LMFDB - Embedded newform 966.4.a.l.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,4,Mod(1,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, 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("966.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	966.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:	$56.9958450655$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 319x^{3} - 666x^{2} + 23460x + 101568 $ x^5 - 319x^3 - 666x^2 + 23460*x + 101568
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-13.4981$ of defining polynomial
Character	$\chi$	$=$	966.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +8.95143 q^{5} +6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +8.95143 q^{5} +6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} -17.9029 q^{10} +61.7033 q^{11} -12.0000 q^{12} -54.4391 q^{13} -14.0000 q^{14} -26.8543 q^{15} +16.0000 q^{16} +29.1814 q^{17} -18.0000 q^{18} -157.317 q^{19} +35.8057 q^{20} -21.0000 q^{21} -123.407 q^{22} -23.0000 q^{23} +24.0000 q^{24} -44.8719 q^{25} +108.878 q^{26} -27.0000 q^{27} +28.0000 q^{28} +25.5868 q^{29} +53.7086 q^{30} -254.749 q^{31} -32.0000 q^{32} -185.110 q^{33} -58.3628 q^{34} +62.6600 q^{35} +36.0000 q^{36} +101.617 q^{37} +314.635 q^{38} +163.317 q^{39} -71.6115 q^{40} -155.506 q^{41} +42.0000 q^{42} +476.770 q^{43} +246.813 q^{44} +80.5629 q^{45} +46.0000 q^{46} -634.239 q^{47} -48.0000 q^{48} +49.0000 q^{49} +89.7437 q^{50} -87.5442 q^{51} -217.757 q^{52} -547.555 q^{53} +54.0000 q^{54} +552.333 q^{55} -56.0000 q^{56} +471.952 q^{57} -51.1736 q^{58} -174.801 q^{59} -107.417 q^{60} -53.4115 q^{61} +509.498 q^{62} +63.0000 q^{63} +64.0000 q^{64} -487.308 q^{65} +370.220 q^{66} +593.651 q^{67} +116.726 q^{68} +69.0000 q^{69} -125.320 q^{70} +416.322 q^{71} -72.0000 q^{72} +378.705 q^{73} -203.234 q^{74} +134.616 q^{75} -629.269 q^{76} +431.923 q^{77} -326.635 q^{78} -423.816 q^{79} +143.223 q^{80} +81.0000 q^{81} +311.012 q^{82} +71.9109 q^{83} -84.0000 q^{84} +261.215 q^{85} -953.540 q^{86} -76.7604 q^{87} -493.627 q^{88} +15.3607 q^{89} -161.126 q^{90} -381.074 q^{91} -92.0000 q^{92} +764.247 q^{93} +1268.48 q^{94} -1408.21 q^{95} +96.0000 q^{96} -1745.01 q^{97} -98.0000 q^{98} +555.330 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 10 q^{2} - 15 q^{3} + 20 q^{4} - 15 q^{5} + 30 q^{6} + 35 q^{7} - 40 q^{8} + 45 q^{9}+O(q^{10}) $ 5 * q - 10 * q^2 - 15 * q^3 + 20 * q^4 - 15 * q^5 + 30 * q^6 + 35 * q^7 - 40 * q^8 + 45 * q^9	\( 5 q - 10 q^{2} - 15 q^{3} + 20 q^{4} - 15 q^{5} + 30 q^{6} + 35 q^{7} - 40 q^{8} + 45 q^{9} + 30 q^{10} - 19 q^{11} - 60 q^{12} - 19 q^{13} - 70 q^{14} + 45 q^{15} + 80 q^{16} - 42 q^{17} - 90 q^{18} - 25 q^{19} - 60 q^{20} - 105 q^{21} + 38 q^{22} - 115 q^{23} + 120 q^{24} + 206 q^{25} + 38 q^{26} - 135 q^{27} + 140 q^{28} - 292 q^{29} - 90 q^{30} - 60 q^{31} - 160 q^{32} + 57 q^{33} + 84 q^{34} - 105 q^{35} + 180 q^{36} + 264 q^{37} + 50 q^{38} + 57 q^{39} + 120 q^{40} + 223 q^{41} + 210 q^{42} + 661 q^{43} - 76 q^{44} - 135 q^{45} + 230 q^{46} - 279 q^{47} - 240 q^{48} + 245 q^{49} - 412 q^{50} + 126 q^{51} - 76 q^{52} - 324 q^{53} + 270 q^{54} + 1077 q^{55} - 280 q^{56} + 75 q^{57} + 584 q^{58} + 26 q^{59} + 180 q^{60} - 460 q^{61} + 120 q^{62} + 315 q^{63} + 320 q^{64} + 528 q^{65} - 114 q^{66} + 1541 q^{67} - 168 q^{68} + 345 q^{69} + 210 q^{70} - 319 q^{71} - 360 q^{72} + 1532 q^{73} - 528 q^{74} - 618 q^{75} - 100 q^{76} - 133 q^{77} - 114 q^{78} + 1242 q^{79} - 240 q^{80} + 405 q^{81} - 446 q^{82} - 1390 q^{83} - 420 q^{84} - 39 q^{85} - 1322 q^{86} + 876 q^{87} + 152 q^{88} - 1171 q^{89} + 270 q^{90} - 133 q^{91} - 460 q^{92} + 180 q^{93} + 558 q^{94} - 3435 q^{95} + 480 q^{96} - 1800 q^{97} - 490 q^{98} - 171 q^{99}+O(q^{100}) \) 5 * q - 10 * q^2 - 15 * q^3 + 20 * q^4 - 15 * q^5 + 30 * q^6 + 35 * q^7 - 40 * q^8 + 45 * q^9 + 30 * q^10 - 19 * q^11 - 60 * q^12 - 19 * q^13 - 70 * q^14 + 45 * q^15 + 80 * q^16 - 42 * q^17 - 90 * q^18 - 25 * q^19 - 60 * q^20 - 105 * q^21 + 38 * q^22 - 115 * q^23 + 120 * q^24 + 206 * q^25 + 38 * q^26 - 135 * q^27 + 140 * q^28 - 292 * q^29 - 90 * q^30 - 60 * q^31 - 160 * q^32 + 57 * q^33 + 84 * q^34 - 105 * q^35 + 180 * q^36 + 264 * q^37 + 50 * q^38 + 57 * q^39 + 120 * q^40 + 223 * q^41 + 210 * q^42 + 661 * q^43 - 76 * q^44 - 135 * q^45 + 230 * q^46 - 279 * q^47 - 240 * q^48 + 245 * q^49 - 412 * q^50 + 126 * q^51 - 76 * q^52 - 324 * q^53 + 270 * q^54 + 1077 * q^55 - 280 * q^56 + 75 * q^57 + 584 * q^58 + 26 * q^59 + 180 * q^60 - 460 * q^61 + 120 * q^62 + 315 * q^63 + 320 * q^64 + 528 * q^65 - 114 * q^66 + 1541 * q^67 - 168 * q^68 + 345 * q^69 + 210 * q^70 - 319 * q^71 - 360 * q^72 + 1532 * q^73 - 528 * q^74 - 618 * q^75 - 100 * q^76 - 133 * q^77 - 114 * q^78 + 1242 * q^79 - 240 * q^80 + 405 * q^81 - 446 * q^82 - 1390 * q^83 - 420 * q^84 - 39 * q^85 - 1322 * q^86 + 876 * q^87 + 152 * q^88 - 1171 * q^89 + 270 * q^90 - 133 * q^91 - 460 * q^92 + 180 * q^93 + 558 * q^94 - 3435 * q^95 + 480 * q^96 - 1800 * q^97 - 490 * q^98 - 171 * 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 $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	4.00000	0.500000
$5$	8.95143	0.800640	0.400320	−	0.916375i	$-0.368899\pi$
$5$	8.95143	0.800640	0.400320	+	0.916375i	$0.368899\pi$
$6$	6.00000	0.408248
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	−17.9029	−0.566138
$11$	61.7033	1.69130	0.845648	−	0.533741i	$-0.179214\pi$
$11$	61.7033	1.69130	0.845648	+	0.533741i	$0.179214\pi$
$12$	−12.0000	−0.288675
$13$	−54.4391	−1.16144	−0.580719	−	0.814104i	$-0.697229\pi$
$13$	−54.4391	−1.16144	−0.580719	+	0.814104i	$0.697229\pi$
$14$	−14.0000	−0.267261
$15$	−26.8543	−0.462250
$16$	16.0000	0.250000
$17$	29.1814	0.416325	0.208163	−	0.978094i	$-0.433252\pi$
$17$	29.1814	0.416325	0.208163	+	0.978094i	$0.433252\pi$
$18$	−18.0000	−0.235702
$19$	−157.317	−1.89953	−0.949765	−	0.312965i	$-0.898678\pi$
$19$	−157.317	−1.89953	−0.949765	+	0.312965i	$0.898678\pi$
$20$	35.8057	0.400320
$21$	−21.0000	−0.218218
$22$	−123.407	−1.19593
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	24.0000	0.204124
$25$	−44.8719	−0.358975
$26$	108.878	0.821261
$27$	−27.0000	−0.192450
$28$	28.0000	0.188982
$29$	25.5868	0.163840	0.0819198	−	0.996639i	$-0.473895\pi$
