LMFDB - Embedded newform 1045.4.a.f.1.2

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:	$1$
Dimension:	$23$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
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)

$f(q)$	$=$	$q-4.98045 q^{2} +6.47284 q^{3} +16.8049 q^{4} -5.00000 q^{5} -32.2376 q^{6} +19.1655 q^{7} -43.8523 q^{8} +14.8976 q^{9} +O(q^{10})$	\(q-4.98045 q^{2} +6.47284 q^{3} +16.8049 q^{4} -5.00000 q^{5} -32.2376 q^{6} +19.1655 q^{7} -43.8523 q^{8} +14.8976 q^{9} +24.9023 q^{10} +11.0000 q^{11} +108.775 q^{12} +55.8698 q^{13} -95.4530 q^{14} -32.3642 q^{15} +83.9652 q^{16} -116.017 q^{17} -74.1968 q^{18} -19.0000 q^{19} -84.0244 q^{20} +124.055 q^{21} -54.7850 q^{22} -108.100 q^{23} -283.849 q^{24} +25.0000 q^{25} -278.257 q^{26} -78.3368 q^{27} +322.075 q^{28} -140.937 q^{29} +161.188 q^{30} +122.433 q^{31} -67.3660 q^{32} +71.2012 q^{33} +577.816 q^{34} -95.8277 q^{35} +250.353 q^{36} -97.6846 q^{37} +94.6286 q^{38} +361.636 q^{39} +219.262 q^{40} -343.550 q^{41} -617.852 q^{42} -164.902 q^{43} +184.854 q^{44} -74.4880 q^{45} +538.387 q^{46} +69.8609 q^{47} +543.493 q^{48} +24.3178 q^{49} -124.511 q^{50} -750.957 q^{51} +938.886 q^{52} -602.505 q^{53} +390.153 q^{54} -55.0000 q^{55} -840.453 q^{56} -122.984 q^{57} +701.930 q^{58} +254.870 q^{59} -543.876 q^{60} -500.048 q^{61} -609.771 q^{62} +285.521 q^{63} -336.209 q^{64} -279.349 q^{65} -354.614 q^{66} +351.385 q^{67} -1949.65 q^{68} -699.714 q^{69} +477.265 q^{70} +435.561 q^{71} -653.295 q^{72} -600.675 q^{73} +486.513 q^{74} +161.821 q^{75} -319.293 q^{76} +210.821 q^{77} -1801.11 q^{78} -630.237 q^{79} -419.826 q^{80} -909.297 q^{81} +1711.03 q^{82} -761.603 q^{83} +2084.74 q^{84} +580.084 q^{85} +821.285 q^{86} -912.263 q^{87} -482.376 q^{88} +549.935 q^{89} +370.984 q^{90} +1070.78 q^{91} -1816.61 q^{92} +792.488 q^{93} -347.939 q^{94} +95.0000 q^{95} -436.049 q^{96} +1043.62 q^{97} -121.114 q^{98} +163.874 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q - 2 q^{2} - 9 q^{3} + 98 q^{4} - 115 q^{5} - 61 q^{6} + 13 q^{7} - 54 q^{8} + 170 q^{9}+O(q^{10}) $ 23 * q - 2 * q^2 - 9 * q^3 + 98 * q^4 - 115 * q^5 - 61 * q^6 + 13 * q^7 - 54 * q^8 + 170 * q^9	\( 23 q - 2 q^{2} - 9 q^{3} + 98 q^{4} - 115 q^{5} - 61 q^{6} + 13 q^{7} - 54 q^{8} + 170 q^{9} + 10 q^{10} + 253 q^{11} - 76 q^{12} - 37 q^{13} - 191 q^{14} + 45 q^{15} + 214 q^{16} - 51 q^{17} - 63 q^{18} - 437 q^{19} - 490 q^{20} - 479 q^{21} - 22 q^{22} + 101 q^{23} - 598 q^{24} + 575 q^{25} - 197 q^{26} - 627 q^{27} + 279 q^{28} - 357 q^{29} + 305 q^{30} - 90 q^{31} - 19 q^{32} - 99 q^{33} + 71 q^{34} - 65 q^{35} + 573 q^{36} - 378 q^{37} + 38 q^{38} + 193 q^{39} + 270 q^{40} - 830 q^{41} + 1480 q^{42} + 260 q^{43} + 1078 q^{44} - 850 q^{45} - 919 q^{46} - 1468 q^{47} + 837 q^{48} + 1200 q^{49} - 50 q^{50} - 1147 q^{51} - 1222 q^{52} + 185 q^{53} - 1406 q^{54} - 1265 q^{55} - 2299 q^{56} + 171 q^{57} - 958 q^{58} - 3665 q^{59} + 380 q^{60} - 2528 q^{61} - 1722 q^{62} + 172 q^{63} - 120 q^{64} + 185 q^{65} - 671 q^{66} + 329 q^{67} - 2240 q^{68} - 1337 q^{69} + 955 q^{70} - 3190 q^{71} - 2488 q^{72} - 2183 q^{73} - 1613 q^{74} - 225 q^{75} - 1862 q^{76} + 143 q^{77} - 2748 q^{78} - 3546 q^{79} - 1070 q^{80} - 2077 q^{81} + 2202 q^{82} - 4324 q^{83} - 8608 q^{84} + 255 q^{85} - 3626 q^{86} + 2921 q^{87} - 594 q^{88} - 4630 q^{89} + 315 q^{90} - 5043 q^{91} + 108 q^{92} - 5644 q^{93} - 8328 q^{94} + 2185 q^{95} - 2016 q^{96} - 774 q^{97} - 6388 q^{98} + 1870 q^{99}+O(q^{100}) \) 23 * q - 2 * q^2 - 9 * q^3 + 98 * q^4 - 115 * q^5 - 61 * q^6 + 13 * q^7 - 54 * q^8 + 170 * q^9 + 10 * q^10 + 253 * q^11 - 76 * q^12 - 37 * q^13 - 191 * q^14 + 45 * q^15 + 214 * q^16 - 51 * q^17 - 63 * q^18 - 437 * q^19 - 490 * q^20 - 479 * q^21 - 22 * q^22 + 101 * q^23 - 598 * q^24 + 575 * q^25 - 197 * q^26 - 627 * q^27 + 279 * q^28 - 357 * q^29 + 305 * q^30 - 90 * q^31 - 19 * q^32 - 99 * q^33 + 71 * q^34 - 65 * q^35 + 573 * q^36 - 378 * q^37 + 38 * q^38 + 193 * q^39 + 270 * q^40 - 830 * q^41 + 1480 * q^42 + 260 * q^43 + 1078 * q^44 - 850 * q^45 - 919 * q^46 - 1468 * q^47 + 837 * q^48 + 1200 * q^49 - 50 * q^50 - 1147 * q^51 - 1222 * q^52 + 185 * q^53 - 1406 * q^54 - 1265 * q^55 - 2299 * q^56 + 171 * q^57 - 958 * q^58 - 3665 * q^59 + 380 * q^60 - 2528 * q^61 - 1722 * q^62 + 172 * q^63 - 120 * q^64 + 185 * q^65 - 671 * q^66 + 329 * q^67 - 2240 * q^68 - 1337 * q^69 + 955 * q^70 - 3190 * q^71 - 2488 * q^72 - 2183 * q^73 - 1613 * q^74 - 225 * q^75 - 1862 * q^76 + 143 * q^77 - 2748 * q^78 - 3546 * q^79 - 1070 * q^80 - 2077 * q^81 + 2202 * q^82 - 4324 * q^83 - 8608 * q^84 + 255 * q^85 - 3626 * q^86 + 2921 * q^87 - 594 * q^88 - 4630 * q^89 + 315 * q^90 - 5043 * q^91 + 108 * q^92 - 5644 * q^93 - 8328 * q^94 + 2185 * q^95 - 2016 * q^96 - 774 * q^97 - 6388 * q^98 + 1870 * 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 $

$2$	−4.98045	−1.76086	−0.880428	−	0.474181i	$-0.842744\pi$
$2$	−4.98045	−1.76086	−0.880428	+	0.474181i	$0.842744\pi$
$3$	6.47284	1.24570	0.622849	−	0.782342i	$-0.285975\pi$
$3$	6.47284	1.24570	0.622849	+	0.782342i	$0.285975\pi$
$4$	16.8049	2.10061
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−32.2376	−2.19349
$7$	19.1655	1.03484	0.517421	−	0.855731i	$-0.326892\pi$
$7$	19.1655	1.03484	0.517421	+	0.855731i	$0.326892\pi$
$8$	−43.8523	−1.93802
$9$	14.8976	0.551763
$10$	24.9023	0.787478
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	108.775	2.61673
$13$	55.8698	1.19196	0.595981	−	0.802999i	$-0.296763\pi$
$13$	55.8698	1.19196	0.595981	+	0.802999i	$0.296763\pi$
$14$	−95.4530	−1.82221
$15$	−32.3642	−0.557093
$16$	83.9652	1.31196
$17$	−116.017	−1.65519	−0.827594	−	0.561328i	$-0.810291\pi$
$17$	−116.017	−1.65519	−0.827594	+	0.561328i	$0.810291\pi$
$18$	−74.1968	−0.971575
$19$	−19.0000	−0.229416
$19$	−19.0000	−0.229416
$20$	−84.0244	−0.939422
$21$	124.055	1.28910
$22$	−54.7850	−0.530918
$23$	−108.100	−0.980018	−0.490009	−	0.871717i	$-0.663007\pi$
$23$	−108.100	−0.980018	−0.490009	+	0.871717i	$0.663007\pi$
$24$	−283.849	−2.41418
$25$	25.0000	0.200000
$26$	−278.257	−2.09887
$27$	−78.3368	−0.558368
$28$	322.075	2.17380
$29$	−140.937	−0.902461	−0.451230	−	0.892407i	$-0.649015\pi$
