LMFDB - Embedded newform 966.4.a.j.1.1

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:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 171x^{2} + 17x + 1050 $ x^4 - x^3 - 171x^2 + 17x + 1050
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.55880$ 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)

$f(q)$	$=$	$q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -17.9067 q^{5} -6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -17.9067 q^{5} -6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +35.8134 q^{10} +37.7207 q^{11} +12.0000 q^{12} -43.6080 q^{13} +14.0000 q^{14} -53.7201 q^{15} +16.0000 q^{16} +94.6311 q^{17} -18.0000 q^{18} -2.78969 q^{19} -71.6268 q^{20} -21.0000 q^{21} -75.4414 q^{22} -23.0000 q^{23} -24.0000 q^{24} +195.650 q^{25} +87.2160 q^{26} +27.0000 q^{27} -28.0000 q^{28} -84.6558 q^{29} +107.440 q^{30} +57.9130 q^{31} -32.0000 q^{32} +113.162 q^{33} -189.262 q^{34} +125.347 q^{35} +36.0000 q^{36} +100.395 q^{37} +5.57938 q^{38} -130.824 q^{39} +143.254 q^{40} -17.2362 q^{41} +42.0000 q^{42} +94.0415 q^{43} +150.883 q^{44} -161.160 q^{45} +46.0000 q^{46} +547.880 q^{47} +48.0000 q^{48} +49.0000 q^{49} -391.300 q^{50} +283.893 q^{51} -174.432 q^{52} -440.777 q^{53} -54.0000 q^{54} -675.453 q^{55} +56.0000 q^{56} -8.36907 q^{57} +169.312 q^{58} +176.587 q^{59} -214.880 q^{60} -572.217 q^{61} -115.826 q^{62} -63.0000 q^{63} +64.0000 q^{64} +780.875 q^{65} -226.324 q^{66} -157.810 q^{67} +378.524 q^{68} -69.0000 q^{69} -250.694 q^{70} -452.971 q^{71} -72.0000 q^{72} -950.747 q^{73} -200.789 q^{74} +586.950 q^{75} -11.1588 q^{76} -264.045 q^{77} +261.648 q^{78} -1143.31 q^{79} -286.507 q^{80} +81.0000 q^{81} +34.4724 q^{82} -946.243 q^{83} -84.0000 q^{84} -1694.53 q^{85} -188.083 q^{86} -253.967 q^{87} -301.766 q^{88} +1203.30 q^{89} +322.321 q^{90} +305.256 q^{91} -92.0000 q^{92} +173.739 q^{93} -1095.76 q^{94} +49.9542 q^{95} -96.0000 q^{96} -920.189 q^{97} -98.0000 q^{98} +339.486 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{2} + 12 q^{3} + 16 q^{4} + 5 q^{5} - 24 q^{6} - 28 q^{7} - 32 q^{8} + 36 q^{9}+O(q^{10}) $ 4 * q - 8 * q^2 + 12 * q^3 + 16 * q^4 + 5 * q^5 - 24 * q^6 - 28 * q^7 - 32 * q^8 + 36 * q^9	\( 4 q - 8 q^{2} + 12 q^{3} + 16 q^{4} + 5 q^{5} - 24 q^{6} - 28 q^{7} - 32 q^{8} + 36 q^{9} - 10 q^{10} + 19 q^{11} + 48 q^{12} - 73 q^{13} + 56 q^{14} + 15 q^{15} + 64 q^{16} - 14 q^{17} - 72 q^{18} - 51 q^{19} + 20 q^{20} - 84 q^{21} - 38 q^{22} - 92 q^{23} - 96 q^{24} + 195 q^{25} + 146 q^{26} + 108 q^{27} - 112 q^{28} - 232 q^{29} - 30 q^{30} + 80 q^{31} - 128 q^{32} + 57 q^{33} + 28 q^{34} - 35 q^{35} + 144 q^{36} - 150 q^{37} + 102 q^{38} - 219 q^{39} - 40 q^{40} - 491 q^{41} + 168 q^{42} - 481 q^{43} + 76 q^{44} + 45 q^{45} + 184 q^{46} - 289 q^{47} + 192 q^{48} + 196 q^{49} - 390 q^{50} - 42 q^{51} - 292 q^{52} - 176 q^{53} - 216 q^{54} - 1067 q^{55} + 224 q^{56} - 153 q^{57} + 464 q^{58} + 212 q^{59} + 60 q^{60} - 2066 q^{61} - 160 q^{62} - 252 q^{63} + 256 q^{64} + 142 q^{65} - 114 q^{66} - 369 q^{67} - 56 q^{68} - 276 q^{69} + 70 q^{70} - 1565 q^{71} - 288 q^{72} - 482 q^{73} + 300 q^{74} + 585 q^{75} - 204 q^{76} - 133 q^{77} + 438 q^{78} - 2146 q^{79} + 80 q^{80} + 324 q^{81} + 982 q^{82} + 1040 q^{83} - 336 q^{84} - 2823 q^{85} + 962 q^{86} - 696 q^{87} - 152 q^{88} + 1963 q^{89} - 90 q^{90} + 511 q^{91} - 368 q^{92} + 240 q^{93} + 578 q^{94} - 283 q^{95} - 384 q^{96} - 818 q^{97} - 392 q^{98} + 171 q^{99}+O(q^{100}) \) 4 * q - 8 * q^2 + 12 * q^3 + 16 * q^4 + 5 * q^5 - 24 * q^6 - 28 * q^7 - 32 * q^8 + 36 * q^9 - 10 * q^10 + 19 * q^11 + 48 * q^12 - 73 * q^13 + 56 * q^14 + 15 * q^15 + 64 * q^16 - 14 * q^17 - 72 * q^18 - 51 * q^19 + 20 * q^20 - 84 * q^21 - 38 * q^22 - 92 * q^23 - 96 * q^24 + 195 * q^25 + 146 * q^26 + 108 * q^27 - 112 * q^28 - 232 * q^29 - 30 * q^30 + 80 * q^31 - 128 * q^32 + 57 * q^33 + 28 * q^34 - 35 * q^35 + 144 * q^36 - 150 * q^37 + 102 * q^38 - 219 * q^39 - 40 * q^40 - 491 * q^41 + 168 * q^42 - 481 * q^43 + 76 * q^44 + 45 * q^45 + 184 * q^46 - 289 * q^47 + 192 * q^48 + 196 * q^49 - 390 * q^50 - 42 * q^51 - 292 * q^52 - 176 * q^53 - 216 * q^54 - 1067 * q^55 + 224 * q^56 - 153 * q^57 + 464 * q^58 + 212 * q^59 + 60 * q^60 - 2066 * q^61 - 160 * q^62 - 252 * q^63 + 256 * q^64 + 142 * q^65 - 114 * q^66 - 369 * q^67 - 56 * q^68 - 276 * q^69 + 70 * q^70 - 1565 * q^71 - 288 * q^72 - 482 * q^73 + 300 * q^74 + 585 * q^75 - 204 * q^76 - 133 * q^77 + 438 * q^78 - 2146 * q^79 + 80 * q^80 + 324 * q^81 + 982 * q^82 + 1040 * q^83 - 336 * q^84 - 2823 * q^85 + 962 * q^86 - 696 * q^87 - 152 * q^88 + 1963 * q^89 - 90 * q^90 + 511 * q^91 - 368 * q^92 + 240 * q^93 + 578 * q^94 - 283 * q^95 - 384 * q^96 - 818 * q^97 - 392 * 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
$5$	−17.9067	−1.60162	−0.800812	−	0.598916i	$-0.795598\pi$
$5$	−17.9067	−1.60162	−0.800812	+	0.598916i	$0.795598\pi$
$6$	−6.00000	−0.408248
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	35.8134	1.13252
$11$	37.7207	1.03393	0.516964	−	0.856007i	$-0.327062\pi$
$11$	37.7207	1.03393	0.516964	+	0.856007i	$0.327062\pi$
$12$	12.0000	0.288675
$13$	−43.6080	−0.930360	−0.465180	−	0.885216i	$-0.654010\pi$
$13$	−43.6080	−0.930360	−0.465180	+	0.885216i	$0.654010\pi$
$14$	14.0000	0.267261
$15$	−53.7201	−0.924698
$16$	16.0000	0.250000
$17$	94.6311	1.35008	0.675042	−	0.737780i	$-0.264126\pi$
$17$	94.6311	1.35008	0.675042	+	0.737780i	$0.264126\pi$
$18$	−18.0000	−0.235702
$19$	−2.78969	−0.0336842	−0.0168421	−	0.999858i	$-0.505361\pi$
$19$	−2.78969	−0.0336842	−0.0168421	+	0.999858i	$0.505361\pi$
$20$	−71.6268	−0.800812
$21$	−21.0000	−0.218218
$22$	−75.4414	−0.731098
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	−24.0000	−0.204124
$25$	195.650	1.56520
$26$	87.2160	0.657864
$27$	27.0000	0.192450
$28$	−28.0000	−0.188982
$29$	−84.6558	−0.542075	−0.271038	−	0.962569i	$-0.587367\pi$
$29$	−84.6558	−0.542075	−0.271038	+	0.962569i	$0.587367\pi$
$30$	107.440	0.653860
$31$	57.9130	0.335532	0.167766	−	0.985827i	$-0.446345\pi$
$31$	57.9130	0.335532	0.167766	+	0.985827i	$0.446345\pi$
$32$	−32.0000	−0.176777
$33$	113.162	0.596939
$34$	−189.262	−0.954653
$35$	125.347	0.605357
$36$	36.0000	0.166667
