LMFDB - Embedded newform 76.5.b.a.39.4

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			39.4
Character	$\chi$	$=$	76.39
Dual form			76.5.b.a.39.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.82653 + 1.16519i) q^{2} -9.98677i q^{3} +(13.2847 - 8.91726i) q^{4} +35.6225 q^{5} +(11.6365 + 38.2147i) q^{6} +14.7837i q^{7} +(-40.4439 + 49.6013i) q^{8} -18.7357 q^{9} +O(q^{10})$	\(q+(-3.82653 + 1.16519i) q^{2} -9.98677i q^{3} +(13.2847 - 8.91726i) q^{4} +35.6225 q^{5} +(11.6365 + 38.2147i) q^{6} +14.7837i q^{7} +(-40.4439 + 49.6013i) q^{8} -18.7357 q^{9} +(-136.310 + 41.5069i) q^{10} -42.5759i q^{11} +(-89.0547 - 132.671i) q^{12} +173.621 q^{13} +(-17.2258 - 56.5703i) q^{14} -355.754i q^{15} +(96.9649 - 236.926i) q^{16} +90.6097 q^{17} +(71.6926 - 21.8306i) q^{18} +82.8191i q^{19} +(473.233 - 317.655i) q^{20} +147.642 q^{21} +(49.6089 + 162.918i) q^{22} -542.932i q^{23} +(495.357 + 403.904i) q^{24} +643.961 q^{25} +(-664.367 + 202.302i) q^{26} -621.820i q^{27} +(131.830 + 196.397i) q^{28} -624.742 q^{29} +(414.520 + 1361.30i) q^{30} -1359.29i q^{31} +(-94.9759 + 1019.59i) q^{32} -425.196 q^{33} +(-346.721 + 105.577i) q^{34} +526.632i q^{35} +(-248.897 + 167.071i) q^{36} -716.024 q^{37} +(-96.4999 - 316.910i) q^{38} -1733.92i q^{39} +(-1440.71 + 1766.92i) q^{40} +268.601 q^{41} +(-564.955 + 172.030i) q^{42} +1116.62i q^{43} +(-379.660 - 565.606i) q^{44} -667.411 q^{45} +(632.618 + 2077.55i) q^{46} +3634.52i q^{47} +(-2366.12 - 968.367i) q^{48} +2182.44 q^{49} +(-2464.13 + 750.336i) q^{50} -904.898i q^{51} +(2306.50 - 1548.23i) q^{52} -4646.79 q^{53} +(724.538 + 2379.41i) q^{54} -1516.66i q^{55} +(-733.291 - 597.911i) q^{56} +827.096 q^{57} +(2390.59 - 727.942i) q^{58} +3785.37i q^{59} +(-3172.35 - 4726.07i) q^{60} +7086.31 q^{61} +(1583.83 + 5201.35i) q^{62} -276.983i q^{63} +(-824.582 - 4012.14i) q^{64} +6184.82 q^{65} +(1627.02 - 495.433i) q^{66} -1301.67i q^{67} +(1203.72 - 807.990i) q^{68} -5422.14 q^{69} +(-613.626 - 2015.17i) q^{70} +1952.12i q^{71} +(757.744 - 929.314i) q^{72} +494.997 q^{73} +(2739.89 - 834.303i) q^{74} -6431.09i q^{75} +(738.519 + 1100.22i) q^{76} +629.429 q^{77} +(2020.34 + 6634.89i) q^{78} -10544.7i q^{79} +(3454.13 - 8439.88i) q^{80} -7727.56 q^{81} +(-1027.81 + 312.971i) q^{82} +8717.27i q^{83} +(1961.37 - 1316.56i) q^{84} +3227.74 q^{85} +(-1301.07 - 4272.78i) q^{86} +6239.15i q^{87} +(2111.82 + 1721.93i) q^{88} -11139.5 q^{89} +(2553.87 - 777.660i) q^{90} +2566.77i q^{91} +(-4841.47 - 7212.67i) q^{92} -13574.9 q^{93} +(-4234.91 - 13907.6i) q^{94} +2950.22i q^{95} +(10182.4 + 948.503i) q^{96} +8562.50 q^{97} +(-8351.18 + 2542.96i) q^{98} +797.687i 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 $

$2$	−3.82653	+	1.16519i	−0.956633	+	0.291297i
$2$	−3.82653	+	1.16519i	−0.956633	+	0.291297i
$3$		−	9.98677i		−	1.10964i	−0.831970	−	0.554821i	$-0.812787\pi$
$3$		−	9.98677i		−	1.10964i	0.831970	−	0.554821i	$-0.187213\pi$
$4$	13.2847	−	8.91726i	0.830292	−	0.557329i
$5$	35.6225			1.42490			0.712449	−	0.701723i	$-0.247586\pi$
$5$	35.6225			1.42490			0.712449	+	0.701723i	$0.247586\pi$
$6$	11.6365	+	38.2147i	0.323236	+	1.06152i
$7$			14.7837i			0.301708i	0.988556	+	0.150854i	$0.0482024\pi$
$7$			14.7837i			0.301708i	−0.988556	+	0.150854i	$0.951798\pi$
$8$	−40.4439	+	49.6013i	−0.631936	+	0.775021i
$9$	−18.7357			−0.231305
$10$	−136.310	+	41.5069i	−1.36310	+	0.415069i
$11$		−	42.5759i		−	0.351867i	−0.984402	−	0.175933i	$-0.943706\pi$
$11$		−	42.5759i		−	0.351867i	0.984402	−	0.175933i	$-0.0562943\pi$
$12$	−89.0547	−	132.671i	−0.618435	−	0.921326i
$13$	173.621			1.02734			0.513672	−	0.857986i	$-0.328285\pi$
$13$	173.621			1.02734			0.513672	+	0.857986i	$0.328285\pi$
$14$	−17.2258	−	56.5703i	−0.0878868	−	0.288624i
$15$		−	355.754i		−	1.58113i
$16$	96.9649	−	236.926i	0.378769	−	0.925491i
$17$	90.6097			0.313528			0.156764	−	0.987636i	$-0.449894\pi$
$17$	90.6097			0.313528			0.156764	+	0.987636i	$0.449894\pi$
$18$	71.6926	−	21.8306i	0.221274	−	0.0673784i
$19$			82.8191i			0.229416i
$19$			82.8191i			0.229416i
$20$	473.233	−	317.655i	1.18308	−	0.794137i
$21$	147.642			0.334788
$22$	49.6089	+	162.918i	0.102498	+	0.336607i
$23$		−	542.932i		−	1.02634i	−0.858288	−	0.513168i	$-0.828472\pi$
$23$		−	542.932i		−	1.02634i	0.858288	−	0.513168i	$-0.171528\pi$
$24$	495.357	+	403.904i	0.859995	+	0.701222i
$25$	643.961			1.03034
$26$	−664.367	+	202.302i	−0.982792	+	0.299263i
$27$		−	621.820i		−	0.852976i
$28$	131.830	+	196.397i	0.168151	+	0.250506i
$29$	−624.742			−0.742856			−0.371428	−	0.928462i	$-0.621132\pi$
$29$	−624.742			−0.742856			−0.371428	+	0.928462i	$0.621132\pi$
$30$	414.520	+	1361.30i	0.460578	+	1.51256i
$31$		−	1359.29i		−	1.41445i	−0.706988	−	0.707225i	$-0.749947\pi$
$31$		−	1359.29i		−	1.41445i	0.706988	−	0.707225i	$-0.250053\pi$
$32$	−94.9759	+	1019.59i	−0.0927499	+	0.995689i
$33$	−425.196			−0.390446
$34$	−346.721	+	105.577i	−0.299931	+	0.0913299i
$35$			526.632i			0.429904i
$36$	−248.897	+	167.071i	−0.192050	+	0.128913i
$37$	−716.024			−0.523027			−0.261514	−	0.965200i	$-0.584222\pi$
$37$	−716.024			−0.523027			−0.261514	+	0.965200i	$0.584222\pi$
$38$	−96.4999	−	316.910i	−0.0668282	−	0.219467i
$39$		−	1733.92i		−	1.13998i
$40$	−1440.71	+	1766.92i	−0.900445	+	1.10433i
$41$	268.601			0.159786			0.0798932	−	0.996803i	$-0.474542\pi$
$41$	268.601			0.159786			0.0798932	+	0.996803i	$0.474542\pi$
$42$	−564.955	+	172.030i	−0.320269	+	0.0975228i
$43$			1116.62i			0.603905i	0.953323	+	0.301952i	$0.0976384\pi$
$43$			1116.62i			0.603905i	−0.953323	+	0.301952i	$0.902362\pi$
$44$	−379.660	−	565.606i	−0.196105	−	0.292152i
$45$	−667.411			−0.329586
$46$	632.618	+	2077.55i	0.298969	+	0.981827i
$47$			3634.52i			1.64533i	0.568529	+	0.822663i	$0.307513\pi$
$47$			3634.52i			1.64533i	−0.568529	+	0.822663i	$0.692487\pi$
$48$	−2366.12	−	968.367i	−1.02696	−	0.420298i
$49$	2182.44			0.908972
$50$	−2464.13	+	750.336i	−0.985654	+	0.300134i
$51$		−	904.898i		−	0.347904i
$52$	2306.50	−	1548.23i	0.852996	−	0.572569i
$53$	−4646.79			−1.65425			−0.827126	−	0.562017i	$-0.810026\pi$
$53$	−4646.79			−1.65425			−0.827126	+	0.562017i	$0.810026\pi$
$54$	724.538	+	2379.41i	0.248470	+	0.815985i
$55$		−	1516.66i		−	0.501374i
$56$	−733.291	−	597.911i	−0.233830	−	0.190660i
$57$	827.096			0.254569
$58$	2390.59	−	727.942i	0.710640	−	0.216392i
$59$			3785.37i			1.08744i	0.839268	+	0.543719i	$0.182984\pi$
$59$			3785.37i			1.08744i	−0.839268	+	0.543719i	$0.817016\pi$
$60$	−3172.35	−	4726.07i	−0.881208	−	1.31280i
$61$	7086.31			1.90441			0.952205	−	0.305460i	$-0.0988103\pi$
$61$	7086.31			1.90441			0.952205	+	0.305460i	$0.0988103\pi$
$62$	1583.83	+	5201.35i	0.412025	+	1.35311i
$63$		−	276.983i		−	0.0697865i
$64$	−824.582	−	4012.14i	−0.201314	−	0.979527i
$65$	6184.82			1.46386
$66$	1627.02	−	495.433i	0.373513	−	0.113736i
$67$		−	1301.67i		−	0.289968i	−0.989434	−	0.144984i	$-0.953687\pi$
$67$		−	1301.67i		−	0.289968i	0.989434	−	0.144984i	$-0.0463131\pi$
$68$	1203.72	−	807.990i	0.260320	−	0.174738i
$69$	−5422.14			−1.13887
$70$	−613.626	−	2015.17i	−0.125230	−	0.411260i
$71$			1952.12i			0.387249i	0.981076	+	0.193624i	$0.0620243\pi$
$71$			1952.12i			0.387249i	−0.981076	+	0.193624i	$0.937976\pi$
$72$	757.744	−	929.314i	0.146170	−	0.179266i
$73$	494.997			0.0928874			0.0464437	−	0.998921i	$-0.485211\pi$
$73$	494.997			0.0928874			0.0464437	+	0.998921i	$0.485211\pi$
$74$	2739.89	−	834.303i	0.500345	−	0.152356i
$75$		−	6431.09i		−	1.14330i
$76$	738.519	+	1100.22i	0.127860	+	0.190482i
$77$	629.429			0.106161
$78$	2020.34	+	6634.89i	0.332074	+	1.09055i
