LMFDB - Embedded newform 1045.4.a.d.1.20

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:	$22$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
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)

$f(q)$	$=$	$q+4.17470 q^{2} +5.44396 q^{3} +9.42811 q^{4} +5.00000 q^{5} +22.7269 q^{6} -28.9642 q^{7} +5.96192 q^{8} +2.63670 q^{9} +O(q^{10})$	\(q+4.17470 q^{2} +5.44396 q^{3} +9.42811 q^{4} +5.00000 q^{5} +22.7269 q^{6} -28.9642 q^{7} +5.96192 q^{8} +2.63670 q^{9} +20.8735 q^{10} -11.0000 q^{11} +51.3262 q^{12} -30.1203 q^{13} -120.917 q^{14} +27.2198 q^{15} -50.5356 q^{16} -74.3057 q^{17} +11.0074 q^{18} -19.0000 q^{19} +47.1405 q^{20} -157.680 q^{21} -45.9217 q^{22} -168.851 q^{23} +32.4565 q^{24} +25.0000 q^{25} -125.743 q^{26} -132.633 q^{27} -273.078 q^{28} +19.0420 q^{29} +113.634 q^{30} +126.226 q^{31} -258.666 q^{32} -59.8836 q^{33} -310.204 q^{34} -144.821 q^{35} +24.8591 q^{36} +338.408 q^{37} -79.3193 q^{38} -163.974 q^{39} +29.8096 q^{40} +235.245 q^{41} -658.266 q^{42} +309.653 q^{43} -103.709 q^{44} +13.1835 q^{45} -704.903 q^{46} +148.629 q^{47} -275.114 q^{48} +495.925 q^{49} +104.367 q^{50} -404.517 q^{51} -283.977 q^{52} -272.854 q^{53} -553.702 q^{54} -55.0000 q^{55} -172.682 q^{56} -103.435 q^{57} +79.4945 q^{58} -216.043 q^{59} +256.631 q^{60} +853.850 q^{61} +526.956 q^{62} -76.3699 q^{63} -675.569 q^{64} -150.601 q^{65} -249.996 q^{66} -290.805 q^{67} -700.562 q^{68} -919.219 q^{69} -604.584 q^{70} -902.814 q^{71} +15.7198 q^{72} +495.199 q^{73} +1412.75 q^{74} +136.099 q^{75} -179.134 q^{76} +318.606 q^{77} -684.541 q^{78} +377.775 q^{79} -252.678 q^{80} -793.239 q^{81} +982.077 q^{82} -812.683 q^{83} -1486.62 q^{84} -371.529 q^{85} +1292.71 q^{86} +103.664 q^{87} -65.5811 q^{88} +117.812 q^{89} +55.0372 q^{90} +872.410 q^{91} -1591.95 q^{92} +687.170 q^{93} +620.483 q^{94} -95.0000 q^{95} -1408.17 q^{96} +674.009 q^{97} +2070.34 q^{98} -29.0037 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 4 q^{2} - 21 q^{3} + 74 q^{4} + 110 q^{5} - 9 q^{6} - 41 q^{7} - 78 q^{8} + 209 q^{9}+O(q^{10}) $ 22 * q - 4 * q^2 - 21 * q^3 + 74 * q^4 + 110 * q^5 - 9 * q^6 - 41 * q^7 - 78 * q^8 + 209 * q^9	\( 22 q - 4 q^{2} - 21 q^{3} + 74 q^{4} + 110 q^{5} - 9 q^{6} - 41 q^{7} - 78 q^{8} + 209 q^{9} - 20 q^{10} - 242 q^{11} - 196 q^{12} - q^{13} - 63 q^{14} - 105 q^{15} + 6 q^{16} + 187 q^{17} - 361 q^{18} - 418 q^{19} + 370 q^{20} - 107 q^{21} + 44 q^{22} - 361 q^{23} + 208 q^{24} + 550 q^{25} - 365 q^{26} - 1467 q^{27} - 773 q^{28} - 319 q^{29} - 45 q^{30} - 402 q^{31} - 873 q^{32} + 231 q^{33} - 717 q^{34} - 205 q^{35} + 725 q^{36} - 838 q^{37} + 76 q^{38} - 607 q^{39} - 390 q^{40} - 392 q^{41} - 1350 q^{42} - 610 q^{43} - 814 q^{44} + 1045 q^{45} - 605 q^{46} - 1866 q^{47} - 1637 q^{48} + 379 q^{49} - 100 q^{50} - 2659 q^{51} - 638 q^{52} - 1303 q^{53} + 2338 q^{54} - 1210 q^{55} + 727 q^{56} + 399 q^{57} + 44 q^{58} - 2417 q^{59} - 980 q^{60} + 918 q^{61} - 1634 q^{62} - 374 q^{63} - 1716 q^{64} - 5 q^{65} + 99 q^{66} - 2339 q^{67} + 4940 q^{68} + 127 q^{69} - 315 q^{70} - 2370 q^{71} - 3306 q^{72} + 2207 q^{73} + 2051 q^{74} - 525 q^{75} - 1406 q^{76} + 451 q^{77} + 1380 q^{78} + 586 q^{79} + 30 q^{80} + 1950 q^{81} - 1566 q^{82} - 2870 q^{83} + 3076 q^{84} + 935 q^{85} - 1246 q^{86} - 1811 q^{87} + 858 q^{88} - 1768 q^{89} - 1805 q^{90} - 2195 q^{91} - 6728 q^{92} - 2916 q^{93} + 672 q^{94} - 2090 q^{95} + 6022 q^{96} - 4022 q^{97} + 1162 q^{98} - 2299 q^{99}+O(q^{100}) \) 22 * q - 4 * q^2 - 21 * q^3 + 74 * q^4 + 110 * q^5 - 9 * q^6 - 41 * q^7 - 78 * q^8 + 209 * q^9 - 20 * q^10 - 242 * q^11 - 196 * q^12 - q^13 - 63 * q^14 - 105 * q^15 + 6 * q^16 + 187 * q^17 - 361 * q^18 - 418 * q^19 + 370 * q^20 - 107 * q^21 + 44 * q^22 - 361 * q^23 + 208 * q^24 + 550 * q^25 - 365 * q^26 - 1467 * q^27 - 773 * q^28 - 319 * q^29 - 45 * q^30 - 402 * q^31 - 873 * q^32 + 231 * q^33 - 717 * q^34 - 205 * q^35 + 725 * q^36 - 838 * q^37 + 76 * q^38 - 607 * q^39 - 390 * q^40 - 392 * q^41 - 1350 * q^42 - 610 * q^43 - 814 * q^44 + 1045 * q^45 - 605 * q^46 - 1866 * q^47 - 1637 * q^48 + 379 * q^49 - 100 * q^50 - 2659 * q^51 - 638 * q^52 - 1303 * q^53 + 2338 * q^54 - 1210 * q^55 + 727 * q^56 + 399 * q^57 + 44 * q^58 - 2417 * q^59 - 980 * q^60 + 918 * q^61 - 1634 * q^62 - 374 * q^63 - 1716 * q^64 - 5 * q^65 + 99 * q^66 - 2339 * q^67 + 4940 * q^68 + 127 * q^69 - 315 * q^70 - 2370 * q^71 - 3306 * q^72 + 2207 * q^73 + 2051 * q^74 - 525 * q^75 - 1406 * q^76 + 451 * q^77 + 1380 * q^78 + 586 * q^79 + 30 * q^80 + 1950 * q^81 - 1566 * q^82 - 2870 * q^83 + 3076 * q^84 + 935 * q^85 - 1246 * q^86 - 1811 * q^87 + 858 * q^88 - 1768 * q^89 - 1805 * q^90 - 2195 * q^91 - 6728 * q^92 - 2916 * q^93 + 672 * q^94 - 2090 * q^95 + 6022 * q^96 - 4022 * q^97 + 1162 * q^98 - 2299 * 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 $

$2$	4.17470	1.47598	0.737989	−	0.674812i	$-0.235775\pi$
$2$	4.17470	1.47598	0.737989	+	0.674812i	$0.235775\pi$
$3$	5.44396	1.04769	0.523845	−	0.851813i	$-0.324497\pi$
$3$	5.44396	1.04769	0.523845	+	0.851813i	$0.324497\pi$
$4$	9.42811	1.17851
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	22.7269	1.54637
$7$	−28.9642	−1.56392	−0.781960	−	0.623329i	$-0.785780\pi$
$7$	−28.9642	−1.56392	−0.781960	+	0.623329i	$0.785780\pi$
$8$	5.96192	0.263482
$9$	2.63670	0.0976556
$10$	20.8735	0.660078
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	51.3262	1.23472
$13$	−30.1203	−0.642605	−0.321303	−	0.946977i	$-0.604121\pi$
$13$	−30.1203	−0.642605	−0.321303	+	0.946977i	$0.604121\pi$
$14$	−120.917	−2.30831
$15$	27.2198	0.468541
$16$	−50.5356	−0.789619
$17$	−74.3057	−1.06010	−0.530052	−	0.847965i	$-0.677828\pi$
$17$	−74.3057	−1.06010	−0.530052	+	0.847965i	$0.677828\pi$
$18$	11.0074	0.144138
$19$	−19.0000	−0.229416
$19$	−19.0000	−0.229416
$20$	47.1405	0.527047
$21$	−157.680	−1.63850
$22$	−45.9217	−0.445024
$23$	−168.851	−1.53078	−0.765389	−	0.643568i	$-0.777454\pi$
$23$	−168.851	−1.53078	−0.765389	+	0.643568i	$0.777454\pi$
$24$	32.4565	0.276048
$25$	25.0000	0.200000
$26$	−125.743	−0.948471
$27$	−132.633	−0.945378
$28$	−273.078	−1.84310
$29$	19.0420	0.121931	0.0609657	−	0.998140i	$-0.480582\pi$
$29$	19.0420	0.121931	0.0609657	+	0.998140i	$0.480582\pi$
