LMFDB - Embedded newform 315.4.d.b.64.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,4,Mod(64,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("315.64");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	315.d (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$18.5856016518$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 37x^{8} + 398x^{6} + 1149x^{4} + 1040x^{2} + 100 $ x^10 + 37x^8 + 398x^6 + 1149x^4 + 1040x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9}\cdot 5 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			64.8
Root			$4.40248i$ of defining polynomial
Character	$\chi$	$=$	315.64
Dual form			315.4.d.b.64.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.33774i q^{2} -3.14050 q^{4} +(-10.1427 + 4.70380i) q^{5} -7.00000i q^{7} +16.2197i q^{8} +O(q^{10})$	\(q+3.33774i q^{2} -3.14050 q^{4} +(-10.1427 + 4.70380i) q^{5} -7.00000i q^{7} +16.2197i q^{8} +(-15.7000 - 33.8537i) q^{10} -18.3258 q^{11} +10.1457i q^{13} +23.3642 q^{14} -79.2613 q^{16} -24.6984i q^{17} -77.4282 q^{19} +(31.8532 - 14.7723i) q^{20} -61.1666i q^{22} -149.411i q^{23} +(80.7486 - 95.4184i) q^{25} -33.8636 q^{26} +21.9835i q^{28} -10.2984 q^{29} +124.423 q^{31} -134.796i q^{32} +82.4367 q^{34} +(32.9266 + 70.9989i) q^{35} -215.905i q^{37} -258.435i q^{38} +(-76.2943 - 164.512i) q^{40} -495.056 q^{41} -220.606i q^{43} +57.5521 q^{44} +498.696 q^{46} +212.957i q^{47} -49.0000 q^{49} +(318.482 + 269.518i) q^{50} -31.8625i q^{52} -532.455i q^{53} +(185.873 - 86.2007i) q^{55} +113.538 q^{56} -34.3732i q^{58} -324.143 q^{59} +653.967 q^{61} +415.292i q^{62} -184.178 q^{64} +(-47.7232 - 102.905i) q^{65} +819.077i q^{67} +77.5653i q^{68} +(-236.976 + 109.900i) q^{70} +466.940 q^{71} +173.066i q^{73} +720.634 q^{74} +243.163 q^{76} +128.280i q^{77} -810.186 q^{79} +(803.923 - 372.829i) q^{80} -1652.37i q^{82} -12.3208i q^{83} +(116.176 + 250.508i) q^{85} +736.326 q^{86} -297.239i q^{88} -33.8297 q^{89} +71.0198 q^{91} +469.227i q^{92} -710.795 q^{94} +(785.330 - 364.206i) q^{95} +810.761i q^{97} -163.549i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 54 q^{4} + 14 q^{5}+O(q^{10}) $ 10 * q - 54 * q^4 + 14 * q^5	$ 10 q - 54 q^{4} + 14 q^{5} + 92 q^{10} - 132 q^{11} + 14 q^{14} + 310 q^{16} - 348 q^{19} - 366 q^{20} - 374 q^{25} - 892 q^{26} + 740 q^{29} + 684 q^{31} - 224 q^{34} - 2156 q^{40} - 1604 q^{41} + 580 q^{44} + 1280 q^{46} - 490 q^{49} + 2504 q^{50} - 452 q^{55} - 462 q^{56} + 1408 q^{59} + 1300 q^{61} - 150 q^{64} + 3296 q^{65} - 882 q^{70} - 2940 q^{71} - 2624 q^{74} + 8740 q^{76} + 1640 q^{79} + 4126 q^{80} - 1704 q^{85} - 1664 q^{86} + 572 q^{89} - 28 q^{91} - 5080 q^{94} - 1268 q^{95}+O(q^{100}) $ 10 * q - 54 * q^4 + 14 * q^5 + 92 * q^10 - 132 * q^11 + 14 * q^14 + 310 * q^16 - 348 * q^19 - 366 * q^20 - 374 * q^25 - 892 * q^26 + 740 * q^29 + 684 * q^31 - 224 * q^34 - 2156 * q^40 - 1604 * q^41 + 580 * q^44 + 1280 * q^46 - 490 * q^49 + 2504 * q^50 - 452 * q^55 - 462 * q^56 + 1408 * q^59 + 1300 * q^61 - 150 * q^64 + 3296 * q^65 - 882 * q^70 - 2940 * q^71 - 2624 * q^74 + 8740 * q^76 + 1640 * q^79 + 4126 * q^80 - 1704 * q^85 - 1664 * q^86 + 572 * q^89 - 28 * q^91 - 5080 * q^94 - 1268 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$			3.33774i			1.18007i	0.807378	+	0.590035i	$0.200886\pi$
$2$			3.33774i			1.18007i	−0.807378	+	0.590035i	$0.799114\pi$
$3$		0			0
$3$		0			0
$4$	−3.14050			−0.392563
$5$	−10.1427	+	4.70380i	−0.907190	+	0.420720i
$5$	−10.1427	+	4.70380i	−0.907190	+	0.420720i
$6$		0			0
$7$		−	7.00000i		−	0.377964i
$7$		−	7.00000i		−	0.377964i
$8$			16.2197i			0.716818i
$9$		0			0
$10$	−15.7000	−	33.8537i	−0.496479	−	1.07055i
$11$	−18.3258			−0.502311			−0.251156	−	0.967947i	$-0.580811\pi$
$11$	−18.3258			−0.502311			−0.251156	+	0.967947i	$0.580811\pi$
$12$		0			0
$13$			10.1457i			0.216454i	0.994126	+	0.108227i	$0.0345174\pi$
$13$			10.1457i			0.216454i	−0.994126	+	0.108227i	$0.965483\pi$
$14$	23.3642			0.446024
$15$		0			0
$16$	−79.2613			−1.23846
$17$		−	24.6984i		−	0.352367i	−0.984357	−	0.176183i	$-0.943625\pi$
$17$		−	24.6984i		−	0.352367i	0.984357	−	0.176183i	$-0.0563752\pi$
$18$		0			0
$19$	−77.4282			−0.934907			−0.467454	−	0.884018i	$-0.654829\pi$
$19$	−77.4282			−0.934907			−0.467454	+	0.884018i	$0.654829\pi$
$20$	31.8532	−	14.7723i	0.356129	−	0.165159i
$21$		0			0
$22$		−	61.1666i		−	0.592762i
$23$		−	149.411i		−	1.35454i	−0.735735	−	0.677270i	$-0.763163\pi$
$23$		−	149.411i		−	1.35454i	0.735735	−	0.677270i	$-0.236837\pi$
$24$		0			0
$25$	80.7486	−	95.4184i	0.645989	−	0.763347i
$26$	−33.8636			−0.255431
$27$		0			0
$28$			21.9835i			0.148375i
$29$	−10.2984			−0.0659434			−0.0329717	−	0.999456i	$-0.510497\pi$
$29$	−10.2984			−0.0659434			−0.0329717	+	0.999456i	$0.510497\pi$
$30$		0			0
$31$	124.423			0.720872			0.360436	−	0.932784i	$-0.382628\pi$
$31$	124.423			0.720872			0.360436	+	0.932784i	$0.382628\pi$
$32$		−	134.796i		−	0.744647i
$33$		0			0
$34$	82.4367			0.415817
$35$	32.9266	+	70.9989i	0.159017	+	0.342886i
$36$		0			0
$37$		−	215.905i		−	0.959312i	−0.877457	−	0.479656i	$-0.840761\pi$
$37$		−	215.905i		−	0.959312i	0.877457	−	0.479656i	$-0.159239\pi$
$38$		−	258.435i		−	1.10326i
$39$		0			0
$40$	−76.2943	−	164.512i	−0.301580	−	0.650290i
$41$	−495.056			−1.88573			−0.942863	−	0.333181i	$-0.891878\pi$
$41$	−495.056			−1.88573			−0.942863	+	0.333181i	$0.891878\pi$
$42$		0			0
$43$		−	220.606i		−	0.782375i	−0.920311	−	0.391188i	$-0.872064\pi$
$43$		−	220.606i		−	0.782375i	0.920311	−	0.391188i	$-0.127936\pi$
$44$	57.5521			0.197189
$45$		0			0
$46$	498.696			1.59845
$47$			212.957i			0.660915i	0.943821	+	0.330457i	$0.107203\pi$
$47$			212.957i			0.660915i	−0.943821	+	0.330457i	$0.892797\pi$
$48$		0			0
$49$	−49.0000			−0.142857
$50$	318.482	+	269.518i	0.900802	+	0.762311i
$51$		0			0
$52$		−	31.8625i		−	0.0849719i
$53$		−	532.455i		−	1.37997i	−0.723825	−	0.689984i	$-0.757618\pi$
$53$		−	532.455i		−	1.37997i	0.723825	−	0.689984i	$-0.242382\pi$
$54$		0			0
$55$	185.873	−	86.2007i	0.455692	−	0.211333i
$56$	113.538			0.270932
$57$		0			0
$58$		−	34.3732i		−	0.0778177i
$59$	−324.143			−0.715252			−0.357626	−	0.933865i	$-0.616414\pi$
