LMFDB - Embedded newform 315.4.d.b.64.2

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			64.2
Root			$-1.37042i$ of defining polynomial
Character	$\chi$	$=$	315.64
Dual form			315.4.d.b.64.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.88936i q^{2} -15.9059 q^{4} +(9.63020 + 5.67972i) q^{5} -7.00000i q^{7} +38.6546i q^{8} +O(q^{10})$	\(q-4.88936i q^{2} -15.9059 q^{4} +(9.63020 + 5.67972i) q^{5} -7.00000i q^{7} +38.6546i q^{8} +(27.7702 - 47.0855i) q^{10} -54.9009 q^{11} -49.7580i q^{13} -34.2255 q^{14} +61.7496 q^{16} +133.661i q^{17} -138.986 q^{19} +(-153.177 - 90.3409i) q^{20} +268.430i q^{22} -7.32751i q^{23} +(60.4815 + 109.394i) q^{25} -243.285 q^{26} +111.341i q^{28} +87.2408 q^{29} -209.479 q^{31} +7.32107i q^{32} +653.519 q^{34} +(39.7580 - 67.4114i) q^{35} +67.9041i q^{37} +679.555i q^{38} +(-219.547 + 372.252i) q^{40} -77.6804 q^{41} -197.692i q^{43} +873.246 q^{44} -35.8269 q^{46} +4.97613i q^{47} -49.0000 q^{49} +(534.865 - 295.716i) q^{50} +791.444i q^{52} +53.0843i q^{53} +(-528.706 - 311.822i) q^{55} +270.582 q^{56} -426.552i q^{58} -683.950 q^{59} -26.8658 q^{61} +1024.22i q^{62} +529.792 q^{64} +(282.612 - 479.180i) q^{65} -149.300i q^{67} -2126.00i q^{68} +(-329.599 - 194.391i) q^{70} -6.15571 q^{71} +294.545i q^{73} +332.008 q^{74} +2210.70 q^{76} +384.306i q^{77} +938.669 q^{79} +(594.661 + 350.720i) q^{80} +379.807i q^{82} -784.907i q^{83} +(-759.160 + 1287.19i) q^{85} -966.590 q^{86} -2122.17i q^{88} +275.928 q^{89} -348.306 q^{91} +116.550i q^{92} +24.3301 q^{94} +(-1338.47 - 789.404i) q^{95} -1165.27i q^{97} +239.579i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	4.88936i		−	1.72865i	−0.502933	−	0.864325i	$-0.667746\pi$
$2$		−	4.88936i		−	1.72865i	0.502933	−	0.864325i	$-0.332254\pi$
$3$		0			0
$3$		0			0
$4$	−15.9059			−1.98823
$5$	9.63020	+	5.67972i	0.861351	+	0.508010i
$5$	9.63020	+	5.67972i	0.861351	+	0.508010i
$6$		0			0
$7$		−	7.00000i		−	0.377964i
$7$		−	7.00000i		−	0.377964i
$8$			38.6546i			1.70831i
$9$		0			0
$10$	27.7702	−	47.0855i	0.878171	−	1.48898i
$11$	−54.9009			−1.50484			−0.752420	−	0.658684i	$-0.771113\pi$
$11$	−54.9009			−1.50484			−0.752420	+	0.658684i	$0.771113\pi$
$12$		0			0
$13$		−	49.7580i		−	1.06157i	−0.847507	−	0.530784i	$-0.821897\pi$
$13$		−	49.7580i		−	1.06157i	0.847507	−	0.530784i	$-0.178103\pi$
$14$	−34.2255			−0.653368
$15$		0			0
$16$	61.7496			0.964837
$17$			133.661i			1.90692i	0.301517	+	0.953461i	$0.402507\pi$
$17$			133.661i			1.90692i	−0.301517	+	0.953461i	$0.597493\pi$
$18$		0			0
$19$	−138.986			−1.67819			−0.839097	−	0.543983i	$-0.816916\pi$
$19$	−138.986			−1.67819			−0.839097	+	0.543983i	$0.816916\pi$
$20$	−153.177	−	90.3409i	−1.71257	−	1.01004i
$21$		0			0
$22$			268.430i			2.60134i
$23$		−	7.32751i		−	0.0664301i	−0.999448	−	0.0332150i	$-0.989425\pi$
$23$		−	7.32751i		−	0.0664301i	0.999448	−	0.0332150i	$-0.0105746\pi$
$24$		0			0
$25$	60.4815	+	109.394i	0.483852	+	0.875150i
$26$	−243.285			−1.83508
$27$		0			0
$28$			111.341i			0.751481i
$29$	87.2408			0.558628			0.279314	−	0.960200i	$-0.409893\pi$
$29$	87.2408			0.558628			0.279314	+	0.960200i	$0.409893\pi$
$30$		0			0
$31$	−209.479			−1.21366			−0.606831	−	0.794831i	$-0.707560\pi$
$31$	−209.479			−1.21366			−0.606831	+	0.794831i	$0.707560\pi$
$32$			7.32107i			0.0404436i
$33$		0			0
$34$	653.519			3.29640
$35$	39.7580	−	67.4114i	0.192010	−	0.325560i
$36$		0			0
$37$			67.9041i			0.301713i	0.988556	+	0.150856i	$0.0482031\pi$
$37$			67.9041i			0.301713i	−0.988556	+	0.150856i	$0.951797\pi$
$38$			679.555i			2.90101i
$39$		0			0
$40$	−219.547	+	372.252i	−0.867838	+	1.47145i
$41$	−77.6804			−0.295894			−0.147947	−	0.988995i	$-0.547266\pi$
$41$	−77.6804			−0.295894			−0.147947	+	0.988995i	$0.547266\pi$
$42$		0			0
$43$		−	197.692i		−	0.701112i	−0.936542	−	0.350556i	$-0.885993\pi$
$43$		−	197.692i		−	0.701112i	0.936542	−	0.350556i	$-0.114007\pi$
$44$	873.246			2.99197
$45$		0			0
$46$	−35.8269			−0.114834
$47$			4.97613i			0.0154435i	0.999970	+	0.00772173i	$0.00245793\pi$
$47$			4.97613i			0.0154435i	−0.999970	+	0.00772173i	$0.997542\pi$
$48$		0			0
$49$	−49.0000			−0.142857
$50$	534.865	−	295.716i	1.51283	−	0.836412i
$51$		0			0
$52$			791.444i			2.11065i
$53$			53.0843i			0.137579i	0.997631	+	0.0687895i	$0.0219137\pi$
$53$			53.0843i			0.137579i	−0.997631	+	0.0687895i	$0.978086\pi$
$54$		0			0
$55$	−528.706	−	311.822i	−1.29620	−	0.764473i
$56$	270.582			0.645680
$57$		0			0
$58$		−	426.552i		−	0.965673i
$59$	−683.950			−1.50920			−0.754599	−	0.656186i	$-0.772169\pi$
$59$	−683.950			−1.50920			−0.754599	+	0.656186i	$0.772169\pi$
$60$		0			0
$61$	−26.8658			−0.0563904			−0.0281952	−	0.999602i	$-0.508976\pi$
$61$	−26.8658			−0.0563904			−0.0281952	+	0.999602i	$0.508976\pi$
$62$			1024.22i			2.09800i
$63$		0			0
$64$	529.792			1.03475
$65$	282.612	−	479.180i	0.539287	−	0.914383i
$66$		0			0
$67$		−	149.300i		−	0.272237i	−0.990693	−	0.136119i	$-0.956537\pi$
$67$		−	149.300i		−	0.272237i	0.990693	−	0.136119i	$-0.0434628\pi$
$68$		−	2126.00i		−	3.79140i
$69$		0			0
$70$	−329.599	−	194.391i	−0.562780	−	0.331918i
$71$	−6.15571			−0.0102894			−0.00514470	−	0.999987i	$-0.501638\pi$
$71$	−6.15571			−0.0102894			−0.00514470	+	0.999987i	$0.501638\pi$
$72$		0			0
$73$			294.545i			0.472245i	0.971723	+	0.236123i	$0.0758767\pi$
$73$			294.545i			0.472245i	−0.971723	+	0.236123i	$0.924123\pi$
$74$	332.008			0.521556
$75$		0			0
$76$	2210.70			3.33664
$77$			384.306i			0.568776i
$78$		0			0
$79$	938.669			1.33682			0.668409	−	0.743794i	$-0.266976\pi$
$79$	938.669			1.33682			0.668409	+	0.743794i	$0.266976\pi$
$80$	594.661	+	350.720i	0.831063	+	0.490146i
$81$		0			0
$82$			379.807i			0.511496i
$83$		−	784.907i		−	1.03801i	−0.854772	−	0.519004i	$-0.826303\pi$
$83$		−	784.907i		−	1.03801i	0.854772	−	0.519004i	$-0.173697\pi$
