LMFDB - Embedded newform 483.4.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,4,Mod(1,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, 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("483.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	483.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:	$28.4979225328$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 34x^{5} + 7x^{4} + 295x^{3} + 84x^{2} - 524x - 288 $ x^7 - x^6 - 34x^5 + 7x^4 + 295x^3 + 84x^2 - 524*x - 288
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-4.12074$ of defining polynomial
Character	$\chi$	$=$	483.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.12074 q^{2} +3.00000 q^{3} +18.2220 q^{4} -15.2134 q^{5} -15.3622 q^{6} +7.00000 q^{7} -52.3444 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-5.12074 q^{2} +3.00000 q^{3} +18.2220 q^{4} -15.2134 q^{5} -15.3622 q^{6} +7.00000 q^{7} -52.3444 q^{8} +9.00000 q^{9} +77.9040 q^{10} -57.9936 q^{11} +54.6661 q^{12} +66.4140 q^{13} -35.8452 q^{14} -45.6402 q^{15} +122.266 q^{16} +133.148 q^{17} -46.0867 q^{18} -89.5681 q^{19} -277.219 q^{20} +21.0000 q^{21} +296.970 q^{22} +23.0000 q^{23} -157.033 q^{24} +106.448 q^{25} -340.089 q^{26} +27.0000 q^{27} +127.554 q^{28} -191.577 q^{29} +233.712 q^{30} +133.974 q^{31} -207.338 q^{32} -173.981 q^{33} -681.817 q^{34} -106.494 q^{35} +163.998 q^{36} -264.506 q^{37} +458.655 q^{38} +199.242 q^{39} +796.337 q^{40} +84.1122 q^{41} -107.536 q^{42} -82.9438 q^{43} -1056.76 q^{44} -136.921 q^{45} -117.777 q^{46} +384.762 q^{47} +366.798 q^{48} +49.0000 q^{49} -545.092 q^{50} +399.444 q^{51} +1210.20 q^{52} +259.677 q^{53} -138.260 q^{54} +882.281 q^{55} -366.411 q^{56} -268.704 q^{57} +981.018 q^{58} +569.768 q^{59} -831.657 q^{60} -33.4713 q^{61} -686.048 q^{62} +63.0000 q^{63} +83.5967 q^{64} -1010.38 q^{65} +890.911 q^{66} -612.990 q^{67} +2426.23 q^{68} +69.0000 q^{69} +545.328 q^{70} -799.550 q^{71} -471.099 q^{72} -357.892 q^{73} +1354.47 q^{74} +319.343 q^{75} -1632.11 q^{76} -405.955 q^{77} -1020.27 q^{78} -397.702 q^{79} -1860.08 q^{80} +81.0000 q^{81} -430.717 q^{82} -5.96537 q^{83} +382.663 q^{84} -2025.64 q^{85} +424.734 q^{86} -574.732 q^{87} +3035.64 q^{88} -370.826 q^{89} +701.136 q^{90} +464.898 q^{91} +419.107 q^{92} +401.923 q^{93} -1970.27 q^{94} +1362.64 q^{95} -622.014 q^{96} -1038.62 q^{97} -250.916 q^{98} -521.942 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 6 q^{2} + 21 q^{3} + 18 q^{4} - 41 q^{5} - 18 q^{6} + 49 q^{7} - 33 q^{8} + 63 q^{9}+O(q^{10}) $ 7 * q - 6 * q^2 + 21 * q^3 + 18 * q^4 - 41 * q^5 - 18 * q^6 + 49 * q^7 - 33 * q^8 + 63 * q^9	\( 7 q - 6 q^{2} + 21 q^{3} + 18 q^{4} - 41 q^{5} - 18 q^{6} + 49 q^{7} - 33 q^{8} + 63 q^{9} + q^{10} - 126 q^{11} + 54 q^{12} - 87 q^{13} - 42 q^{14} - 123 q^{15} + 2 q^{16} - 204 q^{17} - 54 q^{18} - 286 q^{19} - 418 q^{20} + 147 q^{21} + 329 q^{22} + 161 q^{23} - 99 q^{24} + 440 q^{25} - 360 q^{26} + 189 q^{27} + 126 q^{28} - 329 q^{29} + 3 q^{30} + 296 q^{31} - 270 q^{32} - 378 q^{33} - 919 q^{34} - 287 q^{35} + 162 q^{36} - 691 q^{37} - 367 q^{38} - 261 q^{39} + 138 q^{40} - 343 q^{41} - 126 q^{42} - 171 q^{43} - 1279 q^{44} - 369 q^{45} - 138 q^{46} - 1403 q^{47} + 6 q^{48} + 343 q^{49} + 230 q^{50} - 612 q^{51} + 2157 q^{52} - 1024 q^{53} - 162 q^{54} - 158 q^{55} - 231 q^{56} - 858 q^{57} + 2608 q^{58} - 1388 q^{59} - 1254 q^{60} - 52 q^{61} - 309 q^{62} + 441 q^{63} - 187 q^{64} - 1067 q^{65} + 987 q^{66} - 1148 q^{67} + 1293 q^{68} + 483 q^{69} + 7 q^{70} - 1590 q^{71} - 297 q^{72} - 802 q^{73} - 878 q^{74} + 1320 q^{75} - 2505 q^{76} - 882 q^{77} - 1080 q^{78} + 618 q^{79} + 195 q^{80} + 567 q^{81} - 1040 q^{82} - 1818 q^{83} + 378 q^{84} - 1526 q^{85} + 1188 q^{86} - 987 q^{87} + 1664 q^{88} - 354 q^{89} + 9 q^{90} - 609 q^{91} + 414 q^{92} + 888 q^{93} + 663 q^{94} + 78 q^{95} - 810 q^{96} - 1575 q^{97} - 294 q^{98} - 1134 q^{99}+O(q^{100}) \) 7 * q - 6 * q^2 + 21 * q^3 + 18 * q^4 - 41 * q^5 - 18 * q^6 + 49 * q^7 - 33 * q^8 + 63 * q^9 + q^10 - 126 * q^11 + 54 * q^12 - 87 * q^13 - 42 * q^14 - 123 * q^15 + 2 * q^16 - 204 * q^17 - 54 * q^18 - 286 * q^19 - 418 * q^20 + 147 * q^21 + 329 * q^22 + 161 * q^23 - 99 * q^24 + 440 * q^25 - 360 * q^26 + 189 * q^27 + 126 * q^28 - 329 * q^29 + 3 * q^30 + 296 * q^31 - 270 * q^32 - 378 * q^33 - 919 * q^34 - 287 * q^35 + 162 * q^36 - 691 * q^37 - 367 * q^38 - 261 * q^39 + 138 * q^40 - 343 * q^41 - 126 * q^42 - 171 * q^43 - 1279 * q^44 - 369 * q^45 - 138 * q^46 - 1403 * q^47 + 6 * q^48 + 343 * q^49 + 230 * q^50 - 612 * q^51 + 2157 * q^52 - 1024 * q^53 - 162 * q^54 - 158 * q^55 - 231 * q^56 - 858 * q^57 + 2608 * q^58 - 1388 * q^59 - 1254 * q^60 - 52 * q^61 - 309 * q^62 + 441 * q^63 - 187 * q^64 - 1067 * q^65 + 987 * q^66 - 1148 * q^67 + 1293 * q^68 + 483 * q^69 + 7 * q^70 - 1590 * q^71 - 297 * q^72 - 802 * q^73 - 878 * q^74 + 1320 * q^75 - 2505 * q^76 - 882 * q^77 - 1080 * q^78 + 618 * q^79 + 195 * q^80 + 567 * q^81 - 1040 * q^82 - 1818 * q^83 + 378 * q^84 - 1526 * q^85 + 1188 * q^86 - 987 * q^87 + 1664 * q^88 - 354 * q^89 + 9 * q^90 - 609 * q^91 + 414 * q^92 + 888 * q^93 + 663 * q^94 + 78 * q^95 - 810 * q^96 - 1575 * q^97 - 294 * q^98 - 1134 * 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 $

$2$	−5.12074	−1.81046	−0.905228	−	0.424926i	$-0.860300\pi$
$2$	−5.12074	−1.81046	−0.905228	+	0.424926i	$0.860300\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	18.2220	2.27775
$5$	−15.2134	−1.36073	−0.680364	−	0.732874i	$-0.738178\pi$
$5$	−15.2134	−1.36073	−0.680364	+	0.732874i	$0.738178\pi$
$6$	−15.3622	−1.04527
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−52.3444	−2.31332
$9$	9.00000	0.333333
$10$	77.9040	2.46354
$11$	−57.9936	−1.58961	−0.794806	−	0.606864i	$-0.792427\pi$
$11$	−57.9936	−1.58961	−0.794806	+	0.606864i	$0.792427\pi$
$12$	54.6661	1.31506
$13$	66.4140	1.41692	0.708459	−	0.705752i	$-0.249391\pi$
$13$	66.4140	1.41692	0.708459	+	0.705752i	$0.249391\pi$
$14$	−35.8452	−0.684288
$15$	−45.6402	−0.785617
$16$	122.266	1.91041
$17$	133.148	1.89960	0.949799	−	0.312862i	$-0.101288\pi$
$17$	133.148	1.89960	0.949799	+	0.312862i	$0.101288\pi$
$18$	−46.0867	−0.603486
$19$	−89.5681	−1.08149	−0.540745	−	0.841186i	$-0.681858\pi$
