LMFDB - Embedded newform 1045.4.a.i.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,4,Mod(1,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1045.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1045.a (trivial)

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:	yes
Analytic conductor:	$61.6569959560$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.70323 q^{2} +9.22981 q^{3} -5.09901 q^{4} -5.00000 q^{5} +15.7205 q^{6} -12.5263 q^{7} -22.3106 q^{8} +58.1894 q^{9} +O(q^{10})$	\(q+1.70323 q^{2} +9.22981 q^{3} -5.09901 q^{4} -5.00000 q^{5} +15.7205 q^{6} -12.5263 q^{7} -22.3106 q^{8} +58.1894 q^{9} -8.51615 q^{10} +11.0000 q^{11} -47.0629 q^{12} +1.59275 q^{13} -21.3351 q^{14} -46.1491 q^{15} +2.79195 q^{16} +98.5925 q^{17} +99.1100 q^{18} +19.0000 q^{19} +25.4950 q^{20} -115.615 q^{21} +18.7355 q^{22} +130.694 q^{23} -205.923 q^{24} +25.0000 q^{25} +2.71281 q^{26} +287.873 q^{27} +63.8716 q^{28} -151.767 q^{29} -78.6025 q^{30} -223.835 q^{31} +183.240 q^{32} +101.528 q^{33} +167.926 q^{34} +62.6314 q^{35} -296.708 q^{36} +406.522 q^{37} +32.3614 q^{38} +14.7007 q^{39} +111.553 q^{40} +316.354 q^{41} -196.919 q^{42} +315.567 q^{43} -56.0891 q^{44} -290.947 q^{45} +222.602 q^{46} -350.892 q^{47} +25.7692 q^{48} -186.092 q^{49} +42.5807 q^{50} +909.991 q^{51} -8.12143 q^{52} +303.164 q^{53} +490.313 q^{54} -55.0000 q^{55} +279.469 q^{56} +175.366 q^{57} -258.494 q^{58} +520.149 q^{59} +235.314 q^{60} -501.881 q^{61} -381.242 q^{62} -728.897 q^{63} +289.765 q^{64} -7.96373 q^{65} +172.925 q^{66} +878.954 q^{67} -502.724 q^{68} +1206.28 q^{69} +106.676 q^{70} -1084.45 q^{71} -1298.24 q^{72} +773.520 q^{73} +692.400 q^{74} +230.745 q^{75} -96.8812 q^{76} -137.789 q^{77} +25.0387 q^{78} +768.881 q^{79} -13.9598 q^{80} +1085.90 q^{81} +538.823 q^{82} +433.883 q^{83} +589.523 q^{84} -492.963 q^{85} +537.484 q^{86} -1400.78 q^{87} -245.417 q^{88} +1017.63 q^{89} -495.550 q^{90} -19.9512 q^{91} -666.411 q^{92} -2065.95 q^{93} -597.649 q^{94} -95.0000 q^{95} +1691.27 q^{96} +876.662 q^{97} -316.958 q^{98} +640.084 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 2 q^{2} + 9 q^{3} + 122 q^{4} - 125 q^{5} + 11 q^{6} - 15 q^{7} + 60 q^{8} + 300 q^{9}+O(q^{10}) $ 25 * q + 2 * q^2 + 9 * q^3 + 122 * q^4 - 125 * q^5 + 11 * q^6 - 15 * q^7 + 60 * q^8 + 300 * q^9	\( 25 q + 2 q^{2} + 9 q^{3} + 122 q^{4} - 125 q^{5} + 11 q^{6} - 15 q^{7} + 60 q^{8} + 300 q^{9} - 10 q^{10} + 275 q^{11} + 44 q^{12} + 53 q^{13} - 51 q^{14} - 45 q^{15} + 438 q^{16} + 153 q^{17} + 9 q^{18} + 475 q^{19} - 610 q^{20} + 259 q^{21} + 22 q^{22} - 7 q^{23} + 186 q^{24} + 625 q^{25} + 543 q^{26} + 495 q^{27} - 525 q^{28} + 169 q^{29} - 55 q^{30} + 102 q^{31} + 327 q^{32} + 99 q^{33} - 879 q^{34} + 75 q^{35} + 2293 q^{36} - 46 q^{37} + 38 q^{38} + 233 q^{39} - 300 q^{40} + 1190 q^{41} - 684 q^{42} - 408 q^{43} + 1342 q^{44} - 1500 q^{45} + 757 q^{46} + 1068 q^{47} + 715 q^{48} + 1930 q^{49} + 50 q^{50} + 1655 q^{51} - 94 q^{52} + 143 q^{53} + 1970 q^{54} - 1375 q^{55} - 1397 q^{56} + 171 q^{57} + 1366 q^{58} + 2945 q^{59} - 220 q^{60} + 1160 q^{61} + 194 q^{62} + 1804 q^{63} + 3000 q^{64} - 265 q^{65} + 121 q^{66} - 353 q^{67} + 5452 q^{68} + 3289 q^{69} + 255 q^{70} + 230 q^{71} + 196 q^{72} + 1357 q^{73} + 4379 q^{74} + 225 q^{75} + 2318 q^{76} - 165 q^{77} + 2008 q^{78} + 1266 q^{79} - 2190 q^{80} + 1709 q^{81} + 1010 q^{82} + 3856 q^{83} + 9354 q^{84} - 765 q^{85} + 6746 q^{86} + 3113 q^{87} + 660 q^{88} + 3562 q^{89} - 45 q^{90} - 833 q^{91} + 4276 q^{92} + 1312 q^{93} + 5124 q^{94} - 2375 q^{95} + 3828 q^{96} - 914 q^{97} + 2478 q^{98} + 3300 q^{99}+O(q^{100}) \) 25 * q + 2 * q^2 + 9 * q^3 + 122 * q^4 - 125 * q^5 + 11 * q^6 - 15 * q^7 + 60 * q^8 + 300 * q^9 - 10 * q^10 + 275 * q^11 + 44 * q^12 + 53 * q^13 - 51 * q^14 - 45 * q^15 + 438 * q^16 + 153 * q^17 + 9 * q^18 + 475 * q^19 - 610 * q^20 + 259 * q^21 + 22 * q^22 - 7 * q^23 + 186 * q^24 + 625 * q^25 + 543 * q^26 + 495 * q^27 - 525 * q^28 + 169 * q^29 - 55 * q^30 + 102 * q^31 + 327 * q^32 + 99 * q^33 - 879 * q^34 + 75 * q^35 + 2293 * q^36 - 46 * q^37 + 38 * q^38 + 233 * q^39 - 300 * q^40 + 1190 * q^41 - 684 * q^42 - 408 * q^43 + 1342 * q^44 - 1500 * q^45 + 757 * q^46 + 1068 * q^47 + 715 * q^48 + 1930 * q^49 + 50 * q^50 + 1655 * q^51 - 94 * q^52 + 143 * q^53 + 1970 * q^54 - 1375 * q^55 - 1397 * q^56 + 171 * q^57 + 1366 * q^58 + 2945 * q^59 - 220 * q^60 + 1160 * q^61 + 194 * q^62 + 1804 * q^63 + 3000 * q^64 - 265 * q^65 + 121 * q^66 - 353 * q^67 + 5452 * q^68 + 3289 * q^69 + 255 * q^70 + 230 * q^71 + 196 * q^72 + 1357 * q^73 + 4379 * q^74 + 225 * q^75 + 2318 * q^76 - 165 * q^77 + 2008 * q^78 + 1266 * q^79 - 2190 * q^80 + 1709 * q^81 + 1010 * q^82 + 3856 * q^83 + 9354 * q^84 - 765 * q^85 + 6746 * q^86 + 3113 * q^87 + 660 * q^88 + 3562 * q^89 - 45 * q^90 - 833 * q^91 + 4276 * q^92 + 1312 * q^93 + 5124 * q^94 - 2375 * q^95 + 3828 * q^96 - 914 * q^97 + 2478 * q^98 + 3300 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.70323	0.602183	0.301091	−	0.953595i	$-0.402649\pi$
$2$	1.70323	0.602183	0.301091	+	0.953595i	$0.402649\pi$
$3$	9.22981	1.77628	0.888139	−	0.459575i	$-0.151998\pi$
$3$	9.22981	1.77628	0.888139	+	0.459575i	$0.151998\pi$
$4$	−5.09901	−0.637376
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	15.7205	1.06964
$7$	−12.5263	−0.676356	−0.338178	−	0.941082i	$-0.609811\pi$
$7$	−12.5263	−0.676356	−0.338178	+	0.941082i	$0.609811\pi$
$8$	−22.3106	−0.985999
$9$	58.1894	2.15516
$10$	−8.51615	−0.269304
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−47.0629	−1.13216
$13$	1.59275	0.0339806	0.0169903	−	0.999856i	$-0.494592\pi$
$13$	1.59275	0.0339806	0.0169903	+	0.999856i	$0.494592\pi$
$14$	−21.3351	−0.407290
$15$	−46.1491	−0.794376
$16$	2.79195	0.0436243
$17$	98.5925	1.40660	0.703300	−	0.710893i	$-0.251709\pi$
$17$	98.5925	1.40660	0.703300	+	0.710893i	$0.251709\pi$
$18$	99.1100	1.29780
$19$	19.0000	0.229416
$19$	19.0000	0.229416
$20$	25.4950	0.285043
$21$	−115.615	−1.20140
$22$	18.7355	0.181565
$23$	130.694	1.18485	0.592427	−	0.805624i	$-0.298170\pi$
$23$	130.694	1.18485	0.592427	+	0.805624i	$0.298170\pi$
$24$	−205.923	−1.75141
$25$	25.0000	0.200000
$26$	2.71281	0.0204625
$27$	287.873	2.05189
$28$	63.8716	0.431093
