LMFDB - Embedded newform 966.4.a.d.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:	$3$
Coefficient field:	3.3.29901.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 39x + 102 $ x^3 - x^2 - 39*x + 102
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-6.85699$ of defining polynomial
Character	$\chi$	$=$	966.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -8.85699 q^{5} -6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -8.85699 q^{5} -6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +17.7140 q^{10} +29.5332 q^{11} +12.0000 q^{12} -29.0938 q^{13} -14.0000 q^{14} -26.5710 q^{15} +16.0000 q^{16} -27.4772 q^{17} -18.0000 q^{18} -20.9475 q^{19} -35.4280 q^{20} +21.0000 q^{21} -59.0665 q^{22} +23.0000 q^{23} -24.0000 q^{24} -46.5537 q^{25} +58.1876 q^{26} +27.0000 q^{27} +28.0000 q^{28} +60.7313 q^{29} +53.1420 q^{30} -168.461 q^{31} -32.0000 q^{32} +88.5997 q^{33} +54.9544 q^{34} -61.9989 q^{35} +36.0000 q^{36} -139.964 q^{37} +41.8950 q^{38} -87.2814 q^{39} +70.8559 q^{40} +117.773 q^{41} -42.0000 q^{42} +412.795 q^{43} +118.133 q^{44} -79.7129 q^{45} -46.0000 q^{46} -200.089 q^{47} +48.0000 q^{48} +49.0000 q^{49} +93.1074 q^{50} -82.4315 q^{51} -116.375 q^{52} +250.609 q^{53} -54.0000 q^{54} -261.576 q^{55} -56.0000 q^{56} -62.8425 q^{57} -121.463 q^{58} +572.882 q^{59} -106.284 q^{60} -576.362 q^{61} +336.922 q^{62} +63.0000 q^{63} +64.0000 q^{64} +257.684 q^{65} -177.199 q^{66} -792.714 q^{67} -109.909 q^{68} +69.0000 q^{69} +123.998 q^{70} -312.265 q^{71} -72.0000 q^{72} -581.032 q^{73} +279.929 q^{74} -139.661 q^{75} -83.7900 q^{76} +206.733 q^{77} +174.563 q^{78} -880.866 q^{79} -141.712 q^{80} +81.0000 q^{81} -235.547 q^{82} -425.963 q^{83} +84.0000 q^{84} +243.365 q^{85} -825.590 q^{86} +182.194 q^{87} -236.266 q^{88} -905.408 q^{89} +159.426 q^{90} -203.657 q^{91} +92.0000 q^{92} -505.383 q^{93} +400.177 q^{94} +185.532 q^{95} -96.0000 q^{96} +1298.70 q^{97} -98.0000 q^{98} +265.799 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 6 q^{2} + 9 q^{3} + 12 q^{4} - 5 q^{5} - 18 q^{6} + 21 q^{7} - 24 q^{8} + 27 q^{9}+O(q^{10}) $ 3 * q - 6 * q^2 + 9 * q^3 + 12 * q^4 - 5 * q^5 - 18 * q^6 + 21 * q^7 - 24 * q^8 + 27 * q^9	\( 3 q - 6 q^{2} + 9 q^{3} + 12 q^{4} - 5 q^{5} - 18 q^{6} + 21 q^{7} - 24 q^{8} + 27 q^{9} + 10 q^{10} - 3 q^{11} + 36 q^{12} - 79 q^{13} - 42 q^{14} - 15 q^{15} + 48 q^{16} - 26 q^{17} - 54 q^{18} - 15 q^{19} - 20 q^{20} + 63 q^{21} + 6 q^{22} + 69 q^{23} - 72 q^{24} - 288 q^{25} + 158 q^{26} + 81 q^{27} + 84 q^{28} - 74 q^{29} + 30 q^{30} - 378 q^{31} - 96 q^{32} - 9 q^{33} + 52 q^{34} - 35 q^{35} + 108 q^{36} - 260 q^{37} + 30 q^{38} - 237 q^{39} + 40 q^{40} + 293 q^{41} - 126 q^{42} - 625 q^{43} - 12 q^{44} - 45 q^{45} - 138 q^{46} + 163 q^{47} + 144 q^{48} + 147 q^{49} + 576 q^{50} - 78 q^{51} - 316 q^{52} + 178 q^{53} - 162 q^{54} - 353 q^{55} - 168 q^{56} - 45 q^{57} + 148 q^{58} - 624 q^{59} - 60 q^{60} - 502 q^{61} + 756 q^{62} + 189 q^{63} + 192 q^{64} + 102 q^{65} + 18 q^{66} - 141 q^{67} - 104 q^{68} + 207 q^{69} + 70 q^{70} + 29 q^{71} - 216 q^{72} - 1198 q^{73} + 520 q^{74} - 864 q^{75} - 60 q^{76} - 21 q^{77} + 474 q^{78} - 1654 q^{79} - 80 q^{80} + 243 q^{81} - 586 q^{82} - 614 q^{83} + 252 q^{84} + 309 q^{85} + 1250 q^{86} - 222 q^{87} + 24 q^{88} - 549 q^{89} + 90 q^{90} - 553 q^{91} + 276 q^{92} - 1134 q^{93} - 326 q^{94} + 415 q^{95} - 288 q^{96} + 182 q^{97} - 294 q^{98} - 27 q^{99}+O(q^{100}) \) 3 * q - 6 * q^2 + 9 * q^3 + 12 * q^4 - 5 * q^5 - 18 * q^6 + 21 * q^7 - 24 * q^8 + 27 * q^9 + 10 * q^10 - 3 * q^11 + 36 * q^12 - 79 * q^13 - 42 * q^14 - 15 * q^15 + 48 * q^16 - 26 * q^17 - 54 * q^18 - 15 * q^19 - 20 * q^20 + 63 * q^21 + 6 * q^22 + 69 * q^23 - 72 * q^24 - 288 * q^25 + 158 * q^26 + 81 * q^27 + 84 * q^28 - 74 * q^29 + 30 * q^30 - 378 * q^31 - 96 * q^32 - 9 * q^33 + 52 * q^34 - 35 * q^35 + 108 * q^36 - 260 * q^37 + 30 * q^38 - 237 * q^39 + 40 * q^40 + 293 * q^41 - 126 * q^42 - 625 * q^43 - 12 * q^44 - 45 * q^45 - 138 * q^46 + 163 * q^47 + 144 * q^48 + 147 * q^49 + 576 * q^50 - 78 * q^51 - 316 * q^52 + 178 * q^53 - 162 * q^54 - 353 * q^55 - 168 * q^56 - 45 * q^57 + 148 * q^58 - 624 * q^59 - 60 * q^60 - 502 * q^61 + 756 * q^62 + 189 * q^63 + 192 * q^64 + 102 * q^65 + 18 * q^66 - 141 * q^67 - 104 * q^68 + 207 * q^69 + 70 * q^70 + 29 * q^71 - 216 * q^72 - 1198 * q^73 + 520 * q^74 - 864 * q^75 - 60 * q^76 - 21 * q^77 + 474 * q^78 - 1654 * q^79 - 80 * q^80 + 243 * q^81 - 586 * q^82 - 614 * q^83 + 252 * q^84 + 309 * q^85 + 1250 * q^86 - 222 * q^87 + 24 * q^88 - 549 * q^89 + 90 * q^90 - 553 * q^91 + 276 * q^92 - 1134 * q^93 - 326 * q^94 + 415 * q^95 - 288 * q^96 + 182 * q^97 - 294 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	4.00000	0.500000
$5$	−8.85699	−0.792193	−0.396097	−	0.918209i	$-0.629636\pi$
$5$	−8.85699	−0.792193	−0.396097	+	0.918209i	$0.629636\pi$
$6$	−6.00000	−0.408248
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	17.7140	0.560165
$11$	29.5332	0.809510	0.404755	−	0.914425i	$-0.367357\pi$
$11$	29.5332	0.809510	0.404755	+	0.914425i	$0.367357\pi$
$12$	12.0000	0.288675
$13$	−29.0938	−0.620705	−0.310353	−	0.950622i	$-0.600447\pi$
$13$	−29.0938	−0.620705	−0.310353	+	0.950622i	$0.600447\pi$
$14$	−14.0000	−0.267261
$15$	−26.5710	−0.457373
$16$	16.0000	0.250000
$17$	−27.4772	−0.392011	−0.196006	−	0.980603i	$-0.562797\pi$
$17$	−27.4772	−0.392011	−0.196006	+	0.980603i	$0.562797\pi$
$18$	−18.0000	−0.235702
$19$	−20.9475	−0.252931	−0.126465	−	0.991971i	$-0.540363\pi$
$19$	−20.9475	−0.252931	−0.126465	+	0.991971i	$0.540363\pi$
$20$	−35.4280	−0.396097
$21$	21.0000	0.218218
$22$	−59.0665	−0.572410
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	−24.0000	−0.204124
$25$	−46.5537	−0.372430
$26$	58.1876	0.438905
$27$	27.0000	0.192450
$28$	28.0000	0.188982
$29$	60.7313	0.388880	0.194440	−	0.980914i	$-0.437711\pi$
$29$	60.7313	0.388880	0.194440	+	0.980914i	$0.437711\pi$
$30$	53.1420	0.323412
$31$	−168.461	−0.976016	−0.488008	−	0.872839i	$-0.662276\pi$
$31$	−168.461	−0.976016	−0.488008	+	0.872839i	$0.662276\pi$
$32$	−32.0000	−0.176777
$33$	88.5997	0.467371
$34$	54.9544	0.277194
$35$	−61.9989	−0.299421
$36$	36.0000	0.166667
