LMFDB - Embedded newform 1045.4.a.h.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1045.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$61.6569959560$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.40259 q^{2} +2.52468 q^{3} -6.03275 q^{4} +5.00000 q^{5} +3.54108 q^{6} -33.4174 q^{7} -19.6821 q^{8} -20.6260 q^{9} +O(q^{10})$	\(q+1.40259 q^{2} +2.52468 q^{3} -6.03275 q^{4} +5.00000 q^{5} +3.54108 q^{6} -33.4174 q^{7} -19.6821 q^{8} -20.6260 q^{9} +7.01293 q^{10} -11.0000 q^{11} -15.2307 q^{12} +52.2841 q^{13} -46.8708 q^{14} +12.6234 q^{15} +20.6561 q^{16} +17.7211 q^{17} -28.9298 q^{18} +19.0000 q^{19} -30.1638 q^{20} -84.3681 q^{21} -15.4285 q^{22} -23.0164 q^{23} -49.6911 q^{24} +25.0000 q^{25} +73.3329 q^{26} -120.240 q^{27} +201.599 q^{28} -171.243 q^{29} +17.7054 q^{30} -134.783 q^{31} +186.429 q^{32} -27.7714 q^{33} +24.8554 q^{34} -167.087 q^{35} +124.432 q^{36} -334.317 q^{37} +26.6491 q^{38} +132.000 q^{39} -98.4107 q^{40} +519.707 q^{41} -118.334 q^{42} +249.112 q^{43} +66.3603 q^{44} -103.130 q^{45} -32.2825 q^{46} +108.503 q^{47} +52.1500 q^{48} +773.722 q^{49} +35.0647 q^{50} +44.7400 q^{51} -315.417 q^{52} -22.6372 q^{53} -168.647 q^{54} -55.0000 q^{55} +657.726 q^{56} +47.9689 q^{57} -240.183 q^{58} +713.208 q^{59} -76.1537 q^{60} +307.142 q^{61} -189.044 q^{62} +689.267 q^{63} +96.2342 q^{64} +261.420 q^{65} -38.9518 q^{66} +759.172 q^{67} -106.907 q^{68} -58.1089 q^{69} -234.354 q^{70} -350.932 q^{71} +405.964 q^{72} +182.291 q^{73} -468.909 q^{74} +63.1169 q^{75} -114.622 q^{76} +367.591 q^{77} +185.142 q^{78} +214.617 q^{79} +103.280 q^{80} +253.334 q^{81} +728.934 q^{82} +1340.06 q^{83} +508.972 q^{84} +88.6055 q^{85} +349.401 q^{86} -432.334 q^{87} +216.504 q^{88} -1127.45 q^{89} -144.649 q^{90} -1747.20 q^{91} +138.852 q^{92} -340.282 q^{93} +152.185 q^{94} +95.0000 q^{95} +470.673 q^{96} -682.861 q^{97} +1085.21 q^{98} +226.886 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} + 21 q^{3} + 98 q^{4} + 120 q^{5} + 15 q^{6} + 71 q^{7} + 84 q^{8} + 339 q^{9}+O(q^{10}) $ 24 * q + 4 * q^2 + 21 * q^3 + 98 * q^4 + 120 * q^5 + 15 * q^6 + 71 * q^7 + 84 * q^8 + 339 * q^9	\( 24 q + 4 q^{2} + 21 q^{3} + 98 q^{4} + 120 q^{5} + 15 q^{6} + 71 q^{7} + 84 q^{8} + 339 q^{9} + 20 q^{10} - 264 q^{11} + 164 q^{12} - 15 q^{13} + 77 q^{14} + 105 q^{15} + 230 q^{16} + 187 q^{17} - 109 q^{18} + 456 q^{19} + 490 q^{20} + 295 q^{21} - 44 q^{22} + 451 q^{23} + 416 q^{24} + 600 q^{25} + 375 q^{26} + 1335 q^{27} + 815 q^{28} + 271 q^{29} + 75 q^{30} + 302 q^{31} + 1181 q^{32} - 231 q^{33} + 285 q^{34} + 355 q^{35} + 2445 q^{36} + 974 q^{37} + 76 q^{38} + 601 q^{39} + 420 q^{40} + 316 q^{41} + 2158 q^{42} + 686 q^{43} - 1078 q^{44} + 1695 q^{45} - 217 q^{46} + 1798 q^{47} + 353 q^{48} + 1845 q^{49} + 100 q^{50} + 383 q^{51} - 134 q^{52} + 815 q^{53} - 974 q^{54} - 1320 q^{55} + 2001 q^{56} + 399 q^{57} - 888 q^{58} + 1793 q^{59} + 820 q^{60} + 62 q^{61} + 3994 q^{62} + 366 q^{63} - 588 q^{64} - 75 q^{65} - 165 q^{66} + 2363 q^{67} - 1720 q^{68} - 287 q^{69} + 385 q^{70} + 1266 q^{71} + 3838 q^{72} + 127 q^{73} - 2861 q^{74} + 525 q^{75} + 1862 q^{76} - 781 q^{77} - 3916 q^{78} - 1922 q^{79} + 1150 q^{80} + 3688 q^{81} + 2666 q^{82} + 3666 q^{83} + 438 q^{84} + 935 q^{85} + 78 q^{86} + 2685 q^{87} - 924 q^{88} + 2344 q^{89} - 545 q^{90} + 127 q^{91} + 4800 q^{92} + 1344 q^{93} + 1756 q^{94} + 2280 q^{95} + 2874 q^{96} + 1182 q^{97} - 4328 q^{98} - 3729 q^{99}+O(q^{100}) \) 24 * q + 4 * q^2 + 21 * q^3 + 98 * q^4 + 120 * q^5 + 15 * q^6 + 71 * q^7 + 84 * q^8 + 339 * q^9 + 20 * q^10 - 264 * q^11 + 164 * q^12 - 15 * q^13 + 77 * q^14 + 105 * q^15 + 230 * q^16 + 187 * q^17 - 109 * q^18 + 456 * q^19 + 490 * q^20 + 295 * q^21 - 44 * q^22 + 451 * q^23 + 416 * q^24 + 600 * q^25 + 375 * q^26 + 1335 * q^27 + 815 * q^28 + 271 * q^29 + 75 * q^30 + 302 * q^31 + 1181 * q^32 - 231 * q^33 + 285 * q^34 + 355 * q^35 + 2445 * q^36 + 974 * q^37 + 76 * q^38 + 601 * q^39 + 420 * q^40 + 316 * q^41 + 2158 * q^42 + 686 * q^43 - 1078 * q^44 + 1695 * q^45 - 217 * q^46 + 1798 * q^47 + 353 * q^48 + 1845 * q^49 + 100 * q^50 + 383 * q^51 - 134 * q^52 + 815 * q^53 - 974 * q^54 - 1320 * q^55 + 2001 * q^56 + 399 * q^57 - 888 * q^58 + 1793 * q^59 + 820 * q^60 + 62 * q^61 + 3994 * q^62 + 366 * q^63 - 588 * q^64 - 75 * q^65 - 165 * q^66 + 2363 * q^67 - 1720 * q^68 - 287 * q^69 + 385 * q^70 + 1266 * q^71 + 3838 * q^72 + 127 * q^73 - 2861 * q^74 + 525 * q^75 + 1862 * q^76 - 781 * q^77 - 3916 * q^78 - 1922 * q^79 + 1150 * q^80 + 3688 * q^81 + 2666 * q^82 + 3666 * q^83 + 438 * q^84 + 935 * q^85 + 78 * q^86 + 2685 * q^87 - 924 * q^88 + 2344 * q^89 - 545 * q^90 + 127 * q^91 + 4800 * q^92 + 1344 * q^93 + 1756 * q^94 + 2280 * q^95 + 2874 * q^96 + 1182 * q^97 - 4328 * q^98 - 3729 * 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 $

$2$	1.40259	0.495889	0.247945	−	0.968774i	$-0.420245\pi$
$2$	1.40259	0.495889	0.247945	+	0.968774i	$0.420245\pi$
$3$	2.52468	0.485874	0.242937	−	0.970042i	$-0.421889\pi$
$3$	2.52468	0.485874	0.242937	+	0.970042i	$0.421889\pi$
$4$	−6.03275	−0.754094
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	3.54108	0.240940
$7$	−33.4174	−1.80437	−0.902185	−	0.431350i	$-0.858037\pi$
$7$	−33.4174	−1.80437	−0.902185	+	0.431350i	$0.858037\pi$
$8$	−19.6821	−0.869836
$9$	−20.6260	−0.763926
$10$	7.01293	0.221768
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−15.2307	−0.366395
$13$	52.2841	1.11546	0.557731	−	0.830022i	$-0.311672\pi$
$13$	52.2841	1.11546	0.557731	+	0.830022i	$0.311672\pi$
$14$	−46.8708	−0.894767
$15$	12.6234	0.217290
$16$	20.6561	0.322752
$17$	17.7211	0.252823	0.126412	−	0.991978i	$-0.459654\pi$
$17$	17.7211	0.252823	0.126412	+	0.991978i	$0.459654\pi$
$18$	−28.9298	−0.378823
$19$	19.0000	0.229416
$19$	19.0000	0.229416
$20$	−30.1638	−0.337241
$21$	−84.3681	−0.876697
$22$	−15.4285	−0.149516
$23$	−23.0164	−0.208663	−0.104331	−	0.994543i	$-0.533270\pi$
$23$	−23.0164	−0.208663	−0.104331	+	0.994543i	$0.533270\pi$
$24$	−49.6911	−0.422631
$25$	25.0000	0.200000
$26$	73.3329	0.553145
$27$	−120.240	−0.857046
$28$	201.599	1.36066
$29$	−171.243	−1.09652	−0.548260	−	0.836308i	$-0.684710\pi$
$29$	−171.243	−1.09652	−0.548260	+	0.836308i	$0.684710\pi$
