LMFDB - Embedded newform 1045.4.a.d.1.10

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			1.10
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.15290 q^{2} -8.73139 q^{3} -6.67082 q^{4} +5.00000 q^{5} +10.0664 q^{6} +10.3417 q^{7} +16.9140 q^{8} +49.2372 q^{9} +O(q^{10})$	\(q-1.15290 q^{2} -8.73139 q^{3} -6.67082 q^{4} +5.00000 q^{5} +10.0664 q^{6} +10.3417 q^{7} +16.9140 q^{8} +49.2372 q^{9} -5.76450 q^{10} -11.0000 q^{11} +58.2456 q^{12} -78.8239 q^{13} -11.9230 q^{14} -43.6570 q^{15} +33.8664 q^{16} -112.518 q^{17} -56.7656 q^{18} -19.0000 q^{19} -33.3541 q^{20} -90.2977 q^{21} +12.6819 q^{22} +177.413 q^{23} -147.683 q^{24} +25.0000 q^{25} +90.8761 q^{26} -194.162 q^{27} -68.9878 q^{28} +29.0800 q^{29} +50.3321 q^{30} +75.1163 q^{31} -174.357 q^{32} +96.0453 q^{33} +129.722 q^{34} +51.7086 q^{35} -328.453 q^{36} +34.9718 q^{37} +21.9051 q^{38} +688.242 q^{39} +84.5700 q^{40} +194.238 q^{41} +104.104 q^{42} -239.127 q^{43} +73.3790 q^{44} +246.186 q^{45} -204.539 q^{46} +147.264 q^{47} -295.701 q^{48} -236.049 q^{49} -28.8225 q^{50} +982.437 q^{51} +525.820 q^{52} +627.682 q^{53} +223.849 q^{54} -55.0000 q^{55} +174.920 q^{56} +165.896 q^{57} -33.5264 q^{58} -40.4362 q^{59} +291.228 q^{60} +799.006 q^{61} -86.6016 q^{62} +509.198 q^{63} -69.9156 q^{64} -394.119 q^{65} -110.731 q^{66} +42.9490 q^{67} +750.586 q^{68} -1549.06 q^{69} -59.6149 q^{70} +226.440 q^{71} +832.798 q^{72} +518.374 q^{73} -40.3190 q^{74} -218.285 q^{75} +126.746 q^{76} -113.759 q^{77} -793.475 q^{78} +532.146 q^{79} +169.332 q^{80} +365.899 q^{81} -223.937 q^{82} -57.3620 q^{83} +602.360 q^{84} -562.589 q^{85} +275.689 q^{86} -253.909 q^{87} -186.054 q^{88} -755.556 q^{89} -283.828 q^{90} -815.175 q^{91} -1183.49 q^{92} -655.870 q^{93} -169.781 q^{94} -95.0000 q^{95} +1522.38 q^{96} -174.112 q^{97} +272.141 q^{98} -541.609 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.15290	−0.407612	−0.203806	−	0.979011i	$-0.565331\pi$
$2$	−1.15290	−0.407612	−0.203806	+	0.979011i	$0.565331\pi$
$3$	−8.73139	−1.68036	−0.840179	−	0.542310i	$-0.817550\pi$
$3$	−8.73139	−1.68036	−0.840179	+	0.542310i	$0.817550\pi$
$4$	−6.67082	−0.833853
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	10.0664	0.684934
$7$	10.3417	0.558401	0.279200	−	0.960233i	$-0.409931\pi$
$7$	10.3417	0.558401	0.279200	+	0.960233i	$0.409931\pi$
$8$	16.9140	0.747500
$9$	49.2372	1.82360
$10$	−5.76450	−0.182290
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	58.2456	1.40117
$13$	−78.8239	−1.68168	−0.840839	−	0.541286i	$-0.817938\pi$
$13$	−78.8239	−1.68168	−0.840839	+	0.541286i	$0.817938\pi$
$14$	−11.9230	−0.227611
$15$	−43.6570	−0.751479
$16$	33.8664	0.529163
$17$	−112.518	−1.60527	−0.802635	−	0.596471i	$-0.796569\pi$
$17$	−112.518	−1.60527	−0.802635	+	0.596471i	$0.796569\pi$
$18$	−56.7656	−0.743321
$19$	−19.0000	−0.229416
$19$	−19.0000	−0.229416
$20$	−33.3541	−0.372910
$21$	−90.2977	−0.938313
$22$	12.6819	0.122900
$23$	177.413	1.60839	0.804197	−	0.594363i	$-0.202596\pi$
$23$	177.413	1.60839	0.804197	+	0.594363i	$0.202596\pi$
$24$	−147.683	−1.25607
$25$	25.0000	0.200000
$26$	90.8761	0.685472
$27$	−194.162	−1.38394
$28$	−68.9878	−0.465624
$29$	29.0800	0.186208	0.0931039	−	0.995656i	$-0.470321\pi$
$29$	29.0800	0.186208	0.0931039	+	0.995656i	$0.470321\pi$
$30$	50.3321	0.306312
$31$	75.1163	0.435203	0.217601	−	0.976038i	$-0.430177\pi$
$31$	75.1163	0.435203	0.217601	+	0.976038i	$0.430177\pi$
$32$	−174.357	−0.963193
$33$	96.0453	0.506647
$34$	129.722	0.654327
$35$	51.7086	0.249724
$36$	−328.453	−1.52061
$37$	34.9718	0.155387	0.0776936	−	0.996977i	$-0.475244\pi$
$37$	34.9718	0.155387	0.0776936	+	0.996977i	$0.475244\pi$
$38$	21.9051	0.0935126
$39$	688.242	2.82582
$40$	84.5700	0.334292
$41$	194.238	0.739876	0.369938	−	0.929057i	$-0.379379\pi$
$41$	194.238	0.739876	0.369938	+	0.929057i	$0.379379\pi$
$42$	104.104	0.382467
$43$	−239.127	−0.848058	−0.424029	−	0.905649i	$-0.639385\pi$
$43$	−239.127	−0.848058	−0.424029	+	0.905649i	$0.639385\pi$
$44$	73.3790	0.251416
$45$	246.186	0.815539
$46$	−204.539	−0.655601
$47$	147.264	0.457037	0.228518	−	0.973540i	$-0.426612\pi$
$47$	147.264	0.457037	0.228518	+	0.973540i	$0.426612\pi$
$48$	−295.701	−0.889182
$49$	−236.049	−0.688189
$50$	−28.8225	−0.0815224
$51$	982.437	2.69743
$52$	525.820	1.40227
$53$	627.682	1.62677	0.813385	−	0.581726i	$-0.197622\pi$
$53$	627.682	1.62677	0.813385	+	0.581726i	$0.197622\pi$
$54$	223.849	0.564112
$55$	−55.0000	−0.134840
$56$	174.920	0.417405
$57$	165.896	0.385500
$58$	−33.5264	−0.0759005
$59$	−40.4362	−0.0892261	−0.0446130	−	0.999004i	$-0.514205\pi$
$59$	−40.4362	−0.0892261	−0.0446130	+	0.999004i	$0.514205\pi$
$60$	291.228	0.626622
$61$	799.006	1.67709	0.838543	−	0.544835i	$-0.183408\pi$
$61$	799.006	1.67709	0.838543	+	0.544835i	$0.183408\pi$
$62$	−86.6016	−0.177394
$63$	509.198	1.01830
$64$	−69.9156	−0.136554
$65$	−394.119	−0.752069
$66$	−110.731	−0.206515
$67$	42.9490	0.0783143	0.0391571	−	0.999233i	$-0.487533\pi$
$67$	42.9490	0.0783143	0.0391571	+	0.999233i	$0.487533\pi$
$68$	750.586	1.33856
$69$	−1549.06	−2.70268
$70$	−59.6149	−0.101791
$71$	226.440	0.378500	0.189250	−	0.981929i	$-0.439394\pi$
$71$	226.440	0.378500	0.189250	+	0.981929i	$0.439394\pi$
$72$	832.798	1.36314
$73$	518.374	0.831110	0.415555	−	0.909568i	$-0.363587\pi$
$73$	518.374	0.831110	0.415555	+	0.909568i	$0.363587\pi$
$74$	−40.3190	−0.0633377
$75$	−218.285	−0.336071
$76$	126.746	0.191299
$77$	−113.759	−0.168364
$78$	−793.475	−1.15184
$79$	532.146	0.757862	0.378931	−	0.925425i	$-0.376292\pi$
