LMFDB - Embedded newform 483.4.a.d.1.7

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			1.7
Root			$-4.75832$ 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)

$f(q)$	$=$	$q+4.75832 q^{2} -3.00000 q^{3} +14.6416 q^{4} -3.92582 q^{5} -14.2750 q^{6} -7.00000 q^{7} +31.6031 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+4.75832 q^{2} -3.00000 q^{3} +14.6416 q^{4} -3.92582 q^{5} -14.2750 q^{6} -7.00000 q^{7} +31.6031 q^{8} +9.00000 q^{9} -18.6803 q^{10} -72.4684 q^{11} -43.9249 q^{12} +2.47953 q^{13} -33.3083 q^{14} +11.7775 q^{15} +33.2445 q^{16} +20.3668 q^{17} +42.8249 q^{18} +1.34917 q^{19} -57.4805 q^{20} +21.0000 q^{21} -344.828 q^{22} +23.0000 q^{23} -94.8092 q^{24} -109.588 q^{25} +11.7984 q^{26} -27.0000 q^{27} -102.491 q^{28} -214.738 q^{29} +56.0410 q^{30} -236.659 q^{31} -94.6366 q^{32} +217.405 q^{33} +96.9116 q^{34} +27.4808 q^{35} +131.775 q^{36} +6.88941 q^{37} +6.41976 q^{38} -7.43858 q^{39} -124.068 q^{40} +327.639 q^{41} +99.9248 q^{42} +77.6388 q^{43} -1061.06 q^{44} -35.3324 q^{45} +109.441 q^{46} +559.584 q^{47} -99.7334 q^{48} +49.0000 q^{49} -521.455 q^{50} -61.1003 q^{51} +36.3043 q^{52} -584.228 q^{53} -128.475 q^{54} +284.498 q^{55} -221.221 q^{56} -4.04750 q^{57} -1021.79 q^{58} +413.416 q^{59} +172.441 q^{60} -876.841 q^{61} -1126.10 q^{62} -63.0000 q^{63} -716.267 q^{64} -9.73418 q^{65} +1034.48 q^{66} +908.302 q^{67} +298.203 q^{68} -69.0000 q^{69} +130.762 q^{70} +471.005 q^{71} +284.428 q^{72} -657.573 q^{73} +32.7820 q^{74} +328.764 q^{75} +19.7540 q^{76} +507.279 q^{77} -35.3952 q^{78} -852.396 q^{79} -130.512 q^{80} +81.0000 q^{81} +1559.01 q^{82} -11.1534 q^{83} +307.474 q^{84} -79.9563 q^{85} +369.430 q^{86} +644.213 q^{87} -2290.22 q^{88} +186.035 q^{89} -168.123 q^{90} -17.3567 q^{91} +336.758 q^{92} +709.978 q^{93} +2662.68 q^{94} -5.29658 q^{95} +283.910 q^{96} +1296.25 q^{97} +233.158 q^{98} -652.216 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	4.75832	1.68232	0.841161	−	0.540785i	$-0.181873\pi$
$2$	4.75832	1.68232	0.841161	+	0.540785i	$0.181873\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	14.6416	1.83020
$5$	−3.92582	−0.351136	−0.175568	−	0.984467i	$-0.556176\pi$
$5$	−3.92582	−0.351136	−0.175568	+	0.984467i	$0.556176\pi$
$6$	−14.2750	−0.971289
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	31.6031	1.39667
$9$	9.00000	0.333333
$10$	−18.6803	−0.590724
$11$	−72.4684	−1.98637	−0.993184	−	0.116556i	$-0.962815\pi$
$11$	−72.4684	−1.98637	−0.993184	+	0.116556i	$0.962815\pi$
$12$	−43.9249	−1.05667
$13$	2.47953	0.0528998	0.0264499	−	0.999650i	$-0.491580\pi$
$13$	2.47953	0.0528998	0.0264499	+	0.999650i	$0.491580\pi$
$14$	−33.3083	−0.635858
$15$	11.7775	0.202729
$16$	33.2445	0.519445
$17$	20.3668	0.290569	0.145284	−	0.989390i	$-0.453590\pi$
$17$	20.3668	0.290569	0.145284	+	0.989390i	$0.453590\pi$
$18$	42.8249	0.560774
$19$	1.34917	0.0162905	0.00814526	−	0.999967i	$-0.497407\pi$
$19$	1.34917	0.0162905	0.00814526	+	0.999967i	$0.497407\pi$
$20$	−57.4805	−0.642651
$21$	21.0000	0.218218
$22$	−344.828	−3.34171
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	−94.8092	−0.806368
$25$	−109.588	−0.876703
$26$	11.7984	0.0889944
$27$	−27.0000	−0.192450
$28$	−102.491	−0.691752
$29$	−214.738	−1.37503	−0.687513	−	0.726172i	$-0.741298\pi$
$29$	−214.738	−1.37503	−0.687513	+	0.726172i	$0.741298\pi$
$30$	56.0410	0.341055
$31$	−236.659	−1.37114	−0.685569	−	0.728008i	$-0.740446\pi$
$31$	−236.659	−1.37114	−0.685569	+	0.728008i	$0.740446\pi$
$32$	−94.6366	−0.522798
$33$	217.405	1.14683
$34$	96.9116	0.488830
$35$	27.4808	0.132717
$36$	131.775	0.610068
$37$	6.88941	0.0306111	0.0153056	−	0.999883i	$-0.495128\pi$
$37$	6.88941	0.0306111	0.0153056	+	0.999883i	$0.495128\pi$
$38$	6.41976	0.0274059
$39$	−7.43858	−0.0305417
$40$	−124.068	−0.490422
$41$	327.639	1.24801	0.624007	−	0.781419i	$-0.285504\pi$
$41$	327.639	1.24801	0.624007	+	0.781419i	$0.285504\pi$
$42$	99.9248	0.367113
$43$	77.6388	0.275344	0.137672	−	0.990478i	$-0.456038\pi$
$43$	77.6388	0.275344	0.137672	+	0.990478i	$0.456038\pi$
$44$	−1061.06	−3.63546
$45$	−35.3324	−0.117045
$46$	109.441	0.350788
$47$	559.584	1.73667	0.868337	−	0.495975i	$-0.165189\pi$
$47$	559.584	1.73667	0.868337	+	0.495975i	$0.165189\pi$
$48$	−99.7334	−0.299901
$49$	49.0000	0.142857
$50$	−521.455	−1.47490
$51$	−61.1003	−0.167760
$52$	36.3043	0.0968174
$53$	−584.228	−1.51415	−0.757075	−	0.653328i	$-0.773372\pi$
$53$	−584.228	−1.51415	−0.757075	+	0.653328i	$0.773372\pi$
$54$	−128.475	−0.323763
$55$	284.498	0.697486
$56$	−221.221	−0.527892
$57$	−4.04750	−0.00940533
$58$	−1021.79	−2.31324
$59$	413.416	0.912240	0.456120	−	0.889918i	$-0.349239\pi$
$59$	413.416	0.912240	0.456120	+	0.889918i	$0.349239\pi$
$60$	172.441	0.371035
$61$	−876.841	−1.84046	−0.920229	−	0.391380i	$-0.871998\pi$
$61$	−876.841	−1.84046	−0.920229	+	0.391380i	$0.871998\pi$
$62$	−1126.10	−2.30669
$63$	−63.0000	−0.125988
$64$	−716.267	−1.39896
$65$	−9.73418	−0.0185750
$66$	1034.48	1.92934
$67$	908.302	1.65622	0.828110	−	0.560566i	$-0.189416\pi$
$67$	908.302	1.65622	0.828110	+	0.560566i	$0.189416\pi$
$68$	298.203	0.531800
$69$	−69.0000	−0.120386
$70$	130.762	0.223273
$71$	471.005	0.787296	0.393648	−	0.919261i	$-0.371213\pi$
$71$	471.005	0.787296	0.393648	+	0.919261i	$0.371213\pi$
$72$	284.428	0.465557
$73$	−657.573	−1.05429	−0.527145	−	0.849775i	$-0.676737\pi$
$73$	−657.573	−1.05429	−0.527145	+	0.849775i	$0.676737\pi$
$74$	32.7820	0.0514978
$75$	328.764	0.506165
$76$	19.7540	0.0298150
$77$	507.279	0.750777
$78$	−35.3952	−0.0513809
