LMFDB - Embedded newform 354.4.a.b.1.2

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:	$2$
Coefficient field:	$\Q(\sqrt{51}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 51 $ x^2 - 51
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$7.14143$ 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)

$f(q)$	$=$	$q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +20.1414 q^{5} -6.00000 q^{6} -28.5657 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +20.1414 q^{5} -6.00000 q^{6} -28.5657 q^{7} -8.00000 q^{8} +9.00000 q^{9} -40.2829 q^{10} +54.5657 q^{11} +12.0000 q^{12} -16.9900 q^{13} +57.1314 q^{14} +60.4243 q^{15} +16.0000 q^{16} +10.8486 q^{17} -18.0000 q^{18} +34.0000 q^{19} +80.5657 q^{20} -85.6971 q^{21} -109.131 q^{22} +100.849 q^{23} -24.0000 q^{24} +280.677 q^{25} +33.9800 q^{26} +27.0000 q^{27} -114.263 q^{28} +110.727 q^{29} -120.849 q^{30} +0.404283 q^{31} -32.0000 q^{32} +163.697 q^{33} -21.6971 q^{34} -575.354 q^{35} +36.0000 q^{36} -368.990 q^{37} -68.0000 q^{38} -50.9700 q^{39} -161.131 q^{40} -436.546 q^{41} +171.394 q^{42} +326.869 q^{43} +218.263 q^{44} +181.273 q^{45} -201.697 q^{46} +293.374 q^{47} +48.0000 q^{48} +473.000 q^{49} -561.354 q^{50} +32.5457 q^{51} -67.9600 q^{52} +109.273 q^{53} -54.0000 q^{54} +1099.03 q^{55} +228.526 q^{56} +102.000 q^{57} -221.454 q^{58} +59.0000 q^{59} +241.697 q^{60} +460.747 q^{61} -0.808567 q^{62} -257.091 q^{63} +64.0000 q^{64} -342.203 q^{65} -327.394 q^{66} +630.020 q^{67} +43.3943 q^{68} +302.546 q^{69} +1150.71 q^{70} +987.961 q^{71} -72.0000 q^{72} -629.274 q^{73} +737.980 q^{74} +842.031 q^{75} +136.000 q^{76} -1558.71 q^{77} +101.940 q^{78} +715.234 q^{79} +322.263 q^{80} +81.0000 q^{81} +873.091 q^{82} -497.577 q^{83} -342.789 q^{84} +218.506 q^{85} -653.737 q^{86} +332.181 q^{87} -436.526 q^{88} +396.729 q^{89} -362.546 q^{90} +485.331 q^{91} +403.394 q^{92} +1.21285 q^{93} -586.749 q^{94} +684.809 q^{95} -96.0000 q^{96} -1472.39 q^{97} -946.000 q^{98} +491.091 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{2} + 6 q^{3} + 8 q^{4} + 26 q^{5} - 12 q^{6} - 16 q^{8} + 18 q^{9}+O(q^{10}) $ 2 * q - 4 * q^2 + 6 * q^3 + 8 * q^4 + 26 * q^5 - 12 * q^6 - 16 * q^8 + 18 * q^9	\( 2 q - 4 q^{2} + 6 q^{3} + 8 q^{4} + 26 q^{5} - 12 q^{6} - 16 q^{8} + 18 q^{9} - 52 q^{10} + 52 q^{11} + 24 q^{12} + 66 q^{13} + 78 q^{15} + 32 q^{16} - 64 q^{17} - 36 q^{18} + 68 q^{19} + 104 q^{20} - 104 q^{22} + 116 q^{23} - 48 q^{24} + 190 q^{25} - 132 q^{26} + 54 q^{27} + 350 q^{29} - 156 q^{30} - 242 q^{31} - 64 q^{32} + 156 q^{33} + 128 q^{34} - 408 q^{35} + 72 q^{36} - 638 q^{37} - 136 q^{38} + 198 q^{39} - 208 q^{40} - 616 q^{41} + 768 q^{43} + 208 q^{44} + 234 q^{45} - 232 q^{46} + 44 q^{47} + 96 q^{48} + 946 q^{49} - 380 q^{50} - 192 q^{51} + 264 q^{52} + 90 q^{53} - 108 q^{54} + 1084 q^{55} + 204 q^{57} - 700 q^{58} + 118 q^{59} + 312 q^{60} + 1250 q^{61} + 484 q^{62} + 128 q^{64} + 144 q^{65} - 312 q^{66} + 1460 q^{67} - 256 q^{68} + 348 q^{69} + 816 q^{70} + 162 q^{71} - 144 q^{72} + 284 q^{73} + 1276 q^{74} + 570 q^{75} + 272 q^{76} - 1632 q^{77} - 396 q^{78} - 512 q^{79} + 416 q^{80} + 162 q^{81} + 1232 q^{82} + 376 q^{83} - 220 q^{85} - 1536 q^{86} + 1050 q^{87} - 416 q^{88} - 492 q^{89} - 468 q^{90} + 2856 q^{91} + 464 q^{92} - 726 q^{93} - 88 q^{94} + 884 q^{95} - 192 q^{96} - 1088 q^{97} - 1892 q^{98} + 468 q^{99}+O(q^{100}) \) 2 * q - 4 * q^2 + 6 * q^3 + 8 * q^4 + 26 * q^5 - 12 * q^6 - 16 * q^8 + 18 * q^9 - 52 * q^10 + 52 * q^11 + 24 * q^12 + 66 * q^13 + 78 * q^15 + 32 * q^16 - 64 * q^17 - 36 * q^18 + 68 * q^19 + 104 * q^20 - 104 * q^22 + 116 * q^23 - 48 * q^24 + 190 * q^25 - 132 * q^26 + 54 * q^27 + 350 * q^29 - 156 * q^30 - 242 * q^31 - 64 * q^32 + 156 * q^33 + 128 * q^34 - 408 * q^35 + 72 * q^36 - 638 * q^37 - 136 * q^38 + 198 * q^39 - 208 * q^40 - 616 * q^41 + 768 * q^43 + 208 * q^44 + 234 * q^45 - 232 * q^46 + 44 * q^47 + 96 * q^48 + 946 * q^49 - 380 * q^50 - 192 * q^51 + 264 * q^52 + 90 * q^53 - 108 * q^54 + 1084 * q^55 + 204 * q^57 - 700 * q^58 + 118 * q^59 + 312 * q^60 + 1250 * q^61 + 484 * q^62 + 128 * q^64 + 144 * q^65 - 312 * q^66 + 1460 * q^67 - 256 * q^68 + 348 * q^69 + 816 * q^70 + 162 * q^71 - 144 * q^72 + 284 * q^73 + 1276 * q^74 + 570 * q^75 + 272 * q^76 - 1632 * q^77 - 396 * q^78 - 512 * q^79 + 416 * q^80 + 162 * q^81 + 1232 * q^82 + 376 * q^83 - 220 * q^85 - 1536 * q^86 + 1050 * q^87 - 416 * q^88 - 492 * q^89 - 468 * q^90 + 2856 * q^91 + 464 * q^92 - 726 * q^93 - 88 * q^94 + 884 * q^95 - 192 * q^96 - 1088 * q^97 - 1892 * q^98 + 468 * 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
$5$	20.1414	1.80150	0.900752	−	0.434334i	$-0.143016\pi$
$5$	20.1414	1.80150	0.900752	+	0.434334i	$0.143016\pi$
$6$	−6.00000	−0.408248
$7$	−28.5657	−1.54240	−0.771202	−	0.636591i	$-0.780344\pi$
$7$	−28.5657	−1.54240	−0.771202	+	0.636591i	$0.780344\pi$
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	−40.2829	−1.27386
$11$	54.5657	1.49565	0.747826	−	0.663894i	$-0.231098\pi$
$11$	54.5657	1.49565	0.747826	+	0.663894i	$0.231098\pi$
$12$	12.0000	0.288675
$13$	−16.9900	−0.362475	−0.181238	−	0.983439i	$-0.558010\pi$
$13$	−16.9900	−0.362475	−0.181238	+	0.983439i	$0.558010\pi$
$14$	57.1314	1.09064
$15$	60.4243	1.04010
$16$	16.0000	0.250000
$17$	10.8486	0.154774	0.0773872	−	0.997001i	$-0.475342\pi$
$17$	10.8486	0.154774	0.0773872	+	0.997001i	$0.475342\pi$
$18$	−18.0000	−0.235702
$19$	34.0000	0.410533	0.205267	−	0.978706i	$-0.434194\pi$
$19$	34.0000	0.410533	0.205267	+	0.978706i	$0.434194\pi$
$20$	80.5657	0.900752
$21$	−85.6971	−0.890507
$22$	−109.131	−1.05759
$23$	100.849	0.914277	0.457139	−	0.889395i	$-0.348874\pi$
$23$	100.849	0.914277	0.457139	+	0.889395i	$0.348874\pi$
$24$	−24.0000	−0.204124
$25$	280.677	2.24542
$26$	33.9800	0.256309
$27$	27.0000	0.192450
$28$	−114.263	−0.771202
$29$	110.727	0.709018	0.354509	−	0.935053i	$-0.384648\pi$
$29$	110.727	0.709018	0.354509	+	0.935053i	$0.384648\pi$
$30$	−120.849	−0.735461
$31$	0.404283	0.00234230	0.00117115	−	0.999999i	$-0.499627\pi$
$31$	0.404283	0.00234230	0.00117115	+	0.999999i	$0.499627\pi$
$32$	−32.0000	−0.176777
$33$	163.697	0.863516