$59$	−324.143			−0.715252			−0.357626	+	0.933865i	$0.616414\pi$
$60$		0			0
$61$	653.967			1.37265			0.686327	−	0.727293i	$-0.259222\pi$
$61$	653.967			1.37265			0.686327	+	0.727293i	$0.259222\pi$
$62$			415.292i			0.850679i
$63$		0			0
$64$	−184.178			−0.359722
$65$	−47.7232	−	102.905i	−0.0910667	−	0.196365i
$66$		0			0
$67$			819.077i			1.49353i	0.665091	+	0.746763i	$0.268393\pi$
$67$			819.077i			1.49353i	−0.665091	+	0.746763i	$0.731607\pi$
$68$			77.5653i			0.138326i
$69$		0			0
$70$	−236.976	+	109.900i	−0.404629	+	0.187651i
$71$	466.940			0.780501			0.390250	−	0.920709i	$-0.372388\pi$
$71$	466.940			0.780501			0.390250	+	0.920709i	$0.372388\pi$
$72$		0			0
$73$			173.066i			0.277478i	0.990329	+	0.138739i	$0.0443048\pi$
$73$			173.066i			0.277478i	−0.990329	+	0.138739i	$0.955695\pi$
$74$	720.634			1.13205
$75$		0			0
$76$	243.163			0.367010
$77$			128.280i			0.189856i
$78$		0			0
$79$	−810.186			−1.15384			−0.576918	−	0.816802i	$-0.695745\pi$
$79$	−810.186			−1.15384			−0.576918	+	0.816802i	$0.695745\pi$
$80$	803.923	−	372.829i	1.12352	−	0.521044i
$81$		0			0
$82$		−	1652.37i		−	2.22529i
$83$		−	12.3208i		−	0.0162937i	−0.999967	−	0.00814687i	$-0.997407\pi$
$83$		−	12.3208i		−	0.0162937i	0.999967	−	0.00814687i	$-0.00259326\pi$
$84$		0			0
$85$	116.176	+	250.508i	0.148248	+	0.319664i
$86$	736.326			0.923257
$87$		0			0
$88$		−	297.239i		−	0.360066i
$89$	−33.8297			−0.0402914			−0.0201457	−	0.999797i	$-0.506413\pi$
$89$	−33.8297			−0.0402914			−0.0201457	+	0.999797i	$0.506413\pi$
$90$		0			0
$91$	71.0198			0.0818120
$92$			469.227i			0.531742i
$93$		0			0
$94$	−710.795			−0.779925
$95$	785.330	−	364.206i	0.848139	−	0.393335i
$96$		0			0
$97$			810.761i			0.848663i	0.905507	+	0.424331i	$0.139491\pi$
$97$			810.761i			0.848663i	−0.905507	+	0.424331i	$0.860509\pi$
$98$		−	163.549i		−	0.168581i
$99$		0			0
$100$	−253.591	+	299.662i	−0.253591	+	0.299662i
$101$	−1646.84			−1.62245			−0.811223	−	0.584737i	$-0.801198\pi$
$101$	−1646.84			−1.62245			−0.811223	+	0.584737i	$0.801198\pi$
$102$		0			0
$103$		−	921.360i		−	0.881401i	−0.897654	−	0.440700i	$-0.854730\pi$
$103$		−	921.360i		−	0.881401i	0.897654	−	0.440700i	$-0.145270\pi$
$104$	−164.560			−0.155158
$105$		0			0
$106$	1777.19			1.62846
$107$		−	1060.84i		−	0.958464i	−0.877688	−	0.479232i	$-0.840915\pi$
$107$		−	1060.84i		−	0.958464i	0.877688	−	0.479232i	$-0.159085\pi$
$108$		0			0
$109$	−1533.03			−1.34713			−0.673566	−	0.739127i	$-0.735238\pi$
$109$	−1533.03			−1.34713			−0.673566	+	0.739127i	$0.735238\pi$
$110$	287.715	+	620.394i	0.249387	+	0.537748i
$111$		0			0
$112$			554.829i			0.468093i
$113$			2072.67i			1.72549i	0.505637	+	0.862746i	$0.331257\pi$
$113$			2072.67i			1.72549i	−0.505637	+	0.862746i	$0.668743\pi$
$114$		0			0
$115$	702.801	+	1515.43i	0.569883	+	1.22883i
$116$	32.3420			0.0258869
$117$		0			0
$118$		−	1081.91i		−	0.844046i
$119$	−172.889			−0.133182
$120$		0			0
$121$	−995.166			−0.747683
$122$			2182.77i			1.61983i
$123$		0			0
$124$	−390.751			−0.282988
$125$	−370.180	+	1347.62i	−0.264879	+	0.964282i
$126$		0			0
$127$			365.145i			0.255129i	0.991830	+	0.127565i	$0.0407160\pi$
$127$			365.145i			0.255129i	−0.991830	+	0.127565i	$0.959284\pi$
$128$		−	1693.10i		−	1.16914i
$129$		0			0
$130$	343.469	−	159.288i	0.231725	−	0.107465i
$131$	−1300.83			−0.867586			−0.433793	−	0.901013i	$-0.642825\pi$
$131$	−1300.83			−0.867586			−0.433793	+	0.901013i	$0.642825\pi$
$132$		0			0
$133$			541.997i			0.353362i
$134$	−2733.87			−1.76246
$135$		0			0
$136$	400.601			0.252583
$137$		−	2578.40i		−	1.60794i	−0.594670	−	0.803970i	$-0.702717\pi$
$137$		−	2578.40i		−	1.60794i	0.594670	−	0.803970i	$-0.297283\pi$
$138$		0			0
$139$	−3065.49			−1.87059			−0.935294	−	0.353872i	$-0.884865\pi$
$139$	−3065.49			−1.87059			−0.935294	+	0.353872i	$0.884865\pi$
$140$	−103.406	−	222.972i	−0.0624243	−	0.134604i
$141$		0			0
$142$			1558.52i			0.921044i
$143$		−	185.927i		−	0.108727i
$144$		0			0
$145$	104.453	−	48.4414i	0.0598232	−	0.0277437i
$146$	−577.650			−0.327443
$147$		0			0
$148$			678.050i			0.376590i
$149$	−2704.34			−1.48690			−0.743449	−	0.668793i	$-0.766811\pi$
$149$	−2704.34			−1.48690			−0.743449	+	0.668793i	$0.766811\pi$
$150$		0			0
$151$	388.869			0.209574			0.104787	−	0.994495i	$-0.466584\pi$
$151$	388.869			0.209574			0.104787	+	0.994495i	$0.466584\pi$
$152$		−	1255.86i		−	0.670158i
$153$		0			0
$154$	−428.166			−0.224043
$155$	−1261.98	+	585.261i	−0.653968	+	0.303286i
$156$		0			0
$157$			2885.78i			1.46694i	0.679720	+	0.733472i	$0.262101\pi$
$157$			2885.78i			1.46694i	−0.679720	+	0.733472i	$0.737899\pi$
$158$		−	2704.19i		−	1.36161i
$159$		0			0
$160$	634.051	+	1367.19i	0.313288	+	0.675537i
$161$	−1045.88			−0.511968
$162$		0			0
$163$			571.954i			0.274840i	0.990513	+	0.137420i	$0.0438809\pi$
$163$			571.954i			0.274840i	−0.990513	+	0.137420i	$0.956119\pi$
$164$	1554.73			0.740266
$165$		0			0
$166$	41.1235			0.0192277
$167$			2423.96i			1.12319i	0.827414	+	0.561593i	$0.189811\pi$
$167$			2423.96i			1.12319i	−0.827414	+	0.561593i	$0.810189\pi$
$168$		0			0
$169$	2094.07			0.953148
$170$	−836.131	+	387.766i	−0.377225	+	0.174943i
$171$		0			0
$172$			692.815i			0.307131i
$173$		−	626.440i		−	0.275303i	−0.990481	−	0.137651i	$-0.956045\pi$
$173$		−	626.440i		−	0.275303i	0.990481	−	0.137651i	$-0.0439554\pi$
$174$		0			0
$175$	−667.929	−	565.240i	−0.288518	−	0.244161i
$176$	1452.52			0.622091
$177$		0			0
$178$		−	112.915i		−	0.0475467i
$179$	2322.11			0.969623			0.484812	−	0.874619i	$-0.338888\pi$
$179$	2322.11			0.969623			0.484812	+	0.874619i	$0.338888\pi$
$180$		0			0
$181$	−4664.94			−1.91570			−0.957852	−	0.287263i	$-0.907255\pi$
$181$	−4664.94			−1.91570			−0.957852	+	0.287263i	$0.907255\pi$
$182$			237.045i			0.0965438i
$183$		0			0
$184$	2423.41			0.970958
$185$	1015.57	+	2189.86i	0.403602	+	0.870279i
$186$		0			0
$187$			452.617i			0.176998i
$188$		−	668.792i		−	0.259451i
$189$		0			0
$190$	1215.63	+	2621.23i	0.464162	+	1.00086i
$191$	3730.26			1.41315			0.706575	−	0.707638i	$-0.250239\pi$
$191$	3730.26			1.41315			0.706575	+	0.707638i	$0.250239\pi$
$192$		0			0
$193$		−	2585.26i		−	0.964202i	−0.876116	−	0.482101i	$-0.839874\pi$