$30$	113.634	0.691557
$31$	126.226	0.731319	0.365659	−	0.930749i	$-0.380844\pi$
$31$	126.226	0.731319	0.365659	+	0.930749i	$0.380844\pi$
$32$	−258.666	−1.42894
$33$	−59.8836	−0.315891
$34$	−310.204	−1.56469
$35$	−144.821	−0.699406
$36$	24.8591	0.115088
$37$	338.408	1.50362	0.751810	−	0.659380i	$-0.229181\pi$
$37$	338.408	1.50362	0.751810	+	0.659380i	$0.229181\pi$
$38$	−79.3193	−0.338613
$39$	−163.974	−0.673251
$40$	29.8096	0.117833
$41$	235.245	0.896076	0.448038	−	0.894015i	$-0.352123\pi$
$41$	235.245	0.896076	0.448038	+	0.894015i	$0.352123\pi$
$42$	−658.266	−2.41840
$43$	309.653	1.09818	0.549089	−	0.835764i	$-0.314975\pi$
$43$	309.653	1.09818	0.549089	+	0.835764i	$0.314975\pi$
$44$	−103.709	−0.355335
$45$	13.1835	0.0436729
$46$	−704.903	−2.25940
$47$	148.629	0.461273	0.230636	−	0.973040i	$-0.425919\pi$
$47$	148.629	0.461273	0.230636	+	0.973040i	$0.425919\pi$
$48$	−275.114	−0.827277
$49$	495.925	1.44584
$50$	104.367	0.295196
$51$	−404.517	−1.11066
$52$	−283.977	−0.757319
$53$	−272.854	−0.707158	−0.353579	−	0.935405i	$-0.615035\pi$
$53$	−272.854	−0.707158	−0.353579	+	0.935405i	$0.615035\pi$
$54$	−553.702	−1.39536
$55$	−55.0000	−0.134840
$56$	−172.682	−0.412065
$57$	−103.435	−0.240357
$58$	79.4945	0.179968
$59$	−216.043	−0.476718	−0.238359	−	0.971177i	$-0.576609\pi$
$59$	−216.043	−0.476718	−0.238359	+	0.971177i	$0.576609\pi$
$60$	256.631	0.552182
$61$	853.850	1.79220	0.896101	−	0.443851i	$-0.146388\pi$
$61$	853.850	1.79220	0.896101	+	0.443851i	$0.146388\pi$
$62$	526.956	1.07941
$63$	−76.3699	−0.152726
$64$	−675.569	−1.31947
$65$	−150.601	−0.287382
$66$	−249.996	−0.466248
$67$	−290.805	−0.530262	−0.265131	−	0.964212i	$-0.585415\pi$
$67$	−290.805	−0.530262	−0.265131	+	0.964212i	$0.585415\pi$
$68$	−700.562	−1.24935
$69$	−919.219	−1.60378
$70$	−604.584	−1.03231
$71$	−902.814	−1.50907	−0.754537	−	0.656257i	$-0.772139\pi$
$71$	−902.814	−1.50907	−0.754537	+	0.656257i	$0.772139\pi$
$72$	15.7198	0.0257305
$73$	495.199	0.793955	0.396977	−	0.917828i	$-0.370059\pi$
$73$	495.199	0.793955	0.396977	+	0.917828i	$0.370059\pi$
$74$	1412.75	2.21931
$75$	136.099	0.209538
$76$	−179.134	−0.270370
$77$	318.606	0.471540
$78$	−684.541	−0.993705
$79$	377.775	0.538012	0.269006	−	0.963138i	$-0.413305\pi$
$79$	377.775	0.538012	0.269006	+	0.963138i	$0.413305\pi$
$80$	−252.678	−0.353129
$81$	−793.239	−1.08812
$82$	982.077	1.32259
$83$	−812.683	−1.07474	−0.537371	−	0.843346i	$-0.680582\pi$
$83$	−812.683	−1.07474	−0.537371	+	0.843346i	$0.680582\pi$
$84$	−1486.62	−1.93100
$85$	−371.529	−0.474093
$86$	1292.71	1.62089
$87$	103.664	0.127746
$88$	−65.5811	−0.0794428
$89$	117.812	0.140315	0.0701573	−	0.997536i	$-0.477650\pi$
$89$	117.812	0.140315	0.0701573	+	0.997536i	$0.477650\pi$
$90$	55.0372	0.0644603
$91$	872.410	1.00498
$92$	−1591.95	−1.80404
$93$	687.170	0.766196
$94$	620.483	0.680829
$95$	−95.0000	−0.102598
$96$	−1408.17	−1.49709
$97$	674.009	0.705518	0.352759	−	0.935714i	$-0.385244\pi$
$97$	674.009	0.705518	0.352759	+	0.935714i	$0.385244\pi$
$98$	2070.34	2.13404
$99$	−29.0037	−0.0294443
$100$	235.703	0.235703
$101$	−1167.98	−1.15068	−0.575340	−	0.817914i	$-0.695130\pi$
$101$	−1167.98	−1.15068	−0.575340	+	0.817914i	$0.695130\pi$
$102$	−1688.74	−1.63931
$103$	−1889.28	−1.80734	−0.903671	−	0.428228i	$-0.859138\pi$
$103$	−1889.28	−1.80734	−0.903671	+	0.428228i	$0.859138\pi$
$104$	−179.575	−0.169315
$105$	−788.400	−0.732761
$106$	−1139.08	−1.04375
$107$	−64.7691	−0.0585184	−0.0292592	−	0.999572i	$-0.509315\pi$
$107$	−64.7691	−0.0585184	−0.0292592	+	0.999572i	$0.509315\pi$
$108$	−1250.48	−1.11414
$109$	540.212	0.474706	0.237353	−	0.971424i	$-0.423720\pi$
$109$	540.212	0.474706	0.237353	+	0.971424i	$0.423720\pi$
$110$	−229.608	−0.199021
$111$	1842.28	1.57533
$112$	1463.72	1.23490
$113$	−2153.26	−1.79258	−0.896290	−	0.443468i	$-0.853748\pi$
$113$	−2153.26	−1.79258	−0.896290	+	0.443468i	$0.853748\pi$
$114$	−431.811	−0.354761
$115$	−844.256	−0.684585
$116$	179.530	0.143698
$117$	−79.4182	−0.0627540
$118$	−901.913	−0.703626
$119$	2152.21	1.65792
$120$	162.282	0.123452
$121$	121.000	0.0909091
$122$	3564.57	2.64525
$123$	1280.66	0.938810
$124$	1190.07	0.861869
$125$	125.000	0.0894427
$126$	−318.822	−0.225420
$127$	580.387	0.405520	0.202760	−	0.979228i	$-0.435009\pi$
$127$	580.387	0.405520	0.202760	+	0.979228i	$0.435009\pi$
$128$	−750.966	−0.518568
$129$	1685.74	1.15055
$130$	−628.716	−0.424169
$131$	451.893	0.301390	0.150695	−	0.988580i	$-0.451849\pi$
$131$	451.893	0.301390	0.150695	+	0.988580i	$0.451849\pi$
$132$	−564.589	−0.372281
$133$	550.320	0.358788
$134$	−1214.02	−0.782655
$135$	−663.164	−0.422786
$136$	−443.005	−0.279319
$137$	−482.552	−0.300928	−0.150464	−	0.988615i	$-0.548077\pi$
$137$	−482.552	−0.300928	−0.150464	+	0.988615i	$0.548077\pi$
$138$	−3837.46	−2.36715
$139$	1326.05	0.809166	0.404583	−	0.914501i	$-0.367417\pi$
$139$	1326.05	0.809166	0.404583	+	0.914501i	$0.367417\pi$
$140$	−1365.39	−0.824260
$141$	809.132	0.483271
$142$	−3768.98	−2.22736
$143$	331.323	0.193753
$144$	−133.247	−0.0771108
$145$	95.2099	0.0545293
$146$	2067.31	1.17186
$147$	2699.79	1.51480
$148$	3190.55	1.77204
$149$	314.534	0.172937	0.0864684	−	0.996255i	$-0.472442\pi$
$149$	314.534	0.172937	0.0864684	+	0.996255i	$0.472442\pi$
$150$	568.172	0.309274
$151$	3432.42	1.84984	0.924922	−	0.380158i	$-0.124130\pi$
$151$	3432.42	1.84984	0.924922	+	0.380158i	$0.124130\pi$
$152$	−113.276	−0.0604469
$153$	−195.922	−0.103525
$154$	1330.08	0.695982
$155$	631.131	0.327056
$156$	−1545.96	−0.793436
$157$	−583.994	−0.296865	−0.148433	−	0.988923i	$-0.547423\pi$
$157$	−583.994	−0.296865	−0.148433	+	0.988923i	$0.547423\pi$
$158$	1577.10	0.794095
$159$	−1485.41	−0.740883
$160$	−1293.33	−0.639043
$161$	4890.64	2.39401
$162$	−3311.53	−1.60604
$163$	−2026.77	−0.973920	−0.486960	−	0.873424i	$-0.661894\pi$
$163$	−2026.77	−0.973920	−0.486960	+	0.873424i	$0.661894\pi$
$164$	2217.92	1.05604
$165$	−299.418	−0.141271
$166$	−3392.71	−1.58630
$167$	−3249.10	−1.50553	−0.752763	−	0.658292i	$-0.771279\pi$
$167$	−3249.10	−1.50553	−0.752763	+	0.658292i	$0.771279\pi$
$168$	−940.075	−0.431717
$169$	−1289.77	−0.587059
$170$	−1551.02	−0.699752
$171$	−50.0973	−0.0224037
$172$	2919.44	1.29422
