LMFDB - Embedded newform 1045.4.a.e.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1045.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$61.6569959560$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.73543 q^{2} -6.01363 q^{3} +14.4243 q^{4} +5.00000 q^{5} +28.4771 q^{6} +1.72878 q^{7} -30.4218 q^{8} +9.16373 q^{9} +O(q^{10})$	\(q-4.73543 q^{2} -6.01363 q^{3} +14.4243 q^{4} +5.00000 q^{5} +28.4771 q^{6} +1.72878 q^{7} -30.4218 q^{8} +9.16373 q^{9} -23.6772 q^{10} +11.0000 q^{11} -86.7424 q^{12} +53.6748 q^{13} -8.18652 q^{14} -30.0681 q^{15} +28.6661 q^{16} +25.1584 q^{17} -43.3942 q^{18} -19.0000 q^{19} +72.1215 q^{20} -10.3962 q^{21} -52.0897 q^{22} +75.2535 q^{23} +182.946 q^{24} +25.0000 q^{25} -254.173 q^{26} +107.261 q^{27} +24.9365 q^{28} -28.8886 q^{29} +142.386 q^{30} +162.455 q^{31} +107.628 q^{32} -66.1499 q^{33} -119.136 q^{34} +8.64390 q^{35} +132.180 q^{36} +196.875 q^{37} +89.9732 q^{38} -322.780 q^{39} -152.109 q^{40} +191.047 q^{41} +49.2307 q^{42} +367.980 q^{43} +158.667 q^{44} +45.8186 q^{45} -356.358 q^{46} +156.426 q^{47} -172.387 q^{48} -340.011 q^{49} -118.386 q^{50} -151.293 q^{51} +774.221 q^{52} +396.509 q^{53} -507.926 q^{54} +55.0000 q^{55} -52.5927 q^{56} +114.259 q^{57} +136.800 q^{58} +92.0032 q^{59} -433.712 q^{60} -601.444 q^{61} -769.293 q^{62} +15.8421 q^{63} -738.996 q^{64} +268.374 q^{65} +313.248 q^{66} -348.130 q^{67} +362.892 q^{68} -452.547 q^{69} -40.9326 q^{70} +174.994 q^{71} -278.777 q^{72} +31.6544 q^{73} -932.287 q^{74} -150.341 q^{75} -274.062 q^{76} +19.0166 q^{77} +1528.50 q^{78} -396.436 q^{79} +143.330 q^{80} -892.447 q^{81} -904.687 q^{82} -1075.03 q^{83} -149.959 q^{84} +125.792 q^{85} -1742.54 q^{86} +173.725 q^{87} -334.640 q^{88} +605.341 q^{89} -216.971 q^{90} +92.7919 q^{91} +1085.48 q^{92} -976.942 q^{93} -740.746 q^{94} -95.0000 q^{95} -647.238 q^{96} -866.579 q^{97} +1610.10 q^{98} +100.801 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 12 q^{2} + 21 q^{3} + 96 q^{4} + 110 q^{5} + 27 q^{6} + 93 q^{7} + 114 q^{8} + 209 q^{9}+O(q^{10}) $ 22 * q + 12 * q^2 + 21 * q^3 + 96 * q^4 + 110 * q^5 + 27 * q^6 + 93 * q^7 + 114 * q^8 + 209 * q^9	\( 22 q + 12 q^{2} + 21 q^{3} + 96 q^{4} + 110 q^{5} + 27 q^{6} + 93 q^{7} + 114 q^{8} + 209 q^{9} + 60 q^{10} + 242 q^{11} + 164 q^{12} + 207 q^{13} + 129 q^{14} + 105 q^{15} + 604 q^{16} + 209 q^{17} + 869 q^{18} - 418 q^{19} + 480 q^{20} + 45 q^{21} + 132 q^{22} + 191 q^{23} + 458 q^{24} + 550 q^{25} + 363 q^{26} + 45 q^{27} + 577 q^{28} + 389 q^{29} + 135 q^{30} + 198 q^{31} + 1149 q^{32} + 231 q^{33} + 467 q^{34} + 465 q^{35} + 1315 q^{36} + 312 q^{37} - 228 q^{38} + 137 q^{39} + 570 q^{40} + 632 q^{41} - 1794 q^{42} + 1584 q^{43} + 1056 q^{44} + 1045 q^{45} + 681 q^{46} - 54 q^{47} + 2491 q^{48} + 1063 q^{49} + 300 q^{50} + 37 q^{51} + 1246 q^{52} + 343 q^{53} + 1078 q^{54} + 1210 q^{55} - 87 q^{56} - 399 q^{57} - 1424 q^{58} + 2787 q^{59} + 820 q^{60} + 2070 q^{61} - 446 q^{62} + 1696 q^{63} + 1758 q^{64} + 1035 q^{65} + 297 q^{66} + 2423 q^{67} - 524 q^{68} - 997 q^{69} + 645 q^{70} + 2538 q^{71} + 6010 q^{72} + 1397 q^{73} - 1977 q^{74} + 525 q^{75} - 1824 q^{76} + 1023 q^{77} + 202 q^{78} + 878 q^{79} + 3020 q^{80} + 2030 q^{81} - 190 q^{82} + 4932 q^{83} - 4580 q^{84} + 1045 q^{85} - 3394 q^{86} + 6009 q^{87} + 1254 q^{88} + 1812 q^{89} + 4345 q^{90} + 4349 q^{91} - 788 q^{92} - 4848 q^{93} - 2152 q^{94} - 2090 q^{95} + 4032 q^{96} + 988 q^{97} + 1366 q^{98} + 2299 q^{99}+O(q^{100}) \) 22 * q + 12 * q^2 + 21 * q^3 + 96 * q^4 + 110 * q^5 + 27 * q^6 + 93 * q^7 + 114 * q^8 + 209 * q^9 + 60 * q^10 + 242 * q^11 + 164 * q^12 + 207 * q^13 + 129 * q^14 + 105 * q^15 + 604 * q^16 + 209 * q^17 + 869 * q^18 - 418 * q^19 + 480 * q^20 + 45 * q^21 + 132 * q^22 + 191 * q^23 + 458 * q^24 + 550 * q^25 + 363 * q^26 + 45 * q^27 + 577 * q^28 + 389 * q^29 + 135 * q^30 + 198 * q^31 + 1149 * q^32 + 231 * q^33 + 467 * q^34 + 465 * q^35 + 1315 * q^36 + 312 * q^37 - 228 * q^38 + 137 * q^39 + 570 * q^40 + 632 * q^41 - 1794 * q^42 + 1584 * q^43 + 1056 * q^44 + 1045 * q^45 + 681 * q^46 - 54 * q^47 + 2491 * q^48 + 1063 * q^49 + 300 * q^50 + 37 * q^51 + 1246 * q^52 + 343 * q^53 + 1078 * q^54 + 1210 * q^55 - 87 * q^56 - 399 * q^57 - 1424 * q^58 + 2787 * q^59 + 820 * q^60 + 2070 * q^61 - 446 * q^62 + 1696 * q^63 + 1758 * q^64 + 1035 * q^65 + 297 * q^66 + 2423 * q^67 - 524 * q^68 - 997 * q^69 + 645 * q^70 + 2538 * q^71 + 6010 * q^72 + 1397 * q^73 - 1977 * q^74 + 525 * q^75 - 1824 * q^76 + 1023 * q^77 + 202 * q^78 + 878 * q^79 + 3020 * q^80 + 2030 * q^81 - 190 * q^82 + 4932 * q^83 - 4580 * q^84 + 1045 * q^85 - 3394 * q^86 + 6009 * q^87 + 1254 * q^88 + 1812 * q^89 + 4345 * q^90 + 4349 * q^91 - 788 * q^92 - 4848 * q^93 - 2152 * q^94 - 2090 * q^95 + 4032 * q^96 + 988 * q^97 + 1366 * 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 $

$2$	−4.73543	−1.67423	−0.837114	−	0.547029i	$-0.815759\pi$
$2$	−4.73543	−1.67423	−0.837114	+	0.547029i	$0.815759\pi$
$3$	−6.01363	−1.15732	−0.578662	−	0.815568i	$-0.696425\pi$
$3$	−6.01363	−1.15732	−0.578662	+	0.815568i	$0.696425\pi$
$4$	14.4243	1.80304
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	28.4771	1.93762
$7$	1.72878	0.0933454	0.0466727	−	0.998910i	$-0.485138\pi$
$7$	1.72878	0.0933454	0.0466727	+	0.998910i	$0.485138\pi$
$8$	−30.4218	−1.34447
$9$	9.16373	0.339397
$10$	−23.6772	−0.748737
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−86.7424	−2.08670
$13$	53.6748	1.14513	0.572566	−	0.819859i	$-0.305948\pi$
$13$	53.6748	1.14513	0.572566	+	0.819859i	$0.305948\pi$
$14$	−8.18652	−0.156281
$15$	−30.0681	−0.517571
$16$	28.6661	0.447908
$17$	25.1584	0.358930	0.179465	−	0.983764i	$-0.442563\pi$
$17$	25.1584	0.358930	0.179465	+	0.983764i	$0.442563\pi$
$18$	−43.3942	−0.568228
$19$	−19.0000	−0.229416
$19$	−19.0000	−0.229416
$20$	72.1215	0.806343
$21$	−10.3962	−0.108031
$22$	−52.0897	−0.504799
$23$	75.2535	0.682237	0.341118	−	0.940020i	$-0.389194\pi$
$23$	75.2535	0.682237	0.341118	+	0.940020i	$0.389194\pi$
$24$	182.946	1.55598
$25$	25.0000	0.200000
$26$	−254.173	−1.91721
$27$	107.261	0.764531
$28$	24.9365	0.168305
$29$	−28.8886	−0.184982	−0.0924910	−	0.995714i	$-0.529483\pi$