$37$	100.395	0.446075	0.223038	−	0.974810i	$-0.428403\pi$
$37$	100.395	0.446075	0.223038	+	0.974810i	$0.428403\pi$
$38$	5.57938	0.0238183
$39$	−130.824	−0.537144
$40$	143.254	0.566260
$41$	−17.2362	−0.0656548	−0.0328274	−	0.999461i	$-0.510451\pi$
$41$	−17.2362	−0.0656548	−0.0328274	+	0.999461i	$0.510451\pi$
$42$	42.0000	0.154303
$43$	94.0415	0.333516	0.166758	−	0.985998i	$-0.446670\pi$
$43$	94.0415	0.333516	0.166758	+	0.985998i	$0.446670\pi$
$44$	150.883	0.516964
$45$	−161.160	−0.533875
$46$	46.0000	0.147442
$47$	547.880	1.70035	0.850176	−	0.526499i	$-0.176496\pi$
$47$	547.880	1.70035	0.850176	+	0.526499i	$0.176496\pi$
$48$	48.0000	0.144338
$49$	49.0000	0.142857
$50$	−391.300	−1.10676
$51$	283.893	0.779471
$52$	−174.432	−0.465180
$53$	−440.777	−1.14236	−0.571182	−	0.820823i	$-0.693515\pi$
$53$	−440.777	−1.14236	−0.571182	+	0.820823i	$0.693515\pi$
$54$	−54.0000	−0.136083
$55$	−675.453	−1.65596
$56$	56.0000	0.133631
$57$	−8.36907	−0.0194476
$58$	169.312	0.383305
$59$	176.587	0.389654	0.194827	−	0.980838i	$-0.437585\pi$
$59$	176.587	0.389654	0.194827	+	0.980838i	$0.437585\pi$
$60$	−214.880	−0.462349
$61$	−572.217	−1.20106	−0.600532	−	0.799601i	$-0.705044\pi$
$61$	−572.217	−1.20106	−0.600532	+	0.799601i	$0.705044\pi$
$62$	−115.826	−0.237257
$63$	−63.0000	−0.125988
$64$	64.0000	0.125000
$65$	780.875	1.49009
$66$	−226.324	−0.422100
$67$	−157.810	−0.287754	−0.143877	−	0.989596i	$-0.545957\pi$
$67$	−157.810	−0.287754	−0.143877	+	0.989596i	$0.545957\pi$
$68$	378.524	0.675042
$69$	−69.0000	−0.120386
$70$	−250.694	−0.428052
$71$	−452.971	−0.757152	−0.378576	−	0.925570i	$-0.623586\pi$
$71$	−452.971	−0.757152	−0.378576	+	0.925570i	$0.623586\pi$
$72$	−72.0000	−0.117851
$73$	−950.747	−1.52434	−0.762168	−	0.647379i	$-0.775865\pi$
$73$	−950.747	−1.52434	−0.762168	+	0.647379i	$0.775865\pi$
$74$	−200.789	−0.315423
$75$	586.950	0.903668
$76$	−11.1588	−0.0168421
$77$	−264.045	−0.390788
$78$	261.648	0.379818
$79$	−1143.31	−1.62826	−0.814131	−	0.580681i	$-0.802787\pi$
$79$	−1143.31	−1.62826	−0.814131	+	0.580681i	$0.802787\pi$
$80$	−286.507	−0.400406
$81$	81.0000	0.111111
$82$	34.4724	0.0464249
$83$	−946.243	−1.25137	−0.625685	−	0.780076i	$-0.715180\pi$
$83$	−946.243	−1.25137	−0.625685	+	0.780076i	$0.715180\pi$
$84$	−84.0000	−0.109109
$85$	−1694.53	−2.16233
$86$	−188.083	−0.235832
$87$	−253.967	−0.312967
$88$	−301.766	−0.365549
$89$	1203.30	1.43314	0.716571	−	0.697514i	$-0.245710\pi$
$89$	1203.30	1.43314	0.716571	+	0.697514i	$0.245710\pi$
$90$	322.321	0.377506
$91$	305.256	0.351643
$92$	−92.0000	−0.104257
$93$	173.739	0.193719
$94$	−1095.76	−1.20233
$95$	49.9542	0.0539494
$96$	−96.0000	−0.102062
$97$	−920.189	−0.963207	−0.481603	−	0.876389i	$-0.659945\pi$
$97$	−920.189	−0.963207	−0.481603	+	0.876389i	$0.659945\pi$
$98$	−98.0000	−0.101015
$99$	339.486	0.344643
$100$	782.600	0.782600
$101$	1553.77	1.53075	0.765377	−	0.643583i	$-0.222553\pi$
$101$	1553.77	1.53075	0.765377	+	0.643583i	$0.222553\pi$
$102$	−567.787	−0.551169
$103$	196.222	0.187712	0.0938558	−	0.995586i	$-0.470081\pi$
$103$	196.222	0.187712	0.0938558	+	0.995586i	$0.470081\pi$
$104$	348.864	0.328932
$105$	376.041	0.349503
$106$	881.553	0.807774
$107$	−934.215	−0.844055	−0.422028	−	0.906583i	$-0.638682\pi$
$107$	−934.215	−0.844055	−0.422028	+	0.906583i	$0.638682\pi$
$108$	108.000	0.0962250
$109$	−1846.35	−1.62246	−0.811230	−	0.584727i	$-0.801202\pi$
$109$	−1846.35	−1.62246	−0.811230	+	0.584727i	$0.801202\pi$
$110$	1350.91	1.17094
$111$	301.184	0.257542
$112$	−112.000	−0.0944911
$113$	1445.78	1.20361	0.601803	−	0.798644i	$-0.294449\pi$
$113$	1445.78	1.20361	0.601803	+	0.798644i	$0.294449\pi$
$114$	16.7381	0.0137515
$115$	411.854	0.333962
$116$	−338.623	−0.271038
$117$	−392.472	−0.310120
$118$	−353.173	−0.275527
$119$	−662.418	−0.510283
$120$	429.761	0.326930
$121$	91.8505	0.0690086
$122$	1144.43	0.849280
$123$	−51.7087	−0.0379058
$124$	231.652	0.167766
$125$	−1265.11	−0.905236
$126$	126.000	0.0890871
$127$	−909.583	−0.635531	−0.317766	−	0.948169i	$-0.602932\pi$
$127$	−909.583	−0.635531	−0.317766	+	0.948169i	$0.602932\pi$
$128$	−128.000	−0.0883883
$129$	282.124	0.192556
$130$	−1561.75	−1.05365
$131$	−76.8657	−0.0512655	−0.0256328	−	0.999671i	$-0.508160\pi$
$131$	−76.8657	−0.0512655	−0.0256328	+	0.999671i	$0.508160\pi$
$132$	452.648	0.298470
$133$	19.5278	0.0127314
$134$	315.620	0.203473
$135$	−483.481	−0.308233
$136$	−757.049	−0.477327
$137$	1784.06	1.11258	0.556288	−	0.830990i	$-0.312225\pi$
$137$	1784.06	1.11258	0.556288	+	0.830990i	$0.312225\pi$
$138$	138.000	0.0851257
$139$	−1331.08	−0.812237	−0.406119	−	0.913820i	$-0.633118\pi$
$139$	−1331.08	−0.812237	−0.406119	+	0.913820i	$0.633118\pi$
$140$	501.388	0.302678
$141$	1643.64	0.981698
$142$	905.943	0.535388
$143$	−1644.92	−0.961926
$144$	144.000	0.0833333
$145$	1515.91	0.868201
$146$	1901.49	1.07787
$147$	147.000	0.0824786
$148$	401.579	0.223038
$149$	−15.5505	−0.00854999	−0.00427499	−	0.999991i	$-0.501361\pi$
$149$	−15.5505	−0.00854999	−0.00427499	+	0.999991i	$0.501361\pi$
$150$	−1173.90	−0.638990
$151$	−692.882	−0.373417	−0.186708	−	0.982415i	$-0.559782\pi$
$151$	−692.882	−0.373417	−0.186708	+	0.982415i	$0.559782\pi$
$152$	22.3175	0.0119091
$153$	851.680	0.450028
$154$	528.090	0.276329
$155$	−1037.03	−0.537395
$156$	−523.296	−0.268572
$157$	3158.36	1.60551	0.802754	−	0.596311i	$-0.203367\pi$
$157$	3158.36	1.60551	0.802754	+	0.596311i	$0.203367\pi$
$158$	2286.63	1.15136
$159$	−1322.33	−0.659545
$160$	573.014	0.283130
$161$	161.000	0.0788110
$162$	−162.000	−0.0785674
$163$	−1581.84	−0.760118	−0.380059	−	0.924962i	$-0.624096\pi$
$163$	−1581.84	−0.760118	−0.380059	+	0.924962i	$0.624096\pi$
$164$	−68.9449	−0.0328274
$165$	−2026.36	−0.956072
$166$	1892.49	0.884852
$167$	502.539	0.232860	0.116430	−	0.993199i	$-0.462855\pi$
$167$	502.539	0.232860	0.116430	+	0.993199i	$0.462855\pi$
$168$	168.000	0.0771517
$169$	−295.343	−0.134430
$170$	3389.06	1.52900
$171$	−25.1072	−0.0112281
$172$	376.166	0.166758
$173$	−3072.65	−1.35034	−0.675170	−	0.737662i	$-0.735930\pi$
$173$	−3072.65	−1.35034	−0.675170	+	0.737662i	$0.735930\pi$
$174$	507.935	0.221301
$175$	−1369.55	−0.591590
$176$	603.531	0.258482
$177$	529.760	0.224967
