LMFDB - Embedded newform 966.4.a.l.1.3

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			1.3
Root			$15.2907$ 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)

$f(q)$	$=$	$q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +1.26807 q^{5} +6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +1.26807 q^{5} +6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} -2.53613 q^{10} -20.2880 q^{11} -12.0000 q^{12} +5.15056 q^{13} -14.0000 q^{14} -3.80420 q^{15} +16.0000 q^{16} -42.4667 q^{17} -18.0000 q^{18} +126.843 q^{19} +5.07226 q^{20} -21.0000 q^{21} +40.5759 q^{22} -23.0000 q^{23} +24.0000 q^{24} -123.392 q^{25} -10.3011 q^{26} -27.0000 q^{27} +28.0000 q^{28} +31.6088 q^{29} +7.60839 q^{30} -169.866 q^{31} -32.0000 q^{32} +60.8639 q^{33} +84.9334 q^{34} +8.87646 q^{35} +36.0000 q^{36} +311.591 q^{37} -253.687 q^{38} -15.4517 q^{39} -10.1445 q^{40} -366.747 q^{41} +42.0000 q^{42} -100.802 q^{43} -81.1519 q^{44} +11.4126 q^{45} +46.0000 q^{46} +6.97459 q^{47} -48.0000 q^{48} +49.0000 q^{49} +246.784 q^{50} +127.400 q^{51} +20.6022 q^{52} +284.687 q^{53} +54.0000 q^{54} -25.7265 q^{55} -56.0000 q^{56} -380.530 q^{57} -63.2176 q^{58} +162.117 q^{59} -15.2168 q^{60} +582.761 q^{61} +339.732 q^{62} +63.0000 q^{63} +64.0000 q^{64} +6.53124 q^{65} -121.728 q^{66} -539.980 q^{67} -169.867 q^{68} +69.0000 q^{69} -17.7529 q^{70} -179.293 q^{71} -72.0000 q^{72} +913.807 q^{73} -623.182 q^{74} +370.176 q^{75} +507.373 q^{76} -142.016 q^{77} +30.9033 q^{78} -49.7213 q^{79} +20.2890 q^{80} +81.0000 q^{81} +733.495 q^{82} +845.798 q^{83} -84.0000 q^{84} -53.8505 q^{85} +201.604 q^{86} -94.8264 q^{87} +162.304 q^{88} -701.107 q^{89} -22.8252 q^{90} +36.0539 q^{91} -92.0000 q^{92} +509.598 q^{93} -13.9492 q^{94} +160.846 q^{95} +96.0000 q^{96} -1559.33 q^{97} -98.0000 q^{98} -182.592 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	1.26807	0.113419	0.0567096	−	0.998391i	$-0.481939\pi$
$5$	1.26807	0.113419	0.0567096	+	0.998391i	$0.481939\pi$
$6$	6.00000	0.408248
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	−2.53613	−0.0801995
$11$	−20.2880	−0.556096	−0.278048	−	0.960567i	$-0.589687\pi$
$11$	−20.2880	−0.556096	−0.278048	+	0.960567i	$0.589687\pi$
$12$	−12.0000	−0.288675
$13$	5.15056	0.109885	0.0549426	−	0.998490i	$-0.482502\pi$
$13$	5.15056	0.109885	0.0549426	+	0.998490i	$0.482502\pi$
$14$	−14.0000	−0.267261
$15$	−3.80420	−0.0654826
$16$	16.0000	0.250000
$17$	−42.4667	−0.605864	−0.302932	−	0.953012i	$-0.597965\pi$
$17$	−42.4667	−0.605864	−0.302932	+	0.953012i	$0.597965\pi$
$18$	−18.0000	−0.235702
$19$	126.843	1.53157	0.765785	−	0.643096i	$-0.222351\pi$
$19$	126.843	1.53157	0.765785	+	0.643096i	$0.222351\pi$
$20$	5.07226	0.0567096
$21$	−21.0000	−0.218218
$22$	40.5759	0.393219
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	24.0000	0.204124
$25$	−123.392	−0.987136
$26$	−10.3011	−0.0777006
$27$	−27.0000	−0.192450
$28$	28.0000	0.188982
$29$	31.6088	0.202400	0.101200	−	0.994866i	$-0.467732\pi$
$29$	31.6088	0.202400	0.101200	+	0.994866i	$0.467732\pi$
$30$	7.60839	0.0463032
$31$	−169.866	−0.984156	−0.492078	−	0.870551i	$-0.663763\pi$
$31$	−169.866	−0.984156	−0.492078	+	0.870551i	$0.663763\pi$
$32$	−32.0000	−0.176777
$33$	60.8639	0.321062
$34$	84.9334	0.428410
$35$	8.87646	0.0428684
$36$	36.0000	0.166667
$37$	311.591	1.38447	0.692233	−	0.721674i	$-0.256627\pi$
$37$	311.591	1.38447	0.692233	+	0.721674i	$0.256627\pi$
$38$	−253.687	−1.08298
$39$	−15.4517	−0.0634422
$40$	−10.1445	−0.0400997
$41$	−366.747	−1.39698	−0.698492	−	0.715618i	$-0.746145\pi$
$41$	−366.747	−1.39698	−0.698492	+	0.715618i	$0.746145\pi$
$42$	42.0000	0.154303
$43$	−100.802	−0.357491	−0.178746	−	0.983895i	$-0.557204\pi$
$43$	−100.802	−0.357491	−0.178746	+	0.983895i	$0.557204\pi$
$44$	−81.1519	−0.278048
$45$	11.4126	0.0378064
$46$	46.0000	0.147442
$47$	6.97459	0.0216457	0.0108229	−	0.999941i	$-0.496555\pi$
$47$	6.97459	0.0216457	0.0108229	+	0.999941i	$0.496555\pi$
$48$	−48.0000	−0.144338
$49$	49.0000	0.142857
$50$	246.784	0.698011
$51$	127.400	0.349796
$52$	20.6022	0.0549426
$53$	284.687	0.737827	0.368914	−	0.929464i	$-0.379730\pi$
$53$	284.687	0.737827	0.368914	+	0.929464i	$0.379730\pi$
$54$	54.0000	0.136083
$55$	−25.7265	−0.0630719
$56$	−56.0000	−0.133631
$57$	−380.530	−0.884253
$58$	−63.2176	−0.143119
$59$	162.117	0.357725	0.178863	−	0.983874i	$-0.442758\pi$
$59$	162.117	0.357725	0.178863	+	0.983874i	$0.442758\pi$
$60$	−15.2168	−0.0327413
$61$	582.761	1.22319	0.611597	−	0.791169i	$-0.290527\pi$
$61$	582.761	1.22319	0.611597	+	0.791169i	$0.290527\pi$
$62$	339.732	0.695903
$63$	63.0000	0.125988
$64$	64.0000	0.125000
$65$	6.53124	0.0124631
$66$	−121.728	−0.227025
$67$	−539.980	−0.984612	−0.492306	−	0.870422i	$-0.663846\pi$
$67$	−539.980	−0.984612	−0.492306	+	0.870422i	$0.663846\pi$
$68$	−169.867	−0.302932
$69$	69.0000	0.120386
$70$	−17.7529	−0.0303126
$71$	−179.293	−0.299693	−0.149846	−	0.988709i	$-0.547878\pi$
$71$	−179.293	−0.299693	−0.149846	+	0.988709i	$0.547878\pi$
$72$	−72.0000	−0.117851
$73$	913.807	1.46511	0.732555	−	0.680708i	$-0.238328\pi$
$73$	913.807	1.46511	0.732555	+	0.680708i	$0.238328\pi$
$74$	−623.182	−0.978966
$75$	370.176	0.569923
$76$	507.373	0.765785
$77$	−142.016	−0.210184
$78$	30.9033	0.0448604
$79$	−49.7213	−0.0708112	−0.0354056	−	0.999373i	$-0.511272\pi$
$79$	−49.7213	−0.0708112	−0.0354056	+	0.999373i	$0.511272\pi$
$80$	20.2890	0.0283548
$81$	81.0000	0.111111
$82$	733.495	0.987817
$83$	845.798	1.11854	0.559268	−	0.828987i	$-0.311082\pi$
$83$	845.798	1.11854	0.559268	+	0.828987i	$0.311082\pi$
