LMFDB - Embedded newform 483.4.a.d.1.2

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} - 2x^{6} - 37x^{5} + 71x^{4} + 312x^{3} - 629x^{2} + 112x + 180 $ x^7 - 2x^6 - 37x^5 + 71x^4 + 312x^3 - 629x^2 + 112x + 180
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$3.61105$ 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)

$f(q)$	$=$	$q-3.61105 q^{2} -3.00000 q^{3} +5.03969 q^{4} -11.1551 q^{5} +10.8332 q^{6} -7.00000 q^{7} +10.6898 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-3.61105 q^{2} -3.00000 q^{3} +5.03969 q^{4} -11.1551 q^{5} +10.8332 q^{6} -7.00000 q^{7} +10.6898 q^{8} +9.00000 q^{9} +40.2815 q^{10} -12.6051 q^{11} -15.1191 q^{12} -58.3723 q^{13} +25.2774 q^{14} +33.4652 q^{15} -78.9190 q^{16} +46.0793 q^{17} -32.4995 q^{18} +139.291 q^{19} -56.2180 q^{20} +21.0000 q^{21} +45.5175 q^{22} +23.0000 q^{23} -32.0695 q^{24} -0.564718 q^{25} +210.785 q^{26} -27.0000 q^{27} -35.2778 q^{28} +247.832 q^{29} -120.844 q^{30} +42.5308 q^{31} +199.462 q^{32} +37.8152 q^{33} -166.395 q^{34} +78.0854 q^{35} +45.3572 q^{36} -42.7792 q^{37} -502.986 q^{38} +175.117 q^{39} -119.246 q^{40} +407.654 q^{41} -75.8321 q^{42} -6.87794 q^{43} -63.5256 q^{44} -100.396 q^{45} -83.0542 q^{46} -437.329 q^{47} +236.757 q^{48} +49.0000 q^{49} +2.03923 q^{50} -138.238 q^{51} -294.178 q^{52} +245.540 q^{53} +97.4984 q^{54} +140.610 q^{55} -74.8288 q^{56} -417.872 q^{57} -894.936 q^{58} +747.982 q^{59} +168.654 q^{60} -908.216 q^{61} -153.581 q^{62} -63.0000 q^{63} -88.9154 q^{64} +651.146 q^{65} -136.552 q^{66} -286.679 q^{67} +232.225 q^{68} -69.0000 q^{69} -281.970 q^{70} -628.316 q^{71} +96.2085 q^{72} +1023.03 q^{73} +154.478 q^{74} +1.69415 q^{75} +701.982 q^{76} +88.2354 q^{77} -632.356 q^{78} -1012.93 q^{79} +880.346 q^{80} +81.0000 q^{81} -1472.06 q^{82} +327.173 q^{83} +105.833 q^{84} -514.017 q^{85} +24.8366 q^{86} -743.497 q^{87} -134.746 q^{88} -86.1702 q^{89} +362.533 q^{90} +408.606 q^{91} +115.913 q^{92} -127.592 q^{93} +1579.22 q^{94} -1553.80 q^{95} -598.386 q^{96} -1146.54 q^{97} -176.942 q^{98} -113.445 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 2 q^{2} - 21 q^{3} + 22 q^{4} - 11 q^{5} + 6 q^{6} - 49 q^{7} + 15 q^{8} + 63 q^{9}+O(q^{10}) $ 7 * q - 2 * q^2 - 21 * q^3 + 22 * q^4 - 11 * q^5 + 6 * q^6 - 49 * q^7 + 15 * q^8 + 63 * q^9	\( 7 q - 2 q^{2} - 21 q^{3} + 22 q^{4} - 11 q^{5} + 6 q^{6} - 49 q^{7} + 15 q^{8} + 63 q^{9} + 11 q^{10} - 6 q^{11} - 66 q^{12} + 17 q^{13} + 14 q^{14} + 33 q^{15} + 106 q^{16} - 78 q^{17} - 18 q^{18} + 44 q^{19} + 44 q^{20} + 147 q^{21} - 477 q^{22} + 161 q^{23} - 45 q^{24} - 80 q^{25} + 288 q^{26} - 189 q^{27} - 154 q^{28} - 185 q^{29} - 33 q^{30} + 238 q^{31} - 512 q^{32} + 18 q^{33} - 27 q^{34} + 77 q^{35} + 198 q^{36} - 511 q^{37} - 413 q^{38} - 51 q^{39} - 686 q^{40} + 867 q^{41} - 42 q^{42} - 1003 q^{43} - 629 q^{44} - 99 q^{45} - 46 q^{46} + 149 q^{47} - 318 q^{48} + 343 q^{49} - 986 q^{50} + 234 q^{51} - 439 q^{52} - 1244 q^{53} + 54 q^{54} - 270 q^{55} - 105 q^{56} - 132 q^{57} - 2376 q^{58} + 1048 q^{59} - 132 q^{60} - 1380 q^{61} - 809 q^{62} - 441 q^{63} - 1835 q^{64} - 223 q^{65} + 1431 q^{66} - 500 q^{67} - 1387 q^{68} - 483 q^{69} - 77 q^{70} - 14 q^{71} + 135 q^{72} - 530 q^{73} - 738 q^{74} + 240 q^{75} - 1785 q^{76} + 42 q^{77} - 864 q^{78} - 2978 q^{79} + 1043 q^{80} + 567 q^{81} - 1986 q^{82} - 524 q^{83} + 462 q^{84} - 2674 q^{85} + 194 q^{86} + 555 q^{87} - 4504 q^{88} - 648 q^{89} + 99 q^{90} - 119 q^{91} + 506 q^{92} - 714 q^{93} - 801 q^{94} + 154 q^{95} + 1536 q^{96} - 1999 q^{97} - 98 q^{98} - 54 q^{99}+O(q^{100}) \) 7 * q - 2 * q^2 - 21 * q^3 + 22 * q^4 - 11 * q^5 + 6 * q^6 - 49 * q^7 + 15 * q^8 + 63 * q^9 + 11 * q^10 - 6 * q^11 - 66 * q^12 + 17 * q^13 + 14 * q^14 + 33 * q^15 + 106 * q^16 - 78 * q^17 - 18 * q^18 + 44 * q^19 + 44 * q^20 + 147 * q^21 - 477 * q^22 + 161 * q^23 - 45 * q^24 - 80 * q^25 + 288 * q^26 - 189 * q^27 - 154 * q^28 - 185 * q^29 - 33 * q^30 + 238 * q^31 - 512 * q^32 + 18 * q^33 - 27 * q^34 + 77 * q^35 + 198 * q^36 - 511 * q^37 - 413 * q^38 - 51 * q^39 - 686 * q^40 + 867 * q^41 - 42 * q^42 - 1003 * q^43 - 629 * q^44 - 99 * q^45 - 46 * q^46 + 149 * q^47 - 318 * q^48 + 343 * q^49 - 986 * q^50 + 234 * q^51 - 439 * q^52 - 1244 * q^53 + 54 * q^54 - 270 * q^55 - 105 * q^56 - 132 * q^57 - 2376 * q^58 + 1048 * q^59 - 132 * q^60 - 1380 * q^61 - 809 * q^62 - 441 * q^63 - 1835 * q^64 - 223 * q^65 + 1431 * q^66 - 500 * q^67 - 1387 * q^68 - 483 * q^69 - 77 * q^70 - 14 * q^71 + 135 * q^72 - 530 * q^73 - 738 * q^74 + 240 * q^75 - 1785 * q^76 + 42 * q^77 - 864 * q^78 - 2978 * q^79 + 1043 * q^80 + 567 * q^81 - 1986 * q^82 - 524 * q^83 + 462 * q^84 - 2674 * q^85 + 194 * q^86 + 555 * q^87 - 4504 * q^88 - 648 * q^89 + 99 * q^90 - 119 * q^91 + 506 * q^92 - 714 * q^93 - 801 * q^94 + 154 * q^95 + 1536 * q^96 - 1999 * q^97 - 98 * q^98 - 54 * 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 $

$2$	−3.61105	−1.27670	−0.638350	−	0.769747i	$-0.720383\pi$
$2$	−3.61105	−1.27670	−0.638350	+	0.769747i	$0.720383\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	5.03969	0.629961
$5$	−11.1551	−0.997739	−0.498869	−	0.866677i	$-0.666251\pi$
$5$	−11.1551	−0.997739	−0.498869	+	0.866677i	$0.666251\pi$
$6$	10.8332	0.737103
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	10.6898	0.472428
$9$	9.00000	0.333333
$10$	40.2815	1.27381
$11$	−12.6051	−0.345506	−0.172753	−	0.984965i	$-0.555266\pi$
$11$	−12.6051	−0.345506	−0.172753	+	0.984965i	$0.555266\pi$
$12$	−15.1191	−0.363708
$13$	−58.3723	−1.24535	−0.622675	−	0.782480i	$-0.713954\pi$
$13$	−58.3723	−1.24535	−0.622675	+	0.782480i	$0.713954\pi$
$14$	25.2774	0.482547
$15$	33.4652	0.576045
$16$	−78.9190	−1.23311
$17$	46.0793	0.657404	0.328702	−	0.944434i	$-0.393389\pi$
$17$	46.0793	0.657404	0.328702	+	0.944434i	$0.393389\pi$
$18$	−32.4995	−0.425566
$19$	139.291	1.68187	0.840934	−	0.541138i	$-0.182006\pi$
$19$	139.291	1.68187	0.840934	+	0.541138i	$0.182006\pi$
$20$	−56.2180	−0.628537
$21$	21.0000	0.218218
$22$	45.5175	0.441107
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	−32.0695	−0.272757
$25$	−0.564718	−0.00451775
$26$	210.785	1.58994
$27$	−27.0000	−0.192450
$28$	−35.2778	−0.238103
$29$	247.832	1.58694	0.793471	−	0.608608i	$-0.208272\pi$