$79$	532.146	0.757862	0.378931	+	0.925425i	$0.376292\pi$
$80$	169.332	0.236649
$81$	365.899	0.501919
$82$	−223.937	−0.301582
$83$	−57.3620	−0.0758590	−0.0379295	−	0.999280i	$-0.512076\pi$
$83$	−57.3620	−0.0758590	−0.0379295	+	0.999280i	$0.512076\pi$
$84$	602.360	0.782415
$85$	−562.589	−0.717898
$86$	275.689	0.345678
$87$	−253.909	−0.312896
$88$	−186.054	−0.225380
$89$	−755.556	−0.899874	−0.449937	−	0.893060i	$-0.648554\pi$
$89$	−755.556	−0.899874	−0.449937	+	0.893060i	$0.648554\pi$
$90$	−283.828	−0.332423
$91$	−815.175	−0.939050
$92$	−1183.49	−1.34116
$93$	−655.870	−0.731296
$94$	−169.781	−0.186294
$95$	−95.0000	−0.102598
$96$	1522.38	1.61851
$97$	−174.112	−0.182251	−0.0911256	−	0.995839i	$-0.529046\pi$
$97$	−174.112	−0.182251	−0.0911256	+	0.995839i	$0.529046\pi$
$98$	272.141	0.280514
$99$	−541.609	−0.549836
$100$	−166.771	−0.166771
$101$	970.354	0.955979	0.477989	−	0.878366i	$-0.341366\pi$
$101$	970.354	0.955979	0.477989	+	0.878366i	$0.341366\pi$
$102$	−1132.65	−1.09950
$103$	−746.320	−0.713952	−0.356976	−	0.934114i	$-0.616192\pi$
$103$	−746.320	−0.713952	−0.356976	+	0.934114i	$0.616192\pi$
$104$	−1333.23	−1.25705
$105$	−451.488	−0.419626
$106$	−723.655	−0.663091
$107$	−1492.14	−1.34813	−0.674066	−	0.738671i	$-0.735454\pi$
$107$	−1492.14	−1.34813	−0.674066	+	0.738671i	$0.735454\pi$
$108$	1295.22	1.15400
$109$	515.616	0.453092	0.226546	−	0.974000i	$-0.427257\pi$
$109$	515.616	0.453092	0.226546	+	0.974000i	$0.427257\pi$
$110$	63.4095	0.0549624
$111$	−305.352	−0.261106
$112$	350.237	0.295485
$113$	−1367.76	−1.13866	−0.569328	−	0.822111i	$-0.692796\pi$
$113$	−1367.76	−1.13866	−0.569328	+	0.822111i	$0.692796\pi$
$114$	−191.262	−0.157135
$115$	887.063	0.719296
$116$	−193.988	−0.155270
$117$	−3881.07	−3.06671
$118$	46.6189	0.0363696
$119$	−1163.63	−0.896384
$120$	−738.414	−0.561730
$121$	121.000	0.0909091
$122$	−921.175	−0.683600
$123$	−1695.97	−1.24326
$124$	−501.087	−0.362895
$125$	125.000	0.0894427
$126$	−587.054	−0.415071
$127$	−1338.96	−0.935537	−0.467769	−	0.883851i	$-0.654942\pi$
$127$	−1338.96	−0.935537	−0.467769	+	0.883851i	$0.654942\pi$
$128$	1475.46	1.01885
$129$	2087.91	1.42504
$130$	454.380	0.306552
$131$	2672.96	1.78273	0.891365	−	0.453286i	$-0.149748\pi$
$131$	2672.96	1.78273	0.891365	+	0.453286i	$0.149748\pi$
$132$	−640.701	−0.422469
$133$	−196.493	−0.128106
$134$	−49.5159	−0.0319218
$135$	−970.809	−0.618918
$136$	−1903.13	−1.19994
$137$	2030.71	1.26639	0.633194	−	0.773994i	$-0.281744\pi$
$137$	2030.71	1.26639	0.633194	+	0.773994i	$0.281744\pi$
$138$	1785.91	1.10164
$139$	−1028.56	−0.627633	−0.313816	−	0.949484i	$-0.601608\pi$
$139$	−1028.56	−0.627633	−0.313816	+	0.949484i	$0.601608\pi$
$140$	−344.939	−0.208233
$141$	−1285.82	−0.767985
$142$	−261.063	−0.154281
$143$	867.063	0.507045
$144$	1667.49	0.964981
$145$	145.400	0.0832746
$146$	−597.633	−0.338770
$147$	2061.03	1.15640
$148$	−233.290	−0.129570
$149$	−750.965	−0.412896	−0.206448	−	0.978458i	$-0.566190\pi$
$149$	−750.965	−0.412896	−0.206448	+	0.978458i	$0.566190\pi$
$150$	251.661	0.136987
$151$	−229.152	−0.123498	−0.0617489	−	0.998092i	$-0.519668\pi$
$151$	−229.152	−0.123498	−0.0617489	+	0.998092i	$0.519668\pi$
$152$	−321.366	−0.171488
$153$	−5540.06	−2.92737
$154$	131.153	0.0686272
$155$	375.581	0.194629
$156$	−4591.14	−2.35632
$157$	−1690.07	−0.859123	−0.429562	−	0.903038i	$-0.641332\pi$
$157$	−1690.07	−0.859123	−0.429562	+	0.903038i	$0.641332\pi$
$158$	−613.512	−0.308914
$159$	−5480.54	−2.73355
$160$	−871.783	−0.430753
$161$	1834.75	0.898129
$162$	−421.845	−0.204588
$163$	−965.926	−0.464154	−0.232077	−	0.972697i	$-0.574552\pi$
$163$	−965.926	−0.464154	−0.232077	+	0.972697i	$0.574552\pi$
$164$	−1295.73	−0.616947
$165$	480.227	0.226579
$166$	66.1327	0.0309210
$167$	2522.78	1.16897	0.584486	−	0.811404i	$-0.301296\pi$
$167$	2522.78	1.16897	0.584486	+	0.811404i	$0.301296\pi$
$168$	−1527.29	−0.701389
$169$	4016.20	1.82804
$170$	648.609	0.292624
$171$	−935.507	−0.418363
$172$	1595.17	0.707155
$173$	−1356.43	−0.596114	−0.298057	−	0.954548i	$-0.596339\pi$
$173$	−1356.43	−0.596114	−0.298057	+	0.954548i	$0.596339\pi$
$174$	292.732	0.127540
$175$	258.543	0.111680
$176$	−372.531	−0.159549
$177$	353.064	0.149932
$178$	871.081	0.366799
$179$	−2644.42	−1.10421	−0.552105	−	0.833775i	$-0.686175\pi$
$179$	−2644.42	−1.10421	−0.552105	+	0.833775i	$0.686175\pi$
$180$	−1642.26	−0.680039
$181$	−4530.41	−1.86046	−0.930229	−	0.366979i	$-0.880392\pi$
$181$	−4530.41	−1.86046	−0.930229	+	0.366979i	$0.880392\pi$
$182$	939.816	0.382768
$183$	−6976.44	−2.81810
$184$	3000.75	1.20227
$185$	174.859	0.0694913
$186$	756.153	0.298085
$187$	1237.70	0.484007
$188$	−982.374	−0.381101
$189$	−2007.97	−0.772795
$190$	109.526	0.0418201
$191$	2308.29	0.874462	0.437231	−	0.899349i	$-0.355959\pi$
$191$	2308.29	0.874462	0.437231	+	0.899349i	$0.355959\pi$
$192$	610.460	0.229459
$193$	−1902.68	−0.709625	−0.354813	−	0.934937i	$-0.615455\pi$
$193$	−1902.68	−0.709625	−0.354813	+	0.934937i	$0.615455\pi$
$194$	200.734	0.0742878
$195$	3441.21	1.26374
$196$	1574.64	0.573848
$197$	3772.86	1.36449	0.682246	−	0.731123i	$-0.261003\pi$
$197$	3772.86	1.36449	0.682246	+	0.731123i	$0.261003\pi$
$198$	624.422	0.224120
$199$	1228.87	0.437749	0.218875	−	0.975753i	$-0.429761\pi$
$199$	1228.87	0.437749	0.218875	+	0.975753i	$0.429761\pi$
$200$	422.850	0.149500
$201$	−375.005	−0.131596
$202$	−1118.72	−0.389668
$203$	300.738	0.103979
$204$	−6553.66	−2.24926
$205$	971.191	0.330882
$206$	860.432	0.291015
$207$	8735.30	2.93307
$208$	−2669.48	−0.889881
