LMFDB - Embedded newform 354.4.a.i.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,4,Mod(1,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("354.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	354.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:	$20.8866761420$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 492x^{4} + 3376x^{3} + 13255x^{2} - 108942x + 106740 $ x^6 - 2x^5 - 492x^4 + 3376x^3 + 13255x^2 - 108942*x + 106740
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$7.93259$ of defining polynomial
Character	$\chi$	$=$	354.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +10.9326 q^{5} +6.00000 q^{6} +3.94504 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +10.9326 q^{5} +6.00000 q^{6} +3.94504 q^{7} +8.00000 q^{8} +9.00000 q^{9} +21.8652 q^{10} +40.1771 q^{11} +12.0000 q^{12} +9.12380 q^{13} +7.89008 q^{14} +32.7978 q^{15} +16.0000 q^{16} -99.7847 q^{17} +18.0000 q^{18} -68.7298 q^{19} +43.7303 q^{20} +11.8351 q^{21} +80.3543 q^{22} +122.328 q^{23} +24.0000 q^{24} -5.47856 q^{25} +18.2476 q^{26} +27.0000 q^{27} +15.7802 q^{28} +141.483 q^{29} +65.5955 q^{30} +59.3571 q^{31} +32.0000 q^{32} +120.531 q^{33} -199.569 q^{34} +43.1295 q^{35} +36.0000 q^{36} +173.498 q^{37} -137.460 q^{38} +27.3714 q^{39} +87.4607 q^{40} -406.082 q^{41} +23.6703 q^{42} -403.720 q^{43} +160.709 q^{44} +98.3933 q^{45} +244.655 q^{46} +560.374 q^{47} +48.0000 q^{48} -327.437 q^{49} -10.9571 q^{50} -299.354 q^{51} +36.4952 q^{52} -131.018 q^{53} +54.0000 q^{54} +439.240 q^{55} +31.5603 q^{56} -206.189 q^{57} +282.966 q^{58} -59.0000 q^{59} +131.191 q^{60} +846.737 q^{61} +118.714 q^{62} +35.5054 q^{63} +64.0000 q^{64} +99.7467 q^{65} +241.063 q^{66} -250.870 q^{67} -399.139 q^{68} +366.983 q^{69} +86.2590 q^{70} -413.236 q^{71} +72.0000 q^{72} +407.064 q^{73} +346.996 q^{74} -16.4357 q^{75} -274.919 q^{76} +158.500 q^{77} +54.7428 q^{78} -634.622 q^{79} +174.921 q^{80} +81.0000 q^{81} -812.163 q^{82} -455.133 q^{83} +47.3405 q^{84} -1090.90 q^{85} -807.441 q^{86} +424.449 q^{87} +321.417 q^{88} +1439.12 q^{89} +196.787 q^{90} +35.9938 q^{91} +489.311 q^{92} +178.071 q^{93} +1120.75 q^{94} -751.394 q^{95} +96.0000 q^{96} +814.374 q^{97} -654.873 q^{98} +361.594 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 12 q^{2} + 18 q^{3} + 24 q^{4} + 20 q^{5} + 36 q^{6} + 26 q^{7} + 48 q^{8} + 54 q^{9}+O(q^{10}) $ 6 * q + 12 * q^2 + 18 * q^3 + 24 * q^4 + 20 * q^5 + 36 * q^6 + 26 * q^7 + 48 * q^8 + 54 * q^9	\( 6 q + 12 q^{2} + 18 q^{3} + 24 q^{4} + 20 q^{5} + 36 q^{6} + 26 q^{7} + 48 q^{8} + 54 q^{9} + 40 q^{10} + 63 q^{11} + 72 q^{12} + 93 q^{13} + 52 q^{14} + 60 q^{15} + 96 q^{16} + 230 q^{17} + 108 q^{18} + 89 q^{19} + 80 q^{20} + 78 q^{21} + 126 q^{22} + 81 q^{23} + 144 q^{24} + 304 q^{25} + 186 q^{26} + 162 q^{27} + 104 q^{28} + 131 q^{29} + 120 q^{30} + 51 q^{31} + 192 q^{32} + 189 q^{33} + 460 q^{34} - 87 q^{35} + 216 q^{36} - 16 q^{37} + 178 q^{38} + 279 q^{39} + 160 q^{40} + 176 q^{41} + 156 q^{42} + 375 q^{43} + 252 q^{44} + 180 q^{45} + 162 q^{46} - 255 q^{47} + 288 q^{48} - 290 q^{49} + 608 q^{50} + 690 q^{51} + 372 q^{52} - 256 q^{53} + 324 q^{54} - 184 q^{55} + 208 q^{56} + 267 q^{57} + 262 q^{58} - 354 q^{59} + 240 q^{60} + 39 q^{61} + 102 q^{62} + 234 q^{63} + 384 q^{64} - 954 q^{65} + 378 q^{66} + 86 q^{67} + 920 q^{68} + 243 q^{69} - 174 q^{70} - 895 q^{71} + 432 q^{72} + 155 q^{73} - 32 q^{74} + 912 q^{75} + 356 q^{76} - 498 q^{77} + 558 q^{78} - 565 q^{79} + 320 q^{80} + 486 q^{81} + 352 q^{82} + 140 q^{83} + 312 q^{84} + q^{85} + 750 q^{86} + 393 q^{87} + 504 q^{88} - 1769 q^{89} + 360 q^{90} - 422 q^{91} + 324 q^{92} + 153 q^{93} - 510 q^{94} - 2209 q^{95} + 576 q^{96} + 48 q^{97} - 580 q^{98} + 567 q^{99}+O(q^{100}) \) 6 * q + 12 * q^2 + 18 * q^3 + 24 * q^4 + 20 * q^5 + 36 * q^6 + 26 * q^7 + 48 * q^8 + 54 * q^9 + 40 * q^10 + 63 * q^11 + 72 * q^12 + 93 * q^13 + 52 * q^14 + 60 * q^15 + 96 * q^16 + 230 * q^17 + 108 * q^18 + 89 * q^19 + 80 * q^20 + 78 * q^21 + 126 * q^22 + 81 * q^23 + 144 * q^24 + 304 * q^25 + 186 * q^26 + 162 * q^27 + 104 * q^28 + 131 * q^29 + 120 * q^30 + 51 * q^31 + 192 * q^32 + 189 * q^33 + 460 * q^34 - 87 * q^35 + 216 * q^36 - 16 * q^37 + 178 * q^38 + 279 * q^39 + 160 * q^40 + 176 * q^41 + 156 * q^42 + 375 * q^43 + 252 * q^44 + 180 * q^45 + 162 * q^46 - 255 * q^47 + 288 * q^48 - 290 * q^49 + 608 * q^50 + 690 * q^51 + 372 * q^52 - 256 * q^53 + 324 * q^54 - 184 * q^55 + 208 * q^56 + 267 * q^57 + 262 * q^58 - 354 * q^59 + 240 * q^60 + 39 * q^61 + 102 * q^62 + 234 * q^63 + 384 * q^64 - 954 * q^65 + 378 * q^66 + 86 * q^67 + 920 * q^68 + 243 * q^69 - 174 * q^70 - 895 * q^71 + 432 * q^72 + 155 * q^73 - 32 * q^74 + 912 * q^75 + 356 * q^76 - 498 * q^77 + 558 * q^78 - 565 * q^79 + 320 * q^80 + 486 * q^81 + 352 * q^82 + 140 * q^83 + 312 * q^84 + q^85 + 750 * q^86 + 393 * q^87 + 504 * q^88 - 1769 * q^89 + 360 * q^90 - 422 * q^91 + 324 * q^92 + 153 * q^93 - 510 * q^94 - 2209 * q^95 + 576 * q^96 + 48 * q^97 - 580 * q^98 + 567 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	4.00000	0.500000
$5$	10.9326	0.977840	0.488920	−	0.872329i	$-0.337391\pi$
$5$	10.9326	0.977840	0.488920	+	0.872329i	$0.337391\pi$
$6$	6.00000	0.408248
$7$	3.94504	0.213012	0.106506	−	0.994312i	$-0.466034\pi$
$7$	3.94504	0.213012	0.106506	+	0.994312i	$0.466034\pi$
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	21.8652	0.691437
$11$	40.1771	1.10126	0.550630	−	0.834749i	$-0.314388\pi$
$11$	40.1771	1.10126	0.550630	+	0.834749i	$0.314388\pi$
$12$	12.0000	0.288675
$13$	9.12380	0.194653	0.0973264	−	0.995253i	$-0.468971\pi$
$13$	9.12380	0.194653	0.0973264	+	0.995253i	$0.468971\pi$
$14$	7.89008	0.150622
$15$	32.7978	0.564556
$16$	16.0000	0.250000
$17$	−99.7847	−1.42361	−0.711804	−	0.702378i	$-0.752122\pi$
$17$	−99.7847	−1.42361	−0.711804	+	0.702378i	$0.752122\pi$
$18$	18.0000	0.235702
$19$	−68.7298	−0.829879	−0.414939	−	0.909849i	$-0.636197\pi$
$19$	−68.7298	−0.829879	−0.414939	+	0.909849i	$0.636197\pi$
$20$	43.7303	0.488920
$21$	11.8351	0.122983
$22$	80.3543	0.778708
$23$	122.328	1.10900	0.554502	−	0.832182i	$-0.312909\pi$
$23$	122.328	1.10900	0.554502	+	0.832182i	$0.312909\pi$
$24$	24.0000	0.204124
$25$	−5.47856	−0.0438285
$26$	18.2476	0.137640