$79$		−	10544.7i		−	1.68958i	−0.535098	−	0.844790i	$-0.679725\pi$
$79$		−	10544.7i		−	1.68958i	0.535098	−	0.844790i	$-0.320275\pi$
$80$	3454.13	−	8439.88i	0.539708	−	1.31873i
$81$	−7727.56			−1.17780
$82$	−1027.81	+	312.971i	−0.152857	+	0.0465453i
$83$			8717.27i			1.26539i	0.774401	+	0.632695i	$0.218051\pi$
$83$			8717.27i			1.26539i	−0.774401	+	0.632695i	$0.781949\pi$
$84$	1961.37	−	1316.56i	0.277972	−	0.186587i
$85$	3227.74			0.446746
$86$	−1301.07	−	4272.78i	−0.175916	−	0.577715i
$87$			6239.15i			0.824304i
$88$	2111.82	+	1721.93i	0.272704	+	0.222357i
$89$	−11139.5			−1.40633			−0.703163	−	0.711029i	$-0.748230\pi$
$89$	−11139.5			−1.40633			−0.703163	+	0.711029i	$0.748230\pi$
$90$	2553.87	−	777.660i	0.315292	−	0.0960074i
$91$			2566.77i			0.309958i
$92$	−4841.47	−	7212.67i	−0.572007	−	0.852159i
$93$	−13574.9			−1.56953
$94$	−4234.91	−	13907.6i	−0.479279	−	1.57397i
$95$			2950.22i			0.326894i
$96$	10182.4	+	948.503i	1.10486	+	0.102919i
$97$	8562.50			0.910033			0.455017	−	0.890483i	$-0.349633\pi$
$97$	8562.50			0.910033			0.455017	+	0.890483i	$0.349633\pi$
$98$	−8351.18	+	2542.96i	−0.869552	+	0.264781i
$99$			797.687i			0.0813884i
$100$	8554.80	−	5742.36i	0.855480	−	0.574236i
$101$	4696.77			0.460422			0.230211	−	0.973141i	$-0.426058\pi$
$101$	4696.77			0.460422			0.230211	+	0.973141i	$0.426058\pi$
$102$	1054.38	+	3462.62i	0.101343	+	0.332816i
$103$			18600.5i			1.75328i	0.481147	+	0.876640i	$0.340220\pi$
$103$			18600.5i			1.75328i	−0.481147	+	0.876640i	$0.659780\pi$
$104$	−7021.92	+	8611.85i	−0.649216	+	0.796214i
$105$	5259.36			0.477039
$106$	17781.1	−	5414.39i	1.58251	−	0.481879i
$107$			9275.23i			0.810135i	0.914287	+	0.405067i	$0.132752\pi$
$107$			9275.23i			0.810135i	−0.914287	+	0.405067i	$0.867248\pi$
$108$	−5544.93	−	8260.67i	−0.475388	−	0.708219i
$109$	−13047.5			−1.09819			−0.549093	−	0.835761i	$-0.685027\pi$
$109$	−13047.5			−1.09819			−0.549093	+	0.835761i	$0.685027\pi$
$110$	1767.19	+	5803.54i	0.146049	+	0.479631i
$111$			7150.77i			0.580373i
$112$	3502.64	+	1433.50i	0.279228	+	0.114278i
$113$	12050.1			0.943700			0.471850	−	0.881679i	$-0.343586\pi$
$113$	12050.1			0.943700			0.471850	+	0.881679i	$0.343586\pi$
$114$	−3164.91	+	963.722i	−0.243529	+	0.0741553i
$115$		−	19340.6i		−	1.46243i
$116$	−8299.49	+	5570.98i	−0.616787	+	0.414015i
$117$	−3252.91			−0.237630
$118$	−4410.67	−	14484.8i	−0.316767	−	1.04028i
$119$			1339.55i			0.0945941i
$120$	17645.8	+	14388.1i	1.22541	+	0.999171i
$121$	12828.3			0.876190
$122$	−27116.0	+	8256.89i	−1.82182	+	0.554749i
$123$		−	2682.46i		−	0.177306i
$124$	−12121.1	−	18057.7i	−0.788314	−	1.17441i
$125$	675.423			0.0432271
$126$	322.737	+	1059.88i	0.0203286	+	0.0667600i
$127$			21463.1i			1.33072i	0.746524	+	0.665359i	$0.231721\pi$
$127$			21463.1i			1.33072i	−0.746524	+	0.665359i	$0.768279\pi$
$128$	7830.19	+	14391.8i	0.477917	+	0.878405i
$129$	11151.4			0.670118
$130$	−23666.4	+	7206.48i	−1.40038	+	0.426419i
$131$		−	15735.1i		−	0.916912i	−0.888717	−	0.458456i	$-0.848403\pi$
$131$		−	15735.1i		−	0.916912i	0.888717	−	0.458456i	$-0.151597\pi$
$132$	−5648.58	+	3791.58i	−0.324184	+	0.217607i
$133$	−1224.37			−0.0692166
$134$	1516.69	+	4980.87i	0.0844669	+	0.277393i
$135$		−	22150.8i		−	1.21541i
$136$	−3664.61	+	4494.36i	−0.198130	+	0.242991i
$137$	−10365.3			−0.552258			−0.276129	−	0.961121i	$-0.589052\pi$
$137$	−10365.3			−0.552258			−0.276129	+	0.961121i	$0.589052\pi$
$138$	20748.0	−	6317.82i	1.08948	−	0.331749i
$139$			10980.8i			0.568335i	0.958775	+	0.284168i	$0.0917172\pi$
$139$			10980.8i			0.568335i	−0.958775	+	0.284168i	$0.908283\pi$
$140$	4696.12	+	6996.13i	0.239598	+	0.356946i
$141$	36297.2			1.82572
$142$	−2274.59	−	7469.85i	−0.112804	−	0.370455i
$143$		−	7392.08i		−	0.361488i
$144$	−1816.70	+	4438.96i	−0.0876110	+	0.214070i
$145$	−22254.8			−1.05849
$146$	−1894.12	+	576.765i	−0.0888592	+	0.0270579i
$147$		−	21795.6i		−	1.00863i
$148$	−9512.14	+	6384.97i	−0.434265	+	0.291498i
$149$	−21955.8			−0.988957			−0.494478	−	0.869190i	$-0.664641\pi$
$149$	−21955.8			−0.988957			−0.494478	+	0.869190i	$0.664641\pi$
$150$	7493.43	+	24608.8i	0.333042	+	1.09372i
$151$			4282.87i			0.187837i	0.995580	+	0.0939184i	$0.0299393\pi$
$151$			4282.87i			0.187837i	−0.995580	+	0.0939184i	$0.970061\pi$
$152$	−4107.94	−	3349.53i	−0.177802	−	0.144976i
$153$	−1697.63			−0.0725205
$154$	−2408.53	+	733.404i	−0.101557	+	0.0309244i
$155$		−	48421.2i		−	2.01545i
$156$	−15461.8	−	23034.5i	−0.635346	−	0.946520i
$157$	−39796.2			−1.61451			−0.807257	−	0.590200i	$-0.799049\pi$
$157$	−39796.2			−1.61451			−0.807257	+	0.590200i	$0.799049\pi$
$158$	12286.5	+	40349.5i	0.492170	+	1.61631i
$159$			46406.5i			1.83563i
$160$	−3383.28	+	36320.2i	−0.132159	+	1.41876i
$161$	8026.55			0.309654
$162$	29569.8	−	9004.07i	1.12672	−	0.343091i
$163$		−	569.318i		−	0.0214279i	−0.999943	−	0.0107140i	$-0.996590\pi$
$163$		−	569.318i		−	0.0214279i	0.999943	−	0.0107140i	$-0.00341042\pi$
$164$	3568.28	−	2395.19i	0.132669	−	0.0890536i
$165$	−15146.5			−0.556346
$166$	−10157.3	−	33356.9i	−0.368604	−	1.21051i
$167$			37160.1i			1.33243i	0.745760	+	0.666215i	$0.232086\pi$
$167$			37160.1i			1.33243i	−0.745760	+	0.666215i	$0.767914\pi$
$168$	−5971.20	+	7323.21i	−0.211565	+	0.259468i
$169$	1583.35			0.0554376
$170$	−12351.0	+	3760.93i	−0.427372	+	0.130136i
$171$		−	1551.67i		−	0.0530649i
$172$	9957.19	+	14833.9i	0.336574	+	0.501417i
$173$	13975.4			0.466950			0.233475	−	0.972363i	$-0.424990\pi$
$173$	13975.4			0.466950			0.233475	+	0.972363i	$0.424990\pi$
$174$	−7269.79	−	23874.3i	−0.240117	−	0.788556i
$175$			9520.12i			0.310861i
$176$	−10087.3	−	4128.36i	−0.325649	−	0.133276i
$177$	37803.6			1.20667
$178$	42625.7	−	12979.6i	1.34534	−	0.409659i
$179$		−	51453.4i		−	1.60586i	−0.596072	−	0.802931i	$-0.703273\pi$
$179$		−	51453.4i		−	1.60586i	0.596072	−	0.802931i	$-0.296727\pi$
$180$	−8866.33	+	5951.48i	−0.273652	+	0.183688i
$181$	57695.7			1.76111			0.880555	−	0.473944i	$-0.157170\pi$
$181$	57695.7			1.76111			0.880555	+	0.473944i	$0.157170\pi$
$182$	−2990.77	−	9821.81i	−0.0902900	−	0.296516i
$183$		−	70769.4i		−	2.11321i
$184$	26930.2	+	21958.3i	0.795432	+	0.648579i
$185$	−25506.6			−0.745261
$186$	51944.7	−	15817.3i	1.50147	−	0.457201i
$187$		−	3857.78i		−	0.110320i
$188$	32410.0	+	48283.5i	0.916988	+	1.36610i
$189$	9192.80			0.257350
$190$	−3437.56	−	11289.1i	−0.0952234	−	0.312718i
$191$		−	6399.46i		−	0.175419i	−0.996146	−	0.0877095i	$-0.972045\pi$
$191$		−	6399.46i		−	0.175419i	0.996146	−	0.0877095i	$-0.0279547\pi$
$192$	−40068.4	+	8234.92i	−1.08692	+	0.223386i
$193$	−29345.0			−0.787806			−0.393903	−	0.919152i	$-0.628875\pi$
$193$	−29345.0			−0.787806			−0.393903	+	0.919152i	$0.628875\pi$
$194$	−32764.7	+	9976.93i	−0.870567	+	0.265090i
$195$		−	61766.4i		−	1.62436i
$196$	28993.0	−	19461.4i	0.754712	−	0.506596i
$197$	32100.2			0.827134			0.413567	−	0.910474i	$-0.364283\pi$
$197$	32100.2			0.827134			0.413567	+	0.910474i	$0.364283\pi$
$198$	−929.456	−	3052.37i	−0.0237082	−	0.0778588i
$199$		−	19449.5i		−	0.491136i	−0.969379	−	0.245568i	$-0.921025\pi$
$199$		−	19449.5i		−	0.491136i	0.969379	−	0.245568i	$-0.0789745\pi$
$200$	−26044.3	+	31941.3i	−0.651107	+	0.798532i
$201$	−12999.4			−0.321761
$202$	−17972.3	+	5472.62i	−0.440455	+	0.134120i
$203$		−	9236.00i		−	0.224126i
$204$	−8069.22	−	12021.3i	−0.193897	−	0.288862i
$205$	9568.23			0.227680
$206$	−21673.1	−	71175.5i	−0.510725	−	1.67724i
$207$			10172.2i			0.237396i
$208$	16835.2	−	41135.4i	0.389127	−	0.950799i
$209$	3526.09			0.0807237
$210$	−20125.1	+	6128.14i	−0.456351	+	0.138960i
$211$		−	18470.2i		−	0.414865i	−0.978249	−	0.207433i	$-0.933489\pi$
