LMFDB - Embedded newform 966.4.a.m.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("966.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$56.9958450655$
Analytic rank:	$0$
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} - x^{4} - 351x^{3} - 663x^{2} + 18451x - 19243 $ x^5 - x^4 - 351x^3 - 663x^2 + 18451*x - 19243
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$18.8692$ 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)

$f(q)$	$=$	$q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +10.1443 q^{5} +6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +10.1443 q^{5} +6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} -20.2887 q^{10} -47.7648 q^{11} -12.0000 q^{12} -77.2742 q^{13} +14.0000 q^{14} -30.4330 q^{15} +16.0000 q^{16} -26.2302 q^{17} -18.0000 q^{18} +54.9670 q^{19} +40.5774 q^{20} +21.0000 q^{21} +95.5296 q^{22} -23.0000 q^{23} +24.0000 q^{24} -22.0923 q^{25} +154.548 q^{26} -27.0000 q^{27} -28.0000 q^{28} -52.9111 q^{29} +60.8660 q^{30} -97.0969 q^{31} -32.0000 q^{32} +143.294 q^{33} +52.4605 q^{34} -71.0104 q^{35} +36.0000 q^{36} +295.495 q^{37} -109.934 q^{38} +231.823 q^{39} -81.1547 q^{40} +365.501 q^{41} -42.0000 q^{42} +392.207 q^{43} -191.059 q^{44} +91.2991 q^{45} +46.0000 q^{46} +79.9862 q^{47} -48.0000 q^{48} +49.0000 q^{49} +44.1847 q^{50} +78.6907 q^{51} -309.097 q^{52} -146.138 q^{53} +54.0000 q^{54} -484.542 q^{55} +56.0000 q^{56} -164.901 q^{57} +105.822 q^{58} -19.0284 q^{59} -121.732 q^{60} +89.2284 q^{61} +194.194 q^{62} -63.0000 q^{63} +64.0000 q^{64} -783.896 q^{65} -286.589 q^{66} -1020.99 q^{67} -104.921 q^{68} +69.0000 q^{69} +142.021 q^{70} -121.668 q^{71} -72.0000 q^{72} -749.764 q^{73} -590.991 q^{74} +66.2770 q^{75} +219.868 q^{76} +334.354 q^{77} -463.645 q^{78} +548.871 q^{79} +162.309 q^{80} +81.0000 q^{81} -731.003 q^{82} +73.0846 q^{83} +84.0000 q^{84} -266.088 q^{85} -784.414 q^{86} +158.733 q^{87} +382.118 q^{88} +1089.25 q^{89} -182.598 q^{90} +540.919 q^{91} -92.0000 q^{92} +291.291 q^{93} -159.972 q^{94} +557.604 q^{95} +96.0000 q^{96} +724.274 q^{97} -98.0000 q^{98} -429.883 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 10 q^{2} - 15 q^{3} + 20 q^{4} + 10 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 + 10 * q^5 + 30 * q^6 - 35 * q^7 - 40 * q^8 + 45 * q^9	\( 5 q - 10 q^{2} - 15 q^{3} + 20 q^{4} + 10 q^{5} + 30 q^{6} - 35 q^{7} - 40 q^{8} + 45 q^{9} - 20 q^{10} + 4 q^{11} - 60 q^{12} + 24 q^{13} + 70 q^{14} - 30 q^{15} + 80 q^{16} + 28 q^{17} - 90 q^{18} - 160 q^{19} + 40 q^{20} + 105 q^{21} - 8 q^{22} - 115 q^{23} + 120 q^{24} + 219 q^{25} - 48 q^{26} - 135 q^{27} - 140 q^{28} + 79 q^{29} + 60 q^{30} - 162 q^{31} - 160 q^{32} - 12 q^{33} - 56 q^{34} - 70 q^{35} + 180 q^{36} + 301 q^{37} + 320 q^{38} - 72 q^{39} - 80 q^{40} + 251 q^{41} - 210 q^{42} - 380 q^{43} + 16 q^{44} + 90 q^{45} + 230 q^{46} - 505 q^{47} - 240 q^{48} + 245 q^{49} - 438 q^{50} - 84 q^{51} + 96 q^{52} + 93 q^{53} + 270 q^{54} - 503 q^{55} + 280 q^{56} + 480 q^{57} - 158 q^{58} + 637 q^{59} - 120 q^{60} - 679 q^{61} + 324 q^{62} - 315 q^{63} + 320 q^{64} + 961 q^{65} + 24 q^{66} - 1483 q^{67} + 112 q^{68} + 345 q^{69} + 140 q^{70} + 95 q^{71} - 360 q^{72} - 1310 q^{73} - 602 q^{74} - 657 q^{75} - 640 q^{76} - 28 q^{77} + 144 q^{78} + 494 q^{79} + 160 q^{80} + 405 q^{81} - 502 q^{82} - 482 q^{83} + 420 q^{84} - 291 q^{85} + 760 q^{86} - 237 q^{87} - 32 q^{88} + 661 q^{89} - 180 q^{90} - 168 q^{91} - 460 q^{92} + 486 q^{93} + 1010 q^{94} - 629 q^{95} + 480 q^{96} - 1905 q^{97} - 490 q^{98} + 36 q^{99}+O(q^{100}) \) 5 * q - 10 * q^2 - 15 * q^3 + 20 * q^4 + 10 * q^5 + 30 * q^6 - 35 * q^7 - 40 * q^8 + 45 * q^9 - 20 * q^10 + 4 * q^11 - 60 * q^12 + 24 * q^13 + 70 * q^14 - 30 * q^15 + 80 * q^16 + 28 * q^17 - 90 * q^18 - 160 * q^19 + 40 * q^20 + 105 * q^21 - 8 * q^22 - 115 * q^23 + 120 * q^24 + 219 * q^25 - 48 * q^26 - 135 * q^27 - 140 * q^28 + 79 * q^29 + 60 * q^30 - 162 * q^31 - 160 * q^32 - 12 * q^33 - 56 * q^34 - 70 * q^35 + 180 * q^36 + 301 * q^37 + 320 * q^38 - 72 * q^39 - 80 * q^40 + 251 * q^41 - 210 * q^42 - 380 * q^43 + 16 * q^44 + 90 * q^45 + 230 * q^46 - 505 * q^47 - 240 * q^48 + 245 * q^49 - 438 * q^50 - 84 * q^51 + 96 * q^52 + 93 * q^53 + 270 * q^54 - 503 * q^55 + 280 * q^56 + 480 * q^57 - 158 * q^58 + 637 * q^59 - 120 * q^60 - 679 * q^61 + 324 * q^62 - 315 * q^63 + 320 * q^64 + 961 * q^65 + 24 * q^66 - 1483 * q^67 + 112 * q^68 + 345 * q^69 + 140 * q^70 + 95 * q^71 - 360 * q^72 - 1310 * q^73 - 602 * q^74 - 657 * q^75 - 640 * q^76 - 28 * q^77 + 144 * q^78 + 494 * q^79 + 160 * q^80 + 405 * q^81 - 502 * q^82 - 482 * q^83 + 420 * q^84 - 291 * q^85 + 760 * q^86 - 237 * q^87 - 32 * q^88 + 661 * q^89 - 180 * q^90 - 168 * q^91 - 460 * q^92 + 486 * q^93 + 1010 * q^94 - 629 * q^95 + 480 * q^96 - 1905 * q^97 - 490 * q^98 + 36 * 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
$5$	10.1443	0.907337	0.453669	−	0.891170i	$-0.350115\pi$
$5$	10.1443	0.907337	0.453669	+	0.891170i	$0.350115\pi$
$6$	6.00000	0.408248
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	−20.2887	−0.641584
$11$	−47.7648	−1.30924	−0.654619	−	0.755959i	$-0.727171\pi$
$11$	−47.7648	−1.30924	−0.654619	+	0.755959i	$0.727171\pi$
$12$	−12.0000	−0.288675
$13$	−77.2742	−1.64862	−0.824308	−	0.566142i	$-0.808435\pi$
$13$	−77.2742	−1.64862	−0.824308	+	0.566142i	$0.808435\pi$
$14$	14.0000	0.267261
$15$	−30.4330	−0.523852
$16$	16.0000	0.250000
$17$	−26.2302	−0.374222	−0.187111	−	0.982339i	$-0.559912\pi$
$17$	−26.2302	−0.374222	−0.187111	+	0.982339i	$0.559912\pi$
$18$	−18.0000	−0.235702
$19$	54.9670	0.663700	0.331850	−	0.943332i	$-0.392327\pi$
$19$	54.9670	0.663700	0.331850	+	0.943332i	$0.392327\pi$
$20$	40.5774	0.453669
$21$	21.0000	0.218218
$22$	95.5296	0.925772
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	24.0000	0.204124
$25$	−22.0923	−0.176739
$26$	154.548	1.16575
$27$	−27.0000	−0.192450
$28$	−28.0000	−0.188982
$29$	−52.9111	−0.338805	−0.169402	−	0.985547i	$-0.554184\pi$
$29$	−52.9111	−0.338805	−0.169402	+	0.985547i	$0.554184\pi$
$30$	60.8660	0.370419
$31$	−97.0969	−0.562552	−0.281276	−	0.959627i	$-0.590758\pi$
$31$	−97.0969	−0.562552	−0.281276	+	0.959627i	$0.590758\pi$