$84$		0			0
$85$	−759.160	+	1287.19i	−0.968735	+	1.64253i
$86$	−966.590			−1.21198
$87$		0			0
$88$		−	2122.17i		−	2.57073i
$89$	275.928			0.328633			0.164316	−	0.986408i	$-0.447458\pi$
$89$	275.928			0.328633			0.164316	+	0.986408i	$0.447458\pi$
$90$		0			0
$91$	−348.306			−0.401235
$92$			116.550i			0.132078i
$93$		0			0
$94$	24.3301			0.0266963
$95$	−1338.47	−	789.404i	−1.44551	−	0.852538i
$96$		0			0
$97$		−	1165.27i		−	1.21975i	−0.792499	−	0.609873i	$-0.791220\pi$
$97$		−	1165.27i		−	1.21975i	0.792499	−	0.609873i	$-0.208780\pi$
$98$			239.579i			0.246950i
$99$		0			0
$100$	−962.011	−	1740.00i	−0.962011	−	1.74000i
$101$	0.162999			0.000160584			8.02919e−5	−	1.00000i	$-0.499974\pi$
$101$	0.162999			0.000160584			8.02919e−5		1.00000i	$0.499974\pi$
$102$		0			0
$103$			1300.78i			1.24437i	0.782871	+	0.622184i	$0.213755\pi$
$103$			1300.78i			1.24437i	−0.782871	+	0.622184i	$0.786245\pi$
$104$	1923.38			1.81349
$105$		0			0
$106$	259.548			0.237826
$107$			1531.63i			1.38382i	0.721985	+	0.691908i	$0.243230\pi$
$107$			1531.63i			1.38382i	−0.721985	+	0.691908i	$0.756770\pi$
$108$		0			0
$109$	−1971.39			−1.73234			−0.866171	−	0.499748i	$-0.833426\pi$
$109$	−1971.39			−1.73234			−0.866171	+	0.499748i	$0.833426\pi$
$110$	−1524.61	+	2585.04i	−1.32151	+	2.24067i
$111$		0			0
$112$		−	432.247i		−	0.364674i
$113$			262.817i			0.218794i	0.993998	+	0.109397i	$0.0348920\pi$
$113$			262.817i			0.218794i	−0.993998	+	0.109397i	$0.965108\pi$
$114$		0			0
$115$	41.6182	−	70.5654i	0.0337471	−	0.0572196i
$116$	−1387.64			−1.11068
$117$		0			0
$118$			3344.08i			2.60888i
$119$	935.630			0.720749
$120$		0			0
$121$	1683.11			1.26454
$122$			131.357i			0.0974793i
$123$		0			0
$124$	3331.94			2.41304
$125$	−38.8765	+	1397.00i	−0.0278177	+	0.999613i
$126$		0			0
$127$		−	569.649i		−	0.398017i	−0.979998	−	0.199009i	$-0.936228\pi$
$127$		−	569.649i		−	0.398017i	0.979998	−	0.199009i	$-0.0637722\pi$
$128$		−	2531.78i		−	1.74828i
$129$		0			0
$130$	−2342.88	−	1381.79i	−1.58065	−	0.932239i
$131$	−984.808			−0.656817			−0.328409	−	0.944536i	$-0.606512\pi$
$131$	−984.808			−0.656817			−0.328409	+	0.944536i	$0.606512\pi$
$132$		0			0
$133$			972.905i			0.634297i
$134$	−729.982			−0.470603
$135$		0			0
$136$	−5166.63			−3.25761
$137$		−	1377.35i		−	0.858942i	−0.903081	−	0.429471i	$-0.858700\pi$
$137$		−	1377.35i		−	0.858942i	0.903081	−	0.429471i	$-0.141300\pi$
$138$		0			0
$139$	−839.673			−0.512375			−0.256188	−	0.966627i	$-0.582466\pi$
$139$	−839.673			−0.512375			−0.256188	+	0.966627i	$0.582466\pi$
$140$	−632.386	+	1072.24i	−0.381760	+	0.647289i
$141$		0			0
$142$			30.0975i			0.0177868i
$143$			2731.76i			1.59749i
$144$		0			0
$145$	840.147	+	495.504i	0.481175	+	0.283788i
$146$	1440.14			0.816347
$147$		0			0
$148$		−	1080.07i		−	0.599875i
$149$	−1470.33			−0.808416			−0.404208	−	0.914667i	$-0.632453\pi$
$149$	−1470.33			−0.808416			−0.404208	+	0.914667i	$0.632453\pi$
$150$		0			0
$151$	−1695.79			−0.913916			−0.456958	−	0.889488i	$-0.651061\pi$
$151$	−1695.79			−0.913916			−0.456958	+	0.889488i	$0.651061\pi$
$152$		−	5372.47i		−	2.86687i
$153$		0			0
$154$	1879.01			0.983215
$155$	−2017.32	−	1189.78i	−1.04539	−	0.616552i
$156$		0			0
$157$		−	959.433i		−	0.487714i	−0.969811	−	0.243857i	$-0.921587\pi$
$157$		−	959.433i		−	0.487714i	0.969811	−	0.243857i	$-0.0784127\pi$
$158$		−	4589.49i		−	2.31089i
$159$		0			0
$160$	−41.5816	+	70.5033i	−0.0205457	+	0.0348361i
$161$	−51.2926			−0.0251082
$162$		0			0
$163$		−	3865.27i		−	1.85737i	−0.370869	−	0.928685i	$-0.620940\pi$
$163$		−	3865.27i		−	1.85737i	0.370869	−	0.928685i	$-0.379060\pi$
$164$	1235.57			0.588305
$165$		0			0
$166$	−3837.69			−1.79435
$167$		−	465.084i		−	0.215505i	−0.994178	−	0.107752i	$-0.965635\pi$
$167$		−	465.084i		−	0.215505i	0.994178	−	0.107752i	$-0.0343653\pi$
$168$		0			0
$169$	−278.860			−0.126927
$170$	6293.52	+	3711.81i	2.83936	+	1.67460i
$171$		0			0
$172$			3144.47i			1.39397i
$173$		−	2048.04i		−	0.900057i	−0.893014	−	0.450028i	$-0.851414\pi$
$173$		−	2048.04i		−	0.900057i	0.893014	−	0.450028i	$-0.148586\pi$
$174$		0			0
$175$	765.756	−	423.371i	0.330775	−	0.182879i
$176$	−3390.10			−1.45192
$177$		0			0
$178$		−	1349.11i		−	0.568091i
$179$	−911.856			−0.380756			−0.190378	−	0.981711i	$-0.560971\pi$
$179$	−911.856			−0.380756			−0.190378	+	0.981711i	$0.560971\pi$
$180$		0			0
$181$	−2029.81			−0.833562			−0.416781	−	0.909007i	$-0.636842\pi$
$181$	−2029.81			−0.833562			−0.416781	+	0.909007i	$0.636842\pi$
$182$			1702.99i			0.693595i
$183$		0			0
$184$	283.242			0.113483
$185$	−385.677	+	653.930i	−0.153273	+	0.259881i
$186$		0			0
$187$		−	7338.13i		−	2.86961i
$188$		−	79.1496i		−	0.0307052i
$189$		0			0
$190$	−3859.68	+	6544.25i	−1.47374	+	2.49879i
$191$	−4984.11			−1.88815			−0.944077	−	0.329725i	$-0.893044\pi$
$191$	−4984.11			−1.88815			−0.944077	+	0.329725i	$0.893044\pi$
$192$		0			0
$193$		−	3393.44i		−	1.26562i	−0.774306	−	0.632811i	$-0.781901\pi$
$193$		−	3393.44i		−	1.26562i	0.774306	−	0.632811i	$-0.218099\pi$
$194$	−5697.43			−2.10852
$195$		0			0
$196$	779.387			0.284033
$197$			762.475i			0.275757i	0.990449	+	0.137878i	$0.0440283\pi$
$197$			762.475i			0.275757i	−0.990449	+	0.137878i	$0.955972\pi$
$198$		0			0
$199$	1272.32			0.453227			0.226613	−	0.973985i	$-0.427235\pi$
$199$	1272.32			0.453227			0.226613	+	0.973985i	$0.427235\pi$
$200$	−4228.57	+	2337.89i	−1.49503	+	0.826569i
$201$		0			0
$202$		−	0.796959i		−	0.000277593i
$203$		−	610.686i		−	0.211142i
$204$		0			0
$205$	−748.077	−	441.203i	−0.254868	−	0.150317i
$206$	6360.00			2.15108
$207$		0			0
$208$		−	3072.53i		−	1.02424i
$209$	7630.47			2.52541
$210$		0			0
$211$	2010.72			0.656035			0.328017	−	0.944672i	$-0.393620\pi$
$211$	2010.72			0.656035			0.328017	+	0.944672i	$0.393620\pi$
$212$		−	844.351i		−	0.273539i