$19$	−89.5681	−1.08149	−0.540745	+	0.841186i	$0.681858\pi$
$20$	−277.219	−3.09940
$21$	21.0000	0.218218
$22$	296.970	2.87792
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	−157.033	−1.33559
$25$	106.448	0.851583
$26$	−340.089	−2.56527
$27$	27.0000	0.192450
$28$	127.554	0.860910
$29$	−191.577	−1.22672	−0.613362	−	0.789802i	$-0.710183\pi$
$29$	−191.577	−1.22672	−0.613362	+	0.789802i	$0.710183\pi$
$30$	233.712	1.42233
$31$	133.974	0.776209	0.388105	−	0.921615i	$-0.373130\pi$
$31$	133.974	0.776209	0.388105	+	0.921615i	$0.373130\pi$
$32$	−207.338	−1.14539
$33$	−173.981	−0.917763
$34$	−681.817	−3.43914
$35$	−106.494	−0.514307
$36$	163.998	0.759251
$37$	−264.506	−1.17526	−0.587630	−	0.809130i	$-0.699939\pi$
$37$	−264.506	−1.17526	−0.587630	+	0.809130i	$0.699939\pi$
$38$	458.655	1.95799
$39$	199.242	0.818058
$40$	796.337	3.14780
$41$	84.1122	0.320393	0.160197	−	0.987085i	$-0.448787\pi$
$41$	84.1122	0.320393	0.160197	+	0.987085i	$0.448787\pi$
$42$	−107.536	−0.395074
$43$	−82.9438	−0.294158	−0.147079	−	0.989125i	$-0.546987\pi$
$43$	−82.9438	−0.294158	−0.147079	+	0.989125i	$0.546987\pi$
$44$	−1056.76	−3.62074
$45$	−136.921	−0.453576
$46$	−117.777	−0.377506
$47$	384.762	1.19411	0.597056	−	0.802199i	$-0.296337\pi$
$47$	384.762	1.19411	0.597056	+	0.802199i	$0.296337\pi$
$48$	366.798	1.10297
$49$	49.0000	0.142857
$50$	−545.092	−1.54175
$51$	399.444	1.09673
$52$	1210.20	3.22739
$53$	259.677	0.673008	0.336504	−	0.941682i	$-0.390755\pi$
$53$	259.677	0.673008	0.336504	+	0.941682i	$0.390755\pi$
$54$	−138.260	−0.348423
$55$	882.281	2.16303
$56$	−366.411	−0.874352
$57$	−268.704	−0.624399
$58$	981.018	2.22093
$59$	569.768	1.25725	0.628623	−	0.777710i	$-0.283619\pi$
$59$	569.768	1.25725	0.628623	+	0.777710i	$0.283619\pi$
$60$	−831.657	−1.78944
$61$	−33.4713	−0.0702551	−0.0351275	−	0.999383i	$-0.511184\pi$
$61$	−33.4713	−0.0702551	−0.0351275	+	0.999383i	$0.511184\pi$
$62$	−686.048	−1.40529
$63$	63.0000	0.125988
$64$	83.5967	0.163275
$65$	−1010.38	−1.92804
$66$	890.911	1.66157
$67$	−612.990	−1.11774	−0.558870	−	0.829255i	$-0.688765\pi$
$67$	−612.990	−1.11774	−0.558870	+	0.829255i	$0.688765\pi$
$68$	2426.23	4.32681
$69$	69.0000	0.120386
$70$	545.328	0.931131
$71$	−799.550	−1.33647	−0.668233	−	0.743952i	$-0.732949\pi$
$71$	−799.550	−1.33647	−0.668233	+	0.743952i	$0.732949\pi$
$72$	−471.099	−0.771106
$73$	−357.892	−0.573810	−0.286905	−	0.957959i	$-0.592626\pi$
$73$	−357.892	−0.573810	−0.286905	+	0.957959i	$0.592626\pi$
$74$	1354.47	2.12776
$75$	319.343	0.491661
$76$	−1632.11	−2.46337
$77$	−405.955	−0.600817
$78$	−1020.27	−1.48106
$79$	−397.702	−0.566393	−0.283196	−	0.959062i	$-0.591395\pi$
$79$	−397.702	−0.566393	−0.283196	+	0.959062i	$0.591395\pi$
$80$	−1860.08	−2.59954
$81$	81.0000	0.111111
$82$	−430.717	−0.580058
$83$	−5.96537	−0.00788897	−0.00394449	−	0.999992i	$-0.501256\pi$
$83$	−5.96537	−0.00788897	−0.00394449	+	0.999992i	$0.501256\pi$
$84$	382.663	0.497046
$85$	−2025.64	−2.58484
$86$	424.734	0.532561
$87$	−574.732	−0.708250
$88$	3035.64	3.67728
$89$	−370.826	−0.441657	−0.220829	−	0.975313i	$-0.570876\pi$
$89$	−370.826	−0.441657	−0.220829	+	0.975313i	$0.570876\pi$
$90$	701.136	0.821180
$91$	464.898	0.535545
$92$	419.107	0.474944
$93$	401.923	0.448145
$94$	−1970.27	−2.16189
$95$	1362.64	1.47162
$96$	−622.014	−0.661292
$97$	−1038.62	−1.08717	−0.543587	−	0.839353i	$-0.682934\pi$
$97$	−1038.62	−1.08717	−0.543587	+	0.839353i	$0.682934\pi$
$98$	−250.916	−0.258637
$99$	−521.942	−0.529871
$100$	1939.70	1.93970
$101$	−1826.28	−1.79923	−0.899613	−	0.436688i	$-0.856151\pi$
$101$	−1826.28	−1.79923	−0.899613	+	0.436688i	$0.856151\pi$
$102$	−2045.45	−1.98559
$103$	906.822	0.867493	0.433747	−	0.901035i	$-0.357191\pi$
$103$	906.822	0.867493	0.433747	+	0.901035i	$0.357191\pi$
$104$	−3476.40	−3.27778
$105$	−319.482	−0.296935
$106$	−1329.74	−1.21845
$107$	−706.861	−0.638644	−0.319322	−	0.947646i	$-0.603455\pi$
$107$	−706.861	−0.638644	−0.319322	+	0.947646i	$0.603455\pi$
$108$	491.995	0.438354
$109$	−1365.56	−1.19998	−0.599988	−	0.800009i	$-0.704828\pi$
$109$	−1365.56	−1.19998	−0.599988	+	0.800009i	$0.704828\pi$
$110$	−4517.93	−3.91607
$111$	−793.519	−0.678536
$112$	855.862	0.722066
$113$	−1829.93	−1.52341	−0.761705	−	0.647923i	$-0.775638\pi$
$113$	−1829.93	−1.52341	−0.761705	+	0.647923i	$0.775638\pi$
$114$	1375.97	1.13045
$115$	−349.908	−0.283732
$116$	−3490.93	−2.79418
$117$	597.726	0.472306
$118$	−2917.64	−2.27619
$119$	932.037	0.717980
$120$	2389.01	1.81738
$121$	2032.26	1.52687
$122$	171.398	0.127194
$123$	252.337	0.184979
$124$	2441.28	1.76801
$125$	282.242	0.201956
$126$	−322.607	−0.228096
$127$	367.793	0.256979	0.128490	−	0.991711i	$-0.458987\pi$
$127$	367.793	0.256979	0.128490	+	0.991711i	$0.458987\pi$
$128$	1230.63	0.849789
$129$	−248.831	−0.169832
$130$	5173.92	3.49064
$131$	−1967.09	−1.31195	−0.655976	−	0.754782i	$-0.727743\pi$
$131$	−1967.09	−1.31195	−0.655976	+	0.754782i	$0.727743\pi$
$132$	−3170.28	−2.09044
$133$	−626.977	−0.408765
$134$	3138.96	2.02362
$135$	−410.762	−0.261872
$136$	−6969.55	−4.39437
$137$	−1177.49	−0.734306	−0.367153	−	0.930161i	$-0.619667\pi$
$137$	−1177.49	−0.734306	−0.367153	+	0.930161i	$0.619667\pi$
$138$	−353.331	−0.217953
$139$	−1542.66	−0.941341	−0.470671	−	0.882309i	$-0.655988\pi$
$139$	−1542.66	−0.941341	−0.470671	+	0.882309i	$0.655988\pi$
$140$	−1940.53	−1.17146
$141$	1154.29	0.689421
$142$	4094.29	2.41962
$143$	−3851.59	−2.25235
$144$	1100.39	0.636802
$145$	2914.54	1.66924
$146$	1832.68	1.03886
$147$	147.000	0.0824786
$148$	−4819.84	−2.67695
$149$	−1094.49	−0.601775	−0.300887	−	0.953660i	$-0.597283\pi$
$149$	−1094.49	−0.601775	−0.300887	+	0.953660i	$0.597283\pi$
$150$	−1635.28	−0.890132
$151$	2504.75	1.34989	0.674946	−	0.737867i	$-0.264167\pi$
$151$	2504.75	1.34989	0.674946	+	0.737867i	$0.264167\pi$
$152$	4688.39	2.50183
$153$	1198.33	0.633199
$154$	2078.79	1.08775
$155$	−2038.20	−1.05621
$156$	3630.59	1.86333
$157$	−2836.97	−1.44213	−0.721066	−	0.692866i	$-0.756348\pi$
$157$	−2836.97	−1.44213	−0.721066	+	0.692866i	$0.756348\pi$
$158$	2036.53	1.02543
$159$	779.032	0.388561
$160$	3154.32	1.55857
$161$	161.000	0.0788110
$162$	−414.780	−0.201162
$163$	−1886.69	−0.906605	−0.453303	−	0.891357i	$-0.649754\pi$
$163$	−1886.69	−0.906605	−0.453303	+	0.891357i	$0.649754\pi$
