LMFDB - Embedded newform 966.4.a.l.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:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 319x^{3} - 666x^{2} + 23460x + 101568 $ x^5 - 319x^3 - 666x^2 + 23460*x + 101568
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-7.69907$ 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)

$f(q)$	$=$	$q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -20.1660 q^{5} +6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -20.1660 q^{5} +6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +40.3320 q^{10} -63.4858 q^{11} -12.0000 q^{12} -30.9167 q^{13} -14.0000 q^{14} +60.4980 q^{15} +16.0000 q^{16} +84.3337 q^{17} -18.0000 q^{18} +147.764 q^{19} -80.6641 q^{20} -21.0000 q^{21} +126.972 q^{22} -23.0000 q^{23} +24.0000 q^{24} +281.668 q^{25} +61.8333 q^{26} -27.0000 q^{27} +28.0000 q^{28} -88.8615 q^{29} -120.996 q^{30} -69.4903 q^{31} -32.0000 q^{32} +190.457 q^{33} -168.667 q^{34} -141.162 q^{35} +36.0000 q^{36} -190.701 q^{37} -295.529 q^{38} +92.7500 q^{39} +161.328 q^{40} +370.525 q^{41} +42.0000 q^{42} +414.717 q^{43} -253.943 q^{44} -181.494 q^{45} +46.0000 q^{46} -12.5027 q^{47} -48.0000 q^{48} +49.0000 q^{49} -563.336 q^{50} -253.001 q^{51} -123.667 q^{52} +135.318 q^{53} +54.0000 q^{54} +1280.26 q^{55} -56.0000 q^{56} -443.293 q^{57} +177.723 q^{58} -185.868 q^{59} +241.992 q^{60} -579.769 q^{61} +138.981 q^{62} +63.0000 q^{63} +64.0000 q^{64} +623.466 q^{65} -380.915 q^{66} +973.727 q^{67} +337.335 q^{68} +69.0000 q^{69} +282.324 q^{70} +397.175 q^{71} -72.0000 q^{72} -29.1223 q^{73} +381.402 q^{74} -845.004 q^{75} +591.057 q^{76} -444.401 q^{77} -185.500 q^{78} +398.475 q^{79} -322.656 q^{80} +81.0000 q^{81} -741.051 q^{82} -981.129 q^{83} -84.0000 q^{84} -1700.67 q^{85} -829.434 q^{86} +266.585 q^{87} +507.886 q^{88} +870.719 q^{89} +362.988 q^{90} -216.417 q^{91} -92.0000 q^{92} +208.471 q^{93} +25.0055 q^{94} -2979.82 q^{95} +96.0000 q^{96} -19.8829 q^{97} -98.0000 q^{98} -571.372 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 10 q^{2} - 15 q^{3} + 20 q^{4} - 15 q^{5} + 30 q^{6} + 35 q^{7} - 40 q^{8} + 45 q^{9}+O(q^{10}) $ 5 * q - 10 * q^2 - 15 * q^3 + 20 * q^4 - 15 * q^5 + 30 * q^6 + 35 * q^7 - 40 * q^8 + 45 * q^9	\( 5 q - 10 q^{2} - 15 q^{3} + 20 q^{4} - 15 q^{5} + 30 q^{6} + 35 q^{7} - 40 q^{8} + 45 q^{9} + 30 q^{10} - 19 q^{11} - 60 q^{12} - 19 q^{13} - 70 q^{14} + 45 q^{15} + 80 q^{16} - 42 q^{17} - 90 q^{18} - 25 q^{19} - 60 q^{20} - 105 q^{21} + 38 q^{22} - 115 q^{23} + 120 q^{24} + 206 q^{25} + 38 q^{26} - 135 q^{27} + 140 q^{28} - 292 q^{29} - 90 q^{30} - 60 q^{31} - 160 q^{32} + 57 q^{33} + 84 q^{34} - 105 q^{35} + 180 q^{36} + 264 q^{37} + 50 q^{38} + 57 q^{39} + 120 q^{40} + 223 q^{41} + 210 q^{42} + 661 q^{43} - 76 q^{44} - 135 q^{45} + 230 q^{46} - 279 q^{47} - 240 q^{48} + 245 q^{49} - 412 q^{50} + 126 q^{51} - 76 q^{52} - 324 q^{53} + 270 q^{54} + 1077 q^{55} - 280 q^{56} + 75 q^{57} + 584 q^{58} + 26 q^{59} + 180 q^{60} - 460 q^{61} + 120 q^{62} + 315 q^{63} + 320 q^{64} + 528 q^{65} - 114 q^{66} + 1541 q^{67} - 168 q^{68} + 345 q^{69} + 210 q^{70} - 319 q^{71} - 360 q^{72} + 1532 q^{73} - 528 q^{74} - 618 q^{75} - 100 q^{76} - 133 q^{77} - 114 q^{78} + 1242 q^{79} - 240 q^{80} + 405 q^{81} - 446 q^{82} - 1390 q^{83} - 420 q^{84} - 39 q^{85} - 1322 q^{86} + 876 q^{87} + 152 q^{88} - 1171 q^{89} + 270 q^{90} - 133 q^{91} - 460 q^{92} + 180 q^{93} + 558 q^{94} - 3435 q^{95} + 480 q^{96} - 1800 q^{97} - 490 q^{98} - 171 q^{99}+O(q^{100}) \) 5 * q - 10 * q^2 - 15 * q^3 + 20 * q^4 - 15 * q^5 + 30 * q^6 + 35 * q^7 - 40 * q^8 + 45 * q^9 + 30 * q^10 - 19 * q^11 - 60 * q^12 - 19 * q^13 - 70 * q^14 + 45 * q^15 + 80 * q^16 - 42 * q^17 - 90 * q^18 - 25 * q^19 - 60 * q^20 - 105 * q^21 + 38 * q^22 - 115 * q^23 + 120 * q^24 + 206 * q^25 + 38 * q^26 - 135 * q^27 + 140 * q^28 - 292 * q^29 - 90 * q^30 - 60 * q^31 - 160 * q^32 + 57 * q^33 + 84 * q^34 - 105 * q^35 + 180 * q^36 + 264 * q^37 + 50 * q^38 + 57 * q^39 + 120 * q^40 + 223 * q^41 + 210 * q^42 + 661 * q^43 - 76 * q^44 - 135 * q^45 + 230 * q^46 - 279 * q^47 - 240 * q^48 + 245 * q^49 - 412 * q^50 + 126 * q^51 - 76 * q^52 - 324 * q^53 + 270 * q^54 + 1077 * q^55 - 280 * q^56 + 75 * q^57 + 584 * q^58 + 26 * q^59 + 180 * q^60 - 460 * q^61 + 120 * q^62 + 315 * q^63 + 320 * q^64 + 528 * q^65 - 114 * q^66 + 1541 * q^67 - 168 * q^68 + 345 * q^69 + 210 * q^70 - 319 * q^71 - 360 * q^72 + 1532 * q^73 - 528 * q^74 - 618 * q^75 - 100 * q^76 - 133 * q^77 - 114 * q^78 + 1242 * q^79 - 240 * q^80 + 405 * q^81 - 446 * q^82 - 1390 * q^83 - 420 * q^84 - 39 * q^85 - 1322 * q^86 + 876 * q^87 + 152 * q^88 - 1171 * q^89 + 270 * q^90 - 133 * q^91 - 460 * q^92 + 180 * q^93 + 558 * q^94 - 3435 * q^95 + 480 * q^96 - 1800 * q^97 - 490 * q^98 - 171 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	4.00000	0.500000
$5$	−20.1660	−1.80370	−0.901852	−	0.432046i	$-0.857792\pi$
$5$	−20.1660	−1.80370	−0.901852	+	0.432046i	$0.857792\pi$
$6$	6.00000	0.408248
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	40.3320	1.27541
$11$	−63.4858	−1.74015	−0.870077	−	0.492916i	$-0.835931\pi$
$11$	−63.4858	−1.74015	−0.870077	+	0.492916i	$0.835931\pi$
$12$	−12.0000	−0.288675
$13$	−30.9167	−0.659595	−0.329798	−	0.944052i	$-0.606980\pi$
$13$	−30.9167	−0.659595	−0.329798	+	0.944052i	$0.606980\pi$
$14$	−14.0000	−0.267261
$15$	60.4980	1.04137
$16$	16.0000	0.250000
$17$	84.3337	1.20317	0.601586	−	0.798808i	$-0.294536\pi$
$17$	84.3337	1.20317	0.601586	+	0.798808i	$0.294536\pi$
$18$	−18.0000	−0.235702
$19$	147.764	1.78418	0.892091	−	0.451856i	$-0.149238\pi$
$19$	147.764	1.78418	0.892091	+	0.451856i	$0.149238\pi$
$20$	−80.6641	−0.901852
$21$	−21.0000	−0.218218
$22$	126.972	1.23047
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	24.0000	0.204124
$25$	281.668	2.25334
$26$	61.8333	0.466404
$27$	−27.0000	−0.192450
$28$	28.0000	0.188982
$29$	−88.8615	−0.569006	−0.284503	−	0.958675i	$-0.591829\pi$
$29$	−88.8615	−0.569006	−0.284503	+	0.958675i	$0.591829\pi$
$30$	−120.996	−0.736359
$31$	−69.4903	−0.402607	−0.201304	−	0.979529i	$-0.564518\pi$
$31$	−69.4903	−0.402607	−0.201304	+	0.979529i	$0.564518\pi$
$32$	−32.0000	−0.176777