$84$	−84.0000	−0.109109
$85$	−53.8505	−0.0687166
$86$	201.604	0.252785
$87$	−94.8264	−0.116856
$88$	162.304	0.196609
$89$	−701.107	−0.835024	−0.417512	−	0.908671i	$-0.637098\pi$
$89$	−701.107	−0.835024	−0.417512	+	0.908671i	$0.637098\pi$
$90$	−22.8252	−0.0267332
$91$	36.0539	0.0415327
$92$	−92.0000	−0.104257
$93$	509.598	0.568203
$94$	−13.9492	−0.0153058
$95$	160.846	0.173710
$96$	96.0000	0.102062
$97$	−1559.33	−1.63222	−0.816112	−	0.577894i	$-0.803875\pi$
$97$	−1559.33	−1.63222	−0.816112	+	0.577894i	$0.803875\pi$
$98$	−98.0000	−0.101015
$99$	−182.592	−0.185365
$100$	−493.568	−0.493568
$101$	708.180	0.697689	0.348844	−	0.937181i	$-0.386574\pi$
$101$	708.180	0.697689	0.348844	+	0.937181i	$0.386574\pi$
$102$	−254.800	−0.247343
$103$	−867.029	−0.829426	−0.414713	−	0.909952i	$-0.636118\pi$
$103$	−867.029	−0.829426	−0.414713	+	0.909952i	$0.636118\pi$
$104$	−41.2045	−0.0388503
$105$	−26.6294	−0.0247501
$106$	−569.375	−0.521723
$107$	−1059.38	−0.957140	−0.478570	−	0.878049i	$-0.658845\pi$
$107$	−1059.38	−0.957140	−0.478570	+	0.878049i	$0.658845\pi$
$108$	−108.000	−0.0962250
$109$	−643.612	−0.565568	−0.282784	−	0.959184i	$-0.591258\pi$
$109$	−643.612	−0.565568	−0.282784	+	0.959184i	$0.591258\pi$
$110$	51.4529	0.0445986
$111$	−934.773	−0.799322
$112$	112.000	0.0944911
$113$	−353.956	−0.294667	−0.147333	−	0.989087i	$-0.547069\pi$
$113$	−353.956	−0.294667	−0.147333	+	0.989087i	$0.547069\pi$
$114$	761.060	0.625261
$115$	−29.1655	−0.0236495
$116$	126.435	0.101200
$117$	46.3550	0.0366284
$118$	−324.233	−0.252950
$119$	−297.267	−0.228995
$120$	30.4336	0.0231516
$121$	−919.398	−0.690758
$122$	−1165.52	−0.864929
$123$	1100.24	0.806549
$124$	−679.464	−0.492078
$125$	−314.977	−0.225379
$126$	−126.000	−0.0890871
$127$	1534.68	1.07229	0.536144	−	0.844126i	$-0.319880\pi$
$127$	1534.68	1.07229	0.536144	+	0.844126i	$0.319880\pi$
$128$	−128.000	−0.0883883
$129$	302.405	0.206398
$130$	−13.0625	−0.00881274
$131$	−2448.08	−1.63275	−0.816374	−	0.577524i	$-0.804019\pi$
$131$	−2448.08	−1.63275	−0.816374	+	0.577524i	$0.804019\pi$
$132$	243.456	0.160531
$133$	887.903	0.578879
$134$	1079.96	0.696226
$135$	−34.2378	−0.0218275
$136$	339.734	0.214205
$137$	−2498.92	−1.55837	−0.779186	−	0.626793i	$-0.784367\pi$
$137$	−2498.92	−1.55837	−0.779186	+	0.626793i	$0.784367\pi$
$138$	−138.000	−0.0851257
$139$	1013.19	0.618255	0.309128	−	0.951021i	$-0.399963\pi$
$139$	1013.19	0.618255	0.309128	+	0.951021i	$0.399963\pi$
$140$	35.5058	0.0214342
$141$	−20.9238	−0.0124972
$142$	358.586	0.211915
$143$	−104.494	−0.0611067
$144$	144.000	0.0833333
$145$	40.0820	0.0229561
$146$	−1827.61	−1.03599
$147$	−147.000	−0.0824786
$148$	1246.36	0.692233
$149$	−1387.14	−0.762678	−0.381339	−	0.924435i	$-0.624537\pi$
$149$	−1387.14	−0.762678	−0.381339	+	0.924435i	$0.624537\pi$
$150$	−740.352	−0.402997
$151$	1091.22	0.588092	0.294046	−	0.955791i	$-0.404998\pi$
$151$	1091.22	0.588092	0.294046	+	0.955791i	$0.404998\pi$
$152$	−1014.75	−0.541492
$153$	−382.200	−0.201955
$154$	284.032	0.148623
$155$	−215.401	−0.111622
$156$	−61.8067	−0.0317211
$157$	−1413.17	−0.718363	−0.359182	−	0.933268i	$-0.616944\pi$
$157$	−1413.17	−0.718363	−0.359182	+	0.933268i	$0.616944\pi$
$158$	99.4426	0.0500711
$159$	−854.062	−0.425985
$160$	−40.5781	−0.0200499
$161$	−161.000	−0.0788110
$162$	−162.000	−0.0785674
$163$	2960.34	1.42253	0.711263	−	0.702926i	$-0.248123\pi$
$163$	2960.34	1.42253	0.711263	+	0.702926i	$0.248123\pi$
$164$	−1466.99	−0.698492
$165$	77.1794	0.0364146
$166$	−1691.60	−0.790924
$167$	−3107.28	−1.43981	−0.719907	−	0.694071i	$-0.755815\pi$
$167$	−3107.28	−1.43981	−0.719907	+	0.694071i	$0.755815\pi$
$168$	168.000	0.0771517
$169$	−2170.47	−0.987925
$170$	107.701	0.0485900
$171$	1141.59	0.510523
$172$	−403.207	−0.178746
$173$	−839.524	−0.368947	−0.184473	−	0.982837i	$-0.559058\pi$
$173$	−839.524	−0.368947	−0.184473	+	0.982837i	$0.559058\pi$
$174$	189.653	0.0826296
$175$	−863.744	−0.373102
$176$	−324.607	−0.139024
$177$	−486.350	−0.206533
$178$	1402.21	0.590451
$179$	−1822.93	−0.761187	−0.380594	−	0.924742i	$-0.624280\pi$
$179$	−1822.93	−0.761187	−0.380594	+	0.924742i	$0.624280\pi$
$180$	45.6504	0.0189032
$181$	−2728.71	−1.12057	−0.560286	−	0.828299i	$-0.689309\pi$
$181$	−2728.71	−1.12057	−0.560286	+	0.828299i	$0.689309\pi$
$182$	−72.1078	−0.0293681
$183$	−1748.28	−0.706212
$184$	184.000	0.0737210
$185$	395.118	0.157025
$186$	−1019.20	−0.401780
$187$	861.563	0.336918
$188$	27.8984	0.0108229
$189$	−189.000	−0.0727393
$190$	−321.691	−0.122831
$191$	−1323.54	−0.501405	−0.250702	−	0.968064i	$-0.580662\pi$
$191$	−1323.54	−0.501405	−0.250702	+	0.968064i	$0.580662\pi$
$192$	−192.000	−0.0721688
$193$	−1421.65	−0.530220	−0.265110	−	0.964218i	$-0.585408\pi$
$193$	−1421.65	−0.530220	−0.265110	+	0.964218i	$0.585408\pi$
$194$	3118.66	1.15416
$195$	−19.5937	−0.00719557
$196$	196.000	0.0714286
$197$	−2755.34	−0.996495	−0.498248	−	0.867035i	$-0.666023\pi$
$197$	−2755.34	−0.996495	−0.498248	+	0.867035i	$0.666023\pi$
$198$	365.183	0.131073
$199$	−980.307	−0.349207	−0.174603	−	0.984639i	$-0.555864\pi$
$199$	−980.307	−0.349207	−0.174603	+	0.984639i	$0.555864\pi$
$200$	987.136	0.349005
$201$	1619.94	0.568466
$202$	−1416.36	−0.493340
$203$	221.262	0.0765001
$204$	509.600	0.174898
$205$	−465.060	−0.158445
$206$	1734.06	0.586493
$207$	−207.000	−0.0695048
$208$	82.4089	0.0274713
$209$	−2573.39	−0.851700
$210$	53.2587	0.0175010
$211$	−926.237	−0.302203	−0.151101	−	0.988518i	$-0.548282\pi$
$211$	−926.237	−0.302203	−0.151101	+	0.988518i	$0.548282\pi$
