LMFDB - Embedded newform 966.4.a.r.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:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 411x^{4} + 1741x^{3} + 37570x^{2} - 116091x - 993528 $ x^6 - 2x^5 - 411x^4 + 1741x^3 + 37570x^2 - 116091*x - 993528
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-18.6983$ 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)

$f(q)$	$=$	$q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -15.6983 q^{5} +6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -15.6983 q^{5} +6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} -31.3966 q^{10} +9.74242 q^{11} +12.0000 q^{12} +11.9282 q^{13} +14.0000 q^{14} -47.0948 q^{15} +16.0000 q^{16} -16.9753 q^{17} +18.0000 q^{18} +75.0029 q^{19} -62.7931 q^{20} +21.0000 q^{21} +19.4848 q^{22} +23.0000 q^{23} +24.0000 q^{24} +121.436 q^{25} +23.8565 q^{26} +27.0000 q^{27} +28.0000 q^{28} -224.868 q^{29} -94.1897 q^{30} +23.8716 q^{31} +32.0000 q^{32} +29.2273 q^{33} -33.9506 q^{34} -109.888 q^{35} +36.0000 q^{36} +305.540 q^{37} +150.006 q^{38} +35.7847 q^{39} -125.586 q^{40} +336.715 q^{41} +42.0000 q^{42} -51.1745 q^{43} +38.9697 q^{44} -141.285 q^{45} +46.0000 q^{46} +455.653 q^{47} +48.0000 q^{48} +49.0000 q^{49} +242.872 q^{50} -50.9259 q^{51} +47.7129 q^{52} +106.429 q^{53} +54.0000 q^{54} -152.939 q^{55} +56.0000 q^{56} +225.009 q^{57} -449.735 q^{58} +301.874 q^{59} -188.379 q^{60} -233.023 q^{61} +47.7432 q^{62} +63.0000 q^{63} +64.0000 q^{64} -187.253 q^{65} +58.4545 q^{66} +976.173 q^{67} -67.9012 q^{68} +69.0000 q^{69} -219.776 q^{70} -1139.15 q^{71} +72.0000 q^{72} +374.505 q^{73} +611.079 q^{74} +364.308 q^{75} +300.012 q^{76} +68.1969 q^{77} +71.5694 q^{78} +1037.75 q^{79} -251.172 q^{80} +81.0000 q^{81} +673.430 q^{82} +595.327 q^{83} +84.0000 q^{84} +266.483 q^{85} -102.349 q^{86} -674.603 q^{87} +77.9394 q^{88} +796.910 q^{89} -282.569 q^{90} +83.4977 q^{91} +92.0000 q^{92} +71.6148 q^{93} +911.306 q^{94} -1177.42 q^{95} +96.0000 q^{96} +1635.20 q^{97} +98.0000 q^{98} +87.6818 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 12 q^{2} + 18 q^{3} + 24 q^{4} + 20 q^{5} + 36 q^{6} + 42 q^{7} + 48 q^{8} + 54 q^{9}+O(q^{10}) $ 6 * q + 12 * q^2 + 18 * q^3 + 24 * q^4 + 20 * q^5 + 36 * q^6 + 42 * q^7 + 48 * q^8 + 54 * q^9	\( 6 q + 12 q^{2} + 18 q^{3} + 24 q^{4} + 20 q^{5} + 36 q^{6} + 42 q^{7} + 48 q^{8} + 54 q^{9} + 40 q^{10} + 79 q^{11} + 72 q^{12} + 52 q^{13} + 84 q^{14} + 60 q^{15} + 96 q^{16} + 140 q^{17} + 108 q^{18} + 93 q^{19} + 80 q^{20} + 126 q^{21} + 158 q^{22} + 138 q^{23} + 144 q^{24} + 142 q^{25} + 104 q^{26} + 162 q^{27} + 168 q^{28} + 143 q^{29} + 120 q^{30} + 130 q^{31} + 192 q^{32} + 237 q^{33} + 280 q^{34} + 140 q^{35} + 216 q^{36} + 151 q^{37} + 186 q^{38} + 156 q^{39} + 160 q^{40} + 412 q^{41} + 252 q^{42} + 250 q^{43} + 316 q^{44} + 180 q^{45} + 276 q^{46} + 666 q^{47} + 288 q^{48} + 294 q^{49} + 284 q^{50} + 420 q^{51} + 208 q^{52} - 96 q^{53} + 324 q^{54} + 51 q^{55} + 336 q^{56} + 279 q^{57} + 286 q^{58} + 514 q^{59} + 240 q^{60} + 422 q^{61} + 260 q^{62} + 378 q^{63} + 384 q^{64} + 277 q^{65} + 474 q^{66} + 669 q^{67} + 560 q^{68} + 414 q^{69} + 280 q^{70} - 357 q^{71} + 432 q^{72} + 430 q^{73} + 302 q^{74} + 426 q^{75} + 372 q^{76} + 553 q^{77} + 312 q^{78} + 750 q^{79} + 320 q^{80} + 486 q^{81} + 824 q^{82} + 222 q^{83} + 504 q^{84} + 601 q^{85} + 500 q^{86} + 429 q^{87} + 632 q^{88} + 763 q^{89} + 360 q^{90} + 364 q^{91} + 552 q^{92} + 390 q^{93} + 1332 q^{94} - 541 q^{95} + 576 q^{96} + 575 q^{97} + 588 q^{98} + 711 q^{99}+O(q^{100}) \) 6 * q + 12 * q^2 + 18 * q^3 + 24 * q^4 + 20 * q^5 + 36 * q^6 + 42 * q^7 + 48 * q^8 + 54 * q^9 + 40 * q^10 + 79 * q^11 + 72 * q^12 + 52 * q^13 + 84 * q^14 + 60 * q^15 + 96 * q^16 + 140 * q^17 + 108 * q^18 + 93 * q^19 + 80 * q^20 + 126 * q^21 + 158 * q^22 + 138 * q^23 + 144 * q^24 + 142 * q^25 + 104 * q^26 + 162 * q^27 + 168 * q^28 + 143 * q^29 + 120 * q^30 + 130 * q^31 + 192 * q^32 + 237 * q^33 + 280 * q^34 + 140 * q^35 + 216 * q^36 + 151 * q^37 + 186 * q^38 + 156 * q^39 + 160 * q^40 + 412 * q^41 + 252 * q^42 + 250 * q^43 + 316 * q^44 + 180 * q^45 + 276 * q^46 + 666 * q^47 + 288 * q^48 + 294 * q^49 + 284 * q^50 + 420 * q^51 + 208 * q^52 - 96 * q^53 + 324 * q^54 + 51 * q^55 + 336 * q^56 + 279 * q^57 + 286 * q^58 + 514 * q^59 + 240 * q^60 + 422 * q^61 + 260 * q^62 + 378 * q^63 + 384 * q^64 + 277 * q^65 + 474 * q^66 + 669 * q^67 + 560 * q^68 + 414 * q^69 + 280 * q^70 - 357 * q^71 + 432 * q^72 + 430 * q^73 + 302 * q^74 + 426 * q^75 + 372 * q^76 + 553 * q^77 + 312 * q^78 + 750 * q^79 + 320 * q^80 + 486 * q^81 + 824 * q^82 + 222 * q^83 + 504 * q^84 + 601 * q^85 + 500 * q^86 + 429 * q^87 + 632 * q^88 + 763 * q^89 + 360 * q^90 + 364 * q^91 + 552 * q^92 + 390 * q^93 + 1332 * q^94 - 541 * q^95 + 576 * q^96 + 575 * q^97 + 588 * q^98 + 711 * 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
$5$	−15.6983	−1.40410	−0.702048	−	0.712129i	$-0.747731\pi$
$5$	−15.6983	−1.40410	−0.702048	+	0.712129i	$0.747731\pi$
$6$	6.00000	0.408248
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	−31.3966	−0.992846
$11$	9.74242	0.267041	0.133520	−	0.991046i	$-0.457372\pi$
$11$	9.74242	0.267041	0.133520	+	0.991046i	$0.457372\pi$
$12$	12.0000	0.288675
$13$	11.9282	0.254484	0.127242	−	0.991872i	$-0.459387\pi$
$13$	11.9282	0.254484	0.127242	+	0.991872i	$0.459387\pi$
$14$	14.0000	0.267261
$15$	−47.0948	−0.810656
$16$	16.0000	0.250000
$17$	−16.9753	−0.242183	−0.121092	−	0.992641i	$-0.538639\pi$
$17$	−16.9753	−0.242183	−0.121092	+	0.992641i	$0.538639\pi$
$18$	18.0000	0.235702
$19$	75.0029	0.905624	0.452812	−	0.891606i	$-0.350421\pi$
$19$	75.0029	0.905624	0.452812	+	0.891606i	$0.350421\pi$
$20$	−62.7931	−0.702048
$21$	21.0000	0.218218
$22$	19.4848	0.188826
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	24.0000	0.204124
$25$	121.436	0.971488
$26$	23.8565	0.179948
$27$	27.0000	0.192450
$28$	28.0000	0.188982
$29$	−224.868	−1.43989	−0.719946	−	0.694030i	$-0.755833\pi$
$29$	−224.868	−1.43989	−0.719946	+	0.694030i	$0.755833\pi$
$30$	−94.1897	−0.573220
$31$	23.8716	0.138305	0.0691527	−	0.997606i	$-0.477970\pi$
$31$	23.8716	0.138305	0.0691527	+	0.997606i	$0.477970\pi$
