LMFDB - Embedded newform 354.4.a.f.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:	$3$
Coefficient field:	3.3.18989.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 17x + 14 $ x^3 - x^2 - 17*x + 14
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-4.05043$ 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)

$f(q)$	$=$	$q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -17.7453 q^{5} -6.00000 q^{6} -13.9633 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -17.7453 q^{5} -6.00000 q^{6} -13.9633 q^{7} -8.00000 q^{8} +9.00000 q^{9} +35.4906 q^{10} -46.9266 q^{11} +12.0000 q^{12} +12.6240 q^{13} +27.9266 q^{14} -53.2359 q^{15} +16.0000 q^{16} -12.7632 q^{17} -18.0000 q^{18} +62.9633 q^{19} -70.9812 q^{20} -41.8898 q^{21} +93.8531 q^{22} +137.119 q^{23} -24.0000 q^{24} +189.896 q^{25} -25.2479 q^{26} +27.0000 q^{27} -55.8531 q^{28} +36.9137 q^{29} +106.472 q^{30} +148.043 q^{31} -32.0000 q^{32} -140.780 q^{33} +25.5265 q^{34} +247.783 q^{35} +36.0000 q^{36} +7.66392 q^{37} -125.927 q^{38} +37.8719 q^{39} +141.962 q^{40} -108.481 q^{41} +83.7797 q^{42} +228.486 q^{43} -187.706 q^{44} -159.708 q^{45} -274.238 q^{46} -474.446 q^{47} +48.0000 q^{48} -148.027 q^{49} -379.791 q^{50} -38.2897 q^{51} +50.4959 q^{52} +645.954 q^{53} -54.0000 q^{54} +832.726 q^{55} +111.706 q^{56} +188.890 q^{57} -73.8273 q^{58} +59.0000 q^{59} -212.944 q^{60} +134.942 q^{61} -296.087 q^{62} -125.669 q^{63} +64.0000 q^{64} -224.016 q^{65} +281.559 q^{66} -697.004 q^{67} -51.0529 q^{68} +411.357 q^{69} -495.565 q^{70} +276.687 q^{71} -72.0000 q^{72} +1203.43 q^{73} -15.3278 q^{74} +569.687 q^{75} +251.853 q^{76} +655.248 q^{77} -75.7438 q^{78} +951.201 q^{79} -283.925 q^{80} +81.0000 q^{81} +216.963 q^{82} -187.816 q^{83} -167.559 q^{84} +226.487 q^{85} -456.972 q^{86} +110.741 q^{87} +375.412 q^{88} +702.075 q^{89} +319.415 q^{90} -176.272 q^{91} +548.476 q^{92} +444.130 q^{93} +948.892 q^{94} -1117.30 q^{95} -96.0000 q^{96} -98.6825 q^{97} +296.054 q^{98} -422.339 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 6 q^{2} + 9 q^{3} + 12 q^{4} - 28 q^{5} - 18 q^{6} + 26 q^{7} - 24 q^{8} + 27 q^{9}+O(q^{10}) $ 3 * q - 6 * q^2 + 9 * q^3 + 12 * q^4 - 28 * q^5 - 18 * q^6 + 26 * q^7 - 24 * q^8 + 27 * q^9	\( 3 q - 6 q^{2} + 9 q^{3} + 12 q^{4} - 28 q^{5} - 18 q^{6} + 26 q^{7} - 24 q^{8} + 27 q^{9} + 56 q^{10} - 5 q^{11} + 36 q^{12} - 19 q^{13} - 52 q^{14} - 84 q^{15} + 48 q^{16} + 20 q^{17} - 54 q^{18} + 121 q^{19} - 112 q^{20} + 78 q^{21} + 10 q^{22} - 7 q^{23} - 72 q^{24} + 371 q^{25} + 38 q^{26} + 81 q^{27} + 104 q^{28} - 121 q^{29} + 168 q^{30} + 651 q^{31} - 96 q^{32} - 15 q^{33} - 40 q^{34} - 291 q^{35} + 108 q^{36} + 618 q^{37} - 242 q^{38} - 57 q^{39} + 224 q^{40} + 314 q^{41} - 156 q^{42} - 265 q^{43} - 20 q^{44} - 252 q^{45} + 14 q^{46} + 179 q^{47} + 144 q^{48} + 259 q^{49} - 742 q^{50} + 60 q^{51} - 76 q^{52} + 252 q^{53} - 162 q^{54} - 50 q^{55} - 208 q^{56} + 363 q^{57} + 242 q^{58} + 177 q^{59} - 336 q^{60} + 997 q^{61} - 1302 q^{62} + 234 q^{63} + 192 q^{64} + 888 q^{65} + 30 q^{66} + 460 q^{67} + 80 q^{68} - 21 q^{69} + 582 q^{70} + 1263 q^{71} - 216 q^{72} + 1543 q^{73} - 1236 q^{74} + 1113 q^{75} + 484 q^{76} + 2082 q^{77} + 114 q^{78} + 1719 q^{79} - 448 q^{80} + 243 q^{81} - 628 q^{82} - 224 q^{83} + 312 q^{84} + 2285 q^{85} + 530 q^{86} - 363 q^{87} + 40 q^{88} + 1347 q^{89} + 504 q^{90} - 1646 q^{91} - 28 q^{92} + 1953 q^{93} - 358 q^{94} - 1081 q^{95} - 288 q^{96} + 1200 q^{97} - 518 q^{98} - 45 q^{99}+O(q^{100}) \) 3 * q - 6 * q^2 + 9 * q^3 + 12 * q^4 - 28 * q^5 - 18 * q^6 + 26 * q^7 - 24 * q^8 + 27 * q^9 + 56 * q^10 - 5 * q^11 + 36 * q^12 - 19 * q^13 - 52 * q^14 - 84 * q^15 + 48 * q^16 + 20 * q^17 - 54 * q^18 + 121 * q^19 - 112 * q^20 + 78 * q^21 + 10 * q^22 - 7 * q^23 - 72 * q^24 + 371 * q^25 + 38 * q^26 + 81 * q^27 + 104 * q^28 - 121 * q^29 + 168 * q^30 + 651 * q^31 - 96 * q^32 - 15 * q^33 - 40 * q^34 - 291 * q^35 + 108 * q^36 + 618 * q^37 - 242 * q^38 - 57 * q^39 + 224 * q^40 + 314 * q^41 - 156 * q^42 - 265 * q^43 - 20 * q^44 - 252 * q^45 + 14 * q^46 + 179 * q^47 + 144 * q^48 + 259 * q^49 - 742 * q^50 + 60 * q^51 - 76 * q^52 + 252 * q^53 - 162 * q^54 - 50 * q^55 - 208 * q^56 + 363 * q^57 + 242 * q^58 + 177 * q^59 - 336 * q^60 + 997 * q^61 - 1302 * q^62 + 234 * q^63 + 192 * q^64 + 888 * q^65 + 30 * q^66 + 460 * q^67 + 80 * q^68 - 21 * q^69 + 582 * q^70 + 1263 * q^71 - 216 * q^72 + 1543 * q^73 - 1236 * q^74 + 1113 * q^75 + 484 * q^76 + 2082 * q^77 + 114 * q^78 + 1719 * q^79 - 448 * q^80 + 243 * q^81 - 628 * q^82 - 224 * q^83 + 312 * q^84 + 2285 * q^85 + 530 * q^86 - 363 * q^87 + 40 * q^88 + 1347 * q^89 + 504 * q^90 - 1646 * q^91 - 28 * q^92 + 1953 * q^93 - 358 * q^94 - 1081 * q^95 - 288 * q^96 + 1200 * q^97 - 518 * q^98 - 45 * 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
$5$	−17.7453	−1.58719	−0.793594	−	0.608448i	$-0.791793\pi$
$5$	−17.7453	−1.58719	−0.793594	+	0.608448i	$0.791793\pi$
$6$	−6.00000	−0.408248
$7$	−13.9633	−0.753946	−0.376973	−	0.926224i	$-0.623035\pi$
$7$	−13.9633	−0.753946	−0.376973	+	0.926224i	$0.623035\pi$
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	35.4906	1.12231
$11$	−46.9266	−1.28626	−0.643131	−	0.765756i	$-0.722365\pi$
$11$	−46.9266	−1.28626	−0.643131	+	0.765756i	$0.722365\pi$
$12$	12.0000	0.288675
$13$	12.6240	0.269328	0.134664	−	0.990891i	$-0.457005\pi$
$13$	12.6240	0.269328	0.134664	+	0.990891i	$0.457005\pi$
$14$	27.9266	0.533120
$15$	−53.2359	−0.916363
$16$	16.0000	0.250000
$17$	−12.7632	−0.182091	−0.0910453	−	0.995847i	$-0.529021\pi$
$17$	−12.7632	−0.182091	−0.0910453	+	0.995847i	$0.529021\pi$
$18$	−18.0000	−0.235702
$19$	62.9633	0.760251	0.380125	−	0.924935i	$-0.375881\pi$
$19$	62.9633	0.760251	0.380125	+	0.924935i	$0.375881\pi$
$20$	−70.9812	−0.793594
$21$	−41.8898	−0.435291
$22$	93.8531	0.909525
$23$	137.119	1.24310	0.621550	−	0.783375i	$-0.286503\pi$
$23$	137.119	1.24310	0.621550	+	0.783375i	$0.286503\pi$
$24$	−24.0000	−0.204124
$25$	189.896	1.51917
$26$	−25.2479	−0.190443
$27$	27.0000	0.192450
$28$	−55.8531	−0.376973
$29$	36.9137	0.236369	0.118184	−	0.992992i	$-0.462293\pi$
$29$	36.9137	0.236369	0.118184	+	0.992992i	$0.462293\pi$
$30$	106.472	0.647967