$209$	209.000	0.0691714
$210$	520.521	0.171045
$211$	741.820	0.242033	0.121017	−	0.992650i	$-0.461385\pi$
$211$	741.820	0.242033	0.121017	+	0.992650i	$0.461385\pi$
$212$	−4187.16	−1.35649
$213$	−1977.14	−0.636015
$214$	1720.28	0.549515
$215$	−1195.63	−0.379263
$216$	−3284.05	−1.03450
$217$	776.832	0.243018
$218$	−594.454	−0.184686
$219$	−4526.12	−1.39656
$220$	366.895	0.112437
$221$	8869.09	2.69955
$222$	352.041	0.106430
$223$	−6022.97	−1.80865	−0.904323	−	0.426849i	$-0.859624\pi$
$223$	−6022.97	−1.80865	−0.904323	+	0.426849i	$0.859624\pi$
$224$	−1803.15	−0.537848
$225$	1230.93	0.364720
$226$	1576.89	0.464130
$227$	−3972.07	−1.16139	−0.580695	−	0.814121i	$-0.697219\pi$
$227$	−3972.07	−1.16139	−0.580695	+	0.814121i	$0.697219\pi$
$228$	−1106.67	−0.321451
$229$	−3220.31	−0.929275	−0.464638	−	0.885501i	$-0.653815\pi$
$229$	−3220.31	−0.929275	−0.464638	+	0.885501i	$0.653815\pi$
$230$	−1022.69	−0.293193
$231$	993.274	0.282912
$232$	491.859	0.139190
$233$	3519.93	0.989691	0.494845	−	0.868981i	$-0.335225\pi$
$233$	3519.93	0.989691	0.494845	+	0.868981i	$0.335225\pi$
$234$	4474.49	1.25003
$235$	736.322	0.204393
$236$	269.742	0.0744014
$237$	−4646.38	−1.27348
$238$	1341.55	0.365377
$239$	3681.62	0.996419	0.498210	−	0.867057i	$-0.333991\pi$
$239$	3681.62	0.996419	0.498210	+	0.867057i	$0.333991\pi$
$240$	−1478.50	−0.397654
$241$	2979.30	0.796323	0.398161	−	0.917315i	$-0.369648\pi$
$241$	2979.30	0.796323	0.398161	+	0.917315i	$0.369648\pi$
$242$	−139.501	−0.0370556
$243$	2047.56	0.540541
$244$	−5330.03	−1.39844
$245$	−1180.24	−0.307767
$246$	1955.28	0.506766
$247$	1497.65	0.385803
$248$	1270.52	0.325314
$249$	500.850	0.127470
$250$	−144.113	−0.0364579
$251$	−3413.83	−0.858483	−0.429242	−	0.903190i	$-0.641219\pi$
$251$	−3413.83	−0.858483	−0.429242	+	0.903190i	$0.641219\pi$
$252$	−3396.77	−0.849112
$253$	−1951.54	−0.484949
$254$	1543.68	0.381336
$255$	4912.19	1.20633
$256$	−1141.73	−0.278743
$257$	−2104.95	−0.510907	−0.255454	−	0.966821i	$-0.582225\pi$
$257$	−2104.95	−0.510907	−0.255454	+	0.966821i	$0.582225\pi$
$258$	−2407.15	−0.580863
$259$	361.669	0.0867683
$260$	2629.10	0.627115
$261$	1431.82	0.339569
$262$	−3081.66	−0.726662
$263$	−3082.62	−0.722748	−0.361374	−	0.932421i	$-0.617692\pi$
$263$	−3082.62	−0.722748	−0.361374	+	0.932421i	$0.617692\pi$
$264$	1624.51	0.378718
$265$	3138.41	0.727514
$266$	226.537	0.0522175
$267$	6597.06	1.51211
$268$	−286.505	−0.0653026
$269$	−2354.32	−0.533626	−0.266813	−	0.963748i	$-0.585971\pi$
$269$	−2354.32	−0.533626	−0.266813	+	0.963748i	$0.585971\pi$
$270$	1119.25	0.252278
$271$	105.254	0.0235932	0.0117966	−	0.999930i	$-0.496245\pi$
$271$	105.254	0.0235932	0.0117966	+	0.999930i	$0.496245\pi$
$272$	−3810.57	−0.849449
$273$	7117.61	1.57794
$274$	−2341.20	−0.516194
$275$	−275.000	−0.0603023
$276$	10333.5	2.25363
$277$	−7520.07	−1.63118	−0.815590	−	0.578630i	$-0.803588\pi$
$277$	−7520.07	−1.63118	−0.815590	+	0.578630i	$0.803588\pi$
$278$	1185.82	0.255831
$279$	3698.52	0.793636
$280$	874.600	0.186669
$281$	5755.85	1.22194	0.610970	−	0.791654i	$-0.290780\pi$
$281$	5755.85	1.22194	0.610970	+	0.791654i	$0.290780\pi$
$282$	1482.43	0.313040
$283$	−164.079	−0.0344646	−0.0172323	−	0.999852i	$-0.505485\pi$
$283$	−164.079	−0.0344646	−0.0172323	+	0.999852i	$0.505485\pi$
$284$	−1510.54	−0.315613
$285$	829.482	0.172401
$286$	−999.637	−0.206677
$287$	2008.76	0.413147
$288$	−8584.83	−1.75648
$289$	7747.26	1.57689
$290$	−167.632	−0.0339437
$291$	1520.24	0.306247
$292$	−3457.98	−0.693023
$293$	2320.62	0.462703	0.231352	−	0.972870i	$-0.425685\pi$
$293$	2320.62	0.462703	0.231352	+	0.972870i	$0.425685\pi$
$294$	−2376.17	−0.471363
$295$	−202.181	−0.0399031
$296$	591.513	0.116152
$297$	2135.78	0.417275
$298$	865.788	0.168301
$299$	−13984.3	−2.70480
$300$	1456.14	0.280234
$301$	−2472.98	−0.473556
$302$	264.190	0.0503391
$303$	−8472.54	−1.60639
$304$	−643.462	−0.121398
$305$	3995.03	0.750016
$306$	6387.14	1.19323
$307$	671.473	0.124831	0.0624153	−	0.998050i	$-0.480120\pi$
$307$	671.473	0.124831	0.0624153	+	0.998050i	$0.480120\pi$
$308$	758.866	0.140391
$309$	6516.41	1.19969
$310$	−433.008	−0.0793329
$311$	−9950.06	−1.81420	−0.907100	−	0.420915i	$-0.861709\pi$
$311$	−9950.06	−1.81420	−0.907100	+	0.420915i	$0.861709\pi$
$312$	11640.9	2.11230
$313$	−640.305	−0.115630	−0.0578150	−	0.998327i	$-0.518413\pi$
$313$	−640.305	−0.115630	−0.0578150	+	0.998327i	$0.518413\pi$
$314$	1948.48	0.350189
$315$	2545.99	0.455398
$316$	−3549.85	−0.631946
$317$	−8945.57	−1.58496	−0.792482	−	0.609895i	$-0.791211\pi$
$317$	−8945.57	−1.58496	−0.792482	+	0.609895i	$0.791211\pi$
$318$	6318.52	1.11423
$319$	−319.880	−0.0561437
$320$	−349.578	−0.0610687
$321$	13028.4	2.26535
$322$	−2115.29	−0.366088
$323$	2137.84	0.368274
$324$	−2440.85	−0.418526
$325$	−1970.60	−0.336336
$326$	1113.62	0.189195
$327$	−4502.04	−0.761357
$328$	3285.34	0.553057
$329$	1522.97	0.255210
$330$	−553.653	−0.0923564
$331$	6404.50	1.06351	0.531757	−	0.846897i	$-0.321532\pi$
$331$	6404.50	1.06351	0.531757	+	0.846897i	$0.321532\pi$
$332$	382.652	0.0632553
$333$	1721.91	0.283364
$334$	−2908.51	−0.476487
$335$	214.745	0.0350232
$336$	−3058.06	−0.496520
$337$	3153.72	0.509774	0.254887	−	0.966971i	$-0.417962\pi$
$337$	3153.72	0.509774	0.254887	+	0.966971i	$0.417962\pi$
$338$	−4630.28	−0.745131
$339$	11942.5	1.91335
$340$	3752.93	0.598621
$341$	−826.279	−0.131219
$342$	1078.55	0.170530
$343$	−5988.36	−0.942686
$344$	−4044.59	−0.633923
$345$	−7745.29	−1.20867
$346$	1563.83	0.242983
$347$	−10625.9	−1.64388	−0.821939	−	0.569575i	$-0.807108\pi$