$211$		−	18470.2i		−	0.414865i	0.978249	−	0.207433i	$-0.0665107\pi$
$212$	−61731.1	+	41436.7i	−1.37351	+	0.921962i
$213$	19495.4			0.429707
$214$	−10807.4	−	35492.0i	−0.235990	−	0.775001i
$215$			39776.8i			0.860503i
$216$	30843.1	+	25148.8i	0.661074	+	0.539026i
$217$	20095.3			0.426751
$218$	49926.8	−	15202.9i	1.05056	−	0.319899i
$219$		−	4943.43i		−	0.103072i
$220$	−13524.4	−	20148.3i	−0.279430	−	0.416287i
$221$	15731.8			0.322102
$222$	−8332.00	−	27362.6i	−0.169061	−	0.555203i
$223$			75761.3i			1.52348i	0.647881	+	0.761742i	$0.275656\pi$
$223$			75761.3i			1.52348i	−0.647881	+	0.761742i	$0.724344\pi$
$224$	−15073.3	−	1404.10i	−0.300408	−	0.0279834i
$225$	−12065.0			−0.238322
$226$	−46110.1	+	14040.6i	−0.902774	+	0.274897i
$227$			26443.9i			0.513185i	0.966520	+	0.256593i	$0.0825999\pi$
$227$			26443.9i			0.513185i	−0.966520	+	0.256593i	$0.917400\pi$
$228$	10987.7	−	7375.43i	0.211367	−	0.141879i
$229$	36601.4			0.697953			0.348977	−	0.937131i	$-0.386529\pi$
$229$	36601.4			0.697953			0.348977	+	0.937131i	$0.386529\pi$
$230$	22535.4	+	74007.3i	0.426001	+	1.39900i
$231$		−	6285.96i		−	0.117801i
$232$	25267.0	−	30988.0i	0.469437	−	0.575728i
$233$	−61064.1			−1.12480			−0.562398	−	0.826867i	$-0.690121\pi$
$233$	−61064.1			−1.12480			−0.562398	+	0.826867i	$0.690121\pi$
$234$	12447.4	−	3790.26i	0.227324	−	0.0692208i
$235$			129471.i			2.34442i
$236$	33755.1	+	50287.4i	0.606060	+	0.902890i
$237$	−105307.			−1.87483
$238$	−1560.82	−	5125.82i	−0.0275550	−	0.0904918i
$239$			74816.9i			1.30980i	0.755717	+	0.654898i	$0.227289\pi$
$239$			74816.9i			1.30980i	−0.755717	+	0.654898i	$0.772711\pi$
$240$	−84287.2	−	34495.6i	−1.46332	−	0.598882i
$241$	−7030.47			−0.121046			−0.0605230	−	0.998167i	$-0.519277\pi$
$241$	−7030.47			−0.121046			−0.0605230	+	0.998167i	$0.519277\pi$
$242$	−49087.9	+	14947.4i	−0.838192	+	0.255232i
$243$			26806.0i			0.453963i
$244$	94139.3	−	63190.5i	1.58122	−	1.06138i
$245$	77744.0			1.29519
$246$	3125.57	+	10264.5i	0.0516487	+	0.169616i
$247$			14379.2i			0.235689i
$248$	67422.4	+	54974.9i	1.09623	+	0.893842i
$249$	87057.4			1.40413
$250$	−2584.53	+	786.995i	−0.0413524	+	0.0125919i
$251$			58503.9i			0.928618i	0.885673	+	0.464309i	$0.153697\pi$
$251$			58503.9i			0.928618i	−0.885673	+	0.464309i	$0.846303\pi$
$252$	−2469.93	−	3679.62i	−0.0388940	−	0.0579432i
$253$	−23115.8			−0.361134
$254$	−25008.6	−	82129.4i	−0.387634	−	1.27301i
$255$		−	32234.7i		−	0.495728i
$256$	−46731.6	−	45947.0i	−0.713068	−	0.701095i
$257$	−96298.5			−1.45799			−0.728993	−	0.684522i	$-0.760011\pi$
$257$	−96298.5			−1.45799			−0.728993	+	0.684522i	$0.760011\pi$
$258$	−42671.3	+	12993.5i	−0.641057	+	0.195203i
$259$		−	10585.5i		−	0.157802i
$260$	82163.3	−	55151.7i	1.21543	−	0.815853i
$261$	11705.0			0.171826
$262$	18334.4	+	60210.9i	0.267094	+	0.877148i
$263$		−	84353.6i		−	1.21953i	−0.792583	−	0.609764i	$-0.791264\pi$
$263$		−	84353.6i		−	1.21953i	0.792583	−	0.609764i	$-0.208736\pi$
$264$	17196.6	−	21090.3i	0.246737	−	0.302604i
$265$	−165530.			−2.35714
$266$	4685.10	−	1426.63i	0.0662149	−	0.0201626i
$267$			111248.i			1.56052i
$268$	−11607.3	−	17292.2i	−0.161608	−	0.240758i
$269$	−82684.4			−1.14266			−0.571332	−	0.820719i	$-0.693573\pi$
$269$	−82684.4			−1.14266			−0.571332	+	0.820719i	$0.693573\pi$
$270$	25809.8	+	84760.6i	0.354044	+	1.16270i
$271$			111525.i			1.51857i	0.650760	+	0.759284i	$0.274451\pi$
$271$			111525.i			1.51857i	−0.650760	+	0.759284i	$0.725549\pi$
$272$	8785.96	−	21467.8i	0.118755	−	0.290168i
$273$	25633.7			0.343943
$274$	39663.2	−	12077.6i	0.528308	−	0.160871i
$275$		−	27417.2i		−	0.362541i
$276$	−72031.4	+	48350.6i	−0.945591	+	0.634723i
$277$	−62981.0			−0.820824			−0.410412	−	0.911900i	$-0.634615\pi$
$277$	−62981.0			−0.820824			−0.410412	+	0.911900i	$0.634615\pi$
$278$	−12794.7	−	42018.4i	−0.165555	−	0.543688i
$279$			25467.2i			0.327169i
$280$	−26121.6	−	21299.1i	−0.333184	−	0.271672i
$281$	39478.2			0.499971			0.249985	−	0.968250i	$-0.419574\pi$
$281$	39478.2			0.499971			0.249985	+	0.968250i	$0.419574\pi$
$282$	−138892.	+	42293.1i	−1.74655	+	0.531828i
$283$		−	114614.i		−	1.43109i	−0.698568	−	0.715543i	$-0.746179\pi$
$283$		−	114614.i		−	1.43109i	0.698568	−	0.715543i	$-0.253821\pi$
$284$	17407.6	+	25933.3i	0.215825	+	0.321529i
$285$	29463.2			0.362735
$286$	8613.16	+	28286.0i	0.105301	+	0.345812i
$287$			3970.92i			0.0482089i
$288$	1779.44	−	19102.6i	0.0214535	−	0.230308i
$289$	−75310.9			−0.901700
$290$	85158.8	−	25931.1i	1.01259	−	0.308336i
$291$		−	85511.8i		−	1.00981i
$292$	6575.87	−	4414.02i	0.0771237	−	0.0517688i
$293$	−68100.5			−0.793259			−0.396629	−	0.917979i	$-0.629820\pi$
$293$	−68100.5			−0.793259			−0.396629	+	0.917979i	$0.629820\pi$
$294$	25395.9	+	83401.4i	0.293812	+	0.964892i
$295$			134844.i			1.54949i
$296$	28958.8	−	35515.7i	0.330520	−	0.405357i
$297$	−26474.5			−0.300134
$298$	84014.6	−	25582.7i	0.946068	−	0.288080i
$299$		−	94264.6i		−	1.05440i
$300$	−57347.7	−	85434.9i	−0.637197	−	0.949277i
$301$	−16507.8			−0.182203
$302$	−4990.35	−	16388.5i	−0.0547163	−	0.179691i
$303$		−	46905.6i		−	0.510904i
$304$	19622.0	+	8030.54i	0.212322	+	0.0868956i
$305$	252432.			2.71359
$306$	6496.05	−	1978.06i	0.0693755	−	0.0211250i
$307$		−	102846.i		−	1.09122i	−0.838040	−	0.545609i	$-0.816298\pi$
$307$		−	102846.i		−	1.09122i	0.838040	−	0.545609i	$-0.183702\pi$
$308$	8361.75	−	5612.78i	0.0881447	−	0.0591666i
$309$	185759.			1.94551
$310$	56419.8	+	185285.i	0.587095	+	1.92804i
$311$		−	109889.i		−	1.13614i	−0.822981	−	0.568070i	$-0.807690\pi$
$311$		−	109889.i		−	1.13614i	0.822981	−	0.568070i	$-0.192310\pi$
$312$	86004.6	+	70126.4i	0.883512	+	0.720397i
$313$	7434.85			0.0758898			0.0379449	−	0.999280i	$-0.487919\pi$
$313$	7434.85			0.0758898			0.0379449	+	0.999280i	$0.487919\pi$
$314$	152281.	−	46370.0i	1.54450	−	0.470304i
$315$		−	9866.81i		−	0.0994387i
$316$	−94029.6	−	140082.i	−0.941652	−	1.40284i
$317$	78303.0			0.779220			0.389610	−	0.920980i	$-0.372610\pi$
$317$	78303.0			0.779220			0.389610	+	0.920980i	$0.372610\pi$
$318$	−54072.3	−	177576.i	−0.534713	−	1.75602i
$319$			26598.9i			0.261386i
$320$	−29373.7	−	142922.i	−0.286852	−	1.39573i
$321$	92629.7			0.898959
$322$	−30713.8	+	9352.44i	−0.296225	+	0.0902014i
$323$			7504.21i			0.0719283i
$324$	−102658.	+	68908.7i	−0.977920	+	0.656423i
$325$	111805.			1.05851
$326$	663.363	+	2178.51i	0.00624189	+	0.0204986i
$327$			130303.i			1.21859i
$328$	−10863.3	+	13323.0i	−0.100975	+	0.123838i
$329$	−53731.7			−0.496408
$330$	57958.6	−	17648.6i	0.532219	−	0.162062i
$331$		−	20790.0i		−	0.189757i	−0.995489	−	0.0948787i	$-0.969754\pi$
$331$		−	20790.0i		−	0.189757i	0.995489	−	0.0948787i	$-0.0302463\pi$
$332$	77734.2	+	115806.i	0.705238	+	1.05064i
$333$	13415.2			0.120979
$334$	−43298.6	−	142194.i	−0.388133	−	1.27465i
$335$		−	46368.6i		−	0.413175i
$336$	14316.0	−	34980.1i	0.126807	−	0.309843i
$337$	90228.9			0.794485			0.397243	−	0.917714i	$-0.369967\pi$
$337$	90228.9			0.794485			0.397243	+	0.917714i	$0.369967\pi$
$338$	−6058.75	+	1844.91i	−0.0530334	+	0.0161488i
$339$		−	120342.i		−	1.04717i
$340$	42879.5	−	28782.6i	0.370930	−	0.248985i
$341$	−57872.8			−0.497698
$342$	1807.99	+	5937.52i	0.0154577	+	0.0507636i
$343$			67760.3i			0.575953i
$344$	−55385.8	−	45160.5i	−0.468039	−	0.381629i
$345$	−193150.			−1.62277
$346$	−53477.1	+	16283.9i	−0.446700	+	0.136021i
$347$			96041.7i			0.797629i	0.917032	+	0.398815i	$0.130578\pi$
$347$			96041.7i			0.797629i	−0.917032	+	0.398815i	$0.869422\pi$
$348$	55636.2	+	82885.1i	0.459408	+	0.684413i