$79$	−852.396	−1.21395	−0.606975	−	0.794721i	$-0.707617\pi$
$79$	−852.396	−1.21395	−0.606975	+	0.794721i	$0.707617\pi$
$80$	−130.512	−0.182396
$81$	81.0000	0.111111
$82$	1559.01	2.09956
$83$	−11.1534	−0.0147499	−0.00737495	−	0.999973i	$-0.502348\pi$
$83$	−11.1534	−0.0147499	−0.00737495	+	0.999973i	$0.502348\pi$
$84$	307.474	0.399383
$85$	−79.9563	−0.102029
$86$	369.430	0.463217
$87$	644.213	0.793872
$88$	−2290.22	−2.77430
$89$	186.035	0.221569	0.110784	−	0.993844i	$-0.464664\pi$
$89$	186.035	0.221569	0.110784	+	0.993844i	$0.464664\pi$
$90$	−168.123	−0.196908
$91$	−17.3567	−0.0199942
$92$	336.758	0.381624
$93$	709.978	0.791627
$94$	2662.68	2.92164
$95$	−5.29658	−0.00572019
$96$	283.910	0.301838
$97$	1296.25	1.35685	0.678425	−	0.734670i	$-0.262663\pi$
$97$	1296.25	1.35685	0.678425	+	0.734670i	$0.262663\pi$
$98$	233.158	0.240332
$99$	−652.216	−0.662123
$100$	−1604.55	−1.60455
$101$	−152.881	−0.150616	−0.0753079	−	0.997160i	$-0.523994\pi$
$101$	−152.881	−0.150616	−0.0753079	+	0.997160i	$0.523994\pi$
$102$	−290.735	−0.282226
$103$	−683.452	−0.653811	−0.326905	−	0.945057i	$-0.606006\pi$
$103$	−683.452	−0.653811	−0.326905	+	0.945057i	$0.606006\pi$
$104$	78.3606	0.0738836
$105$	−82.4423	−0.0766242
$106$	−2779.95	−2.54729
$107$	84.2718	0.0761389	0.0380695	−	0.999275i	$-0.487879\pi$
$107$	84.2718	0.0761389	0.0380695	+	0.999275i	$0.487879\pi$
$108$	−395.324	−0.352223
$109$	−2123.85	−1.86631	−0.933157	−	0.359469i	$-0.882958\pi$
$109$	−2123.85	−1.86631	−0.933157	+	0.359469i	$0.882958\pi$
$110$	1353.73	1.17340
$111$	−20.6682	−0.0176733
$112$	−232.711	−0.196332
$113$	−681.503	−0.567349	−0.283675	−	0.958921i	$-0.591554\pi$
$113$	−681.503	−0.567349	−0.283675	+	0.958921i	$0.591554\pi$
$114$	−19.2593	−0.0158228
$115$	−90.2939	−0.0732170
$116$	−3144.11	−2.51658
$117$	22.3157	0.0176333
$118$	1967.17	1.53468
$119$	−142.567	−0.109825
$120$	372.204	0.283145
$121$	3920.67	2.94566
$122$	−4172.29	−3.09624
$123$	−982.916	−0.720541
$124$	−3465.08	−2.50946
$125$	920.951	0.658979
$126$	−299.774	−0.211953
$127$	1890.94	1.32121	0.660605	−	0.750734i	$-0.270300\pi$
$127$	1890.94	1.32121	0.660605	+	0.750734i	$0.270300\pi$
$128$	−2651.14	−1.83070
$129$	−232.916	−0.158970
$130$	−46.3184	−0.0312492
$131$	1025.91	0.684229	0.342114	−	0.939658i	$-0.388857\pi$
$131$	1025.91	0.684229	0.342114	+	0.939658i	$0.388857\pi$
$132$	3183.17	2.09893
$133$	−9.44416	−0.00615723
$134$	4321.99	2.78629
$135$	105.997	0.0675762
$136$	643.652	0.405829
$137$	−1303.32	−0.812777	−0.406388	−	0.913700i	$-0.633212\pi$
$137$	−1303.32	−0.812777	−0.406388	+	0.913700i	$0.633212\pi$
$138$	−328.324	−0.202528
$139$	2046.97	1.24908	0.624539	−	0.780994i	$-0.285287\pi$
$139$	2046.97	1.24908	0.624539	+	0.780994i	$0.285287\pi$
$140$	402.363	0.242899
$141$	−1678.75	−1.00267
$142$	2241.19	1.32448
$143$	−179.687	−0.105078
$144$	299.200	0.173148
$145$	843.022	0.482822
$146$	−3128.95	−1.77365
$147$	−147.000	−0.0824786
$148$	100.872	0.0560246
$149$	303.520	0.166881	0.0834407	−	0.996513i	$-0.473409\pi$
$149$	303.520	0.166881	0.0834407	+	0.996513i	$0.473409\pi$
$150$	1564.36	0.851532
$151$	1982.64	1.06851	0.534255	−	0.845323i	$-0.320592\pi$
$151$	1982.64	1.06851	0.534255	+	0.845323i	$0.320592\pi$
$152$	42.6377	0.0227525
$153$	183.301	0.0968562
$154$	2413.80	1.26305
$155$	929.082	0.481456
$156$	−108.913	−0.0558975
$157$	2086.70	1.06074	0.530372	−	0.847765i	$-0.322052\pi$
$157$	2086.70	1.06074	0.530372	+	0.847765i	$0.322052\pi$
$158$	−4055.97	−2.04225
$159$	1752.68	0.874195
$160$	371.527	0.183573
$161$	−161.000	−0.0788110
$162$	385.424	0.186925
$163$	2260.17	1.08608	0.543038	−	0.839708i	$-0.317274\pi$
$163$	2260.17	1.08608	0.543038	+	0.839708i	$0.317274\pi$
$164$	4797.17	2.28412
$165$	−853.494	−0.402694
$166$	−53.0714	−0.0248141
$167$	1943.86	0.900720	0.450360	−	0.892847i	$-0.351296\pi$
$167$	1943.86	0.900720	0.450360	+	0.892847i	$0.351296\pi$
$168$	663.664	0.304779
$169$	−2190.85	−0.997202
$170$	−380.458	−0.171646
$171$	12.1425	0.00543017
$172$	1136.76	0.503936
$173$	−240.277	−0.105595	−0.0527975	−	0.998605i	$-0.516814\pi$
$173$	−240.277	−0.105595	−0.0527975	+	0.998605i	$0.516814\pi$
$174$	3065.37	1.33555
$175$	767.115	0.331363
$176$	−2409.17	−1.03181
$177$	−1240.25	−0.526682
$178$	885.213	0.372750
$179$	−3770.00	−1.57421	−0.787103	−	0.616821i	$-0.788420\pi$
$179$	−3770.00	−1.57421	−0.787103	+	0.616821i	$0.788420\pi$
$180$	−517.324	−0.214217
$181$	−3272.63	−1.34394	−0.671968	−	0.740580i	$-0.734551\pi$
$181$	−3272.63	−1.34394	−0.671968	+	0.740580i	$0.734551\pi$
$182$	−82.5887	−0.0336367
$183$	2630.52	1.06259
$184$	726.870	0.291226
$185$	−27.0466	−0.0107487
$186$	3378.30	1.33177
$187$	−1475.95	−0.577176
$188$	8193.22	3.17847
$189$	189.000	0.0727393
$190$	−25.2029	−0.00962320
$191$	3218.48	1.21927	0.609636	−	0.792681i	$-0.291315\pi$
$191$	3218.48	1.21927	0.609636	+	0.792681i	$0.291315\pi$
$192$	2148.80	0.807690
$193$	169.777	0.0633203	0.0316602	−	0.999499i	$-0.489921\pi$
$193$	169.777	0.0633203	0.0316602	+	0.999499i	$0.489921\pi$
$194$	6167.99	2.28266
$195$	29.2025	0.0107243
$196$	717.440	0.261458
$197$	−187.030	−0.0676412	−0.0338206	−	0.999428i	$-0.510767\pi$
$197$	−187.030	−0.0676412	−0.0338206	+	0.999428i	$0.510767\pi$
$198$	−3103.45	−1.11390
$199$	−3856.15	−1.37364	−0.686822	−	0.726825i	$-0.740995\pi$
$199$	−3856.15	−1.37364	−0.686822	+	0.726825i	$0.740995\pi$
$200$	−3463.31	−1.22447
$201$	−2724.90	−0.956219
$202$	−727.455	−0.253384
$203$	1503.16	0.519711
$204$	−894.608	−0.307035
$205$	−1286.25	−0.438223
$206$	−3252.09	−1.09992
$207$	207.000	0.0695048
$208$	82.4305	0.0274785