$29$	247.832	1.58694	0.793471	+	0.608608i	$0.208272\pi$
$30$	−120.844	−0.735436
$31$	42.5308	0.246411	0.123206	−	0.992381i	$-0.460682\pi$
$31$	42.5308	0.246411	0.123206	+	0.992381i	$0.460682\pi$
$32$	199.462	1.10188
$33$	37.8152	0.199478
$34$	−166.395	−0.839307
$35$	78.0854	0.377110
$36$	45.3572	0.209987
$37$	−42.7792	−0.190077	−0.0950385	−	0.995474i	$-0.530297\pi$
$37$	−42.7792	−0.190077	−0.0950385	+	0.995474i	$0.530297\pi$
$38$	−502.986	−2.14724
$39$	175.117	0.719003
$40$	−119.246	−0.471360
$41$	407.654	1.55280	0.776401	−	0.630240i	$-0.217043\pi$
$41$	407.654	1.55280	0.776401	+	0.630240i	$0.217043\pi$
$42$	−75.8321	−0.278599
$43$	−6.87794	−0.0243925	−0.0121962	−	0.999926i	$-0.503882\pi$
$43$	−6.87794	−0.0243925	−0.0121962	+	0.999926i	$0.503882\pi$
$44$	−63.5256	−0.217655
$45$	−100.396	−0.332580
$46$	−83.0542	−0.266210
$47$	−437.329	−1.35725	−0.678627	−	0.734483i	$-0.737425\pi$
$47$	−437.329	−1.35725	−0.678627	+	0.734483i	$0.737425\pi$
$48$	236.757	0.711936
$49$	49.0000	0.142857
$50$	2.03923	0.00576780
$51$	−138.238	−0.379552
$52$	−294.178	−0.784523
$53$	245.540	0.636369	0.318185	−	0.948029i	$-0.396927\pi$
$53$	245.540	0.636369	0.318185	+	0.948029i	$0.396927\pi$
$54$	97.4984	0.245701
$55$	140.610	0.344725
$56$	−74.8288	−0.178561
$57$	−417.872	−0.971027
$58$	−894.936	−2.02605
$59$	747.982	1.65049	0.825246	−	0.564774i	$-0.191036\pi$
$59$	747.982	1.65049	0.825246	+	0.564774i	$0.191036\pi$
$60$	168.654	0.362886
$61$	−908.216	−1.90631	−0.953157	−	0.302475i	$-0.902187\pi$
$61$	−908.216	−1.90631	−0.953157	+	0.302475i	$0.902187\pi$
$62$	−153.581	−0.314593
$63$	−63.0000	−0.125988
$64$	−88.9154	−0.173663
$65$	651.146	1.24253
$66$	−136.552	−0.254673
$67$	−286.679	−0.522737	−0.261369	−	0.965239i	$-0.584174\pi$
$67$	−286.679	−0.522737	−0.261369	+	0.965239i	$0.584174\pi$
$68$	232.225	0.414139
$69$	−69.0000	−0.120386
$70$	−281.970	−0.481456
$71$	−628.316	−1.05025	−0.525123	−	0.851027i	$-0.675981\pi$
$71$	−628.316	−1.05025	−0.525123	+	0.851027i	$0.675981\pi$
$72$	96.2085	0.157476
$73$	1023.03	1.64023	0.820116	−	0.572197i	$-0.193909\pi$
$73$	1023.03	1.64023	0.820116	+	0.572197i	$0.193909\pi$
$74$	154.478	0.242671
$75$	1.69415	0.00260832
$76$	701.982	1.05951
$77$	88.2354	0.130589
$78$	−632.356	−0.917951
$79$	−1012.93	−1.44258	−0.721289	−	0.692634i	$-0.756450\pi$
$79$	−1012.93	−1.44258	−0.721289	+	0.692634i	$0.756450\pi$
$80$	880.346	1.23032
$81$	81.0000	0.111111
$82$	−1472.06	−1.98246
$83$	327.173	0.432673	0.216337	−	0.976319i	$-0.430589\pi$
$83$	327.173	0.432673	0.216337	+	0.976319i	$0.430589\pi$
$84$	105.833	0.137469
$85$	−514.017	−0.655917
$86$	24.8366	0.0311418
$87$	−743.497	−0.916222
$88$	−134.746	−0.163227
$89$	−86.1702	−0.102629	−0.0513147	−	0.998683i	$-0.516341\pi$
$89$	−86.1702	−0.102629	−0.0513147	+	0.998683i	$0.516341\pi$
$90$	362.533	0.424604
$91$	408.606	0.470698
$92$	115.913	0.131356
$93$	−127.592	−0.142266
$94$	1579.22	1.73281
$95$	−1553.80	−1.67806
$96$	−598.386	−0.636172
$97$	−1146.54	−1.20014	−0.600069	−	0.799948i	$-0.704860\pi$
$97$	−1146.54	−1.20014	−0.600069	+	0.799948i	$0.704860\pi$
$98$	−176.942	−0.182386
$99$	−113.445	−0.115169
$100$	−2.84600	−0.00284600
$101$	−2016.06	−1.98620	−0.993098	−	0.117291i	$-0.962579\pi$
$101$	−2016.06	−1.98620	−0.993098	+	0.117291i	$0.962579\pi$
$102$	499.184	0.484574
$103$	44.8504	0.0429052	0.0214526	−	0.999770i	$-0.493171\pi$
$103$	44.8504	0.0429052	0.0214526	+	0.999770i	$0.493171\pi$
$104$	−623.990	−0.588339
$105$	−234.256	−0.217724
$106$	−886.659	−0.812452
$107$	−1832.37	−1.65554	−0.827768	−	0.561071i	$-0.810390\pi$
$107$	−1832.37	−1.65554	−0.827768	+	0.561071i	$0.810390\pi$
$108$	−136.072	−0.121236
$109$	−946.215	−0.831476	−0.415738	−	0.909484i	$-0.636477\pi$
$109$	−946.215	−0.831476	−0.415738	+	0.909484i	$0.636477\pi$
$110$	−507.750	−0.440110
$111$	128.337	0.109741
$112$	552.433	0.466072
$113$	1007.58	0.838807	0.419403	−	0.907800i	$-0.362239\pi$
$113$	1007.58	0.838807	0.419403	+	0.907800i	$0.362239\pi$
$114$	1508.96	1.23971
$115$	−256.566	−0.208043
$116$	1249.00	0.999712
$117$	−525.351	−0.415117
$118$	−2701.00	−2.10718
$119$	−322.555	−0.248475
$120$	357.737	0.272140
$121$	−1172.11	−0.880626
$122$	3279.62	2.43379
$123$	−1222.96	−0.896510
$124$	214.342	0.155230
$125$	1400.68	1.00225
$126$	227.496	0.160849
$127$	−1163.58	−0.813002	−0.406501	−	0.913650i	$-0.633251\pi$
$127$	−1163.58	−0.813002	−0.406501	+	0.913650i	$0.633251\pi$
$128$	−1274.62	−0.880167
$129$	20.6338	0.0140830
$130$	−2351.32	−1.58634
$131$	140.471	0.0936871	0.0468436	−	0.998902i	$-0.485084\pi$
$131$	140.471	0.0936871	0.0468436	+	0.998902i	$0.485084\pi$
$132$	190.577	0.125663
$133$	−975.035	−0.635686
$134$	1035.21	0.667378
$135$	301.187	0.192015
$136$	492.579	0.310576
$137$	1138.05	0.709707	0.354854	−	0.934922i	$-0.384531\pi$
$137$	1138.05	0.709707	0.354854	+	0.934922i	$0.384531\pi$
$138$	249.163	0.153697
$139$	750.691	0.458078	0.229039	−	0.973417i	$-0.426442\pi$
$139$	750.691	0.458078	0.229039	+	0.973417i	$0.426442\pi$
$140$	393.526	0.237565
$141$	1311.99	0.783611
$142$	2268.88	1.34085
$143$	735.786	0.430276
$144$	−710.271	−0.411037
$145$	−2764.59	−1.58335
$146$	−3694.22	−2.09408
$147$	−147.000	−0.0824786
$148$	−215.594	−0.119741
$149$	737.980	0.405756	0.202878	−	0.979204i	$-0.434970\pi$
$149$	737.980	0.405756	0.202878	+	0.979204i	$0.434970\pi$
$150$	−6.11768	−0.00333004
$151$	2197.99	1.18457	0.592284	−	0.805729i	$-0.298226\pi$
$151$	2197.99	1.18457	0.592284	+	0.805729i	$0.298226\pi$
$152$	1488.99	0.794562
$153$	414.713	0.219135
$154$	−318.622	−0.166723
$155$	−474.433	−0.245854
$156$	882.535	0.452944
$157$	3172.38	1.61263	0.806316	−	0.591485i	$-0.201458\pi$
$157$	3172.38	1.61263	0.806316	+	0.591485i	$0.201458\pi$
$158$	3657.75	1.84174
$159$	−736.621	−0.367408
$160$	−2225.01	−1.09939
$161$	−161.000	−0.0788110
$162$	−292.495	−0.141855
$163$	−1325.66	−0.637018	−0.318509	−	0.947920i	$-0.603182\pi$
$163$	−1325.66	−0.637018	−0.318509	+	0.947920i	$0.603182\pi$
$164$	2054.45	0.978205
$165$	−421.830	−0.199027
$166$	−1181.44	−0.552394
$167$	1905.20	0.882807	0.441404	−	0.897309i	$-0.354481\pi$
$167$	1905.20	0.882807	0.441404	+	0.897309i	$0.354481\pi$
$168$	224.486	0.103092
$169$	1210.32	0.550898
$170$	1856.14	0.837409
$171$	1253.62	0.560623
$172$	−34.6627	−0.0153663