$32$	−32.0000	−0.176777
$33$	143.294	0.755889
$34$	52.4605	0.264615
$35$	−71.0104	−0.342941
$36$	36.0000	0.166667
$37$	295.495	1.31295	0.656475	−	0.754348i	$-0.272047\pi$
$37$	295.495	1.31295	0.656475	+	0.754348i	$0.272047\pi$
$38$	−109.934	−0.469307
$39$	231.823	0.951829
$40$	−81.1547	−0.320792
$41$	365.501	1.39224	0.696119	−	0.717927i	$-0.254909\pi$
$41$	365.501	1.39224	0.696119	+	0.717927i	$0.254909\pi$
$42$	−42.0000	−0.154303
$43$	392.207	1.39095	0.695477	−	0.718548i	$-0.255193\pi$
$43$	392.207	1.39095	0.695477	+	0.718548i	$0.255193\pi$
$44$	−191.059	−0.654619
$45$	91.2991	0.302446
$46$	46.0000	0.147442
$47$	79.9862	0.248238	0.124119	−	0.992267i	$-0.460390\pi$
$47$	79.9862	0.248238	0.124119	+	0.992267i	$0.460390\pi$
$48$	−48.0000	−0.144338
$49$	49.0000	0.142857
$50$	44.1847	0.124973
$51$	78.6907	0.216057
$52$	−309.097	−0.824308
$53$	−146.138	−0.378747	−0.189373	−	0.981905i	$-0.560646\pi$
$53$	−146.138	−0.378747	−0.189373	+	0.981905i	$0.560646\pi$
$54$	54.0000	0.136083
$55$	−484.542	−1.18792
$56$	56.0000	0.133631
$57$	−164.901	−0.383188
$58$	105.822	0.239571
$59$	−19.0284	−0.0419879	−0.0209939	−	0.999780i	$-0.506683\pi$
$59$	−19.0284	−0.0419879	−0.0209939	+	0.999780i	$0.506683\pi$
$60$	−121.732	−0.261926
$61$	89.2284	0.187287	0.0936436	−	0.995606i	$-0.470149\pi$
$61$	89.2284	0.187287	0.0936436	+	0.995606i	$0.470149\pi$
$62$	194.194	0.397784
$63$	−63.0000	−0.125988
$64$	64.0000	0.125000
$65$	−783.896	−1.49585
$66$	−286.589	−0.534495
$67$	−1020.99	−1.86169	−0.930845	−	0.365415i	$-0.880927\pi$
$67$	−1020.99	−1.86169	−0.930845	+	0.365415i	$0.880927\pi$
$68$	−104.921	−0.187111
$69$	69.0000	0.120386
$70$	142.021	0.242496
$71$	−121.668	−0.203370	−0.101685	−	0.994817i	$-0.532423\pi$
$71$	−121.668	−0.203370	−0.101685	+	0.994817i	$0.532423\pi$
$72$	−72.0000	−0.117851
$73$	−749.764	−1.20210	−0.601049	−	0.799212i	$-0.705250\pi$
$73$	−749.764	−1.20210	−0.601049	+	0.799212i	$0.705250\pi$
$74$	−590.991	−0.928395
$75$	66.2770	0.102040
$76$	219.868	0.331850
$77$	334.354	0.494846
$78$	−463.645	−0.673045
$79$	548.871	0.781681	0.390840	−	0.920459i	$-0.372184\pi$
$79$	548.871	0.781681	0.390840	+	0.920459i	$0.372184\pi$
$80$	162.309	0.226834
$81$	81.0000	0.111111
$82$	−731.003	−0.984461
$83$	73.0846	0.0966516	0.0483258	−	0.998832i	$-0.484611\pi$
$83$	73.0846	0.0966516	0.0483258	+	0.998832i	$0.484611\pi$
$84$	84.0000	0.109109
$85$	−266.088	−0.339545
$86$	−784.414	−0.983553
$87$	158.733	0.195609
$88$	382.118	0.462886
$89$	1089.25	1.29731	0.648655	−	0.761082i	$-0.275332\pi$
$89$	1089.25	1.29731	0.648655	+	0.761082i	$0.275332\pi$
$90$	−182.598	−0.213861
$91$	540.919	0.623118
$92$	−92.0000	−0.104257
$93$	291.291	0.324790
$94$	−159.972	−0.175531
$95$	557.604	0.602200
$96$	96.0000	0.102062
$97$	724.274	0.758132	0.379066	−	0.925370i	$-0.376245\pi$
$97$	724.274	0.758132	0.379066	+	0.925370i	$0.376245\pi$
$98$	−98.0000	−0.101015
$99$	−429.883	−0.436413
$100$	−88.3694	−0.0883694
$101$	−159.521	−0.157158	−0.0785788	−	0.996908i	$-0.525038\pi$
$101$	−159.521	−0.157158	−0.0785788	+	0.996908i	$0.525038\pi$
$102$	−157.381	−0.152775
$103$	−184.341	−0.176347	−0.0881733	−	0.996105i	$-0.528103\pi$
$103$	−184.341	−0.176347	−0.0881733	+	0.996105i	$0.528103\pi$
$104$	618.194	0.582874
$105$	213.031	0.197997
$106$	292.276	0.267814
$107$	488.616	0.441461	0.220730	−	0.975335i	$-0.429156\pi$
$107$	488.616	0.441461	0.220730	+	0.975335i	$0.429156\pi$
$108$	−108.000	−0.0962250
$109$	786.623	0.691237	0.345618	−	0.938375i	$-0.387669\pi$
$109$	786.623	0.691237	0.345618	+	0.938375i	$0.387669\pi$
$110$	969.085	0.839987
$111$	−886.486	−0.758032
$112$	−112.000	−0.0944911
$113$	986.714	0.821436	0.410718	−	0.911762i	$-0.365278\pi$
$113$	986.714	0.821436	0.410718	+	0.911762i	$0.365278\pi$
$114$	329.802	0.270955
$115$	−233.320	−0.189193
$116$	−211.644	−0.169402
$117$	−695.468	−0.549539
$118$	38.0568	0.0296899
$119$	183.612	0.141442
$120$	243.464	0.185209
$121$	950.476	0.714107
$122$	−178.457	−0.132432
$123$	−1096.50	−0.803809
$124$	−388.387	−0.281276
$125$	−1492.15	−1.06770
$126$	126.000	0.0890871
$127$	653.081	0.456311	0.228156	−	0.973625i	$-0.426731\pi$
$127$	653.081	0.456311	0.228156	+	0.973625i	$0.426731\pi$
$128$	−128.000	−0.0883883
$129$	−1176.62	−0.803068
$130$	1567.79	1.05773
$131$	1747.44	1.16545	0.582727	−	0.812668i	$-0.301986\pi$
$131$	1747.44	1.16545	0.582727	+	0.812668i	$0.301986\pi$
$132$	573.178	0.377945
$133$	−384.769	−0.250855
$134$	2041.97	1.31641
$135$	−273.897	−0.174617
$136$	209.842	0.132307
$137$	1512.55	0.943251	0.471626	−	0.881799i	$-0.343667\pi$
$137$	1512.55	0.943251	0.471626	+	0.881799i	$0.343667\pi$
$138$	−138.000	−0.0851257
$139$	−581.410	−0.354781	−0.177390	−	0.984141i	$-0.556766\pi$
$139$	−581.410	−0.354781	−0.177390	+	0.984141i	$0.556766\pi$
$140$	−284.042	−0.171471
$141$	−239.958	−0.143320
$142$	243.335	0.143804
$143$	3690.99	2.15843
$144$	144.000	0.0833333
$145$	−536.748	−0.307410
$146$	1499.53	0.850012
$147$	−147.000	−0.0824786
$148$	1181.98	0.656475
$149$	2846.52	1.56508	0.782538	−	0.622603i	$-0.213925\pi$
$149$	2846.52	1.56508	0.782538	+	0.622603i	$0.213925\pi$
$150$	−132.554	−0.0721533
$151$	−2712.86	−1.46205	−0.731025	−	0.682351i	$-0.760958\pi$
$151$	−2712.86	−1.46205	−0.731025	+	0.682351i	$0.760958\pi$
$152$	−439.736	−0.234653
$153$	−236.072	−0.124741
$154$	−668.707	−0.349909
$155$	−984.984	−0.510424
$156$	927.290	0.475914
$157$	2744.44	1.39510	0.697549	−	0.716537i	$-0.254274\pi$
$157$	2744.44	1.39510	0.697549	+	0.716537i	$0.254274\pi$
$158$	−1097.74	−0.552732
$159$	438.413	0.218669
$160$	−324.619	−0.160396
$161$	161.000	0.0788110
$162$	−162.000	−0.0785674
$163$	−2844.94	−1.36707	−0.683536	−	0.729917i	$-0.739559\pi$
$163$	−2844.94	−1.36707	−0.683536	+	0.729917i	$0.739559\pi$
$164$	1462.01	0.696119
$165$	1453.63	0.685847
$166$	−146.169	−0.0683430
$167$	−495.312	−0.229511	−0.114756	−	0.993394i	$-0.536609\pi$
$167$	−495.312	−0.229511	−0.114756	+	0.993394i	$0.536609\pi$
$168$	−168.000	−0.0771517
$169$	3774.30	1.71793
$170$	532.177	0.240095
$171$	494.703	0.221233
$172$	1568.83	0.695477
$173$	3565.79	1.56706	0.783532	−	0.621351i	$-0.213416\pi$
$173$	3565.79	1.56706	0.783532	+	0.621351i	$0.213416\pi$
$174$	−317.467	−0.138317