$34$	−21.6971	−0.109442
$35$	−575.354	−2.77865
$36$	36.0000	0.166667
$37$	−368.990	−1.63950	−0.819751	−	0.572720i	$-0.805888\pi$
$37$	−368.990	−1.63950	−0.819751	+	0.572720i	$0.805888\pi$
$38$	−68.0000	−0.290291
$39$	−50.9700	−0.209275
$40$	−161.131	−0.636928
$41$	−436.546	−1.66285	−0.831427	−	0.555635i	$-0.812475\pi$
$41$	−436.546	−1.66285	−0.831427	+	0.555635i	$0.812475\pi$
$42$	171.394	0.629684
$43$	326.869	1.15923	0.579616	−	0.814890i	$-0.303202\pi$
$43$	326.869	1.15923	0.579616	+	0.814890i	$0.303202\pi$
$44$	218.263	0.747826
$45$	181.273	0.600501
$46$	−201.697	−0.646492
$47$	293.374	0.910490	0.455245	−	0.890366i	$-0.349552\pi$
$47$	293.374	0.910490	0.455245	+	0.890366i	$0.349552\pi$
$48$	48.0000	0.144338
$49$	473.000	1.37901
$50$	−561.354	−1.58775
$51$	32.5457	0.0893590
$52$	−67.9600	−0.181238
$53$	109.273	0.283203	0.141602	−	0.989924i	$-0.454775\pi$
$53$	109.273	0.283203	0.141602	+	0.989924i	$0.454775\pi$
$54$	−54.0000	−0.136083
$55$	1099.03	2.69442
$56$	228.526	0.545322
$57$	102.000	0.237022
$58$	−221.454	−0.501351
$59$	59.0000	0.130189
$59$	59.0000	0.130189
$60$	241.697	0.520049
$61$	460.747	0.967092	0.483546	−	0.875319i	$-0.339349\pi$
$61$	460.747	0.967092	0.483546	+	0.875319i	$0.339349\pi$
$62$	−0.808567	−0.00165626
$63$	−257.091	−0.514135
$64$	64.0000	0.125000
$65$	−342.203	−0.653001
$66$	−327.394	−0.610598
$67$	630.020	1.14879	0.574397	−	0.818577i	$-0.305237\pi$
$67$	630.020	1.14879	0.574397	+	0.818577i	$0.305237\pi$
$68$	43.3943	0.0773872
$69$	302.546	0.527858
$70$	1150.71	1.96480
$71$	987.961	1.65140	0.825700	−	0.564109i	$-0.190780\pi$
$71$	987.961	1.65140	0.825700	+	0.564109i	$0.190780\pi$
$72$	−72.0000	−0.117851
$73$	−629.274	−1.00892	−0.504459	−	0.863436i	$-0.668308\pi$
$73$	−629.274	−1.00892	−0.504459	+	0.863436i	$0.668308\pi$
$74$	737.980	1.15930
$75$	842.031	1.29639
$76$	136.000	0.205267
$77$	−1558.71	−2.30690
$78$	101.940	0.147980
$79$	715.234	1.01861	0.509305	−	0.860586i	$-0.329903\pi$
$79$	715.234	1.01861	0.509305	+	0.860586i	$0.329903\pi$
$80$	322.263	0.450376
$81$	81.0000	0.111111
$82$	873.091	1.17581
$83$	−497.577	−0.658026	−0.329013	−	0.944325i	$-0.606716\pi$
$83$	−497.577	−0.658026	−0.329013	+	0.944325i	$0.606716\pi$
$84$	−342.789	−0.445254
$85$	218.506	0.278827
$86$	−653.737	−0.819701
$87$	332.181	0.409352
$88$	−436.526	−0.528793
$89$	396.729	0.472507	0.236254	−	0.971691i	$-0.424080\pi$
$89$	396.729	0.472507	0.236254	+	0.971691i	$0.424080\pi$
$90$	−362.546	−0.424619
$91$	485.331	0.559083
$92$	403.394	0.457139
$93$	1.21285	0.00135233
$94$	−586.749	−0.643814
$95$	684.809	0.739578
$96$	−96.0000	−0.102062
$97$	−1472.39	−1.54122	−0.770609	−	0.637308i	$-0.780048\pi$
$97$	−1472.39	−1.54122	−0.770609	+	0.637308i	$0.780048\pi$
$98$	−946.000	−0.975106
$99$	491.091	0.498551
$100$	1122.71	1.12271
$101$	630.969	0.621621	0.310810	−	0.950472i	$-0.399400\pi$
$101$	630.969	0.621621	0.310810	+	0.950472i	$0.399400\pi$
$102$	−65.0914	−0.0631864
$103$	1285.78	1.23001	0.615007	−	0.788521i	$-0.289153\pi$
$103$	1285.78	1.23001	0.615007	+	0.788521i	$0.289153\pi$
$104$	135.920	0.128154
$105$	−1726.06	−1.60425
$106$	−218.546	−0.200255
$107$	−1760.57	−1.59066	−0.795330	−	0.606177i	$-0.792702\pi$
$107$	−1760.57	−1.59066	−0.795330	+	0.606177i	$0.792702\pi$
$108$	108.000	0.0962250
$109$	−1227.74	−1.07886	−0.539431	−	0.842030i	$-0.681361\pi$
$109$	−1227.74	−1.07886	−0.539431	+	0.842030i	$0.681361\pi$
$110$	−2198.06	−1.90525
$111$	−1106.97	−0.946567
$112$	−457.051	−0.385601
$113$	−1128.63	−0.939579	−0.469790	−	0.882778i	$-0.655670\pi$
$113$	−1128.63	−0.939579	−0.469790	+	0.882778i	$0.655670\pi$
$114$	−204.000	−0.167600
$115$	2031.23	1.64707
$116$	442.909	0.354509
$117$	−152.910	−0.120825
$118$	−118.000	−0.0920575
$119$	−309.897	−0.238725
$120$	−483.394	−0.367730
$121$	1646.42	1.23698
$122$	−921.494	−0.683837
$123$	−1309.64	−0.960049
$124$	1.61713	0.00117115
$125$	3135.56	2.24362
$126$	514.183	0.363548
$127$	65.9000	0.0460447	0.0230224	−	0.999735i	$-0.492671\pi$
$127$	65.9000	0.0460447	0.0230224	+	0.999735i	$0.492671\pi$
$128$	−128.000	−0.0883883
$129$	980.606	0.669283
$130$	684.406	0.461741
$131$	204.023	0.136073	0.0680365	−	0.997683i	$-0.478327\pi$
$131$	204.023	0.136073	0.0680365	+	0.997683i	$0.478327\pi$
$132$	654.789	0.431758
$133$	−971.234	−0.633208
$134$	−1260.04	−0.812320
$135$	543.819	0.346700
$136$	−86.7886	−0.0547210
$137$	−2129.80	−1.32818	−0.664091	−	0.747652i	$-0.731181\pi$
$137$	−2129.80	−1.32818	−0.664091	+	0.747652i	$0.731181\pi$
$138$	−605.091	−0.373252
$139$	−1297.92	−0.792001	−0.396000	−	0.918250i	$-0.629602\pi$
$139$	−1297.92	−0.792001	−0.396000	+	0.918250i	$0.629602\pi$
$140$	−2301.42	−1.38932
$141$	880.123	0.525672
$142$	−1975.92	−1.16772
$143$	−927.071	−0.542137
$144$	144.000	0.0833333
$145$	2230.20	1.27730
$146$	1258.55	0.713412
$147$	1419.00	0.796171
$148$	−1475.96	−0.819751
$149$	2180.35	1.19880	0.599400	−	0.800450i	$-0.295406\pi$
$149$	2180.35	1.19880	0.599400	+	0.800450i	$0.295406\pi$
$150$	−1684.06	−0.916688
$151$	−3106.06	−1.67396	−0.836980	−	0.547234i	$-0.815681\pi$
$151$	−3106.06	−1.67396	−0.836980	+	0.547234i	$0.815681\pi$
$152$	−272.000	−0.145145
$153$	97.6371	0.0515915
$154$	3117.42	1.63122
$155$	8.14284	0.00421967
$156$	−203.880	−0.104638
$157$	1846.04	0.938410	0.469205	−	0.883089i	$-0.344541\pi$
$157$	1846.04	0.938410	0.469205	+	0.883089i	$0.344541\pi$
$158$	−1430.47	−0.720266
$159$	327.819	0.163508
$160$	−644.526	−0.318464
$161$	−2880.81	−1.41018
$162$	−162.000	−0.0785674
$163$	349.154	0.167778	0.0838892	−	0.996475i	$-0.473266\pi$
$163$	349.154	0.167778	0.0838892	+	0.996475i	$0.473266\pi$
$164$	−1746.18	−0.831427
$165$	3297.09	1.55563
$166$	995.154	0.465295
$167$	−67.2729	−0.0311720	−0.0155860	−	0.999879i	$-0.504961\pi$
$167$	−67.2729	−0.0311720	−0.0155860	+	0.999879i	$0.504961\pi$
$168$	685.577	0.314842
$169$	−1908.34	−0.868612
$170$	−437.011	−0.197160
$171$	306.000	0.136844
$172$	1307.47	0.579616
$173$	3237.08	1.42260	0.711302	−	0.702887i	$-0.248106\pi$
$173$	3237.08	1.42260	0.711302	+	0.702887i	$0.248106\pi$
$174$	−664.363	−0.289455
$175$	−8017.74	−3.46334
$176$	873.051	0.373913
$177$	177.000	0.0751646
$178$	−793.457	−0.334113