$29$	25.5868	0.163840	0.0819198	+	0.996639i	$0.473895\pi$
$30$	53.7086	0.326860
$31$	−254.749	−1.47594	−0.737972	−	0.674831i	$-0.764216\pi$
$31$	−254.749	−1.47594	−0.737972	+	0.674831i	$0.764216\pi$
$32$	−32.0000	−0.176777
$33$	−185.110	−0.976470
$34$	−58.3628	−0.294386
$35$	62.6600	0.302614
$36$	36.0000	0.166667
$37$	101.617	0.451507	0.225754	−	0.974184i	$-0.427516\pi$
$37$	101.617	0.451507	0.225754	+	0.974184i	$0.427516\pi$
$38$	314.635	1.34317
$39$	163.317	0.670557
$40$	−71.6115	−0.283069
$41$	−155.506	−0.592341	−0.296170	−	0.955135i	$-0.595710\pi$
$41$	−155.506	−0.592341	−0.296170	+	0.955135i	$0.595710\pi$
$42$	42.0000	0.154303
$43$	476.770	1.69085	0.845427	−	0.534090i	$-0.179346\pi$
$43$	476.770	1.69085	0.845427	+	0.534090i	$0.179346\pi$
$44$	246.813	0.845648
$45$	80.5629	0.266880
$46$	46.0000	0.147442
$47$	−634.239	−1.96837	−0.984184	−	0.177150i	$-0.943312\pi$
$47$	−634.239	−1.96837	−0.984184	+	0.177150i	$0.943312\pi$
$48$	−48.0000	−0.144338
$49$	49.0000	0.142857
$50$	89.7437	0.253834
$51$	−87.5442	−0.240365
$52$	−217.757	−0.580719
$53$	−547.555	−1.41910	−0.709551	−	0.704654i	$-0.751102\pi$
$53$	−547.555	−1.41910	−0.709551	+	0.704654i	$0.751102\pi$
$54$	54.0000	0.136083
$55$	552.333	1.35412
$56$	−56.0000	−0.133631
$57$	471.952	1.09669
$58$	−51.1736	−0.115852
$59$	−174.801	−0.385715	−0.192857	−	0.981227i	$-0.561775\pi$
$59$	−174.801	−0.385715	−0.192857	+	0.981227i	$0.561775\pi$
$60$	−107.417	−0.231125
$61$	−53.4115	−0.112109	−0.0560545	−	0.998428i	$-0.517852\pi$
$61$	−53.4115	−0.112109	−0.0560545	+	0.998428i	$0.517852\pi$
$62$	509.498	1.04365
$63$	63.0000	0.125988
$64$	64.0000	0.125000
$65$	−487.308	−0.929895
$66$	370.220	0.690469
$67$	593.651	1.08248	0.541239	−	0.840869i	$-0.317956\pi$
$67$	593.651	1.08248	0.541239	+	0.840869i	$0.317956\pi$
$68$	116.726	0.208163
$69$	69.0000	0.120386
$70$	−125.320	−0.213980
$71$	416.322	0.695892	0.347946	−	0.937515i	$-0.386879\pi$
$71$	416.322	0.695892	0.347946	+	0.937515i	$0.386879\pi$
$72$	−72.0000	−0.117851
$73$	378.705	0.607179	0.303589	−	0.952803i	$-0.401815\pi$
$73$	378.705	0.607179	0.303589	+	0.952803i	$0.401815\pi$
$74$	−203.234	−0.319264
$75$	134.616	0.207254
$76$	−629.269	−0.949765
$77$	431.923	0.639250
$78$	−326.635	−0.474155
$79$	−423.816	−0.603583	−0.301791	−	0.953374i	$-0.597585\pi$
$79$	−423.816	−0.603583	−0.301791	+	0.953374i	$0.597585\pi$
$80$	143.223	0.200160
$81$	81.0000	0.111111
$82$	311.012	0.418848
$83$	71.9109	0.0950994	0.0475497	−	0.998869i	$-0.484859\pi$
$83$	71.9109	0.0950994	0.0475497	+	0.998869i	$0.484859\pi$
$84$	−84.0000	−0.109109
$85$	261.215	0.333327
$86$	−953.540	−1.19561
$87$	−76.7604	−0.0945928
$88$	−493.627	−0.597964
$89$	15.3607	0.0182948	0.00914738	−	0.999958i	$-0.497088\pi$
$89$	15.3607	0.0182948	0.00914738	+	0.999958i	$0.497088\pi$
$90$	−161.126	−0.188713
$91$	−381.074	−0.438982
$92$	−92.0000	−0.104257
$93$	764.247	0.852137
$94$	1268.48	1.39185
$95$	−1408.21	−1.52084
$96$	96.0000	0.102062
$97$	−1745.01	−1.82658	−0.913292	−	0.407305i	$-0.866469\pi$
$97$	−1745.01	−1.82658	−0.913292	+	0.407305i	$0.866469\pi$
$98$	−98.0000	−0.101015
$99$	555.330	0.563765
$100$	−179.487	−0.179487
$101$	−78.4142	−0.0772525	−0.0386263	−	0.999254i	$-0.512298\pi$
$101$	−78.4142	−0.0772525	−0.0386263	+	0.999254i	$0.512298\pi$
$102$	175.088	0.169964
$103$	500.302	0.478604	0.239302	−	0.970945i	$-0.423081\pi$
$103$	500.302	0.478604	0.239302	+	0.970945i	$0.423081\pi$
$104$	435.513	0.410630
$105$	−187.980	−0.174714
$106$	1095.11	1.00346
$107$	711.814	0.643119	0.321559	−	0.946889i	$-0.395793\pi$
$107$	711.814	0.643119	0.321559	+	0.946889i	$0.395793\pi$
$108$	−108.000	−0.0962250
$109$	1247.50	1.09623	0.548113	−	0.836405i	$-0.315347\pi$
$109$	1247.50	1.09623	0.548113	+	0.836405i	$0.315347\pi$
$110$	−1104.67	−0.957508
$111$	−304.852	−0.260678
$112$	112.000	0.0944911
$113$	39.6471	0.0330060	0.0165030	−	0.999864i	$-0.494747\pi$
$113$	39.6471	0.0330060	0.0165030	+	0.999864i	$0.494747\pi$
$114$	−943.904	−0.775480
$115$	−205.883	−0.166945
$116$	102.347	0.0819198
$117$	−489.952	−0.387146
$118$	349.602	0.272741
$119$	204.270	0.157356
$120$	214.834	0.163430
$121$	2476.30	1.86048
$122$	106.823	0.0792730
$123$	466.518	0.341988
$124$	−1019.00	−0.737972
$125$	−1520.60	−1.08805
$126$	−126.000	−0.0890871
$127$	−102.105	−0.0713416	−0.0356708	−	0.999364i	$-0.511357\pi$
$127$	−102.105	−0.0713416	−0.0356708	+	0.999364i	$0.511357\pi$
$128$	−128.000	−0.0883883
$129$	−1430.31	−0.976215
$130$	974.616	0.657535
$131$	−638.174	−0.425630	−0.212815	−	0.977093i	$-0.568263\pi$
$131$	−638.174	−0.425630	−0.212815	+	0.977093i	$0.568263\pi$
$132$	−740.440	−0.488235
$133$	−1101.22	−0.717955
$134$	−1187.30	−0.765427
$135$	−241.689	−0.154083
$136$	−233.451	−0.147193
$137$	140.517	0.0876290	0.0438145	−	0.999040i	$-0.486049\pi$
$137$	140.517	0.0876290	0.0438145	+	0.999040i	$0.486049\pi$
$138$	−138.000	−0.0851257
$139$	−2098.79	−1.28070	−0.640348	−	0.768085i	$-0.721210\pi$
$139$	−2098.79	−1.28070	−0.640348	+	0.768085i	$0.721210\pi$
$140$	250.640	0.151307
$141$	1902.72	1.13644
$142$	−832.644	−0.492070
$143$	−3359.08	−1.96434
$144$	144.000	0.0833333
$145$	229.038	0.131177
$146$	−757.410	−0.429340
$147$	−147.000	−0.0824786
$148$	406.469	0.225754
$149$	−3219.34	−1.77006	−0.885030	−	0.465535i	$-0.845862\pi$
$149$	−3219.34	−1.77006	−0.885030	+	0.465535i	$0.845862\pi$
$150$	−269.231	−0.146551
$151$	−3486.65	−1.87907	−0.939536	−	0.342451i	$-0.888743\pi$
$151$	−3486.65	−1.87907	−0.939536	+	0.342451i	$0.888743\pi$
$152$	1258.54	0.671585
$153$	262.633	0.138775
$154$	−863.847	−0.452018
$155$	−2280.37	−1.18170
$156$	653.270	0.335278
$157$	1045.19	0.531306	0.265653	−	0.964069i	$-0.414412\pi$
$157$	1045.19	0.531306	0.265653	+	0.964069i	$0.414412\pi$
$158$	847.632	0.426798
$159$	1642.66	0.819319
$160$	−286.446	−0.141535
$161$	−161.000	−0.0788110
$162$	−162.000	−0.0785674
$163$	−821.434	−0.394722	−0.197361	−	0.980331i	$-0.563237\pi$
$163$	−821.434	−0.394722	−0.197361	+	0.980331i	$0.563237\pi$
$164$	−622.025	−0.296170
$165$	−1657.00	−0.781802
$166$	−143.822	−0.0672454
$167$	3092.89	1.43314	0.716572	−	0.697514i	$-0.245710\pi$
$167$	3092.89	1.43314	0.716572	+	0.697514i	$0.245710\pi$
$168$	168.000	0.0771517
$169$	766.619	0.348939
$170$	−522.431	−0.235698