$213$		0			0
$214$	7488.70			2.39214
$215$	1122.84	−	1903.82i	0.356172	−	0.603904i
$216$		0			0
$217$			1466.35i			0.458721i
$218$			9638.85i			2.99461i
$219$		0			0
$220$	8409.53	+	4959.79i	2.57714	+	1.51995i
$221$	6650.73			2.02433
$222$		0			0
$223$			1516.44i			0.455374i	0.973734	+	0.227687i	$0.0731163\pi$
$223$			1516.44i			0.455374i	−0.973734	+	0.227687i	$0.926884\pi$
$224$	51.2475			0.0152862
$225$		0			0
$226$	1285.01			0.378219
$227$			4101.17i			1.19914i	0.800323	+	0.599568i	$0.204661\pi$
$227$			4101.17i			1.19914i	−0.800323	+	0.599568i	$0.795339\pi$
$228$		0			0
$229$	1029.24			0.297004			0.148502	−	0.988912i	$-0.452555\pi$
$229$	1029.24			0.297004			0.148502	+	0.988912i	$0.452555\pi$
$230$	−345.020	−	203.487i	−0.0989128	−	0.0583370i
$231$		0			0
$232$			3372.26i			0.954309i
$233$		−	5578.41i		−	1.56847i	−0.620463	−	0.784236i	$-0.713055\pi$
$233$		−	5578.41i		−	1.56847i	0.620463	−	0.784236i	$-0.286945\pi$
$234$		0			0
$235$	−28.2630	+	47.9211i	−0.00784543	+	0.0133022i
$236$	10878.8			3.00064
$237$		0			0
$238$		−	4574.64i		−	1.24592i
$239$	5389.67			1.45870			0.729348	−	0.684142i	$-0.239823\pi$
$239$	5389.67			1.45870			0.729348	+	0.684142i	$0.239823\pi$
$240$		0			0
$241$	3976.27			1.06280			0.531399	−	0.847122i	$-0.321667\pi$
$241$	3976.27			1.06280			0.531399	+	0.847122i	$0.321667\pi$
$242$		−	8229.31i		−	2.18595i
$243$		0			0
$244$	427.324			0.112117
$245$	−471.880	−	278.306i	−0.123050	−	0.0725728i
$246$		0			0
$247$			6915.69i			1.78152i
$248$		−	8097.33i		−	2.07331i
$249$		0			0
$250$	6830.45	+	190.081i	1.72798	+	0.0480871i
$251$	−7095.76			−1.78438			−0.892192	−	0.451655i	$-0.850834\pi$
$251$	−7095.76			−1.78438			−0.892192	+	0.451655i	$0.850834\pi$
$252$		0			0
$253$			402.287i			0.0999666i
$254$	−2785.22			−0.688033
$255$		0			0
$256$	−8140.43			−1.98741
$257$		−	2526.56i		−	0.613239i	−0.951832	−	0.306619i	$-0.900802\pi$
$257$		−	2526.56i		−	0.613239i	0.951832	−	0.306619i	$-0.0991979\pi$
$258$		0			0
$259$	475.329			0.114037
$260$	−4495.18	+	7621.77i	−1.07223	+	1.81801i
$261$		0			0
$262$			4815.08i			1.13541i
$263$			3842.34i			0.900871i	0.892809	+	0.450435i	$0.148731\pi$
$263$			3842.34i			0.900871i	−0.892809	+	0.450435i	$0.851269\pi$
$264$		0			0
$265$	−301.504	+	511.212i	−0.0698914	+	0.118504i
$266$	4756.88			1.09648
$267$		0			0
$268$			2374.75i			0.541271i
$269$	−8411.04			−1.90643			−0.953216	−	0.302291i	$-0.902249\pi$
$269$	−8411.04			−1.90643			−0.953216	+	0.302291i	$0.902249\pi$
$270$		0			0
$271$	5659.73			1.26865			0.634325	−	0.773067i	$-0.281278\pi$
$271$	5659.73			1.26865			0.634325	+	0.773067i	$0.281278\pi$
$272$			8253.54i			1.83987i
$273$		0			0
$274$	−6734.37			−1.48481
$275$	−3320.49	−	6005.81i	−0.728120	−	1.31696i
$276$		0			0
$277$			881.409i			0.191187i	0.995420	+	0.0955934i	$0.0304749\pi$
$277$			881.409i			0.191187i	−0.995420	+	0.0955934i	$0.969525\pi$
$278$			4105.47i			0.885718i
$279$		0			0
$280$	2605.76	+	1536.83i	0.556157	+	0.328012i
$281$	3853.71			0.818124			0.409062	−	0.912506i	$-0.365856\pi$
$281$	3853.71			0.818124			0.409062	+	0.912506i	$0.365856\pi$
$282$		0			0
$283$		−	1891.60i		−	0.397328i	−0.980068	−	0.198664i	$-0.936340\pi$
$283$		−	1891.60i		−	0.397328i	0.980068	−	0.198664i	$-0.0636603\pi$
$284$	97.9118			0.0204577
$285$		0			0
$286$	13356.6			2.76150
$287$			543.763i			0.111837i
$288$		0			0
$289$	−12952.4			−2.63635
$290$	2422.70	−	4107.78i	0.490571	−	0.831784i
$291$		0			0
$292$		−	4684.99i		−	0.938933i
$293$			4076.18i			0.812742i	0.913708	+	0.406371i	$0.133206\pi$
$293$			4076.18i			0.812742i	−0.913708	+	0.406371i	$0.866794\pi$
$294$		0			0
$295$	−6586.58	−	3884.65i	−1.29995	−	0.766687i
$296$	−2624.81			−0.515419
$297$		0			0
$298$			7188.97i			1.39747i
$299$	−364.602			−0.0705201
$300$		0			0
$301$	−1383.85			−0.264995
$302$			8291.33i			1.57984i
$303$		0			0
$304$	−8582.35			−1.61918
$305$	−258.723	−	152.590i	−0.0485720	−	0.0286469i
$306$		0			0
$307$		−	6201.87i		−	1.15296i	−0.817110	−	0.576481i	$-0.804425\pi$
$307$		−	6201.87i		−	1.15296i	0.817110	−	0.576481i	$-0.195575\pi$
$308$		−	6112.72i		−	1.13086i
$309$		0			0
$310$	−5817.28	+	9863.43i	−1.06580	+	1.80711i
$311$	6601.95			1.20374			0.601868	−	0.798595i	$-0.294423\pi$
$311$	6601.95			1.20374			0.601868	+	0.798595i	$0.294423\pi$
$312$		0			0
$313$			2291.01i			0.413724i	0.978370	+	0.206862i	$0.0663251\pi$
$313$			2291.01i			0.413724i	−0.978370	+	0.206862i	$0.933675\pi$
$314$	−4691.02			−0.843087
$315$		0			0
$316$	−14930.3			−2.65790
$317$			3124.07i			0.553517i	0.960939	+	0.276759i	$0.0892603\pi$
$317$			3124.07i			0.553517i	−0.960939	+	0.276759i	$0.910740\pi$
$318$		0			0
$319$	−4789.60			−0.840646
$320$	5102.00	+	3009.07i	0.891283	+	0.525663i
$321$		0			0
$322$			250.788i			0.0434033i
$323$		−	18577.1i		−	3.20018i
$324$		0			0
$325$	5443.21	−	3009.44i	0.929031	−	0.513642i
$326$	−18898.7			−3.21074
$327$		0			0
$328$		−	3002.70i		−	0.505478i
$329$	34.8329			0.00583708
$330$		0			0
$331$	9825.49			1.63159			0.815797	−	0.578338i	$-0.196298\pi$
$331$	9825.49			1.63159			0.815797	+	0.578338i	$0.196298\pi$
$332$			12484.6i			2.06380i
$333$		0			0
$334$	−2273.96			−0.372532
$335$	847.983	−	1437.79i	0.138299	−	0.234492i
$336$		0			0
$337$			8526.35i			1.37822i	0.724657	+	0.689110i	$0.241998\pi$
$337$			8526.35i			1.37822i	−0.724657	+	0.689110i	$0.758002\pi$
$338$			1363.45i			0.219413i
$339$		0			0
$340$	12075.1	−	20473.8i	1.92607	−	3.26573i
$341$	11500.6			1.82637
$342$		0			0
$343$			343.000i			0.0539949i
$344$	7641.73			1.19772
$345$		0			0
$346$	−10013.6			−1.55588
$347$			4164.54i			0.644277i	0.946693	+	0.322138i	$0.104402\pi$
$347$			4164.54i			0.644277i	−0.946693	+	0.322138i	$0.895598\pi$
$348$		0			0
$349$	−2584.60			−0.396420			−0.198210	−	0.980160i	$-0.563513\pi$
$349$	−2584.60			−0.396420			−0.198210	+	0.980160i	$0.563513\pi$