$29$	−28.8886	−0.184982	−0.0924910	+	0.995714i	$0.529483\pi$
$30$	142.386	0.866531
$31$	162.455	0.941217	0.470608	−	0.882342i	$-0.344034\pi$
$31$	162.455	0.941217	0.470608	+	0.882342i	$0.344034\pi$
$32$	107.628	0.594569
$33$	−66.1499	−0.348946
$34$	−119.136	−0.600930
$35$	8.64390	0.0417453
$36$	132.180	0.611946
$37$	196.875	0.874758	0.437379	−	0.899277i	$-0.355907\pi$
$37$	196.875	0.874758	0.437379	+	0.899277i	$0.355907\pi$
$38$	89.9732	0.384094
$39$	−322.780	−1.32529
$40$	−152.109	−0.601264
$41$	191.047	0.727718	0.363859	−	0.931454i	$-0.381459\pi$
$41$	191.047	0.727718	0.363859	+	0.931454i	$0.381459\pi$
$42$	49.2307	0.180868
$43$	367.980	1.30503	0.652516	−	0.757775i	$-0.273714\pi$
$43$	367.980	1.30503	0.652516	+	0.757775i	$0.273714\pi$
$44$	158.667	0.543636
$45$	45.8186	0.151783
$46$	−356.358	−1.14222
$47$	156.426	0.485471	0.242736	−	0.970093i	$-0.421955\pi$
$47$	156.426	0.485471	0.242736	+	0.970093i	$0.421955\pi$
$48$	−172.387	−0.518374
$49$	−340.011	−0.991287
$50$	−118.386	−0.334846
$51$	−151.293	−0.415398
$52$	774.221	2.06472
$53$	396.509	1.02764	0.513818	−	0.857899i	$-0.328231\pi$
$53$	396.509	1.02764	0.513818	+	0.857899i	$0.328231\pi$
$54$	−507.926	−1.28000
$55$	55.0000	0.134840
$56$	−52.5927	−0.125500
$57$	114.259	0.265508
$58$	136.800	0.309702
$59$	92.0032	0.203014	0.101507	−	0.994835i	$-0.467634\pi$
$59$	92.0032	0.203014	0.101507	+	0.994835i	$0.467634\pi$
$60$	−433.712	−0.933200
$61$	−601.444	−1.26241	−0.631205	−	0.775616i	$-0.717440\pi$
$61$	−601.444	−1.26241	−0.631205	+	0.775616i	$0.717440\pi$
$62$	−769.293	−1.57581
$63$	15.8421	0.0316812
$64$	−738.996	−1.44335
$65$	268.374	0.512118
$66$	313.248	0.584215
$67$	−348.130	−0.634789	−0.317395	−	0.948294i	$-0.602808\pi$
$67$	−348.130	−0.634789	−0.317395	+	0.948294i	$0.602808\pi$
$68$	362.892	0.647164
$69$	−452.547	−0.789569
$70$	−40.9326	−0.0698912
$71$	174.994	0.292507	0.146253	−	0.989247i	$-0.453279\pi$
$71$	174.994	0.292507	0.146253	+	0.989247i	$0.453279\pi$
$72$	−278.777	−0.456309
$73$	31.6544	0.0507516	0.0253758	−	0.999678i	$-0.491922\pi$
$73$	31.6544	0.0507516	0.0253758	+	0.999678i	$0.491922\pi$
$74$	−932.287	−1.46454
$75$	−150.341	−0.231465
$76$	−274.062	−0.413645
$77$	19.0166	0.0281447
$78$	1528.50	2.21883
$79$	−396.436	−0.564589	−0.282294	−	0.959328i	$-0.591095\pi$
$79$	−396.436	−0.564589	−0.282294	+	0.959328i	$0.591095\pi$
$80$	143.330	0.200310
$81$	−892.447	−1.22421
$82$	−904.687	−1.21837
$83$	−1075.03	−1.42168	−0.710841	−	0.703353i	$-0.751685\pi$
$83$	−1075.03	−1.42168	−0.710841	+	0.703353i	$0.751685\pi$
$84$	−149.959	−0.194784
$85$	125.792	0.160518
$86$	−1742.54	−2.18492
$87$	173.725	0.214084
$88$	−334.640	−0.405372
$89$	605.341	0.720966	0.360483	−	0.932766i	$-0.382612\pi$
$89$	605.341	0.720966	0.360483	+	0.932766i	$0.382612\pi$
$90$	−216.971	−0.254119
$91$	92.7919	0.106893
$92$	1085.48	1.23010
$93$	−976.942	−1.08929
$94$	−740.746	−0.812789
$95$	−95.0000	−0.102598
$96$	−647.238	−0.688108
$97$	−866.579	−0.907090	−0.453545	−	0.891233i	$-0.649841\pi$
$97$	−866.579	−0.907090	−0.453545	+	0.891233i	$0.649841\pi$
$98$	1610.10	1.65964
$99$	100.801	0.102332
$100$	360.608	0.360608
$101$	−290.374	−0.286073	−0.143036	−	0.989717i	$-0.545687\pi$
$101$	−290.374	−0.286073	−0.143036	+	0.989717i	$0.545687\pi$
$102$	716.438	0.695470
$103$	−296.552	−0.283690	−0.141845	−	0.989889i	$-0.545304\pi$
$103$	−296.552	−0.283690	−0.141845	+	0.989889i	$0.545304\pi$
$104$	−1632.89	−1.53959
$105$	−51.9812	−0.0483128
$106$	−1877.64	−1.72050
$107$	−1022.39	−0.923721	−0.461860	−	0.886953i	$-0.652818\pi$
$107$	−1022.39	−0.923721	−0.461860	+	0.886953i	$0.652818\pi$
$108$	1547.16	1.37848
$109$	598.759	0.526154	0.263077	−	0.964775i	$-0.415263\pi$
$109$	598.759	0.526154	0.263077	+	0.964775i	$0.415263\pi$
$110$	−260.449	−0.225753
$111$	−1183.93	−1.01238
$112$	49.5574	0.0418101
$113$	−573.584	−0.477506	−0.238753	−	0.971080i	$-0.576739\pi$
$113$	−573.584	−0.477506	−0.238753	+	0.971080i	$0.576739\pi$
$114$	−541.065	−0.444521
$115$	376.268	0.305106
$116$	−416.698	−0.333529
$117$	491.861	0.388654
$118$	−435.675	−0.339891
$119$	43.4933	0.0335044
$120$	914.728	0.695857
$121$	121.000	0.0909091
$122$	2848.10	2.11356
$123$	−1148.88	−0.842205
$124$	2343.30	1.69705
$125$	125.000	0.0894427
$126$	−75.0190	−0.0530415
$127$	1074.12	0.750496	0.375248	−	0.926925i	$-0.377558\pi$
$127$	1074.12	0.750496	0.375248	+	0.926925i	$0.377558\pi$
$128$	2638.44	1.82193
$129$	−2212.89	−1.51034
$130$	−1270.87	−0.857403
$131$	516.533	0.344501	0.172251	−	0.985053i	$-0.444896\pi$
$131$	516.533	0.344501	0.172251	+	0.985053i	$0.444896\pi$
$132$	−954.166	−0.629163
$133$	−32.8468	−0.0214149
$134$	1648.55	1.06278
$135$	536.304	0.341909
$136$	−765.364	−0.482569
$137$	655.845	0.408997	0.204499	−	0.978867i	$-0.434444\pi$
$137$	655.845	0.408997	0.204499	+	0.978867i	$0.434444\pi$
$138$	2143.00	1.32192
$139$	535.563	0.326805	0.163402	−	0.986559i	$-0.447753\pi$
$139$	535.563	0.326805	0.163402	+	0.986559i	$0.447753\pi$
$140$	124.682	0.0752684
$141$	−940.690	−0.561847
$142$	−828.672	−0.489723
$143$	590.423	0.345270
$144$	262.688	0.152019
$145$	−144.443	−0.0827264
$146$	−149.897	−0.0849697
$147$	2044.70	1.14724
$148$	2839.78	1.57722
$149$	−1966.87	−1.08142	−0.540712	−	0.841208i	$-0.681845\pi$
$149$	−1966.87	−1.08142	−0.540712	+	0.841208i	$0.681845\pi$
$150$	711.928	0.387525
$151$	1083.71	0.584047	0.292024	−	0.956411i	$-0.405671\pi$
$151$	1083.71	0.584047	0.292024	+	0.956411i	$0.405671\pi$
$152$	578.015	0.308442
$153$	230.545	0.121820
$154$	−90.0517	−0.0471206
$155$	812.273	0.420925
$156$	−4655.88	−2.38954
$157$	1524.93	0.775174	0.387587	−	0.921833i	$-0.373309\pi$
$157$	1524.93	0.775174	0.387587	+	0.921833i	$0.373309\pi$
$158$	1877.29	0.945250
$159$	−2384.46	−1.18931
$160$	538.142	0.265899
$161$	130.097	0.0636837
$162$	4226.12	2.04960
$163$	−867.900	−0.417050	−0.208525	−	0.978017i	$-0.566866\pi$
$163$	−867.900	−0.417050	−0.208525	+	0.978017i	$0.566866\pi$
$164$	2755.71	1.31210
$165$	−330.750	−0.156053
$166$	5090.72	2.38022
$167$	2700.04	1.25111	0.625555	−	0.780180i	$-0.284873\pi$
$167$	2700.04	1.25111	0.625555	+	0.780180i	$0.284873\pi$
$168$	316.273	0.145244
$169$	683.983	0.311326
$170$	−595.679	−0.268744
$171$	−174.111	−0.0778631
$172$	5307.85	2.35302