$37$	−139.964	−0.621892	−0.310946	−	0.950428i	$-0.600646\pi$
$37$	−139.964	−0.621892	−0.310946	+	0.950428i	$0.600646\pi$
$38$	41.8950	0.178849
$39$	−87.2814	−0.358364
$40$	70.8559	0.280083
$41$	117.773	0.448612	0.224306	−	0.974519i	$-0.427988\pi$
$41$	117.773	0.448612	0.224306	+	0.974519i	$0.427988\pi$
$42$	−42.0000	−0.154303
$43$	412.795	1.46397	0.731984	−	0.681321i	$-0.238594\pi$
$43$	412.795	1.46397	0.731984	+	0.681321i	$0.238594\pi$
$44$	118.133	0.404755
$45$	−79.7129	−0.264064
$46$	−46.0000	−0.147442
$47$	−200.089	−0.620977	−0.310488	−	0.950577i	$-0.600493\pi$
$47$	−200.089	−0.620977	−0.310488	+	0.950577i	$0.600493\pi$
$48$	48.0000	0.144338
$49$	49.0000	0.142857
$50$	93.1074	0.263347
$51$	−82.4315	−0.226328
$52$	−116.375	−0.310353
$53$	250.609	0.649506	0.324753	−	0.945799i	$-0.394719\pi$
$53$	250.609	0.649506	0.324753	+	0.945799i	$0.394719\pi$
$54$	−54.0000	−0.136083
$55$	−261.576	−0.641288
$56$	−56.0000	−0.133631
$57$	−62.8425	−0.146030
$58$	−121.463	−0.274979
$59$	572.882	1.26412	0.632059	−	0.774920i	$-0.282210\pi$
$59$	572.882	1.26412	0.632059	+	0.774920i	$0.282210\pi$
$60$	−106.284	−0.228687
$61$	−576.362	−1.20976	−0.604881	−	0.796316i	$-0.706779\pi$
$61$	−576.362	−1.20976	−0.604881	+	0.796316i	$0.706779\pi$
$62$	336.922	0.690148
$63$	63.0000	0.125988
$64$	64.0000	0.125000
$65$	257.684	0.491719
$66$	−177.199	−0.330481
$67$	−792.714	−1.44545	−0.722727	−	0.691133i	$-0.757112\pi$
$67$	−792.714	−1.44545	−0.722727	+	0.691133i	$0.757112\pi$
$68$	−109.909	−0.196006
$69$	69.0000	0.120386
$70$	123.998	0.211723
$71$	−312.265	−0.521959	−0.260980	−	0.965344i	$-0.584046\pi$
$71$	−312.265	−0.521959	−0.260980	+	0.965344i	$0.584046\pi$
$72$	−72.0000	−0.117851
$73$	−581.032	−0.931570	−0.465785	−	0.884898i	$-0.654228\pi$
$73$	−581.032	−0.931570	−0.465785	+	0.884898i	$0.654228\pi$
$74$	279.929	0.439744
$75$	−139.661	−0.215022
$76$	−83.7900	−0.126465
$77$	206.733	0.305966
$78$	174.563	0.253402
$79$	−880.866	−1.25450	−0.627248	−	0.778820i	$-0.715819\pi$
$79$	−880.866	−1.25450	−0.627248	+	0.778820i	$0.715819\pi$
$80$	−141.712	−0.198048
$81$	81.0000	0.111111
$82$	−235.547	−0.317217
$83$	−425.963	−0.563319	−0.281660	−	0.959514i	$-0.590885\pi$
$83$	−425.963	−0.563319	−0.281660	+	0.959514i	$0.590885\pi$
$84$	84.0000	0.109109
$85$	243.365	0.310549
$86$	−825.590	−1.03518
$87$	182.194	0.224520
$88$	−236.266	−0.286205
$89$	−905.408	−1.07835	−0.539175	−	0.842194i	$-0.681264\pi$
$89$	−905.408	−1.07835	−0.539175	+	0.842194i	$0.681264\pi$
$90$	159.426	0.186722
$91$	−203.657	−0.234604
$92$	92.0000	0.104257
$93$	−505.383	−0.563503
$94$	400.177	0.439097
$95$	185.532	0.200370
$96$	−96.0000	−0.102062
$97$	1298.70	1.35941	0.679706	−	0.733485i	$-0.262108\pi$
$97$	1298.70	1.35941	0.679706	+	0.733485i	$0.262108\pi$
$98$	−98.0000	−0.101015
$99$	265.799	0.269837
$100$	−186.215	−0.186215
$101$	−821.996	−0.809818	−0.404909	−	0.914357i	$-0.632697\pi$
$101$	−821.996	−0.809818	−0.404909	+	0.914357i	$0.632697\pi$
$102$	164.863	0.160038
$103$	−1680.17	−1.60730	−0.803650	−	0.595102i	$-0.797111\pi$
$103$	−1680.17	−1.60730	−0.803650	+	0.595102i	$0.797111\pi$
$104$	232.750	0.219452
$105$	−185.997	−0.172871
$106$	−501.218	−0.459270
$107$	1352.16	1.22166	0.610832	−	0.791760i	$-0.290835\pi$
$107$	1352.16	1.22166	0.610832	+	0.791760i	$0.290835\pi$
$108$	108.000	0.0962250
$109$	1612.14	1.41665	0.708324	−	0.705888i	$-0.249452\pi$
$109$	1612.14	1.41665	0.708324	+	0.705888i	$0.249452\pi$
$110$	523.151	0.453459
$111$	−419.893	−0.359050
$112$	112.000	0.0944911
$113$	389.328	0.324114	0.162057	−	0.986781i	$-0.448187\pi$
$113$	389.328	0.324114	0.162057	+	0.986781i	$0.448187\pi$
$114$	125.685	0.103259
$115$	−203.711	−0.165184
$116$	242.925	0.194440
$117$	−261.844	−0.206902
$118$	−1145.76	−0.893866
$119$	−192.340	−0.148166
$120$	212.568	0.161706
$121$	−458.787	−0.344694
$122$	1152.72	0.855431
$123$	353.320	0.259006
$124$	−673.844	−0.488008
$125$	1519.45	1.08723
$126$	−126.000	−0.0890871
$127$	−1306.85	−0.913105	−0.456552	−	0.889697i	$-0.650916\pi$
$127$	−1306.85	−0.913105	−0.456552	+	0.889697i	$0.650916\pi$
$128$	−128.000	−0.0883883
$129$	1238.39	0.845223
$130$	−515.367	−0.347698
$131$	−872.359	−0.581819	−0.290910	−	0.956751i	$-0.593958\pi$
$131$	−872.359	−0.581819	−0.290910	+	0.956751i	$0.593958\pi$
$132$	354.399	0.233685
$133$	−146.633	−0.0955989
$134$	1585.43	1.02209
$135$	−239.139	−0.152458
$136$	219.817	0.138597
$137$	523.804	0.326654	0.163327	−	0.986572i	$-0.447777\pi$
$137$	523.804	0.326654	0.163327	+	0.986572i	$0.447777\pi$
$138$	−138.000	−0.0851257
$139$	−1874.99	−1.14413	−0.572066	−	0.820207i	$-0.693858\pi$
$139$	−1874.99	−1.14413	−0.572066	+	0.820207i	$0.693858\pi$
$140$	−247.996	−0.149710
$141$	−600.266	−0.358521
$142$	624.531	0.369081
$143$	−859.234	−0.502467
$144$	144.000	0.0833333
$145$	−537.896	−0.308068
$146$	1162.06	0.658719
$147$	147.000	0.0824786
$148$	−559.858	−0.310946
$149$	−1833.45	−1.00807	−0.504034	−	0.863684i	$-0.668151\pi$
$149$	−1833.45	−1.00807	−0.504034	+	0.863684i	$0.668151\pi$
$150$	279.322	0.152044
$151$	2387.92	1.28693	0.643463	−	0.765477i	$-0.277497\pi$
$151$	2387.92	1.28693	0.643463	+	0.765477i	$0.277497\pi$
$152$	167.580	0.0894246
$153$	−247.295	−0.130670
$154$	−413.465	−0.216351
$155$	1492.06	0.773194
$156$	−349.126	−0.179182
$157$	−1634.62	−0.830938	−0.415469	−	0.909607i	$-0.636382\pi$
$157$	−1634.62	−0.830938	−0.415469	+	0.909607i	$0.636382\pi$
$158$	1761.73	0.887062
$159$	751.827	0.374992
$160$	283.424	0.140041
$161$	161.000	0.0788110
$162$	−162.000	−0.0785674
$163$	−1228.84	−0.590493	−0.295246	−	0.955421i	$-0.595402\pi$
$163$	−1228.84	−0.590493	−0.295246	+	0.955421i	$0.595402\pi$
$164$	471.093	0.224306
$165$	−784.727	−0.370248
$166$	851.926	0.398327
$167$	−2782.43	−1.28929	−0.644644	−	0.764483i	$-0.722994\pi$
$167$	−2782.43	−1.28929	−0.644644	+	0.764483i	$0.722994\pi$
$168$	−168.000	−0.0771517
$169$	−1350.55	−0.614725
$170$	−486.730	−0.219591
$171$	−188.528	−0.0843103
$172$	1651.18	0.731984
$173$	3581.65	1.57403	0.787017	−	0.616932i	$-0.211624\pi$
$173$	3581.65	1.57403	0.787017	+	0.616932i	$0.211624\pi$
$174$	−364.388	−0.158759
$175$	−325.876	−0.140765
$176$	472.532	0.202377
$177$	1718.65	0.729839
$178$	1810.82	0.762508