$29$	−151.767	−0.971808	−0.485904	−	0.874012i	$-0.661510\pi$
$29$	−151.767	−0.971808	−0.485904	+	0.874012i	$0.661510\pi$
$30$	−78.6025	−0.478359
$31$	−223.835	−1.29683	−0.648417	−	0.761285i	$-0.724569\pi$
$31$	−223.835	−1.29683	−0.648417	+	0.761285i	$0.724569\pi$
$32$	183.240	1.01227
$33$	101.528	0.535568
$34$	167.926	0.847030
$35$	62.6314	0.302475
$36$	−296.708	−1.37365
$37$	406.522	1.80626	0.903132	−	0.429363i	$-0.141262\pi$
$37$	406.522	1.80626	0.903132	+	0.429363i	$0.141262\pi$
$38$	32.3614	0.138150
$39$	14.7007	0.0603591
$40$	111.553	0.440952
$41$	316.354	1.20503	0.602514	−	0.798108i	$-0.294166\pi$
$41$	316.354	1.20503	0.602514	+	0.798108i	$0.294166\pi$
$42$	−196.919	−0.723460
$43$	315.567	1.11915	0.559576	−	0.828779i	$-0.310964\pi$
$43$	315.567	1.11915	0.559576	+	0.828779i	$0.310964\pi$
$44$	−56.0891	−0.192176
$45$	−290.947	−0.963819
$46$	222.602	0.713499
$47$	−350.892	−1.08900	−0.544498	−	0.838762i	$-0.683280\pi$
$47$	−350.892	−1.08900	−0.544498	+	0.838762i	$0.683280\pi$
$48$	25.7692	0.0774888
$49$	−186.092	−0.542543
$50$	42.5807	0.120437
$51$	909.991	2.49851
$52$	−8.12143	−0.0216584
$53$	303.164	0.785712	0.392856	−	0.919600i	$-0.371487\pi$
$53$	303.164	0.785712	0.392856	+	0.919600i	$0.371487\pi$
$54$	490.313	1.23561
$55$	−55.0000	−0.134840
$56$	279.469	0.666886
$57$	175.366	0.407506
$58$	−258.494	−0.585206
$59$	520.149	1.14776	0.573878	−	0.818941i	$-0.305438\pi$
$59$	520.149	1.14776	0.573878	+	0.818941i	$0.305438\pi$
$60$	235.314	0.506316
$61$	−501.881	−1.05343	−0.526715	−	0.850042i	$-0.676577\pi$
$61$	−501.881	−1.05343	−0.526715	+	0.850042i	$0.676577\pi$
$62$	−381.242	−0.780931
$63$	−728.897	−1.45766
$64$	289.765	0.565947
$65$	−7.96373	−0.0151966
$66$	172.925	0.322510
$67$	878.954	1.60271	0.801353	−	0.598191i	$-0.204114\pi$
$67$	878.954	1.60271	0.801353	+	0.598191i	$0.204114\pi$
$68$	−502.724	−0.896533
$69$	1206.28	2.10463
$70$	106.676	0.182145
$71$	−1084.45	−1.81268	−0.906338	−	0.422554i	$-0.861134\pi$
$71$	−1084.45	−1.81268	−0.906338	+	0.422554i	$0.861134\pi$
$72$	−1298.24	−2.12499
$73$	773.520	1.24019	0.620094	−	0.784528i	$-0.287095\pi$
$73$	773.520	1.24019	0.620094	+	0.784528i	$0.287095\pi$
$74$	692.400	1.08770
$75$	230.745	0.355256
$76$	−96.8812	−0.146224
$77$	−137.789	−0.203929
$78$	25.0387	0.0363472
$79$	768.881	1.09501	0.547505	−	0.836802i	$-0.315578\pi$
$79$	768.881	1.09501	0.547505	+	0.836802i	$0.315578\pi$
$80$	−13.9598	−0.0195094
$81$	1085.90	1.48957
$82$	538.823	0.725647
$83$	433.883	0.573793	0.286896	−	0.957962i	$-0.407376\pi$
$83$	433.883	0.573793	0.286896	+	0.957962i	$0.407376\pi$
$84$	589.523	0.765741
$85$	−492.963	−0.629051
$86$	537.484	0.673934
$87$	−1400.78	−1.72620
$88$	−245.417	−0.297290
$89$	1017.63	1.21200	0.606002	−	0.795463i	$-0.292772\pi$
$89$	1017.63	1.21200	0.606002	+	0.795463i	$0.292772\pi$
$90$	−495.550	−0.580395
$91$	−19.9512	−0.0229830
$92$	−666.411	−0.755198
$93$	−2065.95	−2.30354
$94$	−597.649	−0.655774
$95$	−95.0000	−0.102598
$96$	1691.27	1.79807
$97$	876.662	0.917644	0.458822	−	0.888528i	$-0.348271\pi$
$97$	876.662	0.917644	0.458822	+	0.888528i	$0.348271\pi$
$98$	−316.958	−0.326710
$99$	640.084	0.649806
$100$	−127.475	−0.127475
$101$	890.007	0.876821	0.438411	−	0.898775i	$-0.355542\pi$
$101$	890.007	0.876821	0.438411	+	0.898775i	$0.355542\pi$
$102$	1549.92	1.50456
$103$	−778.291	−0.744537	−0.372268	−	0.928125i	$-0.621420\pi$
$103$	−778.291	−0.744537	−0.372268	+	0.928125i	$0.621420\pi$
$104$	−35.5352	−0.0335049
$105$	578.076	0.537281
$106$	516.357	0.473142
$107$	1534.27	1.38620	0.693101	−	0.720840i	$-0.256244\pi$
$107$	1534.27	1.38620	0.693101	+	0.720840i	$0.256244\pi$
$108$	−1467.86	−1.30783
$109$	444.610	0.390697	0.195348	−	0.980734i	$-0.437416\pi$
$109$	444.610	0.390697	0.195348	+	0.980734i	$0.437416\pi$
$110$	−93.6776	−0.0811983
$111$	3752.12	3.20843
$112$	−34.9728	−0.0295055
$113$	−1441.35	−1.19992	−0.599960	−	0.800030i	$-0.704817\pi$
$113$	−1441.35	−1.19992	−0.599960	+	0.800030i	$0.704817\pi$
$114$	298.689	0.245393
$115$	−653.471	−0.529883
$116$	773.862	0.619407
$117$	92.6810	0.0732338
$118$	885.933	0.691159
$119$	−1235.00	−0.951362
$120$	1029.61	0.783254
$121$	121.000	0.0909091
$122$	−854.819	−0.634358
$123$	2919.89	2.14047
$124$	1141.33	0.826571
$125$	−125.000	−0.0894427
$126$	−1241.48	−0.877776
$127$	2536.84	1.77250	0.886251	−	0.463205i	$-0.153300\pi$
$127$	2536.84	1.77250	0.886251	+	0.463205i	$0.153300\pi$
$128$	−972.387	−0.671466
$129$	2912.63	1.98793
$130$	−13.5641	−0.00915113
$131$	−2221.38	−1.48155	−0.740774	−	0.671754i	$-0.765541\pi$
$131$	−2221.38	−1.48155	−0.740774	+	0.671754i	$0.765541\pi$
$132$	−517.692	−0.341358
$133$	−237.999	−0.155167
$134$	1497.06	0.965122
$135$	−1439.36	−0.917634
$136$	−2199.66	−1.38691
$137$	−15.7179	−0.00980200	−0.00490100	−	0.999988i	$-0.501560\pi$
$137$	−15.7179	−0.00980200	−0.00490100	+	0.999988i	$0.501560\pi$
$138$	2054.58	1.26737
$139$	−2142.81	−1.30756	−0.653779	−	0.756685i	$-0.726817\pi$
$139$	−2142.81	−1.30756	−0.653779	+	0.756685i	$0.726817\pi$
$140$	−319.358	−0.192791
$141$	−3238.66	−1.93436
$142$	−1847.06	−1.09156
$143$	17.5202	0.0102455
$144$	162.462	0.0940174
$145$	758.836	0.434606
$146$	1317.48	0.746819
$147$	−1717.60	−0.963707
$148$	−2072.86	−1.15127
$149$	−3198.07	−1.75836	−0.879181	−	0.476488i	$-0.841909\pi$
$149$	−3198.07	−1.75836	−0.879181	+	0.476488i	$0.841909\pi$
$150$	393.012	0.213929
$151$	−713.936	−0.384763	−0.192382	−	0.981320i	$-0.561621\pi$
$151$	−713.936	−0.384763	−0.192382	+	0.981320i	$0.561621\pi$
$152$	−423.902	−0.226204
$153$	5737.04	3.03145
$154$	−234.687	−0.122802
$155$	1119.17	0.579962
$156$	−74.9592	−0.0384714
$157$	9.54114	0.00485010	0.00242505	−	0.999997i	$-0.499228\pi$
$157$	9.54114	0.00485010	0.00242505	+	0.999997i	$0.499228\pi$
$158$	1309.58	0.659396
$159$	2798.14	1.39564
$160$	−916.202	−0.452701
$161$	−1637.11	−0.801383
$162$	1849.53	0.896992
$163$	−2141.83	−1.02921	−0.514605	−	0.857427i	$-0.672061\pi$
$163$	−2141.83	−1.02921	−0.514605	+	0.857427i	$0.672061\pi$
$164$	−1613.09	−0.768057
$165$	−507.640	−0.239513
$166$	739.002	0.345528
$167$	441.766	0.204700	0.102350	−	0.994748i	$-0.467364\pi$
$167$	441.766	0.204700	0.102350	+	0.994748i	$0.467364\pi$
$168$	2579.45	1.18458
$169$	−2194.46	−0.998845
$170$	−839.629	−0.378803