$349$	−33501.7			−0.275053			−0.137527	−	0.990498i	$-0.543915\pi$
$349$	−33501.7			−0.275053			−0.137527	+	0.990498i	$0.543915\pi$
$350$	−11092.7	−	36429.0i	−0.0905530	−	0.297380i
$351$		−	107961.i		−	0.876301i
$352$	43409.7	+	4043.68i	0.350350	+	0.0326356i
$353$	−35188.5			−0.282392			−0.141196	−	0.989982i	$-0.545095\pi$
$353$	−35188.5			−0.282392			−0.141196	+	0.989982i	$0.545095\pi$
$354$	−144657.	+	44048.4i	−1.15434	+	0.351498i
$355$			69539.4i			0.551790i
$356$	−147985.	+	99333.9i	−1.16766	+	0.783786i
$357$	13377.8			0.104966
$358$	59952.9	+	196888.i	0.467783	+	1.53622i
$359$			78109.9i			0.606062i	0.952981	+	0.303031i	$0.0979986\pi$
$359$			78109.9i			0.606062i	−0.952981	+	0.303031i	$0.902001\pi$
$360$	26992.7	−	33104.5i	0.208277	−	0.255436i
$361$	−6859.00			−0.0526316
$362$	−220774.	+	67226.4i	−1.68474	+	0.513006i
$363$		−	128113.i		−	0.972257i
$364$	22888.5	+	34098.6i	0.172749	+	0.257356i
$365$	17633.0			0.132355
$366$	82459.7	+	270801.i	0.615573	+	2.02157i
$367$			9286.95i			0.0689511i	0.999406	+	0.0344755i	$0.0109761\pi$
$367$			9286.95i			0.0689511i	−0.999406	+	0.0344755i	$0.989024\pi$
$368$	−128635.	−	52645.4i	−0.949866	−	0.388745i
$369$	−5032.42			−0.0369593
$370$	97601.6	−	29720.0i	0.712941	−	0.217092i
$371$		−	68696.8i		−	0.499101i
$372$	−180338.	+	121051.i	−1.30317	+	0.874746i
$373$	−15140.4			−0.108823			−0.0544114	−	0.998519i	$-0.517328\pi$
$373$	−15140.4			−0.108823			−0.0544114	+	0.998519i	$0.517328\pi$
$374$	4495.05	+	14761.9i	0.0321359	+	0.105536i
$375$		−	6745.29i		−	0.0479665i
$376$	−180277.	−	146994.i	−1.27516	−	1.03974i
$377$	−108468.			−0.763169
$378$	−35176.5	+	10711.3i	−0.246189	+	0.0749653i
$379$		−	30969.0i		−	0.215600i	−0.994173	−	0.107800i	$-0.965619\pi$
$379$		−	30969.0i		−	0.215600i	0.994173	−	0.107800i	$-0.0343806\pi$
$380$	26307.9	+	39192.7i	0.182188	+	0.271418i
$381$	214348.			1.47662
$382$	7456.58	+	24487.7i	0.0510991	+	0.167812i
$383$		−	114940.i		−	0.783562i	−0.920058	−	0.391781i	$-0.871859\pi$
$383$		−	114940.i		−	0.783562i	0.920058	−	0.391781i	$-0.128141\pi$
$384$	143728.	−	78198.4i	0.974715	−	0.530317i
$385$	22421.8			0.151269
$386$	112290.	−	34192.5i	0.753641	−	0.229486i
$387$		−	20920.6i		−	0.139686i
$388$	113750.	−	76354.1i	0.755593	−	0.507188i
$389$	−50645.8			−0.334691			−0.167345	−	0.985898i	$-0.553520\pi$
$389$	−50645.8			−0.334691			−0.167345	+	0.985898i	$0.553520\pi$
$390$	71969.5	+	236351.i	0.473172	+	1.55392i
$391$		−	49194.9i		−	0.321786i
$392$	−88266.5	+	108252.i	−0.574412	+	0.704472i
$393$	−157143.			−1.01744
$394$	−122832.	+	37402.8i	−0.791263	+	0.240942i
$395$		−	375627.i		−	2.40748i
$396$	7113.19	+	10597.0i	0.0453601	+	0.0675761i
$397$	−134024.			−0.850360			−0.425180	−	0.905109i	$-0.639789\pi$
$397$	−134024.			−0.850360			−0.425180	+	0.905109i	$0.639789\pi$
$398$	22662.3	+	74424.1i	0.143067	+	0.469837i
$399$			12227.5i			0.0768056i
$400$	62441.6	−	152571.i	0.390260	−	0.953568i
$401$	154488.			0.960743			0.480372	−	0.877065i	$-0.340502\pi$
$401$	154488.			0.960743			0.480372	+	0.877065i	$0.340502\pi$
$402$	49742.8	−	15146.8i	0.307807	−	0.0937280i
$403$		−	236001.i		−	1.45313i
$404$	62395.0	−	41882.3i	0.382285	−	0.256607i
$405$	−275275.			−1.67825
$406$	10761.7	+	35341.8i	0.0652872	+	0.214406i
$407$			30485.3i			0.184036i
$408$	44884.2	+	36597.6i	0.269633	+	0.219853i
$409$	296093.			1.77003			0.885015	−	0.465562i	$-0.154148\pi$
$409$	296093.			1.77003			0.885015	+	0.465562i	$0.154148\pi$
$410$	−36613.1	+	11148.8i	−0.217806	+	0.0663224i
$411$			103516.i			0.612808i
$412$	165866.	+	247102.i	0.977153	+	1.45573i
$413$	−55961.8			−0.328089
$414$	−11852.5	−	38924.2i	−0.0691529	−	0.227101i
$415$			310531.i			1.80305i
$416$	−16489.8	+	177022.i	−0.0952861	+	1.02292i
$417$	109663.			0.630649
$418$	−13492.7	+	4108.56i	−0.0772230	+	0.0235146i
$419$			216561.i			1.23353i	0.787146	+	0.616767i	$0.211558\pi$
$419$			216561.i			1.23353i	−0.787146	+	0.616767i	$0.788442\pi$
$420$	69868.8	−	46899.1i	0.396082	−	0.265868i
$421$	−163464.			−0.922272			−0.461136	−	0.887330i	$-0.652558\pi$
$421$	−163464.			−0.922272			−0.461136	+	0.887330i	$0.652558\pi$
$422$	21521.3	+	70676.8i	0.120849	+	0.396873i
$423$		−	68095.3i		−	0.380571i
$424$	187934.	−	230487.i	1.04538	−	1.28208i
$425$	58349.1			0.323040
$426$	−74599.7	+	22715.8i	−0.411072	+	0.125173i
$427$			104762.i			0.574576i
$428$	82709.7	+	123218.i	0.451511	+	0.672648i
$429$	−73823.0			−0.401123
$430$	−46347.4	−	152207.i	−0.250662	−	0.823185i
$431$		−	217509.i		−	1.17091i	−0.810706	−	0.585453i	$-0.800917\pi$
$431$		−	217509.i		−	1.17091i	0.810706	−	0.585453i	$-0.199083\pi$
$432$	−147325.	−	60294.7i	−0.789422	−	0.323081i
$433$	169083.			0.901830			0.450915	−	0.892567i	$-0.351098\pi$
$433$	169083.			0.901830			0.450915	+	0.892567i	$0.351098\pi$
$434$	−76895.3	+	23414.8i	−0.408244	+	0.124311i
$435$			222254.i			1.17455i
$436$	−173332.	+	116348.i	−0.911815	+	0.612051i
$437$	44965.1			0.235458
$438$	5760.02	+	18916.2i	0.0300245	+	0.0986018i
$439$			319412.i			1.65738i	0.559707	+	0.828690i	$0.310914\pi$
$439$			319412.i			1.65738i	−0.559707	+	0.828690i	$0.689086\pi$
$440$	75228.2	+	61339.5i	0.388575	+	0.316836i
$441$	−40889.5			−0.210249
$442$	−60198.1	+	18330.5i	−0.308133	+	0.0938273i
$443$		−	37162.0i		−	0.189362i	−0.995508	−	0.0946808i	$-0.969817\pi$
$443$		−	37162.0i		−	0.189362i	0.995508	−	0.0946808i	$-0.0301830\pi$
$444$	63765.3	+	94995.6i	0.323458	+	0.481879i
$445$	−396817.			−2.00387
$446$	−88276.3	−	289903.i	−0.443787	−	1.45741i
$447$			219268.i			1.09739i
$448$	59314.3	−	12190.4i	0.295531	−	0.0607381i
$449$	335550.			1.66443			0.832214	−	0.554455i	$-0.187073\pi$
$449$	335550.			1.66443			0.832214	+	0.554455i	$0.187073\pi$
$450$	46167.2	−	14058.0i	0.227986	−	0.0694224i
$451$		−	11435.9i		−	0.0562235i
$452$	160082.	−	107454.i	0.783546	−	0.525951i
$453$	42772.0			0.208432
$454$	−30812.2	−	101189.i	−0.149489	−	0.490930i
$455$			91434.5i			0.441659i
$456$	−33451.0	+	41025.0i	−0.160871	+	0.197296i
$457$	187048.			0.895616			0.447808	−	0.894130i	$-0.352205\pi$
$457$	187048.			0.895616			0.447808	+	0.894130i	$0.352205\pi$
$458$	−140056.	+	42647.5i	−0.667685	+	0.203312i
$459$		−	56342.9i		−	0.267432i
$460$	−172465.	−	256933.i	−0.815052	−	1.21424i
$461$	−204225.			−0.960962			−0.480481	−	0.877005i	$-0.659538\pi$
$461$	−204225.			−0.960962			−0.480481	+	0.877005i	$0.659538\pi$
$462$	7324.34	+	24053.4i	0.0343150	+	0.112692i
$463$		−	47268.6i		−	0.220501i	−0.993904	−	0.110251i	$-0.964835\pi$
$463$		−	47268.6i		−	0.220501i	0.993904	−	0.110251i	$-0.0351653\pi$
$464$	−60578.0	+	148017.i	−0.281371	+	0.687506i
$465$	−483571.			−2.23643
$466$	233663.	−	71151.2i	1.07602	−	0.327650i
$467$		−	328988.i		−	1.50850i	−0.656586	−	0.754251i	$-0.728000\pi$
$467$		−	328988.i		−	1.50850i	0.656586	−	0.754251i	$-0.272000\pi$
$468$	−43213.9	+	29007.1i	−0.197302	+	0.132438i
$469$	19243.4			0.0874857
$470$	−150858.	−	495424.i	−0.682924	−	2.24275i
$471$			397435.i			1.79153i
$472$	−187759.	−	153095.i	−0.842786	−	0.687191i
$473$	47541.0			0.212494
$474$	402961.	−	122703.i	1.79352	−	0.546132i
$475$			53332.2i			0.236376i
$476$	11945.1	+	17795.4i	0.0527200	+	0.0785407i
$477$	87060.8			0.382636
$478$	−87175.8	−	286289.i	−0.381540	−	1.25299i
$479$		−	246920.i		−	1.07618i	−0.842887	−	0.538091i	$-0.819146\pi$
$479$		−	246920.i		−	1.07618i	0.842887	−	0.538091i	$-0.180854\pi$
$480$	362721.	+	33788.0i	1.57431	+	0.146649i
$481$	−124317.			−0.537329
$482$	26902.3	−	8191.83i	0.115797	−	0.0352604i
$483$		−	80159.3i		−	0.343605i
$484$	170420.	−	114393.i	0.727493	−	0.488326i
$485$	305017.			1.29671
$486$	−31234.1	−	102574.i	−0.132238	−	0.434275i