$29$	−140.937	−0.902461	−0.451230	+	0.892407i	$0.649015\pi$
$30$	161.188	0.980960
$31$	122.433	0.709342	0.354671	−	0.934991i	$-0.384593\pi$
$31$	122.433	0.709342	0.354671	+	0.934991i	$0.384593\pi$
$32$	−67.3660	−0.372148
$33$	71.2012	0.375592
$34$	577.816	2.91455
$35$	−95.8277	−0.462795
$36$	250.353	1.15904
$37$	−97.6846	−0.434034	−0.217017	−	0.976168i	$-0.569633\pi$
$37$	−97.6846	−0.434034	−0.217017	+	0.976168i	$0.569633\pi$
$38$	94.6286	0.403968
$39$	361.636	1.48482
$40$	219.262	0.866708
$41$	−343.550	−1.30862	−0.654310	−	0.756226i	$-0.727041\pi$
$41$	−343.550	−1.30862	−0.654310	+	0.756226i	$0.727041\pi$
$42$	−617.852	−2.26992
$43$	−164.902	−0.584820	−0.292410	−	0.956293i	$-0.594457\pi$
$43$	−164.902	−0.584820	−0.292410	+	0.956293i	$0.594457\pi$
$44$	184.854	0.633358
$45$	−74.4880	−0.246756
$46$	538.387	1.72567
$47$	69.8609	0.216814	0.108407	−	0.994107i	$-0.465425\pi$
$47$	69.8609	0.216814	0.108407	+	0.994107i	$0.465425\pi$
$48$	543.493	1.63430
$49$	24.3178	0.0708974
$50$	−124.511	−0.352171
$51$	−750.957	−2.06186
$52$	938.886	2.50385
$53$	−602.505	−1.56152	−0.780759	−	0.624833i	$-0.785167\pi$
$53$	−602.505	−1.56152	−0.780759	+	0.624833i	$0.785167\pi$
$54$	390.153	0.983205
$55$	−55.0000	−0.134840
$56$	−840.453	−2.00554
$57$	−122.984	−0.285783
$58$	701.930	1.58910
$59$	254.870	0.562394	0.281197	−	0.959650i	$-0.409269\pi$
$59$	254.870	0.562394	0.281197	+	0.959650i	$0.409269\pi$
$60$	−543.876	−1.17024
$61$	−500.048	−1.04958	−0.524792	−	0.851230i	$-0.675857\pi$
$61$	−500.048	−1.04958	−0.524792	+	0.851230i	$0.675857\pi$
$62$	−609.771	−1.24905
$63$	285.521	0.570988
$64$	−336.209	−0.656658
$65$	−279.349	−0.533062
$66$	−354.614	−0.661363
$67$	351.385	0.640724	0.320362	−	0.947295i	$-0.396195\pi$
$67$	351.385	0.640724	0.320362	+	0.947295i	$0.396195\pi$
$68$	−1949.65	−3.47691
$69$	−699.714	−1.22081
$70$	477.265	0.814916
$71$	435.561	0.728051	0.364025	−	0.931389i	$-0.381402\pi$
$71$	435.561	0.728051	0.364025	+	0.931389i	$0.381402\pi$
$72$	−653.295	−1.06933
$73$	−600.675	−0.963065	−0.481532	−	0.876428i	$-0.659920\pi$
$73$	−600.675	−0.963065	−0.481532	+	0.876428i	$0.659920\pi$
$74$	486.513	0.764271
$75$	161.821	0.249140
$76$	−319.293	−0.481913
$77$	210.821	0.312017
$78$	−1801.11	−2.61456
$79$	−630.237	−0.897560	−0.448780	−	0.893642i	$-0.648141\pi$
$79$	−630.237	−0.897560	−0.448780	+	0.893642i	$0.648141\pi$
$80$	−419.826	−0.586725
$81$	−909.297	−1.24732
$82$	1711.03	2.30429
$83$	−761.603	−1.00719	−0.503595	−	0.863940i	$-0.667990\pi$
$83$	−761.603	−1.00719	−0.503595	+	0.863940i	$0.667990\pi$
$84$	2084.74	2.70790
$85$	580.084	0.740222
$86$	821.285	1.02978
$87$	−912.263	−1.12419
$88$	−482.376	−0.584334
$89$	549.935	0.654977	0.327488	−	0.944855i	$-0.393798\pi$
$89$	549.935	0.654977	0.327488	+	0.944855i	$0.393798\pi$
$90$	370.984	0.434502
$91$	1070.78	1.23349
$92$	−1816.61	−2.05864
$93$	792.488	0.883626
$94$	−347.939	−0.381778
$95$	95.0000	0.102598
$96$	−436.049	−0.463584
$97$	1043.62	1.09241	0.546203	−	0.837653i	$-0.316073\pi$
$97$	1043.62	1.09241	0.546203	+	0.837653i	$0.316073\pi$
$98$	−121.114	−0.124840
$99$	163.874	0.166363
$100$	420.122	0.420122
$101$	1296.41	1.27720	0.638601	−	0.769538i	$-0.279513\pi$
$101$	1296.41	1.27720	0.638601	+	0.769538i	$0.279513\pi$
$102$	3740.11	3.63064
$103$	−1289.40	−1.23348	−0.616740	−	0.787167i	$-0.711547\pi$
$103$	−1289.40	−1.23348	−0.616740	+	0.787167i	$0.711547\pi$
$104$	−2450.02	−2.31004
$105$	−620.277	−0.576503
$106$	3000.75	2.74961
$107$	737.883	0.666671	0.333336	−	0.942808i	$-0.391826\pi$
$107$	737.883	0.666671	0.333336	+	0.942808i	$0.391826\pi$
$108$	−1316.44	−1.17291
$109$	−720.067	−0.632751	−0.316376	−	0.948634i	$-0.602466\pi$
$109$	−720.067	−0.632751	−0.316376	+	0.948634i	$0.602466\pi$
$110$	273.925	0.237434
$111$	−632.296	−0.540675
$112$	1609.24	1.35767
$113$	1616.79	1.34597	0.672986	−	0.739655i	$-0.265011\pi$
$113$	1616.79	1.34597	0.672986	+	0.739655i	$0.265011\pi$
$114$	612.515	0.503222
$115$	540.500	0.438277
$116$	−2368.43	−1.89572
$117$	832.327	0.657681
$118$	−1269.37	−0.990294
$119$	−2223.52	−1.71286
$120$	1419.24	1.07966
$121$	121.000	0.0909091
$122$	2490.47	1.84817
$123$	−2223.74	−1.63015
$124$	2057.47	1.49005
$125$	−125.000	−0.0894427
$126$	−1422.02	−1.00543
$127$	381.281	0.266403	0.133202	−	0.991089i	$-0.457474\pi$
$127$	381.281	0.266403	0.133202	+	0.991089i	$0.457474\pi$
$128$	2213.40	1.52843
$129$	−1067.38	−0.728509
$130$	1391.28	0.938644
$131$	−1668.00	−1.11248	−0.556238	−	0.831023i	$-0.687756\pi$
$131$	−1668.00	−1.11248	−0.556238	+	0.831023i	$0.687756\pi$
$132$	1196.53	0.788973
$133$	−364.145	−0.237409
$134$	−1750.06	−1.12822
$135$	391.684	0.249710
$136$	5087.60	3.20778
$137$	2635.77	1.64371	0.821857	−	0.569694i	$-0.192938\pi$
$137$	2635.77	1.64371	0.821857	+	0.569694i	$0.192938\pi$
$138$	3484.89	2.14966
$139$	815.539	0.497649	0.248824	−	0.968549i	$-0.419956\pi$
$139$	815.539	0.497649	0.248824	+	0.968549i	$0.419956\pi$
$140$	−1610.37	−0.972153
$141$	452.198	0.270085
$142$	−2169.29	−1.28199
$143$	614.568	0.359390
$144$	1250.88	0.723889
$145$	704.686	0.403593
$146$	2991.63	1.69582
$147$	157.405	0.0883168
$148$	−1641.58	−0.911736
$149$	−1241.32	−0.682502	−0.341251	−	0.939972i	$-0.610851\pi$
$149$	−1241.32	−0.682502	−0.341251	+	0.939972i	$0.610851\pi$
$150$	−805.941	−0.438699
$151$	−95.5002	−0.0514682	−0.0257341	−	0.999669i	$-0.508192\pi$
$151$	−95.5002	−0.0514682	−0.0257341	+	0.999669i	$0.508192\pi$
$152$	833.194	0.444612
$153$	−1728.37	−0.913271
$154$	−1049.98	−0.549416
$155$	−612.165	−0.317227
$156$	6077.26	3.11904
$157$	3553.47	1.80636	0.903178	−	0.429266i	$-0.141228\pi$
$157$	3553.47	1.80636	0.903178	+	0.429266i	$0.141228\pi$
$158$	3138.87	1.58047
$159$	−3899.91	−1.94518
$160$	336.830	0.166430
$161$	−2071.80	−1.01416
$162$	4528.71	2.19635
$163$	1439.54	0.691740	0.345870	−	0.938282i	$-0.387584\pi$
$163$	1439.54	0.691740	0.345870	+	0.938282i	$0.387584\pi$
$164$	−5773.31	−2.74890
$165$	−356.006	−0.167970
$166$	3793.13	1.77352
$167$	1946.89	0.902126	0.451063	−	0.892492i	$-0.351045\pi$
$167$	1946.89	0.902126	0.451063	+	0.892492i	$0.351045\pi$
$168$	−5440.12	−2.49830
$169$	924.438	0.420773
$170$	−2889.08	−1.30342
$171$	−283.055	−0.126583
$172$	−2771.15	−1.22848