$33$	190.457	1.00468
$34$	−168.667	−0.850771
$35$	−141.162	−0.681736
$36$	36.0000	0.166667
$37$	−190.701	−0.847326	−0.423663	−	0.905820i	$-0.639256\pi$
$37$	−190.701	−0.847326	−0.423663	+	0.905820i	$0.639256\pi$
$38$	−295.529	−1.26161
$39$	92.7500	0.380817
$40$	161.328	0.637705
$41$	370.525	1.41137	0.705687	−	0.708524i	$-0.250638\pi$
$41$	370.525	1.41137	0.705687	+	0.708524i	$0.250638\pi$
$42$	42.0000	0.154303
$43$	414.717	1.47079	0.735393	−	0.677641i	$-0.236998\pi$
$43$	414.717	1.47079	0.735393	+	0.677641i	$0.236998\pi$
$44$	−253.943	−0.870077
$45$	−181.494	−0.601234
$46$	46.0000	0.147442
$47$	−12.5027	−0.0388024	−0.0194012	−	0.999812i	$-0.506176\pi$
$47$	−12.5027	−0.0388024	−0.0194012	+	0.999812i	$0.506176\pi$
$48$	−48.0000	−0.144338
$49$	49.0000	0.142857
$50$	−563.336	−1.59336
$51$	−253.001	−0.694651
$52$	−123.667	−0.329798
$53$	135.318	0.350705	0.175352	−	0.984506i	$-0.443894\pi$
$53$	135.318	0.350705	0.175352	+	0.984506i	$0.443894\pi$
$54$	54.0000	0.136083
$55$	1280.26	3.13872
$56$	−56.0000	−0.133631
$57$	−443.293	−1.03010
$58$	177.723	0.402348
$59$	−185.868	−0.410134	−0.205067	−	0.978748i	$-0.565741\pi$
$59$	−185.868	−0.410134	−0.205067	+	0.978748i	$0.565741\pi$
$60$	241.992	0.520684
$61$	−579.769	−1.21691	−0.608457	−	0.793587i	$-0.708211\pi$
$61$	−579.769	−1.21691	−0.608457	+	0.793587i	$0.708211\pi$
$62$	138.981	0.284686
$63$	63.0000	0.125988
$64$	64.0000	0.125000
$65$	623.466	1.18971
$66$	−380.915	−0.710415
$67$	973.727	1.77552	0.887759	−	0.460309i	$-0.152261\pi$
$67$	973.727	1.77552	0.887759	+	0.460309i	$0.152261\pi$
$68$	337.335	0.601586
$69$	69.0000	0.120386
$70$	282.324	0.482060
$71$	397.175	0.663888	0.331944	−	0.943299i	$-0.392296\pi$
$71$	397.175	0.663888	0.331944	+	0.943299i	$0.392296\pi$
$72$	−72.0000	−0.117851
$73$	−29.1223	−0.0466918	−0.0233459	−	0.999727i	$-0.507432\pi$
$73$	−29.1223	−0.0466918	−0.0233459	+	0.999727i	$0.507432\pi$
$74$	381.402	0.599150
$75$	−845.004	−1.30097
$76$	591.057	0.892091
$77$	−444.401	−0.657716
$78$	−185.500	−0.269279
$79$	398.475	0.567493	0.283746	−	0.958899i	$-0.408423\pi$
$79$	398.475	0.567493	0.283746	+	0.958899i	$0.408423\pi$
$80$	−322.656	−0.450926
$81$	81.0000	0.111111
$82$	−741.051	−0.997992
$83$	−981.129	−1.29750	−0.648752	−	0.761000i	$-0.724709\pi$
$83$	−981.129	−1.29750	−0.648752	+	0.761000i	$0.724709\pi$
$84$	−84.0000	−0.109109
$85$	−1700.67	−2.17016
$86$	−829.434	−1.04000
$87$	266.585	0.328516
$88$	507.886	0.615237
$89$	870.719	1.03703	0.518517	−	0.855067i	$-0.326484\pi$
$89$	870.719	1.03703	0.518517	+	0.855067i	$0.326484\pi$
$90$	362.988	0.425137
$91$	−216.417	−0.249304
$92$	−92.0000	−0.104257
$93$	208.471	0.232445
$94$	25.0055	0.0274374
$95$	−2979.82	−3.21813
$96$	96.0000	0.102062
$97$	−19.8829	−0.0208124	−0.0104062	−	0.999946i	$-0.503312\pi$
$97$	−19.8829	−0.0208124	−0.0104062	+	0.999946i	$0.503312\pi$
$98$	−98.0000	−0.101015
$99$	−571.372	−0.580051
$100$	1126.67	1.12667
$101$	721.859	0.711165	0.355582	−	0.934645i	$-0.384283\pi$
$101$	721.859	0.711165	0.355582	+	0.934645i	$0.384283\pi$
$102$	506.002	0.491193
$103$	−1147.09	−1.09734	−0.548669	−	0.836040i	$-0.684865\pi$
$103$	−1147.09	−1.09734	−0.548669	+	0.836040i	$0.684865\pi$
$104$	247.333	0.233202
$105$	423.486	0.393600
$106$	−270.636	−0.247986
$107$	−961.964	−0.869127	−0.434563	−	0.900641i	$-0.643097\pi$
$107$	−961.964	−0.869127	−0.434563	+	0.900641i	$0.643097\pi$
$108$	−108.000	−0.0962250
$109$	872.037	0.766293	0.383147	−	0.923688i	$-0.374840\pi$
$109$	872.037	0.766293	0.383147	+	0.923688i	$0.374840\pi$
$110$	−2560.51	−2.21941
$111$	572.104	0.489204
$112$	112.000	0.0944911
$113$	−1285.08	−1.06983	−0.534913	−	0.844907i	$-0.679656\pi$
$113$	−1285.08	−1.06983	−0.534913	+	0.844907i	$0.679656\pi$
$114$	886.586	0.728389
$115$	463.818	0.376098
$116$	−355.446	−0.284503
$117$	−278.250	−0.219865
$118$	371.735	0.290009
$119$	590.336	0.454756
$120$	−483.984	−0.368179
$121$	2699.45	2.02813
$122$	1159.54	0.860489
$123$	−1111.58	−0.814857
$124$	−277.961	−0.201304
$125$	−3159.37	−2.26066
$126$	−126.000	−0.0890871
$127$	−2602.55	−1.81842	−0.909210	−	0.416338i	$-0.863313\pi$
$127$	−2602.55	−1.81842	−0.909210	+	0.416338i	$0.863313\pi$
$128$	−128.000	−0.0883883
$129$	−1244.15	−0.849158
$130$	−1246.93	−0.841255
$131$	−707.969	−0.472180	−0.236090	−	0.971731i	$-0.575866\pi$
$131$	−707.969	−0.472180	−0.236090	+	0.971731i	$0.575866\pi$
$132$	761.830	0.502339
$133$	1034.35	0.674357
$134$	−1947.45	−1.25548
$135$	544.482	0.347123
$136$	−674.669	−0.425385
$137$	2472.89	1.54214	0.771072	−	0.636748i	$-0.219721\pi$
$137$	2472.89	1.54214	0.771072	+	0.636748i	$0.219721\pi$
$138$	−138.000	−0.0851257
$139$	−1870.68	−1.14150	−0.570750	−	0.821124i	$-0.693348\pi$
$139$	−1870.68	−1.14150	−0.570750	+	0.821124i	$0.693348\pi$
$140$	−564.648	−0.340868
$141$	37.5082	0.0224026
$142$	−794.350	−0.469439
$143$	1962.77	1.14780
$144$	144.000	0.0833333
$145$	1791.98	1.02632
$146$	58.2445	0.0330161
$147$	−147.000	−0.0824786
$148$	−762.805	−0.423663
$149$	−3232.83	−1.77748	−0.888739	−	0.458414i	$-0.848418\pi$
$149$	−3232.83	−1.77748	−0.888739	+	0.458414i	$0.848418\pi$
$150$	1690.01	0.919924
$151$	−559.226	−0.301385	−0.150692	−	0.988581i	$-0.548150\pi$
$151$	−559.226	−0.301385	−0.150692	+	0.988581i	$0.548150\pi$
$152$	−1182.11	−0.630803
$153$	759.003	0.401057
$154$	888.801	0.465076
$155$	1401.34	0.726184
$156$	371.000	0.190409
$157$	−1933.14	−0.982686	−0.491343	−	0.870966i	$-0.663494\pi$
$157$	−1933.14	−0.982686	−0.491343	+	0.870966i	$0.663494\pi$
$158$	−796.950	−0.401278
$159$	−405.954	−0.202479
$160$	645.312	0.318853
$161$	−161.000	−0.0788110
$162$	−162.000	−0.0785674
$163$	46.9784	0.0225744	0.0112872	−	0.999936i	$-0.496407\pi$
$163$	46.9784	0.0225744	0.0112872	+	0.999936i	$0.496407\pi$
$164$	1482.10	0.705687
$165$	−3840.77	−1.81214
$166$	1962.26	0.917474
$167$	−1086.52	−0.503459	−0.251730	−	0.967798i	$-0.580999\pi$
$167$	−1086.52	−0.503459	−0.251730	+	0.967798i	$0.580999\pi$
$168$	168.000	0.0771517
$169$	−1241.16	−0.564934
$170$	3401.35	1.53454
$171$	1329.88	0.594727
$172$	1658.87	0.735393
$173$	2304.69	1.01285	0.506424	−	0.862285i	$-0.330967\pi$
$173$	2304.69	1.01285	0.506424	+	0.862285i	$0.330967\pi$
$174$	−533.169	−0.232296