$171$	−1415.86	−0.633176
$172$	1907.08	0.845427
$173$	−1770.65	−0.778148	−0.389074	−	0.921206i	$-0.627205\pi$
$173$	−1770.65	−0.778148	−0.389074	+	0.921206i	$0.627205\pi$
$174$	153.521	0.0668872
$175$	−314.103	−0.135680
$176$	987.254	0.422824
$177$	524.403	0.222692
$178$	−30.7214	−0.0129363
$179$	−1906.84	−0.796224	−0.398112	−	0.917337i	$-0.630334\pi$
$179$	−1906.84	−0.796224	−0.398112	+	0.917337i	$0.630334\pi$
$180$	322.252	0.133440
$181$	−3119.21	−1.28094	−0.640468	−	0.767985i	$-0.721260\pi$
$181$	−3119.21	−1.28094	−0.640468	+	0.767985i	$0.721260\pi$
$182$	762.148	0.310407
$183$	160.235	0.0647261
$184$	184.000	0.0737210
$185$	909.620	0.361495
$186$	−1528.49	−0.602552
$187$	1800.59	0.704129
$188$	−2536.96	−0.984184
$189$	−189.000	−0.0727393
$190$	2816.43	1.07540
$191$	−4410.96	−1.67102	−0.835512	−	0.549472i	$-0.814829\pi$
$191$	−4410.96	−1.67102	−0.835512	+	0.549472i	$0.814829\pi$
$192$	−192.000	−0.0721688
$193$	−2901.21	−1.08204	−0.541020	−	0.841010i	$-0.681962\pi$
$193$	−2901.21	−1.08204	−0.541020	+	0.841010i	$0.681962\pi$
$194$	3490.02	1.29159
$195$	1461.92	0.536875
$196$	196.000	0.0714286
$197$	−314.888	−0.113883	−0.0569413	−	0.998378i	$-0.518135\pi$
$197$	−314.888	−0.113883	−0.0569413	+	0.998378i	$0.518135\pi$
$198$	−1110.66	−0.398642
$199$	−1985.00	−0.707101	−0.353551	−	0.935415i	$-0.615026\pi$
$199$	−1985.00	−0.707101	−0.353551	+	0.935415i	$0.615026\pi$
$200$	358.975	0.126917
$201$	−1780.95	−0.624968
$202$	156.828	0.0546258
$203$	179.108	0.0619255
$204$	−350.177	−0.120183
$205$	−1392.00	−0.474252
$206$	−1000.60	−0.338424
$207$	−207.000	−0.0695048
$208$	−871.026	−0.290360
$209$	−9707.00	−3.21267
$210$	375.960	0.123542
$211$	1956.10	0.638215	0.319107	−	0.947719i	$-0.396617\pi$
$211$	1956.10	0.638215	0.319107	+	0.947719i	$0.396617\pi$
$212$	−2190.22	−0.709551
$213$	−1248.97	−0.401773
$214$	−1423.63	−0.454753
$215$	4267.78	1.35377
$216$	216.000	0.0680414
$217$	−1783.24	−0.557854
$218$	−2494.99	−0.775148
$219$	−1136.11	−0.350555
$220$	2209.33	0.677060
$221$	−1588.61	−0.483536
$222$	609.703	0.184327
$223$	−2858.95	−0.858519	−0.429259	−	0.903181i	$-0.641225\pi$
$223$	−2858.95	−0.858519	−0.429259	+	0.903181i	$0.641225\pi$
$224$	−224.000	−0.0668153
$225$	−403.847	−0.119658
$226$	−79.2941	−0.0233388
$227$	1156.28	0.338084	0.169042	−	0.985609i	$-0.445933\pi$
$227$	1156.28	0.338084	0.169042	+	0.985609i	$0.445933\pi$
$228$	1887.81	0.548347
$229$	2035.29	0.587317	0.293658	−	0.955910i	$-0.405127\pi$
$229$	2035.29	0.587317	0.293658	+	0.955910i	$0.405127\pi$
$230$	411.766	0.118048
$231$	−1295.77	−0.369071
$232$	−204.694	−0.0579260
$233$	3940.72	1.10801	0.554003	−	0.832515i	$-0.313100\pi$
$233$	3940.72	1.10801	0.554003	+	0.832515i	$0.313100\pi$
$234$	979.904	0.273754
$235$	−5677.35	−1.57595
$236$	−699.204	−0.192857
$237$	1271.45	0.348479
$238$	−408.540	−0.111268
$239$	−6221.94	−1.68395	−0.841974	−	0.539518i	$-0.818607\pi$
$239$	−6221.94	−1.68395	−0.841974	+	0.539518i	$0.818607\pi$
$240$	−429.669	−0.115562
$241$	6523.72	1.74369	0.871846	−	0.489781i	$-0.162923\pi$
$241$	6523.72	1.74369	0.871846	+	0.489781i	$0.162923\pi$
$242$	−4952.61	−1.31556
$243$	−243.000	−0.0641500
$244$	−213.646	−0.0560545
$245$	438.620	0.114377
$246$	−933.037	−0.241822
$247$	8564.22	2.20619
$248$	2037.99	0.521825
$249$	−215.733	−0.0549057
$250$	3041.19	0.769368
$251$	5833.99	1.46708	0.733542	−	0.679645i	$-0.237866\pi$
$251$	5833.99	1.46708	0.733542	+	0.679645i	$0.237866\pi$
$252$	252.000	0.0629941
$253$	−1419.18	−0.352660
$254$	204.211	0.0504461
$255$	−783.646	−0.192446
$256$	256.000	0.0625000
$257$	2472.23	0.600052	0.300026	−	0.953931i	$-0.403005\pi$
$257$	2472.23	0.600052	0.300026	+	0.953931i	$0.403005\pi$
$258$	2860.62	0.690289
$259$	711.321	0.170654
$260$	−1949.23	−0.464947
$261$	230.281	0.0546132
$262$	1276.35	0.300966
$263$	5966.88	1.39899	0.699493	−	0.714639i	$-0.253409\pi$
$263$	5966.88	1.39899	0.699493	+	0.714639i	$0.253409\pi$
$264$	1480.88	0.345234
$265$	−4901.40	−1.13619
$266$	2202.44	0.507671
$267$	−46.0822	−0.0105625
$268$	2374.60	0.541239
$269$	−2741.67	−0.621423	−0.310712	−	0.950504i	$-0.600567\pi$
$269$	−2741.67	−0.621423	−0.310712	+	0.950504i	$0.600567\pi$
$270$	483.377	0.108953
$271$	6842.72	1.53382	0.766910	−	0.641754i	$-0.221793\pi$
$271$	6842.72	1.53382	0.766910	+	0.641754i	$0.221793\pi$
$272$	466.902	0.104081
$273$	1143.22	0.253447
$274$	−281.034	−0.0619631
$275$	−2768.74	−0.607133
$276$	276.000	0.0601929
$277$	−3914.09	−0.849007	−0.424504	−	0.905426i	$-0.639551\pi$
$277$	−3914.09	−0.849007	−0.424504	+	0.905426i	$0.639551\pi$
$278$	4197.58	0.905589
$279$	−2292.74	−0.491981
$280$	−501.280	−0.106990
$281$	−3185.59	−0.676286	−0.338143	−	0.941095i	$-0.609799\pi$
$281$	−3185.59	−0.676286	−0.338143	+	0.941095i	$0.609799\pi$
$282$	−3805.43	−0.803583
$283$	4069.98	0.854895	0.427447	−	0.904040i	$-0.359413\pi$
$283$	4069.98	0.854895	0.427447	+	0.904040i	$0.359413\pi$
$284$	1665.29	0.347946
$285$	4224.64	0.878057
$286$	6718.15	1.38900
$287$	−1088.54	−0.223884
$288$	−288.000	−0.0589256
$289$	−4061.45	−0.826673
$290$	−458.077	−0.0927559
$291$	5235.02	1.05458
$292$	1514.82	0.303589
$293$	−5645.74	−1.12569	−0.562846	−	0.826562i	$-0.690294\pi$
$293$	−5645.74	−1.12569	−0.562846	+	0.826562i	$0.690294\pi$
$294$	294.000	0.0583212
$295$	−1564.72	−0.308819
$296$	−812.938	−0.159632
$297$	−1665.99	−0.325490
$298$	6438.68	1.25162
$299$	1252.10	0.242177
$300$	538.462	0.103627
$301$	3337.39	0.639083
$302$	6973.31	1.32870
$303$	235.243	0.0446018
$304$	−2517.08	−0.474882
$305$	−478.110	−0.0897589
$306$	−525.265	−0.0981288
$307$	4251.12	0.790307	0.395153	−	0.918615i	$-0.370691\pi$
$307$	4251.12	0.790307	0.395153	+	0.918615i	$0.370691\pi$
$308$	1727.69	0.319625
$309$	−1500.91	−0.276322
$310$	4560.74	0.835589
$311$	2923.74	0.533088	0.266544	−	0.963823i	$-0.414118\pi$
$311$	2923.74	0.533088	0.266544	+	0.963823i	$0.414118\pi$
$312$	−1306.54	−0.237078
$313$	−7942.92	−1.43438	−0.717190	−	0.696878i	$-0.754572\pi$
$313$	−7942.92	−1.43438	−0.717190	+	0.696878i	$0.754572\pi$
$314$	−2090.38	−0.375690
$315$	563.940	0.100871
$316$	−1695.26	−0.301791
$317$	692.119	0.122629	0.0613143	−	0.998119i	$-0.480471\pi$
$317$	692.119	0.122629	0.0613143	+	0.998119i	$0.480471\pi$
$318$	−3285.33	−0.579346
$319$	1578.79	0.277101
