LMFDB - Embedded newform 722.4.a.o.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,4,Mod(1,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("722.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	722.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:	$42.5993790241$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.6719782761.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 75x^{4} + 135x^{3} + 1857x^{2} - 1425x - 14797 $ x^6 - 3x^5 - 75x^4 + 135x^3 + 1857x^2 - 1425*x - 14797
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 19 $
Twist minimal:	no (minimal twist has level 38)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-4.13096$ of defining polynomial
Character	$\chi$	$=$	722.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{2} +5.78366 q^{3} +4.00000 q^{4} +6.19832 q^{5} -11.5673 q^{6} +11.2225 q^{7} -8.00000 q^{8} +6.45071 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} +5.78366 q^{3} +4.00000 q^{4} +6.19832 q^{5} -11.5673 q^{6} +11.2225 q^{7} -8.00000 q^{8} +6.45071 q^{9} -12.3966 q^{10} -45.1020 q^{11} +23.1346 q^{12} -22.6540 q^{13} -22.4449 q^{14} +35.8490 q^{15} +16.0000 q^{16} -31.0319 q^{17} -12.9014 q^{18} +24.7933 q^{20} +64.9070 q^{21} +90.2039 q^{22} -144.310 q^{23} -46.2693 q^{24} -86.5808 q^{25} +45.3081 q^{26} -118.850 q^{27} +44.8899 q^{28} -24.2340 q^{29} -71.6980 q^{30} -303.653 q^{31} -32.0000 q^{32} -260.854 q^{33} +62.0638 q^{34} +69.5605 q^{35} +25.8029 q^{36} +121.394 q^{37} -131.023 q^{39} -49.5866 q^{40} +103.668 q^{41} -129.814 q^{42} -444.382 q^{43} -180.408 q^{44} +39.9836 q^{45} +288.619 q^{46} +481.971 q^{47} +92.5385 q^{48} -217.056 q^{49} +173.162 q^{50} -179.478 q^{51} -90.6162 q^{52} +441.119 q^{53} +237.700 q^{54} -279.557 q^{55} -89.7798 q^{56} +48.4679 q^{58} -242.460 q^{59} +143.396 q^{60} -531.909 q^{61} +607.307 q^{62} +72.3930 q^{63} +64.0000 q^{64} -140.417 q^{65} +521.709 q^{66} +727.654 q^{67} -124.128 q^{68} -834.637 q^{69} -139.121 q^{70} +225.441 q^{71} -51.6057 q^{72} -351.323 q^{73} -242.787 q^{74} -500.754 q^{75} -506.156 q^{77} +262.047 q^{78} +602.658 q^{79} +99.1732 q^{80} -861.558 q^{81} -207.336 q^{82} +248.852 q^{83} +259.628 q^{84} -192.346 q^{85} +888.764 q^{86} -140.161 q^{87} +360.816 q^{88} +1663.61 q^{89} -79.9672 q^{90} -254.234 q^{91} -577.238 q^{92} -1756.23 q^{93} -963.943 q^{94} -185.077 q^{96} +846.301 q^{97} +434.112 q^{98} -290.940 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 12 q^{2} + 9 q^{3} + 24 q^{4} - 27 q^{5} - 18 q^{6} - 21 q^{7} - 48 q^{8} + 33 q^{9}+O(q^{10}) $ 6 * q - 12 * q^2 + 9 * q^3 + 24 * q^4 - 27 * q^5 - 18 * q^6 - 21 * q^7 - 48 * q^8 + 33 * q^9	\( 6 q - 12 q^{2} + 9 q^{3} + 24 q^{4} - 27 q^{5} - 18 q^{6} - 21 q^{7} - 48 q^{8} + 33 q^{9} + 54 q^{10} + 9 q^{11} + 36 q^{12} + 24 q^{13} + 42 q^{14} + 96 q^{16} - 102 q^{17} - 66 q^{18} - 108 q^{20} + 51 q^{21} - 18 q^{22} - 264 q^{23} - 72 q^{24} + 177 q^{25} - 48 q^{26} + 189 q^{27} - 84 q^{28} + 483 q^{29} + 72 q^{31} - 192 q^{32} + 387 q^{33} + 204 q^{34} + 135 q^{35} + 132 q^{36} - 558 q^{37} - 624 q^{39} + 216 q^{40} + 396 q^{41} - 102 q^{42} - 2064 q^{43} + 36 q^{44} - 1296 q^{45} + 528 q^{46} + 858 q^{47} + 144 q^{48} - 1413 q^{49} - 354 q^{50} - 1272 q^{51} + 96 q^{52} + 762 q^{53} - 378 q^{54} - 1107 q^{55} + 168 q^{56} - 966 q^{58} + 393 q^{59} - 627 q^{61} - 144 q^{62} - 84 q^{63} + 384 q^{64} + 495 q^{65} - 774 q^{66} + 2028 q^{67} - 408 q^{68} - 237 q^{69} - 270 q^{70} + 1284 q^{71} - 264 q^{72} - 2688 q^{73} + 1116 q^{74} + 927 q^{75} - 708 q^{77} + 1248 q^{78} + 969 q^{79} - 432 q^{80} - 1398 q^{81} - 792 q^{82} - 927 q^{83} + 204 q^{84} + 396 q^{85} + 4128 q^{86} - 2892 q^{87} - 72 q^{88} - 1257 q^{89} + 2592 q^{90} - 1323 q^{91} - 1056 q^{92} - 1368 q^{93} - 1716 q^{94} - 288 q^{96} - 2403 q^{97} + 2826 q^{98} + 567 q^{99}+O(q^{100}) \) 6 * q - 12 * q^2 + 9 * q^3 + 24 * q^4 - 27 * q^5 - 18 * q^6 - 21 * q^7 - 48 * q^8 + 33 * q^9 + 54 * q^10 + 9 * q^11 + 36 * q^12 + 24 * q^13 + 42 * q^14 + 96 * q^16 - 102 * q^17 - 66 * q^18 - 108 * q^20 + 51 * q^21 - 18 * q^22 - 264 * q^23 - 72 * q^24 + 177 * q^25 - 48 * q^26 + 189 * q^27 - 84 * q^28 + 483 * q^29 + 72 * q^31 - 192 * q^32 + 387 * q^33 + 204 * q^34 + 135 * q^35 + 132 * q^36 - 558 * q^37 - 624 * q^39 + 216 * q^40 + 396 * q^41 - 102 * q^42 - 2064 * q^43 + 36 * q^44 - 1296 * q^45 + 528 * q^46 + 858 * q^47 + 144 * q^48 - 1413 * q^49 - 354 * q^50 - 1272 * q^51 + 96 * q^52 + 762 * q^53 - 378 * q^54 - 1107 * q^55 + 168 * q^56 - 966 * q^58 + 393 * q^59 - 627 * q^61 - 144 * q^62 - 84 * q^63 + 384 * q^64 + 495 * q^65 - 774 * q^66 + 2028 * q^67 - 408 * q^68 - 237 * q^69 - 270 * q^70 + 1284 * q^71 - 264 * q^72 - 2688 * q^73 + 1116 * q^74 + 927 * q^75 - 708 * q^77 + 1248 * q^78 + 969 * q^79 - 432 * q^80 - 1398 * q^81 - 792 * q^82 - 927 * q^83 + 204 * q^84 + 396 * q^85 + 4128 * q^86 - 2892 * q^87 - 72 * q^88 - 1257 * q^89 + 2592 * q^90 - 1323 * q^91 - 1056 * q^92 - 1368 * q^93 - 1716 * q^94 - 288 * q^96 - 2403 * q^97 + 2826 * 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
$3$	5.78366	1.11307	0.556533	−	0.830826i	$-0.312131\pi$
$3$	5.78366	1.11307	0.556533	+	0.830826i	$0.312131\pi$
$4$	4.00000	0.500000
$5$	6.19832	0.554395	0.277197	−	0.960813i	$-0.410594\pi$
$5$	6.19832	0.554395	0.277197	+	0.960813i	$0.410594\pi$
$6$	−11.5673	−0.787056
$7$	11.2225	0.605957	0.302978	−	0.952997i	$-0.402019\pi$
$7$	11.2225	0.605957	0.302978	+	0.952997i	$0.402019\pi$
$8$	−8.00000	−0.353553
$9$	6.45071	0.238915
$10$	−12.3966	−0.392016
$11$	−45.1020	−1.23625	−0.618125	−	0.786080i	$-0.712108\pi$
$11$	−45.1020	−1.23625	−0.618125	+	0.786080i	$0.712108\pi$
$12$	23.1346	0.556533
$13$	−22.6540	−0.483315	−0.241658	−	0.970362i	$-0.577691\pi$
$13$	−22.6540	−0.483315	−0.241658	+	0.970362i	$0.577691\pi$
$14$	−22.4449	−0.428476
$15$	35.8490	0.617078
$16$	16.0000	0.250000
$17$	−31.0319	−0.442726	−0.221363	−	0.975191i	$-0.571051\pi$
$17$	−31.0319	−0.442726	−0.221363	+	0.975191i	$0.571051\pi$
$18$	−12.9014	−0.168939
$19$	0	0
$19$	0	0
$20$	24.7933	0.277197
$21$	64.9070	0.674470
$22$	90.2039	0.874161
$23$	−144.310	−1.30829	−0.654144	−	0.756370i	$-0.726971\pi$