$27$	27.0000	0.192450
$28$	15.7802	0.106506
$29$	141.483	0.905956	0.452978	−	0.891522i	$-0.350362\pi$
$29$	141.483	0.905956	0.452978	+	0.891522i	$0.350362\pi$
$30$	65.5955	0.399202
$31$	59.3571	0.343898	0.171949	−	0.985106i	$-0.444994\pi$
$31$	59.3571	0.343898	0.171949	+	0.985106i	$0.444994\pi$
$32$	32.0000	0.176777
$33$	120.531	0.635813
$34$	−199.569	−1.00664
$35$	43.1295	0.208292
$36$	36.0000	0.166667
$37$	173.498	0.770888	0.385444	−	0.922731i	$-0.374048\pi$
$37$	173.498	0.770888	0.385444	+	0.922731i	$0.374048\pi$
$38$	−137.460	−0.586813
$39$	27.3714	0.112383
$40$	87.4607	0.345719
$41$	−406.082	−1.54681	−0.773406	−	0.633911i	$-0.781449\pi$
$41$	−406.082	−1.54681	−0.773406	+	0.633911i	$0.781449\pi$
$42$	23.6703	0.0869619
$43$	−403.720	−1.43179	−0.715893	−	0.698210i	$-0.753980\pi$
$43$	−403.720	−1.43179	−0.715893	+	0.698210i	$0.753980\pi$
$44$	160.709	0.550630
$45$	98.3933	0.325947
$46$	244.655	0.784184
$47$	560.374	1.73913	0.869564	−	0.493821i	$-0.164400\pi$
$47$	560.374	1.73913	0.869564	+	0.493821i	$0.164400\pi$
$48$	48.0000	0.144338
$49$	−327.437	−0.954626
$50$	−10.9571	−0.0309914
$51$	−299.354	−0.821921
$52$	36.4952	0.0973264
$53$	−131.018	−0.339562	−0.169781	−	0.985482i	$-0.554306\pi$
$53$	−131.018	−0.339562	−0.169781	+	0.985482i	$0.554306\pi$
$54$	54.0000	0.136083
$55$	439.240	1.07686
$56$	31.5603	0.0753112
$57$	−206.189	−0.479131
$58$	282.966	0.640608
$59$	−59.0000	−0.130189
$59$	−59.0000	−0.130189
$60$	131.191	0.282278
$61$	846.737	1.77727	0.888636	−	0.458614i	$-0.151654\pi$
$61$	846.737	1.77727	0.888636	+	0.458614i	$0.151654\pi$
$62$	118.714	0.243173
$63$	35.5054	0.0710041
$64$	64.0000	0.125000
$65$	99.7467	0.190339
$66$	241.063	0.449588
$67$	−250.870	−0.457443	−0.228721	−	0.973492i	$-0.573454\pi$
$67$	−250.870	−0.457443	−0.228721	+	0.973492i	$0.573454\pi$
$68$	−399.139	−0.711804
$69$	366.983	0.640284
$70$	86.2590	0.147285
$71$	−413.236	−0.690734	−0.345367	−	0.938468i	$-0.612246\pi$
$71$	−413.236	−0.690734	−0.345367	+	0.938468i	$0.612246\pi$
$72$	72.0000	0.117851
$73$	407.064	0.652648	0.326324	−	0.945258i	$-0.394190\pi$
$73$	407.064	0.652648	0.326324	+	0.945258i	$0.394190\pi$
$74$	346.996	0.545100
$75$	−16.4357	−0.0253044
$76$	−274.919	−0.414939
$77$	158.500	0.234582
$78$	54.7428	0.0794667
$79$	−634.622	−0.903805	−0.451903	−	0.892067i	$-0.649255\pi$
$79$	−634.622	−0.903805	−0.451903	+	0.892067i	$0.649255\pi$
$80$	174.921	0.244460
$81$	81.0000	0.111111
$82$	−812.163	−1.09376
$83$	−455.133	−0.601896	−0.300948	−	0.953641i	$-0.597303\pi$
$83$	−455.133	−0.601896	−0.300948	+	0.953641i	$0.597303\pi$
$84$	47.3405	0.0614913
$85$	−1090.90	−1.39206
$86$	−807.441	−1.01243
$87$	424.449	0.523054
$88$	321.417	0.389354
$89$	1439.12	1.71401	0.857003	−	0.515311i	$-0.172324\pi$
$89$	1439.12	1.71401	0.857003	+	0.515311i	$0.172324\pi$
$90$	196.787	0.230479
$91$	35.9938	0.0414634
$92$	489.311	0.554502
$93$	178.071	0.198550
$94$	1120.75	1.22975
$95$	−751.394	−0.811489
$96$	96.0000	0.102062
$97$	814.374	0.852445	0.426223	−	0.904618i	$-0.359844\pi$
$97$	814.374	0.852445	0.426223	+	0.904618i	$0.359844\pi$
$98$	−654.873	−0.675022
$99$	361.594	0.367087
$100$	−21.9143	−0.0219143
$101$	−1192.20	−1.17453	−0.587267	−	0.809393i	$-0.699796\pi$
$101$	−1192.20	−1.17453	−0.587267	+	0.809393i	$0.699796\pi$
$102$	−598.708	−0.581186
$103$	−1188.52	−1.13697	−0.568486	−	0.822693i	$-0.692471\pi$
$103$	−1188.52	−1.13697	−0.568486	+	0.822693i	$0.692471\pi$
$104$	72.9904	0.0688202
$105$	129.389	0.120257
$106$	−262.037	−0.240106
$107$	−721.860	−0.652195	−0.326098	−	0.945336i	$-0.605734\pi$
$107$	−721.860	−0.652195	−0.326098	+	0.945336i	$0.605734\pi$
$108$	108.000	0.0962250
$109$	−243.555	−0.214021	−0.107011	−	0.994258i	$-0.534128\pi$
$109$	−243.555	−0.214021	−0.107011	+	0.994258i	$0.534128\pi$
$110$	878.480	0.761452
$111$	520.493	0.445073
$112$	63.1207	0.0532531
$113$	−2220.45	−1.84851	−0.924256	−	0.381773i	$-0.875314\pi$
$113$	−2220.45	−1.84851	−0.924256	+	0.381773i	$0.875314\pi$
$114$	−412.379	−0.338797
$115$	1337.36	1.08443
$116$	565.932	0.452978
$117$	82.1142	0.0648843
$118$	−118.000	−0.0920575
$119$	−393.655	−0.303246
$120$	262.382	0.199601
$121$	283.202	0.212774
$122$	1693.47	1.25672
$123$	−1218.24	−0.893052
$124$	237.428	0.171949
$125$	−1426.47	−1.02070
$126$	71.0108	0.0502075
$127$	−870.282	−0.608071	−0.304036	−	0.952661i	$-0.598334\pi$
$127$	−870.282	−0.608071	−0.304036	+	0.952661i	$0.598334\pi$
$128$	128.000	0.0883883
$129$	−1211.16	−0.826642
$130$	199.493	0.134590
$131$	−953.735	−0.636093	−0.318047	−	0.948075i	$-0.603027\pi$
$131$	−953.735	−0.636093	−0.318047	+	0.948075i	$0.603027\pi$
$132$	482.126	0.317906
$133$	−271.142	−0.176774
$134$	−501.740	−0.323461
$135$	295.180	0.188185
$136$	−798.277	−0.503321
$137$	875.222	0.545805	0.272902	−	0.962042i	$-0.412016\pi$
$137$	875.222	0.545805	0.272902	+	0.962042i	$0.412016\pi$
$138$	733.966	0.452749
$139$	1722.36	1.05100	0.525498	−	0.850795i	$-0.323879\pi$
$139$	1722.36	1.05100	0.525498	+	0.850795i	$0.323879\pi$
$140$	172.518	0.104146
$141$	1681.12	1.00409
$142$	−826.472	−0.488422
$143$	366.568	0.214363
$144$	144.000	0.0833333
$145$	1546.77	0.885880
$146$	814.129	0.461492
$147$	−982.310	−0.551153
$148$	693.991	0.385444
$149$	−1942.48	−1.06802	−0.534008	−	0.845479i	$-0.679315\pi$
$149$	−1942.48	−1.06802	−0.534008	+	0.845479i	$0.679315\pi$
$150$	−32.8714	−0.0178929
$151$	379.401	0.204471	0.102236	−	0.994760i	$-0.467400\pi$
$151$	379.401	0.204471	0.102236	+	0.994760i	$0.467400\pi$
$152$	−549.838	−0.293406
$153$	−898.062	−0.474536
$154$	317.001	0.165874
$155$	648.926	0.336278
$156$	109.486	0.0561914
$157$	231.097	0.117475	0.0587374	−	0.998273i	$-0.481293\pi$
$157$	231.097	0.117475	0.0587374	+	0.998273i	$0.481293\pi$
$158$	−1269.24	−0.639087
$159$	−393.055	−0.196046
$160$	349.843	0.172859
$161$	482.588	0.236231
$162$	162.000	0.0785674
$163$	−1152.44	−0.553778	−0.276889	−	0.960902i	$-0.589303\pi$
$163$	−1152.44	−0.553778	−0.276889	+	0.960902i	$0.589303\pi$
$164$	−1624.33	−0.773406
$165$	1317.72	0.621723
$166$	−910.266	−0.425605
$167$	−1620.13	−0.750713	−0.375357	−	0.926880i	$-0.622480\pi$
$167$	−1620.13	−0.750713	−0.375357	+	0.926880i	$0.622480\pi$
$168$	94.6810	0.0434809
$169$	−2113.76	−0.962110
$170$	−2181.81	−0.984336