$173$	−4085.42	−1.79543	−0.897714	−	0.440580i	$-0.854773\pi$
$173$	−4085.42	−1.79543	−0.897714	+	0.440580i	$0.854773\pi$
$174$	432.765	0.188551
$175$	−724.105	−0.312784
$176$	555.892	0.238079
$177$	−1176.13	−0.499453
$178$	491.828	0.207101
$179$	−1069.44	−0.446559	−0.223279	−	0.974755i	$-0.571676\pi$
$179$	−1069.44	−0.446559	−0.223279	+	0.974755i	$0.571676\pi$
$180$	124.296	0.0514691
$181$	−837.867	−0.344078	−0.172039	−	0.985090i	$-0.555036\pi$
$181$	−837.867	−0.344078	−0.172039	+	0.985090i	$0.555036\pi$
$182$	3642.05	1.48333
$183$	4648.32	1.87767
$184$	−1006.68	−0.403333
$185$	1692.04	0.672439
$186$	2868.73	1.13089
$187$	817.363	0.319634
$188$	1401.29	0.543616
$189$	3841.60	1.47849
$190$	−396.596	−0.151432
$191$	−3081.91	−1.16753	−0.583767	−	0.811921i	$-0.698422\pi$
$191$	−3081.91	−1.16753	−0.583767	+	0.811921i	$0.698422\pi$
$192$	−3677.77	−1.38240
$193$	−2201.37	−0.821026	−0.410513	−	0.911855i	$-0.634650\pi$
$193$	−2201.37	−0.821026	−0.410513	+	0.911855i	$0.634650\pi$
$194$	2813.79	1.04133
$195$	−819.868	−0.301087
$196$	4675.63	1.70395
$197$	−2961.93	−1.07121	−0.535606	−	0.844468i	$-0.679917\pi$
$197$	−2961.93	−1.07121	−0.535606	+	0.844468i	$0.679917\pi$
$198$	−121.082	−0.0434591
$199$	−612.747	−0.218274	−0.109137	−	0.994027i	$-0.534809\pi$
$199$	−612.747	−0.218274	−0.109137	+	0.994027i	$0.534809\pi$
$200$	149.048	0.0526964
$201$	−1583.13	−0.555550
$202$	−4875.98	−1.69838
$203$	−551.536	−0.190691
$204$	−3813.83	−1.30893
$205$	1176.23	0.400737
$206$	−7887.17	−2.66760
$207$	−445.210	−0.149489
$208$	1522.15	0.507413
$209$	209.000	0.0691714
$210$	−3291.33	−1.08154
$211$	−2322.69	−0.757824	−0.378912	−	0.925433i	$-0.623702\pi$
$211$	−2322.69	−0.757824	−0.378912	+	0.925433i	$0.623702\pi$
$212$	−2572.50	−0.833395
$213$	−4914.88	−1.58104
$214$	−270.392	−0.0863719
$215$	1548.27	0.491120
$216$	−790.746	−0.249090
$217$	−3656.04	−1.14372
$218$	2255.22	0.700655
$219$	2695.84	0.831819
$220$	−518.546	−0.158911
$221$	2238.11	0.681229
$222$	7690.97	2.32515
$223$	−2471.92	−0.742297	−0.371148	−	0.928574i	$-0.621036\pi$
$223$	−2471.92	−0.742297	−0.371148	+	0.928574i	$0.621036\pi$
$224$	7492.07	2.23475
$225$	65.9175	0.0195311
$226$	−8989.21	−2.64581
$227$	−1954.57	−0.571494	−0.285747	−	0.958305i	$-0.592242\pi$
$227$	−1954.57	−0.571494	−0.285747	+	0.958305i	$0.592242\pi$
$228$	−975.199	−0.283264
$229$	−783.070	−0.225968	−0.112984	−	0.993597i	$-0.536041\pi$
$229$	−783.070	−0.225968	−0.112984	+	0.993597i	$0.536041\pi$
$230$	−3524.51	−1.01043
$231$	1734.48	0.494028
$232$	113.527	0.0321267
$233$	2341.81	0.658442	0.329221	−	0.944253i	$-0.393214\pi$
$233$	2341.81	0.658442	0.329221	+	0.944253i	$0.393214\pi$
$234$	−331.547	−0.0926236
$235$	743.147	0.206287
$236$	−2036.87	−0.561818
$237$	2056.59	0.563670
$238$	8984.81	2.44705
$239$	−4135.02	−1.11913	−0.559565	−	0.828786i	$-0.689032\pi$
$239$	−4135.02	−1.11913	−0.559565	+	0.828786i	$0.689032\pi$
$240$	−1375.57	−0.369969
$241$	508.209	0.135837	0.0679183	−	0.997691i	$-0.478364\pi$
$241$	508.209	0.135837	0.0679183	+	0.997691i	$0.478364\pi$
$242$	505.139	0.134180
$243$	−737.274	−0.194634
$244$	8050.19	2.11213
$245$	2479.62	0.646601
$246$	5346.39	1.38566
$247$	572.286	0.147424
$248$	752.550	0.192689
$249$	−4424.21	−1.12600
$250$	521.837	0.132016
$251$	−4505.43	−1.13299	−0.566494	−	0.824066i	$-0.691701\pi$
$251$	−4505.43	−1.13299	−0.566494	+	0.824066i	$0.691701\pi$
$252$	−720.024	−0.179989
$253$	1857.36	0.461547
$254$	2422.94	0.598539
$255$	−2022.59	−0.496703
$256$	2269.50	0.554076
$257$	10.9642	0.00266119	0.00133060	−	0.999999i	$-0.499576\pi$
$257$	10.9642	0.00266119	0.00133060	+	0.999999i	$0.499576\pi$
$258$	7037.45	1.69819
$259$	−9801.72	−2.35154
$260$	−1419.89	−0.338683
$261$	50.2080	0.0119073
$262$	1886.52	0.444845
$263$	7016.37	1.64505	0.822524	−	0.568730i	$-0.192565\pi$
$263$	7016.37	1.64505	0.822524	+	0.568730i	$0.192565\pi$
$264$	−357.021	−0.0832315
$265$	−1364.27	−0.316251
$266$	2297.42	0.529563
$267$	641.362	0.147006
$268$	−2741.74	−0.624921
$269$	−4399.75	−0.997240	−0.498620	−	0.866821i	$-0.666160\pi$
$269$	−4399.75	−0.997240	−0.498620	+	0.866821i	$0.666160\pi$
$270$	−2768.51	−0.624023
$271$	6199.88	1.38973	0.694863	−	0.719142i	$-0.255465\pi$
$271$	6199.88	1.38973	0.694863	+	0.719142i	$0.255465\pi$
$272$	3755.09	0.837079
$273$	4749.37	1.05291
$274$	−2014.51	−0.444164
$275$	−275.000	−0.0603023
$276$	−8666.50	−1.89008
$277$	−243.042	−0.0527182	−0.0263591	−	0.999653i	$-0.508391\pi$
$277$	−243.042	−0.0527182	−0.0263591	+	0.999653i	$0.508391\pi$
$278$	5535.86	1.19431
$279$	332.821	0.0714174
$280$	−863.411	−0.184281
$281$	7098.87	1.50706	0.753529	−	0.657415i	$-0.228350\pi$
$281$	7098.87	1.50706	0.753529	+	0.657415i	$0.228350\pi$
$282$	3377.88	0.713298
$283$	−3565.10	−0.748846	−0.374423	−	0.927258i	$-0.622159\pi$
$283$	−3565.10	−0.748846	−0.374423	+	0.927258i	$0.622159\pi$
$284$	−8511.83	−1.77846
$285$	−517.176	−0.107491
$286$	1383.17	0.285975
$287$	−6813.68	−1.40139
$288$	−682.026	−0.139544
$289$	608.338	0.123822
$290$	397.473	0.0804841
$291$	3669.28	0.739165
$292$	4668.79	0.935686
$293$	5822.87	1.16101	0.580504	−	0.814257i	$-0.302855\pi$
$293$	5822.87	1.16101	0.580504	+	0.814257i	$0.302855\pi$
$294$	11270.8	2.23581
$295$	−1080.21	−0.213195
$296$	2017.56	0.396177
$297$	1458.96	0.285042
$298$	1313.08	0.255251
$299$	5085.85	0.983686
$300$	1283.16	0.246944
$301$	−8968.85	−1.71746
$302$	14329.3	2.73033
$303$	−6358.46	−1.20556
$304$	960.177	0.181151
$305$	4269.25	0.801497
$306$	−817.915	−0.152801
$307$	7929.49	1.47414	0.737068	−	0.675819i	$-0.236210\pi$
$307$	7929.49	1.47414	0.737068	+	0.675819i	$0.236210\pi$
$308$	3003.85	0.555716
$309$	−10285.2	−1.89354
$310$	2634.78	0.482727
$311$	4861.06	0.886320	0.443160	−	0.896443i	$-0.353857\pi$
$311$	4861.06	0.886320	0.443160	+	0.896443i	$0.353857\pi$
$312$	−977.598	−0.177390
$313$	−6102.17	−1.10197	−0.550983	−	0.834517i	$-0.685747\pi$
$313$	−6102.17	−1.10197	−0.550983	+	0.834517i	$0.685747\pi$
$314$	−2438.00	−0.438166
$315$	−381.850	−0.0683009
$316$	3561.70	0.634055
$317$	9260.99	1.64085	0.820424	−	0.571755i	$-0.193737\pi$
$317$	9260.99	1.64085	0.820424	+	0.571755i	$0.193737\pi$
$318$	−6201.12	−1.09353
$319$	−209.462	−0.0367637
$320$	−3377.85	−0.590085
$321$	−352.601	−0.0613092
$322$	20416.9	3.53351