$23$	−144.310	−1.30829	−0.654144	+	0.756370i	$0.726971\pi$
$24$	−46.2693	−0.393528
$25$	−86.5808	−0.692646
$26$	45.3081	0.341756
$27$	−118.850	−0.847137
$28$	44.8899	0.302978
$29$	−24.2340	−0.155177	−0.0775885	−	0.996985i	$-0.524722\pi$
$29$	−24.2340	−0.155177	−0.0775885	+	0.996985i	$0.524722\pi$
$30$	−71.6980	−0.436340
$31$	−303.653	−1.75928	−0.879641	−	0.475637i	$-0.842217\pi$
$31$	−303.653	−1.75928	−0.879641	+	0.475637i	$0.842217\pi$
$32$	−32.0000	−0.176777
$33$	−260.854	−1.37603
$34$	62.0638	0.313055
$35$	69.5605	0.335939
$36$	25.8029	0.119458
$37$	121.394	0.539378	0.269689	−	0.962947i	$-0.413079\pi$
$37$	121.394	0.539378	0.269689	+	0.962947i	$0.413079\pi$
$38$	0	0
$39$	−131.023	−0.537962
$40$	−49.5866	−0.196008
$41$	103.668	0.394883	0.197442	−	0.980315i	$-0.436737\pi$
$41$	103.668	0.394883	0.197442	+	0.980315i	$0.436737\pi$
$42$	−129.814	−0.476922
$43$	−444.382	−1.57599	−0.787996	−	0.615681i	$-0.788881\pi$
$43$	−444.382	−1.57599	−0.787996	+	0.615681i	$0.788881\pi$
$44$	−180.408	−0.618125
$45$	39.9836	0.132453
$46$	288.619	0.925099
$47$	481.971	1.49580	0.747902	−	0.663809i	$-0.231061\pi$
$47$	481.971	1.49580	0.747902	+	0.663809i	$0.231061\pi$
$48$	92.5385	0.278266
$49$	−217.056	−0.632817
$50$	173.162	0.489775
$51$	−179.478	−0.492783
$52$	−90.6162	−0.241658
$53$	441.119	1.14325	0.571626	−	0.820514i	$-0.306313\pi$
$53$	441.119	1.14325	0.571626	+	0.820514i	$0.306313\pi$
$54$	237.700	0.599017
$55$	−279.557	−0.685371
$56$	−89.7798	−0.214238
$57$	0	0
$58$	48.4679	0.109727
$59$	−242.460	−0.535011	−0.267506	−	0.963556i	$-0.586199\pi$
$59$	−242.460	−0.535011	−0.267506	+	0.963556i	$0.586199\pi$
$60$	143.396	0.308539
$61$	−531.909	−1.11646	−0.558229	−	0.829687i	$-0.688519\pi$
$61$	−531.909	−1.11646	−0.558229	+	0.829687i	$0.688519\pi$
$62$	607.307	1.24400
$63$	72.3930	0.144772
$64$	64.0000	0.125000
$65$	−140.417	−0.267948
$66$	521.709	0.972999
$67$	727.654	1.32682	0.663411	−	0.748255i	$-0.269108\pi$
$67$	727.654	1.32682	0.663411	+	0.748255i	$0.269108\pi$
$68$	−124.128	−0.221363
$69$	−834.637	−1.45621
$70$	−139.121	−0.237545
$71$	225.441	0.376831	0.188415	−	0.982089i	$-0.439665\pi$
$71$	225.441	0.376831	0.188415	+	0.982089i	$0.439665\pi$
$72$	−51.6057	−0.0844693
$73$	−351.323	−0.563278	−0.281639	−	0.959520i	$-0.590878\pi$
$73$	−351.323	−0.563278	−0.281639	+	0.959520i	$0.590878\pi$
$74$	−242.787	−0.381398
$75$	−500.754	−0.770961
$76$	0	0
$77$	−506.156	−0.749114
$78$	262.047	0.380396
$79$	602.658	0.858283	0.429141	−	0.903237i	$-0.358816\pi$
$79$	602.658	0.858283	0.429141	+	0.903237i	$0.358816\pi$
$80$	99.1732	0.138599
$81$	−861.558	−1.18183
$82$	−207.336	−0.279225
$83$	248.852	0.329098	0.164549	−	0.986369i	$-0.447383\pi$
$83$	248.852	0.329098	0.164549	+	0.986369i	$0.447383\pi$
$84$	259.628	0.337235
$85$	−192.346	−0.245445
$86$	888.764	1.11439
$87$	−140.161	−0.172722
$88$	360.816	0.437080
$89$	1663.61	1.98138	0.990690	−	0.136139i	$-0.0434693\pi$
$89$	1663.61	1.98138	0.990690	+	0.136139i	$0.0434693\pi$
$90$	−79.9672	−0.0936587
$91$	−254.234	−0.292868
$92$	−577.238	−0.654144
$93$	−1756.23	−1.95820
$94$	−963.943	−1.05769
$95$	0	0
$96$	−185.077	−0.196764
$97$	846.301	0.885864	0.442932	−	0.896555i	$-0.353938\pi$
$97$	846.301	0.885864	0.442932	+	0.896555i	$0.353938\pi$
$98$	434.112	0.447469
$99$	−290.940	−0.295359
$100$	−346.323	−0.346323
$101$	1316.51	1.29701	0.648505	−	0.761210i	$-0.275394\pi$
$101$	1316.51	1.29701	0.648505	+	0.761210i	$0.275394\pi$
$102$	358.956	0.348450
$103$	−958.346	−0.916783	−0.458392	−	0.888750i	$-0.651574\pi$
$103$	−958.346	−0.916783	−0.458392	+	0.888750i	$0.651574\pi$
$104$	181.232	0.170878
$105$	402.314	0.373922
$106$	−882.238	−0.808401
$107$	−529.514	−0.478412	−0.239206	−	0.970969i	$-0.576887\pi$
$107$	−529.514	−0.478412	−0.239206	+	0.970969i	$0.576887\pi$
$108$	−475.400	−0.423569
$109$	1719.93	1.51137	0.755685	−	0.654935i	$-0.227304\pi$
$109$	1719.93	1.51137	0.755685	+	0.654935i	$0.227304\pi$
$110$	559.113	0.484630
$111$	702.099	0.600363
$112$	179.560	0.151489
$113$	−1735.05	−1.44442	−0.722210	−	0.691674i	$-0.756874\pi$
$113$	−1735.05	−1.44442	−0.722210	+	0.691674i	$0.756874\pi$
$114$	0	0
$115$	−894.477	−0.725308
$116$	−96.9358	−0.0775885
$117$	−146.135	−0.115471
$118$	484.921	0.378310
$119$	−348.255	−0.268273
$120$	−286.792	−0.218170
$121$	703.187	0.528315
$122$	1063.82	0.789455
$123$	599.580	0.439531
$124$	−1214.61	−0.879641
$125$	−1311.45	−0.938394
$126$	−144.786	−0.102369
$127$	1747.13	1.22073	0.610364	−	0.792121i	$-0.291023\pi$
$127$	1747.13	1.22073	0.610364	+	0.792121i	$0.291023\pi$
$128$	−128.000	−0.0883883
$129$	−2570.15	−1.75418
$130$	280.834	0.189468
$131$	−1777.03	−1.18519	−0.592595	−	0.805500i	$-0.701897\pi$
$131$	−1777.03	−1.18519	−0.592595	+	0.805500i	$0.701897\pi$
$132$	−1043.42	−0.688014
$133$	0	0
$134$	−1455.31	−0.938205
$135$	−736.671	−0.469649
$136$	248.255	0.156527
$137$	−617.687	−0.385201	−0.192600	−	0.981277i	$-0.561692\pi$
$137$	−617.687	−0.385201	−0.192600	+	0.981277i	$0.561692\pi$
$138$	1669.27	1.02970
$139$	−1942.20	−1.18515	−0.592573	−	0.805516i	$-0.701888\pi$
$139$	−1942.20	−1.18515	−0.592573	+	0.805516i	$0.701888\pi$
$140$	278.242	0.167970
$141$	2787.56	1.66493
$142$	−450.883	−0.266460
$143$	1021.74	0.597499
$144$	103.211	0.0597288
$145$	−150.210	−0.0860293
$146$	702.647	0.398298
$147$	−1255.38	−0.704366
$148$	485.575	0.269689
$149$	816.104	0.448710	0.224355	−	0.974507i	$-0.427972\pi$
$149$	816.104	0.448710	0.224355	+	0.974507i	$0.427972\pi$
$150$	1001.51	0.545152
$151$	−905.056	−0.487764	−0.243882	−	0.969805i	$-0.578421\pi$
$151$	−905.056	−0.487764	−0.243882	+	0.969805i	$0.578421\pi$
$152$	0	0
$153$	−200.178	−0.105774
$154$	1012.31	0.529704
$155$	−1882.14	−0.975337
$156$	−524.093	−0.268981
$157$	−1399.90	−0.711620	−0.355810	−	0.934558i	$-0.615795\pi$
$157$	−1399.90	−0.711620	−0.355810	+	0.934558i	$0.615795\pi$
$158$	−1205.32	−0.606898
$159$	2551.28	1.27251
$160$	−198.346	−0.0980041
$161$	−1619.51	−0.792766
$162$	1723.12	0.835683
$163$	440.371	0.211611	0.105805	−	0.994387i	$-0.466258\pi$
$163$	440.371	0.211611	0.105805	+	0.994387i	$0.466258\pi$
$164$	414.672	0.197442
$165$	−1616.86	−0.762863
$166$	−497.705	−0.232707