$175$	1971.68	0.851684
$176$	−1015.77	−0.435038
$177$	557.603	0.236791
$178$	−1741.44	−0.733294
$179$	4150.95	1.73328	0.866639	−	0.498935i	$-0.166275\pi$
$179$	4150.95	1.73328	0.866639	+	0.498935i	$0.166275\pi$
$180$	−725.976	−0.300617
$181$	−2537.46	−1.04203	−0.521017	−	0.853546i	$-0.674447\pi$
$181$	−2537.46	−1.04203	−0.521017	+	0.853546i	$0.674447\pi$
$182$	432.833	0.176284
$183$	1739.31	0.702586
$184$	184.000	0.0737210
$185$	3845.68	1.52833
$186$	−416.942	−0.164364
$187$	−5353.99	−2.09370
$188$	−50.0110	−0.0194012
$189$	−189.000	−0.0727393
$190$	5959.63	2.27556
$191$	−1004.95	−0.380710	−0.190355	−	0.981715i	$-0.560964\pi$
$191$	−1004.95	−0.380710	−0.190355	+	0.981715i	$0.560964\pi$
$192$	−192.000	−0.0721688
$193$	3768.95	1.40567	0.702836	−	0.711352i	$-0.251917\pi$
$193$	3768.95	1.40567	0.702836	+	0.711352i	$0.251917\pi$
$194$	39.7658	0.0147166
$195$	−1870.40	−0.686882
$196$	196.000	0.0714286
$197$	1701.79	0.615469	0.307735	−	0.951472i	$-0.400429\pi$
$197$	1701.79	0.615469	0.307735	+	0.951472i	$0.400429\pi$
$198$	1142.74	0.410158
$199$	−3723.59	−1.32642	−0.663212	−	0.748431i	$-0.730807\pi$
$199$	−3723.59	−1.32642	−0.663212	+	0.748431i	$0.730807\pi$
$200$	−2253.34	−0.796678
$201$	−2921.18	−1.02510
$202$	−1443.72	−0.502869
$203$	−622.031	−0.215064
$204$	−1012.00	−0.347326
$205$	−7472.02	−2.54570
$206$	2294.17	0.775935
$207$	−207.000	−0.0695048
$208$	−494.666	−0.164899
$209$	−9380.93	−3.10475
$210$	−846.973	−0.278317
$211$	2597.26	0.847405	0.423703	−	0.905801i	$-0.360730\pi$
$211$	2597.26	0.847405	0.423703	+	0.905801i	$0.360730\pi$
$212$	541.272	0.175352
$213$	−1191.53	−0.383296
$214$	1923.93	0.614565
$215$	−8363.19	−2.65286
$216$	216.000	0.0680414
$217$	−486.432	−0.152171
$218$	−1744.07	−0.541851
$219$	87.3668	0.0269575
$220$	5121.02	1.56936
$221$	−2607.31	−0.793606
$222$	−1144.21	−0.345920
$223$	−60.8061	−0.0182595	−0.00912977	−	0.999958i	$-0.502906\pi$
$223$	−60.8061	−0.0182595	−0.00912977	+	0.999958i	$0.502906\pi$
$224$	−224.000	−0.0668153
$225$	2535.01	0.751115
$226$	2570.17	0.756482
$227$	−1095.57	−0.320332	−0.160166	−	0.987090i	$-0.551203\pi$
$227$	−1095.57	−0.320332	−0.160166	+	0.987090i	$0.551203\pi$
$228$	−1773.17	−0.515049
$229$	−4716.49	−1.36102	−0.680511	−	0.732737i	$-0.738242\pi$
$229$	−4716.49	−1.36102	−0.680511	+	0.732737i	$0.738242\pi$
$230$	−927.637	−0.265942
$231$	1333.20	0.379733
$232$	710.892	0.201174
$233$	4695.16	1.32013	0.660065	−	0.751208i	$-0.270529\pi$
$233$	4695.16	1.32013	0.660065	+	0.751208i	$0.270529\pi$
$234$	556.500	0.155468
$235$	252.131	0.0699880
$236$	−743.471	−0.205067
$237$	−1195.42	−0.327642
$238$	−1180.67	−0.321561
$239$	−5305.70	−1.43597	−0.717986	−	0.696058i	$-0.754936\pi$
$239$	−5305.70	−1.43597	−0.717986	+	0.696058i	$0.754936\pi$
$240$	967.969	0.260342
$241$	−2204.12	−0.589128	−0.294564	−	0.955632i	$-0.595174\pi$
$241$	−2204.12	−0.589128	−0.294564	+	0.955632i	$0.595174\pi$
$242$	−5398.90	−1.43411
$243$	−243.000	−0.0641500
$244$	−2319.08	−0.608457
$245$	−988.135	−0.257672
$246$	2223.15	0.576191
$247$	−4568.38	−1.17684
$248$	555.922	0.142343
$249$	2943.39	0.749115
$250$	6318.74	1.59853
$251$	−5579.60	−1.40311	−0.701556	−	0.712615i	$-0.747511\pi$
$251$	−5579.60	−1.40311	−0.701556	+	0.712615i	$0.747511\pi$
$252$	252.000	0.0629941
$253$	1460.17	0.362847
$254$	5205.11	1.28582
$255$	5102.02	1.25294
$256$	256.000	0.0625000
$257$	−7405.02	−1.79732	−0.898662	−	0.438642i	$-0.855460\pi$
$257$	−7405.02	−1.79732	−0.898662	+	0.438642i	$0.855460\pi$
$258$	2488.30	0.600446
$259$	−1334.91	−0.320259
$260$	2493.86	0.594857
$261$	−799.754	−0.189669
$262$	1415.94	0.333882
$263$	4373.47	1.02540	0.512699	−	0.858569i	$-0.328646\pi$
$263$	4373.47	1.02540	0.512699	+	0.858569i	$0.328646\pi$
$264$	−1523.66	−0.355207
$265$	−2728.82	−0.632567
$266$	−2068.70	−0.476843
$267$	−2612.16	−0.598732
$268$	3894.91	0.887759
$269$	−11.1956	−0.00253757	−0.00126878	−	0.999999i	$-0.500404\pi$
$269$	−11.1956	−0.00253757	−0.00126878	+	0.999999i	$0.500404\pi$
$270$	−1088.96	−0.245453
$271$	2328.71	0.521989	0.260994	−	0.965340i	$-0.415950\pi$
$271$	2328.71	0.521989	0.260994	+	0.965340i	$0.415950\pi$
$272$	1349.34	0.300793
$273$	649.250	0.143935
$274$	−4945.79	−1.09046
$275$	−17881.9	−3.92117
$276$	276.000	0.0601929
$277$	−5587.72	−1.21203	−0.606017	−	0.795452i	$-0.707234\pi$
$277$	−5587.72	−1.21203	−0.606017	+	0.795452i	$0.707234\pi$
$278$	3741.35	0.807163
$279$	−625.412	−0.134202
$280$	1129.30	0.241030
$281$	1621.27	0.344187	0.172094	−	0.985081i	$-0.444947\pi$
$281$	1621.27	0.344187	0.172094	+	0.985081i	$0.444947\pi$
$282$	−75.0165	−0.0158410
$283$	8494.70	1.78430	0.892151	−	0.451738i	$-0.149196\pi$
$283$	8494.70	1.78430	0.892151	+	0.451738i	$0.149196\pi$
$284$	1588.70	0.331944
$285$	8939.45	1.85799
$286$	−3925.54	−0.811615
$287$	2593.68	0.533449
$288$	−288.000	−0.0589256
$289$	2199.17	0.447622
$290$	−3583.96	−0.725716
$291$	59.6487	0.0120160
$292$	−116.489	−0.0233459
$293$	−3793.34	−0.756346	−0.378173	−	0.925735i	$-0.623448\pi$
$293$	−3793.34	−0.756346	−0.378173	+	0.925735i	$0.623448\pi$
$294$	294.000	0.0583212
$295$	3748.21	0.739760
$296$	1525.61	0.299575
$297$	1714.12	0.334893
$298$	6465.67	1.25687
$299$	711.083	0.137535
$300$	−3380.02	−0.650485
$301$	2903.02	0.555905
$302$	1118.45	0.213111
$303$	−2165.58	−0.410591
$304$	2364.23	0.446045
$305$	11691.6	2.19495
$306$	−1518.01	−0.283590
$307$	4249.62	0.790028	0.395014	−	0.918675i	$-0.370740\pi$
$307$	4249.62	0.790028	0.395014	+	0.918675i	$0.370740\pi$
$308$	−1777.60	−0.328858
$309$	3441.26	0.633548
$310$	−2802.68	−0.513489
$311$	−509.659	−0.0929263	−0.0464632	−	0.998920i	$-0.514795\pi$
$311$	−509.659	−0.0929263	−0.0464632	+	0.998920i	$0.514795\pi$
$312$	−742.000	−0.134639
$313$	8072.59	1.45779	0.728897	−	0.684623i	$-0.240033\pi$
$313$	8072.59	1.45779	0.728897	+	0.684623i	$0.240033\pi$
$314$	3866.29	0.694864
$315$	−1270.46	−0.227245
$316$	1593.90	0.283746
$317$	1320.38	0.233942	0.116971	−	0.993135i	$-0.462681\pi$
$317$	1320.38	0.233942	0.116971	+	0.993135i	$0.462681\pi$
$318$	811.907	0.143175
$319$	5641.44	0.990157
$320$	−1290.62	−0.225463
$321$	2885.89	0.501791
$322$	322.000	0.0557278
$323$	12461.5	2.14668
$324$	324.000	0.0555556