$179$	3341.94	1.39547	0.697733	−	0.716358i	$-0.254192\pi$
$179$	3341.94	1.39547	0.697733	+	0.716358i	$0.254192\pi$
$180$	725.091	0.300251
$181$	−2063.94	−0.847576	−0.423788	−	0.905761i	$-0.639300\pi$
$181$	−2063.94	−0.847576	−0.423788	+	0.905761i	$0.639300\pi$
$182$	−970.663	−0.395331
$183$	1382.24	0.558351
$184$	−806.789	−0.323246
$185$	−7431.99	−2.95357
$186$	−2.42570	−0.000956242 0
$187$	591.960	0.231489
$188$	1173.50	0.455245
$189$	−771.274	−0.296836
$190$	−1369.62	−0.522960
$191$	−4106.47	−1.55567	−0.777837	−	0.628466i	$-0.783683\pi$
$191$	−4106.47	−1.55567	−0.777837	+	0.628466i	$0.783683\pi$
$192$	192.000	0.0721688
$193$	−861.554	−0.321327	−0.160663	−	0.987009i	$-0.551363\pi$
$193$	−861.554	−0.321327	−0.160663	+	0.987009i	$0.551363\pi$
$194$	2944.77	1.08981
$195$	−1026.61	−0.377010
$196$	1892.00	0.689504
$197$	−1209.92	−0.437581	−0.218791	−	0.975772i	$-0.570211\pi$
$197$	−1209.92	−0.437581	−0.218791	+	0.975772i	$0.570211\pi$
$198$	−982.183	−0.352529
$199$	1644.16	0.585687	0.292843	−	0.956160i	$-0.405399\pi$
$199$	1644.16	0.585687	0.292843	+	0.956160i	$0.405399\pi$
$200$	−2245.42	−0.793875
$201$	1890.06	0.663256
$202$	−1261.94	−0.439552
$203$	−3163.00	−1.09359
$204$	130.183	0.0446795
$205$	−8792.65	−2.99564
$206$	−2571.56	−0.869752
$207$	907.637	0.304759
$208$	−271.840	−0.0906188
$209$	1855.23	0.614015
$210$	3452.13	1.13438
$211$	−4746.03	−1.54848	−0.774241	−	0.632890i	$-0.781868\pi$
$211$	−4746.03	−1.54848	−0.774241	+	0.632890i	$0.781868\pi$
$212$	437.091	0.141602
$213$	2963.88	0.953437
$214$	3521.14	1.12477
$215$	6583.60	2.08836
$216$	−216.000	−0.0680414
$217$	−11.5486	−0.00361278
$218$	2455.48	0.762871
$219$	−1887.82	−0.582499
$220$	4396.13	1.34721
$221$	−184.317	−0.0561019
$222$	2213.94	0.669324
$223$	−6515.69	−1.95660	−0.978302	−	0.207185i	$-0.933570\pi$
$223$	−6515.69	−1.95660	−0.978302	+	0.207185i	$0.933570\pi$
$224$	914.103	0.272661
$225$	2526.09	0.748472
$226$	2257.26	0.664383
$227$	565.617	0.165380	0.0826901	−	0.996575i	$-0.473649\pi$
$227$	565.617	0.165380	0.0826901	+	0.996575i	$0.473649\pi$
$228$	408.000	0.118511
$229$	1260.26	0.363670	0.181835	−	0.983329i	$-0.441796\pi$
$229$	1260.26	0.363670	0.181835	+	0.983329i	$0.441796\pi$
$230$	−4062.47	−1.16466
$231$	−4676.13	−1.33189
$232$	−885.817	−0.250676
$233$	−2409.86	−0.677576	−0.338788	−	0.940863i	$-0.610017\pi$
$233$	−2409.86	−0.677576	−0.338788	+	0.940863i	$0.610017\pi$
$234$	305.820	0.0854362
$235$	5908.98	1.64025
$236$	236.000	0.0650945
$237$	2145.70	0.588094
$238$	619.794	0.168804
$239$	−4883.81	−1.32179	−0.660894	−	0.750479i	$-0.729823\pi$
$239$	−4883.81	−1.32179	−0.660894	+	0.750479i	$0.729823\pi$
$240$	966.789	0.260025
$241$	4385.86	1.17227	0.586137	−	0.810212i	$-0.300648\pi$
$241$	4385.86	1.17227	0.586137	+	0.810212i	$0.300648\pi$
$242$	−3292.83	−0.874675
$243$	243.000	0.0641500
$244$	1842.99	0.483546
$245$	9526.90	2.48429
$246$	2619.27	0.678857
$247$	−577.660	−0.148808
$248$	−3.23427	−0.000828129 0
$249$	−1492.73	−0.379912
$250$	−6271.12	−1.58648
$251$	420.891	0.105842	0.0529212	−	0.998599i	$-0.483147\pi$
$251$	420.891	0.105842	0.0529212	+	0.998599i	$0.483147\pi$
$252$	−1028.37	−0.257067
$253$	5502.87	1.36744
$254$	−131.800	−0.0325585
$255$	655.517	0.160981
$256$	256.000	0.0625000
$257$	−5904.43	−1.43311	−0.716553	−	0.697533i	$-0.754281\pi$
$257$	−5904.43	−1.43311	−0.716553	+	0.697533i	$0.754281\pi$
$258$	−1961.21	−0.473255
$259$	10540.5	2.52877
$260$	−1368.81	−0.326500
$261$	996.544	0.236339
$262$	−408.046	−0.0962181
$263$	−7196.30	−1.68723	−0.843617	−	0.536945i	$-0.819578\pi$
$263$	−7196.30	−1.68723	−0.843617	+	0.536945i	$0.819578\pi$
$264$	−1309.58	−0.305299
$265$	2200.91	0.510192
$266$	1942.47	0.447746
$267$	1190.19	0.272802
$268$	2520.08	0.574397
$269$	5610.61	1.27169	0.635846	−	0.771816i	$-0.280651\pi$
$269$	5610.61	1.27169	0.635846	+	0.771816i	$0.280651\pi$
$270$	−1087.64	−0.245154
$271$	5150.07	1.15441	0.577204	−	0.816600i	$-0.304144\pi$
$271$	5150.07	1.15441	0.577204	+	0.816600i	$0.304144\pi$
$272$	173.577	0.0386936
$273$	1455.99	0.322787
$274$	4259.59	0.939166
$275$	15315.3	3.35836
$276$	1210.18	0.263929
$277$	8215.83	1.78210	0.891049	−	0.453907i	$-0.149970\pi$
$277$	8215.83	1.78210	0.891049	+	0.453907i	$0.149970\pi$
$278$	2595.84	0.560029
$279$	3.63855	0.000780768 0
$280$	4602.83	0.982400
$281$	−2793.35	−0.593016	−0.296508	−	0.955030i	$-0.595822\pi$
$281$	−2793.35	−0.593016	−0.296508	+	0.955030i	$0.595822\pi$
$282$	−1760.25	−0.371706
$283$	−133.611	−0.0280649	−0.0140325	−	0.999902i	$-0.504467\pi$
$283$	−133.611	−0.0280649	−0.0140325	+	0.999902i	$0.504467\pi$
$284$	3951.85	0.825700
$285$	2054.43	0.426995
$286$	1854.14	0.383349
$287$	12470.2	2.56479
$288$	−288.000	−0.0589256
$289$	−4795.31	−0.976045
$290$	−4460.41	−0.903186
$291$	−4417.16	−0.889822
$292$	−2517.10	−0.504459
$293$	−8450.25	−1.68488	−0.842439	−	0.538792i	$-0.818881\pi$
$293$	−8450.25	−1.68488	−0.842439	+	0.538792i	$0.818881\pi$
$294$	−2838.00	−0.562978
$295$	1188.34	0.234536
$296$	2951.92	0.579652
$297$	1473.27	0.287839
$298$	−4360.70	−0.847679
$299$	−1713.42	−0.331403
$300$	3368.13	0.648196
$301$	−9337.23	−1.78800
$302$	6212.13	1.18367
$303$	1892.91	0.358893
$304$	544.000	0.102633
$305$	9280.11	1.74222
$306$	−195.274	−0.0364807
$307$	−4184.95	−0.778006	−0.389003	−	0.921236i	$-0.627180\pi$
$307$	−4184.95	−0.778006	−0.389003	+	0.921236i	$0.627180\pi$
$308$	−6234.83	−1.15345
$309$	3857.34	0.710149
$310$	−16.2857	−0.00298376
$311$	−7845.63	−1.43050	−0.715249	−	0.698870i	$-0.753687\pi$
$311$	−7845.63	−1.43050	−0.715249	+	0.698870i	$0.753687\pi$
$312$	407.760	0.0739899
$313$	−3180.87	−0.574420	−0.287210	−	0.957868i	$-0.592728\pi$
$313$	−3180.87	−0.574420	−0.287210	+	0.957868i	$0.592728\pi$
$314$	−3692.09	−0.663556
$315$	−5178.19	−0.926215
$316$	2860.94	0.509305
$317$	−5932.91	−1.05118	−0.525592	−	0.850737i	$-0.676156\pi$
$317$	−5932.91	−1.05118	−0.525592	+	0.850737i	$0.676156\pi$
$318$	−655.637	−0.115617
$319$	6041.91	1.06044
$320$	1289.05	0.225188
$321$	−5281.71	−0.918368
$322$	5761.62	0.997151
$323$	368.851	0.0635401
$324$	324.000	0.0555556
$325$	−4768.70	−0.813908
$326$	−698.309	−0.118637
$327$	−3683.22	−0.622882
$328$	3492.37	0.587907