$193$		−	2585.26i		−	0.964202i	0.876116	−	0.482101i	$-0.160126\pi$
$194$	−2706.11			−1.00148
$195$		0			0
$196$	153.885			0.0560804
$197$			2405.91i			0.870122i	0.900401	+	0.435061i	$0.143273\pi$
$197$			2405.91i			0.870122i	−0.900401	+	0.435061i	$0.856727\pi$
$198$		0			0
$199$	−1192.35			−0.424740			−0.212370	−	0.977189i	$-0.568118\pi$
$199$	−1192.35			−0.424740			−0.212370	+	0.977189i	$0.568118\pi$
$200$	1547.66	+	1309.72i	0.547181	+	0.463056i
$201$		0			0
$202$		−	5496.74i		−	1.91460i
$203$			72.0885i			0.0249243i
$204$		0			0
$205$	5021.20	−	2328.64i	1.71071	−	0.793364i
$206$	3075.26			1.04011
$207$		0			0
$208$		−	804.160i		−	0.268069i
$209$	1418.93			0.469615
$210$		0			0
$211$	−764.904			−0.249565			−0.124782	−	0.992184i	$-0.539823\pi$
$211$	−764.904			−0.249565			−0.124782	+	0.992184i	$0.539823\pi$
$212$			1672.18i			0.541724i
$213$		0			0
$214$	3540.82			1.13105
$215$	1037.69	+	2237.54i	0.329161	+	0.709763i
$216$		0			0
$217$		−	870.961i		−	0.272464i
$218$		−	5116.84i		−	1.58971i
$219$		0			0
$220$	−583.734	+	270.713i	−0.178888	+	0.0829614i
$221$	250.582			0.0762713
$222$		0			0
$223$			1585.18i			0.476016i	0.971263	+	0.238008i	$0.0764945\pi$
$223$			1585.18i			0.476016i	−0.971263	+	0.238008i	$0.923506\pi$
$224$	−943.569			−0.281450
$225$		0			0
$226$	−6918.04			−2.03620
$227$			2363.07i			0.690936i	0.938431	+	0.345468i	$0.112280\pi$
$227$			2363.07i			0.690936i	−0.938431	+	0.345468i	$0.887720\pi$
$228$		0			0
$229$	−1626.44			−0.469337			−0.234669	−	0.972075i	$-0.575401\pi$
$229$	−1626.44			−0.469337			−0.234669	+	0.972075i	$0.575401\pi$
$230$	−5058.12	+	2345.77i	−1.45010	+	0.672501i
$231$		0			0
$232$		−	167.037i		−	0.0472694i
$233$		−	1720.34i		−	0.483705i	−0.970313	−	0.241853i	$-0.922245\pi$
$233$		−	1720.34i		−	0.483705i	0.970313	−	0.241853i	$-0.0777551\pi$
$234$		0			0
$235$	−1001.71	−	2159.96i	−0.278060	−	0.599575i
$236$	1017.97			0.280781
$237$		0			0
$238$		−	577.057i		−	0.157164i
$239$	7217.75			1.95346			0.976732	−	0.214466i	$-0.0688010\pi$
$239$	7217.75			1.95346			0.976732	+	0.214466i	$0.0688010\pi$
$240$		0			0
$241$	5094.78			1.36176			0.680879	−	0.732396i	$-0.261598\pi$
$241$	5094.78			1.36176			0.680879	+	0.732396i	$0.261598\pi$
$242$		−	3321.61i		−	0.882318i
$243$		0			0
$244$	−2053.79			−0.538853
$245$	496.992	−	230.486i	0.129599	−	0.0601029i
$246$		0			0
$247$		−	785.561i		−	0.202365i
$248$			2018.11i			0.516734i
$249$		0			0
$250$	−4498.02	−	1235.56i	−1.13792	−	0.312575i
$251$	4346.51			1.09303			0.546513	−	0.837451i	$-0.315955\pi$
$251$	4346.51			1.09303			0.546513	+	0.837451i	$0.315955\pi$
$252$		0			0
$253$			2738.08i			0.680401i
$254$	−1218.76			−0.301070
$255$		0			0
$256$	4177.71			1.01995
$257$		−	1428.13i		−	0.346632i	−0.984866	−	0.173316i	$-0.944552\pi$
$257$		−	1428.13i		−	0.346632i	0.984866	−	0.173316i	$-0.0554482\pi$
$258$		0			0
$259$	−1511.33			−0.362586
$260$	149.875	+	323.172i	0.0357494	+	0.0770857i
$261$		0			0
$262$		−	4341.82i		−	1.02381i
$263$		−	3447.78i		−	0.808362i	−0.914679	−	0.404181i	$-0.867557\pi$
$263$		−	3447.78i		−	0.808362i	0.914679	−	0.404181i	$-0.132443\pi$
$264$		0			0
$265$	2504.56	+	5400.53i	0.580581	+	1.25189i
$266$	−1809.05			−0.416991
$267$		0			0
$268$		−	2572.31i		−	0.586303i
$269$	−22.3975			−0.00507657			−0.00253829	−	0.999997i	$-0.500808\pi$
$269$	−22.3975			−0.00507657			−0.00253829	+	0.999997i	$0.500808\pi$
$270$		0			0
$271$	−1557.33			−0.349080			−0.174540	−	0.984650i	$-0.555844\pi$
$271$	−1557.33			−0.349080			−0.174540	+	0.984650i	$0.555844\pi$
$272$			1957.62i			0.436391i
$273$		0			0
$274$	8606.03			1.89748
$275$	−1479.78	+	1748.61i	−0.324487	+	0.383438i
$276$		0			0
$277$			3734.92i			0.810142i	0.914285	+	0.405071i	$0.132753\pi$
$277$			3734.92i			0.810142i	−0.914285	+	0.405071i	$0.867247\pi$
$278$		−	10231.8i		−	2.20742i
$279$		0			0
$280$	−1151.58	+	534.060i	−0.245787	+	0.113986i
$281$	2422.37			0.514258			0.257129	−	0.966377i	$-0.417223\pi$
$281$	2422.37			0.514258			0.257129	+	0.966377i	$0.417223\pi$
$282$		0			0
$283$			283.232i			0.0594926i	0.999557	+	0.0297463i	$0.00946994\pi$
$283$			283.232i			0.0594926i	−0.999557	+	0.0297463i	$0.990530\pi$
$284$	−1466.43			−0.306396
$285$		0			0
$286$	620.577			0.128306
$287$			3465.39i			0.712737i
$288$		0			0
$289$	4302.99			0.875838
$290$	161.685	+	348.637i	0.0327395	+	0.0705955i
$291$		0			0
$292$		−	543.515i		−	0.108927i
$293$		−	8481.49i		−	1.69111i	−0.533892	−	0.845553i	$-0.679271\pi$
$293$		−	8481.49i		−	1.69111i	0.533892	−	0.845553i	$-0.320729\pi$
$294$		0			0
$295$	3287.69	−	1524.70i	0.648870	−	0.300921i
$296$	3501.92			0.687652
$297$		0			0
$298$		−	9026.37i		−	1.75464i
$299$	1515.88			0.293196
$300$		0			0
$301$	−1544.24			−0.295710
$302$			1297.94i			0.247312i
$303$		0			0
$304$	6137.05			1.15784
$305$	−6632.99	+	3076.13i	−1.24526	+	0.577504i
$306$		0			0
$307$			2005.50i			0.372834i	0.982471	+	0.186417i	$0.0596875\pi$
$307$			2005.50i			0.372834i	−0.982471	+	0.186417i	$0.940312\pi$
$308$		−	402.865i		−	0.0745304i
$309$		0			0
$310$	−1953.45	−	4212.18i	−0.357898	−	0.771727i
$311$	−10021.4			−1.82720			−0.913602	−	0.406609i	$-0.866711\pi$
$311$	−10021.4			−1.82720			−0.913602	+	0.406609i	$0.866711\pi$
$312$		0			0
$313$		−	631.178i		−	0.113982i	−0.998375	−	0.0569908i	$-0.981849\pi$
$313$		−	631.178i		−	0.113982i	0.998375	−	0.0569908i	$-0.0181506\pi$
$314$	−9631.97			−1.73109
$315$		0			0
$316$	2544.39			0.452953
$317$		−	1202.71i		−	0.213095i	−0.994308	−	0.106547i	$-0.966020\pi$
$317$		−	1202.71i		−	0.213095i	0.994308	−	0.106547i	$-0.0339796\pi$
$318$		0			0
$319$	188.725			0.0331241
$320$	1868.06	−	866.335i	0.326336	−	0.151342i
$321$		0			0
$322$		−	3490.87i		−	0.604158i
$323$			1912.35i			0.329430i
$324$		0			0
$325$	968.084	+	819.249i	0.165230	+	0.139827i
$326$	−1909.03			−0.324330
$327$		0			0
$328$		−	8029.68i		−	1.35172i
$329$	1490.70			0.249802
$330$		0			0
$331$	−9297.55			−1.54393			−0.771963	−	0.635667i	$-0.780725\pi$
$331$	−9297.55			−1.54393			−0.771963	+	0.635667i	$0.780725\pi$
$332$			38.6934i			0.00639632i
$333$		0			0
$334$	−8090.56			−1.32544
$335$	−3852.77	−	8307.65i	−0.628357	−	1.35491i