$167$	−778.900	−0.360917	−0.180458	−	0.983583i	$-0.557758\pi$
$167$	−778.900	−0.360917	−0.180458	+	0.983583i	$0.557758\pi$
$168$	−519.256	−0.238461
$169$	−1683.79	−0.766406
$170$	384.692	0.173556
$171$	0	0
$172$	−1777.53	−0.787996
$173$	−3281.31	−1.44204	−0.721021	−	0.692913i	$-0.756327\pi$
$173$	−3281.31	−1.44204	−0.721021	+	0.692913i	$0.756327\pi$
$174$	280.322	0.122133
$175$	−971.651	−0.419714
$176$	−721.631	−0.309063
$177$	−1402.31	−0.595503
$178$	−3327.23	−1.40105
$179$	−1354.70	−0.565669	−0.282834	−	0.959169i	$-0.591275\pi$
$179$	−1354.70	−0.565669	−0.282834	+	0.959169i	$0.591275\pi$
$180$	159.934	0.0662267
$181$	−3399.81	−1.39616	−0.698082	−	0.716018i	$-0.745963\pi$
$181$	−3399.81	−1.39616	−0.698082	+	0.716018i	$0.745963\pi$
$182$	508.469	0.207089
$183$	−3076.38	−1.24269
$184$	1154.48	0.462550
$185$	752.437	0.299028
$186$	3512.46	1.38465
$187$	1399.60	0.547320
$188$	1927.89	0.747902
$189$	−1333.79	−0.513328
$190$	0	0
$191$	4250.41	1.61020	0.805102	−	0.593136i	$-0.202110\pi$
$191$	4250.41	1.61020	0.805102	+	0.593136i	$0.202110\pi$
$192$	370.154	0.139133
$193$	538.743	0.200930	0.100465	−	0.994941i	$-0.467967\pi$
$193$	538.743	0.200930	0.100465	+	0.994941i	$0.467967\pi$
$194$	−1692.60	−0.626401
$195$	−812.124	−0.298243
$196$	−868.224	−0.316408
$197$	−1549.19	−0.560279	−0.280139	−	0.959959i	$-0.590381\pi$
$197$	−1549.19	−0.560279	−0.280139	+	0.959959i	$0.590381\pi$
$198$	581.880	0.208850
$199$	−233.484	−0.0831722	−0.0415861	−	0.999135i	$-0.513241\pi$
$199$	−233.484	−0.0831722	−0.0415861	+	0.999135i	$0.513241\pi$
$200$	692.646	0.244887
$201$	4208.50	1.47684
$202$	−2633.03	−0.917125
$203$	−271.965	−0.0940305
$204$	−717.912	−0.246392
$205$	642.568	0.218921
$206$	1916.69	0.648264
$207$	−930.900	−0.312570
$208$	−362.465	−0.120829
$209$	0	0
$210$	−804.629	−0.264403
$211$	−3710.13	−1.21050	−0.605252	−	0.796034i	$-0.706927\pi$
$211$	−3710.13	−1.21050	−0.605252	+	0.796034i	$0.706927\pi$
$212$	1764.48	0.571626
$213$	1303.88	0.419437
$214$	1059.03	0.338288
$215$	−2754.42	−0.873721
$216$	950.801	0.299508
$217$	−3407.74	−1.06605
$218$	−3439.86	−1.06870
$219$	−2031.93	−0.626965
$220$	−1118.23	−0.342685
$221$	702.998	0.213976
$222$	−1404.20	−0.424521
$223$	441.958	0.132716	0.0663580	−	0.997796i	$-0.478862\pi$
$223$	441.958	0.132716	0.0663580	+	0.997796i	$0.478862\pi$
$224$	−359.119	−0.107119
$225$	−558.508	−0.165484
$226$	3470.09	1.02136
$227$	5132.39	1.50066	0.750328	−	0.661066i	$-0.229896\pi$
$227$	5132.39	1.50066	0.750328	+	0.661066i	$0.229896\pi$
$228$	0	0
$229$	−157.494	−0.0454476	−0.0227238	−	0.999742i	$-0.507234\pi$
$229$	−157.494	−0.0454476	−0.0227238	+	0.999742i	$0.507234\pi$
$230$	1788.95	0.512870
$231$	−2927.43	−0.833813
$232$	193.872	0.0548634
$233$	6129.92	1.72354	0.861769	−	0.507302i	$-0.169357\pi$
$233$	6129.92	1.72354	0.861769	+	0.507302i	$0.169357\pi$
$234$	292.269	0.0816506
$235$	2987.41	0.829266
$236$	−969.842	−0.267506
$237$	3485.57	0.955325
$238$	696.510	0.189698
$239$	−6313.36	−1.70869	−0.854346	−	0.519705i	$-0.826042\pi$
$239$	−6313.36	−1.70869	−0.854346	+	0.519705i	$0.826042\pi$
$240$	573.584	0.154269
$241$	−3175.75	−0.848829	−0.424414	−	0.905468i	$-0.639520\pi$
$241$	−3175.75	−0.848829	−0.424414	+	0.905468i	$0.639520\pi$
$242$	−1406.37	−0.373575
$243$	−1774.00	−0.468323
$244$	−2127.64	−0.558229
$245$	−1345.38	−0.350830
$246$	−1199.16	−0.310795
$247$	0	0
$248$	2429.23	0.622000
$249$	1439.28	0.366307
$250$	2622.89	0.663545
$251$	3923.04	0.986534	0.493267	−	0.869878i	$-0.335803\pi$
$251$	3923.04	0.986534	0.493267	+	0.869878i	$0.335803\pi$
$252$	289.572	0.0723862
$253$	6508.65	1.61737
$254$	−3494.25	−0.863185
$255$	−1112.46	−0.273197
$256$	256.000	0.0625000
$257$	−1250.61	−0.303543	−0.151772	−	0.988416i	$-0.548498\pi$
$257$	−1250.61	−0.303543	−0.151772	+	0.988416i	$0.548498\pi$
$258$	5140.31	1.24039
$259$	1362.34	0.326840
$260$	−561.668	−0.133974
$261$	−156.326	−0.0370742
$262$	3554.06	0.838056
$263$	4838.44	1.13441	0.567207	−	0.823575i	$-0.308024\pi$
$263$	4838.44	1.13441	0.567207	+	0.823575i	$0.308024\pi$
$264$	2086.83	0.486499
$265$	2734.20	0.633813
$266$	0	0
$267$	9621.78	2.20541
$268$	2910.61	0.663411
$269$	2475.34	0.561057	0.280528	−	0.959846i	$-0.409490\pi$
$269$	2475.34	0.561057	0.280528	+	0.959846i	$0.409490\pi$
$270$	1473.34	0.332092
$271$	−987.601	−0.221374	−0.110687	−	0.993855i	$-0.535305\pi$
$271$	−987.601	−0.221374	−0.110687	+	0.993855i	$0.535305\pi$
$272$	−496.511	−0.110682
$273$	−1470.41	−0.325982
$274$	1235.37	0.272378
$275$	3904.96	0.856284
$276$	−3338.55	−0.728105
$277$	3242.87	0.703412	0.351706	−	0.936110i	$-0.385602\pi$
$277$	3242.87	0.703412	0.351706	+	0.936110i	$0.385602\pi$
$278$	3884.40	0.838025
$279$	−1958.78	−0.420320
$280$	−556.484	−0.118772
$281$	−4950.83	−1.05104	−0.525519	−	0.850782i	$-0.676129\pi$
$281$	−4950.83	−1.05104	−0.525519	+	0.850782i	$0.676129\pi$
$282$	−5575.12	−1.17728
$283$	7723.68	1.62235	0.811176	−	0.584803i	$-0.198828\pi$
$283$	7723.68	1.62235	0.811176	+	0.584803i	$0.198828\pi$
$284$	901.766	0.188415
$285$	0	0
$286$	−2043.48	−0.422495
$287$	1163.41	0.239282
$288$	−206.423	−0.0422347
$289$	−3950.02	−0.803994
$290$	300.420	0.0608319
$291$	4894.72	0.986025
$292$	−1405.29	−0.281639
$293$	1320.00	0.263192	0.131596	−	0.991303i	$-0.457990\pi$
$293$	1320.00	0.263192	0.131596	+	0.991303i	$0.457990\pi$
$294$	2510.76	0.498062
$295$	−1502.85	−0.296607
$296$	−971.149	−0.190699
$297$	5360.37	1.04727
$298$	−1632.21	−0.317286
$299$	3269.20	0.632316
$300$	−2003.02	−0.385480
$301$	−4987.07	−0.954982
$302$	1810.11	0.344901
$303$	7614.27	1.44366
$304$	0	0
$305$	−3296.94	−0.618959
$306$	400.356	0.0747936
$307$	−4946.49	−0.919580	−0.459790	−	0.888028i	$-0.652075\pi$
$307$	−4946.49	−0.919580	−0.459790	+	0.888028i	$0.652075\pi$
$308$	−2024.62	−0.374557
$309$	−5542.75	−1.02044
$310$	3764.28	0.689668
$311$	−2632.00	−0.479894	−0.239947	−	0.970786i	$-0.577130\pi$
$311$	−2632.00	−0.479894	−0.239947	+	0.970786i	$0.577130\pi$
$312$	1048.19	0.190198
$313$	−9391.82	−1.69603	−0.848014	−	0.529974i	$-0.822202\pi$
$313$	−9391.82	−1.69603	−0.848014	+	0.529974i	$0.822202\pi$
$314$	2799.80	0.503191
$315$	448.715	0.0802610
$316$	2410.63	0.429141
$317$	3668.88	0.650046	0.325023	−	0.945706i	$-0.394628\pi$