$209$	−97.7719	−0.0323590
$210$	−392.287	−0.128907
$211$	−3033.02	−0.989580	−0.494790	−	0.869012i	$-0.664755\pi$
$211$	−3033.02	−0.989580	−0.494790	+	0.869012i	$0.664755\pi$
$212$	−8554.06	−2.77120
$213$	−1413.02	−0.454546
$214$	400.993	0.128090
$215$	−304.796	−0.0966833
$216$	−853.283	−0.268789
$217$	1656.62	0.518241
$218$	−10106.0	−3.13974
$219$	1972.72	0.608694
$220$	4165.52	1.27654
$221$	50.4999	0.0153710
$222$	−98.3461	−0.0297322
$223$	286.254	0.0859597	0.0429798	−	0.999076i	$-0.486315\pi$
$223$	286.254	0.0859597	0.0429798	+	0.999076i	$0.486315\pi$
$224$	662.456	0.197599
$225$	−986.291	−0.292234
$226$	−3242.81	−0.954464
$227$	−463.470	−0.135514	−0.0677568	−	0.997702i	$-0.521584\pi$
$227$	−463.470	−0.135514	−0.0677568	+	0.997702i	$0.521584\pi$
$228$	−59.2620	−0.0172137
$229$	−4703.23	−1.35720	−0.678599	−	0.734509i	$-0.737413\pi$
$229$	−4703.23	−1.35720	−0.678599	+	0.734509i	$0.737413\pi$
$230$	−429.648	−0.123174
$231$	−1521.84	−0.433461
$232$	−6786.37	−1.92046
$233$	2629.25	0.739261	0.369630	−	0.929179i	$-0.379484\pi$
$233$	2629.25	0.739261	0.369630	+	0.929179i	$0.379484\pi$
$234$	106.185	0.0296648
$235$	−2196.83	−0.609809
$236$	6053.08	1.66959
$237$	2557.19	0.700874
$238$	−678.382	−0.184760
$239$	−4743.09	−1.28370	−0.641852	−	0.766829i	$-0.721834\pi$
$239$	−4743.09	−1.28370	−0.641852	+	0.766829i	$0.721834\pi$
$240$	391.535	0.105306
$241$	−4392.21	−1.17397	−0.586986	−	0.809597i	$-0.699686\pi$
$241$	−4392.21	−1.17397	−0.586986	+	0.809597i	$0.699686\pi$
$242$	18655.8	4.95554
$243$	−243.000	−0.0641500
$244$	−12838.4	−3.36841
$245$	−192.365	−0.0501623
$246$	−4677.03	−1.21218
$247$	3.34529	0.000861764 0
$248$	−7479.16	−1.91503
$249$	33.4601	0.00851586
$250$	4382.18	1.10861
$251$	−5723.31	−1.43925	−0.719626	−	0.694362i	$-0.755687\pi$
$251$	−5723.31	−1.43925	−0.719626	+	0.694362i	$0.755687\pi$
$252$	−922.423	−0.230584
$253$	−1666.77	−0.414186
$254$	8997.69	2.22270
$255$	239.869	0.0589066
$256$	−6884.83	−1.68087
$257$	654.449	0.158846	0.0794230	−	0.996841i	$-0.474692\pi$
$257$	654.449	0.158846	0.0794230	+	0.996841i	$0.474692\pi$
$258$	−1108.29	−0.267439
$259$	−48.2259	−0.0115699
$260$	−142.524	−0.0339961
$261$	−1932.64	−0.458342
$262$	4881.60	1.15109
$263$	−2414.20	−0.566030	−0.283015	−	0.959116i	$-0.591335\pi$
$263$	−2414.20	−0.566030	−0.283015	+	0.959116i	$0.591335\pi$
$264$	6870.67	1.60174
$265$	2293.58	0.531673
$266$	−44.9383	−0.0103584
$267$	−558.104	−0.127923
$268$	13299.0	3.03122
$269$	7635.96	1.73075	0.865377	−	0.501121i	$-0.167079\pi$
$269$	7635.96	1.73075	0.865377	+	0.501121i	$0.167079\pi$
$270$	504.369	0.113685
$271$	−395.054	−0.0885529	−0.0442764	−	0.999019i	$-0.514098\pi$
$271$	−395.054	−0.0885529	−0.0442764	+	0.999019i	$0.514098\pi$
$272$	677.082	0.150934
$273$	52.0701	0.0115437
$274$	−6201.63	−1.36735
$275$	7941.66	1.74146
$276$	−1010.27	−0.220331
$277$	1092.88	0.237056	0.118528	−	0.992951i	$-0.462182\pi$
$277$	1092.88	0.237056	0.118528	+	0.992951i	$0.462182\pi$
$278$	9740.15	2.10135
$279$	−2129.93	−0.457046
$280$	868.476	0.185362
$281$	3263.73	0.692874	0.346437	−	0.938073i	$-0.387391\pi$
$281$	3263.73	0.692874	0.346437	+	0.938073i	$0.387391\pi$
$282$	−7988.04	−1.68681
$283$	−5179.21	−1.08789	−0.543944	−	0.839122i	$-0.683070\pi$
$283$	−5179.21	−1.08789	−0.543944	+	0.839122i	$0.683070\pi$
$284$	6896.29	1.44091
$285$	15.8897	0.00330255
$286$	−855.010	−0.176776
$287$	−2293.47	−0.471705
$288$	−851.730	−0.174266
$289$	−4498.19	−0.915570
$290$	4011.37	0.812261
$291$	−3888.76	−0.783378
$292$	−9627.95	−1.92957
$293$	2207.71	0.440190	0.220095	−	0.975478i	$-0.429363\pi$
$293$	2207.71	0.440190	0.220095	+	0.975478i	$0.429363\pi$
$294$	−699.473	−0.138756
$295$	−1623.00	−0.320320
$296$	217.726	0.0427537
$297$	1956.65	0.382277
$298$	1444.25	0.280748
$299$	57.0291	0.0110304
$300$	4813.64	0.926385
$301$	−543.471	−0.104070
$302$	9434.04	1.79758
$303$	458.642	0.0869580
$304$	44.8523	0.00846202
$305$	3442.32	0.646251
$306$	872.205	0.162943
$307$	−8832.43	−1.64200	−0.820999	−	0.570930i	$-0.806583\pi$
$307$	−8832.43	−1.64200	−0.820999	+	0.570930i	$0.806583\pi$
$308$	7427.39	1.37407
$309$	2050.36	0.377478
$310$	4420.87	0.809964
$311$	−10173.7	−1.85497	−0.927487	−	0.373856i	$-0.878035\pi$
$311$	−10173.7	−1.85497	−0.927487	+	0.373856i	$0.878035\pi$
$312$	−235.082	−0.0426567
$313$	−4840.06	−0.874046	−0.437023	−	0.899450i	$-0.643967\pi$
$313$	−4840.06	−0.874046	−0.437023	+	0.899450i	$0.643967\pi$
$314$	9929.20	1.78451
$315$	247.327	0.0442390
$316$	−12480.5	−2.22178
$317$	−4471.25	−0.792209	−0.396105	−	0.918205i	$-0.629638\pi$
$317$	−4471.25	−0.792209	−0.396105	+	0.918205i	$0.629638\pi$
$318$	8339.84	1.47068
$319$	15561.7	2.73131
$320$	2811.94	0.491225
$321$	−252.815	−0.0439588
$322$	−766.090	−0.132585
$323$	27.4781	0.00473351
$324$	1185.97	0.203356
$325$	−271.726	−0.0463774
$326$	10754.6	1.82713
$327$	6371.56	1.07752
$328$	10354.4	1.74306
$329$	−3917.09	−0.656401
$330$	−4061.20	−0.677460
$331$	−6151.68	−1.02153	−0.510765	−	0.859720i	$-0.670638\pi$
$331$	−6151.68	−1.02153	−0.510765	+	0.859720i	$0.670638\pi$
$332$	−163.304	−0.0269953
$333$	62.0047	0.0102037
$334$	9249.51	1.51530
$335$	−3565.83	−0.581559
$336$	698.133	0.113352
$337$	−308.576	−0.0498790	−0.0249395	−	0.999689i	$-0.507939\pi$
$337$	−308.576	−0.0498790	−0.0249395	+	0.999689i	$0.507939\pi$
$338$	−10424.8	−1.67761
$339$	2044.51	0.327559
$340$	−1170.69	−0.186734
$341$	17150.3	2.72358
$342$	57.7779	0.00913529
$343$	−343.000	−0.0539949
$344$	2453.62	0.384565
$345$	270.882	0.0422718
$346$	−1143.32	−0.177645
$347$	7211.37	1.11564	0.557820	−	0.829962i	$-0.311638\pi$