$179$	−4147.84	−1.73198	−0.865988	−	0.500065i	$-0.833310\pi$
$179$	−4147.84	−1.73198	−0.865988	+	0.500065i	$0.833310\pi$
$180$	−318.852	−0.132032
$181$	−3574.46	−1.46789	−0.733944	−	0.679210i	$-0.762322\pi$
$181$	−3574.46	−1.46789	−0.733944	+	0.679210i	$0.762322\pi$
$182$	407.313	0.165890
$183$	−1729.08	−0.698457
$184$	−184.000	−0.0737210
$185$	1239.66	0.492659
$186$	1010.77	0.398457
$187$	−811.490	−0.317337
$188$	−800.354	−0.310488
$189$	189.000	0.0727393
$190$	−371.064	−0.141683
$191$	−2346.42	−0.888904	−0.444452	−	0.895803i	$-0.646602\pi$
$191$	−2346.42	−0.888904	−0.444452	+	0.895803i	$0.646602\pi$
$192$	192.000	0.0721688
$193$	−1053.94	−0.393078	−0.196539	−	0.980496i	$-0.562970\pi$
$193$	−1053.94	−0.393078	−0.196539	+	0.980496i	$0.562970\pi$
$194$	−2597.40	−0.961249
$195$	773.051	0.283894
$196$	196.000	0.0714286
$197$	−3496.07	−1.26439	−0.632195	−	0.774810i	$-0.717846\pi$
$197$	−3496.07	−1.26439	−0.632195	+	0.774810i	$0.717846\pi$
$198$	−531.598	−0.190803
$199$	−4418.65	−1.57402	−0.787010	−	0.616940i	$-0.788372\pi$
$199$	−4418.65	−1.57402	−0.787010	+	0.616940i	$0.788372\pi$
$200$	372.430	0.131674
$201$	−2378.14	−0.834534
$202$	1643.99	0.572628
$203$	425.119	0.146983
$204$	−329.726	−0.113164
$205$	−1043.12	−0.355388
$206$	3360.34	1.13653
$207$	207.000	0.0695048
$208$	−465.501	−0.155176
$209$	−618.648	−0.204750
$210$	371.994	0.122238
$211$	1017.48	0.331973	0.165987	−	0.986128i	$-0.446919\pi$
$211$	1017.48	0.331973	0.165987	+	0.986128i	$0.446919\pi$
$212$	1002.44	0.324753
$213$	−936.796	−0.301353
$214$	−2704.32	−0.863848
$215$	−3656.12	−1.15975
$216$	−216.000	−0.0680414
$217$	−1179.23	−0.368899
$218$	−3224.27	−1.00172
$219$	−1743.09	−0.537842
$220$	−1046.30	−0.320644
$221$	799.415	0.243324
$222$	839.787	0.253887
$223$	4397.86	1.32064	0.660320	−	0.750984i	$-0.270421\pi$
$223$	4397.86	1.32064	0.660320	+	0.750984i	$0.270421\pi$
$224$	−224.000	−0.0668153
$225$	−418.983	−0.124143
$226$	−778.655	−0.229183
$227$	−3446.70	−1.00778	−0.503889	−	0.863768i	$-0.668098\pi$
$227$	−3446.70	−1.00778	−0.503889	+	0.863768i	$0.668098\pi$
$228$	−251.370	−0.0730149
$229$	−92.4564	−0.0266799	−0.0133399	−	0.999911i	$-0.504246\pi$
$229$	−92.4564	−0.0266799	−0.0133399	+	0.999911i	$0.504246\pi$
$230$	407.422	0.116803
$231$	620.198	0.176650
$232$	−485.850	−0.137490
$233$	770.884	0.216748	0.108374	−	0.994110i	$-0.465436\pi$
$233$	770.884	0.216748	0.108374	+	0.994110i	$0.465436\pi$
$234$	523.688	0.146302
$235$	1772.18	0.491934
$236$	2291.53	0.632059
$237$	−2642.60	−0.724283
$238$	384.681	0.104769
$239$	1043.11	0.282315	0.141157	−	0.989987i	$-0.454918\pi$
$239$	1043.11	0.282315	0.141157	+	0.989987i	$0.454918\pi$
$240$	−425.136	−0.114343
$241$	−2066.75	−0.552412	−0.276206	−	0.961098i	$-0.589077\pi$
$241$	−2066.75	−0.552412	−0.276206	+	0.961098i	$0.589077\pi$
$242$	917.575	0.243735
$243$	243.000	0.0641500
$244$	−2305.45	−0.604881
$245$	−433.993	−0.113170
$246$	−706.640	−0.183145
$247$	609.442	0.156996
$248$	1347.69	0.345074
$249$	−1277.89	−0.325233
$250$	−3038.90	−0.768787
$251$	2177.33	0.547538	0.273769	−	0.961796i	$-0.411730\pi$
$251$	2177.33	0.547538	0.273769	+	0.961796i	$0.411730\pi$
$252$	252.000	0.0629941
$253$	679.265	0.168794
$254$	2613.70	0.645662
$255$	730.095	0.179295
$256$	256.000	0.0625000
$257$	−4843.96	−1.17571	−0.587856	−	0.808966i	$-0.700028\pi$
$257$	−4843.96	−1.17571	−0.587856	+	0.808966i	$0.700028\pi$
$258$	−2476.77	−0.597663
$259$	−979.751	−0.235053
$260$	1030.73	0.245859
$261$	546.581	0.129627
$262$	1744.72	0.411409
$263$	−2434.90	−0.570883	−0.285441	−	0.958396i	$-0.592140\pi$
$263$	−2434.90	−0.570883	−0.285441	+	0.958396i	$0.592140\pi$
$264$	−708.798	−0.165241
$265$	−2219.64	−0.514534
$266$	293.265	0.0675986
$267$	−2716.22	−0.622585
$268$	−3170.86	−0.722727
$269$	2614.70	0.592644	0.296322	−	0.955088i	$-0.404240\pi$
$269$	2614.70	0.592644	0.296322	+	0.955088i	$0.404240\pi$
$270$	478.278	0.107804
$271$	−902.526	−0.202305	−0.101152	−	0.994871i	$-0.532253\pi$
$271$	−902.526	−0.202305	−0.101152	+	0.994871i	$0.532253\pi$
$272$	−439.635	−0.0980029
$273$	−610.970	−0.135449
$274$	−1047.61	−0.230979
$275$	−1374.88	−0.301485
$276$	276.000	0.0601929
$277$	7011.90	1.52095	0.760477	−	0.649365i	$-0.224965\pi$
$277$	7011.90	1.52095	0.760477	+	0.649365i	$0.224965\pi$
$278$	3749.98	0.809024
$279$	−1516.15	−0.325339
$280$	495.992	0.105861
$281$	4932.86	1.04722	0.523611	−	0.851957i	$-0.324584\pi$
$281$	4932.86	1.04722	0.523611	+	0.851957i	$0.324584\pi$
$282$	1200.53	0.253513
$283$	3384.43	0.710895	0.355448	−	0.934696i	$-0.384328\pi$
$283$	3384.43	0.710895	0.355448	+	0.934696i	$0.384328\pi$
$284$	−1249.06	−0.260980
$285$	556.596	0.115684
$286$	1718.47	0.355298
$287$	824.413	0.169560
$288$	−288.000	−0.0589256
$289$	−4158.00	−0.846327
$290$	1075.79	0.217837
$291$	3896.10	0.784856
$292$	−2324.13	−0.465785
$293$	−4437.54	−0.884791	−0.442395	−	0.896820i	$-0.645871\pi$
$293$	−4437.54	−0.884791	−0.442395	+	0.896820i	$0.645871\pi$
$294$	−294.000	−0.0583212
$295$	−5074.01	−1.00143
$296$	1119.72	0.219872
$297$	797.398	0.155790
$298$	3666.90	0.712812
$299$	−669.157	−0.129426
$300$	−558.644	−0.107511
$301$	2889.57	0.553328
$302$	−4775.83	−0.909995
$303$	−2465.99	−0.467549
$304$	−335.160	−0.0632327
$305$	5104.83	0.958366
$306$	494.589	0.0923980
$307$	−4760.67	−0.885035	−0.442518	−	0.896760i	$-0.645915\pi$
$307$	−4760.67	−0.885035	−0.442518	+	0.896760i	$0.645915\pi$
$308$	826.931	0.152983
$309$	−5040.50	−0.927975
$310$	−2984.12	−0.546730
$311$	−2610.22	−0.475922	−0.237961	−	0.971275i	$-0.576479\pi$
$311$	−2610.22	−0.475922	−0.237961	+	0.971275i	$0.576479\pi$
$312$	698.251	0.126701
$313$	348.408	0.0629176	0.0314588	−	0.999505i	$-0.489985\pi$
$313$	348.408	0.0629176	0.0314588	+	0.999505i	$0.489985\pi$
$314$	3269.25	0.587562
$315$	−557.990	−0.0998070
$316$	−3523.46	−0.627248
$317$	6843.13	1.21246	0.606228	−	0.795291i	$-0.292682\pi$
$317$	6843.13	1.21246	0.606228	+	0.795291i	$0.292682\pi$
$318$	−1503.65	−0.265160
$319$	1793.59	0.314802
$320$	−566.847	−0.0990242
$321$	4056.48	0.705329
$322$	−322.000	−0.0557278
$323$	575.578	0.0991518
$324$	324.000	0.0555556
$325$	1354.42	0.231169
$326$	2457.68	0.417542
$327$	4836.41	0.817902
$328$	−942.187	−0.158608