$175$	154.646	0.0668010
$176$	−764.237	−0.327310
$177$	57.0852	0.0242417
$178$	−2178.51	−0.917337
$179$	−490.581	−0.204848	−0.102424	−	0.994741i	$-0.532660\pi$
$179$	−490.581	−0.204848	−0.102424	+	0.994741i	$0.532660\pi$
$180$	365.196	0.151223
$181$	235.990	0.0969115	0.0484558	−	0.998825i	$-0.484570\pi$
$181$	235.990	0.0969115	0.0484558	+	0.998825i	$0.484570\pi$
$182$	−1081.84	−0.440611
$183$	−267.685	−0.108130
$184$	184.000	0.0737210
$185$	2997.60	1.19129
$186$	−582.581	−0.229661
$187$	1252.88	0.489946
$188$	319.945	0.124119
$189$	189.000	0.0727393
$190$	−1115.21	−0.425820
$191$	306.490	0.116109	0.0580546	−	0.998313i	$-0.481510\pi$
$191$	306.490	0.116109	0.0580546	+	0.998313i	$0.481510\pi$
$192$	−192.000	−0.0721688
$193$	−1142.78	−0.426213	−0.213106	−	0.977029i	$-0.568358\pi$
$193$	−1142.78	−0.426213	−0.213106	+	0.977029i	$0.568358\pi$
$194$	−1448.55	−0.536081
$195$	2351.69	0.863630
$196$	196.000	0.0714286
$197$	3109.77	1.12468	0.562340	−	0.826906i	$-0.309901\pi$
$197$	3109.77	1.12468	0.562340	+	0.826906i	$0.309901\pi$
$198$	859.766	0.308591
$199$	886.066	0.315636	0.157818	−	0.987468i	$-0.449554\pi$
$199$	886.066	0.315636	0.157818	+	0.987468i	$0.449554\pi$
$200$	176.739	0.0624866
$201$	3062.96	1.07485
$202$	319.042	0.111127
$203$	370.378	0.128056
$204$	314.763	0.108028
$205$	3707.77	1.26323
$206$	368.683	0.124696
$207$	−207.000	−0.0695048
$208$	−1236.39	−0.412154
$209$	−2625.49	−0.868942
$210$	−426.062	−0.140005
$211$	393.347	0.128337	0.0641686	−	0.997939i	$-0.479560\pi$
$211$	393.347	0.128337	0.0641686	+	0.997939i	$0.479560\pi$
$212$	−584.551	−0.189373
$213$	365.003	0.117416
$214$	−977.233	−0.312160
$215$	3978.68	1.26206
$216$	216.000	0.0680414
$217$	679.678	0.212625
$218$	−1573.25	−0.488778
$219$	2249.29	0.694032
$220$	−1938.17	−0.593961
$221$	2026.92	0.616948
$222$	1772.97	0.536009
$223$	−4935.73	−1.48216	−0.741079	−	0.671418i	$-0.765685\pi$
$223$	−4935.73	−1.48216	−0.741079	+	0.671418i	$0.765685\pi$
$224$	224.000	0.0668153
$225$	−198.831	−0.0589129
$226$	−1973.43	−0.580843
$227$	67.8077	0.0198262	0.00991311	−	0.999951i	$-0.496845\pi$
$227$	67.8077	0.0198262	0.00991311	+	0.999951i	$0.496845\pi$
$228$	−659.605	−0.191594
$229$	4500.59	1.29872	0.649361	−	0.760481i	$-0.275037\pi$
$229$	4500.59	1.29872	0.649361	+	0.760481i	$0.275037\pi$
$230$	466.640	0.133780
$231$	−1003.06	−0.285699
$232$	423.289	0.119786
$233$	−5112.93	−1.43759	−0.718797	−	0.695220i	$-0.755307\pi$
$233$	−5112.93	−1.43759	−0.718797	+	0.695220i	$0.755307\pi$
$234$	1390.94	0.388582
$235$	811.407	0.225236
$236$	−76.1135	−0.0209939
$237$	−1646.61	−0.451303
$238$	−367.223	−0.100015
$239$	4432.35	1.19960	0.599801	−	0.800149i	$-0.295246\pi$
$239$	4432.35	1.19960	0.599801	+	0.800149i	$0.295246\pi$
$240$	−486.928	−0.130963
$241$	2451.90	0.655355	0.327678	−	0.944790i	$-0.393734\pi$
$241$	2451.90	0.655355	0.327678	+	0.944790i	$0.393734\pi$
$242$	−1900.95	−0.504950
$243$	−243.000	−0.0641500
$244$	356.914	0.0936436
$245$	497.073	0.129620
$246$	2193.01	0.568379
$247$	−4247.53	−1.09419
$248$	776.775	0.198892
$249$	−219.254	−0.0558018
$250$	2984.31	0.754977
$251$	1628.07	0.409414	0.204707	−	0.978823i	$-0.434376\pi$
$251$	1628.07	0.409414	0.204707	+	0.978823i	$0.434376\pi$
$252$	−252.000	−0.0629941
$253$	1098.59	0.272995
$254$	−1306.16	−0.322661
$255$	798.265	0.196037
$256$	256.000	0.0625000
$257$	5757.66	1.39748	0.698741	−	0.715375i	$-0.253744\pi$
$257$	5757.66	1.39748	0.698741	+	0.715375i	$0.253744\pi$
$258$	2353.24	0.567855
$259$	−2068.47	−0.496248
$260$	−3135.58	−0.747925
$261$	−476.200	−0.112935
$262$	−3494.88	−0.824101
$263$	1559.25	0.365580	0.182790	−	0.983152i	$-0.441487\pi$
$263$	1559.25	0.365580	0.182790	+	0.983152i	$0.441487\pi$
$264$	−1146.36	−0.267247
$265$	−1482.47	−0.343651
$266$	769.539	0.177381
$267$	−3267.76	−0.749003
$268$	−4083.94	−0.930845
$269$	6369.88	1.44379	0.721893	−	0.692005i	$-0.243272\pi$
$269$	6369.88	1.44379	0.721893	+	0.692005i	$0.243272\pi$
$270$	547.794	0.123473
$271$	−5526.08	−1.23869	−0.619346	−	0.785119i	$-0.712602\pi$
$271$	−5526.08	−1.23869	−0.619346	+	0.785119i	$0.712602\pi$
$272$	−419.684	−0.0935554
$273$	−1622.76	−0.359757
$274$	−3025.09	−0.666979
$275$	1055.24	0.231393
$276$	276.000	0.0601929
$277$	7349.07	1.59409	0.797045	−	0.603920i	$-0.206395\pi$
$277$	7349.07	1.59409	0.797045	+	0.603920i	$0.206395\pi$
$278$	1162.82	0.250868
$279$	−873.872	−0.187517
$280$	568.083	0.121248
$281$	3432.00	0.728598	0.364299	−	0.931282i	$-0.381309\pi$
$281$	3432.00	0.728598	0.364299	+	0.931282i	$0.381309\pi$
$282$	479.917	0.101343
$283$	−8732.86	−1.83433	−0.917163	−	0.398512i	$-0.869527\pi$
$283$	−8732.86	−1.83433	−0.917163	+	0.398512i	$0.869527\pi$
$284$	−486.670	−0.101685
$285$	−1672.81	−0.347680
$286$	−7381.97	−1.52624
$287$	−2558.51	−0.526216
$288$	−288.000	−0.0589256
$289$	−4224.97	−0.859958
$290$	1073.50	0.217372
$291$	−2172.82	−0.437708
$292$	−2999.05	−0.601049
$293$	−5749.95	−1.14647	−0.573235	−	0.819391i	$-0.694312\pi$
$293$	−5749.95	−1.14647	−0.573235	+	0.819391i	$0.694312\pi$
$294$	294.000	0.0583212
$295$	−193.030	−0.0380972
$296$	−2363.96	−0.464198
$297$	1289.65	0.251963
$298$	−5693.05	−1.10668
$299$	1777.31	0.343760
$300$	265.108	0.0510201
$301$	−2745.45	−0.525731
$302$	5425.72	1.03382
$303$	478.562	0.0907349
$304$	879.473	0.165925
$305$	905.163	0.169933
$306$	472.144	0.0882049
$307$	2069.88	0.384802	0.192401	−	0.981316i	$-0.438373\pi$
$307$	2069.88	0.384802	0.192401	+	0.981316i	$0.438373\pi$
$308$	1337.41	0.247423
$309$	553.024	0.101814
$310$	1969.97	0.360925
$311$	8128.54	1.48208	0.741040	−	0.671460i	$-0.234333\pi$
$311$	8128.54	1.48208	0.741040	+	0.671460i	$0.234333\pi$
$312$	−1854.58	−0.336522
$313$	−2147.81	−0.387865	−0.193932	−	0.981015i	$-0.562124\pi$
$313$	−2147.81	−0.387865	−0.193932	+	0.981015i	$0.562124\pi$
$314$	−5488.89	−0.986483
$315$	−639.093	−0.114314
$316$	2195.48	0.390840
$317$	−5908.90	−1.04693	−0.523465	−	0.852047i	$-0.675361\pi$
$317$	−5908.90	−1.04693	−0.523465	+	0.852047i	$0.675361\pi$
$318$	−876.827	−0.154623
$319$	2527.29	0.443577
$320$	649.238	0.113417
$321$	−1465.85	−0.254878
$322$	−322.000	−0.0557278
$323$	−1441.80	−0.248371
$324$	324.000	0.0555556
$325$	1707.17	0.291374