$347$	7211.37	1.11564	0.557820	+	0.829962i	$0.311638\pi$
$348$	9432.33	1.45295
$349$	−7183.34	−1.10176	−0.550882	−	0.834583i	$-0.685709\pi$
$349$	−7183.34	−1.10176	−0.550882	+	0.834583i	$0.685709\pi$
$350$	3650.18	0.557459
$351$	−66.9472	−0.0101806
$352$	6858.17	1.03847
$353$	−6814.28	−1.02744	−0.513722	−	0.857957i	$-0.671734\pi$
$353$	−6814.28	−1.02744	−0.513722	+	0.857957i	$0.671734\pi$
$354$	−5901.50	−0.886048
$355$	−1849.08	−0.276448
$356$	2723.85	0.405516
$357$	427.702	0.0634073
$358$	−17938.9	−2.64832
$359$	−113.867	−0.0167400	−0.00837001	−	0.999965i	$-0.502664\pi$
$359$	−113.867	−0.0167400	−0.00837001	+	0.999965i	$0.502664\pi$
$360$	−1116.61	−0.163474
$361$	−6857.18	−0.999735
$362$	−15572.2	−2.26093
$363$	−11762.0	−1.70068
$364$	−254.130	−0.0365935
$365$	2581.52	0.370199
$366$	12516.9	1.78762
$367$	3348.94	0.476330	0.238165	−	0.971225i	$-0.423454\pi$
$367$	3348.94	0.476330	0.238165	+	0.971225i	$0.423454\pi$
$368$	764.622	0.108312
$369$	2948.75	0.416005
$370$	−128.696	−0.0180827
$371$	4089.60	0.572295
$372$	10395.2	1.44884
$373$	−6562.26	−0.910940	−0.455470	−	0.890251i	$-0.650529\pi$
$373$	−6562.26	−0.910940	−0.455470	+	0.890251i	$0.650529\pi$
$374$	−7023.03	−0.970996
$375$	−2762.85	−0.380461
$376$	17684.6	2.42556
$377$	−532.448	−0.0727386
$378$	899.323	0.122371
$379$	−3457.77	−0.468637	−0.234319	−	0.972160i	$-0.575286\pi$
$379$	−3457.77	−0.468637	−0.234319	+	0.972160i	$0.575286\pi$
$380$	−77.5506	−0.0104691
$381$	−5672.81	−0.762800
$382$	15314.6	2.05121
$383$	4951.99	0.660665	0.330333	−	0.943865i	$-0.392839\pi$
$383$	4951.99	0.660665	0.330333	+	0.943865i	$0.392839\pi$
$384$	7953.41	1.05696
$385$	−1991.49	−0.263625
$386$	807.854	0.106525
$387$	698.749	0.0917814
$388$	18979.3	2.48331
$389$	8687.00	1.13226	0.566129	−	0.824317i	$-0.308440\pi$
$389$	8687.00	1.13226	0.566129	+	0.824317i	$0.308440\pi$
$390$	138.955	0.0180417
$391$	468.436	0.0605877
$392$	1548.55	0.199524
$393$	−3077.72	−0.395040
$394$	−889.948	−0.113794
$395$	3346.35	0.426262
$396$	−9549.51	−1.21182
$397$	3809.34	0.481575	0.240788	−	0.970578i	$-0.422594\pi$
$397$	3809.34	0.481575	0.240788	+	0.970578i	$0.422594\pi$
$398$	−18348.8	−2.31091
$399$	28.3325	0.00355488
$400$	−3643.19	−0.455399
$401$	−8728.03	−1.08693	−0.543463	−	0.839433i	$-0.682887\pi$
$401$	−8728.03	−1.08693	−0.543463	+	0.839433i	$0.682887\pi$
$402$	−12966.0	−1.60867
$403$	−586.803	−0.0725328
$404$	−2238.42	−0.275658
$405$	−317.992	−0.0390151
$406$	7152.54	0.874321
$407$	−499.265	−0.0608050
$408$	−1930.96	−0.234305
$409$	11204.8	1.35463	0.677313	−	0.735695i	$-0.263144\pi$
$409$	11204.8	1.35463	0.677313	+	0.735695i	$0.263144\pi$
$410$	−6120.40	−0.737232
$411$	3909.97	0.469257
$412$	−10006.9	−1.19661
$413$	−2893.91	−0.344794
$414$	984.973	0.116929
$415$	43.7862	0.00517922
$416$	−234.654	−0.0276559
$417$	−6140.91	−0.721156
$418$	−465.230	−0.0544382
$419$	−1940.20	−0.226217	−0.113108	−	0.993583i	$-0.536081\pi$
$419$	−1940.20	−0.226217	−0.113108	+	0.993583i	$0.536081\pi$
$420$	−1207.09	−0.140238
$421$	−4400.57	−0.509432	−0.254716	−	0.967016i	$-0.581982\pi$
$421$	−4400.57	−0.509432	−0.254716	+	0.967016i	$0.581982\pi$
$422$	−14432.1	−1.66479
$423$	5036.25	0.578891
$424$	−18463.4	−2.11477
$425$	−2231.95	−0.254742
$426$	−6723.58	−0.764692
$427$	6137.88	0.695628
$428$	1233.88	0.139350
$429$	539.062	0.0606670
$430$	−1450.32	−0.162652
$431$	7590.10	0.848266	0.424133	−	0.905600i	$-0.360579\pi$
$431$	7590.10	0.848266	0.424133	+	0.905600i	$0.360579\pi$
$432$	−897.600	−0.0999671
$433$	−2224.82	−0.246923	−0.123462	−	0.992349i	$-0.539400\pi$
$433$	−2224.82	−0.246923	−0.123462	+	0.992349i	$0.539400\pi$
$434$	7882.71	0.871848
$435$	−2529.07	−0.278757
$436$	−31096.7	−3.41574
$437$	31.0308	0.00339681
$438$	9386.84	1.02402
$439$	11239.3	1.22192	0.610958	−	0.791663i	$-0.290784\pi$
$439$	11239.3	1.22192	0.610958	+	0.791663i	$0.290784\pi$
$440$	8991.01	0.974158
$441$	441.000	0.0476190
$442$	240.295	0.0258590
$443$	2342.12	0.251191	0.125595	−	0.992082i	$-0.459916\pi$
$443$	2342.12	0.251191	0.125595	+	0.992082i	$0.459916\pi$
$444$	−302.617	−0.0323458
$445$	−730.339	−0.0778008
$446$	1362.09	0.144612
$447$	−910.560	−0.0963490
$448$	5013.87	0.528757
$449$	−1942.10	−0.204128	−0.102064	−	0.994778i	$-0.532545\pi$
$449$	−1942.10	−0.204128	−0.102064	+	0.994778i	$0.532545\pi$
$450$	−4693.09	−0.491632
$451$	−23743.5	−2.47901
$452$	−9978.33	−1.03837
$453$	−5947.92	−0.616904
$454$	−2205.34	−0.227977
$455$	68.1393	0.00702070
$456$	−127.913	−0.0131362
$457$	3390.95	0.347094	0.173547	−	0.984826i	$-0.444477\pi$
$457$	3390.95	0.347094	0.173547	+	0.984826i	$0.444477\pi$
$458$	−22379.5	−2.28324
$459$	−549.903	−0.0559200
$460$	−1322.05	−0.134002
$461$	3606.13	0.364326	0.182163	−	0.983268i	$-0.441690\pi$
$461$	3606.13	0.364326	0.182163	+	0.983268i	$0.441690\pi$
$462$	−7241.39	−0.729221
$463$	−9393.52	−0.942881	−0.471440	−	0.881898i	$-0.656266\pi$
$463$	−9393.52	−0.942881	−0.471440	+	0.881898i	$0.656266\pi$
$464$	−7138.83	−0.714250
$465$	−2787.25	−0.277969
$466$	12510.8	1.24367
$467$	9668.65	0.958056	0.479028	−	0.877800i	$-0.340989\pi$
$467$	9668.65	0.958056	0.479028	+	0.877800i	$0.340989\pi$
$468$	326.739	0.0322725
$469$	−6358.11	−0.625992
$470$	−10453.2	−1.02589
$471$	−6260.11	−0.612421
$472$	13065.2	1.27410
$473$	−5626.36	−0.546935
$474$	12167.9	1.17910
$475$	−147.852	−0.0142819
$476$	−2087.42	−0.201002
$477$	−5258.05	−0.504717
$478$	−22569.2	−2.15960
$479$	−2942.54	−0.280684	−0.140342	−	0.990103i	$-0.544820\pi$
$479$	−2942.54	−0.280684	−0.140342	+	0.990103i	$0.544820\pi$