$347$	−10625.9	−1.64388	−0.821939	+	0.569575i	$0.807108\pi$
$348$	1693.78	0.260909
$349$	11402.4	1.74887	0.874434	−	0.485144i	$-0.161233\pi$
$349$	11402.4	1.74887	0.874434	+	0.485144i	$0.161233\pi$
$350$	−298.075	−0.0455222
$351$	15304.6	2.32735
$352$	1917.92	0.290414
$353$	−4763.27	−0.718196	−0.359098	−	0.933300i	$-0.616916\pi$
$353$	−4763.27	−0.718196	−0.359098	+	0.933300i	$0.616916\pi$
$354$	−407.048	−0.0611139
$355$	1132.20	0.169270
$356$	5040.18	0.750362
$357$	10160.1	1.50624
$358$	3048.76	0.450089
$359$	775.482	0.114007	0.0570033	−	0.998374i	$-0.481845\pi$
$359$	775.482	0.114007	0.0570033	+	0.998374i	$0.481845\pi$
$360$	4163.99	0.609615
$361$	361.000	0.0526316
$362$	5223.11	0.758345
$363$	−1056.50	−0.152760
$364$	5437.89	0.783029
$365$	2591.87	0.371684
$366$	8043.14	1.14869
$367$	−8399.82	−1.19473	−0.597366	−	0.801968i	$-0.703786\pi$
$367$	−8399.82	−1.19473	−0.597366	+	0.801968i	$0.703786\pi$
$368$	6008.33	0.851102
$369$	9563.75	1.34924
$370$	−201.595	−0.0283255
$371$	6491.32	0.908390
$372$	4375.19	0.609793
$373$	−11559.2	−1.60460	−0.802299	−	0.596923i	$-0.796390\pi$
$373$	−11559.2	−1.60460	−0.802299	+	0.596923i	$0.796390\pi$
$374$	−1426.94	−0.197287
$375$	−1091.42	−0.150296
$376$	2490.83	0.341635
$377$	−2292.20	−0.313141
$378$	2314.99	0.315000
$379$	−10482.5	−1.42072	−0.710359	−	0.703840i	$-0.751467\pi$
$379$	−10482.5	−1.42072	−0.710359	+	0.703840i	$0.751467\pi$
$380$	633.728	0.0855515
$381$	11691.0	1.57204
$382$	−2661.23	−0.356441
$383$	−2765.56	−0.368965	−0.184483	−	0.982836i	$-0.559061\pi$
$383$	−2765.56	−0.368965	−0.184483	+	0.982836i	$0.559061\pi$
$384$	−12882.8	−1.71204
$385$	−568.795	−0.0752947
$386$	2193.60	0.289252
$387$	−11773.9	−1.54652
$388$	1161.47	0.151971
$389$	9514.29	1.24009	0.620043	−	0.784568i	$-0.287115\pi$
$389$	9514.29	1.24009	0.620043	+	0.784568i	$0.287115\pi$
$390$	−3967.37	−0.515117
$391$	−19962.1	−2.58191
$392$	−3992.53	−0.514421
$393$	−23338.7	−2.99562
$394$	−4349.73	−0.556183
$395$	2660.73	0.338926
$396$	3612.98	0.458482
$397$	−6518.23	−0.824032	−0.412016	−	0.911177i	$-0.635175\pi$
$397$	−6518.23	−0.824032	−0.412016	+	0.911177i	$0.635175\pi$
$398$	−1416.76	−0.178432
$399$	1715.66	0.215264
$400$	846.660	0.105833
$401$	6993.49	0.870918	0.435459	−	0.900208i	$-0.356586\pi$
$401$	6993.49	0.870918	0.435459	+	0.900208i	$0.356586\pi$
$402$	432.343	0.0536401
$403$	−5920.96	−0.731871
$404$	−6473.06	−0.797145
$405$	1829.49	0.224465
$406$	−346.721	−0.0423829
$407$	−384.690	−0.0468510
$408$	16616.9	2.01633
$409$	−3853.19	−0.465838	−0.232919	−	0.972496i	$-0.574828\pi$
$409$	−3853.19	−0.465838	−0.232919	+	0.972496i	$0.574828\pi$
$410$	−1119.69	−0.134872
$411$	−17730.9	−2.12798
$412$	4978.56	0.595331
$413$	−418.180	−0.0498239
$414$	−10070.9	−1.19555
$415$	−286.810	−0.0339252
$416$	13743.5	1.61978
$417$	8980.72	1.05465
$418$	−240.956	−0.0281951
$419$	−8945.02	−1.04294	−0.521471	−	0.853269i	$-0.674617\pi$
$419$	−8945.02	−1.04294	−0.521471	+	0.853269i	$0.674617\pi$
$420$	3011.80	0.349906
$421$	5636.18	0.652472	0.326236	−	0.945288i	$-0.394220\pi$
$421$	5636.18	0.652472	0.326236	+	0.945288i	$0.394220\pi$
$422$	−855.244	−0.0986556
$423$	7250.89	0.833452
$424$	10616.6	1.21601
$425$	−2812.95	−0.321054
$426$	2279.44	0.259247
$427$	8263.10	0.936486
$428$	9953.77	1.12414
$429$	−7570.66	−0.852017
$430$	1378.45	0.154592
$431$	2691.15	0.300761	0.150380	−	0.988628i	$-0.451950\pi$
$431$	2691.15	0.300761	0.150380	+	0.988628i	$0.451950\pi$
$432$	−6575.57	−0.732331
$433$	3094.72	0.343470	0.171735	−	0.985143i	$-0.445063\pi$
$433$	3094.72	0.343470	0.171735	+	0.985143i	$0.445063\pi$
$434$	−895.610	−0.0990568
$435$	−1269.55	−0.139931
$436$	−3439.58	−0.377812
$437$	−3370.84	−0.368991
$438$	5218.17	0.569255
$439$	918.569	0.0998654	0.0499327	−	0.998753i	$-0.484099\pi$
$439$	918.569	0.0998654	0.0499327	+	0.998753i	$0.484099\pi$
$440$	−930.270	−0.100793
$441$	−11622.4	−1.25498
$442$	−10225.2	−1.10037
$443$	−17234.6	−1.84840	−0.924199	−	0.381912i	$-0.875266\pi$
$443$	−17234.6	−1.84840	−0.924199	+	0.381912i	$0.875266\pi$
$444$	2036.95	0.217724
$445$	−3777.78	−0.402436
$446$	6943.89	0.737226
$447$	6556.97	0.693812
$448$	−723.048	−0.0762518
$449$	−11847.9	−1.24529	−0.622646	−	0.782503i	$-0.713942\pi$
$449$	−11847.9	−1.24529	−0.622646	+	0.782503i	$0.713942\pi$
$450$	−1419.14	−0.148664
$451$	−2136.62	−0.223081
$452$	9124.08	0.949471
$453$	2000.82	0.207520
$454$	4579.40	0.473396
$455$	−4075.87	−0.419956
$456$	2805.97	0.288162
$457$	18522.1	1.89590	0.947950	−	0.318418i	$-0.103152\pi$
$457$	18522.1	1.89590	0.947950	+	0.318418i	$0.103152\pi$
$458$	3712.70	0.378784
$459$	21846.7	2.22160
$460$	−5917.44	−0.599787
$461$	−5602.48	−0.566017	−0.283008	−	0.959117i	$-0.591332\pi$
$461$	−5602.48	−0.566017	−0.283008	+	0.959117i	$0.591332\pi$
$462$	−1145.15	−0.115318
$463$	1858.68	0.186566	0.0932830	−	0.995640i	$-0.470264\pi$
$463$	1858.68	0.186566	0.0932830	+	0.995640i	$0.470264\pi$
$464$	984.836	0.0985342
$465$	−3279.35	−0.327046
$466$	−4058.12	−0.403410
$467$	−17588.1	−1.74278	−0.871392	−	0.490587i	$-0.836782\pi$
$467$	−17588.1	−1.74278	−0.871392	+	0.490587i	$0.836782\pi$
$468$	25889.9	2.55718
$469$	444.167	0.0437307
$470$	−848.906	−0.0833130
$471$	14756.7	1.44363
$472$	−683.937	−0.0666965
$473$	2630.39	0.255699
$474$	5356.81	0.519085
$475$	−475.000	−0.0458831
$476$	7762.36	0.747452
$477$	30905.3	2.96658
$478$	−4244.54	−0.406152
$479$	4184.90	0.399192	0.199596	−	0.979878i	$-0.436037\pi$
$479$	4184.90	0.399192	0.199596	+	0.979878i	$0.436037\pi$
$480$	7611.88	0.723819