$323$	1411.81	0.243205
$324$	−7478.74	−1.28236
$325$	−753.007	−0.128521
$326$	−8461.16	−1.43749
$327$	2940.89	0.497345
$328$	1402.51	0.236100
$329$	−4304.93	−0.721394
$330$	−1249.98	−0.208512
$331$	5733.77	0.952135	0.476067	−	0.879409i	$-0.342062\pi$
$331$	5733.77	0.952135	0.476067	+	0.879409i	$0.342062\pi$
$332$	−7662.06	−1.26660
$333$	892.281	0.146837
$334$	−13564.0	−2.22212
$335$	−1454.03	−0.237140
$336$	7968.46	1.29379
$337$	−5880.37	−0.950517	−0.475259	−	0.879846i	$-0.657645\pi$
$337$	−5880.37	−0.950517	−0.475259	+	0.879846i	$0.657645\pi$
$338$	−5384.39	−0.866486
$339$	−11722.3	−1.87807
$340$	−3502.81	−0.558725
$341$	−1388.49	−0.220501
$342$	−209.141	−0.0330674
$343$	−4429.34	−0.697265
$344$	1846.13	0.289350
$345$	−4596.10	−0.717233
$346$	−17055.4	−2.65001
$347$	−7584.97	−1.17344	−0.586718	−	0.809791i	$-0.699580\pi$
$347$	−7584.97	−1.17344	−0.586718	+	0.809791i	$0.699580\pi$
$348$	977.354	0.150551
$349$	4967.52	0.761907	0.380953	−	0.924594i	$-0.375596\pi$
$349$	4967.52	0.761907	0.380953	+	0.924594i	$0.375596\pi$
$350$	−3022.92	−0.461662
$351$	3994.94	0.607505
$352$	2845.33	0.430843
$353$	10946.2	1.65045	0.825226	−	0.564802i	$-0.191048\pi$
$353$	10946.2	1.65045	0.825226	+	0.564802i	$0.191048\pi$
$354$	−4909.98	−0.737182
$355$	−4514.07	−0.674879
$356$	1110.74	0.165363
$357$	11716.5	1.73699
$358$	−4464.60	−0.659111
$359$	−13078.4	−1.92271	−0.961356	−	0.275310i	$-0.911220\pi$
$359$	−13078.4	−1.92271	−0.961356	+	0.275310i	$0.911220\pi$
$360$	78.5990	0.0115070
$361$	361.000	0.0526316
$362$	−3497.84	−0.507852
$363$	658.719	0.0952446
$364$	8225.18	1.18439
$365$	2476.00	0.355067
$366$	19405.4	2.77140
$367$	−6344.54	−0.902403	−0.451202	−	0.892422i	$-0.649005\pi$
$367$	−6344.54	−0.902403	−0.451202	+	0.892422i	$0.649005\pi$
$368$	8533.00	1.20873
$369$	620.271	0.0875068
$370$	7063.76	0.992506
$371$	7902.99	1.10594
$372$	6478.71	0.902972
$373$	−3073.71	−0.426677	−0.213338	−	0.976978i	$-0.568434\pi$
$373$	−3073.71	−0.426677	−0.213338	+	0.976978i	$0.568434\pi$
$374$	3412.24	0.471772
$375$	680.495	0.0937083
$376$	886.116	0.121537
$377$	−573.550	−0.0783537
$378$	16037.5	2.18223
$379$	−11005.6	−1.49161	−0.745807	−	0.666162i	$-0.767936\pi$
$379$	−11005.6	−1.49161	−0.745807	+	0.666162i	$0.767936\pi$
$380$	−895.670	−0.120913
$381$	3159.61	0.424860
$382$	−12866.0	−1.72326
$383$	4551.60	0.607247	0.303624	−	0.952792i	$-0.401803\pi$
$383$	4551.60	0.607247	0.303624	+	0.952792i	$0.401803\pi$
$384$	−4088.23	−0.543299
$385$	1593.03	0.210879
$386$	−9190.05	−1.21182
$387$	816.463	0.107243
$388$	6354.63	0.831463
$389$	−10155.7	−1.32368	−0.661841	−	0.749645i	$-0.730224\pi$
$389$	−10155.7	−1.32368	−0.661841	+	0.749645i	$0.730224\pi$
$390$	−3422.70	−0.444398
$391$	12546.6	1.62279
$392$	2956.66	0.380954
$393$	2460.09	0.315763
$394$	−12365.2	−1.58109
$395$	1888.87	0.240606
$396$	−273.450	−0.0347005
$397$	5557.79	0.702613	0.351306	−	0.936261i	$-0.385738\pi$
$397$	5557.79	0.702613	0.351306	+	0.936261i	$0.385738\pi$
$398$	−2558.04	−0.322168
$399$	2995.92	0.375899
$400$	−1263.39	−0.157924
$401$	3227.91	0.401980	0.200990	−	0.979593i	$-0.435584\pi$
$401$	3227.91	0.401980	0.200990	+	0.979593i	$0.435584\pi$
$402$	−6609.10	−0.819980
$403$	−3801.97	−0.469949
$404$	−11011.9	−1.35609
$405$	−3966.19	−0.486622
$406$	−2302.50	−0.281456
$407$	−3722.49	−0.453359
$408$	−2411.70	−0.292640
$409$	10762.1	1.30110	0.650550	−	0.759463i	$-0.274538\pi$
$409$	10762.1	1.30110	0.650550	+	0.759463i	$0.274538\pi$
$410$	4910.39	0.591480
$411$	−2626.99	−0.315280
$412$	−17812.3	−2.12998
$413$	6257.50	0.745549
$414$	−1858.62	−0.220643
$415$	−4063.42	−0.480639
$416$	7791.11	0.918246
$417$	7218.97	0.847756
$418$	872.512	0.102096
$419$	2888.96	0.336838	0.168419	−	0.985716i	$-0.446134\pi$
$419$	2888.96	0.336838	0.168419	+	0.985716i	$0.446134\pi$
$420$	−7433.12	−0.863569
$421$	7146.74	0.827341	0.413671	−	0.910427i	$-0.364246\pi$
$421$	7146.74	0.827341	0.413671	+	0.910427i	$0.364246\pi$
$422$	−9696.54	−1.11853
$423$	391.891	0.0450459
$424$	−1626.73	−0.186323
$425$	−1857.64	−0.212021
$426$	−20518.2	−2.33359
$427$	−24731.1	−2.80286
$428$	−610.650	−0.0689647
$429$	1803.71	0.202993
$430$	6463.54	0.724883
$431$	−7911.52	−0.884187	−0.442094	−	0.896969i	$-0.645764\pi$
$431$	−7911.52	−0.884187	−0.442094	+	0.896969i	$0.645764\pi$
$432$	6702.69	0.746489
$433$	−1085.51	−0.120477	−0.0602383	−	0.998184i	$-0.519186\pi$
$433$	−1085.51	−0.120477	−0.0602383	+	0.998184i	$0.519186\pi$
$434$	−15262.9	−1.68811
$435$	518.319	0.0571299
$436$	5093.18	0.559447
$437$	3208.17	0.351185
$438$	11254.3	1.22775
$439$	12619.3	1.37195	0.685975	−	0.727625i	$-0.259376\pi$
$439$	12619.3	1.37195	0.685975	+	0.727625i	$0.259376\pi$
$440$	−327.906	−0.0355279
$441$	1307.61	0.141195
$442$	9343.43	1.00548
$443$	8853.16	0.949496	0.474748	−	0.880122i	$-0.342539\pi$
$443$	8853.16	0.949496	0.474748	+	0.880122i	$0.342539\pi$
$444$	17369.2	1.85655
$445$	589.058	0.0627506
$446$	−10319.5	−1.09561
$447$	1712.31	0.181184
$448$	19567.3	2.06355
$449$	−11499.4	−1.20867	−0.604334	−	0.796731i	$-0.706561\pi$
$449$	−11499.4	−1.20867	−0.604334	+	0.796731i	$0.706561\pi$
$450$	275.186	0.0288275
$451$	−2587.70	−0.270177
$452$	−20301.2	−2.11258
$453$	18686.0	1.93806
$454$	−8159.73	−0.843513
$455$	4362.05	0.449442
$456$	−616.673	−0.0633297
$457$	3351.85	0.343091	0.171546	−	0.985176i	$-0.445124\pi$
$457$	3351.85	0.343091	0.171546	+	0.985176i	$0.445124\pi$
$458$	−3269.08	−0.333524
$459$	9855.38	1.00220
$460$	−7959.74	−0.806793
$461$	8601.12	0.868967	0.434484	−	0.900680i	$-0.356931\pi$
$461$	8601.12	0.868967	0.434484	+	0.900680i	$0.356931\pi$
$462$	7240.93	0.729174
$463$	−7315.33	−0.734281	−0.367141	−	0.930165i	$-0.619663\pi$
$463$	−7315.33	−0.734281	−0.367141	+	0.930165i	$0.619663\pi$
$464$	−962.299	−0.0962793
$465$	3435.85	0.342653
$466$	9776.35	0.971847
$467$	5570.95	0.552019	0.276010	−	0.961155i	$-0.410988\pi$
$467$	5570.95	0.552019	0.276010	+	0.961155i	$0.410988\pi$
$468$	−748.764	−0.0739564
$469$	8422.94	0.829287
$470$	3102.41	0.304476
$471$	−3179.24	−0.311023
$472$	−1288.03	−0.125607
$473$	−3406.18	−0.331113
$474$	8585.65	0.831966
$475$	−475.000	−0.0458831
$476$	20291.2	1.95388
$477$	−719.434	−0.0690579
$478$	−17262.5	−1.65181