$173$	3930.31	1.72726	0.863631	−	0.504125i	$-0.168185\pi$
$173$	3930.31	1.72726	0.863631	+	0.504125i	$0.168185\pi$
$174$	−822.664	−0.358425
$175$	43.2195	0.0186691
$176$	315.327	0.135049
$177$	−553.273	−0.234952
$178$	−2866.55	−1.20706
$179$	2129.91	0.889369	0.444684	−	0.895687i	$-0.353316\pi$
$179$	2129.91	0.889369	0.444684	+	0.895687i	$0.353316\pi$
$180$	660.902	0.273671
$181$	−1060.59	−0.435542	−0.217771	−	0.976000i	$-0.569879\pi$
$181$	−1060.59	−0.435542	−0.217771	+	0.976000i	$0.569879\pi$
$182$	−439.410	−0.178963
$183$	3616.86	1.46102
$184$	−2289.35	−0.917246
$185$	984.374	0.391204
$186$	4626.24	1.82372
$187$	276.742	0.108221
$188$	2256.34	0.875323
$189$	185.430	0.0713654
$190$	449.866	0.171772
$191$	−2087.65	−0.790873	−0.395437	−	0.918493i	$-0.629407\pi$
$191$	−2087.65	−0.790873	−0.395437	+	0.918493i	$0.629407\pi$
$192$	4444.05	1.67042
$193$	−3530.04	−1.31657	−0.658285	−	0.752768i	$-0.728718\pi$
$193$	−3530.04	−1.31657	−0.658285	+	0.752768i	$0.728718\pi$
$194$	4103.62	1.51868
$195$	−1613.90	−0.592686
$196$	−4904.43	−1.78733
$197$	−1762.43	−0.637401	−0.318701	−	0.947855i	$-0.603246\pi$
$197$	−1762.43	−0.637401	−0.318701	+	0.947855i	$0.603246\pi$
$198$	−477.336	−0.171327
$199$	1238.64	0.441229	0.220615	−	0.975361i	$-0.429194\pi$
$199$	1238.64	0.441229	0.220615	+	0.975361i	$0.429194\pi$
$200$	−760.546	−0.268894
$201$	2093.53	0.734656
$202$	1375.05	0.478951
$203$	−49.9420	−0.0172672
$204$	−2182.30	−0.748978
$205$	955.233	0.325446
$206$	1404.30	0.474962
$207$	689.603	0.231549
$208$	1538.65	0.512913
$209$	−209.000	−0.0691714
$210$	246.153	0.0808867
$211$	4360.13	1.42258	0.711289	−	0.702900i	$-0.248112\pi$
$211$	4360.13	1.42258	0.711289	+	0.702900i	$0.248112\pi$
$212$	5719.37	1.85287
$213$	−1052.35	−0.338525
$214$	4841.45	1.54652
$215$	1839.90	0.583628
$216$	−3263.07	−1.02789
$217$	280.848	0.0878582
$218$	−2835.38	−0.880901
$219$	−190.358	−0.0587360
$220$	793.337	0.243122
$221$	1350.37	0.411022
$222$	5606.43	1.69495
$223$	−3420.57	−1.02717	−0.513583	−	0.858040i	$-0.671682\pi$
$223$	−3420.57	−1.02717	−0.513583	+	0.858040i	$0.671682\pi$
$224$	186.066	0.0555003
$225$	229.093	0.0678795
$226$	2716.17	0.799454
$227$	3512.92	1.02714	0.513570	−	0.858048i	$-0.328323\pi$
$227$	3512.92	1.02714	0.513570	+	0.858048i	$0.328323\pi$
$228$	1648.11	0.478721
$229$	−5074.74	−1.46440	−0.732202	−	0.681088i	$-0.761507\pi$
$229$	−5074.74	−1.46440	−0.732202	+	0.681088i	$0.761507\pi$
$230$	−1781.79	−0.510816
$231$	−114.359	−0.0325725
$232$	878.844	0.248702
$233$	4826.48	1.35705	0.678526	−	0.734576i	$-0.262619\pi$
$233$	4826.48	1.35705	0.678526	+	0.734576i	$0.262619\pi$
$234$	−2329.17	−0.650696
$235$	782.132	0.217109
$236$	1327.08	0.366041
$237$	2384.02	0.653412
$238$	−205.960	−0.0560940
$239$	548.944	0.148570	0.0742851	−	0.997237i	$-0.476333\pi$
$239$	548.944	0.148570	0.0742851	+	0.997237i	$0.476333\pi$
$240$	−861.936	−0.231824
$241$	−5262.96	−1.40671	−0.703355	−	0.710839i	$-0.748315\pi$
$241$	−5262.96	−1.40671	−0.703355	+	0.710839i	$0.748315\pi$
$242$	−572.987	−0.152203
$243$	2470.80	0.652272
$244$	−8675.42	−2.27617
$245$	−1700.06	−0.443317
$246$	5440.45	1.41004
$247$	−1019.82	−0.262711
$248$	−4942.17	−1.26544
$249$	6464.81	1.64535
$250$	−591.929	−0.149747
$251$	−1526.59	−0.383894	−0.191947	−	0.981405i	$-0.561480\pi$
$251$	−1526.59	−0.383894	−0.191947	+	0.981405i	$0.561480\pi$
$252$	228.511	0.0571223
$253$	827.789	0.205702
$254$	−5086.43	−1.25650
$255$	−756.466	−0.185771
$256$	−6582.16	−1.60697
$257$	−30.5055	−0.00740421	−0.00370210	−	0.999993i	$-0.501178\pi$
$257$	−30.5055	−0.00740421	−0.00370210	+	0.999993i	$0.501178\pi$
$258$	10479.0	2.52866
$259$	340.353	0.0816546
$260$	3871.11	0.923369
$261$	−264.727	−0.0627824
$262$	−2446.01	−0.576774
$263$	5094.78	1.19452	0.597258	−	0.802049i	$-0.296257\pi$
$263$	5094.78	1.19452	0.597258	+	0.802049i	$0.296257\pi$
$264$	2012.40	0.469147
$265$	1982.54	0.459573
$266$	155.544	0.0358534
$267$	−3640.29	−0.834391
$268$	−5021.53	−1.14455
$269$	1331.37	0.301765	0.150883	−	0.988552i	$-0.451788\pi$
$269$	1331.37	0.301765	0.150883	+	0.988552i	$0.451788\pi$
$270$	−2539.63	−0.572433
$271$	5463.19	1.22460	0.612298	−	0.790627i	$-0.290245\pi$
$271$	5463.19	1.22460	0.612298	+	0.790627i	$0.290245\pi$
$272$	721.192	0.160767
$273$	−558.016	−0.123709
$274$	−3105.71	−0.684754
$275$	275.000	0.0603023
$276$	−6527.67	−1.42362
$277$	−9063.33	−1.96593	−0.982965	−	0.183794i	$-0.941162\pi$
$277$	−9063.33	−1.96593	−0.982965	+	0.183794i	$0.941162\pi$
$278$	−2536.12	−0.547146
$279$	1488.69	0.319446
$280$	−262.963	−0.0561252
$281$	3511.46	0.745467	0.372733	−	0.927939i	$-0.378421\pi$
$281$	3511.46	0.745467	0.372733	+	0.927939i	$0.378421\pi$
$282$	4454.57	0.940660
$283$	3525.36	0.740498	0.370249	−	0.928932i	$-0.379272\pi$
$283$	3525.36	0.740498	0.370249	+	0.928932i	$0.379272\pi$
$284$	2524.17	0.527401
$285$	571.295	0.118739
$286$	−2795.91	−0.578061
$287$	330.277	0.0679291
$288$	986.278	0.201795
$289$	−4280.06	−0.871170
$290$	683.999	0.138503
$291$	5211.28	1.04980
$292$	456.593	0.0915070
$293$	8717.82	1.73823	0.869114	−	0.494613i	$-0.164690\pi$
$293$	8717.82	1.73823	0.869114	+	0.494613i	$0.164690\pi$
$294$	−9682.54	−1.92074
$295$	460.016	0.0907904
$296$	−5989.30	−1.17608
$297$	1179.87	0.230515
$298$	9313.97	1.81055
$299$	4039.22	0.781251
$300$	−2168.56	−0.417340
$301$	636.156	0.121819
$302$	−5131.84	−0.977828
$303$	1746.20	0.331079
$304$	−544.656	−0.102757
$305$	−3007.22	−0.564567
$306$	−1091.73	−0.203954
$307$	−2750.86	−0.511400	−0.255700	−	0.966756i	$-0.582306\pi$
$307$	−2750.86	−0.511400	−0.255700	+	0.966756i	$0.582306\pi$
$308$	274.301	0.0507459
$309$	1783.35	0.328322
$310$	−3846.46	−0.704724
$311$	6047.70	1.10268	0.551340	−	0.834281i	$-0.314117\pi$
$311$	6047.70	1.10268	0.551340	+	0.834281i	$0.314117\pi$
$312$	9819.57	1.78181
$313$	−297.274	−0.0536834	−0.0268417	−	0.999640i	$-0.508545\pi$
$313$	−297.274	−0.0536834	−0.0268417	+	0.999640i	$0.508545\pi$
$314$	−7221.18	−1.29782
$315$	79.2104	0.0141682
$316$	−5718.31	−1.01797
$317$	−7577.49	−1.34257	−0.671285	−	0.741200i	$-0.734257\pi$
$317$	−7577.49	−1.34257	−0.671285	+	0.741200i	$0.734257\pi$
$318$	11291.4	1.99117
$319$	−317.774	−0.0557742
$320$	−3694.98	−0.645486
$321$	6148.27	1.06904
$322$	−616.065	−0.106621
$323$	−478.009	−0.0823441