$31$	148.043	0.857722	0.428861	−	0.903370i	$-0.358915\pi$
$31$	148.043	0.857722	0.428861	+	0.903370i	$0.358915\pi$
$32$	−32.0000	−0.176777
$33$	−140.780	−0.742624
$34$	25.5265	0.128757
$35$	247.783	1.19665
$36$	36.0000	0.166667
$37$	7.66392	0.0340525	0.0170262	−	0.999855i	$-0.494580\pi$
$37$	7.66392	0.0340525	0.0170262	+	0.999855i	$0.494580\pi$
$38$	−125.927	−0.537579
$39$	37.8719	0.155496
$40$	141.962	0.561156
$41$	−108.481	−0.413218	−0.206609	−	0.978424i	$-0.566243\pi$
$41$	−108.481	−0.413218	−0.206609	+	0.978424i	$0.566243\pi$
$42$	83.7797	0.307797
$43$	228.486	0.810320	0.405160	−	0.914246i	$-0.367216\pi$
$43$	228.486	0.810320	0.405160	+	0.914246i	$0.367216\pi$
$44$	−187.706	−0.643131
$45$	−159.708	−0.529063
$46$	−274.238	−0.879004
$47$	−474.446	−1.47245	−0.736224	−	0.676738i	$-0.763393\pi$
$47$	−474.446	−1.47245	−0.736224	+	0.676738i	$0.763393\pi$
$48$	48.0000	0.144338
$49$	−148.027	−0.431565
$50$	−379.791	−1.07421
$51$	−38.2897	−0.105130
$52$	50.4959	0.134664
$53$	645.954	1.67413	0.837063	−	0.547107i	$-0.184271\pi$
$53$	645.954	1.67413	0.837063	+	0.547107i	$0.184271\pi$
$54$	−54.0000	−0.136083
$55$	832.726	2.04154
$56$	111.706	0.266560
$57$	188.890	0.438931
$58$	−73.8273	−0.167138
$59$	59.0000	0.130189
$59$	59.0000	0.130189
$60$	−212.944	−0.458182
$61$	134.942	0.283240	0.141620	−	0.989921i	$-0.454769\pi$
$61$	134.942	0.283240	0.141620	+	0.989921i	$0.454769\pi$
$62$	−296.087	−0.606501
$63$	−125.669	−0.251315
$64$	64.0000	0.125000
$65$	−224.016	−0.427473
$66$	281.559	0.525114
$67$	−697.004	−1.27093	−0.635467	−	0.772128i	$-0.719193\pi$
$67$	−697.004	−1.27093	−0.635467	+	0.772128i	$0.719193\pi$
$68$	−51.0529	−0.0910453
$69$	411.357	0.717704
$70$	−495.565	−0.846162
$71$	276.687	0.462489	0.231244	−	0.972896i	$-0.425720\pi$
$71$	276.687	0.462489	0.231244	+	0.972896i	$0.425720\pi$
$72$	−72.0000	−0.117851
$73$	1203.43	1.92946	0.964728	−	0.263247i	$-0.0847936\pi$
$73$	1203.43	1.92946	0.964728	+	0.263247i	$0.0847936\pi$
$74$	−15.3278	−0.0240787
$75$	569.687	0.877091
$76$	251.853	0.380125
$77$	655.248	0.969772
$78$	−75.7438	−0.109953
$79$	951.201	1.35466	0.677332	−	0.735678i	$-0.263136\pi$
$79$	951.201	1.35466	0.677332	+	0.735678i	$0.263136\pi$
$80$	−283.925	−0.396797
$81$	81.0000	0.111111
$82$	216.963	0.292190
$83$	−187.816	−0.248380	−0.124190	−	0.992258i	$-0.539633\pi$
$83$	−187.816	−0.248380	−0.124190	+	0.992258i	$0.539633\pi$
$84$	−167.559	−0.217645
$85$	226.487	0.289012
$86$	−456.972	−0.572983
$87$	110.741	0.136468
$88$	375.412	0.454762
$89$	702.075	0.836177	0.418089	−	0.908406i	$-0.362700\pi$
$89$	702.075	0.836177	0.418089	+	0.908406i	$0.362700\pi$
$90$	319.415	0.374104
$91$	−176.272	−0.203058
$92$	548.476	0.621550
$93$	444.130	0.495206
$94$	948.892	1.04118
$95$	−1117.30	−1.20666
$96$	−96.0000	−0.102062
$97$	−98.6825	−0.103296	−0.0516479	−	0.998665i	$-0.516447\pi$
$97$	−98.6825	−0.103296	−0.0516479	+	0.998665i	$0.516447\pi$
$98$	296.054	0.305163
$99$	−422.339	−0.428754
$100$	759.583	0.759583
$101$	619.375	0.610199	0.305099	−	0.952321i	$-0.401310\pi$
$101$	619.375	0.610199	0.305099	+	0.952321i	$0.401310\pi$
$102$	76.5794	0.0743381
$103$	1839.63	1.75984	0.879921	−	0.475120i	$-0.157595\pi$
$103$	1839.63	1.75984	0.879921	+	0.475120i	$0.157595\pi$
$104$	−100.992	−0.0952217
$105$	743.348	0.690889
$106$	−1291.91	−1.18379
$107$	−471.013	−0.425556	−0.212778	−	0.977101i	$-0.568251\pi$
$107$	−471.013	−0.425556	−0.212778	+	0.977101i	$0.568251\pi$
$108$	108.000	0.0962250
$109$	−577.873	−0.507800	−0.253900	−	0.967230i	$-0.581713\pi$
$109$	−577.873	−0.507800	−0.253900	+	0.967230i	$0.581713\pi$
$110$	−1665.45	−1.44359
$111$	22.9918	0.0196602
$112$	−223.412	−0.188487
$113$	−511.137	−0.425520	−0.212760	−	0.977105i	$-0.568245\pi$
$113$	−511.137	−0.425520	−0.212760	+	0.977105i	$0.568245\pi$
$114$	−377.780	−0.310371
$115$	−2433.22	−1.97303
$116$	147.655	0.118184
$117$	113.616	0.0897758
$118$	−118.000	−0.0920575
$119$	178.217	0.137286
$120$	425.887	0.323983
$121$	871.101	0.654471
$122$	−269.885	−0.200281
$123$	−325.444	−0.238572
$124$	592.174	0.428861
$125$	−1151.59	−0.824014
$126$	251.339	0.177707
$127$	−2172.09	−1.51765	−0.758827	−	0.651292i	$-0.774227\pi$
$127$	−2172.09	−1.51765	−0.758827	+	0.651292i	$0.774227\pi$
$128$	−128.000	−0.0883883
$129$	685.458	0.467839
$130$	448.032	0.302269
$131$	−617.010	−0.411515	−0.205757	−	0.978603i	$-0.565966\pi$
$131$	−617.010	−0.411515	−0.205757	+	0.978603i	$0.565966\pi$
$132$	−563.119	−0.371312
$133$	−879.174	−0.573188
$134$	1394.01	0.898687
$135$	−479.123	−0.305454
$136$	102.106	0.0643787
$137$	−85.1682	−0.0531125	−0.0265562	−	0.999647i	$-0.508454\pi$
$137$	−85.1682	−0.0531125	−0.0265562	+	0.999647i	$0.508454\pi$
$138$	−822.714	−0.507493
$139$	559.724	0.341548	0.170774	−	0.985310i	$-0.445373\pi$
$139$	559.724	0.341548	0.170774	+	0.985310i	$0.445373\pi$
$140$	991.130	0.598327
$141$	−1423.34	−0.850118
$142$	−553.374	−0.327029
$143$	−592.399	−0.346426
$144$	144.000	0.0833333
$145$	−655.044	−0.375162
$146$	−2406.85	−1.36433
$147$	−444.081	−0.249164
$148$	30.6557	0.0170262
$149$	1510.48	0.830491	0.415246	−	0.909709i	$-0.363696\pi$
$149$	1510.48	0.830491	0.415246	+	0.909709i	$0.363696\pi$
$150$	−1139.37	−0.620197
$151$	−2847.53	−1.53463	−0.767314	−	0.641271i	$-0.778407\pi$
$151$	−2847.53	−1.53463	−0.767314	+	0.641271i	$0.778407\pi$
$152$	−503.706	−0.268789
$153$	−114.869	−0.0606968
$154$	−1310.50	−0.685733
$155$	−2627.08	−1.36137
$156$	151.488	0.0777482
$157$	422.872	0.214961	0.107480	−	0.994207i	$-0.465722\pi$
$157$	422.872	0.214961	0.107480	+	0.994207i	$0.465722\pi$
$158$	−1902.40	−0.957892
$159$	1937.86	0.966557
$160$	567.850	0.280578
$161$	−1914.63	−0.937230
$162$	−162.000	−0.0785674
$163$	1926.41	0.925694	0.462847	−	0.886438i	$-0.346828\pi$
$163$	1926.41	0.925694	0.462847	+	0.886438i	$0.346828\pi$
$164$	−433.926	−0.206609
$165$	2498.18	1.17868
$166$	375.633	0.175631
$167$	1328.27	0.615477	0.307739	−	0.951471i	$-0.400428\pi$
$167$	1328.27	0.615477	0.307739	+	0.951471i	$0.400428\pi$
$168$	335.119	0.153899
$169$	−2037.64	−0.927463
$170$	−452.975	−0.204362
$171$	566.669	0.253417
$172$	913.943	0.405160
$173$	−1935.45	−0.850577	−0.425288	−	0.905058i	$-0.639827\pi$
$173$	−1935.45	−0.850577	−0.425288	+	0.905058i	$0.639827\pi$