$171$	−618.568	−0.276626
$172$	−1614.88	−0.715893
$173$	−3066.19	−1.34750	−0.673752	−	0.738957i	$-0.735319\pi$
$173$	−3066.19	−1.34750	−0.673752	+	0.738957i	$0.735319\pi$
$174$	848.898	0.369855
$175$	−21.6132	−0.00933601
$176$	642.834	0.275315
$177$	−177.000	−0.0751646
$178$	2878.24	1.21199
$179$	−4356.44	−1.81908	−0.909541	−	0.415614i	$-0.863567\pi$
$179$	−4356.44	−1.81908	−0.909541	+	0.415614i	$0.863567\pi$
$180$	393.573	0.162973
$181$	1424.88	0.585140	0.292570	−	0.956244i	$-0.405490\pi$
$181$	1424.88	0.585140	0.292570	+	0.956244i	$0.405490\pi$
$182$	71.9876	0.0293191
$183$	2540.21	1.02611
$184$	978.622	0.392092
$185$	1896.78	0.753806
$186$	356.142	0.140396
$187$	−4009.06	−1.56776
$188$	2241.50	0.869564
$189$	106.516	0.0409942
$190$	−1502.79	−0.573809
$191$	2078.31	0.787337	0.393668	−	0.919253i	$-0.371206\pi$
$191$	2078.31	0.787337	0.393668	+	0.919253i	$0.371206\pi$
$192$	192.000	0.0721688
$193$	86.7242	0.0323448	0.0161724	−	0.999869i	$-0.494852\pi$
$193$	86.7242	0.0323448	0.0161724	+	0.999869i	$0.494852\pi$
$194$	1628.75	0.602770
$195$	299.240	0.109892
$196$	−1309.75	−0.477313
$197$	2490.98	0.900888	0.450444	−	0.892805i	$-0.351266\pi$
$197$	2490.98	0.900888	0.450444	+	0.892805i	$0.351266\pi$
$198$	723.188	0.259569
$199$	1747.06	0.622341	0.311171	−	0.950354i	$-0.399279\pi$
$199$	1747.06	0.622341	0.311171	+	0.950354i	$0.399279\pi$
$200$	−43.8285	−0.0154957
$201$	−752.610	−0.264105
$202$	−2384.39	−0.830521
$203$	558.156	0.192980
$204$	−1197.42	−0.410960
$205$	−4439.52	−1.51254
$206$	−2377.04	−0.803961
$207$	1100.95	0.369668
$208$	145.981	0.0486632
$209$	−2761.37	−0.913912
$210$	258.777	0.0850348
$211$	4702.52	1.53429	0.767144	−	0.641475i	$-0.221677\pi$
$211$	4702.52	1.53429	0.767144	+	0.641475i	$0.221677\pi$
$212$	−524.074	−0.169781
$213$	−1239.71	−0.398795
$214$	−1443.72	−0.461172
$215$	−4413.71	−1.40006
$216$	216.000	0.0680414
$217$	234.166	0.0732545
$218$	−487.109	−0.151336
$219$	1221.19	0.376806
$220$	1756.96	0.538428
$221$	−910.415	−0.277109
$222$	1040.99	0.314714
$223$	3467.27	1.04119	0.520596	−	0.853803i	$-0.325710\pi$
$223$	3467.27	1.04119	0.520596	+	0.853803i	$0.325710\pi$
$224$	126.241	0.0376556
$225$	−49.3071	−0.0146095
$226$	−4440.89	−1.30710
$227$	−4938.77	−1.44404	−0.722022	−	0.691871i	$-0.756787\pi$
$227$	−4938.77	−1.44404	−0.722022	+	0.691871i	$0.756787\pi$
$228$	−824.757	−0.239565
$229$	4573.50	1.31976	0.659881	−	0.751370i	$-0.270607\pi$
$229$	4573.50	1.31976	0.659881	+	0.751370i	$0.270607\pi$
$230$	2674.72	0.766807
$231$	475.501	0.135436
$232$	1131.86	0.320304
$233$	1449.39	0.407521	0.203761	−	0.979021i	$-0.434684\pi$
$233$	1449.39	0.407521	0.203761	+	0.979021i	$0.434684\pi$
$234$	164.228	0.0458801
$235$	6126.34	1.70059
$236$	−236.000	−0.0650945
$237$	−1903.87	−0.521812
$238$	−787.310	−0.214427
$239$	−4216.84	−1.14128	−0.570638	−	0.821202i	$-0.693304\pi$
$239$	−4216.84	−1.14128	−0.570638	+	0.821202i	$0.693304\pi$
$240$	524.764	0.141139
$241$	801.512	0.214232	0.107116	−	0.994247i	$-0.465838\pi$
$241$	801.512	0.214232	0.107116	+	0.994247i	$0.465838\pi$
$242$	566.403	0.150454
$243$	243.000	0.0641500
$244$	3386.95	0.888636
$245$	−3579.73	−0.933471
$246$	−2436.49	−0.631483
$247$	−627.077	−0.161538
$248$	474.857	0.121586
$249$	−1365.40	−0.347505
$250$	−2852.94	−0.721742
$251$	−4269.12	−1.07356	−0.536782	−	0.843721i	$-0.680360\pi$
$251$	−4269.12	−1.07356	−0.536782	+	0.843721i	$0.680360\pi$
$252$	142.022	0.0355020
$253$	4914.78	1.22130
$254$	−1740.56	−0.429971
$255$	−3272.71	−0.803707
$256$	256.000	0.0625000
$257$	6384.70	1.54968	0.774838	−	0.632159i	$-0.217831\pi$
$257$	6384.70	1.54968	0.774838	+	0.632159i	$0.217831\pi$
$258$	−2422.32	−0.584524
$259$	684.456	0.164209
$260$	398.987	0.0951697
$261$	1273.35	0.301985
$262$	−1907.47	−0.449786
$263$	228.377	0.0535451	0.0267725	−	0.999642i	$-0.491477\pi$
$263$	228.377	0.0535451	0.0267725	+	0.999642i	$0.491477\pi$
$264$	964.251	0.224794
$265$	−1432.37	−0.332037
$266$	−542.284	−0.124998
$267$	4317.36	0.989582
$268$	−1003.48	−0.228721
$269$	2132.40	0.483326	0.241663	−	0.970360i	$-0.422307\pi$
$269$	2132.40	0.483326	0.241663	+	0.970360i	$0.422307\pi$
$270$	590.360	0.133067
$271$	5009.66	1.12293	0.561467	−	0.827499i	$-0.310237\pi$
$271$	5009.66	1.12293	0.561467	+	0.827499i	$0.310237\pi$
$272$	−1596.55	−0.355902
$273$	107.981	0.0239389
$274$	1750.44	0.385942
$275$	−220.113	−0.0482666
$276$	1467.93	0.320142
$277$	3044.10	0.660296	0.330148	−	0.943929i	$-0.392901\pi$
$277$	3044.10	0.660296	0.330148	+	0.943929i	$0.392901\pi$
$278$	3444.72	0.743167
$279$	534.214	0.114633
$280$	345.036	0.0736423
$281$	3170.66	0.673117	0.336559	−	0.941663i	$-0.390737\pi$
$281$	3170.66	0.673117	0.336559	+	0.941663i	$0.390737\pi$
$282$	3362.25	0.709996
$283$	−1213.69	−0.254934	−0.127467	−	0.991843i	$-0.540685\pi$
$283$	−1213.69	−0.254934	−0.127467	+	0.991843i	$0.540685\pi$
$284$	−1652.94	−0.345367
$285$	−2254.18	−0.468513
$286$	733.136	0.151578
$287$	−1602.01	−0.329490
$288$	288.000	0.0589256
$289$	5043.98	1.02666
$290$	3093.55	0.626412
$291$	2443.12	0.492159
$292$	1628.26	0.326324
$293$	−7442.45	−1.48393	−0.741967	−	0.670436i	$-0.766107\pi$
$293$	−7442.45	−1.48393	−0.741967	+	0.670436i	$0.766107\pi$
$294$	−1964.62	−0.389724
$295$	−645.023	−0.127304
$296$	1387.98	0.272550
$297$	1084.78	0.211938
$298$	−3884.97	−0.755201
$299$	1116.09	0.215871
$300$	−65.7428	−0.0126522
$301$	−1592.69	−0.304988
$302$	758.801	0.144583
$303$	−3576.59	−0.678118
$304$	−1099.68	−0.207470
$305$	9257.02	1.73789
$306$	−1796.12	−0.335548
$307$	826.503	0.153651	0.0768257	−	0.997045i	$-0.475521\pi$
$307$	826.503	0.153651	0.0768257	+	0.997045i	$0.475521\pi$
$308$	634.002	0.117291
$309$	−3565.55	−0.656431
$310$	1297.85	0.237784
$311$	−4081.36	−0.744156	−0.372078	−	0.928202i	$-0.621355\pi$
$311$	−4081.36	−0.744156	−0.372078	+	0.928202i	$0.621355\pi$
$312$	218.971	0.0397333
$313$	7738.06	1.39738	0.698691	−	0.715423i	$-0.253766\pi$
$313$	7738.06	1.39738	0.698691	+	0.715423i	$0.253766\pi$
$314$	462.194	0.0830672
$315$	388.166	0.0694307
$316$	−2538.49	−0.451903
$317$	2964.73	0.525287	0.262643	−	0.964893i	$-0.415406\pi$
$317$	2964.73	0.525287	0.262643	+	0.964893i	$0.415406\pi$
$318$	−786.110	−0.138625
$319$	5684.38	0.997693
$320$	699.686	0.122230
$321$	−2165.58	−0.376545