$30$	17.7054	0.107752
$31$	−134.783	−0.780892	−0.390446	−	0.920626i	$-0.627679\pi$
$31$	−134.783	−0.780892	−0.390446	+	0.920626i	$0.627679\pi$
$32$	186.429	1.02989
$33$	−27.7714	−0.146497
$34$	24.8554	0.125372
$35$	−167.087	−0.806938
$36$	124.432	0.576072
$37$	−334.317	−1.48544	−0.742721	−	0.669601i	$-0.766465\pi$
$37$	−334.317	−1.48544	−0.742721	+	0.669601i	$0.766465\pi$
$38$	26.6491	0.113765
$39$	132.000	0.541974
$40$	−98.4107	−0.389003
$41$	519.707	1.97963	0.989813	−	0.142376i	$-0.0454743\pi$
$41$	519.707	1.97963	0.989813	+	0.142376i	$0.0454743\pi$
$42$	−118.334	−0.434744
$43$	249.112	0.883470	0.441735	−	0.897145i	$-0.354363\pi$
$43$	249.112	0.883470	0.441735	+	0.897145i	$0.354363\pi$
$44$	66.3603	0.227368
$45$	−103.130	−0.341638
$46$	−32.2825	−0.103474
$47$	108.503	0.336740	0.168370	−	0.985724i	$-0.446150\pi$
$47$	108.503	0.336740	0.168370	+	0.985724i	$0.446150\pi$
$48$	52.1500	0.156817
$49$	773.722	2.25575
$50$	35.0647	0.0991778
$51$	44.7400	0.122840
$52$	−315.417	−0.841162
$53$	−22.6372	−0.0586691	−0.0293346	−	0.999570i	$-0.509339\pi$
$53$	−22.6372	−0.0586691	−0.0293346	+	0.999570i	$0.509339\pi$
$54$	−168.647	−0.425000
$55$	−55.0000	−0.134840
$56$	657.726	1.56951
$57$	47.9689	0.111467
$58$	−240.183	−0.543752
$59$	713.208	1.57376	0.786879	−	0.617107i	$-0.211696\pi$
$59$	713.208	1.57376	0.786879	+	0.617107i	$0.211696\pi$
$60$	−76.1537	−0.163857
$61$	307.142	0.644680	0.322340	−	0.946624i	$-0.395531\pi$
$61$	307.142	0.644680	0.322340	+	0.946624i	$0.395531\pi$
$62$	−189.044	−0.387236
$63$	689.267	1.37840
$64$	96.2342	0.187957
$65$	261.420	0.498849
$66$	−38.9518	−0.0726461
$67$	759.172	1.38429	0.692146	−	0.721757i	$-0.256665\pi$
$67$	759.172	1.38429	0.692146	+	0.721757i	$0.256665\pi$
$68$	−106.907	−0.190652
$69$	−58.1089	−0.101384
$70$	−234.354	−0.400152
$71$	−350.932	−0.586591	−0.293296	−	0.956022i	$-0.594752\pi$
$71$	−350.932	−0.586591	−0.293296	+	0.956022i	$0.594752\pi$
$72$	405.964	0.664491
$73$	182.291	0.292268	0.146134	−	0.989265i	$-0.453317\pi$
$73$	182.291	0.292268	0.146134	+	0.989265i	$0.453317\pi$
$74$	−468.909	−0.736615
$75$	63.1169	0.0971748
$76$	−114.622	−0.173001
$77$	367.591	0.544038
$78$	185.142	0.268759
$79$	214.617	0.305649	0.152824	−	0.988253i	$-0.451163\pi$
$79$	214.617	0.305649	0.152824	+	0.988253i	$0.451163\pi$
$80$	103.280	0.144339
$81$	253.334	0.347509
$82$	728.934	0.981675
$83$	1340.06	1.77218	0.886090	−	0.463512i	$-0.153411\pi$
$83$	1340.06	1.77218	0.886090	+	0.463512i	$0.153411\pi$
$84$	508.972	0.661112
$85$	88.6055	0.113066
$86$	349.401	0.438103
$87$	−432.334	−0.532771
$88$	216.504	0.262265
$89$	−1127.45	−1.34280	−0.671401	−	0.741094i	$-0.734307\pi$
$89$	−1127.45	−1.34280	−0.671401	+	0.741094i	$0.734307\pi$
$90$	−144.649	−0.169415
$91$	−1747.20	−2.01270
$92$	138.852	0.157351
$93$	−340.282	−0.379415
$94$	152.185	0.166986
$95$	95.0000	0.102598
$96$	470.673	0.500395
$97$	−682.861	−0.714784	−0.357392	−	0.933954i	$-0.616334\pi$
$97$	−682.861	−0.714784	−0.357392	+	0.933954i	$0.616334\pi$
$98$	1085.21	1.11860
$99$	226.886	0.230332
$100$	−150.819	−0.150819
$101$	1017.77	1.00269	0.501347	−	0.865247i	$-0.332838\pi$
$101$	1017.77	1.00269	0.501347	+	0.865247i	$0.332838\pi$
$102$	62.7518	0.0609152
$103$	1083.32	1.03634	0.518168	−	0.855279i	$-0.326614\pi$
$103$	1083.32	1.03634	0.518168	+	0.855279i	$0.326614\pi$
$104$	−1029.06	−0.970268
$105$	−421.840	−0.392071
$106$	−31.7507	−0.0290934
$107$	408.170	0.368778	0.184389	−	0.982853i	$-0.440969\pi$
$107$	408.170	0.368778	0.184389	+	0.982853i	$0.440969\pi$
$108$	725.380	0.646293
$109$	−1996.28	−1.75421	−0.877103	−	0.480302i	$-0.840527\pi$
$109$	−1996.28	−1.75421	−0.877103	+	0.480302i	$0.840527\pi$
$110$	−77.1423	−0.0668657
$111$	−844.042	−0.721738
$112$	−690.273	−0.582363
$113$	−409.153	−0.340619	−0.170309	−	0.985391i	$-0.554477\pi$
$113$	−409.153	−0.340619	−0.170309	+	0.985391i	$0.554477\pi$
$114$	67.2805	0.0552754
$115$	−115.082	−0.0933169
$116$	1033.07	0.826879
$117$	−1078.41	−0.852130
$118$	1000.34	0.780410
$119$	−592.193	−0.456187
$120$	−248.455	−0.189006
$121$	121.000	0.0909091
$122$	430.793	0.319690
$123$	1312.09	0.961849
$124$	813.109	0.588866
$125$	125.000	0.0894427
$126$	966.757	0.683536
$127$	−2572.35	−1.79732	−0.898658	−	0.438650i	$-0.855457\pi$
$127$	−2572.35	−1.79732	−0.898658	+	0.438650i	$0.855457\pi$
$128$	−1356.46	−0.936679
$129$	628.927	0.429256
$130$	366.665	0.247374
$131$	−996.611	−0.664689	−0.332345	−	0.943158i	$-0.607840\pi$
$131$	−996.611	−0.664689	−0.332345	+	0.943158i	$0.607840\pi$
$132$	167.538	0.110472
$133$	−634.930	−0.413951
$134$	1064.80	0.686456
$135$	−601.201	−0.383283
$136$	−348.789	−0.219915
$137$	1333.56	0.831636	0.415818	−	0.909448i	$-0.363495\pi$
$137$	1333.56	0.831636	0.415818	+	0.909448i	$0.363495\pi$
$138$	−81.5028	−0.0502752
$139$	2023.36	1.23467	0.617334	−	0.786701i	$-0.288213\pi$
$139$	2023.36	1.23467	0.617334	+	0.786701i	$0.288213\pi$
$140$	1007.99	0.608507
$141$	273.935	0.163613
$142$	−492.213	−0.290884
$143$	−575.125	−0.336324
$144$	−426.053	−0.246558
$145$	−856.216	−0.490378
$146$	255.679	0.144933
$147$	1953.40	1.09601
$148$	2016.85	1.12016
$149$	2406.44	1.32311	0.661554	−	0.749898i	$-0.269897\pi$
$149$	2406.44	1.32311	0.661554	+	0.749898i	$0.269897\pi$
$150$	88.5269	0.0481880
$151$	1527.81	0.823387	0.411693	−	0.911322i	$-0.364937\pi$
$151$	1527.81	0.823387	0.411693	+	0.911322i	$0.364937\pi$
$152$	−373.961	−0.199554
$153$	−365.515	−0.193138
$154$	515.579	0.269782
$155$	−673.913	−0.349226
$156$	−796.326	−0.408699
$157$	300.681	0.152847	0.0764234	−	0.997075i	$-0.475650\pi$
$157$	300.681	0.152847	0.0764234	+	0.997075i	$0.475650\pi$
$158$	301.018	0.151568
$159$	−57.1517	−0.0285058
$160$	932.146	0.460579
$161$	769.147	0.376505
$162$	355.323	0.172326
$163$	2971.63	1.42795	0.713976	−	0.700170i	$-0.246892\pi$
$163$	2971.63	1.42795	0.713976	+	0.700170i	$0.246892\pi$
$164$	−3135.26	−1.49282
$165$	−138.857	−0.0655153
$166$	1879.55	0.878805
$167$	−67.0698	−0.0310780	−0.0155390	−	0.999879i	$-0.504946\pi$
$167$	−67.0698	−0.0310780	−0.0155390	+	0.999879i	$0.504946\pi$
$168$	1660.55	0.762582
$169$	536.625	0.244253
$170$	124.277	0.0560682
$171$	−391.894	−0.175257
$172$	−1502.83	−0.666220
$173$	−2957.71	−1.29983	−0.649914	−	0.760008i	$-0.725195\pi$