$336$		0			0
$337$		−	507.727i		−	0.0820702i	−0.999158	−	0.0410351i	$-0.986934\pi$
$337$		−	507.727i		−	0.0820702i	0.999158	−	0.0410351i	$-0.0130656\pi$
$338$			6989.44i			1.12478i
$339$		0			0
$340$	−364.852	−	786.722i	−0.0581966	−	0.125488i
$341$	−2280.15			−0.362102
$342$		0			0
$343$			343.000i			0.0539949i
$344$	3578.17			0.560820
$345$		0			0
$346$	2090.89			0.324876
$347$			6860.59i			1.06137i	0.847569	+	0.530685i	$0.178065\pi$
$347$			6860.59i			1.06137i	−0.847569	+	0.530685i	$0.821935\pi$
$348$		0			0
$349$	9236.45			1.41666			0.708332	−	0.705879i	$-0.249448\pi$
$349$	9236.45			1.41666			0.708332	+	0.705879i	$0.249448\pi$
$350$	1886.62	−	2229.37i	0.288127	−	0.340471i
$351$		0			0
$352$			2470.23i			0.374045i
$353$		−	9419.54i		−	1.42026i	−0.704071	−	0.710129i	$-0.748636\pi$
$353$		−	9419.54i		−	1.42026i	0.704071	−	0.710129i	$-0.251364\pi$
$354$		0			0
$355$	−4736.03	+	2196.39i	−0.708063	+	0.328373i
$356$	106.242			0.0158169
$357$		0			0
$358$			7750.59i			1.14422i
$359$	−2890.82			−0.424990			−0.212495	−	0.977162i	$-0.568159\pi$
$359$	−2890.82			−0.424990			−0.212495	+	0.977162i	$0.568159\pi$
$360$		0			0
$361$	−863.879			−0.125948
$362$		−	15570.4i		−	2.26066i
$363$		0			0
$364$	−223.038			−0.0321164
$365$	−814.068	−	1755.36i	−0.116740	−	0.251725i
$366$		0			0
$367$			1570.51i			0.223379i	0.993743	+	0.111690i	$0.0356262\pi$
$367$			1570.51i			0.223379i	−0.993743	+	0.111690i	$0.964374\pi$
$368$			11842.5i			1.67754i
$369$		0			0
$370$	−7309.17	+	3389.72i	−1.02699	+	0.476278i
$371$	−3727.18			−0.521579
$372$		0			0
$373$		−	8713.38i		−	1.20955i	−0.796397	−	0.604774i	$-0.793263\pi$
$373$		−	8713.38i		−	1.20955i	0.796397	−	0.604774i	$-0.206737\pi$
$374$	−1510.72			−0.208870
$375$		0			0
$376$	−3454.11			−0.473755
$377$		−	104.484i		−	0.0142737i
$378$		0			0
$379$	5779.65			0.783326			0.391663	−	0.920109i	$-0.371900\pi$
$379$	5779.65			0.783326			0.391663	+	0.920109i	$0.371900\pi$
$380$	−2466.33	+	1143.79i	−0.332948	+	0.154409i
$381$		0			0
$382$			12450.6i			1.66762i
$383$			12340.2i			1.64636i	0.567780	+	0.823181i	$0.307803\pi$
$383$			12340.2i			1.64636i	−0.567780	+	0.823181i	$0.692197\pi$
$384$		0			0
$385$	−603.405	−	1301.11i	−0.0798762	−	0.172235i
$386$	8628.92			1.13783
$387$		0			0
$388$		−	2546.20i		−	0.333153i
$389$	7948.44			1.03600			0.517998	−	0.855382i	$-0.326678\pi$
$389$	7948.44			1.03600			0.517998	+	0.855382i	$0.326678\pi$
$390$		0			0
$391$	−3690.22			−0.477295
$392$		−	794.767i		−	0.102403i
$393$		0			0
$394$	−8030.30			−1.02680
$395$	8217.47	−	3810.95i	1.04675	−	0.485442i
$396$		0			0
$397$			5363.64i			0.678069i	0.940774	+	0.339034i	$0.110100\pi$
$397$			5363.64i			0.678069i	−0.940774	+	0.339034i	$0.889900\pi$
$398$		−	3979.75i		−	0.501223i
$399$		0			0
$400$	−6400.23	+	7562.98i	−0.800029	+	0.945373i
$401$	−6057.13			−0.754310			−0.377155	−	0.926150i	$-0.623098\pi$
$401$	−6057.13			−0.754310			−0.377155	+	0.926150i	$0.623098\pi$
$402$		0			0
$403$			1262.36i			0.156036i
$404$	5171.92			0.636912
$405$		0			0
$406$	−240.613			−0.0294123
$407$			3956.62i			0.481873i
$408$		0			0
$409$	−1248.52			−0.150942			−0.0754709	−	0.997148i	$-0.524046\pi$
$409$	−1248.52			−0.150942			−0.0754709	+	0.997148i	$0.524046\pi$
$410$	7772.41	+	16759.5i	0.936224	+	2.01876i
$411$		0			0
$412$			2893.53i			0.346005i
$413$			2269.00i			0.270340i
$414$		0			0
$415$	57.9544	+	124.966i	0.00685511	+	0.0147815i
$416$	1367.59			0.161182
$417$		0			0
$418$			4736.02i			0.554178i
$419$	8324.28			0.970567			0.485284	−	0.874357i	$-0.338716\pi$
$419$	8324.28			0.970567			0.485284	+	0.874357i	$0.338716\pi$
$420$		0			0
$421$	1693.40			0.196036			0.0980179	−	0.995185i	$-0.468750\pi$
$421$	1693.40			0.196036			0.0980179	+	0.995185i	$0.468750\pi$
$422$		−	2553.05i		−	0.294504i
$423$		0			0
$424$	8636.27			0.989185
$425$	−2356.68	−	1994.36i	−0.268978	−	0.227625i
$426$		0			0
$427$		−	4577.77i		−	0.518814i
$428$			3331.58i			0.376257i
$429$		0			0
$430$	−7468.33	+	3463.53i	−0.837570	+	0.388433i
$431$	−11754.6			−1.31369			−0.656844	−	0.754026i	$-0.728109\pi$
$431$	−11754.6			−1.31369			−0.656844	+	0.754026i	$0.728109\pi$
$432$		0			0
$433$		−	14614.3i		−	1.62199i	−0.585056	−	0.810993i	$-0.698927\pi$
$433$		−	14614.3i		−	1.62199i	0.585056	−	0.810993i	$-0.301073\pi$
$434$	2907.04			0.321526
$435$		0			0
$436$	4814.48			0.528834
$437$			11568.6i			1.26637i
$438$		0			0
$439$	−1957.52			−0.212819			−0.106409	−	0.994322i	$-0.533935\pi$
$439$	−1957.52			−0.212819			−0.106409	+	0.994322i	$0.533935\pi$
$440$	1398.15	+	3014.80i	0.151487	+	0.326648i
$441$		0			0
$442$			836.377i			0.0900054i
$443$			356.774i			0.0382637i	0.999817	+	0.0191319i	$0.00609023\pi$
$443$			356.774i			0.0382637i	−0.999817	+	0.0191319i	$0.993910\pi$
$444$		0			0
$445$	343.124	−	159.128i	0.0365520	−	0.0169514i
$446$	−5290.92			−0.561732
$447$		0			0
$448$			1289.24i			0.135962i
$449$	7395.30			0.777296			0.388648	−	0.921386i	$-0.372942\pi$
$449$	7395.30			0.777296			0.388648	+	0.921386i	$0.372942\pi$
$450$		0			0
$451$	9072.28			0.947222
$452$		−	6509.23i		−	0.677364i
$453$		0			0
$454$	−7887.31			−0.815352
$455$	−720.332	+	334.063i	−0.0742191	+	0.0344200i
$456$		0			0
$457$		−	12722.2i		−	1.30223i	−0.758979	−	0.651115i	$-0.774302\pi$
$457$		−	12722.2i		−	1.30223i	0.758979	−	0.651115i	$-0.225698\pi$
$458$		−	5428.64i		−	0.553850i
$459$		0			0
$460$	−2207.15	−	4759.23i	−0.223715	−	0.482391i
$461$	2206.45			0.222916			0.111458	−	0.993769i	$-0.464448\pi$
$461$	2206.45			0.222916			0.111458	+	0.993769i	$0.464448\pi$
$462$		0			0
$463$			15912.0i			1.59718i	0.601875	+	0.798591i	$0.294421\pi$
$463$			15912.0i			1.59718i	−0.601875	+	0.798591i	$0.705579\pi$
$464$	816.261			0.0816681
$465$		0			0
$466$	5742.05			0.570806
$467$			7602.65i			0.753337i	0.926348	+	0.376669i	$0.122930\pi$
$467$			7602.65i			0.753337i	−0.926348	+	0.376669i	$0.877070\pi$
$468$		0			0
$469$	5733.54			0.564499
$470$	7209.38	−	3343.44i	0.707540	−	0.328130i
$471$		0			0
$472$		−	5257.52i		−	0.512705i
$473$			4042.78i			0.392996i
$474$		0			0
$475$	−6252.21	+	7388.07i	−0.603940	+	0.713659i
$476$	542.957			0.0522824
$477$		0			0
$478$			24091.0i			2.30522i