$322$	965.176	0.167041
$323$	6858.18	1.18142
$324$	324.000	0.0555556
$325$	−49.9853	−0.00853134
$326$	−2304.87	−0.391580
$327$	−730.664	−0.123565
$328$	−3248.65	−0.546881
$329$	2210.70	0.370455
$330$	2635.44	0.439625
$331$	4556.98	0.756719	0.378360	−	0.925659i	$-0.376488\pi$
$331$	4556.98	0.756719	0.378360	+	0.925659i	$0.376488\pi$
$332$	−1820.53	−0.300948
$333$	1561.48	0.256963
$334$	−3240.25	−0.530834
$335$	−2742.66	−0.447306
$336$	189.362	0.0307457
$337$	−979.231	−0.158285	−0.0791426	−	0.996863i	$-0.525218\pi$
$337$	−979.231	−0.158285	−0.0791426	+	0.996863i	$0.525218\pi$
$338$	−4227.51	−0.680315
$339$	−6661.34	−1.06724
$340$	−4363.62	−0.696031
$341$	2384.80	0.378721
$342$	−1237.14	−0.195604
$343$	−2644.90	−0.416359
$344$	−3229.76	−0.506213
$345$	4012.07	0.626095
$346$	−6132.39	−0.952830
$347$	−3783.94	−0.585397	−0.292698	−	0.956205i	$-0.594553\pi$
$347$	−3783.94	−0.585397	−0.292698	+	0.956205i	$0.594553\pi$
$348$	1697.80	0.261527
$349$	8692.70	1.33327	0.666633	−	0.745386i	$-0.267735\pi$
$349$	8692.70	1.33327	0.666633	+	0.745386i	$0.267735\pi$
$350$	−43.2263	−0.00660155
$351$	246.343	0.0374610
$352$	1285.67	0.194677
$353$	10440.7	1.57423	0.787115	−	0.616806i	$-0.211574\pi$
$353$	10440.7	1.57423	0.787115	+	0.616806i	$0.211574\pi$
$354$	−354.000	−0.0531494
$355$	−4517.74	−0.675427
$356$	5756.49	0.857003
$357$	−1180.96	−0.175079
$358$	−8712.88	−1.28629
$359$	10610.2	1.55985	0.779926	−	0.625872i	$-0.215257\pi$
$359$	10610.2	1.55985	0.779926	+	0.625872i	$0.215257\pi$
$360$	787.146	0.115240
$361$	−2135.22	−0.311301
$362$	2849.75	0.413756
$363$	849.605	0.122845
$364$	143.975	0.0207317
$365$	4450.27	0.638185
$366$	5080.42	0.725568
$367$	2671.50	0.379976	0.189988	−	0.981786i	$-0.439155\pi$
$367$	2671.50	0.379976	0.189988	+	0.981786i	$0.439155\pi$
$368$	1957.24	0.277251
$369$	−3654.73	−0.515604
$370$	3793.56	0.533021
$371$	−516.873	−0.0723308
$372$	712.285	0.0992749
$373$	4782.30	0.663856	0.331928	−	0.943305i	$-0.392301\pi$
$373$	4782.30	0.663856	0.331928	+	0.943305i	$0.392301\pi$
$374$	−8018.12	−1.10858
$375$	−4279.40	−0.589300
$376$	4482.99	0.614874
$377$	1290.86	0.176347
$378$	213.032	0.0289873
$379$	−4197.99	−0.568960	−0.284480	−	0.958682i	$-0.591821\pi$
$379$	−4197.99	−0.568960	−0.284480	+	0.958682i	$0.591821\pi$
$380$	−3005.58	−0.405744
$381$	−2610.85	−0.351070
$382$	4156.62	0.556731
$383$	13951.1	1.86127	0.930637	−	0.365944i	$-0.119254\pi$
$383$	13951.1	1.86127	0.930637	+	0.365944i	$0.119254\pi$
$384$	384.000	0.0510310
$385$	1732.82	0.229384
$386$	173.448	0.0228712
$387$	−3633.48	−0.477262
$388$	3257.50	0.426223
$389$	9807.04	1.27824	0.639122	−	0.769106i	$-0.279298\pi$
$389$	9807.04	1.27824	0.639122	+	0.769106i	$0.279298\pi$
$390$	598.480	0.0777057
$391$	−12206.4	−1.57879
$392$	−2619.49	−0.337511
$393$	−2861.21	−0.367249
$394$	4981.96	0.637024
$395$	−6938.06	−0.883777
$396$	1446.38	0.183543
$397$	4499.09	0.568773	0.284387	−	0.958710i	$-0.408210\pi$
$397$	4499.09	0.568773	0.284387	+	0.958710i	$0.408210\pi$
$398$	3494.12	0.440062
$399$	−813.426	−0.102061
$400$	−87.6570	−0.0109571
$401$	4329.58	0.539174	0.269587	−	0.962976i	$-0.413113\pi$
$401$	4329.58	0.539174	0.269587	+	0.962976i	$0.413113\pi$
$402$	−1505.22	−0.186750
$403$	541.562	0.0669408
$404$	−4768.78	−0.587267
$405$	885.539	0.108649
$406$	1116.31	0.136457
$407$	6970.64	0.848948
$408$	−2394.83	−0.290593
$409$	−5274.11	−0.637623	−0.318812	−	0.947818i	$-0.603284\pi$
$409$	−5274.11	−0.637623	−0.318812	+	0.947818i	$0.603284\pi$
$410$	−8879.04	−1.06952
$411$	2625.66	0.315120
$412$	−4754.07	−0.568486
$413$	−232.757	−0.0277318
$414$	2201.90	0.261395
$415$	−4975.78	−0.588558
$416$	291.962	0.0344101
$417$	5167.08	0.606793
$418$	−5522.73	−0.646234
$419$	4134.55	0.482067	0.241033	−	0.970517i	$-0.422514\pi$
$419$	4134.55	0.482067	0.241033	+	0.970517i	$0.422514\pi$
$420$	517.554	0.0601287
$421$	−11059.6	−1.28031	−0.640155	−	0.768245i	$-0.721130\pi$
$421$	−11059.6	−1.28031	−0.640155	+	0.768245i	$0.721130\pi$
$422$	9405.04	1.08491
$423$	5043.37	0.579709
$424$	−1048.15	−0.120053
$425$	546.677	0.0623946
$426$	−2479.42	−0.281991
$427$	3340.41	0.378581
$428$	−2887.44	−0.326098
$429$	1099.70	0.123763
$430$	−8827.42	−0.989990
$431$	864.369	0.0966013	0.0483007	−	0.998833i	$-0.484619\pi$
$431$	864.369	0.0966013	0.0483007	+	0.998833i	$0.484619\pi$
$432$	432.000	0.0481125
$433$	13365.3	1.48336	0.741681	−	0.670753i	$-0.234029\pi$
$433$	13365.3	1.48336	0.741681	+	0.670753i	$0.234029\pi$
$434$	468.332	0.0517988
$435$	4640.32	0.511463
$436$	−974.219	−0.107011
$437$	−8407.56	−0.920339
$438$	2442.39	0.266442
$439$	−15358.1	−1.66971	−0.834857	−	0.550467i	$-0.814450\pi$
$439$	−15358.1	−1.66971	−0.834857	+	0.550467i	$0.814450\pi$
$440$	3513.92	0.380726
$441$	−2946.93	−0.318209
$442$	−1820.83	−0.195946
$443$	−6972.21	−0.747764	−0.373882	−	0.927476i	$-0.621974\pi$
$443$	−6972.21	−0.747764	−0.373882	+	0.927476i	$0.621974\pi$
$444$	2081.97	0.222536
$445$	15733.3	1.67602
$446$	6934.54	0.736233
$447$	−5827.45	−0.616619
$448$	252.483	0.0266265
$449$	−6211.25	−0.652844	−0.326422	−	0.945224i	$-0.605843\pi$
$449$	−6211.25	−0.652844	−0.326422	+	0.945224i	$0.605843\pi$
$450$	−98.6141	−0.0103305
$451$	−16315.2	−1.70344
$452$	−8881.78	−0.924256
$453$	1138.20	0.118052
$454$	−9877.54	−1.02109
$455$	393.505	0.0405446
$456$	−1649.51	−0.169398
$457$	300.381	0.0307467	0.0153734	−	0.999882i	$-0.495106\pi$
$457$	300.381	0.0307467	0.0153734	+	0.999882i	$0.495106\pi$
$458$	9147.00	0.933213
$459$	−2694.19	−0.273974
$460$	5349.43	0.542214
$461$	11846.1	1.19681	0.598403	−	0.801195i	$-0.295802\pi$
$461$	11846.1	1.19681	0.598403	+	0.801195i	$0.295802\pi$
$462$	951.003	0.0957677
$463$	−16831.1	−1.68943	−0.844717	−	0.535213i	$-0.820231\pi$
$463$	−16831.1	−1.68943	−0.844717	+	0.535213i	$0.820231\pi$
$464$	2263.73	0.226489
$465$	1946.78	0.194150
$466$	2898.77	0.288161
$467$	5535.37	0.548494	0.274247	−	0.961659i	$-0.411571\pi$
$467$	5535.37	0.548494	0.274247	+	0.961659i	$0.411571\pi$
$468$	328.457	0.0324421
$469$	−989.693	−0.0974409
$470$	12252.7	1.20250
$471$	693.291	0.0678241
$472$	−472.000	−0.0460287
$473$	−16220.3	−1.57677
$474$	−3807.73	−0.368977
$475$	376.540	0.0363723
$476$	−1574.62	−0.151623
$477$	−1179.17	−0.113187
$478$	−8433.69	−0.807004