$173$	−2913.29	−1.28031	−0.640155	−	0.768246i	$-0.721130\pi$
$173$	−2913.29	−1.28031	−0.640155	+	0.768246i	$0.721130\pi$
$174$	4543.48	1.97954
$175$	479.138	0.206968
$176$	923.617	0.395570
$177$	1649.73	0.700573
$178$	−2738.92	−1.15332
$179$	−240.269	−0.100327	−0.0501635	−	0.998741i	$-0.515974\pi$
$179$	−240.269	−0.100327	−0.0501635	+	0.998741i	$0.515974\pi$
$180$	−1251.76	−0.518338
$181$	−3792.87	−1.55758	−0.778790	−	0.627285i	$-0.784166\pi$
$181$	−3792.87	−1.55758	−0.778790	+	0.627285i	$0.784166\pi$
$182$	−5332.94	−2.17200
$183$	−3236.73	−1.30746
$184$	4740.44	1.89929
$185$	488.423	0.194106
$186$	−3946.95	−1.55594
$187$	−1276.18	−0.499058
$188$	1174.00	0.455442
$189$	−1501.37	−0.577822
$190$	−473.143	−0.180660
$191$	−2038.24	−0.772158	−0.386079	−	0.922466i	$-0.626171\pi$
$191$	−2038.24	−0.772158	−0.386079	+	0.922466i	$0.626171\pi$
$192$	−2176.22	−0.817997
$193$	−4234.64	−1.57936	−0.789679	−	0.613520i	$-0.789753\pi$
$193$	−4234.64	−1.57936	−0.789679	+	0.613520i	$0.789753\pi$
$194$	−5197.69	−1.92357
$195$	−1808.18	−0.664034
$196$	408.658	0.148928
$197$	−3529.12	−1.27634	−0.638172	−	0.769894i	$-0.720309\pi$
$197$	−3529.12	−1.27634	−0.638172	+	0.769894i	$0.720309\pi$
$198$	−816.165	−0.292941
$199$	1081.07	0.385102	0.192551	−	0.981287i	$-0.438324\pi$
$199$	1081.07	0.385102	0.192551	+	0.981287i	$0.438324\pi$
$200$	−1096.31	−0.387603
$201$	2274.46	0.798149
$202$	−6456.70	−2.24897
$203$	−2701.14	−0.933904
$204$	−12619.8	−4.33117
$205$	1717.75	0.585233
$206$	6421.80	2.17198
$207$	−1610.43	−0.540738
$208$	4691.12	1.56380
$209$	−209.000	−0.0691714
$210$	3089.26	1.01514
$211$	−18.1092	−0.00590848	−0.00295424	−	0.999996i	$-0.500940\pi$
$211$	−18.1092	−0.00590848	−0.00295424	+	0.999996i	$0.500940\pi$
$212$	−10125.0	−3.28014
$213$	2819.32	0.906931
$214$	−3674.99	−1.17391
$215$	824.508	0.261540
$216$	3435.25	1.08213
$217$	2346.49	0.734057
$218$	3586.26	1.11418
$219$	−3888.07	−1.19969
$220$	−924.269	−0.283246
$221$	−6481.83	−1.97292
$222$	3149.12	0.952050
$223$	3537.24	1.06220	0.531101	−	0.847308i	$-0.321778\pi$
$223$	3537.24	1.06220	0.531101	+	0.847308i	$0.321778\pi$
$224$	−1291.11	−0.385114
$225$	372.440	0.110353
$226$	−8052.34	−2.37006
$227$	4248.60	1.24224	0.621122	−	0.783714i	$-0.286677\pi$
$227$	4248.60	1.24224	0.621122	+	0.783714i	$0.286677\pi$
$228$	−2066.73	−0.600318
$229$	−5742.20	−1.65701	−0.828505	−	0.559982i	$-0.810808\pi$
$229$	−5742.20	−1.65701	−0.828505	+	0.559982i	$0.810808\pi$
$230$	−2691.93	−0.771743
$231$	1364.61	0.388678
$232$	6180.42	1.74898
$233$	−4084.98	−1.14857	−0.574284	−	0.818656i	$-0.694719\pi$
$233$	−4084.98	−1.14857	−0.574284	+	0.818656i	$0.694719\pi$
$234$	−4145.36	−1.15808
$235$	−349.304	−0.0969622
$236$	4283.06	1.18137
$237$	−4079.42	−1.11809
$238$	11074.1	3.01609
$239$	1264.71	0.342291	0.171145	−	0.985246i	$-0.445253\pi$
$239$	1264.71	0.342291	0.171145	+	0.985246i	$0.445253\pi$
$240$	−2717.46	−0.730882
$241$	−2985.93	−0.798095	−0.399047	−	0.916930i	$-0.630659\pi$
$241$	−2985.93	−0.798095	−0.399047	+	0.916930i	$0.630659\pi$
$242$	−602.635	−0.160078
$243$	−3770.63	−0.995417
$244$	−8403.26	−2.20477
$245$	−121.589	−0.0317063
$246$	11075.2	2.87045
$247$	−1061.53	−0.273455
$248$	−5368.97	−1.37472
$249$	−4929.73	−1.25465
$250$	622.556	0.157496
$251$	317.774	0.0799113	0.0399557	−	0.999201i	$-0.487278\pi$
$251$	317.774	0.0799113	0.0399557	+	0.999201i	$0.487278\pi$
$252$	4798.14	1.19942
$253$	−1189.10	−0.295487
$254$	−1898.95	−0.469098
$255$	3754.79	0.922093
$256$	−8334.05	−2.03468
$257$	−3024.28	−0.734044	−0.367022	−	0.930212i	$-0.619623\pi$
$257$	−3024.28	−0.734044	−0.367022	+	0.930212i	$0.619623\pi$
$258$	5316.04	1.28280
$259$	−1872.18	−0.449156
$260$	−4694.43	−1.11976
$261$	−2099.63	−0.497945
$262$	8307.41	1.95891
$263$	4378.86	1.02666	0.513331	−	0.858191i	$-0.328411\pi$
$263$	4378.86	1.02666	0.513331	+	0.858191i	$0.328411\pi$
$264$	−3122.34	−0.727904
$265$	3012.52	0.698332
$266$	1813.61	0.418043
$267$	3559.64	0.815903
$268$	5904.99	1.34591
$269$	−3494.60	−0.792080	−0.396040	−	0.918233i	$-0.629616\pi$
$269$	−3494.60	−0.792080	−0.396040	+	0.918233i	$0.629616\pi$
$270$	−1950.76	−0.439702
$271$	−5863.55	−1.31434	−0.657168	−	0.753744i	$-0.728246\pi$
$271$	−5863.55	−1.31434	−0.657168	+	0.753744i	$0.728246\pi$
$272$	−9741.37	−2.17153
$273$	6930.95	1.53656
$274$	−13127.3	−2.89434
$275$	275.000	0.0603023
$276$	−11758.6	−2.56444
$277$	5817.49	1.26187	0.630937	−	0.775834i	$-0.282671\pi$
$277$	5817.49	1.26187	0.630937	+	0.775834i	$0.282671\pi$
$278$	−4061.75	−0.876287
$279$	1823.96	0.391389
$280$	4202.27	0.896905
$281$	−2188.35	−0.464578	−0.232289	−	0.972647i	$-0.574621\pi$
$281$	−2188.35	−0.464578	−0.232289	+	0.972647i	$0.574621\pi$
$282$	−2252.15	−0.475580
$283$	4253.71	0.893487	0.446743	−	0.894662i	$-0.352584\pi$
$283$	4253.71	0.893487	0.446743	+	0.894662i	$0.352584\pi$
$284$	7319.56	1.52935
$285$	614.919	0.127806
$286$	−3060.83	−0.632834
$287$	−6584.31	−1.35422
$288$	−1003.59	−0.205338
$289$	8546.88	1.73965
$290$	−3509.65	−0.710668
$291$	6755.17	1.36081
$292$	−10094.3	−2.02302
$293$	−3476.50	−0.693173	−0.346586	−	0.938018i	$-0.612659\pi$
$293$	−3476.50	−0.693173	−0.346586	+	0.938018i	$0.612659\pi$
$294$	−783.949	−0.155513
$295$	−1274.35	−0.251510
$296$	4283.70	0.841165
$297$	−861.705	−0.168354
$298$	6182.33	1.20179
$299$	−6039.53	−1.16814
$300$	2719.38	0.523345
$301$	−3160.43	−0.605196
$302$	475.634	0.0906280
$303$	8391.44	1.59101
$304$	−1595.34	−0.300983
$305$	2500.24	0.469388
$306$	8608.07	1.60814
$307$	−4491.31	−0.834960	−0.417480	−	0.908686i	$-0.637087\pi$
$307$	−4491.31	−0.834960	−0.417480	+	0.908686i	$0.637087\pi$
$308$	3542.82	0.655425
$309$	−8346.09	−1.53654
$310$	3048.86	0.558591
$311$	2442.18	0.445283	0.222642	−	0.974900i	$-0.428532\pi$
$311$	2442.18	0.445283	0.222642	+	0.974900i	$0.428532\pi$
$312$	−15858.6	−2.87761
$313$	1309.33	0.236447	0.118223	−	0.992987i	$-0.462280\pi$
$313$	1309.33	0.236447	0.118223	+	0.992987i	$0.462280\pi$
$314$	−17697.9	−3.18073
$315$	−1427.60	−0.255353
$316$	−10591.1	−1.88543
$317$	−5409.06	−0.958370	−0.479185	−	0.877714i	$-0.659068\pi$
$317$	−5409.06	−0.958370	−0.479185	+	0.877714i	$0.659068\pi$
$318$	19423.3	3.42518
$319$	−1550.31	−0.272102
$320$	1681.04	0.293666