$324$	−12872.9	−2.20729
$325$	1341.87	0.229026
$326$	4109.88	0.698237
$327$	−3600.72	−0.608930
$328$	−5811.99	−0.978394
$329$	270.427	0.0453165
$330$	1566.24	0.261269
$331$	−2700.98	−0.448518	−0.224259	−	0.974530i	$-0.571996\pi$
$331$	−2700.98	−0.448518	−0.224259	+	0.974530i	$0.571996\pi$
$332$	−15506.5	−2.56335
$333$	1804.11	0.296890
$334$	−12785.8	−2.09464
$335$	−1740.65	−0.283886
$336$	−298.020	−0.0483878
$337$	−2995.97	−0.484276	−0.242138	−	0.970242i	$-0.577849\pi$
$337$	−2995.97	−0.484276	−0.242138	+	0.970242i	$0.577849\pi$
$338$	−3238.95	−0.521230
$339$	3449.32	0.552629
$340$	1814.46	0.289420
$341$	1787.00	0.283788
$342$	824.490	0.130361
$343$	−1180.78	−0.185877
$344$	−11194.6	−1.75457
$345$	−2262.73	−0.353106
$346$	−18611.7	−2.89183
$347$	8762.82	1.35566	0.677828	−	0.735221i	$-0.262921\pi$
$347$	8762.82	1.35566	0.677828	+	0.735221i	$0.262921\pi$
$348$	2505.87	0.386001
$349$	−3307.67	−0.507323	−0.253661	−	0.967293i	$-0.581635\pi$
$349$	−3307.67	−0.507323	−0.253661	+	0.967293i	$0.581635\pi$
$350$	−204.663	−0.0312563
$351$	5757.20	0.875488
$352$	1183.91	0.179269
$353$	−207.671	−0.0313122	−0.0156561	−	0.999877i	$-0.504984\pi$
$353$	−207.671	−0.0313122	−0.0156561	+	0.999877i	$0.504984\pi$
$354$	2619.99	0.393364
$355$	874.970	0.130813
$356$	8731.62	1.29993
$357$	−261.553	−0.0387754
$358$	−10086.0	−1.48901
$359$	9436.93	1.38736	0.693680	−	0.720284i	$-0.255988\pi$
$359$	9436.93	1.38736	0.693680	+	0.720284i	$0.255988\pi$
$360$	−1393.89	−0.204068
$361$	361.000	0.0526316
$362$	5022.36	0.729197
$363$	−727.649	−0.105211
$364$	1338.46	0.192732
$365$	158.272	0.0226968
$366$	−17127.4	−2.44608
$367$	4814.64	0.684802	0.342401	−	0.939554i	$-0.388760\pi$
$367$	4814.64	0.684802	0.342401	+	0.939554i	$0.388760\pi$
$368$	2157.22	0.305579
$369$	1750.70	0.246986
$370$	−4661.44	−0.654964
$371$	685.477	0.0959250
$372$	−14091.7	−1.96403
$373$	788.840	0.109503	0.0547515	−	0.998500i	$-0.482563\pi$
$373$	788.840	0.109503	0.0547515	+	0.998500i	$0.482563\pi$
$374$	−1310.49	−0.181187
$375$	−751.704	−0.103514
$376$	−4758.78	−0.652700
$377$	−1550.59	−0.211829
$378$	−878.092	−0.119482
$379$	1473.64	0.199725	0.0998624	−	0.995001i	$-0.468160\pi$
$379$	1473.64	0.199725	0.0998624	+	0.995001i	$0.468160\pi$
$380$	−1370.31	−0.184988
$381$	−6459.37	−0.868566
$382$	9885.90	1.32410
$383$	6418.08	0.856263	0.428131	−	0.903717i	$-0.359172\pi$
$383$	6418.08	0.856263	0.428131	+	0.903717i	$0.359172\pi$
$384$	−15866.6	−2.10856
$385$	95.0829	0.0125867
$386$	16716.3	2.20424
$387$	3372.07	0.442924
$388$	−12499.8	−1.63552
$389$	−882.624	−0.115041	−0.0575203	−	0.998344i	$-0.518319\pi$
$389$	−882.624	−0.115041	−0.0575203	+	0.998344i	$0.518319\pi$
$390$	7642.52	0.992292
$391$	1893.26	0.244875
$392$	10343.8	1.33275
$393$	−3106.24	−0.398700
$394$	8345.87	1.06715
$395$	−1982.18	−0.252492
$396$	1453.98	0.184509
$397$	12241.3	1.54754	0.773771	−	0.633466i	$-0.218368\pi$
$397$	12241.3	1.54754	0.773771	+	0.633466i	$0.218368\pi$
$398$	−5865.48	−0.738718
$399$	197.529	0.0247840
$400$	716.652	0.0895815
$401$	14641.2	1.82331	0.911655	−	0.410955i	$-0.134805\pi$
$401$	14641.2	1.82331	0.911655	+	0.410955i	$0.134805\pi$
$402$	−9913.74	−1.22998
$403$	8719.72	1.07782
$404$	−4188.45	−0.515800
$405$	−4462.23	−0.547482
$406$	236.497	0.0289092
$407$	2165.62	0.263749
$408$	4602.62	0.558489
$409$	3641.42	0.440236	0.220118	−	0.975473i	$-0.429356\pi$
$409$	3641.42	0.440236	0.220118	+	0.975473i	$0.429356\pi$
$410$	−4523.44	−0.544870
$411$	−3944.01	−0.473342
$412$	−4277.55	−0.511504
$413$	159.053	0.0189504
$414$	−3265.57	−0.387666
$415$	−5375.14	−0.635795
$416$	5776.93	0.680859
$417$	−3220.68	−0.378219
$418$	989.705	0.115809
$419$	−14397.7	−1.67870	−0.839348	−	0.543595i	$-0.817063\pi$
$419$	−14397.7	−1.67870	−0.839348	+	0.543595i	$0.817063\pi$
$420$	−749.793	−0.0871099
$421$	6162.32	0.713380	0.356690	−	0.934223i	$-0.383905\pi$
$421$	6162.32	0.713380	0.356690	+	0.934223i	$0.383905\pi$
$422$	−20647.1	−2.38172
$423$	1433.45	0.164768
$424$	−12062.5	−1.38162
$425$	628.960	0.0717859
$426$	4983.33	0.566768
$427$	−1039.77	−0.117840
$428$	−14747.3	−1.66550
$429$	−3550.58	−0.399589
$430$	−8712.71	−0.977126
$431$	2328.36	0.260216	0.130108	−	0.991500i	$-0.458468\pi$
$431$	2328.36	0.260216	0.130108	+	0.991500i	$0.458468\pi$
$432$	3074.74	0.342439
$433$	42.7643	0.00474624	0.00237312	−	0.999997i	$-0.499245\pi$
$433$	42.7643	0.00474624	0.00237312	+	0.999997i	$0.499245\pi$
$434$	−1329.94	−0.147095
$435$	868.626	0.0957412
$436$	8636.69	0.948675
$437$	−1429.82	−0.156516
$438$	901.426	0.0983374
$439$	−1085.44	−0.118008	−0.0590038	−	0.998258i	$-0.518792\pi$
$439$	−1085.44	−0.118008	−0.0590038	+	0.998258i	$0.518792\pi$
$440$	−1673.20	−0.181288
$441$	−3115.77	−0.336440
$442$	−6394.59	−0.688144
$443$	−6390.49	−0.685376	−0.342688	−	0.939449i	$-0.611337\pi$
$443$	−6390.49	−0.685376	−0.342688	+	0.939449i	$0.611337\pi$
$444$	−17077.4	−1.82535
$445$	3026.70	0.322426
$446$	16197.9	1.71971
$447$	11828.0	1.25156
$448$	−1277.56	−0.134730
$449$	1518.66	0.159621	0.0798105	−	0.996810i	$-0.474568\pi$
$449$	1518.66	0.159621	0.0798105	+	0.996810i	$0.474568\pi$
$450$	−1084.85	−0.113646
$451$	2101.51	0.219415
$452$	−8273.55	−0.860962
$453$	−6517.03	−0.675931
$454$	−16635.2	−1.71966
$455$	463.960	0.0478039
$456$	−3475.97	−0.356967
$457$	−9632.94	−0.986018	−0.493009	−	0.870024i	$-0.664103\pi$
$457$	−9632.94	−0.986018	−0.493009	+	0.870024i	$0.664103\pi$
$458$	24031.1	2.45174
$459$	2698.51	0.274413
$460$	5427.40	0.550117
$461$	−112.596	−0.0113756	−0.00568778	−	0.999984i	$-0.501810\pi$
$461$	−112.596	−0.0113756	−0.00568778	+	0.999984i	$0.501810\pi$
$462$	541.538	0.0545338
$463$	15945.2	1.60051	0.800254	−	0.599662i	$-0.204698\pi$
$463$	15945.2	1.60051	0.800254	+	0.599662i	$0.204698\pi$
$464$	−828.123	−0.0828548
$465$	−4884.71	−0.487146
$466$	−22855.5	−2.27201
$467$	−12287.4	−1.21754	−0.608770	−	0.793347i	$-0.708337\pi$
$467$	−12287.4	−1.21754	−0.608770	+	0.793347i	$0.708337\pi$
$468$	7094.75	0.700759
$469$	−601.841	−0.0592546
$470$	−3703.73	−0.363490
$471$	−9170.34	−0.897127
$472$	−2798.91	−0.272945
$473$	4047.78	0.393482
$474$	−11289.4	−1.09396
$475$	−475.000	−0.0458831
$476$	627.361	0.0604097
$477$	3633.50	0.348777
$478$	−2599.49	−0.248740