$32$	32.0000	0.176777
$33$	29.2273	0.154176
$34$	−33.9506	−0.171249
$35$	−109.888	−0.530699
$36$	36.0000	0.166667
$37$	305.540	1.35758	0.678789	−	0.734333i	$-0.262505\pi$
$37$	305.540	1.35758	0.678789	+	0.734333i	$0.262505\pi$
$38$	150.006	0.640373
$39$	35.7847	0.146927
$40$	−125.586	−0.496423
$41$	336.715	1.28259	0.641293	−	0.767296i	$-0.278398\pi$
$41$	336.715	1.28259	0.641293	+	0.767296i	$0.278398\pi$
$42$	42.0000	0.154303
$43$	−51.1745	−0.181489	−0.0907446	−	0.995874i	$-0.528925\pi$
$43$	−51.1745	−0.181489	−0.0907446	+	0.995874i	$0.528925\pi$
$44$	38.9697	0.133520
$45$	−141.285	−0.468032
$46$	46.0000	0.147442
$47$	455.653	1.41412	0.707062	−	0.707152i	$-0.250020\pi$
$47$	455.653	1.41412	0.707062	+	0.707152i	$0.250020\pi$
$48$	48.0000	0.144338
$49$	49.0000	0.142857
$50$	242.872	0.686946
$51$	−50.9259	−0.139825
$52$	47.7129	0.127242
$53$	106.429	0.275833	0.137917	−	0.990444i	$-0.455959\pi$
$53$	106.429	0.275833	0.137917	+	0.990444i	$0.455959\pi$
$54$	54.0000	0.136083
$55$	−152.939	−0.374951
$56$	56.0000	0.133631
$57$	225.009	0.522862
$58$	−449.735	−1.01816
$59$	301.874	0.666112	0.333056	−	0.942907i	$-0.391920\pi$
$59$	301.874	0.666112	0.333056	+	0.942907i	$0.391920\pi$
$60$	−188.379	−0.405328
$61$	−233.023	−0.489108	−0.244554	−	0.969636i	$-0.578642\pi$
$61$	−233.023	−0.489108	−0.244554	+	0.969636i	$0.578642\pi$
$62$	47.7432	0.0977967
$63$	63.0000	0.125988
$64$	64.0000	0.125000
$65$	−187.253	−0.357321
$66$	58.4545	0.109019
$67$	976.173	1.77998	0.889989	−	0.455982i	$-0.150712\pi$
$67$	976.173	1.77998	0.889989	+	0.455982i	$0.150712\pi$
$68$	−67.9012	−0.121092
$69$	69.0000	0.120386
$70$	−219.776	−0.375261
$71$	−1139.15	−1.90412	−0.952059	−	0.305915i	$-0.901038\pi$
$71$	−1139.15	−1.90412	−0.952059	+	0.305915i	$0.901038\pi$
$72$	72.0000	0.117851
$73$	374.505	0.600446	0.300223	−	0.953869i	$-0.402939\pi$
$73$	374.505	0.600446	0.300223	+	0.953869i	$0.402939\pi$
$74$	611.079	0.959953
$75$	364.308	0.560889
$76$	300.012	0.452812
$77$	68.1969	0.100932
$78$	71.5694	0.103893
$79$	1037.75	1.47792	0.738959	−	0.673751i	$-0.235318\pi$
$79$	1037.75	1.47792	0.738959	+	0.673751i	$0.235318\pi$
$80$	−251.172	−0.351024
$81$	81.0000	0.111111
$82$	673.430	0.906925
$83$	595.327	0.787296	0.393648	−	0.919261i	$-0.371213\pi$
$83$	595.327	0.787296	0.393648	+	0.919261i	$0.371213\pi$
$84$	84.0000	0.109109
$85$	266.483	0.340049
$86$	−102.349	−0.128332
$87$	−674.603	−0.831322
$88$	77.9394	0.0944132
$89$	796.910	0.949127	0.474564	−	0.880221i	$-0.342606\pi$
$89$	796.910	0.949127	0.474564	+	0.880221i	$0.342606\pi$
$90$	−282.569	−0.330949
$91$	83.4977	0.0961861
$92$	92.0000	0.104257
$93$	71.6148	0.0798507
$94$	911.306	0.999936
$95$	−1177.42	−1.27158
$96$	96.0000	0.102062
$97$	1635.20	1.71164	0.855821	−	0.517272i	$-0.173052\pi$
$97$	1635.20	1.71164	0.855821	+	0.517272i	$0.173052\pi$
$98$	98.0000	0.101015
$99$	87.6818	0.0890136
$100$	485.744	0.485744
$101$	841.079	0.828619	0.414309	−	0.910136i	$-0.364023\pi$
$101$	841.079	0.828619	0.414309	+	0.910136i	$0.364023\pi$
$102$	−101.852	−0.0988709
$103$	344.894	0.329936	0.164968	−	0.986299i	$-0.447248\pi$
$103$	344.894	0.329936	0.164968	+	0.986299i	$0.447248\pi$
$104$	95.4259	0.0899738
$105$	−329.664	−0.306399
$106$	212.858	0.195044
$107$	−1169.45	−1.05659	−0.528293	−	0.849062i	$-0.677168\pi$
$107$	−1169.45	−1.05659	−0.528293	+	0.849062i	$0.677168\pi$
$108$	108.000	0.0962250
$109$	−420.070	−0.369132	−0.184566	−	0.982820i	$-0.559088\pi$
$109$	−420.070	−0.369132	−0.184566	+	0.982820i	$0.559088\pi$
$110$	−305.878	−0.265131
$111$	916.619	0.783798
$112$	112.000	0.0944911
$113$	1563.28	1.30143	0.650713	−	0.759324i	$-0.274470\pi$
$113$	1563.28	1.30143	0.650713	+	0.759324i	$0.274470\pi$
$114$	450.018	0.369719
$115$	−361.060	−0.292774
$116$	−899.470	−0.719946
$117$	107.354	0.0848281
$118$	603.748	0.471013
$119$	−118.827	−0.0915367
$120$	−376.759	−0.286610
$121$	−1236.09	−0.928689
$122$	−466.047	−0.345852
$123$	1010.14	0.740501
$124$	95.4864	0.0691527
$125$	55.9491	0.0400339
$126$	126.000	0.0890871
$127$	358.689	0.250618	0.125309	−	0.992118i	$-0.460008\pi$
$127$	358.689	0.250618	0.125309	+	0.992118i	$0.460008\pi$
$128$	128.000	0.0883883
$129$	−153.523	−0.104783
$130$	−374.506	−0.252664
$131$	−1932.50	−1.28888	−0.644438	−	0.764656i	$-0.722909\pi$
$131$	−1932.50	−1.28888	−0.644438	+	0.764656i	$0.722909\pi$
$132$	116.909	0.0770881
$133$	525.021	0.342294
$134$	1952.35	1.25863
$135$	−423.854	−0.270219
$136$	−135.802	−0.0856247
$137$	−1317.89	−0.821861	−0.410930	−	0.911667i	$-0.634796\pi$
$137$	−1317.89	−0.821861	−0.410930	+	0.911667i	$0.634796\pi$
$138$	138.000	0.0851257
$139$	−180.822	−0.110339	−0.0551695	−	0.998477i	$-0.517570\pi$
$139$	−180.822	−0.110339	−0.0551695	+	0.998477i	$0.517570\pi$
$140$	−439.552	−0.265349
$141$	1366.96	0.816444
$142$	−2278.30	−1.34641
$143$	116.210	0.0679577
$144$	144.000	0.0833333
$145$	3530.03	2.02175
$146$	749.011	0.424579
$147$	147.000	0.0824786
$148$	1222.16	0.678789
$149$	−2809.81	−1.54489	−0.772446	−	0.635081i	$-0.780967\pi$
$149$	−2809.81	−1.54489	−0.772446	+	0.635081i	$0.780967\pi$
$150$	728.616	0.396608
$151$	1282.53	0.691198	0.345599	−	0.938382i	$-0.387676\pi$
$151$	1282.53	0.691198	0.345599	+	0.938382i	$0.387676\pi$
$152$	600.023	0.320186
$153$	−152.778	−0.0807278
$154$	136.394	0.0713697
$155$	−374.743	−0.194194
$156$	143.139	0.0734633
$157$	−2430.26	−1.23539	−0.617694	−	0.786418i	$-0.711933\pi$
$157$	−2430.26	−1.23539	−0.617694	+	0.786418i	$0.711933\pi$
$158$	2075.49	1.04505
$159$	319.287	0.159252
$160$	−502.345	−0.248212
$161$	161.000	0.0788110
$162$	162.000	0.0785674
$163$	−239.689	−0.115177	−0.0575887	−	0.998340i	$-0.518341\pi$
$163$	−239.689	−0.115177	−0.0575887	+	0.998340i	$0.518341\pi$
$164$	1346.86	0.641293
$165$	−458.818	−0.216478
$166$	1190.65	0.556703
$167$	−1645.34	−0.762397	−0.381198	−	0.924493i	$-0.624488\pi$
$167$	−1645.34	−0.762397	−0.381198	+	0.924493i	$0.624488\pi$
$168$	168.000	0.0771517
$169$	−2054.72	−0.935238
$170$	532.966	0.240451
$171$	675.026	0.301875
$172$	−204.698	−0.0907446
$173$	99.7237	0.0438257	0.0219129	−	0.999760i	$-0.493024\pi$
$173$	99.7237	0.0438257	0.0219129	+	0.999760i	$0.493024\pi$
$174$	−1349.21	−0.587833
$175$	850.052	0.367188