$480$	−1114.58	−0.105986
$481$	17.0825	0.00161932
$482$	−20899.6	−1.97500
$483$	483.000	0.0455016
$484$	57405.1	5.39116
$485$	−5088.86	−0.476439
$486$	−1156.27	−0.107921
$487$	−14601.4	−1.35863	−0.679317	−	0.733845i	$-0.737724\pi$
$487$	−14601.4	−1.35863	−0.679317	+	0.733845i	$0.737724\pi$
$488$	−27710.8	−2.57051
$489$	−6780.52	−0.627046
$490$	−915.336	−0.0843891
$491$	−6760.98	−0.621423	−0.310712	−	0.950504i	$-0.600567\pi$
$491$	−6760.98	−0.621423	−0.310712	+	0.950504i	$0.600567\pi$
$492$	−14391.5	−1.31874
$493$	−4373.51	−0.399540
$494$	15.9180	0.00144976
$495$	2560.48	0.232495
$496$	−7867.61	−0.712230
$497$	−3297.04	−0.297570
$498$	159.214	0.0143264
$499$	−3884.91	−0.348522	−0.174261	−	0.984700i	$-0.555754\pi$
$499$	−3884.91	−0.348522	−0.174261	+	0.984700i	$0.555754\pi$
$500$	13484.2	1.20607
$501$	−5831.57	−0.520031
$502$	−27233.4	−2.42128
$503$	15873.7	1.40711	0.703554	−	0.710642i	$-0.251595\pi$
$503$	15873.7	1.40711	0.703554	+	0.710642i	$0.251595\pi$
$504$	−1990.99	−0.175964
$505$	600.182	0.0528866
$506$	−7931.05	−0.696795
$507$	6572.56	0.575735
$508$	27686.4	2.41808
$509$	−7783.52	−0.677796	−0.338898	−	0.940823i	$-0.610054\pi$
$509$	−7783.52	−0.677796	−0.338898	+	0.940823i	$0.610054\pi$
$510$	1141.37	0.0990998
$511$	4603.01	0.398484
$512$	−11551.2	−0.997058
$513$	−36.4275	−0.00313511
$514$	3114.08	0.267230
$515$	2683.11	0.229577
$516$	−3410.28	−0.290948
$517$	−40552.2	−3.44967
$518$	−229.474	−0.0194643
$519$	720.831	0.0609653
$520$	−307.630	−0.0259432
$521$	−4296.82	−0.361319	−0.180660	−	0.983546i	$-0.557823\pi$
$521$	−4296.82	−0.361319	−0.180660	+	0.983546i	$0.557823\pi$
$522$	−9196.12	−0.771079
$523$	−4246.90	−0.355074	−0.177537	−	0.984114i	$-0.556813\pi$
$523$	−4246.90	−0.355074	−0.177537	+	0.984114i	$0.556813\pi$
$524$	15021.0	1.25228
$525$	−2301.35	−0.191312
$526$	−11487.5	−0.952244
$527$	−4819.98	−0.398410
$528$	7227.52	0.595715
$529$	529.000	0.0434783
$530$	10913.6	0.894444
$531$	3720.74	0.304080
$532$	−138.278	−0.0112690
$533$	812.389	0.0660196
$534$	−2655.64	−0.215207
$535$	−330.836	−0.0267351
$536$	28705.1	2.31319
$537$	11310.0	0.908868
$538$	36334.4	2.91169
$539$	−3550.95	−0.283767
$540$	1551.97	0.123678
$541$	6425.12	0.510606	0.255303	−	0.966861i	$-0.417825\pi$
$541$	6425.12	0.510606	0.255303	+	0.966861i	$0.417825\pi$
$542$	−1879.80	−0.148974
$543$	9817.88	0.775922
$544$	−1927.44	−0.151909
$545$	8337.87	0.655331
$546$	247.766	0.0194202
$547$	−19375.3	−1.51449	−0.757246	−	0.653130i	$-0.773456\pi$
$547$	−19375.3	−1.51449	−0.757246	+	0.653130i	$0.773456\pi$
$548$	−19082.8	−1.48755
$549$	−7891.57	−0.613486
$550$	37789.0	2.92969
$551$	−289.717	−0.0223999
$552$	−2180.61	−0.168139
$553$	5966.77	0.458830
$554$	5200.26	0.398805
$555$	81.1398	0.00620575
$556$	29971.0	2.28607
$557$	−5844.15	−0.444568	−0.222284	−	0.974982i	$-0.571351\pi$
$557$	−5844.15	−0.444568	−0.222284	+	0.974982i	$0.571351\pi$
$558$	−10134.9	−0.768898
$559$	192.507	0.0145656
$560$	913.583	0.0689391
$561$	4427.84	0.333233
$562$	15529.9	1.16564
$563$	−319.746	−0.0239355	−0.0119677	−	0.999928i	$-0.503810\pi$
$563$	−319.746	−0.0239355	−0.0119677	+	0.999928i	$0.503810\pi$
$564$	−24579.7	−1.83509
$565$	2675.46	0.199217
$566$	−24644.4	−1.83018
$567$	−567.000	−0.0419961
$568$	14885.2	1.09959
$569$	−13495.0	−0.994272	−0.497136	−	0.867673i	$-0.665615\pi$
$569$	−13495.0	−0.994272	−0.497136	+	0.867673i	$0.665615\pi$
$570$	75.6086	0.00555595
$571$	−9577.79	−0.701958	−0.350979	−	0.936383i	$-0.614151\pi$
$571$	−9577.79	−0.701958	−0.350979	+	0.936383i	$0.614151\pi$
$572$	−2630.92	−0.192315
$573$	−9655.44	−0.703948
$574$	−10913.1	−0.793559
$575$	−2520.52	−0.182805
$576$	−6446.40	−0.466320
$577$	−17907.8	−1.29205	−0.646025	−	0.763316i	$-0.723570\pi$
$577$	−17907.8	−1.29205	−0.646025	+	0.763316i	$0.723570\pi$
$578$	−21403.9	−1.54028
$579$	−509.331	−0.0365580
$580$	12343.2	0.883663
$581$	78.0736	0.00557494
$582$	−18504.0	−1.31789
$583$	42338.1	3.00766
$584$	−20781.3	−1.47250
$585$	−87.6076	−0.00619167
$586$	10505.0	0.740541
$587$	16915.4	1.18939	0.594697	−	0.803950i	$-0.297272\pi$
$587$	16915.4	1.18939	0.594697	+	0.803950i	$0.297272\pi$
$588$	−2152.32	−0.150953
$589$	−319.292	−0.0223365
$590$	−7722.74	−0.538882
$591$	561.089	0.0390527
$592$	229.035	0.0159008
$593$	20594.4	1.42616	0.713080	−	0.701083i	$-0.247300\pi$
$593$	20594.4	1.42616	0.713080	+	0.701083i	$0.247300\pi$
$594$	9310.36	0.643112
$595$	559.694	0.0385634
$596$	4444.03	0.305427
$597$	11568.5	0.793074
$598$	271.363	0.0185566
$599$	20057.1	1.36813	0.684065	−	0.729421i	$-0.260211\pi$
$599$	20057.1	1.36813	0.684065	+	0.729421i	$0.260211\pi$
$600$	10389.9	0.706946
$601$	21844.5	1.48262	0.741312	−	0.671160i	$-0.234204\pi$
$601$	21844.5	1.48262	0.741312	+	0.671160i	$0.234204\pi$
$602$	−2586.01	−0.175080
$603$	8174.71	0.552073
$604$	29029.1	1.95559
$605$	−15391.9	−1.03433
$606$	2182.37	0.146291
$607$	17748.4	1.18679	0.593397	−	0.804910i	$-0.297786\pi$
$607$	17748.4	1.18679	0.593397	+	0.804910i	$0.297786\pi$
$608$	−127.680	−0.00851665
$609$	−4509.49	−0.300055
$610$	16379.7	1.08720
$611$	1387.50	0.0918696
$612$	2683.83	0.177267
$613$	9844.81	0.648659	0.324330	−	0.945944i	$-0.394861\pi$
$613$	9844.81	0.648659	0.324330	+	0.945944i	$0.394861\pi$
$614$	−42027.6	−2.76237
$615$	3858.75	0.253008
$616$	16031.6	1.04859
$617$	19329.7	1.26124	0.630620	−	0.776092i	$-0.282801\pi$
$617$	19329.7	1.26124	0.630620	+	0.776092i	$0.282801\pi$
$618$	9756.26	0.635039
$619$	16157.5	1.04915	0.524576	−	0.851364i	$-0.324224\pi$
$619$	16157.5	1.04915	0.524576	+	0.851364i	$0.324224\pi$
$620$	13603.3	0.881163