$326$	5689.87	0.966665
$327$	−2359.87	−0.399086
$328$	−2924.01	−0.492230
$329$	−559.903	−0.0938251
$330$	−2907.25	−0.484967
$331$	−278.062	−0.0461742	−0.0230871	−	0.999733i	$-0.507350\pi$
$331$	−278.062	−0.0461742	−0.0230871	+	0.999733i	$0.507350\pi$
$332$	292.339	0.0483258
$333$	2659.46	0.437650
$334$	990.624	0.162289
$335$	−10357.2	−1.68918
$336$	336.000	0.0545545
$337$	−8355.18	−1.35055	−0.675275	−	0.737566i	$-0.735975\pi$
$337$	−8355.18	−1.35055	−0.675275	+	0.737566i	$0.735975\pi$
$338$	−7548.60	−1.21476
$339$	−2960.14	−0.474256
$340$	−1064.35	−0.169773
$341$	4637.81	0.736515
$342$	−989.407	−0.156436
$343$	−343.000	−0.0539949
$344$	−3137.66	−0.491776
$345$	699.960	0.109231
$346$	−7131.58	−1.10808
$347$	6786.89	1.04997	0.524984	−	0.851112i	$-0.324071\pi$
$347$	6786.89	1.04997	0.524984	+	0.851112i	$0.324071\pi$
$348$	634.933	0.0978046
$349$	−7005.57	−1.07450	−0.537249	−	0.843424i	$-0.680536\pi$
$349$	−7005.57	−1.07450	−0.537249	+	0.843424i	$0.680536\pi$
$350$	−309.293	−0.0472354
$351$	2086.40	0.317276
$352$	1528.47	0.231443
$353$	2040.58	0.307674	0.153837	−	0.988096i	$-0.450837\pi$
$353$	2040.58	0.307674	0.153837	+	0.988096i	$0.450837\pi$
$354$	−114.170	−0.0171415
$355$	−1234.24	−0.184525
$356$	4357.01	0.648655
$357$	−550.835	−0.0816619
$358$	981.162	0.144849
$359$	5503.62	0.809109	0.404555	−	0.914514i	$-0.367427\pi$
$359$	5503.62	0.809109	0.404555	+	0.914514i	$0.367427\pi$
$360$	−730.393	−0.106931
$361$	−3837.62	−0.559502
$362$	−471.980	−0.0685268
$363$	−2851.43	−0.412290
$364$	2163.68	0.311559
$365$	−7605.86	−1.09071
$366$	535.370	0.0764597
$367$	−5167.28	−0.734959	−0.367479	−	0.930032i	$-0.619779\pi$
$367$	−5167.28	−0.734959	−0.367479	+	0.930032i	$0.619779\pi$
$368$	−368.000	−0.0521286
$369$	3289.51	0.464079
$370$	−5995.21	−0.842368
$371$	1022.96	0.143153
$372$	1165.16	0.162395
$373$	−956.629	−0.132795	−0.0663973	−	0.997793i	$-0.521150\pi$
$373$	−956.629	−0.132795	−0.0663973	+	0.997793i	$0.521150\pi$
$374$	−2505.76	−0.346444
$375$	4476.46	0.616436
$376$	−639.889	−0.0877653
$377$	4088.66	0.558559
$378$	−378.000	−0.0514344
$379$	13701.1	1.85694	0.928468	−	0.371413i	$-0.121127\pi$
$379$	13701.1	1.85694	0.928468	+	0.371413i	$0.121127\pi$
$380$	2230.42	0.301100
$381$	−1959.24	−0.263451
$382$	−612.980	−0.0821015
$383$	−5039.42	−0.672330	−0.336165	−	0.941803i	$-0.609130\pi$
$383$	−5039.42	−0.672330	−0.336165	+	0.941803i	$0.609130\pi$
$384$	384.000	0.0510310
$385$	3391.80	0.448992
$386$	2285.56	0.301378
$387$	3529.86	0.463651
$388$	2897.09	0.379066
$389$	−5545.34	−0.722776	−0.361388	−	0.932415i	$-0.617697\pi$
$389$	−5545.34	−0.722776	−0.361388	+	0.932415i	$0.617697\pi$
$390$	−4703.37	−0.610679
$391$	603.296	0.0780306
$392$	−392.000	−0.0505076
$393$	−5242.32	−0.672875
$394$	−6219.54	−0.795269
$395$	5567.93	0.709248
$396$	−1719.53	−0.218206
$397$	3102.14	0.392171	0.196085	−	0.980587i	$-0.437177\pi$
$397$	3102.14	0.392171	0.196085	+	0.980587i	$0.437177\pi$
$398$	−1772.13	−0.223188
$399$	1154.31	0.144831
$400$	−353.478	−0.0441847
$401$	10715.5	1.33443	0.667214	−	0.744866i	$-0.267487\pi$
$401$	10715.5	1.33443	0.667214	+	0.744866i	$0.267487\pi$
$402$	−6125.91	−0.760031
$403$	7503.08	0.927432
$404$	−638.083	−0.0785788
$405$	821.692	0.100815
$406$	−740.755	−0.0905494
$407$	−14114.3	−1.71896
$408$	−629.526	−0.0763877
$409$	11550.2	1.39638	0.698190	−	0.715913i	$-0.253989\pi$
$409$	11550.2	1.39638	0.698190	+	0.715913i	$0.253989\pi$
$410$	−7415.54	−0.893238
$411$	−4537.64	−0.544586
$412$	−737.365	−0.0881733
$413$	133.199	0.0158699
$414$	414.000	0.0491473
$415$	741.396	0.0876956
$416$	2472.77	0.291437
$417$	1744.23	0.204833
$418$	5250.98	0.614435
$419$	2239.70	0.261137	0.130569	−	0.991439i	$-0.458320\pi$
$419$	2239.70	0.261137	0.130569	+	0.991439i	$0.458320\pi$
$420$	852.125	0.0989986
$421$	5738.65	0.664334	0.332167	−	0.943221i	$-0.392220\pi$
$421$	5738.65	0.664334	0.332167	+	0.943221i	$0.392220\pi$
$422$	−786.695	−0.0907481
$423$	719.875	0.0827460
$424$	1169.10	0.133907
$425$	579.488	0.0661395
$426$	−730.005	−0.0830255
$427$	−624.599	−0.0707879
$428$	1954.47	0.220730
$429$	−11073.0	−1.24617
$430$	−7957.36	−0.892414
$431$	2493.21	0.278640	0.139320	−	0.990247i	$-0.455508\pi$
$431$	2493.21	0.278640	0.139320	+	0.990247i	$0.455508\pi$
$432$	−432.000	−0.0481125
$433$	4175.42	0.463414	0.231707	−	0.972786i	$-0.425569\pi$
$433$	4175.42	0.463414	0.231707	+	0.972786i	$0.425569\pi$
$434$	−1359.36	−0.150348
$435$	1610.24	0.177483
$436$	3146.49	0.345618
$437$	−1264.24	−0.138391
$438$	−4498.58	−0.490755
$439$	−10892.5	−1.18422	−0.592109	−	0.805858i	$-0.701704\pi$
$439$	−10892.5	−1.18422	−0.592109	+	0.805858i	$0.701704\pi$
$440$	3876.34	0.419994
$441$	441.000	0.0476190
$442$	−4053.84	−0.436248
$443$	−10500.1	−1.12612	−0.563062	−	0.826415i	$-0.690377\pi$
$443$	−10500.1	−1.12612	−0.563062	+	0.826415i	$0.690377\pi$
$444$	−3545.94	−0.379016
$445$	11049.8	1.17710
$446$	9871.47	1.04804
$447$	−8539.57	−0.903597
$448$	−448.000	−0.0472456
$449$	5069.81	0.532871	0.266435	−	0.963853i	$-0.414154\pi$
$449$	5069.81	0.532871	0.266435	+	0.963853i	$0.414154\pi$
$450$	397.662	0.0416577
$451$	−17458.1	−1.82277
$452$	3946.86	0.410718
$453$	8138.58	0.844114
$454$	−135.615	−0.0140193
$455$	5487.27	0.565379
$456$	1319.21	0.135477
$457$	1772.04	0.181384	0.0906919	−	0.995879i	$-0.471092\pi$
$457$	1772.04	0.181384	0.0906919	+	0.995879i	$0.471092\pi$
$458$	−9001.17	−0.918334
$459$	708.216	0.0720190
$460$	−933.279	−0.0945965
$461$	−12009.1	−1.21328	−0.606639	−	0.794977i	$-0.707483\pi$
$461$	−12009.1	−1.21328	−0.606639	+	0.794977i	$0.707483\pi$
$462$	2006.12	0.202020
$463$	13558.0	1.36089	0.680446	−	0.732799i	$-0.261786\pi$
$463$	13558.0	1.36089	0.680446	+	0.732799i	$0.261786\pi$
$464$	−846.577	−0.0847012
$465$	2954.95	0.294694
$466$	10225.9	1.01653
$467$	7489.21	0.742097	0.371048	−	0.928614i	$-0.378998\pi$
$467$	7489.21	0.742097	0.371048	+	0.928614i	$0.378998\pi$
$468$	−2781.87	−0.274769
$469$	7146.90	0.703652
$470$	−1622.81	−0.159266
$471$	−8233.33	−0.805460
$472$	152.227	0.0148450
$473$	−18733.7	−1.82109
$474$	3293.22	0.319120
$475$	−1214.35	−0.117302
$476$	734.447	0.0707212
$477$	−1315.24	−0.126249
$478$	−8864.71	−0.848247
$479$	−13665.4	−1.30352	−0.651761	−	0.758424i	$-0.725969\pi$