$164$	1532.69	0.729776
$165$	2646.84	1.24883
$166$	30.5471	0.0142826
$167$	−621.821	−0.288131	−0.144066	−	0.989568i	$-0.546018\pi$
$167$	−621.821	−0.288131	−0.144066	+	0.989568i	$0.546018\pi$
$168$	−1099.23	−0.504807
$169$	2213.82	1.00766
$170$	10372.8	4.67973
$171$	−806.113	−0.360497
$172$	−1511.40	−0.670020
$173$	951.440	0.418131	0.209065	−	0.977902i	$-0.432958\pi$
$173$	951.440	0.418131	0.209065	+	0.977902i	$0.432958\pi$
$174$	2943.05	1.28226
$175$	745.135	0.321868
$176$	−7090.65	−3.03680
$177$	1709.30	0.725871
$178$	1898.91	0.799601
$179$	2440.98	1.01926	0.509630	−	0.860394i	$-0.329782\pi$
$179$	2440.98	1.01926	0.509630	+	0.860394i	$0.329782\pi$
$180$	−2494.97	−1.03313
$181$	3128.09	1.28458	0.642289	−	0.766462i	$-0.277985\pi$
$181$	3128.09	1.28458	0.642289	+	0.766462i	$0.277985\pi$
$182$	−2380.62	−0.969581
$183$	−100.414	−0.0405618
$184$	−1203.92	−0.482360
$185$	4024.05	1.59921
$186$	−2058.14	−0.811346
$187$	−7721.74	−3.01962
$188$	7011.14	2.71989
$189$	189.000	0.0727393
$190$	−6977.71	−2.66430
$191$	−2700.27	−1.02296	−0.511478	−	0.859296i	$-0.670902\pi$
$191$	−2700.27	−1.02296	−0.511478	+	0.859296i	$0.670902\pi$
$192$	250.790	0.0942667
$193$	−936.731	−0.349365	−0.174682	−	0.984625i	$-0.555890\pi$
$193$	−936.731	−0.349365	−0.174682	+	0.984625i	$0.555890\pi$
$194$	5318.51	1.96828
$195$	−3031.15	−1.11316
$196$	892.879	0.325393
$197$	−5116.15	−1.85031	−0.925154	−	0.379591i	$-0.876065\pi$
$197$	−5116.15	−1.85031	−0.925154	+	0.379591i	$0.876065\pi$
$198$	2672.73	0.959308
$199$	4579.08	1.63117	0.815584	−	0.578638i	$-0.196416\pi$
$199$	4579.08	1.63117	0.815584	+	0.578638i	$0.196416\pi$
$200$	−5571.95	−1.96998
$201$	−1838.97	−0.645328
$202$	9351.92	3.25742
$203$	−1341.04	−0.463658
$204$	7278.68	2.49809
$205$	−1279.63	−0.435968
$206$	−4643.60	−1.57056
$207$	207.000	0.0695048
$208$	8120.18	2.70689
$209$	5194.38	1.71915
$210$	1635.98	0.537589
$211$	1307.30	0.426532	0.213266	−	0.976994i	$-0.431590\pi$
$211$	1307.30	0.426532	0.213266	+	0.976994i	$0.431590\pi$
$212$	4731.85	1.53295
$213$	−2398.65	−0.771609
$214$	3619.66	1.15624
$215$	1261.86	0.400270
$216$	−1413.30	−0.445198
$217$	937.820	0.293379
$218$	6992.70	2.17250
$219$	−1073.68	−0.331289
$220$	16076.9	4.92685
$221$	8842.90	2.69157
$222$	4063.41	1.22846
$223$	−5358.23	−1.60903	−0.804514	−	0.593933i	$-0.797574\pi$
$223$	−5358.23	−1.60903	−0.804514	+	0.593933i	$0.797574\pi$
$224$	−1451.37	−0.432917
$225$	958.030	0.283861
$226$	9370.61	2.75807
$227$	2270.90	0.663986	0.331993	−	0.943282i	$-0.392279\pi$
$227$	2270.90	0.663986	0.331993	+	0.943282i	$0.392279\pi$
$228$	−4896.34	−1.42223
$229$	−2668.76	−0.770117	−0.385059	−	0.922892i	$-0.625819\pi$
$229$	−2668.76	−0.770117	−0.385059	+	0.922892i	$0.625819\pi$
$230$	1791.79	0.513684
$231$	−1217.87	−0.346882
$232$	10028.0	2.83780
$233$	445.777	0.125338	0.0626692	−	0.998034i	$-0.480039\pi$
$233$	445.777	0.125338	0.0626692	+	0.998034i	$0.480039\pi$
$234$	−3060.80	−0.855090
$235$	−5853.54	−1.62486
$236$	10382.3	2.86369
$237$	−1193.11	−0.327007
$238$	−4772.72	−1.29987
$239$	1039.72	0.281397	0.140698	−	0.990052i	$-0.455065\pi$
$239$	1039.72	0.281397	0.140698	+	0.990052i	$0.455065\pi$
$240$	−5580.25	−1.50085
$241$	−2989.95	−0.799167	−0.399584	−	0.916697i	$-0.630845\pi$
$241$	−2989.95	−0.799167	−0.399584	+	0.916697i	$0.630845\pi$
$242$	−10406.7	−2.76433
$243$	243.000	0.0641500
$244$	−609.915	−0.160024
$245$	−745.457	−0.194390
$246$	−1292.15	−0.334897
$247$	−5948.58	−1.53238
$248$	−7012.80	−1.79562
$249$	−17.8961	−0.00455470
$250$	−1445.29	−0.365632
$251$	−3431.79	−0.862999	−0.431499	−	0.902113i	$-0.642015\pi$
$251$	−3431.79	−0.862999	−0.431499	+	0.902113i	$0.642015\pi$
$252$	1147.99	0.286970
$253$	−1333.85	−0.331457
$254$	−1883.37	−0.465250
$255$	−6076.91	−1.49236
$256$	−6970.50	−1.70178
$257$	3636.37	0.882609	0.441305	−	0.897357i	$-0.354516\pi$
$257$	3636.37	0.882609	0.441305	+	0.897357i	$0.354516\pi$
$258$	1274.20	0.307474
$259$	−1851.55	−0.444206
$260$	−18411.2	−4.39160
$261$	−1724.20	−0.408908
$262$	10073.0	2.37523
$263$	661.168	0.155017	0.0775083	−	0.996992i	$-0.475304\pi$
$263$	661.168	0.155017	0.0775083	+	0.996992i	$0.475304\pi$
$264$	9106.92	2.12308
$265$	−3950.58	−0.915781
$266$	3210.59	0.740052
$267$	−1112.48	−0.254991
$268$	−11169.9	−2.54594
$269$	−6940.30	−1.57308	−0.786539	−	0.617541i	$-0.788129\pi$
$269$	−6940.30	−1.57308	−0.786539	+	0.617541i	$0.788129\pi$
$270$	2103.41	0.474109
$271$	−7247.28	−1.62450	−0.812252	−	0.583306i	$-0.801759\pi$
$271$	−7247.28	−1.62450	−0.812252	+	0.583306i	$0.801759\pi$
$272$	16279.5	3.62900
$273$	1394.69	0.309197
$274$	6029.63	1.32943
$275$	−6173.29	−1.35369
$276$	1257.32	0.274209
$277$	−396.731	−0.0860551	−0.0430276	−	0.999074i	$-0.513700\pi$
$277$	−396.731	−0.0860551	−0.0430276	+	0.999074i	$0.513700\pi$
$278$	7899.55	1.70426
$279$	1205.77	0.258736
$280$	5574.36	1.18976
$281$	1413.45	0.300069	0.150035	−	0.988681i	$-0.452061\pi$
$281$	1413.45	0.300069	0.150035	+	0.988681i	$0.452061\pi$
$282$	−5910.80	−1.24817
$283$	4090.54	0.859213	0.429606	−	0.903016i	$-0.358652\pi$
$283$	4090.54	0.859213	0.429606	+	0.903016i	$0.358652\pi$
$284$	−14569.4	−3.04414
$285$	4087.91	0.849638
$286$	19723.0	4.07778
$287$	588.785	0.121097
$288$	−1866.04	−0.381797
$289$	12815.4	2.60847
$290$	−14924.6	−3.02208
$291$	−3115.86	−0.627681
$292$	−6521.53	−1.30700
$293$	4206.66	0.838756	0.419378	−	0.907812i	$-0.362248\pi$
$293$	4206.66	0.838756	0.419378	+	0.907812i	$0.362248\pi$
$294$	−752.749	−0.149324
$295$	−8668.11	−1.71077
$296$	13845.4	2.71875
$297$	−1565.83	−0.305921
$298$	5604.63	1.08949
$299$	1527.52	0.295448
$300$	5819.09	1.11988
$301$	−580.607	−0.111181
$302$	−12826.2	−2.44392
$303$	−5478.84	−1.03878
$304$	−10951.1	−2.06609
$305$	509.212	0.0955981
$306$	−6136.36	−1.14638
$307$	199.064	0.0370071	0.0185036	−	0.999829i	$-0.494110\pi$
$307$	199.064	0.0370071	0.0185036	+	0.999829i	$0.494110\pi$
$308$	−7397.33	−1.36851
$309$	2720.47	0.500848
$310$	10437.1	1.91222
$311$	146.806	0.0267672	0.0133836	−	0.999910i	$-0.495740\pi$
$311$	146.806	0.0267672	0.0133836	+	0.999910i	$0.495740\pi$
$312$	−10429.2	−1.89243
$313$	−10478.4	−1.89225	−0.946127	−	0.323795i	$-0.895041\pi$
$313$	−10478.4	−1.89225	−0.946127	+	0.323795i	$0.895041\pi$
$314$	14527.4	2.61092
$315$	−958.445	−0.171436