$176$	155.879	0.0667602
$177$	905.622	0.384580
$178$	1593.82	0.671134
$179$	−4178.50	−1.74478	−0.872390	−	0.488811i	$-0.837431\pi$
$179$	−4178.50	−1.74478	−0.872390	+	0.488811i	$0.837431\pi$
$180$	−565.138	−0.234016
$181$	812.335	0.333593	0.166797	−	0.985991i	$-0.446658\pi$
$181$	812.335	0.333593	0.166797	+	0.985991i	$0.446658\pi$
$182$	166.995	0.0680138
$183$	−699.070	−0.282387
$184$	184.000	0.0737210
$185$	−4796.45	−1.90617
$186$	143.230	0.0564629
$187$	−165.381	−0.0646729
$188$	1822.61	0.707062
$189$	189.000	0.0727393
$190$	−2354.83	−0.899145
$191$	−1331.02	−0.504237	−0.252119	−	0.967696i	$-0.581127\pi$
$191$	−1331.02	−0.504237	−0.252119	+	0.967696i	$0.581127\pi$
$192$	192.000	0.0721688
$193$	−2337.14	−0.871662	−0.435831	−	0.900029i	$-0.643545\pi$
$193$	−2337.14	−0.871662	−0.435831	+	0.900029i	$0.643545\pi$
$194$	3270.40	1.21031
$195$	−561.758	−0.206299
$196$	196.000	0.0714286
$197$	2134.94	0.772124	0.386062	−	0.922473i	$-0.373835\pi$
$197$	2134.94	0.772124	0.386062	+	0.922473i	$0.373835\pi$
$198$	175.364	0.0629421
$199$	−3634.97	−1.29486	−0.647428	−	0.762127i	$-0.724155\pi$
$199$	−3634.97	−1.29486	−0.647428	+	0.762127i	$0.724155\pi$
$200$	971.488	0.343473
$201$	2928.52	1.02767
$202$	1682.16	0.585922
$203$	−1574.07	−0.544228
$204$	−203.704	−0.0699123
$205$	−5285.84	−1.80088
$206$	689.787	0.233300
$207$	207.000	0.0695048
$208$	190.852	0.0636211
$209$	730.710	0.241839
$210$	−659.328	−0.216657
$211$	658.364	0.214804	0.107402	−	0.994216i	$-0.465747\pi$
$211$	658.364	0.214804	0.107402	+	0.994216i	$0.465747\pi$
$212$	425.716	0.137917
$213$	−3417.45	−1.09934
$214$	−2338.89	−0.747119
$215$	803.351	0.254828
$216$	216.000	0.0680414
$217$	167.101	0.0522745
$218$	−840.140	−0.261016
$219$	1123.52	0.346668
$220$	−611.757	−0.187476
$221$	−202.485	−0.0616319
$222$	1833.24	0.554229
$223$	−4019.54	−1.20703	−0.603516	−	0.797351i	$-0.706234\pi$
$223$	−4019.54	−1.20703	−0.603516	+	0.797351i	$0.706234\pi$
$224$	224.000	0.0668153
$225$	1092.92	0.323829
$226$	3126.56	0.920246
$227$	534.421	0.156259	0.0781294	−	0.996943i	$-0.475105\pi$
$227$	534.421	0.156259	0.0781294	+	0.996943i	$0.475105\pi$
$228$	900.035	0.261431
$229$	6279.17	1.81196	0.905982	−	0.423317i	$-0.139134\pi$
$229$	6279.17	1.81196	0.905982	+	0.423317i	$0.139134\pi$
$230$	−722.121	−0.207023
$231$	204.591	0.0582731
$232$	−1798.94	−0.509079
$233$	4923.34	1.38429	0.692143	−	0.721760i	$-0.256667\pi$
$233$	4923.34	1.38429	0.692143	+	0.721760i	$0.256667\pi$
$234$	214.708	0.0599826
$235$	−7152.96	−1.98557
$236$	1207.50	0.333056
$237$	3113.24	0.853276
$238$	−237.654	−0.0647262
$239$	6272.79	1.69771	0.848856	−	0.528625i	$-0.177292\pi$
$239$	6272.79	1.69771	0.848856	+	0.528625i	$0.177292\pi$
$240$	−753.517	−0.202664
$241$	5463.63	1.46034	0.730172	−	0.683263i	$-0.239440\pi$
$241$	5463.63	1.46034	0.730172	+	0.683263i	$0.239440\pi$
$242$	−2472.17	−0.656682
$243$	243.000	0.0641500
$244$	−932.094	−0.244554
$245$	−769.216	−0.200585
$246$	2020.29	0.523614
$247$	894.653	0.230467
$248$	190.973	0.0488983
$249$	1785.98	0.454546
$250$	111.898	0.0283082
$251$	−1389.08	−0.349314	−0.174657	−	0.984629i	$-0.555882\pi$
$251$	−1389.08	−0.349314	−0.174657	+	0.984629i	$0.555882\pi$
$252$	252.000	0.0629941
$253$	224.076	0.0556819
$254$	717.379	0.177214
$255$	799.449	0.196327
$256$	256.000	0.0625000
$257$	−534.592	−0.129755	−0.0648773	−	0.997893i	$-0.520666\pi$
$257$	−534.592	−0.129755	−0.0648773	+	0.997893i	$0.520666\pi$
$258$	−307.047	−0.0740926
$259$	2138.78	0.513116
$260$	−749.011	−0.178660
$261$	−2023.81	−0.479964
$262$	−3864.99	−0.911374
$263$	−6658.56	−1.56116	−0.780579	−	0.625057i	$-0.785076\pi$
$263$	−6658.56	−1.56116	−0.780579	+	0.625057i	$0.785076\pi$
$264$	233.818	0.0545095
$265$	−1670.75	−0.387297
$266$	1050.04	0.242038
$267$	2390.73	0.547979
$268$	3904.69	0.889989
$269$	4079.12	0.924567	0.462283	−	0.886732i	$-0.347030\pi$
$269$	4079.12	0.924567	0.462283	+	0.886732i	$0.347030\pi$
$270$	−847.707	−0.191073
$271$	−5494.85	−1.23169	−0.615846	−	0.787867i	$-0.711186\pi$
$271$	−5494.85	−1.23169	−0.615846	+	0.787867i	$0.711186\pi$
$272$	−271.605	−0.0605458
$273$	250.493	0.0555331
$274$	−2635.78	−0.581143
$275$	1183.08	0.259427
$276$	276.000	0.0601929
$277$	5364.37	1.16359	0.581794	−	0.813336i	$-0.302351\pi$
$277$	5364.37	1.16359	0.581794	+	0.813336i	$0.302351\pi$
$278$	−361.644	−0.0780214
$279$	214.844	0.0461018
$280$	−879.104	−0.187630
$281$	3021.97	0.641550	0.320775	−	0.947155i	$-0.396057\pi$
$281$	3021.97	0.641550	0.320775	+	0.947155i	$0.396057\pi$
$282$	2733.92	0.577313
$283$	−2459.51	−0.516616	−0.258308	−	0.966063i	$-0.583165\pi$
$283$	−2459.51	−0.516616	−0.258308	+	0.966063i	$0.583165\pi$
$284$	−4556.60	−0.952059
$285$	−3532.25	−0.734149
$286$	232.420	0.0480534
$287$	2357.00	0.484772
$288$	288.000	0.0589256
$289$	−4624.84	−0.941347
$290$	7060.07	1.42959
$291$	4905.60	0.988217
$292$	1498.02	0.300223
$293$	4380.01	0.873320	0.436660	−	0.899627i	$-0.356161\pi$
$293$	4380.01	0.873320	0.436660	+	0.899627i	$0.356161\pi$
$294$	294.000	0.0583212
$295$	−4738.90	−0.935286
$296$	2444.32	0.479976
$297$	263.045	0.0513920
$298$	−5619.62	−1.09240
$299$	274.349	0.0530637
$300$	1457.23	0.280444
$301$	−358.221	−0.0685965
$302$	2565.06	0.488751
$303$	2523.24	0.478403
$304$	1200.05	0.226406
$305$	3658.07	0.686755
$306$	−305.556	−0.0570832
$307$	8066.45	1.49960	0.749799	−	0.661666i	$-0.230150\pi$
$307$	8066.45	1.49960	0.749799	+	0.661666i	$0.230150\pi$
$308$	272.788	0.0504660
$309$	1034.68	0.190488
$310$	−749.486	−0.137316
$311$	1256.75	0.229144	0.114572	−	0.993415i	$-0.463450\pi$
$311$	1256.75	0.229144	0.114572	+	0.993415i	$0.463450\pi$
$312$	286.278	0.0519464
$313$	8791.91	1.58769	0.793847	−	0.608118i	$-0.208075\pi$
$313$	8791.91	1.58769	0.793847	+	0.608118i	$0.208075\pi$
$314$	−4860.52	−0.873551
$315$	−988.992	−0.176900
$316$	4150.98	0.738959
$317$	−7831.05	−1.38749	−0.693747	−	0.720219i	$-0.744041\pi$
$317$	−7831.05	−1.38749	−0.693747	+	0.720219i	$0.744041\pi$
$318$	638.575	0.112608
$319$	−2190.75	−0.384510
$320$	−1004.69	−0.175512
$321$	−3508.34	−0.610020
$322$	322.000	0.0557278
$323$	−1273.20	−0.219327
$324$	324.000	0.0555556
$325$	1448.52	0.247228
$326$	−479.378	−0.0814427
$327$	−1260.21	−0.213118