$479$	3013.69	0.287472	0.143736	−	0.989616i	$-0.454088\pi$
$479$	3013.69	0.287472	0.143736	+	0.989616i	$0.454088\pi$
$480$	−7040.85	−0.669519
$481$	−10193.0	−0.966234
$482$	2121.62	0.200492
$483$	26624.4	2.50819
$484$	1140.80	0.107138
$485$	3370.05	0.315517
$486$	−3077.90	−0.287276
$487$	19352.2	1.80068	0.900340	−	0.435187i	$-0.143318\pi$
$487$	19352.2	1.80068	0.900340	+	0.435187i	$0.143318\pi$
$488$	5090.58	0.472213
$489$	−11033.7	−1.02037
$490$	10351.7	0.954370
$491$	−285.696	−0.0262593	−0.0131296	−	0.999914i	$-0.504179\pi$
$491$	−285.696	−0.0262593	−0.0131296	+	0.999914i	$0.504179\pi$
$492$	12074.2	1.10640
$493$	−1414.93	−0.129260
$494$	2389.12	0.217594
$495$	−145.019	−0.0131679
$496$	−6378.92	−0.577463
$497$	26149.3	2.36007
$498$	−18469.8	−1.66195
$499$	−17955.4	−1.61081	−0.805405	−	0.592725i	$-0.798052\pi$
$499$	−17955.4	−1.61081	−0.805405	+	0.592725i	$0.798052\pi$
$500$	1178.51	0.105409
$501$	−17688.0	−1.57732
$502$	−18808.8	−1.67227
$503$	6390.39	0.566468	0.283234	−	0.959051i	$-0.408593\pi$
$503$	6390.39	0.566468	0.283234	+	0.959051i	$0.408593\pi$
$504$	−455.312	−0.0402405
$505$	−5839.92	−0.514600
$506$	7753.93	0.681234
$507$	−7021.45	−0.615056
$508$	5471.96	0.477911
$509$	−6332.40	−0.551432	−0.275716	−	0.961239i	$-0.588915\pi$
$509$	−6332.40	−0.551432	−0.275716	+	0.961239i	$0.588915\pi$
$510$	−8443.69	−0.733123
$511$	−14343.0	−1.24168
$512$	15482.2	1.33637
$513$	2520.02	0.216885
$514$	45.7721	0.00392786
$515$	−9446.40	−0.808268
$516$	15893.3	1.35594
$517$	−1634.92	−0.139079
$518$	−40919.2	−3.47083
$519$	−22240.9	−1.88105
$520$	−897.874	−0.0757199
$521$	−7786.00	−0.654724	−0.327362	−	0.944899i	$-0.606160\pi$
$521$	−7786.00	−0.654724	−0.327362	+	0.944899i	$0.606160\pi$
$522$	209.603	0.0175749
$523$	4639.46	0.387896	0.193948	−	0.981012i	$-0.437871\pi$
$523$	4639.46	0.387896	0.193948	+	0.981012i	$0.437871\pi$
$524$	4260.49	0.355192
$525$	−3942.00	−0.327701
$526$	29291.2	2.42806
$527$	−9379.32	−0.775274
$528$	3026.25	0.249433
$529$	16343.7	1.34328
$530$	−5695.41	−0.466779
$531$	−569.640	−0.0465542
$532$	5188.47	0.422836
$533$	−7085.65	−0.575823
$534$	2677.49	0.216978
$535$	−323.846	−0.0261702
$536$	−1733.76	−0.139714
$537$	−5822.01	−0.467855
$538$	−18367.6	−1.47190
$539$	−5455.17	−0.435939
$540$	−6252.38	−0.498259
$541$	18313.5	1.45537	0.727686	−	0.685910i	$-0.240596\pi$
$541$	18313.5	1.45537	0.727686	+	0.685910i	$0.240596\pi$
$542$	25882.6	2.05121
$543$	−4561.32	−0.360488
$544$	19220.4	1.51483
$545$	2701.06	0.212295
$546$	19827.2	1.55407
$547$	−320.442	−0.0250477	−0.0125239	−	0.999922i	$-0.503987\pi$
$547$	−320.442	−0.0250477	−0.0125239	+	0.999922i	$0.503987\pi$
$548$	−4549.55	−0.354648
$549$	2251.35	0.175018
$550$	−1148.04	−0.0890049
$551$	−361.798	−0.0279730
$552$	−5480.31	−0.422568
$553$	−10941.9	−0.841408
$554$	−1014.63	−0.0778110
$555$	9211.40	0.704509
$556$	12502.1	0.953614
$557$	−7727.61	−0.587845	−0.293922	−	0.955829i	$-0.594961\pi$
$557$	−7727.61	−0.587845	−0.293922	+	0.955829i	$0.594961\pi$
$558$	1389.43	0.105411
$559$	−9326.84	−0.705695
$560$	7318.62	0.552265
$561$	4449.69	0.334877
$562$	29635.7	2.22439
$563$	13526.0	1.01253	0.506265	−	0.862378i	$-0.331026\pi$
$563$	13526.0	1.01253	0.506265	+	0.862378i	$0.331026\pi$
$564$	7628.59	0.569542
$565$	−10766.3	−0.801666
$566$	−14883.2	−1.10528
$567$	22975.5	1.70173
$568$	−5382.50	−0.397614
$569$	−7304.94	−0.538205	−0.269103	−	0.963111i	$-0.586727\pi$
$569$	−7304.94	−0.538205	−0.269103	+	0.963111i	$0.586727\pi$
$570$	−2159.05	−0.158654
$571$	−5588.44	−0.409578	−0.204789	−	0.978806i	$-0.565651\pi$
$571$	−5588.44	−0.409578	−0.204789	+	0.978806i	$0.565651\pi$
$572$	3123.75	0.228340
$573$	−16777.8	−1.22322
$574$	−28445.1	−2.06842
$575$	−4221.28	−0.306156
$576$	−1781.27	−0.128854
$577$	20410.6	1.47262	0.736311	−	0.676643i	$-0.236566\pi$
$577$	20410.6	1.47262	0.736311	+	0.676643i	$0.236566\pi$
$578$	2539.63	0.182759
$579$	−11984.2	−0.860181
$580$	897.649	0.0642636
$581$	23538.7	1.68081
$582$	15318.1	1.09099
$583$	3001.39	0.213216
$584$	2952.34	0.209193
$585$	−397.091	−0.0280644
$586$	24308.7	1.71362
$587$	−16302.1	−1.14627	−0.573133	−	0.819463i	$-0.694272\pi$
$587$	−16302.1	−1.14627	−0.573133	+	0.819463i	$0.694272\pi$
$588$	25454.0	1.78521
$589$	−2398.30	−0.167776
$590$	−4509.56	−0.314671
$591$	−16124.6	−1.12230
$592$	−17101.7	−1.18729
$593$	−9849.10	−0.682047	−0.341024	−	0.940055i	$-0.610774\pi$
$593$	−9849.10	−0.682047	−0.341024	+	0.940055i	$0.610774\pi$
$594$	6090.72	0.420716
$595$	10761.0	0.741444
$596$	2965.46	0.203808
$597$	−3335.77	−0.228684
$598$	21231.9	1.45190
$599$	−843.844	−0.0575601	−0.0287801	−	0.999586i	$-0.509162\pi$
$599$	−843.844	−0.0575601	−0.0287801	+	0.999586i	$0.509162\pi$
$600$	811.411	0.0552095
$601$	23655.6	1.60554	0.802771	−	0.596288i	$-0.203358\pi$
$601$	23655.6	1.60554	0.802771	+	0.596288i	$0.203358\pi$
$602$	−37442.3	−2.53494
$603$	−766.767	−0.0517830
$604$	32361.2	2.18006
$605$	605.000	0.0406558
$606$	−26544.7	−1.77938
$607$	−22156.6	−1.48156	−0.740781	−	0.671746i	$-0.765544\pi$
$607$	−22156.6	−1.48156	−0.740781	+	0.671746i	$0.765544\pi$
$608$	4914.66	0.327822
$609$	−3002.54	−0.199785
$610$	17822.8	1.18299
$611$	−4476.76	−0.296416
$612$	−1847.17	−0.122006
$613$	2964.74	0.195342	0.0976711	−	0.995219i	$-0.468861\pi$
$613$	2964.74	0.195342	0.0976711	+	0.995219i	$0.468861\pi$
$614$	33103.2	2.17579
$615$	6403.32	0.419849
$616$	1899.50	0.124242
$617$	10698.4	0.698060	0.349030	−	0.937112i	$-0.386511\pi$
$617$	10698.4	0.698060	0.349030	+	0.937112i	$0.386511\pi$
$618$	−42937.4	−2.79482
$619$	−4160.16	−0.270131	−0.135065	−	0.990837i	$-0.543124\pi$
$619$	−4160.16	−0.270131	−0.135065	+	0.990837i	$0.543124\pi$
$620$	5950.37	0.385440
$621$	22395.2	1.44716
$622$	20293.5	1.30819
$623$	−3412.32	−0.219441
$624$	8286.51	0.531612
$625$	625.000	0.0400000
$626$	−25474.7	−1.62648
$627$	1137.79	0.0724703
$628$	−5505.96	−0.349859
$629$	−25145.7	−1.59400
$630$	−1594.11	−0.100811
$631$	11671.7	0.736361	0.368180	−	0.929754i	$-0.379981\pi$
$631$	11671.7	0.736361	0.368180	+	0.929754i	$0.379981\pi$
$632$	2252.26	0.141757
$633$	−12644.6	−0.793965
$634$	38661.8	2.42186
$635$	2901.94	0.181354
$636$	−14004.6	−0.873140
$637$	−14937.4	−0.929107
$638$	−874.440	−0.0542624
$639$	−2380.45	−0.147370
$640$	−3754.83	−0.231911