$171$	1105.60	0.494429
$172$	−1609.08	−0.713321
$173$	−2061.14	−0.905813	−0.452907	−	0.891558i	$-0.649613\pi$
$173$	−2061.14	−0.905813	−0.452907	+	0.891558i	$0.649613\pi$
$174$	−2385.85	−1.03949
$175$	−313.157	−0.135271
$176$	30.7115	0.0131532
$177$	4800.88	2.03873
$178$	1733.25	0.729848
$179$	−2405.37	−1.00439	−0.502194	−	0.864755i	$-0.667474\pi$
$179$	−2405.37	−1.00439	−0.502194	+	0.864755i	$0.667474\pi$
$180$	1483.54	0.614315
$181$	−1839.47	−0.755397	−0.377698	−	0.925929i	$-0.623284\pi$
$181$	−1839.47	−0.755397	−0.377698	+	0.925929i	$0.623284\pi$
$182$	−33.9815	−0.0138400
$183$	−4632.27	−1.87119
$184$	−2915.87	−1.16827
$185$	−2032.61	−0.807786
$186$	−3518.79	−1.38715
$187$	1084.52	0.424106
$188$	1789.20	0.694100
$189$	−3605.97	−1.38781
$190$	−161.807	−0.0617826
$191$	342.163	0.129623	0.0648117	−	0.997898i	$-0.479355\pi$
$191$	342.163	0.129623	0.0648117	+	0.997898i	$0.479355\pi$
$192$	2674.47	1.00528
$193$	−3756.96	−1.40120	−0.700600	−	0.713554i	$-0.747084\pi$
$193$	−3756.96	−1.40120	−0.700600	+	0.713554i	$0.747084\pi$
$194$	1493.16	0.552590
$195$	−73.5037	−0.0269934
$196$	948.886	0.345804
$197$	−2299.30	−0.831565	−0.415782	−	0.909464i	$-0.636492\pi$
$197$	−2299.30	−0.831565	−0.415782	+	0.909464i	$0.636492\pi$
$198$	1090.21	0.391302
$199$	−568.196	−0.202404	−0.101202	−	0.994866i	$-0.532269\pi$
$199$	−568.196	−0.202404	−0.101202	+	0.994866i	$0.532269\pi$
$200$	−557.766	−0.197200
$201$	8112.58	2.84685
$202$	1515.89	0.528007
$203$	1901.08	0.657288
$204$	−4640.05	−1.59249
$205$	−1581.77	−0.538905
$206$	−1325.61	−0.448347
$207$	7605.03	2.55355
$208$	4.44687	0.00148238
$209$	209.000	0.0691714
$210$	984.597	0.323541
$211$	2245.79	0.732732	0.366366	−	0.930471i	$-0.380602\pi$
$211$	2245.79	0.732732	0.366366	+	0.930471i	$0.380602\pi$
$212$	−1545.83	−0.500794
$213$	−10009.2	−3.21982
$214$	2613.22	0.834747
$215$	−1577.84	−0.500500
$216$	−6422.62	−2.02317
$217$	2803.82	0.877122
$218$	757.274	0.235271
$219$	7139.45	2.20292
$220$	280.445	0.0859438
$221$	157.033	0.0477972
$222$	6390.72	1.93206
$223$	1628.26	0.488952	0.244476	−	0.969655i	$-0.421384\pi$
$223$	1628.26	0.488952	0.244476	+	0.969655i	$0.421384\pi$
$224$	−2295.32	−0.684654
$225$	1454.74	0.431033
$226$	−2454.95	−0.722571
$227$	3507.95	1.02569	0.512843	−	0.858483i	$-0.328592\pi$
$227$	3507.95	1.02569	0.512843	+	0.858483i	$0.328592\pi$
$228$	−894.195	−0.259735
$229$	−2527.55	−0.729369	−0.364685	−	0.931131i	$-0.618823\pi$
$229$	−2527.55	−0.729369	−0.364685	+	0.931131i	$0.618823\pi$
$230$	−1113.01	−0.319086
$231$	−1271.77	−0.362235
$232$	3386.02	0.958203
$233$	−323.312	−0.0909049	−0.0454525	−	0.998967i	$-0.514473\pi$
$233$	−323.312	−0.0909049	−0.0454525	+	0.998967i	$0.514473\pi$
$234$	157.857	0.0441002
$235$	1754.46	0.487014
$236$	−2652.24	−0.731552
$237$	7096.62	1.94504
$238$	−2103.49	−0.572894
$239$	6213.71	1.68172	0.840861	−	0.541251i	$-0.182049\pi$
$239$	6213.71	1.68172	0.840861	+	0.541251i	$0.182049\pi$
$240$	−128.846	−0.0346541
$241$	−850.324	−0.227279	−0.113639	−	0.993522i	$-0.536251\pi$
$241$	−850.324	−0.227279	−0.113639	+	0.993522i	$0.536251\pi$
$242$	206.091	0.0547439
$243$	2250.05	0.593995
$244$	2559.10	0.671432
$245$	930.461	0.242633
$246$	4973.24	1.28895
$247$	30.2622	0.00779569
$248$	4993.89	1.27868
$249$	4004.65	1.01922
$250$	−212.904	−0.0538609
$251$	−4409.74	−1.10893	−0.554463	−	0.832208i	$-0.687076\pi$
$251$	−4409.74	−1.10893	−0.554463	+	0.832208i	$0.687076\pi$
$252$	3716.65	0.929076
$253$	1437.64	0.357247
$254$	4320.82	1.06737
$255$	−4549.95	−1.11737
$256$	−3974.32	−0.970292
$257$	6198.92	1.50458	0.752292	−	0.658829i	$-0.228948\pi$
$257$	6198.92	1.50458	0.752292	+	0.658829i	$0.228948\pi$
$258$	4960.87	1.19709
$259$	−5092.21	−1.22168
$260$	40.6071	0.00968595
$261$	−8831.24	−2.09441
$262$	−3783.52	−0.892162
$263$	−2328.47	−0.545930	−0.272965	−	0.962024i	$-0.588004\pi$
$263$	−2328.47	−0.545930	−0.272965	+	0.962024i	$0.588004\pi$
$264$	−2265.15	−0.528070
$265$	−1515.82	−0.351381
$266$	−405.368	−0.0934387
$267$	9392.51	2.15286
$268$	−4481.79	−1.02153
$269$	−5371.90	−1.21759	−0.608793	−	0.793329i	$-0.708346\pi$
$269$	−5371.90	−1.21759	−0.608793	+	0.793329i	$0.708346\pi$
$270$	−2451.57	−0.552584
$271$	4693.20	1.05200	0.526000	−	0.850485i	$-0.323691\pi$
$271$	4693.20	1.05200	0.526000	+	0.850485i	$0.323691\pi$
$272$	275.266	0.0613619
$273$	−184.146	−0.0408242
$274$	−26.7713	−0.00590259
$275$	275.000	0.0603023
$276$	−6150.85	−1.34144
$277$	−2013.17	−0.436676	−0.218338	−	0.975873i	$-0.570064\pi$
$277$	−2013.17	−0.436676	−0.218338	+	0.975873i	$0.570064\pi$
$278$	−3649.69	−0.787389
$279$	−13024.8	−2.79489
$280$	−1397.35	−0.298241
$281$	−3491.32	−0.741191	−0.370595	−	0.928794i	$-0.620846\pi$
$281$	−3491.32	−0.741191	−0.370595	+	0.928794i	$0.620846\pi$
$282$	−5516.19	−1.16484
$283$	−4026.46	−0.845753	−0.422876	−	0.906187i	$-0.638980\pi$
$283$	−4026.46	−0.845753	−0.422876	+	0.906187i	$0.638980\pi$
$284$	5529.60	1.15536
$285$	−876.832	−0.182242
$286$	29.8409	0.00616969
$287$	−3962.74	−0.815028
$288$	10662.6	2.18161
$289$	4807.49	0.978524
$290$	1292.47	0.261712
$291$	8091.42	1.62999
$292$	−3944.19	−0.790466
$293$	3695.00	0.736738	0.368369	−	0.929680i	$-0.379916\pi$
$293$	3695.00	0.736738	0.368369	+	0.929680i	$0.379916\pi$
$294$	−2925.46	−0.580328
$295$	−2600.74	−0.513292
$296$	−9069.75	−1.78097
$297$	3166.60	0.618669
$298$	−5447.04	−1.05885
$299$	208.163	0.0402621
$300$	−1176.57	−0.226431
$301$	−3952.89	−0.756945
$302$	−1216.00	−0.231698
$303$	8214.59	1.55748
$304$	53.0471	0.0100081
$305$	2509.41	0.471109
$306$	9771.50	1.82549
$307$	6542.76	1.21634	0.608168	−	0.793809i	$-0.291905\pi$
$307$	6542.76	1.21634	0.608168	+	0.793809i	$0.291905\pi$
$308$	702.588	0.129979
$309$	−7183.48	−1.32250
$310$	1906.21	0.349243
$311$	−6152.46	−1.12178	−0.560891	−	0.827890i	$-0.689541\pi$
$311$	−6152.46	−1.12178	−0.560891	+	0.827890i	$0.689541\pi$
$312$	−327.983	−0.0595140
$313$	−4962.48	−0.896154	−0.448077	−	0.893995i	$-0.647891\pi$
$313$	−4962.48	−0.896154	−0.448077	+	0.893995i	$0.647891\pi$
$314$	16.2508	0.00292065
$315$	3644.49	0.651884
$316$	−3920.53	−0.697933
$317$	4601.70	0.815323	0.407661	−	0.913133i	$-0.366344\pi$
$317$	4601.70	0.815323	0.407661	+	0.913133i	$0.366344\pi$
$318$	4765.88	0.840432
$319$	−1669.44	−0.293011