$328$	2693.72	0.453463
$329$	3189.57	0.534488
$330$	−917.635	−0.153073
$331$	−5323.87	−0.884067	−0.442034	−	0.896998i	$-0.645743\pi$
$331$	−5323.87	−0.884067	−0.442034	+	0.896998i	$0.645743\pi$
$332$	2381.31	0.393648
$333$	2749.86	0.452526
$334$	−3290.68	−0.539096
$335$	−15324.2	−2.49926
$336$	336.000	0.0545545
$337$	−1053.39	−0.170272	−0.0851362	−	0.996369i	$-0.527133\pi$
$337$	−1053.39	−0.170272	−0.0851362	+	0.996369i	$0.527133\pi$
$338$	−4109.43	−0.661313
$339$	4689.84	0.751378
$340$	1065.93	0.170024
$341$	232.567	0.0369332
$342$	1350.05	0.213458
$343$	343.000	0.0539949
$344$	−409.396	−0.0641661
$345$	−1083.18	−0.169033
$346$	199.447	0.0309895
$347$	−31.5159	−0.00487569	−0.00243784	−	0.999997i	$-0.500776\pi$
$347$	−31.5159	−0.00487569	−0.00243784	+	0.999997i	$0.500776\pi$
$348$	−2698.41	−0.415661
$349$	−2582.66	−0.396123	−0.198061	−	0.980190i	$-0.563465\pi$
$349$	−2582.66	−0.396123	−0.198061	+	0.980190i	$0.563465\pi$
$350$	1700.10	0.259641
$351$	322.062	0.0489755
$352$	311.757	0.0472066
$353$	−8100.11	−1.22132	−0.610659	−	0.791894i	$-0.709095\pi$
$353$	−8100.11	−1.22132	−0.610659	+	0.791894i	$0.709095\pi$
$354$	1811.24	0.271939
$355$	17882.7	2.67357
$356$	3187.64	0.474564
$357$	−356.481	−0.0528487
$358$	−8356.99	−1.23375
$359$	−3800.95	−0.558793	−0.279396	−	0.960176i	$-0.590134\pi$
$359$	−3800.95	−0.558793	−0.279396	+	0.960176i	$0.590134\pi$
$360$	−1130.28	−0.165474
$361$	−1233.56	−0.179846
$362$	1624.67	0.235886
$363$	−3708.26	−0.536179
$364$	333.991	0.0480930
$365$	−5879.09	−0.843084
$366$	−1398.14	−0.199678
$367$	−7637.36	−1.08629	−0.543143	−	0.839640i	$-0.682766\pi$
$367$	−7637.36	−1.08629	−0.543143	+	0.839640i	$0.682766\pi$
$368$	368.000	0.0521286
$369$	3030.43	0.427529
$370$	−9592.89	−1.34787
$371$	745.004	0.104255
$372$	286.459	0.0399253
$373$	416.035	0.0577520	0.0288760	−	0.999583i	$-0.490807\pi$
$373$	416.035	0.0577520	0.0288760	+	0.999583i	$0.490807\pi$
$374$	−330.761	−0.0457306
$375$	167.847	0.0231136
$376$	3645.22	0.499968
$377$	−2682.27	−0.366430
$378$	378.000	0.0514344
$379$	1810.64	0.245399	0.122700	−	0.992444i	$-0.460845\pi$
$379$	1810.64	0.245399	0.122700	+	0.992444i	$0.460845\pi$
$380$	−4709.67	−0.635792
$381$	1076.07	0.144695
$382$	−2662.04	−0.356550
$383$	−13398.4	−1.78754	−0.893768	−	0.448529i	$-0.851948\pi$
$383$	−13398.4	−1.78754	−0.893768	+	0.448529i	$0.851948\pi$
$384$	384.000	0.0510310
$385$	−1070.57	−0.141718
$386$	−4674.27	−0.616358
$387$	−460.570	−0.0604964
$388$	6540.80	0.855821
$389$	−9932.52	−1.29460	−0.647299	−	0.762236i	$-0.724102\pi$
$389$	−9932.52	−1.29460	−0.647299	+	0.762236i	$0.724102\pi$
$390$	−1123.52	−0.145876
$391$	−390.432	−0.0504987
$392$	392.000	0.0505076
$393$	−5797.49	−0.744133
$394$	4269.89	0.545974
$395$	−16290.8	−2.07514
$396$	350.727	0.0445068
$397$	−4876.50	−0.616484	−0.308242	−	0.951308i	$-0.599741\pi$
$397$	−4876.50	−0.616484	−0.308242	+	0.951308i	$0.599741\pi$
$398$	−7269.94	−0.915601
$399$	1575.06	0.197623
$400$	1942.98	0.242872
$401$	7145.59	0.889860	0.444930	−	0.895565i	$-0.353229\pi$
$401$	7145.59	0.889860	0.444930	+	0.895565i	$0.353229\pi$
$402$	5857.04	0.726673
$403$	284.746	0.0351966
$404$	3364.32	0.414309
$405$	−1271.56	−0.156011
$406$	−3148.15	−0.384827
$407$	2976.69	0.362529
$408$	−407.407	−0.0494355
$409$	−14976.3	−1.81059	−0.905293	−	0.424787i	$-0.860349\pi$
$409$	−14976.3	−1.81059	−0.905293	+	0.424787i	$0.860349\pi$
$410$	−10571.7	−1.27341
$411$	−3953.67	−0.474501
$412$	1379.57	0.164968
$413$	2113.12	0.251767
$414$	414.000	0.0491473
$415$	−9345.61	−1.10544
$416$	381.704	0.0449869
$417$	−542.466	−0.0637042
$418$	1461.42	0.171006
$419$	9165.39	1.06864	0.534318	−	0.845283i	$-0.320568\pi$
$419$	9165.39	1.06864	0.534318	+	0.845283i	$0.320568\pi$
$420$	−1318.66	−0.153200
$421$	11265.7	1.30417	0.652086	−	0.758145i	$-0.273894\pi$
$421$	11265.7	1.30417	0.652086	+	0.758145i	$0.273894\pi$
$422$	1316.73	0.151889
$423$	4100.87	0.471374
$424$	851.433	0.0975218
$425$	−2061.41	−0.235278
$426$	−6834.91	−0.777353
$427$	−1631.16	−0.184865
$428$	−4677.79	−0.528293
$429$	348.630	0.0392354
$430$	1606.70	0.180191
$431$	−956.518	−0.106900	−0.0534499	−	0.998571i	$-0.517022\pi$
$431$	−956.518	−0.106900	−0.0534499	+	0.998571i	$0.517022\pi$
$432$	432.000	0.0481125
$433$	−3271.30	−0.363069	−0.181534	−	0.983385i	$-0.558106\pi$
$433$	−3271.30	−0.363069	−0.181534	+	0.983385i	$0.558106\pi$
$434$	334.203	0.0369637
$435$	10590.1	1.16726
$436$	−1680.28	−0.184566
$437$	1725.07	0.188836
$438$	2247.03	0.245131
$439$	−2581.42	−0.280648	−0.140324	−	0.990106i	$-0.544814\pi$
$439$	−2581.42	−0.280648	−0.140324	+	0.990106i	$0.544814\pi$
$440$	−1223.51	−0.132565
$441$	441.000	0.0476190
$442$	−404.971	−0.0435803
$443$	−1813.65	−0.194512	−0.0972562	−	0.995259i	$-0.531007\pi$
$443$	−1813.65	−0.194512	−0.0972562	+	0.995259i	$0.531007\pi$
$444$	3666.47	0.391899
$445$	−12510.1	−1.33267
$446$	−8039.07	−0.853500
$447$	−8429.44	−0.891943
$448$	448.000	0.0472456
$449$	999.196	0.105022	0.0525111	−	0.998620i	$-0.483277\pi$
$449$	999.196	0.105022	0.0525111	+	0.998620i	$0.483277\pi$
$450$	2185.85	0.228982
$451$	3280.42	0.342503
$452$	6253.12	0.650713
$453$	3847.59	0.399063
$454$	1068.84	0.110492
$455$	−1310.77	−0.135055
$456$	1800.07	0.184860
$457$	5629.44	0.576223	0.288112	−	0.957597i	$-0.406973\pi$
$457$	5629.44	0.576223	0.288112	+	0.957597i	$0.406973\pi$
$458$	12558.3	1.28125
$459$	−458.333	−0.0466082
$460$	−1444.24	−0.146387
$461$	−15561.5	−1.57218	−0.786088	−	0.618115i	$-0.787897\pi$
$461$	−15561.5	−1.57218	−0.786088	+	0.618115i	$0.787897\pi$
$462$	409.182	0.0412053
$463$	12077.9	1.21233	0.606163	−	0.795340i	$-0.292708\pi$
$463$	12077.9	1.21233	0.606163	+	0.795340i	$0.292708\pi$
$464$	−3597.88	−0.359973
$465$	−1124.23	−0.112118
$466$	9846.68	0.978838
$467$	−3194.39	−0.316528	−0.158264	−	0.987397i	$-0.550590\pi$
$467$	−3194.39	−0.316528	−0.158264	+	0.987397i	$0.550590\pi$
$468$	429.416	0.0424141
$469$	6833.21	0.672768
$470$	−14305.9	−1.40401
$471$	−7290.78	−0.713252
$472$	2414.99	0.235506
$473$	−498.563	−0.0484650
$474$	6226.47	0.603357
$475$	9108.05	0.879802
$476$	−475.309	−0.0457683
$477$	957.862	0.0919444
$478$	12545.6	1.20046
$479$	12207.4	1.16445	0.582226	−	0.813027i	$-0.302182\pi$