$316$	−7246.94	−1.29010
$317$	403.214	0.0714408	0.0357204	−	0.999362i	$-0.488627\pi$
$317$	403.214	0.0714408	0.0357204	+	0.999362i	$0.488627\pi$
$318$	−3989.22	−0.703473
$319$	11110.3	1.95002
$320$	−1271.79	−0.222173
$321$	−2120.58	−0.368721
$322$	−824.440	−0.142684
$323$	−11925.8	−2.05440
$324$	1475.98	0.253084
$325$	7069.63	1.20662
$326$	9661.24	1.64137
$327$	−4096.69	−0.692806
$328$	−4402.80	−0.741171
$329$	2693.33	0.451332
$330$	−13553.8	−2.26095
$331$	9512.20	1.57957	0.789786	−	0.613383i	$-0.210192\pi$
$331$	9512.20	1.57957	0.789786	+	0.613383i	$0.210192\pi$
$332$	−108.701	−0.0179691
$333$	−2380.56	−0.391753
$334$	3184.19	0.521649
$335$	9325.66	1.52094
$336$	2567.59	0.416885
$337$	10463.1	1.69128	0.845638	−	0.533757i	$-0.179220\pi$
$337$	10463.1	1.69128	0.845638	+	0.533757i	$0.179220\pi$
$338$	−11336.4	−1.82432
$339$	−5489.79	−0.879542
$340$	−36911.2	−5.88762
$341$	−7769.65	−1.23387
$342$	4127.90	0.652664
$343$	343.000	0.0539949
$344$	4341.64	0.680481
$345$	−1049.73	−0.163812
$346$	−4872.08	−0.757008
$347$	4198.84	0.649584	0.324792	−	0.945785i	$-0.394706\pi$
$347$	4198.84	0.649584	0.324792	+	0.945785i	$0.394706\pi$
$348$	−10472.8	−1.61322
$349$	1988.70	0.305023	0.152511	−	0.988302i	$-0.451264\pi$
$349$	1988.70	0.305023	0.152511	+	0.988302i	$0.451264\pi$
$350$	−3815.64	−0.582728
$351$	1793.18	0.272686
$352$	12024.3	1.82073
$353$	9992.61	1.50666	0.753332	−	0.657640i	$-0.228445\pi$
$353$	9992.61	1.50666	0.753332	+	0.657640i	$0.228445\pi$
$354$	−8752.91	−1.31416
$355$	12163.9	1.81857
$356$	−6757.20	−1.00599
$357$	2796.11	0.414526
$358$	−12499.6	−1.84533
$359$	4260.58	0.626364	0.313182	−	0.949693i	$-0.398605\pi$
$359$	4260.58	0.626364	0.313182	+	0.949693i	$0.398605\pi$
$360$	7167.03	1.04927
$361$	1163.44	0.169622
$362$	−16018.1	−2.32567
$363$	6096.78	0.881537
$364$	8471.39	1.21984
$365$	5444.76	0.780800
$366$	514.194	0.0734353
$367$	9633.94	1.37027	0.685133	−	0.728418i	$-0.259744\pi$
$367$	9633.94	1.37027	0.685133	+	0.728418i	$0.259744\pi$
$368$	2812.12	0.398347
$369$	757.010	0.106798
$370$	−20606.1	−2.89530
$371$	1817.74	0.254373
$372$	7323.85	1.02076
$373$	−10526.0	−1.46117	−0.730583	−	0.682824i	$-0.760752\pi$
$373$	−10526.0	−1.46117	−0.730583	+	0.682824i	$0.760752\pi$
$374$	39541.1	5.46690
$375$	846.725	0.116599
$376$	−20140.1	−2.76236
$377$	−12723.4	−1.73817
$378$	−967.821	−0.131691
$379$	−890.066	−0.120632	−0.0603161	−	0.998179i	$-0.519211\pi$
$379$	−890.066	−0.120632	−0.0603161	+	0.998179i	$0.519211\pi$
$380$	24830.0	3.35198
$381$	1103.38	0.148367
$382$	13827.4	1.85202
$383$	4715.46	0.629109	0.314555	−	0.949239i	$-0.398145\pi$
$383$	4715.46	0.629109	0.314555	+	0.949239i	$0.398145\pi$
$384$	3691.88	0.490626
$385$	6175.96	0.817549
$386$	4796.76	0.632510
$387$	−746.494	−0.0980528
$388$	−18925.8	−2.47632
$389$	5683.76	0.740818	0.370409	−	0.928869i	$-0.379218\pi$
$389$	5683.76	0.740818	0.370409	+	0.928869i	$0.379218\pi$
$390$	15521.8	2.01532
$391$	3062.41	0.396093
$392$	−2564.87	−0.330474
$393$	−5901.27	−0.757455
$394$	26198.5	3.34990
$395$	6050.41	0.770707
$396$	−9510.85	−1.20691
$397$	6327.38	0.799904	0.399952	−	0.916536i	$-0.369027\pi$
$397$	6327.38	0.799904	0.399952	+	0.916536i	$0.369027\pi$
$398$	−23448.3	−2.95316
$399$	−1880.93	−0.236001
$400$	13015.0	1.62687
$401$	−13588.3	−1.69219	−0.846095	−	0.533033i	$-0.821052\pi$
$401$	−13588.3	−1.69219	−0.846095	+	0.533033i	$0.821052\pi$
$402$	9416.89	1.16834
$403$	8897.77	1.09982
$404$	−33278.5	−4.09819
$405$	−1232.29	−0.151192
$406$	6867.13	0.839433
$407$	15339.7	1.86821
$408$	−20908.7	−2.53709
$409$	1686.83	0.203932	0.101966	−	0.994788i	$-0.467487\pi$
$409$	1686.83	0.203932	0.101966	+	0.994788i	$0.467487\pi$
$410$	6552.67	0.789301
$411$	−3532.48	−0.423952
$412$	16524.1	1.97594
$413$	3988.38	0.475194
$414$	−1059.99	−0.125835
$415$	90.7537	0.0107348
$416$	−13770.1	−1.62293
$417$	−4627.97	−0.543484
$418$	−26599.1	−3.11245
$419$	10448.2	1.21821	0.609104	−	0.793091i	$-0.291529\pi$
$419$	10448.2	1.21821	0.609104	+	0.793091i	$0.291529\pi$
$420$	−5821.60	−0.676345
$421$	−7789.11	−0.901705	−0.450853	−	0.892598i	$-0.648880\pi$
$421$	−7789.11	−0.901705	−0.450853	+	0.892598i	$0.648880\pi$
$422$	−6694.35	−0.772218
$423$	3462.86	0.398038
$424$	−13592.6	−1.55688
$425$	14173.3	1.61766
$426$	12282.9	1.39697
$427$	−234.299	−0.0265539
$428$	−12880.4	−1.45467
$429$	−11554.8	−1.30039
$430$	−6461.65	−0.724671
$431$	−16880.5	−1.88655	−0.943276	−	0.332011i	$-0.892273\pi$
$431$	−16880.5	−1.88655	−0.943276	+	0.332011i	$0.892273\pi$
$432$	3301.18	0.367658
$433$	2662.49	0.295500	0.147750	−	0.989025i	$-0.452797\pi$
$433$	2662.49	0.295500	0.147750	+	0.989025i	$0.452797\pi$
$434$	−4802.33	−0.531151
$435$	8743.63	0.963736
$436$	−24883.3	−2.73325
$437$	−2060.07	−0.225506
$438$	5498.03	0.599785
$439$	−8862.45	−0.963512	−0.481756	−	0.876305i	$-0.660001\pi$
$439$	−8862.45	−0.963512	−0.481756	+	0.876305i	$0.660001\pi$
$440$	−46182.4	−5.00378
$441$	441.000	0.0476190
$442$	−45282.2	−4.87298
$443$	4746.29	0.509036	0.254518	−	0.967068i	$-0.418083\pi$
$443$	4746.29	0.509036	0.254518	+	0.967068i	$0.418083\pi$
$444$	−14459.5	−1.54554
$445$	5641.53	0.600975
$446$	27438.1	2.91308
$447$	−3283.48	−0.347435
$448$	585.177	0.0617120
$449$	−14997.9	−1.57638	−0.788190	−	0.615432i	$-0.788982\pi$
$449$	−14997.9	−1.57638	−0.788190	+	0.615432i	$0.788982\pi$
$450$	−4905.83	−0.513918
$451$	−4877.97	−0.509301
$452$	−33345.0	−3.46995
$453$	7514.25	0.779361
$454$	−11628.7	−1.20212
$455$	−7072.69	−0.728731
$456$	14065.2	1.44443
$457$	−2117.45	−0.216739	−0.108370	−	0.994111i	$-0.534563\pi$
$457$	−2117.45	−0.216739	−0.108370	+	0.994111i	$0.534563\pi$
$458$	13666.1	1.39426
$459$	3595.00	0.365578
$460$	−6376.04	−0.646270
$461$	10156.2	1.02607	0.513036	−	0.858367i	$-0.328521\pi$
$461$	10156.2	1.02607	0.513036	+	0.858367i	$0.328521\pi$
$462$	6236.38	0.628014
$463$	8870.74	0.890406	0.445203	−	0.895430i	$-0.353131\pi$
$463$	8870.74	0.890406	0.445203	+	0.895430i	$0.353131\pi$
$464$	−23423.4	−2.34354
$465$	−6114.61	−0.609803
$466$	−2282.71	−0.226920
$467$	2112.02	0.209278	0.104639	−	0.994510i	$-0.466631\pi$
$467$	2112.02	0.209278	0.104639	+	0.994510i	$0.466631\pi$
$468$	10891.8	1.07580
$469$	−4290.93	−0.422466
$470$	29974.5	2.94175
$471$	−8510.90	−0.832615
$472$	−29824.2	−2.90841