$321$	4776.19	0.830471
$322$	10318.5	1.78580
$323$	2204.32	0.379726
$324$	−15280.6	−2.62014
$325$	1396.75	0.238392
$326$	−7169.57	−1.21805
$327$	−4660.87	−0.788217
$328$	15065.4	2.53613
$329$	1338.92	0.224368
$330$	1773.07	0.295771
$331$	7603.80	1.26267	0.631333	−	0.775512i	$-0.282508\pi$
$331$	7603.80	1.26267	0.631333	+	0.775512i	$0.282508\pi$
$332$	−12798.7	−2.11571
$333$	−1455.27	−0.239484
$334$	−9696.40	−1.58851
$335$	−1756.93	−0.286541
$336$	10416.3	1.69124
$337$	6414.73	1.03689	0.518446	−	0.855110i	$-0.326511\pi$
$337$	6414.73	1.03689	0.518446	+	0.855110i	$0.326511\pi$
$338$	−4604.12	−0.740920
$339$	10465.2	1.67667
$340$	9748.24	1.55492
$341$	1346.76	0.213875
$342$	1409.74	0.222895
$343$	−6107.72	−0.961474
$344$	7231.32	1.13339
$345$	3498.57	0.545961
$346$	14509.5	2.25444
$347$	710.307	0.109888	0.0549442	−	0.998489i	$-0.482502\pi$
$347$	710.307	0.109888	0.0549442	+	0.998489i	$0.482502\pi$
$348$	−15330.5	−2.36149
$349$	−6823.66	−1.04660	−0.523298	−	0.852150i	$-0.675298\pi$
$349$	−6823.66	−1.04660	−0.523298	+	0.852150i	$0.675298\pi$
$350$	−2386.33	−0.364441
$351$	−4376.66	−0.665553
$352$	−741.026	−0.112207
$353$	−2298.11	−0.346505	−0.173252	−	0.984877i	$-0.555428\pi$
$353$	−2298.11	−0.346505	−0.173252	+	0.984877i	$0.555428\pi$
$354$	−8216.40	−1.23361
$355$	−2177.81	−0.325594
$356$	9241.59	1.37585
$357$	−14392.5	−2.13370
$358$	1196.65	0.176661
$359$	−11264.6	−1.65605	−0.828023	−	0.560695i	$-0.810534\pi$
$359$	−11264.6	−1.65605	−0.828023	+	0.560695i	$0.810534\pi$
$360$	3266.47	0.478217
$361$	361.000	0.0526316
$362$	18890.2	2.74267
$363$	783.213	0.113245
$364$	17994.3	2.59109
$365$	3003.38	0.430696
$366$	16120.4	2.30226
$367$	−3077.55	−0.437729	−0.218865	−	0.975755i	$-0.570235\pi$
$367$	−3077.55	−0.437729	−0.218865	+	0.975755i	$0.570235\pi$
$368$	−9076.64	−1.28574
$369$	−5118.07	−0.722049
$370$	−2432.57	−0.341792
$371$	−11547.3	−1.61592
$372$	13317.7	1.85615
$373$	−1575.78	−0.218742	−0.109371	−	0.994001i	$-0.534884\pi$
$373$	−1575.78	−0.218742	−0.109371	+	0.994001i	$0.534884\pi$
$374$	6355.97	0.878769
$375$	−809.104	−0.111419
$376$	−3063.56	−0.420189
$377$	−7874.13	−1.07570
$378$	7477.49	1.01746
$379$	−5048.77	−0.684269	−0.342134	−	0.939651i	$-0.611150\pi$
$379$	−5048.77	−0.684269	−0.342134	+	0.939651i	$0.611150\pi$
$380$	1596.46	0.215518
$381$	2467.97	0.331858
$382$	10151.4	1.35966
$383$	5986.38	0.798668	0.399334	−	0.916805i	$-0.369241\pi$
$383$	5986.38	0.798668	0.399334	+	0.916805i	$0.369241\pi$
$384$	14327.0	1.90396
$385$	−1054.10	−0.139538
$386$	21090.4	2.78102
$387$	−2456.64	−0.322682
$388$	17537.9	2.29472
$389$	14681.5	1.91358	0.956791	−	0.290776i	$-0.0939133\pi$
$389$	14681.5	1.91358	0.956791	+	0.290776i	$0.0939133\pi$
$390$	9005.56	1.16927
$391$	12541.4	1.62211
$392$	−1066.39	−0.137400
$393$	−10796.7	−1.38581
$394$	17576.6	2.24746
$395$	3151.19	0.401401
$396$	2753.88	0.349464
$397$	−8393.29	−1.06108	−0.530538	−	0.847661i	$-0.678010\pi$
$397$	−8393.29	−1.06108	−0.530538	+	0.847661i	$0.678010\pi$
$398$	−5384.24	−0.678109
$399$	−2357.05	−0.295740
$400$	2099.13	0.262391
$401$	−5161.18	−0.642735	−0.321368	−	0.946954i	$-0.604143\pi$
$401$	−5161.18	−0.642735	−0.321368	+	0.946954i	$0.604143\pi$
$402$	−11327.8	−1.40543
$403$	6840.31	0.845509
$404$	21786.0	2.68291
$405$	4546.48	0.557819
$406$	13452.9	1.64447
$407$	−1074.53	−0.130866
$408$	32931.2	3.99593
$409$	−982.944	−0.118835	−0.0594174	−	0.998233i	$-0.518924\pi$
$409$	−982.944	−0.118835	−0.0594174	+	0.998233i	$0.518924\pi$
$410$	−8555.16	−1.03051
$411$	17060.9	2.04757
$412$	−21668.3	−2.59106
$413$	4884.72	0.581989
$414$	8020.68	0.952161
$415$	3808.01	0.450429
$416$	−3763.73	−0.443586
$417$	5278.85	0.619920
$418$	1040.91	0.121801
$419$	−1212.03	−0.141316	−0.0706579	−	0.997501i	$-0.522510\pi$
$419$	−1212.03	−0.141316	−0.0706579	+	0.997501i	$0.522510\pi$
$420$	−10423.7	−1.21101
$421$	−12820.6	−1.48417	−0.742086	−	0.670305i	$-0.766163\pi$
$421$	−12820.6	−1.48417	−0.742086	+	0.670305i	$0.766163\pi$
$422$	90.1920	0.0104040
$423$	1040.76	0.119630
$424$	26421.2	3.02625
$425$	−2900.42	−0.331037
$426$	−14041.5	−1.59697
$427$	−9583.70	−1.08615
$428$	12400.0	1.40042
$429$	3978.00	0.447691
$430$	−4106.42	−0.460533
$431$	−14704.8	−1.64340	−0.821701	−	0.569918i	$-0.806975\pi$
$431$	−14704.8	−1.64340	−0.821701	+	0.569918i	$0.806975\pi$
$432$	−6577.57	−0.732554
$433$	−16077.0	−1.78432	−0.892160	−	0.451719i	$-0.850811\pi$
$433$	−16077.0	−1.78432	−0.892160	+	0.451719i	$0.850811\pi$
$434$	−11686.6	−1.29257
$435$	4561.31	0.502755
$436$	−12100.6	−1.32916
$437$	2053.90	0.224832
$438$	19364.4	2.11248
$439$	17004.6	1.84872	0.924359	−	0.381524i	$-0.124601\pi$
$439$	17004.6	1.84872	0.924359	+	0.381524i	$0.124601\pi$
$440$	2411.88	0.261322
$441$	362.277	0.0391186
$442$	32282.5	3.47403
$443$	5528.08	0.592883	0.296441	−	0.955051i	$-0.404200\pi$
$443$	5528.08	0.592883	0.296441	+	0.955051i	$0.404200\pi$
$444$	−10625.7	−1.13575
$445$	−2749.67	−0.292915
$446$	−17617.1	−1.87038
$447$	−8034.86	−0.850192
$448$	−6443.62	−0.679537
$449$	−10484.2	−1.10196	−0.550978	−	0.834519i	$-0.685745\pi$
$449$	−10484.2	−1.10196	−0.550978	+	0.834519i	$0.685745\pi$
$450$	−1854.92	−0.194315
$451$	−3779.05	−0.394564
$452$	27170.0	2.82736
$453$	−618.157	−0.0641138
$454$	−21159.9	−2.18741
$455$	−5353.88	−0.551634
$456$	5393.13	0.553852
$457$	−8239.50	−0.843387	−0.421693	−	0.906739i	$-0.638564\pi$
$457$	−8239.50	−0.843387	−0.421693	+	0.906739i	$0.638564\pi$
$458$	28598.7	2.91775
$459$	9088.38	0.924203
$460$	9083.05	0.920651
$461$	17922.5	1.81070	0.905351	−	0.424665i	$-0.139608\pi$
$461$	17922.5	1.81070	0.905351	+	0.424665i	$0.139608\pi$
$462$	−6796.37	−0.684406
$463$	16502.1	1.65641	0.828205	−	0.560425i	$-0.189362\pi$
$463$	16502.1	1.65641	0.828205	+	0.560425i	$0.189362\pi$
$464$	−11833.8	−1.18399
$465$	−3962.44	−0.395169
$466$	20345.1	2.02246
$467$	5419.62	0.537024	0.268512	−	0.963276i	$-0.413468\pi$
$467$	5419.62	0.537024	0.268512	+	0.963276i	$0.413468\pi$
$468$	13987.2	1.38153
$469$	6734.49	0.663048
$470$	1739.69	0.170736
$471$	23001.0	2.25017
$472$	−11176.6	−1.08993
$473$	−1813.92	−0.176330
$474$	20317.4	1.96879
$475$	−475.000	−0.0458831
$476$	−37366.1	−3.59805
$477$	−8975.88	−0.861588