$174$	−221.482	−0.0964972
$175$	−2651.57	−1.14537
$176$	−750.825	−0.321566
$177$	177.000	0.0751646
$178$	−1404.15	−0.591266
$179$	−2354.19	−0.983021	−0.491510	−	0.870872i	$-0.663555\pi$
$179$	−2354.19	−0.983021	−0.491510	+	0.870872i	$0.663555\pi$
$180$	−638.831	−0.264531
$181$	301.447	0.123792	0.0618961	−	0.998083i	$-0.480285\pi$
$181$	301.447	0.123792	0.0618961	+	0.998083i	$0.480285\pi$
$182$	352.544	0.143584
$183$	404.827	0.163528
$184$	−1096.95	−0.439502
$185$	−135.999	−0.0540477
$186$	−888.261	−0.350164
$187$	598.935	0.234216
$188$	−1897.78	−0.736224
$189$	−377.008	−0.145097
$190$	2234.60	0.853238
$191$	4004.53	1.51706	0.758529	−	0.651640i	$-0.225919\pi$
$191$	4004.53	1.51706	0.758529	+	0.651640i	$0.225919\pi$
$192$	192.000	0.0721688
$193$	1546.16	0.576657	0.288328	−	0.957532i	$-0.406901\pi$
$193$	1546.16	0.576657	0.288328	+	0.957532i	$0.406901\pi$
$194$	197.365	0.0730411
$195$	−672.048	−0.246802
$196$	−592.108	−0.215783
$197$	−3465.33	−1.25327	−0.626636	−	0.779312i	$-0.715569\pi$
$197$	−3465.33	−1.25327	−0.626636	+	0.779312i	$0.715569\pi$
$198$	844.678	0.303175
$199$	4399.56	1.56722	0.783609	−	0.621254i	$-0.213377\pi$
$199$	4399.56	1.56722	0.783609	+	0.621254i	$0.213377\pi$
$200$	−1519.17	−0.537106
$201$	−2091.01	−0.733775
$202$	−1238.75	−0.431476
$203$	−515.436	−0.178209
$204$	−153.159	−0.0525650
$205$	1925.04	0.655855
$206$	−3679.25	−1.24440
$207$	1234.07	0.414366
$208$	201.983	0.0673319
$209$	−2954.65	−0.977882
$210$	−1486.70	−0.488532
$211$	4966.93	1.62056	0.810279	−	0.586044i	$-0.199315\pi$
$211$	4966.93	1.62056	0.810279	+	0.586044i	$0.199315\pi$
$212$	2583.82	0.837063
$213$	830.061	0.267018
$214$	942.025	0.300914
$215$	−4054.55	−1.28613
$216$	−216.000	−0.0680414
$217$	−2067.17	−0.646676
$218$	1155.75	0.359069
$219$	3610.28	1.11397
$220$	3330.90	1.02077
$221$	−161.123	−0.0490420
$222$	−45.9835	−0.0139019
$223$	4178.41	1.25474	0.627370	−	0.778721i	$-0.284131\pi$
$223$	4178.41	1.25474	0.627370	+	0.778721i	$0.284131\pi$
$224$	446.825	0.133280
$225$	1709.06	0.506389
$226$	1022.27	0.300888
$227$	−5149.58	−1.50568	−0.752840	−	0.658204i	$-0.771317\pi$
$227$	−5149.58	−1.50568	−0.752840	+	0.658204i	$0.771317\pi$
$228$	755.559	0.219466
$229$	−3217.17	−0.928370	−0.464185	−	0.885738i	$-0.653653\pi$
$229$	−3217.17	−0.928370	−0.464185	+	0.885738i	$0.653653\pi$
$230$	4866.43	1.39514
$231$	1965.75	0.559898
$232$	−295.309	−0.0835690
$233$	2126.84	0.597998	0.298999	−	0.954253i	$-0.403347\pi$
$233$	2126.84	0.597998	0.298999	+	0.954253i	$0.403347\pi$
$234$	−227.231	−0.0634811
$235$	8419.19	2.33705
$236$	236.000	0.0650945
$237$	2853.60	0.782116
$238$	−356.433	−0.0970762
$239$	5862.07	1.58655	0.793276	−	0.608863i	$-0.208374\pi$
$239$	5862.07	1.58655	0.793276	+	0.608863i	$0.208374\pi$
$240$	−851.774	−0.229091
$241$	−2501.24	−0.668545	−0.334272	−	0.942477i	$-0.608491\pi$
$241$	−2501.24	−0.668545	−0.334272	+	0.942477i	$0.608491\pi$
$242$	−1742.20	−0.462781
$243$	243.000	0.0641500
$244$	539.770	0.141620
$245$	2626.78	0.684975
$246$	650.889	0.168696
$247$	794.846	0.204756
$248$	−1184.35	−0.303251
$249$	−563.449	−0.143402
$250$	2303.19	0.582666
$251$	1625.72	0.408822	0.204411	−	0.978885i	$-0.434472\pi$
$251$	1625.72	0.408822	0.204411	+	0.978885i	$0.434472\pi$
$252$	−502.678	−0.125658
$253$	−6434.52	−1.59895
$254$	4344.18	1.07314
$255$	679.462	0.166861
$256$	256.000	0.0625000
$257$	−3447.00	−0.836647	−0.418323	−	0.908298i	$-0.637382\pi$
$257$	−3447.00	−0.836647	−0.418323	+	0.908298i	$0.637382\pi$
$258$	−1370.92	−0.330812
$259$	−107.013	−0.0256737
$260$	−896.064	−0.213737
$261$	332.223	0.0787896
$262$	1234.02	0.290985
$263$	−4136.63	−0.969869	−0.484934	−	0.874551i	$-0.661157\pi$
$263$	−4136.63	−0.969869	−0.484934	+	0.874551i	$0.661157\pi$
$264$	1126.24	0.262557
$265$	−11462.7	−2.65715
$266$	1758.35	0.405305
$267$	2106.22	0.482767
$268$	−2788.02	−0.635467
$269$	3571.47	0.809503	0.404752	−	0.914427i	$-0.367358\pi$
$269$	3571.47	0.809503	0.404752	+	0.914427i	$0.367358\pi$
$270$	958.246	0.215989
$271$	1176.08	0.263622	0.131811	−	0.991275i	$-0.457921\pi$
$271$	1176.08	0.263622	0.131811	+	0.991275i	$0.457921\pi$
$272$	−204.212	−0.0455226
$273$	−528.816	−0.117236
$274$	170.336	0.0375562
$275$	−8911.15	−1.95405
$276$	1645.43	0.358852
$277$	−3942.78	−0.855229	−0.427615	−	0.903961i	$-0.640646\pi$
$277$	−3942.78	−0.855229	−0.427615	+	0.903961i	$0.640646\pi$
$278$	−1119.45	−0.241511
$279$	1332.39	0.285907
$280$	−1982.26	−0.423081
$281$	8273.14	1.75635	0.878175	−	0.478340i	$-0.158761\pi$
$281$	8273.14	1.75635	0.878175	+	0.478340i	$0.158761\pi$
$282$	2846.68	0.601124
$283$	−3476.20	−0.730173	−0.365086	−	0.930974i	$-0.618961\pi$
$283$	−3476.20	−0.730173	−0.365086	+	0.930974i	$0.618961\pi$
$284$	1106.75	0.231244
$285$	−3351.91	−0.696666
$286$	1184.80	0.244960
$287$	1514.76	0.311544
$288$	−288.000	−0.0589256
$289$	−4750.10	−0.966843
$290$	1310.09	0.265279
$291$	−296.047	−0.0596378
$292$	4813.70	0.964728
$293$	5308.92	1.05853	0.529267	−	0.848456i	$-0.322467\pi$
$293$	5308.92	1.05853	0.529267	+	0.848456i	$0.322467\pi$
$294$	888.162	0.176186
$295$	−1046.97	−0.206634
$296$	−61.3114	−0.0120394
$297$	−1267.02	−0.247541
$298$	−3020.96	−0.587246
$299$	1730.99	0.334801
$300$	2278.75	0.438545
$301$	−3190.41	−0.610938
$302$	5695.06	1.08515
$303$	1858.12	0.352298
$304$	1007.41	0.190063
$305$	−2394.59	−0.449554
$306$	229.738	0.0429191
$307$	780.338	0.145069	0.0725346	−	0.997366i	$-0.476891\pi$
$307$	780.338	0.145069	0.0725346	+	0.997366i	$0.476891\pi$
$308$	2620.99	0.484886
$309$	5518.88	1.01605
$310$	5254.15	0.962632
$311$	6626.70	1.20825	0.604125	−	0.796890i	$-0.293523\pi$
$311$	6626.70	1.20825	0.604125	+	0.796890i	$0.293523\pi$
$312$	−302.975	−0.0549763
$313$	−3748.22	−0.676876	−0.338438	−	0.940989i	$-0.609898\pi$
$313$	−3748.22	−0.676876	−0.338438	+	0.940989i	$0.609898\pi$
$314$	−845.744	−0.152000
$315$	2230.04	0.398885
$316$	3804.80	0.677332
$317$	7211.72	1.27776	0.638881	−	0.769306i	$-0.279398\pi$
$317$	7211.72	1.27776	0.638881	+	0.769306i	$0.279398\pi$
$318$	−3875.73	−0.683459
$319$	−1732.23	−0.304032
$320$	−1135.70	−0.198399
$321$	−1413.04	−0.245695
$322$	3829.26	0.662721
$323$	−803.615	−0.138434
$324$	324.000	0.0555556
$325$	2397.24	0.409153