$350$	−2070.01	−	3744.06i	−0.316134	−	0.571795i
$351$		0			0
$352$		−	401.933i		−	0.0608611i
$353$		−	4199.25i		−	0.633154i	−0.948567	−	0.316577i	$-0.897466\pi$
$353$		−	4199.25i		−	0.633154i	0.948567	−	0.316577i	$-0.102534\pi$
$354$		0			0
$355$	−59.2807	−	34.9627i	−0.00886280	−	0.00522712i
$356$	−4388.87			−0.653398
$357$		0			0
$358$			4458.39i			0.658194i
$359$	−990.277			−0.145584			−0.0727922	−	0.997347i	$-0.523191\pi$
$359$	−990.277			−0.145584			−0.0727922	+	0.997347i	$0.523191\pi$
$360$		0			0
$361$	12458.2			1.81633
$362$			9924.48i			1.44094i
$363$		0			0
$364$	5540.11			0.797749
$365$	−1672.93	+	2836.53i	−0.239905	+	0.406769i
$366$		0			0
$367$		−	4179.24i		−	0.594427i	−0.954811	−	0.297213i	$-0.903943\pi$
$367$		−	4179.24i		−	0.594427i	0.954811	−	0.297213i	$-0.0960573\pi$
$368$		−	452.471i		−	0.0640942i
$369$		0			0
$370$	3197.30	+	1885.71i	0.449243	+	0.264955i
$371$	371.590			0.0519999
$372$		0			0
$373$		−	7365.36i		−	1.02242i	−0.859455	−	0.511212i	$-0.829197\pi$
$373$		−	7365.36i		−	1.02242i	0.859455	−	0.511212i	$-0.170803\pi$
$374$	−35878.8			−4.96056
$375$		0			0
$376$	−192.350			−0.0263822
$377$		−	4340.93i		−	0.593022i
$378$		0			0
$379$	6214.13			0.842213			0.421106	−	0.907011i	$-0.361642\pi$
$379$	6214.13			0.842213			0.421106	+	0.907011i	$0.361642\pi$
$380$	21289.5	+	12556.2i	2.87402	+	1.69504i
$381$		0			0
$382$			24369.1i			3.26396i
$383$			1755.04i			0.234148i	0.993123	+	0.117074i	$0.0373514\pi$
$383$			1755.04i			0.234148i	−0.993123	+	0.117074i	$0.962649\pi$
$384$		0			0
$385$	−2182.75	+	3700.94i	−0.288944	+	0.489916i
$386$	−16591.7			−2.18782
$387$		0			0
$388$			18534.6i			2.42514i
$389$	8805.69			1.14773			0.573864	−	0.818950i	$-0.305444\pi$
$389$	8805.69			1.14773			0.573864	+	0.818950i	$0.305444\pi$
$390$		0			0
$391$	979.406			0.126677
$392$		−	1894.08i		−	0.244044i
$393$		0			0
$394$	3728.01			0.476687
$395$	9039.57	+	5331.38i	1.15147	+	0.679116i
$396$		0			0
$397$			13717.2i			1.73413i	0.498199	+	0.867063i	$0.333995\pi$
$397$			13717.2i			1.73413i	−0.498199	+	0.867063i	$0.666005\pi$
$398$		−	6220.82i		−	0.783471i
$399$		0			0
$400$	3734.71	+	6755.01i	0.466838	+	0.844377i
$401$	−307.220			−0.0382590			−0.0191295	−	0.999817i	$-0.506089\pi$
$401$	−307.220			−0.0382590			−0.0191295	+	0.999817i	$0.506089\pi$
$402$		0			0
$403$			10423.3i			1.28839i
$404$	−2.59263			−0.000319278
$405$		0			0
$406$	−2985.86			−0.364990
$407$		−	3728.00i		−	0.454029i
$408$		0			0
$409$	−12390.7			−1.49799			−0.748997	−	0.662573i	$-0.769464\pi$
$409$	−12390.7			−1.49799			−0.748997	+	0.662573i	$0.769464\pi$
$410$	−2157.20	+	3657.62i	−0.259845	+	0.440578i
$411$		0			0
$412$		−	20690.1i		−	2.47409i
$413$			4787.65i			0.570423i
$414$		0			0
$415$	4458.05	−	7558.81i	0.527318	−	0.894090i
$416$	364.282			0.0429336
$417$		0			0
$418$		−	37308.2i		−	4.36555i
$419$	2664.10			0.310620			0.155310	−	0.987866i	$-0.450362\pi$
$419$	2664.10			0.310620			0.155310	+	0.987866i	$0.450362\pi$
$420$		0			0
$421$	−6851.11			−0.793118			−0.396559	−	0.918009i	$-0.629796\pi$
$421$	−6851.11			−0.793118			−0.396559	+	0.918009i	$0.629796\pi$
$422$		−	9831.12i		−	1.13406i
$423$		0			0
$424$	−2051.95			−0.235027
$425$	−14621.7	+	8084.05i	−1.66884	+	0.922668i
$426$		0			0
$427$			188.061i			0.0213136i
$428$		−	24361.9i		−	2.75135i
$429$		0			0
$430$	−9308.45	−	5489.96i	−1.04394	−	0.615696i
$431$	7651.38			0.855114			0.427557	−	0.903988i	$-0.359374\pi$
$431$	7651.38			0.855114			0.427557	+	0.903988i	$0.359374\pi$
$432$		0			0
$433$			691.572i			0.0767548i	0.999263	+	0.0383774i	$0.0122189\pi$
$433$			691.572i			0.0767548i	−0.999263	+	0.0383774i	$0.987781\pi$
$434$	7169.53			0.792969
$435$		0			0
$436$	31356.7			3.44430
$437$			1018.42i			0.111483i
$438$		0			0
$439$	−10621.7			−1.15478			−0.577389	−	0.816469i	$-0.695928\pi$
$439$	−10621.7			−1.15478			−0.577389	+	0.816469i	$0.695928\pi$
$440$	12053.3	−	20436.9i	1.30596	−	2.21430i
$441$		0			0
$442$		−	32517.8i		−	3.49936i
$443$			3133.67i			0.336084i	0.985780	+	0.168042i	$0.0537444\pi$
$443$			3133.67i			0.336084i	−0.985780	+	0.168042i	$0.946256\pi$
$444$		0			0
$445$	2657.24	+	1567.19i	0.283068	+	0.166949i
$446$	7414.43			0.787182
$447$		0			0
$448$		−	3708.54i		−	0.391099i
$449$	−9144.92			−0.961192			−0.480596	−	0.876942i	$-0.659580\pi$
$449$	−9144.92			−0.961192			−0.480596	+	0.876942i	$0.659580\pi$
$450$		0			0
$451$	4264.72			0.445272
$452$		−	4180.33i		−	0.435014i
$453$		0			0
$454$	20052.1			2.07289
$455$	−3354.26	−	1978.28i	−0.345604	−	0.203831i
$456$		0			0
$457$			8142.60i			0.833468i	0.909029	+	0.416734i	$0.136825\pi$
$457$			8142.60i			0.833468i	−0.909029	+	0.416734i	$0.863175\pi$
$458$		−	5032.32i		−	0.513417i
$459$		0			0
$460$	−661.974	+	1122.40i	−0.0670971	+	0.113766i
$461$	9287.29			0.938291			0.469145	−	0.883121i	$-0.344562\pi$
$461$	9287.29			0.938291			0.469145	+	0.883121i	$0.344562\pi$
$462$		0			0
$463$		−	2440.53i		−	0.244970i	−0.992470	−	0.122485i	$-0.960914\pi$
$463$		−	2440.53i		−	0.244970i	0.992470	−	0.122485i	$-0.0390864\pi$
$464$	5387.08			0.538985
$465$		0			0
$466$	−27274.9			−2.71134
$467$			12066.3i			1.19564i	0.801632	+	0.597818i	$0.203966\pi$
$467$			12066.3i			1.19564i	−0.801632	+	0.597818i	$0.796034\pi$
$468$		0			0
$469$	−1045.10			−0.102896
$470$	234.304	+	138.188i	0.0229949	+	0.0135620i
$471$		0			0
$472$		−	26437.8i		−	2.57818i
$473$			10853.5i			1.05506i
$474$		0			0
$475$	−8406.11	−	15204.2i	−0.811998	−	1.46867i
$476$	−14882.0			−1.43302
$477$		0			0
$478$		−	26352.0i		−	2.52158i
$479$	395.211			0.0376987			0.0188493	−	0.999822i	$-0.494000\pi$
$479$	395.211			0.0376987			0.0188493	+	0.999822i	$0.494000\pi$
$480$		0			0
$481$	3378.77			0.320289
$482$		−	19441.4i		−	1.83721i
$483$		0			0
$484$	−26771.2			−2.51420
$485$	6618.42	−	11221.8i	0.619643	−	1.05063i