$478$	−6298.84	−0.602724
$479$	8915.09	0.850399	0.425199	−	0.905100i	$-0.360204\pi$
$479$	8915.09	0.850399	0.425199	+	0.905100i	$0.360204\pi$
$480$	2180.24	0.207321
$481$	−5457.62	−0.517352
$482$	14871.3	1.40533
$483$	−13410.4	−1.26334
$484$	2033.39	0.190965
$485$	−5218.09	−0.488539
$486$	18779.5	1.75279
$487$	15515.6	1.44370	0.721848	−	0.692052i	$-0.243293\pi$
$487$	15515.6	1.44370	0.721848	+	0.692052i	$0.243293\pi$
$488$	21928.3	2.03411
$489$	9317.92	0.861699
$490$	605.568	0.0558302
$491$	−3761.28	−0.345711	−0.172856	−	0.984947i	$-0.555299\pi$
$491$	−3761.28	−0.345711	−0.172856	+	0.984947i	$0.555299\pi$
$492$	−37369.7	−3.42430
$493$	16351.1	1.49374
$494$	5286.88	0.481514
$495$	−819.368	−0.0743997
$496$	10280.1	0.930626
$497$	8347.76	0.753417
$498$	24552.3	2.20927
$499$	−623.041	−0.0558940	−0.0279470	−	0.999609i	$-0.508897\pi$
$499$	−623.041	−0.0558940	−0.0279470	+	0.999609i	$0.508897\pi$
$500$	−2100.61	−0.187884
$501$	12601.9	1.12378
$502$	−1582.66	−0.140712
$503$	2692.32	0.238657	0.119329	−	0.992855i	$-0.461926\pi$
$503$	2692.32	0.238657	0.119329	+	0.992855i	$0.461926\pi$
$504$	−12520.7	−1.10658
$505$	−6482.04	−0.571182
$506$	5922.26	0.520309
$507$	5983.74	0.524156
$508$	6407.39	0.559610
$509$	−10267.1	−0.894069	−0.447035	−	0.894517i	$-0.647520\pi$
$509$	−10267.1	−0.894069	−0.447035	+	0.894517i	$0.647520\pi$
$510$	−18700.5	−1.62367
$511$	−11512.3	−0.996620
$512$	23800.2	2.05435
$513$	1488.40	0.128098
$514$	15062.3	1.29255
$515$	6447.01	0.551629
$516$	−17937.2	−1.53031
$517$	768.470	0.0653719
$518$	9324.29	0.790899
$519$	−18857.3	−1.59488
$520$	12250.1	1.03308
$521$	3206.96	0.269673	0.134836	−	0.990868i	$-0.456949\pi$
$521$	3206.96	0.269673	0.134836	+	0.990868i	$0.456949\pi$
$522$	10457.1	0.876808
$523$	9103.29	0.761108	0.380554	−	0.924759i	$-0.375733\pi$
$523$	9103.29	0.761108	0.380554	+	0.924759i	$0.375733\pi$
$524$	−28030.6	−2.33688
$525$	3101.38	0.257820
$526$	−21808.7	−1.80780
$527$	−14204.3	−1.17409
$528$	5978.42	0.492760
$529$	−481.380	−0.0395644
$530$	−15003.7	−1.22966
$531$	3796.95	0.310308
$532$	−6119.42	−0.498704
$533$	−19194.1	−1.55983
$534$	−17728.6	−1.43669
$535$	−3689.41	−0.298144
$536$	−15409.1	−1.24173
$537$	−1555.22	−0.124977
$538$	17404.7	1.39474
$539$	267.496	0.0213764
$540$	6582.21	0.524543
$541$	−22482.1	−1.78665	−0.893326	−	0.449409i	$-0.851635\pi$
$541$	−22482.1	−1.78665	−0.893326	+	0.449409i	$0.851635\pi$
$542$	29203.1	2.31436
$543$	−24550.6	−1.94027
$544$	7815.58	0.615975
$545$	3600.33	0.282975
$546$	−34519.3	−2.70566
$547$	15659.4	1.22404	0.612018	−	0.790844i	$-0.290358\pi$
$547$	15659.4	1.22404	0.612018	+	0.790844i	$0.290358\pi$
$548$	44293.8	3.45280
$549$	−7449.52	−0.579122
$550$	−1369.62	−0.106184
$551$	2677.81	0.207039
$552$	30684.1	2.36594
$553$	−12078.8	−0.928833
$554$	−28973.7	−2.22198
$555$	3161.48	0.241797
$556$	13705.0	1.04537
$557$	11982.1	0.911489	0.455744	−	0.890111i	$-0.349373\pi$
$557$	11982.1	0.911489	0.455744	+	0.890111i	$0.349373\pi$
$558$	−9084.13	−0.689179
$559$	−9213.03	−0.697083
$560$	−8046.19	−0.607167
$561$	−8260.53	−0.621675
$562$	10899.0	0.818054
$563$	2730.29	0.204384	0.102192	−	0.994765i	$-0.467414\pi$
$563$	2730.29	0.204384	0.102192	+	0.994765i	$0.467414\pi$
$564$	7599.14	0.567343
$565$	−8083.95	−0.601937
$566$	−21185.4	−1.57330
$567$	−17427.2	−1.29078
$568$	−19100.4	−1.41097
$569$	−12771.1	−0.940937	−0.470469	−	0.882417i	$-0.655915\pi$
$569$	−12771.1	−0.940937	−0.470469	+	0.882417i	$0.655915\pi$
$570$	−3062.58	−0.225048
$571$	23167.9	1.69798	0.848991	−	0.528407i	$-0.177211\pi$
$571$	23167.9	1.69798	0.848991	+	0.528407i	$0.177211\pi$
$572$	10327.8	0.754939
$573$	−13193.2	−0.961875
$574$	32792.8	2.38458
$575$	−2702.50	−0.196004
$576$	−5008.70	−0.362319
$577$	6856.59	0.494703	0.247351	−	0.968926i	$-0.420440\pi$
$577$	6856.59	0.494703	0.247351	+	0.968926i	$0.420440\pi$
$578$	−42567.3	−3.06326
$579$	−27410.1	−1.96740
$580$	11842.2	0.847791
$581$	−14596.5	−1.04228
$582$	−33643.8	−2.39619
$583$	−6627.55	−0.470815
$584$	26341.0	1.86644
$585$	−4161.63	−0.294124
$586$	17314.6	1.22058
$587$	5029.66	0.353656	0.176828	−	0.984242i	$-0.443416\pi$
$587$	5029.66	0.353656	0.176828	+	0.984242i	$0.443416\pi$
$588$	2645.18	0.185519
$589$	−2326.23	−0.162734
$590$	6346.84	0.442873
$591$	−22843.4	−1.58994
$592$	−8202.11	−0.569433
$593$	−19025.7	−1.31753	−0.658763	−	0.752351i	$-0.728920\pi$
$593$	−19025.7	−1.31753	−0.658763	+	0.752351i	$0.728920\pi$
$594$	4291.68	0.296447
$595$	11117.6	0.766013
$596$	−20860.2	−1.43367
$597$	6997.62	0.479721
$598$	30079.6	2.05693
$599$	−21366.0	−1.45741	−0.728707	−	0.684825i	$-0.759879\pi$
$599$	−21366.0	−1.45741	−0.728707	+	0.684825i	$0.759879\pi$
$600$	−7096.22	−0.482837
$601$	−16352.1	−1.10985	−0.554923	−	0.831902i	$-0.687252\pi$
$601$	−16352.1	−1.10985	−0.554923	+	0.831902i	$0.687252\pi$
$602$	15740.4	1.06566
$603$	5234.80	0.353528
$604$	−1604.87	−0.108115
$605$	−605.000	−0.0406558
$606$	−41793.1	−2.80153
$607$	2579.50	0.172485	0.0862426	−	0.996274i	$-0.472514\pi$
$607$	2579.50	0.172485	0.0862426	+	0.996274i	$0.472514\pi$
$608$	1279.95	0.0853766
$609$	−17484.0	−1.16336
$610$	−12452.3	−0.826525
$611$	3903.12	0.258434
$612$	−29045.1	−1.91843
$613$	−12299.9	−0.810421	−0.405210	−	0.914223i	$-0.632802\pi$
$613$	−12299.9	−0.810421	−0.405210	+	0.914223i	$0.632802\pi$
$614$	22368.8	1.47024
$615$	11118.7	0.729023
$616$	−9244.99	−0.604693
$617$	5452.30	0.355756	0.177878	−	0.984053i	$-0.443077\pi$
$617$	5452.30	0.355756	0.177878	+	0.984053i	$0.443077\pi$
$618$	41567.3	2.70563
$619$	−7265.59	−0.471775	−0.235887	−	0.971780i	$-0.575800\pi$
$619$	−7265.59	−0.471775	−0.235887	+	0.971780i	$0.575800\pi$
$620$	−10287.4	−0.666371
$621$	8468.21	0.547210
$622$	−12163.1	−0.784080
$623$	10539.8	0.677798
$624$	30364.9	1.94802
$625$	625.000	0.0400000
$626$	−6521.07	−0.416349
$627$	−1352.82	−0.0861667
$628$	59715.7	3.79445
$629$	11333.0	0.718407
$630$	7110.11	0.449640
$631$	22825.2	1.44003	0.720013	−	0.693960i	$-0.244136\pi$
$631$	22825.2	1.44003	0.720013	+	0.693960i	$0.244136\pi$
$632$	27637.4	1.73949
$633$	−117.218	−0.00736018
$634$	26939.6	1.68755
$635$	−1906.41	−0.119139
$636$	−65537.6	−4.08606
$637$	1358.63	0.0845070
$638$	7721.23	0.479133
$639$	6488.82	0.401712