$212$	1138.75	0.368914
$213$	537.880	0.173028
$214$	2118.76	0.676800
$215$	−127.823	−0.0405464
$216$	216.000	0.0680414
$217$	−1189.06	−0.371976
$218$	1287.22	0.399917
$219$	−2741.42	−0.845881
$220$	−102.906	−0.0315360
$221$	−218.727	−0.0665755
$222$	1869.55	0.565206
$223$	2392.46	0.718434	0.359217	−	0.933254i	$-0.383044\pi$
$223$	2392.46	0.718434	0.359217	+	0.933254i	$0.383044\pi$
$224$	−224.000	−0.0668153
$225$	−1110.53	−0.329045
$226$	707.911	0.208361
$227$	1123.48	0.328492	0.164246	−	0.986419i	$-0.447481\pi$
$227$	1123.48	0.328492	0.164246	+	0.986419i	$0.447481\pi$
$228$	−1522.12	−0.442126
$229$	−2867.35	−0.827424	−0.413712	−	0.910408i	$-0.635768\pi$
$229$	−2867.35	−0.827424	−0.413712	+	0.910408i	$0.635768\pi$
$230$	58.3310	0.0167228
$231$	426.047	0.121350
$232$	−252.870	−0.0715593
$233$	−5972.93	−1.67940	−0.839699	−	0.543052i	$-0.817269\pi$
$233$	−5972.93	−1.67940	−0.839699	+	0.543052i	$0.817269\pi$
$234$	−92.7100	−0.0259002
$235$	8.84424	0.00245504
$236$	648.466	0.178863
$237$	149.164	0.0408829
$238$	594.534	0.161924
$239$	2605.57	0.705191	0.352595	−	0.935776i	$-0.385299\pi$
$239$	2605.57	0.705191	0.352595	+	0.935776i	$0.385299\pi$
$240$	−60.8671	−0.0163707
$241$	−4341.24	−1.16035	−0.580173	−	0.814493i	$-0.697015\pi$
$241$	−4341.24	−1.16035	−0.580173	+	0.814493i	$0.697015\pi$
$242$	1838.80	0.488439
$243$	−243.000	−0.0641500
$244$	2331.04	0.611597
$245$	62.1352	0.0162027
$246$	−2200.48	−0.570316
$247$	653.313	0.168297
$248$	1358.93	0.347952
$249$	−2537.40	−0.645787
$250$	629.955	0.159367
$251$	−7357.85	−1.85029	−0.925147	−	0.379610i	$-0.876058\pi$
$251$	−7357.85	−1.85029	−0.925147	+	0.379610i	$0.876058\pi$
$252$	252.000	0.0629941
$253$	466.623	0.115954
$254$	−3069.36	−0.758222
$255$	161.552	0.0396736
$256$	256.000	0.0625000
$257$	3459.17	0.839600	0.419800	−	0.907617i	$-0.362100\pi$
$257$	3459.17	0.839600	0.419800	+	0.907617i	$0.362100\pi$
$258$	−604.811	−0.145945
$259$	2181.14	0.523279
$260$	26.1250	0.00623155
$261$	284.479	0.0674668
$262$	4896.17	1.15453
$263$	1703.24	0.399340	0.199670	−	0.979863i	$-0.436013\pi$
$263$	1703.24	0.399340	0.199670	+	0.979863i	$0.436013\pi$
$264$	−486.911	−0.113513
$265$	361.002	0.0836838
$266$	−1775.81	−0.409329
$267$	2103.32	0.482101
$268$	−2159.92	−0.492306
$269$	−229.555	−0.0520305	−0.0260153	−	0.999662i	$-0.508282\pi$
$269$	−229.555	−0.0520305	−0.0260153	+	0.999662i	$0.508282\pi$
$270$	68.4755	0.0154344
$271$	1970.90	0.441785	0.220892	−	0.975298i	$-0.429103\pi$
$271$	1970.90	0.441785	0.220892	+	0.975298i	$0.429103\pi$
$272$	−679.467	−0.151466
$273$	−108.162	−0.0239789
$274$	4997.83	1.10194
$275$	2503.37	0.548942
$276$	276.000	0.0601929
$277$	5876.11	1.27459	0.637295	−	0.770620i	$-0.280053\pi$
$277$	5876.11	1.27459	0.637295	+	0.770620i	$0.280053\pi$
$278$	−2026.38	−0.437173
$279$	−1528.79	−0.328052
$280$	−71.0117	−0.0151563
$281$	3693.41	0.784095	0.392047	−	0.919945i	$-0.371767\pi$
$281$	3693.41	0.784095	0.392047	+	0.919945i	$0.371767\pi$
$282$	41.8476	0.00883683
$283$	−262.842	−0.0552096	−0.0276048	−	0.999619i	$-0.508788\pi$
$283$	−262.842	−0.0552096	−0.0276048	+	0.999619i	$0.508788\pi$
$284$	−717.173	−0.149846
$285$	−482.537	−0.100291
$286$	208.989	0.0432089
$287$	−2567.23	−0.528010
$288$	−288.000	−0.0589256
$289$	−3109.58	−0.632929
$290$	−80.1641	−0.0162324
$291$	4677.98	0.942365
$292$	3655.23	0.732555
$293$	−6552.37	−1.30646	−0.653232	−	0.757158i	$-0.726587\pi$
$293$	−6552.37	−1.30646	−0.653232	+	0.757158i	$0.726587\pi$
$294$	294.000	0.0583212
$295$	205.574	0.0405729
$296$	−2492.73	−0.489483
$297$	547.775	0.107021
$298$	2774.28	0.539295
$299$	−118.463	−0.0229126
$300$	1480.70	0.284962
$301$	−705.612	−0.135119
$302$	−2182.43	−0.415844
$303$	−2124.54	−0.402811
$304$	2029.49	0.382893
$305$	738.979	0.138734
$306$	764.401	0.142803
$307$	−5382.37	−1.00061	−0.500306	−	0.865849i	$-0.666779\pi$
$307$	−5382.37	−1.00061	−0.500306	+	0.865849i	$0.666779\pi$
$308$	−568.063	−0.105092
$309$	2601.09	0.478869
$310$	430.802	0.0789288
$311$	−8784.17	−1.60162	−0.800811	−	0.598917i	$-0.795598\pi$
$311$	−8784.17	−1.60162	−0.800811	+	0.598917i	$0.795598\pi$
$312$	123.613	0.0224302
$313$	4134.60	0.746651	0.373325	−	0.927700i	$-0.378218\pi$
$313$	4134.60	0.746651	0.373325	+	0.927700i	$0.378218\pi$
$314$	2826.34	0.507960
$315$	79.8881	0.0142895
$316$	−198.885	−0.0354056
$317$	−165.901	−0.0293941	−0.0146971	−	0.999892i	$-0.504678\pi$
$317$	−165.901	−0.0293941	−0.0146971	+	0.999892i	$0.504678\pi$
$318$	1708.12	0.301217
$319$	−641.278	−0.112554
$320$	81.1562	0.0141774
$321$	3178.14	0.552605
$322$	322.000	0.0557278
$323$	−5386.61	−0.927923
$324$	324.000	0.0555556
$325$	−635.538	−0.108472
$326$	−5920.68	−1.00588
$327$	1930.84	0.326531
$328$	2933.98	0.493908
$329$	48.8221	0.00818131
$330$	−154.359	−0.0257490
$331$	739.050	0.122725	0.0613623	−	0.998116i	$-0.480455\pi$
$331$	739.050	0.122725	0.0613623	+	0.998116i	$0.480455\pi$
$332$	3383.19	0.559268
$333$	2804.32	0.461489
$334$	6214.57	1.01810
$335$	−684.729	−0.111674
$336$	−336.000	−0.0545545
$337$	9964.54	1.61069	0.805346	−	0.592805i	$-0.201979\pi$
$337$	9964.54	1.61069	0.805346	+	0.592805i	$0.201979\pi$
$338$	4340.94	0.698569
$339$	1061.87	0.170126
$340$	−215.402	−0.0343583
$341$	3446.24	0.547285
$342$	−2283.18	−0.360995
$343$	343.000	0.0539949
$344$	806.414	0.126392
$345$	87.4965	0.0136541
$346$	1679.05	0.260885
$347$	2400.95	0.371440	0.185720	−	0.982603i	$-0.440538\pi$
$347$	2400.95	0.371440	0.185720	+	0.982603i	$0.440538\pi$
$348$	−379.306	−0.0584279
$349$	−7225.44	−1.10822	−0.554111	−	0.832443i	$-0.686942\pi$