$317$	3668.88	0.650046	0.325023	+	0.945706i	$0.394628\pi$
$318$	−5102.57	−0.899804
$319$	1093.00	0.191838
$320$	396.693	0.0692994
$321$	−3062.53	−0.532504
$322$	3239.02	0.560570
$323$	0	0
$324$	−3446.23	−0.590917
$325$	1961.40	0.334767
$326$	−880.743	−0.149631
$327$	9947.49	1.68225
$328$	−829.344	−0.139612
$329$	5408.91	0.906392
$330$	3233.72	0.539425
$331$	−5244.49	−0.870885	−0.435443	−	0.900217i	$-0.643408\pi$
$331$	−5244.49	−0.870885	−0.435443	+	0.900217i	$0.643408\pi$
$332$	995.410	0.164549
$333$	783.076	0.128866
$334$	1557.80	0.255207
$335$	4510.23	0.735583
$336$	1038.51	0.168617
$337$	4989.44	0.806505	0.403252	−	0.915089i	$-0.367880\pi$
$337$	4989.44	0.806505	0.403252	+	0.915089i	$0.367880\pi$
$338$	3367.59	0.541931
$339$	−10034.9	−1.60773
$340$	−769.383	−0.122723
$341$	13695.4	2.17491
$342$	0	0
$343$	−6285.21	−0.989416
$344$	3555.06	0.557197
$345$	−5173.35	−0.807316
$346$	6562.62	1.01968
$347$	−2913.31	−0.450705	−0.225353	−	0.974277i	$-0.572353\pi$
$347$	−2913.31	−0.450705	−0.225353	+	0.974277i	$0.572353\pi$
$348$	−560.644	−0.0863611
$349$	−2270.75	−0.348282	−0.174141	−	0.984721i	$-0.555715\pi$
$349$	−2270.75	−0.348282	−0.174141	+	0.984721i	$0.555715\pi$
$350$	1943.30	0.296782
$351$	2692.43	0.409435
$352$	1443.26	0.218540
$353$	5027.04	0.757968	0.378984	−	0.925403i	$-0.376274\pi$
$353$	5027.04	0.757968	0.378984	+	0.925403i	$0.376274\pi$
$354$	2804.62	0.421084
$355$	1397.36	0.208913
$356$	6654.46	0.990690
$357$	−2014.19	−0.298605
$358$	2709.39	0.399988
$359$	5541.79	0.814720	0.407360	−	0.913268i	$-0.366449\pi$
$359$	5541.79	0.814720	0.407360	+	0.913268i	$0.366449\pi$
$360$	−319.869	−0.0468294
$361$	0	0
$362$	6799.61	0.987237
$363$	4066.99	0.588049
$364$	−1016.94	−0.146434
$365$	−2177.62	−0.312278
$366$	6152.76	0.878716
$367$	8489.93	1.20755	0.603775	−	0.797155i	$-0.293663\pi$
$367$	8489.93	1.20755	0.603775	+	0.797155i	$0.293663\pi$
$368$	−2308.95	−0.327072
$369$	668.732	0.0943437
$370$	−1504.87	−0.211445
$371$	4950.45	0.692761
$372$	−7024.91	−0.979099
$373$	10969.6	1.52274	0.761372	−	0.648315i	$-0.224526\pi$
$373$	10969.6	1.52274	0.761372	+	0.648315i	$0.224526\pi$
$374$	−2799.20	−0.387014
$375$	−7584.96	−1.04449
$376$	−3855.77	−0.528846
$377$	548.997	0.0749994
$378$	2667.58	0.362978
$379$	−1753.10	−0.237601	−0.118801	−	0.992918i	$-0.537905\pi$
$379$	−1753.10	−0.237601	−0.118801	+	0.992918i	$0.537905\pi$
$380$	0	0
$381$	10104.8	1.35875
$382$	−8500.83	−1.13859
$383$	−9028.40	−1.20452	−0.602258	−	0.798301i	$-0.705732\pi$
$383$	−9028.40	−1.20452	−0.602258	+	0.798301i	$0.705732\pi$
$384$	−740.308	−0.0983820
$385$	−3137.32	−0.415305
$386$	−1077.49	−0.142079
$387$	−2866.58	−0.376528
$388$	3385.20	0.442932
$389$	−3839.88	−0.500488	−0.250244	−	0.968183i	$-0.580511\pi$
$389$	−3839.88	−0.500488	−0.250244	+	0.968183i	$0.580511\pi$
$390$	1624.25	0.210890
$391$	4478.20	0.579213
$392$	1736.45	0.223734
$393$	−10277.7	−1.31920
$394$	3098.37	0.396177
$395$	3735.47	0.475828
$396$	−1163.76	−0.147680
$397$	−4512.67	−0.570489	−0.285245	−	0.958455i	$-0.592075\pi$
$397$	−4512.67	−0.570489	−0.285245	+	0.958455i	$0.592075\pi$
$398$	466.969	0.0588116
$399$	0	0
$400$	−1385.29	−0.173162
$401$	1877.15	0.233766	0.116883	−	0.993146i	$-0.462710\pi$
$401$	1877.15	0.233766	0.116883	+	0.993146i	$0.462710\pi$
$402$	−8417.00	−1.04428
$403$	6878.98	0.850289
$404$	5266.06	0.648505
$405$	−5340.21	−0.655203
$406$	543.930	0.0664896
$407$	−5475.09	−0.666806
$408$	1435.82	0.174225
$409$	−9743.55	−1.17796	−0.588982	−	0.808146i	$-0.700471\pi$
$409$	−9743.55	−1.17796	−0.588982	+	0.808146i	$0.700471\pi$
$410$	−1285.14	−0.154801
$411$	−3572.49	−0.428754
$412$	−3833.39	−0.458392
$413$	−2721.01	−0.324194
$414$	1861.80	0.221020
$415$	1542.47	0.182450
$416$	724.929	0.0854389
$417$	−11233.0	−1.31915
$418$	0	0
$419$	−5602.13	−0.653179	−0.326589	−	0.945166i	$-0.605899\pi$
$419$	−5602.13	−0.653179	−0.326589	+	0.945166i	$0.605899\pi$
$420$	1609.26	0.186961
$421$	12908.4	1.49434	0.747171	−	0.664632i	$-0.231412\pi$
$421$	12908.4	1.49434	0.747171	+	0.664632i	$0.231412\pi$
$422$	7420.27	0.855955
$423$	3109.06	0.357370
$424$	−3528.95	−0.404201
$425$	2686.77	0.306653
$426$	−2607.75	−0.296587
$427$	−5969.33	−0.676525
$428$	−2118.06	−0.239206
$429$	5909.41	0.665055
$430$	5508.85	0.617814
$431$	7961.65	0.889790	0.444895	−	0.895583i	$-0.353241\pi$
$431$	7961.65	0.889790	0.444895	+	0.895583i	$0.353241\pi$
$432$	−1901.60	−0.211784
$433$	10039.4	1.11423	0.557116	−	0.830434i	$-0.311908\pi$
$433$	10039.4	1.11423	0.557116	+	0.830434i	$0.311908\pi$
$434$	6815.49	0.753811
$435$	−868.763	−0.0957563
$436$	6879.72	0.755685
$437$	0	0
$438$	4063.87	0.443331
$439$	−3860.18	−0.419673	−0.209836	−	0.977737i	$-0.567293\pi$
$439$	−3860.18	−0.419673	−0.209836	+	0.977737i	$0.567293\pi$
$440$	2236.45	0.242315
$441$	−1400.17	−0.151190
$442$	−1406.00	−0.151304
$443$	622.267	0.0667377	0.0333689	−	0.999443i	$-0.489376\pi$
$443$	622.267	0.0667377	0.0333689	+	0.999443i	$0.489376\pi$
$444$	2808.40	0.300182
$445$	10311.6	1.09847
$446$	−883.916	−0.0938444
$447$	4720.07	0.499444
$448$	718.238	0.0757446
$449$	−13387.9	−1.40716	−0.703579	−	0.710617i	$-0.748416\pi$
$449$	−13387.9	−1.40716	−0.703579	+	0.710617i	$0.748416\pi$
$450$	1117.02	0.117015
$451$	−4675.63	−0.488175
$452$	−6940.19	−0.722210
$453$	−5234.54	−0.542914
$454$	−10264.8	−1.06112
$455$	−1575.83	−0.162365
$456$	0	0
$457$	4190.76	0.428962	0.214481	−	0.976728i	$-0.431194\pi$
$457$	4190.76	0.428962	0.214481	+	0.976728i	$0.431194\pi$
$458$	314.988	0.0321363
$459$	3688.15	0.375050
$460$	−3577.91	−0.362654
$461$	3160.96	0.319350	0.159675	−	0.987170i	$-0.448955\pi$
$461$	3160.96	0.319350	0.159675	+	0.987170i	$0.448955\pi$
$462$	5854.86	0.589595
$463$	−8081.65	−0.811202	−0.405601	−	0.914050i	$-0.632938\pi$
$463$	−8081.65	−0.811202	−0.405601	+	0.914050i	$0.632938\pi$
$464$	−387.743	−0.0387943
$465$	−10885.7	−1.08561
$466$	−12259.8	−1.21872
$467$	−4341.82	−0.430225	−0.215113	−	0.976589i	$-0.569012\pi$
$467$	−4341.82	−0.430225	−0.215113	+	0.976589i	$0.569012\pi$
$468$	−584.539	−0.0577357
$469$	8166.08	0.803996
$470$	−5974.83	−0.586379
$471$	−8096.56	−0.792080
$472$	1939.68	0.189155
$473$	20042.5	1.94832