$320$	−1448.82	−0.253099
$321$	14161.0	2.46228
$322$	−2788.38	−0.482579
$323$	1873.26	0.322696
$324$	−5536.99	−0.949415
$325$	39.8187	0.00679613
$326$	−3648.03	−0.619772
$327$	4103.67	0.693986
$328$	−7058.05	−1.18816
$329$	4395.37	0.736549
$330$	−864.627	−0.144231
$331$	8687.91	1.44269	0.721346	−	0.692575i	$-0.243524\pi$
$331$	8687.91	1.44269	0.721346	+	0.692575i	$0.243524\pi$
$332$	−2212.37	−0.365722
$333$	23655.3	3.89279
$334$	752.429	0.123267
$335$	−4394.77	−0.716752
$336$	−322.792	−0.0524100
$337$	−3925.48	−0.634523	−0.317262	−	0.948338i	$-0.602763\pi$
$337$	−3925.48	−0.634523	−0.317262	+	0.948338i	$0.602763\pi$
$338$	−3737.67	−0.601487
$339$	−13303.4	−2.13139
$340$	2513.62	0.400942
$341$	−2462.18	−0.391010
$342$	1883.09	0.297736
$343$	6627.56	1.04331
$344$	−7040.50	−1.10348
$345$	−6031.42	−0.941219
$346$	−3510.60	−0.545465
$347$	−123.140	−0.0190504	−0.00952521	−	0.999955i	$-0.503032\pi$
$347$	−123.140	−0.0190504	−0.00952521	+	0.999955i	$0.503032\pi$
$348$	7142.60	1.10024
$349$	9043.92	1.38713	0.693567	−	0.720392i	$-0.256038\pi$
$349$	9043.92	1.38713	0.693567	+	0.720392i	$0.256038\pi$
$350$	−533.378	−0.0814579
$351$	458.508	0.0697246
$352$	2015.64	0.305211
$353$	−9336.69	−1.40777	−0.703884	−	0.710315i	$-0.748552\pi$
$353$	−9336.69	−1.40777	−0.703884	+	0.710315i	$0.748552\pi$
$354$	8177.00	1.22769
$355$	5422.23	0.810653
$356$	−5188.89	−0.772502
$357$	−11398.8	−1.68988
$358$	−4096.89	−0.604825
$359$	1650.49	0.242645	0.121323	−	0.992613i	$-0.461286\pi$
$359$	1650.49	0.242645	0.121323	+	0.992613i	$0.461286\pi$
$360$	6491.21	0.950325
$361$	361.000	0.0526316
$362$	−3133.04	−0.454887
$363$	1116.81	0.161480
$364$	101.731	0.0146488
$365$	−3867.60	−0.554629
$366$	−7889.82	−1.12680
$367$	9700.49	1.37973	0.689866	−	0.723937i	$-0.257670\pi$
$367$	9700.49	1.37973	0.689866	+	0.723937i	$0.257670\pi$
$368$	364.892	0.0516884
$369$	18408.5	2.59703
$370$	−3462.00	−0.486435
$371$	−3797.51	−0.531421
$372$	10534.3	1.46822
$373$	11595.6	1.60964	0.804821	−	0.593518i	$-0.202261\pi$
$373$	11595.6	1.60964	0.804821	+	0.593518i	$0.202261\pi$
$374$	1847.18	0.255389
$375$	−1153.73	−0.158875
$376$	7828.61	1.07375
$377$	−241.726	−0.0330227
$378$	−6141.80	−0.835715
$379$	−1193.03	−0.161694	−0.0808469	−	0.996727i	$-0.525762\pi$
$379$	−1193.03	−0.161694	−0.0808469	+	0.996727i	$0.525762\pi$
$380$	484.406	0.0653934
$381$	23414.5	3.14846
$382$	582.783	0.0780570
$383$	12565.3	1.67638	0.838192	−	0.545376i	$-0.183613\pi$
$383$	12565.3	1.67638	0.838192	+	0.545376i	$0.183613\pi$
$384$	−8974.95	−1.19271
$385$	688.946	0.0911998
$386$	−6398.96	−0.843778
$387$	18362.7	2.41196
$388$	−4470.11	−0.584885
$389$	2109.66	0.274972	0.137486	−	0.990504i	$-0.456098\pi$
$389$	2109.66	0.274972	0.137486	+	0.990504i	$0.456098\pi$
$390$	−125.194	−0.0162550
$391$	12885.5	1.66662
$392$	4151.83	0.534947
$393$	−20502.9	−2.63164
$394$	−3916.23	−0.500754
$395$	−3844.40	−0.489704
$396$	−3263.79	−0.414171
$397$	−5717.07	−0.722750	−0.361375	−	0.932421i	$-0.617692\pi$
$397$	−5717.07	−0.722750	−0.361375	+	0.932421i	$0.617692\pi$
$398$	−967.768	−0.121884
$399$	−2196.69	−0.275619
$400$	69.7988	0.00872485
$401$	−7980.40	−0.993821	−0.496910	−	0.867802i	$-0.665532\pi$
$401$	−7980.40	−0.993821	−0.496910	+	0.867802i	$0.665532\pi$
$402$	13817.6	1.71433
$403$	−356.512	−0.0440673
$404$	−4538.15	−0.558865
$405$	−5429.48	−0.666155
$406$	3237.97	0.395808
$407$	4471.74	0.544609
$408$	−20302.5	−2.46353
$409$	5367.97	0.648971	0.324485	−	0.945891i	$-0.394809\pi$
$409$	5367.97	0.648971	0.324485	+	0.945891i	$0.394809\pi$
$410$	−2694.12	−0.324519
$411$	−145.074	−0.0174111
$412$	3968.51	0.474550
$413$	−6515.53	−0.776292
$414$	12953.1	1.53771
$415$	−2169.41	−0.256608
$416$	291.855	0.0343976
$417$	−19777.7	−2.32259
$418$	355.975	0.0416538
$419$	14522.5	1.69325	0.846623	−	0.532193i	$-0.178632\pi$
$419$	14522.5	1.69325	0.846623	+	0.532193i	$0.178632\pi$
$420$	−2947.62	−0.342450
$421$	−3723.17	−0.431012	−0.215506	−	0.976503i	$-0.569140\pi$
$421$	−3723.17	−0.431012	−0.215506	+	0.976503i	$0.569140\pi$
$422$	3825.10	0.441239
$423$	−20418.2	−2.34696
$424$	−6763.77	−0.774712
$425$	2464.81	0.281320
$426$	−17048.0	−1.93892
$427$	6286.70	0.712494
$428$	−7823.26	−0.883532
$429$	161.708	0.0181989
$430$	−2687.42	−0.301393
$431$	6265.70	0.700251	0.350125	−	0.936703i	$-0.386139\pi$
$431$	6265.70	0.700251	0.350125	+	0.936703i	$0.386139\pi$
$432$	803.727	0.0895123
$433$	14520.7	1.61159	0.805797	−	0.592192i	$-0.201737\pi$
$433$	14520.7	1.61159	0.805797	+	0.592192i	$0.201737\pi$
$434$	4775.54	0.528187
$435$	7003.91	0.771981
$436$	−2267.07	−0.249021
$437$	2483.19	0.271824
$438$	12160.1	1.32656
$439$	−11629.1	−1.26429	−0.632147	−	0.774848i	$-0.717826\pi$
$439$	−11629.1	−1.26429	−0.632147	+	0.774848i	$0.717826\pi$
$440$	1227.08	0.132952
$441$	−10828.6	−1.16927
$442$	267.463	0.0287826
$443$	−4049.43	−0.434299	−0.217149	−	0.976138i	$-0.569676\pi$
$443$	−4049.43	−0.434299	−0.217149	+	0.976138i	$0.569676\pi$
$444$	−19132.1	−2.04497
$445$	−5088.14	−0.542025
$446$	2773.30	0.294438
$447$	−29517.6	−3.12334
$448$	−3629.68	−0.382781
$449$	−17124.6	−1.79991	−0.899953	−	0.435986i	$-0.856400\pi$
$449$	−17124.6	−1.79991	−0.899953	+	0.435986i	$0.856400\pi$
$450$	2477.75	0.259560
$451$	3479.89	0.363330
$452$	7349.46	0.764800
$453$	−6589.49	−0.683447
$454$	5974.84	0.617650
$455$	99.7559	0.0102783
$456$	−3912.53	−0.401801
$457$	−4685.04	−0.479555	−0.239778	−	0.970828i	$-0.577075\pi$
$457$	−4685.04	−0.479555	−0.239778	+	0.970828i	$0.577075\pi$
$458$	−4305.01	−0.439213
$459$	28382.1	2.88619
$460$	3332.06	0.337735
$461$	16288.7	1.64564	0.822818	−	0.568305i	$-0.192401\pi$
$461$	16288.7	1.64564	0.822818	+	0.568305i	$0.192401\pi$
$462$	−2166.11	−0.218131
$463$	11490.1	1.15332	0.576661	−	0.816983i	$-0.304355\pi$
$463$	11490.1	1.15332	0.576661	+	0.816983i	$0.304355\pi$
$464$	−423.727	−0.0423944
$465$	10329.8	1.03017
$466$	−550.674	−0.0547414
$467$	−12052.3	−1.19425	−0.597125	−	0.802148i	$-0.703691\pi$
$467$	−12052.3	−1.19425	−0.597125	+	0.802148i	$0.703691\pi$
$468$	−472.581	−0.0466775
$469$	−11010.0	−1.08400
$470$	2988.25	0.293271
$471$	88.0629	0.00861513
$472$	−11604.8	−1.13169
$473$	3471.24	0.337437
$474$	12087.2	1.17127
$475$	475.000	0.0458831
$476$	6297.27	0.606375
$477$	17640.9	1.69334
$478$	10583.4	1.01270