$349$	−7225.44	−1.10822	−0.554111	+	0.832443i	$0.686942\pi$
$350$	1727.49	0.263823
$351$	−139.065	−0.0211474
$352$	649.215	0.0983047
$353$	5795.71	0.873865	0.436933	−	0.899494i	$-0.356065\pi$
$353$	5795.71	0.873865	0.436933	+	0.899494i	$0.356065\pi$
$354$	972.699	0.146041
$355$	−227.355	−0.0339909
$356$	−2804.43	−0.417512
$357$	891.801	0.132210
$358$	3645.87	0.538241
$359$	1363.87	0.200507	0.100254	−	0.994962i	$-0.468035\pi$
$359$	1363.87	0.200507	0.100254	+	0.994962i	$0.468035\pi$
$360$	−91.3007	−0.0133666
$361$	9230.21	1.34571
$362$	5457.43	0.792365
$363$	2758.20	0.398809
$364$	144.216	0.0207663
$365$	1158.77	0.166172
$366$	3496.56	0.499367
$367$	1366.59	0.194374	0.0971870	−	0.995266i	$-0.469015\pi$
$367$	1366.59	0.194374	0.0971870	+	0.995266i	$0.469015\pi$
$368$	−368.000	−0.0521286
$369$	−3300.73	−0.465661
$370$	−790.236	−0.111033
$371$	1992.81	0.278872
$372$	2038.39	0.284101
$373$	−799.766	−0.111020	−0.0555098	−	0.998458i	$-0.517678\pi$
$373$	−799.766	−0.111020	−0.0555098	+	0.998458i	$0.517678\pi$
$374$	−1723.13	−0.238237
$375$	944.932	0.130123
$376$	−55.7967	−0.00765292
$377$	162.803	0.0222408
$378$	378.000	0.0514344
$379$	1265.74	0.171548	0.0857738	−	0.996315i	$-0.472664\pi$
$379$	1265.74	0.171548	0.0857738	+	0.996315i	$0.472664\pi$
$380$	643.382	0.0868548
$381$	−4604.03	−0.619086
$382$	2647.09	0.354547
$383$	4043.99	0.539526	0.269763	−	0.962927i	$-0.413055\pi$
$383$	4043.99	0.539526	0.269763	+	0.962927i	$0.413055\pi$
$384$	384.000	0.0510310
$385$	−180.085	−0.0238389
$386$	2843.29	0.374922
$387$	−907.216	−0.119164
$388$	−6237.31	−0.816112
$389$	−1763.05	−0.229795	−0.114897	−	0.993377i	$-0.536654\pi$
$389$	−1763.05	−0.229795	−0.114897	+	0.993377i	$0.536654\pi$
$390$	39.1875	0.00508804
$391$	976.734	0.126331
$392$	−392.000	−0.0505076
$393$	7344.25	0.942667
$394$	5510.67	0.704628
$395$	−63.0499	−0.00803135
$396$	−730.367	−0.0926826
$397$	−4469.97	−0.565092	−0.282546	−	0.959254i	$-0.591179\pi$
$397$	−4469.97	−0.565092	−0.282546	+	0.959254i	$0.591179\pi$
$398$	1960.61	0.246926
$399$	−2663.71	−0.334216
$400$	−1974.27	−0.246784
$401$	−7022.40	−0.874519	−0.437259	−	0.899335i	$-0.644051\pi$
$401$	−7022.40	−0.874519	−0.437259	+	0.899335i	$0.644051\pi$
$402$	−3239.88	−0.401966
$403$	−874.905	−0.108144
$404$	2832.72	0.348844
$405$	102.713	0.0126021
$406$	−442.523	−0.0540937
$407$	−6321.55	−0.769896
$408$	−1019.20	−0.123671
$409$	7280.64	0.880207	0.440103	−	0.897947i	$-0.354942\pi$
$409$	7280.64	0.880207	0.440103	+	0.897947i	$0.354942\pi$
$410$	930.120	0.112037
$411$	7496.75	0.899726
$412$	−3468.12	−0.414713
$413$	1134.82	0.135207
$414$	414.000	0.0491473
$415$	1072.53	0.126863
$416$	−164.818	−0.0194251
$417$	−3039.56	−0.356950
$418$	5146.78	0.602243
$419$	−6819.12	−0.795073	−0.397537	−	0.917586i	$-0.630135\pi$
$419$	−6819.12	−0.795073	−0.397537	+	0.917586i	$0.630135\pi$
$420$	−106.517	−0.0123751
$421$	3450.67	0.399466	0.199733	−	0.979850i	$-0.435992\pi$
$421$	3450.67	0.399466	0.199733	+	0.979850i	$0.435992\pi$
$422$	1852.47	0.213690
$423$	62.7713	0.00721524
$424$	−2277.50	−0.260861
$425$	5240.05	0.598070
$426$	−1075.76	−0.122349
$427$	4079.33	0.462324
$428$	−4237.51	−0.478570
$429$	313.483	0.0352800
$430$	255.646	0.0286706
$431$	7474.52	0.835348	0.417674	−	0.908597i	$-0.362845\pi$
$431$	7474.52	0.835348	0.417674	+	0.908597i	$0.362845\pi$
$432$	−432.000	−0.0481125
$433$	−6035.32	−0.669836	−0.334918	−	0.942247i	$-0.608709\pi$
$433$	−6035.32	−0.669836	−0.334918	+	0.942247i	$0.608709\pi$
$434$	2378.12	0.263027
$435$	−120.246	−0.0132537
$436$	−2574.45	−0.282784
$437$	−2917.39	−0.319355
$438$	5482.84	0.598128
$439$	1823.31	0.198228	0.0991140	−	0.995076i	$-0.468399\pi$
$439$	1823.31	0.198228	0.0991140	+	0.995076i	$0.468399\pi$
$440$	205.812	0.0222993
$441$	441.000	0.0476190
$442$	437.454	0.0470760
$443$	14030.3	1.50474	0.752369	−	0.658742i	$-0.228911\pi$
$443$	14030.3	1.50474	0.752369	+	0.658742i	$0.228911\pi$
$444$	−3739.09	−0.399661
$445$	−889.049	−0.0947078
$446$	−4784.92	−0.508010
$447$	4161.42	0.440333
$448$	448.000	0.0472456
$449$	−15636.3	−1.64348	−0.821739	−	0.569864i	$-0.806996\pi$
$449$	−15636.3	−1.64348	−0.821739	+	0.569864i	$0.806996\pi$
$450$	2221.06	0.232670
$451$	7440.56	0.776857
$452$	−1415.82	−0.147333
$453$	−3273.65	−0.339535
$454$	−2246.95	−0.232279
$455$	45.7187	0.00471061
$456$	3044.24	0.312630
$457$	122.585	0.0125477	0.00627386	−	0.999980i	$-0.498003\pi$
$457$	122.585	0.0125477	0.00627386	+	0.999980i	$0.498003\pi$
$458$	5734.71	0.585077
$459$	1146.60	0.116599
$460$	−116.662	−0.0118248
$461$	−7869.94	−0.795097	−0.397548	−	0.917581i	$-0.630139\pi$
$461$	−7869.94	−0.795097	−0.397548	+	0.917581i	$0.630139\pi$
$462$	−852.095	−0.0858074
$463$	16581.2	1.66435	0.832177	−	0.554511i	$-0.187095\pi$
$463$	16581.2	1.66435	0.832177	+	0.554511i	$0.187095\pi$
$464$	505.741	0.0506001
$465$	646.204	0.0644451
$466$	11945.9	1.18751
$467$	−4883.25	−0.483875	−0.241938	−	0.970292i	$-0.577783\pi$
$467$	−4883.25	−0.483875	−0.241938	+	0.970292i	$0.577783\pi$
$468$	185.420	0.0183142
$469$	−3779.86	−0.372148
$470$	−17.6885	−0.00173598
$471$	4239.50	0.414747
$472$	−1296.93	−0.126475
$473$	2045.06	0.198799
$474$	−298.328	−0.0289085
$475$	−15651.4	−1.51187
$476$	−1189.07	−0.114498
$477$	2562.19	0.245942
$478$	−5211.15	−0.498645
$479$	12174.9	1.16135	0.580676	−	0.814135i	$-0.302788\pi$
$479$	12174.9	1.16135	0.580676	+	0.814135i	$0.302788\pi$
$480$	121.734	0.0115758
$481$	1604.87	0.152132
$482$	8682.47	0.820489
$483$	483.000	0.0455016
$484$	−3677.59	−0.345379