$325$	−8708.23	−1.48630
$326$	−93.9568	−0.0159625
$327$	−2616.11	−0.442420
$328$	−2964.20	−0.498996
$329$	−87.5192	−0.0146659
$330$	7681.53	1.28138
$331$	5727.19	0.951042	0.475521	−	0.879704i	$-0.342260\pi$
$331$	5727.19	0.951042	0.475521	+	0.879704i	$0.342260\pi$
$332$	−3924.52	−0.648752
$333$	−1716.31	−0.282442
$334$	2173.05	0.355999
$335$	−19636.2	−3.20251
$336$	−336.000	−0.0545545
$337$	−9063.94	−1.46512	−0.732558	−	0.680704i	$-0.761674\pi$
$337$	−9063.94	−1.46512	−0.732558	+	0.680704i	$0.761674\pi$
$338$	2482.32	0.399469
$339$	3855.25	0.617665
$340$	−6802.70	−1.08508
$341$	4411.64	0.700598
$342$	−2659.76	−0.420536
$343$	343.000	0.0539949
$344$	−3317.74	−0.520001
$345$	−1391.45	−0.217140
$346$	−4609.39	−0.716191
$347$	5122.97	0.792552	0.396276	−	0.918131i	$-0.370302\pi$
$347$	5122.97	0.792552	0.396276	+	0.918131i	$0.370302\pi$
$348$	1066.34	0.164258
$349$	8349.58	1.28064	0.640319	−	0.768109i	$-0.278802\pi$
$349$	8349.58	1.28064	0.640319	+	0.768109i	$0.278802\pi$
$350$	−3943.35	−0.602232
$351$	834.750	0.126939
$352$	2031.55	0.307619
$353$	−12778.4	−1.92671	−0.963354	−	0.268232i	$-0.913561\pi$
$353$	−12778.4	−1.92671	−0.963354	+	0.268232i	$0.913561\pi$
$354$	−1115.21	−0.167437
$355$	−8009.44	−1.19746
$356$	3482.88	0.518517
$357$	−1771.01	−0.262554
$358$	−8301.91	−1.22561
$359$	10205.6	1.50036	0.750180	−	0.661234i	$-0.229967\pi$
$359$	10205.6	1.50036	0.750180	+	0.661234i	$0.229967\pi$
$360$	1451.95	0.212568
$361$	14975.3	2.18330
$362$	5074.93	0.736830
$363$	−8098.34	−1.17094
$364$	−865.666	−0.124652
$365$	587.280	0.0842182
$366$	−3478.61	−0.496803
$367$	−4086.69	−0.581263	−0.290632	−	0.956835i	$-0.593865\pi$
$367$	−4086.69	−0.581263	−0.290632	+	0.956835i	$0.593865\pi$
$368$	−368.000	−0.0521286
$369$	3334.73	0.470458
$370$	−7691.36	−1.08069
$371$	947.225	0.132554
$372$	833.883	0.116223
$373$	443.862	0.0616147	0.0308074	−	0.999525i	$-0.490192\pi$
$373$	443.862	0.0616147	0.0308074	+	0.999525i	$0.490192\pi$
$374$	10708.0	1.48047
$375$	9478.11	1.30519
$376$	100.022	0.0137187
$377$	2747.30	0.375313
$378$	378.000	0.0514344
$379$	35.7039	0.00483902	0.00241951	−	0.999997i	$-0.499230\pi$
$379$	35.7039	0.00483902	0.00241951	+	0.999997i	$0.499230\pi$
$380$	−11919.3	−1.60907
$381$	7807.66	1.04986
$382$	2009.90	0.269202
$383$	10971.7	1.46378	0.731891	−	0.681422i	$-0.238638\pi$
$383$	10971.7	1.46378	0.731891	+	0.681422i	$0.238638\pi$
$384$	384.000	0.0510310
$385$	8961.79	1.18632
$386$	−7537.89	−0.993960
$387$	3732.45	0.490262
$388$	−79.5316	−0.0104062
$389$	2471.82	0.322175	0.161088	−	0.986940i	$-0.448500\pi$
$389$	2471.82	0.322175	0.161088	+	0.986940i	$0.448500\pi$
$390$	3740.79	0.485699
$391$	−1939.67	−0.250879
$392$	−392.000	−0.0505076
$393$	2123.91	0.272613
$394$	−3403.58	−0.435202
$395$	−8035.65	−1.02359
$396$	−2285.49	−0.290026
$397$	7037.81	0.889717	0.444859	−	0.895601i	$-0.353254\pi$
$397$	7037.81	0.889717	0.444859	+	0.895601i	$0.353254\pi$
$398$	7447.19	0.937924
$399$	−3103.05	−0.389340
$400$	4506.69	0.563336
$401$	9668.25	1.20401	0.602007	−	0.798491i	$-0.294368\pi$
$401$	9668.25	1.20401	0.602007	+	0.798491i	$0.294368\pi$
$402$	5842.36	0.724852
$403$	2148.41	0.265558
$404$	2887.44	0.355582
$405$	−1633.45	−0.200411
$406$	1244.06	0.152073
$407$	12106.8	1.47448
$408$	2024.01	0.245596
$409$	−12873.2	−1.55633	−0.778166	−	0.628059i	$-0.783850\pi$
$409$	−12873.2	−1.55633	−0.778166	+	0.628059i	$0.783850\pi$
$410$	14944.0	1.80008
$411$	−7418.68	−0.890357
$412$	−4588.35	−0.548669
$413$	−1301.07	−0.155016
$414$	414.000	0.0491473
$415$	19785.5	2.34031
$416$	989.333	0.116601
$417$	5612.03	0.659046
$418$	18761.9	2.19539
$419$	−4602.86	−0.536669	−0.268335	−	0.963326i	$-0.586473\pi$
$419$	−4602.86	−0.536669	−0.268335	+	0.963326i	$0.586473\pi$
$420$	1693.95	0.196800
$421$	−2274.90	−0.263353	−0.131677	−	0.991293i	$-0.542036\pi$
$421$	−2274.90	−0.263353	−0.131677	+	0.991293i	$0.542036\pi$
$422$	−5194.51	−0.599206
$423$	−112.525	−0.0129341
$424$	−1082.54	−0.123993
$425$	23754.1	2.71116
$426$	2383.05	0.271031
$427$	−4058.38	−0.459950
$428$	−3847.86	−0.434563
$429$	−5888.31	−0.662681
$430$	16726.4	1.87586
$431$	10662.3	1.19161	0.595807	−	0.803128i	$-0.296832\pi$
$431$	10662.3	1.19161	0.595807	+	0.803128i	$0.296832\pi$
$432$	−432.000	−0.0481125
$433$	8262.71	0.917045	0.458522	−	0.888683i	$-0.348379\pi$
$433$	8262.71	0.917045	0.458522	+	0.888683i	$0.348379\pi$
$434$	972.864	0.107601
$435$	−5375.95	−0.592545
$436$	3488.15	0.383147
$437$	−3398.58	−0.372028
$438$	−174.734	−0.0190619
$439$	−14808.6	−1.60997	−0.804986	−	0.593294i	$-0.797827\pi$
$439$	−14808.6	−1.60997	−0.804986	+	0.593294i	$0.797827\pi$
$440$	−10242.0	−1.10971
$441$	441.000	0.0476190
$442$	5214.63	0.561164
$443$	−17487.5	−1.87553	−0.937763	−	0.347275i	$-0.887107\pi$
$443$	−17487.5	−1.87553	−0.937763	+	0.347275i	$0.887107\pi$
$444$	2288.41	0.244602
$445$	−17558.9	−1.87050
$446$	121.612	0.0129115
$447$	9698.50	1.02623
$448$	448.000	0.0472456
$449$	−13879.2	−1.45880	−0.729398	−	0.684089i	$-0.760200\pi$
$449$	−13879.2	−1.45880	−0.729398	+	0.684089i	$0.760200\pi$
$450$	−5070.03	−0.531118
$451$	−23523.1	−2.45601
$452$	−5140.33	−0.534913
$453$	1677.68	0.174005
$454$	2191.13	0.226509
$455$	4364.26	0.449670
$456$	3546.34	0.364194
$457$	4840.59	0.495477	0.247739	−	0.968827i	$-0.420313\pi$
$457$	4840.59	0.495477	0.247739	+	0.968827i	$0.420313\pi$
$458$	9432.97	0.962389
$459$	−2277.01	−0.231550
$460$	1855.27	0.188049
$461$	2282.31	0.230581	0.115290	−	0.993332i	$-0.463220\pi$
$461$	2282.31	0.230581	0.115290	+	0.993332i	$0.463220\pi$
$462$	−2666.40	−0.268512
$463$	15762.5	1.58217	0.791087	−	0.611704i	$-0.209515\pi$
$463$	15762.5	1.58217	0.791087	+	0.611704i	$0.209515\pi$
$464$	−1421.78	−0.142251
$465$	−4204.02	−0.419262
$466$	−9390.33	−0.933473
$467$	−13180.4	−1.30603	−0.653014	−	0.757346i	$-0.726496\pi$
$467$	−13180.4	−1.30603	−0.653014	+	0.757346i	$0.726496\pi$
$468$	−1113.00	−0.109933
$469$	6816.09	0.671083
$470$	−504.261	−0.0494890
$471$	5799.43	0.567354
$472$	1486.94	0.145004
$473$	−26328.7	−2.55939
$474$	2390.85	0.231678
$475$	41620.5	4.02038
$476$	2361.34	0.227378
$477$	1217.86	0.116902
$478$	10611.4	1.01539
$479$	13891.8	1.32512	0.662562	−	0.749007i	$-0.269469\pi$