$621$	−621.000	−0.0401286
$622$	−48409.7	−3.12066
$623$	−1302.24	−0.0837451
$624$	−247.291	−0.0158647
$625$	10083.0	0.645312
$626$	−23030.6	−1.47043
$627$	293.316	0.0186825
$628$	30552.7	1.94138
$629$	140.315	0.00889463
$630$	1176.86	0.0744242
$631$	−7188.34	−0.453508	−0.226754	−	0.973952i	$-0.572811\pi$
$631$	−7188.34	−0.453508	−0.226754	+	0.973952i	$0.572811\pi$
$632$	−26938.3	−1.69549
$633$	9099.05	0.571335
$634$	−21275.7	−1.33275
$635$	−7423.48	−0.463924
$636$	25662.2	1.59996
$637$	121.497	0.00755711
$638$	74047.6	4.59494
$639$	4239.05	0.262432
$640$	10407.9	0.642825
$641$	26948.4	1.66053	0.830264	−	0.557371i	$-0.188190\pi$
$641$	26948.4	1.66053	0.830264	+	0.557371i	$0.188190\pi$
$642$	−1202.98	−0.0739529
$643$	−22091.4	−1.35490	−0.677451	−	0.735568i	$-0.736915\pi$
$643$	−22091.4	−1.35490	−0.677451	+	0.735568i	$0.736915\pi$
$644$	−2357.30	−0.144240
$645$	914.388	0.0558201
$646$	130.750	0.00796329
$647$	−3547.94	−0.215585	−0.107793	−	0.994173i	$-0.534378\pi$
$647$	−3547.94	−0.215585	−0.107793	+	0.994173i	$0.534378\pi$
$648$	2559.85	0.155186
$649$	−29959.6	−1.81204
$650$	−1292.96	−0.0780217
$651$	−4969.85	−0.299207
$652$	33092.6	1.98774
$653$	−10818.5	−0.648332	−0.324166	−	0.946000i	$-0.605084\pi$
$653$	−10818.5	−0.648332	−0.324166	+	0.946000i	$0.605084\pi$
$654$	30317.9	1.81273
$655$	−4027.53	−0.240257
$656$	10892.2	0.648274
$657$	−5918.16	−0.351430
$658$	−18638.8	−1.10428
$659$	8103.29	0.478998	0.239499	−	0.970897i	$-0.423017\pi$
$659$	8103.29	0.478998	0.239499	+	0.970897i	$0.423017\pi$
$660$	−12496.6	−0.737012
$661$	16663.9	0.980560	0.490280	−	0.871565i	$-0.336895\pi$
$661$	16663.9	0.980560	0.490280	+	0.871565i	$0.336895\pi$
$662$	−29271.7	−1.71854
$663$	−151.500	−0.00887446
$664$	−352.481	−0.0206008
$665$	37.0761	0.00216203
$666$	295.038	0.0171659
$667$	−4938.97	−0.286713
$668$	28461.3	1.64850
$669$	−858.763	−0.0496288
$670$	−16967.4	−0.978368
$671$	63543.3	3.65583
$672$	−1987.37	−0.114084
$673$	9771.33	0.559669	0.279834	−	0.960048i	$-0.409720\pi$
$673$	9771.33	0.559669	0.279834	+	0.960048i	$0.409720\pi$
$674$	−1468.30	−0.0839124
$675$	2958.87	0.168722
$676$	−32077.7	−1.82508
$677$	−27957.2	−1.58712	−0.793561	−	0.608491i	$-0.791775\pi$
$677$	−27957.2	−1.58712	−0.793561	+	0.608491i	$0.791775\pi$
$678$	9728.44	0.551060
$679$	−9073.76	−0.512841
$680$	−2526.86	−0.142501
$681$	1390.41	0.0782388
$682$	81606.8	4.58194
$683$	−6864.31	−0.384562	−0.192281	−	0.981340i	$-0.561588\pi$
$683$	−6864.31	−0.384562	−0.192281	+	0.981340i	$0.561588\pi$
$684$	177.786	0.00993832
$685$	5116.61	0.285395
$686$	−1632.10	−0.0908368
$687$	14109.7	0.783579
$688$	2581.06	0.143026
$689$	−1448.61	−0.0800982
$690$	1288.94	0.0711148
$691$	35684.5	1.96455	0.982275	−	0.187446i	$-0.0600210\pi$
$691$	35684.5	1.96455	0.982275	+	0.187446i	$0.0600210\pi$
$692$	−3518.05	−0.193260
$693$	4565.51	0.250259
$694$	34314.0	1.87686
$695$	−8036.05	−0.438597
$696$	20359.1	1.10878
$697$	6672.94	0.362634
$698$	−34180.7	−1.85352
$699$	−7887.74	−0.426812
$700$	11231.8	0.606462
$701$	−7316.05	−0.394185	−0.197092	−	0.980385i	$-0.563150\pi$
$701$	−7316.05	−0.394185	−0.197092	+	0.980385i	$0.563150\pi$
$702$	−318.556	−0.0171270
$703$	9.29495	0.000498671 0
$704$	51906.8	2.77885
$705$	6590.48	0.352074
$706$	−32424.5	−1.72849
$707$	1070.16	0.0569274
$708$	−18159.2	−0.963935
$709$	15019.3	0.795574	0.397787	−	0.917478i	$-0.369778\pi$
$709$	15019.3	0.795574	0.397787	+	0.917478i	$0.369778\pi$
$710$	−8798.53	−0.465075
$711$	−7671.56	−0.404650
$712$	5879.26	0.309459
$713$	−5443.16	−0.285902
$714$	2035.14	0.106671
$715$	705.421	0.0368968
$716$	−55199.0	−2.88112
$717$	14229.3	0.741147
$718$	−541.816	−0.0281621
$719$	19785.9	1.02627	0.513137	−	0.858307i	$-0.328483\pi$
$719$	19785.9	1.02627	0.513137	+	0.858307i	$0.328483\pi$
$720$	−1174.61	−0.0607986
$721$	4784.16	0.247117
$722$	−32628.7	−1.68187
$723$	13176.6	0.677793
$724$	−47916.6	−2.45968
$725$	23532.6	1.20549
$726$	−55967.5	−2.86108
$727$	−24691.8	−1.25965	−0.629827	−	0.776735i	$-0.716874\pi$
$727$	−24691.8	−1.25965	−0.629827	+	0.776735i	$0.716874\pi$
$728$	−548.524	−0.0279254
$729$	729.000	0.0370370
$730$	12283.7	0.622794
$731$	1581.25	0.0800064
$732$	38515.1	1.94476
$733$	−7689.20	−0.387459	−0.193729	−	0.981055i	$-0.562058\pi$
$733$	−7689.20	−0.387459	−0.193729	+	0.981055i	$0.562058\pi$
$734$	15935.3	0.801341
$735$	577.096	0.0289612
$736$	−2176.64	−0.109011
$737$	−65823.2	−3.28986
$738$	14031.1	0.699853
$739$	12502.7	0.622355	0.311177	−	0.950352i	$-0.399277\pi$
$739$	12502.7	0.622355	0.311177	+	0.950352i	$0.399277\pi$
$740$	−396.006	−0.0196723
$741$	−10.0359	−0.000497540 0
$742$	19459.6	0.962784
$743$	−22052.4	−1.08886	−0.544432	−	0.838805i	$-0.683255\pi$
$743$	−22052.4	−1.08886	−0.544432	+	0.838805i	$0.683255\pi$
$744$	22437.5	1.10564
$745$	−1191.57	−0.0585981
$746$	−31225.3	−1.53249
$747$	−100.380	−0.00491663
$748$	−21610.3	−1.05635
$749$	−589.903	−0.0287778
$750$	−13146.5	−0.640058
$751$	−6982.67	−0.339283	−0.169641	−	0.985506i	$-0.554261\pi$
$751$	−6982.67	−0.339283	−0.169641	+	0.985506i	$0.554261\pi$
$752$	18603.1	0.902106
$753$	17169.9	0.830952
$754$	−2533.56	−0.122370
$755$	−7783.49	−0.375193
$756$	2767.27	0.133128
$757$	−26844.8	−1.28889	−0.644446	−	0.764650i	$-0.722912\pi$
$757$	−26844.8	−1.28889	−0.644446	+	0.764650i	$0.722912\pi$
$758$	−16453.2	−0.788399
$759$	5000.32	0.239131
$760$	−167.388	−0.00798922
$761$	−10788.4	−0.513901	−0.256951	−	0.966425i	$-0.582718\pi$
$761$	−10788.4	−0.513901	−0.256951	+	0.966425i	$0.582718\pi$
$762$	−26993.1	−1.28328
$763$	14867.0	0.705400
$764$	47123.8	2.23152