$479$	−13665.4	−1.30352	−0.651761	+	0.758424i	$0.725969\pi$
$480$	973.857	0.0926047
$481$	−22834.2	−2.16455
$482$	−4903.79	−0.463406
$483$	−483.000	−0.0455016
$484$	3801.90	0.357053
$485$	7347.28	0.687882
$486$	486.000	0.0453609
$487$	687.947	0.0640121	0.0320060	−	0.999488i	$-0.489810\pi$
$487$	687.947	0.0640121	0.0320060	+	0.999488i	$0.489810\pi$
$488$	−713.827	−0.0662161
$489$	8534.81	0.789279
$490$	−994.145	−0.0916549
$491$	7748.27	0.712168	0.356084	−	0.934454i	$-0.384112\pi$
$491$	7748.27	0.712168	0.356084	+	0.934454i	$0.384112\pi$
$492$	−4386.02	−0.401904
$493$	1387.87	0.126788
$494$	8495.07	0.773707
$495$	−4360.88	−0.395974
$496$	−1553.55	−0.140638
$497$	851.673	0.0768667
$498$	438.508	0.0394578
$499$	−11221.2	−1.00667	−0.503335	−	0.864091i	$-0.667894\pi$
$499$	−11221.2	−1.00667	−0.503335	+	0.864091i	$0.667894\pi$
$500$	−5968.62	−0.533850
$501$	1485.94	0.132508
$502$	−3256.14	−0.289499
$503$	12631.4	1.11969	0.559845	−	0.828597i	$-0.310861\pi$
$503$	12631.4	1.11969	0.559845	+	0.828597i	$0.310861\pi$
$504$	504.000	0.0445435
$505$	−1618.23	−0.142595
$506$	−2197.18	−0.193037
$507$	−11322.9	−0.991850
$508$	2612.32	0.228156
$509$	−10373.2	−0.903307	−0.451653	−	0.892193i	$-0.649166\pi$
$509$	−10373.2	−0.903307	−0.451653	+	0.892193i	$0.649166\pi$
$510$	−1596.53	−0.138619
$511$	5248.34	0.454350
$512$	−512.000	−0.0441942
$513$	−1484.11	−0.127729
$514$	−11515.3	−0.988169
$515$	−1870.02	−0.160006
$516$	−4706.48	−0.401534
$517$	−3820.52	−0.325003
$518$	4136.93	0.350900
$519$	−10697.4	−0.904745
$520$	6271.17	0.528863
$521$	−18433.9	−1.55010	−0.775051	−	0.631898i	$-0.782276\pi$
$521$	−18433.9	−1.55010	−0.775051	+	0.631898i	$0.782276\pi$
$522$	952.400	0.0798571
$523$	10811.1	0.903894	0.451947	−	0.892045i	$-0.350730\pi$
$523$	10811.1	0.903894	0.451947	+	0.892045i	$0.350730\pi$
$524$	6989.76	0.582727
$525$	−463.939	−0.0385676
$526$	−3118.50	−0.258504
$527$	2546.87	0.210519
$528$	2292.71	0.188972
$529$	529.000	0.0434783
$530$	2964.94	0.242998
$531$	−171.255	−0.0139960
$532$	−1539.08	−0.125428
$533$	−28243.8	−2.29527
$534$	6535.52	0.529625
$535$	4956.69	0.400554
$536$	8167.88	0.658207
$537$	1471.74	0.118269
$538$	−12739.8	−1.02091
$539$	−2340.48	−0.187034
$540$	−1095.59	−0.0873086
$541$	7964.67	0.632954	0.316477	−	0.948600i	$-0.397500\pi$
$541$	7964.67	0.632954	0.316477	+	0.948600i	$0.397500\pi$
$542$	11052.2	0.875887
$543$	−707.969	−0.0559519
$544$	839.368	0.0661537
$545$	7979.77	0.627185
$546$	3245.52	0.254387
$547$	−19077.6	−1.49122	−0.745611	−	0.666382i	$-0.767842\pi$
$547$	−19077.6	−1.49122	−0.745611	+	0.666382i	$0.767842\pi$
$548$	6050.18	0.471626
$549$	803.055	0.0624291
$550$	−2110.47	−0.163620
$551$	−2908.37	−0.224865
$552$	−552.000	−0.0425628
$553$	−3842.09	−0.295447
$554$	−14698.1	−1.12719
$555$	−8992.81	−0.687790
$556$	−2325.64	−0.177390
$557$	18414.8	1.40083	0.700414	−	0.713737i	$-0.252999\pi$
$557$	18414.8	1.40083	0.700414	+	0.713737i	$0.252999\pi$
$558$	1747.74	0.132595
$559$	−30307.5	−2.29315
$560$	−1136.17	−0.0857353
$561$	−3758.65	−0.282870
$562$	−6864.00	−0.515196
$563$	−8660.61	−0.648314	−0.324157	−	0.946003i	$-0.605081\pi$
$563$	−8660.61	−0.648314	−0.324157	+	0.946003i	$0.605081\pi$
$564$	−959.834	−0.0716601
$565$	10009.6	0.745320
$566$	17465.7	1.29706
$567$	−567.000	−0.0419961
$568$	973.341	0.0719022
$569$	14435.5	1.06357	0.531783	−	0.846881i	$-0.321522\pi$
$569$	14435.5	1.06357	0.531783	+	0.846881i	$0.321522\pi$
$570$	3345.63	0.245847
$571$	15744.4	1.15391	0.576954	−	0.816776i	$-0.304241\pi$
$571$	15744.4	1.15391	0.576954	+	0.816776i	$0.304241\pi$
$572$	14763.9	1.07922
$573$	−919.470	−0.0670356
$574$	5117.02	0.372091
$575$	508.124	0.0368526
$576$	576.000	0.0416667
$577$	14990.4	1.08156	0.540780	−	0.841164i	$-0.318129\pi$
$577$	14990.4	1.08156	0.540780	+	0.841164i	$0.318129\pi$
$578$	8449.95	0.608082
$579$	3428.34	0.246074
$580$	−2146.99	−0.153705
$581$	−511.592	−0.0365309
$582$	4345.64	0.309506
$583$	6980.24	0.495870
$584$	5998.11	0.425006
$585$	−7055.06	−0.498617
$586$	11499.9	0.810677
$587$	−6469.75	−0.454915	−0.227457	−	0.973788i	$-0.573041\pi$
$587$	−6469.75	−0.454915	−0.227457	+	0.973788i	$0.573041\pi$
$588$	−588.000	−0.0412393
$589$	−5337.13	−0.373366
$590$	386.061	0.0269388
$591$	−9329.31	−0.649334
$592$	4727.92	0.328237
$593$	−2693.71	−0.186539	−0.0932693	−	0.995641i	$-0.529732\pi$
$593$	−2693.71	−0.186539	−0.0932693	+	0.995641i	$0.529732\pi$
$594$	−2579.30	−0.178165
$595$	1862.62	0.128336
$596$	11386.1	0.782538
$597$	−2658.20	−0.182233
$598$	−3554.61	−0.243075
$599$	15387.1	1.04958	0.524790	−	0.851232i	$-0.324144\pi$
$599$	15387.1	1.04958	0.524790	+	0.851232i	$0.324144\pi$
$600$	−530.216	−0.0360767
$601$	−5907.39	−0.400944	−0.200472	−	0.979699i	$-0.564248\pi$
$601$	−5907.39	−0.400944	−0.200472	+	0.979699i	$0.564248\pi$
$602$	5490.90	0.371748
$603$	−9188.87	−0.620563
$604$	−10851.4	−0.731025
$605$	9641.95	0.647936
$606$	−957.125	−0.0641593
$607$	6209.90	0.415243	0.207621	−	0.978209i	$-0.433428\pi$
$607$	6209.90	0.415243	0.207621	+	0.978209i	$0.433428\pi$
$608$	−1758.95	−0.117327
$609$	−1111.13	−0.0739333
$610$	−1810.33	−0.120161
$611$	−6180.87	−0.409249
$612$	−944.289	−0.0623703
$613$	4419.34	0.291183	0.145592	−	0.989345i	$-0.453491\pi$
$613$	4419.34	0.291183	0.145592	+	0.989345i	$0.453491\pi$
$614$	−4139.75	−0.272096
$615$	−11123.3	−0.729326
$616$	−2674.83	−0.174954
$617$	−9736.05	−0.635265	−0.317633	−	0.948214i	$-0.602888\pi$
$617$	−9736.05	−0.635265	−0.317633	+	0.948214i	$0.602888\pi$
$618$	−1106.05	−0.0719932
$619$	16608.5	1.07844	0.539218	−	0.842166i	$-0.318720\pi$
$619$	16608.5	1.07844	0.539218	+	0.842166i	$0.318720\pi$
$620$	−3939.93	−0.255212
$621$	621.000	0.0401286
$622$	−16257.1	−1.04799
$623$	−7624.77	−0.490337
$624$	3709.16	0.237957
$625$	−12375.4	−0.792025
$626$	4295.63	0.274262
$627$	7876.47	0.501684
$628$	10977.8	0.697549
$629$	−7750.91	−0.491334
$630$	1278.19	0.0808320
$631$	15115.7	0.953640	0.476820	−	0.879001i	$-0.341789\pi$
$631$	15115.7	0.953640	0.476820	+	0.879001i	$0.341789\pi$
$632$	−4390.96	−0.276366
$633$	−1180.04	−0.0740955
$634$	11817.8	0.740291
$635$	6625.07	0.414028
$636$	1753.65	0.109335
$637$	−3786.44	−0.235517