$481$	−2756.61	−0.261311
$482$	−3434.84	−0.324591
$483$	−16019.9	−1.50918
$484$	−807.169	−0.0758048
$485$	−870.559	−0.0815052
$486$	−2360.64	−0.220331
$487$	−9191.30	−0.855231	−0.427616	−	0.903961i	$-0.640646\pi$
$487$	−9191.30	−0.855231	−0.427616	+	0.903961i	$0.640646\pi$
$488$	13514.4	1.25362
$489$	8433.88	0.779945
$490$	1360.70	0.125450
$491$	−18158.2	−1.66898	−0.834488	−	0.551026i	$-0.814236\pi$
$491$	−18158.2	−1.66898	−0.834488	+	0.551026i	$0.814236\pi$
$492$	11313.5	1.03669
$493$	−3272.02	−0.298914
$494$	−1726.65	−0.157258
$495$	−2708.05	−0.245894
$496$	2543.92	0.230293
$497$	2341.78	0.211355
$498$	−577.431	−0.0519584
$499$	2940.13	0.263764	0.131882	−	0.991265i	$-0.457898\pi$
$499$	2940.13	0.263764	0.131882	+	0.991265i	$0.457898\pi$
$500$	−833.853	−0.0745820
$501$	−22027.4	−1.96429
$502$	3935.81	0.349928
$503$	−11037.7	−0.978421	−0.489210	−	0.872166i	$-0.662715\pi$
$503$	−11037.7	−0.978421	−0.489210	+	0.872166i	$0.662715\pi$
$504$	8612.57	0.761179
$505$	4851.77	0.427527
$506$	2249.93	0.197671
$507$	−35067.0	−3.07176
$508$	8931.94	0.780100
$509$	−12424.0	−1.08189	−0.540947	−	0.841057i	$-0.681934\pi$
$509$	−12424.0	−1.08189	−0.540947	+	0.841057i	$0.681934\pi$
$510$	−5663.26	−0.491713
$511$	5360.88	0.464093
$512$	−10487.4	−0.905235
$513$	3689.08	0.317498
$514$	2426.80	0.208252
$515$	−3731.60	−0.319289
$516$	−13928.1	−1.18827
$517$	−1619.91	−0.137802
$518$	−416.968	−0.0353678
$519$	11843.5	1.00168
$520$	−6666.13	−0.562172
$521$	−6789.73	−0.570947	−0.285473	−	0.958387i	$-0.592151\pi$
$521$	−6789.73	−0.570947	−0.285473	+	0.958387i	$0.592151\pi$
$522$	−1650.74	−0.138412
$523$	−5430.31	−0.454017	−0.227009	−	0.973893i	$-0.572895\pi$
$523$	−5430.31	−0.454017	−0.227009	+	0.973893i	$0.572895\pi$
$524$	−17830.8	−1.48653
$525$	−2257.44	−0.187663
$526$	3553.96	0.294601
$527$	−8451.92	−0.698618
$528$	3252.71	0.268099
$529$	19308.2	1.58693
$530$	−3618.28	−0.296543
$531$	−1990.96	−0.162713
$532$	1310.77	0.106821
$533$	−15310.6	−1.24423
$534$	−7605.75	−0.616354
$535$	−7460.68	−0.602903
$536$	726.439	0.0585399
$537$	23089.5	1.85547
$538$	2714.29	0.217512
$539$	2596.54	0.207497
$540$	6476.10	0.516087
$541$	5578.94	0.443360	0.221680	−	0.975120i	$-0.428846\pi$
$541$	5578.94	0.443360	0.221680	+	0.975120i	$0.428846\pi$
$542$	−121.348	−0.00961686
$543$	39556.8	3.12623
$544$	19618.2	1.54618
$545$	2578.08	0.202629
$546$	−8205.90	−0.643187
$547$	−11516.6	−0.900207	−0.450103	−	0.892976i	$-0.648613\pi$
$547$	−11516.6	−0.900207	−0.450103	+	0.892976i	$0.648613\pi$
$548$	−13546.5	−1.05598
$549$	39340.8	3.05834
$550$	317.048	0.0245799
$551$	−552.520	−0.0427190
$552$	−26200.8	−2.02025
$553$	5503.31	0.423191
$554$	8669.89	0.664889
$555$	−1526.76	−0.116770
$556$	6861.31	0.523353
$557$	18350.4	1.39593	0.697964	−	0.716133i	$-0.254090\pi$
$557$	18350.4	1.39593	0.697964	+	0.716133i	$0.254090\pi$
$558$	−4264.02	−0.323495
$559$	18848.9	1.42616
$560$	1751.19	0.132145
$561$	−10806.8	−0.813305
$562$	−6635.92	−0.498077
$563$	24798.7	1.85638	0.928189	−	0.372109i	$-0.121365\pi$
$563$	24798.7	1.85638	0.928189	+	0.372109i	$0.121365\pi$
$564$	8577.50	0.640386
$565$	−6838.80	−0.509222
$566$	189.167	0.0140482
$567$	3784.03	0.280272
$568$	3830.01	0.282929
$569$	−5300.34	−0.390513	−0.195257	−	0.980752i	$-0.562554\pi$
$569$	−5300.34	−0.390513	−0.195257	+	0.980752i	$0.562554\pi$
$570$	−956.310	−0.0702727
$571$	24095.3	1.76595	0.882975	−	0.469420i	$-0.155537\pi$
$571$	24095.3	1.76595	0.882975	+	0.469420i	$0.155537\pi$
$572$	−5784.02	−0.422801
$573$	−20154.6	−1.46941
$574$	−2315.90	−0.168404
$575$	4435.31	0.321679
$576$	−3442.45	−0.249020
$577$	19008.8	1.37148	0.685741	−	0.727846i	$-0.259478\pi$
$577$	19008.8	1.37148	0.685741	+	0.727846i	$0.259478\pi$
$578$	−8931.82	−0.642759
$579$	16613.0	1.19242
$580$	−969.938	−0.0694388
$581$	−593.222	−0.0423597
$582$	−1752.68	−0.124830
$583$	−6904.51	−0.490490
$584$	8767.77	0.621255
$585$	−19405.3	−1.37147
$586$	−2675.44	−0.188603
$587$	−7408.03	−0.520890	−0.260445	−	0.965489i	$-0.583869\pi$
$587$	−7408.03	−0.520890	−0.260445	+	0.965489i	$0.583869\pi$
$588$	−13748.8	−0.964269
$589$	−1427.21	−0.0998424
$590$	233.094	0.0162650
$591$	−32942.3	−2.29283
$592$	1184.37	0.0822251
$593$	20839.0	1.44310	0.721548	−	0.692364i	$-0.243431\pi$
$593$	20839.0	1.44310	0.721548	+	0.692364i	$0.243431\pi$
$594$	−2462.34	−0.170086
$595$	−5818.14	−0.400875
$596$	5009.55	0.344294
$597$	−10729.7	−0.735575
$598$	16122.6	1.10251
$599$	−1943.54	−0.132573	−0.0662863	−	0.997801i	$-0.521115\pi$
$599$	−1943.54	−0.132573	−0.0662863	+	0.997801i	$0.521115\pi$
$600$	−3692.07	−0.251213
$601$	15283.0	1.03728	0.518642	−	0.854992i	$-0.326438\pi$
$601$	15283.0	1.03728	0.518642	+	0.854992i	$0.326438\pi$
$602$	2851.10	0.193027
$603$	2114.69	0.142814
$604$	1528.63	0.102979
$605$	605.000	0.0406558
$606$	9768.00	0.654782
$607$	−18291.9	−1.22314	−0.611570	−	0.791191i	$-0.709462\pi$
$607$	−18291.9	−1.22314	−0.611570	+	0.791191i	$0.709462\pi$
$608$	3312.77	0.220972
$609$	−2625.86	−0.174721
$610$	−4605.87	−0.305715
$611$	−11607.9	−0.768588
$612$	36956.8	2.44100
$613$	−16459.8	−1.08451	−0.542256	−	0.840213i	$-0.682430\pi$
$613$	−16459.8	−1.08451	−0.542256	+	0.840213i	$0.682430\pi$
$614$	−774.142	−0.0508825
$615$	−8479.85	−0.556001
$616$	−1924.12	−0.125852
$617$	24470.6	1.59668	0.798340	−	0.602207i	$-0.205712\pi$
$617$	24470.6	1.59668	0.798340	+	0.602207i	$0.205712\pi$
$618$	−7512.77	−0.489010
$619$	−18291.8	−1.18774	−0.593868	−	0.804563i	$-0.702400\pi$
$619$	−18291.8	−1.18774	−0.593868	+	0.804563i	$0.702400\pi$
