LMFDB - Embedded newform 315.4.d.b.64.4

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			64.4
Root			$1.35311i$ of defining polynomial
Character	$\chi$	$=$	315.64
Dual form			315.4.d.b.64.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.20666i q^{2} +3.13065 q^{4} +(1.50045 - 11.0792i) q^{5} -7.00000i q^{7} -24.5616i q^{8} +O(q^{10})$	\(q-2.20666i q^{2} +3.13065 q^{4} +(1.50045 - 11.0792i) q^{5} -7.00000i q^{7} -24.5616i q^{8} +(-24.4480 - 3.31098i) q^{10} -56.2010 q^{11} +38.9026i q^{13} -15.4466 q^{14} -29.1538 q^{16} -119.322i q^{17} +13.0045 q^{19} +(4.69738 - 34.6851i) q^{20} +124.016i q^{22} +130.565i q^{23} +(-120.497 - 33.2475i) q^{25} +85.8448 q^{26} -21.9146i q^{28} +77.9925 q^{29} +61.0660 q^{31} -132.160i q^{32} -263.303 q^{34} +(-77.5544 - 10.5031i) q^{35} -167.391i q^{37} -28.6964i q^{38} +(-272.122 - 36.8533i) q^{40} -436.142 q^{41} -393.030i q^{43} -175.946 q^{44} +288.112 q^{46} +365.271i q^{47} -49.0000 q^{49} +(-73.3659 + 265.897i) q^{50} +121.791i q^{52} +282.048i q^{53} +(-84.3266 + 622.662i) q^{55} -171.931 q^{56} -172.103i q^{58} +414.842 q^{59} -563.802 q^{61} -134.752i q^{62} -524.862 q^{64} +(431.009 + 58.3713i) q^{65} -395.230i q^{67} -373.556i q^{68} +(-23.1768 + 171.136i) q^{70} -103.990 q^{71} -128.026i q^{73} -369.376 q^{74} +40.7125 q^{76} +393.407i q^{77} +641.999 q^{79} +(-43.7437 + 323.000i) q^{80} +962.417i q^{82} -512.010i q^{83} +(-1321.99 - 179.037i) q^{85} -867.283 q^{86} +1380.38i q^{88} +1225.10 q^{89} +272.318 q^{91} +408.753i q^{92} +806.028 q^{94} +(19.5125 - 144.079i) q^{95} -186.760i q^{97} +108.126i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	2.20666i		−	0.780172i	−0.920778	−	0.390086i	$-0.872445\pi$
$2$		−	2.20666i		−	0.780172i	0.920778	−	0.390086i	$-0.127555\pi$
$3$		0			0
$3$		0			0
$4$	3.13065			0.391332
$5$	1.50045	−	11.0792i	0.134204	−	0.990954i
$5$	1.50045	−	11.0792i	0.134204	−	0.990954i
$6$		0			0
$7$		−	7.00000i		−	0.377964i
$7$		−	7.00000i		−	0.377964i
$8$		−	24.5616i		−	1.08548i
$9$		0			0
$10$	−24.4480	−	3.31098i	−0.773114	−	0.104702i
$11$	−56.2010			−1.54048			−0.770238	−	0.637757i	$-0.779862\pi$
$11$	−56.2010			−1.54048			−0.770238	+	0.637757i	$0.779862\pi$
$12$		0			0
$13$			38.9026i			0.829972i	0.909828	+	0.414986i	$0.136214\pi$
$13$			38.9026i			0.829972i	−0.909828	+	0.414986i	$0.863786\pi$
$14$	−15.4466			−0.294877
$15$		0			0
$16$	−29.1538			−0.455528
$17$		−	119.322i		−	1.70235i	−0.524886	−	0.851173i	$-0.675892\pi$
$17$		−	119.322i		−	1.70235i	0.524886	−	0.851173i	$-0.324108\pi$
$18$		0			0
$19$	13.0045			0.157023			0.0785113	−	0.996913i	$-0.474983\pi$
$19$	13.0045			0.157023			0.0785113	+	0.996913i	$0.474983\pi$
$20$	4.69738	−	34.6851i	0.0525183	−	0.387792i
$21$		0			0
$22$			124.016i			1.20184i
$23$			130.565i			1.18368i	0.806055	+	0.591840i	$0.201598\pi$
$23$			130.565i			1.18368i	−0.806055	+	0.591840i	$0.798402\pi$
$24$		0			0
$25$	−120.497	−	33.2475i	−0.963979	−	0.265980i
$26$	85.8448			0.647521
$27$		0			0
$28$		−	21.9146i		−	0.147910i
$29$	77.9925			0.499408			0.249704	−	0.968322i	$-0.419667\pi$
$29$	77.9925			0.499408			0.249704	+	0.968322i	$0.419667\pi$
$30$		0			0
$31$	61.0660			0.353799			0.176900	−	0.984229i	$-0.443393\pi$
$31$	61.0660			0.353799			0.176900	+	0.984229i	$0.443393\pi$
$32$		−	132.160i		−	0.730088i
$33$		0			0
$34$	−263.303			−1.32812
$35$	−77.5544	−	10.5031i	−0.374545	−	0.0507244i
$36$		0			0
$37$		−	167.391i		−	0.743757i	−0.928282	−	0.371878i	$-0.878714\pi$
$37$		−	167.391i		−	0.743757i	0.928282	−	0.371878i	$-0.121286\pi$
$38$		−	28.6964i		−	0.122505i
$39$		0			0
$40$	−272.122	−	36.8533i	−1.07566	−	0.145676i
$41$	−436.142			−1.66132			−0.830658	−	0.556783i	$-0.812036\pi$
$41$	−436.142			−1.66132			−0.830658	+	0.556783i	$0.812036\pi$
$42$		0			0
$43$		−	393.030i		−	1.39387i	−0.717134	−	0.696936i	$-0.754546\pi$
$43$		−	393.030i		−	1.39387i	0.717134	−	0.696936i	$-0.245454\pi$
$44$	−175.946			−0.602837
$45$		0			0
$46$	288.112			0.923474
$47$			365.271i			1.13362i	0.823848	+	0.566811i	$0.191823\pi$
$47$			365.271i			1.13362i	−0.823848	+	0.566811i	$0.808177\pi$
$48$		0			0
$49$	−49.0000			−0.142857
$50$	−73.3659	+	265.897i	−0.207510	+	0.752069i
$51$		0			0
$52$			121.791i			0.324794i
$53$			282.048i			0.730987i	0.930814	+	0.365494i	$0.119100\pi$
$53$			282.048i			0.730987i	−0.930814	+	0.365494i	$0.880900\pi$
$54$		0			0
$55$	−84.3266	+	622.662i	−0.206738	+	1.52654i
$56$	−171.931			−0.410272
$57$		0			0
$58$		−	172.103i		−	0.389624i
$59$	414.842			0.915388			0.457694	−	0.889110i	$-0.348676\pi$
$59$	414.842			0.915388			0.457694	+	0.889110i	$0.348676\pi$
$60$		0			0
$61$	−563.802			−1.18340			−0.591701	−	0.806158i	$-0.701543\pi$
$61$	−563.802			−1.18340			−0.591701	+	0.806158i	$0.701543\pi$
$62$		−	134.752i		−	0.276024i
$63$		0			0
$64$	−524.862			−1.02512
$65$	431.009	+	58.3713i	0.822464	+	0.111386i
$66$		0			0
$67$		−	395.230i		−	0.720673i	−0.932822	−	0.360336i	$-0.882662\pi$
$67$		−	395.230i		−	0.720673i	0.932822	−	0.360336i	$-0.117338\pi$