$487$			98309.7i			0.414513i	0.978287	+	0.207257i	$0.0664535\pi$
$487$			98309.7i			0.414513i	−0.978287	+	0.207257i	$0.933546\pi$
$488$	−286598.	+	351490.i	−1.20346	+	1.47596i
$489$	−5685.65			−0.0237773
$490$	−297490.	+	90586.4i	−1.23902	+	0.377286i
$491$			76479.9i			0.317237i	0.987340	+	0.158619i	$0.0507041\pi$
$491$			76479.9i			0.317237i	−0.987340	+	0.158619i	$0.949296\pi$
$492$	−23920.2	−	35635.6i	−0.0988176	−	0.147215i
$493$	−56607.6			−0.232906
$494$	−16754.4	−	55022.3i	−0.0686556	−	0.225468i
$495$			28415.6i			0.115970i
$496$	−322050.	−	131803.i	−1.30906	−	0.535750i
$497$	−28859.6			−0.116836
$498$	−333128.	+	101438.i	−1.34324	+	0.409019i
$499$		−	106598.i		−	0.428101i	−0.976823	−	0.214051i	$-0.931334\pi$
$499$		−	106598.i		−	0.428101i	0.976823	−	0.214051i	$-0.0686657\pi$
$500$	8972.77	−	6022.92i	0.0358911	−	0.0240917i
$501$	371110.			1.47852
$502$	−68168.1	−	223867.i	−0.270504	−	0.888347i
$503$		−	222230.i		−	0.878348i	−0.898402	−	0.439174i	$-0.855271\pi$
$503$		−	222230.i		−	0.878348i	0.898402	−	0.439174i	$-0.144729\pi$
$504$	13738.7	+	11202.3i	0.0540860	+	0.0441006i
$505$	167310.			0.656055
$506$	88453.3	−	26934.3i	0.345472	−	0.105197i
$507$		−	15812.6i		−	0.0615159i
$508$	191392.	+	285131.i	0.741647	+	1.10488i
$509$	−85304.0			−0.329256			−0.164628	−	0.986356i	$-0.552642\pi$
$509$	−85304.0			−0.329256			−0.164628	+	0.986356i	$0.552642\pi$
$510$	37559.5	+	123347.i	0.144404	+	0.474230i
$511$			7317.89i			0.0280249i
$512$	232357.	+	121366.i	0.886371	+	0.462976i
$513$	51498.5			0.195686
$514$	368489.	−	112206.i	1.39476	−	0.424707i
$515$			662597.i			2.49825i
$516$	148143.	−	99440.2i	0.556393	−	0.373476i
$517$	154743.			0.578935
$518$	12334.1	+	40505.7i	0.0459672	+	0.150958i
$519$		−	139569.i		−	0.518147i
$520$	−250138.	+	306775.i	−0.925067	+	1.13452i
$521$	318613.			1.17378			0.586892	−	0.809665i	$-0.300351\pi$
$521$	318613.			1.17378			0.586892	+	0.809665i	$0.300351\pi$
$522$	−44789.4	+	13638.5i	−0.164374	+	0.0500524i
$523$			201919.i			0.738199i	0.929390	+	0.369099i	$0.120334\pi$
$523$			201919.i			0.738199i	−0.929390	+	0.369099i	$0.879666\pi$
$524$	−140314.	−	209036.i	−0.511022	−	0.761305i
$525$	95075.3			0.344944
$526$	98287.9	+	322782.i	0.355245	+	1.16664i
$527$		−	123165.i		−	0.443470i
$528$	−41229.0	+	100740.i	−0.147889	+	0.361354i
$529$	−14934.3			−0.0533671
$530$	633406.	−	192874.i	2.25492	−	0.686629i
$531$		−	70921.4i		−	0.251529i
$532$	−16265.4	+	10918.1i	−0.0574700	+	0.0385764i
$533$	46634.9			0.164156
$534$	−129625.	−	425693.i	−0.454574	−	1.49284i
$535$			330407.i			1.15436i
$536$	64564.4	+	52644.5i	0.224731	+	0.183241i
$537$	−513854.			−1.78193
$538$	316394.	−	96342.9i	1.09311	−	0.332855i
$539$		−	92919.3i		−	0.319837i
$540$	−197524.	−	294266.i	−0.677380	−	1.00914i
$541$	−359658.			−1.22884			−0.614419	−	0.788980i	$-0.710610\pi$
$541$	−359658.			−1.22884			−0.614419	+	0.788980i	$0.710610\pi$
$542$	−129948.	−	426754.i	−0.442355	−	1.45271i
$543$		−	576194.i		−	1.95420i
$544$	−8605.73	+	92384.4i	−0.0290797	+	0.312177i
$545$	−464786.			−1.56480
$546$	−98088.2	+	29868.1i	−0.329027	+	0.100190i
$547$			12140.4i			0.0405749i	0.999794	+	0.0202874i	$0.00645814\pi$
$547$			12140.4i			0.0405749i	−0.999794	+	0.0202874i	$0.993542\pi$
$548$	−137700.	+	92430.3i	−0.458535	+	0.307789i
$549$	−132767.			−0.440499
$550$	31946.2	+	104913.i	0.105607	+	0.346819i
$551$		−	51740.5i		−	0.170423i
$552$	219293.	−	268945.i	0.719690	−	0.882645i
$553$	155889.			0.509760
$554$	240999.	−	73384.8i	0.785227	−	0.239104i
$555$			254728.i			0.826972i
$556$	97918.7	+	145876.i	0.316750	+	0.471884i
$557$	−179094.			−0.577259			−0.288630	−	0.957441i	$-0.593200\pi$
$557$	−179094.			−0.577259			−0.288630	+	0.957441i	$0.593200\pi$
$558$	−29674.0	−	97450.8i	−0.0953034	−	0.312980i
$559$			193869.i			0.620418i
$560$	124773.	+	51064.8i	0.397872	+	0.162834i
$561$	−38526.8			−0.122416
$562$	−151064.	+	45999.5i	−0.478288	+	0.145640i
$563$			252148.i			0.795498i	0.917494	+	0.397749i	$0.130209\pi$
$563$			252148.i			0.795498i	−0.917494	+	0.397749i	$0.869791\pi$
$564$	482196.	−	323671.i	1.51588	−	1.01753i
$565$	429254.			1.34468
$566$	133547.	+	438575.i	0.416872	+	1.36902i
$567$		−	114242.i		−	0.355353i
$568$	−96827.8	−	78951.4i	−0.300126	−	0.244716i
$569$	10674.6			0.0329705			0.0164852	−	0.999864i	$-0.494752\pi$
$569$	10674.6			0.0329705			0.0164852	+	0.999864i	$0.494752\pi$
$570$	−112742.	+	34330.2i	−0.347005	+	0.105664i
$571$		−	304884.i		−	0.935108i	−0.883964	−	0.467554i	$-0.845135\pi$
$571$		−	304884.i		−	0.935108i	0.883964	−	0.467554i	$-0.154865\pi$
$572$	−65917.1	−	98201.3i	−0.201468	−	0.300141i
$573$	−63910.0			−0.194652
$574$	−4626.87	−	15194.8i	−0.0140431	−	0.0461182i
$575$		−	349627.i		−	1.05747i
$576$	15449.1	+	75170.2i	0.0465649	+	0.226569i
$577$	−147748.			−0.443781			−0.221891	−	0.975072i	$-0.571223\pi$
$577$	−147748.			−0.443781			−0.221891	+	0.975072i	$0.571223\pi$
$578$	288179.	−	87751.4i	0.862596	−	0.262663i
$579$			293062.i			0.874183i
$580$	−295648.	+	198452.i	−0.878859	+	0.589929i
$581$	−128874.			−0.381778
$582$	99637.4	+	327213.i	0.294155	+	0.966018i
$583$			197841.i			0.582076i
$584$	−20019.6	+	24552.5i	−0.0586989	+	0.0719897i
$585$	−115877.			−0.338598
$586$	260589.	−	79349.9i	0.758857	−	0.231074i
$587$			274871.i			0.797724i	0.917011	+	0.398862i	$0.130595\pi$
$587$			274871.i			0.797724i	−0.917011	+	0.398862i	$0.869405\pi$
$588$	−194357.	−	289547.i	−0.562140	−	0.837460i
$589$	112575.			0.324497
$590$	−157119.	−	515985.i	−0.451362	−	1.48229i
$591$		−	320578.i		−	0.917822i
$592$	−69429.2	+	169645.i	−0.198107	+	0.484057i
$593$	681908.			1.93917			0.969586	−	0.244751i	$-0.0787062\pi$
$593$	681908.			1.93917			0.969586	+	0.244751i	$0.0787062\pi$
$594$	101306.	−	30847.8i	0.287118	−	0.0874282i
$595$			47718.0i			0.134787i
$596$	−291676.	+	195786.i	−0.821123	+	0.551174i
$597$	−194238.			−0.544985
$598$	109836.	+	360706.i	0.307144	+	1.00868i
$599$		−	217785.i		−	0.606981i	−0.952835	−	0.303490i	$-0.901848\pi$
$599$		−	217785.i		−	0.606981i	0.952835	−	0.303490i	$-0.0981520\pi$
$600$	318991.	+	260098.i	0.886085	+	0.722495i
$601$	−283943.			−0.786107			−0.393054	−	0.919516i	$-0.628581\pi$
$601$	−283943.			−0.786107			−0.393054	+	0.919516i	$0.628581\pi$
$602$	63167.5	−	19234.7i	0.174301	−	0.0530752i
$603$			24387.6i			0.0670709i
$604$	38191.4	+	56896.5i	0.104687	+	0.155959i
$605$	456976.			1.24848
$606$	54653.8	+	179486.i	0.148825	+	0.488747i
$607$		−	494014.i		−	1.34079i	−0.742003	−	0.670397i	$-0.766124\pi$
$607$		−	494014.i		−	1.34079i	0.742003	−	0.670397i	$-0.233876\pi$
$608$	−84441.2	−	7865.81i	−0.228427	−	0.0212783i
$609$	−92237.8			−0.248699
$610$	−965938.	+	294131.i	−2.59591	+	0.790462i
$611$			631031.i			1.69032i
$612$	−22552.5	+	15138.2i	−0.0602132	+	0.0404178i
$613$	−540838.			−1.43928			−0.719642	−	0.694345i	$-0.755694\pi$
$613$	−540838.			−1.43928			−0.719642	+	0.694345i	$0.755694\pi$
$614$	119835.	+	393544.i	0.317869	+	1.04390i
$615$		−	95555.8i		−	0.252643i
$616$	−25456.6	+	31220.5i	−0.0670870	+	0.0822770i
$617$	175957.			0.462207			0.231103	−	0.972929i	$-0.425766\pi$
$617$	175957.			0.462207			0.231103	+	0.972929i	$0.425766\pi$
$618$	−710814.	+	216445.i	−1.86114	+	0.566722i
$619$			324704.i			0.847435i	0.905794	+	0.423717i	$0.139275\pi$
$619$			324704.i			0.847435i	−0.905794	+	0.423717i	$0.860725\pi$
$620$	−431784.	−	643259.i	−1.12327	−	1.67341i
$621$	−337606.			−0.875441
$622$	128041.	+	420492.i	0.330954	+	1.08687i
$623$		−	164683.i		−	0.424300i
$624$	−410810.	−	168129.i	−1.05505	−	0.431791i
$625$	−378415.			−0.968743
$626$	−28449.7	+	8663.00i	−0.0725986	+	0.0221065i