$474$	−6971.14	−0.675517
$475$	0	0
$476$	−1393.02	−0.134136
$477$	2845.53	0.273140
$478$	12626.7	1.20823
$479$	−7929.68	−0.756402	−0.378201	−	0.925724i	$-0.623457\pi$
$479$	−7929.68	−0.756402	−0.378201	+	0.925724i	$0.623457\pi$
$480$	−1147.17	−0.109085
$481$	−2750.06	−0.260690
$482$	6351.49	0.600213
$483$	−9366.70	−0.882401
$484$	2812.75	0.264157
$485$	5245.65	0.491119
$486$	3548.01	0.331154
$487$	−18066.3	−1.68103	−0.840515	−	0.541788i	$-0.817748\pi$
$487$	−18066.3	−1.68103	−0.840515	+	0.541788i	$0.817748\pi$
$488$	4255.27	0.394728
$489$	2546.96	0.235537
$490$	2690.77	0.248074
$491$	16813.8	1.54541	0.772707	−	0.634763i	$-0.218902\pi$
$491$	16813.8	1.54541	0.772707	+	0.634763i	$0.218902\pi$
$492$	2398.32	0.219766
$493$	752.026	0.0687009
$494$	0	0
$495$	−1803.34	−0.163746
$496$	−4858.46	−0.439821
$497$	2530.01	0.228343
$498$	−2878.56	−0.259018
$499$	10323.6	0.926151	0.463076	−	0.886319i	$-0.346746\pi$
$499$	10323.6	0.926151	0.463076	+	0.886319i	$0.346746\pi$
$500$	−5245.78	−0.469197
$501$	−4504.89	−0.401724
$502$	−7846.08	−0.697585
$503$	13793.7	1.22272	0.611362	−	0.791351i	$-0.290622\pi$
$503$	13793.7	1.22272	0.611362	+	0.791351i	$0.290622\pi$
$504$	−579.144	−0.0511847
$505$	8160.18	0.719056
$506$	−13017.3	−1.14365
$507$	−9738.49	−0.853060
$508$	6988.51	0.610364
$509$	5016.70	0.436859	0.218430	−	0.975853i	$-0.429907\pi$
$509$	5016.70	0.436859	0.218430	+	0.975853i	$0.429907\pi$
$510$	2224.93	0.193179
$511$	−3942.72	−0.341322
$512$	−512.000	−0.0441942
$513$	0	0
$514$	2501.21	0.214638
$515$	−5940.14	−0.508260
$516$	−10280.6	−0.877091
$517$	−21737.9	−1.84919
$518$	−2724.67	−0.231111
$519$	−18978.0	−1.60509
$520$	1123.34	0.0947338
$521$	5813.15	0.488827	0.244413	−	0.969671i	$-0.421405\pi$
$521$	5813.15	0.488827	0.244413	+	0.969671i	$0.421405\pi$
$522$	312.653	0.0262154
$523$	−18488.9	−1.54582	−0.772911	−	0.634514i	$-0.781200\pi$
$523$	−18488.9	−1.54582	−0.772911	+	0.634514i	$0.781200\pi$
$524$	−7108.13	−0.592595
$525$	−5619.70	−0.467169
$526$	−9676.88	−0.802152
$527$	9422.95	0.778881
$528$	−4173.67	−0.344007
$529$	8658.25	0.711618
$530$	−5468.40	−0.448174
$531$	−1564.04	−0.127822
$532$	0	0
$533$	−2348.50	−0.190853
$534$	−19243.6	−1.55946
$535$	−3282.10	−0.265229
$536$	−5821.23	−0.469102
$537$	−7835.10	−0.629627
$538$	−4950.68	−0.396727
$539$	9789.65	0.782320
$540$	−2946.68	−0.234824
$541$	1026.37	0.0815658	0.0407829	−	0.999168i	$-0.487015\pi$
$541$	1026.37	0.0815658	0.0407829	+	0.999168i	$0.487015\pi$
$542$	1975.20	0.156535
$543$	−19663.3	−1.55402
$544$	993.021	0.0782637
$545$	10660.7	0.837896
$546$	2940.81	0.230504
$547$	−646.489	−0.0505336	−0.0252668	−	0.999681i	$-0.508044\pi$
$547$	−646.489	−0.0505336	−0.0252668	+	0.999681i	$0.508044\pi$
$548$	−2470.75	−0.192600
$549$	−3431.19	−0.266739
$550$	−7809.93	−0.605484
$551$	0	0
$552$	6677.10	0.514848
$553$	6763.32	0.520082
$554$	−6485.74	−0.497388
$555$	4351.84	0.332838
$556$	−7768.81	−0.592573
$557$	−21815.9	−1.65955	−0.829774	−	0.558100i	$-0.811531\pi$
$557$	−21815.9	−1.65955	−0.829774	+	0.558100i	$0.811531\pi$
$558$	3917.56	0.297211
$559$	10067.0	0.761701
$560$	1112.97	0.0839848
$561$	8094.81	0.609204
$562$	9901.66	0.743196
$563$	8004.63	0.599209	0.299605	−	0.954063i	$-0.403145\pi$
$563$	8004.63	0.599209	0.299605	+	0.954063i	$0.403145\pi$
$564$	11150.2	0.832464
$565$	−10754.4	−0.800779
$566$	−15447.4	−1.14718
$567$	−9668.81	−0.716141
$568$	−1803.53	−0.133230
$569$	−23734.5	−1.74869	−0.874344	−	0.485307i	$-0.838708\pi$
$569$	−23734.5	−1.74869	−0.874344	+	0.485307i	$0.838708\pi$
$570$	0	0
$571$	−23049.1	−1.68927	−0.844635	−	0.535342i	$-0.820183\pi$
$571$	−23049.1	−1.68927	−0.844635	+	0.535342i	$0.820183\pi$
$572$	4086.97	0.298749
$573$	24582.9	1.79226
$574$	−2326.82	−0.169198
$575$	12494.4	0.906181
$576$	412.846	0.0298644
$577$	4211.76	0.303878	0.151939	−	0.988390i	$-0.451448\pi$
$577$	4211.76	0.303878	0.151939	+	0.988390i	$0.451448\pi$
$578$	7900.04	0.568509
$579$	3115.91	0.223649
$580$	−600.840	−0.0430147
$581$	2792.74	0.199419
$582$	−9789.43	−0.697225
$583$	−19895.3	−1.41335
$584$	2810.59	0.199149
$585$	−905.790	−0.0640168
$586$	−2640.00	−0.186105
$587$	−5783.74	−0.406679	−0.203339	−	0.979108i	$-0.565179\pi$
$587$	−5783.74	−0.406679	−0.203339	+	0.979108i	$0.565179\pi$
$588$	−5021.51	−0.352183
$589$	0	0
$590$	3005.70	0.209733
$591$	−8959.97	−0.623627
$592$	1942.30	0.134845
$593$	4633.12	0.320842	0.160421	−	0.987049i	$-0.448715\pi$
$593$	4633.12	0.320842	0.160421	+	0.987049i	$0.448715\pi$
$594$	−10720.7	−0.740534
$595$	−2158.60	−0.148729
$596$	3264.42	0.224355
$597$	−1350.39	−0.0925762
$598$	−6538.39	−0.447115
$599$	14215.3	0.969653	0.484827	−	0.874610i	$-0.338883\pi$
$599$	14215.3	0.969653	0.484827	+	0.874610i	$0.338883\pi$
$600$	4006.03	0.272576
$601$	3846.80	0.261089	0.130544	−	0.991442i	$-0.458327\pi$
$601$	3846.80	0.261089	0.130544	+	0.991442i	$0.458327\pi$
$602$	9974.13	0.675275
$603$	4693.89	0.316998
$604$	−3620.22	−0.243882
$605$	4358.58	0.292895
$606$	−15228.5	−1.02082
$607$	−15984.6	−1.06886	−0.534428	−	0.845214i	$-0.679473\pi$
$607$	−15984.6	−1.06886	−0.534428	+	0.845214i	$0.679473\pi$
$608$	0	0
$609$	−1572.95	−0.104662
$610$	6593.89	0.437670
$611$	−10918.6	−0.722945
$612$	−800.712	−0.0528870
$613$	11540.6	0.760394	0.380197	−	0.924905i	$-0.375856\pi$
$613$	11540.6	0.760394	0.380197	+	0.924905i	$0.375856\pi$
$614$	9892.98	0.650241
$615$	3716.39	0.243674
$616$	4049.24	0.264852
$617$	18127.4	1.18279	0.591394	−	0.806383i	$-0.298578\pi$
$617$	18127.4	1.18279	0.591394	+	0.806383i	$0.298578\pi$
$618$	11085.5	0.721560
$619$	−21146.2	−1.37308	−0.686542	−	0.727090i	$-0.740872\pi$
$619$	−21146.2	−1.37308	−0.686542	+	0.727090i	$0.740872\pi$
$620$	−7528.57	−0.487669
$621$	17151.2	1.10830
$622$	5264.00	0.339337
$623$	18669.9	1.20063
$624$	−2096.37	−0.134490
$625$	2693.83	0.172405
$626$	18783.6	1.19927
$627$	0	0
$628$	−5599.61	−0.355810
$629$	−3767.08	−0.238797
$630$	−897.430	−0.0567531
$631$	−5656.94	−0.356893	−0.178446	−	0.983950i	$-0.557107\pi$
$631$	−5656.94	−0.356893	−0.178446	+	0.983950i	$0.557107\pi$
$632$	−4821.27	−0.303449
$633$	−21458.2	−1.34737
$634$	−7337.75	−0.459652
$635$	10829.3	0.676765
$636$	10205.1	0.636257
$637$	4917.20	0.305850