$68$		−	373.556i		−	0.666182i
$69$		0			0
$70$	−23.1768	+	171.136i	−0.0395737	+	0.292210i
$71$	−103.990			−0.173821			−0.0869107	−	0.996216i	$-0.527699\pi$
$71$	−103.990			−0.173821			−0.0869107	+	0.996216i	$0.527699\pi$
$72$		0			0
$73$		−	128.026i		−	0.205264i	−0.994719	−	0.102632i	$-0.967274\pi$
$73$		−	128.026i		−	0.205264i	0.994719	−	0.102632i	$-0.0327264\pi$
$74$	−369.376			−0.580258
$75$		0			0
$76$	40.7125			0.0614479
$77$			393.407i			0.582245i
$78$		0			0
$79$	641.999			0.914310			0.457155	−	0.889387i	$-0.348868\pi$
$79$	641.999			0.914310			0.457155	+	0.889387i	$0.348868\pi$
$80$	−43.7437	+	323.000i	−0.0611337	+	0.451407i
$81$		0			0
$82$			962.417i			1.29611i
$83$		−	512.010i		−	0.677113i	−0.940946	−	0.338557i	$-0.890061\pi$
$83$		−	512.010i		−	0.677113i	0.940946	−	0.338557i	$-0.109939\pi$
$84$		0			0
$85$	−1321.99	−	179.037i	−1.68695	−	0.228462i
$86$	−867.283			−1.08746
$87$		0			0
$88$			1380.38i			1.67215i
$89$	1225.10			1.45911			0.729554	−	0.683923i	$-0.239728\pi$
$89$	1225.10			1.45911			0.729554	+	0.683923i	$0.239728\pi$
$90$		0			0
$91$	272.318			0.313700
$92$			408.753i			0.463212i
$93$		0			0
$94$	806.028			0.884420
$95$	19.5125	−	144.079i	0.0210731	−	0.155602i
$96$		0			0
$97$		−	186.760i		−	0.195491i	−0.995211	−	0.0977454i	$-0.968837\pi$
$97$		−	186.760i		−	0.195491i	0.995211	−	0.0977454i	$-0.0311631\pi$
$98$			108.126i			0.111453i
$99$		0			0
$100$	−377.235	−	104.086i	−0.377235	−	0.104086i
$101$	−1650.68			−1.62623			−0.813114	−	0.582104i	$-0.802230\pi$
$101$	−1650.68			−1.62623			−0.813114	+	0.582104i	$0.802230\pi$
$102$		0			0
$103$		−	72.1876i		−	0.0690568i	−0.999404	−	0.0345284i	$-0.989007\pi$
$103$		−	72.1876i		−	0.0690568i	0.999404	−	0.0345284i	$-0.0109929\pi$
$104$	955.508			0.900916
$105$		0			0
$106$	622.385			0.570296
$107$		−	1202.55i		−	1.08649i	−0.839574	−	0.543246i	$-0.817195\pi$
$107$		−	1202.55i		−	1.08649i	0.839574	−	0.543246i	$-0.182805\pi$
$108$		0			0
$109$	1551.36			1.36324			0.681622	−	0.731704i	$-0.261275\pi$
$109$	1551.36			1.36324			0.681622	+	0.731704i	$0.261275\pi$
$110$	1374.00	+	186.080i	1.19096	+	0.161291i
$111$		0			0
$112$			204.076i			0.172173i
$113$		−	2080.90i		−	1.73234i	−0.499749	−	0.866170i	$-0.666574\pi$
$113$		−	2080.90i		−	1.73234i	0.499749	−	0.866170i	$-0.333426\pi$
$114$		0			0
$115$	1446.55	+	195.906i	1.17297	+	0.158855i
$116$	244.167			0.195434
$117$		0			0
$118$		−	915.416i		−	0.714160i
$119$	−835.255			−0.643426
$120$		0			0
$121$	1827.55			1.37306
$122$			1244.12i			0.923257i
$123$		0			0
$124$	191.177			0.138453
$125$	−549.156	+	1285.13i	−0.392944	+	0.919562i
$126$		0			0
$127$		−	1414.70i		−	0.988461i	−0.869331	−	0.494231i	$-0.835450\pi$
$127$		−	1414.70i		−	0.988461i	0.869331	−	0.494231i	$-0.164550\pi$
$128$			100.912i			0.0696832i
$129$		0			0
$130$	128.806	−	951.091i	0.0869000	−	0.641663i
$131$	2472.51			1.64904			0.824520	−	0.565833i	$-0.191445\pi$
$131$	2472.51			1.64904			0.824520	+	0.565833i	$0.191445\pi$
$132$		0			0
$133$		−	91.0313i		−	0.0593490i
$134$	−872.139			−0.562249
$135$		0			0
$136$	−2930.74			−1.84786
$137$		−	214.391i		−	0.133698i	−0.997763	−	0.0668491i	$-0.978705\pi$
$137$		−	214.391i		−	0.133698i	0.997763	−	0.0668491i	$-0.0212946\pi$
$138$		0			0
$139$	−942.774			−0.575288			−0.287644	−	0.957737i	$-0.592872\pi$
$139$	−942.774			−0.575288			−0.287644	+	0.957737i	$0.592872\pi$
$140$	−242.796	−	32.8817i	−0.146571	−	0.0198501i
$141$		0			0
$142$			229.470i			0.135611i
$143$		−	2186.36i		−	1.27855i
$144$		0			0
$145$	117.024	−	864.094i	0.0670226	−	0.494890i
$146$	−282.509			−0.160141
$147$		0			0
$148$		−	524.045i		−	0.291056i
$149$	1693.07			0.930882			0.465441	−	0.885079i	$-0.345896\pi$
$149$	1693.07			0.930882			0.465441	+	0.885079i	$0.345896\pi$
$150$		0			0
$151$	2519.69			1.35795			0.678973	−	0.734163i	$-0.262425\pi$
$151$	2519.69			1.35795			0.678973	+	0.734163i	$0.262425\pi$
$152$		−	319.410i		−	0.170445i
$153$		0			0
$154$	868.115			0.454251
$155$	91.6263	−	676.562i	0.0474813	−	0.350599i
$156$		0			0
$157$		−	1621.48i		−	0.824258i	−0.911125	−	0.412129i	$-0.864785\pi$
$157$		−	1621.48i		−	0.824258i	0.911125	−	0.412129i	$-0.135215\pi$
$158$		−	1416.67i		−	0.713319i
$159$		0			0
$160$	−1464.23	−	198.299i	−0.723484	−	0.0979808i
$161$	913.954			0.447389
$162$		0			0
$163$			925.194i			0.444582i	0.974980	+	0.222291i	$0.0713534\pi$
$163$			925.194i			0.444582i	−0.974980	+	0.222291i	$0.928647\pi$
$164$	−1365.41			−0.650126
$165$		0			0
$166$	−1129.83			−0.528265
$167$			2681.55i			1.24254i	0.783596	+	0.621271i	$0.213383\pi$
$167$			2681.55i			1.24254i	−0.783596	+	0.621271i	$0.786617\pi$
$168$		0			0
$169$	683.589			0.311147
$170$	−395.073	+	2917.19i	−0.178239	+	1.31611i
$171$		0			0
$172$		−	1230.44i		−	0.545466i
$173$		−	287.591i		−	0.126388i	−0.998001	−	0.0631940i	$-0.979871\pi$
$173$		−	287.591i		−	0.126388i	0.998001	−	0.0631940i	$-0.0201287\pi$
$174$		0			0
$175$	−232.733	+	843.481i	−0.100531	+	0.364350i
$176$	1638.47			0.701729
$177$		0			0
$178$		−	2703.38i		−	1.13835i