$627$		−	35214.3i		−	0.0895744i
$628$	−528679.	+	354873.i	−1.34052	+	0.899815i
$629$	−64878.7			−0.163984
$630$	11496.7	+	37755.6i	0.0289662	+	0.0951263i
$631$		−	228748.i		−	0.574511i	−0.957854	−	0.287256i	$-0.907257\pi$
$631$		−	228748.i		−	0.574511i	0.957854	−	0.287256i	$-0.0927429\pi$
$632$	523029.	+	426467.i	1.30946	+	1.06771i
$633$	−184458.			−0.460351
$634$	−299629.	+	91237.8i	−0.745427	+	0.226985i
$635$			764570.i			1.89614i
$636$	413819.	+	616495.i	1.02305	+	1.52411i
$637$	378918.			0.933828
$638$	−30992.8	−	101782.i	−0.0761410	−	0.250050i
$639$		−	36574.3i		−	0.0895724i
$640$	278931.	+	512671.i	0.680983	+	1.25164i
$641$	−345075.			−0.839841			−0.419921	−	0.907561i	$-0.637942\pi$
$641$	−345075.			−0.839841			−0.419921	+	0.907561i	$0.637942\pi$
$642$	−354450.	+	107931.i	−0.859974	+	0.261864i
$643$		−	736664.i		−	1.78175i	−0.454244	−	0.890877i	$-0.650091\pi$
$643$		−	736664.i		−	1.78175i	0.454244	−	0.890877i	$-0.349909\pi$
$644$	106630.	−	71574.8i	0.257103	−	0.172579i
$645$	397242.			0.954850
$646$	−8743.82	−	28715.1i	−0.0209525	−	0.0688090i
$647$			166880.i			0.398654i	0.979933	+	0.199327i	$0.0638755\pi$
$647$			166880.i			0.398654i	−0.979933	+	0.199327i	$0.936124\pi$
$648$	312533.	−	383297.i	0.744296	−	0.912821i
$649$	161165.			0.382633
$650$	−427826.	+	130274.i	−1.01261	+	0.308341i
$651$		−	200687.i		−	0.473541i
$652$	−5076.76	−	7563.20i	−0.0119424	−	0.0177914i
$653$	492960.			1.15607			0.578036	−	0.816011i	$-0.303819\pi$
$653$	492960.			1.15607			0.578036	+	0.816011i	$0.303819\pi$
$654$	−151828.	−	498608.i	−0.354973	−	1.16575i
$655$		−	560524.i		−	1.30651i
$656$	26044.9	−	63638.5i	0.0605222	−	0.147881i
$657$	−9274.10			−0.0214853
$658$	205606.	−	62607.6i	0.474880	−	0.144602i
$659$		−	211337.i		−	0.486636i	−0.969947	−	0.243318i	$-0.921764\pi$
$659$		−	211337.i		−	0.486636i	0.969947	−	0.243318i	$-0.0782359\pi$
$660$	−201216.	+	135065.i	−0.461929	+	0.310068i
$661$	520844.			1.19208			0.596039	−	0.802955i	$-0.296740\pi$
$661$	520844.			1.19208			0.596039	+	0.802955i	$0.296740\pi$
$662$	24224.3	+	79553.6i	0.0552758	+	0.181528i
$663$		−	157110.i		−	0.357417i
$664$	−432388.	−	352560.i	−0.980703	−	0.799645i
$665$	−43615.2			−0.0986267
$666$	−51333.6	+	15631.2i	−0.115732	+	0.0352407i
$667$			339192.i			0.762420i
$668$	331366.	+	493660.i	0.742601	+	1.10630i
$669$	756611.			1.69052
$670$	54028.1	+	177431.i	0.120357	+	0.395257i
$671$		−	301706.i		−	0.670098i
$672$	−14022.4	+	150533.i	−0.0310516	+	0.333345i
$673$	757014.			1.67137			0.835687	−	0.549206i	$-0.185070\pi$
$673$	757014.			1.67137			0.835687	+	0.549206i	$0.185070\pi$
$674$	−345264.	+	105134.i	−0.760031	+	0.231431i
$675$		−	400427.i		−	0.878853i
$676$	21034.3	−	14119.2i	0.0460294	−	0.0308970i
$677$	191190.			0.417145			0.208573	−	0.978007i	$-0.433118\pi$
$677$	191190.			0.417145			0.208573	+	0.978007i	$0.433118\pi$
$678$	140221.	+	460491.i	0.305037	+	1.00176i
$679$			126585.i			0.274564i
$680$	−130542.	+	160100.i	−0.282315	+	0.346237i
$681$	264090.			0.569452
$682$	221452.	−	67432.7i	0.476114	−	0.144978i
$683$			18669.5i			0.0400213i	0.999800	+	0.0200107i	$0.00637002\pi$
$683$			18669.5i			0.0400213i	−0.999800	+	0.0200107i	$0.993630\pi$
$684$	−13836.7	−	20613.4i	−0.0295746	−	0.0440594i
$685$	−369238.			−0.786911
$686$	−78953.5	−	259287.i	−0.167773	−	0.550975i
$687$		−	365530.i		−	0.774478i
$688$	264556.	+	108273.i	0.558909	+	0.228740i
$689$	−806782.			−1.69949
$690$	739095.	−	225056.i	1.55239	−	0.472708i
$691$		−	555397.i		−	1.16318i	−0.813481	−	0.581591i	$-0.802430\pi$
$691$		−	555397.i		−	1.16318i	0.813481	−	0.581591i	$-0.197570\pi$
$692$	185658.	−	124622.i	0.387705	−	0.260245i
$693$	−11792.8			−0.0245555
$694$	−111907.	−	367507.i	−0.232347	−	0.763038i
$695$			391164.i			0.809820i
$696$	−309470.	−	252336.i	−0.638852	−	0.520907i
$697$	24337.9			0.0500976
$698$	128195.	−	39035.8i	0.263125	−	0.0801222i
$699$			609833.i			1.24812i
$700$	84893.4	+	126472.i	0.173252	+	0.258105i
$701$	−813758.			−1.65600			−0.827998	−	0.560731i	$-0.810520\pi$
$701$	−813758.			−1.65600			−0.827998	+	0.560731i	$0.810520\pi$
$702$	125795.	+	413117.i	0.255264	+	0.838298i
$703$		−	59300.5i		−	0.119991i
$704$	−170820.	+	35107.3i	−0.344663	+	0.0708357i
$705$	1.29300e6			2.60147
$706$	134650.	−	41001.3i	0.270145	−	0.0822599i
$707$			69435.6i			0.138913i
$708$	502209.	−	337105.i	1.00188	−	0.672509i
$709$	−797738.			−1.58697			−0.793484	−	0.608591i	$-0.791735\pi$
$709$	−797738.			−1.58697			−0.793484	+	0.608591i	$0.791735\pi$
$710$	−81026.5	−	266094.i	−0.160735	−	0.527861i
$711$			197561.i			0.390808i
$712$	450525.	−	552534.i	0.888708	−	1.08993i
$713$	−738000.			−1.45170
$714$	−51190.4	+	15587.6i	−0.100413	+	0.0305762i
$715$		−	263324.i		−	0.515084i
$716$	−458823.	−	683542.i	−0.894993	−	1.33333i
$717$	747179.			1.45340
$718$	−91012.8	−	298890.i	−0.176544	−	0.579779i
$719$			156363.i			0.302466i	0.988498	+	0.151233i	$0.0483243\pi$
$719$			156363.i			0.302466i	−0.988498	+	0.151233i	$0.951676\pi$
$720$	−64715.4	+	158127.i	−0.124837	+	0.305029i
$721$	−274985.			−0.528979
$722$	26246.2	−	7992.03i	0.0503491	−	0.0153314i
$723$			70211.8i			0.134318i
$724$	766469.	−	514488.i	1.46224	−	0.981517i
$725$	−402309.			−0.765392
$726$	149276.	+	490229.i	0.283216	+	0.930093i
$727$		−	754590.i		−	1.42772i	−0.700289	−	0.713859i	$-0.746946\pi$
$727$		−	754590.i		−	1.42772i	0.700289	−	0.713859i	$-0.253054\pi$
$728$	−127315.	−	103810.i	−0.240224	−	0.195874i
$729$	−358227.			−0.674067
$730$	−67473.3	+	20545.8i	−0.126615	+	0.0385547i
$731$			101177.i			0.189341i
$732$	−631069.	−	940148.i	−1.17775	−	1.75458i
$733$	972655.			1.81030			0.905150	−	0.425091i	$-0.139758\pi$
$733$	972655.			1.81030			0.905150	+	0.425091i	$0.139758\pi$
$734$	−10821.1	−	35536.8i	−0.0200853	−	0.0659608i
$735$		−	776412.i		−	1.43720i
$736$	553566.	+	51565.5i	1.02191	+	0.0951926i
$737$	−55419.6			−0.102030
$738$	19256.7	−	5863.72i	0.0353565	−	0.0107662i
$739$		−	578463.i		−	1.05922i	−0.848241	−	0.529611i	$-0.822338\pi$
$739$		−	578463.i		−	1.05922i	0.848241	−	0.529611i	$-0.177662\pi$
$740$	−338846.	+	227449.i	−0.618784	+	0.415355i
$741$	143601.			0.261530
$742$	80044.7	+	262870.i	0.145387	+	0.477457i
$743$			689504.i			1.24899i	0.781029	+	0.624495i	$0.214695\pi$
$743$			689504.i			1.24899i	−0.781029	+	0.624495i	$0.785305\pi$
$744$	549022.	−	673333.i	0.991844	−	1.21642i
$745$	−782121.			−1.40916
$746$	57935.2	−	17641.4i	0.104103	−	0.0316998i
$747$		−	163324.i		−	0.292690i
$748$	−34400.9	−	51249.4i	−0.0614846	−	0.0915979i
$749$	−137122.			−0.244424
$750$	7859.54	+	25811.1i	0.0139725	+	0.0458864i
$751$		−	434757.i		−	0.770845i	−0.922740	−	0.385423i	$-0.874056\pi$
$751$		−	434757.i		−	0.770845i	0.922740	−	0.385423i	$-0.125944\pi$
$752$	861112.	+	352421.i	1.52273	+	0.623199i
$753$	584265.			1.03043
$754$	415058.	−	126386.i	0.730072	−	0.222309i
$755$			152566.i			0.267648i
$756$	122123.	−	81974.6i	0.213676	−	0.143429i
$757$	152072.			0.265373			0.132686	−	0.991158i	$-0.457640\pi$
$757$	152072.			0.265373			0.132686	+	0.991158i	$0.457640\pi$
$758$	36084.7	+	118504.i	0.0628036	+	0.206250i
$759$			230852.i			0.400729i
$760$	−146335.	−	119318.i	−0.253350	−	0.206576i
$761$	251169.			0.433707			0.216853	−	0.976204i	$-0.430421\pi$
$761$	251169.			0.433707			0.216853	+	0.976204i	$0.430421\pi$
$762$	−820208.	+	249755.i	−1.41258	+	0.430135i
$763$		−	192891.i		−	0.331332i
$764$	−57065.7	−	85014.7i	−0.0977661	−	0.145649i
$765$	−60473.9			−0.103334
$766$	133927.	+	439821.i	0.228249	+	0.749581i
$767$			657221.i			1.11717i
$768$	−458862.	+	466698.i	−0.777964	+	0.791250i