$173$	79.9645	0.0351421	0.0175711	−	0.999846i	$-0.494407\pi$
$173$	79.9645	0.0351421	0.0175711	+	0.999846i	$0.494407\pi$
$174$	2684.81	1.16974
$175$	3.95303	0.00170755
$176$	994.779	0.426047
$177$	−2243.95	−0.952912
$178$	311.165	0.131027
$179$	−2084.01	−0.870200	−0.435100	−	0.900382i	$-0.643287\pi$
$179$	−2084.01	−0.870200	−0.435100	+	0.900382i	$0.643287\pi$
$180$	−505.962	−0.209512
$181$	−1081.92	−0.444300	−0.222150	−	0.975013i	$-0.571307\pi$
$181$	−1081.92	−0.444300	−0.222150	+	0.975013i	$0.571307\pi$
$182$	−1475.50	−0.600940
$183$	2724.65	1.10061
$184$	245.866	0.0985081
$185$	477.204	0.189647
$186$	460.743	0.181631
$187$	−580.832	−0.227137
$188$	−2204.00	−0.855018
$189$	189.000	0.0727393
$190$	5610.84	2.14238
$191$	1051.61	0.398388	0.199194	−	0.979960i	$-0.436168\pi$
$191$	1051.61	0.398388	0.199194	+	0.979960i	$0.436168\pi$
$192$	266.746	0.100264
$193$	−4329.32	−1.61467	−0.807335	−	0.590093i	$-0.799091\pi$
$193$	−4329.32	−1.61467	−0.807335	+	0.590093i	$0.799091\pi$
$194$	4140.21	1.53222
$195$	−1953.44	−0.717377
$196$	246.945	0.0899945
$197$	−3758.62	−1.35934	−0.679671	−	0.733517i	$-0.737877\pi$
$197$	−3758.62	−1.35934	−0.679671	+	0.733517i	$0.737877\pi$
$198$	409.657	0.147036
$199$	4799.77	1.70978	0.854891	−	0.518808i	$-0.173624\pi$
$199$	4799.77	1.70978	0.854891	+	0.518808i	$0.173624\pi$
$200$	−6.03674	−0.00213431
$201$	860.036	0.301802
$202$	7280.10	2.53577
$203$	−1734.83	−0.599808
$204$	−696.676	−0.239103
$205$	−4547.40	−1.54929
$206$	−161.957	−0.0547771
$207$	207.000	0.0695048
$208$	4606.68	1.53565
$209$	−1755.77	−0.581096
$210$	845.911	0.277969
$211$	4652.75	1.51805	0.759025	−	0.651062i	$-0.225676\pi$
$211$	4652.75	1.51805	0.759025	+	0.651062i	$0.225676\pi$
$212$	1237.45	0.400888
$213$	1884.95	0.606359
$214$	6616.80	2.11362
$215$	76.7238	0.0243373
$216$	−288.625	−0.0909188
$217$	−297.716	−0.0931348
$218$	3416.83	1.06155
$219$	−3069.10	−0.946988
$220$	708.631	0.217163
$221$	−2689.75	−0.818698
$222$	−463.433	−0.140106
$223$	−5739.51	−1.72352	−0.861762	−	0.507313i	$-0.830639\pi$
$223$	−5739.51	−1.72352	−0.861762	+	0.507313i	$0.830639\pi$
$224$	−1396.23	−0.416472
$225$	−5.08246	−0.00150592
$226$	−3638.42	−1.07090
$227$	−171.194	−0.0500552	−0.0250276	−	0.999687i	$-0.507967\pi$
$227$	−171.194	−0.0500552	−0.0250276	+	0.999687i	$0.507967\pi$
$228$	−2105.95	−0.611709
$229$	−1349.74	−0.389491	−0.194745	−	0.980854i	$-0.562388\pi$
$229$	−1349.74	−0.389491	−0.194745	+	0.980854i	$0.562388\pi$
$230$	926.474	0.265608
$231$	−264.706	−0.0753956
$232$	2649.29	0.749716
$233$	1817.41	0.510997	0.255499	−	0.966809i	$-0.417760\pi$
$233$	1817.41	0.510997	0.255499	+	0.966809i	$0.417760\pi$
$234$	1897.07	0.529979
$235$	4878.43	1.35418
$236$	3769.60	1.03975
$237$	3038.79	0.832873
$238$	1164.76	0.317228
$239$	5672.21	1.53517	0.767583	−	0.640949i	$-0.221459\pi$
$239$	5672.21	1.53517	0.767583	+	0.640949i	$0.221459\pi$
$240$	−2641.04	−0.710326
$241$	716.259	0.191445	0.0957226	−	0.995408i	$-0.469484\pi$
$241$	716.259	0.191445	0.0957226	+	0.995408i	$0.469484\pi$
$242$	4232.56	1.12429
$243$	−243.000	−0.0641500
$244$	−4577.13	−1.20090
$245$	−546.598	−0.142534
$246$	4416.18	1.14457
$247$	−8130.72	−2.09452
$248$	454.647	0.116412
$249$	−981.518	−0.249804
$250$	−5057.93	−1.27957
$251$	6498.73	1.63425	0.817124	−	0.576462i	$-0.195567\pi$
$251$	6498.73	1.63425	0.817124	+	0.576462i	$0.195567\pi$
$252$	−317.500	−0.0793677
$253$	−289.916	−0.0720430
$254$	4201.76	1.03796
$255$	1542.05	0.378694
$256$	5314.04	1.29737
$257$	2203.43	0.534810	0.267405	−	0.963584i	$-0.413834\pi$
$257$	2203.43	0.534810	0.267405	+	0.963584i	$0.413834\pi$
$258$	−74.5097	−0.0179797
$259$	299.454	0.0718424
$260$	3281.57	0.782749
$261$	2230.49	0.528981
$262$	−507.248	−0.119610
$263$	−5481.52	−1.28519	−0.642595	−	0.766206i	$-0.722142\pi$
$263$	−5481.52	−1.28519	−0.642595	+	0.766206i	$0.722142\pi$
$264$	404.238	0.0942390
$265$	−2739.02	−0.634930
$266$	3520.90	0.811580
$267$	258.511	0.0592531
$268$	−1444.77	−0.329304
$269$	−586.966	−0.133041	−0.0665203	−	0.997785i	$-0.521190\pi$
$269$	−586.966	−0.133041	−0.0665203	+	0.997785i	$0.521190\pi$
$270$	−1087.60	−0.245145
$271$	2152.88	0.482577	0.241289	−	0.970453i	$-0.422430\pi$
$271$	2152.88	0.482577	0.241289	+	0.970453i	$0.422430\pi$
$272$	−3636.53	−0.810651
$273$	−1225.82	−0.271758
$274$	−4109.54	−0.906083
$275$	7.11830	0.00156091
$276$	−347.739	−0.0758384
$277$	−1723.34	−0.373811	−0.186905	−	0.982378i	$-0.559846\pi$
$277$	−1723.34	−0.373811	−0.186905	+	0.982378i	$0.559846\pi$
$278$	−2710.79	−0.584828
$279$	382.777	0.0821371
$280$	834.720	0.178157
$281$	−1540.87	−0.327120	−0.163560	−	0.986533i	$-0.552298\pi$
$281$	−1540.87	−0.327120	−0.163560	+	0.986533i	$0.552298\pi$
$282$	−4737.65	−1.00044
$283$	−7908.71	−1.66122	−0.830608	−	0.556857i	$-0.812007\pi$
$283$	−7908.71	−1.66122	−0.830608	+	0.556857i	$0.812007\pi$
$284$	−3166.52	−0.661614
$285$	4661.39	0.968831
$286$	−2656.96	−0.549333
$287$	−2853.58	−0.586904
$288$	1795.16	0.367294
$289$	−2789.70	−0.567820
$290$	9983.06	2.02147
$291$	3439.62	0.692900
$292$	5155.77	1.03328
$293$	−8367.82	−1.66844	−0.834220	−	0.551431i	$-0.814082\pi$
$293$	−8367.82	−1.66844	−0.834220	+	0.551431i	$0.814082\pi$
$294$	530.825	0.105300
$295$	−8343.79	−1.64676
$296$	−457.302	−0.0897978
$297$	340.336	0.0664927
$298$	−2664.89	−0.518029
$299$	−1342.56	−0.259674
$300$	8.53801	0.00164314
$301$	48.1456	0.00921948
$302$	−7937.05	−1.51234
$303$	6048.19	1.14673
$304$	−10992.7	−2.07393
$305$	10131.2	1.90200
$306$	−1497.55	−0.279769
$307$	−5330.83	−0.991032	−0.495516	−	0.868599i	$-0.665021\pi$
$307$	−5330.83	−0.991032	−0.495516	+	0.868599i	$0.665021\pi$
$308$	444.679	0.0822660
$309$	−134.551	−0.0247713
$310$	1713.20	0.313882
$311$	−2881.19	−0.525330	−0.262665	−	0.964887i	$-0.584601\pi$
$311$	−2881.19	−0.525330	−0.262665	+	0.964887i	$0.584601\pi$
$312$	1871.97	0.339678
$313$	1032.35	0.186428	0.0932138	−	0.995646i	$-0.470286\pi$
$313$	1032.35	0.186428	0.0932138	+	0.995646i	$0.470286\pi$
$314$	−11455.6	−2.05885
$315$	702.769	0.125703
$316$	−5104.86	−0.908769
$317$	−7477.11	−1.32478	−0.662391	−	0.749158i	$-0.730458\pi$
$317$	−7477.11	−1.32478	−0.662391	+	0.749158i	$0.730458\pi$
$318$	2659.98	0.469069
$319$	−3123.94	−0.548298
$320$	991.856	0.173270
$321$	5497.12	0.955824
$322$	581.379	0.100618
$323$	6418.42	1.10567