$178$	−2406.60	−1.01338
$179$	−3867.06	−1.61474	−0.807369	−	0.590047i	$-0.799109\pi$
$179$	−3867.06	−1.61474	−0.807369	+	0.590047i	$0.799109\pi$
$180$	−644.641	−0.266937
$181$	571.802	0.234816	0.117408	−	0.993084i	$-0.462541\pi$
$181$	571.802	0.234816	0.117408	+	0.993084i	$0.462541\pi$
$182$	−610.512	−0.248649
$183$	−1716.65	−0.693434
$184$	184.000	0.0737210
$185$	−1797.74	−0.714445
$186$	−347.478	−0.136980
$187$	3569.55	1.39589
$188$	2191.52	0.850176
$189$	−189.000	−0.0727393
$190$	−99.9083	−0.0381480
$191$	−3044.22	−1.15326	−0.576628	−	0.817007i	$-0.695632\pi$
$191$	−3044.22	−1.15326	−0.576628	+	0.817007i	$0.695632\pi$
$192$	192.000	0.0721688
$193$	−1927.08	−0.718727	−0.359363	−	0.933198i	$-0.617006\pi$
$193$	−1927.08	−0.718727	−0.359363	+	0.933198i	$0.617006\pi$
$194$	1840.38	0.681090
$195$	2342.63	0.860302
$196$	196.000	0.0714286
$197$	−3584.24	−1.29628	−0.648138	−	0.761523i	$-0.724452\pi$
$197$	−3584.24	−1.29628	−0.648138	+	0.761523i	$0.724452\pi$
$198$	−678.972	−0.243699
$199$	−4800.19	−1.70993	−0.854965	−	0.518685i	$-0.826422\pi$
$199$	−4800.19	−1.70993	−0.854965	+	0.518685i	$0.826422\pi$
$200$	−1565.20	−0.553381
$201$	−473.430	−0.166135
$202$	−3107.54	−1.08241
$203$	592.591	0.204885
$204$	1135.57	0.389735
$205$	308.644	0.105154
$206$	−392.444	−0.132732
$207$	−207.000	−0.0695048
$208$	−697.728	−0.232590
$209$	−105.229	−0.0348270
$210$	−752.081	−0.247136
$211$	−4202.42	−1.37112	−0.685560	−	0.728016i	$-0.740443\pi$
$211$	−4202.42	−1.37112	−0.685560	+	0.728016i	$0.740443\pi$
$212$	−1763.11	−0.571182
$213$	−1358.91	−0.437142
$214$	1868.43	0.596837
$215$	−1683.97	−0.534167
$216$	−216.000	−0.0680414
$217$	−405.391	−0.126819
$218$	3692.70	1.14725
$219$	−2852.24	−0.880076
$220$	−2701.81	−0.827982
$221$	−4126.67	−1.25606
$222$	−602.368	−0.182110
$223$	2662.06	0.799393	0.399696	−	0.916648i	$-0.369116\pi$
$223$	2662.06	0.799393	0.399696	+	0.916648i	$0.369116\pi$
$224$	224.000	0.0668153
$225$	1760.85	0.521733
$226$	−2891.56	−0.851079
$227$	2040.26	0.596549	0.298274	−	0.954480i	$-0.403589\pi$
$227$	2040.26	0.596549	0.298274	+	0.954480i	$0.403589\pi$
$228$	−33.4763	−0.00972378
$229$	−1852.06	−0.534443	−0.267222	−	0.963635i	$-0.586106\pi$
$229$	−1852.06	−0.534443	−0.267222	+	0.963635i	$0.586106\pi$
$230$	−823.708	−0.236147
$231$	−792.134	−0.225622
$232$	677.246	0.191653
$233$	−1788.26	−0.502800	−0.251400	−	0.967883i	$-0.580891\pi$
$233$	−1788.26	−0.502800	−0.251400	+	0.967883i	$0.580891\pi$
$234$	784.944	0.219288
$235$	−9810.72	−2.72332
$236$	706.346	0.194827
$237$	−3429.94	−0.940078
$238$	1324.84	0.360825
$239$	1946.66	0.526858	0.263429	−	0.964679i	$-0.415147\pi$
$239$	1946.66	0.526858	0.263429	+	0.964679i	$0.415147\pi$
$240$	−859.522	−0.231174
$241$	1461.24	0.390568	0.195284	−	0.980747i	$-0.437437\pi$
$241$	1461.24	0.390568	0.195284	+	0.980747i	$0.437437\pi$
$242$	−183.701	−0.0487965
$243$	243.000	0.0641500
$244$	−2288.87	−0.600532
$245$	−877.428	−0.228803
$246$	103.417	0.0268034
$247$	121.653	0.0313384
$248$	−463.304	−0.118628
$249$	−2838.73	−0.722479
$250$	2530.21	0.640099
$251$	−3537.29	−0.889530	−0.444765	−	0.895647i	$-0.646713\pi$
$251$	−3537.29	−0.889530	−0.444765	+	0.895647i	$0.646713\pi$
$252$	−252.000	−0.0629941
$253$	−867.576	−0.215589
$254$	1819.17	0.449388
$255$	−5083.59	−1.24842
$256$	256.000	0.0625000
$257$	5741.59	1.39358	0.696791	−	0.717274i	$-0.254610\pi$
$257$	5741.59	1.39358	0.696791	+	0.717274i	$0.254610\pi$
$258$	−564.249	−0.136157
$259$	−702.763	−0.168601
$260$	3123.50	0.745043
$261$	−761.902	−0.180692
$262$	153.731	0.0362502
$263$	1868.89	0.438177	0.219089	−	0.975705i	$-0.429692\pi$
$263$	1868.89	0.438177	0.219089	+	0.975705i	$0.429692\pi$
$264$	−905.297	−0.211050
$265$	7892.85	1.82964
$266$	−39.0557	−0.00900247
$267$	3609.90	0.827425
$268$	−631.240	−0.143877
$269$	−3679.66	−0.834025	−0.417012	−	0.908901i	$-0.636923\pi$
$269$	−3679.66	−0.834025	−0.417012	+	0.908901i	$0.636923\pi$
$270$	966.962	0.217953
$271$	2834.49	0.635362	0.317681	−	0.948198i	$-0.397096\pi$
$271$	2834.49	0.635362	0.317681	+	0.948198i	$0.397096\pi$
$272$	1514.10	0.337521
$273$	915.768	0.203021
$274$	−3568.13	−0.786710
$275$	7380.05	1.61830
$276$	−276.000	−0.0601929
$277$	1388.08	0.301089	0.150544	−	0.988603i	$-0.451897\pi$
$277$	1388.08	0.301089	0.150544	+	0.988603i	$0.451897\pi$
$278$	2662.17	0.574339
$279$	521.217	0.111844
$280$	−1002.78	−0.214026
$281$	590.442	0.125348	0.0626740	−	0.998034i	$-0.480037\pi$
$281$	590.442	0.125348	0.0626740	+	0.998034i	$0.480037\pi$
$282$	−3287.28	−0.694166
$283$	5273.40	1.10767	0.553836	−	0.832626i	$-0.313164\pi$
$283$	5273.40	1.10767	0.553836	+	0.832626i	$0.313164\pi$
$284$	−1811.89	−0.378576
$285$	149.862	0.0311477
$286$	3289.85	0.680184
$287$	120.654	0.0248152
$288$	−288.000	−0.0589256
$289$	4042.05	0.822725
$290$	−3031.81	−0.613911
$291$	−2760.57	−0.556108
$292$	−3802.99	−0.762168
$293$	5525.49	1.10171	0.550857	−	0.834599i	$-0.314301\pi$
$293$	5525.49	1.10171	0.550857	+	0.834599i	$0.314301\pi$
$294$	−294.000	−0.0583212
$295$	−3162.08	−0.624080
$296$	−803.158	−0.157711
$297$	1018.46	0.198980
$298$	31.1010	0.00604575
$299$	1002.98	0.193993
$300$	2347.80	0.451834
$301$	−658.290	−0.126057
$302$	1385.76	0.264046
$303$	4661.32	0.883781
$304$	−44.6351	−0.00842104
$305$	10246.5	1.92365
$306$	−1703.36	−0.318218
$307$	−3.75914	−0.000698845 0	−0.000349423	−	1.00000i	$-0.500111\pi$
$307$	−3.75914	−0.000698845 0	−0.000349423		1.00000i	$0.500111\pi$
$308$	−1056.18	−0.195394
$309$	588.665	0.108375
$310$	2074.06	0.379996
$311$	−1432.04	−0.261105	−0.130552	−	0.991441i	$-0.541675\pi$
$311$	−1432.04	−0.261105	−0.130552	+	0.991441i	$0.541675\pi$
$312$	1046.59	0.189909
$313$	−8189.13	−1.47884	−0.739420	−	0.673244i	$-0.764900\pi$
$313$	−8189.13	−1.47884	−0.739420	+	0.673244i	$0.764900\pi$
$314$	−6316.72	−1.13526
$315$	1128.12	0.201786
$316$	−4573.25	−0.814131
$317$	−5273.51	−0.934352	−0.467176	−	0.884164i	$-0.654729\pi$
$317$	−5273.51	−0.934352	−0.467176	+	0.884164i	$0.654729\pi$
$318$	2644.66	0.466368
$319$	−3193.28	−0.560467
$320$	−1146.03	−0.200203
$321$	−2802.64	−0.487316
$322$	−322.000	−0.0557278
$323$	−263.992	−0.0454764
$324$	324.000	0.0555556
$325$	−8531.90	−1.45620
$326$	3163.68	0.537485
$327$	−5539.05	−0.936728