$769$	−3848.83			−0.00650843			−0.00325421	−	0.999995i	$-0.501036\pi$
$769$	−3848.83			−0.00650843			−0.00325421	+	0.999995i	$0.501036\pi$
$770$	−85797.8	+	26125.6i	−0.144709	+	0.0440642i
$771$			961711.i			1.61784i
$772$	−389839.	+	261677.i	−0.654109	+	0.439067i
$773$	−176467.			−0.295327			−0.147664	−	0.989038i	$-0.547175\pi$
$773$	−176467.			−0.295327			−0.147664	+	0.989038i	$0.547175\pi$
$774$	24376.5	+	80053.4i	0.0406901	+	0.133628i
$775$		−	875327.i		−	1.45736i
$776$	−346301.	+	424711.i	−0.575083	+	0.705294i
$777$	−105715.			−0.175103
$778$	193798.	−	59011.9i	0.320176	−	0.0974945i
$779$			22245.3i			0.0366575i
$780$	−550787.	−	820546.i	−0.905304	−	1.34870i
$781$	83113.2			0.136260
$782$	57321.4	+	188246.i	0.0937353	+	0.307831i
$783$			388477.i			0.633638i
$784$	211620.	−	517077.i	0.344291	−	0.841246i
$785$	−1.41764e6			−2.30052
$786$	601313.	−	183101.i	0.973320	−	0.296379i
$787$		−	616043.i		−	0.994629i	−0.867570	−	0.497315i	$-0.834319\pi$
$787$		−	616043.i		−	0.994629i	0.867570	−	0.497315i	$-0.165681\pi$
$788$	426441.	−	286246.i	0.686762	−	0.460985i
$789$	−842420.			−1.35324
$790$	437677.	+	1.43735e6i	0.701292	+	2.30307i
$791$			178145.i			0.284722i
$792$	−39566.3	−	32261.6i	−0.0630777	−	0.0514322i
$793$	1.23033e6			1.95649
$794$	512849.	−	156164.i	0.813482	−	0.247708i
$795$			1.65311e6i			2.61558i
$796$	−173436.	−	258380.i	−0.273724	−	0.407787i
$797$	−864478.			−1.36094			−0.680468	−	0.732778i	$-0.738223\pi$
$797$	−864478.			−1.36094			−0.680468	+	0.732778i	$0.738223\pi$
$798$	−14247.4	−	46789.0i	−0.0223733	−	0.0734748i
$799$			329323.i			0.515856i
$800$	−61160.7	+	656573.i	−0.0955636	+	1.02590i
$801$	208706.			0.325290
$802$	−591155.	+	180008.i	−0.919078	+	0.279862i
$803$		−	21074.9i		−	0.0326840i
$804$	−172693.	+	115919.i	−0.267155	+	0.179326i
$805$	285925.			0.441226
$806$	274986.	+	903065.i	0.423292	+	1.39011i
$807$			825750.i			1.26795i
$808$	−189956.	+	232966.i	−0.290957	+	0.356837i
$809$	−425135.			−0.649577			−0.324788	−	0.945787i	$-0.605293\pi$
$809$	−425135.			−0.649577			−0.324788	+	0.945787i	$0.605293\pi$
$810$	1.05335e6	−	320747.i	1.60547	−	0.488870i
$811$		−	675387.i		−	1.02686i	−0.858132	−	0.513430i	$-0.828375\pi$
$811$		−	675387.i		−	1.02686i	0.858132	−	0.513430i	$-0.171625\pi$
$812$	−82359.8	−	122697.i	−0.124912	−	0.186090i
$813$	1.11378e6			1.68507
$814$	−35521.2	−	116653.i	−0.0536091	−	0.176055i
$815$		−	20280.5i		−	0.0305326i
$816$	−214394.	−	87743.4i	−0.321982	−	0.131775i
$817$	−92477.4			−0.138545
$818$	−1.13301e6	+	345004.i	−1.69327	+	0.515605i
$819$		−	48090.1i		−	0.0716948i
$820$	127111.	−	85322.4i	0.189040	−	0.126892i
$821$	153021.			0.227020			0.113510	−	0.993537i	$-0.463791\pi$
$821$	153021.			0.227020			0.113510	+	0.993537i	$0.463791\pi$
$822$	−120616.	−	396108.i	−0.178509	−	0.586232i
$823$			203532.i			0.300492i	0.988649	+	0.150246i	$0.0480066\pi$
$823$			203532.i			0.300492i	−0.988649	+	0.150246i	$0.951993\pi$
$824$	−922612.	−	752278.i	−1.35883	−	1.10796i
$825$	−273809.			−0.402291
$826$	214139.	−	65206.0i	0.313860	−	0.0955713i
$827$		−	140842.i		−	0.205930i	−0.994685	−	0.102965i	$-0.967167\pi$
$827$		−	140842.i		−	0.205930i	0.994685	−	0.102965i	$-0.0328330\pi$
$828$	90708.2	+	135134.i	0.132308	+	0.197108i
$829$	696347.			1.01325			0.506625	−	0.862166i	$-0.330893\pi$
$829$	696347.			1.01325			0.506625	+	0.862166i	$0.330893\pi$
$830$	−361827.	−	1.18826e6i	−0.525224	−	1.72486i
$831$			628977.i			0.910821i
$832$	−143165.	−	696593.i	−0.206819	−	1.00631i
$833$	197750.			0.284988
$834$	−419628.	+	127778.i	−0.603299	+	0.183706i
$835$			1.32374e6i			1.89858i
$836$	46843.0	−	31443.1i	0.0670243	−	0.0449897i
$837$	−845231.			−1.20649
$838$	−252334.	−	828676.i	−0.359325	−	1.18004i
$839$			1.14173e6i			1.62195i	0.585079	+	0.810976i	$0.301063\pi$
$839$			1.14173e6i			1.62195i	−0.585079	+	0.810976i	$0.698937\pi$
$840$	−212709.	+	260871.i	−0.301458	+	0.369715i
$841$	−316979.			−0.448165
$842$	625501.	−	190467.i	0.882275	−	0.268655i
$843$		−	394260.i		−	0.554788i
$844$	−164704.	−	245371.i	−0.231216	−	0.344459i
$845$	56402.9			0.0789930
$846$	79343.8	+	260569.i	0.110859	+	0.364067i
$847$			189650.i			0.264354i
$848$	−450576.	+	1.10094e6i	−0.626579	+	1.53100i
$849$	−1.14463e6			−1.58799
$850$	−223274.	+	67987.7i	−0.309030	+	0.0941006i
$851$			388753.i			0.536802i
$852$	258990.	−	173845.i	0.356782	−	0.239488i
$853$	123535.			0.169782			0.0848910	−	0.996390i	$-0.472946\pi$
$853$	123535.			0.169782			0.0848910	+	0.996390i	$0.472946\pi$
$854$	−122067.	−	400875.i	−0.167372	−	0.549658i
$855$		−	55274.4i		−	0.0756121i
$856$	−460064.	−	375127.i	−0.627871	−	0.511953i
$857$	991442.			1.34991			0.674957	−	0.737857i	$-0.264162\pi$
$857$	991442.			1.34991			0.674957	+	0.737857i	$0.264162\pi$
$858$	282486.	−	86017.7i	0.383727	−	0.116846i
$859$			456137.i			0.618172i	0.951034	+	0.309086i	$0.100023\pi$
$859$			456137.i			0.618172i	−0.951034	+	0.309086i	$0.899977\pi$
$860$	354700.	+	528421.i	0.479583	+	0.714469i
$861$	39656.7			0.0534946
$862$	253439.	+	832303.i	0.341082	+	1.12013i
$863$		−	599038.i		−	0.804327i	−0.915568	−	0.402164i	$-0.868258\pi$
$863$		−	599038.i		−	0.804327i	0.915568	−	0.402164i	$-0.131742\pi$
$864$	633999.	+	59057.9i	0.849300	+	0.0791135i
$865$	497837.			0.665357
$866$	−647002.	+	197014.i	−0.862720	+	0.262701i
$867$			752113.i			1.00056i
$868$	266959.	−	179195.i	0.354328	−	0.237841i
$869$	−448948.			−0.594507
$870$	−258968.	−	850462.i	−0.342143	−	1.12361i
$871$		−	225997.i		−	0.297897i
$872$	527694.	−	647176.i	0.693983	−	0.851117i
$873$	−160424.			−0.210495
$874$	−172060.	+	52392.9i	−0.225247	+	0.0685882i
$875$			9985.25i			0.0130420i
$876$	−44081.8	−	65671.8i	−0.0574449	−	0.0855797i
$877$	−887326.			−1.15368			−0.576839	−	0.816858i	$-0.695714\pi$
$877$	−887326.			−1.15368			−0.576839	+	0.816858i	$0.695714\pi$
$878$	−372175.	−	1.22224e6i	−0.482790	−	1.58550i
$879$			680104.i			0.880233i
$880$	−359335.	−	147063.i	−0.464018	−	0.189905i
$881$	7753.73			0.00998985			0.00499492	−	0.999988i	$-0.498410\pi$
$881$	7753.73			0.00998985			0.00499492	+	0.999988i	$0.498410\pi$
$882$	156465.	−	47644.0i	0.201131	−	0.0612451i
$883$		−	835709.i		−	1.07185i	−0.844266	−	0.535925i	$-0.819963\pi$
$883$		−	835709.i		−	1.07185i	0.844266	−	0.535925i	$-0.180037\pi$
$884$	208991.	−	140284.i	0.267438	−	0.179517i
$885$	1.34666e6			1.71938
$886$	43300.8	+	142202.i	0.0551605	+	0.181149i
$887$		−	251965.i		−	0.320252i	−0.987097	−	0.160126i	$-0.948810\pi$
$887$		−	251965.i		−	0.320252i	0.987097	−	0.160126i	$-0.0511901\pi$
$888$	−354688.	−	289205.i	−0.449801	−	0.366758i
$889$	−317305.			−0.401489
$890$	1.51843e6	−	462366.i	1.91697	−	0.583722i
$891$			329008.i			0.414429i
$892$	675584.	+	1.00646e6i	0.849081	+	1.26494i
$893$	−301008.			−0.377464
$894$	−255489.	−	839035.i	−0.319666	−	1.04980i
$895$		−	1.83290e6i		−	2.28819i
$896$	−212764.	+	115759.i	−0.265022	+	0.144191i
$897$	−941399.			−1.17001
$898$	−1.28399e6	+	390979.i	−1.59225	+	0.484843i
$899$			849203.i			1.05073i
$900$	−160280.	+	107587.i	−0.197877	+	0.132824i
$901$	−421044.			−0.518655
$902$	13325.0	+	43759.9i	0.0163778	+	0.0537852i
$903$			164859.i			0.202180i
$904$	−487353.	+	597701.i	−0.596358	+	0.731387i
$905$	2.05526e6			2.50940
$906$	−163668.	+	49837.5i	−0.199392	+	0.0607155i
$907$			1.59671e6i			1.94093i	0.241236	+	0.970466i	$0.422447\pi$
$907$			1.59671e6i			1.94093i	−0.241236	+	0.970466i	$0.577553\pi$
$908$	235807.	+	351299.i	0.286013	+	0.426094i
$909$	−87997.1			−0.106498
$910$	−106539.	−	349877.i	−0.128654	−	0.422506i
$911$		−	1.21908e6i		−	1.46891i	−0.678655	−	0.734457i	$-0.737437\pi$