$324$	408.215	0.0699957
$325$	32.9639	0.00562618
$326$	4787.04	0.813281
$327$	2838.64	0.480053
$328$	4357.75	0.733587
$329$	3061.30	0.512994
$330$	1523.25	0.254098
$331$	6743.30	1.11977	0.559887	−	0.828569i	$-0.310845\pi$
$331$	6743.30	1.11977	0.559887	+	0.828569i	$0.310845\pi$
$332$	1648.85	0.272567
$333$	−385.012	−0.0633590
$334$	−6879.77	−1.12708
$335$	3197.92	0.521555
$336$	−1657.30	−0.269087
$337$	7505.30	1.21317	0.606587	−	0.795017i	$-0.292538\pi$
$337$	7505.30	1.21317	0.606587	+	0.795017i	$0.292538\pi$
$338$	−4370.54	−0.703331
$339$	−3022.74	−0.484285
$340$	−2590.49	−0.413202
$341$	−536.103	−0.0851367
$342$	−4526.88	−0.715747
$343$	−343.000	−0.0539949
$344$	−73.5240	−0.0115237
$345$	769.699	0.120114
$346$	−288.756	−0.0448659
$347$	−12727.8	−1.96905	−0.984527	−	0.175234i	$-0.943932\pi$
$347$	−12727.8	−1.96905	−0.984527	+	0.175234i	$0.943932\pi$
$348$	−3747.00	−0.577184
$349$	−3837.11	−0.588527	−0.294264	−	0.955724i	$-0.595074\pi$
$349$	−3837.11	−0.588527	−0.294264	+	0.955724i	$0.595074\pi$
$350$	−14.2746	−0.00218002
$351$	1576.05	0.239668
$352$	−2514.23	−0.380707
$353$	110.485	0.0166587	0.00832936	−	0.999965i	$-0.497349\pi$
$353$	110.485	0.0166587	0.00832936	+	0.999965i	$0.497349\pi$
$354$	8103.01	1.21658
$355$	7008.90	1.04787
$356$	−434.271	−0.0646526
$357$	967.664	0.143457
$358$	7525.45	1.11098
$359$	−529.690	−0.0778718	−0.0389359	−	0.999242i	$-0.512397\pi$
$359$	−529.690	−0.0778718	−0.0389359	+	0.999242i	$0.512397\pi$
$360$	−1073.21	−0.157120
$361$	12542.9	1.82868
$362$	3906.86	0.567237
$363$	3516.34	0.508429
$364$	2059.25	0.296522
$365$	−11412.0	−1.63652
$366$	−9838.85	−1.40515
$367$	11598.9	1.64974	0.824872	−	0.565320i	$-0.191247\pi$
$367$	11598.9	1.64974	0.824872	+	0.565320i	$0.191247\pi$
$368$	−1815.14	−0.257121
$369$	3668.89	0.517600
$370$	−1723.21	−0.242122
$371$	−1718.78	−0.240525
$372$	−643.026	−0.0896219
$373$	−903.243	−0.125384	−0.0626919	−	0.998033i	$-0.519969\pi$
$373$	−903.243	−0.125384	−0.0626919	+	0.998033i	$0.519969\pi$
$374$	2097.41	0.289986
$375$	−4202.04	−0.578647
$376$	−4674.97	−0.641205
$377$	−14466.5	−1.97630
$378$	−682.489	−0.0928662
$379$	3033.13	0.411085	0.205542	−	0.978648i	$-0.434104\pi$
$379$	3033.13	0.411085	0.205542	+	0.978648i	$0.434104\pi$
$380$	−7830.65	−1.05712
$381$	3490.75	0.469387
$382$	−3797.43	−0.508622
$383$	−3638.47	−0.485423	−0.242711	−	0.970099i	$-0.578037\pi$
$383$	−3638.47	−0.485423	−0.242711	+	0.970099i	$0.578037\pi$
$384$	3823.86	0.508165
$385$	−984.271	−0.130294
$386$	15633.4	2.06145
$387$	−61.9014	−0.00813082
$388$	−5778.20	−0.756040
$389$	1793.71	0.233792	0.116896	−	0.993144i	$-0.462706\pi$
$389$	1793.71	0.233792	0.116896	+	0.993144i	$0.462706\pi$
$390$	7053.97	0.915875
$391$	1059.82	0.137078
$392$	523.802	0.0674897
$393$	−421.413	−0.0540903
$394$	13572.6	1.73547
$395$	11299.3	1.43932
$396$	−571.730	−0.0725518
$397$	−12508.8	−1.58135	−0.790676	−	0.612234i	$-0.790271\pi$
$397$	−12508.8	−1.58135	−0.790676	+	0.612234i	$0.790271\pi$
$398$	−17332.2	−2.18288
$399$	2925.11	0.367014
$400$	44.5670	0.00557088
$401$	−4110.34	−0.511872	−0.255936	−	0.966694i	$-0.582384\pi$
$401$	−4110.34	−0.511872	−0.255936	+	0.966694i	$0.582384\pi$
$402$	−3105.63	−0.385311
$403$	−2482.62	−0.306869
$404$	−10160.3	−1.25123
$405$	−903.560	−0.110860
$406$	6264.55	0.765774
$407$	539.234	0.0656728
$408$	−1477.74	−0.179311
$409$	−5599.41	−0.676951	−0.338476	−	0.940975i	$-0.609911\pi$
$409$	−5599.41	−0.676951	−0.338476	+	0.940975i	$0.609911\pi$
$410$	16420.9	1.97798
$411$	−3414.14	−0.409750
$412$	226.032	0.0270286
$413$	−5235.88	−0.623827
$414$	−747.488	−0.0887367
$415$	−3649.63	−0.431695
$416$	−11643.1	−1.37223
$417$	−2252.07	−0.264471
$418$	6340.17	0.741884
$419$	−15453.4	−1.80179	−0.900895	−	0.434038i	$-0.857089\pi$
$419$	−15453.4	−1.80179	−0.900895	+	0.434038i	$0.857089\pi$
$420$	−1180.58	−0.137158
$421$	−4674.14	−0.541102	−0.270551	−	0.962706i	$-0.587206\pi$
$421$	−4674.14	−0.541102	−0.270551	+	0.962706i	$0.587206\pi$
$422$	−16801.3	−1.93809
$423$	−3935.96	−0.452418
$424$	2624.78	0.300639
$425$	−26.0218	−0.00296998
$426$	−6806.65	−0.774139
$427$	6357.52	0.720519
$428$	−9234.60	−1.04292
$429$	−2207.36	−0.248420
$430$	−277.053	−0.0310714
$431$	−4662.18	−0.521043	−0.260521	−	0.965468i	$-0.583894\pi$
$431$	−4662.18	−0.521043	−0.260521	+	0.965468i	$0.583894\pi$
$432$	2130.81	0.237312
$433$	−2125.77	−0.235930	−0.117965	−	0.993018i	$-0.537637\pi$
$433$	−2125.77	−0.235930	−0.117965	+	0.993018i	$0.537637\pi$
$434$	1075.07	0.118905
$435$	8293.76	0.914150
$436$	−4768.63	−0.523798
$437$	3203.69	0.350694
$438$	11082.7	1.20902
$439$	2412.52	0.262285	0.131143	−	0.991363i	$-0.458135\pi$
$439$	2412.52	0.262285	0.131143	+	0.991363i	$0.458135\pi$
$440$	1503.10	0.162858
$441$	441.000	0.0476190
$442$	9712.83	1.04523
$443$	−7856.42	−0.842595	−0.421298	−	0.906922i	$-0.638425\pi$
$443$	−7856.42	−0.842595	−0.421298	+	0.906922i	$0.638425\pi$
$444$	646.781	0.0691326
$445$	961.233	0.102397
$446$	20725.7	2.20042
$447$	−2213.94	−0.234264
$448$	622.408	0.0656384
$449$	−4752.88	−0.499559	−0.249780	−	0.968303i	$-0.580358\pi$
$449$	−4752.88	−0.499559	−0.249780	+	0.968303i	$0.580358\pi$
$450$	18.3530	0.00192260
$451$	−5138.50	−0.536502
$452$	5077.89	0.528416
$453$	−6593.96	−0.683911
$454$	618.189	0.0639054
$455$	−4558.02	−0.469634
$456$	−4466.98	−0.458741
$457$	11210.0	1.14745	0.573723	−	0.819049i	$-0.305499\pi$
$457$	11210.0	1.14745	0.573723	+	0.819049i	$0.305499\pi$
$458$	4873.98	0.497262
$459$	−1244.14	−0.126517
$460$	−1293.01	−0.131059
$461$	14981.0	1.51352	0.756762	−	0.653690i	$-0.226780\pi$
$461$	14981.0	1.51352	0.756762	+	0.653690i	$0.226780\pi$
$462$	955.867	0.0962575
$463$	−15215.6	−1.52728	−0.763640	−	0.645642i	$-0.776590\pi$
$463$	−15215.6	−1.52728	−0.763640	+	0.645642i	$0.776590\pi$
$464$	−19558.7	−1.95687
$465$	1423.30	0.141944
$466$	−6562.75	−0.652390
$467$	8203.41	0.812866	0.406433	−	0.913681i	$-0.366772\pi$
$467$	8203.41	0.812866	0.406433	+	0.913681i	$0.366772\pi$
$468$	−2647.60	−0.261508
$469$	2006.75	0.197576
$470$	−17616.2	−1.72889
$471$	−9517.13	−0.931054
$472$	7995.80	0.779739
$473$	86.6968	0.00842774
$474$	−10973.2	−1.06333
$475$	−78.6600	−0.00759825
$476$	−1625.58	−0.156530
$477$	2209.86	0.212123
$478$	−20482.6	−1.95995
$479$	18664.2	1.78035	0.890176	−	0.455616i	$-0.150581\pi$