$320$	572.892	0.100080
$321$	−2135.44	−0.371305
$322$	322.000	0.0557278
$323$	−4590.74	−0.790822
$324$	324.000	0.0555556
$325$	2442.78	0.416927
$326$	1642.87	0.279111
$327$	−3742.49	−0.632906
$328$	1244.05	0.209424
$329$	−4439.67	−0.743973
$330$	3314.00	0.552817
$331$	4956.62	0.823083	0.411542	−	0.911391i	$-0.364991\pi$
$331$	4956.62	0.823083	0.411542	+	0.911391i	$0.364991\pi$
$332$	287.644	0.0475497
$333$	914.555	0.150502
$334$	−6185.78	−1.01339
$335$	5314.02	0.866675
$336$	−336.000	−0.0545545
$337$	−7374.83	−1.19208	−0.596042	−	0.802953i	$-0.703261\pi$
$337$	−7374.83	−1.19208	−0.596042	+	0.802953i	$0.703261\pi$
$338$	−1533.24	−0.246737
$339$	−118.941	−0.0190560
$340$	1044.86	0.166663
$341$	−15718.9	−2.49626
$342$	2831.71	0.447723
$343$	343.000	0.0539949
$344$	−3814.16	−0.597807
$345$	617.649	0.0963858
$346$	3541.29	0.550234
$347$	4250.12	0.657517	0.328758	−	0.944414i	$-0.393370\pi$
$347$	4250.12	0.657517	0.328758	+	0.944414i	$0.393370\pi$
$348$	−307.041	−0.0472964
$349$	−2241.11	−0.343735	−0.171868	−	0.985120i	$-0.554980\pi$
$349$	−2241.11	−0.343735	−0.171868	+	0.985120i	$0.554980\pi$
$350$	628.206	0.0959401
$351$	1469.86	0.223519
$352$	−1974.51	−0.298982
$353$	−1501.11	−0.226335	−0.113167	−	0.993576i	$-0.536100\pi$
$353$	−1501.11	−0.226335	−0.113167	+	0.993576i	$0.536100\pi$
$354$	−1048.81	−0.157467
$355$	3726.68	0.557159
$356$	61.4429	0.00914738
$357$	−612.809	−0.0908496
$358$	3813.68	0.563015
$359$	−2551.16	−0.375056	−0.187528	−	0.982259i	$-0.560048\pi$
$359$	−2551.16	−0.375056	−0.187528	+	0.982259i	$0.560048\pi$
$360$	−644.503	−0.0943564
$361$	17889.7	2.60821
$362$	6238.43	0.905758
$363$	−7428.91	−1.07415
$364$	−1524.30	−0.219491
$365$	3389.95	0.486132
$366$	−320.469	−0.0457683
$367$	12196.4	1.73473	0.867367	−	0.497668i	$-0.165810\pi$
$367$	12196.4	1.73473	0.867367	+	0.497668i	$0.165810\pi$
$368$	−368.000	−0.0521286
$369$	−1399.56	−0.197447
$370$	−1819.24	−0.255616
$371$	−3832.88	−0.536370
$372$	3056.99	0.426068
$373$	−8484.96	−1.17784	−0.588920	−	0.808191i	$-0.700447\pi$
$373$	−8484.96	−1.17784	−0.588920	+	0.808191i	$0.700447\pi$
$374$	−3601.18	−0.497895
$375$	4561.79	0.628186
$376$	5073.91	0.695923
$377$	−1392.92	−0.190290
$378$	378.000	0.0514344
$379$	3702.20	0.501766	0.250883	−	0.968017i	$-0.419279\pi$
$379$	3702.20	0.501766	0.250883	+	0.968017i	$0.419279\pi$
$380$	−5632.86	−0.760420
$381$	306.316	0.0411891
$382$	8821.91	1.18159
$383$	2878.06	0.383974	0.191987	−	0.981397i	$-0.438507\pi$
$383$	2878.06	0.383974	0.191987	+	0.981397i	$0.438507\pi$
$384$	384.000	0.0510310
$385$	3866.33	0.511809
$386$	5802.42	0.765118
$387$	4290.93	0.563618
$388$	−6980.03	−0.913292
$389$	−15006.0	−1.95587	−0.977937	−	0.208902i	$-0.933011\pi$
$389$	−15006.0	−1.95587	−0.977937	+	0.208902i	$0.933011\pi$
$390$	−2923.85	−0.379628
$391$	−671.172	−0.0868098
$392$	−392.000	−0.0505076
$393$	1914.52	0.245738
$394$	629.777	0.0805271
$395$	−3793.76	−0.483253
$396$	2221.32	0.281883
$397$	1001.33	0.126588	0.0632941	−	0.997995i	$-0.479839\pi$
$397$	1001.33	0.126588	0.0632941	+	0.997995i	$0.479839\pi$
$398$	3970.01	0.499996
$399$	3303.66	0.414511
$400$	−717.950	−0.0897437
$401$	−1779.78	−0.221641	−0.110821	−	0.993840i	$-0.535348\pi$
$401$	−1779.78	−0.221641	−0.110821	+	0.993840i	$0.535348\pi$
$402$	3561.90	0.441919
$403$	13868.3	1.71422
$404$	−313.657	−0.0386263
$405$	725.066	0.0889601
$406$	−358.215	−0.0437880
$407$	6270.12	0.763633
$408$	700.354	0.0849820
$409$	5952.40	0.719626	0.359813	−	0.933024i	$-0.382840\pi$
$409$	5952.40	0.719626	0.359813	+	0.933024i	$0.382840\pi$
$410$	2784.01	0.335347
$411$	−421.551	−0.0505926
$412$	2001.21	0.239302
$413$	−1223.61	−0.145786
$414$	414.000	0.0491473
$415$	643.706	0.0761404
$416$	1742.05	0.205315
$417$	6296.36	0.739411
$418$	19414.0	2.27170
$419$	−14634.3	−1.70628	−0.853140	−	0.521682i	$-0.825305\pi$
$419$	−14634.3	−1.70628	−0.853140	+	0.521682i	$0.825305\pi$
$420$	−751.920	−0.0873570
$421$	−12874.4	−1.49041	−0.745204	−	0.666836i	$-0.767648\pi$
$421$	−12874.4	−1.49041	−0.745204	+	0.666836i	$0.767648\pi$
$422$	−3912.19	−0.451286
$423$	−5708.15	−0.656123
$424$	4380.44	0.501728
$425$	−1309.42	−0.149450
$426$	2497.93	0.284097
$427$	−373.881	−0.0423732
$428$	2847.26	0.321559
$429$	10077.2	1.13411
$430$	−8535.55	−0.957258
$431$	−4216.57	−0.471241	−0.235620	−	0.971845i	$-0.575712\pi$
$431$	−4216.57	−0.471241	−0.235620	+	0.971845i	$0.575712\pi$
$432$	−432.000	−0.0481125
$433$	−7989.43	−0.886714	−0.443357	−	0.896345i	$-0.646213\pi$
$433$	−7989.43	−0.886714	−0.443357	+	0.896345i	$0.646213\pi$
$434$	3566.49	0.394463
$435$	−687.115	−0.0757348
$436$	4989.99	0.548113
$437$	3618.30	0.396079
$438$	2272.23	0.247880
$439$	−3189.74	−0.346783	−0.173392	−	0.984853i	$-0.555473\pi$
$439$	−3189.74	−0.346783	−0.173392	+	0.984853i	$0.555473\pi$
$440$	−4418.67	−0.478754
$441$	441.000	0.0476190
$442$	3177.22	0.341912
$443$	554.007	0.0594169	0.0297084	−	0.999559i	$-0.490542\pi$
$443$	554.007	0.0594169	0.0297084	+	0.999559i	$0.490542\pi$
$444$	−1219.41	−0.130339
$445$	137.500	0.0146475
$446$	5717.91	0.607065
$447$	9658.03	1.02194
$448$	448.000	0.0472456
$449$	8490.20	0.892377	0.446189	−	0.894939i	$-0.352781\pi$
$449$	8490.20	0.892377	0.446189	+	0.894939i	$0.352781\pi$
$450$	807.693	0.0846112
$451$	−9595.25	−1.00182
$452$	158.588	0.0165030
$453$	10460.0	1.08488
$454$	−2312.56	−0.239061
$455$	−3411.16	−0.351467
$456$	−3775.61	−0.387740
$457$	5292.78	0.541763	0.270881	−	0.962613i	$-0.412685\pi$
$457$	5292.78	0.541763	0.270881	+	0.962613i	$0.412685\pi$
$458$	−4070.57	−0.415296
$459$	−787.898	−0.0801218
$460$	−823.532	−0.0834725
$461$	−175.243	−0.0177047	−0.00885234	−	0.999961i	$-0.502818\pi$
$461$	−175.243	−0.0177047	−0.00885234	+	0.999961i	$0.502818\pi$
$462$	2591.54	0.260973
$463$	8239.16	0.827011	0.413506	−	0.910502i	$-0.364304\pi$
$463$	8239.16	0.827011	0.413506	+	0.910502i	$0.364304\pi$
$464$	409.389	0.0409599
$465$	6841.10	0.682255
$466$	−7881.44	−0.783478
$467$	15280.0	1.51407	0.757037	−	0.653372i	$-0.226646\pi$
$467$	15280.0	1.51407	0.757037	+	0.653372i	$0.226646\pi$
$468$	−1959.81	−0.193573
$469$	4155.55	0.409138
$470$	11354.7	1.11437
$471$	−3135.56	−0.306750
$472$	1398.41	0.136371
$473$	29418.3	2.85974
$474$	−2542.90	−0.246412
$475$	7059.12	0.681883
$476$	817.079	0.0786781