$479$	12207.4	1.16445	0.582226	+	0.813027i	$0.302182\pi$
$480$	−1507.03	−0.143305
$481$	3644.55	0.345483
$482$	10927.3	1.03262
$483$	483.000	0.0455016
$484$	−4944.34	−0.464345
$485$	−25669.8	−2.40331
$486$	486.000	0.0453609
$487$	10022.3	0.932557	0.466278	−	0.884638i	$-0.345594\pi$
$487$	10022.3	0.932557	0.466278	+	0.884638i	$0.345594\pi$
$488$	−1864.19	−0.172926
$489$	−719.068	−0.0664977
$490$	−1538.43	−0.141835
$491$	−10389.0	−0.954887	−0.477444	−	0.878662i	$-0.658437\pi$
$491$	−10389.0	−0.954887	−0.477444	+	0.878662i	$0.658437\pi$
$492$	4040.58	0.370251
$493$	3817.20	0.348718
$494$	1789.31	0.162965
$495$	−1376.45	−0.124984
$496$	381.946	0.0345764
$497$	−7974.06	−0.719689
$498$	3571.96	0.321412
$499$	15575.8	1.39733	0.698667	−	0.715447i	$-0.253777\pi$
$499$	15575.8	1.39733	0.698667	+	0.715447i	$0.253777\pi$
$500$	223.796	0.0200170
$501$	−4936.02	−0.440170
$502$	−2778.16	−0.247002
$503$	10865.2	0.963128	0.481564	−	0.876411i	$-0.340069\pi$
$503$	10865.2	0.963128	0.481564	+	0.876411i	$0.340069\pi$
$504$	504.000	0.0445435
$505$	−13203.5	−1.16346
$506$	448.151	0.0393730
$507$	−6164.15	−0.539960
$508$	1434.76	0.125309
$509$	−3741.52	−0.325815	−0.162908	−	0.986641i	$-0.552087\pi$
$509$	−3741.52	−0.325815	−0.162908	+	0.986641i	$0.552087\pi$
$510$	1598.90	0.138824
$511$	2621.54	0.226947
$512$	512.000	0.0441942
$513$	2025.08	0.174287
$514$	−1069.18	−0.0917504
$515$	−5414.24	−0.463262
$516$	−614.094	−0.0523914
$517$	4439.16	0.377629
$518$	4277.55	0.362828
$519$	299.171	0.0253028
$520$	−1498.02	−0.126332
$521$	1444.82	0.121494	0.0607472	−	0.998153i	$-0.480652\pi$
$521$	1444.82	0.121494	0.0607472	+	0.998153i	$0.480652\pi$
$522$	−4047.62	−0.339386
$523$	−3104.71	−0.259578	−0.129789	−	0.991542i	$-0.541430\pi$
$523$	−3104.71	−0.259578	−0.129789	+	0.991542i	$0.541430\pi$
$524$	−7729.98	−0.644438
$525$	2550.16	0.211996
$526$	−13317.1	−1.10391
$527$	−405.228	−0.0334953
$528$	467.636	0.0385440
$529$	529.000	0.0434783
$530$	−3341.51	−0.273860
$531$	2716.86	0.222037
$532$	2100.08	0.171147
$533$	4016.41	0.326398
$534$	4781.46	0.387480
$535$	18358.3	1.48355
$536$	7809.39	0.629317
$537$	−12535.5	−1.00735
$538$	8158.24	0.653767
$539$	477.379	0.0381487
$540$	−1695.41	−0.135109
$541$	7861.19	0.624730	0.312365	−	0.949962i	$-0.398879\pi$
$541$	7861.19	0.624730	0.312365	+	0.949962i	$0.398879\pi$
$542$	−10989.7	−0.870938
$543$	2437.00	0.192600
$544$	−543.210	−0.0428124
$545$	6594.37	0.518297
$546$	500.986	0.0392678
$547$	−14895.1	−1.16429	−0.582147	−	0.813083i	$-0.697787\pi$
$547$	−14895.1	−1.16429	−0.582147	+	0.813083i	$0.697787\pi$
$548$	−5271.56	−0.410930
$549$	−2097.21	−0.163036
$550$	2366.16	0.183443
$551$	−16865.7	−1.30400
$552$	552.000	0.0425628
$553$	7264.22	0.558600
$554$	10728.7	0.822781
$555$	−14389.3	−1.10053
$556$	−723.288	−0.0551695
$557$	−3992.33	−0.303699	−0.151850	−	0.988404i	$-0.548523\pi$
$557$	−3992.33	−0.303699	−0.151850	+	0.988404i	$0.548523\pi$
$558$	429.689	0.0325989
$559$	−610.421	−0.0461862
$560$	−1758.21	−0.132675
$561$	−496.142	−0.0373389
$562$	6043.93	0.453644
$563$	−3404.15	−0.254827	−0.127414	−	0.991850i	$-0.540668\pi$
$563$	−3404.15	−0.254827	−0.127414	+	0.991850i	$0.540668\pi$
$564$	5467.83	0.408222
$565$	−24540.8	−1.82733
$566$	−4919.01	−0.365303
$567$	567.000	0.0419961
$568$	−9113.21	−0.673207
$569$	−7798.22	−0.574549	−0.287274	−	0.957848i	$-0.592749\pi$
$569$	−7798.22	−0.574549	−0.287274	+	0.957848i	$0.592749\pi$
$570$	−7064.50	−0.519122
$571$	12449.3	0.912413	0.456207	−	0.889874i	$-0.349208\pi$
$571$	12449.3	0.912413	0.456207	+	0.889874i	$0.349208\pi$
$572$	464.839	0.0339789
$573$	−3993.06	−0.291122
$574$	4714.01	0.342786
$575$	2793.03	0.202569
$576$	576.000	0.0416667
$577$	2817.69	0.203296	0.101648	−	0.994820i	$-0.467588\pi$
$577$	2817.69	0.203296	0.101648	+	0.994820i	$0.467588\pi$
$578$	−9249.68	−0.665633
$579$	−7011.41	−0.503254
$580$	14120.1	1.01087
$581$	4167.29	0.297570
$582$	9811.19	0.698775
$583$	1036.88	0.0736588
$584$	2996.04	0.212290
$585$	−1685.27	−0.119107
$586$	8760.01	0.617530
$587$	−22982.6	−1.61600	−0.808001	−	0.589181i	$-0.799450\pi$
$587$	−22982.6	−1.61600	−0.808001	+	0.589181i	$0.799450\pi$
$588$	588.000	0.0412393
$589$	1790.44	0.125253
$590$	−9477.80	−0.661347
$591$	6404.83	0.445786
$592$	4888.63	0.339395
$593$	16896.4	1.17007	0.585037	−	0.811007i	$-0.301080\pi$
$593$	16896.4	1.17007	0.585037	+	0.811007i	$0.301080\pi$
$594$	526.091	0.0363397
$595$	1865.38	0.128526
$596$	−11239.2	−0.772446
$597$	−10904.9	−0.747585
$598$	548.699	0.0375217
$599$	−3570.35	−0.243540	−0.121770	−	0.992558i	$-0.538857\pi$
$599$	−3570.35	−0.243540	−0.121770	+	0.992558i	$0.538857\pi$
$600$	2914.46	0.198304
$601$	16020.2	1.08732	0.543660	−	0.839306i	$-0.317038\pi$
$601$	16020.2	1.08732	0.543660	+	0.839306i	$0.317038\pi$
$602$	−716.443	−0.0485050
$603$	8785.56	0.593326
$604$	5130.13	0.345599
$605$	19404.4	1.30397
$606$	5046.48	0.338282
$607$	14321.8	0.957667	0.478833	−	0.877906i	$-0.341060\pi$
$607$	14321.8	0.957667	0.478833	+	0.877906i	$0.341060\pi$
$608$	2400.09	0.160093
$609$	−4722.22	−0.314210
$610$	7316.13	0.485609
$611$	5435.13	0.359872
$612$	−611.111	−0.0403639
$613$	−11976.1	−0.789088	−0.394544	−	0.918877i	$-0.629097\pi$
$613$	−11976.1	−0.789088	−0.394544	+	0.918877i	$0.629097\pi$
$614$	16132.9	1.06038
$615$	−15857.5	−1.03974
$616$	545.575	0.0356848
$617$	17445.1	1.13827	0.569135	−	0.822244i	$-0.307278\pi$
$617$	17445.1	1.13827	0.569135	+	0.822244i	$0.307278\pi$
$618$	2069.36	0.134696
$619$	12068.3	0.783626	0.391813	−	0.920045i	$-0.371848\pi$
$619$	12068.3	0.783626	0.391813	+	0.920045i	$0.371848\pi$
$620$	−1498.97	−0.0970971
$621$	621.000	0.0401286
$622$	2513.50	0.162029
$623$	5578.37	0.358736
$624$	572.555	0.0367317
$625$	−16057.8	−1.02770
$626$	17583.8	1.12267
$627$	2192.13	0.139626
$628$	−9721.04	−0.617694
$629$	−5186.63	−0.328783
$630$	−1977.98	−0.125087
$631$	−6106.29	−0.385242	−0.192621	−	0.981273i	$-0.561699\pi$
$631$	−6106.29	−0.385242	−0.192621	+	0.981273i	$0.561699\pi$
$632$	8301.96	0.522523
$633$	1975.09	0.124017
$634$	−15662.1	−0.981106
$635$	−5630.80	−0.351892
$636$	1277.15	0.0796262
$637$	584.484	0.0363549
$638$	−4381.51	−0.271890
$639$	−10252.4	−0.634706
$640$	−2009.38	−0.124106