$479$	18664.2	1.78035	0.890176	+	0.455616i	$0.150581\pi$
$480$	6675.03	0.634734
$481$	2497.12	0.236713
$482$	−2586.45	−0.244418
$483$	483.000	0.0455016
$484$	−5907.08	−0.554760
$485$	12789.7	1.19742
$486$	877.485	0.0819003
$487$	2339.11	0.217649	0.108825	−	0.994061i	$-0.465291\pi$
$487$	2339.11	0.217649	0.108825	+	0.994061i	$0.465291\pi$
$488$	−9708.68	−0.900597
$489$	3976.99	0.367783
$490$	1973.79	0.181973
$491$	−10104.1	−0.928703	−0.464351	−	0.885651i	$-0.653713\pi$
$491$	−10104.1	−0.928703	−0.464351	+	0.885651i	$0.653713\pi$
$492$	−6163.35	−0.564767
$493$	11419.9	1.04326
$494$	29360.4	2.67407
$495$	1265.49	0.114908
$496$	−3356.49	−0.303852
$497$	4398.21	0.396955
$498$	3544.31	0.318925
$499$	10665.5	0.956822	0.478411	−	0.878136i	$-0.341213\pi$
$499$	10665.5	0.956822	0.478411	+	0.878136i	$0.341213\pi$
$500$	7059.00	0.631376
$501$	−5715.60	−0.509689
$502$	−23467.2	−2.08644
$503$	−9776.43	−0.866620	−0.433310	−	0.901245i	$-0.642654\pi$
$503$	−9776.43	−0.866620	−0.433310	+	0.901245i	$0.642654\pi$
$504$	−673.459	−0.0595204
$505$	22489.3	1.98170
$506$	1046.90	0.0919773
$507$	−3630.97	−0.318061
$508$	−5864.09	−0.512160
$509$	−17897.9	−1.55857	−0.779283	−	0.626672i	$-0.784417\pi$
$509$	−17897.9	−1.55857	−0.779283	+	0.626672i	$0.784417\pi$
$510$	−5568.42	−0.483478
$511$	−7161.23	−0.619949
$512$	−8992.31	−0.776187
$513$	−3760.85	−0.323676
$514$	−7956.70	−0.682792
$515$	−500.308	−0.0428082
$516$	103.988	0.00887174
$517$	5512.55	0.468940
$518$	−1081.34	−0.0917211
$519$	−239.893	−0.0202893
$520$	6960.64	0.587008
$521$	3183.02	0.267659	0.133830	−	0.991004i	$-0.457272\pi$
$521$	3183.02	0.267659	0.133830	+	0.991004i	$0.457272\pi$
$522$	−8054.42	−0.675350
$523$	3.79211	0.000317051 0	0.000158525	−	1.00000i	$-0.499950\pi$
$523$	3.79211	0.000317051 0	0.000158525		1.00000i	$0.499950\pi$
$524$	707.931	0.0590193
$525$	−11.8591	−0.000985853 0
$526$	19794.0	1.64080
$527$	1959.79	0.161992
$528$	−2984.34	−0.245978
$529$	529.000	0.0434783
$530$	9890.73	0.810615
$531$	6731.84	0.550164
$532$	−4913.88	−0.400458
$533$	−23795.7	−1.93378
$534$	−933.495	−0.0756485
$535$	20440.2	1.65179
$536$	−3064.55	−0.246956
$537$	6252.02	0.502410
$538$	2119.56	0.169853
$539$	−617.648	−0.0493580
$540$	1517.89	0.120962
$541$	−11461.2	−0.910821	−0.455410	−	0.890282i	$-0.650507\pi$
$541$	−11461.2	−0.910821	−0.455410	+	0.890282i	$0.650507\pi$
$542$	−7774.17	−0.616106
$543$	3245.75	0.256517
$544$	9191.06	0.724382
$545$	10555.1	0.829596
$546$	4426.49	0.346953
$547$	−8285.96	−0.647682	−0.323841	−	0.946112i	$-0.604974\pi$
$547$	−8285.96	−0.647682	−0.323841	+	0.946112i	$0.604974\pi$
$548$	5735.40	0.447088
$549$	−8173.95	−0.635438
$550$	−25.7046	−0.00199281
$551$	34520.8	2.66903
$552$	−737.598	−0.0568737
$553$	7090.52	0.545243
$554$	6223.07	0.477244
$555$	−1431.61	−0.109493
$556$	3783.25	0.288571
$557$	−13490.6	−1.02624	−0.513119	−	0.858318i	$-0.671510\pi$
$557$	−13490.6	−1.02624	−0.513119	+	0.858318i	$0.671510\pi$
$558$	−1382.23	−0.104864
$559$	401.481	0.0303772
$560$	−6162.42	−0.465018
$561$	1742.49	0.131138
$562$	5564.17	0.417634
$563$	5318.81	0.398154	0.199077	−	0.979984i	$-0.436206\pi$
$563$	5318.81	0.398154	0.199077	+	0.979984i	$0.436206\pi$
$564$	6612.00	0.493645
$565$	−11239.6	−0.836910
$566$	28558.8	2.12087
$567$	−567.000	−0.0419961
$568$	−6716.59	−0.496166
$569$	−15975.8	−1.17705	−0.588526	−	0.808479i	$-0.700291\pi$
$569$	−15975.8	−1.17705	−0.588526	+	0.808479i	$0.700291\pi$
$570$	−16832.5	−1.23691
$571$	−9367.25	−0.686528	−0.343264	−	0.939239i	$-0.611532\pi$
$571$	−9367.25	−0.686528	−0.343264	+	0.939239i	$0.611532\pi$
$572$	3708.13	0.271057
$573$	−3154.84	−0.230010
$574$	10304.4	0.749300
$575$	−12.9885	−0.000942015 0
$576$	−800.238	−0.0578876
$577$	7538.95	0.543935	0.271968	−	0.962306i	$-0.412326\pi$
$577$	7538.95	0.543935	0.271968	+	0.962306i	$0.412326\pi$
$578$	10073.8	0.724936
$579$	12988.0	0.932230
$580$	−13932.7	−0.997452
$581$	−2290.21	−0.163535
$582$	−12420.6	−0.884625
$583$	−3095.05	−0.219869
$584$	10936.0	0.774892
$585$	5860.31	0.414178
$586$	30216.6	2.13010
$587$	19349.4	1.36054	0.680268	−	0.732964i	$-0.261864\pi$
$587$	19349.4	1.36054	0.680268	+	0.732964i	$0.261864\pi$
$588$	−740.834	−0.0519583
$589$	5924.15	0.414432
$590$	30129.8	2.10242
$591$	11275.9	0.784817
$592$	3376.09	0.234386
$593$	−7635.66	−0.528767	−0.264384	−	0.964418i	$-0.585169\pi$
$593$	−7635.66	−0.528767	−0.264384	+	0.964418i	$0.585169\pi$
$594$	−1228.97	−0.0848912
$595$	3598.12	0.247913
$596$	3719.19	0.255611
$597$	−14399.3	−0.987143
$598$	4848.06	0.331525
$599$	7679.82	0.523855	0.261927	−	0.965088i	$-0.415642\pi$
$599$	7679.82	0.523855	0.261927	+	0.965088i	$0.415642\pi$
$600$	18.1102	0.00123224
$601$	16514.4	1.12086	0.560429	−	0.828203i	$-0.310636\pi$
$601$	16514.4	1.12086	0.560429	+	0.828203i	$0.310636\pi$
$602$	−173.856	−0.0117705
$603$	−2580.11	−0.174246
$604$	11077.2	0.746232
$605$	13075.0	0.878634
$606$	−21840.3	−1.46403
$607$	23440.5	1.56741	0.783707	−	0.621130i	$-0.213326\pi$
$607$	23440.5	1.56741	0.783707	+	0.621130i	$0.213326\pi$
$608$	27783.2	1.85322
$609$	5204.48	0.346299
$610$	−36584.3	−2.42829
$611$	25527.9	1.69026
$612$	2090.03	0.138046
$613$	11002.9	0.724966	0.362483	−	0.931990i	$-0.381929\pi$
$613$	11002.9	0.724966	0.362483	+	0.931990i	$0.381929\pi$
$614$	19249.9	1.26525
$615$	13642.2	0.894483
$616$	943.221	0.0616939
$617$	−13491.6	−0.880309	−0.440155	−	0.897922i	$-0.645076\pi$
$617$	−13491.6	−0.880309	−0.440155	+	0.897922i	$0.645076\pi$
$618$	485.871	0.0316256
$619$	−26907.4	−1.74717	−0.873585	−	0.486672i	$-0.838211\pi$
$619$	−26907.4	−1.74717	−0.873585	+	0.486672i	$0.838211\pi$
$620$	−2391.00	−0.154879
$621$	−621.000	−0.0401286
$622$	10404.1	0.670688
$623$	603.191	0.0387903
$624$	−13820.1	−0.886610
$625$	−15554.1	−0.995462
$626$	−3727.87	−0.238012
$627$	5267.30	0.335496
$628$	15987.8	1.01590
$629$	−1971.23	−0.124957
$630$	−2537.73	−0.160485
$631$	19881.2	1.25429	0.627145	−	0.778902i	$-0.284223\pi$
$631$	19881.2	1.25429	0.627145	+	0.778902i	$0.284223\pi$
$632$	−10828.1	−0.681515
$633$	−13958.2	−0.876446
$634$	27000.2	1.69135
$635$	12979.8	0.811163
$636$	−3712.34	−0.231453
$637$	−2860.24	−0.177907
$638$	11280.7	0.700012
$639$	−5654.85	−0.350082
$640$	14218.4	0.878177