$479$	13891.8	1.32512	0.662562	+	0.749007i	$0.269469\pi$
$480$	−1935.94	−0.184090
$481$	5895.84	0.558892
$482$	4408.24	0.416576
$483$	483.000	0.0455016
$484$	10797.8	1.01407
$485$	400.959	0.0375394
$486$	486.000	0.0453609
$487$	11610.6	1.08034	0.540169	−	0.841557i	$-0.318360\pi$
$487$	11610.6	1.08034	0.540169	+	0.841557i	$0.318360\pi$
$488$	4638.15	0.430244
$489$	−140.935	−0.0130333
$490$	1976.27	0.182202
$491$	−4927.58	−0.452909	−0.226455	−	0.974022i	$-0.572713\pi$
$491$	−4927.58	−0.452909	−0.226455	+	0.974022i	$0.572713\pi$
$492$	−4446.30	−0.407429
$493$	−7494.02	−0.684612
$494$	9136.75	0.832150
$495$	11522.3	1.04624
$496$	−1111.84	−0.100652
$497$	2780.23	0.250926
$498$	−5886.77	−0.529704
$499$	−3735.22	−0.335093	−0.167546	−	0.985864i	$-0.553584\pi$
$499$	−3735.22	−0.335093	−0.167546	+	0.985864i	$0.553584\pi$
$500$	−12637.5	−1.13033
$501$	3259.57	0.290672
$502$	11159.2	0.992150
$503$	−8622.73	−0.764351	−0.382175	−	0.924090i	$-0.624825\pi$
$503$	−8622.73	−0.764351	−0.382175	+	0.924090i	$0.624825\pi$
$504$	−504.000	−0.0445435
$505$	−14557.0	−1.28273
$506$	−2920.35	−0.256572
$507$	3723.48	0.326165
$508$	−10410.2	−0.909210
$509$	−2993.45	−0.260673	−0.130336	−	0.991470i	$-0.541606\pi$
$509$	−2993.45	−0.260673	−0.130336	+	0.991470i	$0.541606\pi$
$510$	−10204.0	−0.885966
$511$	−203.856	−0.0176478
$512$	−512.000	−0.0441942
$513$	−3989.63	−0.343366
$514$	14810.0	1.27090
$515$	23132.2	1.97927
$516$	−4976.61	−0.424579
$517$	793.747	0.0675221
$518$	2669.82	0.226458
$519$	−6914.08	−0.584768
$520$	−4987.72	−0.420627
$521$	45.6884	0.00384193	0.00192096	−	0.999998i	$-0.499389\pi$
$521$	45.6884	0.00384193	0.00192096	+	0.999998i	$0.499389\pi$
$522$	1599.51	0.134116
$523$	−1862.07	−0.155683	−0.0778417	−	0.996966i	$-0.524803\pi$
$523$	−1862.07	−0.155683	−0.0778417	+	0.996966i	$0.524803\pi$
$524$	−2831.88	−0.236090
$525$	−5915.03	−0.491720
$526$	−8746.93	−0.725065
$527$	−5860.37	−0.484405
$528$	3047.32	0.251170
$529$	529.000	0.0434783
$530$	5457.65	0.447292
$531$	−1672.81	−0.136711
$532$	4137.40	0.337179
$533$	−11455.4	−0.930935
$534$	5224.31	0.423367
$535$	19399.0	1.56765
$536$	−7789.82	−0.627740
$537$	−12452.9	−1.00071
$538$	22.3911	0.00179433
$539$	−3110.80	−0.248593
$540$	2177.93	0.173561
$541$	−9564.76	−0.760113	−0.380056	−	0.924963i	$-0.624095\pi$
$541$	−9564.76	−0.760113	−0.380056	+	0.924963i	$0.624095\pi$
$542$	−4657.42	−0.369102
$543$	7612.39	0.601619
$544$	−2698.68	−0.212693
$545$	−17585.5	−1.38217
$546$	−1298.50	−0.101778
$547$	6442.21	0.503563	0.251781	−	0.967784i	$-0.418984\pi$
$547$	6442.21	0.503563	0.251781	+	0.967784i	$0.418984\pi$
$548$	9891.58	0.771072
$549$	−5217.92	−0.405638
$550$	35763.9	2.77268
$551$	−13130.6	−1.01521
$552$	−552.000	−0.0425628
$553$	2789.32	0.214492
$554$	11175.4	0.857037
$555$	−11537.0	−0.882379
$556$	−7482.70	−0.570750
$557$	13148.5	1.00021	0.500107	−	0.865964i	$-0.333294\pi$
$557$	13148.5	1.00021	0.500107	+	0.865964i	$0.333294\pi$
$558$	1250.82	0.0948954
$559$	−12821.7	−0.970123
$560$	−2258.59	−0.170434
$561$	16062.0	1.20880
$562$	−3242.53	−0.243377
$563$	20156.8	1.50889	0.754446	−	0.656362i	$-0.227906\pi$
$563$	20156.8	1.50889	0.754446	+	0.656362i	$0.227906\pi$
$564$	150.033	0.0112013
$565$	25915.0	1.92965
$566$	−16989.4	−1.26169
$567$	567.000	0.0419961
$568$	−3177.40	−0.234720
$569$	−19363.0	−1.42661	−0.713304	−	0.700855i	$-0.752802\pi$
$569$	−19363.0	−1.42661	−0.713304	+	0.700855i	$0.752802\pi$
$570$	−17878.9	−1.31380
$571$	−15499.8	−1.13598	−0.567992	−	0.823034i	$-0.692279\pi$
$571$	−15499.8	−1.13598	−0.567992	+	0.823034i	$0.692279\pi$
$572$	7851.07	0.573898
$573$	3014.85	0.219803
$574$	−5187.36	−0.377206
$575$	−6478.37	−0.469855
$576$	576.000	0.0416667
$577$	−7523.85	−0.542846	−0.271423	−	0.962460i	$-0.587494\pi$
$577$	−7523.85	−0.542846	−0.271423	+	0.962460i	$0.587494\pi$
$578$	−4398.33	−0.316517
$579$	−11306.8	−0.811565
$580$	7167.93	0.513159
$581$	−6867.90	−0.490411
$582$	−119.297	−0.00849663
$583$	−8590.77	−0.610280
$584$	232.978	0.0165081
$585$	5611.19	0.396571
$586$	7586.69	0.534818
$587$	−8791.90	−0.618195	−0.309097	−	0.951030i	$-0.600027\pi$
$587$	−8791.90	−0.618195	−0.309097	+	0.951030i	$0.600027\pi$
$588$	−588.000	−0.0412393
$589$	−10268.2	−0.718324
$590$	−7496.42	−0.523090
$591$	−5105.37	−0.355341
$592$	−3051.22	−0.211832
$593$	−10096.7	−0.699193	−0.349597	−	0.936900i	$-0.613681\pi$
$593$	−10096.7	−0.699193	−0.349597	+	0.936900i	$0.613681\pi$
$594$	−3428.23	−0.236805
$595$	−11904.7	−0.820245
$596$	−12931.3	−0.888739
$597$	11170.8	0.765812
$598$	−1422.17	−0.0972520
$599$	−12647.3	−0.862696	−0.431348	−	0.902186i	$-0.641962\pi$
$599$	−12647.3	−0.862696	−0.431348	+	0.902186i	$0.641962\pi$
$600$	6760.03	0.459962
$601$	−12922.4	−0.877064	−0.438532	−	0.898716i	$-0.644501\pi$
$601$	−12922.4	−0.877064	−0.438532	+	0.898716i	$0.644501\pi$
$602$	−5806.04	−0.393084
$603$	8763.54	0.591839
$604$	−2236.90	−0.150692
$605$	−54437.1	−3.65815
$606$	4331.15	0.290332
$607$	5911.64	0.395298	0.197649	−	0.980273i	$-0.436669\pi$
$607$	5911.64	0.395298	0.197649	+	0.980273i	$0.436669\pi$
$608$	−4728.46	−0.315402
$609$	1866.09	0.124167
$610$	−23383.3	−1.55207
$611$	386.543	0.0255939
$612$	3036.01	0.200529
$613$	−19067.1	−1.25630	−0.628149	−	0.778093i	$-0.716187\pi$
$613$	−19067.1	−1.25630	−0.628149	+	0.778093i	$0.716187\pi$
$614$	−8499.23	−0.558634
$615$	22416.1	1.46976
$616$	3555.21	0.232538
$617$	−14627.2	−0.954409	−0.477205	−	0.878792i	$-0.658350\pi$
$617$	−14627.2	−0.954409	−0.477205	+	0.878792i	$0.658350\pi$
$618$	−6882.52	−0.447986
$619$	−7712.66	−0.500804	−0.250402	−	0.968142i	$-0.580563\pi$
$619$	−7712.66	−0.500804	−0.250402	+	0.968142i	$0.580563\pi$
$620$	5605.37	0.363092
$621$	621.000	0.0401286
$622$	1019.32	0.0657088
$623$	6095.03	0.391962
$624$	1484.00	0.0952043
$625$	28503.4	1.82422
$626$	−16145.2	−1.03082
$627$	28142.8	1.79253
$628$	−7732.57	−0.491343
$629$	−16082.5	−1.01948
$630$	2540.92	0.160687
$631$	18049.4	1.13872	0.569362	−	0.822087i	$-0.307190\pi$
$631$	18049.4	1.13872	0.569362	+	0.822087i	$0.307190\pi$
$632$	−3187.80	−0.200639
$633$	−7791.77	−0.489250
$634$	−2640.75	−0.165422
$635$	52483.1	3.27989
$636$	−1623.81	−0.101240
$637$	−1514.92	−0.0942279