$328$	137.890	0.0232125
$329$	−3835.16	−0.642673
$330$	4052.72	0.676045
$331$	8147.14	1.35289	0.676446	−	0.736492i	$-0.263519\pi$
$331$	8147.14	1.35289	0.676446	+	0.736492i	$0.263519\pi$
$332$	−3784.97	−0.625685
$333$	903.553	0.148692
$334$	−1005.08	−0.164657
$335$	2825.85	0.460874
$336$	−336.000	−0.0545545
$337$	578.599	0.0935261	0.0467631	−	0.998906i	$-0.485109\pi$
$337$	578.599	0.0935261	0.0467631	+	0.998906i	$0.485109\pi$
$338$	590.686	0.0950565
$339$	4337.34	0.694903
$340$	−6778.12	−1.08116
$341$	2184.52	0.346916
$342$	50.2144	0.00793943
$343$	−343.000	−0.0539949
$344$	−752.332	−0.117916
$345$	1235.56	0.192813
$346$	6145.29	0.954835
$347$	−12673.0	−1.96058	−0.980292	−	0.197556i	$-0.936700\pi$
$347$	−12673.0	−1.96058	−0.980292	+	0.197556i	$0.936700\pi$
$348$	−1015.87	−0.156484
$349$	−6216.23	−0.953431	−0.476715	−	0.879058i	$-0.658173\pi$
$349$	−6216.23	−0.953431	−0.476715	+	0.879058i	$0.658173\pi$
$350$	2739.10	0.418317
$351$	−1177.42	−0.179048
$352$	−1207.06	−0.182775
$353$	7377.24	1.11233	0.556163	−	0.831073i	$-0.312273\pi$
$353$	7377.24	1.11233	0.556163	+	0.831073i	$0.312273\pi$
$354$	−1059.52	−0.159076
$355$	8111.22	1.21267
$356$	4813.20	0.716571
$357$	−1987.25	−0.294612
$358$	7734.13	1.14179
$359$	−4800.00	−0.705667	−0.352834	−	0.935686i	$-0.614782\pi$
$359$	−4800.00	−0.705667	−0.352834	+	0.935686i	$0.614782\pi$
$360$	1289.28	0.188753
$361$	−6851.22	−0.998865
$362$	−1143.60	−0.166040
$363$	275.551	0.0398421
$364$	1221.02	0.175822
$365$	17024.7	2.44141
$366$	3433.30	0.490332
$367$	−5947.05	−0.845868	−0.422934	−	0.906160i	$-0.639000\pi$
$367$	−5947.05	−0.845868	−0.422934	+	0.906160i	$0.639000\pi$
$368$	−368.000	−0.0521286
$369$	−155.126	−0.0218849
$370$	3595.48	0.505189
$371$	3085.44	0.431773
$372$	694.956	0.0968596
$373$	5785.78	0.803154	0.401577	−	0.915825i	$-0.368462\pi$
$373$	5785.78	0.803154	0.401577	+	0.915825i	$0.368462\pi$
$374$	−7139.10	−0.987043
$375$	−3795.32	−0.522639
$376$	−4383.04	−0.601165
$377$	3691.67	0.504325
$378$	378.000	0.0514344
$379$	8649.11	1.17223	0.586114	−	0.810228i	$-0.300657\pi$
$379$	8649.11	1.17223	0.586114	+	0.810228i	$0.300657\pi$
$380$	199.817	0.0269747
$381$	−2728.75	−0.366924
$382$	6088.43	0.815475
$383$	−3417.70	−0.455970	−0.227985	−	0.973665i	$-0.573214\pi$
$383$	−3417.70	−0.455970	−0.227985	+	0.973665i	$0.573214\pi$
$384$	−384.000	−0.0510310
$385$	4728.17	0.625896
$386$	3854.16	0.508217
$387$	846.373	0.111172
$388$	−3680.76	−0.481603
$389$	8632.59	1.12517	0.562583	−	0.826741i	$-0.309808\pi$
$389$	8632.59	1.12517	0.562583	+	0.826741i	$0.309808\pi$
$390$	−4685.25	−0.608325
$391$	−2176.52	−0.281512
$392$	−392.000	−0.0505076
$393$	−230.597	−0.0295982
$394$	7168.48	0.916606
$395$	20473.0	2.60786
$396$	1357.94	0.172321
$397$	2970.13	0.375482	0.187741	−	0.982219i	$-0.439883\pi$
$397$	2970.13	0.375482	0.187741	+	0.982219i	$0.439883\pi$
$398$	9600.37	1.20910
$399$	58.5835	0.00735049
$400$	3130.40	0.391300
$401$	−6092.78	−0.758750	−0.379375	−	0.925243i	$-0.623861\pi$
$401$	−6092.78	−0.758750	−0.379375	+	0.925243i	$0.623861\pi$
$402$	946.859	0.117475
$403$	−2525.47	−0.312165
$404$	6215.09	0.765377
$405$	−1450.44	−0.177958
$406$	−1185.18	−0.144876
$407$	3786.96	0.461210
$408$	−2271.15	−0.275585
$409$	15246.1	1.84320	0.921601	−	0.388138i	$-0.126882\pi$
$409$	15246.1	1.84320	0.921601	+	0.388138i	$0.126882\pi$
$410$	−617.288	−0.0743553
$411$	5352.19	0.642346
$412$	784.887	0.0938558
$413$	−1236.11	−0.147276
$414$	414.000	0.0491473
$415$	16944.1	2.00422
$416$	1395.46	0.164466
$417$	−3993.25	−0.468946
$418$	210.458	0.0246264
$419$	−9177.09	−1.07000	−0.535000	−	0.844852i	$-0.679688\pi$
$419$	−9177.09	−1.07000	−0.535000	+	0.844852i	$0.679688\pi$
$420$	1504.16	0.174751
$421$	−9160.85	−1.06051	−0.530253	−	0.847840i	$-0.677903\pi$
$421$	−9160.85	−1.06051	−0.530253	+	0.847840i	$0.677903\pi$
$422$	8404.83	0.969528
$423$	4930.92	0.566784
$424$	3526.21	0.403887
$425$	18514.6	2.11315
$426$	2717.83	0.309106
$427$	4005.52	0.453959
$428$	−3736.86	−0.422028
$429$	−4934.77	−0.555368
$430$	3367.95	0.377713
$431$	2844.85	0.317939	0.158969	−	0.987284i	$-0.449183\pi$
$431$	2844.85	0.317939	0.158969	+	0.987284i	$0.449183\pi$
$432$	432.000	0.0481125
$433$	13518.8	1.50039	0.750196	−	0.661215i	$-0.229959\pi$
$433$	13518.8	1.50039	0.750196	+	0.661215i	$0.229959\pi$
$434$	810.782	0.0896746
$435$	4547.72	0.501256
$436$	−7385.40	−0.811230
$437$	64.1629	0.00702363
$438$	5704.48	0.622308
$439$	−2813.10	−0.305836	−0.152918	−	0.988239i	$-0.548867\pi$
$439$	−2813.10	−0.305836	−0.152918	+	0.988239i	$0.548867\pi$
$440$	5403.62	0.585472
$441$	441.000	0.0476190
$442$	8253.34	0.888171
$443$	8807.91	0.944642	0.472321	−	0.881427i	$-0.343416\pi$
$443$	8807.91	0.944642	0.472321	+	0.881427i	$0.343416\pi$
$444$	1204.74	0.128771
$445$	−21547.2	−2.29536
$446$	−5324.12	−0.565256
$447$	−46.6515	−0.00493634
$448$	−448.000	−0.0472456
$449$	5526.96	0.580921	0.290460	−	0.956887i	$-0.406192\pi$
$449$	5526.96	0.580921	0.290460	+	0.956887i	$0.406192\pi$
$450$	−3521.70	−0.368921
$451$	−650.162	−0.0678824
$452$	5783.12	0.601803
$453$	−2078.65	−0.215592
$454$	−4080.51	−0.421824
$455$	−5466.13	−0.563200
$456$	66.9526	0.00687575
$457$	6030.12	0.617236	0.308618	−	0.951186i	$-0.400133\pi$
$457$	6030.12	0.617236	0.308618	+	0.951186i	$0.400133\pi$
$458$	3704.12	0.377908
$459$	2555.04	0.259824
$460$	1647.42	0.166981
$461$	−7913.78	−0.799526	−0.399763	−	0.916619i	$-0.630908\pi$
$461$	−7913.78	−0.799526	−0.399763	+	0.916619i	$0.630908\pi$
$462$	1584.27	0.159539
$463$	−7969.83	−0.799977	−0.399989	−	0.916520i	$-0.630986\pi$
$463$	−7969.83	−0.799977	−0.399989	+	0.916520i	$0.630986\pi$
$464$	−1354.49	−0.135519
$465$	−3111.09	−0.310265
$466$	3576.51	0.355534
$467$	−865.537	−0.0857650	−0.0428825	−	0.999080i	$-0.513654\pi$
$467$	−865.537	−0.0857650	−0.0428825	+	0.999080i	$0.513654\pi$
$468$	−1569.89	−0.155060
$469$	1104.67	0.108761
$470$	19621.4	1.92568
$471$	9475.08	0.926940
$472$	−1412.69	−0.137764
$473$	3547.31	0.344832
$474$	6859.88	0.664736
$475$	−545.803	−0.0527224
$476$	−2649.67	−0.255142
$477$	−3966.99	−0.380788
$478$	−3893.32	−0.372545
$479$	9904.47	0.944774	0.472387	−	0.881391i	$-0.343393\pi$
$479$	9904.47	0.944774	0.472387	+	0.881391i	$0.343393\pi$