$179$	3683.47			1.53808			0.769038	−	0.639203i	$-0.220735\pi$
$179$	3683.47			1.53808			0.769038	+	0.639203i	$0.220735\pi$
$180$		0			0
$181$	3132.65			1.28645			0.643227	−	0.765676i	$-0.277595\pi$
$181$	3132.65			1.28645			0.643227	+	0.765676i	$0.277595\pi$
$182$		−	600.913i		−	0.244740i
$183$		0			0
$184$	3206.88			1.28486
$185$	−1854.56	−	251.162i	−0.737028	−	0.0998152i
$186$		0			0
$187$			6706.02i			2.62242i
$188$			1143.54i			0.443622i
$189$		0			0
$190$	−317.933	−	43.0575i	−0.121396	−	0.0164406i
$191$	−1586.93			−0.601184			−0.300592	−	0.953753i	$-0.597184\pi$
$191$	−1586.93			−0.601184			−0.300592	+	0.953753i	$0.597184\pi$
$192$		0			0
$193$		−	5179.00i		−	1.93157i	−0.259352	−	0.965783i	$-0.583509\pi$
$193$		−	5179.00i		−	1.93157i	0.259352	−	0.965783i	$-0.416491\pi$
$194$	−412.116			−0.152516
$195$		0			0
$196$	−153.402			−0.0559045
$197$			903.798i			0.326868i	0.986554	+	0.163434i	$0.0522570\pi$
$197$			903.798i			0.326868i	−0.986554	+	0.163434i	$0.947743\pi$
$198$		0			0
$199$	1171.51			0.417317			0.208659	−	0.977989i	$-0.433090\pi$
$199$	1171.51			0.417317			0.208659	+	0.977989i	$0.433090\pi$
$200$	−816.611	+	2959.60i	−0.288716	+	1.04638i
$201$		0			0
$202$			3642.50i			1.26874i
$203$		−	545.947i		−	0.188759i
$204$		0			0
$205$	−654.409	+	4832.11i	−0.222955	+	1.64629i
$206$	−159.293			−0.0538762
$207$		0			0
$208$		−	1134.16i		−	0.378075i
$209$	−730.864			−0.241889
$210$		0			0
$211$	−1103.16			−0.359928			−0.179964	−	0.983673i	$-0.557598\pi$
$211$	−1103.16			−0.359928			−0.179964	+	0.983673i	$0.557598\pi$
$212$			882.996i			0.286059i
$213$		0			0
$214$	−2653.61			−0.847651
$215$	−4354.45	−	589.721i	−1.38126	−	0.187063i
$216$		0			0
$217$		−	427.462i		−	0.133724i
$218$		−	3423.33i		−	1.06357i
$219$		0			0
$220$	−263.997	+	1949.34i	−0.0809032	+	0.597383i
$221$	4641.94			1.41290
$222$		0			0
$223$			4079.95i			1.22517i	0.790404	+	0.612586i	$0.209871\pi$
$223$			4079.95i			1.22517i	−0.790404	+	0.612586i	$0.790129\pi$
$224$	−925.120			−0.275947
$225$		0			0
$226$	−4591.83			−1.35152
$227$			931.964i			0.272496i	0.990675	+	0.136248i	$0.0435044\pi$
$227$			931.964i			0.272496i	−0.990675	+	0.136248i	$0.956496\pi$
$228$		0			0
$229$	1471.55			0.424641			0.212321	−	0.977200i	$-0.431898\pi$
$229$	1471.55			0.424641			0.212321	+	0.977200i	$0.431898\pi$
$230$	432.297	−	3192.05i	0.123934	−	0.915120i
$231$		0			0
$232$		−	1915.62i		−	0.542097i
$233$		−	2479.06i		−	0.697034i	−0.937303	−	0.348517i	$-0.886685\pi$
$233$		−	2479.06i		−	0.697034i	0.937303	−	0.348517i	$-0.113315\pi$
$234$		0			0
$235$	4046.91	+	548.070i	1.12337	+	0.152137i
$236$	1298.73			0.358220
$237$		0			0
$238$			1843.12i			0.501983i
$239$	−954.068			−0.258216			−0.129108	−	0.991631i	$-0.541211\pi$
$239$	−954.068			−0.258216			−0.129108	+	0.991631i	$0.541211\pi$
$240$		0			0
$241$	−5297.02			−1.41581			−0.707906	−	0.706306i	$-0.750360\pi$
$241$	−5297.02			−1.41581			−0.707906	+	0.706306i	$0.750360\pi$
$242$		−	4032.77i		−	1.07123i
$243$		0			0
$244$	−1765.07			−0.463103
$245$	−73.5219	+	542.881i	−0.0191720	+	0.141565i
$246$		0			0
$247$			505.907i			0.130324i
$248$		−	1499.88i		−	0.384041i
$249$		0			0
$250$	2835.84	+	1211.80i	0.717417	+	0.306564i
$251$	−1855.17			−0.466524			−0.233262	−	0.972414i	$-0.574940\pi$
$251$	−1855.17			−0.466524			−0.233262	+	0.972414i	$0.574940\pi$
$252$		0			0
$253$		−	7337.87i		−	1.82343i
$254$	−3121.77			−0.771170
$255$		0			0
$256$	−3976.22			−0.970757
$257$			6233.09i			1.51288i	0.654065	+	0.756438i	$0.273062\pi$
$257$			6233.09i			1.51288i	−0.654065	+	0.756438i	$0.726938\pi$
$258$		0			0
$259$	−1171.74			−0.281114
$260$	1349.34	+	182.740i	0.321856	+	0.0435887i
$261$		0			0
$262$		−	5455.99i		−	1.28653i
$263$		−	1184.50i		−	0.277716i	−0.990312	−	0.138858i	$-0.955657\pi$
$263$		−	1184.50i		−	0.277716i	0.990312	−	0.138858i	$-0.0443432\pi$
$264$		0			0
$265$	3124.87	+	423.199i	0.724375	+	0.0981015i
$266$	−200.875			−0.0463024
$267$		0			0
$268$		−	1237.33i		−	0.282022i
$269$	−1916.03			−0.434283			−0.217141	−	0.976140i	$-0.569673\pi$
$269$	−1916.03			−0.434283			−0.217141	+	0.976140i	$0.569673\pi$
$270$		0			0
$271$	−1168.95			−0.262025			−0.131013	−	0.991381i	$-0.541823\pi$
$271$	−1168.95			−0.262025			−0.131013	+	0.991381i	$0.541823\pi$
$272$			3478.69i			0.775465i
$273$		0			0
$274$	−473.088			−0.104308
$275$	6772.06	+	1868.54i	1.48498	+	0.409736i
$276$		0			0
$277$			7269.54i			1.57684i	0.615138	+	0.788419i	$0.289100\pi$
$277$			7269.54i			1.57684i	−0.615138	+	0.788419i	$0.710900\pi$
$278$			2080.38i			0.448824i
$279$		0			0
$280$	−257.973	+	1904.86i	−0.0550602	+	0.406561i
$281$	−298.126			−0.0632908			−0.0316454	−	0.999499i	$-0.510075\pi$
$281$	−298.126			−0.0632908			−0.0316454	+	0.999499i	$0.510075\pi$
$282$		0			0
$283$			4496.30i			0.944444i	0.881480	+	0.472222i	$0.156548\pi$
$283$			4496.30i			0.944444i	−0.881480	+	0.472222i	$0.843452\pi$
$284$	−325.556			−0.0680218
$285$		0			0
$286$	−4824.56			−0.997490
$287$			3053.00i			0.627919i
$288$		0			0
$289$	−9324.77			−1.89798