$479$	1681.93			0.160437			0.0802184	−	0.996777i	$-0.474438\pi$
$479$	1681.93			0.160437			0.0802184	+	0.996777i	$0.474438\pi$
$480$		0			0
$481$	2190.50			0.207647
$482$			17005.0i			1.60697i
$483$		0			0
$484$	3125.32			0.293513
$485$	−3813.65	−	8223.30i	−0.357050	−	0.769898i
$486$		0			0
$487$			14107.0i			1.31263i	0.754487	+	0.656314i	$0.227886\pi$
$487$			14107.0i			1.31263i	−0.754487	+	0.656314i	$0.772114\pi$
$488$			10607.2i			0.983943i
$489$		0			0
$490$	769.302	+	1658.83i	0.0709256	+	0.152935i
$491$	−9010.20			−0.828156			−0.414078	−	0.910241i	$-0.635896\pi$
$491$	−9010.20			−0.828156			−0.414078	+	0.910241i	$0.635896\pi$
$492$		0			0
$493$			254.353i			0.0232363i
$494$	2622.00			0.238804
$495$		0			0
$496$	−9861.92			−0.892769
$497$		−	3268.58i		−	0.295001i
$498$		0			0
$499$	−2655.07			−0.238191			−0.119096	−	0.992883i	$-0.538000\pi$
$499$	−2655.07			−0.238191			−0.119096	+	0.992883i	$0.538000\pi$
$500$	1162.55	−	4232.22i	0.103982	−	0.378541i
$501$		0			0
$502$			14507.5i			1.28985i
$503$		−	16559.4i		−	1.46789i	−0.679208	−	0.733946i	$-0.737677\pi$
$503$		−	16559.4i		−	1.46789i	0.679208	−	0.733946i	$-0.262323\pi$
$504$		0			0
$505$	16703.4	−	7746.42i	1.47187	−	0.682596i
$506$	−9138.99			−0.802920
$507$		0			0
$508$		−	1146.74i		−	0.100154i
$509$	−12308.6			−1.07184			−0.535922	−	0.844268i	$-0.680036\pi$
$509$	−12308.6			−1.07184			−0.535922	+	0.844268i	$0.680036\pi$
$510$		0			0
$511$	1211.46			0.104877
$512$			399.294i			0.0344658i
$513$		0			0
$514$	4766.74			0.409050
$515$	4333.89	+	9345.07i	0.370823	+	0.799598i
$516$		0			0
$517$		−	3902.60i		−	0.331985i
$518$		−	5044.44i		−	0.427876i
$519$		0			0
$520$	1669.08	−	774.058i	0.140758	−	0.0652783i
$521$	15045.9			1.26521			0.632605	−	0.774475i	$-0.281986\pi$
$521$	15045.9			1.26521			0.632605	+	0.774475i	$0.281986\pi$
$522$		0			0
$523$			6372.16i			0.532763i	0.963868	+	0.266381i	$0.0858281\pi$
$523$			6372.16i			0.532763i	−0.963868	+	0.266381i	$0.914172\pi$
$524$	4085.25			0.340582
$525$		0			0
$526$	11507.8			0.953923
$527$		−	3073.05i		−	0.254011i
$528$		0			0
$529$	−10156.8			−0.834779
$530$	−18025.5	+	8359.57i	−1.47732	+	0.685125i
$531$		0			0
$532$		−	1702.14i		−	0.138717i
$533$		−	5022.68i		−	0.408173i
$534$		0			0
$535$	4989.99	+	10759.8i	0.403245	+	0.869509i
$536$	−13285.2			−1.07059
$537$		0			0
$538$		−	74.7569i		−	0.00599071i
$539$	897.962			0.0717588
$540$		0			0
$541$	4128.72			0.328110			0.164055	−	0.986451i	$-0.447543\pi$
$541$	4128.72			0.328110			0.164055	+	0.986451i	$0.447543\pi$
$542$		−	5197.95i		−	0.411939i
$543$		0			0
$544$	−3329.23			−0.262389
$545$	15549.0	−	7211.05i	1.22210	−	0.566766i
$546$		0			0
$547$		−	17987.6i		−	1.40602i	−0.711179	−	0.703011i	$-0.751838\pi$
$547$		−	17987.6i		−	1.40602i	0.711179	−	0.703011i	$-0.248162\pi$
$548$			8097.48i			0.631217i
$549$		0			0
$550$	−5836.42	−	4939.12i	−0.452483	−	0.382918i
$551$	797.383			0.0616509
$552$		0			0
$553$			5671.30i			0.436109i
$554$	−12466.2			−0.956024
$555$		0			0
$556$	9627.19			0.734323
$557$		−	13278.6i		−	1.01011i	−0.863086	−	0.505057i	$-0.831471\pi$
$557$		−	13278.6i		−	1.01011i	0.863086	−	0.505057i	$-0.168529\pi$
$558$		0			0
$559$	2238.20			0.169348
$560$	−2609.80	−	5627.46i	−0.196936	−	0.424649i
$561$		0			0
$562$			8085.24i			0.606860i
$563$		−	517.822i		−	0.0387630i	−0.999812	−	0.0193815i	$-0.993830\pi$
$563$		−	517.822i		−	0.0387630i	0.999812	−	0.0193815i	$-0.00616971\pi$
$564$		0			0
$565$	−9749.43	−	21022.5i	−0.725950	−	1.56535i
$566$	−945.355			−0.0702054
$567$		0			0
$568$			7573.64i			0.559477i
$569$	1071.91			0.0789750			0.0394875	−	0.999220i	$-0.487427\pi$
$569$	1071.91			0.0789750			0.0394875	+	0.999220i	$0.487427\pi$
$570$		0			0
$571$	−24489.8			−1.79486			−0.897430	−	0.441157i	$-0.854568\pi$
$571$	−24489.8			−1.79486			−0.897430	+	0.441157i	$0.854568\pi$
$572$			583.905i			0.0426824i
$573$		0			0
$574$	−11566.6			−0.841079
$575$	−14256.6	−	12064.8i	−1.03398	−	0.875018i
$576$		0			0
$577$		−	22765.1i		−	1.64250i	−0.570568	−	0.821251i	$-0.693277\pi$
$577$		−	22765.1i		−	1.64250i	0.570568	−	0.821251i	$-0.306723\pi$
$578$			14362.3i			1.03355i
$579$		0			0
$580$	−328.035	+	152.130i	−0.0234844	+	0.0108912i
$581$	−86.2454			−0.00615846
$582$		0			0
$583$			9757.64i			0.693173i
$584$	−2807.09			−0.198901
$585$		0			0
$586$	28309.0			1.99562
$587$		−	10106.8i		−	0.710651i	−0.934743	−	0.355325i	$-0.884370\pi$
$587$		−	10106.8i		−	0.710651i	0.934743	−	0.355325i	$-0.115630\pi$
$588$		0			0
$589$	−9633.85			−0.673949
$590$	5089.07	+	10973.4i	0.355108	+	0.765711i
$591$		0			0
$592$			17112.9i			1.18807i
$593$			4241.04i			0.293691i	0.989159	+	0.146845i	$0.0469120\pi$
$593$			4241.04i			0.293691i	−0.989159	+	0.146845i	$0.953088\pi$
$594$		0			0
$595$	1753.56	−	813.233i	0.120822	−	0.0560324i
$596$	8492.97			0.583701
$597$		0			0
$598$			5059.61i			0.345992i
$599$	−16536.6			−1.12799			−0.563995	−	0.825778i	$-0.690736\pi$
$599$	−16536.6			−1.12799			−0.563995	+	0.825778i	$0.690736\pi$
$600$		0			0
$601$	−6030.83			−0.409322			−0.204661	−	0.978833i	$-0.565609\pi$
$601$	−6030.83			−0.409322			−0.204661	+	0.978833i	$0.565609\pi$
$602$		−	5154.28i		−	0.348958i
$603$		0			0
$604$	−1221.24			−0.0822710
$605$	10093.7	−	4681.06i	0.678291	−	0.314566i
$606$		0			0
$607$		−	12639.0i		−	0.845143i	−0.906330	−	0.422572i	$-0.861128\pi$
$607$		−	12639.0i		−	0.845143i	0.906330	−	0.422572i	$-0.138872\pi$
$608$			10437.0i			0.696176i
$609$		0			0
$610$	−10267.3	−	22139.2i	−0.681494	−	1.46949i
$611$	−2160.59			−0.143058
$612$		0			0
$613$		−	226.217i		−	0.0149051i	−0.999972	−	0.00745254i	$-0.997628\pi$
$613$		−	226.217i		−	0.0149051i	0.999972	−	0.00745254i	$-0.00237224\pi$
$614$	−6693.84			−0.439970
$615$		0			0
$616$	−2080.67			−0.136092
$617$		−	6491.49i		−	0.423561i	−0.977317	−	0.211781i	$-0.932074\pi$
$617$		−	6491.49i		−	0.423561i	0.977317	−	0.211781i	$-0.0679263\pi$
$618$		0			0
$619$	−19224.9			−1.24833			−0.624163	−	0.781294i	$-0.714560\pi$
$619$	−19224.9			−1.24833			−0.624163	+	0.781294i	$0.714560\pi$
$620$	3963.27	−	1838.01i	0.256724	−	0.119059i
$621$		0			0
$622$		−	33448.8i		−	2.15623i
$623$			236.808i			0.0152287i
$624$		0			0