$326$	−3852.82	−0.654565
$327$	−1733.62	−0.293178
$328$	867.852	0.146095
$329$	6624.82	1.11015
$330$	−4996.35	−0.833455
$331$	−10980.1	−1.82333	−0.911663	−	0.410938i	$-0.865201\pi$
$331$	−10980.1	−1.82333	−0.911663	+	0.410938i	$0.865201\pi$
$332$	−751.266	−0.124190
$333$	68.9753	0.0113508
$334$	−2656.54	−0.435208
$335$	12368.6	2.01721
$336$	−670.237	−0.108823
$337$	10224.9	1.65278	0.826391	−	0.563097i	$-0.190390\pi$
$337$	10224.9	1.65278	0.826391	+	0.563097i	$0.190390\pi$
$338$	4075.27	0.655815
$339$	−1533.41	−0.245674
$340$	905.950	0.144506
$341$	−6947.17	−1.10326
$342$	−1133.34	−0.179193
$343$	6856.34	1.07932
$344$	−1827.89	−0.286491
$345$	−7299.65	−1.13913
$346$	3870.91	0.601449
$347$	5169.44	0.799741	0.399870	−	0.916572i	$-0.369055\pi$
$347$	5169.44	0.799741	0.399870	+	0.916572i	$0.369055\pi$
$348$	442.964	0.0682338
$349$	−597.944	−0.0917112	−0.0458556	−	0.998948i	$-0.514601\pi$
$349$	−597.944	−0.0917112	−0.0458556	+	0.998948i	$0.514601\pi$
$350$	5303.13	0.809898
$351$	340.847	0.0518321
$352$	1501.65	0.227381
$353$	477.685	0.0720243	0.0360122	−	0.999351i	$-0.488534\pi$
$353$	477.685	0.0720243	0.0360122	+	0.999351i	$0.488534\pi$
$354$	−354.000	−0.0531494
$355$	−4909.89	−0.734056
$356$	2808.30	0.418089
$357$	534.650	0.0792623
$358$	4708.39	0.695101
$359$	11885.2	1.74729	0.873646	−	0.486563i	$-0.161749\pi$
$359$	11885.2	1.74729	0.873646	+	0.486563i	$0.161749\pi$
$360$	1277.66	0.187052
$361$	−2894.63	−0.422019
$362$	−602.894	−0.0875343
$363$	2613.30	0.377859
$364$	−705.088	−0.101529
$365$	−21355.2	−3.06241
$366$	−809.655	−0.115632
$367$	610.587	0.0868457	0.0434228	−	0.999057i	$-0.486174\pi$
$367$	610.587	0.0868457	0.0434228	+	0.999057i	$0.486174\pi$
$368$	2193.90	0.310775
$369$	−976.333	−0.137739
$370$	271.997	0.0382175
$371$	−9019.64	−1.26220
$372$	1776.52	0.247603
$373$	−7024.04	−0.975042	−0.487521	−	0.873111i	$-0.662099\pi$
$373$	−7024.04	−0.975042	−0.487521	+	0.873111i	$0.662099\pi$
$374$	−1197.87	−0.165616
$375$	−3454.78	−0.475745
$376$	3795.57	0.520589
$377$	465.997	0.0636606
$378$	754.017	0.102599
$379$	8622.74	1.16865	0.584327	−	0.811518i	$-0.301358\pi$
$379$	8622.74	1.16865	0.584327	+	0.811518i	$0.301358\pi$
$380$	−4469.21	−0.603331
$381$	−6516.28	−0.876218
$382$	−8009.07	−1.07272
$383$	8392.45	1.11967	0.559836	−	0.828603i	$-0.310864\pi$
$383$	8392.45	1.11967	0.559836	+	0.828603i	$0.310864\pi$
$384$	−384.000	−0.0510310
$385$	−11627.6	−1.53921
$386$	−3092.31	−0.407758
$387$	2056.37	0.270107
$388$	−394.730	−0.0516479
$389$	5386.95	0.702132	0.351066	−	0.936351i	$-0.385819\pi$
$389$	5386.95	0.702132	0.351066	+	0.936351i	$0.385819\pi$
$390$	1344.10	0.174515
$391$	−1750.08	−0.226357
$392$	1184.22	0.152581
$393$	−1851.03	−0.237588
$394$	6930.66	0.886197
$395$	−16879.3	−2.15011
$396$	−1689.36	−0.214377
$397$	−10341.5	−1.30737	−0.653687	−	0.756765i	$-0.726779\pi$
$397$	−10341.5	−1.30737	−0.653687	+	0.756765i	$0.726779\pi$
$398$	−8799.12	−1.10819
$399$	−2637.52	−0.330930
$400$	3038.33	0.379791
$401$	9524.52	1.18611	0.593057	−	0.805160i	$-0.297921\pi$
$401$	9524.52	1.18611	0.593057	+	0.805160i	$0.297921\pi$
$402$	4182.03	0.518857
$403$	1868.90	0.231008
$404$	2477.50	0.305099
$405$	−1437.37	−0.176354
$406$	1030.87	0.126013
$407$	−359.642	−0.0438004
$408$	306.318	0.0371691
$409$	−4649.39	−0.562096	−0.281048	−	0.959694i	$-0.590682\pi$
$409$	−4649.39	−0.562096	−0.281048	+	0.959694i	$0.590682\pi$
$410$	−3850.07	−0.463760
$411$	−255.505	−0.0306645
$412$	7358.51	0.879921
$413$	−823.833	−0.0981554
$414$	−2468.14	−0.293001
$415$	3332.86	0.394225
$416$	−403.967	−0.0476108
$417$	1679.17	0.197193
$418$	5909.30	0.691467
$419$	2510.26	0.292684	0.146342	−	0.989234i	$-0.453250\pi$
$419$	2510.26	0.292684	0.146342	+	0.989234i	$0.453250\pi$
$420$	2973.39	0.345444
$421$	9011.84	1.04325	0.521627	−	0.853174i	$-0.325325\pi$
$421$	9011.84	1.04325	0.521627	+	0.853174i	$0.325325\pi$
$422$	−9933.87	−1.14591
$423$	−4270.01	−0.490816
$424$	−5167.64	−0.591893
$425$	−2423.68	−0.276626
$426$	−1660.12	−0.188810
$427$	−1884.24	−0.213547
$428$	−1884.05	−0.212778
$429$	−1777.20	−0.200009
$430$	8109.10	0.909432
$431$	2283.00	0.255147	0.127574	−	0.991829i	$-0.459281\pi$
$431$	2283.00	0.255147	0.127574	+	0.991829i	$0.459281\pi$
$432$	432.000	0.0481125
$433$	−3417.07	−0.379247	−0.189623	−	0.981857i	$-0.560727\pi$
$433$	−3417.07	−0.379247	−0.189623	+	0.981857i	$0.560727\pi$
$434$	4134.34	0.457269
$435$	−1965.13	−0.216600
$436$	−2311.49	−0.253900
$437$	8633.46	0.945067
$438$	−7220.55	−0.787697
$439$	−9424.78	−1.02465	−0.512324	−	0.858792i	$-0.671215\pi$
$439$	−9424.78	−1.02465	−0.512324	+	0.858792i	$0.671215\pi$
$440$	−6661.81	−0.721794
$441$	−1332.24	−0.143855
$442$	322.245	0.0346779
$443$	−1192.29	−0.127872	−0.0639360	−	0.997954i	$-0.520365\pi$
$443$	−1192.29	−0.127872	−0.0639360	+	0.997954i	$0.520365\pi$
$444$	91.9671	0.00983010
$445$	−12458.5	−1.32717
$446$	−8356.82	−0.887235
$447$	4531.43	0.479484
$448$	−893.650	−0.0942433
$449$	4705.61	0.494591	0.247296	−	0.968940i	$-0.420458\pi$
$449$	4705.61	0.494591	0.247296	+	0.968940i	$0.420458\pi$
$450$	−3418.12	−0.358071
$451$	5090.66	0.531507
$452$	−2044.55	−0.212760
$453$	−8542.60	−0.886018
$454$	10299.2	1.06468
$455$	3128.00	0.322292
$456$	−1511.12	−0.155186
$457$	−2758.31	−0.282338	−0.141169	−	0.989986i	$-0.545086\pi$
$457$	−2758.31	−0.282338	−0.141169	+	0.989986i	$0.545086\pi$
$458$	6434.34	0.656457
$459$	−344.607	−0.0350433
$460$	−9732.87	−0.986516
$461$	14774.7	1.49268	0.746339	−	0.665567i	$-0.231810\pi$
$461$	14774.7	1.49268	0.746339	+	0.665567i	$0.231810\pi$
$462$	−3931.49	−0.395908
$463$	10574.5	1.06142	0.530709	−	0.847554i	$-0.321926\pi$
$463$	10574.5	1.06142	0.530709	+	0.847554i	$0.321926\pi$
$464$	590.619	0.0590922
$465$	−7881.23	−0.785986
$466$	−4253.67	−0.422849
$467$	10332.7	1.02386	0.511928	−	0.859028i	$-0.328931\pi$
$467$	10332.7	1.02386	0.511928	+	0.859028i	$0.328931\pi$
$468$	454.463	0.0448879
$469$	9732.46	0.958216
$470$	−16838.4	−1.65254
$471$	1268.62	0.124108
$472$	−472.000	−0.0460287
$473$	−10722.1	−1.04228
$474$	−5707.20	−0.553039
$475$	11956.5	1.15495
$476$	712.866	0.0686432
$477$	5813.59	0.558042
$478$	−11724.1	−1.12186
$479$	5927.37	0.565404	0.282702	−	0.959208i	$-0.408769\pi$