$641$	−25620.7	−1.57872	−0.789358	−	0.613933i	$-0.789586\pi$
$641$	−25620.7	−1.57872	−0.789358	+	0.613933i	$0.789586\pi$
$642$	−7016.68	−0.431349
$643$	14432.6	0.885174	0.442587	−	0.896726i	$-0.354061\pi$
$643$	14432.6	0.885174	0.442587	+	0.896726i	$0.354061\pi$
$644$	644.000	0.0394055
$645$	2410.05	0.147125
$646$	−2546.40	−0.155088
$647$	14953.8	0.908649	0.454324	−	0.890836i	$-0.349881\pi$
$647$	14953.8	0.908649	0.454324	+	0.890836i	$0.349881\pi$
$648$	648.000	0.0392837
$649$	2940.98	0.177879
$650$	2897.03	0.174817
$651$	501.304	0.0301807
$652$	−958.757	−0.0575887
$653$	−9258.13	−0.554821	−0.277411	−	0.960751i	$-0.589476\pi$
$653$	−9258.13	−0.554821	−0.277411	+	0.960751i	$0.589476\pi$
$654$	−2520.42	−0.150698
$655$	30336.8	1.80971
$656$	5387.44	0.320647
$657$	3370.55	0.200149
$658$	6379.14	0.377940
$659$	−20908.4	−1.23593	−0.617963	−	0.786207i	$-0.712042\pi$
$659$	−20908.4	−1.23593	−0.617963	+	0.786207i	$0.712042\pi$
$660$	−1835.27	−0.108239
$661$	2548.73	0.149976	0.0749880	−	0.997184i	$-0.476108\pi$
$661$	2548.73	0.149976	0.0749880	+	0.997184i	$0.476108\pi$
$662$	−10647.7	−0.625130
$663$	−607.456	−0.0355832
$664$	4762.61	0.278351
$665$	−8241.92	−0.480613
$666$	5499.71	0.319984
$667$	−5171.95	−0.300238
$668$	−6581.36	−0.381198
$669$	−12058.6	−0.696880
$670$	−30648.5	−1.76724
$671$	−2270.21	−0.130612
$672$	672.000	0.0385758
$673$	−9284.90	−0.531808	−0.265904	−	0.964000i	$-0.585670\pi$
$673$	−9284.90	−0.531808	−0.265904	+	0.964000i	$0.585670\pi$
$674$	−2106.78	−0.120401
$675$	3278.77	0.186963
$676$	−8218.87	−0.467619
$677$	−30248.6	−1.71720	−0.858602	−	0.512642i	$-0.828667\pi$
$677$	−30248.6	−1.71720	−0.858602	+	0.512642i	$0.828667\pi$
$678$	9379.68	0.531305
$679$	11446.4	0.646940
$680$	2131.86	0.120225
$681$	1603.26	0.0902161
$682$	465.134	0.0261157
$683$	−7107.36	−0.398178	−0.199089	−	0.979981i	$-0.563798\pi$
$683$	−7107.36	−0.398178	−0.199089	+	0.979981i	$0.563798\pi$
$684$	2700.11	0.150937
$685$	20688.6	1.15397
$686$	686.000	0.0381802
$687$	18837.5	1.04614
$688$	−818.792	−0.0453723
$689$	1269.51	0.0701953
$690$	−2166.36	−0.119525
$691$	−78.1562	−0.00430275	−0.00215138	−	0.999998i	$-0.500685\pi$
$691$	−78.1562	−0.00430275	−0.00215138	+	0.999998i	$0.500685\pi$
$692$	398.895	0.0219129
$693$	613.772	0.0336440
$694$	−63.0319	−0.00344763
$695$	2838.59	0.154927
$696$	−5396.82	−0.293917
$697$	−5715.84	−0.310621
$698$	−5165.33	−0.280101
$699$	14770.0	0.799218
$700$	3400.21	0.183594
$701$	4373.65	0.235650	0.117825	−	0.993034i	$-0.462408\pi$
$701$	4373.65	0.235650	0.117825	+	0.993034i	$0.462408\pi$
$702$	644.125	0.0346309
$703$	22916.4	1.22946
$704$	623.515	0.0333801
$705$	−21458.9	−1.14637
$706$	−16200.2	−0.863602
$707$	5887.56	0.313189
$708$	3622.49	0.192290
$709$	−22379.1	−1.18542	−0.592711	−	0.805415i	$-0.701942\pi$
$709$	−22379.1	−1.18542	−0.592711	+	0.805415i	$0.701942\pi$
$710$	35765.4	1.89050
$711$	9339.71	0.492639
$712$	6375.28	0.335567
$713$	549.047	0.0288387
$714$	−712.963	−0.0373697
$715$	−1824.30	−0.0954193
$716$	−16714.0	−0.872390
$717$	18818.4	0.980174
$718$	−7601.90	−0.395126
$719$	12740.5	0.660836	0.330418	−	0.943835i	$-0.392810\pi$
$719$	12740.5	0.660836	0.330418	+	0.943835i	$0.392810\pi$
$720$	−2260.55	−0.117008
$721$	2414.25	0.124704
$722$	−2467.12	−0.127170
$723$	16390.9	0.843130
$724$	3249.34	0.166797
$725$	−27307.0	−1.39884
$726$	−7416.51	−0.379136
$727$	11475.8	0.585439	0.292720	−	0.956198i	$-0.405440\pi$
$727$	11475.8	0.585439	0.292720	+	0.956198i	$0.405440\pi$
$728$	667.981	0.0340069
$729$	729.000	0.0370370
$730$	−11758.2	−0.596151
$731$	868.702	0.0439537
$732$	−2796.28	−0.141193
$733$	−13902.2	−0.700533	−0.350266	−	0.936650i	$-0.613909\pi$
$733$	−13902.2	−0.700533	−0.350266	+	0.936650i	$0.613909\pi$
$734$	−15274.7	−0.768120
$735$	−2307.65	−0.115808
$736$	736.000	0.0368605
$737$	9510.29	0.475327
$738$	6060.87	0.302308
$739$	−3775.51	−0.187935	−0.0939677	−	0.995575i	$-0.529955\pi$
$739$	−3775.51	−0.187935	−0.0939677	+	0.995575i	$0.529955\pi$
$740$	−19185.8	−0.953086
$741$	2683.96	0.133060
$742$	1490.01	0.0737195
$743$	22225.4	1.09740	0.548701	−	0.836018i	$-0.315122\pi$
$743$	22225.4	1.09740	0.548701	+	0.836018i	$0.315122\pi$
$744$	572.919	0.0282315
$745$	44109.2	2.16918
$746$	832.070	0.0408368
$747$	5357.94	0.262432
$748$	−661.522	−0.0323364
$749$	−8186.13	−0.399352
$750$	335.694	0.0163438
$751$	−30574.3	−1.48558	−0.742791	−	0.669523i	$-0.766499\pi$
$751$	−30574.3	−1.48558	−0.742791	+	0.669523i	$0.766499\pi$
$752$	7290.44	0.353531
$753$	−4167.24	−0.201677
$754$	−5364.55	−0.259105
$755$	−20133.5	−0.970509
$756$	756.000	0.0363696
$757$	3765.58	0.180796	0.0903978	−	0.995906i	$-0.471186\pi$
$757$	3765.58	0.180796	0.0903978	+	0.995906i	$0.471186\pi$
$758$	3621.28	0.173523
$759$	672.227	0.0321479
$760$	−9419.34	−0.449573
$761$	−4613.25	−0.219750	−0.109875	−	0.993945i	$-0.535045\pi$
$761$	−4613.25	−0.219750	−0.109875	+	0.993945i	$0.535045\pi$
$762$	2152.14	0.102315
$763$	−2940.49	−0.139519
$764$	−5324.09	−0.252119
$765$	2398.35	0.113350
$766$	−26796.8	−1.26398
$767$	3600.82	0.169515
$768$	768.000	0.0360844
$769$	18049.6	0.846403	0.423202	−	0.906035i	$-0.360906\pi$
$769$	18049.6	0.846403	0.423202	+	0.906035i	$0.360906\pi$
$770$	−2141.15	−0.100210
$771$	−1603.78	−0.0749138
$772$	−9348.54	−0.435831
$773$	19278.5	0.897022	0.448511	−	0.893777i	$-0.351954\pi$
$773$	19278.5	0.897022	0.448511	+	0.893777i	$0.351954\pi$
$774$	−921.141	−0.0427774
$775$	2898.87	0.134362
$776$	13081.6	0.605157
$777$	6416.33	0.296248
$778$	−19865.0	−0.915419
$779$	25254.6	1.16154
$780$	−2247.03	−0.103150
$781$	−11098.1	−0.508477
$782$	−780.864	−0.0357080
$783$	−6071.43	−0.277107
$784$	784.000	0.0357143
$785$	38150.9	1.73460
$786$	−11595.0	−0.526182
$787$	20397.1	0.923860	0.461930	−	0.886916i	$-0.347157\pi$
$787$	20397.1	0.923860	0.461930	+	0.886916i	$0.347157\pi$
$788$	8539.77	0.386062
$789$	−19975.7	−0.901335
$790$	−32581.6	−1.46734
$791$	10943.0	0.491892
$792$	701.454	0.0314711
$793$	−2779.56	−0.124470
$794$	−9752.99	−0.435920
$795$	−5012.26	−0.223606
$796$	−14539.9	−0.647428
$797$	−13249.2	−0.588846	−0.294423	−	0.955675i	$-0.595127\pi$
$797$	−13249.2	−0.588846	−0.294423	+	0.955675i	$0.595127\pi$
$798$	3150.12	0.139741