$477$	−4927.99	−0.473034
$478$	12443.9	1.19073
$479$	8168.52	0.779184	0.389592	−	0.920987i	$-0.372616\pi$
$479$	8168.52	0.779184	0.389592	+	0.920987i	$0.372616\pi$
$480$	859.338	0.0817150
$481$	−5531.95	−0.524398
$482$	−13047.4	−1.23298
$483$	483.000	0.0455016
$484$	9905.21	0.930242
$485$	−15620.3	−1.46244
$486$	486.000	0.0453609
$487$	2249.02	0.209266	0.104633	−	0.994511i	$-0.466633\pi$
$487$	2249.02	0.209266	0.104633	+	0.994511i	$0.466633\pi$
$488$	427.292	0.0396365
$489$	2464.30	0.227893
$490$	−877.240	−0.0808769
$491$	−2655.49	−0.244075	−0.122037	−	0.992526i	$-0.538943\pi$
$491$	−2655.49	−0.244075	−0.122037	+	0.992526i	$0.538943\pi$
$492$	1866.07	0.170994
$493$	746.658	0.0682105
$494$	−17128.4	−1.56001
$495$	4971.00	0.451373
$496$	−4075.98	−0.368986
$497$	2914.25	0.263022
$498$	431.466	0.0388242
$499$	−3099.72	−0.278081	−0.139041	−	0.990287i	$-0.544402\pi$
$499$	−3099.72	−0.278081	−0.139041	+	0.990287i	$0.544402\pi$
$500$	−6082.39	−0.544025
$501$	−9278.66	−0.827426
$502$	−11668.0	−1.03738
$503$	−8156.81	−0.723050	−0.361525	−	0.932362i	$-0.617744\pi$
$503$	−8156.81	−0.723050	−0.361525	+	0.932362i	$0.617744\pi$
$504$	−504.000	−0.0445435
$505$	−701.919	−0.0618515
$506$	2838.35	0.249368
$507$	−2299.86	−0.201460
$508$	−408.421	−0.0356708
$509$	10163.9	0.885082	0.442541	−	0.896748i	$-0.354077\pi$
$509$	10163.9	0.885082	0.442541	+	0.896748i	$0.354077\pi$
$510$	1567.29	0.136080
$511$	2650.93	0.229492
$512$	−512.000	−0.0441942
$513$	4247.57	0.365565
$514$	−4944.45	−0.424301
$515$	4478.42	0.383190
$516$	−5721.24	−0.488108
$517$	−39134.7	−3.32909
$518$	−1422.64	−0.120670
$519$	5311.94	0.449264
$520$	3898.47	0.328767
$521$	−1048.80	−0.0881931	−0.0440966	−	0.999027i	$-0.514041\pi$
$521$	−1048.80	−0.0881931	−0.0440966	+	0.999027i	$0.514041\pi$
$522$	−460.562	−0.0386174
$523$	1225.73	0.102481	0.0512405	−	0.998686i	$-0.483682\pi$
$523$	1225.73	0.102481	0.0512405	+	0.998686i	$0.483682\pi$
$524$	−2552.70	−0.212815
$525$	942.309	0.0783347
$526$	−11933.8	−0.989233
$527$	−7433.93	−0.614473
$528$	−2961.76	−0.244118
$529$	529.000	0.0434783
$530$	9802.79	0.803408
$531$	−1573.21	−0.128572
$532$	−4404.88	−0.358977
$533$	8465.62	0.687967
$534$	92.1643	0.00746880
$535$	6371.76	0.514907
$536$	−4749.20	−0.382713
$537$	5720.53	0.459700
$538$	5483.35	0.439412
$539$	3023.46	0.241614
$540$	−966.755	−0.0770417
$541$	−18028.3	−1.43271	−0.716356	−	0.697735i	$-0.754191\pi$
$541$	−18028.3	−1.43271	−0.716356	+	0.697735i	$0.754191\pi$
$542$	−13685.4	−1.08458
$543$	9357.64	0.739549
$544$	−933.805	−0.0735966
$545$	11166.9	0.877682
$546$	−2286.44	−0.179214
$547$	1327.43	0.103760	0.0518802	−	0.998653i	$-0.483479\pi$
$547$	1327.43	0.103760	0.0518802	+	0.998653i	$0.483479\pi$
$548$	562.068	0.0438145
$549$	−480.704	−0.0373696
$550$	5537.49	0.429308
$551$	−4025.24	−0.311218
$552$	−552.000	−0.0425628
$553$	−2966.71	−0.228133
$554$	7828.18	0.600339
$555$	−2728.86	−0.208709
$556$	−8395.15	−0.640348
$557$	11658.1	0.886841	0.443420	−	0.896314i	$-0.353765\pi$
$557$	11658.1	0.886841	0.443420	+	0.896314i	$0.353765\pi$
$558$	4585.48	0.347883
$559$	−25955.0	−1.96382
$560$	1002.56	0.0756534
$561$	−5401.77	−0.406529
$562$	6371.18	0.478206
$563$	−3715.96	−0.278169	−0.139084	−	0.990281i	$-0.544416\pi$
$563$	−3715.96	−0.278169	−0.139084	+	0.990281i	$0.544416\pi$
$564$	7610.87	0.568219
$565$	354.898	0.0264260
$566$	−8139.96	−0.604502
$567$	567.000	0.0419961
$568$	−3330.58	−0.246035
$569$	−168.062	−0.0123823	−0.00619113	−	0.999981i	$-0.501971\pi$
$569$	−168.062	−0.0123823	−0.00619113	+	0.999981i	$0.501971\pi$
$570$	−8449.29	−0.620880
$571$	4028.01	0.295213	0.147607	−	0.989046i	$-0.452843\pi$
$571$	4028.01	0.295213	0.147607	+	0.989046i	$0.452843\pi$
$572$	−13436.3	−0.982168
$573$	13232.9	0.964766
$574$	2177.09	0.158310
$575$	1032.05	0.0748514
$576$	576.000	0.0416667
$577$	9778.23	0.705499	0.352750	−	0.935718i	$-0.385247\pi$
$577$	9778.23	0.705499	0.352750	+	0.935718i	$0.385247\pi$
$578$	8122.89	0.584546
$579$	8703.63	0.624716
$580$	916.154	0.0655883
$581$	503.377	0.0359442
$582$	−10470.0	−0.745700
$583$	−33785.9	−2.40012
$584$	−3029.64	−0.214670
$585$	−4385.77	−0.309965
$586$	11291.5	0.795985
$587$	16928.6	1.19032	0.595162	−	0.803606i	$-0.297088\pi$
$587$	16928.6	1.19032	0.595162	+	0.803606i	$0.297088\pi$
$588$	−588.000	−0.0412393
$589$	40076.4	2.80360
$590$	3129.44	0.218368
$591$	944.665	0.0657501
$592$	1625.88	0.112877
$593$	−5427.49	−0.375852	−0.187926	−	0.982183i	$-0.560176\pi$
$593$	−5427.49	−0.375852	−0.187926	+	0.982183i	$0.560176\pi$
$594$	3331.98	0.230156
$595$	1828.51	0.125986
$596$	−12877.4	−0.885030
$597$	5955.01	0.408245
$598$	−2504.20	−0.171245
$599$	17801.2	1.21425	0.607125	−	0.794606i	$-0.292323\pi$
$599$	17801.2	1.21425	0.607125	+	0.794606i	$0.292323\pi$
$600$	−1076.92	−0.0732754
$601$	−16228.9	−1.10148	−0.550742	−	0.834675i	$-0.685655\pi$
$601$	−16228.9	−1.10148	−0.550742	+	0.834675i	$0.685655\pi$
$602$	−6674.78	−0.451900
$603$	5342.86	0.360826
$604$	−13946.6	−0.939536
$605$	22166.5	1.48958
$606$	−470.485	−0.0315382
$607$	−11664.1	−0.779955	−0.389977	−	0.920824i	$-0.627517\pi$
$607$	−11664.1	−0.779955	−0.389977	+	0.920824i	$0.627517\pi$
$608$	5034.15	0.335792
$609$	−537.323	−0.0357527
$610$	956.219	0.0634691
$611$	34527.4	2.28614
$612$	1050.53	0.0693875
$613$	29211.2	1.92468	0.962339	−	0.271852i	$-0.0876360\pi$
$613$	29211.2	1.92468	0.962339	+	0.271852i	$0.0876360\pi$
$614$	−8502.24	−0.558831
$615$	4176.01	0.273810
$616$	−3455.39	−0.226009
$617$	−7861.91	−0.512980	−0.256490	−	0.966547i	$-0.582566\pi$
$617$	−7861.91	−0.512980	−0.256490	+	0.966547i	$0.582566\pi$
$618$	3001.81	0.195389
$619$	−11316.2	−0.734795	−0.367398	−	0.930064i	$-0.619751\pi$
$619$	−11316.2	−0.734795	−0.367398	+	0.930064i	$0.619751\pi$
$620$	−9121.47	−0.590850
$621$	621.000	0.0401286
$622$	−5847.49	−0.376950
$623$	107.525	0.00691477
$624$	2613.08	0.167639
$625$	−8002.53	−0.512162
$626$	15885.8	1.01426
$627$	29121.0	1.85483
$628$	4180.75	0.265653
$629$	2965.33	0.187974
$630$	−1127.88	−0.0713267
$631$	21926.6	1.38333	0.691667	−	0.722217i	$-0.256877\pi$
$631$	21926.6	1.38333	0.691667	+	0.722217i	$0.256877\pi$
$632$	3390.53	0.213399
$633$	−5868.29	−0.368473
$634$	−1384.24	−0.0867115
$635$	−913.989	−0.0571190
$636$	6570.65	0.409659