$473$	4810.21	0.467598
$474$	6109.60	0.592032
$475$	−9534.33	−0.920979
$476$	16983.6	1.63538
$477$	2337.10	0.224336
$478$	−5324.14	−0.509457
$479$	3634.81	0.346720	0.173360	−	0.984859i	$-0.444538\pi$
$479$	3634.81	0.346720	0.173360	+	0.984859i	$0.444538\pi$
$480$	9462.95	0.899839
$481$	−17566.9	−1.66525
$482$	15310.8	1.44686
$483$	483.000	0.0455016
$484$	37031.9	3.47782
$485$	15801.0	1.47935
$486$	−1244.34	−0.116141
$487$	−18068.0	−1.68119	−0.840595	−	0.541664i	$-0.817795\pi$
$487$	−18068.0	−1.68119	−0.840595	+	0.541664i	$0.817795\pi$
$488$	1752.03	0.162522
$489$	−5660.06	−0.523429
$490$	3817.30	0.351934
$491$	−7353.48	−0.675882	−0.337941	−	0.941167i	$-0.609730\pi$
$491$	−7353.48	−0.675882	−0.337941	+	0.941167i	$0.609730\pi$
$492$	4598.08	0.421337
$493$	−25508.1	−2.33028
$494$	30461.1	2.77431
$495$	7940.52	0.721010
$496$	16380.5	1.48287
$497$	−5596.85	−0.505137
$498$	91.6414	0.00824609
$499$	146.855	0.0131746	0.00658732	−	0.999978i	$-0.497903\pi$
$499$	146.855	0.0131746	0.00658732	+	0.999978i	$0.497903\pi$
$500$	5143.02	0.460005
$501$	−1865.46	−0.166353
$502$	17573.3	1.56242
$503$	21568.2	1.91188	0.955942	−	0.293555i	$-0.0948383\pi$
$503$	21568.2	1.91188	0.955942	+	0.293555i	$0.0948383\pi$
$504$	−3297.70	−0.291451
$505$	27784.0	2.44826
$506$	6830.32	0.600089
$507$	6641.47	0.581771
$508$	6701.94	0.585335
$509$	10287.7	0.895867	0.447933	−	0.894067i	$-0.352160\pi$
$509$	10287.7	0.895867	0.447933	+	0.894067i	$0.352160\pi$
$510$	31118.3	2.70185
$511$	−2505.25	−0.216880
$512$	25849.1	2.23121
$513$	−2418.34	−0.208133
$514$	−18620.9	−1.59793
$515$	−13795.9	−1.18042
$516$	−4534.21	−0.386836
$517$	−22313.7	−1.89818
$518$	9481.29	0.804216
$519$	2854.32	0.241408
$520$	52887.9	4.46017
$521$	−17627.0	−1.48225	−0.741126	−	0.671366i	$-0.765708\pi$
$521$	−17627.0	−1.48225	−0.741126	+	0.671366i	$0.765708\pi$
$522$	8829.16	0.740310
$523$	−13227.0	−1.10588	−0.552939	−	0.833222i	$-0.686494\pi$
$523$	−13227.0	−1.10588	−0.552939	+	0.833222i	$0.686494\pi$
$524$	−35844.4	−2.98830
$525$	2235.40	0.185831
$526$	−3385.67	−0.280651
$527$	17838.4	1.47448
$528$	−21271.9	−1.75330
$529$	529.000	0.0434783
$530$	20229.9	1.65798
$531$	5127.91	0.419082
$532$	−11424.8	−0.931066
$533$	5586.23	0.453971
$534$	5696.72	0.461650
$535$	10753.8	0.869021
$536$	32086.6	2.58569
$537$	7322.94	0.588470
$538$	35539.5	2.84799
$539$	−2841.69	−0.227087
$540$	−7484.92	−0.596481
$541$	9147.09	0.726921	0.363460	−	0.931610i	$-0.381595\pi$
$541$	9147.09	0.726921	0.363460	+	0.931610i	$0.381595\pi$
$542$	37111.5	2.94110
$543$	9384.26	0.741652
$544$	−27606.7	−2.17578
$545$	20774.9	1.63284
$546$	−7141.87	−0.559788
$547$	13279.9	1.03804	0.519019	−	0.854763i	$-0.326297\pi$
$547$	13279.9	1.03804	0.519019	+	0.854763i	$0.326297\pi$
$548$	−21456.3	−1.67257
$549$	−301.242	−0.0234184
$550$	31611.9	2.45079
$551$	17159.2	1.32669
$552$	−3611.76	−0.278491
$553$	−2783.92	−0.214076
$554$	2031.56	0.155799
$555$	12072.1	0.923304
$556$	−28110.3	−2.14414
$557$	−6886.26	−0.523842	−0.261921	−	0.965089i	$-0.584356\pi$
$557$	−6886.26	−0.523842	−0.261921	+	0.965089i	$0.584356\pi$
$558$	−6174.43	−0.468431
$559$	−5508.63	−0.416798
$560$	−13020.6	−0.982536
$561$	−23165.2	−1.74338
$562$	−7237.92	−0.543262
$563$	−15927.9	−1.19233	−0.596165	−	0.802862i	$-0.703310\pi$
$563$	−15927.9	−1.19233	−0.596165	+	0.802862i	$0.703310\pi$
$564$	21033.4	1.57033
$565$	27839.5	2.07295
$566$	−20946.6	−1.55557
$567$	567.000	0.0419961
$568$	41852.0	3.09167
$569$	13013.3	0.958782	0.479391	−	0.877601i	$-0.340858\pi$
$569$	13013.3	0.958782	0.479391	+	0.877601i	$0.340858\pi$
$570$	−20933.1	−1.53823
$571$	6936.69	0.508391	0.254196	−	0.967153i	$-0.418189\pi$
$571$	6936.69	0.508391	0.254196	+	0.967153i	$0.418189\pi$
$572$	−70183.8	−5.13030
$573$	−8100.81	−0.590604
$574$	−3015.02	−0.219241
$575$	2448.30	0.177567
$576$	752.370	0.0544249
$577$	−19392.5	−1.39917	−0.699584	−	0.714551i	$-0.746631\pi$
$577$	−19392.5	−1.39917	−0.699584	+	0.714551i	$0.746631\pi$
$578$	−65624.5	−4.72252
$579$	−2810.19	−0.201706
$580$	53108.9	3.80211
$581$	−41.7576	−0.00298175
$582$	15955.5	1.13639
$583$	−15059.6	−1.06982
$584$	18733.7	1.32740
$585$	−9093.45	−0.642680
$586$	−21541.2	−1.51853
$587$	−16866.2	−1.18593	−0.592967	−	0.805227i	$-0.702044\pi$
$587$	−16866.2	−1.18593	−0.592967	+	0.805227i	$0.702044\pi$
$588$	2678.64	0.187866
$589$	−11999.8	−0.839463
$590$	44387.2	3.09727
$591$	−15348.5	−1.06828
$592$	−32340.1	−2.24522
$593$	9005.97	0.623661	0.311830	−	0.950138i	$-0.399058\pi$
$593$	9005.97	0.623661	0.311830	+	0.950138i	$0.399058\pi$
$594$	8018.20	0.553857
$595$	−14179.5	−0.976976
$596$	−19943.9	−1.37069
$597$	13737.2	0.941756
$598$	−7822.05	−0.534896
$599$	18711.9	1.27637	0.638185	−	0.769883i	$-0.279685\pi$
$599$	18711.9	1.27637	0.638185	+	0.769883i	$0.279685\pi$
$600$	−16715.8	−1.13737
$601$	10868.4	0.737659	0.368829	−	0.929497i	$-0.379759\pi$
$601$	10868.4	0.737659	0.368829	+	0.929497i	$0.379759\pi$
$602$	2973.14	0.201289
$603$	−5516.91	−0.372580
$604$	45641.6	3.07472
$605$	−30917.6	−2.07765
$606$	28055.8	1.88067
$607$	−2436.55	−0.162927	−0.0814635	−	0.996676i	$-0.525959\pi$
$607$	−2436.55	−0.162927	−0.0814635	+	0.996676i	$0.525959\pi$
$608$	18570.9	1.23873
$609$	−4023.12	−0.267693
$610$	−2607.55	−0.173076
$611$	25553.6	1.69196
$612$	21836.1	1.44227
$613$	9165.75	0.603917	0.301958	−	0.953321i	$-0.402360\pi$
$613$	9165.75	0.603917	0.301958	+	0.953321i	$0.402360\pi$
$614$	−1019.36	−0.0669998
$615$	−3838.90	−0.251706
$616$	21249.5	1.38988
$617$	16817.2	1.09730	0.548651	−	0.836052i	$-0.315142\pi$
$617$	16817.2	1.09730	0.548651	+	0.836052i	$0.315142\pi$
$618$	−13930.8	−0.906763
$619$	−9310.80	−0.604576	−0.302288	−	0.953217i	$-0.597750\pi$
$619$	−9310.80	−0.604576	−0.302288	+	0.953217i	$0.597750\pi$
$620$	−37140.2	−2.40579
$621$	621.000	0.0401286
$622$	−751.756	−0.0484609
$623$	−2595.78	−0.166931
$624$	24360.5	1.56282
$625$	−17599.8	−1.12639
$626$	53657.3	3.42584
$627$	15583.1	0.992552
$628$	−51695.3	−3.28482
$629$	−35218.5	−2.23252
$630$	4907.95	0.310377
$631$	21008.2	1.32539	0.662697	−	0.748888i	$-0.269412\pi$
$631$	21008.2	1.32539	0.662697	+	0.748888i	$0.269412\pi$
$632$	20817.5	1.31025
$633$	3921.90	0.246258
$634$	−2064.75	−0.129341
$635$	−5595.39	−0.349679
$636$	14195.5	0.885047
$637$	3254.29	0.202417