$799$	−7734.85	−0.342477
$800$	3885.95	0.171736
$801$	7172.19	0.316376
$802$	14291.2	0.629226
$803$	3648.59	0.160344
$804$	11714.1	0.513835
$805$	−2527.42	−0.110658
$806$	569.492	0.0248877
$807$	12237.4	0.533799
$808$	6728.63	0.292961
$809$	−3506.56	−0.152391	−0.0761953	−	0.997093i	$-0.524277\pi$
$809$	−3506.56	−0.152391	−0.0761953	+	0.997093i	$0.524277\pi$
$810$	−2543.12	−0.110316
$811$	32143.3	1.39174	0.695871	−	0.718167i	$-0.255019\pi$
$811$	32143.3	1.39174	0.695871	+	0.718167i	$0.255019\pi$
$812$	−6296.29	−0.272114
$813$	−16484.6	−0.711118
$814$	5953.39	0.256347
$815$	3762.71	0.161720
$816$	−814.815	−0.0349562
$817$	−3838.24	−0.164361
$818$	−29952.6	−1.28028
$819$	751.479	0.0320620
$820$	−21143.4	−0.900438
$821$	−37363.3	−1.58829	−0.794146	−	0.607727i	$-0.792082\pi$
$821$	−37363.3	−1.58829	−0.794146	+	0.607727i	$0.792082\pi$
$822$	−7907.34	−0.335523
$823$	17032.8	0.721415	0.360708	−	0.932679i	$-0.382535\pi$
$823$	17032.8	0.721415	0.360708	+	0.932679i	$0.382535\pi$
$824$	2759.15	0.116650
$825$	3549.24	0.149780
$826$	4226.23	0.178026
$827$	11926.2	0.501469	0.250735	−	0.968056i	$-0.419328\pi$
$827$	11926.2	0.501469	0.250735	+	0.968056i	$0.419328\pi$
$828$	828.000	0.0347524
$829$	−36866.7	−1.54455	−0.772276	−	0.635287i	$-0.780882\pi$
$829$	−36866.7	−1.54455	−0.772276	+	0.635287i	$0.780882\pi$
$830$	−18691.2	−0.781664
$831$	16093.1	0.671798
$832$	763.407	0.0318106
$833$	−831.790	−0.0345976
$834$	−1084.93	−0.0450457
$835$	25829.0	1.07048
$836$	2922.84	0.120919
$837$	644.533	0.0266169
$838$	18330.8	0.755640
$839$	12740.6	0.524261	0.262131	−	0.965032i	$-0.415575\pi$
$839$	12740.6	0.524261	0.262131	+	0.965032i	$0.415575\pi$
$840$	−2637.31	−0.108328
$841$	26176.4	1.07329
$842$	22531.4	0.922189
$843$	9065.90	0.370399
$844$	2633.45	0.107402
$845$	32255.5	1.31316
$846$	8201.75	0.333312
$847$	−8652.60	−0.351012
$848$	1702.87	0.0689583
$849$	−7378.52	−0.298269
$850$	−4122.83	−0.166367
$851$	7027.41	0.283075
$852$	−13669.8	−0.549671
$853$	−16534.0	−0.663674	−0.331837	−	0.943337i	$-0.607668\pi$
$853$	−16534.0	−0.663674	−0.331837	+	0.943337i	$0.607668\pi$
$854$	−3262.33	−0.130720
$855$	−10596.8	−0.423861
$856$	−9355.57	−0.373560
$857$	11966.0	0.476956	0.238478	−	0.971148i	$-0.423352\pi$
$857$	11966.0	0.476956	0.238478	+	0.971148i	$0.423352\pi$
$858$	697.259	0.0277436
$859$	1515.58	0.0601991	0.0300995	−	0.999547i	$-0.490418\pi$
$859$	1515.58	0.0601991	0.0300995	+	0.999547i	$0.490418\pi$
$860$	3213.40	0.127414
$861$	7071.01	0.279883
$862$	−1913.04	−0.0755896
$863$	9696.09	0.382455	0.191228	−	0.981546i	$-0.438753\pi$
$863$	9696.09	0.382455	0.191228	+	0.981546i	$0.438753\pi$
$864$	864.000	0.0340207
$865$	−1565.49	−0.0615356
$866$	−6542.60	−0.256728
$867$	−13874.5	−0.543487
$868$	668.405	0.0261373
$869$	10110.1	0.394664
$870$	21180.2	0.825375
$871$	11644.0	0.452977
$872$	−3360.56	−0.130508
$873$	14716.8	0.570547
$874$	3450.13	0.133527
$875$	391.644	0.0151314
$876$	4494.07	0.173334
$877$	−6821.69	−0.262659	−0.131330	−	0.991339i	$-0.541925\pi$
$877$	−6821.69	−0.262659	−0.131330	+	0.991339i	$0.541925\pi$
$878$	−5162.83	−0.198448
$879$	13140.0	0.504211
$880$	−2447.03	−0.0937378
$881$	11382.6	0.435290	0.217645	−	0.976028i	$-0.430162\pi$
$881$	11382.6	0.435290	0.217645	+	0.976028i	$0.430162\pi$
$882$	882.000	0.0336718
$883$	−1024.76	−0.0390553	−0.0195276	−	0.999809i	$-0.506216\pi$
$883$	−1024.76	−0.0390553	−0.0195276	+	0.999809i	$0.506216\pi$
$884$	−809.942	−0.0308159
$885$	−14216.7	−0.539988
$886$	−3627.30	−0.137541
$887$	−33552.6	−1.27011	−0.635054	−	0.772467i	$-0.719022\pi$
$887$	−33552.6	−1.27011	−0.635054	+	0.772467i	$0.719022\pi$
$888$	7332.95	0.277115
$889$	2510.82	0.0947248
$890$	−25020.2	−0.942338
$891$	789.136	0.0296712
$892$	−16078.1	−0.603516
$893$	34175.3	1.28066
$894$	−16858.9	−0.630699
$895$	65595.2	2.44984
$896$	896.000	0.0334077
$897$	823.048	0.0306363
$898$	1998.39	0.0742619
$899$	−5367.95	−0.199145
$900$	4371.70	0.161915
$901$	−1806.67	−0.0668022
$902$	6560.84	0.242186
$903$	−1074.66	−0.0396042
$904$	12506.2	0.460123
$905$	−12752.3	−0.468397
$906$	7695.19	0.282181
$907$	24661.7	0.902843	0.451422	−	0.892311i	$-0.350917\pi$
$907$	24661.7	0.902843	0.451422	+	0.892311i	$0.350917\pi$
$908$	2137.68	0.0781294
$909$	7569.71	0.276206
$910$	−2621.54	−0.0954980
$911$	−6419.99	−0.233484	−0.116742	−	0.993162i	$-0.537245\pi$
$911$	−6419.99	−0.233484	−0.116742	+	0.993162i	$0.537245\pi$
$912$	3600.14	0.130716
$913$	5799.92	0.210240
$914$	11258.9	0.407451
$915$	10974.2	0.396498
$916$	25116.7	0.905982
$917$	−13527.5	−0.487150
$918$	−916.667	−0.0329570
$919$	27367.1	0.982327	0.491164	−	0.871067i	$-0.336572\pi$
$919$	27367.1	0.982327	0.491164	+	0.871067i	$0.336572\pi$
$920$	−2888.48	−0.103511
$921$	24199.3	0.865793
$922$	−31123.1	−1.11170
$923$	−13588.1	−0.484568
$924$	818.363	0.0291366
$925$	37103.5	1.31887
$926$	24155.8	0.857244
$927$	3104.04	0.109979
$928$	−7195.76	−0.254539
$929$	15002.1	0.529818	0.264909	−	0.964273i	$-0.414658\pi$
$929$	15002.1	0.529818	0.264909	+	0.964273i	$0.414658\pi$
$930$	−2248.46	−0.0792794
$931$	3675.14	0.129375
$932$	19693.4	0.692143
$933$	3770.25	0.132296
$934$	−6388.78	−0.223819
$935$	2596.19	0.0908069
$936$	858.833	0.0299913
$937$	28290.3	0.986342	0.493171	−	0.869932i	$-0.335838\pi$
$937$	28290.3	0.986342	0.493171	+	0.869932i	$0.335838\pi$
$938$	13666.4	0.475719
$939$	26375.7	0.916655
$940$	−28611.9	−0.992783
$941$	6324.56	0.219102	0.109551	−	0.993981i	$-0.465059\pi$
$941$	6324.56	0.219102	0.109551	+	0.993981i	$0.465059\pi$
$942$	−14581.6	−0.504345
$943$	7744.44	0.267438
$944$	4829.98	0.166528
$945$	−2966.97	−0.102133
$946$	−997.126	−0.0342700
$947$	21075.9	0.723204	0.361602	−	0.932333i	$-0.382230\pi$
$947$	21075.9	0.723204	0.361602	+	0.932333i	$0.382230\pi$
$948$	12452.9	0.426638
$949$	4467.19	0.152804
$950$	18216.1	0.622114
$951$	−23493.1	−0.801070
$952$	−950.617	−0.0323631
$953$	27463.8	0.933516	0.466758	−	0.884385i	$-0.345422\pi$
$953$	27463.8	0.933516	0.466758	+	0.884385i	$0.345422\pi$
$954$	1915.72	0.0650145
$955$	20894.7	0.707998
$956$	25091.2	0.848856
$957$	−6572.26	−0.221997
$958$	24414.9	0.823392
$959$	−9225.23	−0.310634
$960$	−3014.07	−0.101332
$961$	−29221.1	−0.980872
$962$	7289.10	0.244293