$329$	−8380.45	−1.40434
$330$	−6594.19	−1.09999
$331$	−6091.14	−1.01148	−0.505739	−	0.862686i	$-0.668780\pi$
$331$	−6091.14	−1.01148	−0.505739	+	0.862686i	$0.668780\pi$
$332$	−1990.31	−0.329013
$333$	−3320.91	−0.546501
$334$	134.546	0.0220420
$335$	12689.5	2.06956
$336$	−1371.15	−0.222627
$337$	−8467.33	−1.36868	−0.684340	−	0.729163i	$-0.739909\pi$
$337$	−8467.33	−1.36868	−0.684340	+	0.729163i	$0.739909\pi$
$338$	3816.68	0.614201
$339$	−3385.89	−0.542466
$340$	874.023	0.139413
$341$	22.0600	0.00350327
$342$	−612.000	−0.0967637
$343$	−3713.54	−0.584584
$344$	−2614.95	−0.409851
$345$	6093.70	0.950939
$346$	−6474.15	−1.00593
$347$	−941.766	−0.145696	−0.0728482	−	0.997343i	$-0.523209\pi$
$347$	−941.766	−0.145696	−0.0728482	+	0.997343i	$0.523209\pi$
$348$	1328.73	0.204676
$349$	−3556.31	−0.545458	−0.272729	−	0.962091i	$-0.587926\pi$
$349$	−3556.31	−0.545458	−0.272729	+	0.962091i	$0.587926\pi$
$350$	16035.5	2.44895
$351$	−458.730	−0.0697584
$352$	−1746.10	−0.264397
$353$	4004.32	0.603763	0.301882	−	0.953345i	$-0.402385\pi$
$353$	4004.32	0.603763	0.301882	+	0.953345i	$0.402385\pi$
$354$	−354.000	−0.0531494
$355$	19899.0	2.97501
$356$	1586.91	0.236254
$357$	−929.691	−0.137828
$358$	−6683.89	−0.986744
$359$	1206.03	0.177303	0.0886514	−	0.996063i	$-0.471744\pi$
$359$	1206.03	0.177303	0.0886514	+	0.996063i	$0.471744\pi$
$360$	−1450.18	−0.212309
$361$	−5703.00	−0.831462
$362$	4127.87	0.599327
$363$	4939.25	0.714169
$364$	1941.33	0.279542
$365$	−12674.5	−1.81757
$366$	−2764.48	−0.394814
$367$	−5836.89	−0.830199	−0.415099	−	0.909776i	$-0.636253\pi$
$367$	−5836.89	−0.830199	−0.415099	+	0.909776i	$0.636253\pi$
$368$	1613.58	0.228569
$369$	−3928.91	−0.554284
$370$	14864.0	2.08849
$371$	−3121.46	−0.436814
$372$	4.85140	0.000676165 0
$373$	12644.3	1.75522	0.877611	−	0.479373i	$-0.159136\pi$
$373$	12644.3	1.75522	0.877611	+	0.479373i	$0.159136\pi$
$374$	−1183.92	−0.163687
$375$	9406.68	1.29536
$376$	−2346.99	−0.321907
$377$	−1881.25	−0.257001
$378$	1542.55	0.209895
$379$	7096.13	0.961751	0.480875	−	0.876789i	$-0.340319\pi$
$379$	7096.13	0.961751	0.480875	+	0.876789i	$0.340319\pi$
$380$	2739.23	0.369789
$381$	197.700	0.0265839
$382$	8212.94	1.10003
$383$	6841.83	0.912797	0.456399	−	0.889775i	$-0.349139\pi$
$383$	6841.83	0.912797	0.456399	+	0.889775i	$0.349139\pi$
$384$	−384.000	−0.0510310
$385$	−31394.6	−4.15589
$386$	1723.11	0.227212
$387$	2941.82	0.386411
$388$	−5889.54	−0.770609
$389$	−6292.35	−0.820141	−0.410070	−	0.912054i	$-0.634496\pi$
$389$	−6292.35	−0.820141	−0.410070	+	0.912054i	$0.634496\pi$
$390$	2053.22	0.266586
$391$	1094.06	0.141507
$392$	−3784.00	−0.487553
$393$	612.068	0.0785618
$394$	2419.85	0.309417
$395$	14405.8	1.83503
$396$	1964.37	0.249275
$397$	−92.7015	−0.0117193	−0.00585964	−	0.999983i	$-0.501865\pi$
$397$	−92.7015	−0.0117193	−0.00585964	+	0.999983i	$0.501865\pi$
$398$	−3288.33	−0.414143
$399$	−2913.70	−0.365583
$400$	4490.83	0.561354
$401$	−6882.75	−0.857128	−0.428564	−	0.903512i	$-0.640980\pi$
$401$	−6882.75	−0.857128	−0.428564	+	0.903512i	$0.640980\pi$
$402$	−3780.12	−0.468993
$403$	−6.86877	−0.000849027 0
$404$	2523.87	0.310810
$405$	1631.46	0.200167
$406$	6326.00	0.773286
$407$	−20134.2	−2.45213
$408$	−260.366	−0.0315932
$409$	4425.96	0.535085	0.267543	−	0.963546i	$-0.413788\pi$
$409$	4425.96	0.535085	0.267543	+	0.963546i	$0.413788\pi$
$410$	17585.3	2.11824
$411$	−6389.39	−0.766826
$412$	5143.11	0.615007
$413$	−1685.38	−0.200804
$414$	−1815.27	−0.215497
$415$	−10021.9	−1.18544
$416$	543.680	0.0640772
$417$	−3893.76	−0.457262
$418$	−3710.47	−0.434175
$419$	14575.7	1.69945	0.849726	−	0.527224i	$-0.176767\pi$
$419$	14575.7	1.69945	0.849726	+	0.527224i	$0.176767\pi$
$420$	−6904.25	−0.802126
$421$	−10203.0	−1.18115	−0.590575	−	0.806983i	$-0.701099\pi$
$421$	−10203.0	−1.18115	−0.590575	+	0.806983i	$0.701099\pi$
$422$	9492.05	1.09494
$423$	2640.37	0.303497
$424$	−874.183	−0.100128
$425$	3044.95	0.347533
$426$	−5927.77	−0.674182
$427$	−13161.6	−1.49165
$428$	−7042.27	−0.795330
$429$	−2781.21	−0.313003
$430$	−13167.2	−1.47669
$431$	−5149.80	−0.575538	−0.287769	−	0.957700i	$-0.592914\pi$
$431$	−5149.80	−0.575538	−0.287769	+	0.957700i	$0.592914\pi$
$432$	432.000	0.0481125
$433$	−11095.8	−1.23148	−0.615742	−	0.787948i	$-0.711143\pi$
$433$	−11095.8	−1.23148	−0.615742	+	0.787948i	$0.711143\pi$
$434$	23.0973	0.00255462
$435$	6690.61	0.737449
$436$	−4910.95	−0.539431
$437$	3428.85	0.375341
$438$	3775.65	0.411889
$439$	6504.20	0.707126	0.353563	−	0.935411i	$-0.384970\pi$
$439$	6504.20	0.707126	0.353563	+	0.935411i	$0.384970\pi$
$440$	−8792.25	−0.952623
$441$	4257.00	0.459670
$442$	368.634	0.0396700
$443$	12954.2	1.38933	0.694666	−	0.719332i	$-0.255552\pi$
$443$	12954.2	1.38933	0.694666	+	0.719332i	$0.255552\pi$
$444$	−4427.88	−0.473284
$445$	7990.68	0.851224
$446$	13031.4	1.38353
$447$	6541.05	0.692127
$448$	−1828.21	−0.192800
$449$	4722.80	0.496398	0.248199	−	0.968709i	$-0.420161\pi$
$449$	4722.80	0.496398	0.248199	+	0.968709i	$0.420161\pi$
$450$	−5052.19	−0.529250
$451$	−23820.4	−2.48705
$452$	−4514.51	−0.469790
$453$	−9318.19	−0.966461
$454$	−1131.23	−0.116942
$455$	9775.27	1.00719
$456$	−816.000	−0.0837998
$457$	13763.6	1.40883	0.704416	−	0.709788i	$-0.251209\pi$
$457$	13763.6	1.40883	0.704416	+	0.709788i	$0.251209\pi$
$458$	−2520.52	−0.257153
$459$	292.911	0.0297863
$460$	8124.94	0.823537
$461$	4564.32	0.461131	0.230565	−	0.973057i	$-0.425942\pi$
$461$	4564.32	0.461131	0.230565	+	0.973057i	$0.425942\pi$
$462$	9352.25	0.941788
$463$	627.841	0.0630200	0.0315100	−	0.999503i	$-0.489968\pi$
$463$	627.841	0.0630200	0.0315100	+	0.999503i	$0.489968\pi$
$464$	1771.63	0.177254
$465$	24.4285	0.00243623
$466$	4819.72	0.479118
$467$	6716.18	0.665499	0.332749	−	0.943015i	$-0.392024\pi$
$467$	6716.18	0.665499	0.332749	+	0.943015i	$0.392024\pi$
$468$	−611.640	−0.0604125
$469$	−17997.0	−1.77190
$470$	−11818.0	−1.15983
$471$	5538.13	0.541791
$472$	−472.000	−0.0460287
$473$	17835.8	1.73381
$474$	−4291.41	−0.415846
$475$	9543.02	0.921819
$476$	−1239.59	−0.119362
$477$	983.456	0.0944011
$478$	9767.61	0.934645
$479$	−10237.9	−0.976583	−0.488291	−	0.872681i	$-0.662380\pi$