$173$	−2957.71	−1.29983	−0.649914	+	0.760008i	$0.725195\pi$
$174$	−606.386	−0.264195
$175$	−835.435	−0.360874
$176$	−227.217	−0.0973132
$177$	1800.62	0.764648
$178$	−1581.35	−0.665881
$179$	159.698	0.0666837	0.0333418	−	0.999444i	$-0.489385\pi$
$179$	159.698	0.0666837	0.0333418	+	0.999444i	$0.489385\pi$
$180$	622.158	0.257627
$181$	170.509	0.0700210	0.0350105	−	0.999387i	$-0.488854\pi$
$181$	170.509	0.0700210	0.0350105	+	0.999387i	$0.488854\pi$
$182$	−2450.60	−0.998078
$183$	775.434	0.313233
$184$	453.012	0.181503
$185$	−1671.59	−0.664310
$186$	−477.275	−0.188148
$187$	−194.932	−0.0762291
$188$	−654.571	−0.253933
$189$	4018.12	1.54643
$190$	133.246	0.0508772
$191$	868.199	0.328904	0.164452	−	0.986385i	$-0.447414\pi$
$191$	868.199	0.328904	0.164452	+	0.986385i	$0.447414\pi$
$192$	242.960	0.0913237
$193$	2821.45	1.05229	0.526146	−	0.850394i	$-0.323637\pi$
$193$	2821.45	1.05229	0.526146	+	0.850394i	$0.323637\pi$
$194$	−957.772	−0.354454
$195$	660.002	0.242378
$196$	−4667.67	−1.70105
$197$	−3242.60	−1.17272	−0.586360	−	0.810051i	$-0.699440\pi$
$197$	−3242.60	−1.17272	−0.586360	+	0.810051i	$0.699440\pi$
$198$	318.227	0.114219
$199$	4791.18	1.70672	0.853361	−	0.521320i	$-0.174560\pi$
$199$	4791.18	1.70672	0.853361	+	0.521320i	$0.174560\pi$
$200$	−492.054	−0.173967
$201$	1916.66	0.672592
$202$	1427.51	0.497225
$203$	5722.50	1.97853
$204$	−269.905	−0.0926331
$205$	2598.54	0.885315
$206$	1519.45	0.513908
$207$	474.736	0.159403
$208$	1079.99	0.360017
$209$	−209.000	−0.0691714
$210$	−591.668	−0.194424
$211$	−1512.84	−0.493594	−0.246797	−	0.969067i	$-0.579378\pi$
$211$	−1512.84	−0.493594	−0.246797	+	0.969067i	$0.579378\pi$
$212$	136.565	0.0442420
$213$	−885.990	−0.285010
$214$	572.493	0.182873
$215$	1245.56	0.395100
$216$	2366.59	0.745490
$217$	4504.08	1.40902
$218$	−2799.95	−0.869892
$219$	460.226	0.142006
$220$	331.801	0.101682
$221$	926.531	0.282015
$222$	−1183.84	−0.357902
$223$	−4300.08	−1.29128	−0.645638	−	0.763643i	$-0.723409\pi$
$223$	−4300.08	−1.29128	−0.645638	+	0.763643i	$0.723409\pi$
$224$	−6229.97	−1.85829
$225$	−515.650	−0.152785
$226$	−573.873	−0.168909
$227$	1509.17	0.441264	0.220632	−	0.975357i	$-0.429188\pi$
$227$	1509.17	0.441264	0.220632	+	0.975357i	$0.429188\pi$
$228$	−289.384	−0.0840567
$229$	488.994	0.141107	0.0705537	−	0.997508i	$-0.477523\pi$
$229$	488.994	0.141107	0.0705537	+	0.997508i	$0.477523\pi$
$230$	−161.412	−0.0462748
$231$	928.049	0.264334
$232$	3370.43	0.953793
$233$	−5809.92	−1.63356	−0.816782	−	0.576946i	$-0.804244\pi$
$233$	−5809.92	−1.63356	−0.816782	+	0.576946i	$0.804244\pi$
$234$	−1512.57	−0.422562
$235$	542.514	0.150595
$236$	−4302.60	−1.18676
$237$	541.837	0.148507
$238$	−830.601	−0.226218
$239$	−4077.19	−1.10348	−0.551740	−	0.834016i	$-0.686036\pi$
$239$	−4077.19	−1.10348	−0.551740	+	0.834016i	$0.686036\pi$
$240$	260.750	0.0701305
$241$	−3678.93	−0.983323	−0.491661	−	0.870786i	$-0.663610\pi$
$241$	−3678.93	−0.983323	−0.491661	+	0.870786i	$0.663610\pi$
$242$	169.713	0.0450808
$243$	3886.07	1.02589
$244$	−1852.91	−0.486149
$245$	3868.61	1.00880
$246$	1840.32	0.476970
$247$	993.397	0.255904
$248$	2652.81	0.679248
$249$	3383.23	0.861057
$250$	175.323	0.0443537
$251$	1248.18	0.313882	0.156941	−	0.987608i	$-0.449837\pi$
$251$	1248.18	0.313882	0.156941	+	0.987608i	$0.449837\pi$
$252$	−4158.18	−1.03945
$253$	253.180	0.0629142
$254$	−3607.94	−0.891270
$255$	223.700	0.0549359
$256$	−2672.42	−0.652447
$257$	1830.22	0.444225	0.222113	−	0.975021i	$-0.428705\pi$
$257$	1830.22	0.444225	0.222113	+	0.975021i	$0.428705\pi$
$258$	882.125	0.212863
$259$	11172.0	2.68029
$260$	−1577.08	−0.376179
$261$	3532.06	0.837660
$262$	−1397.83	−0.329612
$263$	1993.71	0.467443	0.233722	−	0.972304i	$-0.424910\pi$
$263$	1993.71	0.467443	0.233722	+	0.972304i	$0.424910\pi$
$264$	546.602	0.127428
$265$	−113.186	−0.0262376
$266$	−890.545	−0.205274
$267$	−2846.45	−0.652433
$268$	−4579.90	−1.04389
$269$	−902.313	−0.204517	−0.102258	−	0.994758i	$-0.532607\pi$
$269$	−902.313	−0.204517	−0.102258	+	0.994758i	$0.532607\pi$
$270$	−843.237	−0.190066
$271$	−1678.52	−0.376246	−0.188123	−	0.982145i	$-0.560240\pi$
$271$	−1678.52	−0.376246	−0.188123	+	0.982145i	$0.560240\pi$
$272$	366.049	0.0815991
$273$	−4411.11	−0.977921
$274$	1870.44	0.412399
$275$	−275.000	−0.0603023
$276$	350.557	0.0764530
$277$	−8653.16	−1.87696	−0.938480	−	0.345334i	$-0.887766\pi$
$277$	−8653.16	−1.87696	−0.938480	+	0.345334i	$0.887766\pi$
$278$	2837.93	0.612259
$279$	2780.03	0.596544
$280$	3288.63	0.701904
$281$	−6159.24	−1.30758	−0.653789	−	0.756677i	$-0.726822\pi$
$281$	−6159.24	−1.30758	−0.653789	+	0.756677i	$0.726822\pi$
$282$	384.217	0.0811340
$283$	−1993.28	−0.418687	−0.209343	−	0.977842i	$-0.567133\pi$
$283$	−1993.28	−0.418687	−0.209343	+	0.977842i	$0.567133\pi$
$284$	2117.09	0.442345
$285$	239.844	0.0498496
$286$	−806.662	−0.166780
$287$	−17367.3	−3.57197
$288$	−3845.29	−0.786756
$289$	−4598.96	−0.936080
$290$	−1200.92	−0.243173
$291$	−1724.00	−0.347295
$292$	−1099.72	−0.220398
$293$	−7304.01	−1.45633	−0.728165	−	0.685402i	$-0.759627\pi$
$293$	−7304.01	−1.45633	−0.728165	+	0.685402i	$0.759627\pi$
$294$	2739.81	0.543500
$295$	3566.04	0.703806
$296$	6580.08	1.29209
$297$	1322.64	0.258409
$298$	3375.24	0.656115
$299$	−1203.39	−0.232755
$300$	−380.769	−0.0732790
$301$	−8324.67	−1.59411
$302$	2142.89	0.408309
$303$	2569.54	0.487183
$304$	392.466	0.0740443
$305$	1535.71	0.288310
$306$	−512.667	−0.0957752
$307$	9075.14	1.68712	0.843560	−	0.537035i	$-0.180456\pi$
$307$	9075.14	1.68712	0.843560	+	0.537035i	$0.180456\pi$
$308$	−2217.59	−0.410256
$309$	2735.03	0.503529
$310$	−945.221	−0.173177
$311$	475.164	0.0866370	0.0433185	−	0.999061i	$-0.486207\pi$
$311$	475.164	0.0866370	0.0433185	+	0.999061i	$0.486207\pi$
$312$	−2598.05	−0.471428
$313$	7622.57	1.37653	0.688264	−	0.725461i	$-0.258373\pi$
$313$	7622.57	1.37653	0.688264	+	0.725461i	$0.258373\pi$
$314$	421.731	0.0757950
$315$	3446.34	0.616441
$316$	−1294.73	−0.230488
$317$	−4047.14	−0.717066	−0.358533	−	0.933517i	$-0.616723\pi$
$317$	−4047.14	−0.717066	−0.358533	+	0.933517i	$0.616723\pi$
$318$	−80.1602	−0.0141357
$319$	1883.68	0.330613
$320$	481.171	0.0840571
$321$	1030.50	0.179180
$322$	1078.80	0.186705
$323$	336.701	0.0580016