$329$	−1400.62	−0.234707
$330$	1569.45	0.261805
$331$	−9011.01	−1.49634	−0.748172	−	0.663505i	$-0.769068\pi$
$331$	−9011.01	−1.49634	−0.748172	+	0.663505i	$0.769068\pi$
$332$	−1703.85	−0.281660
$333$	−1259.68	−0.207297
$334$	5564.86	0.911664
$335$	7021.06	1.14508
$336$	336.000	0.0545545
$337$	9160.80	1.48077	0.740387	−	0.672181i	$-0.234642\pi$
$337$	9160.80	1.48077	0.740387	+	0.672181i	$0.234642\pi$
$338$	2701.10	0.434676
$339$	1167.98	0.187127
$340$	973.461	0.155274
$341$	−4975.20	−0.790095
$342$	377.055	0.0596164
$343$	343.000	0.0539949
$344$	−3302.36	−0.517591
$345$	−611.132	−0.0953689
$346$	−7163.30	−1.11301
$347$	4943.00	0.764709	0.382355	−	0.924016i	$-0.375113\pi$
$347$	4943.00	0.764709	0.382355	+	0.924016i	$0.375113\pi$
$348$	728.775	0.112260
$349$	−2976.36	−0.456506	−0.228253	−	0.973602i	$-0.573301\pi$
$349$	−2976.36	−0.456506	−0.228253	+	0.973602i	$0.573301\pi$
$350$	651.752	0.0995360
$351$	−785.532	−0.119455
$352$	−945.064	−0.143102
$353$	5301.30	0.799320	0.399660	−	0.916663i	$-0.369128\pi$
$353$	5301.30	0.799320	0.399660	+	0.916663i	$0.369128\pi$
$354$	−3437.29	−0.516074
$355$	2765.73	0.413493
$356$	−3621.63	−0.539175
$357$	−577.021	−0.0855439
$358$	8295.67	1.22469
$359$	1078.19	0.158509	0.0792547	−	0.996854i	$-0.474746\pi$
$359$	1078.19	0.158509	0.0792547	+	0.996854i	$0.474746\pi$
$360$	637.703	0.0933609
$361$	−6420.20	−0.936026
$362$	7148.92	1.03795
$363$	−1376.36	−0.199009
$364$	−814.626	−0.117302
$365$	5146.19	0.737984
$366$	3458.17	0.493884
$367$	−66.4551	−0.00945212	−0.00472606	−	0.999989i	$-0.501504\pi$
$367$	−66.4551	−0.00945212	−0.00472606	+	0.999989i	$0.501504\pi$
$368$	368.000	0.0521286
$369$	1059.96	0.149537
$370$	−2479.33	−0.348363
$371$	1754.26	0.245490
$372$	−2021.53	−0.281752
$373$	−9204.71	−1.27775	−0.638876	−	0.769309i	$-0.720600\pi$
$373$	−9204.71	−1.27775	−0.638876	+	0.769309i	$0.720600\pi$
$374$	1622.98	0.224391
$375$	4558.35	0.627712
$376$	1600.71	0.219548
$377$	−1766.90	−0.241380
$378$	−378.000	−0.0514344
$379$	−3012.50	−0.408289	−0.204145	−	0.978941i	$-0.565441\pi$
$379$	−3012.50	−0.408289	−0.204145	+	0.978941i	$0.565441\pi$
$380$	742.128	0.100185
$381$	−3920.55	−0.527181
$382$	4692.83	0.628550
$383$	10158.1	1.35523	0.677616	−	0.735416i	$-0.263013\pi$
$383$	10158.1	1.35523	0.677616	+	0.735416i	$0.263013\pi$
$384$	−384.000	−0.0510310
$385$	−1831.03	−0.242384
$386$	2107.88	0.277948
$387$	3715.16	0.487990
$388$	5194.79	0.679706
$389$	8969.84	1.16912	0.584562	−	0.811349i	$-0.301267\pi$
$389$	8969.84	1.16912	0.584562	+	0.811349i	$0.301267\pi$
$390$	−1546.10	−0.200743
$391$	−631.975	−0.0817400
$392$	−392.000	−0.0505076
$393$	−2617.08	−0.335914
$394$	6992.14	0.894058
$395$	7801.82	0.993803
$396$	1063.20	0.134918
$397$	1986.03	0.251074	0.125537	−	0.992089i	$-0.459935\pi$
$397$	1986.03	0.251074	0.125537	+	0.992089i	$0.459935\pi$
$398$	8837.30	1.11300
$399$	−439.898	−0.0551941
$400$	−744.859	−0.0931074
$401$	10927.8	1.36087	0.680435	−	0.732808i	$-0.261791\pi$
$401$	10927.8	1.36087	0.680435	+	0.732808i	$0.261791\pi$
$402$	4756.29	0.590104
$403$	4901.17	0.605818
$404$	−3287.98	−0.404909
$405$	−717.416	−0.0880215
$406$	−850.238	−0.103932
$407$	−4133.61	−0.503428
$408$	659.452	0.0800190
$409$	7791.23	0.941935	0.470968	−	0.882151i	$-0.343905\pi$
$409$	7791.23	0.941935	0.470968	+	0.882151i	$0.343905\pi$
$410$	2086.23	0.251297
$411$	1571.41	0.188594
$412$	−6720.67	−0.803650
$413$	4010.18	0.477792
$414$	−414.000	−0.0491473
$415$	3772.75	0.446258
$416$	931.001	0.109726
$417$	−5624.97	−0.660565
$418$	1237.30	0.144780
$419$	5092.02	0.593703	0.296851	−	0.954924i	$-0.404063\pi$
$419$	5092.02	0.593703	0.296851	+	0.954924i	$0.404063\pi$
$420$	−743.987	−0.0864354
$421$	2858.50	0.330914	0.165457	−	0.986217i	$-0.447090\pi$
$421$	2858.50	0.330914	0.165457	+	0.986217i	$0.447090\pi$
$422$	−2034.97	−0.234741
$423$	−1800.80	−0.206992
$424$	−2004.87	−0.229635
$425$	1279.16	0.145997
$426$	1873.59	0.213089
$427$	−4034.53	−0.457247
$428$	5408.64	0.610832
$429$	−2577.70	−0.290099
$430$	7312.25	0.820065
$431$	8370.26	0.935455	0.467728	−	0.883873i	$-0.345073\pi$
$431$	8370.26	0.935455	0.467728	+	0.883873i	$0.345073\pi$
$432$	432.000	0.0481125
$433$	8136.78	0.903069	0.451535	−	0.892254i	$-0.350877\pi$
$433$	8136.78	0.903069	0.451535	+	0.892254i	$0.350877\pi$
$434$	2358.45	0.260851
$435$	−1613.69	−0.177863
$436$	6448.54	0.708324
$437$	−481.793	−0.0527397
$438$	3486.19	0.380312
$439$	10996.7	1.19555	0.597774	−	0.801664i	$-0.296052\pi$
$439$	10996.7	1.19555	0.597774	+	0.801664i	$0.296052\pi$
$440$	2092.61	0.226730
$441$	441.000	0.0476190
$442$	−1598.83	−0.172056
$443$	−15596.1	−1.67267	−0.836334	−	0.548220i	$-0.815305\pi$
$443$	−15596.1	−1.67267	−0.836334	+	0.548220i	$0.815305\pi$
$444$	−1679.57	−0.179525
$445$	8019.19	0.854261
$446$	−8795.73	−0.933833
$447$	−5500.35	−0.582008
$448$	448.000	0.0472456
$449$	1713.63	0.180114	0.0900568	−	0.995937i	$-0.471295\pi$
$449$	1713.63	0.180114	0.0900568	+	0.995937i	$0.471295\pi$
$450$	837.967	0.0877825
$451$	3478.23	0.363156
$452$	1557.31	0.162057
$453$	7163.75	0.743008
$454$	6893.40	0.712607
$455$	1803.78	0.185852
$456$	502.740	0.0516293
$457$	−7747.69	−0.793045	−0.396523	−	0.918025i	$-0.629783\pi$
$457$	−7747.69	−0.793045	−0.396523	+	0.918025i	$0.629783\pi$
$458$	184.913	0.0188655
$459$	−741.884	−0.0754426
$460$	−814.843	−0.0825919
$461$	5876.37	0.593688	0.296844	−	0.954926i	$-0.404066\pi$
$461$	5876.37	0.593688	0.296844	+	0.954926i	$0.404066\pi$
$462$	−1240.40	−0.124910
$463$	802.324	0.0805338	0.0402669	−	0.999189i	$-0.487179\pi$
$463$	802.324	0.0805338	0.0402669	+	0.999189i	$0.487179\pi$
$464$	971.700	0.0972199
$465$	4476.17	0.446404
$466$	−1541.77	−0.153264
$467$	14833.9	1.46987	0.734935	−	0.678138i	$-0.237213\pi$
$467$	14833.9	1.46987	0.734935	+	0.678138i	$0.237213\pi$
$468$	−1047.38	−0.103451
$469$	−5549.00	−0.546330
$470$	−3544.36	−0.347850
$471$	−4903.87	−0.479742
$472$	−4583.06	−0.446933
$473$	12191.2	1.18510
$474$	5285.20	0.512146
$475$	975.184	0.0941990
$476$	−769.361	−0.0740832
$477$	2255.48	0.216502
$478$	−2086.22	−0.199627
$479$	−5064.06	−0.483054	−0.241527	−	0.970394i	$-0.577648\pi$
$479$	−5064.06	−0.483054	−0.241527	+	0.970394i	$0.577648\pi$