$641$	−10961.6	−0.675438	−0.337719	−	0.941247i	$-0.609655\pi$
$641$	−10961.6	−0.675438	−0.337719	+	0.941247i	$0.609655\pi$
$642$	−19850.4	−1.22030
$643$	−4591.60	−0.281610	−0.140805	−	0.990037i	$-0.544969\pi$
$643$	−4591.60	−0.281610	−0.140805	+	0.990037i	$0.544969\pi$
$644$	−811.390	−0.0496479
$645$	−230.171	−0.0140511
$646$	−23177.2	−1.41160
$647$	10949.1	0.665305	0.332653	−	0.943049i	$-0.392056\pi$
$647$	10949.1	0.665305	0.332653	+	0.943049i	$0.392056\pi$
$648$	865.876	0.0524920
$649$	−9428.36	−0.570255
$650$	−119.034	−0.00718294
$651$	893.147	0.0537714
$652$	−6680.93	−0.401297
$653$	−14133.1	−0.846968	−0.423484	−	0.905904i	$-0.639193\pi$
$653$	−14133.1	−0.846968	−0.423484	+	0.905904i	$0.639193\pi$
$654$	−10250.5	−0.612883
$655$	−1566.96	−0.0934752
$656$	−32171.7	−1.91477
$657$	9207.29	0.546744
$658$	−11054.5	−0.654939
$659$	−127.473	−0.00753514	−0.00376757	−	0.999993i	$-0.501199\pi$
$659$	−127.473	−0.00753514	−0.00376757	+	0.999993i	$0.501199\pi$
$660$	−2125.89	−0.125379
$661$	−33256.0	−1.95689	−0.978447	−	0.206497i	$-0.933793\pi$
$661$	−33256.0	−1.95689	−0.978447	+	0.206497i	$0.933793\pi$
$662$	−24350.4	−1.42961
$663$	8069.25	0.472675
$664$	3497.42	0.204407
$665$	10876.6	0.634249
$666$	1390.30	0.0808904
$667$	5700.15	0.330900
$668$	9601.62	0.556134
$669$	17218.5	0.995077
$670$	−11547.8	−0.665869
$671$	11448.1	0.658643
$672$	4188.70	0.240451
$673$	3774.61	0.216197	0.108099	−	0.994140i	$-0.465524\pi$
$673$	3774.61	0.216197	0.108099	+	0.994140i	$0.465524\pi$
$674$	−27102.0	−1.54886
$675$	15.2474	0.000869440 0
$676$	6099.65	0.347044
$677$	−6941.91	−0.394090	−0.197045	−	0.980394i	$-0.563135\pi$
$677$	−6941.91	−0.394090	−0.197045	+	0.980394i	$0.563135\pi$
$678$	10915.3	0.618287
$679$	8025.77	0.453609
$680$	−5494.75	−0.309874
$681$	513.581	0.0288994
$682$	1935.89	0.108694
$683$	6454.02	0.361576	0.180788	−	0.983522i	$-0.442135\pi$
$683$	6454.02	0.361576	0.180788	+	0.983522i	$0.442135\pi$
$684$	6317.84	0.353171
$685$	−12695.0	−0.708102
$686$	1238.59	0.0689353
$687$	4049.22	0.224873
$688$	542.800	0.0300786
$689$	−14332.8	−0.792503
$690$	−2779.42	−0.153349
$691$	−12474.3	−0.686749	−0.343374	−	0.939199i	$-0.611570\pi$
$691$	−12474.3	−0.686749	−0.343374	+	0.939199i	$0.611570\pi$
$692$	402.996	0.0221382
$693$	794.118	0.0435297
$694$	45960.6	2.51389
$695$	−8374.01	−0.457042
$696$	−7947.86	−0.432849
$697$	18784.4	1.02082
$698$	13856.0	0.751372
$699$	−5452.22	−0.295024
$700$	19.9220	0.00107569
$701$	−2119.68	−0.114207	−0.0571037	−	0.998368i	$-0.518187\pi$
$701$	−2119.68	−0.114207	−0.0571037	+	0.998368i	$0.518187\pi$
$702$	−5691.20	−0.305984
$703$	−5958.74	−0.319685
$704$	1120.78	0.0600016
$705$	−14635.3	−0.781839
$706$	−398.967	−0.0212682
$707$	14112.4	0.750711
$708$	−11308.8	−0.600298
$709$	−639.637	−0.0338816	−0.0169408	−	0.999856i	$-0.505393\pi$
$709$	−639.637	−0.0338816	−0.0169408	+	0.999856i	$0.505393\pi$
$710$	−25309.5	−1.33782
$711$	−9116.38	−0.480860
$712$	−921.145	−0.0484851
$713$	978.208	0.0513803
$714$	−3494.29	−0.183152
$715$	−8207.73	−0.429303
$716$	−10502.7	−0.548192
$717$	−17016.6	−0.886329
$718$	1912.74	0.0994189
$719$	35787.8	1.85627	0.928136	−	0.372241i	$-0.121411\pi$
$719$	35787.8	1.85627	0.928136	+	0.372241i	$0.121411\pi$
$720$	7923.12	0.410107
$721$	−313.953	−0.0162167
$722$	−45293.1	−2.33468
$723$	−2148.78	−0.110531
$724$	−5452.53	−0.279892
$725$	−139.956	−0.00716940
$726$	−12697.7	−0.649111
$727$	−9877.40	−0.503896	−0.251948	−	0.967741i	$-0.581071\pi$
$727$	−9877.40	−0.503896	−0.251948	+	0.967741i	$0.581071\pi$
$728$	4367.93	0.222371
$729$	729.000	0.0370370
$730$	41209.3	2.08935
$731$	−316.930	−0.0160357
$732$	13731.4	0.693343
$733$	−31571.6	−1.59089	−0.795446	−	0.606024i	$-0.792764\pi$
$733$	−31571.6	−1.59089	−0.795446	+	0.606024i	$0.792764\pi$
$734$	−41884.1	−2.10623
$735$	1639.79	0.0822921
$736$	4587.63	0.229758
$737$	3613.60	0.180609
$738$	−13248.5	−0.660820
$739$	−2685.46	−0.133676	−0.0668378	−	0.997764i	$-0.521291\pi$
$739$	−2685.46	−0.133676	−0.0668378	+	0.997764i	$0.521291\pi$
$740$	2404.96	0.119470
$741$	24392.2	1.20927
$742$	6206.61	0.307078
$743$	3228.38	0.159405	0.0797025	−	0.996819i	$-0.474603\pi$
$743$	3228.38	0.159405	0.0797025	+	0.996819i	$0.474603\pi$
$744$	−1363.94	−0.0672103
$745$	−8232.21	−0.404839
$746$	3261.66	0.160077
$747$	2944.56	0.144224
$748$	−2927.21	−0.143087
$749$	12826.6	0.625734
$750$	15173.8	0.738758
$751$	−20143.6	−0.978761	−0.489380	−	0.872070i	$-0.662777\pi$
$751$	−20143.6	−0.978761	−0.489380	+	0.872070i	$0.662777\pi$
$752$	34513.6	1.67364
$753$	−19496.2	−0.943533
$754$	52239.4	2.52314
$755$	−24518.7	−1.18189
$756$	952.501	0.0458229
$757$	−7963.78	−0.382363	−0.191181	−	0.981555i	$-0.561232\pi$
$757$	−7963.78	−0.382363	−0.191181	+	0.981555i	$0.561232\pi$
$758$	−10952.8	−0.524832
$759$	869.749	0.0415940
$760$	−16609.8	−0.792765
$761$	−14773.9	−0.703748	−0.351874	−	0.936047i	$-0.614455\pi$
$761$	−14773.9	−0.703748	−0.351874	+	0.936047i	$0.614455\pi$
$762$	−12605.3	−0.599266
$763$	6623.50	0.314268
$764$	5299.81	0.250969
$765$	−4626.15	−0.218639
$766$	13138.7	0.619739
$767$	−43661.4	−2.05544
$768$	−15942.1	−0.749038
$769$	−4845.31	−0.227213	−0.113606	−	0.993526i	$-0.536240\pi$
$769$	−4845.31	−0.227213	−0.113606	+	0.993526i	$0.536240\pi$
$770$	3554.25	0.166346
$771$	−6610.30	−0.308773
$772$	−21818.4	−1.01718
$773$	27892.1	1.29781	0.648906	−	0.760869i	$-0.275227\pi$
$773$	27892.1	1.29781	0.648906	+	0.760869i	$0.275227\pi$
$774$	223.529	0.0103806
$775$	−24.0179	−0.00111322
$776$	−12256.3	−0.566979
$777$	−898.362	−0.0414782
$778$	−6477.20	−0.298482
$779$	56782.4	2.61161
$780$	−9844.72	−0.451920
$781$	7919.96	0.362866
$782$	−3827.07	−0.175008
$783$	−6691.48	−0.305407
$784$	−3867.03	−0.176159
$785$	−35388.1	−1.60899
$786$	1521.74	0.0690570
$787$	−2683.32	−0.121538	−0.0607688	−	0.998152i	$-0.519355\pi$
$787$	−2683.32	−0.121538	−0.0607688	+	0.998152i	$0.519355\pi$
$788$	−18942.3	−0.856333
$789$	16444.5	0.742004
$790$	−40802.4	−1.83757
$791$	−7053.06	−0.317039
$792$	−1212.71	−0.0544089
$793$	53014.7	2.37403
$794$	45169.8	2.01891
$795$	8217.05	0.366577
$796$	24189.3	1.07710
$797$	18140.1	0.806217	0.403109	−	0.915152i	$-0.367930\pi$
$797$	18140.1	0.806217	0.403109	+	0.915152i	$0.367930\pi$
$798$	−10562.7	−0.468566
$799$	−20151.8	−0.892264
$800$	−112.640	−0.00497803