$638$	−2186.00	−0.135650
$639$	1454.26	0.0900306
$640$	−793.385	−0.0490020
$641$	−1494.58	−0.0920939	−0.0460469	−	0.998939i	$-0.514662\pi$
$641$	−1494.58	−0.0920939	−0.0460469	+	0.998939i	$0.514662\pi$
$642$	6125.06	0.376537
$643$	−26752.6	−1.64078	−0.820389	−	0.571806i	$-0.806243\pi$
$643$	−26752.6	−1.64078	−0.820389	+	0.571806i	$0.806243\pi$
$644$	−6478.04	−0.396383
$645$	−15930.6	−0.972509
$646$	0	0
$647$	−13915.0	−0.845527	−0.422763	−	0.906240i	$-0.638940\pi$
$647$	−13915.0	−0.845527	−0.422763	+	0.906240i	$0.638940\pi$
$648$	6892.46	0.417842
$649$	10935.4	0.661408
$650$	−3922.81	−0.236716
$651$	−19709.2	−1.18658
$652$	1761.49	0.105805
$653$	−13472.5	−0.807383	−0.403692	−	0.914895i	$-0.632273\pi$
$653$	−13472.5	−0.807383	−0.403692	+	0.914895i	$0.632273\pi$
$654$	−19895.0	−1.18953
$655$	−11014.6	−0.657064
$656$	1658.69	0.0987208
$657$	−2266.29	−0.134576
$658$	−10817.8	−0.640916
$659$	10423.0	0.616119	0.308060	−	0.951367i	$-0.400320\pi$
$659$	10423.0	0.616119	0.308060	+	0.951367i	$0.400320\pi$
$660$	−6467.44	−0.381431
$661$	−4530.89	−0.266613	−0.133307	−	0.991075i	$-0.542559\pi$
$661$	−4530.89	−0.266613	−0.133307	+	0.991075i	$0.542559\pi$
$662$	10489.0	0.615809
$663$	4065.90	0.238170
$664$	−1990.82	−0.116354
$665$	0	0
$666$	−1566.15	−0.0911218
$667$	3497.19	0.203016
$668$	−3115.60	−0.180458
$669$	2556.13	0.147722
$670$	−9020.47	−0.520136
$671$	23990.1	1.38022
$672$	−2077.02	−0.119231
$673$	20324.7	1.16413	0.582064	−	0.813143i	$-0.302245\pi$
$673$	20324.7	1.16413	0.582064	+	0.813143i	$0.302245\pi$
$674$	−9978.88	−0.570285
$675$	10290.1	0.586767
$676$	−6735.18	−0.383203
$677$	12363.0	0.701846	0.350923	−	0.936404i	$-0.385868\pi$
$677$	12363.0	0.701846	0.350923	+	0.936404i	$0.385868\pi$
$678$	20069.8	1.13684
$679$	9497.59	0.536795
$680$	1538.77	0.0867779
$681$	29684.0	1.67033
$682$	−27390.7	−1.53790
$683$	−12962.3	−0.726189	−0.363095	−	0.931752i	$-0.618280\pi$
$683$	−12962.3	−0.726189	−0.363095	+	0.931752i	$0.618280\pi$
$684$	0	0
$685$	−3828.62	−0.213553
$686$	12570.4	0.699623
$687$	−910.892	−0.0505862
$688$	−7110.11	−0.393998
$689$	−9993.13	−0.552551
$690$	10346.7	0.570858
$691$	24256.9	1.33542	0.667710	−	0.744422i	$-0.267275\pi$
$691$	24256.9	1.33542	0.667710	+	0.744422i	$0.267275\pi$
$692$	−13125.2	−0.721021
$693$	−3265.06	−0.178975
$694$	5826.62	0.318697
$695$	−12038.4	−0.657039
$696$	1121.29	0.0610665
$697$	−3217.02	−0.174825
$698$	4541.50	0.246272
$699$	35453.3	1.91841
$700$	−3886.60	−0.209857
$701$	−17999.5	−0.969800	−0.484900	−	0.874570i	$-0.661144\pi$
$701$	−17999.5	−0.969800	−0.484900	+	0.874570i	$0.661144\pi$
$702$	−5384.87	−0.289514
$703$	0	0
$704$	−2886.53	−0.154531
$705$	17278.2	0.923027
$706$	−10054.1	−0.535964
$707$	14774.6	0.785932
$708$	−5609.23	−0.297751
$709$	31485.1	1.66777	0.833884	−	0.551940i	$-0.186112\pi$
$709$	31485.1	1.66777	0.833884	+	0.551940i	$0.186112\pi$
$710$	−2794.72	−0.147724
$711$	3887.58	0.205057
$712$	−13308.9	−0.700523
$713$	43820.1	2.30165
$714$	4028.38	0.211146
$715$	6333.08	0.331250
$716$	−5418.78	−0.282834
$717$	−36514.3	−1.90189
$718$	−11083.6	−0.576094
$719$	6816.34	0.353556	0.176778	−	0.984251i	$-0.443433\pi$
$719$	6816.34	0.353556	0.176778	+	0.984251i	$0.443433\pi$
$720$	639.738	0.0331134
$721$	−10755.0	−0.555531
$722$	0	0
$723$	−18367.4	−0.944802
$724$	−13599.2	−0.698082
$725$	2098.20	0.107483
$726$	−8133.99	−0.415813
$727$	30735.7	1.56798	0.783991	−	0.620773i	$-0.213181\pi$
$727$	30735.7	1.56798	0.783991	+	0.620773i	$0.213181\pi$
$728$	2033.88	0.103545
$729$	13001.8	0.660561
$730$	4355.23	0.220814
$731$	13790.0	0.697733
$732$	−12305.5	−0.621346
$733$	−15839.4	−0.798147	−0.399073	−	0.916919i	$-0.630668\pi$
$733$	−15839.4	−0.798147	−0.399073	+	0.916919i	$0.630668\pi$
$734$	−16979.9	−0.853867
$735$	−7781.24	−0.390497
$736$	4617.91	0.231275
$737$	−32818.6	−1.64028
$738$	−1337.46	−0.0667111
$739$	−26798.4	−1.33396	−0.666978	−	0.745077i	$-0.732413\pi$
$739$	−26798.4	−1.33396	−0.666978	+	0.745077i	$0.732413\pi$
$740$	3009.75	0.149514
$741$	0	0
$742$	−9900.90	−0.489856
$743$	32212.1	1.59051	0.795255	−	0.606276i	$-0.207337\pi$
$743$	32212.1	1.59051	0.795255	+	0.606276i	$0.207337\pi$
$744$	14049.8	0.692327
$745$	5058.48	0.248763
$746$	−21939.2	−1.07674
$747$	1605.28	0.0786265
$748$	5598.40	0.273660
$749$	−5942.46	−0.289897
$750$	15169.9	0.738569
$751$	−31780.6	−1.54420	−0.772098	−	0.635504i	$-0.780792\pi$
$751$	−31780.6	−1.54420	−0.772098	+	0.635504i	$0.780792\pi$
$752$	7711.54	0.373951
$753$	22689.5	1.09808
$754$	−1097.99	−0.0530326
$755$	−5609.83	−0.270414
$756$	−5335.17	−0.256664
$757$	−36512.1	−1.75304	−0.876522	−	0.481362i	$-0.840142\pi$
$757$	−36512.1	−1.75304	−0.876522	+	0.481362i	$0.840142\pi$
$758$	3506.21	0.168010
$759$	37643.8	1.80024
$760$	0	0
$761$	22879.6	1.08986	0.544931	−	0.838481i	$-0.316556\pi$
$761$	22879.6	1.08986	0.544931	+	0.838481i	$0.316556\pi$
$762$	−20209.6	−0.960782
$763$	19301.9	0.915825
$764$	17001.7	0.805102
$765$	−1240.77	−0.0586406
$766$	18056.8	0.851722
$767$	5492.71	0.258579
$768$	1480.62	0.0695666
$769$	31256.1	1.46570	0.732851	−	0.680390i	$-0.238189\pi$
$769$	31256.1	1.46570	0.732851	+	0.680390i	$0.238189\pi$
$770$	6274.63	0.293665
$771$	−7233.08	−0.337864
$772$	2154.97	0.100465
$773$	865.830	0.0402868	0.0201434	−	0.999797i	$-0.493588\pi$
$773$	865.830	0.0402868	0.0201434	+	0.999797i	$0.493588\pi$
$774$	5733.16	0.266246
$775$	26290.6	1.21856
$776$	−6770.41	−0.313200
$777$	7879.29	0.363794
$778$	7679.76	0.353898
$779$	0	0
$780$	−3248.50	−0.149122
$781$	−10167.9	−0.465857
$782$	−8956.41	−0.409566
$783$	2880.21	0.131456
$784$	−3472.90	−0.158204
$785$	−8677.05	−0.394519
$786$	20555.5	0.932812
$787$	19285.1	0.873492	0.436746	−	0.899585i	$-0.356131\pi$
$787$	19285.1	0.873492	0.436746	+	0.899585i	$0.356131\pi$
$788$	−6196.74	−0.280139
$789$	27983.9	1.26268
$790$	−7470.94	−0.336461
$791$	−19471.5	−0.875256
$792$	2327.52	0.104425
$793$	12049.9	0.539602
$794$	9025.33	0.403397
$795$	15813.7	0.705476
$796$	−933.938	−0.0415861
$797$	−5666.00	−0.251819	−0.125910	−	0.992042i	$-0.540185\pi$
$797$	−5666.00	−0.251819	−0.125910	+	0.992042i	$0.540185\pi$
$798$	0	0
$799$	−14956.5	−0.662231
$800$	2770.59	0.122444