$641$	−22269.9	−1.37224	−0.686122	−	0.727487i	$-0.740688\pi$
$641$	−22269.9	−1.37224	−0.686122	+	0.727487i	$0.740688\pi$
$642$	−1472.00	−0.0904910
$643$	18546.7	1.13750	0.568750	−	0.822511i	$-0.307427\pi$
$643$	18546.7	1.13750	0.568750	+	0.822511i	$0.307427\pi$
$644$	46109.5	2.82138
$645$	8428.70	0.514542
$646$	5893.87	0.358965
$647$	10024.2	0.609106	0.304553	−	0.952495i	$-0.401493\pi$
$647$	10024.2	0.609106	0.304553	+	0.952495i	$0.401493\pi$
$648$	−4729.23	−0.286700
$649$	2376.47	0.143736
$650$	−3143.58	−0.189694
$651$	−19903.3	−1.19827
$652$	−19108.6	−1.14778
$653$	22284.7	1.33548	0.667739	−	0.744396i	$-0.267262\pi$
$653$	22284.7	1.33548	0.667739	+	0.744396i	$0.267262\pi$
$654$	12277.3	0.734070
$655$	2259.46	0.134786
$656$	−11888.3	−0.707559
$657$	1305.69	0.0775341
$658$	−17971.8	−1.06476
$659$	28111.7	1.66173	0.830863	−	0.556478i	$-0.187848\pi$
$659$	28111.7	1.66173	0.830863	+	0.556478i	$0.187848\pi$
$660$	−2822.94	−0.166489
$661$	9016.51	0.530562	0.265281	−	0.964171i	$-0.414535\pi$
$661$	9016.51	0.530562	0.265281	+	0.964171i	$0.414535\pi$
$662$	23936.8	1.40533
$663$	12184.2	0.713717
$664$	−4845.15	−0.283175
$665$	2751.60	0.160455
$666$	3725.01	0.216728
$667$	−3215.26	−0.186650
$668$	−30632.8	−1.77428
$669$	−13457.0	−0.777697
$670$	−6070.12	−0.350014
$671$	−9392.35	−0.540369
$672$	40786.5	2.34133
$673$	−33094.1	−1.89552	−0.947759	−	0.318988i	$-0.896657\pi$
$673$	−33094.1	−1.89552	−0.947759	+	0.318988i	$0.896657\pi$
$674$	−24548.8	−1.40294
$675$	−3315.82	−0.189076
$676$	−12160.1	−0.691857
$677$	5388.35	0.305895	0.152948	−	0.988234i	$-0.451123\pi$
$677$	5388.35	0.305895	0.152948	+	0.988234i	$0.451123\pi$
$678$	−48936.9	−2.77199
$679$	−19522.1	−1.10337
$680$	−2215.02	−0.124915
$681$	−10640.6	−0.598749
$682$	−5796.52	−0.325455
$683$	−10134.9	−0.567789	−0.283894	−	0.958856i	$-0.591627\pi$
$683$	−10134.9	−0.567789	−0.283894	+	0.958856i	$0.591627\pi$
$684$	−472.323	−0.0264031
$685$	−2412.76	−0.134579
$686$	−18491.2	−1.02915
$687$	−4263.00	−0.236745
$688$	−15648.5	−0.867143
$689$	8218.44	0.454423
$690$	−19187.3	−1.05862
$691$	19957.3	1.09872	0.549358	−	0.835587i	$-0.314872\pi$
$691$	19957.3	1.09872	0.549358	+	0.835587i	$0.314872\pi$
$692$	−38517.8	−2.11594
$693$	840.069	0.0460485
$694$	−31664.9	−1.73197
$695$	6630.25	0.361870
$696$	618.035	0.0336589
$697$	−17480.0	−0.949934
$698$	20737.9	1.12456
$699$	12748.7	0.689844
$700$	−6826.94	−0.368620
$701$	35577.4	1.91689	0.958445	−	0.285277i	$-0.0920857\pi$
$701$	35577.4	1.91689	0.958445	+	0.285277i	$0.0920857\pi$
$702$	16677.7	0.896664
$703$	−6429.75	−0.344954
$704$	7431.26	0.397836
$705$	4045.66	0.216125
$706$	45697.3	2.43603
$707$	33829.7	1.79957
$708$	−11088.7	−0.588612
$709$	−23215.3	−1.22972	−0.614859	−	0.788637i	$-0.710787\pi$
$709$	−23215.3	−1.22972	−0.614859	+	0.788637i	$0.710787\pi$
$710$	−18844.9	−0.996107
$711$	996.079	0.0525399
$712$	702.383	0.0369704
$713$	−21313.4	−1.11949
$714$	48912.9	2.56375
$715$	1656.62	0.0866488
$716$	−10082.8	−0.526275
$717$	−22510.9	−1.17250
$718$	−54598.5	−2.83788
$719$	−3875.91	−0.201039	−0.100520	−	0.994935i	$-0.532051\pi$
$719$	−3875.91	−0.201039	−0.100520	+	0.994935i	$0.532051\pi$
$720$	−666.237	−0.0344850
$721$	54721.5	2.82654
$722$	1507.07	0.0776831
$723$	2766.67	0.142315
$724$	−7899.50	−0.405501
$725$	476.050	0.0243863
$726$	2749.95	0.140579
$727$	8593.89	0.438418	0.219209	−	0.975678i	$-0.429652\pi$
$727$	8593.89	0.438418	0.219209	+	0.975678i	$0.429652\pi$
$728$	5201.24	0.264795
$729$	17403.8	0.884202
$730$	10336.5	0.524072
$731$	−23009.0	−1.16418
$732$	43824.9	2.21286
$733$	−16774.0	−0.845243	−0.422621	−	0.906306i	$-0.638890\pi$
$733$	−16774.0	−0.845243	−0.422621	+	0.906306i	$0.638890\pi$
$734$	−26486.5	−1.33193
$735$	13499.0	0.677438
$736$	43676.1	2.18740
$737$	3198.86	0.159880
$738$	2589.44	0.129158
$739$	−37484.4	−1.86588	−0.932939	−	0.360034i	$-0.882765\pi$
$739$	−37484.4	−1.86588	−0.932939	+	0.360034i	$0.882765\pi$
$740$	15952.7	0.792479
$741$	3115.50	0.154454
$742$	32992.6	1.63234
$743$	−2505.16	−0.123695	−0.0618474	−	0.998086i	$-0.519699\pi$
$743$	−2505.16	−0.123695	−0.0618474	+	0.998086i	$0.519699\pi$
$744$	4096.85	0.201879
$745$	1572.67	0.0773397
$746$	−12831.8	−0.629766
$747$	−2142.80	−0.104955
$748$	7706.18	0.376693
$749$	1875.99	0.0915181
$750$	2840.86	0.138311
$751$	16307.5	0.792369	0.396184	−	0.918171i	$-0.370334\pi$
$751$	16307.5	0.792369	0.396184	+	0.918171i	$0.370334\pi$
$752$	−7511.08	−0.364230
$753$	−24527.4	−1.18702
$754$	−2394.40	−0.115648
$755$	17162.1	0.827275
$756$	36219.1	1.74243
$757$	−18197.4	−0.873705	−0.436852	−	0.899533i	$-0.643907\pi$
$757$	−18197.4	−0.873705	−0.436852	+	0.899533i	$0.643907\pi$
$758$	−45945.3	−2.20159
$759$	10111.4	0.483559
$760$	−566.382	−0.0270327
$761$	−19847.0	−0.945405	−0.472702	−	0.881222i	$-0.656721\pi$
$761$	−19847.0	−0.945405	−0.472702	+	0.881222i	$0.656721\pi$
$762$	13190.4	0.627084
$763$	−15646.8	−0.742401
$764$	−29056.6	−1.37596
$765$	−979.610	−0.0462979
$766$	19001.5	0.896284
$767$	6507.27	0.306341
$768$	12355.0	0.580500
$769$	16521.4	0.774743	0.387371	−	0.921924i	$-0.373383\pi$
$769$	16521.4	0.774743	0.387371	+	0.921924i	$0.373383\pi$
$770$	6650.42	0.311253
$771$	59.6885	0.00278810
$772$	−20754.7	−0.967590
$773$	5080.11	0.236376	0.118188	−	0.992991i	$-0.462291\pi$
$773$	5080.11	0.236376	0.118188	+	0.992991i	$0.462291\pi$
$774$	3408.49	0.158289
$775$	3155.65	0.146264
$776$	4018.39	0.185891
$777$	−53360.2	−2.46369
$778$	−42396.8	−1.95373
$779$	−4469.66	−0.205574
$780$	−7729.81	−0.354835
$781$	9930.95	0.455003
$782$	52378.3	2.39520
$783$	−2525.59	−0.115271
$784$	−25061.9	−1.14167
$785$	−2919.97	−0.132762
$786$	10270.1	0.466060
$787$	6030.81	0.273158	0.136579	−	0.990629i	$-0.456389\pi$
$787$	6030.81	0.273158	0.136579	+	0.990629i	$0.456389\pi$
$788$	−27925.4	−1.26244
$789$	38196.8	1.72350
$790$	7885.48	0.355130
$791$	62367.4	2.80345
$792$	−172.918	−0.00775804
$793$	−25718.2	−1.15168
$794$	23202.1	1.03704
$795$	−7427.03	−0.331333
$796$	−5777.05	−0.257239
$797$	12063.8	0.536164	0.268082	−	0.963396i	$-0.413610\pi$
$797$	12063.8	0.536164	0.268082	+	0.963396i	$0.413610\pi$
$798$	12507.1	0.554818
$799$	−11044.0	−0.488998
$800$	−6466.66	−0.285789
$801$	310.634	0.0137025
$802$	13475.5	0.593314