$479$	8145.51	0.776989	0.388494	−	0.921451i	$-0.372995\pi$
$479$	8145.51	0.776989	0.388494	+	0.921451i	$0.372995\pi$
$480$	1049.53	0.0998004
$481$	1582.96	0.150056
$482$	1603.02	0.151485
$483$	1447.76	0.136388
$484$	1132.81	0.106387
$485$	8903.22	0.833555
$486$	486.000	0.0453609
$487$	−8121.21	−0.755661	−0.377831	−	0.925875i	$-0.623330\pi$
$487$	−8121.21	−0.755661	−0.377831	+	0.925875i	$0.623330\pi$
$488$	6773.90	0.628360
$489$	−3457.31	−0.319724
$490$	−7159.46	−0.660064
$491$	10205.4	0.938010	0.469005	−	0.883196i	$-0.344613\pi$
$491$	10205.4	0.938010	0.469005	+	0.883196i	$0.344613\pi$
$492$	−4872.98	−0.446526
$493$	−14117.8	−1.28973
$494$	−1254.15	−0.114225
$495$	3953.16	0.358952
$496$	949.713	0.0859746
$497$	−1630.23	−0.147135
$498$	−2730.80	−0.245723
$499$	−16509.1	−1.48106	−0.740529	−	0.672024i	$-0.765425\pi$
$499$	−16509.1	−1.48106	−0.740529	+	0.672024i	$0.765425\pi$
$500$	−5705.87	−0.510349
$501$	−4860.38	−0.433424
$502$	−8538.25	−0.759125
$503$	−13168.2	−1.16728	−0.583638	−	0.812014i	$-0.698371\pi$
$503$	−13168.2	−1.16728	−0.583638	+	0.812014i	$0.698371\pi$
$504$	284.043	0.0251037
$505$	−13033.8	−1.14851
$506$	9829.55	0.863591
$507$	−6341.27	−0.555475
$508$	−3481.13	−0.304036
$509$	8102.42	0.705566	0.352783	−	0.935705i	$-0.385235\pi$
$509$	8102.42	0.705566	0.352783	+	0.935705i	$0.385235\pi$
$510$	−6545.43	−0.568307
$511$	1605.89	0.139022
$512$	512.000	0.0441942
$513$	−1855.70	−0.159710
$514$	12769.4	1.09579
$515$	−12993.6	−1.11178
$516$	−4844.64	−0.413321
$517$	22514.2	1.91523
$518$	1368.91	0.116113
$519$	−9198.58	−0.777982
$520$	797.974	0.0672951
$521$	−7409.71	−0.623081	−0.311541	−	0.950233i	$-0.600845\pi$
$521$	−7409.71	−0.623081	−0.311541	+	0.950233i	$0.600845\pi$
$522$	2546.69	0.213536
$523$	−4231.45	−0.353782	−0.176891	−	0.984230i	$-0.556604\pi$
$523$	−4231.45	−0.353782	−0.176891	+	0.984230i	$0.556604\pi$
$524$	−3814.94	−0.318047
$525$	−64.8395	−0.00539015
$526$	456.755	0.0378621
$527$	−5922.93	−0.489576
$528$	1928.50	0.158953
$529$	2797.06	0.229889
$530$	−2864.74	−0.234786
$531$	−531.000	−0.0433963
$532$	−1084.57	−0.0883872
$533$	−3705.01	−0.301091
$534$	8634.73	0.699740
$535$	−7891.80	−0.637743
$536$	−2006.96	−0.161730
$537$	−13069.3	−1.05025
$538$	4264.80	0.341763
$539$	−13155.5	−1.05129
$540$	1180.72	0.0940927
$541$	7423.25	0.589927	0.294963	−	0.955509i	$-0.404693\pi$
$541$	7423.25	0.589927	0.294963	+	0.955509i	$0.404693\pi$
$542$	10019.3	0.794034
$543$	4274.63	0.337831
$544$	−3193.11	−0.251661
$545$	−2662.68	−0.209278
$546$	215.963	0.0169274
$547$	−15576.1	−1.21752	−0.608762	−	0.793353i	$-0.708333\pi$
$547$	−15576.1	−1.21752	−0.608762	+	0.793353i	$0.708333\pi$
$548$	3500.89	0.272902
$549$	7620.63	0.592424
$550$	−440.226	−0.0341296
$551$	−9724.09	−0.751834
$552$	2935.86	0.226374
$553$	−2503.61	−0.192522
$554$	6088.20	0.466900
$555$	5690.34	0.435210
$556$	6889.43	0.525498
$557$	−4073.41	−0.309867	−0.154934	−	0.987925i	$-0.549516\pi$
$557$	−4073.41	−0.309867	−0.154934	+	0.987925i	$0.549516\pi$
$558$	1068.43	0.0810576
$559$	−3683.46	−0.278701
$560$	690.072	0.0520730
$561$	−12027.2	−0.905148
$562$	6341.33	0.475966
$563$	−16053.1	−1.20170	−0.600852	−	0.799361i	$-0.705172\pi$
$563$	−16053.1	−1.20170	−0.600852	+	0.799361i	$0.705172\pi$
$564$	6724.49	0.502043
$565$	−24275.2	−1.80755
$566$	−2427.38	−0.180265
$567$	319.548	0.0236680
$568$	−3305.89	−0.244211
$569$	20835.4	1.53509	0.767544	−	0.640997i	$-0.221479\pi$
$569$	20835.4	1.53509	0.767544	+	0.640997i	$0.221479\pi$
$570$	−4508.37	−0.331289
$571$	3598.10	0.263706	0.131853	−	0.991269i	$-0.457907\pi$
$571$	3598.10	0.263706	0.131853	+	0.991269i	$0.457907\pi$
$572$	1466.27	0.107182
$573$	6234.93	0.454569
$574$	−3204.02	−0.232985
$575$	−670.180	−0.0486060
$576$	576.000	0.0416667
$577$	16311.2	1.17685	0.588426	−	0.808551i	$-0.299748\pi$
$577$	16311.2	1.17685	0.588426	+	0.808551i	$0.299748\pi$
$578$	10088.0	0.725958
$579$	260.172	0.0186743
$580$	6187.10	0.442940
$581$	−1795.52	−0.128211
$582$	4886.25	0.348009
$583$	−5263.94	−0.373946
$584$	3256.51	0.230746
$585$	897.721	0.0634465
$586$	−14884.9	−1.04930
$587$	−14335.5	−1.00799	−0.503994	−	0.863707i	$-0.668137\pi$
$587$	−14335.5	−1.00799	−0.503994	+	0.863707i	$0.668137\pi$
$588$	−3929.24	−0.275577
$589$	−4079.60	−0.285394
$590$	−1290.05	−0.0900175
$591$	7472.94	0.520128
$592$	2775.97	0.192722
$593$	−15021.7	−1.04025	−0.520124	−	0.854091i	$-0.674114\pi$
$593$	−15021.7	−1.04025	−0.520124	+	0.854091i	$0.674114\pi$
$594$	2169.56	0.149863
$595$	−4303.66	−0.296526
$596$	−7769.93	−0.534008
$597$	5241.18	0.359309
$598$	2232.19	0.152644
$599$	−10456.6	−0.713267	−0.356633	−	0.934244i	$-0.616075\pi$
$599$	−10456.6	−0.713267	−0.356633	+	0.934244i	$0.616075\pi$
$600$	−131.486	−0.00894646
$601$	−884.454	−0.0600294	−0.0300147	−	0.999549i	$-0.509555\pi$
$601$	−884.454	−0.0600294	−0.0300147	+	0.999549i	$0.509555\pi$
$602$	−3185.39	−0.215659
$603$	−2257.83	−0.152481
$604$	1517.60	0.102236
$605$	3096.13	0.208059
$606$	−7153.18	−0.479502
$607$	20768.0	1.38871	0.694356	−	0.719632i	$-0.255689\pi$
$607$	20768.0	1.38871	0.694356	+	0.719632i	$0.255689\pi$
$608$	−2199.35	−0.146703
$609$	1674.47	0.111417
$610$	18514.0	1.22887
$611$	5112.74	0.338526
$612$	−3592.25	−0.237268
$613$	580.563	0.0382524	0.0191262	−	0.999817i	$-0.493912\pi$
$613$	580.563	0.0382524	0.0191262	+	0.999817i	$0.493912\pi$
$614$	1653.01	0.108648
$615$	−13318.6	−0.873262
$616$	1268.00	0.0829372
$617$	22745.9	1.48414	0.742070	−	0.670323i	$-0.233844\pi$
$617$	22745.9	1.48414	0.742070	+	0.670323i	$0.233844\pi$
$618$	−7131.11	−0.464167
$619$	242.266	0.0157310	0.00786549	−	0.999969i	$-0.497496\pi$
$619$	242.266	0.0157310	0.00786549	+	0.999969i	$0.497496\pi$
$620$	2595.71	0.168139
$621$	3302.85	0.213428
$622$	−8162.71	−0.526198
$623$	5677.39	0.365104
$624$	437.942	0.0280957
$625$	−14910.2	−0.954251
$626$	15476.1	0.988099
$627$	−8284.10	−0.527647
$628$	924.388	0.0587374
$629$	−17312.4	−1.09744
$630$	776.331	0.0490949
$631$	18727.1	1.18148	0.590740	−	0.806862i	$-0.298836\pi$
$631$	18727.1	1.18148	0.590740	+	0.806862i	$0.298836\pi$
$632$	−5076.98	−0.319543
$633$	14107.6	0.885822
$634$	5929.46	0.371434
$635$	−9514.44	−0.594597
$636$	−1572.22	−0.0980230
$637$	−2987.47	−0.185821
$638$	11368.8	0.705476
$639$	−3719.12	−0.230245