$638$	−5054.58	−0.313656
$639$	−1095.01	−0.0677901
$640$	−1298.48	−0.0801981
$641$	−11613.9	−0.715633	−0.357816	−	0.933792i	$-0.616479\pi$
$641$	−11613.9	−0.715633	−0.357816	+	0.933792i	$0.616479\pi$
$642$	2931.70	0.180226
$643$	−13410.3	−0.822471	−0.411236	−	0.911529i	$-0.634903\pi$
$643$	−13410.3	−0.822471	−0.411236	+	0.911529i	$0.634903\pi$
$644$	644.000	0.0394055
$645$	−11936.0	−0.728653
$646$	2883.60	0.175625
$647$	−8032.34	−0.488074	−0.244037	−	0.969766i	$-0.578472\pi$
$647$	−8032.34	−0.488074	−0.244037	+	0.969766i	$0.578472\pi$
$648$	−648.000	−0.0392837
$649$	908.887	0.0549722
$650$	−3414.34	−0.206033
$651$	−2039.03	−0.122759
$652$	−11379.7	−0.683536
$653$	29290.6	1.75533	0.877664	−	0.479276i	$-0.159101\pi$
$653$	29290.6	1.75533	0.877664	+	0.479276i	$0.159101\pi$
$654$	4719.74	0.282196
$655$	17726.6	1.05746
$656$	5848.02	0.348059
$657$	−6747.87	−0.400699
$658$	1119.81	0.0663444
$659$	−8361.11	−0.494237	−0.247119	−	0.968985i	$-0.579484\pi$
$659$	−8361.11	−0.494237	−0.247119	+	0.968985i	$0.579484\pi$
$660$	5814.51	0.342923
$661$	12471.7	0.733877	0.366938	−	0.930245i	$-0.380406\pi$
$661$	12471.7	0.733877	0.366938	+	0.930245i	$0.380406\pi$
$662$	556.124	0.0326501
$663$	−6080.76	−0.356195
$664$	−584.677	−0.0341715
$665$	−3903.23	−0.227610
$666$	−5318.92	−0.309465
$667$	1216.96	0.0706457
$668$	−1981.25	−0.114756
$669$	14807.2	0.855724
$670$	20714.4	1.19443
$671$	−4261.98	−0.245204
$672$	−672.000	−0.0385758
$673$	−18614.5	−1.06617	−0.533087	−	0.846061i	$-0.678968\pi$
$673$	−18614.5	−1.06617	−0.533087	+	0.846061i	$0.678968\pi$
$674$	16710.4	0.954983
$675$	596.493	0.0340134
$676$	15097.2	0.858967
$677$	10930.2	0.620504	0.310252	−	0.950654i	$-0.399587\pi$
$677$	10930.2	0.620504	0.310252	+	0.950654i	$0.399587\pi$
$678$	5920.29	0.335350
$679$	−5069.92	−0.286547
$680$	2128.71	0.120047
$681$	−203.423	−0.0114467
$682$	−9275.62	−0.520795
$683$	18745.1	1.05016	0.525082	−	0.851052i	$-0.324035\pi$
$683$	18745.1	1.05016	0.525082	+	0.851052i	$0.324035\pi$
$684$	1978.81	0.110617
$685$	15343.8	0.855847
$686$	686.000	0.0381802
$687$	−13501.8	−0.749817
$688$	6275.31	0.347738
$689$	11292.7	0.624408
$690$	−1399.92	−0.0772377
$691$	−26682.8	−1.46898	−0.734488	−	0.678622i	$-0.762577\pi$
$691$	−26682.8	−1.46898	−0.734488	+	0.678622i	$0.762577\pi$
$692$	14263.2	0.783532
$693$	3009.18	0.164949
$694$	−13573.8	−0.742440
$695$	−5898.02	−0.321906
$696$	−1269.87	−0.0691583
$697$	−9587.19	−0.521005
$698$	14011.1	0.759784
$699$	15338.8	0.829995
$700$	618.586	0.0334005
$701$	−16576.7	−0.893144	−0.446572	−	0.894748i	$-0.647355\pi$
$701$	−16576.7	−0.893144	−0.446572	+	0.894748i	$0.647355\pi$
$702$	−4172.81	−0.224348
$703$	16242.5	0.871405
$704$	−3056.95	−0.163655
$705$	−2434.22	−0.130040
$706$	−4081.15	−0.217558
$707$	1116.65	0.0594000
$708$	228.341	0.0121209
$709$	10566.8	0.559723	0.279862	−	0.960040i	$-0.409711\pi$
$709$	10566.8	0.559723	0.279862	+	0.960040i	$0.409711\pi$
$710$	2468.47	0.130479
$711$	4939.84	0.260560
$712$	−8714.03	−0.458669
$713$	2233.23	0.117300
$714$	1101.67	0.0577436
$715$	37442.6	1.95843
$716$	−1962.32	−0.102424
$717$	−13297.1	−0.692591
$718$	−11007.2	−0.572127
$719$	−26143.1	−1.35601	−0.678006	−	0.735056i	$-0.737156\pi$
$719$	−26143.1	−1.35601	−0.678006	+	0.735056i	$0.737156\pi$
$720$	1460.79	0.0756115
$721$	1290.39	0.0666527
$722$	7675.25	0.395628
$723$	−7355.69	−0.378369
$724$	943.959	0.0484558
$725$	1168.93	0.0598800
$726$	5702.86	0.291533
$727$	−30744.5	−1.56843	−0.784216	−	0.620488i	$-0.786934\pi$
$727$	−30744.5	−1.56843	−0.784216	+	0.620488i	$0.786934\pi$
$728$	−4327.36	−0.220306
$729$	729.000	0.0370370
$730$	15211.7	0.771248
$731$	−10287.7	−0.520525
$732$	−1070.74	−0.0540652
$733$	−5053.21	−0.254631	−0.127316	−	0.991862i	$-0.540636\pi$
$733$	−5053.21	−0.254631	−0.127316	+	0.991862i	$0.540636\pi$
$734$	10334.6	0.519694
$735$	−1491.22	−0.0748359
$736$	736.000	0.0368605
$737$	48767.1	2.43740
$738$	−6579.03	−0.328154
$739$	15337.4	0.763460	0.381730	−	0.924274i	$-0.375328\pi$
$739$	15337.4	0.763460	0.381730	+	0.924274i	$0.375328\pi$
$740$	11990.4	0.595644
$741$	12742.6	0.631729
$742$	−2045.93	−0.101224
$743$	40357.0	1.99267	0.996336	−	0.0855253i	$-0.0272568\pi$
$743$	40357.0	1.99267	0.996336	+	0.0855253i	$0.0272568\pi$
$744$	−2330.32	−0.114830
$745$	28876.1	1.42005
$746$	1913.26	0.0938999
$747$	657.762	0.0322172
$748$	5011.53	0.244973
$749$	−3420.31	−0.166857
$750$	−8952.93	−0.435886
$751$	15971.2	0.776027	0.388013	−	0.921654i	$-0.373161\pi$
$751$	15971.2	0.776027	0.388013	+	0.921654i	$0.373161\pi$
$752$	1279.78	0.0620595
$753$	−4884.21	−0.236375
$754$	−8177.32	−0.394961
$755$	−27520.2	−1.32657
$756$	756.000	0.0363696
$757$	−18896.1	−0.907251	−0.453626	−	0.891192i	$-0.649870\pi$
$757$	−18896.1	−0.907251	−0.453626	+	0.891192i	$0.649870\pi$
$758$	−27402.2	−1.31305
$759$	−3295.77	−0.157614
$760$	−4460.84	−0.212910
$761$	10130.8	0.482577	0.241289	−	0.970453i	$-0.422430\pi$
$761$	10130.8	0.482577	0.241289	+	0.970453i	$0.422430\pi$
$762$	3918.48	0.186288
$763$	−5506.36	−0.261263
$764$	1225.96	0.0580546
$765$	−2394.80	−0.113182
$766$	10078.8	0.475409
$767$	1470.40	0.0692219
$768$	−768.000	−0.0360844
$769$	9225.09	0.432594	0.216297	−	0.976328i	$-0.430602\pi$
$769$	9225.09	0.432594	0.216297	+	0.976328i	$0.430602\pi$
$770$	−6783.59	−0.317485
$771$	−17273.0	−0.806837
$772$	−4571.12	−0.213106
$773$	1879.77	0.0874652	0.0437326	−	0.999043i	$-0.486075\pi$
$773$	1879.77	0.0874652	0.0437326	+	0.999043i	$0.486075\pi$
$774$	−7059.73	−0.327851
$775$	2145.10	0.0994247
$776$	−5794.19	−0.268040
$777$	6205.40	0.286509
$778$	11090.7	0.511080
$779$	20090.5	0.924029
$780$	9406.75	0.431815
$781$	5811.43	0.266260
$782$	−1206.59	−0.0551760
$783$	1428.60	0.0652030
$784$	784.000	0.0357143
$785$	27840.6	1.26582
$786$	10484.6	0.475795
$787$	−1579.70	−0.0715506	−0.0357753	−	0.999360i	$-0.511390\pi$
$787$	−1579.70	−0.0715506	−0.0357753	+	0.999360i	$0.511390\pi$
$788$	12439.1	0.562340
$789$	−4677.75	−0.211068
$790$	−11135.9	−0.501514
$791$	−6907.00	−0.310474
$792$	3439.07	0.154295
$793$	−6895.05	−0.308765
$794$	−6204.27	−0.277307
$795$	4447.41	0.198407
$796$	3544.27	0.157818
$797$	10146.4	0.450946	0.225473	−	0.974249i	$-0.427607\pi$