$324$	−1528.30	−0.262055
$325$	1307.10	0.223092
$326$	4167.97	0.708106
$327$	−5039.95	−0.852324
$328$	−10229.0	−1.72195
$329$	−3625.88	−0.607603
$330$	−194.759	−0.0324883
$331$	6852.41	1.13789	0.568946	−	0.822375i	$-0.307351\pi$
$331$	6852.41	1.13789	0.568946	+	0.822375i	$0.307351\pi$
$332$	−8084.27	−1.33639
$333$	6895.63	1.13477
$334$	−94.0712	−0.0154112
$335$	3795.86	0.619075
$336$	−1742.72	−0.282955
$337$	−483.735	−0.0781920	−0.0390960	−	0.999235i	$-0.512448\pi$
$337$	−483.735	−0.0781920	−0.0390960	+	0.999235i	$0.512448\pi$
$338$	752.663	0.121123
$339$	−1032.98	−0.165498
$340$	−534.535	−0.0852624
$341$	1482.61	0.235448
$342$	−549.665	−0.0869079
$343$	−14393.6	−2.26583
$344$	−4903.06	−0.768475
$345$	−290.545	−0.0453403
$346$	−4148.44	−0.644571
$347$	6836.19	1.05760	0.528798	−	0.848747i	$-0.322643\pi$
$347$	6836.19	1.05760	0.528798	+	0.848747i	$0.322643\pi$
$348$	2608.16	0.401759
$349$	12518.1	1.91999	0.959997	−	0.280009i	$-0.0903375\pi$
$349$	12518.1	1.91999	0.959997	+	0.280009i	$0.0903375\pi$
$350$	−1171.77	−0.178953
$351$	−6286.65	−0.956002
$352$	−2050.72	−0.310522
$353$	−3648.36	−0.550092	−0.275046	−	0.961431i	$-0.588693\pi$
$353$	−3648.36	−0.550092	−0.275046	+	0.961431i	$0.588693\pi$
$354$	2525.52	0.379181
$355$	−1754.66	−0.262332
$356$	6801.62	1.01260
$357$	−1495.09	−0.221649
$358$	223.990	0.0330677
$359$	858.838	0.126261	0.0631305	−	0.998005i	$-0.479892\pi$
$359$	858.838	0.126261	0.0631305	+	0.998005i	$0.479892\pi$
$360$	2029.82	0.297169
$361$	361.000	0.0526316
$362$	239.153	0.0347226
$363$	305.486	0.0441704
$364$	10540.4	1.51777
$365$	911.456	0.130706
$366$	1087.61	0.155329
$367$	12682.9	1.80393	0.901964	−	0.431811i	$-0.142125\pi$
$367$	12682.9	1.80393	0.901964	+	0.431811i	$0.142125\pi$
$368$	−475.429	−0.0673463
$369$	−10719.5	−1.51229
$370$	−2344.54	−0.329424
$371$	756.477	0.105861
$372$	2052.84	0.286115
$373$	11741.3	1.62987	0.814933	−	0.579555i	$-0.196774\pi$
$373$	11741.3	1.62987	0.814933	+	0.579555i	$0.196774\pi$
$374$	−273.409	−0.0378012
$375$	315.585	0.0434579
$376$	−2135.57	−0.292908
$377$	−8953.29	−1.22313
$378$	5635.75	0.766857
$379$	13049.8	1.76866	0.884329	−	0.466865i	$-0.154616\pi$
$379$	13049.8	1.76866	0.884329	+	0.466865i	$0.154616\pi$
$380$	−573.111	−0.0773684
$381$	−6494.35	−0.873269
$382$	1217.72	0.163100
$383$	8223.96	1.09719	0.548596	−	0.836088i	$-0.315163\pi$
$383$	8223.96	1.09719	0.548596	+	0.836088i	$0.315163\pi$
$384$	−3424.61	−0.455108
$385$	1837.96	0.243301
$386$	3957.32	0.521820
$387$	−5138.19	−0.674906
$388$	4119.53	0.539014
$389$	10967.6	1.42951	0.714757	−	0.699373i	$-0.246537\pi$
$389$	10967.6	1.42951	0.714757	+	0.699373i	$0.246537\pi$
$390$	925.710	0.120193
$391$	−407.875	−0.0527548
$392$	−15228.5	−1.96213
$393$	−2516.12	−0.322955
$394$	−4548.03	−0.581539
$395$	1073.08	0.136690
$396$	−1368.75	−0.173692
$397$	−6267.93	−0.792389	−0.396195	−	0.918167i	$-0.629669\pi$
$397$	−6267.93	−0.792389	−0.396195	+	0.918167i	$0.629669\pi$
$398$	6720.04	0.846345
$399$	−1602.99	−0.201128
$400$	516.402	0.0645503
$401$	10362.6	1.29048	0.645241	−	0.763979i	$-0.276757\pi$
$401$	10362.6	1.29048	0.645241	+	0.763979i	$0.276757\pi$
$402$	2688.29	0.333531
$403$	−7046.98	−0.871055
$404$	−6139.96	−0.756125
$405$	1266.67	0.155411
$406$	8026.30	0.981130
$407$	3677.49	0.447878
$408$	−880.580	−0.106851
$409$	1150.73	0.139120	0.0695598	−	0.997578i	$-0.477841\pi$
$409$	1150.73	0.139120	0.0695598	+	0.997578i	$0.477841\pi$
$410$	3644.67	0.439018
$411$	3366.82	0.404070
$412$	−6535.39	−0.781494
$413$	−23833.5	−2.83964
$414$	665.858	0.0790463
$415$	6700.31	0.792543
$416$	9747.28	1.14880
$417$	5108.32	0.599894
$418$	−293.141	−0.0343014
$419$	−1701.17	−0.198348	−0.0991739	−	0.995070i	$-0.531620\pi$
$419$	−1701.17	−0.198348	−0.0991739	+	0.995070i	$0.531620\pi$
$420$	2544.86	0.295658
$421$	5307.27	0.614395	0.307198	−	0.951646i	$-0.400609\pi$
$421$	5307.27	0.614395	0.307198	+	0.951646i	$0.400609\pi$
$422$	−2121.89	−0.244768
$423$	−2237.98	−0.257244
$424$	445.549	0.0510325
$425$	443.027	0.0505647
$426$	−1242.68	−0.141333
$427$	−10263.9	−1.16324
$428$	−2462.39	−0.278093
$429$	−1452.00	−0.163411
$430$	1747.01	0.195926
$431$	−10215.9	−1.14172	−0.570861	−	0.821047i	$-0.693391\pi$
$431$	−10215.9	−1.14172	−0.570861	+	0.821047i	$0.693391\pi$
$432$	−2483.69	−0.276613
$433$	1920.32	0.213128	0.106564	−	0.994306i	$-0.466015\pi$
$433$	1920.32	0.213128	0.106564	+	0.994306i	$0.466015\pi$
$434$	6317.36	0.698717
$435$	−2161.67	−0.238262
$436$	12043.0	1.32284
$437$	−437.311	−0.0478706
$438$	645.507	0.0704190
$439$	4686.53	0.509512	0.254756	−	0.967005i	$-0.418005\pi$
$439$	4686.53	0.509512	0.254756	+	0.967005i	$0.418005\pi$
$440$	1082.52	0.117289
$441$	−15958.8	−1.72323
$442$	1299.54	0.139848
$443$	1308.61	0.140347	0.0701736	−	0.997535i	$-0.477645\pi$
$443$	1308.61	0.140347	0.0701736	+	0.997535i	$0.477645\pi$
$444$	5091.90	0.544259
$445$	−5637.25	−0.600520
$446$	−6031.23	−0.640330
$447$	6075.48	0.642864
$448$	−3215.90	−0.339145
$449$	10264.4	1.07886	0.539428	−	0.842032i	$-0.318640\pi$
$449$	10264.4	1.07886	0.539428	+	0.842032i	$0.318640\pi$
$450$	−723.244	−0.0757646
$451$	−5716.78	−0.596879
$452$	2468.32	0.256858
$453$	3857.23	0.400062
$454$	2116.74	0.218818
$455$	−8735.99	−0.900108
$456$	−944.130	−0.0969582
$457$	13506.6	1.38252	0.691262	−	0.722604i	$-0.257055\pi$
$457$	13506.6	1.38252	0.691262	+	0.722604i	$0.257055\pi$
$458$	685.856	0.0699737
$459$	−2130.79	−0.216681
$460$	694.260	0.0703697
$461$	−18150.5	−1.83374	−0.916869	−	0.399187i	$-0.869292\pi$
$461$	−18150.5	−1.83374	−0.916869	+	0.399187i	$0.869292\pi$
$462$	1301.67	0.131080
$463$	11506.0	1.15492	0.577460	−	0.816419i	$-0.304044\pi$
$463$	11506.0	1.15492	0.577460	+	0.816419i	$0.304044\pi$
$464$	−3537.22	−0.353903
$465$	−1701.41	−0.169680
$466$	−8148.92	−0.810067
$467$	7242.42	0.717643	0.358821	−	0.933406i	$-0.383179\pi$
$467$	7242.42	0.717643	0.358821	+	0.933406i	$0.383179\pi$
$468$	6505.79	0.642586
$469$	−25369.5	−2.49778
$470$	760.923	0.0746782
$471$	759.122	0.0742643
$472$	−14037.5	−1.36891
$473$	−2740.23	−0.266376
$474$	759.974	0.0736429
$475$	475.000	0.0458831
$476$	3572.55	0.344008
$477$	466.916	0.0448189
$478$	−5718.61	−0.547204
$479$	−3977.89	−0.379446	−0.189723	−	0.981838i	$-0.560759\pi$