$480$	850.271	0.0808529
$481$	4072.10	0.386012
$482$	4133.51	0.390614
$483$	483.000	0.0455016
$484$	−1835.15	−0.172347
$485$	−11502.6	−1.07692
$486$	−486.000	−0.0453609
$487$	18392.5	1.71139	0.855694	−	0.517482i	$-0.173131\pi$
$487$	18392.5	1.71139	0.855694	+	0.517482i	$0.173131\pi$
$488$	4610.89	0.427716
$489$	−3686.53	−0.340921
$490$	867.985	0.0800236
$491$	3424.59	0.314765	0.157382	−	0.987538i	$-0.449695\pi$
$491$	3424.59	0.314765	0.157382	+	0.987538i	$0.449695\pi$
$492$	1413.28	0.129503
$493$	−1668.72	−0.152445
$494$	−1218.88	−0.111013
$495$	−2354.18	−0.213763
$496$	−2695.38	−0.244004
$497$	−2185.86	−0.197282
$498$	2555.78	0.229974
$499$	−5691.53	−0.510597	−0.255298	−	0.966862i	$-0.582174\pi$
$499$	−5691.53	−0.510597	−0.255298	+	0.966862i	$0.582174\pi$
$500$	6077.80	0.543615
$501$	−8347.29	−0.744370
$502$	−4354.66	−0.387168
$503$	−10599.5	−0.939582	−0.469791	−	0.882778i	$-0.655671\pi$
$503$	−10599.5	−0.939582	−0.469791	+	0.882778i	$0.655671\pi$
$504$	−504.000	−0.0445435
$505$	7280.41	0.641533
$506$	−1358.53	−0.119356
$507$	−4051.65	−0.354912
$508$	−5227.40	−0.456552
$509$	5261.77	0.458200	0.229100	−	0.973403i	$-0.426422\pi$
$509$	5261.77	0.458200	0.229100	+	0.973403i	$0.426422\pi$
$510$	−1460.19	−0.126781
$511$	−4067.22	−0.352100
$512$	−512.000	−0.0441942
$513$	−565.583	−0.0486766
$514$	9687.92	0.831354
$515$	14881.2	1.27329
$516$	4953.54	0.422611
$517$	−5909.26	−0.502687
$518$	1959.50	0.166208
$519$	10745.0	0.908769
$520$	−2061.47	−0.173849
$521$	1792.17	0.150703	0.0753515	−	0.997157i	$-0.475992\pi$
$521$	1792.17	0.150703	0.0753515	+	0.997157i	$0.475992\pi$
$522$	−1093.16	−0.0916598
$523$	−1034.28	−0.0864742	−0.0432371	−	0.999065i	$-0.513767\pi$
$523$	−1034.28	−0.0864742	−0.0432371	+	0.999065i	$0.513767\pi$
$524$	−3489.44	−0.290910
$525$	−977.628	−0.0812708
$526$	4869.79	0.403675
$527$	4628.84	0.382610
$528$	1417.60	0.116843
$529$	529.000	0.0434783
$530$	4439.29	0.363831
$531$	5155.94	0.421373
$532$	−586.530	−0.0477995
$533$	−3426.47	−0.278456
$534$	5432.45	0.440234
$535$	−11976.1	−0.967795
$536$	6341.71	0.511045
$537$	−12443.5	−0.999957
$538$	−5229.41	−0.419063
$539$	1447.13	0.115644
$540$	−956.555	−0.0762288
$541$	−16294.6	−1.29493	−0.647466	−	0.762094i	$-0.724171\pi$
$541$	−16294.6	−1.29493	−0.647466	+	0.762094i	$0.724171\pi$
$542$	1805.05	0.143051
$543$	−10723.4	−0.847485
$544$	879.270	0.0692985
$545$	−14278.7	−1.12226
$546$	1221.94	0.0957769
$547$	12339.7	0.964548	0.482274	−	0.876021i	$-0.339811\pi$
$547$	12339.7	0.964548	0.482274	+	0.876021i	$0.339811\pi$
$548$	2095.22	0.163327
$549$	−5187.25	−0.403254
$550$	2749.76	0.213182
$551$	−1272.17	−0.0983597
$552$	−552.000	−0.0425628
$553$	−6166.06	−0.474155
$554$	−14023.8	−1.07548
$555$	3718.99	0.284437
$556$	−7499.96	−0.572066
$557$	−16015.3	−1.21830	−0.609148	−	0.793056i	$-0.708489\pi$
$557$	−16015.3	−1.21830	−0.609148	+	0.793056i	$0.708489\pi$
$558$	3032.30	0.230049
$559$	−12009.8	−0.908693
$560$	−991.983	−0.0748552
$561$	−2434.47	−0.183215
$562$	−9865.72	−0.740498
$563$	−22606.2	−1.69225	−0.846127	−	0.532981i	$-0.821072\pi$
$563$	−22606.2	−1.69225	−0.846127	+	0.532981i	$0.821072\pi$
$564$	−2401.06	−0.179261
$565$	−3448.27	−0.256761
$566$	−6768.86	−0.502679
$567$	567.000	0.0419961
$568$	2498.12	0.184540
$569$	1026.88	0.0756577	0.0378289	−	0.999284i	$-0.487956\pi$
$569$	1026.88	0.0756577	0.0378289	+	0.999284i	$0.487956\pi$
$570$	−1113.19	−0.0818008
$571$	3383.21	0.247956	0.123978	−	0.992285i	$-0.460435\pi$
$571$	3383.21	0.247956	0.123978	+	0.992285i	$0.460435\pi$
$572$	−3436.94	−0.251233
$573$	−7039.25	−0.513209
$574$	−1648.83	−0.119897
$575$	−1070.74	−0.0776569
$576$	576.000	0.0416667
$577$	7313.32	0.527656	0.263828	−	0.964570i	$-0.415015\pi$
$577$	7313.32	0.527656	0.263828	+	0.964570i	$0.415015\pi$
$578$	8316.01	0.598444
$579$	−3161.81	−0.226944
$580$	−2151.59	−0.154034
$581$	−2981.74	−0.212915
$582$	−7792.19	−0.554977
$583$	7401.30	0.525781
$584$	4648.25	0.329360
$585$	2319.15	0.163906
$586$	8875.08	0.625642
$587$	18271.7	1.28476	0.642379	−	0.766387i	$-0.277947\pi$
$587$	18271.7	1.28476	0.642379	+	0.766387i	$0.277947\pi$
$588$	588.000	0.0412393
$589$	3528.84	0.246865
$590$	10148.0	0.708115
$591$	−10488.2	−0.729995
$592$	−2239.43	−0.155473
$593$	22015.5	1.52457	0.762283	−	0.647244i	$-0.224078\pi$
$593$	22015.5	1.52457	0.762283	+	0.647244i	$0.224078\pi$
$594$	−1594.80	−0.110160
$595$	1703.56	0.117376
$596$	−7333.80	−0.504034
$597$	−13256.0	−0.908761
$598$	1338.31	0.0915180
$599$	−237.828	−0.0162227	−0.00811133	−	0.999967i	$-0.502582\pi$
$599$	−237.828	−0.0162227	−0.00811133	+	0.999967i	$0.502582\pi$
$600$	1117.29	0.0760219
$601$	13839.9	0.939340	0.469670	−	0.882842i	$-0.344373\pi$
$601$	13839.9	0.939340	0.469670	+	0.882842i	$0.344373\pi$
$602$	−5779.13	−0.391262
$603$	−7134.43	−0.481818
$604$	9551.67	0.643463
$605$	4063.48	0.273064
$606$	4931.98	0.330607
$607$	3856.41	0.257869	0.128935	−	0.991653i	$-0.458844\pi$
$607$	3856.41	0.257869	0.128935	+	0.991653i	$0.458844\pi$
$608$	670.320	0.0447123
$609$	1275.36	0.0848605
$610$	−10209.7	−0.677667
$611$	5821.33	0.385443
$612$	−989.178	−0.0653352
$613$	−8038.93	−0.529673	−0.264836	−	0.964293i	$-0.585318\pi$
$613$	−8038.93	−0.529673	−0.264836	+	0.964293i	$0.585318\pi$
$614$	9521.34	0.625814
$615$	−3129.35	−0.205183
$616$	−1653.86	−0.108175
$617$	−5384.54	−0.351335	−0.175667	−	0.984450i	$-0.556208\pi$
$617$	−5384.54	−0.351335	−0.175667	+	0.984450i	$0.556208\pi$
$618$	10081.0	0.656177
$619$	12809.5	0.831759	0.415880	−	0.909420i	$-0.363474\pi$
$619$	12809.5	0.831759	0.415880	+	0.909420i	$0.363474\pi$
$620$	5968.23	0.386597
$621$	621.000	0.0401286
$622$	5220.44	0.336528
$623$	−6337.86	−0.407578
$624$	−1396.50	−0.0895911
$625$	−7638.54	−0.488867
$626$	−696.817	−0.0444895
$627$	−1855.94	−0.118213
$628$	−6538.50	−0.415469
$629$	3845.83	0.243789
$630$	1115.98	0.0705742
$631$	−29515.0	−1.86208	−0.931041	−	0.364914i	$-0.881099\pi$
$631$	−29515.0	−1.86208	−0.931041	+	0.364914i	$0.881099\pi$
$632$	7046.93	0.443531
$633$	3052.45	0.191665
$634$	−13686.3	−0.857335
$635$	11574.8	0.723355
$636$	3007.31	0.187496
$637$	−1425.60	−0.0886722
$638$	−3587.18	−0.222599
$639$	−2810.39	−0.173986
$640$	1133.69	0.0700207