$486$		0			0
$487$		−	9609.06i		−	0.894102i	−0.894508	−	0.447051i	$-0.852474\pi$
$487$		−	9609.06i		−	0.894102i	0.894508	−	0.447051i	$-0.147526\pi$
$488$		−	1038.49i		−	0.0963323i
$489$		0			0
$490$	−1360.74	+	2307.19i	−0.125453	+	0.212711i
$491$	−10941.0			−1.00562			−0.502810	−	0.864397i	$-0.667701\pi$
$491$	−10941.0			−1.00562			−0.502810	+	0.864397i	$0.667701\pi$
$492$		0			0
$493$			11660.7i			1.06526i
$494$	33813.3			3.07962
$495$		0			0
$496$	−12935.2			−1.17099
$497$			43.0899i			0.00388903i
$498$		0			0
$499$	−9269.90			−0.831618			−0.415809	−	0.909452i	$-0.636502\pi$
$499$	−9269.90			−0.831618			−0.415809	+	0.909452i	$0.636502\pi$
$500$	618.363	−	22220.5i	0.0553081	−	1.98746i
$501$		0			0
$502$			34693.8i			3.08458i
$503$			15085.4i			1.33723i	0.743609	+	0.668615i	$0.233112\pi$
$503$			15085.4i			1.33723i	−0.743609	+	0.668615i	$0.766888\pi$
$504$		0			0
$505$	1.56971	+	0.925787i	0.000138319	+	8.15781e-5i
$506$	1966.93			0.172807
$507$		0			0
$508$			9060.76i			0.791351i
$509$	8650.44			0.753289			0.376645	−	0.926358i	$-0.377078\pi$
$509$	8650.44			0.753289			0.376645	+	0.926358i	$0.377078\pi$
$510$		0			0
$511$	2061.82			0.178492
$512$			19547.3i			1.68726i
$513$		0			0
$514$	−12353.3			−1.06008
$515$	−7388.09	+	12526.8i	−0.632151	+	1.07184i
$516$		0			0
$517$		−	273.194i		−	0.0232399i
$518$		−	2324.06i		−	0.197130i
$519$		0			0
$520$	18522.5	+	10924.2i	1.56205	+	0.921269i
$521$	−10661.6			−0.896535			−0.448268	−	0.893899i	$-0.647959\pi$
$521$	−10661.6			−0.896535			−0.448268	+	0.893899i	$0.647959\pi$
$522$		0			0
$523$		−	3449.22i		−	0.288382i	−0.989550	−	0.144191i	$-0.953942\pi$
$523$		−	3449.22i		−	0.288382i	0.989550	−	0.144191i	$-0.0460580\pi$
$524$	15664.2			1.30591
$525$		0			0
$526$	18786.6			1.55729
$527$		−	27999.3i		−	2.31436i
$528$		0			0
$529$	12113.3			0.995587
$530$	2499.50	+	1474.16i	0.204852	+	0.120818i
$531$		0			0
$532$		−	15474.9i		−	1.26113i
$533$			3865.22i			0.314111i
$534$		0			0
$535$	−8699.24	+	14749.9i	−0.702992	+	1.19195i
$536$	5771.14			0.465066
$537$		0			0
$538$			41124.6i			3.29555i
$539$	2690.14			0.214977
$540$		0			0
$541$	13403.2			1.06516			0.532578	−	0.846381i	$-0.321223\pi$
$541$	13403.2			1.06516			0.532578	+	0.846381i	$0.321223\pi$
$542$		−	27672.5i		−	2.19305i
$543$		0			0
$544$	−978.544			−0.0771227
$545$	−18984.9	−	11197.0i	−1.49215	−	0.880046i
$546$		0			0
$547$			3670.29i			0.286893i	0.989658	+	0.143446i	$0.0458184\pi$
$547$			3670.29i			0.286893i	−0.989658	+	0.143446i	$0.954182\pi$
$548$			21907.9i			1.70778i
$549$		0			0
$550$	−29364.6	+	16235.1i	−2.27656	+	1.25867i
$551$	−12125.3			−0.937486
$552$		0			0
$553$		−	6570.69i		−	0.505269i
$554$	4309.53			0.330495
$555$		0			0
$556$	13355.7			1.01872
$557$			521.169i			0.0396456i	0.999804	+	0.0198228i	$0.00631021\pi$
$557$			521.169i			0.0396456i	−0.999804	+	0.0198228i	$0.993690\pi$
$558$		0			0
$559$	−9836.78			−0.744278
$560$	2455.04	−	4162.62i	0.185258	−	0.314112i
$561$		0			0
$562$		−	18842.2i		−	1.41425i
$563$			17970.2i			1.34521i	0.740000	+	0.672606i	$0.234825\pi$
$563$			17970.2i			1.34521i	−0.740000	+	0.672606i	$0.765175\pi$
$564$		0			0
$565$	−1492.73	+	2530.98i	−0.111150	+	0.188459i
$566$	−9248.71			−0.686842
$567$		0			0
$568$		−	237.947i		−	0.0175775i
$569$	−21808.6			−1.60679			−0.803396	−	0.595445i	$-0.796976\pi$
$569$	−21808.6			−1.60679			−0.803396	+	0.595445i	$0.796976\pi$
$570$		0			0
$571$	6604.75			0.484064			0.242032	−	0.970268i	$-0.422186\pi$
$571$	6604.75			0.484064			0.242032	+	0.970268i	$0.422186\pi$
$572$		−	43451.0i		−	3.17618i
$573$		0			0
$574$	2658.65			0.193327
$575$	801.584	−	443.179i	0.0581363	−	0.0321423i
$576$		0			0
$577$			25886.9i			1.86774i	0.357618	+	0.933868i	$0.383589\pi$
$577$			25886.9i			1.86774i	−0.357618	+	0.933868i	$0.616411\pi$
$578$			63328.9i			4.55733i
$579$		0			0
$580$	−13363.3	−	7881.41i	−0.956688	−	0.564238i
$581$	−5494.35			−0.392330
$582$		0			0
$583$		−	2914.37i		−	0.207034i
$584$	−11385.5			−0.806741
$585$		0			0
$586$	19929.9			1.40495
$587$		−	4949.88i		−	0.348046i	−0.984742	−	0.174023i	$-0.944323\pi$
$587$		−	4949.88i		−	0.348046i	0.984742	−	0.174023i	$-0.0556768\pi$
$588$		0			0
$589$	29114.7			2.03676
$590$	−18993.4	+	32204.2i	−1.32533	+	2.24716i
$591$		0			0
$592$			4193.05i			0.291104i
$593$		−	31.3988i		−	0.00217436i	−0.999999	−	0.00108718i	$-0.999654\pi$
$593$		−	31.3988i		−	0.00217436i	0.999999	−	0.00108718i	$-0.000346059\pi$
$594$		0			0
$595$	9010.31	+	5314.12i	0.620818	+	0.366147i
$596$	23386.8			1.60732
$597$		0			0
$598$			1782.67i			0.121905i
$599$	−11870.4			−0.809704			−0.404852	−	0.914382i	$-0.632677\pi$
$599$	−11870.4			−0.809704			−0.404852	+	0.914382i	$0.632677\pi$
$600$		0			0
$601$	−967.320			−0.0656536			−0.0328268	−	0.999461i	$-0.510451\pi$
$601$	−967.320			−0.0656536			−0.0328268	+	0.999461i	$0.510451\pi$
$602$			6766.13i			0.458084i
$603$		0			0
$604$	26973.0			1.81708
$605$	16208.6	+	9559.57i	1.08922	+	0.642400i
$606$		0			0
$607$			9518.28i			0.636466i	0.948013	+	0.318233i	$0.103089\pi$
$607$			9518.28i			0.636466i	−0.948013	+	0.318233i	$0.896911\pi$
$608$		−	1017.53i		−	0.0678721i
$609$		0			0
$610$	−746.070	+	1264.99i	−0.0495205	+	0.0839640i
$611$	247.602			0.0163943
$612$		0			0
$613$		−	3607.19i		−	0.237672i	−0.992914	−	0.118836i	$-0.962084\pi$
$613$		−	3607.19i		−	0.237672i	0.992914	−	0.118836i	$-0.0379163\pi$
$614$	−30323.2			−1.99307
$615$		0			0
$616$	−14855.2			−0.971645
$617$			22473.2i			1.46635i	0.680042	+	0.733173i	$0.261962\pi$
$617$			22473.2i			1.46635i	−0.680042	+	0.733173i	$0.738038\pi$
$618$		0			0
$619$	−19200.1			−1.24672			−0.623358	−	0.781936i	$-0.714232\pi$
$619$	−19200.1			−1.24672			−0.623358	+	0.781936i	$0.714232\pi$
$620$	32087.3	+	18924.5i	2.07848	+	1.22585i
$621$		0			0
$622$		−	32279.3i		−	2.08084i