$640$	−11067.0	−0.683533
$641$	5746.27	0.354078	0.177039	−	0.984204i	$-0.443348\pi$
$641$	5746.27	0.354078	0.177039	+	0.984204i	$0.443348\pi$
$642$	−23787.6	−1.46234
$643$	7930.34	0.486379	0.243190	−	0.969979i	$-0.421806\pi$
$643$	7930.34	0.486379	0.243190	+	0.969979i	$0.421806\pi$
$644$	−34816.3	−2.13036
$645$	5336.91	0.325799
$646$	−10978.5	−0.668643
$647$	−7936.68	−0.482261	−0.241131	−	0.970493i	$-0.577518\pi$
$647$	−7936.68	−0.482261	−0.241131	+	0.970493i	$0.577518\pi$
$648$	39874.8	2.41733
$649$	2803.57	0.169568
$650$	−6956.42	−0.419774
$651$	15188.5	0.914413
$652$	24191.3	1.45308
$653$	20519.0	1.22966	0.614831	−	0.788659i	$-0.289224\pi$
$653$	20519.0	1.22966	0.614831	+	0.788659i	$0.289224\pi$
$654$	23213.3	1.38794
$655$	8340.02	0.497514
$656$	−28846.2	−1.71685
$657$	−8948.63	−0.531384
$658$	−6668.43	−0.395080
$659$	−7430.67	−0.439238	−0.219619	−	0.975586i	$-0.570481\pi$
$659$	−7430.67	−0.439238	−0.219619	+	0.975586i	$0.570481\pi$
$660$	−5982.64	−0.352839
$661$	859.190	0.0505577	0.0252788	−	0.999680i	$-0.491953\pi$
$661$	859.190	0.0505577	0.0252788	+	0.999680i	$0.491953\pi$
$662$	−37870.3	−2.22337
$663$	−41955.9	−2.45766
$664$	33398.1	1.95195
$665$	1820.73	0.106173
$666$	7247.88	0.421696
$667$	15235.3	0.884428
$668$	32717.3	1.89502
$669$	22896.0	1.32318
$670$	8750.28	0.504557
$671$	−5500.53	−0.316462
$672$	−8357.11	−0.479736
$673$	−25939.8	−1.48575	−0.742873	−	0.669432i	$-0.766537\pi$
$673$	−25939.8	−1.48575	−0.742873	+	0.669432i	$0.766537\pi$
$674$	−31948.3	−1.82582
$675$	−1958.42	−0.111674
$676$	15535.1	0.883881
$677$	21373.4	1.21337	0.606683	−	0.794944i	$-0.292500\pi$
$677$	21373.4	1.21337	0.606683	+	0.794944i	$0.292500\pi$
$678$	−52121.5	−2.95238
$679$	20001.5	1.13047
$680$	−25438.0	−1.43456
$681$	27500.5	1.54746
$682$	−6707.48	−0.376602
$683$	−10658.4	−0.597122	−0.298561	−	0.954391i	$-0.596507\pi$
$683$	−10658.4	−0.597122	−0.298561	+	0.954391i	$0.596507\pi$
$684$	−4756.70	−0.265902
$685$	−13178.8	−0.735091
$686$	30419.2	1.69302
$687$	−37168.3	−2.06413
$688$	−13846.0	−0.767259
$689$	−33661.8	−1.86127
$690$	−17424.5	−0.961359
$691$	25468.0	1.40210	0.701048	−	0.713114i	$-0.252716\pi$
$691$	25468.0	1.40210	0.701048	+	0.713114i	$0.252716\pi$
$692$	−48957.6	−2.68943
$693$	3140.73	0.172159
$694$	−3537.65	−0.193498
$695$	−4077.70	−0.222555
$696$	40004.8	2.17871
$697$	39857.5	2.16601
$698$	33984.9	1.84290
$699$	−26441.4	−1.43077
$700$	8051.87	0.434760
$701$	6309.62	0.339958	0.169979	−	0.985448i	$-0.445630\pi$
$701$	6309.62	0.339958	0.169979	+	0.985448i	$0.445630\pi$
$702$	21797.8	1.17194
$703$	1856.01	0.0995742
$704$	−3698.30	−0.197990
$705$	−2260.99	−0.120786
$706$	11445.6	0.610144
$707$	24846.4	1.32170
$708$	27723.5	1.47163
$709$	10498.3	0.556095	0.278047	−	0.960567i	$-0.410313\pi$
$709$	10498.3	0.556095	0.278047	+	0.960567i	$0.410313\pi$
$710$	10846.5	0.573324
$711$	−9389.03	−0.495241
$712$	−24115.9	−1.26936
$713$	−13235.0	−0.695168
$714$	71681.1	3.75714
$715$	−3072.84	−0.160724
$716$	−4037.69	−0.210748
$717$	8186.27	0.426391
$718$	56102.5	2.91606
$719$	−23467.4	−1.21723	−0.608615	−	0.793466i	$-0.708275\pi$
$719$	−23467.4	−1.21723	−0.608615	+	0.793466i	$0.708275\pi$
$720$	−6254.40	−0.323733
$721$	−24712.1	−1.27646
$722$	−1797.94	−0.0926766
$723$	−19327.5	−0.994185
$724$	−63738.8	−3.27187
$725$	−3523.43	−0.180492
$726$	−3900.75	−0.199409
$727$	−20560.8	−1.04891	−0.524455	−	0.851438i	$-0.675731\pi$
$727$	−20560.8	−1.04891	−0.524455	+	0.851438i	$0.675731\pi$
$728$	−46956.0	−2.39053
$729$	144.313	0.00733186
$730$	−14958.2	−0.758393
$731$	19131.4	0.967987
$732$	−54392.9	−2.74648
$733$	25487.2	1.28430	0.642148	−	0.766580i	$-0.278043\pi$
$733$	25487.2	1.28430	0.642148	+	0.766580i	$0.278043\pi$
$734$	15327.6	0.770778
$735$	−787.026	−0.0394965
$736$	7282.26	0.364712
$737$	3865.24	0.193186
$738$	25490.3	1.27142
$739$	−28553.7	−1.42133	−0.710665	−	0.703530i	$-0.751606\pi$
$739$	−28553.7	−1.42133	−0.710665	+	0.703530i	$0.751606\pi$
$740$	8207.90	0.407741
$741$	−6871.09	−0.340642
$742$	57510.9	2.84541
$743$	36899.1	1.82193	0.910966	−	0.412482i	$-0.135338\pi$
$743$	36899.1	1.82193	0.910966	+	0.412482i	$0.135338\pi$
$744$	−34752.4	−1.71248
$745$	6206.60	0.305224
$746$	7848.10	0.385173
$747$	−11346.1	−0.555730
$748$	−21446.1	−1.04833
$749$	14141.9	0.689899
$750$	4029.71	0.196192
$751$	13080.7	0.635583	0.317792	−	0.948161i	$-0.397059\pi$
$751$	13080.7	0.635583	0.317792	+	0.948161i	$0.397059\pi$
$752$	5865.88	0.284450
$753$	2056.90	0.0995453
$754$	39216.7	1.89415
$755$	477.501	0.0230173
$756$	−25230.3	−1.21378
$757$	−19450.5	−0.933874	−0.466937	−	0.884291i	$-0.654642\pi$
$757$	−19450.5	−0.933874	−0.466937	+	0.884291i	$0.654642\pi$
$758$	25145.1	1.20490
$759$	−7696.85	−0.368087
$760$	−4165.97	−0.198836
$761$	5098.27	0.242854	0.121427	−	0.992600i	$-0.461253\pi$
$761$	5098.27	0.242854	0.121427	+	0.992600i	$0.461253\pi$
$762$	−12291.6	−0.584354
$763$	−13800.5	−0.654797
$764$	−34252.5	−1.62200
$765$	8641.86	0.408427
$766$	−29814.9	−1.40634
$767$	14239.5	0.670352
$768$	−53945.0	−2.53460
$769$	20592.8	0.965664	0.482832	−	0.875713i	$-0.339608\pi$
$769$	20592.8	0.965664	0.482832	+	0.875713i	$0.339608\pi$
$770$	5249.92	0.245706
$771$	−19575.7	−0.914397
$772$	−71162.7	−3.31762
$773$	30860.2	1.43592	0.717959	−	0.696085i	$-0.245076\pi$
$773$	30860.2	1.43592	0.717959	+	0.696085i	$0.245076\pi$
$774$	12235.2	0.568197
$775$	3060.82	0.141868
$776$	−45765.1	−2.11710
$777$	−12118.3	−0.559513
$778$	−73120.7	−3.36954
$779$	6527.44	0.300218
$780$	−30386.3	−1.39488
$781$	4791.17	0.219516
$782$	−62461.9	−2.85631
$783$	11040.6	0.503905
$784$	2041.85	0.0930143
$785$	−17767.4	−0.807827
$786$	53772.5	2.44021
$787$	−14815.1	−0.671030	−0.335515	−	0.942035i	$-0.608910\pi$
$787$	−14815.1	−0.671030	−0.335515	+	0.942035i	$0.608910\pi$
$788$	−59306.5	−2.68110
$789$	28343.6	1.27891
$790$	−15694.3	−0.706809
$791$	30986.7	1.39287
$792$	−7186.24	−0.322414
$793$	−27937.6	−1.25106
$794$	41802.3	1.86840
$795$	19499.6	0.869910
$796$	18167.3	0.808950
$797$	26710.5	1.18712	0.593560	−	0.804790i	$-0.297722\pi$
$797$	26710.5	1.18712	0.593560	+	0.804790i	$0.297722\pi$
$798$	11739.2	0.520755
$799$	−8105.03	−0.358868
$800$	−1684.15	−0.0744296
$801$	8192.71	0.361392