$479$	−3977.89	−0.379446	−0.189723	+	0.981838i	$0.560759\pi$
$480$	2353.37	0.223783
$481$	−17479.5	−1.65695
$482$	−5160.02	−0.487619
$483$	1941.85	0.182934
$484$	−729.963	−0.0685540
$485$	−3414.31	−0.319661
$486$	5450.56	0.508729
$487$	−4706.69	−0.437948	−0.218974	−	0.975731i	$-0.570271\pi$
$487$	−4706.69	−0.437948	−0.218974	+	0.975731i	$0.570271\pi$
$488$	−6045.21	−0.560766
$489$	7502.41	0.693806
$490$	5426.06	0.500254
$491$	15221.9	1.39910	0.699549	−	0.714585i	$-0.253384\pi$
$491$	15221.9	1.39910	0.699549	+	0.714585i	$0.253384\pi$
$492$	−7915.53	−0.725324
$493$	−3034.62	−0.277226
$494$	1393.33	0.126900
$495$	1134.43	0.103008
$496$	−2784.08	−0.252034
$497$	11727.2	1.05843
$498$	4745.27	0.426989
$499$	−13742.2	−1.23283	−0.616417	−	0.787420i	$-0.711416\pi$
$499$	−13742.2	−1.23283	−0.616417	+	0.787420i	$0.711416\pi$
$500$	−754.094	−0.0674482
$501$	−169.330	−0.0151000
$502$	1750.68	0.155651
$503$	−7004.63	−0.620916	−0.310458	−	0.950587i	$-0.600482\pi$
$503$	−7004.63	−0.620916	−0.310458	+	0.950587i	$0.600482\pi$
$504$	−13566.3	−1.19899
$505$	5088.86	0.448418
$506$	355.107	0.0311985
$507$	1354.80	0.118676
$508$	15518.3	1.35534
$509$	548.780	0.0477883	0.0238942	−	0.999714i	$-0.492394\pi$
$509$	548.780	0.0477883	0.0238942	+	0.999714i	$0.492394\pi$
$510$	313.759	0.0272421
$511$	−6091.69	−0.527360
$512$	7103.35	0.613138
$513$	−2284.57	−0.196620
$514$	2567.04	0.220287
$515$	5416.59	0.463463
$516$	−3794.16	−0.323699
$517$	−1193.53	−0.101531
$518$	15669.7	1.32913
$519$	−7467.25	−0.631553
$520$	−5145.31	−0.433917
$521$	−16053.4	−1.34993	−0.674964	−	0.737850i	$-0.735841\pi$
$521$	−16053.4	−1.34993	−0.674964	+	0.737850i	$0.735841\pi$
$522$	4954.03	0.415387
$523$	−10306.8	−0.861729	−0.430865	−	0.902417i	$-0.641791\pi$
$523$	−10306.8	−0.861729	−0.430865	+	0.902417i	$0.641791\pi$
$524$	6012.31	0.501238
$525$	−2109.20	−0.175339
$526$	2796.35	0.231800
$527$	−2388.49	−0.197428
$528$	−573.650	−0.0472820
$529$	−11637.2	−0.956460
$530$	−158.753	−0.0130110
$531$	−14710.6	−1.20223
$532$	3830.38	0.312158
$533$	27172.4	2.20819
$534$	−3992.39	−0.323535
$535$	2040.85	0.164923
$536$	−14942.1	−1.20411
$537$	403.185	0.0323999
$538$	−1265.57	−0.101418
$539$	−8510.94	−0.680134
$540$	3626.90	0.289031
$541$	12681.8	1.00783	0.503914	−	0.863754i	$-0.331893\pi$
$541$	12681.8	1.00783	0.503914	+	0.863754i	$0.331893\pi$
$542$	−2354.27	−0.186576
$543$	430.479	0.0340214
$544$	3303.73	0.260379
$545$	−9981.38	−0.784505
$546$	−6186.96	−0.484940
$547$	−2413.03	−0.188618	−0.0943089	−	0.995543i	$-0.530064\pi$
$547$	−2413.03	−0.188618	−0.0943089	+	0.995543i	$0.530064\pi$
$548$	−8045.06	−0.627132
$549$	−6335.11	−0.492488
$550$	−385.711	−0.0299032
$551$	−3253.62	−0.251559
$552$	1143.71	0.0881874
$553$	−7171.92	−0.551503
$554$	−12136.8	−0.930764
$555$	−4220.21	−0.322771
$556$	−12206.4	−0.931056
$557$	11999.9	0.912838	0.456419	−	0.889765i	$-0.349132\pi$
$557$	11999.9	0.912838	0.456419	+	0.889765i	$0.349132\pi$
$558$	3899.23	0.295820
$559$	13024.6	0.985477
$560$	−3451.36	−0.260441
$561$	−492.140	−0.0370378
$562$	−8638.87	−0.648414
$563$	−17802.5	−1.33265	−0.666327	−	0.745659i	$-0.732135\pi$
$563$	−17802.5	−1.33265	−0.666327	+	0.745659i	$0.732135\pi$
$564$	−1652.58	−0.123380
$565$	−2045.77	−0.152329
$566$	−2795.75	−0.207622
$567$	−8465.77	−0.627035
$568$	6907.10	0.510238
$569$	−1937.35	−0.142738	−0.0713691	−	0.997450i	$-0.522737\pi$
$569$	−1937.35	−0.142738	−0.0713691	+	0.997450i	$0.522737\pi$
$570$	336.402	0.0247199
$571$	−10530.8	−0.771805	−0.385903	−	0.922540i	$-0.626110\pi$
$571$	−10530.8	−0.771805	−0.385903	+	0.922540i	$0.626110\pi$
$572$	3469.59	0.253620
$573$	2191.92	0.159806
$574$	−24359.1	−1.77130
$575$	−575.409	−0.0417326
$576$	−1984.93	−0.143586
$577$	21213.7	1.53057	0.765283	−	0.643694i	$-0.222599\pi$
$577$	21213.7	1.53057	0.765283	+	0.643694i	$0.222599\pi$
$578$	−6450.44	−0.464192
$579$	7123.24	0.511281
$580$	5165.34	0.369791
$581$	−44781.4	−3.19767
$582$	−2418.06	−0.172220
$583$	249.010	0.0176894
$584$	−3587.88	−0.254225
$585$	−5392.06	−0.381084
$586$	−10244.5	−0.722178
$587$	2146.72	0.150945	0.0754723	−	0.997148i	$-0.475954\pi$
$587$	2146.72	0.150945	0.0754723	+	0.997148i	$0.475954\pi$
$588$	−11784.4	−0.826495
$589$	−2560.87	−0.179149
$590$	5001.68	0.349010
$591$	−8186.52	−0.569794
$592$	−6905.69	−0.479429
$593$	21620.4	1.49721	0.748604	−	0.663017i	$-0.230724\pi$
$593$	21620.4	1.49721	0.748604	+	0.663017i	$0.230724\pi$
$594$	1855.12	0.128142
$595$	−2960.96	−0.204013
$596$	−14517.4	−0.997747
$597$	12096.2	0.829253
$598$	−1687.86	−0.115421
$599$	9754.85	0.665397	0.332698	−	0.943033i	$-0.392041\pi$
$599$	9754.85	0.665397	0.332698	+	0.943033i	$0.392041\pi$
$600$	−1242.28	−0.0845262
$601$	−7511.66	−0.509829	−0.254914	−	0.966964i	$-0.582047\pi$
$601$	−7511.66	−0.509829	−0.254914	+	0.966964i	$0.582047\pi$
$602$	−11676.1	−0.790500
$603$	−15658.7	−1.05750
$604$	−9216.90	−0.620911
$605$	605.000	0.0406558
$606$	3604.01	0.241589
$607$	21106.2	1.41132	0.705661	−	0.708549i	$-0.250650\pi$
$607$	21106.2	1.41132	0.705661	+	0.708549i	$0.250650\pi$
$608$	3542.15	0.236272
$609$	14447.5	0.961315
$610$	2153.96	0.142970
$611$	5672.97	0.375620
$612$	2205.06	0.145644
$613$	−11745.4	−0.773887	−0.386943	−	0.922103i	$-0.626469\pi$
$613$	−11745.4	−0.773887	−0.386943	+	0.922103i	$0.626469\pi$
$614$	12728.7	0.836624
$615$	6560.46	0.430152
$616$	−7234.98	−0.473224
$617$	−14056.8	−0.917191	−0.458595	−	0.888645i	$-0.651647\pi$
$617$	−14056.8	−0.917191	−0.458595	+	0.888645i	$0.651647\pi$
$618$	3836.12	0.249694
$619$	14270.6	0.926628	0.463314	−	0.886194i	$-0.346660\pi$
$619$	14270.6	0.926628	0.463314	+	0.886194i	$0.346660\pi$
$620$	4065.55	0.263349
$621$	2767.50	0.178834
$622$	666.459	0.0429623
$623$	37676.4	2.42291
$624$	2726.61	0.174923
$625$	625.000	0.0400000
$626$	10691.3	0.682605
$627$	−527.657	−0.0336086
$628$	−1813.93	−0.115261
$629$	−5924.46	−0.375555
$630$	4833.78	0.305687
$631$	−1909.77	−0.120486	−0.0602430	−	0.998184i	$-0.519188\pi$
$631$	−1909.77	−0.120486	−0.0602430	+	0.998184i	$0.519188\pi$
$632$	−4224.11	−0.265864
$633$	−3819.44	−0.239825
$634$	−5676.46	−0.355585
$635$	−12861.7	−0.803784
$636$	344.782	0.0214961
$637$	40453.3	2.51620
$638$	2642.02	0.163947
$639$	7238.33	0.448112
$640$	−6782.28	−0.418896