$797$	10146.4	0.450946	0.225473	+	0.974249i	$0.427607\pi$
$798$	−2308.62	−0.102411
$799$	−2098.06	−0.0928960
$800$	706.955	0.0312433
$801$	9803.28	0.432437
$802$	−21431.0	−0.943583
$803$	35812.3	1.57383
$804$	12251.8	0.537423
$805$	1633.24	0.0715082
$806$	−15006.2	−0.655794
$807$	−19109.6	−0.833570
$808$	1276.17	0.0555636
$809$	−9235.53	−0.401365	−0.200682	−	0.979656i	$-0.564316\pi$
$809$	−9235.53	−0.401365	−0.200682	+	0.979656i	$0.564316\pi$
$810$	−1643.38	−0.0712872
$811$	31367.8	1.35817	0.679083	−	0.734062i	$-0.262378\pi$
$811$	31367.8	1.35817	0.679083	+	0.734062i	$0.262378\pi$
$812$	1481.51	0.0640281
$813$	16578.2	0.715159
$814$	28228.5	1.21549
$815$	−28860.0	−1.24040
$816$	1259.05	0.0540142
$817$	21558.5	0.923176
$818$	−23100.3	−0.987390
$819$	4868.27	0.207706
$820$	14831.1	0.631615
$821$	−1449.02	−0.0615971	−0.0307985	−	0.999526i	$-0.509805\pi$
$821$	−1449.02	−0.0615971	−0.0307985	+	0.999526i	$0.509805\pi$
$822$	9075.27	0.385081
$823$	−6671.39	−0.282564	−0.141282	−	0.989969i	$-0.545122\pi$
$823$	−6671.39	−0.282564	−0.141282	+	0.989969i	$0.545122\pi$
$824$	1474.73	0.0623479
$825$	−3165.71	−0.133595
$826$	−266.397	−0.0112217
$827$	−19290.9	−0.811139	−0.405570	−	0.914064i	$-0.632927\pi$
$827$	−19290.9	−0.811139	−0.405570	+	0.914064i	$0.632927\pi$
$828$	−828.000	−0.0347524
$829$	−17190.7	−0.720213	−0.360107	−	0.932911i	$-0.617260\pi$
$829$	−17190.7	−0.720213	−0.360107	+	0.932911i	$0.617260\pi$
$830$	−1482.79	−0.0620102
$831$	−22047.2	−0.920348
$832$	−4945.55	−0.206077
$833$	−1285.28	−0.0534602
$834$	−3488.46	−0.144839
$835$	−5024.61	−0.208244
$836$	−10502.0	−0.434471
$837$	2621.62	0.108263
$838$	−4479.40	−0.184652
$839$	−47293.3	−1.94606	−0.973032	−	0.230670i	$-0.925908\pi$
$839$	−47293.3	−1.94606	−0.973032	+	0.230670i	$0.925908\pi$
$840$	−1704.25	−0.0700026
$841$	−21589.4	−0.885211
$842$	−11477.3	−0.469755
$843$	−10296.0	−0.420656
$844$	1573.39	0.0641686
$845$	38287.8	1.55875
$846$	−1439.75	−0.0585102
$847$	−6653.33	−0.269907
$848$	−2338.20	−0.0946866
$849$	26198.6	1.05905
$850$	−1158.98	−0.0467677
$851$	−6796.39	−0.273769
$852$	1460.01	0.0587079
$853$	−29185.6	−1.17151	−0.585754	−	0.810489i	$-0.699202\pi$
$853$	−29185.6	−1.17151	−0.585754	+	0.810489i	$0.699202\pi$
$854$	1249.20	0.0500546
$855$	5018.44	0.200733
$856$	−3908.93	−0.156080
$857$	−3922.80	−0.156360	−0.0781798	−	0.996939i	$-0.524911\pi$
$857$	−3922.80	−0.156360	−0.0781798	+	0.996939i	$0.524911\pi$
$858$	22145.9	0.881176
$859$	18335.8	0.728300	0.364150	−	0.931340i	$-0.381359\pi$
$859$	18335.8	0.728300	0.364150	+	0.931340i	$0.381359\pi$
$860$	15914.7	0.631032
$861$	7675.53	0.303811
$862$	−4986.42	−0.197028
$863$	−30425.0	−1.20009	−0.600045	−	0.799966i	$-0.704851\pi$
$863$	−30425.0	−1.20009	−0.600045	+	0.799966i	$0.704851\pi$
$864$	864.000	0.0340207
$865$	36172.6	1.42186
$866$	−8350.85	−0.327683
$867$	12674.9	0.496497
$868$	2718.71	0.106312
$869$	−26216.7	−1.02341
$870$	−3220.49	−0.125500
$871$	78895.8	3.06921
$872$	−6292.98	−0.244389
$873$	6518.46	0.252711
$874$	2528.48	0.0978573
$875$	10445.1	0.403552
$876$	8997.16	0.347016
$877$	−23.1326	−0.000890685 0	−0.000445343	−	1.00000i	$-0.500142\pi$
$877$	−23.1326	−0.000890685 0	−0.000445343		1.00000i	$0.500142\pi$
$878$	21785.0	0.837368
$879$	17249.9	0.661915
$880$	−7752.68	−0.296980
$881$	41825.9	1.59949	0.799744	−	0.600341i	$-0.204968\pi$
$881$	41825.9	1.59949	0.799744	+	0.600341i	$0.204968\pi$
$882$	−882.000	−0.0336718
$883$	25536.2	0.973230	0.486615	−	0.873617i	$-0.338232\pi$
$883$	25536.2	0.973230	0.486615	+	0.873617i	$0.338232\pi$
$884$	8107.68	0.308474
$885$	579.091	0.0219954
$886$	21000.1	0.796289
$887$	−16939.0	−0.641213	−0.320606	−	0.947213i	$-0.603887\pi$
$887$	−16939.0	−0.641213	−0.320606	+	0.947213i	$0.603887\pi$
$888$	7091.89	0.268005
$889$	−4571.56	−0.172469
$890$	−22099.5	−0.832334
$891$	−3868.95	−0.145471
$892$	−19742.9	−0.741079
$893$	4396.60	0.164756
$894$	17079.1	0.638940
$895$	−4976.62	−0.185866
$896$	896.000	0.0334077
$897$	−5331.92	−0.198470
$898$	−10139.6	−0.376797
$899$	5137.50	0.190595
$900$	−795.324	−0.0294565
$901$	3833.23	0.141735
$902$	34916.2	1.28889
$903$	8236.35	0.303531
$904$	−7893.71	−0.290421
$905$	2393.96	0.0879314
$906$	−16277.2	−0.596879
$907$	−53400.9	−1.95496	−0.977479	−	0.211032i	$-0.932318\pi$
$907$	−53400.9	−1.95496	−0.977479	+	0.211032i	$0.932318\pi$
$908$	271.231	0.00991311
$909$	−1435.69	−0.0523858
$910$	−10974.5	−0.399783
$911$	−5253.70	−0.191068	−0.0955339	−	0.995426i	$-0.530456\pi$
$911$	−5253.70	−0.191068	−0.0955339	+	0.995426i	$0.530456\pi$
$912$	−2638.42	−0.0957969
$913$	−3490.87	−0.126540
$914$	−3544.07	−0.128258
$915$	−2715.49	−0.0981107
$916$	18002.3	0.649361
$917$	−12232.1	−0.440500
$918$	−1416.43	−0.0509251
$919$	23492.6	0.843253	0.421627	−	0.906770i	$-0.361459\pi$
$919$	23492.6	0.843253	0.421627	+	0.906770i	$0.361459\pi$
$920$	1866.56	0.0668898
$921$	−6209.63	−0.222165
$922$	24018.3	0.857917
$923$	9401.76	0.335279
$924$	−4012.24	−0.142850
$925$	−6528.18	−0.232049
$926$	−27116.0	−0.962295
$927$	−1659.07	−0.0587822
$928$	1693.15	0.0598928
$929$	4184.83	0.147793	0.0738966	−	0.997266i	$-0.476457\pi$
$929$	4184.83	0.147793	0.0738966	+	0.997266i	$0.476457\pi$
$930$	−5909.90	−0.208380
$931$	2693.39	0.0948143
$932$	−20451.7	−0.718797
$933$	−24385.6	−0.855680
$934$	−14978.4	−0.524742
$935$	12709.7	0.444546
$936$	5563.74	0.194291
$937$	−24593.9	−0.857470	−0.428735	−	0.903430i	$-0.641041\pi$
$937$	−24593.9	−0.857470	−0.428735	+	0.903430i	$0.641041\pi$
$938$	−14293.8	−0.497557
$939$	6443.44	0.223934
$940$	3245.63	0.112618
$941$	6895.77	0.238890	0.119445	−	0.992841i	$-0.461888\pi$
$941$	6895.77	0.238890	0.119445	+	0.992841i	$0.461888\pi$
$942$	16466.7	0.569546
$943$	−8406.53	−0.290302
$944$	−304.454	−0.0104970
$945$	1917.28	0.0659991
$946$	37467.4	1.28771
$947$	780.389	0.0267785	0.0133892	−	0.999910i	$-0.495738\pi$
$947$	780.389	0.0267785	0.0133892	+	0.999910i	$0.495738\pi$
$948$	−6586.45	−0.225652
$949$	57937.4	1.98180
$950$	2428.70	0.0829447
$951$	17726.7	0.604445
$952$	−1468.89	−0.0500075
$953$	27383.7	0.930791	0.465396	−	0.885103i	$-0.345912\pi$
$953$	27383.7	0.930791	0.465396	+	0.885103i	$0.345912\pi$
$954$	2630.48	0.0892714
$955$	3109.14	0.105350