$802$	25705.0	1.13176
$803$	−6607.43	−0.290375
$804$	38222.0	1.67660
$805$	10359.0	0.453548
$806$	−34067.8	−1.48882
$807$	−22620.0	−0.986693
$808$	−56850.5	−2.47524
$809$	−5025.64	−0.218408	−0.109204	−	0.994019i	$-0.534830\pi$
$809$	−5025.64	−0.218408	−0.109204	+	0.994019i	$0.534830\pi$
$810$	−22643.5	−0.982238
$811$	37183.8	1.60999	0.804994	−	0.593282i	$-0.202168\pi$
$811$	37183.8	1.60999	0.804994	+	0.593282i	$0.202168\pi$
$812$	−45392.3	−1.96177
$813$	−37953.8	−1.63727
$814$	5351.65	0.230436
$815$	−7197.71	−0.309356
$816$	−63054.3	−2.70507
$817$	3133.13	0.134167
$818$	4895.50	0.209251
$819$	15952.0	0.680595
$820$	28866.6	1.22935
$821$	22201.2	0.943760	0.471880	−	0.881663i	$-0.343576\pi$
$821$	22201.2	0.943760	0.471880	+	0.881663i	$0.343576\pi$
$822$	−84970.9	−3.60548
$823$	21410.9	0.906851	0.453426	−	0.891294i	$-0.350202\pi$
$823$	21410.9	0.906851	0.453426	+	0.891294i	$0.350202\pi$
$824$	56543.3	2.39051
$825$	1780.03	0.0751184
$826$	−24328.1	−1.02480
$827$	21480.8	0.903217	0.451609	−	0.892216i	$-0.350850\pi$
$827$	21480.8	0.903217	0.451609	+	0.892216i	$0.350850\pi$
$828$	−27063.1	−1.13588
$829$	7767.78	0.325436	0.162718	−	0.986673i	$-0.447974\pi$
$829$	7767.78	0.325436	0.162718	+	0.986673i	$0.447974\pi$
$830$	−18965.6	−0.793140
$831$	37655.6	1.57191
$832$	−18783.9	−0.782711
$833$	−2821.27	−0.117349
$834$	−26291.1	−1.09159
$835$	−9734.46	−0.403443
$836$	−3512.22	−0.145302
$837$	−9591.00	−0.396074
$838$	6036.44	0.248837
$839$	36434.2	1.49922	0.749611	−	0.661879i	$-0.230241\pi$
$839$	36434.2	1.49922	0.749611	+	0.661879i	$0.230241\pi$
$840$	27200.6	1.11727
$841$	−4525.73	−0.185564
$842$	63852.2	2.61341
$843$	−14164.9	−0.578723
$844$	−304.323	−0.0124114
$845$	−4622.19	−0.188175
$846$	−5183.45	−0.210651
$847$	2319.03	0.0940765
$848$	−50589.4	−2.04864
$849$	27533.6	1.11301
$850$	14445.4	0.582909
$851$	10559.7	0.425361
$852$	47378.3	1.90511
$853$	−6606.67	−0.265191	−0.132596	−	0.991170i	$-0.542331\pi$
$853$	−6606.67	−0.265191	−0.132596	+	0.991170i	$0.542331\pi$
$854$	47731.1	1.91256
$855$	1415.27	0.0566097
$856$	−32357.9	−1.29202
$857$	−18824.3	−0.750324	−0.375162	−	0.926959i	$-0.622413\pi$
$857$	−18824.3	−0.750324	−0.375162	+	0.926959i	$0.622413\pi$
$858$	−19812.2	−0.788320
$859$	10677.7	0.424121	0.212060	−	0.977257i	$-0.431983\pi$
$859$	10677.7	0.424121	0.212060	+	0.977257i	$0.431983\pi$
$860$	13855.8	0.549393
$861$	−42619.2	−1.68694
$862$	73236.7	2.89379
$863$	−25715.5	−1.01433	−0.507164	−	0.861849i	$-0.669306\pi$
$863$	−25715.5	−1.01433	−0.507164	+	0.861849i	$0.669306\pi$
$864$	5277.24	0.207795
$865$	14566.5	0.572572
$866$	80070.7	3.14193
$867$	55322.5	2.16707
$868$	39432.5	1.54197
$869$	−6932.61	−0.270625
$870$	−22717.4	−0.885278
$871$	19631.8	0.763719
$872$	31576.6	1.22628
$873$	15547.4	0.602749
$874$	−10229.4	−0.395896
$875$	−2395.69	−0.0925591
$876$	−65338.6	−2.52008
$877$	−30379.1	−1.16970	−0.584851	−	0.811140i	$-0.698847\pi$
$877$	−30379.1	−1.16970	−0.584851	+	0.811140i	$0.698847\pi$
$878$	−84690.8	−3.25532
$879$	−22502.8	−0.863484
$880$	−4618.09	−0.176904
$881$	−31496.8	−1.20449	−0.602244	−	0.798312i	$-0.705727\pi$
$881$	−31496.8	−1.20449	−0.602244	+	0.798312i	$0.705727\pi$
$882$	−1804.30	−0.0688822
$883$	30973.9	1.18047	0.590235	−	0.807231i	$-0.299035\pi$
$883$	30973.9	1.18047	0.590235	+	0.807231i	$0.299035\pi$
$884$	−108927.	−4.14434
$885$	−8248.66	−0.313306
$886$	−27532.3	−1.04398
$887$	38573.0	1.46015	0.730076	−	0.683366i	$-0.239485\pi$
$887$	38573.0	1.46015	0.730076	+	0.683366i	$0.239485\pi$
$888$	27727.7	1.04784
$889$	7307.46	0.275685
$890$	13694.6	0.515780
$891$	−10002.3	−0.376081
$892$	59442.9	2.23127
$893$	−1327.36	−0.0497405
$894$	40017.2	1.49706
$895$	1201.34	0.0448676
$896$	42421.0	1.58168
$897$	−39092.9	−1.45515
$898$	52215.9	1.94039
$899$	−17255.3	−0.640153
$900$	6258.82	0.231808
$901$	69900.6	2.58460
$902$	18821.4	0.694770
$903$	−20456.9	−0.753892
$904$	−70900.0	−2.60852
$905$	18964.4	0.696571
$906$	3078.70	0.112895
$907$	−34862.2	−1.27627	−0.638137	−	0.769923i	$-0.720295\pi$
$907$	−34862.2	−1.27627	−0.638137	+	0.769923i	$0.720295\pi$
$908$	71397.3	2.60947
$909$	19313.4	0.704713
$910$	26664.7	0.971348
$911$	−19316.3	−0.702502	−0.351251	−	0.936281i	$-0.614244\pi$
$911$	−19316.3	−0.702502	−0.351251	+	0.936281i	$0.614244\pi$
$912$	−10326.4	−0.374934
$913$	−8377.63	−0.303679
$914$	41036.4	1.48508
$915$	16183.7	0.584716
$916$	−96497.0	−3.48073
$917$	−31968.2	−1.15124
$918$	−45264.2	−1.62739
$919$	−30301.7	−1.08766	−0.543831	−	0.839195i	$-0.683027\pi$
$919$	−30301.7	−1.08766	−0.543831	+	0.839195i	$0.683027\pi$
$920$	−23702.2	−0.849389
$921$	−29071.5	−1.04011
$922$	−89262.0	−3.18838
$923$	24334.7	0.867809
$924$	22932.1	0.816462
$925$	−2442.12	−0.0868068
$926$	−82187.9	−2.91670
$927$	−19209.0	−0.680589
$928$	9494.37	0.335849
$929$	44877.6	1.58491	0.792457	−	0.609927i	$-0.208801\pi$
$929$	44877.6	1.58491	0.792457	+	0.609927i	$0.208801\pi$
$930$	19734.7	0.695836
$931$	−462.038	−0.0162650
$932$	−68647.7	−2.41269
$933$	15807.8	0.554689
$934$	−26992.2	−0.945621
$935$	6380.92	0.223185
$936$	−36499.5	−1.27460
$937$	882.702	0.0307755	0.0153877	−	0.999882i	$-0.495102\pi$
$937$	882.702	0.0307755	0.0153877	+	0.999882i	$0.495102\pi$
$938$	−33540.8	−1.16753
$939$	8475.10	0.294541
$940$	−5870.02	−0.203680
$941$	−17222.6	−0.596641	−0.298320	−	0.954466i	$-0.596426\pi$
$941$	−17222.6	−0.596641	−0.298320	+	0.954466i	$0.596426\pi$
$942$	−114556.	−3.96223
$943$	37137.7	1.28247
$944$	21400.2	0.737836
$945$	7506.84	0.258410
$946$	9034.13	0.310491
$947$	34647.2	1.18889	0.594447	−	0.804135i	$-0.297371\pi$
$947$	34647.2	1.18889	0.594447	+	0.804135i	$0.297371\pi$
$948$	−68554.3	−2.34867
$949$	−33559.6	−1.14794
$950$	2365.71	0.0807936
$951$	−35012.0	−1.19384
$952$	97506.6	3.31955
$953$	2654.11	0.0902151	0.0451075	−	0.998982i	$-0.485637\pi$
$953$	2654.11	0.0902151	0.0451075	+	0.998982i	$0.485637\pi$
$954$	44703.9	1.51713
$955$	10191.2	0.345319
$956$	21253.3	0.719019
$957$	−10034.9	−0.338957
$958$	−44401.2	−1.49743
$959$	50515.9	1.70098
$960$	10881.1	0.365819
$961$	−14801.2	−0.496834
$962$	27181.4	0.910982
$963$	10992.7	0.367845
$964$	−50178.3	−1.67649
$965$	21173.2	0.706311
$966$	66789.8	2.22456