$641$	12938.8	0.797276	0.398638	−	0.917108i	$-0.369483\pi$
$641$	12938.8	0.797276	0.398638	+	0.917108i	$0.369483\pi$
$642$	−8112.95	−0.498743
$643$	15561.5	0.954408	0.477204	−	0.878792i	$-0.341650\pi$
$643$	15561.5	0.954408	0.477204	+	0.878792i	$0.341650\pi$
$644$	644.000	0.0394055
$645$	−10968.4	−0.669580
$646$	−1151.16	−0.0701109
$647$	8936.17	0.542994	0.271497	−	0.962439i	$-0.412481\pi$
$647$	8936.17	0.542994	0.271497	+	0.962439i	$0.412481\pi$
$648$	−648.000	−0.0392837
$649$	16919.1	1.02332
$650$	−2708.85	−0.163461
$651$	−3537.68	−0.212984
$652$	−4915.37	−0.295246
$653$	−18584.7	−1.11374	−0.556872	−	0.830598i	$-0.687999\pi$
$653$	−18584.7	−1.11374	−0.556872	+	0.830598i	$0.687999\pi$
$654$	−9672.81	−0.578344
$655$	7726.48	0.460914
$656$	1884.37	0.112153
$657$	−5229.28	−0.310523
$658$	2801.24	0.165963
$659$	10204.1	0.603182	0.301591	−	0.953437i	$-0.402482\pi$
$659$	10204.1	0.603182	0.301591	+	0.953437i	$0.402482\pi$
$660$	−3138.91	−0.185124
$661$	8725.73	0.513452	0.256726	−	0.966484i	$-0.417356\pi$
$661$	8725.73	0.513452	0.256726	+	0.966484i	$0.417356\pi$
$662$	18022.0	1.05808
$663$	2398.25	0.140483
$664$	3407.70	0.199163
$665$	1298.72	0.0757328
$666$	2519.36	0.146581
$667$	1396.82	0.0810870
$668$	−11129.7	−0.644644
$669$	13193.6	0.762472
$670$	−14042.1	−0.809694
$671$	−17021.8	−0.979315
$672$	−672.000	−0.0385758
$673$	−21590.4	−1.23663	−0.618314	−	0.785931i	$-0.712184\pi$
$673$	−21590.4	−1.23663	−0.618314	+	0.785931i	$0.712184\pi$
$674$	−18321.6	−1.04706
$675$	−1256.95	−0.0716741
$676$	−5402.20	−0.307363
$677$	−7030.93	−0.399144	−0.199572	−	0.979883i	$-0.563955\pi$
$677$	−7030.93	−0.399144	−0.199572	+	0.979883i	$0.563955\pi$
$678$	−2335.97	−0.132319
$679$	9090.89	0.513809
$680$	−1946.92	−0.109796
$681$	−10340.1	−0.581841
$682$	9950.40	0.558681
$683$	4944.99	0.277035	0.138517	−	0.990360i	$-0.455766\pi$
$683$	4944.99	0.277035	0.138517	+	0.990360i	$0.455766\pi$
$684$	−754.110	−0.0421552
$685$	−4639.33	−0.258773
$686$	−686.000	−0.0381802
$687$	−277.369	−0.0154036
$688$	6604.72	0.365992
$689$	−7291.17	−0.403152
$690$	1222.26	0.0674360
$691$	4369.11	0.240533	0.120267	−	0.992742i	$-0.461625\pi$
$691$	4369.11	0.240533	0.120267	+	0.992742i	$0.461625\pi$
$692$	14326.6	0.787017
$693$	1860.59	0.101989
$694$	−9886.00	−0.540731
$695$	16606.8	0.906375
$696$	−1457.55	−0.0793797
$697$	−3236.08	−0.175861
$698$	5952.71	0.322799
$699$	2312.65	0.125139
$700$	−1303.50	−0.0703826
$701$	−8967.45	−0.483161	−0.241581	−	0.970381i	$-0.577666\pi$
$701$	−8967.45	−0.483161	−0.241581	+	0.970381i	$0.577666\pi$
$702$	1571.06	0.0844673
$703$	2931.91	0.157296
$704$	1890.13	0.101189
$705$	5316.55	0.284018
$706$	−10602.6	−0.565205
$707$	−5753.97	−0.306083
$708$	6874.59	0.364919
$709$	−26058.9	−1.38034	−0.690170	−	0.723647i	$-0.742464\pi$
$709$	−26058.9	−1.38034	−0.690170	+	0.723647i	$0.742464\pi$
$710$	−5531.47	−0.292383
$711$	−7927.79	−0.418165
$712$	7243.27	0.381254
$713$	−3874.60	−0.203513
$714$	1154.04	0.0604887
$715$	7610.23	0.398051
$716$	−16591.3	−0.865988
$717$	3129.33	0.162995
$718$	−2156.39	−0.112083
$719$	−18232.0	−0.945671	−0.472835	−	0.881151i	$-0.656769\pi$
$719$	−18232.0	−0.945671	−0.472835	+	0.881151i	$0.656769\pi$
$720$	−1275.41	−0.0660161
$721$	−11761.2	−0.607502
$722$	12840.4	0.661870
$723$	−6200.26	−0.318935
$724$	−14297.8	−0.733944
$725$	−2827.26	−0.144830
$726$	2752.72	0.140721
$727$	−26773.8	−1.36587	−0.682933	−	0.730481i	$-0.739296\pi$
$727$	−26773.8	−1.36587	−0.682933	+	0.730481i	$0.739296\pi$
$728$	1629.25	0.0829452
$729$	729.000	0.0370370
$730$	−10292.4	−0.521833
$731$	−11342.4	−0.573893
$732$	−6916.34	−0.349228
$733$	−668.285	−0.0336749	−0.0168374	−	0.999858i	$-0.505360\pi$
$733$	−668.285	−0.0336749	−0.0168374	+	0.999858i	$0.505360\pi$
$734$	132.910	0.00668366
$735$	−1301.98	−0.0653390
$736$	−736.000	−0.0368605
$737$	−23411.4	−1.17011
$738$	−2119.92	−0.105739
$739$	25944.6	1.29146	0.645728	−	0.763568i	$-0.276554\pi$
$739$	25944.6	1.29146	0.645728	+	0.763568i	$0.276554\pi$
$740$	4958.66	0.246330
$741$	1828.33	0.0906414
$742$	−3508.53	−0.173588
$743$	23417.1	1.15625	0.578123	−	0.815950i	$-0.303785\pi$
$743$	23417.1	1.15625	0.578123	+	0.815950i	$0.303785\pi$
$744$	4043.07	0.199228
$745$	16238.9	0.798585
$746$	18409.4	0.903508
$747$	−3833.67	−0.187773
$748$	−3245.96	−0.158669
$749$	9465.11	0.461746
$750$	−9116.70	−0.443860
$751$	28847.8	1.40169	0.700846	−	0.713312i	$-0.252806\pi$
$751$	28847.8	1.40169	0.700846	+	0.713312i	$0.252806\pi$
$752$	−3201.42	−0.155244
$753$	6532.00	0.316121
$754$	3533.81	0.170681
$755$	−21149.8	−1.01949
$756$	756.000	0.0363696
$757$	18894.7	0.907188	0.453594	−	0.891208i	$-0.350142\pi$
$757$	18894.7	0.907188	0.453594	+	0.891208i	$0.350142\pi$
$758$	6025.00	0.288704
$759$	2037.79	0.0974535
$760$	−1484.26	−0.0708416
$761$	24596.8	1.17166	0.585830	−	0.810434i	$-0.300768\pi$
$761$	24596.8	1.17166	0.585830	+	0.810434i	$0.300768\pi$
$762$	7841.11	0.372773
$763$	11284.9	0.535442
$764$	−9385.66	−0.444452
$765$	2190.29	0.103516
$766$	−20316.2	−0.958293
$767$	−16667.3	−0.784644
$768$	768.000	0.0360844
$769$	32441.3	1.52128	0.760639	−	0.649175i	$-0.224886\pi$
$769$	32441.3	1.52128	0.760639	+	0.649175i	$0.224886\pi$
$770$	3662.06	0.171392
$771$	−14531.9	−0.678798
$772$	−4215.75	−0.196539
$773$	−16718.0	−0.777885	−0.388943	−	0.921262i	$-0.627160\pi$
$773$	−16718.0	−0.777885	−0.388943	+	0.921262i	$0.627160\pi$
$774$	−7430.31	−0.345061
$775$	7842.49	0.363497
$776$	−10389.6	−0.480624
$777$	−2939.25	−0.135708
$778$	−17939.7	−0.826695
$779$	−2467.06	−0.113468
$780$	3092.20	0.141947
$781$	−9222.21	−0.422531
$782$	1263.95	0.0577989
$783$	1639.74	0.0748399
$784$	784.000	0.0357143
$785$	14477.9	0.658263
$786$	5234.15	0.237527
$787$	−36642.5	−1.65968	−0.829838	−	0.558005i	$-0.811567\pi$
$787$	−36642.5	−1.65968	−0.829838	+	0.558005i	$0.811567\pi$
$788$	−13984.3	−0.632195
$789$	−7304.69	−0.329599
$790$	−15603.6	−0.702725
$791$	2725.29	0.122504
$792$	−2126.39	−0.0954017
$793$	16768.5	0.750906
$794$	−3972.07	−0.177536
$795$	−6658.93	−0.297066
$796$	−17674.6	−0.787010
$797$	−12941.7	−0.575178	−0.287589	−	0.957754i	$-0.592854\pi$
$797$	−12941.7	−0.575178	−0.287589	+	0.957754i	$0.592854\pi$
$798$	879.795	0.0390281