$480$	1719.04	0.163465
$481$	−4378.01	−0.415011
$482$	−2922.48	−0.276173
$483$	483.000	0.0455016
$484$	367.402	0.0345043
$485$	16477.6	1.54270
$486$	−486.000	−0.0453609
$487$	−6518.36	−0.606520	−0.303260	−	0.952908i	$-0.598075\pi$
$487$	−6518.36	−0.606520	−0.303260	+	0.952908i	$0.598075\pi$
$488$	4577.74	0.424640
$489$	−4745.52	−0.438854
$490$	1754.86	0.161788
$491$	−6512.54	−0.598588	−0.299294	−	0.954161i	$-0.596751\pi$
$491$	−6512.54	−0.598588	−0.299294	+	0.954161i	$0.596751\pi$
$492$	−206.835	−0.0189529
$493$	−8011.07	−0.731847
$494$	−243.306	−0.0221596
$495$	−6079.08	−0.551988
$496$	926.608	0.0838829
$497$	3170.80	0.286177
$498$	5677.46	0.510870
$499$	19569.1	1.75558	0.877789	−	0.479047i	$-0.159018\pi$
$499$	19569.1	1.75558	0.877789	+	0.479047i	$0.159018\pi$
$500$	−5060.43	−0.452618
$501$	1507.62	0.134442
$502$	7074.59	0.628992
$503$	−14122.9	−1.25191	−0.625953	−	0.779861i	$-0.715290\pi$
$503$	−14122.9	−1.25191	−0.625953	+	0.779861i	$0.715290\pi$
$504$	504.000	0.0445435
$505$	−27822.9	−2.45169
$506$	1735.15	0.152444
$507$	−886.030	−0.0776133
$508$	−3638.33	−0.317766
$509$	−14550.6	−1.26708	−0.633540	−	0.773710i	$-0.718399\pi$
$509$	−14550.6	−1.26708	−0.633540	+	0.773710i	$0.718399\pi$
$510$	10167.2	0.882766
$511$	6655.23	0.576145
$512$	−512.000	−0.0441942
$513$	−75.3217	−0.00648252
$514$	−11483.2	−0.985412
$515$	−3513.68	−0.300644
$516$	1128.50	0.0962778
$517$	20666.4	1.75804
$518$	1405.53	0.119219
$519$	−9217.94	−0.779620
$520$	−6247.00	−0.526825
$521$	−15468.5	−1.30074	−0.650371	−	0.759617i	$-0.725386\pi$
$521$	−15468.5	−1.30074	−0.650371	+	0.759617i	$0.725386\pi$
$522$	1523.80	0.127768
$523$	−12757.5	−1.06662	−0.533312	−	0.845918i	$-0.679053\pi$
$523$	−12757.5	−1.06662	−0.533312	+	0.845918i	$0.679053\pi$
$524$	−307.463	−0.0256328
$525$	−4108.65	−0.341554
$526$	−3737.78	−0.309838
$527$	5480.37	0.452996
$528$	1810.59	0.149235
$529$	529.000	0.0434783
$530$	−15785.7	−1.29375
$531$	1589.28	0.129885
$532$	78.1113	0.00636571
$533$	751.637	0.0610826
$534$	−7219.81	−0.585078
$535$	16728.7	1.35186
$536$	1262.48	0.101737
$537$	−11601.2	−0.932269
$538$	7359.31	0.589744
$539$	1848.31	0.147704
$540$	−1933.92	−0.154116
$541$	17502.7	1.39094	0.695470	−	0.718555i	$-0.255196\pi$
$541$	17502.7	1.39094	0.695470	+	0.718555i	$0.255196\pi$
$542$	−5668.99	−0.449269
$543$	1715.41	0.135571
$544$	−3028.20	−0.238663
$545$	33062.0	2.59857
$546$	−1831.54	−0.143558
$547$	−7143.52	−0.558382	−0.279191	−	0.960236i	$-0.590066\pi$
$547$	−7143.52	−0.558382	−0.279191	+	0.960236i	$0.590066\pi$
$548$	7136.25	0.556288
$549$	−5149.95	−0.400354
$550$	−14760.1	−1.14431
$551$	236.164	0.0182594
$552$	552.000	0.0425628
$553$	8003.19	0.615426
$554$	−2776.16	−0.212902
$555$	−5393.21	−0.412485
$556$	−5324.33	−0.406119
$557$	20032.1	1.52386	0.761929	−	0.647661i	$-0.224253\pi$
$557$	20032.1	1.52386	0.761929	+	0.647661i	$0.224253\pi$
$558$	−1042.43	−0.0790856
$559$	−4100.96	−0.310290
$560$	2005.55	0.151339
$561$	10708.7	0.805917
$562$	−1180.88	−0.0886344
$563$	8588.58	0.642922	0.321461	−	0.946923i	$-0.395826\pi$
$563$	8588.58	0.642922	0.321461	+	0.946923i	$0.395826\pi$
$564$	6574.56	0.490849
$565$	−25889.2	−1.92773
$566$	−10546.8	−0.783242
$567$	−567.000	−0.0419961
$568$	3623.77	0.267694
$569$	14991.8	1.10455	0.552276	−	0.833662i	$-0.313760\pi$
$569$	14991.8	1.10455	0.552276	+	0.833662i	$0.313760\pi$
$570$	−299.725	−0.0220247
$571$	3881.34	0.284464	0.142232	−	0.989833i	$-0.454572\pi$
$571$	3881.34	0.284464	0.142232	+	0.989833i	$0.454572\pi$
$572$	−6579.69	−0.480963
$573$	−9132.65	−0.665832
$574$	−241.307	−0.0175470
$575$	−4499.95	−0.326367
$576$	576.000	0.0416667
$577$	299.986	0.0216440	0.0108220	−	0.999941i	$-0.496555\pi$
$577$	299.986	0.0216440	0.0108220	+	0.999941i	$0.496555\pi$
$578$	−8084.09	−0.581754
$579$	−5781.24	−0.414957
$580$	6063.62	0.434100
$581$	6623.70	0.472973
$582$	5521.14	0.393228
$583$	−16626.4	−1.18112
$584$	7605.98	0.538934
$585$	7027.88	0.496696
$586$	−11051.0	−0.779030
$587$	10093.7	0.709730	0.354865	−	0.934918i	$-0.384527\pi$
$587$	10093.7	0.709730	0.354865	+	0.934918i	$0.384527\pi$
$588$	588.000	0.0412393
$589$	−161.559	−0.0113021
$590$	6324.17	0.441291
$591$	−10752.7	−0.748406
$592$	1606.32	0.111519
$593$	−18091.5	−1.25283	−0.626416	−	0.779489i	$-0.715479\pi$
$593$	−18091.5	−1.25283	−0.626416	+	0.779489i	$0.715479\pi$
$594$	−2036.92	−0.140700
$595$	11861.7	0.817282
$596$	−62.2021	−0.00427499
$597$	−14400.6	−0.987229
$598$	−2005.97	−0.137174
$599$	−12889.2	−0.879195	−0.439598	−	0.898195i	$-0.644879\pi$
$599$	−12889.2	−0.879195	−0.439598	+	0.898195i	$0.644879\pi$
$600$	−4695.60	−0.319495
$601$	−3968.40	−0.269342	−0.134671	−	0.990890i	$-0.542998\pi$
$601$	−3968.40	−0.269342	−0.134671	+	0.990890i	$0.542998\pi$
$602$	1316.58	0.0891359
$603$	−1420.29	−0.0959182
$604$	−2771.53	−0.186708
$605$	−1644.74	−0.110526
$606$	−9322.63	−0.624927
$607$	671.872	0.0449266	0.0224633	−	0.999748i	$-0.492849\pi$
$607$	671.872	0.0449266	0.0224633	+	0.999748i	$0.492849\pi$
$608$	89.2701	0.00595457
$609$	1777.77	0.118291
$610$	−20493.0	−1.36023
$611$	−23892.0	−1.58194
$612$	3406.72	0.225014
$613$	−27514.6	−1.81289	−0.906446	−	0.422322i	$-0.861215\pi$
$613$	−27514.6	−1.81289	−0.906446	+	0.422322i	$0.861215\pi$
$614$	7.51828	0.000494158 0
$615$	925.932	0.0607108
$616$	2112.36	0.138165
$617$	−13598.4	−0.887280	−0.443640	−	0.896205i	$-0.646313\pi$
$617$	−13598.4	−0.887280	−0.443640	+	0.896205i	$0.646313\pi$
$618$	−1177.33	−0.0766330
$619$	−28521.1	−1.85195	−0.925977	−	0.377580i	$-0.876756\pi$
$619$	−28521.1	−1.85195	−0.925977	+	0.377580i	$0.876756\pi$
$620$	−4148.12	−0.268698
$621$	−621.000	−0.0401286
$622$	2864.08	0.184629
$623$	−8423.11	−0.541677
$624$	−2093.18	−0.134286
$625$	−1802.36	−0.115351
$626$	16378.3	1.04570
$627$	−315.687	−0.0201074
$628$	12633.4	0.802754
$629$	9500.46	0.602239
$630$	−2256.24	−0.142684
$631$	11893.7	0.750364	0.375182	−	0.926951i	$-0.377580\pi$
$631$	11893.7	0.750364	0.375182	+	0.926951i	$0.377580\pi$
$632$	9146.50	0.575678
$633$	−12607.3	−0.791616
$634$	10547.0	0.660687
$635$	16287.6	1.01788
$636$	−5289.32	−0.329772
$637$	−2136.79	−0.132909
$638$	6386.55	0.396310
$639$	−4076.74	−0.252384
$640$	2292.06	0.141565