$620$	−2505.44	−0.162292
$621$	−34446.7	−2.22593
$622$	11471.4	0.739490
$623$	−7813.75	−0.502490
$624$	23308.3	1.49532
$625$	625.000	0.0400000
$626$	738.208	0.0471321
$627$	−1824.86	−0.116233
$628$	11274.2	0.716382
$629$	−3934.95	−0.249438
$630$	−2935.27	−0.185625
$631$	20527.9	1.29509	0.647547	−	0.762026i	$-0.275795\pi$
$631$	20527.9	1.29509	0.647547	+	0.762026i	$0.275795\pi$
$632$	9000.72	0.566502
$633$	−6477.12	−0.406702
$634$	10313.4	0.646050
$635$	−6694.79	−0.418385
$636$	36559.7	2.27938
$637$	18606.3	1.15731
$638$	368.790	0.0228849
$639$	11149.3	0.690233
$640$	7377.29	0.455645
$641$	19832.1	1.22203	0.611013	−	0.791620i	$-0.290762\pi$
$641$	19832.1	1.22203	0.611013	+	0.791620i	$0.290762\pi$
$642$	−15020.5	−0.923381
$643$	−14212.9	−0.871697	−0.435848	−	0.900020i	$-0.643552\pi$
$643$	−14212.9	−0.871697	−0.435848	+	0.900020i	$0.643552\pi$
$644$	−12239.3	−0.748907
$645$	10439.5	0.637297
$646$	−2464.71	−0.150113
$647$	9940.39	0.604014	0.302007	−	0.953306i	$-0.402343\pi$
$647$	9940.39	0.604014	0.302007	+	0.953306i	$0.402343\pi$
$648$	6188.81	0.375184
$649$	444.798	0.0269027
$650$	2271.90	0.137094
$651$	−6782.83	−0.408356
$652$	6443.52	0.387036
$653$	−12745.8	−0.763831	−0.381915	−	0.924197i	$-0.624735\pi$
$653$	−12745.8	−0.763831	−0.381915	+	0.924197i	$0.624735\pi$
$654$	5190.41	0.310338
$655$	13364.8	0.797261
$656$	6578.15	0.391515
$657$	25523.3	1.51561
$658$	−1755.83	−0.104026
$659$	11123.6	0.657531	0.328766	−	0.944412i	$-0.393367\pi$
$659$	11123.6	0.657531	0.328766	+	0.944412i	$0.393367\pi$
$660$	−3203.51	−0.188934
$661$	6180.42	0.363677	0.181838	−	0.983328i	$-0.441795\pi$
$661$	6180.42	0.363677	0.181838	+	0.983328i	$0.441795\pi$
$662$	−7383.75	−0.433501
$663$	−77439.5	−4.53620
$664$	−970.221	−0.0567046
$665$	−982.464	−0.0572907
$666$	−1985.19	−0.115503
$667$	5159.16	0.299495
$668$	−16829.0	−0.974751
$669$	52588.9	3.03917
$670$	−247.580	−0.0142759
$671$	−8789.07	−0.505661
$672$	15744.0	0.903776
$673$	5266.32	0.301637	0.150818	−	0.988561i	$-0.451809\pi$
$673$	5266.32	0.301637	0.150818	+	0.988561i	$0.451809\pi$
$674$	−3635.92	−0.207790
$675$	−4854.05	−0.276789
$676$	−26791.4	−1.52432
$677$	5209.75	0.295756	0.147878	−	0.989006i	$-0.452756\pi$
$677$	5209.75	0.295756	0.147878	+	0.989006i	$0.452756\pi$
$678$	−13768.5	−0.779903
$679$	−1800.62	−0.101769
$680$	−9515.63	−0.536629
$681$	34681.7	1.95155
$682$	952.618	0.0534862
$683$	−8844.50	−0.495498	−0.247749	−	0.968824i	$-0.579691\pi$
$683$	−8844.50	−0.495498	−0.247749	+	0.968824i	$0.579691\pi$
$684$	6240.60	0.348853
$685$	10153.5	0.566346
$686$	6903.99	0.384250
$687$	28117.8	1.56151
$688$	−8098.37	−0.448761
$689$	−49476.4	−2.73570
$690$	8929.55	0.492670
$691$	−12755.9	−0.702253	−0.351126	−	0.936328i	$-0.614201\pi$
$691$	−12755.9	−0.702253	−0.351126	+	0.936328i	$0.614201\pi$
$692$	9048.52	0.497071
$693$	−5601.18	−0.307029
$694$	12250.6	0.670064
$695$	−5142.78	−0.280686
$696$	−4294.62	−0.233889
$697$	−21855.3	−1.18770
$698$	−13145.8	−0.712859
$699$	−30733.9	−1.66303
$700$	−1724.70	−0.0931248
$701$	−18674.3	−1.00616	−0.503079	−	0.864240i	$-0.667800\pi$
$701$	−18674.3	−1.00616	−0.503079	+	0.864240i	$0.667800\pi$
$702$	−17644.7	−0.948654
$703$	−664.464	−0.0356483
$704$	769.071	0.0411725
$705$	−6429.12	−0.343453
$706$	5491.57	0.292745
$707$	10035.1	0.533819
$708$	−2355.23	−0.125021
$709$	−11100.1	−0.587973	−0.293987	−	0.955810i	$-0.594982\pi$
$709$	−11100.1	−0.587973	−0.293987	+	0.955810i	$0.594982\pi$
$710$	−1305.31	−0.0689966
$711$	26201.4	1.38204
$712$	−12779.5	−0.672656
$713$	13326.6	0.699978
$714$	−11713.6	−0.613963
$715$	4335.31	0.226757
$716$	17640.5	0.920748
$717$	−32145.7	−1.67434
$718$	−894.053	−0.0464704
$719$	28033.5	1.45406	0.727032	−	0.686604i	$-0.240899\pi$
$719$	28033.5	1.45406	0.727032	+	0.686604i	$0.240899\pi$
$720$	8337.44	0.431553
$721$	−7718.23	−0.398671
$722$	−416.197	−0.0214533
$723$	−26013.5	−1.33811
$724$	30221.6	1.55135
$725$	727.000	0.0372415
$726$	1218.04	0.0622667
$727$	−24100.2	−1.22948	−0.614738	−	0.788732i	$-0.710738\pi$
$727$	−24100.2	−1.22948	−0.614738	+	0.788732i	$0.710738\pi$
$728$	−13787.9	−0.701940
$729$	−27757.4	−1.41022
$730$	−2988.17	−0.151503
$731$	26906.0	1.36136
$732$	46538.6	2.34988
$733$	31924.9	1.60869	0.804346	−	0.594161i	$-0.202516\pi$
$733$	31924.9	1.60869	0.804346	+	0.594161i	$0.202516\pi$
$734$	9684.15	0.486987
$735$	10305.2	0.517159
$736$	−30933.0	−1.54919
$737$	−472.439	−0.0236126
$738$	−11026.0	−0.549965
$739$	25963.5	1.29240	0.646200	−	0.763168i	$-0.276357\pi$
$739$	25963.5	1.29240	0.646200	+	0.763168i	$0.276357\pi$
$740$	−1166.45	−0.0579455
$741$	−13076.6	−0.648287
$742$	−7483.84	−0.370270
$743$	−23393.2	−1.15506	−0.577532	−	0.816368i	$-0.695984\pi$
$743$	−23393.2	−1.15506	−0.577532	+	0.816368i	$0.695984\pi$
$744$	−11093.4	−0.546644
$745$	−3754.82	−0.184653
$746$	13326.7	0.654053
$747$	−2824.35	−0.138337
$748$	−8256.45	−0.403590
$749$	−15431.3	−0.752798
$750$	1258.30	0.0612623
$751$	−8033.98	−0.390365	−0.195183	−	0.980767i	$-0.562530\pi$
$751$	−8033.98	−0.390365	−0.195183	+	0.980767i	$0.562530\pi$
$752$	4987.32	0.241847
$753$	29807.5	1.44256
$754$	2642.68	0.127640
$755$	−1145.76	−0.0552299
$756$	13394.8	0.644397
$757$	882.147	0.0423543	0.0211771	−	0.999776i	$-0.493259\pi$
$757$	882.147	0.0423543	0.0211771	+	0.999776i	$0.493259\pi$
$758$	12085.3	0.579101
$759$	17039.6	0.814888
$760$	−1606.83	−0.0766919
$761$	−16293.7	−0.776143	−0.388072	−	0.921629i	$-0.626859\pi$
$761$	−16293.7	−0.776143	−0.388072	+	0.921629i	$0.626859\pi$
$762$	−13478.5	−0.640781
$763$	5332.36	0.253007