$637$	−2667.52	−0.165920
$638$	−3157.58	−0.195940
$639$	3746.90	0.231964
$640$	−1145.78	−0.0707673
$641$	−14045.1	−0.865445	−0.432722	−	0.901527i	$-0.642447\pi$
$641$	−14045.1	−0.865445	−0.432722	+	0.901527i	$0.642447\pi$
$642$	4270.89	0.262552
$643$	80.6338	0.00494539	0.00247270	−	0.999997i	$-0.499213\pi$
$643$	80.6338	0.00494539	0.00247270	+	0.999997i	$0.499213\pi$
$644$	−644.000	−0.0394055
$645$	−12803.3	−0.781598
$646$	9181.47	0.559195
$647$	−23027.4	−1.39923	−0.699615	−	0.714520i	$-0.746645\pi$
$647$	−23027.4	−1.39923	−0.699615	+	0.714520i	$0.746645\pi$
$648$	−648.000	−0.0392837
$649$	−10785.8	−0.652358
$650$	−4885.57	−0.294812
$651$	5349.73	0.322077
$652$	−3285.74	−0.197361
$653$	−18908.8	−1.13317	−0.566583	−	0.824005i	$-0.691735\pi$
$653$	−18908.8	−1.13317	−0.566583	+	0.824005i	$0.691735\pi$
$654$	7484.98	0.447532
$655$	−5712.57	−0.340777
$656$	−2488.10	−0.148085
$657$	3408.34	0.202393
$658$	8879.35	0.526068
$659$	−28856.6	−1.70576	−0.852880	−	0.522107i	$-0.825146\pi$
$659$	−28856.6	−1.70576	−0.852880	+	0.522107i	$0.825146\pi$
$660$	−6628.00	−0.390901
$661$	5176.62	0.304610	0.152305	−	0.988334i	$-0.451330\pi$
$661$	5176.62	0.304610	0.152305	+	0.988334i	$0.451330\pi$
$662$	−9913.24	−0.582008
$663$	4765.83	0.279170
$664$	−575.287	−0.0336227
$665$	−9857.50	−0.574823
$666$	−1829.11	−0.106421
$667$	−588.496	−0.0341629
$668$	12371.6	0.716572
$669$	8576.86	0.495666
$670$	−10628.0	−0.612832
$671$	−3295.67	−0.189609
$672$	672.000	0.0385758
$673$	−1549.88	−0.0887717	−0.0443859	−	0.999014i	$-0.514133\pi$
$673$	−1549.88	−0.0887717	−0.0443859	+	0.999014i	$0.514133\pi$
$674$	14749.7	0.842931
$675$	1211.54	0.0690847
$676$	3066.48	0.174470
$677$	−14967.7	−0.849711	−0.424855	−	0.905261i	$-0.639675\pi$
$677$	−14967.7	−0.849711	−0.424855	+	0.905261i	$0.639675\pi$
$678$	237.882	0.0134747
$679$	−12215.1	−0.690384
$680$	−2089.72	−0.117849
$681$	−3468.84	−0.195193
$682$	31437.7	1.76512
$683$	−4263.48	−0.238855	−0.119427	−	0.992843i	$-0.538106\pi$
$683$	−4263.48	−0.238855	−0.119427	+	0.992843i	$0.538106\pi$
$684$	−5663.42	−0.316588
$685$	1257.83	0.0701594
$686$	−686.000	−0.0381802
$687$	−6105.86	−0.339087
$688$	7628.32	0.422714
$689$	29808.4	1.64820
$690$	−1235.30	−0.0681550
$691$	14242.3	0.784086	0.392043	−	0.919947i	$-0.371768\pi$
$691$	14242.3	0.784086	0.392043	+	0.919947i	$0.371768\pi$
$692$	−7082.58	−0.389074
$693$	3887.31	0.213083
$694$	−8500.24	−0.464935
$695$	−18787.2	−1.02538
$696$	614.083	0.0334436
$697$	−4537.89	−0.246606
$698$	4482.21	0.243058
$699$	−11822.2	−0.639707
$700$	−1256.41	−0.0678399
$701$	−21308.5	−1.14809	−0.574046	−	0.818823i	$-0.694627\pi$
$701$	−21308.5	−1.14809	−0.574046	+	0.818823i	$0.694627\pi$
$702$	−2939.71	−0.158052
$703$	−15986.1	−0.857651
$704$	3949.01	0.211412
$705$	17032.0	0.909878
$706$	3002.23	0.160043
$707$	−548.899	−0.0291987
$708$	2097.61	0.111346
$709$	32219.6	1.70668	0.853338	−	0.521357i	$-0.174574\pi$
$709$	32219.6	1.70668	0.853338	+	0.521357i	$0.174574\pi$
$710$	−7453.35	−0.393971
$711$	−3814.35	−0.201194
$712$	−122.886	−0.00646817
$713$	5859.23	0.307756
$714$	1225.62	0.0642404
$715$	−30068.5	−1.57273
$716$	−7627.37	−0.398112
$717$	18665.8	0.972228
$718$	5102.32	0.265205
$719$	4439.50	0.230272	0.115136	−	0.993350i	$-0.463270\pi$
$719$	4439.50	0.230272	0.115136	+	0.993350i	$0.463270\pi$
$720$	1289.01	0.0667200
$721$	3502.12	0.180895
$722$	−35779.4	−1.84428
$723$	−19571.2	−1.00672
$724$	−12476.9	−0.640468
$725$	−1148.13	−0.0588143
$726$	14857.8	0.759539
$727$	15591.2	0.795387	0.397694	−	0.917518i	$-0.369811\pi$
$727$	15591.2	0.795387	0.397694	+	0.917518i	$0.369811\pi$
$728$	3048.59	0.155204
$729$	729.000	0.0370370
$730$	−6779.90	−0.343747
$731$	13912.8	0.703945
$732$	640.938	0.0323631
$733$	−11149.4	−0.561820	−0.280910	−	0.959734i	$-0.590636\pi$
$733$	−11149.4	−0.561820	−0.280910	+	0.959734i	$0.590636\pi$
$734$	−24392.8	−1.22664
$735$	−1315.86	−0.0660357
$736$	736.000	0.0368605
$737$	36630.2	1.83079
$738$	2799.11	0.139616
$739$	−22740.9	−1.13199	−0.565993	−	0.824410i	$-0.691507\pi$
$739$	−22740.9	−1.13199	−0.565993	+	0.824410i	$0.691507\pi$
$740$	3638.48	0.180747
$741$	−25692.6	−1.27374
$742$	7665.76	0.379271
$743$	−35703.0	−1.76287	−0.881437	−	0.472301i	$-0.843424\pi$
$743$	−35703.0	−1.76287	−0.881437	+	0.472301i	$0.843424\pi$
$744$	−6113.98	−0.301276
$745$	−28817.7	−1.41718
$746$	16969.9	0.832859
$747$	647.198	0.0316998
$748$	7202.36	0.352065
$749$	4982.70	0.243076
$750$	−9123.58	−0.444195
$751$	2573.48	0.125043	0.0625217	−	0.998044i	$-0.480086\pi$
$751$	2573.48	0.125043	0.0625217	+	0.998044i	$0.480086\pi$
$752$	−10147.8	−0.492092
$753$	−17502.0	−0.847021
$754$	2785.85	0.134555
$755$	−31210.5	−1.50446
$756$	−756.000	−0.0363696
$757$	25328.2	1.21607	0.608037	−	0.793908i	$-0.291957\pi$
$757$	25328.2	1.21607	0.608037	+	0.793908i	$0.291957\pi$
$758$	−7404.41	−0.354802
$759$	4257.53	0.203608
$760$	11265.7	0.537698
$761$	−24762.0	−1.17953	−0.589766	−	0.807574i	$-0.700780\pi$
$761$	−24762.0	−1.17953	−0.589766	+	0.807574i	$0.700780\pi$
$762$	−612.632	−0.0291251
$763$	8732.48	0.414334
$764$	−17643.8	−0.835512
$765$	2350.94	0.111109
$766$	−5756.12	−0.271510
$767$	9516.02	0.447984
$768$	−768.000	−0.0360844
$769$	−32296.6	−1.51449	−0.757246	−	0.653130i	$-0.773455\pi$
$769$	−32296.6	−1.51449	−0.757246	+	0.653130i	$0.773455\pi$
$770$	−7732.67	−0.361904
$771$	−7416.68	−0.346440
$772$	−11604.8	−0.541020
$773$	−24479.8	−1.13904	−0.569520	−	0.821977i	$-0.692871\pi$
$773$	−24479.8	−1.13904	−0.569520	+	0.821977i	$0.692871\pi$
$774$	−8581.86	−0.398538
$775$	11431.1	0.529827
$776$	13960.1	0.645795
$777$	−2133.96	−0.0985270
$778$	30012.0	1.38301
$779$	24463.8	1.12517
$780$	5847.70	0.268437
$781$	25688.5	1.17696
$782$	1342.34	0.0613838
$783$	−690.843	−0.0315309
$784$	784.000	0.0357143
$785$	9355.93	0.425385
$786$	−3829.05	−0.173763
$787$	−10135.3	−0.459066	−0.229533	−	0.973301i	$-0.573720\pi$
$787$	−10135.3	−0.459066	−0.229533	+	0.973301i	$0.573720\pi$
$788$	−1259.55	−0.0569413
$789$	−17900.6	−0.807705
$790$	7587.53	0.341711
$791$	277.529	0.0124751
$792$	−4442.64	−0.199321
$793$	2907.68	0.130208
$794$	−2002.67	−0.0895114
$795$	14704.2	0.655980
$796$	−7940.01	−0.353551
$797$	−27368.2	−1.21635	−0.608176	−	0.793802i	$-0.708099\pi$