$479$	−6543.44	−0.624170	−0.312085	−	0.950054i	$-0.601027\pi$
$479$	−6543.44	−0.624170	−0.312085	+	0.950054i	$0.601027\pi$
$480$	−8456.37	−0.804122
$481$	647.486	0.0613780
$482$	−1448.30	−0.136863
$483$	−15110.3	−1.42348
$484$	−616.980	−0.0579433
$485$	−4383.31	−0.410383
$486$	3832.35	0.357693
$487$	−18675.1	−1.73768	−0.868839	−	0.495094i	$-0.835134\pi$
$487$	−18675.1	−1.73768	−0.868839	+	0.495094i	$0.835134\pi$
$488$	11197.3	1.03868
$489$	−19768.7	−1.82816
$490$	1584.79	0.146109
$491$	−13406.9	−1.23227	−0.616135	−	0.787640i	$-0.711303\pi$
$491$	−13406.9	−1.23227	−0.616135	+	0.787640i	$0.711303\pi$
$492$	−14888.5	−1.36428
$493$	−14963.1	−1.36695
$494$	51.5434	0.00469443
$495$	−3200.42	−0.290602
$496$	−624.936	−0.0565735
$497$	13584.1	1.22601
$498$	6820.85	0.613754
$499$	−12109.8	−1.08639	−0.543196	−	0.839606i	$-0.682786\pi$
$499$	−12109.8	−1.08639	−0.543196	+	0.839606i	$0.682786\pi$
$500$	637.376	0.0570086
$501$	4077.41	0.363604
$502$	−7510.81	−0.667776
$503$	16085.8	1.42591	0.712954	−	0.701211i	$-0.247357\pi$
$503$	16085.8	1.42591	0.712954	+	0.701211i	$0.247357\pi$
$504$	16262.2	1.43725
$505$	−4450.03	−0.392126
$506$	2448.63	0.215128
$507$	−20254.5	−1.77423
$508$	−12935.4	−1.12975
$509$	7383.26	0.642941	0.321471	−	0.946920i	$-0.395823\pi$
$509$	7383.26	0.642941	0.321471	+	0.946920i	$0.395823\pi$
$510$	−7749.62	−0.672860
$511$	−9689.33	−0.838808
$512$	1009.92	0.0871730
$513$	5469.58	0.470737
$514$	10558.2	0.906035
$515$	3891.45	0.332967
$516$	−14851.5	−1.26706
$517$	−3859.81	−0.328345
$518$	−8673.20	−0.735673
$519$	−19023.9	−1.60898
$520$	177.676	0.0149838
$521$	11938.3	1.00389	0.501943	−	0.864901i	$-0.332619\pi$
$521$	11938.3	1.00389	0.501943	+	0.864901i	$0.332619\pi$
$522$	−15041.6	−1.26122
$523$	−964.059	−0.0806030	−0.0403015	−	0.999188i	$-0.512832\pi$
$523$	−964.059	−0.0806030	−0.0403015	+	0.999188i	$0.512832\pi$
$524$	11326.8	0.944303
$525$	−2890.38	−0.240279
$526$	−3965.92	−0.328749
$527$	−22068.4	−1.82413
$528$	283.461	0.0233638
$529$	4913.99	0.403879
$530$	−2581.79	−0.211596
$531$	30267.2	2.47360
$532$	1213.56	0.0988995
$533$	503.871	0.0409476
$534$	15997.6	1.29641
$535$	−7671.36	−0.619928
$536$	−19610.0	−1.58027
$537$	−22201.1	−1.78407
$538$	−9149.58	−0.733209
$539$	−2047.01	−0.163583
$540$	7339.32	0.584878
$541$	−11382.4	−0.904560	−0.452280	−	0.891876i	$-0.649389\pi$
$541$	−11382.4	−0.904560	−0.452280	+	0.891876i	$0.649389\pi$
$542$	7993.60	0.633496
$543$	−16978.0	−1.34179
$544$	18066.1	1.42386
$545$	−2223.05	−0.174725
$546$	−313.642	−0.0245836
$547$	4471.95	0.349555	0.174778	−	0.984608i	$-0.444079\pi$
$547$	4471.95	0.349555	0.174778	+	0.984608i	$0.444079\pi$
$548$	80.1459	0.00624756
$549$	−29204.2	−2.27032
$550$	468.388	0.0363130
$551$	−2883.58	−0.222948
$552$	−26912.9	−2.07516
$553$	−9631.22	−0.740617
$554$	−3428.88	−0.262959
$555$	−18760.6	−1.43485
$556$	10926.2	0.833406
$557$	18965.1	1.44269	0.721344	−	0.692577i	$-0.243525\pi$
$557$	18965.1	1.44269	0.721344	+	0.692577i	$0.243525\pi$
$558$	−22184.2	−1.68304
$559$	502.619	0.0380295
$560$	174.864	0.0131953
$561$	10009.9	0.753330
$562$	−5946.52	−0.446332
$563$	−25130.4	−1.88121	−0.940605	−	0.339503i	$-0.889741\pi$
$563$	−25130.4	−1.88121	−0.940605	+	0.339503i	$0.889741\pi$
$564$	16514.0	1.23291
$565$	7206.76	0.536621
$566$	−6857.98	−0.509298
$567$	−13602.2	−1.00748
$568$	24194.6	1.78730
$569$	−17162.0	−1.26445	−0.632224	−	0.774786i	$-0.717858\pi$
$569$	−17162.0	−1.26445	−0.632224	+	0.774786i	$0.717858\pi$
$570$	−1493.45	−0.109743
$571$	−3990.90	−0.292494	−0.146247	−	0.989248i	$-0.546719\pi$
$571$	−3990.90	−0.292494	−0.146247	+	0.989248i	$0.546719\pi$
$572$	−89.3357	−0.00653027
$573$	3158.10	0.230247
$574$	−6749.46	−0.490796
$575$	3267.36	0.236971
$576$	16861.2	1.21971
$577$	7903.20	0.570216	0.285108	−	0.958495i	$-0.407971\pi$
$577$	7903.20	0.570216	0.285108	+	0.958495i	$0.407971\pi$
$578$	8188.26	0.589250
$579$	−34676.0	−2.48892
$580$	−3869.31	−0.277007
$581$	−5434.94	−0.388088
$582$	13781.6	0.981553
$583$	3334.80	0.236901
$584$	−17257.7	−1.22282
$585$	−463.405	−0.0327512
$586$	6293.44	0.443651
$587$	−21378.3	−1.50319	−0.751597	−	0.659622i	$-0.770716\pi$
$587$	−21378.3	−1.50319	−0.751597	+	0.659622i	$0.770716\pi$
$588$	8758.04	0.614244
$589$	−4252.86	−0.297514
$590$	−4429.67	−0.309096
$591$	−21222.1	−1.47709
$592$	1134.99	0.0787969
$593$	−6632.79	−0.459319	−0.229659	−	0.973271i	$-0.573761\pi$
$593$	−6632.79	−0.459319	−0.229659	+	0.973271i	$0.573761\pi$
$594$	5393.45	0.372552
$595$	6174.99	0.425462
$596$	16307.0	1.12074
$597$	−5244.34	−0.359525
$598$	354.549	0.0242451
$599$	−3617.10	−0.246729	−0.123364	−	0.992361i	$-0.539368\pi$
$599$	−3617.10	−0.246729	−0.123364	+	0.992361i	$0.539368\pi$
$600$	−5148.07	−0.350282
$601$	19179.5	1.30175	0.650874	−	0.759186i	$-0.274403\pi$
$601$	19179.5	1.30175	0.650874	+	0.759186i	$0.274403\pi$
$602$	−6732.67	−0.455819
$603$	51145.8	3.45410
$604$	3640.36	0.245239
$605$	−605.000	−0.0406558
$606$	13991.3	0.937887
$607$	−17841.2	−1.19300	−0.596500	−	0.802613i	$-0.703443\pi$
$607$	−17841.2	−1.19300	−0.596500	+	0.802613i	$0.703443\pi$
$608$	3481.57	0.232230
$609$	17546.6	1.16753
$610$	4274.09	0.283693
$611$	−558.881	−0.0370048
$612$	−29253.2	−1.93218
$613$	9219.23	0.607441	0.303720	−	0.952761i	$-0.401771\pi$
$613$	9219.23	0.607441	0.303720	+	0.952761i	$0.401771\pi$
$614$	11143.8	0.732456
$615$	−14599.4	−0.957246
$616$	3074.16	0.201074
$617$	−419.816	−0.0273925	−0.0136962	−	0.999906i	$-0.504360\pi$
$617$	−419.816	−0.0273925	−0.0136962	+	0.999906i	$0.504360\pi$
$618$	−12235.1	−0.796389
$619$	21157.4	1.37381	0.686904	−	0.726748i	$-0.258969\pi$
$619$	21157.4	1.37381	0.686904	+	0.726748i	$0.258969\pi$
$620$	−5706.67	−0.369654
$621$	37623.3	2.43119
$622$	−10479.1	−0.675518
$623$	−12747.1	−0.819746
$624$	41.0438	0.00263312
$625$	625.000	0.0400000
$626$	−8452.25	−0.539648
$627$	1929.03	0.122868
$628$	−48.6504	−0.00309134
$629$	40080.0	2.54069
$630$	6207.40	0.392553
$631$	1987.76	0.125406	0.0627032	−	0.998032i	$-0.480028\pi$
$631$	1987.76	0.125406	0.0627032	+	0.998032i	$0.480028\pi$
$632$	−17154.2	−1.07968
$633$	20728.2	1.30154
$634$	7837.76	0.490973
$635$	−12684.2	−0.792687
$636$	−14267.8	−0.889549
$637$	−296.398	−0.0184360
$638$	−2843.44	−0.176446
$639$	−63103.3	−3.90661