$803$	−5447.19	−0.239386
$804$	−14925.9	−0.654723
$805$	24453.2	1.07064
$806$	−15872.1	−0.693635
$807$	−23952.1	−1.04480
$808$	−6963.43	−0.303184
$809$	19621.0	0.852705	0.426352	−	0.904557i	$-0.359798\pi$
$809$	19621.0	0.852705	0.426352	+	0.904557i	$0.359798\pi$
$810$	−16557.7	−0.718243
$811$	−13341.5	−0.577661	−0.288831	−	0.957380i	$-0.593266\pi$
$811$	−13341.5	−0.577661	−0.288831	+	0.957380i	$0.593266\pi$
$812$	−5199.94	−0.224732
$813$	33751.9	1.45600
$814$	−15540.3	−0.669148
$815$	−10133.9	−0.435550
$816$	20442.5	0.877000
$817$	−5883.41	−0.251939
$818$	44928.4	1.92040
$819$	2300.29	0.0981422
$820$	11089.6	0.472274
$821$	2968.29	0.126180	0.0630902	−	0.998008i	$-0.479904\pi$
$821$	2968.29	0.126180	0.0630902	+	0.998008i	$0.479904\pi$
$822$	−10966.9	−0.465346
$823$	27348.8	1.15835	0.579173	−	0.815205i	$-0.303376\pi$
$823$	27348.8	1.15835	0.579173	+	0.815205i	$0.303376\pi$
$824$	−11263.7	−0.476202
$825$	−1497.09	−0.0631781
$826$	26123.2	1.10041
$827$	17900.0	0.752654	0.376327	−	0.926487i	$-0.377187\pi$
$827$	17900.0	0.752654	0.376327	+	0.926487i	$0.377187\pi$
$828$	−4197.49	−0.176175
$829$	−38422.5	−1.60973	−0.804866	−	0.593457i	$-0.797763\pi$
$829$	−38422.5	−1.60973	−0.804866	+	0.593457i	$0.797763\pi$
$830$	−16963.5	−0.709413
$831$	−1323.11	−0.0552324
$832$	20348.3	0.847899
$833$	−36850.0	−1.53275
$834$	30137.0	1.25127
$835$	−16245.5	−0.673291
$836$	1970.47	0.0815195
$837$	−16741.7	−0.691372
$838$	12060.5	0.497165
$839$	17488.7	0.719637	0.359819	−	0.933022i	$-0.382839\pi$
$839$	17488.7	0.719637	0.359819	+	0.933022i	$0.382839\pi$
$840$	−4700.38	−0.193069
$841$	−24026.4	−0.985133
$842$	29835.5	1.22114
$843$	38646.0	1.57893
$844$	−21898.6	−0.893105
$845$	−6448.84	−0.262541
$846$	1636.03	0.0664868
$847$	−3504.67	−0.142175
$848$	13788.8	0.558386
$849$	−19408.3	−0.784559
$850$	−7755.10	−0.312938
$851$	−57140.6	−2.30171
$852$	−46338.1	−1.86328
$853$	−38427.6	−1.54248	−0.771241	−	0.636544i	$-0.780363\pi$
$853$	−38427.6	−1.54248	−0.771241	+	0.636544i	$0.780363\pi$
$854$	−103245.	−4.13696
$855$	−250.487	−0.0100193
$856$	−386.148	−0.0154186
$857$	−22282.9	−0.888179	−0.444090	−	0.895982i	$-0.646473\pi$
$857$	−22282.9	−0.888179	−0.444090	+	0.895982i	$0.646473\pi$
$858$	7529.95	0.299613
$859$	11259.8	0.447240	0.223620	−	0.974676i	$-0.428213\pi$
$859$	11259.8	0.447240	0.223620	+	0.974676i	$0.428213\pi$
$860$	14597.2	0.578792
$861$	−37093.4	−1.46822
$862$	−33028.2	−1.30504
$863$	422.116	0.0166501	0.00832503	−	0.999965i	$-0.497350\pi$
$863$	422.116	0.0166501	0.00832503	+	0.999965i	$0.497350\pi$
$864$	34307.7	1.35089
$865$	−20427.1	−0.802939
$866$	−4531.68	−0.177821
$867$	3311.77	0.129727
$868$	−34469.5	−1.34789
$869$	−4155.52	−0.162217
$870$	2163.83	0.0843225
$871$	8759.14	0.340749
$872$	3220.70	0.125076
$873$	1777.16	0.0688978
$874$	13393.2	0.518341
$875$	−3620.52	−0.139881
$876$	25416.7	0.980310
$877$	38823.8	1.49485	0.747426	−	0.664345i	$-0.231289\pi$
$877$	38823.8	1.49485	0.747426	+	0.664345i	$0.231289\pi$
$878$	52681.8	2.02497
$879$	31699.5	1.21638
$880$	2779.46	0.106472
$881$	−12266.3	−0.469083	−0.234541	−	0.972106i	$-0.575359\pi$
$881$	−12266.3	−0.469083	−0.234541	+	0.972106i	$0.575359\pi$
$882$	5458.86	0.208401
$883$	9975.47	0.380183	0.190091	−	0.981766i	$-0.439122\pi$
$883$	9975.47	0.380183	0.190091	+	0.981766i	$0.439122\pi$
$884$	21101.1	0.802837
$885$	−5880.64	−0.223362
$886$	36959.3	1.40144
$887$	−4188.06	−0.158536	−0.0792680	−	0.996853i	$-0.525258\pi$
$887$	−4188.06	−0.158536	−0.0792680	+	0.996853i	$0.525258\pi$
$888$	10983.5	0.415071
$889$	−16810.5	−0.634201
$890$	2459.14	0.0926186
$891$	8725.63	0.328080
$892$	−23305.5	−0.874807
$893$	−2823.96	−0.105823
$894$	7148.37	0.267424
$895$	−5347.22	−0.199707
$896$	21751.1	0.810998
$897$	27687.1	1.03060
$898$	−48006.7	−1.78397
$899$	2403.60	0.0891706
$900$	621.478	0.0230177
$901$	20274.6	0.749661
$902$	−10802.8	−0.398775
$903$	−48826.1	−1.79937
$904$	−12837.6	−0.472313
$905$	−4189.34	−0.153877
$906$	78008.2	2.86054
$907$	26883.2	0.984170	0.492085	−	0.870547i	$-0.336235\pi$
$907$	26883.2	0.984170	0.492085	+	0.870547i	$0.336235\pi$
$908$	−18427.9	−0.673514
$909$	−3079.63	−0.112370
$910$	18210.2	0.663367
$911$	48221.6	1.75374	0.876868	−	0.480731i	$-0.159629\pi$
$911$	48221.6	1.75374	0.876868	+	0.480731i	$0.159629\pi$
$912$	5227.17	0.189790
$913$	8939.51	0.324047
$914$	13992.9	0.506396
$915$	23241.6	0.839721
$916$	−7382.86	−0.266306
$917$	−13088.7	−0.471349
$918$	41143.2	1.47923
$919$	−33326.3	−1.19623	−0.598113	−	0.801411i	$-0.704083\pi$
$919$	−33326.3	−1.19623	−0.598113	+	0.801411i	$0.704083\pi$
$920$	−5033.39	−0.180376
$921$	43167.8	1.54444
$922$	35907.1	1.28258
$923$	27193.0	0.969739
$924$	16352.9	0.582218
$925$	8460.20	0.300724
$926$	−30539.3	−1.08378
$927$	−4981.47	−0.176497
$928$	−4925.52	−0.174233
$929$	−53989.7	−1.90672	−0.953361	−	0.301832i	$-0.902402\pi$
$929$	−53989.7	−1.90672	−0.953361	+	0.301832i	$0.902402\pi$
$930$	14343.6	0.505749
$931$	−9422.57	−0.331700
$932$	22078.8	0.775983
$933$	26463.4	0.928589
$934$	23257.1	0.814769
$935$	4086.81	0.142945
$936$	−473.485	−0.0165346
$937$	−30161.7	−1.05159	−0.525795	−	0.850612i	$-0.676232\pi$
$937$	−30161.7	−1.05159	−0.525795	+	0.850612i	$0.676232\pi$
$938$	35163.3	1.22401
$939$	−33220.0	−1.15452
$940$	7006.47	0.243113
$941$	32202.6	1.11560	0.557798	−	0.829977i	$-0.311646\pi$
$941$	32202.6	1.11560	0.557798	+	0.829977i	$0.311646\pi$
$942$	−13272.4	−0.459063
$943$	−39721.4	−1.37169
$944$	10917.9	0.376426
$945$	19208.0	0.661203
$946$	−14219.8	−0.488716
$947$	−35098.4	−1.20438	−0.602189	−	0.798354i	$-0.705704\pi$
$947$	−35098.4	−1.20438	−0.602189	+	0.798354i	$0.705704\pi$
$948$	19389.8	0.664293
$949$	−14915.5	−0.510199
$950$	−1982.98	−0.0677226
$951$	50416.5	1.71910
$952$	12831.3	0.436832
$953$	−25993.9	−0.883552	−0.441776	−	0.897125i	$-0.645651\pi$
$953$	−25993.9	−0.883552	−0.441776	+	0.897125i	$0.645651\pi$
$954$	−3003.42	−0.101928
$955$	−15409.5	−0.522137
$956$	−38985.4	−1.31891
$957$	−1140.30	−0.0385170
$958$	12581.2	0.424302
$959$	13976.7	0.470628
$960$	−18388.9	−0.618227
$961$	−13858.0	−0.465173
$962$	−42552.5	−1.42614
$963$	−170.777	−0.00571465
$964$	4791.45	0.160085
$965$	−11006.8	−0.367174
$966$	111149.	3.70203