$640$	1399.37	0.0864297
$641$	22798.1	1.40479	0.702395	−	0.711788i	$-0.252114\pi$
$641$	22798.1	1.40479	0.702395	+	0.711788i	$0.252114\pi$
$642$	−4331.16	−0.266258
$643$	12761.3	0.782667	0.391334	−	0.920249i	$-0.372014\pi$
$643$	12761.3	0.782667	0.391334	+	0.920249i	$0.372014\pi$
$644$	1930.35	0.118116
$645$	−13241.1	−0.808324
$646$	13716.4	0.835392
$647$	11113.7	0.675308	0.337654	−	0.941270i	$-0.390367\pi$
$647$	11113.7	0.675308	0.337654	+	0.941270i	$0.390367\pi$
$648$	648.000	0.0392837
$649$	−2370.45	−0.143372
$650$	−99.9706	−0.00603257
$651$	702.498	0.0422935
$652$	−4609.75	−0.276889
$653$	−28729.1	−1.72168	−0.860838	−	0.508879i	$-0.830060\pi$
$653$	−28729.1	−1.72168	−0.860838	+	0.508879i	$0.830060\pi$
$654$	−1461.33	−0.0873738
$655$	−10426.8	−0.621998
$656$	−6497.31	−0.386703
$657$	3663.58	0.217549
$658$	4421.40	0.261952
$659$	3724.82	0.220180	0.110090	−	0.993922i	$-0.464886\pi$
$659$	3724.82	0.220180	0.110090	+	0.993922i	$0.464886\pi$
$660$	5270.88	0.310862
$661$	13133.8	0.772836	0.386418	−	0.922324i	$-0.373712\pi$
$661$	13133.8	0.772836	0.386418	+	0.922324i	$0.373712\pi$
$662$	9113.95	0.535081
$663$	−2731.25	−0.159989
$664$	−3641.07	−0.212802
$665$	−2964.28	−0.172857
$666$	3122.96	0.181700
$667$	17307.3	1.00471
$668$	−6480.50	−0.375357
$669$	10401.8	0.601132
$670$	−5485.32	−0.316293
$671$	34019.5	1.95724
$672$	378.724	0.0217405
$673$	18479.1	1.05842	0.529209	−	0.848492i	$-0.322489\pi$
$673$	18479.1	1.05842	0.529209	+	0.848492i	$0.322489\pi$
$674$	−1958.46	−0.111925
$675$	−147.921	−0.00843480
$676$	−8455.03	−0.481055
$677$	2171.63	0.123283	0.0616413	−	0.998098i	$-0.480367\pi$
$677$	2171.63	0.123283	0.0616413	+	0.998098i	$0.480367\pi$
$678$	−13322.7	−0.754652
$679$	3212.74	0.181581
$680$	−8727.24	−0.492168
$681$	−14816.3	−0.833719
$682$	4769.59	0.267796
$683$	26443.8	1.48147	0.740736	−	0.671796i	$-0.234477\pi$
$683$	26443.8	1.48147	0.740736	+	0.671796i	$0.234477\pi$
$684$	−2474.27	−0.138313
$685$	9568.44	0.533710
$686$	−5289.80	−0.294410
$687$	13720.5	0.761965
$688$	−6459.53	−0.357946
$689$	−1195.39	−0.0660966
$690$	8024.15	0.442716
$691$	7730.66	0.425598	0.212799	−	0.977096i	$-0.431742\pi$
$691$	7730.66	0.425598	0.212799	+	0.977096i	$0.431742\pi$
$692$	−12264.8	−0.673752
$693$	1426.50	0.0781940
$694$	−7567.88	−0.413938
$695$	18829.8	1.02771
$696$	3395.59	0.184928
$697$	40520.7	2.20205
$698$	17385.4	0.942761
$699$	4348.16	0.235282
$700$	−86.4526	−0.00466800
$701$	−21558.6	−1.16156	−0.580782	−	0.814059i	$-0.697253\pi$
$701$	−21558.6	−1.16156	−0.580782	+	0.814059i	$0.697253\pi$
$702$	492.685	0.0264889
$703$	−11924.5	−0.639744
$704$	2571.34	0.137658
$705$	18379.0	0.981835
$706$	20881.4	1.11315
$707$	−4703.26	−0.250190
$708$	−708.000	−0.0375823
$709$	−4963.38	−0.262911	−0.131455	−	0.991322i	$-0.541965\pi$
$709$	−4963.38	−0.262911	−0.131455	+	0.991322i	$0.541965\pi$
$710$	−9035.48	−0.477599
$711$	−5711.60	−0.301268
$712$	11513.0	0.605993
$713$	7261.01	0.381384
$714$	−2361.93	−0.123800
$715$	4007.54	0.209613
$716$	−17425.8	−0.909541
$717$	−12650.5	−0.658916
$718$	21220.5	1.10298
$719$	−24972.0	−1.29527	−0.647633	−	0.761952i	$-0.724241\pi$
$719$	−24972.0	−1.29527	−0.647633	+	0.761952i	$0.724241\pi$
$720$	1574.29	0.0814867
$721$	−4688.75	−0.242189
$722$	−4270.43	−0.220123
$723$	2404.54	0.123687
$724$	5699.51	0.292570
$725$	−775.123	−0.0397067
$726$	1699.21	0.0868645
$727$	−27903.9	−1.42352	−0.711759	−	0.702424i	$-0.752101\pi$
$727$	−27903.9	−1.42352	−0.711759	+	0.702424i	$0.752101\pi$
$728$	287.950	0.0146595
$729$	729.000	0.0370370
$730$	8900.53	0.451265
$731$	40285.1	2.03830
$732$	10160.8	0.513054
$733$	27029.3	1.36200	0.681002	−	0.732281i	$-0.261544\pi$
$733$	27029.3	1.36200	0.681002	+	0.732281i	$0.261544\pi$
$734$	5343.01	0.268684
$735$	−10739.2	−0.538940
$736$	3914.49	0.196046
$737$	−10079.2	−0.503763
$738$	−7309.47	−0.364587
$739$	−7799.07	−0.388218	−0.194109	−	0.980980i	$-0.562182\pi$
$739$	−7799.07	−0.388218	−0.194109	+	0.980980i	$0.562182\pi$
$740$	7587.12	0.376903
$741$	−1881.23	−0.0932641
$742$	−1033.75	−0.0511456
$743$	6451.04	0.318527	0.159264	−	0.987236i	$-0.449088\pi$
$743$	6451.04	0.318527	0.159264	+	0.987236i	$0.449088\pi$
$744$	1424.57	0.0701979
$745$	−21236.4	−1.04435
$746$	9564.60	0.469417
$747$	−4096.20	−0.200632
$748$	−16036.2	−0.783881
$749$	−2847.77	−0.138926
$750$	−8558.81	−0.416698
$751$	8047.29	0.391012	0.195506	−	0.980703i	$-0.437365\pi$
$751$	8047.29	0.391012	0.195506	+	0.980703i	$0.437365\pi$
$752$	8965.99	0.434782
$753$	−12807.4	−0.619823
$754$	2581.72	0.124696
$755$	4147.83	0.199940
$756$	426.065	0.0204971
$757$	1418.66	0.0681138	0.0340569	−	0.999420i	$-0.489157\pi$
$757$	1418.66	0.0681138	0.0340569	+	0.999420i	$0.489157\pi$
$758$	−8395.97	−0.402316
$759$	14744.3	0.705119
$760$	−6011.15	−0.286905
$761$	−13656.7	−0.650533	−0.325267	−	0.945622i	$-0.605454\pi$
$761$	−13656.7	−0.650533	−0.325267	+	0.945622i	$0.605454\pi$
$762$	−5221.69	−0.248244
$763$	−960.833	−0.0455891
$764$	8313.25	0.393668
$765$	−9818.14	−0.464020
$766$	27902.2	1.31612
$767$	−538.304	−0.0253416
$768$	768.000	0.0360844
$769$	34973.1	1.64000	0.820001	−	0.572362i	$-0.193973\pi$
$769$	34973.1	1.64000	0.820001	+	0.572362i	$0.193973\pi$
$770$	3465.64	0.162199
$771$	19154.1	0.894706
$772$	346.897	0.0161724
$773$	−9855.67	−0.458582	−0.229291	−	0.973358i	$-0.573641\pi$
$773$	−9855.67	−0.458582	−0.229291	+	0.973358i	$0.573641\pi$
$774$	−7266.97	−0.337475
$775$	−325.191	−0.0150725
$776$	6514.99	0.301385
$777$	2053.37	0.0948059
$778$	19614.1	0.903855
$779$	27909.9	1.28367
$780$	1196.96	0.0549462
$781$	−16602.6	−0.760677
$782$	−24412.9	−1.11637
$783$	3820.04	0.174351
$784$	−5238.99	−0.238656
$785$	2526.49	0.114872
$786$	−5722.41	−0.259684
$787$	14567.6	0.659822	0.329911	−	0.944012i	$-0.392981\pi$
$787$	14567.6	0.659822	0.329911	+	0.944012i	$0.392981\pi$
$788$	9963.91	0.450444
$789$	685.132	0.0309143
$790$	−13876.1	−0.624925
$791$	−8759.75	−0.393756
$792$	2892.75	0.129785
$793$	7725.46	0.345951
$794$	8998.19	0.402183
$795$	−4297.11	−0.191702
$796$	6988.25	0.311171
$797$	1791.84	0.0796363	0.0398182	−	0.999207i	$-0.487322\pi$
$797$	1791.84	0.0796363	0.0398182	+	0.999207i	$0.487322\pi$
$798$	−1626.85	−0.0721678
$799$	−55916.8	−2.47584
$800$	−175.314	−0.00774786
$801$	12952.1	0.571335