$638$	−56892.8	−3.53042
$639$	−7195.95	−0.445489
$640$	−18722.0	−1.15633
$641$	−19188.2	−1.18235	−0.591177	−	0.806542i	$-0.701336\pi$
$641$	−19188.2	−1.18235	−0.591177	+	0.806542i	$0.701336\pi$
$642$	10859.0	0.667553
$643$	−9930.29	−0.609039	−0.304520	−	0.952506i	$-0.598496\pi$
$643$	−9930.29	−0.609039	−0.304520	+	0.952506i	$0.598496\pi$
$644$	2933.75	0.179512
$645$	3785.57	0.231096
$646$	61069.1	3.71940
$647$	−11377.6	−0.691343	−0.345671	−	0.938356i	$-0.612349\pi$
$647$	−11377.6	−0.691343	−0.345671	+	0.938356i	$0.612349\pi$
$648$	−4239.89	−0.257035
$649$	−33042.9	−1.99853
$650$	−36201.8	−2.18454
$651$	2813.46	0.169383
$652$	−34379.2	−2.06502
$653$	−31649.1	−1.89667	−0.948334	−	0.317274i	$-0.897233\pi$
$653$	−31649.1	−1.89667	−0.948334	+	0.317274i	$0.897233\pi$
$654$	20978.1	1.25430
$655$	29926.2	1.78521
$656$	10284.1	0.612081
$657$	−3221.03	−0.191270
$658$	−13791.9	−0.817117
$659$	−26315.5	−1.55555	−0.777774	−	0.628544i	$-0.783651\pi$
$659$	−26315.5	−1.55555	−0.777774	+	0.628544i	$0.783651\pi$
$660$	48230.8	2.84452
$661$	−26124.5	−1.53725	−0.768627	−	0.639697i	$-0.779060\pi$
$661$	−26124.5	−1.53725	−0.768627	+	0.639697i	$0.779060\pi$
$662$	−48709.6	−2.85975
$663$	26528.7	1.55398
$664$	312.254	0.0182497
$665$	9538.45	0.556218
$666$	12190.2	0.709252
$667$	−4406.28	−0.255790
$668$	−11330.8	−0.656292
$669$	−16074.7	−0.928973
$670$	−47754.3	−2.75360
$671$	1941.12	0.111678
$672$	−4354.10	−0.249945
$673$	−3770.14	−0.215941	−0.107970	−	0.994154i	$-0.534435\pi$
$673$	−3770.14	−0.215941	−0.107970	+	0.994154i	$0.534435\pi$
$674$	−53578.7	−3.06198
$675$	2874.09	0.163887
$676$	40340.3	2.29519
$677$	−541.021	−0.0307136	−0.0153568	−	0.999882i	$-0.504888\pi$
$677$	−541.021	−0.0307136	−0.0153568	+	0.999882i	$0.504888\pi$
$678$	28111.8	1.59237
$679$	−7270.35	−0.410913
$680$	106031.	5.97955
$681$	6812.70	0.383353
$682$	39786.4	2.23387
$683$	14396.6	0.806544	0.403272	−	0.915080i	$-0.367873\pi$
$683$	14396.6	0.806544	0.403272	+	0.915080i	$0.367873\pi$
$684$	−14689.0	−0.821123
$685$	17913.7	0.999191
$686$	−1756.42	−0.0977555
$687$	−8006.29	−0.444627
$688$	−10141.2	−0.561962
$689$	17246.2	0.953597
$690$	5375.37	0.296575
$691$	19648.0	1.08169	0.540844	−	0.841123i	$-0.318105\pi$
$691$	19648.0	1.08169	0.540844	+	0.841123i	$0.318105\pi$
$692$	17337.2	0.952399
$693$	−3653.60	−0.200272
$694$	−21501.2	−1.17604
$695$	23469.1	1.28091
$696$	30084.0	1.63841
$697$	11199.4	0.608618
$698$	−10183.6	−0.552230
$699$	1337.33	0.0723641
$700$	13577.9	0.733136
$701$	−3496.36	−0.188382	−0.0941910	−	0.995554i	$-0.530026\pi$
$701$	−3496.36	−0.188382	−0.0941910	+	0.995554i	$0.530026\pi$
$702$	−9182.41	−0.493686
$703$	23691.3	1.27103
$704$	−4848.07	−0.259543
$705$	−17560.6	−0.938115
$706$	−51169.6	−2.72775
$707$	−12784.0	−0.680043
$708$	31147.0	1.65335
$709$	−25956.4	−1.37491	−0.687456	−	0.726226i	$-0.741273\pi$
$709$	−25956.4	−1.37491	−0.687456	+	0.726226i	$0.741273\pi$
$710$	−62288.1	−3.29244
$711$	−3579.32	−0.188798
$712$	19410.7	1.02169
$713$	3081.41	0.161851
$714$	−14318.2	−0.750482
$715$	58595.8	3.06484
$716$	44479.6	2.32162
$717$	3119.16	0.162465
$718$	−21817.3	−1.13401
$719$	−12185.0	−0.632023	−0.316011	−	0.948755i	$-0.602344\pi$
$719$	−12185.0	−0.632023	−0.316011	+	0.948755i	$0.602344\pi$
$720$	−16740.7	−0.866515
$721$	6347.75	0.327882
$722$	−5957.68	−0.307094
$723$	−8969.84	−0.461400
$724$	57000.0	2.92595
$725$	−20393.0	−1.04466
$726$	−31220.0	−1.59598
$727$	9280.12	0.473426	0.236713	−	0.971580i	$-0.423930\pi$
$727$	9280.12	0.473426	0.236713	+	0.971580i	$0.423930\pi$
$728$	−24334.8	−1.23888
$729$	729.000	0.0370370
$730$	−27881.2	−1.41360
$731$	−11043.8	−0.558782
$732$	−1829.74	−0.0923897
$733$	20304.0	1.02312	0.511560	−	0.859248i	$-0.329068\pi$
$733$	20304.0	1.02312	0.511560	+	0.859248i	$0.329068\pi$
$734$	−49333.0	−2.48081
$735$	−2236.37	−0.112231
$736$	−4768.77	−0.238831
$737$	35549.5	1.77677
$738$	−3876.45	−0.193353
$739$	22928.7	1.14133	0.570667	−	0.821182i	$-0.306685\pi$
$739$	22928.7	1.14133	0.570667	+	0.821182i	$0.306685\pi$
$740$	73326.3	3.64260
$741$	−17845.7	−0.884722
$742$	−9308.19	−0.460531
$743$	−33778.0	−1.66782	−0.833912	−	0.551898i	$-0.813904\pi$
$743$	−33778.0	−1.66782	−0.833912	+	0.551898i	$0.813904\pi$
$744$	−21038.4	−1.03670
$745$	16651.0	0.818852
$746$	53900.9	2.64538
$747$	−53.6884	−0.00262966
$748$	−140706.	−6.87796
$749$	−4948.03	−0.241385
$750$	−4335.86	−0.211098
$751$	−23349.6	−1.13454	−0.567270	−	0.823532i	$-0.692000\pi$
$751$	−23349.6	−1.13454	−0.567270	+	0.823532i	$0.692000\pi$
$752$	47043.3	2.28124
$753$	−10295.4	−0.498253
$754$	65153.4	3.14688
$755$	−38105.8	−1.83684
$756$	3443.96	0.165682
$757$	−33119.0	−1.59013	−0.795065	−	0.606524i	$-0.792563\pi$
$757$	−33119.0	−1.59013	−0.795065	+	0.606524i	$0.792563\pi$
$758$	4557.80	0.218400
$759$	−4001.56	−0.191367
$760$	−71326.3	−3.40431
$761$	23625.0	1.12537	0.562685	−	0.826671i	$-0.309768\pi$
$761$	23625.0	1.12537	0.562685	+	0.826671i	$0.309768\pi$
$762$	−5650.12	−0.268612
$763$	−9558.95	−0.453548
$764$	−49204.4	−2.33004
$765$	−18230.7	−0.861612
$766$	−24146.7	−1.13898
$767$	37840.6	1.78141
$768$	−20911.5	−0.982524
$769$	−18207.6	−0.853814	−0.426907	−	0.904296i	$-0.640397\pi$
$769$	−18207.6	−0.853814	−0.426907	+	0.904296i	$0.640397\pi$
$770$	−31625.5	−1.48014
$771$	10909.1	0.509575
$772$	−17069.1	−0.795767
$773$	−5657.88	−0.263260	−0.131630	−	0.991299i	$-0.542021\pi$
$773$	−5657.88	−0.263260	−0.131630	+	0.991299i	$0.542021\pi$
$774$	3822.61	0.177520
$775$	14261.3	0.661006
$776$	54366.0	2.51498
$777$	−5554.64	−0.256463
$778$	−29105.1	−1.34122
$779$	−7533.77	−0.346502
$780$	−55233.7	−2.53549
$781$	46368.8	2.12446
$782$	−15681.8	−0.717110
$783$	−5172.59	−0.236083
$784$	5991.03	0.272915
$785$	43160.0	1.96235
$786$	30218.9	1.37134
$787$	26430.7	1.19714	0.598572	−	0.801069i	$-0.295735\pi$
$787$	26430.7	1.19714	0.598572	+	0.801069i	$0.295735\pi$
$788$	−93226.7	−4.21455
$789$	1983.50	0.0894989
$790$	−30982.6	−1.39533
$791$	−12809.5	−0.575795
$792$	27320.8	1.22576
$793$	−2222.96	−0.0995457
$794$	−32400.9	−1.44819
$795$	−11851.7	−0.528726
$796$	83440.1	3.71540
$797$	31830.4	1.41467	0.707333	−	0.706880i	$-0.249898\pi$
$797$	31830.4	1.41467	0.707333	+	0.706880i	$0.249898\pi$
$798$	9631.76	0.427269
$799$	51230.3	2.26833
$800$	−22070.7	−0.975395