$625$	−2584.33	−	15409.8i	−0.165397	−	0.986227i
$626$	2106.71			0.134506
$627$		0			0
$628$		−	9062.79i		−	0.575868i
$629$	−5332.50			−0.338030
$630$		0			0
$631$	21123.5			1.33267			0.666334	−	0.745653i	$-0.267862\pi$
$631$	21123.5			1.33267			0.666334	+	0.745653i	$0.267862\pi$
$632$		−	13141.0i		−	0.827090i
$633$		0			0
$634$	4014.34			0.251467
$635$	−1717.57	−	3703.56i	−0.107338	−	0.231451i
$636$		0			0
$637$		−	497.138i		−	0.0309220i
$638$			629.916i			0.0390887i
$639$		0			0
$640$	7964.01	+	17172.6i	0.491883	+	1.06064i
$641$	8079.31			0.497837			0.248918	−	0.968524i	$-0.419925\pi$
$641$	8079.31			0.497837			0.248918	+	0.968524i	$0.419925\pi$
$642$		0			0
$643$		−	28025.8i		−	1.71887i	−0.511249	−	0.859433i	$-0.670817\pi$
$643$		−	28025.8i		−	1.71887i	0.511249	−	0.859433i	$-0.329183\pi$
$644$	3284.59			0.200980
$645$		0			0
$646$	−6382.93			−0.388751
$647$			9585.95i			0.582477i	0.956650	+	0.291239i	$0.0940674\pi$
$647$			9585.95i			0.582477i	−0.956650	+	0.291239i	$0.905933\pi$
$648$		0			0
$649$	5940.17			0.359279
$650$	−2734.44	+	3231.21i	−0.165006	+	0.194982i
$651$		0			0
$652$		−	1796.22i		−	0.107892i
$653$			6356.08i			0.380908i	0.981696	+	0.190454i	$0.0609959\pi$
$653$			6356.08i			0.380908i	−0.981696	+	0.190454i	$0.939004\pi$
$654$		0			0
$655$	13193.9	−	6118.82i	0.787065	−	0.365011i
$656$	39238.8			2.33539
$657$		0			0
$658$			4975.57i			0.294784i
$659$	2394.70			0.141554			0.0707772	−	0.997492i	$-0.477452\pi$
$659$	2394.70			0.141554			0.0707772	+	0.997492i	$0.477452\pi$
$660$		0			0
$661$	−23502.0			−1.38294			−0.691470	−	0.722406i	$-0.743036\pi$
$661$	−23502.0			−1.38294			−0.691470	+	0.722406i	$0.743036\pi$
$662$		−	31032.8i		−	1.82194i
$663$		0			0
$664$	199.840			0.0116796
$665$	−2549.44	−	5497.31i	−0.148667	−	0.320566i
$666$		0			0
$667$			1538.69i			0.0893229i
$668$		−	7612.46i		−	0.440921i
$669$		0			0
$670$	27728.8	−	12859.5i	1.59889	−	0.741504i
$671$	−11984.4			−0.689500
$672$		0			0
$673$		−	31304.2i		−	1.79300i	−0.443047	−	0.896498i	$-0.646103\pi$
$673$		−	31304.2i		−	1.79300i	0.443047	−	0.896498i	$-0.353897\pi$
$674$	1694.66			0.0968486
$675$		0			0
$676$	−6576.42			−0.374170
$677$			16821.3i			0.954940i	0.878648	+	0.477470i	$0.158446\pi$
$677$			16821.3i			0.954940i	−0.878648	+	0.477470i	$0.841554\pi$
$678$		0			0
$679$	5675.32			0.320764
$680$	−4063.17	+	1884.35i	−0.229141	+	0.106267i
$681$		0			0
$682$		−	7610.53i		−	0.427306i
$683$			106.287i			0.00595453i	0.999996	+	0.00297726i	$0.000947694\pi$
$683$			106.287i			0.00595453i	−0.999996	+	0.00297726i	$0.999052\pi$
$684$		0			0
$685$	12128.3	+	26151.9i	0.676493	+	1.45871i
$686$	−1144.84			−0.0637177
$687$		0			0
$688$			17485.5i			0.968938i
$689$	5402.12			0.298700
$690$		0			0
$691$	−19383.5			−1.06712			−0.533562	−	0.845761i	$-0.679147\pi$
$691$	−19383.5			−1.06712			−0.533562	+	0.845761i	$0.679147\pi$
$692$			1967.34i			0.108074i
$693$		0			0
$694$	−22898.9			−1.25249
$695$	31092.4	−	14419.5i	1.69698	−	0.786995i
$696$		0			0
$697$			12227.1i			0.664467i
$698$			30828.9i			1.67176i
$699$		0			0
$700$	2097.63	+	1775.14i	0.113261	+	0.0958484i
$701$	13338.2			0.718652			0.359326	−	0.933212i	$-0.383007\pi$
$701$	13338.2			0.718652			0.359326	+	0.933212i	$0.383007\pi$
$702$		0			0
$703$			16717.1i			0.896868i
$704$	3375.20			0.180692
$705$		0			0
$706$	31440.0			1.67600
$707$			11527.9i			0.613227i
$708$		0			0
$709$	−15225.3			−0.806487			−0.403243	−	0.915093i	$-0.632117\pi$
$709$	−15225.3			−0.806487			−0.403243	+	0.915093i	$0.632117\pi$
$710$	−7330.98	−	15807.6i	−0.387502	−	0.835563i
$711$		0			0
$712$		−	548.708i		−	0.0288816i
$713$		−	18590.2i		−	0.976450i
$714$		0			0
$715$	874.565	+	1885.80i	0.0457439	+	0.0986365i
$716$	−7292.59			−0.380638
$717$		0			0
$718$		−	9648.79i		−	0.501518i
$719$	−23884.3			−1.23885			−0.619427	−	0.785054i	$-0.712635\pi$
$719$	−23884.3			−1.23885			−0.619427	+	0.785054i	$0.712635\pi$
$720$		0			0
$721$	−6449.52			−0.333138
$722$		−	2883.40i		−	0.148628i
$723$		0			0
$724$	14650.3			0.752034
$725$	−831.578	+	982.653i	−0.0425987	+	0.0503377i
$726$		0			0
$727$			27929.5i			1.42482i	0.701761	+	0.712412i	$0.252397\pi$
$727$			27929.5i			1.42482i	−0.701761	+	0.712412i	$0.747603\pi$
$728$			1151.92i			0.0586443i
$729$		0			0
$730$	5858.93	−	2717.15i	0.297053	−	0.137762i
$731$	−5448.62			−0.275683
$732$		0			0
$733$		−	17970.8i		−	0.905548i	−0.891625	−	0.452774i	$-0.850434\pi$
$733$		−	17970.8i		−	0.905548i	0.891625	−	0.452774i	$-0.149566\pi$
$734$	−5241.97			−0.263603
$735$		0			0
$736$	−20140.0			−1.00865
$737$		−	15010.2i		−	0.750215i
$738$		0			0
$739$	1280.61			0.0637455			0.0318728	−	0.999492i	$-0.489853\pi$
$739$	1280.61			0.0637455			0.0318728	+	0.999492i	$0.489853\pi$
$740$	−3189.41	−	6877.25i	−0.158439	−	0.341639i
$741$		0			0
$742$		−	12440.4i		−	0.615499i
$743$			28570.1i			1.41068i	0.708869	+	0.705340i	$0.249206\pi$
$743$			28570.1i			1.41068i	−0.708869	+	0.705340i	$0.750794\pi$
$744$		0			0
$745$	27429.3	−	12720.6i	1.34890	−	0.625568i
$746$	29083.0			1.42735
$747$		0			0
$748$		−	1421.44i		−	0.0694828i
$749$	−7425.91			−0.362265
$750$		0			0
$751$	32836.7			1.59551			0.797754	−	0.602982i	$-0.206021\pi$
$751$	32836.7			1.59551			0.797754	+	0.602982i	$0.206021\pi$
$752$		−	16879.2i		−	0.818514i
$753$		0			0
$754$	348.740			0.0168440
$755$	−3944.18	+	1829.16i	−0.190123	+	0.0881721i
$756$		0			0
$757$			1086.72i			0.0521763i	0.999660	+	0.0260882i	$0.00830507\pi$
$757$			1086.72i			0.0521763i	−0.999660	+	0.0260882i	$0.991695\pi$
$758$			19291.0i			0.924379i
$759$		0			0
$760$	5907.33	+	12737.8i	0.281949	+	0.607961i
$761$	17097.7			0.814443			0.407221	−	0.913329i	$-0.366498\pi$
$761$	17097.7			0.814443			0.407221	+	0.913329i	$0.366498\pi$
$762$		0			0
$763$			10731.2i			0.509168i
$764$	−11714.9			−0.554751
$765$		0			0
$766$	−41188.5			−1.94282
$767$		−	3288.65i		−	0.154819i
$768$		0			0
$769$	24796.1			1.16277			0.581386	−	0.813628i	$-0.302511\pi$
$769$	24796.1			1.16277			0.581386	+	0.813628i	$0.302511\pi$
$770$	4342.76	−	2014.01i	0.203250	−	0.0942595i
$771$		0			0
$772$			8119.01i			0.378510i
$773$			33325.8i			1.55064i	0.631567	+	0.775321i	$0.282412\pi$