$623$		−	1931.50i		−	0.124211i
$624$		0			0
$625$	−8308.97	+	13232.6i	−0.531774	+	0.846886i
$626$	11201.6			0.715184
$627$		0			0
$628$			15260.6i			0.969689i
$629$	−9076.17			−0.575343
$630$		0			0
$631$	−6980.64			−0.440404			−0.220202	−	0.975454i	$-0.570672\pi$
$631$	−6980.64			−0.440404			−0.220202	+	0.975454i	$0.570672\pi$
$632$			36283.9i			2.28370i
$633$		0			0
$634$	15274.7			0.956838
$635$	3235.45	−	5485.83i	0.202197	−	0.342833i
$636$		0			0
$637$			2438.14i			0.151653i
$638$			23418.1i			1.45318i
$639$		0			0
$640$	14379.8	−	24381.5i	0.888142	−	1.50588i
$641$	1083.82			0.0667837			0.0333919	−	0.999442i	$-0.489369\pi$
$641$	1083.82			0.0667837			0.0333919	+	0.999442i	$0.489369\pi$
$642$		0			0
$643$			4151.42i			0.254613i	0.991863	+	0.127307i	$0.0406332\pi$
$643$			4151.42i			0.254613i	−0.991863	+	0.127307i	$0.959367\pi$
$644$	815.853			0.0499210
$645$		0			0
$646$	−90830.3			−5.53200
$647$			3014.99i			0.183202i	0.995796	+	0.0916008i	$0.0291984\pi$
$647$			3014.99i			0.183202i	−0.995796	+	0.0916008i	$0.970802\pi$
$648$		0			0
$649$	37549.4			2.27110
$650$	−14714.2	−	26613.8i	−0.887908	−	1.60597i
$651$		0			0
$652$			61480.5i			3.69288i
$653$		−	21130.7i		−	1.26632i	−0.774019	−	0.633162i	$-0.781757\pi$
$653$		−	21130.7i		−	1.26632i	0.774019	−	0.633162i	$-0.218243\pi$
$654$		0			0
$655$	−9483.90	−	5593.44i	−0.565751	−	0.333670i
$656$	−4796.73			−0.285489
$657$		0			0
$658$		−	170.311i		−	0.0100903i
$659$	−9961.24			−0.588824			−0.294412	−	0.955679i	$-0.595124\pi$
$659$	−9961.24			−0.588824			−0.294412	+	0.955679i	$0.595124\pi$
$660$		0			0
$661$	1581.43			0.0930569			0.0465285	−	0.998917i	$-0.485184\pi$
$661$	1581.43			0.0930569			0.0465285	+	0.998917i	$0.485184\pi$
$662$		−	48040.4i		−	2.82046i
$663$		0			0
$664$	30340.3			1.77324
$665$	−5525.83	+	9369.27i	−0.322229	+	0.546353i
$666$		0			0
$667$		−	639.258i		−	0.0371097i
$668$			7397.56i			0.428473i
$669$		0			0
$670$	−7029.87	−	4146.09i	−0.405355	−	0.239071i
$671$	1474.96			0.0848586
$672$		0			0
$673$		−	11101.6i		−	0.635865i	−0.948113	−	0.317932i	$-0.897012\pi$
$673$		−	11101.6i		−	0.635865i	0.948113	−	0.317932i	$-0.102988\pi$
$674$	41688.4			2.38246
$675$		0			0
$676$	4435.50			0.252361
$677$			18249.8i			1.03603i	0.855370	+	0.518017i	$0.173330\pi$
$677$			18249.8i			1.03603i	−0.855370	+	0.518017i	$0.826670\pi$
$678$		0			0
$679$	−8156.90			−0.461021
$680$	−49755.7	−	29345.0i	−2.80595	−	1.65490i
$681$		0			0
$682$		−	56230.5i		−	3.15715i
$683$		−	14144.2i		−	0.792403i	−0.918164	−	0.396202i	$-0.870328\pi$
$683$		−	14144.2i		−	0.792403i	0.918164	−	0.396202i	$-0.129672\pi$
$684$		0			0
$685$	7822.97	−	13264.2i	0.436351	−	0.739851i
$686$	1677.05			0.0933384
$687$		0			0
$688$		−	12207.4i		−	0.676458i
$689$	2641.37			0.146049
$690$		0			0
$691$	19621.7			1.08024			0.540120	−	0.841588i	$-0.318379\pi$
$691$	19621.7			1.08024			0.540120	+	0.841588i	$0.318379\pi$
$692$			32575.9i			1.78952i
$693$		0			0
$694$	20361.9			1.11373
$695$	−8086.22	−	4769.11i	−0.441335	−	0.260292i
$696$		0			0
$697$		−	10382.9i		−	0.564246i
$698$			12637.1i			0.685272i
$699$		0			0
$700$	−12180.0	+	6734.08i	−0.657659	+	0.363606i
$701$	−21609.1			−1.16428			−0.582142	−	0.813087i	$-0.697785\pi$
$701$	−21609.1			−1.16428			−0.582142	+	0.813087i	$0.697785\pi$
$702$		0			0
$703$		−	9437.75i		−	0.506332i
$704$	−29086.0			−1.55713
$705$		0			0
$706$	−20531.6			−1.09450
$707$		−	1.14099i		−	6.06950e-5i
$708$		0			0
$709$	12557.2			0.665158			0.332579	−	0.943075i	$-0.392081\pi$
$709$	12557.2			0.665158			0.332579	+	0.943075i	$0.392081\pi$
$710$	−170.945	+	289.845i	−0.00903586	+	0.0153207i
$711$		0			0
$712$			10665.9i			0.561406i
$713$			1534.96i			0.0806237i
$714$		0			0
$715$	−15515.6	+	26307.4i	−0.811540	+	1.37600i
$716$	14503.9			0.757031
$717$		0			0
$718$			4841.82i			0.251665i
$719$	36151.9			1.87516			0.937580	−	0.347771i	$-0.113061\pi$
$719$	36151.9			1.87516			0.937580	+	0.347771i	$0.113061\pi$
$720$		0			0
$721$	9105.48			0.470327
$722$		−	60912.8i		−	3.13980i
$723$		0			0
$724$	32285.9			1.65731
$725$	5276.46	+	9543.60i	0.270293	+	0.488883i
$726$		0			0
$727$			12007.2i			0.612550i	0.951943	+	0.306275i	$0.0990828\pi$
$727$			12007.2i			0.612550i	−0.951943	+	0.306275i	$0.900917\pi$
$728$		−	13463.6i		−	0.685434i
$729$		0			0
$730$	13868.8	+	8179.58i	0.703162	+	0.414712i
$731$	26423.9			1.33697
$732$		0			0
$733$			15920.2i			0.802220i	0.916030	+	0.401110i	$0.131375\pi$
$733$			15920.2i			0.802220i	−0.916030	+	0.401110i	$0.868625\pi$
$734$	−20433.8			−1.02756
$735$		0			0
$736$	53.6452			0.00268667
$737$			8196.70i			0.409674i
$738$		0			0
$739$	26581.1			1.32314			0.661571	−	0.749882i	$-0.269890\pi$
$739$	26581.1			1.32314			0.661571	+	0.749882i	$0.269890\pi$
$740$	6134.52	−	10401.3i	0.304742	−	0.516703i
$741$		0			0
$742$		−	1816.84i		−	0.0898897i
$743$		−	6601.38i		−	0.325950i	−0.986630	−	0.162975i	$-0.947891\pi$
$743$		−	6601.38i		−	0.325950i	0.986630	−	0.162975i	$-0.0521090\pi$
$744$		0			0
$745$	−14159.6	−	8351.06i	−0.696330	−	0.410683i
$746$	−36011.9			−1.76741
$747$		0			0
$748$			116719.i			5.70546i
$749$	10721.4			0.523034
$750$		0			0
$751$	−29809.6			−1.44842			−0.724212	−	0.689578i	$-0.757796\pi$
$751$	−29809.6			−1.44842			−0.724212	+	0.689578i	$0.757796\pi$
$752$			307.274i			0.0149004i
$753$		0			0
$754$	−21224.4			−1.02513
$755$	−16330.8	−	9631.61i	−0.787203	−	0.464278i
$756$		0			0
$757$		−	8179.09i		−	0.392700i	−0.980534	−	0.196350i	$-0.937091\pi$
$757$		−	8179.09i		−	0.392700i	0.980534	−	0.196350i	$-0.0629089\pi$
$758$		−	30383.2i		−	1.45589i
$759$		0			0
$760$	30514.1	−	51737.9i	1.45640	−	2.46938i
$761$	31616.8			1.50605			0.753027	−	0.657990i	$-0.228593\pi$
$761$	31616.8			1.50605			0.753027	+	0.657990i	$0.228593\pi$
$762$		0			0
$763$			13799.8i			0.654763i
$764$	79276.5			3.75409
$765$		0			0