$640$	4861.93	0.300289
$641$	−6041.39	−0.372263	−0.186132	−	0.982525i	$-0.559595\pi$
$641$	−6041.39	−0.372263	−0.186132	+	0.982525i	$0.559595\pi$
$642$	24119.5	1.48274
$643$	−3459.16	−0.212155	−0.106078	−	0.994358i	$-0.533829\pi$
$643$	−3459.16	−0.212155	−0.106078	+	0.994358i	$0.533829\pi$
$644$	8347.66	0.510782
$645$	−14563.1	−0.889028
$646$	3190.59	0.194322
$647$	25147.8	1.52807	0.764036	−	0.645174i	$-0.223215\pi$
$647$	25147.8	1.52807	0.764036	+	0.645174i	$0.223215\pi$
$648$	−24227.0	−1.46871
$649$	5721.64	0.346062
$650$	67.8203	0.00409251
$651$	25878.7	1.55801
$652$	10921.2	0.655994
$653$	1595.99	0.0956445	0.0478223	−	0.998856i	$-0.484772\pi$
$653$	1595.99	0.0956445	0.0478223	+	0.998856i	$0.484772\pi$
$654$	6989.50	0.417907
$655$	11106.9	0.662568
$656$	883.245	0.0525685
$657$	45010.7	2.67281
$658$	7486.32	0.443537
$659$	22303.3	1.31838	0.659192	−	0.751975i	$-0.270899\pi$
$659$	22303.3	1.31838	0.659192	+	0.751975i	$0.270899\pi$
$660$	2588.46	0.152660
$661$	−7938.63	−0.467136	−0.233568	−	0.972340i	$-0.575040\pi$
$661$	−7938.63	−0.467136	−0.233568	+	0.972340i	$0.575040\pi$
$662$	14797.5	0.868764
$663$	1449.38	0.0849011
$664$	−9680.19	−0.565759
$665$	1190.00	0.0693926
$666$	40290.4	2.34417
$667$	−19835.1	−1.15145
$668$	−2252.57	−0.130471
$669$	15028.5	0.868514
$670$	−7485.30	−0.431616
$671$	−5520.69	−0.317621
$672$	−21185.4	−1.21614
$673$	12236.9	0.700890	0.350445	−	0.936583i	$-0.386030\pi$
$673$	12236.9	0.700890	0.350445	+	0.936583i	$0.386030\pi$
$674$	−6685.99	−0.382099
$675$	7196.81	0.410379
$676$	11189.6	0.636640
$677$	9780.60	0.555242	0.277621	−	0.960691i	$-0.410454\pi$
$677$	9780.60	0.555242	0.277621	+	0.960691i	$0.410454\pi$
$678$	−22658.8	−1.28349
$679$	−10981.3	−0.620654
$680$	10998.3	0.620244
$681$	32377.7	1.82190
$682$	−4193.66	−0.235460
$683$	−20108.4	−1.12654	−0.563271	−	0.826272i	$-0.690457\pi$
$683$	−20108.4	−1.12654	−0.563271	+	0.826272i	$0.690457\pi$
$684$	−5637.46	−0.315137
$685$	78.5897	0.00438359
$686$	11288.3	0.628262
$687$	−23328.9	−1.29556
$688$	881.049	0.0488222
$689$	482.863	0.0266990
$690$	−10272.9	−0.566786
$691$	−15423.0	−0.849084	−0.424542	−	0.905408i	$-0.639565\pi$
$691$	−15423.0	−0.849084	−0.424542	+	0.905408i	$0.639565\pi$
$692$	10509.8	0.577344
$693$	−8017.87	−0.439500
$694$	−209.736	−0.0114718
$695$	10714.0	0.584758
$696$	31252.3	1.70203
$697$	31190.1	1.69499
$698$	15403.9	0.835308
$699$	−2984.11	−0.161472
$700$	1596.79	0.0862186
$701$	−15724.7	−0.847237	−0.423618	−	0.905841i	$-0.639240\pi$
$701$	−15724.7	−0.847237	−0.423618	+	0.905841i	$0.639240\pi$
$702$	780.944	0.0419870
$703$	7723.91	0.414385
$704$	3187.41	0.170639
$705$	16193.3	0.865072
$706$	−15902.5	−0.847733
$707$	−11148.5	−0.593043
$708$	−24479.7	−1.29944
$709$	15866.9	0.840473	0.420236	−	0.907415i	$-0.361947\pi$
$709$	15866.9	0.840473	0.420236	+	0.907415i	$0.361947\pi$
$710$	9235.30	0.488161
$711$	44740.7	2.35993
$712$	−22703.9	−1.19503
$713$	−29253.9	−1.53656
$714$	−19414.8	−1.01762
$715$	−87.6010	−0.00458195
$716$	12265.0	0.640173
$717$	57351.4	2.98721
$718$	2811.17	0.146117
$719$	−16152.5	−0.837812	−0.418906	−	0.908030i	$-0.637586\pi$
$719$	−16152.5	−0.837812	−0.418906	+	0.908030i	$0.637586\pi$
$720$	−812.311	−0.0420459
$721$	9749.09	0.503572
$722$	614.866	0.0316938
$723$	−7848.33	−0.403710
$724$	9379.48	0.481472
$725$	−3794.18	−0.194362
$726$	1902.18	0.0972404
$727$	−20389.0	−1.04014	−0.520072	−	0.854123i	$-0.674095\pi$
$727$	−20389.0	−1.04014	−0.520072	+	0.854123i	$0.674095\pi$
$728$	445.123	0.0226612
$729$	−8551.64	−0.434468
$730$	−6587.41	−0.333988
$731$	31112.6	1.57420
$732$	23620.0	1.19265
$733$	5046.82	0.254309	0.127155	−	0.991883i	$-0.459416\pi$
$733$	5046.82	0.254309	0.127155	+	0.991883i	$0.459416\pi$
$734$	16522.2	0.830850
$735$	8587.98	0.430983
$736$	23948.5	1.19939
$737$	9668.50	0.483234
$738$	31353.8	1.56389
$739$	−36381.4	−1.81097	−0.905487	−	0.424373i	$-0.860494\pi$
$739$	−36381.4	−1.81097	−0.905487	+	0.424373i	$0.860494\pi$
$740$	10364.3	0.514863
$741$	279.314	0.0138473
$742$	−6468.04	−0.320012
$743$	−11575.3	−0.571543	−0.285771	−	0.958298i	$-0.592250\pi$
$743$	−11575.3	−0.571543	−0.285771	+	0.958298i	$0.592250\pi$
$744$	46092.7	2.27129
$745$	15990.3	0.786363
$746$	19749.9	0.969298
$747$	25247.4	1.23662
$748$	−5529.97	−0.270315
$749$	−19218.7	−0.937566
$750$	−1965.06	−0.0956719
$751$	12129.9	0.589384	0.294692	−	0.955592i	$-0.404783\pi$
$751$	12129.9	0.589384	0.294692	+	0.955592i	$0.404783\pi$
$752$	−979.673	−0.0475066
$753$	−40701.1	−1.96976
$754$	−411.716	−0.0198857
$755$	3569.68	0.172071
$756$	18386.9	0.884557
$757$	37954.6	1.82230	0.911151	−	0.412072i	$-0.135195\pi$
$757$	37954.6	1.82230	0.911151	+	0.412072i	$0.135195\pi$
$758$	−2032.01	−0.0973692
$759$	13269.1	0.634570
$760$	2119.51	0.101161
$761$	3826.98	0.182297	0.0911483	−	0.995837i	$-0.470946\pi$
$761$	3826.98	0.182297	0.0911483	+	0.995837i	$0.470946\pi$
$762$	39880.3	1.89595
$763$	−5569.32	−0.264250
$764$	−1744.69	−0.0826189
$765$	−28685.2	−1.35571
$766$	21401.5	1.00949
$767$	828.465	0.0390015
$768$	−36682.2	−1.72351
$769$	2792.61	0.130954	0.0654772	−	0.997854i	$-0.479143\pi$
$769$	2792.61	0.130954	0.0654772	+	0.997854i	$0.479143\pi$
$770$	1173.43	0.0549189
$771$	57214.9	2.67256
$772$	19156.8	0.893091
$773$	9605.29	0.446932	0.223466	−	0.974712i	$-0.428263\pi$
$773$	9605.29	0.446932	0.223466	+	0.974712i	$0.428263\pi$
$774$	31275.9	1.45244
$775$	−5595.86	−0.259367
$776$	−19558.9	−0.904797
$777$	−47000.1	−2.17004
$778$	3593.23	0.165583
$779$	6010.72	0.276453
$780$	374.796	0.0172049
$781$	−11928.9	−0.546542
$782$	21946.9	1.00361
$783$	−43689.6	−1.99405
$784$	−519.561	−0.0236680
$785$	−47.7057	−0.00216903
$786$	−34921.2	−1.58473
$787$	3854.41	0.174580	0.0872902	−	0.996183i	$-0.472179\pi$
$787$	3854.41	0.174580	0.0872902	+	0.996183i	$0.472179\pi$
$788$	11724.1	0.530019
$789$	−21491.3	−0.969723
$790$	−6547.90	−0.294891
$791$	18054.8	0.811573
$792$	−14280.7	−0.640709
$793$	−799.369	−0.0357963
$794$	−9737.49	−0.435227
$795$	−13990.7	−0.624151
$796$	2897.23	0.129007
$797$	12130.4	0.539121	0.269560	−	0.962983i	$-0.413122\pi$
$797$	12130.4	0.539121	0.269560	+	0.962983i	$0.413122\pi$
$798$	−3741.47	−0.165973
$799$	−34595.3	−1.53178
$800$	4581.01	0.202454
$801$	59215.2	2.61207
$802$	−13592.5	−0.598462