$911$		−	1.21908e6i		−	1.46891i	0.678655	−	0.734457i	$-0.262563\pi$
$912$	80199.2	−	195960.i	0.0964230	−	0.235602i
$913$	371145.			0.445248
$914$	−715747.	+	217947.i	−0.856775	+	0.260890i
$915$		−	2.52098e6i		−	3.01111i
$916$	486237.	−	326384.i	0.579505	−	0.388989i
$917$	232623.			0.276640
$918$	65650.1	+	215598.i	0.0779023	+	0.255834i
$919$			1.55862e6i			1.84547i	0.385429	+	0.922737i	$0.374053\pi$
$919$			1.55862e6i			1.84547i	−0.385429	+	0.922737i	$0.625947\pi$
$920$	959319.	+	782209.i	1.13341	+	0.924160i
$921$	−1.02710e6			−1.21086
$922$	781472.	−	237960.i	0.919288	−	0.279926i
$923$			338930.i			0.397838i
$924$	−56053.6	−	83507.0i	−0.0656537	−	0.0978090i
$925$	−461091.			−0.538894
$926$	55076.9	+	180875.i	0.0642314	+	0.210939i
$927$		−	348494.i		−	0.405542i
$928$	59335.4	−	636978.i	0.0688998	−	0.739654i
$929$	1.17254e6			1.35862			0.679309	−	0.733852i	$-0.262279\pi$
$929$	1.17254e6			1.35862			0.679309	+	0.733852i	$0.262279\pi$
$930$	1.85040e6	−	563452.i	2.13944	−	0.651465i
$931$			180748.i			0.208533i
$932$	−811216.	+	544524.i	−0.933909	+	0.626881i
$933$	−1.09743e6			−1.26071
$934$	383333.	+	1.25888e6i	0.439423	+	1.44308i
$935$		−	137424.i		−	0.157195i
$936$	131560.	−	161349.i	0.150167	−	0.184168i
$937$	931268.			1.06071			0.530353	−	0.847777i	$-0.322059\pi$
$937$	931268.			1.06071			0.530353	+	0.847777i	$0.322059\pi$
$938$	−73635.6	+	22422.3i	−0.0836917	+	0.0254844i
$939$		−	74250.1i		−	0.0842105i
$940$	1.15452e6	+	1.71998e6i	1.30661	+	1.94656i
$941$	−391705.			−0.442364			−0.221182	−	0.975233i	$-0.570992\pi$
$941$	−391705.			−0.442364			−0.221182	+	0.975233i	$0.570992\pi$
$942$	−463087.	−	1.52080e6i	−0.521868	−	1.71384i
$943$		−	145832.i		−	0.163995i
$944$	896851.	+	367048.i	1.00641	+	0.411888i
$945$	327470.			0.366698
$946$	−181917.	+	55394.3i	−0.203279	+	0.0618989i
$947$		−	936349.i		−	1.04409i	−0.852918	−	0.522045i	$-0.825169\pi$
$947$		−	936349.i		−	1.04409i	0.852918	−	0.522045i	$-0.174831\pi$
$948$	−1.39897e6	+	939052.i	−1.55665	+	1.04490i
$949$	85942.0			0.0954274
$950$	−62142.1	−	204077.i	−0.0688555	−	0.226125i
$951$		−	781995.i		−	0.864655i
$952$	−66443.3	−	54176.5i	−0.0733124	−	0.0597774i
$953$	1.21879e6			1.34197			0.670987	−	0.741469i	$-0.265871\pi$
$953$	1.21879e6			1.34197			0.670987	+	0.741469i	$0.265871\pi$
$954$	−333141.	+	101442.i	−0.366042	+	0.111461i
$955$		−	227965.i		−	0.249954i
$956$	667162.	+	993918.i	0.729987	+	1.08751i
$957$	265637.			0.290045
$958$	287709.	+	944847.i	0.313489	+	1.02951i
$959$		−	153238.i		−	0.166621i
$960$	−1.42733e6	+	293348.i	−1.54876	+	0.318303i
$961$	−924139.			−1.00067
$962$	475703.	−	144853.i	0.514027	−	0.156523i
$963$		−	173778.i		−	0.187388i
$964$	−93397.5	+	62692.6i	−0.100504	+	0.0674624i
$965$	−1.04534e6			−1.12254
$966$	93400.8	+	306732.i	0.100091	+	0.328704i
$967$		−	1.65552e6i		−	1.77044i	−0.465170	−	0.885221i	$-0.654007\pi$
$967$		−	1.65552e6i		−	1.77044i	0.465170	−	0.885221i	$-0.345993\pi$
$968$	−518826.	+	636300.i	−0.553696	+	0.679065i
$969$	74942.9			0.0798147
$970$	−1.16716e6	+	355403.i	−1.24047	+	0.377727i
$971$		−	799368.i		−	0.847829i	−0.905702	−	0.423914i	$-0.860656\pi$
$971$		−	799368.i		−	0.847829i	0.905702	−	0.423914i	$-0.139344\pi$
$972$	239036.	+	356109.i	0.253006	+	0.376921i
$973$	−162337.			−0.171471
$974$	−114549.	−	376185.i	−0.120747	−	0.396537i
$975$		−	1.11657e6i		−	1.17457i
$976$	687123.	−	1.67893e6i	0.721332	−	1.76251i
$977$	−517725.			−0.542388			−0.271194	−	0.962525i	$-0.587418\pi$
$977$	−517725.			−0.542388			−0.271194	+	0.962525i	$0.587418\pi$
$978$	21756.3	−	6624.86i	0.0227461	−	0.00692626i
$979$			474274.i			0.494839i
$980$	1.03280e6	−	693263.i	1.07539	−	0.721849i
$981$	244455.			0.254015
$982$	−89113.5	−	292653.i	−0.0924104	−	0.303480i
$983$		−	1.56050e6i		−	1.61494i	−0.589909	−	0.807470i	$-0.700836\pi$
$983$		−	1.56050e6i		−	1.61494i	0.589909	−	0.807470i	$-0.299164\pi$
$984$	133053.	+	108489.i	0.137416	+	0.112046i
$985$	1.14349e6			1.17858
$986$	216611.	−	65958.6i	0.222806	−	0.0678450i
$987$			536607.i			0.550835i
$988$	128223.	+	191022.i	0.131356	+	0.195691i
$989$	606249.			0.619810
$990$	−33109.5	−	108733.i	−0.0337818	−	0.110941i
$991$			648617.i			0.660452i	0.943902	+	0.330226i	$0.107125\pi$
$991$			648617.i			0.660452i	−0.943902	+	0.330226i	$0.892875\pi$
$992$	1.38591e6	+	129099.i	1.40835	+	0.131190i
$993$	−207625.			−0.210563
$994$	110432.	−	33626.9i	0.111769	−	0.0340340i
$995$		−	692839.i		−	0.699820i
$996$	1.15653e6	−	776314.i	1.16584	−	0.782562i
$997$	−639650.			−0.643505			−0.321752	−	0.946824i	$-0.604272\pi$
$997$	−639650.			−0.643505			−0.321752	+	0.946824i	$0.604272\pi$
$998$	124206.	+	407899.i	0.124705	+	0.409536i
$999$			445238.i			0.446130i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.5.b.a.39.4	yes	36
4.3	odd	2	inner	76.5.b.a.39.3	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.5.b.a.39.3	✓	36	4.3	odd	2	inner
76.5.b.a.39.4	yes	36	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-3.82653 + 1.16519i) q^{2} -9.98677i q^{3} +(13.2847 - 8.91726i) q^{4} +35.6225 q^{5} +(11.6365 + 38.2147i) q^{6} +14.7837i q^{7} +(-40.4439 + 49.6013i) q^{8} -18.7357 q^{9} +O(q^{10})\)	\(q+(-3.82653 + 1.16519i) q^{2} -9.98677i q^{3} +(13.2847 - 8.91726i) q^{4} +35.6225 q^{5} +(11.6365 + 38.2147i) q^{6} +14.7837i q^{7} +(-40.4439 + 49.6013i) q^{8} -18.7357 q^{9} +(-136.310 + 41.5069i) q^{10} -42.5759i q^{11} +(-89.0547 - 132.671i) q^{12} +173.621 q^{13} +(-17.2258 - 56.5703i) q^{14} -355.754i q^{15} +(96.9649 - 236.926i) q^{16} +90.6097 q^{17} +(71.6926 - 21.8306i) q^{18} +82.8191i q^{19} +(473.233 - 317.655i) q^{20} +147.642 q^{21} +(49.6089 + 162.918i) q^{22} -542.932i q^{23} +(495.357 + 403.904i) q^{24} +643.961 q^{25} +(-664.367 + 202.302i) q^{26} -621.820i q^{27} +(131.830 + 196.397i) q^{28} -624.742 q^{29} +(414.520 + 1361.30i) q^{30} -1359.29i q^{31} +(-94.9759 + 1019.59i) q^{32} -425.196 q^{33} +(-346.721 + 105.577i) q^{34} +526.632i q^{35} +(-248.897 + 167.071i) q^{36} -716.024 q^{37} +(-96.4999 - 316.910i) q^{38} -1733.92i q^{39} +(-1440.71 + 1766.92i) q^{40} +268.601 q^{41} +(-564.955 + 172.030i) q^{42} +1116.62i q^{43} +(-379.660 - 565.606i) q^{44} -667.411 q^{45} +(632.618 + 2077.55i) q^{46} +3634.52i q^{47} +(-2366.12 - 968.367i) q^{48} +2182.44 q^{49} +(-2464.13 + 750.336i) q^{50} -904.898i q^{51} +(2306.50 - 1548.23i) q^{52} -4646.79 q^{53} +(724.538 + 2379.41i) q^{54} -1516.66i q^{55} +(-733.291 - 597.911i) q^{56} +827.096 q^{57} +(2390.59 - 727.942i) q^{58} +3785.37i q^{59} +(-3172.35 - 4726.07i) q^{60} +7086.31 q^{61} +(1583.83 + 5201.35i) q^{62} -276.983i q^{63} +(-824.582 - 4012.14i) q^{64} +6184.82 q^{65} +(1627.02 - 495.433i) q^{66} -1301.67i q^{67} +(1203.72 - 807.990i) q^{68} -5422.14 q^{69} +(-613.626 - 2015.17i) q^{70} +1952.12i q^{71} +(757.744 - 929.314i) q^{72} +494.997 q^{73} +(2739.89 - 834.303i) q^{74} -6431.09i q^{75} +(738.519 + 1100.22i) q^{76} +629.429 q^{77} +(2020.34 + 6634.89i) q^{78} -10544.7i q^{79} +(3454.13 - 8439.88i) q^{80} -7727.56 q^{81} +(-1027.81 + 312.971i) q^{82} +8717.27i q^{83} +(1961.37 - 1316.56i) q^{84} +3227.74 q^{85} +(-1301.07 - 4272.78i) q^{86} +6239.15i q^{87} +(2111.82 + 1721.93i) q^{88} -11139.5 q^{89} +(2553.87 - 777.660i) q^{90} +2566.77i q^{91} +(-4841.47 - 7212.67i) q^{92} -13574.9 q^{93} +(-4234.91 - 13907.6i) q^{94} +2950.22i q^{95} +(10182.4 + 948.503i) q^{96} +8562.50 q^{97} +(-8351.18 + 2542.96i) q^{98} +797.687i 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

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Database

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