$766$	8581.05			0.404760
$767$			34032.0i			1.60212i
$768$		0			0
$769$	−24651.3			−1.15598			−0.577991	−	0.816043i	$-0.696163\pi$
$769$	−24651.3			−1.15598			−0.577991	+	0.816043i	$0.696163\pi$
$770$	18095.3	+	10672.3i	0.846893	+	0.499483i
$771$		0			0
$772$			53975.6i			2.51635i
$773$		−	7888.63i		−	0.367056i	−0.983015	−	0.183528i	$-0.941248\pi$
$773$		−	7888.63i		−	0.367056i	0.983015	−	0.183528i	$-0.0587518\pi$
$774$		0			0
$775$	−12669.6	−	22915.7i	−0.587233	−	1.06214i
$776$	45043.1			2.08370
$777$		0			0
$778$		−	43054.2i		−	1.98402i
$779$	10796.5			0.496566
$780$		0			0
$781$	337.954			0.0154839
$782$		−	4788.67i		−	0.218980i
$783$		0			0
$784$	−3025.73			−0.137834
$785$	5449.31	−	9239.53i	0.247763	−	0.420093i
$786$		0			0
$787$		−	8592.94i		−	0.389206i	−0.980882	−	0.194603i	$-0.937658\pi$
$787$		−	8592.94i		−	0.389206i	0.980882	−	0.194603i	$-0.0623419\pi$
$788$		−	12127.8i		−	0.548268i
$789$		0			0
$790$	26067.1	−	44197.8i	1.17395	−	1.99049i
$791$	1839.72			0.0826964
$792$		0			0
$793$			1336.79i			0.0598623i
$794$	67068.5			2.99770
$795$		0			0
$796$	−20237.3			−0.901120
$797$			37498.1i			1.66656i	0.552848	+	0.833282i	$0.313541\pi$
$797$			37498.1i			1.66656i	−0.552848	+	0.833282i	$0.686459\pi$
$798$		0			0
$799$	−665.116			−0.0294495
$800$	−800.878	+	442.789i	−0.0353942	+	0.0195687i
$801$		0			0
$802$			1502.11i			0.0661364i
$803$		−	16170.8i		−	0.710653i
$804$		0			0
$805$	−493.958	−	291.328i	−0.0216270	−	0.0127552i
$806$	50963.1			2.22717
$807$		0			0
$808$			6.30065i			0.000274327i
$809$	33834.0			1.47039			0.735193	−	0.677858i	$-0.237092\pi$
$809$	33834.0			1.47039			0.735193	+	0.677858i	$0.237092\pi$
$810$		0			0
$811$	16234.0			0.702899			0.351450	−	0.936207i	$-0.385689\pi$
$811$	16234.0			0.702899			0.351450	+	0.936207i	$0.385689\pi$
$812$			9713.48i			0.419799i
$813$		0			0
$814$	−18227.5			−0.784858
$815$	21953.7	−	37223.3i	0.943562	−	1.59985i
$816$		0			0
$817$			27476.6i			1.17660i
$818$			60582.5i			2.58951i
$819$		0			0
$820$	11898.8	+	7017.71i	0.506737	+	0.298865i
$821$	26551.4			1.12868			0.564342	−	0.825541i	$-0.309130\pi$
$821$	26551.4			1.12868			0.564342	+	0.825541i	$0.309130\pi$
$822$		0			0
$823$		−	651.954i		−	0.0276132i	−0.999905	−	0.0138066i	$-0.995605\pi$
$823$		−	651.954i		−	0.0276132i	0.999905	−	0.0138066i	$-0.00439492\pi$
$824$	−50281.3			−2.12577
$825$		0			0
$826$	23408.6			0.986063
$827$		−	13248.0i		−	0.557046i	−0.960430	−	0.278523i	$-0.910155\pi$
$827$		−	13248.0i		−	0.557046i	0.960430	−	0.278523i	$-0.0898448\pi$
$828$		0			0
$829$	36828.9			1.54297			0.771484	−	0.636248i	$-0.219515\pi$
$829$	36828.9			1.54297			0.771484	+	0.636248i	$0.219515\pi$
$830$	−36957.7	−	21797.0i	−1.54557	−	0.911549i
$831$		0			0
$832$		−	26361.4i		−	1.09846i
$833$		−	6549.41i		−	0.272417i
$834$		0			0
$835$	2641.55	−	4478.85i	0.109478	−	0.185625i
$836$	−121369.			−5.02111
$837$		0			0
$838$		−	13025.7i		−	0.536953i
$839$	−10641.5			−0.437884			−0.218942	−	0.975738i	$-0.570261\pi$
$839$	−10641.5			−0.437884			−0.218942	+	0.975738i	$0.570261\pi$
$840$		0			0
$841$	−16778.0			−0.687935
$842$			33497.6i			1.37102i
$843$		0			0
$844$	−31982.2			−1.30435
$845$	−2685.47	−	1583.84i	−0.109329	−	0.0644804i
$846$		0			0
$847$		−	11781.7i		−	0.477952i
$848$			3277.93i			0.132741i
$849$		0			0
$850$	39525.9	+	71490.9i	1.59497	+	2.88484i
$851$	497.568			0.0200428
$852$		0			0
$853$		−	2819.13i		−	0.113160i	−0.998398	−	0.0565799i	$-0.981980\pi$
$853$		−	2819.13i		−	0.113160i	0.998398	−	0.0565799i	$-0.0180196\pi$
$854$	919.497			0.0368437
$855$		0			0
$856$	−59204.6			−2.36399
$857$			38853.9i			1.54869i	0.632766	+	0.774343i	$0.281919\pi$
$857$			38853.9i			1.54869i	−0.632766	+	0.774343i	$0.718081\pi$
$858$		0			0
$859$	−8959.42			−0.355869			−0.177935	−	0.984042i	$-0.556942\pi$
$859$	−8959.42			−0.355869			−0.177935	+	0.984042i	$0.556942\pi$
$860$	−17859.7	+	30281.9i	−0.708152	+	1.20070i
$861$		0			0
$862$		−	37410.4i		−	1.47819i
$863$		−	32649.8i		−	1.28785i	−0.765090	−	0.643924i	$-0.777305\pi$
$863$		−	32649.8i		−	1.28785i	0.765090	−	0.643924i	$-0.222695\pi$
$864$		0			0
$865$	11632.3	−	19723.1i	0.457238	−	0.775265i
$866$	3381.35			0.132682
$867$		0			0
$868$		−	23323.6i		−	0.912045i
$869$	−51533.8			−2.01170
$870$		0			0
$871$	−7428.87			−0.288999
$872$		−	76203.5i		−	2.95937i
$873$		0			0
$874$	4979.45			0.192714
$875$	9779.01	+	272.135i	0.377818	+	0.0105141i
$876$		0			0
$877$		−	20229.3i		−	0.778899i	−0.921048	−	0.389450i	$-0.872665\pi$
$877$		−	20229.3i		−	0.778899i	0.921048	−	0.389450i	$-0.127335\pi$
$878$			51933.5i			1.99621i
$879$		0			0
$880$	−32647.4	−	19254.8i	−1.25062	−	0.737592i
$881$	−4356.08			−0.166584			−0.0832918	−	0.996525i	$-0.526543\pi$
$881$	−4356.08			−0.166584			−0.0832918	+	0.996525i	$0.526543\pi$
$882$		0			0
$883$		−	43349.9i		−	1.65214i	−0.563567	−	0.826070i	$-0.690571\pi$
$883$		−	43349.9i		−	1.65214i	0.563567	−	0.826070i	$-0.309429\pi$
$884$	−105786.			−4.02484
$885$		0			0
$886$	15321.6			0.580971
$887$			9754.67i			0.369256i	0.982809	+	0.184628i	$0.0591080\pi$
$887$			9754.67i			0.369256i	−0.982809	+	0.184628i	$0.940892\pi$
$888$		0			0
$889$	−3987.54			−0.150436
$890$	7662.58	−	12992.2i	0.288596	−	0.489326i
$891$		0			0
$892$		−	24120.3i		−	0.905389i
$893$		−	691.614i		−	0.0259171i
$894$		0			0
$895$	−8781.35	−	5179.09i	−0.327965	−	0.193428i
$896$	−17722.4			−0.660786
$897$		0			0
$898$			44712.8i			1.66157i
$899$	−18275.1			−0.677986
$900$		0			0
$901$	−7095.32			−0.262352
$902$		−	20851.8i		−	0.769720i
$903$		0			0
$904$	−10159.1			−0.373768
$905$	−19547.5	−	11528.8i	−0.717989	−	0.423457i
$906$		0			0
$907$		−	7155.16i		−	0.261944i	−0.991386	−	0.130972i	$-0.958190\pi$
$907$		−	7155.16i		−	0.261944i	0.991386	−	0.130972i	$-0.0418098\pi$
$908$		−	65232.6i		−	2.38416i
$909$		0			0