$764$	−15398.2	−0.729173
$765$	−27700.3	−1.30916
$766$	3188.42	0.150395
$767$	3187.33	0.150050
$768$	9968.91	0.468388
$769$	−16671.5	−0.781780	−0.390890	−	0.920437i	$-0.627833\pi$
$769$	−16671.5	−0.781780	−0.390890	+	0.920437i	$0.627833\pi$
$770$	655.764	0.0306910
$771$	18379.1	0.858507
$772$	12692.4	0.591723
$773$	−20899.0	−0.972425	−0.486213	−	0.873841i	$-0.661622\pi$
$773$	−20899.0	−0.972425	−0.486213	+	0.873841i	$0.661622\pi$
$774$	13574.2	0.630379
$775$	1877.91	0.0870405
$776$	−2944.93	−0.136233
$777$	−3157.87	−0.145802
$778$	−10969.0	−0.505474
$779$	−3690.52	−0.169739
$780$	−22955.7	−1.05378
$781$	−2490.84	−0.114122
$782$	23014.3	1.05242
$783$	−5646.23	−0.257701
$784$	−7994.12	−0.364164
$785$	−8450.36	−0.384212
$786$	26907.2	1.22105
$787$	14887.7	0.674318	0.337159	−	0.941448i	$-0.390534\pi$
$787$	14887.7	0.674318	0.337159	+	0.941448i	$0.390534\pi$
$788$	−25168.0	−1.13778
$789$	26915.6	1.21447
$790$	−3067.56	−0.138150
$791$	−14145.0	−0.635826
$792$	−9160.78	−0.411003
$793$	−62980.8	−2.82032
$794$	7514.87	0.335885
$795$	−27402.7	−1.22248
$796$	−8197.55	−0.365018
$797$	4711.72	0.209408	0.104704	−	0.994503i	$-0.466611\pi$
$797$	4711.72	0.209408	0.104704	+	0.994503i	$0.466611\pi$
$798$	−1977.98	−0.0877440
$799$	−16569.9	−0.733667
$800$	−4358.91	−0.192639
$801$	−37201.5	−1.64101
$802$	−8062.80	−0.354997
$803$	−5702.11	−0.250589
$804$	2501.59	0.109732
$805$	9173.76	0.401655
$806$	6826.27	0.298319
$807$	20556.5	0.896682
$808$	16412.6	0.714594
$809$	17247.7	0.749565	0.374782	−	0.927113i	$-0.377717\pi$
$809$	17247.7	0.749565	0.374782	+	0.927113i	$0.377717\pi$
$810$	−2109.22	−0.0914946
$811$	−27844.7	−1.20562	−0.602811	−	0.797884i	$-0.705953\pi$
$811$	−27844.7	−1.20562	−0.602811	+	0.797884i	$0.705953\pi$
$812$	−2006.17	−0.0867028
$813$	−919.018	−0.0396450
$814$	443.509	0.0190970
$815$	−4829.63	−0.207576
$816$	33271.6	1.42738
$817$	4543.41	0.194558
$818$	4442.34	0.189881
$819$	−40136.9	−1.71245
$820$	−6478.64	−0.275907
$821$	25206.7	1.07152	0.535761	−	0.844370i	$-0.320025\pi$
$821$	25206.7	1.07152	0.535761	+	0.844370i	$0.320025\pi$
$822$	20442.0	0.867391
$823$	14553.6	0.616409	0.308205	−	0.951320i	$-0.400272\pi$
$823$	14553.6	0.616409	0.308205	+	0.951320i	$0.400272\pi$
$824$	−12623.2	−0.533679
$825$	2401.13	0.101329
$826$	482.120	0.0203088
$827$	−18111.2	−0.761534	−0.380767	−	0.924671i	$-0.624340\pi$
$827$	−18111.2	−0.761534	−0.380767	+	0.924671i	$0.624340\pi$
$828$	−58271.6	−2.44575
$829$	−41456.6	−1.73685	−0.868425	−	0.495821i	$-0.834867\pi$
$829$	−41456.6	−1.73685	−0.868425	+	0.495821i	$0.834867\pi$
$830$	330.664	0.0138283
$831$	65660.7	2.74097
$832$	5511.01	0.229639
$833$	26559.7	1.10473
$834$	−10353.9	−0.429887
$835$	12613.9	0.522780
$836$	−1394.20	−0.0576788
$837$	−14584.7	−0.602296
$838$	10312.7	0.425116
$839$	−42115.3	−1.73299	−0.866497	−	0.499182i	$-0.833634\pi$
$839$	−42115.3	−1.73299	−0.866497	+	0.499182i	$0.833634\pi$
$840$	−7636.47	−0.313671
$841$	−23543.4	−0.965327
$842$	−6497.95	−0.265955
$843$	−50256.6	−2.05330
$844$	−4948.55	−0.201820
$845$	20081.0	0.817524
$846$	−8359.55	−0.339725
$847$	1251.35	0.0507637
$848$	21257.3	0.860826
$849$	1432.64	0.0579128
$850$	3243.05	0.130865
$851$	6204.43	0.249924
$852$	13189.1	0.530343
$853$	16302.3	0.654373	0.327186	−	0.944960i	$-0.393899\pi$
$853$	16302.3	0.654373	0.327186	+	0.944960i	$0.393899\pi$
$854$	−9526.54	−0.381723
$855$	−4677.54	−0.187097
$856$	−25238.0	−1.00773
$857$	24843.6	0.990246	0.495123	−	0.868823i	$-0.335123\pi$
$857$	24843.6	0.990246	0.495123	+	0.868823i	$0.335123\pi$
$858$	8728.22	0.347292
$859$	8939.42	0.355075	0.177537	−	0.984114i	$-0.443187\pi$
$859$	8939.42	0.355075	0.177537	+	0.984114i	$0.443187\pi$
$860$	7975.86	0.316249
$861$	−17539.3	−0.694235
$862$	−3102.62	−0.122594
$863$	48069.9	1.89608	0.948041	−	0.318149i	$-0.103061\pi$
$863$	48069.9	1.89608	0.948041	+	0.318149i	$0.103061\pi$
$864$	33853.4	1.33300
$865$	−6782.16	−0.266590
$866$	−3567.90	−0.140003
$867$	−67644.4	−2.64974
$868$	−5182.11	−0.202641
$869$	−5853.61	−0.228504
$870$	1463.66	0.0570376
$871$	−3385.41	−0.131699
$872$	8721.12	0.338686
$873$	−8572.78	−0.332353
$874$	3886.24	0.150405
$875$	1292.72	0.0499449
$876$	30193.0	1.16453
$877$	28501.2	1.09740	0.548699	−	0.836020i	$-0.315123\pi$
$877$	28501.2	1.09740	0.548699	+	0.836020i	$0.315123\pi$
$878$	−1059.02	−0.0407063
$879$	−20262.2	−0.777507
$880$	−1862.65	−0.0713523
$881$	2625.58	0.100407	0.0502033	−	0.998739i	$-0.484013\pi$
$881$	2625.58	0.100407	0.0502033	+	0.998739i	$0.484013\pi$
$882$	13399.4	0.511545
$883$	30898.4	1.17759	0.588796	−	0.808281i	$-0.299602\pi$
$883$	30898.4	1.17759	0.588796	+	0.808281i	$0.299602\pi$
$884$	−59164.1	−2.25102
$885$	1765.32	0.0670515
$886$	19869.8	0.753429
$887$	11201.5	0.424024	0.212012	−	0.977267i	$-0.431998\pi$
$887$	11201.5	0.424024	0.212012	+	0.977267i	$0.431998\pi$
$888$	−5164.73	−0.195177
$889$	−13847.1	−0.522405
$890$	4355.40	0.164038
$891$	−4024.89	−0.151334
$892$	40178.2	1.50814
$893$	−2798.02	−0.104851
$894$	−7559.53	−0.282806
$895$	−13222.1	−0.493818
$896$	15258.8	0.568929
$897$	122103.	4.54503
$898$	13659.4	0.507596
$899$	2184.38	0.0810381
$900$	−8211.32	−0.304123
$901$	−70625.4	−2.61140
$902$	2463.31	0.0909304
$903$	21592.6	0.795744
$904$	−23134.3	−0.851145
$905$	−22652.1	−0.832022
$906$	−2306.75	−0.0845878
$907$	37016.6	1.35515	0.677573	−	0.735456i	$-0.263032\pi$
$907$	37016.6	1.35515	0.677573	+	0.735456i	$0.263032\pi$
$908$	26497.0	0.968428
$909$	47777.5	1.74332
$910$	4699.08	0.171179
$911$	−41797.9	−1.52012	−0.760059	−	0.649855i	$-0.774830\pi$