$479$	−10237.9	−0.976583	−0.488291	+	0.872681i	$0.662380\pi$
$480$	−1933.58	−0.183865
$481$	6269.14	0.594279
$482$	−8771.72	−0.828923
$483$	−8642.43	−0.814171
$484$	6585.67	0.618489
$485$	−29656.0	−2.77651
$486$	−486.000	−0.0453609
$487$	10027.8	0.933069	0.466535	−	0.884503i	$-0.345502\pi$
$487$	10027.8	0.933069	0.466535	+	0.884503i	$0.345502\pi$
$488$	−3685.98	−0.341919
$489$	1047.46	0.0968669
$490$	−19053.8	−1.75666
$491$	−9590.92	−0.881532	−0.440766	−	0.897622i	$-0.645293\pi$
$491$	−9590.92	−0.881532	−0.440766	+	0.897622i	$0.645293\pi$
$492$	−5238.55	−0.480024
$493$	1201.23	0.109738
$494$	1155.32	0.105223
$495$	9891.28	0.898142
$496$	6.46853	0.000585576 0
$497$	−28221.8	−2.54713
$498$	2985.46	0.268638
$499$	−1320.95	−0.118505	−0.0592523	−	0.998243i	$-0.518872\pi$
$499$	−1320.95	−0.118505	−0.0592523	+	0.998243i	$0.518872\pi$
$500$	12542.2	1.12181
$501$	−201.819	−0.0179972
$502$	−841.783	−0.0748418
$503$	16075.0	1.42495	0.712475	−	0.701697i	$-0.247574\pi$
$503$	16075.0	1.42495	0.712475	+	0.701697i	$0.247574\pi$
$504$	2056.73	0.181774
$505$	12708.6	1.11985
$506$	−11005.7	−0.966927
$507$	−5725.02	−0.501493
$508$	263.600	0.0230224
$509$	10444.5	0.909519	0.454760	−	0.890614i	$-0.349725\pi$
$509$	10444.5	0.909519	0.454760	+	0.890614i	$0.349725\pi$
$510$	−1311.03	−0.113831
$511$	17975.7	1.55616
$512$	−512.000	−0.0441942
$513$	918.000	0.0790072
$514$	11808.9	1.01336
$515$	25897.4	2.21588
$516$	3922.42	0.334642
$517$	16008.2	1.36178
$518$	−21080.9	−1.78811
$519$	9711.23	0.821341
$520$	2737.62	0.230871
$521$	−5162.05	−0.434076	−0.217038	−	0.976163i	$-0.569640\pi$
$521$	−5162.05	−0.434076	−0.217038	+	0.976163i	$0.569640\pi$
$522$	−1993.09	−0.167117
$523$	−11606.8	−0.970423	−0.485212	−	0.874397i	$-0.661257\pi$
$523$	−11606.8	−0.970423	−0.485212	+	0.874397i	$0.661257\pi$
$524$	816.091	0.0680365
$525$	−24053.2	−1.99956
$526$	14392.6	1.19305
$527$	4.38590	0.000362529 0
$528$	2619.15	0.215879
$529$	−1996.57	−0.164097
$530$	−4401.82	−0.360760
$531$	531.000	0.0433963
$532$	−3884.94	−0.316604
$533$	7416.91	0.602743
$534$	−2380.37	−0.192900
$535$	−35460.4	−2.86558
$536$	−5040.16	−0.406160
$537$	10025.8	0.805673
$538$	−11221.2	−0.899222
$539$	25809.6	2.06252
$540$	2175.27	0.173350
$541$	12568.2	0.998794	0.499397	−	0.866373i	$-0.333555\pi$
$541$	12568.2	0.998794	0.499397	+	0.866373i	$0.333555\pi$
$542$	−10300.1	−0.816289
$543$	−6191.81	−0.489348
$544$	−347.154	−0.0273605
$545$	−24728.4	−1.94358
$546$	−2911.99	−0.228245
$547$	13248.3	1.03557	0.517785	−	0.855511i	$-0.326757\pi$
$547$	13248.3	1.03557	0.517785	+	0.855511i	$0.326757\pi$
$548$	−8519.19	−0.664091
$549$	4146.72	0.322364
$550$	−30630.7	−2.37472
$551$	3764.72	0.291075
$552$	−2420.37	−0.186626
$553$	−20431.2	−1.57111
$554$	−16431.7	−1.26013
$555$	−22296.0	−1.70524
$556$	−5191.68	−0.396000
$557$	18075.5	1.37502	0.687508	−	0.726177i	$-0.258705\pi$
$557$	18075.5	1.37502	0.687508	+	0.726177i	$0.258705\pi$
$558$	−7.27710	−0.000552086 0
$559$	−5553.50	−0.420193
$560$	−9205.67	−0.694662
$561$	1775.88	0.133650
$562$	5586.71	0.419326
$563$	−8401.40	−0.628911	−0.314455	−	0.949272i	$-0.601822\pi$
$563$	−8401.40	−0.628911	−0.314455	+	0.949272i	$0.601822\pi$
$564$	3520.49	0.262836
$565$	−22732.2	−1.69266
$566$	267.223	0.0198449
$567$	−2313.82	−0.171378
$568$	−7903.69	−0.583858
$569$	7993.77	0.588956	0.294478	−	0.955658i	$-0.404854\pi$
$569$	7993.77	0.588956	0.294478	+	0.955658i	$0.404854\pi$
$570$	−4108.85	−0.301931
$571$	15831.5	1.16030	0.580149	−	0.814511i	$-0.302994\pi$
$571$	15831.5	1.16030	0.580149	+	0.814511i	$0.302994\pi$
$572$	−3708.29	−0.271069
$573$	−12319.4	−0.898169
$574$	−24940.5	−1.81358
$575$	28305.9	2.05293
$576$	576.000	0.0416667
$577$	11060.2	0.797996	0.398998	−	0.916952i	$-0.369358\pi$
$577$	11060.2	0.797996	0.398998	+	0.916952i	$0.369358\pi$
$578$	9590.62	0.690168
$579$	−2584.66	−0.185518
$580$	8920.81	0.638649
$581$	14213.6	1.01494
$582$	8834.31	0.629199
$583$	5962.55	0.423574
$584$	5034.19	0.356706
$585$	−3079.83	−0.217667
$586$	16900.5	1.19139
$587$	−19130.0	−1.34511	−0.672554	−	0.740048i	$-0.734803\pi$
$587$	−19130.0	−1.34511	−0.672554	+	0.740048i	$0.734803\pi$
$588$	5676.00	0.398086
$589$	13.7456	0.000961594 0
$590$	−2376.69	−0.165842
$591$	−3629.77	−0.252638
$592$	−5903.84	−0.409876
$593$	8882.23	0.615092	0.307546	−	0.951533i	$-0.400492\pi$
$593$	8882.23	0.615092	0.307546	+	0.951533i	$0.400492\pi$
$594$	−2946.55	−0.203533
$595$	−6241.77	−0.430063
$596$	8721.39	0.599400
$597$	4932.49	0.338146
$598$	3426.83	0.234337
$599$	−18682.7	−1.27438	−0.637192	−	0.770705i	$-0.719904\pi$
$599$	−18682.7	−1.27438	−0.637192	+	0.770705i	$0.719904\pi$
$600$	−6736.25	−0.458344
$601$	15263.7	1.03597	0.517987	−	0.855388i	$-0.326681\pi$
$601$	15263.7	1.03597	0.517987	+	0.855388i	$0.326681\pi$
$602$	18674.5	1.26431
$603$	5670.18	0.382931
$604$	−12424.3	−0.836980
$605$	33161.2	2.22842
$606$	−3785.81	−0.253776
$607$	−354.528	−0.0237065	−0.0118533	−	0.999930i	$-0.503773\pi$
$607$	−354.528	−0.0237065	−0.0118533	+	0.999930i	$0.503773\pi$
$608$	−1088.00	−0.0725727
$609$	−9489.00	−0.631385
$610$	−18560.2	−1.23194
$611$	−4984.43	−0.330030
$612$	390.549	0.0257957
$613$	−16873.7	−1.11178	−0.555892	−	0.831254i	$-0.687623\pi$
$613$	−16873.7	−1.11178	−0.555892	+	0.831254i	$0.687623\pi$
$614$	8369.91	0.550134
$615$	−26378.0	−1.72953
$616$	12469.7	0.815612
$617$	17512.0	1.14264	0.571318	−	0.820729i	$-0.306432\pi$
$617$	17512.0	1.14264	0.571318	+	0.820729i	$0.306432\pi$
$618$	−7714.67	−0.502151
$619$	−1787.91	−0.116094	−0.0580471	−	0.998314i	$-0.518487\pi$
$619$	−1787.91	−0.116094	−0.0580471	+	0.998314i	$0.518487\pi$
$620$	32.5714	0.00210984
$621$	2722.91	0.175953
$622$	15691.3	1.01151
$623$	−11332.8	−0.728797
$624$	−815.520	−0.0523188
$625$	28070.0	1.79648
$626$	6361.74	0.406176
$627$	5565.70	0.354502
$628$	7384.18	0.469205
$629$	−4003.01	−0.253753
$630$	10356.4	0.654933
$631$	16319.4	1.02958	0.514789	−	0.857317i	$-0.327870\pi$
$631$	16319.4	1.02958	0.514789	+	0.857317i	$0.327870\pi$
$632$	−5721.87	−0.360133
$633$	−14238.1	−0.894017
$634$	11865.8	0.743300
$635$	1327.32	0.0829497
$636$	1311.27	0.0817538
$637$	−8036.27	−0.499857
$638$	−12083.8	−0.749847
$639$	8891.65	0.550467