$910$	−9672.53	+	16400.2i	−0.352353	+	0.597429i
$911$	47255.4			1.71860			0.859298	−	0.511475i	$-0.170901\pi$
$911$	47255.4			1.71860			0.859298	+	0.511475i	$0.170901\pi$
$912$		0			0
$913$			43092.1i			1.56204i
$914$	39812.1			1.44077
$915$		0			0
$916$	−16370.9			−0.590514
$917$			6893.66i			0.248254i
$918$		0			0
$919$	−30942.1			−1.11065			−0.555324	−	0.831634i	$-0.687406\pi$
$919$	−30942.1			−1.11065			−0.555324	+	0.831634i	$0.687406\pi$
$920$	2727.68	+	1608.74i	0.0977488	+	0.0576505i
$921$		0			0
$922$		−	45408.9i		−	1.62198i
$923$			306.296i			0.0109229i
$924$		0			0
$925$	−7428.29	+	4106.95i	−0.264044	+	0.145984i
$926$	−11932.6			−0.423468
$927$		0			0
$928$			638.696i			0.0225929i
$929$	12147.4			0.429004			0.214502	−	0.976724i	$-0.431187\pi$
$929$	12147.4			0.429004			0.214502	+	0.976724i	$0.431187\pi$
$930$		0			0
$931$	6810.33			0.239742
$932$			88729.4i			3.11849i
$933$		0			0
$934$	58996.6			2.06684
$935$	41678.5	−	70667.7i	1.45779	−	2.47174i
$936$		0			0
$937$		−	13388.6i		−	0.466794i	−0.972381	−	0.233397i	$-0.925016\pi$
$937$		−	13388.6i		−	0.466794i	0.972381	−	0.233397i	$-0.0749842\pi$
$938$			5109.87i			0.177871i
$939$		0			0
$940$	449.548	−	762.226i	0.0155985	−	0.0264480i
$941$	8035.36			0.278369			0.139184	−	0.990266i	$-0.455552\pi$
$941$	8035.36			0.278369			0.139184	+	0.990266i	$0.455552\pi$
$942$		0			0
$943$			569.204i			0.0196562i
$944$	−42233.6			−1.45613
$945$		0			0
$946$	53066.6			1.82383
$947$		−	17647.7i		−	0.605567i	−0.953059	−	0.302784i	$-0.902084\pi$
$947$		−	17647.7i		−	0.605567i	0.953059	−	0.302784i	$-0.0979160\pi$
$948$		0			0
$949$	14656.0			0.501321
$950$	−74339.0	+	41100.5i	−2.53882	+	1.40366i
$951$		0			0
$952$			36166.4i			1.23126i
$953$			35629.1i			1.21106i	0.795823	+	0.605529i	$0.207039\pi$
$953$			35629.1i			1.21106i	−0.795823	+	0.605529i	$0.792961\pi$
$954$		0			0
$955$	−47998.0	−	28308.3i	−1.62636	−	0.959200i
$956$	−85727.3			−2.90023
$957$		0			0
$958$		−	1932.33i		−	0.0651679i
$959$	−9641.45			−0.324649
$960$		0			0
$961$	14090.4			0.472977
$962$		−	16520.1i		−	0.553667i
$963$		0			0
$964$	−63246.0			−2.11309
$965$	19273.8	−	32679.5i	0.642948	−	1.09015i
$966$		0			0
$967$			35954.1i			1.19566i	0.801622	+	0.597831i	$0.203971\pi$
$967$			35954.1i			1.19566i	−0.801622	+	0.597831i	$0.796029\pi$
$968$			65059.8i			2.16023i
$969$		0			0
$970$	−54867.4	−	32359.8i	−1.81617	−	1.07115i
$971$	−59266.0			−1.95874			−0.979370	−	0.202074i	$-0.935232\pi$
$971$	−59266.0			−1.95874			−0.979370	+	0.202074i	$0.935232\pi$
$972$		0			0
$973$			5877.71i			0.193660i
$974$	−46982.2			−1.54559
$975$		0			0
$976$	−1658.95			−0.0544076
$977$		−	35518.9i		−	1.16310i	−0.813510	−	0.581551i	$-0.802446\pi$
$977$		−	35518.9i		−	1.16310i	0.813510	−	0.581551i	$-0.197554\pi$
$978$		0			0
$979$	−15148.7			−0.494540
$980$	7505.66	+	4426.70i	0.244652	+	0.144292i
$981$		0			0
$982$			53494.4i			1.73837i
$983$		−	37683.6i		−	1.22271i	−0.791358	−	0.611353i	$-0.790626\pi$
$983$		−	37683.6i		−	1.22271i	0.791358	−	0.611353i	$-0.209374\pi$
$984$		0			0
$985$	−4330.64	+	7342.78i	−0.140087	+	0.237523i
$986$	57013.6			1.84146
$987$		0			0
$988$		−	110000.i		−	3.54207i
$989$	−1448.59			−0.0465749
$990$		0			0
$991$	21371.1			0.685041			0.342521	−	0.939510i	$-0.388719\pi$
$991$	21371.1			0.685041			0.342521	+	0.939510i	$0.388719\pi$
$992$		−	1533.61i		−	0.0490848i
$993$		0			0
$994$	210.682			0.00672278
$995$	12252.7	+	7226.40i	0.390387	+	0.230244i
$996$		0			0
$997$			42934.0i			1.36383i	0.731434	+	0.681913i	$0.238852\pi$
$997$			42934.0i			1.36383i	−0.731434	+	0.681913i	$0.761148\pi$
$998$			45323.9i			1.43758i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.4.d.b.64.2		10
3.2	odd	2		105.4.d.b.64.9	yes	10
5.2	odd	4		1575.4.a.bo.1.5		5
5.3	odd	4		1575.4.a.bp.1.1		5
5.4	even	2	inner	315.4.d.b.64.9		10
15.2	even	4		525.4.a.x.1.1		5
15.8	even	4		525.4.a.w.1.5		5
15.14	odd	2		105.4.d.b.64.2	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.d.b.64.2	✓	10	15.14	odd	2
105.4.d.b.64.9	yes	10	3.2	odd	2
315.4.d.b.64.2		10	1.1	even	1	trivial
315.4.d.b.64.9		10	5.4	even	2	inner
525.4.a.w.1.5		5	15.8	even	4
525.4.a.x.1.1		5	15.2	even	4
1575.4.a.bo.1.5		5	5.2	odd	4
1575.4.a.bp.1.1		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)

\(f(q)\)	\(=\)	\(q-4.88936i q^{2} -15.9059 q^{4} +(9.63020 + 5.67972i) q^{5} -7.00000i q^{7} +38.6546i q^{8} +O(q^{10})\)	\(q-4.88936i q^{2} -15.9059 q^{4} +(9.63020 + 5.67972i) q^{5} -7.00000i q^{7} +38.6546i q^{8} +(27.7702 - 47.0855i) q^{10} -54.9009 q^{11} -49.7580i q^{13} -34.2255 q^{14} +61.7496 q^{16} +133.661i q^{17} -138.986 q^{19} +(-153.177 - 90.3409i) q^{20} +268.430i q^{22} -7.32751i q^{23} +(60.4815 + 109.394i) q^{25} -243.285 q^{26} +111.341i q^{28} +87.2408 q^{29} -209.479 q^{31} +7.32107i q^{32} +653.519 q^{34} +(39.7580 - 67.4114i) q^{35} +67.9041i q^{37} +679.555i q^{38} +(-219.547 + 372.252i) q^{40} -77.6804 q^{41} -197.692i q^{43} +873.246 q^{44} -35.8269 q^{46} +4.97613i q^{47} -49.0000 q^{49} +(534.865 - 295.716i) q^{50} +791.444i q^{52} +53.0843i q^{53} +(-528.706 - 311.822i) q^{55} +270.582 q^{56} -426.552i q^{58} -683.950 q^{59} -26.8658 q^{61} +1024.22i q^{62} +529.792 q^{64} +(282.612 - 479.180i) q^{65} -149.300i q^{67} -2126.00i q^{68} +(-329.599 - 194.391i) q^{70} -6.15571 q^{71} +294.545i q^{73} +332.008 q^{74} +2210.70 q^{76} +384.306i q^{77} +938.669 q^{79} +(594.661 + 350.720i) q^{80} +379.807i q^{82} -784.907i q^{83} +(-759.160 + 1287.19i) q^{85} -966.590 q^{86} -2122.17i q^{88} +275.928 q^{89} -348.306 q^{91} +116.550i q^{92} +24.3301 q^{94} +(-1338.47 - 789.404i) q^{95} -1165.27i q^{97} +239.579i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 54 q^{4} + 14 q^{5}+O(q^{10}) \) 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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