$479$	5927.37	0.565404	0.282702	+	0.959208i	$0.408769\pi$
$480$	1703.55	0.161992
$481$	96.7491	0.00917127
$482$	5002.49	0.472733
$483$	−5743.89	−0.541110
$484$	3484.40	0.327236
$485$	1751.15	0.163950
$486$	−486.000	−0.0453609
$487$	8489.04	0.789887	0.394944	−	0.918705i	$-0.370764\pi$
$487$	8489.04	0.789887	0.394944	+	0.918705i	$0.370764\pi$
$488$	−1079.54	−0.100140
$489$	5779.23	0.534450
$490$	−5253.57	−0.484351
$491$	−4906.00	−0.450926	−0.225463	−	0.974252i	$-0.572390\pi$
$491$	−4906.00	−0.450926	−0.225463	+	0.974252i	$0.572390\pi$
$492$	−1301.78	−0.119286
$493$	−471.138	−0.0430405
$494$	−1589.69	−0.144785
$495$	7494.53	0.680513
$496$	2368.70	0.214431
$497$	−3863.46	−0.348691
$498$	1126.90	0.101401
$499$	−3595.39	−0.322548	−0.161274	−	0.986910i	$-0.551560\pi$
$499$	−3595.39	−0.322548	−0.161274	+	0.986910i	$0.551560\pi$
$500$	−4606.38	−0.412007
$501$	3984.81	0.355346
$502$	−3251.44	−0.289081
$503$	12817.7	1.13621	0.568104	−	0.822957i	$-0.307677\pi$
$503$	12817.7	1.13621	0.568104	+	0.822957i	$0.307677\pi$
$504$	1005.36	0.0888534
$505$	−10991.0	−0.968500
$506$	12869.0	1.13063
$507$	−6112.91	−0.535471
$508$	−8688.37	−0.758827
$509$	4607.28	0.401207	0.200603	−	0.979673i	$-0.435710\pi$
$509$	4607.28	0.401207	0.200603	+	0.979673i	$0.435710\pi$
$510$	−1358.92	−0.117989
$511$	−16803.8	−1.45471
$512$	−512.000	−0.0441942
$513$	1700.01	0.146310
$514$	6894.01	0.591599
$515$	−32644.7	−2.79320
$516$	2741.83	0.233919
$517$	22264.1	1.89395
$518$	214.027	0.0181541
$519$	−5806.36	−0.491081
$520$	1792.13	0.151135
$521$	−7331.06	−0.616467	−0.308234	−	0.951311i	$-0.599738\pi$
$521$	−7331.06	−0.616467	−0.308234	+	0.951311i	$0.599738\pi$
$522$	−664.446	−0.0557127
$523$	−1666.64	−0.139344	−0.0696721	−	0.997570i	$-0.522195\pi$
$523$	−1666.64	−0.139344	−0.0696721	+	0.997570i	$0.522195\pi$
$524$	−2468.04	−0.205757
$525$	−7954.70	−0.661279
$526$	8273.26	0.685801
$527$	−1889.51	−0.156183
$528$	−2252.47	−0.185656
$529$	6634.61	0.545295
$530$	22925.3	1.87889
$531$	531.000	0.0433963
$532$	−3516.69	−0.286594
$533$	−1369.47	−0.111291
$534$	−4212.45	−0.341368
$535$	8358.26	0.675438
$536$	5576.03	0.449343
$537$	−7062.58	−0.567547
$538$	−7142.94	−0.572405
$539$	6946.39	0.555106
$540$	−1916.49	−0.152727
$541$	14458.9	1.14905	0.574524	−	0.818488i	$-0.305187\pi$
$541$	14458.9	1.14905	0.574524	+	0.818488i	$0.305187\pi$
$542$	−2352.15	−0.186409
$543$	904.341	0.0714714
$544$	408.423	0.0321894
$545$	10254.5	0.805974
$546$	1057.63	0.0828983
$547$	−11804.7	−0.922729	−0.461365	−	0.887211i	$-0.652640\pi$
$547$	−11804.7	−0.922729	−0.461365	+	0.887211i	$0.652640\pi$
$548$	−340.673	−0.0265562
$549$	1214.48	0.0944132
$550$	17822.3	1.38172
$551$	2324.21	0.179700
$552$	−3290.86	−0.253747
$553$	−13281.9	−1.02134
$554$	7885.55	0.604738
$555$	−407.996	−0.0312044
$556$	2238.90	0.170774
$557$	−11483.5	−0.873560	−0.436780	−	0.899568i	$-0.643881\pi$
$557$	−11483.5	−0.873560	−0.436780	+	0.899568i	$0.643881\pi$
$558$	−2664.78	−0.202167
$559$	2884.40	0.218242
$560$	3964.52	0.299164
$561$	1796.80	0.135225
$562$	−16546.3	−1.24193
$563$	7458.56	0.558332	0.279166	−	0.960243i	$-0.409942\pi$
$563$	7458.56	0.558332	0.279166	+	0.960243i	$0.409942\pi$
$564$	−5693.35	−0.425059
$565$	9070.28	0.675380
$566$	6952.41	0.516310
$567$	−1131.03	−0.0837718
$568$	−2213.50	−0.163514
$569$	11126.6	0.819776	0.409888	−	0.912136i	$-0.365568\pi$
$569$	11126.6	0.819776	0.409888	+	0.912136i	$0.365568\pi$
$570$	6703.81	0.492617
$571$	2287.87	0.167678	0.0838391	−	0.996479i	$-0.473282\pi$
$571$	2287.87	0.167678	0.0838391	+	0.996479i	$0.473282\pi$
$572$	−2369.60	−0.173213
$573$	12013.6	0.875873
$574$	−3029.51	−0.220295
$575$	26038.3	1.88847
$576$	576.000	0.0416667
$577$	−5716.82	−0.412469	−0.206234	−	0.978503i	$-0.566121\pi$
$577$	−5716.82	−0.412469	−0.206234	+	0.978503i	$0.566121\pi$
$578$	9500.20	0.683661
$579$	4638.47	0.332933
$580$	−2620.18	−0.187581
$581$	2622.53	0.187265
$582$	592.095	0.0421703
$583$	−30312.4	−2.15337
$584$	−9627.41	−0.682166
$585$	−2016.14	−0.142491
$586$	−10617.8	−0.748496
$587$	1197.58	0.0842070	0.0421035	−	0.999113i	$-0.486594\pi$
$587$	1197.58	0.0842070	0.0421035	+	0.999113i	$0.486594\pi$
$588$	−1776.32	−0.124582
$589$	9321.30	0.652084
$590$	2093.95	0.146113
$591$	−10396.0	−0.723577
$592$	122.623	0.00851312
$593$	−23618.5	−1.63558	−0.817789	−	0.575519i	$-0.804800\pi$
$593$	−23618.5	−1.63558	−0.817789	+	0.575519i	$0.804800\pi$
$594$	2534.03	0.175038
$595$	−3162.51	−0.217899
$596$	6041.91	0.415246
$597$	13198.7	0.904834
$598$	−3461.97	−0.236740
$599$	−23194.2	−1.58212	−0.791059	−	0.611740i	$-0.790470\pi$
$599$	−23194.2	−1.58212	−0.791059	+	0.611740i	$0.790470\pi$
$600$	−4557.50	−0.310098
$601$	−6322.19	−0.429097	−0.214549	−	0.976713i	$-0.568828\pi$
$601$	−6322.19	−0.429097	−0.214549	+	0.976713i	$0.568828\pi$
$602$	6380.82	0.431998
$603$	−6273.04	−0.423645
$604$	−11390.1	−0.767314
$605$	−15458.0	−1.03877
$606$	−3716.25	−0.249113
$607$	11797.3	0.788862	0.394431	−	0.918926i	$-0.370942\pi$
$607$	11797.3	0.788862	0.394431	+	0.918926i	$0.370942\pi$
$608$	−2014.82	−0.134395
$609$	−1546.31	−0.102889
$610$	4789.19	0.317883
$611$	−5989.39	−0.396571
$612$	−459.476	−0.0303484
$613$	−19451.2	−1.28161	−0.640803	−	0.767705i	$-0.721399\pi$
$613$	−19451.2	−1.28161	−0.640803	+	0.767705i	$0.721399\pi$
$614$	−1560.68	−0.102579
$615$	5775.11	0.378658
$616$	−5241.99	−0.342866
$617$	−7734.31	−0.504654	−0.252327	−	0.967642i	$-0.581196\pi$
$617$	−7734.31	−0.504654	−0.252327	+	0.967642i	$0.581196\pi$
$618$	−11037.8	−0.718453
$619$	−24623.3	−1.59886	−0.799430	−	0.600759i	$-0.794865\pi$
$619$	−24623.3	−1.59886	−0.799430	+	0.600759i	$0.794865\pi$
$620$	−10508.3	−0.680683
$621$	3702.21	0.239235
$622$	−13253.4	−0.854361
$623$	−9803.26	−0.630432
$624$	605.950	0.0388741
$625$	−3301.58	−0.211301
$626$	7496.44	0.478623
$627$	−8863.95	−0.564581
$628$	1691.49	0.107480
$629$	−97.8164	−0.00620063
$630$	−4460.09	−0.282054
$631$	12254.0	0.773099	0.386550	−	0.922269i	$-0.373667\pi$
$631$	12254.0	0.773099	0.386550	+	0.922269i	$0.373667\pi$
$632$	−7609.61	−0.478946
$633$	14900.8	0.935630
$634$	−14423.4	−0.903514
$635$	38544.4	2.40880
$636$	7751.45	0.483278
$637$	−1868.69	−0.116232
$638$	3464.46	0.214983
$639$	2490.18	0.154163
$640$	2271.40	0.140289