$485$	−1977.33	−0.185126
$486$	486.000	0.0453609
$487$	13936.8	1.29679	0.648396	−	0.761303i	$-0.275440\pi$
$487$	13936.8	1.29679	0.648396	+	0.761303i	$0.275440\pi$
$488$	−4662.09	−0.432465
$489$	−8881.02	−0.821296
$490$	−124.270	−0.0114571
$491$	−9267.11	−0.851769	−0.425885	−	0.904777i	$-0.640037\pi$
$491$	−9267.11	−0.851769	−0.425885	+	0.904777i	$0.640037\pi$
$492$	4400.97	0.403274
$493$	−1342.32	−0.122627
$494$	−1306.63	−0.119004
$495$	−231.538	−0.0210240
$496$	−2717.86	−0.246039
$497$	−1255.05	−0.113273
$498$	5074.79	0.456640
$499$	10361.9	0.929585	0.464792	−	0.885420i	$-0.346129\pi$
$499$	10361.9	0.929585	0.464792	+	0.885420i	$0.346129\pi$
$500$	−1259.91	−0.112690
$501$	9321.85	0.831277
$502$	14715.7	1.30835
$503$	14611.6	1.29522	0.647612	−	0.761970i	$-0.275768\pi$
$503$	14611.6	1.29522	0.647612	+	0.761970i	$0.275768\pi$
$504$	−504.000	−0.0445435
$505$	898.018	0.0791313
$506$	−933.246	−0.0819918
$507$	6511.42	0.570379
$508$	6138.71	0.536144
$509$	12331.1	1.07381	0.536903	−	0.843644i	$-0.319594\pi$
$509$	12331.1	1.07381	0.536903	+	0.843644i	$0.319594\pi$
$510$	−323.103	−0.0280534
$511$	6396.65	0.553759
$512$	−512.000	−0.0441942
$513$	−3424.77	−0.294751
$514$	−6918.34	−0.593687
$515$	−1099.45	−0.0940729
$516$	1209.62	0.103199
$517$	−141.500	−0.0120371
$518$	−4362.27	−0.370014
$519$	2518.57	0.213012
$520$	−52.2499	−0.00440637
$521$	1058.72	0.0890274	0.0445137	−	0.999009i	$-0.485826\pi$
$521$	1058.72	0.0890274	0.0445137	+	0.999009i	$0.485826\pi$
$522$	−568.958	−0.0477062
$523$	−16023.6	−1.33970	−0.669849	−	0.742498i	$-0.733641\pi$
$523$	−16023.6	−1.33970	−0.669849	+	0.742498i	$0.733641\pi$
$524$	−9792.33	−0.816374
$525$	2591.23	0.215411
$526$	−3406.48	−0.282376
$527$	7213.65	0.596265
$528$	973.822	0.0802655
$529$	529.000	0.0434783
$530$	−722.005	−0.0591734
$531$	1459.05	0.119242
$532$	3551.61	0.289440
$533$	−1888.95	−0.153508
$534$	−4206.64	−0.340897
$535$	−1343.36	−0.108558
$536$	4319.84	0.348113
$537$	5468.80	0.439472
$538$	459.110	0.0367911
$539$	−994.110	−0.0794422
$540$	−136.951	−0.0109138
$541$	−13974.6	−1.11056	−0.555281	−	0.831663i	$-0.687389\pi$
$541$	−13974.6	−1.11056	−0.555281	+	0.831663i	$0.687389\pi$
$542$	−3941.80	−0.312389
$543$	8186.14	0.646963
$544$	1358.93	0.107103
$545$	−816.143	−0.0641463
$546$	216.323	0.0169557
$547$	−21251.3	−1.66113	−0.830566	−	0.556920i	$-0.811983\pi$
$547$	−21251.3	−1.66113	−0.830566	+	0.556920i	$0.811983\pi$
$548$	−9995.67	−0.779186
$549$	5244.85	0.407732
$550$	−5006.75	−0.388161
$551$	4009.36	0.309990
$552$	−552.000	−0.0425628
$553$	−348.049	−0.0267641
$554$	−11752.2	−0.901271
$555$	−1185.35	−0.0906585
$556$	4052.75	0.309128
$557$	−8322.33	−0.633085	−0.316543	−	0.948578i	$-0.602522\pi$
$557$	−8322.33	−0.633085	−0.316543	+	0.948578i	$0.602522\pi$
$558$	3057.59	0.231968
$559$	−519.185	−0.0392830
$560$	142.023	0.0107171
$561$	−2584.69	−0.194520
$562$	−7386.83	−0.554439
$563$	−10834.4	−0.811037	−0.405518	−	0.914087i	$-0.632909\pi$
$563$	−10834.4	−0.811037	−0.405518	+	0.914087i	$0.632909\pi$
$564$	−83.6951	−0.00624858
$565$	−448.839	−0.0334209
$566$	525.684	0.0390391
$567$	567.000	0.0419961
$568$	1434.35	0.105957
$569$	−9210.45	−0.678598	−0.339299	−	0.940679i	$-0.610190\pi$
$569$	−9210.45	−0.678598	−0.339299	+	0.940679i	$0.610190\pi$
$570$	965.073	0.0709166
$571$	21182.3	1.55245	0.776226	−	0.630454i	$-0.217131\pi$
$571$	21182.3	1.55245	0.776226	+	0.630454i	$0.217131\pi$
$572$	−417.977	−0.0305533
$573$	3970.63	0.289486
$574$	5134.46	0.373360
$575$	2838.02	0.205832
$576$	576.000	0.0416667
$577$	−18407.6	−1.32811	−0.664054	−	0.747685i	$-0.731166\pi$
$577$	−18407.6	−1.32811	−0.664054	+	0.747685i	$0.731166\pi$
$578$	6219.16	0.447548
$579$	4264.94	0.306123
$580$	160.328	0.0114780
$581$	5920.59	0.422767
$582$	−9355.97	−0.666353
$583$	−5775.73	−0.410302
$584$	−7310.45	−0.517994
$585$	58.7812	0.00415436
$586$	13104.7	0.923809
$587$	11534.0	0.811000	0.405500	−	0.914095i	$-0.367097\pi$
$587$	11534.0	0.811000	0.405500	+	0.914095i	$0.367097\pi$
$588$	−588.000	−0.0412393
$589$	−21546.4	−1.50730
$590$	−411.149	−0.0286894
$591$	8266.01	0.575327
$592$	4985.46	0.346117
$593$	−4747.74	−0.328780	−0.164390	−	0.986395i	$-0.552566\pi$
$593$	−4747.74	−0.328780	−0.164390	+	0.986395i	$0.552566\pi$
$594$	−1095.55	−0.0756750
$595$	−376.954	−0.0259724
$596$	−5548.57	−0.381339
$597$	2940.92	0.201615
$598$	236.926	0.0162017
$599$	27354.8	1.86592	0.932959	−	0.359983i	$-0.117217\pi$
$599$	27354.8	1.86592	0.932959	+	0.359983i	$0.117217\pi$
$600$	−2961.41	−0.201498
$601$	14716.2	0.998815	0.499408	−	0.866367i	$-0.333551\pi$
$601$	14716.2	0.998815	0.499408	+	0.866367i	$0.333551\pi$
$602$	1411.22	0.0955436
$603$	−4859.82	−0.328204
$604$	4364.86	0.294046
$605$	−1165.86	−0.0783452
$606$	4249.08	0.284830
$607$	−14724.3	−0.984583	−0.492291	−	0.870431i	$-0.663841\pi$
$607$	−14724.3	−0.984583	−0.492291	+	0.870431i	$0.663841\pi$
$608$	−4058.98	−0.270746
$609$	−663.785	−0.0441674
$610$	−1477.96	−0.0980996
$611$	35.9230	0.00237854
$612$	−1528.80	−0.100977
$613$	10901.8	0.718302	0.359151	−	0.933279i	$-0.383066\pi$
$613$	10901.8	0.718302	0.359151	+	0.933279i	$0.383066\pi$
$614$	10764.7	0.707539
$615$	1395.18	0.0914781
$616$	1136.13	0.0743114
$617$	−26980.5	−1.76044	−0.880221	−	0.474565i	$-0.842605\pi$
$617$	−26980.5	−1.76044	−0.880221	+	0.474565i	$0.842605\pi$
$618$	−5202.17	−0.338612
$619$	2985.00	0.193825	0.0969123	−	0.995293i	$-0.469103\pi$
$619$	2985.00	0.193825	0.0969123	+	0.995293i	$0.469103\pi$
$620$	−861.605	−0.0558111
$621$	621.000	0.0401286
$622$	17568.3	1.13252