$797$	−27368.2	−1.21635	−0.608176	+	0.793802i	$0.708099\pi$
$798$	−6607.32	−0.293104
$799$	−18508.0	−0.819481
$800$	1435.90	0.0634584
$801$	138.246	0.00609825
$802$	3559.57	0.156724
$803$	23367.4	1.02692
$804$	−7123.81	−0.312484
$805$	−1441.18	−0.0630993
$806$	−27736.6	−1.21214
$807$	8225.02	0.358779
$808$	627.314	0.0273129
$809$	−27434.5	−1.19227	−0.596134	−	0.802885i	$-0.703297\pi$
$809$	−27434.5	−1.19227	−0.596134	+	0.802885i	$0.703297\pi$
$810$	−1450.13	−0.0629043
$811$	16073.7	0.695960	0.347980	−	0.937502i	$-0.386868\pi$
$811$	16073.7	0.695960	0.347980	+	0.937502i	$0.386868\pi$
$812$	716.430	0.0309628
$813$	−20528.1	−0.885552
$814$	−12540.2	−0.539970
$815$	−7353.01	−0.316030
$816$	−1400.71	−0.0600914
$817$	−75004.2	−3.21183
$818$	−11904.8	−0.508853
$819$	−3429.67	−0.146327
$820$	−5568.01	−0.237126
$821$	23515.9	0.999649	0.499825	−	0.866127i	$-0.333398\pi$
$821$	23515.9	0.999649	0.499825	+	0.866127i	$0.333398\pi$
$822$	843.102	0.0357744
$823$	11327.6	0.479777	0.239888	−	0.970800i	$-0.422889\pi$
$823$	11327.6	0.479777	0.239888	+	0.970800i	$0.422889\pi$
$824$	−4002.42	−0.169212
$825$	8306.23	0.350528
$826$	2447.22	0.103087
$827$	−7143.58	−0.300371	−0.150185	−	0.988658i	$-0.547987\pi$
$827$	−7143.58	−0.300371	−0.150185	+	0.988658i	$0.547987\pi$
$828$	−828.000	−0.0347524
$829$	39986.1	1.67524	0.837620	−	0.546253i	$-0.183946\pi$
$829$	39986.1	1.67524	0.837620	+	0.546253i	$0.183946\pi$
$830$	−1287.41	−0.0538394
$831$	11742.3	0.490174
$832$	−3484.10	−0.145180
$833$	1429.89	0.0594750
$834$	−12592.7	−0.522842
$835$	27685.8	1.14743
$836$	−38828.0	−1.60633
$837$	6878.22	0.284046
$838$	29268.6	1.20652
$839$	22081.6	0.908632	0.454316	−	0.890841i	$-0.349884\pi$
$839$	22081.6	0.908632	0.454316	+	0.890841i	$0.349884\pi$
$840$	1503.84	0.0617708
$841$	−23734.3	−0.973157
$842$	25748.9	1.05388
$843$	9556.76	0.390454
$844$	7824.39	0.319107
$845$	6862.34	0.279375
$846$	11416.3	0.463949
$847$	17334.1	0.703196
$848$	−8760.87	−0.354775
$849$	−12209.9	−0.493574
$850$	2618.85	0.105677
$851$	−2337.20	−0.0941458
$852$	−4995.86	−0.200887
$853$	10476.6	0.420529	0.210264	−	0.977645i	$-0.432568\pi$
$853$	10476.6	0.420529	0.210264	+	0.977645i	$0.432568\pi$
$854$	747.761	0.0299624
$855$	−12673.9	−0.506947
$856$	−5694.51	−0.227377
$857$	−27665.6	−1.10273	−0.551365	−	0.834264i	$-0.685893\pi$
$857$	−27665.6	−1.10273	−0.551365	+	0.834264i	$0.685893\pi$
$858$	−20154.5	−0.801937
$859$	40063.5	1.59133	0.795663	−	0.605740i	$-0.207123\pi$
$859$	40063.5	1.59133	0.795663	+	0.605740i	$0.207123\pi$
$860$	17071.1	0.676883
$861$	3265.63	0.129259
$862$	8433.13	0.333218
$863$	29605.3	1.16776	0.583881	−	0.811840i	$-0.301534\pi$
$863$	29605.3	1.16776	0.583881	+	0.811840i	$0.301534\pi$
$864$	864.000	0.0340207
$865$	−15849.8	−0.623017
$866$	15978.9	0.627002
$867$	12184.3	0.477280
$868$	−7132.97	−0.278927
$869$	−26150.9	−1.02084
$870$	1374.23	0.0535526
$871$	−32317.8	−1.25723
$872$	−9979.98	−0.387574
$873$	−15705.1	−0.608862
$874$	−7236.59	−0.280070
$875$	−10644.2	−0.411244
$876$	−4544.46	−0.175277
$877$	−14289.7	−0.550203	−0.275101	−	0.961415i	$-0.588711\pi$
$877$	−14289.7	−0.550203	−0.275101	+	0.961415i	$0.588711\pi$
$878$	6379.48	0.245213
$879$	16937.2	0.649919
$880$	8837.33	0.338530
$881$	30345.1	1.16044	0.580222	−	0.814458i	$-0.302966\pi$
$881$	30345.1	1.16044	0.580222	+	0.814458i	$0.302966\pi$
$882$	−882.000	−0.0336718
$883$	536.806	0.0204586	0.0102293	−	0.999948i	$-0.496744\pi$
$883$	536.806	0.0204586	0.0102293	+	0.999948i	$0.496744\pi$
$884$	−6354.44	−0.241768
$885$	4694.16	0.178297
$886$	−1108.01	−0.0420141
$887$	26443.9	1.00101	0.500507	−	0.865732i	$-0.333147\pi$
$887$	26443.9	1.00101	0.500507	+	0.865732i	$0.333147\pi$
$888$	2438.81	0.0921635
$889$	−714.737	−0.0269646
$890$	−275.001	−0.0103574
$891$	4997.97	0.187922
$892$	−11435.8	−0.429259
$893$	99776.8	3.73897
$894$	−19316.1	−0.722624
$895$	−17069.0	−0.637489
$896$	−896.000	−0.0334077
$897$	−3756.30	−0.139821
$898$	−16980.4	−0.631006
$899$	−6518.21	−0.241818
$900$	−1615.39	−0.0598291
$901$	−15978.4	−0.590808
$902$	19190.5	0.708397
$903$	−10012.2	−0.368975
$904$	−317.176	−0.0116694
$905$	−27921.4	−1.02557
$906$	−20919.9	−0.767128
$907$	1779.42	0.0651430	0.0325715	−	0.999469i	$-0.489630\pi$
$907$	1779.42	0.0651430	0.0325715	+	0.999469i	$0.489630\pi$
$908$	4625.12	0.169042
$909$	−705.728	−0.0257508
$910$	6822.32	0.248525
$911$	1884.26	0.0685274	0.0342637	−	0.999413i	$-0.489091\pi$
$911$	1884.26	0.0685274	0.0342637	+	0.999413i	$0.489091\pi$
$912$	7551.23	0.274173
$913$	4437.15	0.160841
$914$	−10585.6	−0.383084
$915$	1434.33	0.0518223
$916$	8141.15	0.293658
$917$	−4467.22	−0.160873
$918$	1575.80	0.0566547
$919$	−16039.0	−0.575712	−0.287856	−	0.957674i	$-0.592942\pi$
$919$	−16039.0	−0.575712	−0.287856	+	0.957674i	$0.592942\pi$
$920$	1647.06	0.0590240
$921$	−12753.4	−0.456284
$922$	350.485	0.0125191
$923$	−22664.2	−0.808235
$924$	−5183.08	−0.184536
$925$	−4559.75	−0.162080
$926$	−16478.3	−0.584785
$927$	4502.72	0.159535
$928$	−818.777	−0.0289630
$929$	51517.3	1.81941	0.909703	−	0.415259i	$-0.136309\pi$
$929$	51517.3	1.81941	0.909703	+	0.415259i	$0.136309\pi$
$930$	−13682.2	−0.482427
$931$	−7708.55	−0.271361
$932$	15762.9	0.554003
$933$	−8771.23	−0.307778
$934$	−30560.0	−1.07061
$935$	16117.9	0.563754
$936$	3919.62	0.136877
$937$	−47237.4	−1.64694	−0.823468	−	0.567362i	$-0.807964\pi$
$937$	−47237.4	−1.64694	−0.823468	+	0.567362i	$0.807964\pi$
$938$	−8311.11	−0.289304
$939$	23828.8	0.828139
$940$	−22709.4	−0.787977
$941$	−29890.1	−1.03548	−0.517742	−	0.855537i	$-0.673227\pi$
$941$	−29890.1	−1.03548	−0.517742	+	0.855537i	$0.673227\pi$
$942$	6271.13	0.216905
$943$	3576.64	0.123512
$944$	−2796.82	−0.0964287
$945$	−1691.82	−0.0582380
$946$	−58836.6	−2.02214
$947$	15944.1	0.547110	0.273555	−	0.961856i	$-0.411800\pi$
$947$	15944.1	0.547110	0.273555	+	0.961856i	$0.411800\pi$
$948$	5085.79	0.174239
$949$	−20616.4	−0.705201
$950$	−14118.2	−0.482164
$951$	−2076.36	−0.0707997
$952$	−1634.16	−0.0556338
$953$	−29235.0	−0.993718	−0.496859	−	0.867831i	$-0.665513\pi$
$953$	−29235.0	−0.993718	−0.496859	+	0.867831i	$0.665513\pi$
$954$	9855.98	0.334486
$955$	−39484.4	−1.33789
$956$	−24887.8	−0.841974
$957$	−4736.37	−0.159984
$958$	−16337.0	−0.550967
$959$	983.619	0.0331207