$641$	−26493.9	−1.63252	−0.816261	−	0.577684i	$-0.803957\pi$
$641$	−26493.9	−1.63252	−0.816261	+	0.577684i	$0.803957\pi$
$642$	2826.08	0.173733
$643$	10758.3	0.659822	0.329911	−	0.944012i	$-0.392981\pi$
$643$	10758.3	0.659822	0.329911	+	0.944012i	$0.392981\pi$
$644$	−7658.52	−0.468615
$645$	−12163.7	−0.742548
$646$	1607.23	0.0978879
$647$	3993.15	0.242639	0.121319	−	0.992614i	$-0.461288\pi$
$647$	3993.15	0.242639	0.121319	+	0.992614i	$0.461288\pi$
$648$	−648.000	−0.0392837
$649$	−2768.67	−0.167457
$650$	−4794.47	−0.289315
$651$	−6201.52	−0.373359
$652$	7705.64	0.462847
$653$	−17363.6	−1.04056	−0.520282	−	0.853994i	$-0.674173\pi$
$653$	−17363.6	−1.04056	−0.520282	+	0.853994i	$0.674173\pi$
$654$	3467.24	0.207308
$655$	10949.0	0.653151
$656$	−1735.70	−0.103305
$657$	10830.8	0.643152
$658$	−13249.6	−0.784992
$659$	27613.6	1.63228	0.816141	−	0.577852i	$-0.196109\pi$
$659$	27613.6	1.63228	0.816141	+	0.577852i	$0.196109\pi$
$660$	9992.71	0.589342
$661$	14305.6	0.841790	0.420895	−	0.907109i	$-0.361716\pi$
$661$	14305.6	0.841790	0.420895	+	0.907109i	$0.361716\pi$
$662$	21960.2	1.28929
$663$	−483.368	−0.0283144
$664$	1502.53	0.0878155
$665$	15601.2	0.909757
$666$	−137.951	−0.00802624
$667$	5061.56	0.293830
$668$	5313.08	0.307739
$669$	12535.2	0.724425
$670$	−24737.1	−1.42638
$671$	−6332.38	−0.364320
$672$	1340.47	0.0769493
$673$	−15.2265	−0.000872122 0	−0.000436061	−	1.00000i	$-0.500139\pi$
$673$	−15.2265	−0.000872122 0	−0.000436061		1.00000i	$0.500139\pi$
$674$	−20449.9	−1.16869
$675$	5127.18	0.292364
$676$	−8150.54	−0.463731
$677$	−16165.4	−0.917708	−0.458854	−	0.888512i	$-0.651740\pi$
$677$	−16165.4	−0.917708	−0.458854	+	0.888512i	$0.651740\pi$
$678$	3066.82	0.173718
$679$	1377.93	0.0778794
$680$	−1811.90	−0.102181
$681$	−15448.7	−0.869305
$682$	13894.3	0.780120
$683$	19411.3	1.08748	0.543742	−	0.839252i	$-0.317007\pi$
$683$	19411.3	1.08748	0.543742	+	0.839252i	$0.317007\pi$
$684$	2266.68	0.126708
$685$	1511.34	0.0842995
$686$	−13712.7	−0.763197
$687$	−9651.52	−0.535995
$688$	3655.77	0.202580
$689$	8154.51	0.450888
$690$	14599.3	0.805487
$691$	26949.4	1.48365	0.741825	−	0.670594i	$-0.233961\pi$
$691$	26949.4	1.48365	0.741825	+	0.670594i	$0.233961\pi$
$692$	−7741.81	−0.425288
$693$	5897.24	0.323257
$694$	−10338.9	−0.565502
$695$	−9932.47	−0.542101
$696$	−885.928	−0.0482486
$697$	1384.57	0.0752432
$698$	1195.89	0.0648496
$699$	6380.51	0.345254
$700$	−10606.3	−0.572685
$701$	6042.73	0.325579	0.162789	−	0.986661i	$-0.447951\pi$
$701$	6042.73	0.325579	0.162789	+	0.986661i	$0.447951\pi$
$702$	−681.694	−0.0366508
$703$	482.546	0.0258884
$704$	−3003.30	−0.160783
$705$	25257.6	1.34930
$706$	−955.369	−0.0509289
$707$	−8648.50	−0.460057
$708$	708.000	0.0375823
$709$	−3530.34	−0.187003	−0.0935013	−	0.995619i	$-0.529806\pi$
$709$	−3530.34	−0.187003	−0.0935013	+	0.995619i	$0.529806\pi$
$710$	9819.79	0.519056
$711$	8560.81	0.451555
$712$	−5616.60	−0.295633
$713$	20299.6	1.06623
$714$	−1069.30	−0.0560469
$715$	10512.3	0.549843
$716$	−9416.77	−0.491510
$717$	17586.2	0.915996
$718$	−23770.4	−1.23552
$719$	35664.2	1.84986	0.924929	−	0.380139i	$-0.124124\pi$
$719$	35664.2	1.84986	0.924929	+	0.380139i	$0.124124\pi$
$720$	−2555.32	−0.132266
$721$	−25687.2	−1.32683
$722$	5789.25	0.298412
$723$	−7503.73	−0.385985
$724$	1205.79	0.0618961
$725$	7009.75	0.359083
$726$	−5226.61	−0.267187
$727$	21718.9	1.10799	0.553995	−	0.832520i	$-0.313103\pi$
$727$	21718.9	1.10799	0.553995	+	0.832520i	$0.313103\pi$
$728$	1410.18	0.0717920
$729$	729.000	0.0370370
$730$	42710.3	2.16545
$731$	−2916.22	−0.147552
$732$	1619.31	0.0817642
$733$	26954.6	1.35824	0.679122	−	0.734026i	$-0.262361\pi$
$733$	26954.6	1.35824	0.679122	+	0.734026i	$0.262361\pi$
$734$	−1221.17	−0.0614092
$735$	7880.35	0.395471
$736$	−4387.81	−0.219751
$737$	32708.0	1.63476
$738$	1952.67	0.0973965
$739$	−13324.0	−0.663237	−0.331619	−	0.943414i	$-0.607595\pi$
$739$	−13324.0	−0.663237	−0.331619	+	0.943414i	$0.607595\pi$
$740$	−543.995	−0.0270238
$741$	2384.54	0.118216
$742$	18039.3	0.892510
$743$	5997.59	0.296138	0.148069	−	0.988977i	$-0.452694\pi$
$743$	5997.59	0.296138	0.148069	+	0.988977i	$0.452694\pi$
$744$	−3553.04	−0.175082
$745$	−26803.9	−1.31815
$746$	14048.1	0.689459
$747$	−1690.35	−0.0827933
$748$	2395.74	0.117108
$749$	6576.88	0.320846
$750$	6909.57	0.336402
$751$	−37290.4	−1.81191	−0.905957	−	0.423371i	$-0.860847\pi$
$751$	−37290.4	−1.81191	−0.905957	+	0.423371i	$0.860847\pi$
$752$	−7591.13	−0.368112
$753$	4877.15	0.236034
$754$	−931.994	−0.0450149
$755$	50530.3	2.43574
$756$	−1508.03	−0.0725485
$757$	6010.23	0.288567	0.144284	−	0.989536i	$-0.453912\pi$
$757$	6010.23	0.288567	0.144284	+	0.989536i	$0.453912\pi$
$758$	−17245.5	−0.826364
$759$	−19303.6	−0.923155
$760$	8938.42	0.426619
$761$	−497.976	−0.0237209	−0.0118605	−	0.999930i	$-0.503775\pi$
$761$	−497.976	−0.0237209	−0.0118605	+	0.999930i	$0.503775\pi$
$762$	13032.6	0.619580
$763$	8069.00	0.382854
$764$	16018.1	0.758529
$765$	2038.39	0.0963373
$766$	−16784.9	−0.791728
$767$	744.814	0.0350635
$768$	768.000	0.0360844
$769$	23928.1	1.12207	0.561034	−	0.827793i	$-0.310404\pi$
$769$	23928.1	1.12207	0.561034	+	0.827793i	$0.310404\pi$
$770$	23255.2	1.08839
$771$	−10341.0	−0.483038
$772$	6184.62	0.288328
$773$	−25391.6	−1.18146	−0.590732	−	0.806868i	$-0.701161\pi$
$773$	−25391.6	−1.18146	−0.590732	+	0.806868i	$0.701161\pi$
$774$	−4112.75	−0.190994
$775$	28112.8	1.30302
$776$	789.460	0.0365206
$777$	−321.040	−0.0148227
$778$	−10773.9	−0.496482
$779$	−6830.35	−0.314150
$780$	−2688.19	−0.123401
$781$	−12984.0	−0.594882
$782$	3500.16	0.160058
$783$	996.669	0.0454892
$784$	−2368.43	−0.107891
$785$	−7503.99	−0.341183
$786$	3702.06	0.168000
$787$	34400.6	1.55813	0.779065	−	0.626943i	$-0.215694\pi$
$787$	34400.6	1.55813	0.779065	+	0.626943i	$0.215694\pi$
$788$	−13861.3	−0.626636
$789$	−12409.9	−0.559954
$790$	33758.7	1.52035
$791$	7137.15	0.320819
$792$	3378.71	0.151587
$793$	1703.51	0.0762842
$794$	20683.1	0.924453
$795$	−34388.0	−1.53411
$796$	17598.2	0.783609
$797$	−31464.7	−1.39841	−0.699207	−	0.714919i	$-0.746463\pi$
$797$	−31464.7	−1.39841	−0.699207	+	0.714919i	$0.746463\pi$
$798$	5275.04	0.234003
$799$	6055.46	0.268119
$800$	−6076.66	−0.268553
$801$	6318.67	0.278726