$803$	8508.72	0.373931
$804$	−41366.1	−1.81452
$805$	8185.57	0.358389
$806$	−607.221	−0.0265365
$807$	−49581.6	−2.16277
$808$	−19856.6	−0.864545
$809$	−13468.0	−0.585303	−0.292651	−	0.956219i	$-0.594538\pi$
$809$	−13468.0	−0.585303	−0.292651	+	0.956219i	$0.594538\pi$
$810$	−9247.65	−0.401147
$811$	−20879.1	−0.904024	−0.452012	−	0.892012i	$-0.649293\pi$
$811$	−20879.1	−0.904024	−0.452012	+	0.892012i	$0.649293\pi$
$812$	−9693.61	−0.418940
$813$	43317.4	1.86864
$814$	7616.40	0.327954
$815$	10709.2	0.460277
$816$	2540.65	0.108996
$817$	5995.78	0.256751
$818$	9142.89	0.390799
$819$	−1160.95	−0.0495321
$820$	8065.46	0.343485
$821$	−38252.0	−1.62607	−0.813035	−	0.582214i	$-0.802186\pi$
$821$	−38252.0	−1.62607	−0.813035	+	0.582214i	$0.802186\pi$
$822$	−247.094	−0.0104846
$823$	−21066.0	−0.892243	−0.446121	−	0.894972i	$-0.647195\pi$
$823$	−21066.0	−0.892243	−0.446121	+	0.894972i	$0.647195\pi$
$824$	17364.2	0.734113
$825$	2538.20	0.107114
$826$	−11097.5	−0.467469
$827$	29860.8	1.25557	0.627787	−	0.778385i	$-0.283961\pi$
$827$	29860.8	1.25557	0.627787	+	0.778385i	$0.283961\pi$
$828$	−38778.1	−1.62757
$829$	−34160.2	−1.43116	−0.715581	−	0.698530i	$-0.753838\pi$
$829$	−34160.2	−1.43116	−0.715581	+	0.698530i	$0.753838\pi$
$830$	−3695.01	−0.154525
$831$	−18581.1	−0.775659
$832$	461.522	0.0192312
$833$	−18347.3	−0.763141
$834$	−33686.0	−1.39862
$835$	−2208.83	−0.0915445
$836$	−1065.69	−0.0440882
$837$	−64435.8	−2.66097
$838$	24735.1	1.01964
$839$	32762.1	1.34812	0.674060	−	0.738676i	$-0.264549\pi$
$839$	32762.1	1.34812	0.674060	+	0.738676i	$0.264549\pi$
$840$	−12897.2	−0.529758
$841$	−1355.74	−0.0555883
$842$	−6341.41	−0.259548
$843$	−32224.2	−1.31656
$844$	−11451.3	−0.467026
$845$	10972.3	0.446697
$846$	−34776.9	−1.41330
$847$	−1515.68	−0.0614869
$848$	846.419	0.0342761
$849$	−37163.4	−1.50229
$850$	4198.14	0.169406
$851$	53130.1	2.14016
$852$	51037.1	2.05223
$853$	−14198.2	−0.569914	−0.284957	−	0.958540i	$-0.591979\pi$
$853$	−14198.2	−0.569914	−0.284957	+	0.958540i	$0.591979\pi$
$854$	10707.7	0.429052
$855$	−5528.00	−0.221115
$856$	−34230.6	−1.36679
$857$	34027.6	1.35631	0.678157	−	0.734917i	$-0.262779\pi$
$857$	34027.6	1.35631	0.678157	+	0.734917i	$0.262779\pi$
$858$	275.426	0.0109591
$859$	−16594.5	−0.659135	−0.329567	−	0.944132i	$-0.606903\pi$
$859$	−16594.5	−0.659135	−0.329567	+	0.944132i	$0.606903\pi$
$860$	8045.40	0.319007
$861$	−36575.3	−1.44772
$862$	10671.9	0.421679
$863$	−33165.4	−1.30818	−0.654092	−	0.756415i	$-0.726949\pi$
$863$	−33165.4	−1.30818	−0.654092	+	0.756415i	$0.726949\pi$
$864$	52749.9	2.07707
$865$	10305.7	0.405092
$866$	24732.1	0.970474
$867$	44372.2	1.73813
$868$	−14296.7	−0.559056
$869$	8457.69	0.330158
$870$	11929.3	0.464874
$871$	1399.95	0.0544610
$872$	−9919.54	−0.385227
$873$	51012.4	1.97767
$874$	4229.45	0.163688
$875$	1565.79	0.0604951
$876$	−36404.1	−1.40409
$877$	18697.6	0.719925	0.359962	−	0.932967i	$-0.382789\pi$
$877$	18697.6	0.719925	0.359962	+	0.932967i	$0.382789\pi$
$878$	−19807.0	−0.761336
$879$	34104.2	1.30865
$880$	−153.557	−0.00588229
$881$	−11250.2	−0.430225	−0.215113	−	0.976589i	$-0.569012\pi$
$881$	−11250.2	−0.430225	−0.215113	+	0.976589i	$0.569012\pi$
$882$	−18443.6	−0.704114
$883$	3962.37	0.151013	0.0755064	−	0.997145i	$-0.475943\pi$
$883$	3962.37	0.151013	0.0755064	+	0.997145i	$0.475943\pi$
$884$	−800.712	−0.0304648
$885$	−24004.4	−0.911750
$886$	−6897.11	−0.261527
$887$	−38322.0	−1.45065	−0.725325	−	0.688406i	$-0.758311\pi$
$887$	−38322.0	−1.45065	−0.725325	+	0.688406i	$0.758311\pi$
$888$	−83712.1	−3.16351
$889$	−31777.1	−1.19884
$890$	−8666.27	−0.326398
$891$	11944.8	0.449122
$892$	−8302.50	−0.311646
$893$	−6666.94	−0.249833
$894$	−50275.2	−1.88082
$895$	12026.8	0.449176
$896$	12180.4	0.454150
$897$	1921.30	0.0715167
$898$	−29167.1	−1.08387
$899$	33970.7	1.26027
$900$	−7417.71	−0.274730
$901$	29889.7	1.10518
$902$	5927.06	0.218791
$903$	−36484.4	−1.34455
$904$	32157.5	1.18312
$905$	9197.36	0.337824
$906$	−11223.4	−0.411560
$907$	−29733.5	−1.08852	−0.544258	−	0.838918i	$-0.683189\pi$
$907$	−29733.5	−1.08852	−0.544258	+	0.838918i	$0.683189\pi$
$908$	−17887.0	−0.653747
$909$	51789.0	1.88969
$910$	169.907	0.00618942
$911$	16146.1	0.587204	0.293602	−	0.955928i	$-0.405146\pi$
$911$	16146.1	0.587204	0.293602	+	0.955928i	$0.405146\pi$
$912$	489.615	0.0177772
$913$	4772.71	0.173005
$914$	−7979.69	−0.288780
$915$	23161.3	0.836820
$916$	12888.0	0.464882
$917$	27825.6	1.00205
$918$	48341.2	1.73802
$919$	39814.7	1.42912	0.714562	−	0.699572i	$-0.246626\pi$
$919$	39814.7	1.42912	0.714562	+	0.699572i	$0.246626\pi$
$920$	14579.4	0.522464
$921$	60388.4	2.16055
$922$	27743.3	0.990974
$923$	−1727.25	−0.0615959
$924$	6484.75	0.230880
$925$	10163.0	0.361253
$926$	19570.2	0.694511
$927$	−45288.3	−1.60460
$928$	−27809.9	−0.983732
$929$	16256.1	0.574106	0.287053	−	0.957915i	$-0.407324\pi$
$929$	16256.1	0.574106	0.287053	+	0.957915i	$0.407324\pi$
$930$	17593.9	0.620353
$931$	−3535.75	−0.124468
$932$	1648.57	0.0579406
$933$	−56786.1	−1.99260
$934$	−20527.9	−0.719157
$935$	−5422.59	−0.189666
$936$	−2067.77	−0.0722085
$937$	15579.6	0.543185	0.271593	−	0.962412i	$-0.412450\pi$
$937$	15579.6	0.543185	0.271593	+	0.962412i	$0.412450\pi$
$938$	−18752.6	−0.652766
$939$	−45802.8	−1.59182
$940$	−8946.00	−0.310411
$941$	−19427.2	−0.673015	−0.336508	−	0.941681i	$-0.609246\pi$
$941$	−19427.2	−0.673015	−0.336508	+	0.941681i	$0.609246\pi$
$942$	149.991	0.00518788
$943$	41345.6	1.42778
$944$	1452.23	0.0500700
$945$	18029.9	0.620647
$946$	5912.32	0.203199
$947$	5265.35	0.180677	0.0903383	−	0.995911i	$-0.471205\pi$
$947$	5265.35	0.180677	0.0903383	+	0.995911i	$0.471205\pi$
$948$	−36185.7	−1.23972
$949$	1232.02	0.0421424
$950$	809.034	0.0276300
$951$	42472.9	1.44824
$952$	27553.6	0.938042
$953$	41714.3	1.41790	0.708949	−	0.705259i	$-0.249170\pi$
$953$	41714.3	1.41790	0.708949	+	0.705259i	$0.249170\pi$
$954$	30046.5	1.01970
$955$	−1710.82	−0.0579694
$956$	−31683.8	−1.07189
$957$	−15408.6	−0.520470
$958$	−11145.0	−0.375864
$959$	196.887	0.00662964
$960$	−13372.4	−0.449574
$961$	20310.9	0.681780
$962$	1102.82	0.0369608
$963$	89278.4	2.98749
$964$	4335.81	0.144862
$965$	18784.8	0.626636
$966$	−25736.2	−0.857194
$967$	34920.1	1.16128	0.580638	−	0.814162i	$-0.302803\pi$