$765$	−719.607	−0.0340097
$766$	23563.2	1.11145
$767$	1025.07	0.0482573
$768$	20654.5	0.970449
$769$	−190.056	−0.00891233	−0.00445617	−	0.999990i	$-0.501418\pi$
$769$	−190.056	−0.00891233	−0.00445617	+	0.999990i	$0.501418\pi$
$770$	−9476.14	−0.443502
$771$	−1963.35	−0.0917098
$772$	2485.81	0.115889
$773$	−17706.2	−0.823863	−0.411932	−	0.911215i	$-0.635146\pi$
$773$	−17706.2	−0.823863	−0.411932	+	0.911215i	$0.635146\pi$
$774$	3324.87	0.154406
$775$	25935.0	1.20208
$776$	40965.5	1.89507
$777$	144.678	0.00667990
$778$	41335.5	1.90482
$779$	442.039	0.0203308
$780$	427.573	0.0196277
$781$	−34133.0	−1.56386
$782$	2228.97	0.101928
$783$	5797.92	0.264624
$784$	1628.98	0.0742064
$785$	−8192.02	−0.372466
$786$	−14644.8	−0.664584
$787$	27026.4	1.22413	0.612063	−	0.790809i	$-0.290340\pi$
$787$	27026.4	1.22413	0.612063	+	0.790809i	$0.290340\pi$
$788$	−2738.42	−0.123797
$789$	7242.60	0.326797
$790$	15923.0	0.717109
$791$	4770.52	0.214438
$792$	−20612.0	−0.924768
$793$	−2174.15	−0.0973598
$794$	18126.1	0.810164
$795$	−6880.73	−0.306961
$796$	−56460.4	−2.51405
$797$	−29863.9	−1.32727	−0.663635	−	0.748057i	$-0.730987\pi$
$797$	−29863.9	−1.32727	−0.663635	+	0.748057i	$0.730987\pi$
$798$	134.815	0.00598045
$799$	11396.9	0.504623
$800$	10371.0	0.458339
$801$	1674.31	0.0738563
$802$	−41530.8	−1.82856
$803$	47653.3	2.09421
$804$	−39897.1	−1.75008
$805$	632.057	0.0276734
$806$	−2792.20	−0.122024
$807$	−22907.9	−0.999252
$808$	−4831.49	−0.210361
$809$	704.045	0.0305969	0.0152984	−	0.999883i	$-0.495130\pi$
$809$	704.045	0.0305969	0.0152984	+	0.999883i	$0.495130\pi$
$810$	−1513.11	−0.0656360
$811$	1021.00	0.0442074	0.0221037	−	0.999756i	$-0.492964\pi$
$811$	1021.00	0.0442074	0.0221037	+	0.999756i	$0.492964\pi$
$812$	22008.8	0.951178
$813$	1185.16	0.0511260
$814$	−2375.66	−0.102294
$815$	−8873.04	−0.381361
$816$	−2031.25	−0.0871419
$817$	104.748	0.00448550
$818$	53316.1	2.27892
$819$	−156.210	−0.00666474
$820$	−18832.8	−0.802037
$821$	26117.4	1.11023	0.555117	−	0.831772i	$-0.312673\pi$
$821$	26117.4	1.11023	0.555117	+	0.831772i	$0.312673\pi$
$822$	18604.9	0.789441
$823$	3169.00	0.134222	0.0671109	−	0.997746i	$-0.478622\pi$
$823$	3169.00	0.134222	0.0671109	+	0.997746i	$0.478622\pi$
$824$	−21599.2	−0.913159
$825$	−23825.0	−1.00543
$826$	−13770.2	−0.580055
$827$	32496.2	1.36639	0.683194	−	0.730237i	$-0.260590\pi$
$827$	32496.2	1.36639	0.683194	+	0.730237i	$0.260590\pi$
$828$	3030.82	0.127208
$829$	35533.5	1.48870	0.744348	−	0.667792i	$-0.232760\pi$
$829$	35533.5	1.48870	0.744348	+	0.667792i	$0.232760\pi$
$830$	208.349	0.00871312
$831$	−3278.63	−0.136865
$832$	−1776.00	−0.0740046
$833$	997.971	0.0415098
$834$	−29220.5	−1.21322
$835$	−7631.24	−0.316275
$836$	−1431.54	−0.0592235
$837$	6389.80	0.263876
$838$	−9232.08	−0.380569
$839$	16751.0	0.689285	0.344642	−	0.938734i	$-0.388000\pi$
$839$	16751.0	0.689285	0.344642	+	0.938734i	$0.388000\pi$
$840$	−2605.43	−0.107019
$841$	21723.2	0.890699
$842$	−20939.3	−0.857028
$843$	−9791.18	−0.400031
$844$	−44408.3	−1.81113
$845$	8600.90	0.350154
$846$	23964.1	0.973881
$847$	−27444.7	−1.11335
$848$	−19422.3	−0.786517
$849$	15537.6	0.628092
$850$	−10620.3	−0.428559
$851$	158.456	0.00638286
$852$	−20688.9	−0.831911
$853$	−40511.6	−1.62613	−0.813066	−	0.582171i	$-0.802203\pi$
$853$	−40511.6	−1.62613	−0.813066	+	0.582171i	$0.802203\pi$
$854$	29206.0	1.17027
$855$	−47.6692	−0.00190673
$856$	2663.25	0.106341
$857$	−11149.6	−0.444416	−0.222208	−	0.974999i	$-0.571326\pi$
$857$	−11149.6	−0.444416	−0.222208	+	0.974999i	$0.571326\pi$
$858$	2565.03	0.102061
$859$	3477.23	0.138116	0.0690580	−	0.997613i	$-0.478001\pi$
$859$	3477.23	0.138116	0.0690580	+	0.997613i	$0.478001\pi$
$860$	−4462.71	−0.176950
$861$	6880.41	0.272339
$862$	36116.2	1.42706
$863$	18152.6	0.716015	0.358008	−	0.933719i	$-0.383456\pi$
$863$	18152.6	0.716015	0.358008	+	0.933719i	$0.383456\pi$
$864$	2555.19	0.100613
$865$	943.285	0.0370782
$866$	−10586.4	−0.415405
$867$	13494.6	0.528605
$868$	24255.6	0.948488
$869$	61771.8	2.41135
$870$	−12034.1	−0.468959
$871$	2252.16	0.0876136
$872$	−67120.3	−2.60663
$873$	11666.3	0.452283
$874$	147.655	0.00571452
$875$	−6446.65	−0.249070
$876$	28883.9	1.11404
$877$	−3333.00	−0.128332	−0.0641661	−	0.997939i	$-0.520439\pi$
$877$	−3333.00	−0.128332	−0.0641661	+	0.997939i	$0.520439\pi$
$878$	53480.1	2.05566
$879$	−6623.12	−0.254144
$880$	9457.98	0.362305
$881$	−16157.4	−0.617886	−0.308943	−	0.951080i	$-0.599975\pi$
$881$	−16157.4	−0.617886	−0.308943	+	0.951080i	$0.599975\pi$
$882$	2098.42	0.0801105
$883$	−2299.44	−0.0876358	−0.0438179	−	0.999040i	$-0.513952\pi$
$883$	−2299.44	−0.0876358	−0.0438179	+	0.999040i	$0.513952\pi$
$884$	739.402	0.0281321
$885$	4868.99	0.184937
$886$	11144.6	0.422583
$887$	−21805.4	−0.825426	−0.412713	−	0.910861i	$-0.635419\pi$
$887$	−21805.4	−0.825426	−0.412713	+	0.910861i	$0.635419\pi$
$888$	−653.179	−0.0246838
$889$	−13236.6	−0.499370
$890$	−3475.19	−0.130886
$891$	−5869.94	−0.220708
$892$	4191.23	0.157324
$893$	754.971	0.0282913
$894$	−4332.74	−0.162090
$895$	14800.3	0.552761
$896$	18558.0	0.691940
$897$	−171.087	−0.00636838
$898$	−9241.15	−0.343409
$899$	50819.7	1.88535
$900$	−14440.9	−0.534849
$901$	−11898.8	−0.439964
$902$	−112979.	−4.17050
$903$	1630.41	0.0600850
$904$	−21537.6	−0.792400
$905$	12847.8	0.471905
$906$	−28302.1	−1.03783
$907$	46108.8	1.68800	0.844001	−	0.536342i	$-0.180194\pi$
$907$	46108.8	1.68800	0.844001	+	0.536342i	$0.180194\pi$
$908$	−6785.96	−0.248018
$909$	−1375.93	−0.0502052
$910$	324.229	0.0118111
$911$	15208.3	0.553101	0.276550	−	0.960999i	$-0.410809\pi$