$479$	−9076.30	−0.865776	−0.432888	−	0.901448i	$-0.642505\pi$
$479$	−9076.30	−0.865776	−0.432888	+	0.901448i	$0.642505\pi$
$480$	−3236.19	−0.307731
$481$	10567.2	1.00171
$482$	24922.4	2.35515
$483$	−782.354	−0.0737026
$484$	1745.34	0.163913
$485$	−4332.89	−0.405663
$486$	−11700.3	−1.09205
$487$	−3858.91	−0.359063	−0.179532	−	0.983752i	$-0.557458\pi$
$487$	−3858.91	−0.359063	−0.179532	+	0.983752i	$0.557458\pi$
$488$	18297.0	1.69727
$489$	5219.23	0.482662
$490$	8050.50	0.742213
$491$	4472.32	0.411065	0.205533	−	0.978650i	$-0.434107\pi$
$491$	4472.32	0.411065	0.205533	+	0.978650i	$0.434107\pi$
$492$	−16571.8	−1.51853
$493$	−726.790	−0.0663955
$494$	4829.29	0.439838
$495$	504.005	0.0457643
$496$	4656.94	0.421578
$497$	302.526	0.0273041
$498$	−30613.7	−2.75468
$499$	−4054.80	−0.363763	−0.181881	−	0.983320i	$-0.558219\pi$
$499$	−4054.80	−0.363763	−0.181881	+	0.983320i	$0.558219\pi$
$500$	1803.04	0.161269
$501$	−16237.0	−1.44794
$502$	7229.04	0.642725
$503$	−5864.31	−0.519835	−0.259917	−	0.965631i	$-0.583695\pi$
$503$	−5864.31	−0.519835	−0.259917	+	0.965631i	$0.583695\pi$
$504$	−481.945	−0.0425943
$505$	−1451.87	−0.127936
$506$	−3919.94	−0.344392
$507$	−4113.22	−0.360305
$508$	15493.5	1.35317
$509$	−1874.33	−0.163218	−0.0816091	−	0.996664i	$-0.526006\pi$
$509$	−1874.33	−0.163218	−0.0816091	+	0.996664i	$0.526006\pi$
$510$	3582.19	0.311024
$511$	54.7235	0.00473743
$512$	10061.9	0.868509
$513$	−2037.95	−0.175395
$514$	144.457	0.0123963
$515$	−1482.76	−0.126870
$516$	−31919.4	−2.72321
$517$	1720.69	0.146375
$518$	−1611.72	−0.136708
$519$	−23635.4	−1.99900
$520$	−8164.43	−0.688527
$521$	3175.75	0.267048	0.133524	−	0.991046i	$-0.457371\pi$
$521$	3175.75	0.267048	0.133524	+	0.991046i	$0.457371\pi$
$522$	1253.60	0.105112
$523$	3216.46	0.268921	0.134461	−	0.990919i	$-0.457070\pi$
$523$	3216.46	0.268921	0.134461	+	0.990919i	$0.457070\pi$
$524$	7450.63	0.621149
$525$	−259.906	−0.0216062
$526$	−24126.0	−1.99989
$527$	4087.10	0.337831
$528$	−1896.26	−0.156296
$529$	−6503.90	−0.534553
$530$	−9388.20	−0.769429
$531$	843.093	0.0689023
$532$	−473.793	−0.0386119
$533$	10254.4	0.833333
$534$	17238.4	1.39696
$535$	−5111.95	−0.413100
$536$	10590.8	0.853454
$537$	−12808.5	−1.02929
$538$	−6304.60	−0.505224
$539$	−3740.12	−0.298884
$540$	7735.81	0.616474
$541$	4605.81	0.366024	0.183012	−	0.983111i	$-0.441415\pi$
$541$	4605.81	0.366024	0.183012	+	0.983111i	$0.441415\pi$
$542$	−25870.6	−2.05025
$543$	6378.00	0.504063
$544$	2707.76	0.213408
$545$	2993.80	0.235303
$546$	2642.45	0.207118
$547$	−6175.23	−0.482694	−0.241347	−	0.970439i	$-0.577589\pi$
$547$	−6175.23	−0.482694	−0.241347	+	0.970439i	$0.577589\pi$
$548$	9460.10	0.737437
$549$	−5511.47	−0.428459
$550$	−1302.24	−0.100960
$551$	548.883	0.0424378
$552$	13767.3	1.06155
$553$	−685.351	−0.0527018
$554$	42918.8	3.29141
$555$	−5919.66	−0.452749
$556$	7725.13	0.589242
$557$	23267.1	1.76994	0.884971	−	0.465646i	$-0.154178\pi$
$557$	23267.1	1.76994	0.884971	+	0.465646i	$0.154178\pi$
$558$	−7049.59	−0.534826
$559$	19751.2	1.49443
$560$	247.787	0.0186980
$561$	−1664.22	−0.125247
$562$	−16628.3	−1.24808
$563$	14996.2	1.12259	0.561293	−	0.827617i	$-0.310304\pi$
$563$	14996.2	1.12259	0.561293	+	0.827617i	$0.310304\pi$
$564$	−13568.8	−1.01303
$565$	−2867.92	−0.213547
$566$	−16694.1	−1.23976
$567$	−1542.84	−0.114274
$568$	−5323.64	−0.393266
$569$	−6937.07	−0.511102	−0.255551	−	0.966796i	$-0.582257\pi$
$569$	−6937.07	−0.511102	−0.255551	+	0.966796i	$0.582257\pi$
$570$	−2705.33	−0.198796
$571$	26664.2	1.95423	0.977113	−	0.212723i	$-0.0682332\pi$
$571$	26664.2	1.95423	0.977113	+	0.212723i	$0.0682332\pi$
$572$	8516.44	0.622535
$573$	12554.3	0.915296
$574$	−1564.01	−0.113729
$575$	1881.34	0.136447
$576$	−6771.96	−0.489869
$577$	5809.11	0.419127	0.209563	−	0.977795i	$-0.432796\pi$
$577$	5809.11	0.419127	0.209563	+	0.977795i	$0.432796\pi$
$578$	20267.9	1.45854
$579$	21228.4	1.52370
$580$	−2083.49	−0.149159
$581$	−1858.49	−0.132707
$582$	−24677.7	−1.75760
$583$	4361.60	0.309844
$584$	−962.985	−0.0682339
$585$	2459.31	0.173812
$586$	−41282.6	−2.91019
$587$	−20099.3	−1.41327	−0.706633	−	0.707581i	$-0.749787\pi$
$587$	−20099.3	−1.41327	−0.706633	+	0.707581i	$0.749787\pi$
$588$	29493.4	2.06852
$589$	−3086.64	−0.215930
$590$	−2178.37	−0.152004
$591$	10598.6	0.737679
$592$	5643.63	0.391811
$593$	12953.4	0.897017	0.448508	−	0.893779i	$-0.351955\pi$
$593$	12953.4	0.897017	0.448508	+	0.893779i	$0.351955\pi$
$594$	−5587.18	−0.385934
$595$	217.467	0.0149836
$596$	−28370.7	−1.94985
$597$	−7448.70	−0.510645
$598$	−19127.4	−1.30799
$599$	4093.72	0.279240	0.139620	−	0.990205i	$-0.455412\pi$
$599$	4093.72	0.279240	0.139620	+	0.990205i	$0.455412\pi$
$600$	4573.64	0.311197
$601$	13143.0	0.892035	0.446017	−	0.895024i	$-0.352842\pi$
$601$	13143.0	0.892035	0.446017	+	0.895024i	$0.352842\pi$
$602$	−3012.47	−0.203952
$603$	−3190.17	−0.215446
$604$	15631.8	1.05306
$605$	605.000	0.0406558
$606$	−8269.03	−0.554301
$607$	−2724.47	−0.182180	−0.0910898	−	0.995843i	$-0.529035\pi$
$607$	−2724.47	−0.182180	−0.0910898	+	0.995843i	$0.529035\pi$
$608$	−2044.94	−0.136403
$609$	300.333	0.0199837
$610$	14240.5	0.945214
$611$	8396.16	0.555928
$612$	3325.44	0.219646
$613$	15838.0	1.04354	0.521771	−	0.853086i	$-0.325272\pi$
$613$	15838.0	1.04354	0.521771	+	0.853086i	$0.325272\pi$
$614$	13026.5	0.856201
$615$	−5744.41	−0.376646
$616$	−578.519	−0.0378396
$617$	−9894.27	−0.645589	−0.322795	−	0.946469i	$-0.604622\pi$
$617$	−9894.27	−0.645589	−0.322795	+	0.946469i	$0.604622\pi$
$618$	−8444.94	−0.549685
$619$	5808.39	0.377155	0.188578	−	0.982058i	$-0.439612\pi$
$619$	5808.39	0.377155	0.188578	+	0.982058i	$0.439612\pi$
$620$	11716.5	0.758944
$621$	8071.75	0.521591
$622$	−28638.5	−1.84614
$623$	1046.50	0.0672988
$624$	−9252.84	−0.593606
$625$	625.000	0.0400000
$626$	1407.72	0.0898783
$627$	1256.85	0.0800537
$628$	21996.0	1.39767
$629$	4953.05	0.313976
$630$	−375.095	−0.0237209
$631$	−14129.2	−0.891404	−0.445702	−	0.895181i	$-0.647046\pi$
$631$	−14129.2	−0.891404	−0.445702	+	0.895181i	$0.647046\pi$
$632$	12060.3	0.759072
$633$	−26220.2	−1.64638
$634$	35882.7	2.24777
$635$	5370.61	0.335632
$636$	−34394.1	−2.14437
$637$	−18250.0	−1.13515
$638$	1504.80	0.0933786
$639$	1603.60	0.0992760