$641$	8972.85	0.552896	0.276448	−	0.961029i	$-0.410843\pi$
$641$	8972.85	0.552896	0.276448	+	0.961029i	$0.410843\pi$
$642$	1445.36	0.0888533
$643$	−26868.2	−1.64786	−0.823932	−	0.566688i	$-0.808224\pi$
$643$	−26868.2	−1.64786	−0.823932	+	0.566688i	$0.808224\pi$
$644$	−4640.07	−0.283920
$645$	3144.64	0.191969
$646$	472.252	0.0287624
$647$	41.0024	0.00249145	0.00124573	−	0.999999i	$-0.499603\pi$
$647$	41.0024	0.00249145	0.00124573	+	0.999999i	$0.499603\pi$
$648$	−4986.17	−0.302276
$649$	−7845.28	−0.474506
$650$	1833.32	0.110629
$651$	11371.3	0.684605
$652$	−17927.1	−1.07681
$653$	22251.7	1.33350	0.666751	−	0.745281i	$-0.267685\pi$
$653$	22251.7	1.33350	0.666751	+	0.745281i	$0.267685\pi$
$654$	−7068.97	−0.422658
$655$	−4983.05	−0.297258
$656$	10735.1	0.638927
$657$	−3759.94	−0.223271
$658$	−5085.61	−0.301304
$659$	14660.7	0.866614	0.433307	−	0.901246i	$-0.357347\pi$
$659$	14660.7	0.866614	0.433307	+	0.901246i	$0.357347\pi$
$660$	837.691	0.0494047
$661$	455.344	0.0267940	0.0133970	−	0.999910i	$-0.495735\pi$
$661$	455.344	0.0267940	0.0133970	+	0.999910i	$0.495735\pi$
$662$	9611.09	0.564268
$663$	2339.19	0.137024
$664$	−26375.3	−1.54151
$665$	−3174.65	−0.185124
$666$	9671.71	0.562720
$667$	3941.40	0.228803
$668$	404.615	0.0234357
$669$	−10856.3	−0.627398
$670$	5324.02	0.306992
$671$	−3378.56	−0.194378
$672$	−15728.7	−0.902897
$673$	26027.1	1.49074	0.745372	−	0.666648i	$-0.232272\pi$
$673$	26027.1	1.49074	0.745372	+	0.666648i	$0.232272\pi$
$674$	−678.480	−0.0387746
$675$	−3006.01	−0.171409
$676$	−3237.32	−0.184190
$677$	9116.58	0.517546	0.258773	−	0.965938i	$-0.416682\pi$
$677$	9116.58	0.517546	0.258773	+	0.965938i	$0.416682\pi$
$678$	−1448.84	−0.0820686
$679$	22819.4	1.28973
$680$	−1743.95	−0.0983489
$681$	3810.16	0.214399
$682$	2079.49	0.116756
$683$	14895.2	0.834482	0.417241	−	0.908796i	$-0.362997\pi$
$683$	14895.2	0.834482	0.417241	+	0.908796i	$0.362997\pi$
$684$	2364.20	0.132160
$685$	6667.82	0.371919
$686$	−20188.3	−1.12360
$687$	1234.55	0.0685605
$688$	5145.68	0.285141
$689$	−1183.57	−0.0654431
$690$	−407.514	−0.0224838
$691$	−25488.6	−1.40323	−0.701615	−	0.712556i	$-0.747537\pi$
$691$	−25488.6	−1.40323	−0.701615	+	0.712556i	$0.747537\pi$
$692$	17843.1	0.980192
$693$	−7581.94	−0.415605
$694$	9588.35	0.524451
$695$	10116.8	0.552161
$696$	8509.26	0.463423
$697$	9209.78	0.500495
$698$	17557.7	0.952105
$699$	−14668.2	−0.793707
$700$	5039.97	0.272133
$701$	30815.0	1.66029	0.830147	−	0.557544i	$-0.188256\pi$
$701$	30815.0	1.66029	0.830147	+	0.557544i	$0.188256\pi$
$702$	−8817.57	−0.474071
$703$	−6352.02	−0.340784
$704$	−1058.58	−0.0566713
$705$	1369.67	0.0731700
$706$	−5117.14	−0.272785
$707$	−34011.3	−1.80923
$708$	−10862.7	−0.576617
$709$	−12418.4	−0.657802	−0.328901	−	0.944364i	$-0.606678\pi$
$709$	−12418.4	−0.657802	−0.328901	+	0.944364i	$0.606678\pi$
$710$	−2461.06	−0.130087
$711$	−4426.68	−0.233493
$712$	22190.6	1.16802
$713$	3102.21	0.162943
$714$	−2097.00	−0.109913
$715$	−2875.62	−0.150409
$716$	−963.417	−0.0502857
$717$	−10293.6	−0.536152
$718$	1204.59	0.0626115
$719$	25259.9	1.31020	0.655102	−	0.755540i	$-0.272626\pi$
$719$	25259.9	1.31020	0.655102	+	0.755540i	$0.272626\pi$
$720$	−2130.26	−0.110264
$721$	−36201.7	−1.86993
$722$	506.334	0.0260994
$723$	−9288.11	−0.477771
$724$	−1028.64	−0.0528024
$725$	−4281.08	−0.219304
$726$	428.470	0.0219036
$727$	4150.96	0.211761	0.105881	−	0.994379i	$-0.466234\pi$
$727$	4150.96	0.211761	0.105881	+	0.994379i	$0.466234\pi$
$728$	34388.6	1.75072
$729$	2971.05	0.150945
$730$	1278.40	0.0648158
$731$	4414.54	0.223362
$732$	−4678.00	−0.236207
$733$	5485.84	0.276431	0.138216	−	0.990402i	$-0.455863\pi$
$733$	5485.84	0.276431	0.138216	+	0.990402i	$0.455863\pi$
$734$	17788.9	0.894549
$735$	9766.99	0.490151
$736$	−4290.92	−0.214899
$737$	−8350.89	−0.417380
$738$	−15035.0	−0.749927
$739$	−6036.24	−0.300469	−0.150235	−	0.988650i	$-0.548003\pi$
$739$	−6036.24	−0.300469	−0.150235	+	0.988650i	$0.548003\pi$
$740$	10084.3	0.500952
$741$	2508.01	0.124337
$742$	1061.02	0.0524952
$743$	39199.7	1.93553	0.967763	−	0.251862i	$-0.0810430\pi$
$743$	39199.7	1.93553	0.967763	+	0.251862i	$0.0810430\pi$
$744$	6697.49	0.330029
$745$	12032.2	0.591712
$746$	16468.2	0.808233
$747$	−27640.1	−1.35382
$748$	1175.98	0.0574839
$749$	−13640.0	−0.665412
$750$	442.635	0.0215503
$751$	18988.6	0.922642	0.461321	−	0.887233i	$-0.347376\pi$
$751$	18988.6	0.922642	0.461321	+	0.887233i	$0.347376\pi$
$752$	2241.25	0.108683
$753$	3151.25	0.152507
$754$	−12557.8	−0.606534
$755$	7639.05	0.368230
$756$	−24240.3	−1.16615
$757$	−11298.1	−0.542454	−0.271227	−	0.962515i	$-0.587429\pi$
$757$	−11298.1	−0.542454	−0.271227	+	0.962515i	$0.587429\pi$
$758$	18303.4	0.877058
$759$	639.198	0.0305684
$760$	−1869.80	−0.0892433
$761$	33944.2	1.61692	0.808459	−	0.588552i	$-0.200302\pi$
$761$	33944.2	1.61692	0.808459	+	0.588552i	$0.200302\pi$
$762$	−9108.89	−0.433045
$763$	66710.3	3.16524
$764$	−5237.63	−0.248025
$765$	−1827.58	−0.0863741
$766$	11534.8	0.544086
$767$	37289.4	1.75547
$768$	−6747.00	−0.317007
$769$	−36924.2	−1.73150	−0.865749	−	0.500478i	$-0.833158\pi$
$769$	−36924.2	−1.73150	−0.865749	+	0.500478i	$0.833158\pi$
$770$	2577.89	0.120650
$771$	4620.71	0.215838
$772$	−17021.1	−0.793526
$773$	39125.2	1.82049	0.910243	−	0.414073i	$-0.135894\pi$
$773$	39125.2	1.82049	0.910243	+	0.414073i	$0.135894\pi$
$774$	−7206.75	−0.334679
$775$	−3369.56	−0.156178
$776$	13440.2	0.621745
$777$	28205.7	1.30228
$778$	15383.0	0.708880
$779$	9874.44	0.454157
$780$	−3981.63	−0.182776
$781$	3860.25	0.176864
$782$	−572.080	−0.0261606
$783$	20590.3	0.939768
$784$	15982.1	0.728046
$785$	1503.40	0.0683551
$786$	−3529.08	−0.160150
$787$	−25778.3	−1.16760	−0.583798	−	0.811899i	$-0.698434\pi$
$787$	−25778.3	−1.16760	−0.583798	+	0.811899i	$0.698434\pi$
$788$	19561.8	0.884341
$789$	5033.48	0.227119
$790$	1505.09	0.0677832
$791$	13672.8	0.614602
$792$	−4465.61	−0.200351
$793$	16058.6	0.719115
$794$	−8791.32	−0.392937
$795$	−285.759	−0.0127482
$796$	−28904.0	−1.28703
$797$	−32702.6	−1.45343	−0.726717	−	0.686937i	$-0.758955\pi$
$797$	−32702.6	−1.45343	−0.726717	+	0.686937i	$0.758955\pi$
$798$	−2248.34	−0.0997372
$799$	1922.79	0.0851356
$800$	4660.73	0.205977
$801$	23254.8	1.02580
$802$	14534.4	0.639936