$801$	−3337.43	−0.147219
$802$	69582.3	3.06364
$803$	20755.5	0.912136
$804$	−33509.7	−1.46990
$805$	−2449.36	−0.107240
$806$	−45563.2	−1.99118
$807$	−20820.9	−0.908217
$808$	95595.6	4.16218
$809$	8216.14	0.357063	0.178531	−	0.983934i	$-0.442865\pi$
$809$	8216.14	0.357063	0.178531	+	0.983934i	$0.442865\pi$
$810$	6310.22	0.273727
$811$	24454.8	1.05884	0.529422	−	0.848358i	$-0.322409\pi$
$811$	24454.8	1.05884	0.529422	+	0.848358i	$0.322409\pi$
$812$	−24436.5	−1.05610
$813$	−21741.8	−0.937908
$814$	−78550.6	−3.38231
$815$	28702.9	1.23364
$816$	48838.5	2.09521
$817$	7429.12	0.318130
$818$	−8637.82	−0.369211
$819$	4184.08	0.178515
$820$	−23317.5	−0.993028
$821$	1928.88	0.0819956	0.0409978	−	0.999159i	$-0.486946\pi$
$821$	1928.88	0.0819956	0.0409978	+	0.999159i	$0.486946\pi$
$822$	18088.9	0.767546
$823$	−7076.32	−0.299715	−0.149857	−	0.988708i	$-0.547881\pi$
$823$	−7076.32	−0.299715	−0.149857	+	0.988708i	$0.547881\pi$
$824$	−47467.0	−2.00679
$825$	−18519.9	−0.781551
$826$	−20423.5	−0.860318
$827$	24803.9	1.04294	0.521472	−	0.853268i	$-0.325383\pi$
$827$	24803.9	1.04294	0.521472	+	0.853268i	$0.325383\pi$
$828$	3771.96	0.158315
$829$	−7408.67	−0.310391	−0.155195	−	0.987884i	$-0.549601\pi$
$829$	−7408.67	−0.310391	−0.155195	+	0.987884i	$0.549601\pi$
$830$	−464.726	−0.0194348
$831$	−1190.19	−0.0496840
$832$	5551.99	0.231347
$833$	6524.26	0.271371
$834$	23698.7	0.983954
$835$	9460.02	0.392069
$836$	94652.1	3.91580
$837$	3617.30	0.149382
$838$	−53502.7	−2.20551
$839$	−35686.3	−1.46845	−0.734225	−	0.678906i	$-0.762454\pi$
$839$	−35686.3	−1.46845	−0.734225	+	0.678906i	$0.762454\pi$
$840$	16723.1	0.686906
$841$	12312.9	0.504853
$842$	39886.0	1.63250
$843$	4240.35	0.173245
$844$	23821.7	0.971535
$845$	−33679.8	−1.37115
$846$	−17732.4	−0.720630
$847$	14225.8	0.577101
$848$	31749.7	1.28572
$849$	12271.6	0.496067
$850$	−72578.0	−2.92871
$851$	−6083.65	−0.245059
$852$	−43708.3	−1.75754
$853$	2490.07	0.0999513	0.0499757	−	0.998750i	$-0.484086\pi$
$853$	2490.07	0.0999513	0.0499757	+	0.998750i	$0.484086\pi$
$854$	1199.79	0.0480747
$855$	12263.7	0.490539
$856$	37000.2	1.47738
$857$	−19071.1	−0.760161	−0.380081	−	0.924953i	$-0.624104\pi$
$857$	−19071.1	−0.760161	−0.380081	+	0.924953i	$0.624104\pi$
$858$	59169.0	2.35431
$859$	20121.9	0.799244	0.399622	−	0.916680i	$-0.369141\pi$
$859$	20121.9	0.799244	0.399622	+	0.916680i	$0.369141\pi$
$860$	22993.6	0.911716
$861$	1766.36	0.0699155
$862$	86440.6	3.41552
$863$	−27350.0	−1.07880	−0.539401	−	0.842049i	$-0.681349\pi$
$863$	−27350.0	−1.07880	−0.539401	+	0.842049i	$0.681349\pi$
$864$	−5598.12	−0.220431
$865$	−14474.6	−0.568963
$866$	−13634.0	−0.534989
$867$	38446.2	1.50600
$868$	17089.0	0.668246
$869$	23064.2	0.900345
$870$	−44773.9	−1.74480
$871$	−40711.1	−1.58375
$872$	71479.6	2.77592
$873$	−9347.59	−0.362392
$874$	10549.1	0.408270
$875$	1975.69	0.0763321
$876$	−19564.6	−0.754596
$877$	−25360.5	−0.976469	−0.488235	−	0.872712i	$-0.662359\pi$
$877$	−25360.5	−0.976469	−0.488235	+	0.872712i	$0.662359\pi$
$878$	45382.4	1.74440
$879$	12620.0	0.484256
$880$	107873.	4.13227
$881$	33883.7	1.29577	0.647885	−	0.761739i	$-0.275654\pi$
$881$	33883.7	1.29577	0.647885	+	0.761739i	$0.275654\pi$
$882$	−2258.25	−0.0862122
$883$	32217.8	1.22788	0.613939	−	0.789354i	$-0.289584\pi$
$883$	32217.8	1.22788	0.613939	+	0.789354i	$0.289584\pi$
$884$	161136.	6.13074
$885$	−26004.3	−0.987713
$886$	−24304.5	−0.921588
$887$	−42587.7	−1.61213	−0.806063	−	0.591829i	$-0.798406\pi$
$887$	−42587.7	−1.61213	−0.806063	+	0.591829i	$0.798406\pi$
$888$	41536.3	1.56967
$889$	2574.55	0.0971290
$890$	−28888.8	−1.08804
$891$	−4697.48	−0.176624
$892$	−97637.7	−3.66497
$893$	−34462.4	−1.29142
$894$	16813.9	0.629016
$895$	−37135.6	−1.38694
$896$	8614.39	0.321190
$897$	4582.57	0.170577
$898$	76800.4	2.85397
$899$	−25666.4	−0.952195
$900$	17457.3	0.646565
$901$	34575.5	1.27844
$902$	24978.8	0.922067
$903$	−1741.82	−0.0641906
$904$	95786.6	3.52413
$905$	−47588.8	−1.74796
$906$	−38478.6	−1.41100
$907$	3838.71	0.140532	0.0702659	−	0.997528i	$-0.477615\pi$
$907$	3838.71	0.140532	0.0702659	+	0.997528i	$0.477615\pi$
$908$	41380.4	1.51240
$909$	−16436.5	−0.599742
$910$	36217.4	1.31934
$911$	−11916.3	−0.433376	−0.216688	−	0.976241i	$-0.569525\pi$
$911$	−11916.3	−0.433376	−0.216688	+	0.976241i	$0.569525\pi$
$912$	−32853.4	−1.19286
$913$	345.953	0.0125404
$914$	10842.9	0.392397
$915$	1527.64	0.0551936
$916$	−48630.3	−1.75414
$917$	−13769.6	−0.495871
$918$	−18409.1	−0.661863
$919$	−14700.6	−0.527669	−0.263834	−	0.964568i	$-0.584987\pi$
$919$	−14700.6	−0.527669	−0.263834	+	0.964568i	$0.584987\pi$
$920$	18315.7	0.656361
$921$	597.192	0.0213661
$922$	−52007.1	−1.85766
$923$	−53101.3	−1.89366
$924$	−22192.0	−0.790111
$925$	−28156.1	−1.00083
$926$	−45424.8	−1.61204
$927$	8161.40	0.289164
$928$	39721.2	1.40508
$929$	−8092.81	−0.285809	−0.142904	−	0.989736i	$-0.545644\pi$
$929$	−8092.81	−0.285809	−0.142904	+	0.989736i	$0.545644\pi$
$930$	31311.4	1.10402
$931$	−4388.84	−0.154499
$932$	8122.96	0.285490
$933$	440.418	0.0154541
$934$	−10815.1	−0.378888
$935$	117474.	4.10889
$936$	−31287.6	−1.09259
$937$	4956.55	0.172811	0.0864053	−	0.996260i	$-0.472462\pi$
$937$	4956.55	0.172811	0.0864053	+	0.996260i	$0.472462\pi$
$938$	21972.7	0.764857
$939$	−31435.3	−1.09249
$940$	−106663.	−3.70104
$941$	24858.1	0.861160	0.430580	−	0.902552i	$-0.358309\pi$
$941$	24858.1	0.861160	0.430580	+	0.902552i	$0.358309\pi$
$942$	43582.2	1.50741
$943$	1934.58	0.0668066
$944$	69663.3	2.40185
$945$	−2875.33	−0.0989784
$946$	−24631.9	−0.846565
$947$	−20112.8	−0.690156	−0.345078	−	0.938574i	$-0.612148\pi$
$947$	−20112.8	−0.690156	−0.345078	+	0.938574i	$0.612148\pi$
$948$	−21740.8	−0.744841
$949$	−23769.1	−0.813042
$950$	48822.9	1.66739
$951$	1209.64	0.0412464
$952$	−48786.9	−1.66092
$953$	22644.0	0.769687	0.384844	−	0.922982i	$-0.374255\pi$
$953$	22644.0	0.769687	0.384844	+	0.922982i	$0.374255\pi$
$954$	−11967.7	−0.406150
$955$	41080.3	1.39197
$956$	18945.8	0.640953
$957$	33330.8	1.12584
$958$	−18612.9	−0.627721
$959$	−8242.44	−0.277542
$960$	−3815.37	−0.128271
$961$	−11841.9	−0.397500
$962$	89955.8	3.01486
$963$	−6361.75	−0.212881
$964$	−54482.9	−1.82031
$965$	14250.9	0.475391
$966$	−2473.32	−0.0823786
$967$	−16667.4	−0.554277	−0.277139	−	0.960830i	$-0.589386\pi$