$641$	2115.46	0.130352	0.0651759	−	0.997874i	$-0.479239\pi$
$641$	2115.46	0.130352	0.0651759	+	0.997874i	$0.479239\pi$
$642$	5605.29	0.344584
$643$	24479.9	1.50139	0.750695	−	0.660649i	$-0.229719\pi$
$643$	24479.9	1.50139	0.750695	+	0.660649i	$0.229719\pi$
$644$	644.000	0.0394055
$645$	−5051.92	−0.308402
$646$	527.983	0.0321567
$647$	19777.5	1.20175	0.600875	−	0.799343i	$-0.294819\pi$
$647$	19777.5	1.20175	0.600875	+	0.799343i	$0.294819\pi$
$648$	−648.000	−0.0392837
$649$	6660.97	0.402875
$650$	17063.8	1.02969
$651$	−1216.17	−0.0732190
$652$	−6327.36	−0.380059
$653$	18931.4	1.13452	0.567260	−	0.823539i	$-0.308003\pi$
$653$	18931.4	1.13452	0.567260	+	0.823539i	$0.308003\pi$
$654$	11078.1	0.662367
$655$	1376.41	0.0821081
$656$	−275.780	−0.0164137
$657$	−8556.72	−0.508112
$658$	7670.32	0.454438
$659$	9973.71	0.589561	0.294780	−	0.955565i	$-0.404753\pi$
$659$	9973.71	0.589561	0.294780	+	0.955565i	$0.404753\pi$
$660$	−8105.44	−0.478036
$661$	−8244.27	−0.485121	−0.242561	−	0.970136i	$-0.577987\pi$
$661$	−8244.27	−0.485121	−0.242561	+	0.970136i	$0.577987\pi$
$662$	−16294.3	−0.956639
$663$	−12380.0	−0.725189
$664$	7569.95	0.442426
$665$	−349.679	−0.0203909
$666$	−1807.11	−0.105141
$667$	1947.08	0.113031
$668$	2010.16	0.116430
$669$	7986.17	0.461530
$670$	−5651.71	−0.325887
$671$	−21584.4	−1.24181
$672$	672.000	0.0385758
$673$	−13078.4	−0.749086	−0.374543	−	0.927209i	$-0.622200\pi$
$673$	−13078.4	−0.749086	−0.374543	+	0.927209i	$0.622200\pi$
$674$	−1157.20	−0.0661330
$675$	5282.55	0.301223
$676$	−1181.37	−0.0672151
$677$	−9591.12	−0.544486	−0.272243	−	0.962229i	$-0.587765\pi$
$677$	−9591.12	−0.544486	−0.272243	+	0.962229i	$0.587765\pi$
$678$	−8674.68	−0.491370
$679$	6441.32	0.364058
$680$	13556.2	0.764498
$681$	6120.77	0.344418
$682$	−4369.04	−0.245306
$683$	−23703.5	−1.32795	−0.663976	−	0.747754i	$-0.731132\pi$
$683$	−23703.5	−1.32795	−0.663976	+	0.747754i	$0.731132\pi$
$684$	−100.429	−0.00561403
$685$	−31946.7	−1.78193
$686$	686.000	0.0381802
$687$	−5556.18	−0.308561
$688$	1504.66	0.0833790
$689$	19221.4	1.06281
$690$	−2471.12	−0.136339
$691$	−9347.10	−0.514588	−0.257294	−	0.966333i	$-0.582831\pi$
$691$	−9347.10	−0.514588	−0.257294	+	0.966333i	$0.582831\pi$
$692$	−12290.6	−0.675170
$693$	−2376.40	−0.130263
$694$	25346.0	1.38634
$695$	23835.3	1.30090
$696$	2031.74	0.110651
$697$	−1631.08	−0.0886394
$698$	12432.5	0.674177
$699$	−5364.77	−0.290292
$700$	−5478.20	−0.295795
$701$	8810.29	0.474693	0.237347	−	0.971425i	$-0.423722\pi$
$701$	8810.29	0.474693	0.237347	+	0.971425i	$0.423722\pi$
$702$	2354.83	0.126606
$703$	−280.070	−0.0150257
$704$	2414.12	0.129241
$705$	−29432.2	−1.57231
$706$	−14754.5	−0.786533
$707$	−10876.4	−0.578570
$708$	2119.04	0.112484
$709$	26357.3	1.39615	0.698073	−	0.716026i	$-0.254041\pi$
$709$	26357.3	1.39615	0.698073	+	0.716026i	$0.254041\pi$
$710$	−16222.4	−0.857489
$711$	−10289.8	−0.542754
$712$	−9626.41	−0.506692
$713$	−1332.00	−0.0699632
$714$	3974.51	0.208322
$715$	29455.2	1.54064
$716$	−15468.3	−0.807369
$717$	5839.98	0.304182
$718$	9600.01	0.498982
$719$	−3769.93	−0.195542	−0.0977709	−	0.995209i	$-0.531171\pi$
$719$	−3769.93	−0.195542	−0.0977709	+	0.995209i	$0.531171\pi$
$720$	−2578.56	−0.133469
$721$	−1373.55	−0.0709484
$722$	13702.4	0.706304
$723$	4383.72	0.225494
$724$	2287.21	0.117408
$725$	−16562.9	−0.848456
$726$	−551.103	−0.0281727
$727$	31827.8	1.62370	0.811849	−	0.583867i	$-0.198461\pi$
$727$	31827.8	1.62370	0.811849	+	0.583867i	$0.198461\pi$
$728$	−2442.05	−0.124325
$729$	729.000	0.0370370
$730$	−34049.5	−1.72634
$731$	8899.25	0.450275
$732$	−6866.60	−0.346717
$733$	−1983.71	−0.0999592	−0.0499796	−	0.998750i	$-0.515916\pi$
$733$	−1983.71	−0.0999592	−0.0499796	+	0.998750i	$0.515916\pi$
$734$	11894.1	0.598119
$735$	−2632.28	−0.132100
$736$	736.000	0.0368605
$737$	−5952.70	−0.297518
$738$	310.252	0.0154750
$739$	34.1793	0.00170136	0.000850681	−	1.00000i	$-0.499729\pi$
$739$	34.1793	0.00170136	0.000850681		1.00000i	$0.499729\pi$
$740$	−7190.95	−0.357223
$741$	364.958	0.0180932
$742$	−6170.87	−0.305310
$743$	17071.8	0.842937	0.421469	−	0.906843i	$-0.361515\pi$
$743$	17071.8	0.842937	0.421469	+	0.906843i	$0.361515\pi$
$744$	−1389.91	−0.0684901
$745$	278.458	0.0136939
$746$	−11571.6	−0.567916
$747$	−8516.19	−0.417123
$748$	14278.2	0.697945
$749$	6539.50	0.319023
$750$	7590.64	0.369561
$751$	18998.3	0.923111	0.461555	−	0.887111i	$-0.347292\pi$
$751$	18998.3	0.923111	0.461555	+	0.887111i	$0.347292\pi$
$752$	8766.08	0.425088
$753$	−10611.9	−0.513570
$754$	−7383.34	−0.356612
$755$	12407.2	0.598073
$756$	−756.000	−0.0363696
$757$	7101.78	0.340975	0.170488	−	0.985360i	$-0.445466\pi$
$757$	7101.78	0.340975	0.170488	+	0.985360i	$0.445466\pi$
$758$	−17298.2	−0.828891
$759$	−2602.73	−0.124470
$760$	−399.633	−0.0190740
$761$	−30578.4	−1.45659	−0.728297	−	0.685262i	$-0.759688\pi$
$761$	−30578.4	−1.45659	−0.728297	+	0.685262i	$0.759688\pi$
$762$	5457.50	0.259454
$763$	12924.4	0.613232
$764$	−12176.9	−0.576628
$765$	−15250.8	−0.720775
$766$	6835.41	0.322420
$767$	−7700.59	−0.362519
$768$	768.000	0.0360844
$769$	−2911.61	−0.136535	−0.0682675	−	0.997667i	$-0.521747\pi$
$769$	−2911.61	−0.136535	−0.0682675	+	0.997667i	$0.521747\pi$
$770$	−9456.34	−0.442575
$771$	17224.8	0.804585
$772$	−7708.32	−0.359363
$773$	7982.51	0.371424	0.185712	−	0.982604i	$-0.440541\pi$
$773$	7982.51	0.371424	0.185712	+	0.982604i	$0.440541\pi$
$774$	−1692.75	−0.0786105
$775$	11330.7	0.525174
$776$	7361.51	0.340545
$777$	−2108.29	−0.0973416
$778$	−17265.2	−0.795613
$779$	48.0837	0.00221153
$780$	9370.50	0.430151
$781$	−17086.4	−0.782841
$782$	4353.03	0.199059
$783$	−2285.71	−0.104322
$784$	784.000	0.0357143
$785$	−56555.8	−2.57142
$786$	461.194	0.0209291
$787$	26408.3	1.19613	0.598065	−	0.801447i	$-0.295936\pi$
$787$	26408.3	1.19613	0.598065	+	0.801447i	$0.295936\pi$
$788$	−14337.0	−0.648138
$789$	5606.67	0.252982
$790$	−40945.9	−1.84404
$791$	−10120.5	−0.454921
$792$	−2715.89	−0.121850
$793$	24953.2	1.11742
$794$	−5940.25	−0.265506
$795$	23678.6	1.05634
$796$	−19200.7	−0.854965
$797$	−10617.6	−0.471889	−0.235944	−	0.971767i	$-0.575818\pi$
$797$	−10617.6	−0.471889	−0.235944	+	0.971767i	$0.575818\pi$
$798$	−117.167	−0.00519758