$623$	−4907.75	−0.315609
$624$	−247.227	−0.0158606
$625$	15024.6	0.961574
$626$	−8269.21	−0.527962
$627$	7720.17	0.491729
$628$	−5652.67	−0.359182
$629$	−13232.2	−0.838798
$630$	−159.776	−0.0101042
$631$	7820.54	0.493392	0.246696	−	0.969093i	$-0.420655\pi$
$631$	7820.54	0.493392	0.246696	+	0.969093i	$0.420655\pi$
$632$	397.770	0.0250355
$633$	2778.71	0.174477
$634$	331.802	0.0207848
$635$	1946.07	0.121618
$636$	−3416.25	−0.212992
$637$	252.377	0.0156979
$638$	1282.56	0.0795876
$639$	−1613.64	−0.0998976
$640$	−162.312	−0.0100249
$641$	−23683.8	−1.45937	−0.729683	−	0.683785i	$-0.760332\pi$
$641$	−23683.8	−1.45937	−0.729683	+	0.683785i	$0.760332\pi$
$642$	−6356.27	−0.390751
$643$	−28934.9	−1.77462	−0.887309	−	0.461176i	$-0.847428\pi$
$643$	−28934.9	−1.77462	−0.887309	+	0.461176i	$0.847428\pi$
$644$	−644.000	−0.0394055
$645$	383.470	0.0234095
$646$	10773.2	0.656141
$647$	−11131.1	−0.676365	−0.338183	−	0.941080i	$-0.609812\pi$
$647$	−11131.1	−0.676365	−0.338183	+	0.941080i	$0.609812\pi$
$648$	−648.000	−0.0392837
$649$	−3289.02	−0.198929
$650$	1271.08	0.0767010
$651$	3567.19	0.214760
$652$	11841.4	0.711263
$653$	−3843.07	−0.230308	−0.115154	−	0.993348i	$-0.536736\pi$
$653$	−3843.07	−0.230308	−0.115154	+	0.993348i	$0.536736\pi$
$654$	−3861.67	−0.230892
$655$	−3104.33	−0.185185
$656$	−5867.96	−0.349246
$657$	8224.26	0.488370
$658$	−97.6443	−0.00578506
$659$	27714.8	1.63826	0.819132	−	0.573605i	$-0.194456\pi$
$659$	27714.8	1.63826	0.819132	+	0.573605i	$0.194456\pi$
$660$	308.718	0.0182073
$661$	−27437.4	−1.61451	−0.807254	−	0.590204i	$-0.799047\pi$
$661$	−27437.4	−1.61451	−0.807254	+	0.590204i	$0.799047\pi$
$662$	−1478.10	−0.0867794
$663$	656.181	0.0384374
$664$	−6766.39	−0.395462
$665$	1125.92	0.0656560
$666$	−5608.64	−0.326322
$667$	−727.002	−0.0422034
$668$	−12429.1	−0.719907
$669$	−7177.37	−0.414788
$670$	1369.46	0.0789654
$671$	−11823.0	−0.680213
$672$	672.000	0.0385758
$673$	−4701.44	−0.269283	−0.134641	−	0.990894i	$-0.542988\pi$
$673$	−4701.44	−0.269283	−0.134641	+	0.990894i	$0.542988\pi$
$674$	−19929.1	−1.13893
$675$	3331.58	0.189974
$676$	−8681.89	−0.493963
$677$	8853.14	0.502591	0.251295	−	0.967910i	$-0.419143\pi$
$677$	8853.14	0.502591	0.251295	+	0.967910i	$0.419143\pi$
$678$	−2123.73	−0.120297
$679$	−10915.3	−0.616923
$680$	430.804	0.0242950
$681$	−3370.43	−0.189655
$682$	−6892.47	−0.386989
$683$	6219.18	0.348419	0.174210	−	0.984709i	$-0.444263\pi$
$683$	6219.18	0.348419	0.174210	+	0.984709i	$0.444263\pi$
$684$	4566.36	0.255262
$685$	−3168.79	−0.176749
$686$	−686.000	−0.0381802
$687$	8602.06	0.477713
$688$	−1612.83	−0.0893728
$689$	1466.30	0.0810763
$690$	−174.993	−0.00965488
$691$	6897.57	0.379733	0.189867	−	0.981810i	$-0.439194\pi$
$691$	6897.57	0.379733	0.189867	+	0.981810i	$0.439194\pi$
$692$	−3358.10	−0.184473
$693$	−1278.14	−0.0700615
$694$	−4801.89	−0.262647
$695$	1284.79	0.0701220
$696$	758.611	0.0413148
$697$	15574.6	0.846382
$698$	14450.9	0.783631
$699$	17918.8	0.969601
$700$	−3454.98	−0.186551
$701$	36177.6	1.94923	0.974614	−	0.223893i	$-0.0718765\pi$
$701$	36177.6	1.94923	0.974614	+	0.223893i	$0.0718765\pi$
$702$	278.130	0.0149535
$703$	39523.2	2.12041
$704$	−1298.43	−0.0695120
$705$	−26.5327	−0.00141742
$706$	−11591.4	−0.617916
$707$	4957.26	0.263701
$708$	−1945.40	−0.103266
$709$	9309.77	0.493139	0.246570	−	0.969125i	$-0.420697\pi$
$709$	9309.77	0.493139	0.246570	+	0.969125i	$0.420697\pi$
$710$	454.711	0.0240352
$711$	−447.492	−0.0236037
$712$	5608.85	0.295226
$713$	3906.92	0.205211
$714$	−1783.60	−0.0934868
$715$	−132.506	−0.00693067
$716$	−7291.74	−0.380594
$717$	−7816.72	−0.407142
$718$	−2727.73	−0.141780
$719$	28025.4	1.45364	0.726822	−	0.686825i	$-0.240996\pi$
$719$	28025.4	1.45364	0.726822	+	0.686825i	$0.240996\pi$
$720$	182.601	0.00945160
$721$	−6069.20	−0.313494
$722$	−18460.4	−0.951559
$723$	13023.7	0.669927
$724$	−10914.9	−0.560286
$725$	−3900.27	−0.199797
$726$	−5516.39	−0.282001
$727$	−25646.0	−1.30833	−0.654165	−	0.756352i	$-0.726980\pi$
$727$	−25646.0	−1.30833	−0.654165	+	0.756352i	$0.726980\pi$
$728$	−288.431	−0.0146840
$729$	729.000	0.0370370
$730$	−2317.53	−0.117501
$731$	4280.72	0.216591
$732$	−6993.13	−0.353106
$733$	21957.2	1.10642	0.553211	−	0.833041i	$-0.313403\pi$
$733$	21957.2	1.10642	0.553211	+	0.833041i	$0.313403\pi$
$734$	−2733.17	−0.137443
$735$	−186.406	−0.00935466
$736$	736.000	0.0368605
$737$	10955.1	0.547538
$738$	6601.45	0.329272
$739$	−38775.1	−1.93013	−0.965064	−	0.262015i	$-0.915613\pi$
$739$	−38775.1	−1.93013	−0.965064	+	0.262015i	$0.915613\pi$
$740$	1580.47	0.0785125
$741$	−1959.94	−0.0971663
$742$	−3985.62	−0.197193
$743$	−13662.5	−0.674602	−0.337301	−	0.941397i	$-0.609514\pi$
$743$	−13662.5	−0.674602	−0.337301	+	0.941397i	$0.609514\pi$
$744$	−4076.78	−0.200890
$745$	−1758.99	−0.0865024
$746$	1599.53	0.0785027
$747$	7612.19	0.372845
$748$	3446.25	0.168459
$749$	−7415.65	−0.361765
$750$	−1889.86	−0.0920108
$751$	17422.9	0.846567	0.423283	−	0.905997i	$-0.360877\pi$
$751$	17422.9	0.846567	0.423283	+	0.905997i	$0.360877\pi$
$752$	111.593	0.00541143
$753$	22073.6	1.06827
$754$	−325.606	−0.0157266
$755$	1383.73	0.0667009
$756$	−756.000	−0.0363696
$757$	−21472.3	−1.03094	−0.515472	−	0.856907i	$-0.672383\pi$
$757$	−21472.3	−1.03094	−0.515472	+	0.856907i	$0.672383\pi$
$758$	−2531.48	−0.121303
$759$	−1399.87	−0.0669460
$760$	−1286.76	−0.0614156
$761$	−8329.76	−0.396785	−0.198393	−	0.980123i	$-0.563572\pi$
$761$	−8329.76	−0.396785	−0.198393	+	0.980123i	$0.563572\pi$
$762$	9208.07	0.437760
$763$	−4505.29	−0.213765