$802$	8659.16	0.381254
$803$	16354.7	0.718735
$804$	−3010.44	−0.132052
$805$	5275.93	0.230997
$806$	1083.12	0.0473343
$807$	6397.20	0.279049
$808$	−9537.57	−0.415261
$809$	−37826.2	−1.64388	−0.821940	−	0.569574i	$-0.807108\pi$
$809$	−37826.2	−1.64388	−0.821940	+	0.569574i	$0.807108\pi$
$810$	1771.08	0.0768264
$811$	14489.8	0.627379	0.313690	−	0.949526i	$-0.398435\pi$
$811$	14489.8	0.627379	0.313690	+	0.949526i	$0.398435\pi$
$812$	2232.63	0.0964899
$813$	15029.0	0.648326
$814$	13941.3	0.600297
$815$	−12599.1	−0.541507
$816$	−4789.66	−0.205480
$817$	27747.6	1.18821
$818$	−10548.2	−0.450868
$819$	323.944	0.0138211
$820$	−17758.1	−0.756268
$821$	14253.7	0.605918	0.302959	−	0.953004i	$-0.402026\pi$
$821$	14253.7	0.605918	0.302959	+	0.953004i	$0.402026\pi$
$822$	5251.33	0.222824
$823$	−99.5030	−0.00421440	−0.00210720	−	0.999998i	$-0.500671\pi$
$823$	−99.5030	−0.00421440	−0.00210720	+	0.999998i	$0.500671\pi$
$824$	−9508.14	−0.401980
$825$	−660.339	−0.0278667
$826$	−465.515	−0.0196094
$827$	−6761.69	−0.284313	−0.142157	−	0.989844i	$-0.545404\pi$
$827$	−6761.69	−0.284313	−0.142157	+	0.989844i	$0.545404\pi$
$828$	4403.80	0.184834
$829$	−21141.6	−0.885739	−0.442870	−	0.896586i	$-0.646040\pi$
$829$	−21141.6	−0.885739	−0.442870	+	0.896586i	$0.646040\pi$
$830$	−9951.57	−0.416173
$831$	9132.29	0.381222
$832$	583.923	0.0243316
$833$	32673.2	1.35901
$834$	10334.2	0.429068
$835$	−17712.2	−0.734078
$836$	−11045.5	−0.456956
$837$	1602.64	0.0661832
$838$	8269.10	0.340873
$839$	18871.5	0.776539	0.388270	−	0.921546i	$-0.373073\pi$
$839$	18871.5	0.776539	0.388270	+	0.921546i	$0.373073\pi$
$840$	1035.11	0.0425174
$841$	−4371.57	−0.179244
$842$	−22119.2	−0.905317
$843$	9511.99	0.388624
$844$	18810.1	0.767144
$845$	−23108.8	−0.940790
$846$	10086.7	0.409916
$847$	1117.24	0.0453234
$848$	−2096.29	−0.0848904
$849$	−3641.06	−0.147186
$850$	1093.35	0.0441197
$851$	21223.6	0.854918
$852$	−4958.83	−0.199398
$853$	−8345.26	−0.334978	−0.167489	−	0.985874i	$-0.553566\pi$
$853$	−8345.26	−0.334978	−0.167489	+	0.985874i	$0.553566\pi$
$854$	6680.83	0.267697
$855$	−6762.55	−0.270496
$856$	−5774.88	−0.230586
$857$	−8964.73	−0.357327	−0.178664	−	0.983910i	$-0.557177\pi$
$857$	−8964.73	−0.357327	−0.178664	+	0.983910i	$0.557177\pi$
$858$	2199.41	0.0875135
$859$	−14343.7	−0.569733	−0.284866	−	0.958567i	$-0.591949\pi$
$859$	−14343.7	−0.569733	−0.284866	+	0.958567i	$0.591949\pi$
$860$	−17654.8	−0.700029
$861$	−4806.03	−0.190231
$862$	1728.74	0.0683075
$863$	−109.142	−0.00430503	−0.00215251	−	0.999998i	$-0.500685\pi$
$863$	−109.142	−0.00430503	−0.00215251	+	0.999998i	$0.500685\pi$
$864$	864.000	0.0340207
$865$	−33521.4	−1.31764
$866$	26730.6	1.04889
$867$	15131.9	0.592743
$868$	936.665	0.0366273
$869$	−25497.3	−0.995324
$870$	9280.65	0.361659
$871$	−2288.89	−0.0890425
$872$	−1948.44	−0.0756679
$873$	7329.37	0.284148
$874$	−16815.1	−0.650778
$875$	−5627.48	−0.217421
$876$	4884.77	0.188403
$877$	10193.4	0.392481	0.196240	−	0.980556i	$-0.437127\pi$
$877$	10193.4	0.392481	0.196240	+	0.980556i	$0.437127\pi$
$878$	−30716.3	−1.18067
$879$	−22327.4	−0.856750
$880$	7027.84	0.269214
$881$	18041.0	0.689918	0.344959	−	0.938618i	$-0.387893\pi$
$881$	18041.0	0.689918	0.344959	+	0.938618i	$0.387893\pi$
$882$	−5893.86	−0.225007
$883$	−5031.25	−0.191750	−0.0958748	−	0.995393i	$-0.530565\pi$
$883$	−5031.25	−0.191750	−0.0958748	+	0.995393i	$0.530565\pi$
$884$	−3641.66	−0.138555
$885$	−1935.07	−0.0734990
$886$	−13944.4	−0.528749
$887$	40222.6	1.52260	0.761298	−	0.648402i	$-0.224562\pi$
$887$	40222.6	1.52260	0.761298	+	0.648402i	$0.224562\pi$
$888$	4163.95	0.157357
$889$	−3433.30	−0.129527
$890$	31466.6	1.18513
$891$	3254.35	0.122362
$892$	13869.1	0.520596
$893$	−38514.4	−1.44326
$894$	−11654.9	−0.436016
$895$	−47627.2	−1.77877
$896$	504.965	0.0188278
$897$	3348.28	0.124633
$898$	−12422.5	−0.461631
$899$	8398.01	0.311557
$900$	−197.228	−0.00730475
$901$	13073.6	0.483403
$902$	−32630.4	−1.20452
$903$	−4778.08	−0.176085
$904$	−17763.6	−0.653548
$905$	15577.6	0.572173
$906$	2276.40	0.0834751
$907$	−25772.5	−0.943508	−0.471754	−	0.881730i	$-0.656379\pi$
$907$	−25772.5	−0.943508	−0.471754	+	0.881730i	$0.656379\pi$
$908$	−19755.1	−0.722022
$909$	−10729.8	−0.391511
$910$	787.010	0.0286694
$911$	−23859.7	−0.867736	−0.433868	−	0.900976i	$-0.642852\pi$
$911$	−23859.7	−0.867736	−0.433868	+	0.900976i	$0.642852\pi$
$912$	−3299.03	−0.119783
$913$	−18285.9	−0.662844
$914$	600.763	0.0217412
$915$	27771.1	1.00337
$916$	18294.0	0.659881
$917$	−3762.53	−0.135496
$918$	−5388.37	−0.193729
$919$	24580.2	0.882292	0.441146	−	0.897435i	$-0.354572\pi$
$919$	24580.2	0.882292	0.441146	+	0.897435i	$0.354572\pi$
$920$	10698.9	0.383403
$921$	2479.51	0.0887107
$922$	23692.2	0.846270
$923$	−3770.28	−0.134453
$924$	1902.01	0.0677180
$925$	−950.519	−0.0337869
$926$	−33662.2	−1.19461
$927$	−10696.7	−0.378991
$928$	4527.45	0.160152
$929$	−36621.9	−1.29335	−0.646677	−	0.762764i	$-0.723842\pi$
$929$	−36621.9	−1.29335	−0.646677	+	0.762764i	$0.723842\pi$
$930$	3893.56	0.137285
$931$	22504.7	0.792224
$932$	5797.54	0.203761
$933$	−12244.1	−0.429639
$934$	11070.7	0.387844
$935$	−43829.4	−1.53302
$936$	656.914	0.0229401
$937$	−13726.7	−0.478583	−0.239292	−	0.970948i	$-0.576915\pi$
$937$	−13726.7	−0.478583	−0.239292	+	0.970948i	$0.576915\pi$
$938$	−1979.39	−0.0689011
$939$	23214.2	0.806779
$940$	24505.4	0.850294
$941$	−4351.46	−0.150748	−0.0753739	−	0.997155i	$-0.524015\pi$
$941$	−4351.46	−0.150748	−0.0753739	+	0.997155i	$0.524015\pi$
$942$	1386.58	0.0479589
$943$	−49675.0	−1.71542
$944$	−944.000	−0.0325472
$945$	1164.50	0.0400858
$946$	−32440.7	−1.11494
$947$	6162.37	0.211457	0.105729	−	0.994395i	$-0.466282\pi$
$947$	6162.37	0.211457	0.105729	+	0.994395i	$0.466282\pi$
$948$	−7615.47	−0.260906
$949$	3713.97	0.127040
$950$	753.081	0.0257191
$951$	8894.20	0.303275
$952$	−3149.24	−0.107214
$953$	−43691.2	−1.48510	−0.742549	−	0.669792i	$-0.766383\pi$
$953$	−43691.2	−1.48510	−0.742549	+	0.669792i	$0.766383\pi$
$954$	−2358.33	−0.0800354
$955$	22721.3	0.769890
$956$	−16867.4	−0.570638
$957$	17053.1	0.576018
$958$	16291.0	0.549414
$959$	3452.79	0.116263
$960$	2099.06	0.0705695
$961$	−26267.7	−0.881734
$962$	3165.92	0.106105
$963$	−6496.74	−0.217398
$964$	3206.05	0.107116