$801$	10731.5	0.473382
$802$	−3754.29	−0.165298
$803$	15845.4	0.696352
$804$	16834.0	0.738420
$805$	−10038.2	−0.439505
$806$	−13758.0	−0.601245
$807$	14316.5	0.624493
$808$	−10532.1	−0.458563
$809$	33219.1	1.44366	0.721829	−	0.692071i	$-0.243302\pi$
$809$	33219.1	1.44366	0.721829	+	0.692071i	$0.243302\pi$
$810$	10680.4	0.463299
$811$	−36696.8	−1.58890	−0.794451	−	0.607329i	$-0.792241\pi$
$811$	−36696.8	−1.58890	−0.794451	+	0.607329i	$0.792241\pi$
$812$	−1087.86	−0.0470153
$813$	−5711.95	−0.246404
$814$	10950.2	0.471503
$815$	2729.56	0.117316
$816$	−2871.65	−0.123196
$817$	0	0
$818$	19487.1	0.832947
$819$	−1639.99	−0.0699707
$820$	2570.27	0.109461
$821$	−27751.9	−1.17972	−0.589859	−	0.807506i	$-0.700817\pi$
$821$	−27751.9	−1.17972	−0.589859	+	0.807506i	$0.700817\pi$
$822$	7144.98	0.303175
$823$	−39401.7	−1.66884	−0.834420	−	0.551128i	$-0.814197\pi$
$823$	−39401.7	−1.66884	−0.834420	+	0.551128i	$0.814197\pi$
$824$	7666.77	0.324132
$825$	22585.0	0.953101
$826$	5442.01	0.229239
$827$	4732.17	0.198977	0.0994883	−	0.995039i	$-0.468279\pi$
$827$	4732.17	0.198977	0.0994883	+	0.995039i	$0.468279\pi$
$828$	−3723.60	−0.156285
$829$	30108.8	1.26142	0.630712	−	0.776017i	$-0.282763\pi$
$829$	30108.8	1.26142	0.630712	+	0.776017i	$0.282763\pi$
$830$	−3084.94	−0.129012
$831$	18755.7	0.782944
$832$	−1449.86	−0.0604144
$833$	6735.67	0.280164
$834$	22466.1	0.932777
$835$	−4827.87	−0.200090
$836$	0	0
$837$	36089.2	1.49035
$838$	11204.3	0.461867
$839$	−1431.07	−0.0588866	−0.0294433	−	0.999566i	$-0.509373\pi$
$839$	−1431.07	−0.0588866	−0.0294433	+	0.999566i	$0.509373\pi$
$840$	−3218.51	−0.132202
$841$	−23801.7	−0.975920
$842$	−25816.8	−1.05666
$843$	−28633.9	−1.16987
$844$	−14840.5	−0.605252
$845$	−10436.7	−0.424892
$846$	−6218.12	−0.252699
$847$	7891.50	0.320136
$848$	7057.91	0.285813
$849$	44671.2	1.80578
$850$	−5373.54	−0.216836
$851$	−17518.3	−0.705662
$852$	5215.51	0.209719
$853$	25783.5	1.03495	0.517475	−	0.855699i	$-0.326872\pi$
$853$	25783.5	1.03495	0.517475	+	0.855699i	$0.326872\pi$
$854$	11938.7	0.478376
$855$	0	0
$856$	4236.11	0.169144
$857$	12567.8	0.500941	0.250470	−	0.968124i	$-0.419415\pi$
$857$	12567.8	0.500941	0.250470	+	0.968124i	$0.419415\pi$
$858$	−11818.8	−0.470265
$859$	−24956.0	−0.991254	−0.495627	−	0.868535i	$-0.665062\pi$
$859$	−24956.0	−0.991254	−0.495627	+	0.868535i	$0.665062\pi$
$860$	−11017.7	−0.436861
$861$	6728.77	0.266337
$862$	−15923.3	−0.629176
$863$	−24082.5	−0.949916	−0.474958	−	0.880008i	$-0.657537\pi$
$863$	−24082.5	−0.949916	−0.474958	+	0.880008i	$0.657537\pi$
$864$	3803.20	0.149754
$865$	−20338.6	−0.799461
$866$	−20078.8	−0.787881
$867$	−22845.6	−0.894898
$868$	−13631.0	−0.533025
$869$	−27181.1	−1.06105
$870$	1737.53	0.0677099
$871$	−16484.3	−0.641273
$872$	−13759.4	−0.534350
$873$	5459.24	0.211647
$874$	0	0
$875$	−14717.7	−0.568626
$876$	−8127.74	−0.313483
$877$	−4449.06	−0.171305	−0.0856523	−	0.996325i	$-0.527297\pi$
$877$	−4449.06	−0.171305	−0.0856523	+	0.996325i	$0.527297\pi$
$878$	7720.36	0.296753
$879$	7634.43	0.292950
$880$	−4472.90	−0.171343
$881$	−25016.3	−0.956664	−0.478332	−	0.878179i	$-0.658758\pi$
$881$	−25016.3	−0.956664	−0.478332	+	0.878179i	$0.658758\pi$
$882$	2800.33	0.106907
$883$	−11244.7	−0.428555	−0.214278	−	0.976773i	$-0.568740\pi$
$883$	−11244.7	−0.428555	−0.214278	+	0.976773i	$0.568740\pi$
$884$	2811.99	0.106988
$885$	−8691.96	−0.330144
$886$	−1244.53	−0.0471907
$887$	−31794.9	−1.20357	−0.601787	−	0.798657i	$-0.705544\pi$
$887$	−31794.9	−1.20357	−0.601787	+	0.798657i	$0.705544\pi$
$888$	−5616.80	−0.212261
$889$	19607.1	0.739708
$890$	−20623.2	−0.776733
$891$	38857.9	1.46104
$892$	1767.83	0.0663580
$893$	0	0
$894$	−9440.14	−0.353160
$895$	−8396.84	−0.313604
$896$	−1436.48	−0.0535595
$897$	18907.9	0.703809
$898$	26775.8	0.995011
$899$	7358.73	0.273000
$900$	−2234.03	−0.0827419
$901$	−13688.8	−0.506148
$902$	9351.26	0.345192
$903$	−28843.5	−1.06296
$904$	13880.4	0.510680
$905$	−21073.1	−0.774026
$906$	10469.1	0.383898
$907$	29117.2	1.06595	0.532976	−	0.846130i	$-0.321073\pi$
$907$	29117.2	1.06595	0.532976	+	0.846130i	$0.321073\pi$
$908$	20529.6	0.750328
$909$	8492.46	0.309876
$910$	3151.65	0.114809
$911$	28129.5	1.02302	0.511510	−	0.859277i	$-0.329086\pi$
$911$	28129.5	1.02302	0.511510	+	0.859277i	$0.329086\pi$
$912$	0	0
$913$	−11223.7	−0.406847
$914$	−8381.52	−0.303322
$915$	−19068.4	−0.688942
$916$	−629.977	−0.0227238
$917$	−19942.7	−0.718174
$918$	−7376.29	−0.265200
$919$	−6300.00	−0.226135	−0.113067	−	0.993587i	$-0.536068\pi$
$919$	−6300.00	−0.226135	−0.113067	+	0.993587i	$0.536068\pi$
$920$	7155.82	0.256435
$921$	−28608.8	−1.02355
$922$	−6321.91	−0.225815
$923$	−5107.16	−0.182128
$924$	−11709.7	−0.416907
$925$	−10510.4	−0.373598
$926$	16163.3	0.573606
$927$	−6182.02	−0.219034
$928$	775.487	0.0274317
$929$	50683.0	1.78994	0.894970	−	0.446126i	$-0.147197\pi$
$929$	50683.0	1.78994	0.894970	+	0.446126i	$0.147197\pi$
$930$	21771.3	0.767645
$931$	0	0
$932$	24519.7	0.861769
$933$	−15222.6	−0.534154
$934$	8683.63	0.304215
$935$	8675.17	0.303432
$936$	1169.08	0.0408253
$937$	−5891.95	−0.205423	−0.102712	−	0.994711i	$-0.532752\pi$
$937$	−5891.95	−0.205423	−0.102712	+	0.994711i	$0.532752\pi$
$938$	−16332.2	−0.568511
$939$	−54319.1	−1.88779
$940$	11949.7	0.414633
$941$	16345.3	0.566249	0.283125	−	0.959083i	$-0.408629\pi$
$941$	16345.3	0.566249	0.283125	+	0.959083i	$0.408629\pi$
$942$	16193.1	0.560085
$943$	−14960.3	−0.516621
$944$	−3879.37	−0.133753
$945$	−8267.27	−0.284587
$946$	−40085.0	−1.37767
$947$	−47136.0	−1.61744	−0.808720	−	0.588194i	$-0.799839\pi$
$947$	−47136.0	−1.61744	−0.808720	+	0.588194i	$0.799839\pi$
$948$	13942.3	0.477663
$949$	7958.89	0.272241
$950$	0	0
$951$	21219.5	0.723544
$952$	2786.04	0.0948488
$953$	28882.9	0.981752	0.490876	−	0.871229i	$-0.336677\pi$
$953$	28882.9	0.981752	0.490876	+	0.871229i	$0.336677\pi$
$954$	−5691.07	−0.193139
$955$	26345.4	0.892689
$956$	−25253.4	−0.854346
$957$	6321.53	0.213528
$958$	15859.4	0.534857
$959$	−6931.97	−0.233415
$960$	2294.34	0.0771347
$961$	62414.4	2.09508
$962$	5500.11	0.184336
$963$	−3415.74	−0.114300
$964$	−12703.0	−0.424414
$965$	3339.30	0.111395
$966$	18733.4	0.623951