$290$	−1906.76	−	258.231i	−0.386100	−	0.0522892i
$291$		0			0
$292$		−	400.804i		−	0.0803264i
$293$		−	1644.33i		−	0.327859i	−0.986472	−	0.163929i	$-0.947583\pi$
$293$		−	1644.33i		−	0.327859i	0.986472	−	0.163929i	$-0.0524169\pi$
$294$		0			0
$295$	622.449	−	4596.12i	0.122849	−	0.907107i
$296$	−4111.40			−0.807331
$297$		0			0
$298$		−	3736.02i		−	0.726248i
$299$	−5079.31			−0.982421
$300$		0			0
$301$	−2751.21			−0.526834
$302$		−	5560.11i		−	1.05943i
$303$		0			0
$304$	−379.129			−0.0715281
$305$	−845.956	+	6246.48i	−0.158817	+	1.17270i
$306$		0			0
$307$		−	4726.18i		−	0.878623i	−0.898335	−	0.439312i	$-0.855222\pi$
$307$		−	4726.18i		−	0.878623i	0.898335	−	0.439312i	$-0.144778\pi$
$308$			1231.62i			0.227851i
$309$		0			0
$310$	−1492.94	−	202.188i	−0.273527	−	0.0370436i
$311$	4853.99			0.885031			0.442515	−	0.896761i	$-0.354086\pi$
$311$	4853.99			0.885031			0.442515	+	0.896761i	$0.354086\pi$
$312$		0			0
$313$		−	1690.87i		−	0.305348i	−0.988277	−	0.152674i	$-0.951212\pi$
$313$		−	1690.87i		−	0.305348i	0.988277	−	0.152674i	$-0.0487884\pi$
$314$	−3578.06			−0.643063
$315$		0			0
$316$	2009.88			0.357799
$317$			3878.38i			0.687166i	0.939122	+	0.343583i	$0.111641\pi$
$317$			3878.38i			0.687166i	−0.939122	+	0.343583i	$0.888359\pi$
$318$		0			0
$319$	−4383.25			−0.769326
$320$	−787.529	+	5815.06i	−0.137576	+	1.01585i
$321$		0			0
$322$		−	2016.78i		−	0.349040i
$323$		−	1551.72i		−	0.267307i
$324$		0			0
$325$	1293.41	−	4687.66i	0.220756	−	0.800075i
$326$	2041.59			0.346850
$327$		0			0
$328$			10712.3i			1.80332i
$329$	2556.90			0.428469
$330$		0			0
$331$	9927.71			1.64857			0.824284	−	0.566176i	$-0.191578\pi$
$331$	9927.71			1.64857			0.824284	+	0.566176i	$0.191578\pi$
$332$		−	1602.93i		−	0.264976i
$333$		0			0
$334$	5917.26			0.969396
$335$	−4378.84	−	593.023i	−0.714153	−	0.0967173i
$336$		0			0
$337$		−	5283.88i		−	0.854099i	−0.904228	−	0.427050i	$-0.859553\pi$
$337$		−	5283.88i		−	0.854099i	0.904228	−	0.427050i	$-0.140447\pi$
$338$		−	1508.45i		−	0.242748i
$339$		0			0
$340$	−4138.71	−	560.502i	−0.660155	−	0.0894043i
$341$	−3431.97			−0.545019
$342$		0			0
$343$			343.000i			0.0539949i
$344$	−9653.42			−1.51302
$345$		0			0
$346$	−634.615			−0.0986044
$347$		−	10548.3i		−	1.63188i	−0.578137	−	0.815940i	$-0.696220\pi$
$347$		−	10548.3i		−	1.63188i	0.578137	−	0.815940i	$-0.303780\pi$
$348$		0			0
$349$	−628.411			−0.0963841			−0.0481921	−	0.998838i	$-0.515346\pi$
$349$	−628.411			−0.0963841			−0.0481921	+	0.998838i	$0.515346\pi$
$350$	1861.28	+	513.562i	0.284255	+	0.0784315i
$351$		0			0
$352$			7427.52i			1.12468i
$353$		−	2548.17i		−	0.384209i	−0.981375	−	0.192104i	$-0.938469\pi$
$353$		−	2548.17i		−	0.384209i	0.981375	−	0.192104i	$-0.0615312\pi$
$354$		0			0
$355$	−156.031	+	1152.12i	−0.0233275	+	0.172249i
$356$	3835.37			0.570995
$357$		0			0
$358$		−	8128.17i		−	1.19996i
$359$	13046.3			1.91799			0.958996	−	0.283420i	$-0.0914689\pi$
$359$	13046.3			1.91799			0.958996	+	0.283420i	$0.0914689\pi$
$360$		0			0
$361$	−6689.88			−0.975344
$362$		−	6912.69i		−	1.00366i
$363$		0			0
$364$	852.534			0.122761
$365$	−1418.42	−	192.096i	−0.203407	−	0.0275473i
$366$		0			0
$367$		−	8068.23i		−	1.14757i	−0.819006	−	0.573785i	$-0.805475\pi$
$367$		−	8068.23i		−	1.14757i	0.819006	−	0.573785i	$-0.194525\pi$
$368$		−	3806.46i		−	0.539199i
$369$		0			0
$370$	−554.229	+	4092.39i	−0.0778730	+	0.575009i
$371$	1974.34			0.276287
$372$		0			0
$373$		−	3623.32i		−	0.502972i	−0.967861	−	0.251486i	$-0.919081\pi$
$373$		−	3623.32i		−	0.502972i	0.967861	−	0.251486i	$-0.0809193\pi$
$374$	14797.9			2.04594
$375$		0			0
$376$	8971.62			1.23052
$377$			3034.11i			0.414495i
$378$		0			0
$379$	−7486.58			−1.01467			−0.507335	−	0.861749i	$-0.669369\pi$
$379$	−7486.58			−1.01467			−0.507335	+	0.861749i	$0.669369\pi$
$380$	61.0870	−	451.062i	0.00824657	−	0.0608921i
$381$		0			0
$382$			3501.81i			0.469027i
$383$		−	8926.58i		−	1.19093i	−0.803381	−	0.595466i	$-0.796967\pi$
$383$		−	8926.58i		−	1.19093i	0.803381	−	0.595466i	$-0.203033\pi$
$384$		0			0
$385$	4358.63	+	590.286i	0.576978	+	0.0781397i
$386$	−11428.3			−1.50695
$387$		0			0
$388$		−	584.681i		−	0.0765018i
$389$	−12600.1			−1.64228			−0.821141	−	0.570725i	$-0.806662\pi$
$389$	−12600.1			−1.64228			−0.821141	+	0.570725i	$0.806662\pi$
$390$		0			0
$391$	15579.3			2.01503
$392$			1203.52i			0.155068i
$393$		0			0
$394$	1994.37			0.255013
$395$	963.286	−	7112.83i	0.122704	−	0.906039i
$396$		0			0
$397$			12713.4i			1.60722i	0.595154	+	0.803612i	$0.297091\pi$
$397$			12713.4i			1.60722i	−0.595154	+	0.803612i	$0.702909\pi$
$398$		−	2585.12i		−	0.325579i
$399$		0			0
$400$	3512.95	+	969.290i	0.439119	+	0.121161i
$401$	6133.51			0.763822			0.381911	−	0.924199i	$-0.375266\pi$
$401$	6133.51			0.763822			0.381911	+	0.924199i	$0.375266\pi$
$402$		0			0
$403$			2375.62i			0.293643i
$404$	−5167.72			−0.636395
$405$		0			0
$406$	−1204.72			−0.147264
$407$			9407.56i			1.14574i
$408$		0			0
$409$	−10600.3			−1.28154			−0.640769	−	0.767733i	$-0.721385\pi$