$799$	51846.5	2.29562
$800$	−6260.80	−0.276691
$801$	10829.7	0.477714
$802$	12185.6	0.536517
$803$	−35862.8	−1.57605
$804$	−1893.72	−0.0830676
$805$	−2882.98	−0.126226
$806$	5050.94	0.220734
$807$	−11039.0	−0.481524
$808$	−12430.2	−0.541203
$809$	−2371.92	−0.103081	−0.0515404	−	0.998671i	$-0.516413\pi$
$809$	−2371.92	−0.103081	−0.0515404	+	0.998671i	$0.516413\pi$
$810$	2900.89	0.125835
$811$	−20773.1	−0.899436	−0.449718	−	0.893171i	$-0.648476\pi$
$811$	−20773.1	−0.899436	−0.449718	+	0.893171i	$0.648476\pi$
$812$	2370.36	0.102443
$813$	8503.48	0.366827
$814$	−7573.92	−0.326125
$815$	28325.5	1.21742
$816$	4542.29	0.194868
$817$	−262.347	−0.0112342
$818$	−30492.2	−1.30334
$819$	2747.30	0.117214
$820$	1234.58	0.0525771
$821$	−13388.9	−0.569155	−0.284577	−	0.958653i	$-0.591853\pi$
$821$	−13388.9	−0.569155	−0.284577	+	0.958653i	$0.591853\pi$
$822$	−10704.4	−0.454207
$823$	15677.1	0.663998	0.331999	−	0.943280i	$-0.392277\pi$
$823$	15677.1	0.663998	0.331999	+	0.943280i	$0.392277\pi$
$824$	−1569.77	−0.0663661
$825$	22140.1	0.934328
$826$	2472.21	0.104140
$827$	26391.3	1.10969	0.554846	−	0.831953i	$-0.312777\pi$
$827$	26391.3	1.10969	0.554846	+	0.831953i	$0.312777\pi$
$828$	−828.000	−0.0347524
$829$	−11286.2	−0.472843	−0.236421	−	0.971651i	$-0.575975\pi$
$829$	−11286.2	−0.472843	−0.236421	+	0.971651i	$0.575975\pi$
$830$	−33888.2	−1.41720
$831$	4164.24	0.173834
$832$	−2790.91	−0.116295
$833$	4636.92	0.192869
$834$	7986.50	0.331595
$835$	−8998.82	−0.372954
$836$	−420.916	−0.0174135
$837$	1563.65	0.0645731
$838$	18354.2	0.756604
$839$	23985.1	0.986960	0.493480	−	0.869757i	$-0.335725\pi$
$839$	23985.1	0.986960	0.493480	+	0.869757i	$0.335725\pi$
$840$	−3008.33	−0.123568
$841$	−17222.4	−0.706154
$842$	18321.7	0.749890
$843$	1771.33	0.0723697
$844$	−16809.7	−0.685560
$845$	5288.62	0.215307
$846$	−9861.84	−0.400777
$847$	−642.953	−0.0260828
$848$	−7052.43	−0.285591
$849$	15820.2	0.639514
$850$	−37029.1	−1.49422
$851$	−2309.08	−0.0930132
$852$	−5435.66	−0.218571
$853$	−28528.5	−1.14513	−0.572566	−	0.819859i	$-0.694052\pi$
$853$	−28528.5	−1.14513	−0.572566	+	0.819859i	$0.694052\pi$
$854$	−8011.04	−0.320998
$855$	449.587	0.0179831
$856$	7473.72	0.298419
$857$	32131.3	1.28073	0.640363	−	0.768072i	$-0.278784\pi$
$857$	32131.3	1.28073	0.640363	+	0.768072i	$0.278784\pi$
$858$	9869.54	0.392705
$859$	15614.2	0.620196	0.310098	−	0.950705i	$-0.399638\pi$
$859$	15614.2	0.620196	0.310098	+	0.950705i	$0.399638\pi$
$860$	−6735.89	−0.267084
$861$	361.961	0.0143270
$862$	−5689.70	−0.224817
$863$	−40084.0	−1.58108	−0.790542	−	0.612407i	$-0.790201\pi$
$863$	−40084.0	−1.58108	−0.790542	+	0.612407i	$0.790201\pi$
$864$	−864.000	−0.0340207
$865$	55021.0	2.16274
$866$	−27037.5	−1.06094
$867$	12126.1	0.475000
$868$	−1621.56	−0.0634095
$869$	−43126.6	−1.68351
$870$	−9095.44	−0.354442
$871$	6881.77	0.267715
$872$	14770.8	0.573626
$873$	−8281.70	−0.321069
$874$	−128.326	−0.00496646
$875$	8855.75	0.342147
$876$	−11409.0	−0.440038
$877$	−34773.6	−1.33891	−0.669453	−	0.742854i	$-0.733471\pi$
$877$	−34773.6	−1.33891	−0.669453	+	0.742854i	$0.733471\pi$
$878$	5626.20	0.216259
$879$	16576.5	0.636075
$880$	−10807.2	−0.413991
$881$	−19623.3	−0.750428	−0.375214	−	0.926938i	$-0.622431\pi$
$881$	−19623.3	−0.750428	−0.375214	+	0.926938i	$0.622431\pi$
$882$	−882.000	−0.0336718
$883$	31233.5	1.19036	0.595182	−	0.803591i	$-0.297080\pi$
$883$	31233.5	1.19036	0.595182	+	0.803591i	$0.297080\pi$
$884$	−16506.7	−0.628032
$885$	−9486.25	−0.360313
$886$	−17615.8	−0.667963
$887$	−22032.4	−0.834021	−0.417011	−	0.908902i	$-0.636922\pi$
$887$	−22032.4	−0.834021	−0.417011	+	0.908902i	$0.636922\pi$
$888$	−2409.47	−0.0910548
$889$	6367.08	0.240208
$890$	43094.3	1.62306
$891$	3055.38	0.114881
$892$	10648.2	0.399696
$893$	−1528.42	−0.0572749
$894$	93.3031	0.00349052
$895$	69246.4	2.58620
$896$	896.000	0.0334077
$897$	3008.95	0.112002
$898$	−11053.9	−0.410773
$899$	−4902.67	−0.181883
$900$	7043.40	0.260867
$901$	−41711.2	−1.54229
$902$	1300.32	0.0480001
$903$	−1974.87	−0.0727792
$904$	−11566.2	−0.425539
$905$	−10239.1	−0.376087
$906$	4157.29	0.152447
$907$	−13533.7	−0.495458	−0.247729	−	0.968829i	$-0.579684\pi$
$907$	−13533.7	−0.495458	−0.247729	+	0.968829i	$0.579684\pi$
$908$	8161.02	0.298274
$909$	13983.9	0.510251
$910$	10932.3	0.398242
$911$	−20822.5	−0.757278	−0.378639	−	0.925544i	$-0.623608\pi$
$911$	−20822.5	−0.757278	−0.378639	+	0.925544i	$0.623608\pi$
$912$	−133.905	−0.00486189
$913$	−35693.0	−1.29383
$914$	−12060.2	−0.436452
$915$	30739.6	1.11062
$916$	−7408.24	−0.267222
$917$	538.060	0.0193766
$918$	−5110.08	−0.183723
$919$	5753.79	0.206529	0.103264	−	0.994654i	$-0.467071\pi$
$919$	5753.79	0.206529	0.103264	+	0.994654i	$0.467071\pi$
$920$	−3294.83	−0.118073
$921$	−11.2774	−0.000403479 0
$922$	15827.6	0.565350
$923$	19753.2	0.704424
$924$	−3168.54	−0.112811
$925$	19642.2	0.698197
$926$	15939.7	0.565669
$927$	1766.00	0.0625706
$928$	2708.99	0.0958263
$929$	−47229.0	−1.66796	−0.833980	−	0.551795i	$-0.813943\pi$
$929$	−47229.0	−1.66796	−0.833980	+	0.551795i	$0.813943\pi$
$930$	6222.18	0.219391
$931$	−136.695	−0.00481202
$932$	−7153.02	−0.251400
$933$	−4296.12	−0.150749
$934$	1731.07	0.0606450
$935$	−63918.9	−2.23569
$936$	3139.78	0.109644
$937$	−13530.9	−0.471756	−0.235878	−	0.971783i	$-0.575797\pi$
$937$	−13530.9	−0.471756	−0.235878	+	0.971783i	$0.575797\pi$
$938$	−2209.34	−0.0769056
$939$	−24567.4	−0.853809
$940$	−39242.9	−1.36166
$941$	−42741.2	−1.48068	−0.740342	−	0.672230i	$-0.765337\pi$
$941$	−42741.2	−1.48068	−0.740342	+	0.672230i	$0.765337\pi$
$942$	−18950.2	−0.655446
$943$	396.433	0.0136900
$944$	2825.39	0.0974136
$945$	3384.37	0.116501
$946$	−7094.62	−0.243833
$947$	−42792.7	−1.46840	−0.734201	−	0.678932i	$-0.762443\pi$
$947$	−42792.7	−1.46840	−0.734201	+	0.678932i	$0.762443\pi$
$948$	−13719.8	−0.470039
$949$	41460.2	1.41818
$950$	1091.61	0.0372804
$951$	−15820.5	−0.539448
$952$	5299.34	0.180412
$953$	−11015.5	−0.374426	−0.187213	−	0.982319i	$-0.559945\pi$
$953$	−11015.5	−0.374426	−0.187213	+	0.982319i	$0.559945\pi$
$954$	7933.98	0.269258
$955$	54511.9	1.84708
$956$	7786.65	0.263429
$957$	−9579.83	−0.323586
$958$	−19808.9	−0.668056
$959$	−12488.4	−0.420514
$960$	−3438.09	−0.115587