$640$	−2578.10	−0.159232
$641$	7001.57	0.431428	0.215714	−	0.976457i	$-0.430792\pi$
$641$	7001.57	0.431428	0.215714	+	0.976457i	$0.430792\pi$
$642$	10563.4	0.649384
$643$	6756.97	0.414415	0.207207	−	0.978297i	$-0.433563\pi$
$643$	6756.97	0.414415	0.207207	+	0.978297i	$0.433563\pi$
$644$	−11523.2	−0.705092
$645$	19750.8	1.20572
$646$	−737.703	−0.0449296
$647$	−24709.5	−1.50144	−0.750720	−	0.660621i	$-0.770293\pi$
$647$	−24709.5	−1.50144	−0.750720	+	0.660621i	$0.770293\pi$
$648$	−648.000	−0.0392837
$649$	3219.38	0.194717
$650$	9537.41	0.575520
$651$	−34.6459	−0.00208584
$652$	1396.62	0.0838892
$653$	7674.59	0.459923	0.229962	−	0.973200i	$-0.426140\pi$
$653$	7674.59	0.459923	0.229962	+	0.973200i	$0.426140\pi$
$654$	7366.43	0.440444
$655$	4109.31	0.245136
$656$	−6984.73	−0.415713
$657$	−5663.47	−0.336306
$658$	16760.9	0.993021
$659$	−600.920	−0.0355213	−0.0177606	−	0.999842i	$-0.505654\pi$
$659$	−600.920	−0.0355213	−0.0177606	+	0.999842i	$0.505654\pi$
$660$	13188.4	0.777813
$661$	−16815.7	−0.989495	−0.494748	−	0.869037i	$-0.664740\pi$
$661$	−16815.7	−0.989495	−0.494748	+	0.869037i	$0.664740\pi$
$662$	12182.3	0.715224
$663$	−552.952	−0.0323904
$664$	3980.62	0.232647
$665$	−19562.0	−1.14073
$666$	6641.82	0.386434
$667$	11166.7	0.648239
$668$	−269.091	−0.0155860
$669$	−19547.1	−1.12965
$670$	−25379.0	−1.46340
$671$	25141.0	1.44643
$672$	2742.31	0.157421
$673$	−10123.9	−0.579865	−0.289933	−	0.957047i	$-0.593633\pi$
$673$	−10123.9	−0.579865	−0.289933	+	0.957047i	$0.593633\pi$
$674$	16934.7	0.967802
$675$	7578.28	0.432131
$676$	−7633.36	−0.434306
$677$	−34456.7	−1.95610	−0.978049	−	0.208377i	$-0.933182\pi$
$677$	−34456.7	−1.95610	−0.978049	+	0.208377i	$0.933182\pi$
$678$	6771.77	0.383582
$679$	42059.7	2.37718
$680$	−1748.05	−0.0985801
$681$	1696.85	0.0954824
$682$	−44.1200	−0.00247719
$683$	−2080.93	−0.116581	−0.0582904	−	0.998300i	$-0.518565\pi$
$683$	−2080.93	−0.116581	−0.0582904	+	0.998300i	$0.518565\pi$
$684$	1224.00	0.0684222
$685$	−42897.2	−2.39272
$686$	7427.09	0.413364
$687$	3780.78	0.209965
$688$	5229.90	0.289808
$689$	−1856.55	−0.102654
$690$	−12187.4	−0.672415
$691$	32006.1	1.76204	0.881019	−	0.473081i	$-0.156858\pi$
$691$	32006.1	1.76204	0.881019	+	0.473081i	$0.156858\pi$
$692$	12948.3	0.711302
$693$	−14028.4	−0.768967
$694$	1883.53	0.103023
$695$	−26142.0	−1.42679
$696$	−2657.45	−0.144728
$697$	−4735.90	−0.257367
$698$	7112.62	0.385697
$699$	−7229.58	−0.391199
$700$	−32071.0	−1.73167
$701$	17360.4	0.935369	0.467685	−	0.883895i	$-0.345088\pi$
$701$	17360.4	0.935369	0.467685	+	0.883895i	$0.345088\pi$
$702$	917.460	0.0493266
$703$	−12545.7	−0.673070
$704$	3492.21	0.186957
$705$	17726.9	0.947000
$706$	−8008.64	−0.426925
$707$	−18024.1	−0.958790
$708$	708.000	0.0375823
$709$	−2143.27	−0.113529	−0.0567646	−	0.998388i	$-0.518078\pi$
$709$	−2143.27	−0.113529	−0.0567646	+	0.998388i	$0.518078\pi$
$710$	−39797.9	−2.10365
$711$	6437.11	0.339536
$712$	−3173.83	−0.167057
$713$	40.7714	0.00214152
$714$	1859.38	0.0974589
$715$	−18672.5	−0.976662
$716$	13367.8	0.697733
$717$	−14651.4	−0.763134
$718$	−2412.05	−0.125372
$719$	−7603.20	−0.394369	−0.197185	−	0.980366i	$-0.563180\pi$
$719$	−7603.20	−0.394369	−0.197185	+	0.980366i	$0.563180\pi$
$720$	2900.37	0.150125
$721$	−36729.2	−1.89718
$722$	11406.0	0.587933
$723$	13157.6	0.676813
$724$	−8255.75	−0.423788
$725$	31078.6	1.59204
$726$	−9878.50	−0.504994
$727$	−2483.49	−0.126695	−0.0633477	−	0.997992i	$-0.520178\pi$
$727$	−2483.49	−0.126695	−0.0633477	+	0.997992i	$0.520178\pi$
$728$	−3882.65	−0.197666
$729$	729.000	0.0370370
$730$	25349.0	1.28522
$731$	3546.06	0.179419
$732$	5528.97	0.279175
$733$	−16382.6	−0.825520	−0.412760	−	0.910840i	$-0.635435\pi$
$733$	−16382.6	−0.825520	−0.412760	+	0.910840i	$0.635435\pi$
$734$	11673.8	0.587039
$735$	28580.7	1.43431
$736$	−3227.15	−0.161623
$737$	34377.5	1.71820
$738$	7857.82	0.391938
$739$	35353.3	1.75980	0.879901	−	0.475157i	$-0.157609\pi$
$739$	35353.3	1.75980	0.879901	+	0.475157i	$0.157609\pi$
$740$	−29727.9	−1.47679
$741$	−1732.98	−0.0859144
$742$	6242.91	0.308874
$743$	−34651.2	−1.71094	−0.855470	−	0.517853i	$-0.826732\pi$
$743$	−34651.2	−1.71094	−0.855470	+	0.517853i	$0.826732\pi$
$744$	−9.70280	−0.000478121 0
$745$	43915.3	2.15964
$746$	−25288.6	−1.24113
$747$	−4478.19	−0.219342
$748$	2367.84	0.115744
$749$	50291.9	2.45344
$750$	−18813.4	−0.915956
$751$	28892.0	1.40384	0.701919	−	0.712256i	$-0.252327\pi$
$751$	28892.0	1.40384	0.701919	+	0.712256i	$0.252327\pi$
$752$	4693.99	0.227623
$753$	1262.67	0.0611081
$754$	3762.51	0.181727
$755$	−62560.6	−3.01565
$756$	−3085.10	−0.148418
$757$	7659.14	0.367736	0.183868	−	0.982951i	$-0.441138\pi$
$757$	7659.14	0.367736	0.183868	+	0.982951i	$0.441138\pi$
$758$	−14192.3	−0.680060
$759$	16508.6	0.789493
$760$	−5478.47	−0.261480
$761$	8765.23	0.417528	0.208764	−	0.977966i	$-0.433056\pi$
$761$	8765.23	0.417528	0.208764	+	0.977966i	$0.433056\pi$
$762$	−395.400	−0.0187977
$763$	35071.2	1.66404
$764$	−16425.9	−0.777837
$765$	1966.55	0.0929422
$766$	−13683.7	−0.645445
$767$	−1002.41	−0.0471903
$768$	768.000	0.0360844
$769$	−21094.2	−0.989177	−0.494588	−	0.869127i	$-0.664681\pi$
$769$	−21094.2	−0.989177	−0.494588	+	0.869127i	$0.664681\pi$
$770$	62789.2	2.93866
$771$	−17713.3	−0.827404
$772$	−3446.22	−0.160663
$773$	−2971.39	−0.138258	−0.0691291	−	0.997608i	$-0.522022\pi$
$773$	−2971.39	−0.138258	−0.0691291	+	0.997608i	$0.522022\pi$
$774$	−5883.63	−0.273234
$775$	113.473	0.00525945
$776$	11779.1	0.544903
$777$	31621.4	1.45999
$778$	12584.7	0.579927
$779$	−14842.6	−0.682657
$780$	−4106.43	−0.188505
$781$	53908.8	2.46992
$782$	−2188.13	−0.100060
$783$	2989.63	0.136451
$784$	7568.00	0.344752
$785$	37182.0	1.69055
$786$	−1224.14	−0.0555516
$787$	16024.0	0.725785	0.362893	−	0.931831i	$-0.381789\pi$
$787$	16024.0	0.725785	0.362893	+	0.931831i	$0.381789\pi$
$788$	−4839.70	−0.218791
$789$	−21588.9	−0.974125
$790$	−28811.7	−1.29756
$791$	32240.1	1.44921
$792$	−3928.73	−0.176264
$793$	−7828.09	−0.350547
$794$	185.403	0.00828678
$795$	6602.73	0.294560
$796$	6576.65	0.292843
$797$	43476.9	1.93228	0.966142	−	0.258011i	$-0.0830669\pi$
$797$	43476.9	1.93228	0.966142	+	0.258011i	$0.0830669\pi$