$960$	−1718.68	−0.0577812
$961$	35106.0	1.17841
$962$	11063.9	0.370805
$963$	6406.33	0.214373
$964$	26094.9	0.871846
$965$	−25970.0	−0.866325
$966$	−966.000	−0.0321745
$967$	10942.5	0.363897	0.181948	−	0.983308i	$-0.441760\pi$
$967$	10942.5	0.363897	0.181948	+	0.983308i	$0.441760\pi$
$968$	−19810.4	−0.657780
$969$	13772.2	0.456581
$970$	31240.6	1.03410
$971$	−6474.15	−0.213971	−0.106985	−	0.994261i	$-0.534120\pi$
$971$	−6474.15	−0.213971	−0.106985	+	0.994261i	$0.534120\pi$
$972$	−972.000	−0.0320750
$973$	−14691.5	−0.484058
$974$	−4498.03	−0.147974
$975$	−7328.35	−0.240713
$976$	−854.584	−0.0280272
$977$	19461.4	0.637281	0.318641	−	0.947876i	$-0.396774\pi$
$977$	19461.4	0.637281	0.318641	+	0.947876i	$0.396774\pi$
$978$	−4928.60	−0.161145
$979$	947.808	0.0309419
$980$	1754.48	0.0571886
$981$	11227.5	0.365408
$982$	5310.98	0.172587
$983$	47485.6	1.54075	0.770374	−	0.637592i	$-0.220070\pi$
$983$	47485.6	1.54075	0.770374	+	0.637592i	$0.220070\pi$
$984$	−3732.15	−0.120911
$985$	−2818.70	−0.0911790
$986$	−1493.32	−0.0482321
$987$	13319.0	0.429533
$988$	34256.9	1.10309
$989$	−10965.7	−0.352568
$990$	−9942.00	−0.319169
$991$	43221.5	1.38544	0.692722	−	0.721204i	$-0.256411\pi$
$991$	43221.5	1.38544	0.692722	+	0.721204i	$0.256411\pi$
$992$	8151.97	0.260913
$993$	−14869.9	−0.475207
$994$	−5828.51	−0.185985
$995$	−17768.6	−0.566134
$996$	−862.931	−0.0274528
$997$	−34237.3	−1.08757	−0.543784	−	0.839225i	$-0.683009\pi$
$997$	−34237.3	−1.08757	−0.543784	+	0.839225i	$0.683009\pi$
$998$	6199.44	0.196633
$999$	−2743.66	−0.0868926

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.4.a.l.1.4	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.4.a.l.1.4	✓	5	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	966.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +8.95143 q^{5} +6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +8.95143 q^{5} +6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} -17.9029 q^{10} +61.7033 q^{11} -12.0000 q^{12} -54.4391 q^{13} -14.0000 q^{14} -26.8543 q^{15} +16.0000 q^{16} +29.1814 q^{17} -18.0000 q^{18} -157.317 q^{19} +35.8057 q^{20} -21.0000 q^{21} -123.407 q^{22} -23.0000 q^{23} +24.0000 q^{24} -44.8719 q^{25} +108.878 q^{26} -27.0000 q^{27} +28.0000 q^{28} +25.5868 q^{29} +53.7086 q^{30} -254.749 q^{31} -32.0000 q^{32} -185.110 q^{33} -58.3628 q^{34} +62.6600 q^{35} +36.0000 q^{36} +101.617 q^{37} +314.635 q^{38} +163.317 q^{39} -71.6115 q^{40} -155.506 q^{41} +42.0000 q^{42} +476.770 q^{43} +246.813 q^{44} +80.5629 q^{45} +46.0000 q^{46} -634.239 q^{47} -48.0000 q^{48} +49.0000 q^{49} +89.7437 q^{50} -87.5442 q^{51} -217.757 q^{52} -547.555 q^{53} +54.0000 q^{54} +552.333 q^{55} -56.0000 q^{56} +471.952 q^{57} -51.1736 q^{58} -174.801 q^{59} -107.417 q^{60} -53.4115 q^{61} +509.498 q^{62} +63.0000 q^{63} +64.0000 q^{64} -487.308 q^{65} +370.220 q^{66} +593.651 q^{67} +116.726 q^{68} +69.0000 q^{69} -125.320 q^{70} +416.322 q^{71} -72.0000 q^{72} +378.705 q^{73} -203.234 q^{74} +134.616 q^{75} -629.269 q^{76} +431.923 q^{77} -326.635 q^{78} -423.816 q^{79} +143.223 q^{80} +81.0000 q^{81} +311.012 q^{82} +71.9109 q^{83} -84.0000 q^{84} +261.215 q^{85} -953.540 q^{86} -76.7604 q^{87} -493.627 q^{88} +15.3607 q^{89} -161.126 q^{90} -381.074 q^{91} -92.0000 q^{92} +764.247 q^{93} +1268.48 q^{94} -1408.21 q^{95} +96.0000 q^{96} -1745.01 q^{97} -98.0000 q^{98} +555.330 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 10 q^{2} - 15 q^{3} + 20 q^{4} - 15 q^{5} + 30 q^{6} + 35 q^{7} - 40 q^{8} + 45 q^{9}+O(q^{10}) \) 5 * q - 10 * q^2 - 15 * q^3 + 20 * q^4 - 15 * q^5 + 30 * q^6 + 35 * q^7 - 40 * q^8 + 45 * q^9	\( 5 q - 10 q^{2} - 15 q^{3} + 20 q^{4} - 15 q^{5} + 30 q^{6} + 35 q^{7} - 40 q^{8} + 45 q^{9} + 30 q^{10} - 19 q^{11} - 60 q^{12} - 19 q^{13} - 70 q^{14} + 45 q^{15} + 80 q^{16} - 42 q^{17} - 90 q^{18} - 25 q^{19} - 60 q^{20} - 105 q^{21} + 38 q^{22} - 115 q^{23} + 120 q^{24} + 206 q^{25} + 38 q^{26} - 135 q^{27} + 140 q^{28} - 292 q^{29} - 90 q^{30} - 60 q^{31} - 160 q^{32} + 57 q^{33} + 84 q^{34} - 105 q^{35} + 180 q^{36} + 264 q^{37} + 50 q^{38} + 57 q^{39} + 120 q^{40} + 223 q^{41} + 210 q^{42} + 661 q^{43} - 76 q^{44} - 135 q^{45} + 230 q^{46} - 279 q^{47} - 240 q^{48} + 245 q^{49} - 412 q^{50} + 126 q^{51} - 76 q^{52} - 324 q^{53} + 270 q^{54} + 1077 q^{55} - 280 q^{56} + 75 q^{57} + 584 q^{58} + 26 q^{59} + 180 q^{60} - 460 q^{61} + 120 q^{62} + 315 q^{63} + 320 q^{64} + 528 q^{65} - 114 q^{66} + 1541 q^{67} - 168 q^{68} + 345 q^{69} + 210 q^{70} - 319 q^{71} - 360 q^{72} + 1532 q^{73} - 528 q^{74} - 618 q^{75} - 100 q^{76} - 133 q^{77} - 114 q^{78} + 1242 q^{79} - 240 q^{80} + 405 q^{81} - 446 q^{82} - 1390 q^{83} - 420 q^{84} - 39 q^{85} - 1322 q^{86} + 876 q^{87} + 152 q^{88} - 1171 q^{89} + 270 q^{90} - 133 q^{91} - 460 q^{92} + 180 q^{93} + 558 q^{94} - 3435 q^{95} + 480 q^{96} - 1800 q^{97} - 490 q^{98} - 171 q^{99}+O(q^{100}) \) 5 * q - 10 * q^2 - 15 * q^3 + 20 * q^4 - 15 * q^5 + 30 * q^6 + 35 * q^7 - 40 * q^8 + 45 * q^9 + 30 * q^10 - 19 * q^11 - 60 * q^12 - 19 * q^13 - 70 * q^14 + 45 * q^15 + 80 * q^16 - 42 * q^17 - 90 * q^18 - 25 * q^19 - 60 * q^20 - 105 * q^21 + 38 * q^22 - 115 * q^23 + 120 * q^24 + 206 * q^25 + 38 * q^26 - 135 * q^27 + 140 * q^28 - 292 * q^29 - 90 * q^30 - 60 * q^31 - 160 * q^32 + 57 * q^33 + 84 * q^34 - 105 * q^35 + 180 * q^36 + 264 * q^37 + 50 * q^38 + 57 * q^39 + 120 * q^40 + 223 * q^41 + 210 * q^42 + 661 * q^43 - 76 * q^44 - 135 * q^45 + 230 * q^46 - 279 * q^47 - 240 * q^48 + 245 * q^49 - 412 * q^50 + 126 * q^51 - 76 * q^52 - 324 * q^53 + 270 * q^54 + 1077 * q^55 - 280 * q^56 + 75 * q^57 + 584 * q^58 + 26 * q^59 + 180 * q^60 - 460 * q^61 + 120 * q^62 + 315 * q^63 + 320 * q^64 + 528 * q^65 - 114 * q^66 + 1541 * q^67 - 168 * q^68 + 345 * q^69 + 210 * q^70 - 319 * q^71 - 360 * q^72 + 1532 * q^73 - 528 * q^74 - 618 * q^75 - 100 * q^76 - 133 * q^77 - 114 * q^78 + 1242 * q^79 - 240 * q^80 + 405 * q^81 - 446 * q^82 - 1390 * q^83 - 420 * q^84 - 39 * q^85 - 1322 * q^86 + 876 * q^87 + 152 * q^88 - 1171 * q^89 + 270 * q^90 - 133 * q^91 - 460 * q^92 + 180 * q^93 + 558 * q^94 - 3435 * q^95 + 480 * q^96 - 1800 * q^97 - 490 * q^98 - 171 * q^99

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