$409$	−10600.3			−1.28154			−0.640769	+	0.767733i	$0.721385\pi$
$410$	10662.8	+	1444.06i	1.28439	+	0.173944i
$411$		0			0
$412$		−	225.994i		−	0.0270241i
$413$		−	2903.90i		−	0.345984i
$414$		0			0
$415$	−5672.66	−	768.244i	−0.670988	−	0.0908714i
$416$	5141.37			0.605953
$417$		0			0
$418$			1612.77i			0.188715i
$419$	4296.43			0.500941			0.250470	−	0.968124i	$-0.419415\pi$
$419$	4296.43			0.500941			0.250470	+	0.968124i	$0.419415\pi$
$420$		0			0
$421$	3916.78			0.453425			0.226713	−	0.973962i	$-0.427202\pi$
$421$	3916.78			0.453425			0.226713	+	0.973962i	$0.427202\pi$
$422$			2434.30i			0.280806i
$423$		0			0
$424$	6927.55			0.793471
$425$	−3967.16	+	14378.0i	−0.452790	+	1.64102i
$426$		0			0
$427$			3946.62i			0.447284i
$428$		−	3764.76i		−	0.425179i
$429$		0			0
$430$	−1301.31	+	9608.80i	−0.145942	+	1.07762i
$431$	−13408.9			−1.49857			−0.749287	−	0.662246i	$-0.769604\pi$
$431$	−13408.9			−1.49857			−0.749287	+	0.662246i	$0.769604\pi$
$432$		0			0
$433$			7792.31i			0.864837i	0.901673	+	0.432419i	$0.142340\pi$
$433$			7792.31i			0.864837i	−0.901673	+	0.432419i	$0.857660\pi$
$434$	−943.263			−0.104327
$435$		0			0
$436$	4856.78			0.533481
$437$			1697.93i			0.185865i
$438$		0			0
$439$	−1039.29			−0.112990			−0.0564948	−	0.998403i	$-0.517992\pi$
$439$	−1039.29			−0.112990			−0.0564948	+	0.998403i	$0.517992\pi$
$440$	15293.5	+	2071.19i	1.65702	+	0.224410i
$441$		0			0
$442$		−	10243.2i		−	1.10230i
$443$			2846.33i			0.305267i	0.988283	+	0.152633i	$0.0487754\pi$
$443$			2846.33i			0.305267i	−0.988283	+	0.152633i	$0.951225\pi$
$444$		0			0
$445$	1838.20	−	13573.2i	0.195818	−	1.44591i
$446$	9003.05			0.955845
$447$		0			0
$448$			3674.04i			0.387460i
$449$	7472.64			0.785425			0.392713	−	0.919661i	$-0.371537\pi$
$449$	7472.64			0.785425			0.392713	+	0.919661i	$0.371537\pi$
$450$		0			0
$451$	24511.6			2.55922
$452$		−	6514.57i		−	0.677920i
$453$		0			0
$454$	2056.53			0.212594
$455$	408.599	−	3017.07i	0.0420998	−	0.310862i
$456$		0			0
$457$			11014.3i			1.12742i	0.825974	+	0.563708i	$0.190626\pi$
$457$			11014.3i			1.12742i	−0.825974	+	0.563708i	$0.809374\pi$
$458$		−	3247.21i		−	0.331293i
$459$		0			0
$460$	4528.66	+	613.313i	0.459021	+	0.0621649i
$461$	−7944.67			−0.802647			−0.401323	−	0.915936i	$-0.631450\pi$
$461$	−7944.67			−0.802647			−0.401323	+	0.915936i	$0.631450\pi$
$462$		0			0
$463$		−	7627.25i		−	0.765591i	−0.923833	−	0.382795i	$-0.874961\pi$
$463$		−	7627.25i		−	0.765591i	0.923833	−	0.382795i	$-0.125039\pi$
$464$	−2273.77			−0.227494
$465$		0			0
$466$	−5470.45			−0.543806
$467$		−	3284.28i		−	0.325436i	−0.986673	−	0.162718i	$-0.947974\pi$
$467$		−	3284.28i		−	0.325436i	0.986673	−	0.162718i	$-0.0520260\pi$
$468$		0			0
$469$	−2766.61			−0.272389
$470$	1209.40	−	8930.15i	0.118693	−	0.876419i
$471$		0			0
$472$		−	10189.2i		−	0.993633i
$473$			22088.6i			2.14722i
$474$		0			0
$475$	−1567.00	−	432.366i	−0.151366	−	0.0417649i
$476$	−2614.89			−0.251793
$477$		0			0
$478$			2105.30i			0.201453i
$479$	−2909.45			−0.277528			−0.138764	−	0.990325i	$-0.544313\pi$
$479$	−2909.45			−0.277528			−0.138764	+	0.990325i	$0.544313\pi$
$480$		0			0
$481$	6511.96			0.617297
$482$			11688.7i			1.10458i
$483$		0			0
$484$	5721.42			0.537323
$485$	−2069.15	−	280.224i	−0.193722	−	0.0262357i
$486$		0			0
$487$			2201.84i			0.204876i	0.994739	+	0.102438i	$0.0326644\pi$
$487$			2201.84i			0.204876i	−0.994739	+	0.102438i	$0.967336\pi$
$488$			13847.9i			1.28456i
$489$		0			0
$490$	1197.95	+	162.238i	0.110445	+	0.0149575i
$491$	11827.6			1.08711			0.543556	−	0.839373i	$-0.317078\pi$
$491$	11827.6			1.08711			0.543556	+	0.839373i	$0.317078\pi$
$492$		0			0
$493$		−	9306.23i		−	0.850165i
$494$	1116.37			0.101675
$495$		0			0
$496$	−1780.30			−0.161165
$497$			727.928i			0.0656983i
$498$		0			0
$499$	−1408.66			−0.126374			−0.0631868	−	0.998002i	$-0.520126\pi$
$499$	−1408.66			−0.126374			−0.0631868	+	0.998002i	$0.520126\pi$
$500$	−1719.22	+	4023.29i	−0.153771	+	0.359854i
$501$		0			0
$502$			4093.74i			0.363969i
$503$			11018.9i			0.976758i	0.872632	+	0.488379i	$0.162412\pi$
$503$			11018.9i			0.976758i	−0.872632	+	0.488379i	$0.837588\pi$
$504$		0			0
$505$	−2476.76	+	18288.2i	−0.218247	+	1.61152i
$506$	−16192.2			−1.42259
$507$		0			0
$508$		−	4428.95i		−	0.386816i
$509$	7032.93			0.612434			0.306217	−	0.951962i	$-0.400937\pi$
$509$	7032.93			0.612434			0.306217	+	0.951962i	$0.400937\pi$
$510$		0			0
$511$	−896.180			−0.0775825
$512$			9581.46i			0.827041i
$513$		0			0
$514$	13754.3			1.18030
$515$	−799.781	−	108.314i	−0.0684321	−	0.00926771i
$516$		0			0
$517$		−	20528.6i		−	1.74632i
$518$			2585.63i			0.219317i
$519$		0			0
$520$	1433.69	−	10586.3i	0.120907	−	0.892766i
$521$	−3049.04			−0.256394			−0.128197	−	0.991749i	$-0.540919\pi$
$521$	−3049.04			−0.256394			−0.128197	+	0.991749i	$0.540919\pi$
$522$		0			0
$523$			8714.06i			0.728564i	0.931289	+	0.364282i	$0.118686\pi$
$523$			8714.06i			0.728564i	−0.931289	+	0.364282i	$0.881314\pi$
$524$	7740.58			0.645322