$764$	−5294.18	−0.250702
$765$	−484.655	−0.0229055
$766$	−8087.99	−0.381502
$767$	834.991	0.0393087
$768$	−768.000	−0.0360844
$769$	−5632.32	−0.264118	−0.132059	−	0.991242i	$-0.542159\pi$
$769$	−5632.32	−0.264118	−0.132059	+	0.991242i	$0.542159\pi$
$770$	360.171	0.0168567
$771$	−10377.5	−0.484743
$772$	−5686.59	−0.265110
$773$	−7363.22	−0.342609	−0.171304	−	0.985218i	$-0.554798\pi$
$773$	−7363.22	−0.342609	−0.171304	+	0.985218i	$0.554798\pi$
$774$	1814.43	0.0842615
$775$	20960.1	0.971496
$776$	12474.6	0.577078
$777$	−6543.41	−0.302115
$778$	3526.10	0.162489
$779$	−46519.4	−2.13958
$780$	−78.3749	−0.00359778
$781$	3637.49	0.166658
$782$	−1953.47	−0.0893298
$783$	−853.438	−0.0389519
$784$	784.000	0.0357143
$785$	−1791.99	−0.0814762
$786$	−14688.5	−0.666567
$787$	9039.98	0.409454	0.204727	−	0.978819i	$-0.434369\pi$
$787$	9039.98	0.409454	0.204727	+	0.978819i	$0.434369\pi$
$788$	−11021.3	−0.498248
$789$	−5109.73	−0.230559
$790$	126.100	0.00567902
$791$	−2477.69	−0.111374
$792$	1460.73	0.0655365
$793$	3001.54	0.134411
$794$	8939.94	0.399580
$795$	−1083.01	−0.0483148
$796$	−3921.23	−0.174603
$797$	23549.8	1.04664	0.523322	−	0.852135i	$-0.324693\pi$
$797$	23549.8	1.04664	0.523322	+	0.852135i	$0.324693\pi$
$798$	5327.42	0.236326
$799$	−296.188	−0.0131144
$800$	3948.54	0.174503
$801$	−6309.96	−0.278341
$802$	14044.8	0.618378
$803$	−18539.3	−0.814741
$804$	6479.75	0.284233
$805$	−204.159	−0.00893869
$806$	1749.81	0.0764695
$807$	688.665	0.0300398
$808$	−5665.44	−0.246670
$809$	25393.3	1.10356	0.551780	−	0.833990i	$-0.313949\pi$
$809$	25393.3	1.10356	0.551780	+	0.833990i	$0.313949\pi$
$810$	−205.427	−0.00891105
$811$	−17694.8	−0.766149	−0.383075	−	0.923717i	$-0.625135\pi$
$811$	−17694.8	−0.766149	−0.383075	+	0.923717i	$0.625135\pi$
$812$	885.047	0.0382501
$813$	−5912.70	−0.255065
$814$	12643.1	0.544398
$815$	3753.91	0.161342
$816$	2038.40	0.0874489
$817$	−12786.0	−0.547523
$818$	−14561.3	−0.622400
$819$	324.485	0.0138442
$820$	−1860.24	−0.0792224
$821$	8750.42	0.371975	0.185988	−	0.982552i	$-0.440452\pi$
$821$	8750.42	0.371975	0.185988	+	0.982552i	$0.440452\pi$
$822$	−14993.5	−0.636203
$823$	12945.1	0.548283	0.274141	−	0.961689i	$-0.411606\pi$
$823$	12945.1	0.548283	0.274141	+	0.961689i	$0.411606\pi$
$824$	6936.23	0.293246
$825$	−7510.12	−0.316932
$826$	−2269.63	−0.0956060
$827$	−8855.38	−0.372348	−0.186174	−	0.982517i	$-0.559609\pi$
$827$	−8855.38	−0.372348	−0.186174	+	0.982517i	$0.559609\pi$
$828$	−828.000	−0.0347524
$829$	−36626.8	−1.53450	−0.767251	−	0.641347i	$-0.778376\pi$
$829$	−36626.8	−1.53450	−0.767251	+	0.641347i	$0.778376\pi$
$830$	−2145.06	−0.0897060
$831$	−17628.3	−0.735885
$832$	329.636	0.0137356
$833$	−2080.87	−0.0865520
$834$	6079.13	0.252402
$835$	−3940.24	−0.163303
$836$	−10293.6	−0.425850
$837$	4586.38	0.189401
$838$	13638.2	0.562202
$839$	−46220.0	−1.90190	−0.950949	−	0.309347i	$-0.899890\pi$
$839$	−46220.0	−1.90190	−0.950949	+	0.309347i	$0.899890\pi$
$840$	213.035	0.00875048
$841$	−23389.9	−0.959034
$842$	−6901.34	−0.282465
$843$	−11080.2	−0.452697
$844$	−3704.95	−0.151101
$845$	−2752.30	−0.112050
$846$	−125.543	−0.00510195
$847$	−6435.79	−0.261082
$848$	4555.00	0.184457
$849$	788.525	0.0318753
$850$	−10480.1	−0.422899
$851$	−7166.59	−0.288681
$852$	2151.52	0.0865138
$853$	−28368.7	−1.13872	−0.569358	−	0.822089i	$-0.692808\pi$
$853$	−28368.7	−1.13872	−0.569358	+	0.822089i	$0.692808\pi$
$854$	−8158.65	−0.326913
$855$	1447.61	0.0579032
$856$	8475.03	0.338400
$857$	38387.7	1.53011	0.765053	−	0.643968i	$-0.222713\pi$
$857$	38387.7	1.53011	0.765053	+	0.643968i	$0.222713\pi$
$858$	−626.966	−0.0249467
$859$	−3472.57	−0.137931	−0.0689653	−	0.997619i	$-0.521970\pi$
$859$	−3472.57	−0.137931	−0.0689653	+	0.997619i	$0.521970\pi$
$860$	−511.293	−0.0202732
$861$	7701.70	0.304847
$862$	−14949.0	−0.590680
$863$	17407.0	0.686606	0.343303	−	0.939225i	$-0.388454\pi$
$863$	17407.0	0.686606	0.343303	+	0.939225i	$0.388454\pi$
$864$	864.000	0.0340207
$865$	−1064.57	−0.0418457
$866$	12070.6	0.473645
$867$	9328.74	0.365422
$868$	−4756.25	−0.185988
$869$	1008.74	0.0393778
$870$	240.492	0.00937178
$871$	−2781.20	−0.108194
$872$	5148.90	0.199958
$873$	−14034.0	−0.544075
$874$	5834.79	0.225818
$875$	−2204.84	−0.0851854
$876$	−10965.7	−0.422941
$877$	−34576.3	−1.33131	−0.665655	−	0.746260i	$-0.731848\pi$
$877$	−34576.3	−1.33131	−0.665655	+	0.746260i	$0.731848\pi$
$878$	−3646.63	−0.140168
$879$	19657.1	0.754287
$880$	−411.623	−0.0157680
$881$	−40887.7	−1.56361	−0.781806	−	0.623522i	$-0.785701\pi$
$881$	−40887.7	−1.56361	−0.781806	+	0.623522i	$0.785701\pi$
$882$	−882.000	−0.0336718
$883$	7295.27	0.278035	0.139018	−	0.990290i	$-0.455606\pi$
$883$	7295.27	0.278035	0.139018	+	0.990290i	$0.455606\pi$
$884$	−874.909	−0.0332877
$885$	−616.723	−0.0234248
$886$	−28060.6	−1.06401
$887$	28163.9	1.06612	0.533061	−	0.846077i	$-0.321042\pi$
$887$	28163.9	1.06612	0.533061	+	0.846077i	$0.321042\pi$
$888$	7478.19	0.282603
$889$	10742.7	0.405287
$890$	1778.10	0.0669685
$891$	−1643.33	−0.0617884
$892$	9569.83	0.359217
$893$	884.680	0.0331519
$894$	−8322.85	−0.311362
$895$	−2311.60	−0.0863333
$896$	−896.000	−0.0334077
$897$	355.388	0.0132286
$898$	31272.6	1.16211
$899$	−5369.26	−0.199193
$900$	−4442.11	−0.164523
$901$	−12089.7	−0.447023
$902$	−14881.1	−0.549321
$903$	2116.84	0.0780110
$904$	2831.64	0.104180
$905$	−3460.19	−0.127094
$906$	6547.29	0.240087
$907$	36823.2	1.34806	0.674031	−	0.738703i	$-0.264561\pi$
$907$	36823.2	1.34806	0.674031	+	0.738703i	$0.264561\pi$
$908$	4493.90	0.164246
$909$	6373.62	0.232563