$640$	13192.2	0.814792
$641$	6363.05	0.392083	0.196041	−	0.980596i	$-0.437191\pi$
$641$	6363.05	0.392083	0.196041	+	0.980596i	$0.437191\pi$
$642$	−29114.7	−1.78982
$643$	2927.71	0.179561	0.0897806	−	0.995962i	$-0.471383\pi$
$643$	2927.71	0.179561	0.0897806	+	0.995962i	$0.471383\pi$
$644$	1876.56	0.114824
$645$	−11064.5	−0.675446
$646$	2263.58	0.137863
$647$	20186.1	1.22658	0.613290	−	0.789857i	$-0.289846\pi$
$647$	20186.1	1.22658	0.613290	+	0.789857i	$0.289846\pi$
$648$	27149.9	1.64591
$649$	1012.04	0.0612109
$650$	−6354.33	−0.383442
$651$	−1688.92	−0.101680
$652$	−12518.9	−0.751957
$653$	23871.7	1.43058	0.715291	−	0.698827i	$-0.246294\pi$
$653$	23871.7	1.43058	0.715291	+	0.698827i	$0.246294\pi$
$654$	17050.9	1.01949
$655$	2582.66	0.154066
$656$	5476.56	0.325951
$657$	290.072	0.0172250
$658$	−1280.59	−0.0758701
$659$	13970.7	0.825827	0.412913	−	0.910770i	$-0.364511\pi$
$659$	13970.7	0.825827	0.412913	+	0.910770i	$0.364511\pi$
$660$	−4770.83	−0.281370
$661$	−32400.2	−1.90654	−0.953269	−	0.302123i	$-0.902305\pi$
$661$	−32400.2	−1.90654	−0.953269	+	0.302123i	$0.902305\pi$
$662$	12790.3	0.750922
$663$	−8120.63	−0.475685
$664$	32704.3	1.91141
$665$	−164.234	−0.00957703
$666$	−8543.23	−0.497062
$667$	−2173.97	−0.126201
$668$	38946.2	2.25580
$669$	20570.0	1.18876
$670$	8242.73	0.475290
$671$	−6615.89	−0.380631
$672$	−1118.93	−0.0642317
$673$	10598.6	0.607051	0.303526	−	0.952823i	$-0.401836\pi$
$673$	10598.6	0.607051	0.303526	+	0.952823i	$0.401836\pi$
$674$	14187.2	0.810788
$675$	2681.52	0.152906
$676$	9865.97	0.561332
$677$	−18706.0	−1.06193	−0.530967	−	0.847392i	$-0.678171\pi$
$677$	−18706.0	−1.06193	−0.530967	+	0.847392i	$0.678171\pi$
$678$	−16334.0	−0.925227
$679$	−1498.12	−0.0846727
$680$	−3826.82	−0.215812
$681$	−21125.4	−1.18873
$682$	−8462.22	−0.475125
$683$	11201.9	0.627566	0.313783	−	0.949495i	$-0.398404\pi$
$683$	11201.9	0.627566	0.313783	+	0.949495i	$0.398404\pi$
$684$	−2511.43	−0.140390
$685$	3279.22	0.182909
$686$	5591.49	0.311201
$687$	30517.6	1.69479
$688$	10548.5	0.584534
$689$	21282.5	1.17678
$690$	10715.0	0.591180
$691$	−11252.5	−0.619488	−0.309744	−	0.950820i	$-0.600243\pi$
$691$	−11252.5	−0.619488	−0.309744	+	0.950820i	$0.600243\pi$
$692$	56692.0	3.11432
$693$	174.263	0.00955223
$694$	−41495.7	−2.26968
$695$	2677.82	0.146152
$696$	−5285.04	−0.287829
$697$	4806.42	0.261200
$698$	15663.3	0.849374
$699$	−29024.7	−1.57055
$700$	623.411	0.0336610
$701$	24918.2	1.34258	0.671291	−	0.741194i	$-0.265740\pi$
$701$	24918.2	1.34258	0.671291	+	0.741194i	$0.265740\pi$
$702$	−27262.8	−1.46577
$703$	−3740.62	−0.200683
$704$	−8128.95	−0.435187
$705$	−4703.45	−0.251266
$706$	983.411	0.0524237
$707$	−501.994	−0.0267036
$708$	−7980.58	−0.423628
$709$	25731.4	1.36299	0.681497	−	0.731821i	$-0.261329\pi$
$709$	25731.4	1.36299	0.681497	+	0.731821i	$0.261329\pi$
$710$	−4143.36	−0.219011
$711$	−3632.83	−0.191620
$712$	−18415.6	−0.969316
$713$	12225.3	0.642133
$714$	1238.56	0.0649189
$715$	2952.11	0.154409
$716$	30722.5	1.60357
$717$	−3301.15	−0.171944
$718$	−44687.9	−2.32276
$719$	5469.45	0.283694	0.141847	−	0.989889i	$-0.454696\pi$
$719$	5469.45	0.283694	0.141847	+	0.989889i	$0.454696\pi$
$720$	1313.44	0.0679848
$721$	−512.673	−0.0264812
$722$	−1709.49	−0.0881172
$723$	31649.5	1.62802
$724$	−15298.3	−0.785299
$725$	−722.215	−0.0369964
$726$	3445.73	0.176148
$727$	−31075.6	−1.58532	−0.792662	−	0.609661i	$-0.791306\pi$
$727$	−31075.6	−1.58532	−0.792662	+	0.609661i	$0.791306\pi$
$728$	−2822.90	−0.143714
$729$	9237.57	0.469317
$730$	−749.486	−0.0379996
$731$	9257.77	0.468415
$732$	52170.7	2.63427
$733$	16744.4	0.843752	0.421876	−	0.906654i	$-0.361372\pi$
$733$	16744.4	0.843752	0.421876	+	0.906654i	$0.361372\pi$
$734$	−22799.4	−1.14651
$735$	10223.5	0.513061
$736$	8099.42	0.405637
$737$	−3829.43	−0.191396
$738$	−8290.31	−0.413510
$739$	−20006.3	−0.995864	−0.497932	−	0.867216i	$-0.665907\pi$
$739$	−20006.3	−0.995864	−0.497932	+	0.867216i	$0.665907\pi$
$740$	14198.9	0.705355
$741$	6132.82	0.304042
$742$	−3246.03	−0.160600
$743$	−6053.87	−0.298916	−0.149458	−	0.988768i	$-0.547753\pi$
$743$	−6053.87	−0.298916	−0.149458	+	0.988768i	$0.547753\pi$
$744$	29720.4	1.46452
$745$	−9834.35	−0.483628
$746$	−3735.50	−0.183333
$747$	−9851.25	−0.482515
$748$	3991.81	0.195127
$749$	−1767.49	−0.0862251
$750$	3559.64	0.173306
$751$	4045.37	0.196562	0.0982808	−	0.995159i	$-0.468666\pi$
$751$	4045.37	0.196562	0.0982808	+	0.995159i	$0.468666\pi$
$752$	4484.13	0.217446
$753$	9180.32	0.444289
$754$	7342.71	0.354649
$755$	5418.55	0.261194
$756$	2674.70	0.128675
$757$	−27413.3	−1.31618	−0.658092	−	0.752937i	$-0.728636\pi$
$757$	−27413.3	−1.31618	−0.658092	+	0.752937i	$0.728636\pi$
$758$	−6978.31	−0.334385
$759$	−4978.02	−0.238064
$760$	2890.07	0.137940
$761$	−6938.38	−0.330507	−0.165254	−	0.986251i	$-0.552844\pi$
$761$	−6938.38	−0.330507	−0.165254	+	0.986251i	$0.552844\pi$
$762$	30587.9	1.45418
$763$	1035.12	0.0491140
$764$	−30112.8	−1.42597
$765$	1152.72	0.0544794
$766$	−30392.4	−1.43358
$767$	4938.25	0.232477
$768$	39582.7	1.85979
$769$	−17491.7	−0.820242	−0.410121	−	0.912031i	$-0.634513\pi$
$769$	−17491.7	−0.820242	−0.410121	+	0.912031i	$0.634513\pi$
$770$	−450.259	−0.0210730
$771$	183.449	0.00856906
$772$	−50918.4	−2.37383
$773$	−468.006	−0.0217762	−0.0108881	−	0.999941i	$-0.503466\pi$
$773$	−468.006	−0.0217762	−0.0108881	+	0.999941i	$0.503466\pi$
$774$	−15968.2	−0.741556
$775$	4061.37	0.188243
$776$	26362.9	1.21955
$777$	−2046.76	−0.0945007
$778$	4179.60	0.192604
$779$	−3629.88	−0.166950
$780$	−23279.4	−1.06864
$781$	1924.93	0.0881941
$782$	−8965.39	−0.409977
$783$	−3098.61	−0.141424
$784$	−9746.79	−0.444005
$785$	7624.63	0.346668
$786$	14709.4	0.667514
$787$	−27066.8	−1.22595	−0.612977	−	0.790101i	$-0.710028\pi$
$787$	−27066.8	−1.22595	−0.612977	+	0.790101i	$0.710028\pi$
$788$	−25421.8	−1.14926
$789$	−30638.1	−1.38244
$790$	9386.47	0.422729
$791$	−991.601	−0.0445730
$792$	−3066.55	−0.137582
$793$	−32282.4	−1.44563
$794$	−57967.9	−2.59094
$795$	−11922.3	−0.531874
$796$	17866.5	0.795553
$797$	−39944.8	−1.77530	−0.887651	−	0.460516i	$-0.847664\pi$
$797$	−39944.8	−1.77530	−0.887651	+	0.460516i	$0.847664\pi$
$798$	−935.383	−0.0414940
$799$	3935.44	0.174250
$800$	2690.71	0.118914