$956$	17729.4	0.599801
$957$	−7581.86	−0.256099
$958$	27330.8	0.921729
$959$	−10587.8	−0.356516
$960$	−1947.71	−0.0654814
$961$	−20363.2	−0.683535
$962$	45668.3	1.53057
$963$	4397.55	0.147154
$964$	9807.59	0.327678
$965$	−11592.7	−0.386719
$966$	966.000	0.0321745
$967$	1541.70	0.0512698	0.0256349	−	0.999671i	$-0.491839\pi$
$967$	1541.70	0.0512698	0.0256349	+	0.999671i	$0.491839\pi$
$968$	−7603.81	−0.252475
$969$	4325.40	0.143397
$970$	−14694.6	−0.486406
$971$	25166.5	0.831753	0.415876	−	0.909421i	$-0.363475\pi$
$971$	25166.5	0.831753	0.415876	+	0.909421i	$0.363475\pi$
$972$	−972.000	−0.0320750
$973$	4069.87	0.134095
$974$	−1375.89	−0.0452634
$975$	−5121.51	−0.168225
$976$	1427.65	0.0468218
$977$	33468.8	1.09597	0.547985	−	0.836488i	$-0.315395\pi$
$977$	33468.8	1.09597	0.547985	+	0.836488i	$0.315395\pi$
$978$	−17069.6	−0.558105
$979$	−52028.0	−1.69849
$980$	1988.29	0.0648098
$981$	7079.61	0.230412
$982$	−15496.5	−0.503579
$983$	−32986.5	−1.07030	−0.535150	−	0.844757i	$-0.679745\pi$
$983$	−32986.5	−1.07030	−0.535150	+	0.844757i	$0.679745\pi$
$984$	8772.04	0.284189
$985$	31546.6	1.02046
$986$	−2775.74	−0.0896527
$987$	1679.71	0.0541699
$988$	−16990.1	−0.547093
$989$	−9020.76	−0.290034
$990$	8721.76	0.279996
$991$	15665.5	0.502152	0.251076	−	0.967967i	$-0.419216\pi$
$991$	15665.5	0.502152	0.251076	+	0.967967i	$0.419216\pi$
$992$	3107.10	0.0994461
$993$	834.186	0.0266587
$994$	−1703.35	−0.0543530
$995$	8988.56	0.286388
$996$	−877.016	−0.0279009
$997$	−14588.1	−0.463400	−0.231700	−	0.972787i	$-0.574429\pi$
$997$	−14588.1	−0.463400	−0.231700	+	0.972787i	$0.574429\pi$
$998$	22442.3	0.711824
$999$	−7978.37	−0.252677

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.4.a.m.1.4	✓	5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +10.1443 q^{5} +6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +10.1443 q^{5} +6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} -20.2887 q^{10} -47.7648 q^{11} -12.0000 q^{12} -77.2742 q^{13} +14.0000 q^{14} -30.4330 q^{15} +16.0000 q^{16} -26.2302 q^{17} -18.0000 q^{18} +54.9670 q^{19} +40.5774 q^{20} +21.0000 q^{21} +95.5296 q^{22} -23.0000 q^{23} +24.0000 q^{24} -22.0923 q^{25} +154.548 q^{26} -27.0000 q^{27} -28.0000 q^{28} -52.9111 q^{29} +60.8660 q^{30} -97.0969 q^{31} -32.0000 q^{32} +143.294 q^{33} +52.4605 q^{34} -71.0104 q^{35} +36.0000 q^{36} +295.495 q^{37} -109.934 q^{38} +231.823 q^{39} -81.1547 q^{40} +365.501 q^{41} -42.0000 q^{42} +392.207 q^{43} -191.059 q^{44} +91.2991 q^{45} +46.0000 q^{46} +79.9862 q^{47} -48.0000 q^{48} +49.0000 q^{49} +44.1847 q^{50} +78.6907 q^{51} -309.097 q^{52} -146.138 q^{53} +54.0000 q^{54} -484.542 q^{55} +56.0000 q^{56} -164.901 q^{57} +105.822 q^{58} -19.0284 q^{59} -121.732 q^{60} +89.2284 q^{61} +194.194 q^{62} -63.0000 q^{63} +64.0000 q^{64} -783.896 q^{65} -286.589 q^{66} -1020.99 q^{67} -104.921 q^{68} +69.0000 q^{69} +142.021 q^{70} -121.668 q^{71} -72.0000 q^{72} -749.764 q^{73} -590.991 q^{74} +66.2770 q^{75} +219.868 q^{76} +334.354 q^{77} -463.645 q^{78} +548.871 q^{79} +162.309 q^{80} +81.0000 q^{81} -731.003 q^{82} +73.0846 q^{83} +84.0000 q^{84} -266.088 q^{85} -784.414 q^{86} +158.733 q^{87} +382.118 q^{88} +1089.25 q^{89} -182.598 q^{90} +540.919 q^{91} -92.0000 q^{92} +291.291 q^{93} -159.972 q^{94} +557.604 q^{95} +96.0000 q^{96} +724.274 q^{97} -98.0000 q^{98} -429.883 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 10 q^{2} - 15 q^{3} + 20 q^{4} + 10 q^{5} + 30 q^{6} - 35 q^{7} - 40 q^{8} + 45 q^{9}+O(q^{10}) \) 5 * q - 10 * q^2 - 15 * q^3 + 20 * q^4 + 10 * q^5 + 30 * q^6 - 35 * q^7 - 40 * q^8 + 45 * q^9	\( 5 q - 10 q^{2} - 15 q^{3} + 20 q^{4} + 10 q^{5} + 30 q^{6} - 35 q^{7} - 40 q^{8} + 45 q^{9} - 20 q^{10} + 4 q^{11} - 60 q^{12} + 24 q^{13} + 70 q^{14} - 30 q^{15} + 80 q^{16} + 28 q^{17} - 90 q^{18} - 160 q^{19} + 40 q^{20} + 105 q^{21} - 8 q^{22} - 115 q^{23} + 120 q^{24} + 219 q^{25} - 48 q^{26} - 135 q^{27} - 140 q^{28} + 79 q^{29} + 60 q^{30} - 162 q^{31} - 160 q^{32} - 12 q^{33} - 56 q^{34} - 70 q^{35} + 180 q^{36} + 301 q^{37} + 320 q^{38} - 72 q^{39} - 80 q^{40} + 251 q^{41} - 210 q^{42} - 380 q^{43} + 16 q^{44} + 90 q^{45} + 230 q^{46} - 505 q^{47} - 240 q^{48} + 245 q^{49} - 438 q^{50} - 84 q^{51} + 96 q^{52} + 93 q^{53} + 270 q^{54} - 503 q^{55} + 280 q^{56} + 480 q^{57} - 158 q^{58} + 637 q^{59} - 120 q^{60} - 679 q^{61} + 324 q^{62} - 315 q^{63} + 320 q^{64} + 961 q^{65} + 24 q^{66} - 1483 q^{67} + 112 q^{68} + 345 q^{69} + 140 q^{70} + 95 q^{71} - 360 q^{72} - 1310 q^{73} - 602 q^{74} - 657 q^{75} - 640 q^{76} - 28 q^{77} + 144 q^{78} + 494 q^{79} + 160 q^{80} + 405 q^{81} - 502 q^{82} - 482 q^{83} + 420 q^{84} - 291 q^{85} + 760 q^{86} - 237 q^{87} - 32 q^{88} + 661 q^{89} - 180 q^{90} - 168 q^{91} - 460 q^{92} + 486 q^{93} + 1010 q^{94} - 629 q^{95} + 480 q^{96} - 1905 q^{97} - 490 q^{98} + 36 q^{99}+O(q^{100}) \) 5 * q - 10 * q^2 - 15 * q^3 + 20 * q^4 + 10 * q^5 + 30 * q^6 - 35 * q^7 - 40 * q^8 + 45 * q^9 - 20 * q^10 + 4 * q^11 - 60 * q^12 + 24 * q^13 + 70 * q^14 - 30 * q^15 + 80 * q^16 + 28 * q^17 - 90 * q^18 - 160 * q^19 + 40 * q^20 + 105 * q^21 - 8 * q^22 - 115 * q^23 + 120 * q^24 + 219 * q^25 - 48 * q^26 - 135 * q^27 - 140 * q^28 + 79 * q^29 + 60 * q^30 - 162 * q^31 - 160 * q^32 - 12 * q^33 - 56 * q^34 - 70 * q^35 + 180 * q^36 + 301 * q^37 + 320 * q^38 - 72 * q^39 - 80 * q^40 + 251 * q^41 - 210 * q^42 - 380 * q^43 + 16 * q^44 + 90 * q^45 + 230 * q^46 - 505 * q^47 - 240 * q^48 + 245 * q^49 - 438 * q^50 - 84 * q^51 + 96 * q^52 + 93 * q^53 + 270 * q^54 - 503 * q^55 + 280 * q^56 + 480 * q^57 - 158 * q^58 + 637 * q^59 - 120 * q^60 - 679 * q^61 + 324 * q^62 - 315 * q^63 + 320 * q^64 + 961 * q^65 + 24 * q^66 - 1483 * q^67 + 112 * q^68 + 345 * q^69 + 140 * q^70 + 95 * q^71 - 360 * q^72 - 1310 * q^73 - 602 * q^74 - 657 * q^75 - 640 * q^76 - 28 * q^77 + 144 * q^78 + 494 * q^79 + 160 * q^80 + 405 * q^81 - 502 * q^82 - 482 * q^83 + 420 * q^84 - 291 * q^85 + 760 * q^86 - 237 * q^87 - 32 * q^88 + 661 * q^89 - 180 * q^90 - 168 * q^91 - 460 * q^92 + 486 * q^93 + 1010 * q^94 - 629 * q^95 + 480 * q^96 - 1905 * q^97 - 490 * q^98 + 36 * q^99

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