$799$	5497.87	0.243430
$800$	1489.72	0.0658369
$801$	−8148.67	−0.359450
$802$	−21855.6	−0.962280
$803$	−17159.7	−0.754115
$804$	−9512.57	−0.417267
$805$	−1425.98	−0.0624336
$806$	−9802.34	−0.428378
$807$	7844.11	0.342163
$808$	6575.97	0.286314
$809$	5965.81	0.259266	0.129633	−	0.991562i	$-0.458620\pi$
$809$	5965.81	0.259266	0.129633	+	0.991562i	$0.458620\pi$
$810$	1434.83	0.0622406
$811$	−12539.9	−0.542953	−0.271477	−	0.962445i	$-0.587512\pi$
$811$	−12539.9	−0.542953	−0.271477	+	0.962445i	$0.587512\pi$
$812$	1700.48	0.0734914
$813$	−2707.58	−0.116801
$814$	8267.21	0.355977
$815$	10883.8	0.467785
$816$	−1318.90	−0.0565820
$817$	−8647.03	−0.370283
$818$	−15582.5	−0.666049
$819$	−1832.91	−0.0782015
$820$	−4172.47	−0.177694
$821$	−8806.58	−0.374363	−0.187181	−	0.982325i	$-0.559935\pi$
$821$	−8806.58	−0.374363	−0.187181	+	0.982325i	$0.559935\pi$
$822$	−3142.82	−0.133356
$823$	42125.9	1.78423	0.892113	−	0.451813i	$-0.149223\pi$
$823$	42125.9	1.78423	0.892113	+	0.451813i	$0.149223\pi$
$824$	13441.3	0.568266
$825$	−4124.65	−0.174063
$826$	−8020.35	−0.337850
$827$	−12270.3	−0.515936	−0.257968	−	0.966153i	$-0.583053\pi$
$827$	−12270.3	−0.515936	−0.257968	+	0.966153i	$0.583053\pi$
$828$	828.000	0.0347524
$829$	−3338.07	−0.139850	−0.0699252	−	0.997552i	$-0.522276\pi$
$829$	−3338.07	−0.139850	−0.0699252	+	0.997552i	$0.522276\pi$
$830$	−7545.50	−0.315552
$831$	21035.7	0.878123
$832$	−1862.00	−0.0775881
$833$	−1346.38	−0.0560016
$834$	11249.9	0.467090
$835$	24644.0	1.02137
$836$	−2474.59	−0.102375
$837$	−4548.45	−0.187834
$838$	−10184.0	−0.419811
$839$	−15892.1	−0.653940	−0.326970	−	0.945035i	$-0.606028\pi$
$839$	−15892.1	−0.653940	−0.326970	+	0.945035i	$0.606028\pi$
$840$	1487.97	0.0611190
$841$	−20700.7	−0.848773
$842$	−5717.01	−0.233992
$843$	14798.6	0.604614
$844$	4069.93	0.165987
$845$	11961.8	0.486981
$846$	3601.59	0.146366
$847$	−3211.51	−0.130282
$848$	4009.75	0.162376
$849$	10153.3	0.410436
$850$	−2558.33	−0.103235
$851$	−3219.18	−0.129674
$852$	−3747.19	−0.150677
$853$	−36304.3	−1.45725	−0.728626	−	0.684912i	$-0.759841\pi$
$853$	−36304.3	−1.45725	−0.728626	+	0.684912i	$0.759841\pi$
$854$	8069.06	0.323323
$855$	1669.79	0.0667901
$856$	−10817.3	−0.431924
$857$	−24565.2	−0.979151	−0.489576	−	0.871961i	$-0.662848\pi$
$857$	−24565.2	−0.979151	−0.489576	+	0.871961i	$0.662848\pi$
$858$	5155.41	0.205131
$859$	40733.8	1.61795	0.808976	−	0.587842i	$-0.200022\pi$
$859$	40733.8	1.61795	0.808976	+	0.587842i	$0.200022\pi$
$860$	−14624.5	−0.579873
$861$	2473.24	0.0978952
$862$	−16740.5	−0.661467
$863$	25575.5	1.00881	0.504403	−	0.863469i	$-0.331713\pi$
$863$	25575.5	1.00881	0.504403	+	0.863469i	$0.331713\pi$
$864$	−864.000	−0.0340207
$865$	−31722.6	−1.24694
$866$	−16273.6	−0.638566
$867$	−12474.0	−0.488627
$868$	−4716.91	−0.184450
$869$	−26014.8	−1.01553
$870$	3227.38	0.125768
$871$	23063.1	0.897201
$872$	−12897.1	−0.500860
$873$	11688.3	0.453137
$874$	963.585	0.0372926
$875$	10636.1	0.410934
$876$	−6972.38	−0.268921
$877$	2355.15	0.0906815	0.0453407	−	0.998972i	$-0.485563\pi$
$877$	2355.15	0.0906815	0.0453407	+	0.998972i	$0.485563\pi$
$878$	−21993.5	−0.845381
$879$	−13312.6	−0.510834
$880$	−4185.21	−0.160322
$881$	−39783.8	−1.52140	−0.760698	−	0.649106i	$-0.775143\pi$
$881$	−39783.8	−1.52140	−0.760698	+	0.649106i	$0.775143\pi$
$882$	−882.000	−0.0336718
$883$	31049.6	1.18336	0.591678	−	0.806175i	$-0.298466\pi$
$883$	31049.6	1.18336	0.591678	+	0.806175i	$0.298466\pi$
$884$	3197.66	0.121662
$885$	−15222.0	−0.578173
$886$	31192.1	1.18275
$887$	29474.2	1.11572	0.557862	−	0.829934i	$-0.311622\pi$
$887$	29474.2	1.11572	0.557862	+	0.829934i	$0.311622\pi$
$888$	3359.15	0.126943
$889$	−9147.96	−0.345121
$890$	−16038.4	−0.604054
$891$	2392.19	0.0899455
$892$	17591.5	0.660320
$893$	4191.36	0.157064
$894$	11000.7	0.411542
$895$	36737.3	1.37206
$896$	−896.000	−0.0334077
$897$	−2007.47	−0.0747241
$898$	−3427.25	−0.127360
$899$	−10230.9	−0.379553
$900$	−1675.93	−0.0620716
$901$	−6886.03	−0.254614
$902$	−6956.46	−0.256790
$903$	8668.70	0.319464
$904$	−3114.62	−0.114592
$905$	31659.0	1.16285
$906$	−14327.5	−0.525386
$907$	20933.4	0.766355	0.383177	−	0.923675i	$-0.374830\pi$
$907$	20933.4	0.766355	0.383177	+	0.923675i	$0.374830\pi$
$908$	−13786.8	−0.503889
$909$	−7397.96	−0.269939
$910$	−3607.57	−0.131417
$911$	−40749.6	−1.48199	−0.740996	−	0.671509i	$-0.765646\pi$
$911$	−40749.6	−1.48199	−0.740996	+	0.671509i	$0.765646\pi$
$912$	−1005.48	−0.0365074
$913$	−12580.1	−0.456013
$914$	15495.4	0.560768
$915$	15314.5	0.553313
$916$	−369.826	−0.0133399
$917$	−6106.51	−0.219907
$918$	1483.77	0.0533460
$919$	12094.2	0.434115	0.217058	−	0.976159i	$-0.430354\pi$
$919$	12094.2	0.434115	0.217058	+	0.976159i	$0.430354\pi$
$920$	1629.69	0.0584013
$921$	−14282.0	−0.510975
$922$	−11752.7	−0.419801
$923$	9084.99	0.323983
$924$	2480.79	0.0883248
$925$	6515.86	0.231611
$926$	−1604.65	−0.0569460
$927$	−15121.5	−0.535767
$928$	−1943.40	−0.0687449
$929$	−7199.03	−0.254244	−0.127122	−	0.991887i	$-0.540574\pi$
$929$	−7199.03	−0.254244	−0.127122	+	0.991887i	$0.540574\pi$
$930$	−8952.35	−0.315655
$931$	−1026.43	−0.0361330
$932$	3083.53	0.108374
$933$	−7830.65	−0.274774
$934$	−29667.7	−1.03935
$935$	7187.36	0.251392
$936$	2094.75	0.0731508
$937$	−724.357	−0.0252548	−0.0126274	−	0.999920i	$-0.504020\pi$
$937$	−724.357	−0.0252548	−0.0126274	+	0.999920i	$0.504020\pi$
$938$	11098.0	0.386314
$939$	1045.23	0.0363255
$940$	7088.73	0.245967
$941$	−35844.8	−1.24177	−0.620886	−	0.783901i	$-0.713227\pi$
$941$	−35844.8	−1.24177	−0.620886	+	0.783901i	$0.713227\pi$
$942$	9807.75	0.339229
$943$	2708.79	0.0935421
$944$	9166.12	0.316029
$945$	−1673.97	−0.0576236
$946$	−24382.4	−0.837990
$947$	42495.0	1.45818	0.729092	−	0.684415i	$-0.239943\pi$
$947$	42495.0	1.45818	0.729092	+	0.684415i	$0.239943\pi$
$948$	−10570.4	−0.362142
$949$	16904.4	0.578230
$950$	−1950.37	−0.0666087
$951$	20529.4	0.700011
$952$	1538.72	0.0523847
$953$	−18860.2	−0.641074	−0.320537	−	0.947236i	$-0.603863\pi$
$953$	−18860.2	−0.641074	−0.320537	+	0.947236i	$0.603863\pi$
$954$	−4510.96	−0.153090
$955$	20782.2	0.704184
$956$	4172.44	0.141157
$957$	5380.77	0.181751
$958$	10128.1	0.341571
$959$	3666.63	0.123464