$798$	5827.41	0.258506
$799$	3182.69	0.140921
$800$	−8981.67	−0.396937
$801$	3570.56	0.157502
$802$	13765.5	0.606081
$803$	−34336.8	−1.50899
$804$	7560.24	0.331628
$805$	−58023.7	−2.54045
$806$	13.7375	0.000600353 0
$807$	16831.8	0.734211
$808$	−5047.75	−0.219776
$809$	−20829.5	−0.905223	−0.452611	−	0.891708i	$-0.649508\pi$
$809$	−20829.5	−0.905223	−0.452611	+	0.891708i	$0.649508\pi$
$810$	−3262.91	−0.141540
$811$	−37858.8	−1.63921	−0.819607	−	0.572926i	$-0.805808\pi$
$811$	−37858.8	−1.63921	−0.819607	+	0.572926i	$0.805808\pi$
$812$	−12652.0	−0.546796
$813$	15450.2	0.666497
$814$	40268.4	1.73392
$815$	7032.47	0.302253
$816$	520.731	0.0223398
$817$	11113.5	0.475904
$818$	−8851.93	−0.378362
$819$	4367.98	0.186361
$820$	−35170.6	−1.49782
$821$	−27071.8	−1.15081	−0.575403	−	0.817870i	$-0.695155\pi$
$821$	−27071.8	−1.15081	−0.575403	+	0.817870i	$0.695155\pi$
$822$	12778.8	0.542228
$823$	−9426.19	−0.399242	−0.199621	−	0.979873i	$-0.563971\pi$
$823$	−9426.19	−0.399242	−0.199621	+	0.979873i	$0.563971\pi$
$824$	−10286.2	−0.434876
$825$	45946.0	1.93895
$826$	3370.75	0.141990
$827$	2097.55	0.0881970	0.0440985	−	0.999027i	$-0.485958\pi$
$827$	2097.55	0.0881970	0.0440985	+	0.999027i	$0.485958\pi$
$828$	3630.55	0.152380
$829$	1011.67	0.0423847	0.0211923	−	0.999775i	$-0.493254\pi$
$829$	1011.67	0.0423847	0.0211923	+	0.999775i	$0.493254\pi$
$830$	20043.8	0.838231
$831$	24647.5	1.02889
$832$	−1087.36	−0.0453094
$833$	5131.37	0.213435
$834$	7787.52	0.323333
$835$	−1354.97	−0.0561566
$836$	7420.94	0.307008
$837$	10.9156	0.000450777 0
$838$	−29151.4	−1.20169
$839$	28850.7	1.18717	0.593586	−	0.804771i	$-0.297712\pi$
$839$	28850.7	1.18717	0.593586	+	0.804771i	$0.297712\pi$
$840$	13808.5	0.567189
$841$	−12128.5	−0.497294
$842$	20406.0	0.835199
$843$	−8380.06	−0.342378
$844$	−18984.1	−0.774241
$845$	−38436.7	−1.56481
$846$	−5280.74	−0.214605
$847$	−47031.1	−1.90792
$848$	1748.37	0.0708009
$849$	−400.834	−0.0162033
$850$	−6089.89	−0.245743
$851$	−37212.1	−1.49896
$852$	11855.5	0.476718
$853$	44788.4	1.79780	0.898901	−	0.438151i	$-0.144366\pi$
$853$	44788.4	1.79780	0.898901	+	0.438151i	$0.144366\pi$
$854$	26323.1	1.05475
$855$	6163.28	0.246526
$856$	14084.5	0.562383
$857$	−3403.85	−0.135675	−0.0678374	−	0.997696i	$-0.521610\pi$
$857$	−3403.85	−0.135675	−0.0678374	+	0.997696i	$0.521610\pi$
$858$	5562.43	0.221327
$859$	−20755.4	−0.824407	−0.412203	−	0.911092i	$-0.635241\pi$
$859$	−20755.4	−0.824407	−0.412203	+	0.911092i	$0.635241\pi$
$860$	26334.4	1.04418
$861$	37410.7	1.48078
$862$	10299.6	0.406967
$863$	129.134	0.00509359	0.00254679	−	0.999997i	$-0.499189\pi$
$863$	129.134	0.00509359	0.00254679	+	0.999997i	$0.499189\pi$
$864$	−864.000	−0.0340207
$865$	65199.4	2.56283
$866$	22191.7	0.870790
$867$	−14385.9	−0.563520
$868$	−46.1946	−0.00180639
$869$	39027.3	1.52349
$870$	−13381.2	−0.521455
$871$	−10704.0	−0.416409
$872$	9821.91	0.381436
$873$	−13251.5	−0.513739
$874$	−6857.70	−0.265406
$875$	−89569.5	−3.46057
$876$	−7551.29	−0.291249
$877$	11326.3	0.436102	0.218051	−	0.975937i	$-0.430030\pi$
$877$	11326.3	0.436102	0.218051	+	0.975937i	$0.430030\pi$
$878$	−13008.4	−0.500014
$879$	−25350.8	−0.972764
$880$	17584.5	0.673606
$881$	11445.9	0.437708	0.218854	−	0.975758i	$-0.429768\pi$
$881$	11445.9	0.437708	0.218854	+	0.975758i	$0.429768\pi$
$882$	−8514.00	−0.325035
$883$	−31.3773	−0.00119584	−0.000597922	−	1.00000i	$-0.500190\pi$
$883$	−31.3773	−0.00119584	−0.000597922		1.00000i	$0.500190\pi$
$884$	−737.269	−0.0280509
$885$	3565.03	0.135409
$886$	−25908.5	−0.982406
$887$	23118.1	0.875117	0.437558	−	0.899190i	$-0.355843\pi$
$887$	23118.1	0.875117	0.437558	+	0.899190i	$0.355843\pi$
$888$	8855.76	0.334662
$889$	−1882.48	−0.0710195
$890$	−15981.4	−0.601906
$891$	4419.82	0.166184
$892$	−26062.7	−0.978302
$893$	9974.73	0.373787
$894$	−13082.1	−0.489408
$895$	67311.5	2.51394
$896$	3656.41	0.136331
$897$	−5140.25	−0.191336
$898$	−9445.59	−0.351006
$899$	44.7651	0.00166074
$900$	10104.4	0.374236
$901$	1185.45	0.0438326
$902$	47640.9	1.75861
$903$	−28011.7	−1.03230
$904$	9029.03	0.332191
$905$	−41570.6	−1.52691
$906$	18636.4	0.683391
$907$	17582.7	0.643688	0.321844	−	0.946793i	$-0.395697\pi$
$907$	17582.7	0.643688	0.321844	+	0.946793i	$0.395697\pi$
$908$	2262.47	0.0826901
$909$	5678.72	0.207207
$910$	−19550.5	−0.712191
$911$	18975.5	0.690104	0.345052	−	0.938583i	$-0.387861\pi$
$911$	18975.5	0.690104	0.345052	+	0.938583i	$0.387861\pi$
$912$	1632.00	0.0592554
$913$	−27150.7	−0.984179
$914$	−27527.3	−0.996194
$915$	27840.3	1.00587
$916$	5041.05	0.181835
$917$	−5828.06	−0.209879
$918$	−585.823	−0.0210621
$919$	35075.0	1.25900	0.629498	−	0.777002i	$-0.283260\pi$
$919$	35075.0	1.25900	0.629498	+	0.777002i	$0.283260\pi$
$920$	−16249.9	−0.582329
$921$	−12554.9	−0.449182
$922$	−9128.63	−0.326069
$923$	−16785.5	−0.598592
$924$	−18704.5	−0.665945
$925$	−103567.	−3.68137
$926$	−1255.68	−0.0445619
$927$	11572.0	0.410005
$928$	−3543.27	−0.125338
$929$	−14369.6	−0.507482	−0.253741	−	0.967272i	$-0.581661\pi$
$929$	−14369.6	−0.507482	−0.253741	+	0.967272i	$0.581661\pi$
$930$	−48.8571	−0.00172267
$931$	16082.0	0.566129
$932$	−9639.44	−0.338788
$933$	−23536.9	−0.825898
$934$	−13432.4	−0.470579
$935$	11922.9	0.417028
$936$	1223.28	0.0427181
$937$	11260.5	0.392598	0.196299	−	0.980544i	$-0.437108\pi$
$937$	11260.5	0.392598	0.196299	+	0.980544i	$0.437108\pi$
$938$	35993.9	1.25293
$939$	−9542.61	−0.331642
$940$	23635.9	0.820126
$941$	41046.7	1.42198	0.710991	−	0.703201i	$-0.248247\pi$
$941$	41046.7	1.42198	0.710991	+	0.703201i	$0.248247\pi$
$942$	−11076.3	−0.383104
$943$	−44025.0	−1.52031
$944$	944.000	0.0325472
$945$	−15534.6	−0.534751
$946$	−35671.6	−1.22599
$947$	−13131.7	−0.450604	−0.225302	−	0.974289i	$-0.572337\pi$
$947$	−13131.7	−0.450604	−0.225302	+	0.974289i	$0.572337\pi$
$948$	8582.81	0.294047
$949$	10691.4	0.365708
$950$	−19086.0	−0.651824
$951$	−17798.7	−0.606902
$952$	2479.18	0.0844019
$953$	−46349.4	−1.57545	−0.787725	−	0.616027i	$-0.788741\pi$
$953$	−46349.4	−1.57545	−0.787725	+	0.616027i	$0.788741\pi$
$954$	−1966.91	−0.0667517
$955$	−82710.2	−2.80255
$956$	−19535.2	−0.660894
$957$	18125.7	0.612248