$967$	−28982.8	−0.963830	−0.481915	−	0.876218i	$-0.660059\pi$
$967$	−28982.8	−0.963830	−0.481915	+	0.876218i	$0.660059\pi$
$968$	−5625.50	−0.186787
$969$	0	0
$970$	−10491.3	−0.347273
$971$	−48710.6	−1.60988	−0.804942	−	0.593354i	$-0.797803\pi$
$971$	−48710.6	−1.60988	−0.804942	+	0.593354i	$0.797803\pi$
$972$	−7096.01	−0.234161
$973$	−21796.3	−0.718148
$974$	36132.6	1.18867
$975$	11344.1	0.372617
$976$	−8510.54	−0.279115
$977$	−8805.79	−0.288354	−0.144177	−	0.989552i	$-0.546054\pi$
$977$	−8805.79	−0.288354	−0.144177	+	0.989552i	$0.546054\pi$
$978$	−5093.92	−0.166550
$979$	−75032.3	−2.44948
$980$	−5381.53	−0.175415
$981$	11094.8	0.361090
$982$	−33627.7	−1.09277
$983$	−46354.3	−1.50404	−0.752020	−	0.659140i	$-0.770921\pi$
$983$	−46354.3	−1.50404	−0.752020	+	0.659140i	$0.770921\pi$
$984$	−4796.64	−0.155398
$985$	−9602.36	−0.310616
$986$	−1504.05	−0.0485789
$987$	31283.3	1.00887
$988$	0	0
$989$	64128.6	2.06185
$990$	3606.68	0.115786
$991$	−29195.3	−0.935842	−0.467921	−	0.883770i	$-0.654997\pi$
$991$	−29195.3	−0.935842	−0.467921	+	0.883770i	$0.654997\pi$
$992$	9716.91	0.311000
$993$	−30332.3	−0.969352
$994$	−5060.02	−0.161463
$995$	−1447.21	−0.0461103
$996$	5757.11	0.183154
$997$	−35662.1	−1.13283	−0.566415	−	0.824120i	$-0.691670\pi$
$997$	−35662.1	−1.13283	−0.566415	+	0.824120i	$0.691670\pi$
$998$	−20647.3	−0.654888
$999$	−14427.6	−0.456927

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.4.a.o.1.5		6
19.3	odd	18		38.4.e.a.9.1	✓	12
19.13	odd	18		38.4.e.a.17.1	yes	12
19.18	odd	2		722.4.a.p.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.4.e.a.9.1	✓	12	19.3	odd	18
38.4.e.a.17.1	yes	12	19.13	odd	18
722.4.a.o.1.5		6	1.1	even	1	trivial
722.4.a.p.1.2		6	19.18	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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	722.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +5.78366 q^{3} +4.00000 q^{4} +6.19832 q^{5} -11.5673 q^{6} +11.2225 q^{7} -8.00000 q^{8} +6.45071 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} +5.78366 q^{3} +4.00000 q^{4} +6.19832 q^{5} -11.5673 q^{6} +11.2225 q^{7} -8.00000 q^{8} +6.45071 q^{9} -12.3966 q^{10} -45.1020 q^{11} +23.1346 q^{12} -22.6540 q^{13} -22.4449 q^{14} +35.8490 q^{15} +16.0000 q^{16} -31.0319 q^{17} -12.9014 q^{18} +24.7933 q^{20} +64.9070 q^{21} +90.2039 q^{22} -144.310 q^{23} -46.2693 q^{24} -86.5808 q^{25} +45.3081 q^{26} -118.850 q^{27} +44.8899 q^{28} -24.2340 q^{29} -71.6980 q^{30} -303.653 q^{31} -32.0000 q^{32} -260.854 q^{33} +62.0638 q^{34} +69.5605 q^{35} +25.8029 q^{36} +121.394 q^{37} -131.023 q^{39} -49.5866 q^{40} +103.668 q^{41} -129.814 q^{42} -444.382 q^{43} -180.408 q^{44} +39.9836 q^{45} +288.619 q^{46} +481.971 q^{47} +92.5385 q^{48} -217.056 q^{49} +173.162 q^{50} -179.478 q^{51} -90.6162 q^{52} +441.119 q^{53} +237.700 q^{54} -279.557 q^{55} -89.7798 q^{56} +48.4679 q^{58} -242.460 q^{59} +143.396 q^{60} -531.909 q^{61} +607.307 q^{62} +72.3930 q^{63} +64.0000 q^{64} -140.417 q^{65} +521.709 q^{66} +727.654 q^{67} -124.128 q^{68} -834.637 q^{69} -139.121 q^{70} +225.441 q^{71} -51.6057 q^{72} -351.323 q^{73} -242.787 q^{74} -500.754 q^{75} -506.156 q^{77} +262.047 q^{78} +602.658 q^{79} +99.1732 q^{80} -861.558 q^{81} -207.336 q^{82} +248.852 q^{83} +259.628 q^{84} -192.346 q^{85} +888.764 q^{86} -140.161 q^{87} +360.816 q^{88} +1663.61 q^{89} -79.9672 q^{90} -254.234 q^{91} -577.238 q^{92} -1756.23 q^{93} -963.943 q^{94} -185.077 q^{96} +846.301 q^{97} +434.112 q^{98} -290.940 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 12 q^{2} + 9 q^{3} + 24 q^{4} - 27 q^{5} - 18 q^{6} - 21 q^{7} - 48 q^{8} + 33 q^{9}+O(q^{10}) \) 6 * q - 12 * q^2 + 9 * q^3 + 24 * q^4 - 27 * q^5 - 18 * q^6 - 21 * q^7 - 48 * q^8 + 33 * q^9	\( 6 q - 12 q^{2} + 9 q^{3} + 24 q^{4} - 27 q^{5} - 18 q^{6} - 21 q^{7} - 48 q^{8} + 33 q^{9} + 54 q^{10} + 9 q^{11} + 36 q^{12} + 24 q^{13} + 42 q^{14} + 96 q^{16} - 102 q^{17} - 66 q^{18} - 108 q^{20} + 51 q^{21} - 18 q^{22} - 264 q^{23} - 72 q^{24} + 177 q^{25} - 48 q^{26} + 189 q^{27} - 84 q^{28} + 483 q^{29} + 72 q^{31} - 192 q^{32} + 387 q^{33} + 204 q^{34} + 135 q^{35} + 132 q^{36} - 558 q^{37} - 624 q^{39} + 216 q^{40} + 396 q^{41} - 102 q^{42} - 2064 q^{43} + 36 q^{44} - 1296 q^{45} + 528 q^{46} + 858 q^{47} + 144 q^{48} - 1413 q^{49} - 354 q^{50} - 1272 q^{51} + 96 q^{52} + 762 q^{53} - 378 q^{54} - 1107 q^{55} + 168 q^{56} - 966 q^{58} + 393 q^{59} - 627 q^{61} - 144 q^{62} - 84 q^{63} + 384 q^{64} + 495 q^{65} - 774 q^{66} + 2028 q^{67} - 408 q^{68} - 237 q^{69} - 270 q^{70} + 1284 q^{71} - 264 q^{72} - 2688 q^{73} + 1116 q^{74} + 927 q^{75} - 708 q^{77} + 1248 q^{78} + 969 q^{79} - 432 q^{80} - 1398 q^{81} - 792 q^{82} - 927 q^{83} + 204 q^{84} + 396 q^{85} + 4128 q^{86} - 2892 q^{87} - 72 q^{88} - 1257 q^{89} + 2592 q^{90} - 1323 q^{91} - 1056 q^{92} - 1368 q^{93} - 1716 q^{94} - 288 q^{96} - 2403 q^{97} + 2826 q^{98} + 567 q^{99}+O(q^{100}) \) 6 * q - 12 * q^2 + 9 * q^3 + 24 * q^4 - 27 * q^5 - 18 * q^6 - 21 * q^7 - 48 * q^8 + 33 * q^9 + 54 * q^10 + 9 * q^11 + 36 * q^12 + 24 * q^13 + 42 * q^14 + 96 * q^16 - 102 * q^17 - 66 * q^18 - 108 * q^20 + 51 * q^21 - 18 * q^22 - 264 * q^23 - 72 * q^24 + 177 * q^25 - 48 * q^26 + 189 * q^27 - 84 * q^28 + 483 * q^29 + 72 * q^31 - 192 * q^32 + 387 * q^33 + 204 * q^34 + 135 * q^35 + 132 * q^36 - 558 * q^37 - 624 * q^39 + 216 * q^40 + 396 * q^41 - 102 * q^42 - 2064 * q^43 + 36 * q^44 - 1296 * q^45 + 528 * q^46 + 858 * q^47 + 144 * q^48 - 1413 * q^49 - 354 * q^50 - 1272 * q^51 + 96 * q^52 + 762 * q^53 - 378 * q^54 - 1107 * q^55 + 168 * q^56 - 966 * q^58 + 393 * q^59 - 627 * q^61 - 144 * q^62 - 84 * q^63 + 384 * q^64 + 495 * q^65 - 774 * q^66 + 2028 * q^67 - 408 * q^68 - 237 * q^69 - 270 * q^70 + 1284 * q^71 - 264 * q^72 - 2688 * q^73 + 1116 * q^74 + 927 * q^75 - 708 * q^77 + 1248 * q^78 + 969 * q^79 - 432 * q^80 - 1398 * q^81 - 792 * q^82 - 927 * q^83 + 204 * q^84 + 396 * q^85 + 4128 * q^86 - 2892 * q^87 - 72 * q^88 - 1257 * q^89 + 2592 * q^90 - 1323 * q^91 - 1056 * q^92 - 1368 * q^93 - 1716 * q^94 - 288 * q^96 - 2403 * q^97 + 2826 * q^98 + 567 * q^99

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