$803$	−2005.20	−0.0881221
$804$	−11562.8	−0.507198
$805$	3845.74	0.168378
$806$	−9884.00	−0.431947
$807$	−2278.05	−0.0993694
$808$	−20031.9	−0.872179
$809$	−15886.5	−0.690407	−0.345203	−	0.938528i	$-0.612190\pi$
$809$	−15886.5	−0.690407	−0.345203	+	0.938528i	$0.612190\pi$
$810$	1776.62	0.0770666
$811$	−26616.2	−1.15243	−0.576216	−	0.817297i	$-0.695471\pi$
$811$	−26616.2	−1.15243	−0.576216	+	0.817297i	$0.695471\pi$
$812$	−34522.4	−1.49199
$813$	−4237.72	−0.182808
$814$	5157.99	0.222098
$815$	14858.2	0.638600
$816$	924.154	0.0396469
$817$	4733.13	0.202682
$818$	1614.00	0.0689879
$819$	36037.7	1.53756
$820$	−15676.3	−0.667611
$821$	−14976.2	−0.636631	−0.318316	−	0.947985i	$-0.603117\pi$
$821$	−14976.2	−0.636631	−0.318316	+	0.947985i	$0.603117\pi$
$822$	4722.26	0.200374
$823$	24281.2	1.02842	0.514209	−	0.857665i	$-0.328086\pi$
$823$	24281.2	1.02842	0.514209	+	0.857665i	$0.328086\pi$
$824$	−21322.0	−0.901442
$825$	−694.286	−0.0292993
$826$	−33428.6	−1.40815
$827$	−4610.83	−0.193874	−0.0969372	−	0.995290i	$-0.530905\pi$
$827$	−4610.83	−0.193874	−0.0969372	+	0.995290i	$0.530905\pi$
$828$	−2863.96	−0.120205
$829$	−22819.1	−0.956019	−0.478010	−	0.878355i	$-0.658642\pi$
$829$	−22819.1	−0.956019	−0.478010	+	0.878355i	$0.658642\pi$
$830$	9397.77	0.393014
$831$	−21846.4	−0.911967
$832$	5031.52	0.209659
$833$	13711.2	0.570306
$834$	7164.87	0.297481
$835$	−335.349	−0.0138985
$836$	1260.85	0.0521618
$837$	16206.3	0.669261
$838$	−2386.04	−0.0983585
$839$	−33784.8	−1.39020	−0.695102	−	0.718911i	$-0.744641\pi$
$839$	−33784.8	−1.39020	−0.695102	+	0.718911i	$0.744641\pi$
$840$	8302.73	0.341037
$841$	4935.24	0.202355
$842$	7443.90	0.304672
$843$	−15550.1	−0.635319
$844$	9126.61	0.372217
$845$	2683.12	0.109233
$846$	−3138.96	−0.127565
$847$	−4043.50	−0.164034
$848$	−467.597	−0.0189356
$849$	−5032.40	−0.203429
$850$	621.384	0.0250745
$851$	7694.77	0.309957
$852$	5344.96	0.214924
$853$	36970.5	1.48399	0.741996	−	0.670404i	$-0.233879\pi$
$853$	36970.5	1.48399	0.741996	+	0.670404i	$0.233879\pi$
$854$	−14396.0	−0.576838
$855$	−1959.47	−0.0783772
$856$	−8033.65	−0.320776
$857$	25534.6	1.01779	0.508894	−	0.860829i	$-0.330055\pi$
$857$	25534.6	1.01779	0.508894	+	0.860829i	$0.330055\pi$
$858$	−2036.56	−0.0810339
$859$	−26422.3	−1.04949	−0.524747	−	0.851258i	$-0.675840\pi$
$859$	−26422.3	−1.04949	−0.524747	+	0.851258i	$0.675840\pi$
$860$	−7514.15	−0.297942
$861$	−43846.7	−1.73553
$862$	−14328.7	−0.566168
$863$	20207.6	0.797075	0.398537	−	0.917152i	$-0.369518\pi$
$863$	20207.6	0.797075	0.398537	+	0.917152i	$0.369518\pi$
$864$	−22416.3	−0.882659
$865$	−14788.5	−0.581301
$866$	2693.41	0.105688
$867$	−11610.9	−0.454817
$868$	−27172.0	−1.06253
$869$	−2360.78	−0.0921565
$870$	−3031.93	−0.118152
$871$	39692.6	1.54412
$872$	39291.0	1.52587
$873$	14084.7	0.546042
$874$	−613.367	−0.0237385
$875$	−4177.17	−0.161388
$876$	−2776.43	−0.107086
$877$	−9790.82	−0.376981	−0.188491	−	0.982075i	$-0.560359\pi$
$877$	−9790.82	−0.376981	−0.188491	+	0.982075i	$0.560359\pi$
$878$	6573.26	0.252662
$879$	−18440.3	−0.707593
$880$	−1136.09	−0.0435198
$881$	−14142.4	−0.540830	−0.270415	−	0.962744i	$-0.587161\pi$
$881$	−14142.4	−0.540830	−0.270415	+	0.962744i	$0.587161\pi$
$882$	−22383.6	−0.854529
$883$	−3031.50	−0.115536	−0.0577680	−	0.998330i	$-0.518398\pi$
$883$	−3031.50	−0.115536	−0.0577680	+	0.998330i	$0.518398\pi$
$884$	−5589.53	−0.212665
$885$	9003.09	0.341961
$886$	1835.44	0.0695967
$887$	−20211.0	−0.765071	−0.382536	−	0.923941i	$-0.624949\pi$
$887$	−20211.0	−0.765071	−0.382536	+	0.923941i	$0.624949\pi$
$888$	16612.6	0.627794
$889$	85961.2	3.24302
$890$	−7906.73	−0.297791
$891$	−2786.68	−0.104778
$892$	25941.3	0.973744
$893$	2061.55	0.0772534
$894$	8521.38	0.318789
$895$	798.489	0.0298218
$896$	45329.2	1.69012
$897$	−3038.17	−0.113090
$898$	14396.7	0.534993
$899$	23080.6	0.856263
$900$	3110.79	0.115214
$901$	−401.157	−0.0148329
$902$	−8018.28	−0.295986
$903$	−21017.1	−0.774535
$904$	8053.02	0.296282
$905$	852.543	0.0313143
$906$	5410.09	0.198387
$907$	12842.8	0.470162	0.235081	−	0.971976i	$-0.424464\pi$
$907$	12842.8	0.470162	0.235081	+	0.971976i	$0.424464\pi$
$908$	−9104.42	−0.332754
$909$	−20992.6	−0.765984
$910$	−12253.0	−0.446354
$911$	−6817.61	−0.247944	−0.123972	−	0.992286i	$-0.539563\pi$
$911$	−6817.61	−0.247944	−0.123972	+	0.992286i	$0.539563\pi$
$912$	990.849	0.0359762
$913$	−14740.7	−0.534333
$914$	18944.2	0.685579
$915$	3877.17	0.140082
$916$	−2949.98	−0.106408
$917$	33304.1	1.19934
$918$	−2988.62	−0.107450
$919$	8407.04	0.301766	0.150883	−	0.988552i	$-0.451788\pi$
$919$	8407.04	0.301766	0.150883	+	0.988552i	$0.451788\pi$
$920$	2265.06	0.0811704
$921$	22911.8	0.819728
$922$	−25457.7	−0.909331
$923$	−18348.2	−0.654320
$924$	−5598.69	−0.199333
$925$	−8357.93	−0.297089
$926$	16138.1	0.572713
$927$	−22344.5	−0.791684
$928$	−31924.7	−1.12929
$929$	3104.46	0.109638	0.0548192	−	0.998496i	$-0.482542\pi$
$929$	3104.46	0.109638	0.0548192	+	0.998496i	$0.482542\pi$
$930$	−2386.38	−0.0841423
$931$	14700.7	0.517504
$932$	35049.8	1.23186
$933$	1199.64	0.0420947
$934$	10158.1	0.355871
$935$	−974.660	−0.0340907
$936$	21225.5	0.741214
$937$	32949.1	1.14877	0.574386	−	0.818585i	$-0.305241\pi$
$937$	32949.1	1.14877	0.574386	+	0.818585i	$0.305241\pi$
$938$	−35583.0	−1.23862
$939$	19244.5	0.668819
$940$	−3272.85	−0.113562
$941$	−49959.0	−1.73073	−0.865365	−	0.501141i	$-0.832914\pi$
$941$	−49959.0	−1.73073	−0.865365	+	0.501141i	$0.832914\pi$
$942$	1064.73	0.0368269
$943$	−11961.8	−0.413074
$944$	14732.1	0.507933
$945$	20090.6	0.691584
$946$	−3843.41	−0.132093
$947$	−16151.4	−0.554225	−0.277112	−	0.960838i	$-0.589377\pi$
$947$	−16151.4	−0.554225	−0.277112	+	0.960838i	$0.589377\pi$
$948$	−3268.77	−0.111988
$949$	9530.93	0.326014
$950$	666.229	0.0227530
$951$	−10217.7	−0.348404
$952$	11655.6	0.396808
$953$	−16781.7	−0.570421	−0.285210	−	0.958465i	$-0.592064\pi$
$953$	−16781.7	−0.570421	−0.285210	+	0.958465i	$0.592064\pi$
$954$	654.890	0.0222252
$955$	4340.99	0.147090
$956$	24596.7	0.832127
$957$	4755.67	0.160636
$958$	−5579.34	−0.188163
$959$	−44564.2	−1.50058
$960$	1214.80	0.0408412
$961$	−11624.7	−0.390208
$962$	−24516.5	−0.821665
$963$	−8418.91	−0.281719
$964$	22194.1	0.741518
$965$	14107.2	0.470599
$966$	2723.61	0.0907150