$773$			33325.8i			1.55064i	−0.631567	+	0.775321i	$0.717588\pi$
$774$		0			0
$775$	10047.0	−	11872.2i	0.465675	−	0.550275i
$776$	−13150.3			−0.608336
$777$		0			0
$778$			26529.8i			1.22255i
$779$	38331.3			1.76298
$780$		0			0
$781$	−8557.02			−0.392054
$782$		−	12317.0i		−	0.563241i
$783$		0			0
$784$	3883.80			0.176922
$785$	−13574.1	−	29269.6i	−0.617173	−	1.33080i
$786$		0			0
$787$			30195.2i			1.36765i	0.729645	+	0.683826i	$0.239685\pi$
$787$			30195.2i			1.36765i	−0.729645	+	0.683826i	$0.760315\pi$
$788$		−	7555.77i		−	0.341578i
$789$		0			0
$790$	12720.0	+	27427.8i	0.572856	+	1.23524i
$791$	14508.7			0.652175
$792$		0			0
$793$			6634.94i			0.297117i
$794$	−17902.4			−0.800168
$795$		0			0
$796$	3744.57			0.166737
$797$			24226.2i			1.07671i	0.842720	+	0.538353i	$0.180953\pi$
$797$			24226.2i			1.07671i	−0.842720	+	0.538353i	$0.819047\pi$
$798$		0			0
$799$	5259.69			0.232884
$800$	−12862.0	−	10884.6i	−0.568424	−	0.481034i
$801$		0			0
$802$		−	20217.1i		−	0.890138i
$803$		−	3171.57i		−	0.139380i
$804$		0			0
$805$	10608.0	−	4919.61i	0.464452	−	0.215395i
$806$	−4213.42			−0.184133
$807$		0			0
$808$		−	26711.4i		−	1.16300i
$809$	−16039.7			−0.697065			−0.348533	−	0.937297i	$-0.613320\pi$
$809$	−16039.7			−0.697065			−0.348533	+	0.937297i	$0.613320\pi$
$810$		0			0
$811$	33767.0			1.46205			0.731024	−	0.682352i	$-0.239043\pi$
$811$	33767.0			1.46205			0.731024	+	0.682352i	$0.239043\pi$
$812$		−	226.394i		−	0.00978434i
$813$		0			0
$814$	−13206.2			−0.568644
$815$	−2690.35	−	5801.15i	−0.115631	−	0.249332i
$816$		0			0
$817$			17081.1i			0.731448i
$818$		−	4167.22i		−	0.178122i
$819$		0			0
$820$	−15769.1	+	7313.11i	−0.671562	+	0.311445i
$821$	−631.743			−0.0268550			−0.0134275	−	0.999910i	$-0.504274\pi$
$821$	−631.743			−0.0268550			−0.0134275	+	0.999910i	$0.504274\pi$
$822$		0			0
$823$		−	30565.3i		−	1.29458i	−0.762244	−	0.647290i	$-0.775902\pi$
$823$		−	30565.3i		−	1.29458i	0.762244	−	0.647290i	$-0.224098\pi$
$824$	14944.2			0.631804
$825$		0			0
$826$	−7573.34			−0.319020
$827$			24472.5i			1.02901i	0.857487	+	0.514505i	$0.172024\pi$
$827$			24472.5i			1.02901i	−0.857487	+	0.514505i	$0.827976\pi$
$828$		0			0
$829$	9613.32			0.402756			0.201378	−	0.979514i	$-0.435458\pi$
$829$	9613.32			0.402756			0.201378	+	0.979514i	$0.435458\pi$
$830$	−417.104	+	193.437i	−0.0174432	+	0.00808951i
$831$		0			0
$832$		−	1868.61i		−	0.0778634i
$833$			1210.22i			0.0503381i
$834$		0			0
$835$	−11401.8	−	24585.5i	−0.472547	−	1.01894i
$836$	−4456.15			−0.184353
$837$		0			0
$838$			27784.3i			1.14534i
$839$	−23320.5			−0.959609			−0.479805	−	0.877375i	$-0.659293\pi$
$839$	−23320.5			−0.959609			−0.479805	+	0.877375i	$0.659293\pi$
$840$		0			0
$841$	−24282.9			−0.995651
$842$			5652.11i			0.231336i
$843$		0			0
$844$	2402.18			0.0979699
$845$	−21239.5	+	9850.06i	−0.864686	+	0.401009i
$846$		0			0
$847$			6966.17i			0.282598i
$848$			42203.0i			1.70903i
$849$		0			0
$850$	6656.65	−	7865.98i	0.268613	−	0.317413i
$851$	−32258.6			−1.29943
$852$		0			0
$853$			2992.19i			0.120106i	0.998195	+	0.0600531i	$0.0191270\pi$
$853$			2992.19i			0.120106i	−0.998195	+	0.0600531i	$0.980873\pi$
$854$	15279.4			0.612237
$855$		0			0
$856$	17206.6			0.687044
$857$			20796.2i			0.828919i	0.910068	+	0.414459i	$0.136029\pi$
$857$			20796.2i			0.828919i	−0.910068	+	0.414459i	$0.863971\pi$
$858$		0			0
$859$	5302.17			0.210603			0.105301	−	0.994440i	$-0.466419\pi$
$859$	5302.17			0.210603			0.105301	+	0.994440i	$0.466419\pi$
$860$	−3258.86	−	7027.01i	−0.129216	−	0.278627i
$861$		0			0
$862$		−	39233.8i		−	1.55024i
$863$			27066.7i			1.06762i	0.845603	+	0.533812i	$0.179241\pi$
$863$			27066.7i			1.06762i	−0.845603	+	0.533812i	$0.820759\pi$
$864$		0			0
$865$	2946.65	+	6353.79i	0.115825	+	0.249752i
$866$	48778.8			1.91406
$867$		0			0
$868$			2735.26i			0.106959i
$869$	14847.3			0.579585
$870$		0			0
$871$	−8310.09			−0.323280
$872$		−	24865.3i		−	0.965648i
$873$		0			0
$874$	−38613.1			−1.49440
$875$	9433.37	+	2591.26i	0.364464	+	0.100115i
$876$		0			0
$877$		−	26825.0i		−	1.03286i	−0.856330	−	0.516429i	$-0.827261\pi$
$877$		−	26825.0i		−	1.03286i	0.856330	−	0.516429i	$-0.172739\pi$
$878$		−	6533.69i		−	0.251141i
$879$		0			0
$880$	−14732.5	+	6832.37i	−0.564355	+	0.261726i
$881$	47701.8			1.82420			0.912098	−	0.409973i	$-0.134462\pi$
$881$	47701.8			1.82420			0.912098	+	0.409973i	$0.134462\pi$
$882$		0			0
$883$			28447.5i			1.08418i	0.840319	+	0.542092i	$0.182368\pi$
$883$			28447.5i			1.08418i	−0.840319	+	0.542092i	$0.817632\pi$
$884$	−786.953			−0.0299413
$885$		0			0
$886$	−1190.82			−0.0451538
$887$		−	35046.9i		−	1.32667i	−0.748321	−	0.663337i	$-0.769140\pi$
$887$		−	35046.9i		−	1.32667i	0.748321	−	0.663337i	$-0.230860\pi$
$888$		0			0
$889$	2556.02			0.0964297
$890$	531.128	+	1145.26i	0.0200039	+	0.0431339i
$891$		0			0
$892$		−	4978.27i		−	0.186866i
$893$		−	16488.9i		−	0.617894i
$894$		0			0
$895$	−23552.4	+	10922.7i	−0.879633	+	0.407940i
$896$	−11851.7			−0.441895
$897$		0			0
$898$			24683.6i			0.917262i
$899$	−1281.35			−0.0475367
$900$		0			0
$901$	−13150.8			−0.486255
$902$			30280.9i			1.11779i
$903$		0			0
$904$	−33618.2			−1.23686
$905$	47315.1	−	21942.9i	1.73791	−	0.805976i
$906$		0			0
$907$			19761.2i			0.723439i	0.932287	+	0.361720i	$0.117810\pi$
$907$			19761.2i			0.723439i	−0.932287	+	0.361720i	$0.882190\pi$
$908$		−	7421.23i		−	0.271236i
$909$		0			0
$910$	−1115.01	−	2404.28i	−0.0406180	−	0.0875836i
$911$	−23563.4			−0.856960			−0.428480	−	0.903551i	$-0.640951\pi$
$911$	−23563.4			−0.856960			−0.428480	+	0.903551i	$0.640951\pi$
$912$		0			0
$913$			225.788i			0.00818453i
$914$	42463.4			1.53672
$915$		0			0
$916$	5107.84			0.184244
$917$			9105.78i			0.327917i
$918$		0			0
$919$	37601.1			1.34967			0.674834	−	0.737970i	$-0.264215\pi$
$919$	37601.1			1.34967			0.674834	+	0.737970i	$0.264215\pi$
$920$	−24579.9	+	11399.2i	−0.880844	+	0.408502i
$921$		0			0
$922$			7364.54i			0.263057i
$923$			4737.42i			0.168943i
$924$		0			0
$925$	−20601.3	−	17434.0i	−0.732288	−	0.619705i
$926$	−53110.2			−1.88478
$927$		0			0
$928$			1388.17i			0.0491046i
$929$	−17616.6			−0.622154			−0.311077	−	0.950385i	$-0.600690\pi$