$967$	−16667.4	−0.554277	−0.277139	+	0.960830i	$0.589386\pi$
$968$	−106377.	−3.53213
$969$	−35777.5	−1.18611
$970$	−80912.7	−2.67830
$971$	−13164.6	−0.435088	−0.217544	−	0.976050i	$-0.569805\pi$
$971$	−13164.6	−0.435088	−0.217544	+	0.976050i	$0.569805\pi$
$972$	4427.95	0.146118
$973$	−10798.6	−0.355794
$974$	92521.7	3.04372
$975$	21208.9	0.696644
$976$	−4092.40	−0.134216
$977$	−11011.0	−0.360566	−0.180283	−	0.983615i	$-0.557701\pi$
$977$	−11011.0	−0.360566	−0.180283	+	0.983615i	$0.557701\pi$
$978$	28983.7	0.947645
$979$	21505.5	0.702063
$980$	−13583.7	−0.442772
$981$	−12290.1	−0.399992
$982$	37655.3	1.22366
$983$	42455.1	1.37753	0.688763	−	0.724986i	$-0.258154\pi$
$983$	42455.1	1.37753	0.688763	+	0.724986i	$0.258154\pi$
$984$	−13208.4	−0.427915
$985$	77834.1	2.51777
$986$	130621.	4.21888
$987$	8080.00	0.260577
$988$	−108395.	−3.49039
$989$	−1907.71	−0.0613363
$990$	−40661.4	−1.30536
$991$	−27832.9	−0.892170	−0.446085	−	0.894991i	$-0.647182\pi$
$991$	−27832.9	−0.892170	−0.446085	+	0.894991i	$0.647182\pi$
$992$	−27777.9	−0.889063
$993$	28536.6	0.911966
$994$	28660.0	0.914529
$995$	−69663.4	−2.21958
$996$	−326.104	−0.0103745
$997$	49018.5	1.55710	0.778552	−	0.627581i	$-0.215955\pi$
$997$	49018.5	1.55710	0.778552	+	0.627581i	$0.215955\pi$
$998$	−752.008	−0.0238521
$999$	−7141.67	−0.226179

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.4.a.c.1.1	✓	7
3.2	odd	2		1449.4.a.h.1.7		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.4.a.c.1.1	✓	7	1.1	even	1	trivial
1449.4.a.h.1.7		7	3.2	odd	2

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	483.a (trivial)

\(f(q)\)	\(=\)	\(q-5.12074 q^{2} +3.00000 q^{3} +18.2220 q^{4} -15.2134 q^{5} -15.3622 q^{6} +7.00000 q^{7} -52.3444 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-5.12074 q^{2} +3.00000 q^{3} +18.2220 q^{4} -15.2134 q^{5} -15.3622 q^{6} +7.00000 q^{7} -52.3444 q^{8} +9.00000 q^{9} +77.9040 q^{10} -57.9936 q^{11} +54.6661 q^{12} +66.4140 q^{13} -35.8452 q^{14} -45.6402 q^{15} +122.266 q^{16} +133.148 q^{17} -46.0867 q^{18} -89.5681 q^{19} -277.219 q^{20} +21.0000 q^{21} +296.970 q^{22} +23.0000 q^{23} -157.033 q^{24} +106.448 q^{25} -340.089 q^{26} +27.0000 q^{27} +127.554 q^{28} -191.577 q^{29} +233.712 q^{30} +133.974 q^{31} -207.338 q^{32} -173.981 q^{33} -681.817 q^{34} -106.494 q^{35} +163.998 q^{36} -264.506 q^{37} +458.655 q^{38} +199.242 q^{39} +796.337 q^{40} +84.1122 q^{41} -107.536 q^{42} -82.9438 q^{43} -1056.76 q^{44} -136.921 q^{45} -117.777 q^{46} +384.762 q^{47} +366.798 q^{48} +49.0000 q^{49} -545.092 q^{50} +399.444 q^{51} +1210.20 q^{52} +259.677 q^{53} -138.260 q^{54} +882.281 q^{55} -366.411 q^{56} -268.704 q^{57} +981.018 q^{58} +569.768 q^{59} -831.657 q^{60} -33.4713 q^{61} -686.048 q^{62} +63.0000 q^{63} +83.5967 q^{64} -1010.38 q^{65} +890.911 q^{66} -612.990 q^{67} +2426.23 q^{68} +69.0000 q^{69} +545.328 q^{70} -799.550 q^{71} -471.099 q^{72} -357.892 q^{73} +1354.47 q^{74} +319.343 q^{75} -1632.11 q^{76} -405.955 q^{77} -1020.27 q^{78} -397.702 q^{79} -1860.08 q^{80} +81.0000 q^{81} -430.717 q^{82} -5.96537 q^{83} +382.663 q^{84} -2025.64 q^{85} +424.734 q^{86} -574.732 q^{87} +3035.64 q^{88} -370.826 q^{89} +701.136 q^{90} +464.898 q^{91} +419.107 q^{92} +401.923 q^{93} -1970.27 q^{94} +1362.64 q^{95} -622.014 q^{96} -1038.62 q^{97} -250.916 q^{98} -521.942 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 6 q^{2} + 21 q^{3} + 18 q^{4} - 41 q^{5} - 18 q^{6} + 49 q^{7} - 33 q^{8} + 63 q^{9}+O(q^{10}) \) 7 * q - 6 * q^2 + 21 * q^3 + 18 * q^4 - 41 * q^5 - 18 * q^6 + 49 * q^7 - 33 * q^8 + 63 * q^9	\( 7 q - 6 q^{2} + 21 q^{3} + 18 q^{4} - 41 q^{5} - 18 q^{6} + 49 q^{7} - 33 q^{8} + 63 q^{9} + q^{10} - 126 q^{11} + 54 q^{12} - 87 q^{13} - 42 q^{14} - 123 q^{15} + 2 q^{16} - 204 q^{17} - 54 q^{18} - 286 q^{19} - 418 q^{20} + 147 q^{21} + 329 q^{22} + 161 q^{23} - 99 q^{24} + 440 q^{25} - 360 q^{26} + 189 q^{27} + 126 q^{28} - 329 q^{29} + 3 q^{30} + 296 q^{31} - 270 q^{32} - 378 q^{33} - 919 q^{34} - 287 q^{35} + 162 q^{36} - 691 q^{37} - 367 q^{38} - 261 q^{39} + 138 q^{40} - 343 q^{41} - 126 q^{42} - 171 q^{43} - 1279 q^{44} - 369 q^{45} - 138 q^{46} - 1403 q^{47} + 6 q^{48} + 343 q^{49} + 230 q^{50} - 612 q^{51} + 2157 q^{52} - 1024 q^{53} - 162 q^{54} - 158 q^{55} - 231 q^{56} - 858 q^{57} + 2608 q^{58} - 1388 q^{59} - 1254 q^{60} - 52 q^{61} - 309 q^{62} + 441 q^{63} - 187 q^{64} - 1067 q^{65} + 987 q^{66} - 1148 q^{67} + 1293 q^{68} + 483 q^{69} + 7 q^{70} - 1590 q^{71} - 297 q^{72} - 802 q^{73} - 878 q^{74} + 1320 q^{75} - 2505 q^{76} - 882 q^{77} - 1080 q^{78} + 618 q^{79} + 195 q^{80} + 567 q^{81} - 1040 q^{82} - 1818 q^{83} + 378 q^{84} - 1526 q^{85} + 1188 q^{86} - 987 q^{87} + 1664 q^{88} - 354 q^{89} + 9 q^{90} - 609 q^{91} + 414 q^{92} + 888 q^{93} + 663 q^{94} + 78 q^{95} - 810 q^{96} - 1575 q^{97} - 294 q^{98} - 1134 q^{99}+O(q^{100}) \) 7 * q - 6 * q^2 + 21 * q^3 + 18 * q^4 - 41 * q^5 - 18 * q^6 + 49 * q^7 - 33 * q^8 + 63 * q^9 + q^10 - 126 * q^11 + 54 * q^12 - 87 * q^13 - 42 * q^14 - 123 * q^15 + 2 * q^16 - 204 * q^17 - 54 * q^18 - 286 * q^19 - 418 * q^20 + 147 * q^21 + 329 * q^22 + 161 * q^23 - 99 * q^24 + 440 * q^25 - 360 * q^26 + 189 * q^27 + 126 * q^28 - 329 * q^29 + 3 * q^30 + 296 * q^31 - 270 * q^32 - 378 * q^33 - 919 * q^34 - 287 * q^35 + 162 * q^36 - 691 * q^37 - 367 * q^38 - 261 * q^39 + 138 * q^40 - 343 * q^41 - 126 * q^42 - 171 * q^43 - 1279 * q^44 - 369 * q^45 - 138 * q^46 - 1403 * q^47 + 6 * q^48 + 343 * q^49 + 230 * q^50 - 612 * q^51 + 2157 * q^52 - 1024 * q^53 - 162 * q^54 - 158 * q^55 - 231 * q^56 - 858 * q^57 + 2608 * q^58 - 1388 * q^59 - 1254 * q^60 - 52 * q^61 - 309 * q^62 + 441 * q^63 - 187 * q^64 - 1067 * q^65 + 987 * q^66 - 1148 * q^67 + 1293 * q^68 + 483 * q^69 + 7 * q^70 - 1590 * q^71 - 297 * q^72 - 802 * q^73 - 878 * q^74 + 1320 * q^75 - 2505 * q^76 - 882 * q^77 - 1080 * q^78 + 618 * q^79 + 195 * q^80 + 567 * q^81 - 1040 * q^82 - 1818 * q^83 + 378 * q^84 - 1526 * q^85 + 1188 * q^86 - 987 * q^87 + 1664 * q^88 - 354 * q^89 + 9 * q^90 - 609 * q^91 + 414 * q^92 + 888 * q^93 + 663 * q^94 + 78 * q^95 - 810 * q^96 - 1575 * q^97 - 294 * q^98 - 1134 * q^99

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