$525$		0			0
$526$	−2613.79			−0.216666
$527$		−	7286.52i		−	0.602288i
$528$		0			0
$529$	−4880.17			−0.401099
$530$	933.856	−	6895.53i	0.0765361	−	0.565137i
$531$		0			0
$532$		−	284.987i		−	0.0232251i
$533$		−	16967.1i		−	1.37885i
$534$		0			0
$535$	−13323.3	−	1804.36i	−1.07666	−	0.145812i
$536$	−9707.48			−0.782275
$537$		0			0
$538$			4228.02i			0.338815i
$539$	2753.85			0.220068
$540$		0			0
$541$	−5999.45			−0.476778			−0.238389	−	0.971170i	$-0.576619\pi$
$541$	−5999.45			−0.476778			−0.238389	+	0.971170i	$0.576619\pi$
$542$			2579.48i			0.204425i
$543$		0			0
$544$	−15769.6			−1.24286
$545$	2327.74	−	17187.9i	0.182953	−	1.35091i
$546$		0			0
$547$		−	7759.95i		−	0.606566i	−0.952901	−	0.303283i	$-0.901917\pi$
$547$		−	7759.95i		−	0.606566i	0.952901	−	0.303283i	$-0.0980828\pi$
$548$		−	671.184i		−	0.0523203i
$549$		0			0
$550$	4123.24	−	14943.6i	0.319664	−	1.15854i
$551$	1014.25			0.0784184
$552$		0			0
$553$		−	4493.99i		−	0.345577i
$554$	16041.4			1.23021
$555$		0			0
$556$	−2951.50			−0.225128
$557$		−	6392.82i		−	0.486306i	−0.969988	−	0.243153i	$-0.921818\pi$
$557$		−	6392.82i		−	0.486306i	0.969988	−	0.243153i	$-0.0781817\pi$
$558$		0			0
$559$	15289.9			1.15687
$560$	2261.00	+	306.206i	0.170616	+	0.0231064i
$561$		0			0
$562$			657.863i			0.0493777i
$563$			7682.70i			0.575111i	0.957764	+	0.287555i	$0.0928425\pi$
$563$			7682.70i			0.575111i	−0.957764	+	0.287555i	$0.907157\pi$
$564$		0			0
$565$	−23054.7	−	3122.28i	−1.71667	−	0.232487i
$566$	9921.81			0.736828
$567$		0			0
$568$			2554.15i			0.188679i
$569$	143.175			0.0105487			0.00527434	−	0.999986i	$-0.498321\pi$
$569$	143.175			0.0105487			0.00527434	+	0.999986i	$0.498321\pi$
$570$		0			0
$571$	1077.72			0.0789863			0.0394932	−	0.999220i	$-0.487426\pi$
$571$	1077.72			0.0789863			0.0394932	+	0.999220i	$0.487426\pi$
$572$		−	6844.74i		−	0.500338i
$573$		0			0
$574$	6736.92			0.489884
$575$	4340.96	−	15732.7i	0.314835	−	1.14104i
$576$		0			0
$577$			12651.7i			0.912818i	0.889770	+	0.456409i	$0.150865\pi$
$577$			12651.7i			0.912818i	−0.889770	+	0.456409i	$0.849135\pi$
$578$			20576.6i			1.48075i
$579$		0			0
$580$	366.361	−	2705.18i	0.0262281	−	0.193666i
$581$	−3584.07			−0.255925
$582$		0			0
$583$		−	15851.4i		−	1.12607i
$584$	−3144.51			−0.222810
$585$		0			0
$586$	−3628.47			−0.255786
$587$		−	2920.89i		−	0.205380i	−0.994713	−	0.102690i	$-0.967255\pi$
$587$		−	2920.89i		−	0.205380i	0.994713	−	0.102690i	$-0.0327450\pi$
$588$		0			0
$589$	794.131			0.0555545
$590$	−10142.1	−	1373.53i	−0.707699	−	0.0958432i
$591$		0			0
$592$			4880.09i			0.338802i
$593$			9801.70i			0.678765i	0.940648	+	0.339382i	$0.110218\pi$
$593$			9801.70i			0.678765i	−0.940648	+	0.339382i	$0.889782\pi$
$594$		0			0
$595$	−1253.26	+	9253.96i	−0.0863504	+	0.637605i
$596$	5300.41			0.364284
$597$		0			0
$598$			11208.3i			0.766458i
$599$	−6992.54			−0.476974			−0.238487	−	0.971146i	$-0.576651\pi$
$599$	−6992.54			−0.476974			−0.238487	+	0.971146i	$0.576651\pi$
$600$		0			0
$601$	−26159.1			−1.77546			−0.887730	−	0.460364i	$-0.847719\pi$
$601$	−26159.1			−1.77546			−0.887730	+	0.460364i	$0.847719\pi$
$602$			6070.98i			0.411021i
$603$		0			0
$604$	7888.29			0.531407
$605$	2742.14	−	20247.8i	0.184271	−	1.36064i
$606$		0			0
$607$		−	264.526i		−	0.0176883i	−0.999961	−	0.00884415i	$-0.997185\pi$
$607$		−	264.526i		−	0.0176883i	0.999961	−	0.00884415i	$-0.00281522\pi$
$608$		−	1718.67i		−	0.114640i
$609$		0			0
$610$	13783.9	+	1866.74i	0.914905	+	0.123905i
$611$	−14210.0			−0.940875
$612$		0			0
$613$			29371.1i			1.93521i	0.252461	+	0.967607i	$0.418760\pi$
$613$			29371.1i			1.93521i	−0.252461	+	0.967607i	$0.581240\pi$
$614$	−10429.1			−0.685477
$615$		0			0
$616$	9662.68			0.632014
$617$		−	26226.1i		−	1.71122i	−0.517622	−	0.855609i	$-0.673183\pi$
$617$		−	26226.1i		−	1.71122i	0.517622	−	0.855609i	$-0.326817\pi$
$618$		0			0
$619$	8903.12			0.578105			0.289052	−	0.957313i	$-0.406660\pi$
$619$	8903.12			0.578105			0.289052	+	0.957313i	$0.406660\pi$
$620$	286.850	−	2118.08i	0.0185809	−	0.137200i
$621$		0			0
$622$		−	10711.1i		−	0.690476i
$623$		−	8575.72i		−	0.551491i
$624$		0			0
$625$	13414.2	+	8012.47i	0.858509	+	0.512798i
$626$	−3731.18			−0.238224
$627$		0			0
$628$		−	5076.31i		−	0.322558i
$629$	−19973.5			−1.26613
$630$		0			0
$631$	−14136.0			−0.891832			−0.445916	−	0.895075i	$-0.647122\pi$
$631$	−14136.0			−0.891832			−0.445916	+	0.895075i	$0.647122\pi$
$632$		−	15768.5i		−	0.992464i
$633$		0			0
$634$	8558.27			0.536108
$635$	−15673.8	−	2122.69i	−0.979519	−	0.132656i
$636$		0			0
$637$		−	1906.23i		−	0.118567i
$638$			9672.34i			0.600206i
$639$		0			0
$640$	1118.02	+	151.413i	0.0690528	+	0.00935177i
$641$	−17665.7			−1.08854			−0.544270	−	0.838910i	$-0.683193\pi$
$641$	−17665.7			−1.08854			−0.544270	+	0.838910i	$0.683193\pi$
$642$		0			0
$643$			10890.0i			0.667901i	0.942591	+	0.333951i	$0.108382\pi$
$643$			10890.0i			0.667901i	−0.942591	+	0.333951i	$0.891618\pi$
$644$	2861.27			0.175078
$645$		0			0
$646$	−3424.12			−0.208545