$967$	34920.1	1.16128	0.580638	+	0.814162i	$0.302803\pi$
$968$	−2699.59	−0.0896363
$969$	17289.8	0.573198
$970$	−7465.78	−0.247126
$971$	53847.4	1.77966	0.889828	−	0.456297i	$-0.150825\pi$
$971$	53847.4	1.77966	0.889828	+	0.456297i	$0.150825\pi$
$972$	−11473.0	−0.378598
$973$	26841.4	0.884375
$974$	−31808.0	−1.04640
$975$	367.519	0.0120718
$976$	−1401.23	−0.0459551
$977$	50470.5	1.65271	0.826353	−	0.563153i	$-0.190412\pi$
$977$	50470.5	1.65271	0.826353	+	0.563153i	$0.190412\pi$
$978$	−33670.6	−1.10089
$979$	11193.9	0.365433
$980$	−4744.43	−0.154648
$981$	25871.6	0.842016
$982$	−22835.0	−0.742052
$983$	42909.6	1.39227	0.696136	−	0.717910i	$-0.254901\pi$
$983$	42909.6	1.39227	0.696136	+	0.717910i	$0.254901\pi$
$984$	−65144.5	−2.11050
$985$	11496.5	0.371887
$986$	−25485.6	−0.823151
$987$	40568.4	1.30832
$988$	−154.307	−0.00496879
$989$	41242.8	1.32603
$990$	−5451.05	−0.174996
$991$	−6984.74	−0.223893	−0.111946	−	0.993714i	$-0.535708\pi$
$991$	−6984.74	−0.223893	−0.111946	+	0.993714i	$0.535708\pi$
$992$	−41015.5	−1.31275
$993$	80187.8	2.56262
$994$	23136.8	0.738284
$995$	2840.98	0.0905177
$996$	−20419.8	−0.649624
$997$	−13535.9	−0.429975	−0.214988	−	0.976617i	$-0.568971\pi$
$997$	−13535.9	−0.429975	−0.214988	+	0.976617i	$0.568971\pi$
$998$	−20625.8	−0.654207
$999$	117026.	3.70626

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.4.a.i.1.15	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.4.a.i.1.15	✓	25	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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1045.a (trivial)

\(f(q)\)	\(=\)	\(q+1.70323 q^{2} +9.22981 q^{3} -5.09901 q^{4} -5.00000 q^{5} +15.7205 q^{6} -12.5263 q^{7} -22.3106 q^{8} +58.1894 q^{9} +O(q^{10})\)	\(q+1.70323 q^{2} +9.22981 q^{3} -5.09901 q^{4} -5.00000 q^{5} +15.7205 q^{6} -12.5263 q^{7} -22.3106 q^{8} +58.1894 q^{9} -8.51615 q^{10} +11.0000 q^{11} -47.0629 q^{12} +1.59275 q^{13} -21.3351 q^{14} -46.1491 q^{15} +2.79195 q^{16} +98.5925 q^{17} +99.1100 q^{18} +19.0000 q^{19} +25.4950 q^{20} -115.615 q^{21} +18.7355 q^{22} +130.694 q^{23} -205.923 q^{24} +25.0000 q^{25} +2.71281 q^{26} +287.873 q^{27} +63.8716 q^{28} -151.767 q^{29} -78.6025 q^{30} -223.835 q^{31} +183.240 q^{32} +101.528 q^{33} +167.926 q^{34} +62.6314 q^{35} -296.708 q^{36} +406.522 q^{37} +32.3614 q^{38} +14.7007 q^{39} +111.553 q^{40} +316.354 q^{41} -196.919 q^{42} +315.567 q^{43} -56.0891 q^{44} -290.947 q^{45} +222.602 q^{46} -350.892 q^{47} +25.7692 q^{48} -186.092 q^{49} +42.5807 q^{50} +909.991 q^{51} -8.12143 q^{52} +303.164 q^{53} +490.313 q^{54} -55.0000 q^{55} +279.469 q^{56} +175.366 q^{57} -258.494 q^{58} +520.149 q^{59} +235.314 q^{60} -501.881 q^{61} -381.242 q^{62} -728.897 q^{63} +289.765 q^{64} -7.96373 q^{65} +172.925 q^{66} +878.954 q^{67} -502.724 q^{68} +1206.28 q^{69} +106.676 q^{70} -1084.45 q^{71} -1298.24 q^{72} +773.520 q^{73} +692.400 q^{74} +230.745 q^{75} -96.8812 q^{76} -137.789 q^{77} +25.0387 q^{78} +768.881 q^{79} -13.9598 q^{80} +1085.90 q^{81} +538.823 q^{82} +433.883 q^{83} +589.523 q^{84} -492.963 q^{85} +537.484 q^{86} -1400.78 q^{87} -245.417 q^{88} +1017.63 q^{89} -495.550 q^{90} -19.9512 q^{91} -666.411 q^{92} -2065.95 q^{93} -597.649 q^{94} -95.0000 q^{95} +1691.27 q^{96} +876.662 q^{97} -316.958 q^{98} +640.084 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 2 q^{2} + 9 q^{3} + 122 q^{4} - 125 q^{5} + 11 q^{6} - 15 q^{7} + 60 q^{8} + 300 q^{9}+O(q^{10}) \) 25 * q + 2 * q^2 + 9 * q^3 + 122 * q^4 - 125 * q^5 + 11 * q^6 - 15 * q^7 + 60 * q^8 + 300 * q^9	\( 25 q + 2 q^{2} + 9 q^{3} + 122 q^{4} - 125 q^{5} + 11 q^{6} - 15 q^{7} + 60 q^{8} + 300 q^{9} - 10 q^{10} + 275 q^{11} + 44 q^{12} + 53 q^{13} - 51 q^{14} - 45 q^{15} + 438 q^{16} + 153 q^{17} + 9 q^{18} + 475 q^{19} - 610 q^{20} + 259 q^{21} + 22 q^{22} - 7 q^{23} + 186 q^{24} + 625 q^{25} + 543 q^{26} + 495 q^{27} - 525 q^{28} + 169 q^{29} - 55 q^{30} + 102 q^{31} + 327 q^{32} + 99 q^{33} - 879 q^{34} + 75 q^{35} + 2293 q^{36} - 46 q^{37} + 38 q^{38} + 233 q^{39} - 300 q^{40} + 1190 q^{41} - 684 q^{42} - 408 q^{43} + 1342 q^{44} - 1500 q^{45} + 757 q^{46} + 1068 q^{47} + 715 q^{48} + 1930 q^{49} + 50 q^{50} + 1655 q^{51} - 94 q^{52} + 143 q^{53} + 1970 q^{54} - 1375 q^{55} - 1397 q^{56} + 171 q^{57} + 1366 q^{58} + 2945 q^{59} - 220 q^{60} + 1160 q^{61} + 194 q^{62} + 1804 q^{63} + 3000 q^{64} - 265 q^{65} + 121 q^{66} - 353 q^{67} + 5452 q^{68} + 3289 q^{69} + 255 q^{70} + 230 q^{71} + 196 q^{72} + 1357 q^{73} + 4379 q^{74} + 225 q^{75} + 2318 q^{76} - 165 q^{77} + 2008 q^{78} + 1266 q^{79} - 2190 q^{80} + 1709 q^{81} + 1010 q^{82} + 3856 q^{83} + 9354 q^{84} - 765 q^{85} + 6746 q^{86} + 3113 q^{87} + 660 q^{88} + 3562 q^{89} - 45 q^{90} - 833 q^{91} + 4276 q^{92} + 1312 q^{93} + 5124 q^{94} - 2375 q^{95} + 3828 q^{96} - 914 q^{97} + 2478 q^{98} + 3300 q^{99}+O(q^{100}) \) 25 * q + 2 * q^2 + 9 * q^3 + 122 * q^4 - 125 * q^5 + 11 * q^6 - 15 * q^7 + 60 * q^8 + 300 * q^9 - 10 * q^10 + 275 * q^11 + 44 * q^12 + 53 * q^13 - 51 * q^14 - 45 * q^15 + 438 * q^16 + 153 * q^17 + 9 * q^18 + 475 * q^19 - 610 * q^20 + 259 * q^21 + 22 * q^22 - 7 * q^23 + 186 * q^24 + 625 * q^25 + 543 * q^26 + 495 * q^27 - 525 * q^28 + 169 * q^29 - 55 * q^30 + 102 * q^31 + 327 * q^32 + 99 * q^33 - 879 * q^34 + 75 * q^35 + 2293 * q^36 - 46 * q^37 + 38 * q^38 + 233 * q^39 - 300 * q^40 + 1190 * q^41 - 684 * q^42 - 408 * q^43 + 1342 * q^44 - 1500 * q^45 + 757 * q^46 + 1068 * q^47 + 715 * q^48 + 1930 * q^49 + 50 * q^50 + 1655 * q^51 - 94 * q^52 + 143 * q^53 + 1970 * q^54 - 1375 * q^55 - 1397 * q^56 + 171 * q^57 + 1366 * q^58 + 2945 * q^59 - 220 * q^60 + 1160 * q^61 + 194 * q^62 + 1804 * q^63 + 3000 * q^64 - 265 * q^65 + 121 * q^66 - 353 * q^67 + 5452 * q^68 + 3289 * q^69 + 255 * q^70 + 230 * q^71 + 196 * q^72 + 1357 * q^73 + 4379 * q^74 + 225 * q^75 + 2318 * q^76 - 165 * q^77 + 2008 * q^78 + 1266 * q^79 - 2190 * q^80 + 1709 * q^81 + 1010 * q^82 + 3856 * q^83 + 9354 * q^84 - 765 * q^85 + 6746 * q^86 + 3113 * q^87 + 660 * q^88 + 3562 * q^89 - 45 * q^90 - 833 * q^91 + 4276 * q^92 + 1312 * q^93 + 5124 * q^94 - 2375 * q^95 + 3828 * q^96 - 914 * q^97 + 2478 * q^98 + 3300 * q^99

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