$963$	−10525.0	−0.352195
$964$	21854.5	0.730172
$965$	36689.0	1.22390
$966$	966.000	0.0321745
$967$	25578.8	0.850631	0.425315	−	0.905045i	$-0.360163\pi$
$967$	25578.8	0.850631	0.425315	+	0.905045i	$0.360163\pi$
$968$	−9888.68	−0.328341
$969$	−3819.59	−0.126628
$970$	−51339.6	−1.69940
$971$	18396.6	0.608007	0.304003	−	0.952671i	$-0.401677\pi$
$971$	18396.6	0.608007	0.304003	+	0.952671i	$0.401677\pi$
$972$	972.000	0.0320750
$973$	−1265.75	−0.0417042
$974$	20044.7	0.659417
$975$	4345.55	0.142737
$976$	−3728.37	−0.122277
$977$	−43408.7	−1.42146	−0.710730	−	0.703465i	$-0.751635\pi$
$977$	−43408.7	−1.42146	−0.710730	+	0.703465i	$0.751635\pi$
$978$	−1438.14	−0.0470210
$979$	7763.84	0.253456
$980$	−3076.86	−0.100293
$981$	−3780.63	−0.123044
$982$	−20778.0	−0.675207
$983$	−57534.9	−1.86682	−0.933408	−	0.358818i	$-0.883180\pi$
$983$	−57534.9	−1.86682	−0.933408	+	0.358818i	$0.883180\pi$
$984$	8081.16	0.261807
$985$	−33514.9	−1.08414
$986$	7634.39	0.246581
$987$	9568.71	0.308587
$988$	3578.61	0.115234
$989$	−1177.01	−0.0378431
$990$	−2752.91	−0.0883769
$991$	−51860.2	−1.66236	−0.831178	−	0.556007i	$-0.812333\pi$
$991$	−51860.2	−1.66236	−0.831178	+	0.556007i	$0.812333\pi$
$992$	763.891	0.0244492
$993$	−15971.6	−0.510417
$994$	−15948.1	−0.508897
$995$	57062.8	1.81810
$996$	7143.92	0.227273
$997$	−24141.5	−0.766870	−0.383435	−	0.923568i	$-0.625259\pi$
$997$	−24141.5	−0.766870	−0.383435	+	0.923568i	$0.625259\pi$
$998$	31151.6	0.988064
$999$	8249.57	0.261266

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.4.a.r.1.1	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.4.a.r.1.1	✓	6	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)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -15.6983 q^{5} +6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -15.6983 q^{5} +6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} -31.3966 q^{10} +9.74242 q^{11} +12.0000 q^{12} +11.9282 q^{13} +14.0000 q^{14} -47.0948 q^{15} +16.0000 q^{16} -16.9753 q^{17} +18.0000 q^{18} +75.0029 q^{19} -62.7931 q^{20} +21.0000 q^{21} +19.4848 q^{22} +23.0000 q^{23} +24.0000 q^{24} +121.436 q^{25} +23.8565 q^{26} +27.0000 q^{27} +28.0000 q^{28} -224.868 q^{29} -94.1897 q^{30} +23.8716 q^{31} +32.0000 q^{32} +29.2273 q^{33} -33.9506 q^{34} -109.888 q^{35} +36.0000 q^{36} +305.540 q^{37} +150.006 q^{38} +35.7847 q^{39} -125.586 q^{40} +336.715 q^{41} +42.0000 q^{42} -51.1745 q^{43} +38.9697 q^{44} -141.285 q^{45} +46.0000 q^{46} +455.653 q^{47} +48.0000 q^{48} +49.0000 q^{49} +242.872 q^{50} -50.9259 q^{51} +47.7129 q^{52} +106.429 q^{53} +54.0000 q^{54} -152.939 q^{55} +56.0000 q^{56} +225.009 q^{57} -449.735 q^{58} +301.874 q^{59} -188.379 q^{60} -233.023 q^{61} +47.7432 q^{62} +63.0000 q^{63} +64.0000 q^{64} -187.253 q^{65} +58.4545 q^{66} +976.173 q^{67} -67.9012 q^{68} +69.0000 q^{69} -219.776 q^{70} -1139.15 q^{71} +72.0000 q^{72} +374.505 q^{73} +611.079 q^{74} +364.308 q^{75} +300.012 q^{76} +68.1969 q^{77} +71.5694 q^{78} +1037.75 q^{79} -251.172 q^{80} +81.0000 q^{81} +673.430 q^{82} +595.327 q^{83} +84.0000 q^{84} +266.483 q^{85} -102.349 q^{86} -674.603 q^{87} +77.9394 q^{88} +796.910 q^{89} -282.569 q^{90} +83.4977 q^{91} +92.0000 q^{92} +71.6148 q^{93} +911.306 q^{94} -1177.42 q^{95} +96.0000 q^{96} +1635.20 q^{97} +98.0000 q^{98} +87.6818 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 12 q^{2} + 18 q^{3} + 24 q^{4} + 20 q^{5} + 36 q^{6} + 42 q^{7} + 48 q^{8} + 54 q^{9}+O(q^{10}) \) 6 * q + 12 * q^2 + 18 * q^3 + 24 * q^4 + 20 * q^5 + 36 * q^6 + 42 * q^7 + 48 * q^8 + 54 * q^9	\( 6 q + 12 q^{2} + 18 q^{3} + 24 q^{4} + 20 q^{5} + 36 q^{6} + 42 q^{7} + 48 q^{8} + 54 q^{9} + 40 q^{10} + 79 q^{11} + 72 q^{12} + 52 q^{13} + 84 q^{14} + 60 q^{15} + 96 q^{16} + 140 q^{17} + 108 q^{18} + 93 q^{19} + 80 q^{20} + 126 q^{21} + 158 q^{22} + 138 q^{23} + 144 q^{24} + 142 q^{25} + 104 q^{26} + 162 q^{27} + 168 q^{28} + 143 q^{29} + 120 q^{30} + 130 q^{31} + 192 q^{32} + 237 q^{33} + 280 q^{34} + 140 q^{35} + 216 q^{36} + 151 q^{37} + 186 q^{38} + 156 q^{39} + 160 q^{40} + 412 q^{41} + 252 q^{42} + 250 q^{43} + 316 q^{44} + 180 q^{45} + 276 q^{46} + 666 q^{47} + 288 q^{48} + 294 q^{49} + 284 q^{50} + 420 q^{51} + 208 q^{52} - 96 q^{53} + 324 q^{54} + 51 q^{55} + 336 q^{56} + 279 q^{57} + 286 q^{58} + 514 q^{59} + 240 q^{60} + 422 q^{61} + 260 q^{62} + 378 q^{63} + 384 q^{64} + 277 q^{65} + 474 q^{66} + 669 q^{67} + 560 q^{68} + 414 q^{69} + 280 q^{70} - 357 q^{71} + 432 q^{72} + 430 q^{73} + 302 q^{74} + 426 q^{75} + 372 q^{76} + 553 q^{77} + 312 q^{78} + 750 q^{79} + 320 q^{80} + 486 q^{81} + 824 q^{82} + 222 q^{83} + 504 q^{84} + 601 q^{85} + 500 q^{86} + 429 q^{87} + 632 q^{88} + 763 q^{89} + 360 q^{90} + 364 q^{91} + 552 q^{92} + 390 q^{93} + 1332 q^{94} - 541 q^{95} + 576 q^{96} + 575 q^{97} + 588 q^{98} + 711 q^{99}+O(q^{100}) \) 6 * q + 12 * q^2 + 18 * q^3 + 24 * q^4 + 20 * q^5 + 36 * q^6 + 42 * q^7 + 48 * q^8 + 54 * q^9 + 40 * q^10 + 79 * q^11 + 72 * q^12 + 52 * q^13 + 84 * q^14 + 60 * q^15 + 96 * q^16 + 140 * q^17 + 108 * q^18 + 93 * q^19 + 80 * q^20 + 126 * q^21 + 158 * q^22 + 138 * q^23 + 144 * q^24 + 142 * q^25 + 104 * q^26 + 162 * q^27 + 168 * q^28 + 143 * q^29 + 120 * q^30 + 130 * q^31 + 192 * q^32 + 237 * q^33 + 280 * q^34 + 140 * q^35 + 216 * q^36 + 151 * q^37 + 186 * q^38 + 156 * q^39 + 160 * q^40 + 412 * q^41 + 252 * q^42 + 250 * q^43 + 316 * q^44 + 180 * q^45 + 276 * q^46 + 666 * q^47 + 288 * q^48 + 294 * q^49 + 284 * q^50 + 420 * q^51 + 208 * q^52 - 96 * q^53 + 324 * q^54 + 51 * q^55 + 336 * q^56 + 279 * q^57 + 286 * q^58 + 514 * q^59 + 240 * q^60 + 422 * q^61 + 260 * q^62 + 378 * q^63 + 384 * q^64 + 277 * q^65 + 474 * q^66 + 669 * q^67 + 560 * q^68 + 414 * q^69 + 280 * q^70 - 357 * q^71 + 432 * q^72 + 430 * q^73 + 302 * q^74 + 426 * q^75 + 372 * q^76 + 553 * q^77 + 312 * q^78 + 750 * q^79 + 320 * q^80 + 486 * q^81 + 824 * q^82 + 222 * q^83 + 504 * q^84 + 601 * q^85 + 500 * q^86 + 429 * q^87 + 632 * q^88 + 763 * q^89 + 360 * q^90 + 364 * q^91 + 552 * q^92 + 390 * q^93 + 1332 * q^94 - 541 * q^95 + 576 * q^96 + 575 * q^97 + 588 * q^98 + 711 * q^99

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