$647$			24281.0i			1.47540i	0.675128	+	0.737701i	$0.264089\pi$
$647$			24281.0i			1.47540i	−0.675128	+	0.737701i	$0.735911\pi$
$648$		0			0
$649$	−23314.5			−1.41013
$650$	−10344.1	−	2854.12i	−0.624196	−	0.172228i
$651$		0			0
$652$			2896.46i			0.173979i
$653$		−	1865.16i		−	0.111776i	−0.998437	−	0.0558878i	$-0.982201\pi$
$653$		−	1865.16i		−	0.111776i	0.998437	−	0.0558878i	$-0.0177989\pi$
$654$		0			0
$655$	3709.87	−	27393.4i	0.221308	−	1.63412i
$656$	12715.2			0.756775
$657$		0			0
$658$		−	5642.20i		−	0.334279i
$659$	−8327.14			−0.492230			−0.246115	−	0.969241i	$-0.579154\pi$
$659$	−8327.14			−0.492230			−0.246115	+	0.969241i	$0.579154\pi$
$660$		0			0
$661$	−20665.7			−1.21604			−0.608021	−	0.793921i	$-0.708036\pi$
$661$	−20665.7			−1.21604			−0.608021	+	0.793921i	$0.708036\pi$
$662$		−	21907.1i		−	1.28617i
$663$		0			0
$664$	−12575.8			−0.734991
$665$	−1008.55	−	136.588i	−0.0588121	−	0.00796488i
$666$		0			0
$667$			10183.1i			0.591140i
$668$			8395.00i			0.486246i
$669$		0			0
$670$	−1308.60	+	9662.60i	−0.0754561	+	0.557163i
$671$	31686.2			1.82300
$672$		0			0
$673$		−	1283.48i		−	0.0735136i	−0.999324	−	0.0367568i	$-0.988297\pi$
$673$		−	1283.48i		−	0.0735136i	0.999324	−	0.0367568i	$-0.0117027\pi$
$674$	−11659.7			−0.666344
$675$		0			0
$676$	2140.08			0.121762
$677$		−	13783.2i		−	0.782467i	−0.920291	−	0.391234i	$-0.872048\pi$
$677$		−	13783.2i		−	0.782467i	0.920291	−	0.391234i	$-0.127952\pi$
$678$		0			0
$679$	−1307.32			−0.0738886
$680$	−4397.42	+	32470.2i	−0.247990	+	1.83114i
$681$		0			0
$682$			7573.18i			0.425208i
$683$		−	10796.5i		−	0.604856i	−0.953172	−	0.302428i	$-0.902203\pi$
$683$		−	10796.5i		−	0.604856i	0.953172	−	0.302428i	$-0.0977972\pi$
$684$		0			0
$685$	−2375.28	−	321.682i	−0.132489	−	0.0179428i
$686$	756.884			0.0421253
$687$		0			0
$688$			11458.3i			0.634947i
$689$	−10972.4			−0.606699
$690$		0			0
$691$	−12082.4			−0.665173			−0.332587	−	0.943073i	$-0.607921\pi$
$691$	−12082.4			−0.665173			−0.332587	+	0.943073i	$0.607921\pi$
$692$		−	900.348i		−	0.0494597i
$693$		0			0
$694$	−23276.5			−1.27315
$695$	−1414.58	+	10445.2i	−0.0772060	+	0.570084i
$696$		0			0
$697$			52041.4i			2.82813i
$698$			1386.69i			0.0751962i
$699$		0			0
$700$	−728.605	+	2640.65i	−0.0393410	+	0.142582i
$701$	28753.5			1.54922			0.774610	−	0.632439i	$-0.217946\pi$
$701$	28753.5			1.54922			0.774610	+	0.632439i	$0.217946\pi$
$702$		0			0
$703$		−	2176.84i		−	0.116787i
$704$	29497.8			1.57917
$705$		0			0
$706$	−5622.95			−0.299749
$707$			11554.8i			0.614657i
$708$		0			0
$709$	−4577.21			−0.242455			−0.121228	−	0.992625i	$-0.538683\pi$
$709$	−4577.21			−0.242455			−0.121228	+	0.992625i	$0.538683\pi$
$710$	2542.34	+	344.308i	0.134384	+	0.0181995i
$711$		0			0
$712$		−	30090.4i		−	1.58383i
$713$			7973.07i			0.418785i
$714$		0			0
$715$	−24223.1	−	3280.52i	−1.26698	−	0.171587i
$716$	11531.7			0.601898
$717$		0			0
$718$		−	28788.8i		−	1.49636i
$719$	30875.9			1.60150			0.800749	−	0.599000i	$-0.204435\pi$
$719$	30875.9			1.60150			0.800749	+	0.599000i	$0.204435\pi$
$720$		0			0
$721$	−505.313			−0.0261010
$722$			14762.3i			0.760936i
$723$		0			0
$724$	9807.25			0.503430
$725$	−9397.88	−	2593.06i	−0.481419	−	0.132833i
$726$		0			0
$727$			520.090i			0.0265324i	0.999912	+	0.0132662i	$0.00422289\pi$
$727$			520.090i			0.0265324i	−0.999912	+	0.0132662i	$0.995777\pi$
$728$		−	6688.56i		−	0.340514i
$729$		0			0
$730$	−423.890	+	3129.98i	−0.0214916	+	0.158693i
$731$	−46897.1			−2.37285
$732$		0			0
$733$			393.396i			0.0198232i	0.999951	+	0.00991160i	$0.00315501\pi$
$733$			393.396i			0.0198232i	−0.999951	+	0.00991160i	$0.996845\pi$
$734$	−17803.8			−0.895301
$735$		0			0
$736$	17255.5			0.864191
$737$			22212.3i			1.11018i
$738$		0			0
$739$	9348.92			0.465366			0.232683	−	0.972553i	$-0.425250\pi$
$739$	9348.92			0.465366			0.232683	+	0.972553i	$0.425250\pi$
$740$	−5806.00	−	786.302i	−0.288423	−	0.0390609i
$741$		0			0
$742$		−	4356.69i		−	0.215552i
$743$			33710.8i			1.66451i	0.554394	+	0.832254i	$0.312950\pi$
$743$			33710.8i			1.66451i	−0.554394	+	0.832254i	$0.687050\pi$
$744$		0			0
$745$	2540.36	−	18757.8i	0.124928	−	0.922461i
$746$	−7995.44			−0.392405
$747$		0			0
$748$			20994.2i			1.02624i
$749$	−8417.83			−0.410655
$750$		0			0
$751$	−21116.6			−1.02604			−0.513019	−	0.858377i	$-0.671473\pi$
$751$	−21116.6			−1.02604			−0.513019	+	0.858377i	$0.671473\pi$
$752$		−	10649.0i		−	0.516396i
$753$		0			0
$754$	6695.24			0.323377
$755$	3780.67	−	27916.2i	0.182242	−	1.34566i
$756$		0			0
$757$		−	7385.25i		−	0.354586i	−0.984158	−	0.177293i	$-0.943266\pi$
$757$		−	7385.25i		−	0.354586i	0.984158	−	0.177293i	$-0.0567340\pi$
$758$			16520.3i			0.791616i
$759$		0			0
$760$	−3538.81	−	479.258i	−0.168903	−	0.0228744i
$761$	27682.0			1.31862			0.659311	−	0.751871i	$-0.270848\pi$
$761$	27682.0			1.31862			0.659311	+	0.751871i	$0.270848\pi$
$762$		0			0
$763$		−	10859.5i		−	0.515258i
$764$	−4968.12			−0.235262
$765$		0			0
$766$	−19697.9			−0.929132
$767$			16138.4i			0.759746i