$960$	−1700.54	−0.0571716
$961$	−1411.87	−0.0473925
$962$	−8144.20	−0.272952
$963$	12169.4	0.407222
$964$	−8267.01	−0.276206
$965$	9334.72	0.311394
$966$	−966.000	−0.0321745
$967$	24405.1	0.811598	0.405799	−	0.913962i	$-0.366993\pi$
$967$	24405.1	0.811598	0.405799	+	0.913962i	$0.366993\pi$
$968$	3670.30	0.121868
$969$	1726.74	0.0572453
$970$	23005.1	0.761495
$971$	−32226.9	−1.06510	−0.532549	−	0.846399i	$-0.678766\pi$
$971$	−32226.9	−1.06510	−0.532549	+	0.846399i	$0.678766\pi$
$972$	972.000	0.0320750
$973$	−13124.9	−0.432442
$974$	−36785.1	−1.21013
$975$	4063.27	0.133465
$976$	−9221.78	−0.302441
$977$	−40.9102	−0.00133964	−0.000669822	−	1.00000i	$-0.500213\pi$
$977$	−40.9102	−0.00133964	−0.000669822		1.00000i	$0.500213\pi$
$978$	7373.05	0.241068
$979$	−26739.6	−0.872934
$980$	−1735.97	−0.0565852
$981$	14509.2	0.472216
$982$	−6849.17	−0.222572
$983$	−53906.8	−1.74910	−0.874548	−	0.484940i	$-0.838842\pi$
$983$	−53906.8	−1.74910	−0.874548	+	0.484940i	$0.838842\pi$
$984$	−2826.56	−0.0915726
$985$	30964.7	1.00164
$986$	3337.45	0.107795
$987$	−4201.86	−0.135508
$988$	2437.77	0.0784978
$989$	9494.29	0.305259
$990$	4708.36	0.151153
$991$	14732.6	0.472246	0.236123	−	0.971723i	$-0.424123\pi$
$991$	14732.6	0.472246	0.236123	+	0.971723i	$0.424123\pi$
$992$	5390.75	0.172537
$993$	−27033.0	−0.863915
$994$	4371.72	0.139499
$995$	39136.0	1.24693
$996$	−5111.56	−0.162616
$997$	4611.16	0.146476	0.0732381	−	0.997314i	$-0.476667\pi$
$997$	4611.16	0.146476	0.0732381	+	0.997314i	$0.476667\pi$
$998$	11383.1	0.361047
$999$	−3779.04	−0.119683

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.4.a.d.1.1	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.4.a.d.1.1	✓	3	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	966.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -8.85699 q^{5} -6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -8.85699 q^{5} -6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +17.7140 q^{10} +29.5332 q^{11} +12.0000 q^{12} -29.0938 q^{13} -14.0000 q^{14} -26.5710 q^{15} +16.0000 q^{16} -27.4772 q^{17} -18.0000 q^{18} -20.9475 q^{19} -35.4280 q^{20} +21.0000 q^{21} -59.0665 q^{22} +23.0000 q^{23} -24.0000 q^{24} -46.5537 q^{25} +58.1876 q^{26} +27.0000 q^{27} +28.0000 q^{28} +60.7313 q^{29} +53.1420 q^{30} -168.461 q^{31} -32.0000 q^{32} +88.5997 q^{33} +54.9544 q^{34} -61.9989 q^{35} +36.0000 q^{36} -139.964 q^{37} +41.8950 q^{38} -87.2814 q^{39} +70.8559 q^{40} +117.773 q^{41} -42.0000 q^{42} +412.795 q^{43} +118.133 q^{44} -79.7129 q^{45} -46.0000 q^{46} -200.089 q^{47} +48.0000 q^{48} +49.0000 q^{49} +93.1074 q^{50} -82.4315 q^{51} -116.375 q^{52} +250.609 q^{53} -54.0000 q^{54} -261.576 q^{55} -56.0000 q^{56} -62.8425 q^{57} -121.463 q^{58} +572.882 q^{59} -106.284 q^{60} -576.362 q^{61} +336.922 q^{62} +63.0000 q^{63} +64.0000 q^{64} +257.684 q^{65} -177.199 q^{66} -792.714 q^{67} -109.909 q^{68} +69.0000 q^{69} +123.998 q^{70} -312.265 q^{71} -72.0000 q^{72} -581.032 q^{73} +279.929 q^{74} -139.661 q^{75} -83.7900 q^{76} +206.733 q^{77} +174.563 q^{78} -880.866 q^{79} -141.712 q^{80} +81.0000 q^{81} -235.547 q^{82} -425.963 q^{83} +84.0000 q^{84} +243.365 q^{85} -825.590 q^{86} +182.194 q^{87} -236.266 q^{88} -905.408 q^{89} +159.426 q^{90} -203.657 q^{91} +92.0000 q^{92} -505.383 q^{93} +400.177 q^{94} +185.532 q^{95} -96.0000 q^{96} +1298.70 q^{97} -98.0000 q^{98} +265.799 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 6 q^{2} + 9 q^{3} + 12 q^{4} - 5 q^{5} - 18 q^{6} + 21 q^{7} - 24 q^{8} + 27 q^{9}+O(q^{10}) \) 3 * q - 6 * q^2 + 9 * q^3 + 12 * q^4 - 5 * q^5 - 18 * q^6 + 21 * q^7 - 24 * q^8 + 27 * q^9	\( 3 q - 6 q^{2} + 9 q^{3} + 12 q^{4} - 5 q^{5} - 18 q^{6} + 21 q^{7} - 24 q^{8} + 27 q^{9} + 10 q^{10} - 3 q^{11} + 36 q^{12} - 79 q^{13} - 42 q^{14} - 15 q^{15} + 48 q^{16} - 26 q^{17} - 54 q^{18} - 15 q^{19} - 20 q^{20} + 63 q^{21} + 6 q^{22} + 69 q^{23} - 72 q^{24} - 288 q^{25} + 158 q^{26} + 81 q^{27} + 84 q^{28} - 74 q^{29} + 30 q^{30} - 378 q^{31} - 96 q^{32} - 9 q^{33} + 52 q^{34} - 35 q^{35} + 108 q^{36} - 260 q^{37} + 30 q^{38} - 237 q^{39} + 40 q^{40} + 293 q^{41} - 126 q^{42} - 625 q^{43} - 12 q^{44} - 45 q^{45} - 138 q^{46} + 163 q^{47} + 144 q^{48} + 147 q^{49} + 576 q^{50} - 78 q^{51} - 316 q^{52} + 178 q^{53} - 162 q^{54} - 353 q^{55} - 168 q^{56} - 45 q^{57} + 148 q^{58} - 624 q^{59} - 60 q^{60} - 502 q^{61} + 756 q^{62} + 189 q^{63} + 192 q^{64} + 102 q^{65} + 18 q^{66} - 141 q^{67} - 104 q^{68} + 207 q^{69} + 70 q^{70} + 29 q^{71} - 216 q^{72} - 1198 q^{73} + 520 q^{74} - 864 q^{75} - 60 q^{76} - 21 q^{77} + 474 q^{78} - 1654 q^{79} - 80 q^{80} + 243 q^{81} - 586 q^{82} - 614 q^{83} + 252 q^{84} + 309 q^{85} + 1250 q^{86} - 222 q^{87} + 24 q^{88} - 549 q^{89} + 90 q^{90} - 553 q^{91} + 276 q^{92} - 1134 q^{93} - 326 q^{94} + 415 q^{95} - 288 q^{96} + 182 q^{97} - 294 q^{98} - 27 q^{99}+O(q^{100}) \) 3 * q - 6 * q^2 + 9 * q^3 + 12 * q^4 - 5 * q^5 - 18 * q^6 + 21 * q^7 - 24 * q^8 + 27 * q^9 + 10 * q^10 - 3 * q^11 + 36 * q^12 - 79 * q^13 - 42 * q^14 - 15 * q^15 + 48 * q^16 - 26 * q^17 - 54 * q^18 - 15 * q^19 - 20 * q^20 + 63 * q^21 + 6 * q^22 + 69 * q^23 - 72 * q^24 - 288 * q^25 + 158 * q^26 + 81 * q^27 + 84 * q^28 - 74 * q^29 + 30 * q^30 - 378 * q^31 - 96 * q^32 - 9 * q^33 + 52 * q^34 - 35 * q^35 + 108 * q^36 - 260 * q^37 + 30 * q^38 - 237 * q^39 + 40 * q^40 + 293 * q^41 - 126 * q^42 - 625 * q^43 - 12 * q^44 - 45 * q^45 - 138 * q^46 + 163 * q^47 + 144 * q^48 + 147 * q^49 + 576 * q^50 - 78 * q^51 - 316 * q^52 + 178 * q^53 - 162 * q^54 - 353 * q^55 - 168 * q^56 - 45 * q^57 + 148 * q^58 - 624 * q^59 - 60 * q^60 - 502 * q^61 + 756 * q^62 + 189 * q^63 + 192 * q^64 + 102 * q^65 + 18 * q^66 - 141 * q^67 - 104 * q^68 + 207 * q^69 + 70 * q^70 + 29 * q^71 - 216 * q^72 - 1198 * q^73 + 520 * q^74 - 864 * q^75 - 60 * q^76 - 21 * q^77 + 474 * q^78 - 1654 * q^79 - 80 * q^80 + 243 * q^81 - 586 * q^82 - 614 * q^83 + 252 * q^84 + 309 * q^85 + 1250 * q^86 - 222 * q^87 + 24 * q^88 - 549 * q^89 + 90 * q^90 - 553 * q^91 + 276 * q^92 - 1134 * q^93 - 326 * q^94 + 415 * q^95 - 288 * q^96 + 182 * q^97 - 294 * q^98 - 27 * q^99

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