$638$	−11282.9	−0.700147
$639$	3574.58	0.221296
$640$	2581.25	0.159426
$641$	−16721.5	−1.03036	−0.515179	−	0.857083i	$-0.672274\pi$
$641$	−16721.5	−1.03036	−0.515179	+	0.857083i	$0.672274\pi$
$642$	−5771.78	−0.354820
$643$	11507.4	0.705764	0.352882	−	0.935668i	$-0.385202\pi$
$643$	11507.4	0.705764	0.352882	+	0.935668i	$0.385202\pi$
$644$	−644.000	−0.0394055
$645$	25089.6	1.53163
$646$	−24923.0	−1.51793
$647$	22004.8	1.33709	0.668544	−	0.743672i	$-0.266918\pi$
$647$	22004.8	1.33709	0.668544	+	0.743672i	$0.266918\pi$
$648$	−648.000	−0.0392837
$649$	11800.0	0.713697
$650$	17416.5	1.05097
$651$	1459.30	0.0878561
$652$	187.914	0.0112872
$653$	−22250.6	−1.33343	−0.666717	−	0.745311i	$-0.732301\pi$
$653$	−22250.6	−1.33343	−0.666717	+	0.745311i	$0.732301\pi$
$654$	5232.22	0.312838
$655$	14276.9	0.851672
$656$	5928.41	0.352844
$657$	−262.100	−0.0155639
$658$	175.038	0.0103704
$659$	−862.049	−0.0509570	−0.0254785	−	0.999675i	$-0.508111\pi$
$659$	−862.049	−0.0509570	−0.0254785	+	0.999675i	$0.508111\pi$
$660$	−15363.1	−0.906071
$661$	−6407.18	−0.377020	−0.188510	−	0.982071i	$-0.560366\pi$
$661$	−6407.18	−0.377020	−0.188510	+	0.982071i	$0.560366\pi$
$662$	−11454.4	−0.672488
$663$	7821.94	0.458189
$664$	7849.03	0.458737
$665$	−20858.7	−1.21634
$666$	3432.62	0.199717
$667$	2043.81	0.118646
$668$	−4346.09	−0.251730
$669$	182.418	0.0105422
$670$	39272.4	2.26451
$671$	36807.1	2.11762
$672$	672.000	0.0385758
$673$	−22671.8	−1.29857	−0.649283	−	0.760547i	$-0.724931\pi$
$673$	−22671.8	−1.29857	−0.649283	+	0.760547i	$0.724931\pi$
$674$	18127.9	1.03599
$675$	−7605.04	−0.433656
$676$	−4964.64	−0.282467
$677$	15637.0	0.887709	0.443855	−	0.896099i	$-0.353611\pi$
$677$	15637.0	0.887709	0.443855	+	0.896099i	$0.353611\pi$
$678$	−7710.50	−0.436755
$679$	−139.180	−0.00786635
$680$	13605.4	0.767269
$681$	3286.70	0.184944
$682$	−8823.29	−0.495398
$683$	−4857.24	−0.272119	−0.136059	−	0.990701i	$-0.543444\pi$
$683$	−4857.24	−0.272119	−0.136059	+	0.990701i	$0.543444\pi$
$684$	5319.51	0.297364
$685$	−49868.4	−2.78157
$686$	−686.000	−0.0381802
$687$	14149.5	0.785787
$688$	6635.48	0.367696
$689$	−4183.58	−0.231323
$690$	2782.91	0.153541
$691$	−6622.05	−0.364565	−0.182283	−	0.983246i	$-0.558349\pi$
$691$	−6622.05	−0.364565	−0.182283	+	0.983246i	$0.558349\pi$
$692$	9218.78	0.506424
$693$	−3999.61	−0.219239
$694$	−10245.9	−0.560419
$695$	37724.1	2.05893
$696$	−2132.68	−0.116148
$697$	31247.8	1.69813
$698$	−16699.2	−0.905548
$699$	−14085.5	−0.762178
$700$	7886.71	0.425842
$701$	16371.5	0.882088	0.441044	−	0.897486i	$-0.354608\pi$
$701$	16371.5	0.882088	0.441044	+	0.897486i	$0.354608\pi$
$702$	−1669.50	−0.0897595
$703$	−28178.8	−1.51178
$704$	−4063.09	−0.217519
$705$	−756.392	−0.0404076
$706$	25556.9	1.36239
$707$	5053.01	0.268795
$708$	2230.41	0.118396
$709$	−18407.0	−0.975019	−0.487509	−	0.873118i	$-0.662094\pi$
$709$	−18407.0	−0.975019	−0.487509	+	0.873118i	$0.662094\pi$
$710$	16018.9	0.846729
$711$	3586.27	0.189164
$712$	−6965.75	−0.366647
$713$	1598.28	0.0839494
$714$	3542.01	0.185653
$715$	−39581.2	−2.07028
$716$	16603.8	0.866639
$717$	15917.1	0.829058
$718$	−20411.1	−1.06091
$719$	11243.2	0.583170	0.291585	−	0.956545i	$-0.405817\pi$
$719$	11243.2	0.583170	0.291585	+	0.956545i	$0.405817\pi$
$720$	−2903.91	−0.150309
$721$	−8029.61	−0.414755
$722$	−29950.5	−1.54383
$723$	6612.36	0.340133
$724$	−10149.9	−0.521017
$725$	−25029.5	−1.28217
$726$	16196.7	0.827983
$727$	14670.4	0.748409	0.374204	−	0.927346i	$-0.377916\pi$
$727$	14670.4	0.748409	0.374204	+	0.927346i	$0.377916\pi$
$728$	1731.33	0.0881421
$729$	729.000	0.0370370
$730$	−1174.56	−0.0595512
$731$	34974.6	1.76961
$732$	6957.23	0.351293
$733$	29916.8	1.50751	0.753754	−	0.657156i	$-0.228241\pi$
$733$	29916.8	1.50751	0.753754	+	0.657156i	$0.228241\pi$
$734$	8173.38	0.411015
$735$	2964.40	0.148767
$736$	736.000	0.0368605
$737$	−61817.8	−3.08967
$738$	−6669.46	−0.332664
$739$	12933.4	0.643793	0.321897	−	0.946775i	$-0.395680\pi$
$739$	12933.4	0.643793	0.321897	+	0.946775i	$0.395680\pi$
$740$	15382.7	0.764163
$741$	13705.1	0.679447
$742$	−1894.45	−0.0937298
$743$	33296.1	1.64403	0.822015	−	0.569466i	$-0.192850\pi$
$743$	33296.1	1.64403	0.822015	+	0.569466i	$0.192850\pi$
$744$	−1667.77	−0.0821818
$745$	65193.4	3.20604
$746$	−887.723	−0.0435682
$747$	−8830.16	−0.432502
$748$	−21416.0	−1.04685
$749$	−6733.75	−0.328499
$750$	−18956.2	−0.922911
$751$	−39801.9	−1.93394	−0.966972	−	0.254885i	$-0.917963\pi$
$751$	−39801.9	−1.93394	−0.966972	+	0.254885i	$0.917963\pi$
$752$	−200.044	−0.00970060
$753$	16738.8	0.810087
$754$	−5494.60	−0.265387
$755$	11277.4	0.543609
$756$	−756.000	−0.0363696
$757$	−3971.32	−0.190674	−0.0953369	−	0.995445i	$-0.530393\pi$
$757$	−3971.32	−0.190674	−0.0953369	+	0.995445i	$0.530393\pi$
$758$	−71.4078	−0.00342170
$759$	−4380.52	−0.209490
$760$	23838.5	1.13778
$761$	−13403.2	−0.638457	−0.319228	−	0.947678i	$-0.603424\pi$
$761$	−13403.2	−0.638457	−0.319228	+	0.947678i	$0.603424\pi$
$762$	−15615.3	−0.742367
$763$	6104.26	0.289632
$764$	−4019.80	−0.190355
$765$	−15306.1	−0.723388
$766$	−21943.4	−1.03505
$767$	5746.41	0.270522
$768$	−768.000	−0.0360844
$769$	6693.50	0.313880	0.156940	−	0.987608i	$-0.449837\pi$
$769$	6693.50	0.313880	0.156940	+	0.987608i	$0.449837\pi$
$770$	−17923.6	−0.838858
$771$	22215.1	1.03769
$772$	15075.8	0.702836
$773$	23471.5	1.09212	0.546062	−	0.837745i	$-0.316126\pi$
$773$	23471.5	1.09212	0.546062	+	0.837745i	$0.316126\pi$
$774$	−7464.91	−0.346667
$775$	−19573.2	−0.907212
$776$	159.063	0.00735830
$777$	4004.72	0.184902
$778$	−4943.64	−0.227812
$779$	54750.4	2.51815
$780$	−7481.59	−0.343441
$781$	−25215.0	−1.15527
$782$	3879.35	0.177398
$783$	2399.26	0.109505
$784$	784.000	0.0357143
$785$	38983.8	1.77247
$786$	−4247.81	−0.192767
$787$	−17609.8	−0.797613	−0.398806	−	0.917035i	$-0.630575\pi$
$787$	−17609.8	−0.797613	−0.398806	+	0.917035i	$0.630575\pi$
$788$	6807.15	0.307735
$789$	−13120.4	−0.592013
$790$	16071.3	0.723786
$791$	−8995.58	−0.404356
$792$	4570.98	0.205079
$793$	17924.5	0.802671
$794$	−14075.6	−0.629125
$795$	8186.47	0.365213
$796$	−14894.4	−0.663212
$797$	1460.74	0.0649212	0.0324606	−	0.999473i	$-0.489666\pi$
$797$	1460.74	0.0649212	0.0324606	+	0.999473i	$0.489666\pi$