$958$	20475.9	0.690548
$959$	60839.2	2.04859
$960$	3867.15	0.130012
$961$	−29790.8	−0.999995
$962$	−12538.3	−0.420219
$963$	−15845.1	−0.530220
$964$	17543.4	0.586137
$965$	−17352.9	−0.578871
$966$	17284.9	0.575706
$967$	28322.6	0.941875	0.470937	−	0.882167i	$-0.343916\pi$
$967$	28322.6	0.941875	0.470937	+	0.882167i	$0.343916\pi$
$968$	−13171.3	−0.437338
$969$	1106.55	0.0366849
$970$	59311.9	1.96329
$971$	−11450.1	−0.378424	−0.189212	−	0.981936i	$-0.560593\pi$
$971$	−11450.1	−0.378424	−0.189212	+	0.981936i	$0.560593\pi$
$972$	972.000	0.0320750
$973$	37076.0	1.22159
$974$	−20055.7	−0.659780
$975$	−14306.1	−0.469910
$976$	7371.95	0.241773
$977$	−28464.8	−0.932107	−0.466054	−	0.884756i	$-0.654325\pi$
$977$	−28464.8	−0.932107	−0.466054	+	0.884756i	$0.654325\pi$
$978$	−2094.93	−0.0684952
$979$	21647.8	0.706707
$980$	38107.6	1.24214
$981$	−11049.6	−0.359621
$982$	19181.8	0.623337
$983$	−24122.9	−0.782708	−0.391354	−	0.920240i	$-0.627993\pi$
$983$	−24122.9	−0.782708	−0.391354	+	0.920240i	$0.627993\pi$
$984$	10477.1	0.339429
$985$	−24369.6	−0.788305
$986$	−2402.46	−0.0775963
$987$	−25141.3	−0.810798
$988$	−2310.64	−0.0744041
$989$	32964.2	1.05986
$990$	−19782.6	−0.635082
$991$	4710.10	0.150980	0.0754901	−	0.997147i	$-0.475948\pi$
$991$	4710.10	0.150980	0.0754901	+	0.997147i	$0.475948\pi$
$992$	−12.9371	−0.000414065 0
$993$	−18273.4	−0.583978
$994$	56443.6	1.80109
$995$	33115.8	1.05512
$996$	−5970.93	−0.189956
$997$	21534.7	0.684064	0.342032	−	0.939688i	$-0.388885\pi$
$997$	21534.7	0.684064	0.342032	+	0.939688i	$0.388885\pi$
$998$	2641.90	0.0837954
$999$	−9962.73	−0.315522

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.4.a.b.1.2	✓	2
3.2	odd	2		1062.4.a.g.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.4.a.b.1.2	✓	2	1.1	even	1	trivial
1062.4.a.g.1.1		2	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)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +20.1414 q^{5} -6.00000 q^{6} -28.5657 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +20.1414 q^{5} -6.00000 q^{6} -28.5657 q^{7} -8.00000 q^{8} +9.00000 q^{9} -40.2829 q^{10} +54.5657 q^{11} +12.0000 q^{12} -16.9900 q^{13} +57.1314 q^{14} +60.4243 q^{15} +16.0000 q^{16} +10.8486 q^{17} -18.0000 q^{18} +34.0000 q^{19} +80.5657 q^{20} -85.6971 q^{21} -109.131 q^{22} +100.849 q^{23} -24.0000 q^{24} +280.677 q^{25} +33.9800 q^{26} +27.0000 q^{27} -114.263 q^{28} +110.727 q^{29} -120.849 q^{30} +0.404283 q^{31} -32.0000 q^{32} +163.697 q^{33} -21.6971 q^{34} -575.354 q^{35} +36.0000 q^{36} -368.990 q^{37} -68.0000 q^{38} -50.9700 q^{39} -161.131 q^{40} -436.546 q^{41} +171.394 q^{42} +326.869 q^{43} +218.263 q^{44} +181.273 q^{45} -201.697 q^{46} +293.374 q^{47} +48.0000 q^{48} +473.000 q^{49} -561.354 q^{50} +32.5457 q^{51} -67.9600 q^{52} +109.273 q^{53} -54.0000 q^{54} +1099.03 q^{55} +228.526 q^{56} +102.000 q^{57} -221.454 q^{58} +59.0000 q^{59} +241.697 q^{60} +460.747 q^{61} -0.808567 q^{62} -257.091 q^{63} +64.0000 q^{64} -342.203 q^{65} -327.394 q^{66} +630.020 q^{67} +43.3943 q^{68} +302.546 q^{69} +1150.71 q^{70} +987.961 q^{71} -72.0000 q^{72} -629.274 q^{73} +737.980 q^{74} +842.031 q^{75} +136.000 q^{76} -1558.71 q^{77} +101.940 q^{78} +715.234 q^{79} +322.263 q^{80} +81.0000 q^{81} +873.091 q^{82} -497.577 q^{83} -342.789 q^{84} +218.506 q^{85} -653.737 q^{86} +332.181 q^{87} -436.526 q^{88} +396.729 q^{89} -362.546 q^{90} +485.331 q^{91} +403.394 q^{92} +1.21285 q^{93} -586.749 q^{94} +684.809 q^{95} -96.0000 q^{96} -1472.39 q^{97} -946.000 q^{98} +491.091 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{2} + 6 q^{3} + 8 q^{4} + 26 q^{5} - 12 q^{6} - 16 q^{8} + 18 q^{9}+O(q^{10}) \) 2 * q - 4 * q^2 + 6 * q^3 + 8 * q^4 + 26 * q^5 - 12 * q^6 - 16 * q^8 + 18 * q^9	\( 2 q - 4 q^{2} + 6 q^{3} + 8 q^{4} + 26 q^{5} - 12 q^{6} - 16 q^{8} + 18 q^{9} - 52 q^{10} + 52 q^{11} + 24 q^{12} + 66 q^{13} + 78 q^{15} + 32 q^{16} - 64 q^{17} - 36 q^{18} + 68 q^{19} + 104 q^{20} - 104 q^{22} + 116 q^{23} - 48 q^{24} + 190 q^{25} - 132 q^{26} + 54 q^{27} + 350 q^{29} - 156 q^{30} - 242 q^{31} - 64 q^{32} + 156 q^{33} + 128 q^{34} - 408 q^{35} + 72 q^{36} - 638 q^{37} - 136 q^{38} + 198 q^{39} - 208 q^{40} - 616 q^{41} + 768 q^{43} + 208 q^{44} + 234 q^{45} - 232 q^{46} + 44 q^{47} + 96 q^{48} + 946 q^{49} - 380 q^{50} - 192 q^{51} + 264 q^{52} + 90 q^{53} - 108 q^{54} + 1084 q^{55} + 204 q^{57} - 700 q^{58} + 118 q^{59} + 312 q^{60} + 1250 q^{61} + 484 q^{62} + 128 q^{64} + 144 q^{65} - 312 q^{66} + 1460 q^{67} - 256 q^{68} + 348 q^{69} + 816 q^{70} + 162 q^{71} - 144 q^{72} + 284 q^{73} + 1276 q^{74} + 570 q^{75} + 272 q^{76} - 1632 q^{77} - 396 q^{78} - 512 q^{79} + 416 q^{80} + 162 q^{81} + 1232 q^{82} + 376 q^{83} - 220 q^{85} - 1536 q^{86} + 1050 q^{87} - 416 q^{88} - 492 q^{89} - 468 q^{90} + 2856 q^{91} + 464 q^{92} - 726 q^{93} - 88 q^{94} + 884 q^{95} - 192 q^{96} - 1088 q^{97} - 1892 q^{98} + 468 q^{99}+O(q^{100}) \) 2 * q - 4 * q^2 + 6 * q^3 + 8 * q^4 + 26 * q^5 - 12 * q^6 - 16 * q^8 + 18 * q^9 - 52 * q^10 + 52 * q^11 + 24 * q^12 + 66 * q^13 + 78 * q^15 + 32 * q^16 - 64 * q^17 - 36 * q^18 + 68 * q^19 + 104 * q^20 - 104 * q^22 + 116 * q^23 - 48 * q^24 + 190 * q^25 - 132 * q^26 + 54 * q^27 + 350 * q^29 - 156 * q^30 - 242 * q^31 - 64 * q^32 + 156 * q^33 + 128 * q^34 - 408 * q^35 + 72 * q^36 - 638 * q^37 - 136 * q^38 + 198 * q^39 - 208 * q^40 - 616 * q^41 + 768 * q^43 + 208 * q^44 + 234 * q^45 - 232 * q^46 + 44 * q^47 + 96 * q^48 + 946 * q^49 - 380 * q^50 - 192 * q^51 + 264 * q^52 + 90 * q^53 - 108 * q^54 + 1084 * q^55 + 204 * q^57 - 700 * q^58 + 118 * q^59 + 312 * q^60 + 1250 * q^61 + 484 * q^62 + 128 * q^64 + 144 * q^65 - 312 * q^66 + 1460 * q^67 - 256 * q^68 + 348 * q^69 + 816 * q^70 + 162 * q^71 - 144 * q^72 + 284 * q^73 + 1276 * q^74 + 570 * q^75 + 272 * q^76 - 1632 * q^77 - 396 * q^78 - 512 * q^79 + 416 * q^80 + 162 * q^81 + 1232 * q^82 + 376 * q^83 - 220 * q^85 - 1536 * q^86 + 1050 * q^87 - 416 * q^88 - 492 * q^89 - 468 * q^90 + 2856 * q^91 + 464 * q^92 - 726 * q^93 - 88 * q^94 + 884 * q^95 - 192 * q^96 - 1088 * q^97 - 1892 * q^98 + 468 * q^99

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