$801$	5547.18	0.244694
$802$	−69332.5	−3.05264
$803$	348.198	0.0153022
$804$	30197.6	1.32461
$805$	650.484	0.0284802
$806$	−41291.6	−1.80451
$807$	−8006.35	−0.349240
$808$	8833.72	0.384616
$809$	−42005.1	−1.82549	−0.912745	−	0.408530i	$-0.866041\pi$
$809$	−42005.1	−1.82549	−0.912745	+	0.408530i	$0.866041\pi$
$810$	21130.6	0.916609
$811$	43668.6	1.89077	0.945383	−	0.325962i	$-0.105688\pi$
$811$	43668.6	1.89077	0.945383	+	0.325962i	$0.105688\pi$
$812$	−720.379	−0.0311334
$813$	−32853.6	−1.41725
$814$	−10255.2	−0.441576
$815$	−4339.50	−0.186511
$816$	−4336.98	−0.186060
$817$	−6991.61	−0.299395
$818$	−17243.7	−0.737055
$819$	850.320	0.0362791
$820$	13778.6	0.586791
$821$	−9211.19	−0.391562	−0.195781	−	0.980648i	$-0.562724\pi$
$821$	−9211.19	−0.391562	−0.195781	+	0.980648i	$0.562724\pi$
$822$	18676.6	0.792482
$823$	16306.4	0.690648	0.345324	−	0.938483i	$-0.387769\pi$
$823$	16306.4	0.690648	0.345324	+	0.938483i	$0.387769\pi$
$824$	9021.65	0.381413
$825$	−1653.75	−0.0697892
$826$	−753.186	−0.0317272
$827$	37257.0	1.56657	0.783285	−	0.621663i	$-0.213543\pi$
$827$	37257.0	1.56657	0.783285	+	0.621663i	$0.213543\pi$
$828$	9947.04	0.417492
$829$	5762.95	0.241442	0.120721	−	0.992686i	$-0.461479\pi$
$829$	5762.95	0.241442	0.120721	+	0.992686i	$0.461479\pi$
$830$	25453.6	1.06447
$831$	54503.5	2.27522
$832$	−39665.4	−1.65283
$833$	−8554.13	−0.355802
$834$	15251.3	0.633225
$835$	13500.2	0.559513
$836$	−3014.68	−0.124719
$837$	17425.0	0.719589
$838$	68179.3	2.81052
$839$	25975.1	1.06884	0.534422	−	0.845218i	$-0.320529\pi$
$839$	25975.1	1.06884	0.534422	+	0.845218i	$0.320529\pi$
$840$	1581.36	0.0649551
$841$	−23554.4	−0.965782
$842$	−29181.2	−1.19436
$843$	−21116.6	−0.862746
$844$	62891.9	2.56496
$845$	3419.91	0.139229
$846$	−6788.00	−0.275858
$847$	209.182	0.00848594
$848$	11366.4	0.460286
$849$	−21200.2	−0.856996
$850$	−2978.39	−0.120186
$851$	14815.5	0.596792
$852$	−15179.4	−0.610373
$853$	34485.1	1.38423	0.692114	−	0.721788i	$-0.256680\pi$
$853$	34485.1	1.38423	0.692114	+	0.721788i	$0.256680\pi$
$854$	4923.74	0.197291
$855$	−870.554	−0.0348214
$856$	31103.0	1.24191
$857$	5258.40	0.209596	0.104798	−	0.994494i	$-0.466580\pi$
$857$	5258.40	0.209596	0.104798	+	0.994494i	$0.466580\pi$
$858$	16813.5	0.669003
$859$	37848.9	1.50336	0.751681	−	0.659527i	$-0.229244\pi$
$859$	37848.9	1.50336	0.751681	+	0.659527i	$0.229244\pi$
$860$	26539.3	1.05230
$861$	−1986.17	−0.0786160
$862$	−11025.8	−0.435660
$863$	23378.8	0.922160	0.461080	−	0.887359i	$-0.347462\pi$
$863$	23378.8	0.922160	0.461080	+	0.887359i	$0.347462\pi$
$864$	11544.3	0.454566
$865$	19651.6	0.772455
$866$	−202.507	−0.00794628
$867$	25738.7	1.00822
$868$	4051.04	0.158412
$869$	−4360.79	−0.170230
$870$	−4113.32	−0.160293
$871$	−18685.8	−0.726917
$872$	−18215.4	−0.707397
$873$	−7941.09	−0.307864
$874$	6770.80	0.262043
$875$	216.098	0.00834906
$876$	−2745.78	−0.105903
$877$	17154.7	0.660516	0.330258	−	0.943891i	$-0.392864\pi$
$877$	17154.7	0.660516	0.330258	+	0.943891i	$0.392864\pi$
$878$	5140.03	0.197571
$879$	−52425.7	−2.01169
$880$	1576.63	0.0603958
$881$	−22880.4	−0.874982	−0.437491	−	0.899223i	$-0.644133\pi$
$881$	−22880.4	−0.874982	−0.437491	+	0.899223i	$0.644133\pi$
$882$	14754.5	0.563277
$883$	7342.92	0.279852	0.139926	−	0.990162i	$-0.455314\pi$
$883$	7342.92	0.279852	0.139926	+	0.990162i	$0.455314\pi$
$884$	19478.2	0.741087
$885$	−2766.37	−0.105074
$886$	30261.7	1.14748
$887$	−1590.30	−0.0601995	−0.0300997	−	0.999547i	$-0.509582\pi$
$887$	−1590.30	−0.0601995	−0.0300997	+	0.999547i	$0.509582\pi$
$888$	36017.4	1.36111
$889$	1856.92	0.0700553
$890$	−14332.7	−0.539814
$891$	−9816.91	−0.369112
$892$	−49339.3	−1.85202
$893$	−2972.10	−0.111375
$894$	−56010.8	−2.09539
$895$	10649.6	0.397738
$896$	4561.28	0.170069
$897$	−24290.4	−0.904160
$898$	−7191.49	−0.267242
$899$	−4693.09	−0.174108
$900$	3304.51	0.122389
$901$	9975.52	0.368849
$902$	−9951.56	−0.367351
$903$	−3825.61	−0.140984
$904$	17449.5	0.641992
$905$	−5302.96	−0.194780
$906$	30861.0	1.13166
$907$	−16149.0	−0.591200	−0.295600	−	0.955312i	$-0.595520\pi$
$907$	−16149.0	−0.591200	−0.295600	+	0.955312i	$0.595520\pi$
$908$	50671.4	1.85197
$909$	−2660.91	−0.0970923
$910$	−2197.05	−0.0800346
$911$	42737.6	1.55429	0.777146	−	0.629320i	$-0.216667\pi$
$911$	42737.6	1.55429	0.777146	+	0.629320i	$0.216667\pi$
$912$	3275.36	0.118923
$913$	−11825.3	−0.428653
$914$	45616.1	1.65082
$915$	18084.3	0.653387
$916$	−73199.6	−2.64037
$917$	892.972	0.0321576
$918$	−12778.6	−0.459429
$919$	−20208.7	−0.725380	−0.362690	−	0.931910i	$-0.618142\pi$
$919$	−20208.7	−0.725380	−0.362690	+	0.931910i	$0.618142\pi$
$920$	−11446.8	−0.410205
$921$	16542.7	0.591856
$922$	533.192	0.0190453
$923$	9392.77	0.334959
$924$	−1649.54	−0.0587295
$925$	4921.87	0.174952
$926$	−75507.2	−2.67961
$927$	−2717.52	−0.0962838
$928$	−3109.23	−0.109984
$929$	−53424.5	−1.88676	−0.943381	−	0.331712i	$-0.892374\pi$
$929$	−53424.5	−1.88676	−0.943381	+	0.331712i	$0.892374\pi$
$930$	23131.2	0.815594
$931$	6460.22	0.227417
$932$	69618.6	2.44682
$933$	−36368.6	−1.27616
$934$	58186.0	2.03844
$935$	1383.71	0.0483981
$936$	−14963.3	−0.522534
$937$	45963.8	1.60253	0.801266	−	0.598308i	$-0.204160\pi$
$937$	45963.8	1.60253	0.801266	+	0.598308i	$0.204160\pi$
$938$	2849.97	0.0992057
$939$	1787.69	0.0621291
$940$	11281.7	0.391456
$941$	−12160.2	−0.421265	−0.210632	−	0.977565i	$-0.567552\pi$
$941$	−12160.2	−0.421265	−0.210632	+	0.977565i	$0.567552\pi$
$942$	43425.5	1.50199
$943$	14376.9	0.496476
$944$	2637.37	0.0909313
$945$	927.151	0.0319156
$946$	−19168.0	−0.658778
$947$	21326.8	0.731815	0.365908	−	0.930651i	$-0.380759\pi$
$947$	21326.8	0.731815	0.365908	+	0.930651i	$0.380759\pi$
$948$	34387.8	1.17813
$949$	1699.04	0.0581172
$950$	2249.33	0.0768188
$951$	45568.2	1.55379
$952$	−1323.15	−0.0450456
$953$	20429.1	0.694399	0.347199	−	0.937791i	$-0.387133\pi$
$953$	20429.1	0.694399	0.347199	+	0.937791i	$0.387133\pi$
$954$	−17206.2	−0.583932
$955$	−10438.2	−0.353689
$956$	7918.14	0.267878
$957$	1910.98	0.0645487
$958$	42980.2	1.44951
$959$	1133.81	0.0381780
$960$	22220.2	0.747036
$961$	−3399.48	−0.114111
$962$	−50040.3	−1.67709
$963$	−9368.90	−0.313508
$964$	−75914.5	−2.53635
$965$	−17650.2	−0.588788
$966$	3704.78	0.123395