$802$	−19049.0	−0.838709
$803$	−56472.6	−2.48179
$804$	−8364.05	−0.366887
$805$	33975.7	1.48756
$806$	−3737.79	−0.163348
$807$	10714.4	0.467367
$808$	−4955.00	−0.215738
$809$	40499.9	1.76007	0.880037	−	0.474906i	$-0.157518\pi$
$809$	40499.9	1.76007	0.880037	+	0.474906i	$0.157518\pi$
$810$	2874.74	0.124701
$811$	37794.2	1.63642	0.818209	−	0.574921i	$-0.194967\pi$
$811$	37794.2	1.63642	0.818209	+	0.574921i	$0.194967\pi$
$812$	−2061.74	−0.0891047
$813$	3528.23	0.152202
$814$	719.283	0.0309716
$815$	−34184.7	−1.46925
$816$	−612.635	−0.0262825
$817$	14386.2	0.616047
$818$	9298.78	0.397462
$819$	−1586.45	−0.0676861
$820$	7700.15	0.327928
$821$	−2223.58	−0.0945232	−0.0472616	−	0.998883i	$-0.515049\pi$
$821$	−2223.58	−0.0945232	−0.0472616	+	0.998883i	$0.515049\pi$
$822$	511.009	0.0216831
$823$	13780.3	0.583659	0.291829	−	0.956470i	$-0.405736\pi$
$823$	13780.3	0.583659	0.291829	+	0.956470i	$0.405736\pi$
$824$	−14717.0	−0.622198
$825$	−26733.5	−1.12817
$826$	1647.67	0.0694064
$827$	−28841.6	−1.21272	−0.606360	−	0.795190i	$-0.707371\pi$
$827$	−28841.6	−1.21272	−0.606360	+	0.795190i	$0.707371\pi$
$828$	4936.28	0.207183
$829$	−26844.8	−1.12468	−0.562339	−	0.826907i	$-0.690098\pi$
$829$	−26844.8	−1.12468	−0.562339	+	0.826907i	$0.690098\pi$
$830$	−6665.72	−0.278760
$831$	−11828.3	−0.493767
$832$	807.934	0.0336659
$833$	1889.30	0.0785840
$834$	−3358.35	−0.139436
$835$	−23570.6	−0.976878
$836$	−11818.6	−0.488941
$837$	3997.17	0.165069
$838$	−5020.53	−0.206958
$839$	−35477.6	−1.45986	−0.729931	−	0.683521i	$-0.760448\pi$
$839$	−35477.6	−1.45986	−0.729931	+	0.683521i	$0.760448\pi$
$840$	−5946.78	−0.244266
$841$	−23026.4	−0.944130
$842$	−18023.7	−0.737692
$843$	24819.4	1.01403
$844$	19867.7	0.810279
$845$	36158.5	1.47206
$846$	8540.03	0.347059
$847$	−12163.4	−0.493436
$848$	10335.3	0.418531
$849$	−10428.6	−0.421565
$850$	4847.37	0.195604
$851$	1050.87	0.0423306
$852$	3320.24	0.133509
$853$	−26512.6	−1.06422	−0.532108	−	0.846677i	$-0.678600\pi$
$853$	−26512.6	−1.06422	−0.532108	+	0.846677i	$0.678600\pi$
$854$	3768.48	0.151001
$855$	−10055.7	−0.402220
$856$	3768.10	0.150457
$857$	−21167.8	−0.843732	−0.421866	−	0.906658i	$-0.638625\pi$
$857$	−21167.8	−0.843732	−0.421866	+	0.906658i	$0.638625\pi$
$858$	3554.39	0.141428
$859$	48177.3	1.91361	0.956804	−	0.290735i	$-0.0938999\pi$
$859$	48177.3	1.91361	0.956804	+	0.290735i	$0.0938999\pi$
$860$	−16218.2	−0.643065
$861$	4544.27	0.179870
$862$	−4566.01	−0.180416
$863$	−34255.1	−1.35117	−0.675583	−	0.737284i	$-0.736108\pi$
$863$	−34255.1	−1.35117	−0.675583	+	0.737284i	$0.736108\pi$
$864$	−864.000	−0.0340207
$865$	34345.2	1.35003
$866$	6834.14	0.268168
$867$	−14250.3	−0.558207
$868$	−8268.69	−0.323338
$869$	−44636.6	−1.74245
$870$	3930.26	0.153159
$871$	−8798.96	−0.342298
$872$	4622.98	0.179534
$873$	−888.142	−0.0344319
$874$	−17266.9	−0.668263
$875$	16080.0	0.621262
$876$	14441.1	0.556986
$877$	−33119.1	−1.27520	−0.637601	−	0.770367i	$-0.720073\pi$
$877$	−33119.1	−1.27520	−0.637601	+	0.770367i	$0.720073\pi$
$878$	18849.6	0.724535
$879$	15926.8	0.611144
$880$	13323.6	0.510385
$881$	39629.1	1.51548	0.757740	−	0.652556i	$-0.226303\pi$
$881$	39629.1	1.51548	0.757740	+	0.652556i	$0.226303\pi$
$882$	2664.48	0.101721
$883$	172.223	0.00656371	0.00328186	−	0.999995i	$-0.498955\pi$
$883$	172.223	0.00656371	0.00328186	+	0.999995i	$0.498955\pi$
$884$	−644.490	−0.0245210
$885$	−3140.92	−0.119300
$886$	2384.58	0.0904192
$887$	17522.4	0.663297	0.331648	−	0.943403i	$-0.392395\pi$
$887$	17522.4	0.663297	0.331648	+	0.943403i	$0.392395\pi$
$888$	−183.934	−0.00695093
$889$	30329.5	1.14423
$890$	24917.1	0.938451
$891$	−3801.05	−0.142918
$892$	16713.6	0.627370
$893$	−29872.7	−1.11943
$894$	−9062.87	−0.339047
$895$	41775.9	1.56024
$896$	1787.30	0.0666400
$897$	5192.96	0.193297
$898$	−9411.22	−0.349729
$899$	5464.83	0.202739
$900$	6836.25	0.253194
$901$	−8244.47	−0.304842
$902$	−10181.3	−0.375833
$903$	−9571.23	−0.352725
$904$	4089.10	0.150444
$905$	−5349.27	−0.196481
$906$	17085.2	0.626509
$907$	−1466.53	−0.0536884	−0.0268442	−	0.999640i	$-0.508546\pi$
$907$	−1466.53	−0.0536884	−0.0268442	+	0.999640i	$0.508546\pi$
$908$	−20598.3	−0.752840
$909$	5574.37	0.203400
$910$	−6256.00	−0.227895
$911$	49065.7	1.78443	0.892216	−	0.451608i	$-0.149149\pi$
$911$	49065.7	1.78443	0.892216	+	0.451608i	$0.149149\pi$
$912$	3022.24	0.109733
$913$	8813.57	0.319482
$914$	5516.63	0.199643
$915$	−7183.78	−0.259550
$916$	−12868.7	−0.464185
$917$	8615.48	0.310260
$918$	689.215	0.0247794
$919$	−16191.0	−0.581165	−0.290583	−	0.956850i	$-0.593849\pi$
$919$	−16191.0	−0.581165	−0.290583	+	0.956850i	$0.593849\pi$
$920$	19465.7	0.697572
$921$	2341.02	0.0837558
$922$	−29549.3	−1.05548
$923$	3492.89	0.124561
$924$	7862.98	0.279949
$925$	1455.35	0.0517313
$926$	−21148.9	−0.750536
$927$	16556.6	0.586614
$928$	−1181.24	−0.0417845
$929$	−48294.4	−1.70558	−0.852792	−	0.522250i	$-0.825093\pi$
$929$	−48294.4	−1.70558	−0.852792	+	0.522250i	$0.825093\pi$
$930$	15762.5	0.555776
$931$	−9320.26	−0.328098
$932$	8507.34	0.298999
$933$	19880.1	0.697583
$934$	−20665.4	−0.723976
$935$	−10628.3	−0.371745
$936$	−908.925	−0.0317406
$937$	−27619.9	−0.962970	−0.481485	−	0.876454i	$-0.659902\pi$
$937$	−27619.9	−0.962970	−0.481485	+	0.876454i	$0.659902\pi$
$938$	−19464.9	−0.677561
$939$	−11244.7	−0.390794
$940$	33676.7	1.16853
$941$	−50167.6	−1.73796	−0.868979	−	0.494849i	$-0.835223\pi$
$941$	−50167.6	−1.73796	−0.868979	+	0.494849i	$0.835223\pi$
$942$	−2537.23	−0.0877574
$943$	−14874.9	−0.513672
$944$	944.000	0.0325472
$945$	6690.13	0.230296
$946$	21444.1	0.737006
$947$	−4200.09	−0.144123	−0.0720615	−	0.997400i	$-0.522958\pi$
$947$	−4200.09	−0.144123	−0.0720615	+	0.997400i	$0.522958\pi$
$948$	11414.4	0.391058
$949$	15192.0	0.519656
$950$	−23912.9	−0.816671
$951$	21635.1	0.737716
$952$	−1425.73	−0.0485381
$953$	−2057.23	−0.0699267	−0.0349633	−	0.999389i	$-0.511131\pi$
$953$	−2057.23	−0.0699267	−0.0349633	+	0.999389i	$0.511131\pi$
$954$	−11627.2	−0.394595
$955$	−71061.7	−2.40786
$956$	23448.3	0.793276
$957$	−5196.69	−0.175533
$958$	−11854.7	−0.399801
$959$	1189.23	0.0400439
$960$	−3407.10	−0.114545
$961$	−7874.12	−0.264312
$962$	−193.498	−0.00648507
$963$	−4239.11	−0.141852