$967$	11349.6	0.377434	0.188717	−	0.982032i	$-0.439567\pi$
$967$	11349.6	0.377434	0.188717	+	0.982032i	$0.439567\pi$
$968$	−2381.54	−0.0790760
$969$	850.060	0.0281815
$970$	−4788.86	−0.158516
$971$	−31009.1	−1.02485	−0.512426	−	0.858732i	$-0.671253\pi$
$971$	−31009.1	−1.02485	−0.512426	+	0.858732i	$0.671253\pi$
$972$	−23443.7	−0.773619
$973$	−67615.3	−2.22780
$974$	−6601.54	−0.217174
$975$	3300.01	0.108395
$976$	6344.35	0.208071
$977$	−10739.9	−0.351689	−0.175844	−	0.984418i	$-0.556266\pi$
$977$	−10739.9	−0.351689	−0.175844	+	0.984418i	$0.556266\pi$
$978$	10522.8	0.344051
$979$	12401.9	0.404870
$980$	−23338.4	−0.760731
$981$	41175.2	1.34008
$982$	21350.1	0.693797
$983$	4841.43	0.157088	0.0785440	−	0.996911i	$-0.474973\pi$
$983$	4841.43	0.157088	0.0785440	+	0.996911i	$0.474973\pi$
$984$	−25824.8	−0.836651
$985$	−16213.0	−0.524456
$986$	−4256.31	−0.137473
$987$	−9154.18	−0.295219
$988$	−5992.92	−0.192976
$989$	−5733.66	−0.184347
$990$	1591.14	0.0510805
$991$	34230.1	1.09723	0.548615	−	0.836075i	$-0.315155\pi$
$991$	34230.1	1.09723	0.548615	+	0.836075i	$0.315155\pi$
$992$	−25127.4	−0.804229
$993$	17300.1	0.552873
$994$	16448.5	0.524863
$995$	23955.9	0.763270
$996$	−20410.2	−0.649318
$997$	37066.6	1.17744	0.588722	−	0.808335i	$-0.299631\pi$
$997$	37066.6	1.17744	0.588722	+	0.808335i	$0.299631\pi$
$998$	−19274.6	−0.611349
$999$	40198.4	1.27309

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.4.a.h.1.15	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.4.a.h.1.15	✓	24	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)

\(f(q)\)	\(=\)	\(q+1.40259 q^{2} +2.52468 q^{3} -6.03275 q^{4} +5.00000 q^{5} +3.54108 q^{6} -33.4174 q^{7} -19.6821 q^{8} -20.6260 q^{9} +O(q^{10})\)	\(q+1.40259 q^{2} +2.52468 q^{3} -6.03275 q^{4} +5.00000 q^{5} +3.54108 q^{6} -33.4174 q^{7} -19.6821 q^{8} -20.6260 q^{9} +7.01293 q^{10} -11.0000 q^{11} -15.2307 q^{12} +52.2841 q^{13} -46.8708 q^{14} +12.6234 q^{15} +20.6561 q^{16} +17.7211 q^{17} -28.9298 q^{18} +19.0000 q^{19} -30.1638 q^{20} -84.3681 q^{21} -15.4285 q^{22} -23.0164 q^{23} -49.6911 q^{24} +25.0000 q^{25} +73.3329 q^{26} -120.240 q^{27} +201.599 q^{28} -171.243 q^{29} +17.7054 q^{30} -134.783 q^{31} +186.429 q^{32} -27.7714 q^{33} +24.8554 q^{34} -167.087 q^{35} +124.432 q^{36} -334.317 q^{37} +26.6491 q^{38} +132.000 q^{39} -98.4107 q^{40} +519.707 q^{41} -118.334 q^{42} +249.112 q^{43} +66.3603 q^{44} -103.130 q^{45} -32.2825 q^{46} +108.503 q^{47} +52.1500 q^{48} +773.722 q^{49} +35.0647 q^{50} +44.7400 q^{51} -315.417 q^{52} -22.6372 q^{53} -168.647 q^{54} -55.0000 q^{55} +657.726 q^{56} +47.9689 q^{57} -240.183 q^{58} +713.208 q^{59} -76.1537 q^{60} +307.142 q^{61} -189.044 q^{62} +689.267 q^{63} +96.2342 q^{64} +261.420 q^{65} -38.9518 q^{66} +759.172 q^{67} -106.907 q^{68} -58.1089 q^{69} -234.354 q^{70} -350.932 q^{71} +405.964 q^{72} +182.291 q^{73} -468.909 q^{74} +63.1169 q^{75} -114.622 q^{76} +367.591 q^{77} +185.142 q^{78} +214.617 q^{79} +103.280 q^{80} +253.334 q^{81} +728.934 q^{82} +1340.06 q^{83} +508.972 q^{84} +88.6055 q^{85} +349.401 q^{86} -432.334 q^{87} +216.504 q^{88} -1127.45 q^{89} -144.649 q^{90} -1747.20 q^{91} +138.852 q^{92} -340.282 q^{93} +152.185 q^{94} +95.0000 q^{95} +470.673 q^{96} -682.861 q^{97} +1085.21 q^{98} +226.886 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 21 q^{3} + 98 q^{4} + 120 q^{5} + 15 q^{6} + 71 q^{7} + 84 q^{8} + 339 q^{9}+O(q^{10}) \) 24 * q + 4 * q^2 + 21 * q^3 + 98 * q^4 + 120 * q^5 + 15 * q^6 + 71 * q^7 + 84 * q^8 + 339 * q^9	\( 24 q + 4 q^{2} + 21 q^{3} + 98 q^{4} + 120 q^{5} + 15 q^{6} + 71 q^{7} + 84 q^{8} + 339 q^{9} + 20 q^{10} - 264 q^{11} + 164 q^{12} - 15 q^{13} + 77 q^{14} + 105 q^{15} + 230 q^{16} + 187 q^{17} - 109 q^{18} + 456 q^{19} + 490 q^{20} + 295 q^{21} - 44 q^{22} + 451 q^{23} + 416 q^{24} + 600 q^{25} + 375 q^{26} + 1335 q^{27} + 815 q^{28} + 271 q^{29} + 75 q^{30} + 302 q^{31} + 1181 q^{32} - 231 q^{33} + 285 q^{34} + 355 q^{35} + 2445 q^{36} + 974 q^{37} + 76 q^{38} + 601 q^{39} + 420 q^{40} + 316 q^{41} + 2158 q^{42} + 686 q^{43} - 1078 q^{44} + 1695 q^{45} - 217 q^{46} + 1798 q^{47} + 353 q^{48} + 1845 q^{49} + 100 q^{50} + 383 q^{51} - 134 q^{52} + 815 q^{53} - 974 q^{54} - 1320 q^{55} + 2001 q^{56} + 399 q^{57} - 888 q^{58} + 1793 q^{59} + 820 q^{60} + 62 q^{61} + 3994 q^{62} + 366 q^{63} - 588 q^{64} - 75 q^{65} - 165 q^{66} + 2363 q^{67} - 1720 q^{68} - 287 q^{69} + 385 q^{70} + 1266 q^{71} + 3838 q^{72} + 127 q^{73} - 2861 q^{74} + 525 q^{75} + 1862 q^{76} - 781 q^{77} - 3916 q^{78} - 1922 q^{79} + 1150 q^{80} + 3688 q^{81} + 2666 q^{82} + 3666 q^{83} + 438 q^{84} + 935 q^{85} + 78 q^{86} + 2685 q^{87} - 924 q^{88} + 2344 q^{89} - 545 q^{90} + 127 q^{91} + 4800 q^{92} + 1344 q^{93} + 1756 q^{94} + 2280 q^{95} + 2874 q^{96} + 1182 q^{97} - 4328 q^{98} - 3729 q^{99}+O(q^{100}) \) 24 * q + 4 * q^2 + 21 * q^3 + 98 * q^4 + 120 * q^5 + 15 * q^6 + 71 * q^7 + 84 * q^8 + 339 * q^9 + 20 * q^10 - 264 * q^11 + 164 * q^12 - 15 * q^13 + 77 * q^14 + 105 * q^15 + 230 * q^16 + 187 * q^17 - 109 * q^18 + 456 * q^19 + 490 * q^20 + 295 * q^21 - 44 * q^22 + 451 * q^23 + 416 * q^24 + 600 * q^25 + 375 * q^26 + 1335 * q^27 + 815 * q^28 + 271 * q^29 + 75 * q^30 + 302 * q^31 + 1181 * q^32 - 231 * q^33 + 285 * q^34 + 355 * q^35 + 2445 * q^36 + 974 * q^37 + 76 * q^38 + 601 * q^39 + 420 * q^40 + 316 * q^41 + 2158 * q^42 + 686 * q^43 - 1078 * q^44 + 1695 * q^45 - 217 * q^46 + 1798 * q^47 + 353 * q^48 + 1845 * q^49 + 100 * q^50 + 383 * q^51 - 134 * q^52 + 815 * q^53 - 974 * q^54 - 1320 * q^55 + 2001 * q^56 + 399 * q^57 - 888 * q^58 + 1793 * q^59 + 820 * q^60 + 62 * q^61 + 3994 * q^62 + 366 * q^63 - 588 * q^64 - 75 * q^65 - 165 * q^66 + 2363 * q^67 - 1720 * q^68 - 287 * q^69 + 385 * q^70 + 1266 * q^71 + 3838 * q^72 + 127 * q^73 - 2861 * q^74 + 525 * q^75 + 1862 * q^76 - 781 * q^77 - 3916 * q^78 - 1922 * q^79 + 1150 * q^80 + 3688 * q^81 + 2666 * q^82 + 3666 * q^83 + 438 * q^84 + 935 * q^85 + 78 * q^86 + 2685 * q^87 - 924 * q^88 + 2344 * q^89 - 545 * q^90 + 127 * q^91 + 4800 * q^92 + 1344 * q^93 + 1756 * q^94 + 2280 * q^95 + 2874 * q^96 + 1182 * q^97 - 4328 * q^98 - 3729 * q^99

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