$967$	−2545.79	−0.0846609	−0.0423305	−	0.999104i	$-0.513478\pi$
$967$	−2545.79	−0.0846609	−0.0423305	+	0.999104i	$0.513478\pi$
$968$	721.392	0.0239529
$969$	7685.83	0.254803
$970$	14068.9	0.465697
$971$	−1079.00	−0.0356611	−0.0178305	−	0.999841i	$-0.505676\pi$
$971$	−1079.00	−0.0356611	−0.0178305	+	0.999841i	$0.505676\pi$
$972$	−6951.10	−0.229379
$973$	−38408.0	−1.26547
$974$	80789.5	2.65777
$975$	−4099.34	−0.134650
$976$	−43149.8	−1.41516
$977$	52134.1	1.70718	0.853592	−	0.520942i	$-0.174419\pi$
$977$	52134.1	1.70718	0.853592	+	0.520942i	$0.174419\pi$
$978$	−46062.2	−1.50604
$979$	−1295.93	−0.0423065
$980$	23378.2	0.762029
$981$	1424.38	0.0463577
$982$	−1192.70	−0.0387581
$983$	30696.6	0.996000	0.498000	−	0.867177i	$-0.334068\pi$
$983$	30696.6	0.996000	0.498000	+	0.867177i	$0.334068\pi$
$984$	7635.22	0.247360
$985$	−14809.7	−0.479061
$986$	−5906.90	−0.190785
$987$	−23435.9	−0.755797
$988$	5395.57	0.173741
$989$	−52285.3	−1.68107
$990$	−605.409	−0.0194355
$991$	9357.60	0.299954	0.149977	−	0.988690i	$-0.452080\pi$
$991$	9357.60	0.299954	0.149977	+	0.988690i	$0.452080\pi$
$992$	−32650.5	−1.04501
$993$	31214.4	0.997542
$994$	109165.	3.48342
$995$	−3063.74	−0.0976151
$996$	−41712.0	−1.32700
$997$	18484.1	0.587158	0.293579	−	0.955935i	$-0.405154\pi$
$997$	18484.1	0.587158	0.293579	+	0.955935i	$0.405154\pi$
$998$	−74958.4	−2.37752
$999$	−44884.0	−1.42149

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.4.a.d.1.20	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.4.a.d.1.20	✓	22	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)

\(f(q)\)	\(=\)	\(q+4.17470 q^{2} +5.44396 q^{3} +9.42811 q^{4} +5.00000 q^{5} +22.7269 q^{6} -28.9642 q^{7} +5.96192 q^{8} +2.63670 q^{9} +O(q^{10})\)	\(q+4.17470 q^{2} +5.44396 q^{3} +9.42811 q^{4} +5.00000 q^{5} +22.7269 q^{6} -28.9642 q^{7} +5.96192 q^{8} +2.63670 q^{9} +20.8735 q^{10} -11.0000 q^{11} +51.3262 q^{12} -30.1203 q^{13} -120.917 q^{14} +27.2198 q^{15} -50.5356 q^{16} -74.3057 q^{17} +11.0074 q^{18} -19.0000 q^{19} +47.1405 q^{20} -157.680 q^{21} -45.9217 q^{22} -168.851 q^{23} +32.4565 q^{24} +25.0000 q^{25} -125.743 q^{26} -132.633 q^{27} -273.078 q^{28} +19.0420 q^{29} +113.634 q^{30} +126.226 q^{31} -258.666 q^{32} -59.8836 q^{33} -310.204 q^{34} -144.821 q^{35} +24.8591 q^{36} +338.408 q^{37} -79.3193 q^{38} -163.974 q^{39} +29.8096 q^{40} +235.245 q^{41} -658.266 q^{42} +309.653 q^{43} -103.709 q^{44} +13.1835 q^{45} -704.903 q^{46} +148.629 q^{47} -275.114 q^{48} +495.925 q^{49} +104.367 q^{50} -404.517 q^{51} -283.977 q^{52} -272.854 q^{53} -553.702 q^{54} -55.0000 q^{55} -172.682 q^{56} -103.435 q^{57} +79.4945 q^{58} -216.043 q^{59} +256.631 q^{60} +853.850 q^{61} +526.956 q^{62} -76.3699 q^{63} -675.569 q^{64} -150.601 q^{65} -249.996 q^{66} -290.805 q^{67} -700.562 q^{68} -919.219 q^{69} -604.584 q^{70} -902.814 q^{71} +15.7198 q^{72} +495.199 q^{73} +1412.75 q^{74} +136.099 q^{75} -179.134 q^{76} +318.606 q^{77} -684.541 q^{78} +377.775 q^{79} -252.678 q^{80} -793.239 q^{81} +982.077 q^{82} -812.683 q^{83} -1486.62 q^{84} -371.529 q^{85} +1292.71 q^{86} +103.664 q^{87} -65.5811 q^{88} +117.812 q^{89} +55.0372 q^{90} +872.410 q^{91} -1591.95 q^{92} +687.170 q^{93} +620.483 q^{94} -95.0000 q^{95} -1408.17 q^{96} +674.009 q^{97} +2070.34 q^{98} -29.0037 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 4 q^{2} - 21 q^{3} + 74 q^{4} + 110 q^{5} - 9 q^{6} - 41 q^{7} - 78 q^{8} + 209 q^{9}+O(q^{10}) \) 22 * q - 4 * q^2 - 21 * q^3 + 74 * q^4 + 110 * q^5 - 9 * q^6 - 41 * q^7 - 78 * q^8 + 209 * q^9	\( 22 q - 4 q^{2} - 21 q^{3} + 74 q^{4} + 110 q^{5} - 9 q^{6} - 41 q^{7} - 78 q^{8} + 209 q^{9} - 20 q^{10} - 242 q^{11} - 196 q^{12} - q^{13} - 63 q^{14} - 105 q^{15} + 6 q^{16} + 187 q^{17} - 361 q^{18} - 418 q^{19} + 370 q^{20} - 107 q^{21} + 44 q^{22} - 361 q^{23} + 208 q^{24} + 550 q^{25} - 365 q^{26} - 1467 q^{27} - 773 q^{28} - 319 q^{29} - 45 q^{30} - 402 q^{31} - 873 q^{32} + 231 q^{33} - 717 q^{34} - 205 q^{35} + 725 q^{36} - 838 q^{37} + 76 q^{38} - 607 q^{39} - 390 q^{40} - 392 q^{41} - 1350 q^{42} - 610 q^{43} - 814 q^{44} + 1045 q^{45} - 605 q^{46} - 1866 q^{47} - 1637 q^{48} + 379 q^{49} - 100 q^{50} - 2659 q^{51} - 638 q^{52} - 1303 q^{53} + 2338 q^{54} - 1210 q^{55} + 727 q^{56} + 399 q^{57} + 44 q^{58} - 2417 q^{59} - 980 q^{60} + 918 q^{61} - 1634 q^{62} - 374 q^{63} - 1716 q^{64} - 5 q^{65} + 99 q^{66} - 2339 q^{67} + 4940 q^{68} + 127 q^{69} - 315 q^{70} - 2370 q^{71} - 3306 q^{72} + 2207 q^{73} + 2051 q^{74} - 525 q^{75} - 1406 q^{76} + 451 q^{77} + 1380 q^{78} + 586 q^{79} + 30 q^{80} + 1950 q^{81} - 1566 q^{82} - 2870 q^{83} + 3076 q^{84} + 935 q^{85} - 1246 q^{86} - 1811 q^{87} + 858 q^{88} - 1768 q^{89} - 1805 q^{90} - 2195 q^{91} - 6728 q^{92} - 2916 q^{93} + 672 q^{94} - 2090 q^{95} + 6022 q^{96} - 4022 q^{97} + 1162 q^{98} - 2299 q^{99}+O(q^{100}) \) 22 * q - 4 * q^2 - 21 * q^3 + 74 * q^4 + 110 * q^5 - 9 * q^6 - 41 * q^7 - 78 * q^8 + 209 * q^9 - 20 * q^10 - 242 * q^11 - 196 * q^12 - q^13 - 63 * q^14 - 105 * q^15 + 6 * q^16 + 187 * q^17 - 361 * q^18 - 418 * q^19 + 370 * q^20 - 107 * q^21 + 44 * q^22 - 361 * q^23 + 208 * q^24 + 550 * q^25 - 365 * q^26 - 1467 * q^27 - 773 * q^28 - 319 * q^29 - 45 * q^30 - 402 * q^31 - 873 * q^32 + 231 * q^33 - 717 * q^34 - 205 * q^35 + 725 * q^36 - 838 * q^37 + 76 * q^38 - 607 * q^39 - 390 * q^40 - 392 * q^41 - 1350 * q^42 - 610 * q^43 - 814 * q^44 + 1045 * q^45 - 605 * q^46 - 1866 * q^47 - 1637 * q^48 + 379 * q^49 - 100 * q^50 - 2659 * q^51 - 638 * q^52 - 1303 * q^53 + 2338 * q^54 - 1210 * q^55 + 727 * q^56 + 399 * q^57 + 44 * q^58 - 2417 * q^59 - 980 * q^60 + 918 * q^61 - 1634 * q^62 - 374 * q^63 - 1716 * q^64 - 5 * q^65 + 99 * q^66 - 2339 * q^67 + 4940 * q^68 + 127 * q^69 - 315 * q^70 - 2370 * q^71 - 3306 * q^72 + 2207 * q^73 + 2051 * q^74 - 525 * q^75 - 1406 * q^76 + 451 * q^77 + 1380 * q^78 + 586 * q^79 + 30 * q^80 + 1950 * q^81 - 1566 * q^82 - 2870 * q^83 + 3076 * q^84 + 935 * q^85 - 1246 * q^86 - 1811 * q^87 + 858 * q^88 - 1768 * q^89 - 1805 * q^90 - 2195 * q^91 - 6728 * q^92 - 2916 * q^93 + 672 * q^94 - 2090 * q^95 + 6022 * q^96 - 4022 * q^97 + 1162 * q^98 - 2299 * q^99

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