$911$	−41797.9	−1.52012	−0.760059	+	0.649855i	$0.774830\pi$
$912$	5618.32	0.203992
$913$	630.982	0.0228724
$914$	−21354.1	−0.772792
$915$	−34882.2	−1.26029
$916$	21482.1	0.774878
$917$	27643.0	0.995478
$918$	−25187.0	−0.905551
$919$	4673.78	0.167762	0.0838812	−	0.996476i	$-0.473268\pi$
$919$	4673.78	0.167762	0.0838812	+	0.996476i	$0.473268\pi$
$920$	15003.8	0.537674
$921$	−5862.90	−0.209760
$922$	6459.11	0.230715
$923$	−17848.9	−0.636515
$924$	−6625.96	−0.235907
$925$	874.295	0.0310774
$926$	−2142.87	−0.0760465
$927$	−36746.7	−1.30196
$928$	−5070.29	−0.179354
$929$	−51473.5	−1.81786	−0.908929	−	0.416950i	$-0.863099\pi$
$929$	−51473.5	−1.81786	−0.908929	+	0.416950i	$0.863099\pi$
$930$	3780.76	0.133308
$931$	4484.92	0.157881
$932$	−23480.8	−0.825256
$933$	86877.9	3.04851
$934$	20277.3	0.710379
$935$	6188.48	0.216454
$936$	−65644.4	−2.29236
$937$	9993.25	0.348415	0.174208	−	0.984709i	$-0.444264\pi$
$937$	9993.25	0.348415	0.174208	+	0.984709i	$0.444264\pi$
$938$	−512.080	−0.0178252
$939$	5590.75	0.194300
$940$	−4911.87	−0.170434
$941$	−46578.0	−1.61360	−0.806801	−	0.590824i	$-0.798803\pi$
$941$	−46578.0	−1.61360	−0.806801	+	0.590824i	$0.798803\pi$
$942$	−17013.0	−0.588442
$943$	34460.3	1.19001
$944$	−1369.43	−0.0472151
$945$	−10039.8	−0.345604
$946$	−3032.58	−0.104226
$947$	8763.15	0.300701	0.150351	−	0.988633i	$-0.451960\pi$
$947$	8763.15	0.300701	0.150351	+	0.988633i	$0.451960\pi$
$948$	30995.2	1.06189
$949$	−40860.2	−1.39766
$950$	547.628	0.0187025
$951$	78107.3	2.66331
$952$	−19681.6	−0.670047
$953$	−42474.6	−1.44374	−0.721871	−	0.692028i	$-0.756718\pi$
$953$	−42474.6	−1.44374	−0.721871	+	0.692028i	$0.756718\pi$
$954$	−35630.8	−1.20921
$955$	11541.5	0.391071
$956$	−24559.4	−0.830867
$957$	2793.00	0.0943415
$958$	−4824.77	−0.162715
$959$	21001.0	0.707152
$960$	3052.30	0.102617
$961$	−24148.5	−0.810599
$962$	3178.10	0.106514
$963$	−73468.6	−2.45846
$964$	−19874.4	−0.664016
$965$	−9513.38	−0.317354
$966$	18469.4	0.615158
$967$	31580.5	1.05022	0.525109	−	0.851035i	$-0.324025\pi$
$967$	31580.5	1.05022	0.525109	+	0.851035i	$0.324025\pi$
$968$	2046.59	0.0679545
$969$	−18666.3	−0.618832
$970$	1003.67	0.0332225
$971$	−39383.0	−1.30161	−0.650804	−	0.759246i	$-0.725568\pi$
$971$	−39383.0	−1.30161	−0.650804	+	0.759246i	$0.725568\pi$
$972$	−13658.9	−0.450731
$973$	−10637.0	−0.350471
$974$	10596.7	0.348602
$975$	17206.1	0.565164
$976$	27059.5	0.887451
$977$	−52396.6	−1.71578	−0.857889	−	0.513835i	$-0.828224\pi$
$977$	−52396.6	−1.71578	−0.857889	+	0.513835i	$0.828224\pi$
$978$	−9723.42	−0.317915
$979$	8311.12	0.271322
$980$	7873.19	0.256633
$981$	25387.5	0.826259
$982$	20934.6	0.680294
$983$	−7121.45	−0.231067	−0.115534	−	0.993304i	$-0.536858\pi$
$983$	−7121.45	−0.231067	−0.115534	+	0.993304i	$0.536858\pi$
$984$	−28685.6	−0.929333
$985$	18864.3	0.610219
$986$	3772.31	0.121841
$987$	−13297.6	−0.428843
$988$	−9990.58	−0.321703
$989$	−42424.1	−1.36401
$990$	3122.11	0.100229
$991$	25881.8	0.829630	0.414815	−	0.909906i	$-0.363846\pi$
$991$	25881.8	0.829630	0.414815	+	0.909906i	$0.363846\pi$
$992$	−13097.0	−0.419184
$993$	−55920.2	−1.78708
$994$	−2699.84	−0.0861507
$995$	6144.33	0.195767
$996$	−3341.08	−0.106291
$997$	58898.4	1.87094	0.935471	−	0.353403i	$-0.114975\pi$
$997$	58898.4	1.87094	0.935471	+	0.353403i	$0.114975\pi$
$998$	−3389.68	−0.107513
$999$	−6790.19	−0.215047

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.4.a.d.1.10	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.4.a.d.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-1.15290 q^{2} -8.73139 q^{3} -6.67082 q^{4} +5.00000 q^{5} +10.0664 q^{6} +10.3417 q^{7} +16.9140 q^{8} +49.2372 q^{9} +O(q^{10})\)	\(q-1.15290 q^{2} -8.73139 q^{3} -6.67082 q^{4} +5.00000 q^{5} +10.0664 q^{6} +10.3417 q^{7} +16.9140 q^{8} +49.2372 q^{9} -5.76450 q^{10} -11.0000 q^{11} +58.2456 q^{12} -78.8239 q^{13} -11.9230 q^{14} -43.6570 q^{15} +33.8664 q^{16} -112.518 q^{17} -56.7656 q^{18} -19.0000 q^{19} -33.3541 q^{20} -90.2977 q^{21} +12.6819 q^{22} +177.413 q^{23} -147.683 q^{24} +25.0000 q^{25} +90.8761 q^{26} -194.162 q^{27} -68.9878 q^{28} +29.0800 q^{29} +50.3321 q^{30} +75.1163 q^{31} -174.357 q^{32} +96.0453 q^{33} +129.722 q^{34} +51.7086 q^{35} -328.453 q^{36} +34.9718 q^{37} +21.9051 q^{38} +688.242 q^{39} +84.5700 q^{40} +194.238 q^{41} +104.104 q^{42} -239.127 q^{43} +73.3790 q^{44} +246.186 q^{45} -204.539 q^{46} +147.264 q^{47} -295.701 q^{48} -236.049 q^{49} -28.8225 q^{50} +982.437 q^{51} +525.820 q^{52} +627.682 q^{53} +223.849 q^{54} -55.0000 q^{55} +174.920 q^{56} +165.896 q^{57} -33.5264 q^{58} -40.4362 q^{59} +291.228 q^{60} +799.006 q^{61} -86.6016 q^{62} +509.198 q^{63} -69.9156 q^{64} -394.119 q^{65} -110.731 q^{66} +42.9490 q^{67} +750.586 q^{68} -1549.06 q^{69} -59.6149 q^{70} +226.440 q^{71} +832.798 q^{72} +518.374 q^{73} -40.3190 q^{74} -218.285 q^{75} +126.746 q^{76} -113.759 q^{77} -793.475 q^{78} +532.146 q^{79} +169.332 q^{80} +365.899 q^{81} -223.937 q^{82} -57.3620 q^{83} +602.360 q^{84} -562.589 q^{85} +275.689 q^{86} -253.909 q^{87} -186.054 q^{88} -755.556 q^{89} -283.828 q^{90} -815.175 q^{91} -1183.49 q^{92} -655.870 q^{93} -169.781 q^{94} -95.0000 q^{95} +1522.38 q^{96} -174.112 q^{97} +272.141 q^{98} -541.609 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 4 q^{2} - 21 q^{3} + 74 q^{4} + 110 q^{5} - 9 q^{6} - 41 q^{7} - 78 q^{8} + 209 q^{9}+O(q^{10}) \) 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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