$967$	1005.88	0.0334507	0.0167253	−	0.999860i	$-0.494676\pi$
$967$	1005.88	0.0334507	0.0167253	+	0.999860i	$0.494676\pi$
$968$	−3681.04	−0.122224
$969$	2874.57	0.0952988
$970$	20518.1	0.679172
$971$	28570.9	0.944267	0.472133	−	0.881527i	$-0.343484\pi$
$971$	28570.9	0.944267	0.472133	+	0.881527i	$0.343484\pi$
$972$	35639.6	1.17607
$973$	925.872	0.0305057
$974$	18273.6	0.601153
$975$	−8069.51	−0.265057
$976$	−17241.1	−0.565443
$977$	−8545.27	−0.279823	−0.139912	−	0.990164i	$-0.544682\pi$
$977$	−8545.27	−0.279823	−0.139912	+	0.990164i	$0.544682\pi$
$978$	−24715.3	−0.808086
$979$	6658.75	0.217379
$980$	−24522.1	−0.799317
$981$	5486.87	0.178575
$982$	−21178.4	−0.688216
$983$	−587.670	−0.0190679	−0.00953397	−	0.999955i	$-0.503035\pi$
$983$	−587.670	−0.0190679	−0.00953397	+	0.999955i	$0.503035\pi$
$984$	34951.1	1.13232
$985$	−8812.16	−0.285055
$986$	3441.66	0.111161
$987$	−1626.25	−0.0524458
$988$	−14710.2	−0.473678
$989$	27691.8	0.890341
$990$	−2386.68	−0.0766199
$991$	49743.8	1.59451	0.797257	−	0.603640i	$-0.206284\pi$
$991$	49743.8	1.59451	0.797257	+	0.603640i	$0.206284\pi$
$992$	17484.7	0.559618
$993$	16242.7	0.519081
$994$	−1432.59	−0.0457134
$995$	6193.18	0.197324
$996$	93250.4	2.96662
$997$	−19432.5	−0.617285	−0.308643	−	0.951178i	$-0.599875\pi$
$997$	−19432.5	−0.617285	−0.308643	+	0.951178i	$0.599875\pi$
$998$	19201.2	0.609021
$999$	21116.9	0.668779

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.4.a.e.1.2	✓	22

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

\(f(q)\)	\(=\)	\(q-4.73543 q^{2} -6.01363 q^{3} +14.4243 q^{4} +5.00000 q^{5} +28.4771 q^{6} +1.72878 q^{7} -30.4218 q^{8} +9.16373 q^{9} +O(q^{10})\)	\(q-4.73543 q^{2} -6.01363 q^{3} +14.4243 q^{4} +5.00000 q^{5} +28.4771 q^{6} +1.72878 q^{7} -30.4218 q^{8} +9.16373 q^{9} -23.6772 q^{10} +11.0000 q^{11} -86.7424 q^{12} +53.6748 q^{13} -8.18652 q^{14} -30.0681 q^{15} +28.6661 q^{16} +25.1584 q^{17} -43.3942 q^{18} -19.0000 q^{19} +72.1215 q^{20} -10.3962 q^{21} -52.0897 q^{22} +75.2535 q^{23} +182.946 q^{24} +25.0000 q^{25} -254.173 q^{26} +107.261 q^{27} +24.9365 q^{28} -28.8886 q^{29} +142.386 q^{30} +162.455 q^{31} +107.628 q^{32} -66.1499 q^{33} -119.136 q^{34} +8.64390 q^{35} +132.180 q^{36} +196.875 q^{37} +89.9732 q^{38} -322.780 q^{39} -152.109 q^{40} +191.047 q^{41} +49.2307 q^{42} +367.980 q^{43} +158.667 q^{44} +45.8186 q^{45} -356.358 q^{46} +156.426 q^{47} -172.387 q^{48} -340.011 q^{49} -118.386 q^{50} -151.293 q^{51} +774.221 q^{52} +396.509 q^{53} -507.926 q^{54} +55.0000 q^{55} -52.5927 q^{56} +114.259 q^{57} +136.800 q^{58} +92.0032 q^{59} -433.712 q^{60} -601.444 q^{61} -769.293 q^{62} +15.8421 q^{63} -738.996 q^{64} +268.374 q^{65} +313.248 q^{66} -348.130 q^{67} +362.892 q^{68} -452.547 q^{69} -40.9326 q^{70} +174.994 q^{71} -278.777 q^{72} +31.6544 q^{73} -932.287 q^{74} -150.341 q^{75} -274.062 q^{76} +19.0166 q^{77} +1528.50 q^{78} -396.436 q^{79} +143.330 q^{80} -892.447 q^{81} -904.687 q^{82} -1075.03 q^{83} -149.959 q^{84} +125.792 q^{85} -1742.54 q^{86} +173.725 q^{87} -334.640 q^{88} +605.341 q^{89} -216.971 q^{90} +92.7919 q^{91} +1085.48 q^{92} -976.942 q^{93} -740.746 q^{94} -95.0000 q^{95} -647.238 q^{96} -866.579 q^{97} +1610.10 q^{98} +100.801 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 12 q^{2} + 21 q^{3} + 96 q^{4} + 110 q^{5} + 27 q^{6} + 93 q^{7} + 114 q^{8} + 209 q^{9}+O(q^{10}) \) 22 * q + 12 * q^2 + 21 * q^3 + 96 * q^4 + 110 * q^5 + 27 * q^6 + 93 * q^7 + 114 * q^8 + 209 * q^9	\( 22 q + 12 q^{2} + 21 q^{3} + 96 q^{4} + 110 q^{5} + 27 q^{6} + 93 q^{7} + 114 q^{8} + 209 q^{9} + 60 q^{10} + 242 q^{11} + 164 q^{12} + 207 q^{13} + 129 q^{14} + 105 q^{15} + 604 q^{16} + 209 q^{17} + 869 q^{18} - 418 q^{19} + 480 q^{20} + 45 q^{21} + 132 q^{22} + 191 q^{23} + 458 q^{24} + 550 q^{25} + 363 q^{26} + 45 q^{27} + 577 q^{28} + 389 q^{29} + 135 q^{30} + 198 q^{31} + 1149 q^{32} + 231 q^{33} + 467 q^{34} + 465 q^{35} + 1315 q^{36} + 312 q^{37} - 228 q^{38} + 137 q^{39} + 570 q^{40} + 632 q^{41} - 1794 q^{42} + 1584 q^{43} + 1056 q^{44} + 1045 q^{45} + 681 q^{46} - 54 q^{47} + 2491 q^{48} + 1063 q^{49} + 300 q^{50} + 37 q^{51} + 1246 q^{52} + 343 q^{53} + 1078 q^{54} + 1210 q^{55} - 87 q^{56} - 399 q^{57} - 1424 q^{58} + 2787 q^{59} + 820 q^{60} + 2070 q^{61} - 446 q^{62} + 1696 q^{63} + 1758 q^{64} + 1035 q^{65} + 297 q^{66} + 2423 q^{67} - 524 q^{68} - 997 q^{69} + 645 q^{70} + 2538 q^{71} + 6010 q^{72} + 1397 q^{73} - 1977 q^{74} + 525 q^{75} - 1824 q^{76} + 1023 q^{77} + 202 q^{78} + 878 q^{79} + 3020 q^{80} + 2030 q^{81} - 190 q^{82} + 4932 q^{83} - 4580 q^{84} + 1045 q^{85} - 3394 q^{86} + 6009 q^{87} + 1254 q^{88} + 1812 q^{89} + 4345 q^{90} + 4349 q^{91} - 788 q^{92} - 4848 q^{93} - 2152 q^{94} - 2090 q^{95} + 4032 q^{96} + 988 q^{97} + 1366 q^{98} + 2299 q^{99}+O(q^{100}) \) 22 * q + 12 * q^2 + 21 * q^3 + 96 * q^4 + 110 * q^5 + 27 * q^6 + 93 * q^7 + 114 * q^8 + 209 * q^9 + 60 * q^10 + 242 * q^11 + 164 * q^12 + 207 * q^13 + 129 * q^14 + 105 * q^15 + 604 * q^16 + 209 * q^17 + 869 * q^18 - 418 * q^19 + 480 * q^20 + 45 * q^21 + 132 * q^22 + 191 * q^23 + 458 * q^24 + 550 * q^25 + 363 * q^26 + 45 * q^27 + 577 * q^28 + 389 * q^29 + 135 * q^30 + 198 * q^31 + 1149 * q^32 + 231 * q^33 + 467 * q^34 + 465 * q^35 + 1315 * q^36 + 312 * q^37 - 228 * q^38 + 137 * q^39 + 570 * q^40 + 632 * q^41 - 1794 * q^42 + 1584 * q^43 + 1056 * q^44 + 1045 * q^45 + 681 * q^46 - 54 * q^47 + 2491 * q^48 + 1063 * q^49 + 300 * q^50 + 37 * q^51 + 1246 * q^52 + 343 * q^53 + 1078 * q^54 + 1210 * q^55 - 87 * q^56 - 399 * q^57 - 1424 * q^58 + 2787 * q^59 + 820 * q^60 + 2070 * q^61 - 446 * q^62 + 1696 * q^63 + 1758 * q^64 + 1035 * q^65 + 297 * q^66 + 2423 * q^67 - 524 * q^68 - 997 * q^69 + 645 * q^70 + 2538 * q^71 + 6010 * q^72 + 1397 * q^73 - 1977 * q^74 + 525 * q^75 - 1824 * q^76 + 1023 * q^77 + 202 * q^78 + 878 * q^79 + 3020 * q^80 + 2030 * q^81 - 190 * q^82 + 4932 * q^83 - 4580 * q^84 + 1045 * q^85 - 3394 * q^86 + 6009 * q^87 + 1254 * q^88 + 1812 * q^89 + 4345 * q^90 + 4349 * q^91 - 788 * q^92 - 4848 * q^93 - 2152 * q^94 - 2090 * q^95 + 4032 * q^96 + 988 * q^97 + 1366 * q^98 + 2299 * q^99

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