$798$	6206.10	0.275305
$799$	−1054.40	−0.0466859
$800$	−9013.38	−0.398339
$801$	7836.47	0.345678
$802$	−19336.5	−0.851366
$803$	1848.85	0.0812509
$804$	−11684.7	−0.512548
$805$	3246.73	0.142152
$806$	−4296.81	−0.187778
$807$	33.5867	0.00146506
$808$	−5774.87	−0.251435
$809$	−4493.24	−0.195271	−0.0976353	−	0.995222i	$-0.531128\pi$
$809$	−4493.24	−0.195271	−0.0976353	+	0.995222i	$0.531128\pi$
$810$	3266.89	0.141712
$811$	−32207.3	−1.39451	−0.697256	−	0.716822i	$-0.745596\pi$
$811$	−32207.3	−1.39451	−0.697256	+	0.716822i	$0.745596\pi$
$812$	−2488.12	−0.107532
$813$	−6986.13	−0.301370
$814$	−24213.6	−1.04261
$815$	−947.367	−0.0407176
$816$	−4048.02	−0.173663
$817$	61280.4	2.62415
$818$	25746.4	1.10049
$819$	−1947.75	−0.0831012
$820$	−29888.1	−1.27285
$821$	−18336.7	−0.779482	−0.389741	−	0.920925i	$-0.627435\pi$
$821$	−18336.7	−0.779482	−0.389741	+	0.920925i	$0.627435\pi$
$822$	14837.4	0.629577
$823$	3524.71	0.149288	0.0746438	−	0.997210i	$-0.476218\pi$
$823$	3524.71	0.149288	0.0746438	+	0.997210i	$0.476218\pi$
$824$	9176.69	0.387968
$825$	53645.8	2.26389
$826$	2602.15	0.109613
$827$	−5119.25	−0.215253	−0.107626	−	0.994191i	$-0.534325\pi$
$827$	−5119.25	−0.215253	−0.107626	+	0.994191i	$0.534325\pi$
$828$	−828.000	−0.0347524
$829$	−40403.2	−1.69272	−0.846358	−	0.532615i	$-0.821210\pi$
$829$	−40403.2	−1.69272	−0.846358	+	0.532615i	$0.821210\pi$
$830$	−39570.9	−1.65485
$831$	16763.1	0.699768
$832$	−1978.67	−0.0824494
$833$	4132.35	0.171882
$834$	−11224.1	−0.466016
$835$	21910.8	0.908091
$836$	−37523.7	−1.55237
$837$	1876.24	0.0774818
$838$	9205.72	0.379483
$839$	21536.5	0.886202	0.443101	−	0.896472i	$-0.353878\pi$
$839$	21536.5	0.886202	0.443101	+	0.896472i	$0.353878\pi$
$840$	−3387.89	−0.139159
$841$	−16492.6	−0.676232
$842$	4549.79	0.186219
$843$	−4863.80	−0.198717
$844$	10389.0	0.423703
$845$	25029.3	1.01897
$846$	225.049	0.00914581
$847$	18896.1	0.766563
$848$	2165.09	0.0876762
$849$	−25484.1	−1.03017
$850$	−47508.2	−1.91708
$851$	4386.13	0.176680
$852$	−4766.10	−0.191648
$853$	−44892.0	−1.80196	−0.900981	−	0.433858i	$-0.857152\pi$
$853$	−44892.0	−1.80196	−0.900981	+	0.433858i	$0.857152\pi$
$854$	8116.76	0.325234
$855$	−26818.3	−1.07271
$856$	7695.71	0.307283
$857$	−32327.5	−1.28855	−0.644273	−	0.764795i	$-0.722840\pi$
$857$	−32327.5	−1.28855	−0.644273	+	0.764795i	$0.722840\pi$
$858$	11776.6	0.468586
$859$	−24691.2	−0.980737	−0.490369	−	0.871515i	$-0.663138\pi$
$859$	−24691.2	−0.980737	−0.490369	+	0.871515i	$0.663138\pi$
$860$	−33452.8	−1.32643
$861$	−7781.03	−0.307987
$862$	−21324.6	−0.842598
$863$	−45597.2	−1.79855	−0.899274	−	0.437385i	$-0.855905\pi$
$863$	−45597.2	−1.79855	−0.899274	+	0.437385i	$0.855905\pi$
$864$	864.000	0.0340207
$865$	−46476.5	−1.82688
$866$	−16525.4	−0.648448
$867$	−6597.50	−0.258435
$868$	−1945.73	−0.0760856
$869$	−25297.5	−0.987525
$870$	10751.9	0.418992
$871$	−30104.4	−1.17112
$872$	−6976.29	−0.270926
$873$	−178.946	−0.00693747
$874$	6797.16	0.263063
$875$	−22115.6	−0.854450
$876$	349.467	0.0134788
$877$	−45955.5	−1.76945	−0.884725	−	0.466113i	$-0.845654\pi$
$877$	−45955.5	−1.76945	−0.884725	+	0.466113i	$0.845654\pi$
$878$	29617.3	1.13842
$879$	11380.0	0.436677
$880$	20484.1	0.784680
$881$	4234.06	0.161917	0.0809586	−	0.996717i	$-0.474202\pi$
$881$	4234.06	0.161917	0.0809586	+	0.996717i	$0.474202\pi$
$882$	−882.000	−0.0336718
$883$	−23061.9	−0.878928	−0.439464	−	0.898260i	$-0.644832\pi$
$883$	−23061.9	−0.878928	−0.439464	+	0.898260i	$0.644832\pi$
$884$	−10429.3	−0.396803
$885$	−11244.6	−0.427101
$886$	34975.1	1.32620
$887$	−22572.6	−0.854469	−0.427235	−	0.904141i	$-0.640512\pi$
$887$	−22572.6	−0.854469	−0.427235	+	0.904141i	$0.640512\pi$
$888$	−4576.83	−0.172960
$889$	−18217.9	−0.687298
$890$	35117.9	1.32264
$891$	−5142.35	−0.193350
$892$	−243.225	−0.00912977
$893$	−1847.46	−0.0692305
$894$	−19397.0	−0.725652
$895$	−83708.2	−3.12632
$896$	−896.000	−0.0334077
$897$	−2133.25	−0.0794059
$898$	27758.4	1.03153
$899$	6175.01	0.229086
$900$	10140.1	0.375557
$901$	11411.9	0.421958
$902$	47046.2	1.73666
$903$	−8709.06	−0.320952
$904$	10280.7	0.378241
$905$	51170.5	1.87952
$906$	−3355.35	−0.123040
$907$	39552.4	1.44798	0.723988	−	0.689812i	$-0.242307\pi$
$907$	39552.4	1.44798	0.723988	+	0.689812i	$0.242307\pi$
$908$	−4382.27	−0.160166
$909$	6496.73	0.237055
$910$	−8728.52	−0.317964
$911$	−6762.38	−0.245936	−0.122968	−	0.992411i	$-0.539241\pi$
$911$	−6762.38	−0.245936	−0.122968	+	0.992411i	$0.539241\pi$
$912$	−7092.68	−0.257524
$913$	62287.8	2.25786
$914$	−9681.18	−0.350355
$915$	−35074.9	−1.26726
$916$	−18865.9	−0.680511
$917$	−4955.78	−0.178467
$918$	4554.02	0.163731
$919$	39591.2	1.42110	0.710551	−	0.703646i	$-0.248446\pi$
$919$	39591.2	1.42110	0.710551	+	0.703646i	$0.248446\pi$
$920$	−3710.55	−0.132971
$921$	−12748.9	−0.456123
$922$	−4564.62	−0.163045
$923$	−12279.3	−0.437897
$924$	5332.81	0.189866
$925$	−53714.4	−1.90932
$926$	−31525.0	−1.11877
$927$	−10323.8	−0.365779
$928$	2843.57	0.100587
$929$	−7336.85	−0.259111	−0.129556	−	0.991572i	$-0.541355\pi$
$929$	−7336.85	−0.259111	−0.129556	+	0.991572i	$0.541355\pi$
$930$	8408.05	0.296463
$931$	7240.45	0.254883
$932$	18780.7	0.660065
$933$	1528.98	0.0536510
$934$	26360.7	0.923501
$935$	107969.	3.77642
$936$	2226.00	0.0777340
$937$	−22032.3	−0.768159	−0.384079	−	0.923300i	$-0.625481\pi$
$937$	−22032.3	−0.768159	−0.384079	+	0.923300i	$0.625481\pi$
$938$	−13632.2	−0.474527
$939$	−24217.8	−0.841658
$940$	1008.52	0.0349940
$941$	1710.12	0.0592436	0.0296218	−	0.999561i	$-0.490570\pi$
$941$	1710.12	0.0592436	0.0296218	+	0.999561i	$0.490570\pi$
$942$	−11598.9	−0.401180
$943$	−8522.08	−0.294292
$944$	−2973.88	−0.102534
$945$	3811.38	0.131200
$946$	52657.3	1.80976
$947$	−37346.4	−1.28152	−0.640758	−	0.767743i	$-0.721380\pi$
$947$	−37346.4	−1.28152	−0.640758	+	0.767743i	$0.721380\pi$
$948$	−4781.70	−0.163821
$949$	900.363	0.0307977
$950$	−83241.0	−2.84283
$951$	−3961.13	−0.135067
$952$	−4722.69	−0.160781
$953$	34960.2	1.18832	0.594161	−	0.804346i	$-0.297484\pi$
$953$	34960.2	1.18832	0.594161	+	0.804346i	$0.297484\pi$
$954$	−2435.72	−0.0826619
$955$	20265.8	0.686687
$956$	−21222.8	−0.717986
$957$	−16924.3	−0.571668