$910$	−91.4374	−0.00333090
$911$	23711.8	0.862355	0.431178	−	0.902267i	$-0.358098\pi$
$911$	23711.8	0.862355	0.431178	+	0.902267i	$0.358098\pi$
$912$	−6088.48	−0.221063
$913$	−17159.5	−0.622013
$914$	−245.171	−0.00887257
$915$	−2216.94	−0.0800980
$916$	−11469.4	−0.413712
$917$	−17136.6	−0.617121
$918$	−2293.20	−0.0824476
$919$	−35818.8	−1.28569	−0.642847	−	0.765995i	$-0.722247\pi$
$919$	−35818.8	−1.28569	−0.642847	+	0.765995i	$0.722247\pi$
$920$	233.324	0.00836138
$921$	16147.1	0.577703
$922$	15739.9	0.562218
$923$	−923.460	−0.0329318
$924$	1704.19	0.0606750
$925$	−38447.8	−1.36666
$926$	−33162.5	−1.17688
$927$	−7803.26	−0.276475
$928$	−1011.48	−0.0357796
$929$	−31777.2	−1.12226	−0.561128	−	0.827729i	$-0.689632\pi$
$929$	−31777.2	−1.12226	−0.561128	+	0.827729i	$0.689632\pi$
$930$	−1292.41	−0.0455696
$931$	6215.32	0.218796
$932$	−23891.7	−0.839699
$933$	26352.5	0.924697
$934$	9766.50	0.342152
$935$	1092.52	0.0382130
$936$	−370.840	−0.0129501
$937$	53675.3	1.87139	0.935697	−	0.352805i	$-0.114772\pi$
$937$	53675.3	1.87139	0.935697	+	0.352805i	$0.114772\pi$
$938$	7559.71	0.263149
$939$	−12403.8	−0.431079
$940$	35.3770	0.00122752
$941$	−42558.4	−1.47435	−0.737175	−	0.675702i	$-0.763841\pi$
$941$	−42558.4	−1.47435	−0.737175	+	0.675702i	$0.763841\pi$
$942$	−8479.01	−0.293271
$943$	8435.19	0.291291
$944$	2593.86	0.0894313
$945$	−239.664	−0.00825003
$946$	−4090.13	−0.140572
$947$	−5778.46	−0.198284	−0.0991418	−	0.995073i	$-0.531610\pi$
$947$	−5778.46	−0.198284	−0.0991418	+	0.995073i	$0.531610\pi$
$948$	596.656	0.0204414
$949$	4706.61	0.160994
$950$	31302.9	1.06905
$951$	497.703	0.0169707
$952$	2378.13	0.0809620
$953$	1814.63	0.0616807	0.0308403	−	0.999524i	$-0.490182\pi$
$953$	1814.63	0.0616807	0.0308403	+	0.999524i	$0.490182\pi$
$954$	−5124.37	−0.173908
$955$	−1678.34	−0.0568689
$956$	10422.3	0.352595
$957$	1923.83	0.0649830
$958$	−24349.9	−0.821200
$959$	−17492.4	−0.589009
$960$	−243.469	−0.00818533
$961$	−936.530	−0.0314367
$962$	−3209.74	−0.107574
$963$	−9534.41	−0.319047
$964$	−17364.9	−0.580173
$965$	−1802.74	−0.0601371
$966$	−966.000	−0.0321745
$967$	35059.8	1.16592	0.582961	−	0.812500i	$-0.301894\pi$
$967$	35059.8	1.16592	0.582961	+	0.812500i	$0.301894\pi$
$968$	7355.19	0.244220
$969$	16159.8	0.535737
$970$	3954.66	0.130904
$971$	−22521.6	−0.744339	−0.372170	−	0.928165i	$-0.621386\pi$
$971$	−22521.6	−0.744339	−0.372170	+	0.928165i	$0.621386\pi$
$972$	−972.000	−0.0320750
$973$	7092.32	0.233679
$974$	−27873.7	−0.916971
$975$	1906.61	0.0626261
$976$	9324.17	0.305799
$977$	36937.3	1.20955	0.604774	−	0.796397i	$-0.293263\pi$
$977$	36937.3	1.20955	0.604774	+	0.796397i	$0.293263\pi$
$978$	17762.0	0.580744
$979$	14224.0	0.464353
$980$	248.541	0.00810137
$981$	−5792.51	−0.188523
$982$	18534.2	0.602292
$983$	−6569.10	−0.213145	−0.106573	−	0.994305i	$-0.533988\pi$
$983$	−6569.10	−0.213145	−0.106573	+	0.994305i	$0.533988\pi$
$984$	−8801.94	−0.285158
$985$	−3493.95	−0.113022
$986$	2684.64	0.0867104
$987$	−146.466	−0.00472348
$988$	2613.25	0.0841485
$989$	2318.44	0.0745421
$990$	463.076	0.0148662
$991$	−41759.4	−1.33858	−0.669290	−	0.743002i	$-0.733401\pi$
$991$	−41759.4	−1.33858	−0.669290	+	0.743002i	$0.733401\pi$
$992$	5435.71	0.173976
$993$	−2217.15	−0.0708551
$994$	2510.10	0.0800963
$995$	−1243.09	−0.0396067
$996$	−10149.6	−0.322893
$997$	39129.5	1.24297	0.621487	−	0.783425i	$-0.286529\pi$
$997$	39129.5	1.24297	0.621487	+	0.783425i	$0.286529\pi$
$998$	−20723.8	−0.657316
$999$	−8412.96	−0.266441

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.4.a.l.1.3	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.4.a.l.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +1.26807 q^{5} +6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +1.26807 q^{5} +6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} -2.53613 q^{10} -20.2880 q^{11} -12.0000 q^{12} +5.15056 q^{13} -14.0000 q^{14} -3.80420 q^{15} +16.0000 q^{16} -42.4667 q^{17} -18.0000 q^{18} +126.843 q^{19} +5.07226 q^{20} -21.0000 q^{21} +40.5759 q^{22} -23.0000 q^{23} +24.0000 q^{24} -123.392 q^{25} -10.3011 q^{26} -27.0000 q^{27} +28.0000 q^{28} +31.6088 q^{29} +7.60839 q^{30} -169.866 q^{31} -32.0000 q^{32} +60.8639 q^{33} +84.9334 q^{34} +8.87646 q^{35} +36.0000 q^{36} +311.591 q^{37} -253.687 q^{38} -15.4517 q^{39} -10.1445 q^{40} -366.747 q^{41} +42.0000 q^{42} -100.802 q^{43} -81.1519 q^{44} +11.4126 q^{45} +46.0000 q^{46} +6.97459 q^{47} -48.0000 q^{48} +49.0000 q^{49} +246.784 q^{50} +127.400 q^{51} +20.6022 q^{52} +284.687 q^{53} +54.0000 q^{54} -25.7265 q^{55} -56.0000 q^{56} -380.530 q^{57} -63.2176 q^{58} +162.117 q^{59} -15.2168 q^{60} +582.761 q^{61} +339.732 q^{62} +63.0000 q^{63} +64.0000 q^{64} +6.53124 q^{65} -121.728 q^{66} -539.980 q^{67} -169.867 q^{68} +69.0000 q^{69} -17.7529 q^{70} -179.293 q^{71} -72.0000 q^{72} +913.807 q^{73} -623.182 q^{74} +370.176 q^{75} +507.373 q^{76} -142.016 q^{77} +30.9033 q^{78} -49.7213 q^{79} +20.2890 q^{80} +81.0000 q^{81} +733.495 q^{82} +845.798 q^{83} -84.0000 q^{84} -53.8505 q^{85} +201.604 q^{86} -94.8264 q^{87} +162.304 q^{88} -701.107 q^{89} -22.8252 q^{90} +36.0539 q^{91} -92.0000 q^{92} +509.598 q^{93} -13.9492 q^{94} +160.846 q^{95} +96.0000 q^{96} -1559.33 q^{97} -98.0000 q^{98} -182.592 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 10 q^{2} - 15 q^{3} + 20 q^{4} - 15 q^{5} + 30 q^{6} + 35 q^{7} - 40 q^{8} + 45 q^{9}+O(q^{10}) \) 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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