$929$	−17616.6			−0.622154			−0.311077	+	0.950385i	$0.600690\pi$
$930$		0			0
$931$	3793.98			0.133558
$932$			5402.74i			0.189885i
$933$		0			0
$934$	−25375.6			−0.888990
$935$	−2129.02	−	4590.75i	−0.0744666	−	0.160571i
$936$		0			0
$937$			36717.2i			1.28015i	0.768313	+	0.640074i	$0.221096\pi$
$937$			36717.2i			1.28015i	−0.768313	+	0.640074i	$0.778904\pi$
$938$			19137.1i			0.666148i
$939$		0			0
$940$	3145.86	+	6783.36i	0.109156	+	0.235371i
$941$	−21861.7			−0.757354			−0.378677	−	0.925529i	$-0.623621\pi$
$941$	−21861.7			−0.757354			−0.378677	+	0.925529i	$0.623621\pi$
$942$		0			0
$943$			73967.0i			2.55429i
$944$	25692.0			0.885809
$945$		0			0
$946$	−13493.7			−0.463762
$947$		−	17752.1i		−	0.609149i	−0.952488	−	0.304575i	$-0.901486\pi$
$947$		−	17752.1i		−	0.609149i	0.952488	−	0.304575i	$-0.0985143\pi$
$948$		0			0
$949$	−1755.87			−0.0600612
$950$	−24659.5	−	20868.3i	−0.842167	−	0.712690i
$951$		0			0
$952$		−	2804.21i		−	0.0954673i
$953$		−	26764.9i		−	0.909758i	−0.890553	−	0.454879i	$-0.849683\pi$
$953$		−	26764.9i		−	0.909758i	0.890553	−	0.454879i	$-0.150317\pi$
$954$		0			0
$955$	−37834.9	+	17546.4i	−1.28200	+	0.594542i
$956$	−22667.4			−0.766857
$957$		0			0
$958$			5613.83i			0.189326i
$959$	−18048.8			−0.607744
$960$		0			0
$961$	−14309.9			−0.480344
$962$			7311.32i			0.245038i
$963$		0			0
$964$	−16000.2			−0.534575
$965$	12160.5	+	26221.5i	0.405660	+	0.874715i
$966$		0			0
$967$			31173.9i			1.03669i	0.855170	+	0.518347i	$0.173453\pi$
$967$			31173.9i			1.03669i	−0.855170	+	0.518347i	$0.826547\pi$
$968$		−	16141.3i		−	0.535953i
$969$		0			0
$970$	27447.2	−	12729.0i	0.908533	−	0.421343i
$971$	35414.7			1.17046			0.585228	−	0.810869i	$-0.301005\pi$
$971$	35414.7			1.17046			0.585228	+	0.810869i	$0.301005\pi$
$972$		0			0
$973$			21458.5i			0.707016i
$974$	−47085.6			−1.54899
$975$		0			0
$976$	−51834.3			−1.69997
$977$			20952.6i			0.686112i	0.939315	+	0.343056i	$0.111462\pi$
$977$			20952.6i			0.686112i	−0.939315	+	0.343056i	$0.888538\pi$
$978$		0			0
$979$	619.955			0.0202388
$980$	−1560.81	+	723.842i	−0.0508756	+	0.0235942i
$981$		0			0
$982$		−	30073.7i		−	0.977281i
$983$		−	20858.6i		−	0.676793i	−0.941004	−	0.338396i	$-0.890116\pi$
$983$		−	20858.6i		−	0.676793i	0.941004	−	0.338396i	$-0.109884\pi$
$984$		0			0
$985$	−11316.9	−	24402.4i	−0.366078	−	0.789366i
$986$	−848.963			−0.0274204
$987$		0			0
$988$			2467.06i			0.0794409i
$989$	−32961.1			−1.05976
$990$		0			0
$991$	−13565.0			−0.434820			−0.217410	−	0.976080i	$-0.569761\pi$
$991$	−13565.0			−0.434820			−0.217410	+	0.976080i	$0.569761\pi$
$992$		−	16771.7i		−	0.536795i
$993$		0			0
$994$	10909.7			0.348122
$995$	12093.6	−	5608.57i	0.385320	−	0.178697i
$996$		0			0
$997$		−	12520.7i		−	0.397727i	−0.980027	−	0.198864i	$-0.936275\pi$
$997$		−	12520.7i		−	0.397727i	0.980027	−	0.198864i	$-0.0637251\pi$
$998$		−	8861.94i		−	0.281082i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.4.d.b.64.8		10
3.2	odd	2		105.4.d.b.64.3	✓	10
5.2	odd	4		1575.4.a.bo.1.2		5
5.3	odd	4		1575.4.a.bp.1.4		5
5.4	even	2	inner	315.4.d.b.64.3		10
15.2	even	4		525.4.a.x.1.4		5
15.8	even	4		525.4.a.w.1.2		5
15.14	odd	2		105.4.d.b.64.8	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.d.b.64.3	✓	10	3.2	odd	2
105.4.d.b.64.8	yes	10	15.14	odd	2
315.4.d.b.64.3		10	5.4	even	2	inner
315.4.d.b.64.8		10	1.1	even	1	trivial
525.4.a.w.1.2		5	15.8	even	4
525.4.a.x.1.4		5	15.2	even	4
1575.4.a.bo.1.2		5	5.2	odd	4
1575.4.a.bp.1.4		5	5.3	odd	4

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	315.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+3.33774i q^{2} -3.14050 q^{4} +(-10.1427 + 4.70380i) q^{5} -7.00000i q^{7} +16.2197i q^{8} +O(q^{10})\)	\(q+3.33774i q^{2} -3.14050 q^{4} +(-10.1427 + 4.70380i) q^{5} -7.00000i q^{7} +16.2197i q^{8} +(-15.7000 - 33.8537i) q^{10} -18.3258 q^{11} +10.1457i q^{13} +23.3642 q^{14} -79.2613 q^{16} -24.6984i q^{17} -77.4282 q^{19} +(31.8532 - 14.7723i) q^{20} -61.1666i q^{22} -149.411i q^{23} +(80.7486 - 95.4184i) q^{25} -33.8636 q^{26} +21.9835i q^{28} -10.2984 q^{29} +124.423 q^{31} -134.796i q^{32} +82.4367 q^{34} +(32.9266 + 70.9989i) q^{35} -215.905i q^{37} -258.435i q^{38} +(-76.2943 - 164.512i) q^{40} -495.056 q^{41} -220.606i q^{43} +57.5521 q^{44} +498.696 q^{46} +212.957i q^{47} -49.0000 q^{49} +(318.482 + 269.518i) q^{50} -31.8625i q^{52} -532.455i q^{53} +(185.873 - 86.2007i) q^{55} +113.538 q^{56} -34.3732i q^{58} -324.143 q^{59} +653.967 q^{61} +415.292i q^{62} -184.178 q^{64} +(-47.7232 - 102.905i) q^{65} +819.077i q^{67} +77.5653i q^{68} +(-236.976 + 109.900i) q^{70} +466.940 q^{71} +173.066i q^{73} +720.634 q^{74} +243.163 q^{76} +128.280i q^{77} -810.186 q^{79} +(803.923 - 372.829i) q^{80} -1652.37i q^{82} -12.3208i q^{83} +(116.176 + 250.508i) q^{85} +736.326 q^{86} -297.239i q^{88} -33.8297 q^{89} +71.0198 q^{91} +469.227i q^{92} -710.795 q^{94} +(785.330 - 364.206i) q^{95} +810.761i q^{97} -163.549i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 54 q^{4} + 14 q^{5}+O(q^{10}) \) 10 * q - 54 * q^4 + 14 * q^5	\( 10 q - 54 q^{4} + 14 q^{5} + 92 q^{10} - 132 q^{11} + 14 q^{14} + 310 q^{16} - 348 q^{19} - 366 q^{20} - 374 q^{25} - 892 q^{26} + 740 q^{29} + 684 q^{31} - 224 q^{34} - 2156 q^{40} - 1604 q^{41} + 580 q^{44} + 1280 q^{46} - 490 q^{49} + 2504 q^{50} - 452 q^{55} - 462 q^{56} + 1408 q^{59} + 1300 q^{61} - 150 q^{64} + 3296 q^{65} - 882 q^{70} - 2940 q^{71} - 2624 q^{74} + 8740 q^{76} + 1640 q^{79} + 4126 q^{80} - 1704 q^{85} - 1664 q^{86} + 572 q^{89} - 28 q^{91} - 5080 q^{94} - 1268 q^{95}+O(q^{100}) \) 10 * q - 54 * q^4 + 14 * q^5 + 92 * q^10 - 132 * q^11 + 14 * q^14 + 310 * q^16 - 348 * q^19 - 366 * q^20 - 374 * q^25 - 892 * q^26 + 740 * q^29 + 684 * q^31 - 224 * q^34 - 2156 * q^40 - 1604 * q^41 + 580 * q^44 + 1280 * q^46 - 490 * q^49 + 2504 * q^50 - 452 * q^55 - 462 * q^56 + 1408 * q^59 + 1300 * q^61 - 150 * q^64 + 3296 * q^65 - 882 * q^70 - 2940 * q^71 - 2624 * q^74 + 8740 * q^76 + 1640 * q^79 + 4126 * q^80 - 1704 * q^85 - 1664 * q^86 + 572 * q^89 - 28 * q^91 - 5080 * q^94 - 1268 * q^95

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