$958$	−27783.7	−0.937005
$959$	17310.3	0.582875
$960$	3871.87	0.130171
$961$	−24962.1	−0.837908
$962$	−11791.7	−0.395197
$963$	−8657.68	−0.289709
$964$	−8816.48	−0.294564
$965$	−76004.6	−2.53542
$966$	−966.000	−0.0321745
$967$	2230.28	0.0741685	0.0370843	−	0.999312i	$-0.488193\pi$
$967$	2230.28	0.0741685	0.0370843	+	0.999312i	$0.488193\pi$
$968$	−21595.6	−0.717054
$969$	−37384.5	−1.23938
$970$	−801.918	−0.0265444
$971$	−9139.22	−0.302051	−0.151026	−	0.988530i	$-0.548258\pi$
$971$	−9139.22	−0.302051	−0.151026	+	0.988530i	$0.548258\pi$
$972$	−972.000	−0.0320750
$973$	−13094.7	−0.431447
$974$	−23221.1	−0.763914
$975$	26124.7	0.858113
$976$	−9276.30	−0.304229
$977$	10162.7	0.332788	0.166394	−	0.986059i	$-0.446788\pi$
$977$	10162.7	0.332788	0.166394	+	0.986059i	$0.446788\pi$
$978$	281.870	0.00921597
$979$	−55278.3	−1.80460
$980$	−3952.54	−0.128836
$981$	7848.33	0.255431
$982$	9855.15	0.320255
$983$	340.359	0.0110435	0.00552176	−	0.999985i	$-0.498242\pi$
$983$	340.359	0.0110435	0.00552176	+	0.999985i	$0.498242\pi$
$984$	8892.61	0.288096
$985$	−34318.3	−1.11012
$986$	14988.0	0.484093
$987$	262.558	0.00846738
$988$	−18273.5	−0.588419
$989$	−9538.50	−0.306680
$990$	−23044.6	−0.739804
$991$	−25091.3	−0.804290	−0.402145	−	0.915576i	$-0.631735\pi$
$991$	−25091.3	−0.804290	−0.402145	+	0.915576i	$0.631735\pi$
$992$	2223.69	0.0711715
$993$	−17181.6	−0.549084
$994$	−5560.45	−0.177431
$995$	75090.0	2.39248
$996$	11773.5	0.374557
$997$	43443.7	1.38001	0.690007	−	0.723802i	$-0.257607\pi$
$997$	43443.7	1.38001	0.690007	+	0.723802i	$0.257607\pi$
$998$	7470.43	0.236946
$999$	5148.93	0.163068

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.4.a.l.1.1	✓	5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -20.1660 q^{5} +6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -20.1660 q^{5} +6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +40.3320 q^{10} -63.4858 q^{11} -12.0000 q^{12} -30.9167 q^{13} -14.0000 q^{14} +60.4980 q^{15} +16.0000 q^{16} +84.3337 q^{17} -18.0000 q^{18} +147.764 q^{19} -80.6641 q^{20} -21.0000 q^{21} +126.972 q^{22} -23.0000 q^{23} +24.0000 q^{24} +281.668 q^{25} +61.8333 q^{26} -27.0000 q^{27} +28.0000 q^{28} -88.8615 q^{29} -120.996 q^{30} -69.4903 q^{31} -32.0000 q^{32} +190.457 q^{33} -168.667 q^{34} -141.162 q^{35} +36.0000 q^{36} -190.701 q^{37} -295.529 q^{38} +92.7500 q^{39} +161.328 q^{40} +370.525 q^{41} +42.0000 q^{42} +414.717 q^{43} -253.943 q^{44} -181.494 q^{45} +46.0000 q^{46} -12.5027 q^{47} -48.0000 q^{48} +49.0000 q^{49} -563.336 q^{50} -253.001 q^{51} -123.667 q^{52} +135.318 q^{53} +54.0000 q^{54} +1280.26 q^{55} -56.0000 q^{56} -443.293 q^{57} +177.723 q^{58} -185.868 q^{59} +241.992 q^{60} -579.769 q^{61} +138.981 q^{62} +63.0000 q^{63} +64.0000 q^{64} +623.466 q^{65} -380.915 q^{66} +973.727 q^{67} +337.335 q^{68} +69.0000 q^{69} +282.324 q^{70} +397.175 q^{71} -72.0000 q^{72} -29.1223 q^{73} +381.402 q^{74} -845.004 q^{75} +591.057 q^{76} -444.401 q^{77} -185.500 q^{78} +398.475 q^{79} -322.656 q^{80} +81.0000 q^{81} -741.051 q^{82} -981.129 q^{83} -84.0000 q^{84} -1700.67 q^{85} -829.434 q^{86} +266.585 q^{87} +507.886 q^{88} +870.719 q^{89} +362.988 q^{90} -216.417 q^{91} -92.0000 q^{92} +208.471 q^{93} +25.0055 q^{94} -2979.82 q^{95} +96.0000 q^{96} -19.8829 q^{97} -98.0000 q^{98} -571.372 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 10 q^{2} - 15 q^{3} + 20 q^{4} - 15 q^{5} + 30 q^{6} + 35 q^{7} - 40 q^{8} + 45 q^{9}+O(q^{10}) \) 5 * q - 10 * q^2 - 15 * q^3 + 20 * q^4 - 15 * q^5 + 30 * q^6 + 35 * q^7 - 40 * q^8 + 45 * q^9	\( 5 q - 10 q^{2} - 15 q^{3} + 20 q^{4} - 15 q^{5} + 30 q^{6} + 35 q^{7} - 40 q^{8} + 45 q^{9} + 30 q^{10} - 19 q^{11} - 60 q^{12} - 19 q^{13} - 70 q^{14} + 45 q^{15} + 80 q^{16} - 42 q^{17} - 90 q^{18} - 25 q^{19} - 60 q^{20} - 105 q^{21} + 38 q^{22} - 115 q^{23} + 120 q^{24} + 206 q^{25} + 38 q^{26} - 135 q^{27} + 140 q^{28} - 292 q^{29} - 90 q^{30} - 60 q^{31} - 160 q^{32} + 57 q^{33} + 84 q^{34} - 105 q^{35} + 180 q^{36} + 264 q^{37} + 50 q^{38} + 57 q^{39} + 120 q^{40} + 223 q^{41} + 210 q^{42} + 661 q^{43} - 76 q^{44} - 135 q^{45} + 230 q^{46} - 279 q^{47} - 240 q^{48} + 245 q^{49} - 412 q^{50} + 126 q^{51} - 76 q^{52} - 324 q^{53} + 270 q^{54} + 1077 q^{55} - 280 q^{56} + 75 q^{57} + 584 q^{58} + 26 q^{59} + 180 q^{60} - 460 q^{61} + 120 q^{62} + 315 q^{63} + 320 q^{64} + 528 q^{65} - 114 q^{66} + 1541 q^{67} - 168 q^{68} + 345 q^{69} + 210 q^{70} - 319 q^{71} - 360 q^{72} + 1532 q^{73} - 528 q^{74} - 618 q^{75} - 100 q^{76} - 133 q^{77} - 114 q^{78} + 1242 q^{79} - 240 q^{80} + 405 q^{81} - 446 q^{82} - 1390 q^{83} - 420 q^{84} - 39 q^{85} - 1322 q^{86} + 876 q^{87} + 152 q^{88} - 1171 q^{89} + 270 q^{90} - 133 q^{91} - 460 q^{92} + 180 q^{93} + 558 q^{94} - 3435 q^{95} + 480 q^{96} - 1800 q^{97} - 490 q^{98} - 171 q^{99}+O(q^{100}) \) 5 * q - 10 * q^2 - 15 * q^3 + 20 * q^4 - 15 * q^5 + 30 * q^6 + 35 * q^7 - 40 * q^8 + 45 * q^9 + 30 * q^10 - 19 * q^11 - 60 * q^12 - 19 * q^13 - 70 * q^14 + 45 * q^15 + 80 * q^16 - 42 * q^17 - 90 * q^18 - 25 * q^19 - 60 * q^20 - 105 * q^21 + 38 * q^22 - 115 * q^23 + 120 * q^24 + 206 * q^25 + 38 * q^26 - 135 * q^27 + 140 * q^28 - 292 * q^29 - 90 * q^30 - 60 * q^31 - 160 * q^32 + 57 * q^33 + 84 * q^34 - 105 * q^35 + 180 * q^36 + 264 * q^37 + 50 * q^38 + 57 * q^39 + 120 * q^40 + 223 * q^41 + 210 * q^42 + 661 * q^43 - 76 * q^44 - 135 * q^45 + 230 * q^46 - 279 * q^47 - 240 * q^48 + 245 * q^49 - 412 * q^50 + 126 * q^51 - 76 * q^52 - 324 * q^53 + 270 * q^54 + 1077 * q^55 - 280 * q^56 + 75 * q^57 + 584 * q^58 + 26 * q^59 + 180 * q^60 - 460 * q^61 + 120 * q^62 + 315 * q^63 + 320 * q^64 + 528 * q^65 - 114 * q^66 + 1541 * q^67 - 168 * q^68 + 345 * q^69 + 210 * q^70 - 319 * q^71 - 360 * q^72 + 1532 * q^73 - 528 * q^74 - 618 * q^75 - 100 * q^76 - 133 * q^77 - 114 * q^78 + 1242 * q^79 - 240 * q^80 + 405 * q^81 - 446 * q^82 - 1390 * q^83 - 420 * q^84 - 39 * q^85 - 1322 * q^86 + 876 * q^87 + 152 * q^88 - 1171 * q^89 + 270 * q^90 - 133 * q^91 - 460 * q^92 + 180 * q^93 + 558 * q^94 - 3435 * q^95 + 480 * q^96 - 1800 * q^97 - 490 * q^98 - 171 * q^99

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