$964$	−10005.0	−0.334272
$965$	−27437.0	−0.915263
$966$	11487.8	0.382622
$967$	−43167.5	−1.43554	−0.717772	−	0.696278i	$-0.754838\pi$
$967$	−43167.5	−1.43554	−0.717772	+	0.696278i	$0.754838\pi$
$968$	−6968.81	−0.231391
$969$	−2410.84	−0.0799252
$970$	−3502.30	−0.115930
$971$	−7326.54	−0.242142	−0.121071	−	0.992644i	$-0.538633\pi$
$971$	−7326.54	−0.242142	−0.121071	+	0.992644i	$0.538633\pi$
$972$	972.000	0.0320750
$973$	−7815.58	−0.257509
$974$	−16978.1	−0.558535
$975$	7191.71	0.236225
$976$	2159.08	0.0708099
$977$	40058.4	1.31175	0.655876	−	0.754869i	$-0.272299\pi$
$977$	40058.4	1.31175	0.655876	+	0.754869i	$0.272299\pi$
$978$	−11558.5	−0.377913
$979$	−32945.9	−1.07554
$980$	10507.1	0.342488
$981$	−5200.86	−0.169267
$982$	9812.00	0.318853
$983$	−20309.6	−0.658979	−0.329490	−	0.944159i	$-0.606877\pi$
$983$	−20309.6	−0.658979	−0.329490	+	0.944159i	$0.606877\pi$
$984$	2603.56	0.0843479
$985$	61493.3	1.98918
$986$	942.275	0.0304342
$987$	19874.5	0.640943
$988$	3179.38	0.102378
$989$	31329.7	1.00731
$990$	−14989.1	−0.481196
$991$	33235.0	1.06533	0.532666	−	0.846326i	$-0.321190\pi$
$991$	33235.0	1.06533	0.532666	+	0.846326i	$0.321190\pi$
$992$	−4737.39	−0.151625
$993$	−32940.3	−1.05270
$994$	7726.91	0.246562
$995$	−78071.5	−2.48747
$996$	−2253.80	−0.0717011
$997$	−55876.2	−1.77494	−0.887470	−	0.460865i	$-0.847539\pi$
$997$	−55876.2	−1.77494	−0.887470	+	0.460865i	$0.847539\pi$
$998$	7190.78	0.228076
$999$	206.926	0.00655340

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.4.a.f.1.2	✓	3
3.2	odd	2		1062.4.a.m.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.4.a.f.1.2	✓	3	1.1	even	1	trivial
1062.4.a.m.1.2		3	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)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -17.7453 q^{5} -6.00000 q^{6} -13.9633 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -17.7453 q^{5} -6.00000 q^{6} -13.9633 q^{7} -8.00000 q^{8} +9.00000 q^{9} +35.4906 q^{10} -46.9266 q^{11} +12.0000 q^{12} +12.6240 q^{13} +27.9266 q^{14} -53.2359 q^{15} +16.0000 q^{16} -12.7632 q^{17} -18.0000 q^{18} +62.9633 q^{19} -70.9812 q^{20} -41.8898 q^{21} +93.8531 q^{22} +137.119 q^{23} -24.0000 q^{24} +189.896 q^{25} -25.2479 q^{26} +27.0000 q^{27} -55.8531 q^{28} +36.9137 q^{29} +106.472 q^{30} +148.043 q^{31} -32.0000 q^{32} -140.780 q^{33} +25.5265 q^{34} +247.783 q^{35} +36.0000 q^{36} +7.66392 q^{37} -125.927 q^{38} +37.8719 q^{39} +141.962 q^{40} -108.481 q^{41} +83.7797 q^{42} +228.486 q^{43} -187.706 q^{44} -159.708 q^{45} -274.238 q^{46} -474.446 q^{47} +48.0000 q^{48} -148.027 q^{49} -379.791 q^{50} -38.2897 q^{51} +50.4959 q^{52} +645.954 q^{53} -54.0000 q^{54} +832.726 q^{55} +111.706 q^{56} +188.890 q^{57} -73.8273 q^{58} +59.0000 q^{59} -212.944 q^{60} +134.942 q^{61} -296.087 q^{62} -125.669 q^{63} +64.0000 q^{64} -224.016 q^{65} +281.559 q^{66} -697.004 q^{67} -51.0529 q^{68} +411.357 q^{69} -495.565 q^{70} +276.687 q^{71} -72.0000 q^{72} +1203.43 q^{73} -15.3278 q^{74} +569.687 q^{75} +251.853 q^{76} +655.248 q^{77} -75.7438 q^{78} +951.201 q^{79} -283.925 q^{80} +81.0000 q^{81} +216.963 q^{82} -187.816 q^{83} -167.559 q^{84} +226.487 q^{85} -456.972 q^{86} +110.741 q^{87} +375.412 q^{88} +702.075 q^{89} +319.415 q^{90} -176.272 q^{91} +548.476 q^{92} +444.130 q^{93} +948.892 q^{94} -1117.30 q^{95} -96.0000 q^{96} -98.6825 q^{97} +296.054 q^{98} -422.339 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 6 q^{2} + 9 q^{3} + 12 q^{4} - 28 q^{5} - 18 q^{6} + 26 q^{7} - 24 q^{8} + 27 q^{9}+O(q^{10}) \) 3 * q - 6 * q^2 + 9 * q^3 + 12 * q^4 - 28 * q^5 - 18 * q^6 + 26 * q^7 - 24 * q^8 + 27 * q^9	\( 3 q - 6 q^{2} + 9 q^{3} + 12 q^{4} - 28 q^{5} - 18 q^{6} + 26 q^{7} - 24 q^{8} + 27 q^{9} + 56 q^{10} - 5 q^{11} + 36 q^{12} - 19 q^{13} - 52 q^{14} - 84 q^{15} + 48 q^{16} + 20 q^{17} - 54 q^{18} + 121 q^{19} - 112 q^{20} + 78 q^{21} + 10 q^{22} - 7 q^{23} - 72 q^{24} + 371 q^{25} + 38 q^{26} + 81 q^{27} + 104 q^{28} - 121 q^{29} + 168 q^{30} + 651 q^{31} - 96 q^{32} - 15 q^{33} - 40 q^{34} - 291 q^{35} + 108 q^{36} + 618 q^{37} - 242 q^{38} - 57 q^{39} + 224 q^{40} + 314 q^{41} - 156 q^{42} - 265 q^{43} - 20 q^{44} - 252 q^{45} + 14 q^{46} + 179 q^{47} + 144 q^{48} + 259 q^{49} - 742 q^{50} + 60 q^{51} - 76 q^{52} + 252 q^{53} - 162 q^{54} - 50 q^{55} - 208 q^{56} + 363 q^{57} + 242 q^{58} + 177 q^{59} - 336 q^{60} + 997 q^{61} - 1302 q^{62} + 234 q^{63} + 192 q^{64} + 888 q^{65} + 30 q^{66} + 460 q^{67} + 80 q^{68} - 21 q^{69} + 582 q^{70} + 1263 q^{71} - 216 q^{72} + 1543 q^{73} - 1236 q^{74} + 1113 q^{75} + 484 q^{76} + 2082 q^{77} + 114 q^{78} + 1719 q^{79} - 448 q^{80} + 243 q^{81} - 628 q^{82} - 224 q^{83} + 312 q^{84} + 2285 q^{85} + 530 q^{86} - 363 q^{87} + 40 q^{88} + 1347 q^{89} + 504 q^{90} - 1646 q^{91} - 28 q^{92} + 1953 q^{93} - 358 q^{94} - 1081 q^{95} - 288 q^{96} + 1200 q^{97} - 518 q^{98} - 45 q^{99}+O(q^{100}) \) 3 * q - 6 * q^2 + 9 * q^3 + 12 * q^4 - 28 * q^5 - 18 * q^6 + 26 * q^7 - 24 * q^8 + 27 * q^9 + 56 * q^10 - 5 * q^11 + 36 * q^12 - 19 * q^13 - 52 * q^14 - 84 * q^15 + 48 * q^16 + 20 * q^17 - 54 * q^18 + 121 * q^19 - 112 * q^20 + 78 * q^21 + 10 * q^22 - 7 * q^23 - 72 * q^24 + 371 * q^25 + 38 * q^26 + 81 * q^27 + 104 * q^28 - 121 * q^29 + 168 * q^30 + 651 * q^31 - 96 * q^32 - 15 * q^33 - 40 * q^34 - 291 * q^35 + 108 * q^36 + 618 * q^37 - 242 * q^38 - 57 * q^39 + 224 * q^40 + 314 * q^41 - 156 * q^42 - 265 * q^43 - 20 * q^44 - 252 * q^45 + 14 * q^46 + 179 * q^47 + 144 * q^48 + 259 * q^49 - 742 * q^50 + 60 * q^51 - 76 * q^52 + 252 * q^53 - 162 * q^54 - 50 * q^55 - 208 * q^56 + 363 * q^57 + 242 * q^58 + 177 * q^59 - 336 * q^60 + 997 * q^61 - 1302 * q^62 + 234 * q^63 + 192 * q^64 + 888 * q^65 + 30 * q^66 + 460 * q^67 + 80 * q^68 - 21 * q^69 + 582 * q^70 + 1263 * q^71 - 216 * q^72 + 1543 * q^73 - 1236 * q^74 + 1113 * q^75 + 484 * q^76 + 2082 * q^77 + 114 * q^78 + 1719 * q^79 - 448 * q^80 + 243 * q^81 - 628 * q^82 - 224 * q^83 + 312 * q^84 + 2285 * q^85 + 530 * q^86 - 363 * q^87 + 40 * q^88 + 1347 * q^89 + 504 * q^90 - 1646 * q^91 - 28 * q^92 + 1953 * q^93 - 358 * q^94 - 1081 * q^95 - 288 * q^96 + 1200 * q^97 - 518 * q^98 - 45 * q^99

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