$961$	−26437.1	−0.887419
$962$	8756.02	0.293457
$963$	−8407.93	−0.281352
$964$	5844.96	0.195284
$965$	34507.6	1.15113
$966$	−966.000	−0.0321745
$967$	−11212.9	−0.372889	−0.186444	−	0.982466i	$-0.559696\pi$
$967$	−11212.9	−0.372889	−0.186444	+	0.982466i	$0.559696\pi$
$968$	−734.804	−0.0243982
$969$	−791.975	−0.0262558
$970$	−32955.1	−1.09085
$971$	−37111.3	−1.22653	−0.613264	−	0.789878i	$-0.710144\pi$
$971$	−37111.3	−1.22653	−0.613264	+	0.789878i	$0.710144\pi$
$972$	972.000	0.0320750
$973$	9317.58	0.306997
$974$	13036.7	0.428874
$975$	−25595.7	−0.840737
$976$	−9155.47	−0.300266
$977$	−4343.67	−0.142238	−0.0711189	−	0.997468i	$-0.522657\pi$
$977$	−4343.67	−0.142238	−0.0711189	+	0.997468i	$0.522657\pi$
$978$	9491.04	0.310317
$979$	45389.4	1.48177
$980$	−3509.71	−0.114402
$981$	−16617.1	−0.540820
$982$	13025.1	0.423266
$983$	44326.6	1.43825	0.719125	−	0.694881i	$-0.244543\pi$
$983$	44326.6	1.43825	0.719125	+	0.694881i	$0.244543\pi$
$984$	413.669	0.0134017
$985$	64181.9	2.07615
$986$	16022.1	0.517494
$987$	−11505.5	−0.371047
$988$	486.611	0.0156692
$989$	−2162.95	−0.0695429
$990$	12158.2	0.390315
$991$	23611.0	0.756839	0.378420	−	0.925634i	$-0.376468\pi$
$991$	23611.0	0.756839	0.378420	+	0.925634i	$0.376468\pi$
$992$	−1853.22	−0.0593142
$993$	24441.4	0.781093
$994$	−6341.60	−0.202357
$995$	85955.5	2.73867
$996$	−11354.9	−0.361239
$997$	6353.81	0.201833	0.100916	−	0.994895i	$-0.467823\pi$
$997$	6353.81	0.201833	0.100916	+	0.994895i	$0.467823\pi$
$998$	−39138.2	−1.24138
$999$	2710.66	0.0858473

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.4.a.j.1.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.4.a.j.1.1	✓	4	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)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -17.9067 q^{5} -6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -17.9067 q^{5} -6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +35.8134 q^{10} +37.7207 q^{11} +12.0000 q^{12} -43.6080 q^{13} +14.0000 q^{14} -53.7201 q^{15} +16.0000 q^{16} +94.6311 q^{17} -18.0000 q^{18} -2.78969 q^{19} -71.6268 q^{20} -21.0000 q^{21} -75.4414 q^{22} -23.0000 q^{23} -24.0000 q^{24} +195.650 q^{25} +87.2160 q^{26} +27.0000 q^{27} -28.0000 q^{28} -84.6558 q^{29} +107.440 q^{30} +57.9130 q^{31} -32.0000 q^{32} +113.162 q^{33} -189.262 q^{34} +125.347 q^{35} +36.0000 q^{36} +100.395 q^{37} +5.57938 q^{38} -130.824 q^{39} +143.254 q^{40} -17.2362 q^{41} +42.0000 q^{42} +94.0415 q^{43} +150.883 q^{44} -161.160 q^{45} +46.0000 q^{46} +547.880 q^{47} +48.0000 q^{48} +49.0000 q^{49} -391.300 q^{50} +283.893 q^{51} -174.432 q^{52} -440.777 q^{53} -54.0000 q^{54} -675.453 q^{55} +56.0000 q^{56} -8.36907 q^{57} +169.312 q^{58} +176.587 q^{59} -214.880 q^{60} -572.217 q^{61} -115.826 q^{62} -63.0000 q^{63} +64.0000 q^{64} +780.875 q^{65} -226.324 q^{66} -157.810 q^{67} +378.524 q^{68} -69.0000 q^{69} -250.694 q^{70} -452.971 q^{71} -72.0000 q^{72} -950.747 q^{73} -200.789 q^{74} +586.950 q^{75} -11.1588 q^{76} -264.045 q^{77} +261.648 q^{78} -1143.31 q^{79} -286.507 q^{80} +81.0000 q^{81} +34.4724 q^{82} -946.243 q^{83} -84.0000 q^{84} -1694.53 q^{85} -188.083 q^{86} -253.967 q^{87} -301.766 q^{88} +1203.30 q^{89} +322.321 q^{90} +305.256 q^{91} -92.0000 q^{92} +173.739 q^{93} -1095.76 q^{94} +49.9542 q^{95} -96.0000 q^{96} -920.189 q^{97} -98.0000 q^{98} +339.486 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{2} + 12 q^{3} + 16 q^{4} + 5 q^{5} - 24 q^{6} - 28 q^{7} - 32 q^{8} + 36 q^{9}+O(q^{10}) \) 4 * q - 8 * q^2 + 12 * q^3 + 16 * q^4 + 5 * q^5 - 24 * q^6 - 28 * q^7 - 32 * q^8 + 36 * q^9	\( 4 q - 8 q^{2} + 12 q^{3} + 16 q^{4} + 5 q^{5} - 24 q^{6} - 28 q^{7} - 32 q^{8} + 36 q^{9} - 10 q^{10} + 19 q^{11} + 48 q^{12} - 73 q^{13} + 56 q^{14} + 15 q^{15} + 64 q^{16} - 14 q^{17} - 72 q^{18} - 51 q^{19} + 20 q^{20} - 84 q^{21} - 38 q^{22} - 92 q^{23} - 96 q^{24} + 195 q^{25} + 146 q^{26} + 108 q^{27} - 112 q^{28} - 232 q^{29} - 30 q^{30} + 80 q^{31} - 128 q^{32} + 57 q^{33} + 28 q^{34} - 35 q^{35} + 144 q^{36} - 150 q^{37} + 102 q^{38} - 219 q^{39} - 40 q^{40} - 491 q^{41} + 168 q^{42} - 481 q^{43} + 76 q^{44} + 45 q^{45} + 184 q^{46} - 289 q^{47} + 192 q^{48} + 196 q^{49} - 390 q^{50} - 42 q^{51} - 292 q^{52} - 176 q^{53} - 216 q^{54} - 1067 q^{55} + 224 q^{56} - 153 q^{57} + 464 q^{58} + 212 q^{59} + 60 q^{60} - 2066 q^{61} - 160 q^{62} - 252 q^{63} + 256 q^{64} + 142 q^{65} - 114 q^{66} - 369 q^{67} - 56 q^{68} - 276 q^{69} + 70 q^{70} - 1565 q^{71} - 288 q^{72} - 482 q^{73} + 300 q^{74} + 585 q^{75} - 204 q^{76} - 133 q^{77} + 438 q^{78} - 2146 q^{79} + 80 q^{80} + 324 q^{81} + 982 q^{82} + 1040 q^{83} - 336 q^{84} - 2823 q^{85} + 962 q^{86} - 696 q^{87} - 152 q^{88} + 1963 q^{89} - 90 q^{90} + 511 q^{91} - 368 q^{92} + 240 q^{93} + 578 q^{94} - 283 q^{95} - 384 q^{96} - 818 q^{97} - 392 q^{98} + 171 q^{99}+O(q^{100}) \) 4 * q - 8 * q^2 + 12 * q^3 + 16 * q^4 + 5 * q^5 - 24 * q^6 - 28 * q^7 - 32 * q^8 + 36 * q^9 - 10 * q^10 + 19 * q^11 + 48 * q^12 - 73 * q^13 + 56 * q^14 + 15 * q^15 + 64 * q^16 - 14 * q^17 - 72 * q^18 - 51 * q^19 + 20 * q^20 - 84 * q^21 - 38 * q^22 - 92 * q^23 - 96 * q^24 + 195 * q^25 + 146 * q^26 + 108 * q^27 - 112 * q^28 - 232 * q^29 - 30 * q^30 + 80 * q^31 - 128 * q^32 + 57 * q^33 + 28 * q^34 - 35 * q^35 + 144 * q^36 - 150 * q^37 + 102 * q^38 - 219 * q^39 - 40 * q^40 - 491 * q^41 + 168 * q^42 - 481 * q^43 + 76 * q^44 + 45 * q^45 + 184 * q^46 - 289 * q^47 + 192 * q^48 + 196 * q^49 - 390 * q^50 - 42 * q^51 - 292 * q^52 - 176 * q^53 - 216 * q^54 - 1067 * q^55 + 224 * q^56 - 153 * q^57 + 464 * q^58 + 212 * q^59 + 60 * q^60 - 2066 * q^61 - 160 * q^62 - 252 * q^63 + 256 * q^64 + 142 * q^65 - 114 * q^66 - 369 * q^67 - 56 * q^68 - 276 * q^69 + 70 * q^70 - 1565 * q^71 - 288 * q^72 - 482 * q^73 + 300 * q^74 + 585 * q^75 - 204 * q^76 - 133 * q^77 + 438 * q^78 - 2146 * q^79 + 80 * q^80 + 324 * q^81 + 982 * q^82 + 1040 * q^83 - 336 * q^84 - 2823 * q^85 + 962 * q^86 - 696 * q^87 - 152 * q^88 + 1963 * q^89 - 90 * q^90 + 511 * q^91 - 368 * q^92 + 240 * q^93 + 578 * q^94 - 283 * q^95 - 384 * q^96 - 818 * q^97 - 392 * q^98 + 171 * q^99

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