$967$	51397.1	1.70922	0.854611	−	0.519268i	$-0.173795\pi$
$967$	51397.1	1.70922	0.854611	+	0.519268i	$0.173795\pi$
$968$	−5306.13	−0.176183
$969$	14268.2	0.473024
$970$	25988.4	0.860246
$971$	40678.5	1.34442	0.672212	−	0.740358i	$-0.265344\pi$
$971$	40678.5	1.34442	0.672212	+	0.740358i	$0.265344\pi$
$972$	−63365.1	−2.09098
$973$	15630.3	0.514988
$974$	−77274.8	−2.54214
$975$	9040.91	0.296965
$976$	−41986.7	−1.37701
$977$	12501.3	0.409368	0.204684	−	0.978828i	$-0.434383\pi$
$977$	12501.3	0.409368	0.204684	+	0.978828i	$0.434383\pi$
$978$	−46407.4	−1.51733
$979$	6049.28	0.197483
$980$	−2043.29	−0.0666026
$981$	−10727.3	−0.349129
$982$	18732.9	0.608747
$983$	−44714.2	−1.45083	−0.725413	−	0.688313i	$-0.758351\pi$
$983$	−44714.2	−1.45083	−0.725413	+	0.688313i	$0.758351\pi$
$984$	97516.2	3.15925
$985$	17645.6	0.570798
$986$	−81435.7	−2.63026
$987$	8666.62	0.279495
$988$	−17838.8	−0.574422
$989$	17825.9	0.573134
$990$	4080.82	0.131007
$991$	−44553.7	−1.42815	−0.714074	−	0.700071i	$-0.753152\pi$
$991$	−44553.7	−1.42815	−0.714074	+	0.700071i	$0.753152\pi$
$992$	−8247.81	−0.263980
$993$	49218.1	1.57290
$994$	−41575.6	−1.32666
$995$	−5405.37	−0.172223
$996$	−82843.6	−2.63554
$997$	−32756.7	−1.04054	−0.520269	−	0.854002i	$-0.674168\pi$
$997$	−32756.7	−1.04054	−0.520269	+	0.854002i	$0.674168\pi$
$998$	3103.02	0.0984213
$999$	7652.30	0.242350

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.4.a.f.1.2	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.4.a.f.1.2	✓	23	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)

\(f(q)\)	\(=\)	\(q-4.98045 q^{2} +6.47284 q^{3} +16.8049 q^{4} -5.00000 q^{5} -32.2376 q^{6} +19.1655 q^{7} -43.8523 q^{8} +14.8976 q^{9} +O(q^{10})\)	\(q-4.98045 q^{2} +6.47284 q^{3} +16.8049 q^{4} -5.00000 q^{5} -32.2376 q^{6} +19.1655 q^{7} -43.8523 q^{8} +14.8976 q^{9} +24.9023 q^{10} +11.0000 q^{11} +108.775 q^{12} +55.8698 q^{13} -95.4530 q^{14} -32.3642 q^{15} +83.9652 q^{16} -116.017 q^{17} -74.1968 q^{18} -19.0000 q^{19} -84.0244 q^{20} +124.055 q^{21} -54.7850 q^{22} -108.100 q^{23} -283.849 q^{24} +25.0000 q^{25} -278.257 q^{26} -78.3368 q^{27} +322.075 q^{28} -140.937 q^{29} +161.188 q^{30} +122.433 q^{31} -67.3660 q^{32} +71.2012 q^{33} +577.816 q^{34} -95.8277 q^{35} +250.353 q^{36} -97.6846 q^{37} +94.6286 q^{38} +361.636 q^{39} +219.262 q^{40} -343.550 q^{41} -617.852 q^{42} -164.902 q^{43} +184.854 q^{44} -74.4880 q^{45} +538.387 q^{46} +69.8609 q^{47} +543.493 q^{48} +24.3178 q^{49} -124.511 q^{50} -750.957 q^{51} +938.886 q^{52} -602.505 q^{53} +390.153 q^{54} -55.0000 q^{55} -840.453 q^{56} -122.984 q^{57} +701.930 q^{58} +254.870 q^{59} -543.876 q^{60} -500.048 q^{61} -609.771 q^{62} +285.521 q^{63} -336.209 q^{64} -279.349 q^{65} -354.614 q^{66} +351.385 q^{67} -1949.65 q^{68} -699.714 q^{69} +477.265 q^{70} +435.561 q^{71} -653.295 q^{72} -600.675 q^{73} +486.513 q^{74} +161.821 q^{75} -319.293 q^{76} +210.821 q^{77} -1801.11 q^{78} -630.237 q^{79} -419.826 q^{80} -909.297 q^{81} +1711.03 q^{82} -761.603 q^{83} +2084.74 q^{84} +580.084 q^{85} +821.285 q^{86} -912.263 q^{87} -482.376 q^{88} +549.935 q^{89} +370.984 q^{90} +1070.78 q^{91} -1816.61 q^{92} +792.488 q^{93} -347.939 q^{94} +95.0000 q^{95} -436.049 q^{96} +1043.62 q^{97} -121.114 q^{98} +163.874 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 2 q^{2} - 9 q^{3} + 98 q^{4} - 115 q^{5} - 61 q^{6} + 13 q^{7} - 54 q^{8} + 170 q^{9}+O(q^{10}) \) 23 * q - 2 * q^2 - 9 * q^3 + 98 * q^4 - 115 * q^5 - 61 * q^6 + 13 * q^7 - 54 * q^8 + 170 * q^9	\( 23 q - 2 q^{2} - 9 q^{3} + 98 q^{4} - 115 q^{5} - 61 q^{6} + 13 q^{7} - 54 q^{8} + 170 q^{9} + 10 q^{10} + 253 q^{11} - 76 q^{12} - 37 q^{13} - 191 q^{14} + 45 q^{15} + 214 q^{16} - 51 q^{17} - 63 q^{18} - 437 q^{19} - 490 q^{20} - 479 q^{21} - 22 q^{22} + 101 q^{23} - 598 q^{24} + 575 q^{25} - 197 q^{26} - 627 q^{27} + 279 q^{28} - 357 q^{29} + 305 q^{30} - 90 q^{31} - 19 q^{32} - 99 q^{33} + 71 q^{34} - 65 q^{35} + 573 q^{36} - 378 q^{37} + 38 q^{38} + 193 q^{39} + 270 q^{40} - 830 q^{41} + 1480 q^{42} + 260 q^{43} + 1078 q^{44} - 850 q^{45} - 919 q^{46} - 1468 q^{47} + 837 q^{48} + 1200 q^{49} - 50 q^{50} - 1147 q^{51} - 1222 q^{52} + 185 q^{53} - 1406 q^{54} - 1265 q^{55} - 2299 q^{56} + 171 q^{57} - 958 q^{58} - 3665 q^{59} + 380 q^{60} - 2528 q^{61} - 1722 q^{62} + 172 q^{63} - 120 q^{64} + 185 q^{65} - 671 q^{66} + 329 q^{67} - 2240 q^{68} - 1337 q^{69} + 955 q^{70} - 3190 q^{71} - 2488 q^{72} - 2183 q^{73} - 1613 q^{74} - 225 q^{75} - 1862 q^{76} + 143 q^{77} - 2748 q^{78} - 3546 q^{79} - 1070 q^{80} - 2077 q^{81} + 2202 q^{82} - 4324 q^{83} - 8608 q^{84} + 255 q^{85} - 3626 q^{86} + 2921 q^{87} - 594 q^{88} - 4630 q^{89} + 315 q^{90} - 5043 q^{91} + 108 q^{92} - 5644 q^{93} - 8328 q^{94} + 2185 q^{95} - 2016 q^{96} - 774 q^{97} - 6388 q^{98} + 1870 q^{99}+O(q^{100}) \) 23 * q - 2 * q^2 - 9 * q^3 + 98 * q^4 - 115 * q^5 - 61 * q^6 + 13 * q^7 - 54 * q^8 + 170 * q^9 + 10 * q^10 + 253 * q^11 - 76 * q^12 - 37 * q^13 - 191 * q^14 + 45 * q^15 + 214 * q^16 - 51 * q^17 - 63 * q^18 - 437 * q^19 - 490 * q^20 - 479 * q^21 - 22 * q^22 + 101 * q^23 - 598 * q^24 + 575 * q^25 - 197 * q^26 - 627 * q^27 + 279 * q^28 - 357 * q^29 + 305 * q^30 - 90 * q^31 - 19 * q^32 - 99 * q^33 + 71 * q^34 - 65 * q^35 + 573 * q^36 - 378 * q^37 + 38 * q^38 + 193 * q^39 + 270 * q^40 - 830 * q^41 + 1480 * q^42 + 260 * q^43 + 1078 * q^44 - 850 * q^45 - 919 * q^46 - 1468 * q^47 + 837 * q^48 + 1200 * q^49 - 50 * q^50 - 1147 * q^51 - 1222 * q^52 + 185 * q^53 - 1406 * q^54 - 1265 * q^55 - 2299 * q^56 + 171 * q^57 - 958 * q^58 - 3665 * q^59 + 380 * q^60 - 2528 * q^61 - 1722 * q^62 + 172 * q^63 - 120 * q^64 + 185 * q^65 - 671 * q^66 + 329 * q^67 - 2240 * q^68 - 1337 * q^69 + 955 * q^70 - 3190 * q^71 - 2488 * q^72 - 2183 * q^73 - 1613 * q^74 - 225 * q^75 - 1862 * q^76 + 143 * q^77 - 2748 * q^78 - 3546 * q^79 - 1070 * q^80 - 2077 * q^81 + 2202 * q^82 - 4324 * q^83 - 8608 * q^84 + 255 * q^85 - 3626 * q^86 + 2921 * q^87 - 594 * q^88 - 4630 * q^89 + 315 * q^90 - 5043 * q^91 + 108 * q^92 - 5644 * q^93 - 8328 * q^94 + 2185 * q^95 - 2016 * q^96 - 774 * q^97 - 6388 * q^98 + 1870 * q^99

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