$911$	15208.3	0.553101	0.276550	+	0.960999i	$0.410809\pi$
$912$	−134.557	−0.00488555
$913$	808.267	0.0292987
$914$	16135.2	0.583924
$915$	−10327.0	−0.373113
$916$	−68863.1	−2.48395
$917$	−7181.35	−0.258614
$918$	−2616.61	−0.0940753
$919$	−54929.6	−1.97167	−0.985833	−	0.167732i	$-0.946356\pi$
$919$	−54929.6	−1.97167	−0.985833	+	0.167732i	$0.946356\pi$
$920$	−2853.56	−0.102260
$921$	26497.3	0.948008
$922$	17159.1	0.612914
$923$	1167.87	0.0416478
$924$	−22282.2	−0.793323
$925$	−754.996	−0.0268369
$926$	−44697.4	−1.58623
$927$	−6151.07	−0.217937
$928$	20322.0	0.718862
$929$	−41910.6	−1.48013	−0.740065	−	0.672535i	$-0.765205\pi$
$929$	−41910.6	−1.48013	−0.740065	+	0.672535i	$0.765205\pi$
$930$	−13262.6	−0.467633
$931$	66.1091	0.00232722
$932$	38496.5	1.35300
$933$	30521.1	1.07097
$934$	46006.6	1.61176
$935$	5794.31	0.202667
$936$	705.245	0.0246279
$937$	44168.6	1.53994	0.769971	−	0.638079i	$-0.220271\pi$
$937$	44168.6	1.53994	0.769971	+	0.638079i	$0.220271\pi$
$938$	−30253.9	−1.05312
$939$	14520.2	0.504631
$940$	−32165.1	−1.11608
$941$	−43211.4	−1.49697	−0.748487	−	0.663150i	$-0.769219\pi$
$941$	−43211.4	−1.49697	−0.748487	+	0.663150i	$0.769219\pi$
$942$	−29787.6	−1.03029
$943$	7535.69	0.260229
$944$	13743.8	0.473858
$945$	−741.980	−0.0255414
$946$	−26772.0	−0.920120
$947$	12693.2	0.435558	0.217779	−	0.975998i	$-0.430119\pi$
$947$	12693.2	0.435558	0.217779	+	0.975998i	$0.430119\pi$
$948$	37441.4	1.28274
$949$	−1630.47	−0.0557717
$950$	−703.529	−0.0240268
$951$	13413.7	0.457382
$952$	−4505.56	−0.153389
$953$	16487.3	0.560415	0.280208	−	0.959939i	$-0.409597\pi$
$953$	16487.3	0.560415	0.280208	+	0.959939i	$0.409597\pi$
$954$	−25019.5	−0.849095
$955$	−12635.2	−0.428131
$956$	−69446.6	−2.34944
$957$	−46685.1	−1.57692
$958$	−14001.5	−0.472201
$959$	9123.26	0.307201
$960$	−8435.81	−0.283609
$961$	26216.6	0.880018
$962$	81.2839	0.00272422
$963$	758.446	0.0253796
$964$	−64309.2	−2.14861
$965$	−666.515	−0.0222341
$966$	2298.27	0.0765483
$967$	−7799.29	−0.259367	−0.129684	−	0.991555i	$-0.541396\pi$
$967$	−7799.29	−0.259367	−0.129684	+	0.991555i	$0.541396\pi$
$968$	123905.	4.11412
$969$	−82.4344	−0.00273289
$970$	−24214.4	−0.801524
$971$	20854.1	0.689227	0.344614	−	0.938745i	$-0.388010\pi$
$971$	20854.1	0.689227	0.344614	+	0.938745i	$0.388010\pi$
$972$	−3557.92	−0.117408
$973$	−14328.8	−0.472107
$974$	−69478.4	−2.28566
$975$	815.178	0.0267760
$976$	−29150.1	−0.956016
$977$	34868.8	1.14181	0.570907	−	0.821015i	$-0.306592\pi$
$977$	34868.8	1.14181	0.570907	+	0.821015i	$0.306592\pi$
$978$	−32263.9	−1.05489
$979$	−13481.6	−0.440117
$980$	−2816.54	−0.0918073
$981$	−19114.7	−0.622105
$982$	−32170.9	−1.04543
$983$	49052.4	1.59159	0.795794	−	0.605568i	$-0.207054\pi$
$983$	49052.4	1.59159	0.795794	+	0.605568i	$0.207054\pi$
$984$	−31063.1	−1.00636
$985$	734.245	0.0237513
$986$	−20810.6	−0.672154
$987$	11751.3	0.378973
$988$	48.9805	0.00157720
$989$	1785.69	0.0574132
$990$	12183.6	0.391132
$991$	−38206.2	−1.22468	−0.612341	−	0.790594i	$-0.709772\pi$
$991$	−38206.2	−1.22468	−0.612341	+	0.790594i	$0.709772\pi$
$992$	22396.6	0.716829
$993$	18455.0	0.589781
$994$	−15688.4	−0.500608
$995$	15138.6	0.482336
$996$	489.911	0.0155858
$997$	16820.5	0.534313	0.267156	−	0.963653i	$-0.413916\pi$
$997$	16820.5	0.534313	0.267156	+	0.963653i	$0.413916\pi$
$998$	−18485.6	−0.586325
$999$	−186.014	−0.00589111

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.4.a.d.1.7	✓	7	1.1	even	1	trivial
1449.4.a.g.1.1		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)

\(f(q)\)	\(=\)	\(q+4.75832 q^{2} -3.00000 q^{3} +14.6416 q^{4} -3.92582 q^{5} -14.2750 q^{6} -7.00000 q^{7} +31.6031 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+4.75832 q^{2} -3.00000 q^{3} +14.6416 q^{4} -3.92582 q^{5} -14.2750 q^{6} -7.00000 q^{7} +31.6031 q^{8} +9.00000 q^{9} -18.6803 q^{10} -72.4684 q^{11} -43.9249 q^{12} +2.47953 q^{13} -33.3083 q^{14} +11.7775 q^{15} +33.2445 q^{16} +20.3668 q^{17} +42.8249 q^{18} +1.34917 q^{19} -57.4805 q^{20} +21.0000 q^{21} -344.828 q^{22} +23.0000 q^{23} -94.8092 q^{24} -109.588 q^{25} +11.7984 q^{26} -27.0000 q^{27} -102.491 q^{28} -214.738 q^{29} +56.0410 q^{30} -236.659 q^{31} -94.6366 q^{32} +217.405 q^{33} +96.9116 q^{34} +27.4808 q^{35} +131.775 q^{36} +6.88941 q^{37} +6.41976 q^{38} -7.43858 q^{39} -124.068 q^{40} +327.639 q^{41} +99.9248 q^{42} +77.6388 q^{43} -1061.06 q^{44} -35.3324 q^{45} +109.441 q^{46} +559.584 q^{47} -99.7334 q^{48} +49.0000 q^{49} -521.455 q^{50} -61.1003 q^{51} +36.3043 q^{52} -584.228 q^{53} -128.475 q^{54} +284.498 q^{55} -221.221 q^{56} -4.04750 q^{57} -1021.79 q^{58} +413.416 q^{59} +172.441 q^{60} -876.841 q^{61} -1126.10 q^{62} -63.0000 q^{63} -716.267 q^{64} -9.73418 q^{65} +1034.48 q^{66} +908.302 q^{67} +298.203 q^{68} -69.0000 q^{69} +130.762 q^{70} +471.005 q^{71} +284.428 q^{72} -657.573 q^{73} +32.7820 q^{74} +328.764 q^{75} +19.7540 q^{76} +507.279 q^{77} -35.3952 q^{78} -852.396 q^{79} -130.512 q^{80} +81.0000 q^{81} +1559.01 q^{82} -11.1534 q^{83} +307.474 q^{84} -79.9563 q^{85} +369.430 q^{86} +644.213 q^{87} -2290.22 q^{88} +186.035 q^{89} -168.123 q^{90} -17.3567 q^{91} +336.758 q^{92} +709.978 q^{93} +2662.68 q^{94} -5.29658 q^{95} +283.910 q^{96} +1296.25 q^{97} +233.158 q^{98} -652.216 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 2 q^{2} - 21 q^{3} + 22 q^{4} - 11 q^{5} + 6 q^{6} - 49 q^{7} + 15 q^{8} + 63 q^{9}+O(q^{10}) \) 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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