$801$	−775.532	−0.0342098
$802$	14842.6	0.653506
$803$	−12895.4	−0.566710
$804$	4334.32	0.190124
$805$	1795.96	0.0786328
$806$	8964.86	0.391779
$807$	1760.90	0.0768111
$808$	−21551.4	−0.938335
$809$	−32318.9	−1.40454	−0.702270	−	0.711911i	$-0.747830\pi$
$809$	−32318.9	−1.40454	−0.702270	+	0.711911i	$0.747830\pi$
$810$	3262.80	0.141535
$811$	8994.66	0.389452	0.194726	−	0.980858i	$-0.437618\pi$
$811$	8994.66	0.389452	0.194726	+	0.980858i	$0.437618\pi$
$812$	−8742.99	−0.377856
$813$	−6458.65	−0.278616
$814$	−1947.20	−0.0838444
$815$	14787.8	0.635578
$816$	10909.6	0.468030
$817$	−958.033	−0.0410249
$818$	20219.8	0.864263
$819$	3677.45	0.156899
$820$	−22917.5	−0.975992
$821$	1958.84	0.0832690	0.0416345	−	0.999133i	$-0.486743\pi$
$821$	1958.84	0.0832690	0.0416345	+	0.999133i	$0.486743\pi$
$822$	12328.6	0.523127
$823$	−18829.8	−0.797527	−0.398764	−	0.917054i	$-0.630561\pi$
$823$	−18829.8	−0.797527	−0.398764	+	0.917054i	$0.630561\pi$
$824$	479.443	0.0202696
$825$	−21.3549	−0.000901191 0
$826$	18907.0	0.796440
$827$	−8910.55	−0.374668	−0.187334	−	0.982296i	$-0.559985\pi$
$827$	−8910.55	−0.374668	−0.187334	+	0.982296i	$0.559985\pi$
$828$	1043.22	0.0437853
$829$	−19895.5	−0.833534	−0.416767	−	0.909013i	$-0.636837\pi$
$829$	−19895.5	−0.833534	−0.416767	+	0.909013i	$0.636837\pi$
$830$	13179.0	0.551144
$831$	5170.02	0.215820
$832$	5190.19	0.216271
$833$	2257.88	0.0939148
$834$	8132.36	0.337650
$835$	−21252.6	−0.880811
$836$	−8848.53	−0.366068
$837$	−1148.33	−0.0474219
$838$	55803.2	2.30034
$839$	38581.5	1.58758	0.793791	−	0.608190i	$-0.208104\pi$
$839$	38581.5	1.58758	0.793791	+	0.608190i	$0.208104\pi$
$840$	−2504.16	−0.102859
$841$	37031.9	1.51839
$842$	16878.6	0.690824
$843$	4622.62	0.188863
$844$	23448.4	0.956312
$845$	−13501.2	−0.549652
$846$	14212.9	0.577602
$847$	8204.79	0.332845
$848$	−19377.8	−0.784713
$849$	23726.1	0.959104
$850$	93.9660	0.00379177
$851$	−983.921	−0.0396338
$852$	9499.56	0.381983
$853$	31921.4	1.28132	0.640660	−	0.767824i	$-0.278661\pi$
$853$	31921.4	1.28132	0.640660	+	0.767824i	$0.278661\pi$
$854$	−22957.3	−0.919887
$855$	−13984.2	−0.559355
$856$	−19587.8	−0.782122
$857$	20560.0	0.819507	0.409754	−	0.912196i	$-0.365615\pi$
$857$	20560.0	0.819507	0.409754	+	0.912196i	$0.365615\pi$
$858$	7970.88	0.317158
$859$	46617.9	1.85167	0.925834	−	0.377929i	$-0.123364\pi$
$859$	46617.9	1.85167	0.925834	+	0.377929i	$0.123364\pi$
$860$	386.664	0.0153316
$861$	8560.73	0.338849
$862$	16835.4	0.665215
$863$	−27344.5	−1.07858	−0.539291	−	0.842119i	$-0.681308\pi$
$863$	−27344.5	−1.07858	−0.539291	+	0.842119i	$0.681308\pi$
$864$	−5385.48	−0.212057
$865$	−892.008	−0.0350626
$866$	7676.25	0.301212
$867$	8369.11	0.327831
$868$	−1500.39	−0.0586713
$869$	12768.1	0.498420
$870$	−29949.2	−1.16709
$871$	16734.1	0.650991
$872$	−10114.9	−0.392813
$873$	−10318.8	−0.400046
$874$	−11568.7	−0.447731
$875$	−9804.77	−0.378813
$876$	−15467.3	−0.596566
$877$	−50442.3	−1.94221	−0.971104	−	0.238656i	$-0.923293\pi$
$877$	−50442.3	−1.94221	−0.971104	+	0.238656i	$0.923293\pi$
$878$	−8711.73	−0.334860
$879$	25103.4	0.963275
$880$	−11096.8	−0.425084
$881$	22242.3	0.850583	0.425292	−	0.905056i	$-0.360172\pi$
$881$	22242.3	0.850583	0.425292	+	0.905056i	$0.360172\pi$
$882$	−1592.47	−0.0607952
$883$	4630.53	0.176478	0.0882389	−	0.996099i	$-0.471876\pi$
$883$	4630.53	0.176478	0.0882389	+	0.996099i	$0.471876\pi$
$884$	−13555.5	−0.515748
$885$	25031.4	0.950757
$886$	28369.9	1.07574
$887$	45089.2	1.70682	0.853408	−	0.521243i	$-0.174531\pi$
$887$	45089.2	1.70682	0.853408	+	0.521243i	$0.174531\pi$
$888$	1371.91	0.0518448
$889$	8145.08	0.307286
$890$	−3471.06	−0.130731
$891$	−1021.01	−0.0383896
$892$	−28925.3	−1.08575
$893$	−60915.9	−2.28272
$894$	7994.66	0.299084
$895$	23247.2	0.868232
$896$	8922.33	0.332672
$897$	4027.69	0.149923
$898$	17162.9	0.637787
$899$	10540.5	0.391041
$900$	−25.6140	−0.000948668 0
$901$	11314.3	0.418351
$902$	18555.4	0.684952
$903$	−144.437	−0.00532287
$904$	10770.9	0.396276
$905$	12068.9	0.443295
$906$	23811.1	0.873148
$907$	−15103.7	−0.552932	−0.276466	−	0.961024i	$-0.589163\pi$
$907$	−15103.7	−0.552932	−0.276466	+	0.961024i	$0.589163\pi$
$908$	−862.763	−0.0315328
$909$	−18144.6	−0.662065
$910$	16459.3	0.599581
$911$	27769.5	1.00993	0.504965	−	0.863140i	$-0.331505\pi$
$911$	27769.5	1.00993	0.504965	+	0.863140i	$0.331505\pi$
$912$	32978.1	1.19738
$913$	−4124.03	−0.149491
$914$	−40480.0	−1.46494
$915$	−30393.6	−1.09812
$916$	−6802.27	−0.245364
$917$	−983.297	−0.0354104
$918$	4492.65	0.161525
$919$	−34220.8	−1.22834	−0.614168	−	0.789175i	$-0.710508\pi$
$919$	−34220.8	−1.22834	−0.614168	+	0.789175i	$0.710508\pi$
$920$	−2742.65	−0.0982853
$921$	15992.5	0.572172
$922$	−54097.2	−1.93232
$923$	36676.3	1.30792
$924$	−1334.04	−0.0474963
$925$	24.1582	0.000858720 0
$926$	54944.4	1.94988
$927$	403.653	0.0143017
$928$	49433.2	1.74862
$929$	−8972.86	−0.316889	−0.158445	−	0.987368i	$-0.550648\pi$
$929$	−8972.86	−0.316889	−0.158445	+	0.987368i	$0.550648\pi$
$930$	−5139.61	−0.181220
$931$	6825.25	0.240267
$932$	9159.17	0.321909
$933$	8643.58	0.303299
$934$	−29622.9	−1.03779
$935$	6479.21	0.226623
$936$	−5615.91	−0.196113
$937$	−49330.3	−1.71990	−0.859952	−	0.510374i	$-0.829507\pi$
$937$	−49330.3	−1.71990	−0.859952	+	0.510374i	$0.829507\pi$
$938$	−7246.48	−0.252245
$939$	−3097.05	−0.107634
$940$	24585.8	0.853084
$941$	−6142.65	−0.212800	−0.106400	−	0.994323i	$-0.533932\pi$
$941$	−6142.65	−0.212800	−0.106400	+	0.994323i	$0.533932\pi$
$942$	34366.9	1.18868
$943$	9376.04	0.323781
$944$	−59030.1	−2.03524
$945$	−2108.31	−0.0725748
$946$	−313.066	−0.0107597
$947$	22650.3	0.777230	0.388615	−	0.921400i	$-0.372954\pi$
$947$	22650.3	0.777230	0.388615	+	0.921400i	$0.372954\pi$
$948$	15314.6	0.524678
$949$	−59716.7	−2.04266
$950$	284.045	0.00970068
$951$	22431.3	0.764864
$952$	−3448.06	−0.117387
$953$	−48634.1	−1.65311	−0.826555	−	0.562856i	$-0.809703\pi$
$953$	−48634.1	−1.65311	−0.826555	+	0.562856i	$0.809703\pi$
$954$	−7979.93	−0.270817
$955$	−11730.8	−0.397487
$956$	28586.2	0.967095
$957$	9371.83	0.316560
$958$	−67397.4	−2.27298
$959$	−7966.33	−0.268244
$960$	−2975.57	−0.100038
$961$	−27982.1	−0.939281
$962$	−9017.22	−0.302211
$963$	−16491.4	−0.551845
$964$	3609.72	0.120603
$965$	48293.8	1.61102
$966$	−1744.14	−0.0580918