$965$	948.119	0.0316280
$966$	2895.53	0.0964411
$967$	46203.4	1.53651	0.768253	−	0.640147i	$-0.221126\pi$
$967$	46203.4	1.53651	0.768253	+	0.640147i	$0.221126\pi$
$968$	2265.61	0.0752268
$969$	20574.5	0.682094
$970$	17806.4	0.589412
$971$	−8135.12	−0.268865	−0.134433	−	0.990923i	$-0.542921\pi$
$971$	−8135.12	−0.268865	−0.134433	+	0.990923i	$0.542921\pi$
$972$	972.000	0.0320750
$973$	6794.78	0.223875
$974$	−16242.4	−0.534333
$975$	−149.956	−0.00492557
$976$	13547.8	0.444318
$977$	33349.1	1.09205	0.546024	−	0.837769i	$-0.316141\pi$
$977$	33349.1	1.09205	0.546024	+	0.837769i	$0.316141\pi$
$978$	−6914.62	−0.226079
$979$	57819.8	1.88757
$980$	−14318.9	−0.466736
$981$	−2191.99	−0.0713404
$982$	20410.8	0.663273
$983$	−52603.8	−1.70682	−0.853408	−	0.521244i	$-0.825468\pi$
$983$	−52603.8	−1.70682	−0.853408	+	0.521244i	$0.825468\pi$
$984$	−9745.96	−0.315742
$985$	27232.8	0.880924
$986$	−28235.7	−0.911974
$987$	6632.10	0.213883
$988$	−2508.31	−0.0807691
$989$	−49386.2	−1.58786
$990$	7906.32	0.253817
$991$	12810.6	0.410639	0.205319	−	0.978695i	$-0.434177\pi$
$991$	12810.6	0.410639	0.205319	+	0.978695i	$0.434177\pi$
$992$	1899.43	0.0607932
$993$	13670.9	0.436892
$994$	−3260.47	−0.104040
$995$	19099.9	0.608550
$996$	−5461.60	−0.173752
$997$	55780.7	1.77191	0.885954	−	0.463774i	$-0.153505\pi$
$997$	55780.7	1.77191	0.885954	+	0.463774i	$0.153505\pi$
$998$	−33018.2	−1.04727
$999$	4684.44	0.148358

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.4.a.i.1.5	✓	6
3.2	odd	2		1062.4.a.s.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.4.a.i.1.5	✓	6	1.1	even	1	trivial
1062.4.a.s.1.2		6	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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	354.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +10.9326 q^{5} +6.00000 q^{6} +3.94504 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +10.9326 q^{5} +6.00000 q^{6} +3.94504 q^{7} +8.00000 q^{8} +9.00000 q^{9} +21.8652 q^{10} +40.1771 q^{11} +12.0000 q^{12} +9.12380 q^{13} +7.89008 q^{14} +32.7978 q^{15} +16.0000 q^{16} -99.7847 q^{17} +18.0000 q^{18} -68.7298 q^{19} +43.7303 q^{20} +11.8351 q^{21} +80.3543 q^{22} +122.328 q^{23} +24.0000 q^{24} -5.47856 q^{25} +18.2476 q^{26} +27.0000 q^{27} +15.7802 q^{28} +141.483 q^{29} +65.5955 q^{30} +59.3571 q^{31} +32.0000 q^{32} +120.531 q^{33} -199.569 q^{34} +43.1295 q^{35} +36.0000 q^{36} +173.498 q^{37} -137.460 q^{38} +27.3714 q^{39} +87.4607 q^{40} -406.082 q^{41} +23.6703 q^{42} -403.720 q^{43} +160.709 q^{44} +98.3933 q^{45} +244.655 q^{46} +560.374 q^{47} +48.0000 q^{48} -327.437 q^{49} -10.9571 q^{50} -299.354 q^{51} +36.4952 q^{52} -131.018 q^{53} +54.0000 q^{54} +439.240 q^{55} +31.5603 q^{56} -206.189 q^{57} +282.966 q^{58} -59.0000 q^{59} +131.191 q^{60} +846.737 q^{61} +118.714 q^{62} +35.5054 q^{63} +64.0000 q^{64} +99.7467 q^{65} +241.063 q^{66} -250.870 q^{67} -399.139 q^{68} +366.983 q^{69} +86.2590 q^{70} -413.236 q^{71} +72.0000 q^{72} +407.064 q^{73} +346.996 q^{74} -16.4357 q^{75} -274.919 q^{76} +158.500 q^{77} +54.7428 q^{78} -634.622 q^{79} +174.921 q^{80} +81.0000 q^{81} -812.163 q^{82} -455.133 q^{83} +47.3405 q^{84} -1090.90 q^{85} -807.441 q^{86} +424.449 q^{87} +321.417 q^{88} +1439.12 q^{89} +196.787 q^{90} +35.9938 q^{91} +489.311 q^{92} +178.071 q^{93} +1120.75 q^{94} -751.394 q^{95} +96.0000 q^{96} +814.374 q^{97} -654.873 q^{98} +361.594 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 12 q^{2} + 18 q^{3} + 24 q^{4} + 20 q^{5} + 36 q^{6} + 26 q^{7} + 48 q^{8} + 54 q^{9}+O(q^{10}) \) 6 * q + 12 * q^2 + 18 * q^3 + 24 * q^4 + 20 * q^5 + 36 * q^6 + 26 * q^7 + 48 * q^8 + 54 * q^9	\( 6 q + 12 q^{2} + 18 q^{3} + 24 q^{4} + 20 q^{5} + 36 q^{6} + 26 q^{7} + 48 q^{8} + 54 q^{9} + 40 q^{10} + 63 q^{11} + 72 q^{12} + 93 q^{13} + 52 q^{14} + 60 q^{15} + 96 q^{16} + 230 q^{17} + 108 q^{18} + 89 q^{19} + 80 q^{20} + 78 q^{21} + 126 q^{22} + 81 q^{23} + 144 q^{24} + 304 q^{25} + 186 q^{26} + 162 q^{27} + 104 q^{28} + 131 q^{29} + 120 q^{30} + 51 q^{31} + 192 q^{32} + 189 q^{33} + 460 q^{34} - 87 q^{35} + 216 q^{36} - 16 q^{37} + 178 q^{38} + 279 q^{39} + 160 q^{40} + 176 q^{41} + 156 q^{42} + 375 q^{43} + 252 q^{44} + 180 q^{45} + 162 q^{46} - 255 q^{47} + 288 q^{48} - 290 q^{49} + 608 q^{50} + 690 q^{51} + 372 q^{52} - 256 q^{53} + 324 q^{54} - 184 q^{55} + 208 q^{56} + 267 q^{57} + 262 q^{58} - 354 q^{59} + 240 q^{60} + 39 q^{61} + 102 q^{62} + 234 q^{63} + 384 q^{64} - 954 q^{65} + 378 q^{66} + 86 q^{67} + 920 q^{68} + 243 q^{69} - 174 q^{70} - 895 q^{71} + 432 q^{72} + 155 q^{73} - 32 q^{74} + 912 q^{75} + 356 q^{76} - 498 q^{77} + 558 q^{78} - 565 q^{79} + 320 q^{80} + 486 q^{81} + 352 q^{82} + 140 q^{83} + 312 q^{84} + q^{85} + 750 q^{86} + 393 q^{87} + 504 q^{88} - 1769 q^{89} + 360 q^{90} - 422 q^{91} + 324 q^{92} + 153 q^{93} - 510 q^{94} - 2209 q^{95} + 576 q^{96} + 48 q^{97} - 580 q^{98} + 567 q^{99}+O(q^{100}) \) 6 * q + 12 * q^2 + 18 * q^3 + 24 * q^4 + 20 * q^5 + 36 * q^6 + 26 * q^7 + 48 * q^8 + 54 * q^9 + 40 * q^10 + 63 * q^11 + 72 * q^12 + 93 * q^13 + 52 * q^14 + 60 * q^15 + 96 * q^16 + 230 * q^17 + 108 * q^18 + 89 * q^19 + 80 * q^20 + 78 * q^21 + 126 * q^22 + 81 * q^23 + 144 * q^24 + 304 * q^25 + 186 * q^26 + 162 * q^27 + 104 * q^28 + 131 * q^29 + 120 * q^30 + 51 * q^31 + 192 * q^32 + 189 * q^33 + 460 * q^34 - 87 * q^35 + 216 * q^36 - 16 * q^37 + 178 * q^38 + 279 * q^39 + 160 * q^40 + 176 * q^41 + 156 * q^42 + 375 * q^43 + 252 * q^44 + 180 * q^45 + 162 * q^46 - 255 * q^47 + 288 * q^48 - 290 * q^49 + 608 * q^50 + 690 * q^51 + 372 * q^52 - 256 * q^53 + 324 * q^54 - 184 * q^55 + 208 * q^56 + 267 * q^57 + 262 * q^58 - 354 * q^59 + 240 * q^60 + 39 * q^61 + 102 * q^62 + 234 * q^63 + 384 * q^64 - 954 * q^65 + 378 * q^66 + 86 * q^67 + 920 * q^68 + 243 * q^69 - 174 * q^70 - 895 * q^71 + 432 * q^72 + 155 * q^73 - 32 * q^74 + 912 * q^75 + 356 * q^76 - 498 * q^77 + 558 * q^78 - 565 * q^79 + 320 * q^80 + 486 * q^81 + 352 * q^82 + 140 * q^83 + 312 * q^84 + q^85 + 750 * q^86 + 393 * q^87 + 504 * q^88 - 1769 * q^89 + 360 * q^90 - 422 * q^91 + 324 * q^92 + 153 * q^93 - 510 * q^94 - 2209 * q^95 + 576 * q^96 + 48 * q^97 - 580 * q^98 + 567 * q^99

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