$967$	20718.3	0.688991	0.344496	−	0.938788i	$-0.388050\pi$
$967$	20718.3	0.688991	0.344496	+	0.938788i	$0.388050\pi$
$968$	−12529.7	−0.416032
$969$	−19255.2	−0.638357
$970$	−46184.3	−1.52875
$971$	2779.24	0.0918539	0.0459269	−	0.998945i	$-0.485376\pi$
$971$	2779.24	0.0918539	0.0459269	+	0.998945i	$0.485376\pi$
$972$	−1224.64	−0.0404120
$973$	−5254.84	−0.173137
$974$	−8446.64	−0.277872
$975$	−98.8917	−0.00324827
$976$	71675.6	2.35070
$977$	−55624.6	−1.82148	−0.910742	−	0.412976i	$-0.864490\pi$
$977$	−55624.6	−1.82148	−0.910742	+	0.412976i	$0.864490\pi$
$978$	−14361.1	−0.469548
$979$	1086.18	0.0354591
$980$	−2754.68	−0.0897910
$981$	−8515.93	−0.277159
$982$	36486.5	1.18567
$983$	−3906.50	−0.126753	−0.0633764	−	0.997990i	$-0.520187\pi$
$983$	−3906.50	−0.126753	−0.0633764	+	0.997990i	$0.520187\pi$
$984$	−13073.3	−0.423537
$985$	41927.6	1.35627
$986$	−41238.0	−1.33193
$987$	−9183.90	−0.296177
$988$	−40976.3	−1.31946
$989$	−158.193	−0.00508618
$990$	−4569.75	−0.146703
$991$	−1288.85	−0.0413134	−0.0206567	−	0.999787i	$-0.506576\pi$
$991$	−1288.85	−0.0413134	−0.0206567	+	0.999787i	$0.506576\pi$
$992$	8483.28	0.271516
$993$	−20229.9	−0.646502
$994$	−15882.2	−0.506793
$995$	−53541.7	−1.70592
$996$	−4946.55	−0.157367
$997$	1421.22	0.0451459	0.0225730	−	0.999745i	$-0.492814\pi$
$997$	1421.22	0.0451459	0.0225730	+	0.999745i	$0.492814\pi$
$998$	−38513.7	−1.22157
$999$	1155.04	0.0365803

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.4.a.d.1.2	✓	7
3.2	odd	2		1449.4.a.g.1.6		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.4.a.d.1.2	✓	7	1.1	even	1	trivial
1449.4.a.g.1.6		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)

\(f(q)\)	\(=\)	\(q-3.61105 q^{2} -3.00000 q^{3} +5.03969 q^{4} -11.1551 q^{5} +10.8332 q^{6} -7.00000 q^{7} +10.6898 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-3.61105 q^{2} -3.00000 q^{3} +5.03969 q^{4} -11.1551 q^{5} +10.8332 q^{6} -7.00000 q^{7} +10.6898 q^{8} +9.00000 q^{9} +40.2815 q^{10} -12.6051 q^{11} -15.1191 q^{12} -58.3723 q^{13} +25.2774 q^{14} +33.4652 q^{15} -78.9190 q^{16} +46.0793 q^{17} -32.4995 q^{18} +139.291 q^{19} -56.2180 q^{20} +21.0000 q^{21} +45.5175 q^{22} +23.0000 q^{23} -32.0695 q^{24} -0.564718 q^{25} +210.785 q^{26} -27.0000 q^{27} -35.2778 q^{28} +247.832 q^{29} -120.844 q^{30} +42.5308 q^{31} +199.462 q^{32} +37.8152 q^{33} -166.395 q^{34} +78.0854 q^{35} +45.3572 q^{36} -42.7792 q^{37} -502.986 q^{38} +175.117 q^{39} -119.246 q^{40} +407.654 q^{41} -75.8321 q^{42} -6.87794 q^{43} -63.5256 q^{44} -100.396 q^{45} -83.0542 q^{46} -437.329 q^{47} +236.757 q^{48} +49.0000 q^{49} +2.03923 q^{50} -138.238 q^{51} -294.178 q^{52} +245.540 q^{53} +97.4984 q^{54} +140.610 q^{55} -74.8288 q^{56} -417.872 q^{57} -894.936 q^{58} +747.982 q^{59} +168.654 q^{60} -908.216 q^{61} -153.581 q^{62} -63.0000 q^{63} -88.9154 q^{64} +651.146 q^{65} -136.552 q^{66} -286.679 q^{67} +232.225 q^{68} -69.0000 q^{69} -281.970 q^{70} -628.316 q^{71} +96.2085 q^{72} +1023.03 q^{73} +154.478 q^{74} +1.69415 q^{75} +701.982 q^{76} +88.2354 q^{77} -632.356 q^{78} -1012.93 q^{79} +880.346 q^{80} +81.0000 q^{81} -1472.06 q^{82} +327.173 q^{83} +105.833 q^{84} -514.017 q^{85} +24.8366 q^{86} -743.497 q^{87} -134.746 q^{88} -86.1702 q^{89} +362.533 q^{90} +408.606 q^{91} +115.913 q^{92} -127.592 q^{93} +1579.22 q^{94} -1553.80 q^{95} -598.386 q^{96} -1146.54 q^{97} -176.942 q^{98} -113.445 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 2 q^{2} - 21 q^{3} + 22 q^{4} - 11 q^{5} + 6 q^{6} - 49 q^{7} + 15 q^{8} + 63 q^{9}+O(q^{10}) \) 7 * q - 2 * q^2 - 21 * q^3 + 22 * q^4 - 11 * q^5 + 6 * q^6 - 49 * q^7 + 15 * q^8 + 63 * q^9	\( 7 q - 2 q^{2} - 21 q^{3} + 22 q^{4} - 11 q^{5} + 6 q^{6} - 49 q^{7} + 15 q^{8} + 63 q^{9} + 11 q^{10} - 6 q^{11} - 66 q^{12} + 17 q^{13} + 14 q^{14} + 33 q^{15} + 106 q^{16} - 78 q^{17} - 18 q^{18} + 44 q^{19} + 44 q^{20} + 147 q^{21} - 477 q^{22} + 161 q^{23} - 45 q^{24} - 80 q^{25} + 288 q^{26} - 189 q^{27} - 154 q^{28} - 185 q^{29} - 33 q^{30} + 238 q^{31} - 512 q^{32} + 18 q^{33} - 27 q^{34} + 77 q^{35} + 198 q^{36} - 511 q^{37} - 413 q^{38} - 51 q^{39} - 686 q^{40} + 867 q^{41} - 42 q^{42} - 1003 q^{43} - 629 q^{44} - 99 q^{45} - 46 q^{46} + 149 q^{47} - 318 q^{48} + 343 q^{49} - 986 q^{50} + 234 q^{51} - 439 q^{52} - 1244 q^{53} + 54 q^{54} - 270 q^{55} - 105 q^{56} - 132 q^{57} - 2376 q^{58} + 1048 q^{59} - 132 q^{60} - 1380 q^{61} - 809 q^{62} - 441 q^{63} - 1835 q^{64} - 223 q^{65} + 1431 q^{66} - 500 q^{67} - 1387 q^{68} - 483 q^{69} - 77 q^{70} - 14 q^{71} + 135 q^{72} - 530 q^{73} - 738 q^{74} + 240 q^{75} - 1785 q^{76} + 42 q^{77} - 864 q^{78} - 2978 q^{79} + 1043 q^{80} + 567 q^{81} - 1986 q^{82} - 524 q^{83} + 462 q^{84} - 2674 q^{85} + 194 q^{86} + 555 q^{87} - 4504 q^{88} - 648 q^{89} + 99 q^{90} - 119 q^{91} + 506 q^{92} - 714 q^{93} - 801 q^{94} + 154 q^{95} + 1536 q^{96} - 1999 q^{97} - 98 q^{98} - 54 q^{99}+O(q^{100}) \) 7 * q - 2 * q^2 - 21 * q^3 + 22 * q^4 - 11 * q^5 + 6 * q^6 - 49 * q^7 + 15 * q^8 + 63 * q^9 + 11 * q^10 - 6 * q^11 - 66 * q^12 + 17 * q^13 + 14 * q^14 + 33 * q^15 + 106 * q^16 - 78 * q^17 - 18 * q^18 + 44 * q^19 + 44 * q^20 + 147 * q^21 - 477 * q^22 + 161 * q^23 - 45 * q^24 - 80 * q^25 + 288 * q^26 - 189 * q^27 - 154 * q^28 - 185 * q^29 - 33 * q^30 + 238 * q^31 - 512 * q^32 + 18 * q^33 - 27 * q^34 + 77 * q^35 + 198 * q^36 - 511 * q^37 - 413 * q^38 - 51 * q^39 - 686 * q^40 + 867 * q^41 - 42 * q^42 - 1003 * q^43 - 629 * q^44 - 99 * q^45 - 46 * q^46 + 149 * q^47 - 318 * q^48 + 343 * q^49 - 986 * q^50 + 234 * q^51 - 439 * q^52 - 1244 * q^53 + 54 * q^54 - 270 * q^55 - 105 * q^56 - 132 * q^57 - 2376 * q^58 + 1048 * q^59 - 132 * q^60 - 1380 * q^61 - 809 * q^62 - 441 * q^63 - 1835 * q^64 - 223 * q^65 + 1431 * q^66 - 500 * q^67 - 1387 * q^68 - 483 * q^69 - 77 * q^70 - 14 * q^71 + 135 * q^72 - 530 * q^73 - 738 * q^74 + 240 * q^75 - 1785 * q^76 + 42 * q^77 - 864 * q^78 - 2978 * q^79 + 1043 * q^80 + 567 * q^81 - 1986 * q^82 - 524 * q^83 + 462 * q^84 - 2674 * q^85 + 194 * q^86 + 555 * q^87 - 4504 * q^88 - 648 * q^89 + 99 * q^90 - 119 * q^91 + 506 * q^92 - 714 * q^93 - 801 * q^94 + 154 * q^95 + 1536 * q^96 - 1999 * q^97 - 98 * q^98 - 54 * q^99

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