$768$		0			0
$769$	22248.6			1.04331			0.521654	−	0.853157i	$-0.325315\pi$
$769$	22248.6			1.04331			0.521654	+	0.853157i	$0.325315\pi$
$770$	1302.56	−	9618.01i	0.0609624	−	0.450142i
$771$		0			0
$772$		−	16213.6i		−	0.755883i
$773$		−	11372.3i		−	0.529152i	−0.964365	−	0.264576i	$-0.914768\pi$
$773$		−	11372.3i		−	0.529152i	0.964365	−	0.264576i	$-0.0852321\pi$
$774$		0			0
$775$	−7358.29	−	2030.29i	−0.341055	−	0.0941036i
$776$	−4587.12			−0.212201
$777$		0			0
$778$			27804.0i			1.28126i
$779$	−5671.80			−0.260864
$780$		0			0
$781$	5844.32			0.267767
$782$		−	34378.1i		−	1.57207i
$783$		0			0
$784$	1428.53			0.0650754
$785$	−17964.7	−	2432.95i	−0.816802	−	0.110619i
$786$		0			0
$787$		−	36561.9i		−	1.65602i	−0.560710	−	0.828012i	$-0.689472\pi$
$787$		−	36561.9i		−	1.65602i	0.560710	−	0.828012i	$-0.310528\pi$
$788$			2829.48i			0.127914i
$789$		0			0
$790$	−15695.6	−	2125.64i	−0.706866	−	0.0957304i
$791$	−14566.3			−0.654763
$792$		0			0
$793$		−	21933.4i		−	0.982190i
$794$	28054.2			1.25391
$795$		0			0
$796$	3667.59			0.163309
$797$			7436.80i			0.330521i	0.986250	+	0.165260i	$0.0528465\pi$
$797$			7436.80i			0.330521i	−0.986250	+	0.165260i	$0.947154\pi$
$798$		0			0
$799$	43584.9			1.92982
$800$	−4393.99	+	15924.9i	−0.194189	+	0.703789i
$801$		0			0
$802$		−	13534.6i		−	0.595913i
$803$			7195.17i			0.316204i
$804$		0			0
$805$	1371.34	−	10125.9i	0.0600415	−	0.443342i
$806$	5242.20			0.229092
$807$		0			0
$808$			40543.4i			1.76524i
$809$	−30585.4			−1.32920			−0.664601	−	0.747198i	$-0.731399\pi$
$809$	−30585.4			−1.32920			−0.664601	+	0.747198i	$0.731399\pi$
$810$		0			0
$811$	23756.0			1.02859			0.514294	−	0.857614i	$-0.328054\pi$
$811$	23756.0			1.02859			0.514294	+	0.857614i	$0.328054\pi$
$812$		−	1709.17i		−	0.0738672i
$813$		0			0
$814$	20759.3			0.893873
$815$	10250.4	+	1388.21i	0.440560	+	0.0596647i
$816$		0			0
$817$		−	5111.14i		−	0.218869i
$818$			23391.2i			0.999821i
$819$		0			0
$820$	−2048.73	+	15127.7i	−0.0872496	+	0.644245i
$821$	33842.2			1.43861			0.719306	−	0.694694i	$-0.244460\pi$
$821$	33842.2			1.43861			0.719306	+	0.694694i	$0.244460\pi$
$822$		0			0
$823$			18730.9i			0.793340i	0.917961	+	0.396670i	$0.129834\pi$
$823$			18730.9i			0.793340i	−0.917961	+	0.396670i	$0.870166\pi$
$824$	−1773.04			−0.0749597
$825$		0			0
$826$	−6407.91			−0.269927
$827$			19107.1i			0.803409i	0.915769	+	0.401705i	$0.131582\pi$
$827$			19107.1i			0.803409i	−0.915769	+	0.401705i	$0.868418\pi$
$828$		0			0
$829$	−9942.59			−0.416551			−0.208275	−	0.978070i	$-0.566785\pi$
$829$	−9942.59			−0.416551			−0.208275	+	0.978070i	$0.566785\pi$
$830$	−1695.25	+	12517.6i	−0.0708953	+	0.523486i
$831$		0			0
$832$		−	20418.5i		−	0.850822i
$833$			5846.78i			0.243192i
$834$		0			0
$835$	29709.4	+	4023.52i	1.23130	+	0.166754i
$836$	−2288.08			−0.0946590
$837$		0			0
$838$		−	9480.75i		−	0.390820i
$839$	37144.9			1.52847			0.764233	−	0.644940i	$-0.223118\pi$
$839$	37144.9			1.52847			0.764233	+	0.644940i	$0.223118\pi$
$840$		0			0
$841$	−18306.2			−0.750591
$842$		−	8642.99i		−	0.353750i
$843$		0			0
$844$	−3453.62			−0.140851
$845$	1025.69	−	7573.62i	0.0417572	−	0.308332i
$846$		0			0
$847$		−	12792.8i		−	0.518969i
$848$		−	8222.78i		−	0.332985i
$849$		0			0
$850$	31727.3	+	8754.18i	1.28028	+	0.353254i
$851$	21855.4			0.880370
$852$		0			0
$853$			31377.2i			1.25948i	0.776807	+	0.629739i	$0.216838\pi$
$853$			31377.2i			1.25948i	−0.776807	+	0.629739i	$0.783162\pi$
$854$	8708.84			0.348958
$855$		0			0
$856$	−29536.4			−1.17936
$857$			24561.3i			0.978993i	0.872005	+	0.489496i	$0.162819\pi$
$857$			24561.3i			0.978993i	−0.872005	+	0.489496i	$0.837181\pi$
$858$		0			0
$859$	39819.1			1.58162			0.790809	−	0.612063i	$-0.209660\pi$
$859$	39819.1			1.58162			0.790809	+	0.612063i	$0.209660\pi$
$860$	−13632.3	−	1846.21i	−0.540532	−	0.0732038i
$861$		0			0
$862$			29588.9i			1.16914i
$863$			14702.2i			0.579919i	0.957039	+	0.289959i	$0.0936418\pi$
$863$			14702.2i			0.579919i	−0.957039	+	0.289959i	$0.906358\pi$
$864$		0			0
$865$	−3186.28	−	431.515i	−0.125245	−	0.0169618i
$866$	17195.0			0.674722
$867$		0			0
$868$		−	1338.24i		−	0.0523303i
$869$	−36081.0			−1.40847
$870$		0			0
$871$	15375.5			0.598138
$872$		−	38103.9i		−	1.47977i
$873$		0			0
$874$	3746.74			0.145006
$875$	8995.89	+	3844.09i	0.347562	+	0.148519i
$876$		0			0
$877$			7208.31i			0.277546i	0.990324	+	0.138773i	$0.0443158\pi$
$877$			7208.31i			0.277546i	−0.990324	+	0.138773i	$0.955684\pi$
$878$			2293.35i			0.0881512i
$879$		0			0
$880$	2458.44	−	18152.9i	0.0941749	−	0.695381i
$881$	−3789.00			−0.144898			−0.0724488	−	0.997372i	$-0.523081\pi$
$881$	−3789.00			−0.144898			−0.0724488	+	0.997372i	$0.523081\pi$
$882$		0			0
$883$			26953.7i			1.02725i	0.858014	+	0.513626i	$0.171698\pi$
$883$			26953.7i			1.02725i	−0.858014	+	0.513626i	$0.828302\pi$
$884$	14532.3			0.552912
$885$		0			0
$886$	6280.88			0.238160
$887$			37869.8i			1.43353i	0.697314	+	0.716766i	$0.254379\pi$
$887$			37869.8i			1.43353i	−0.697314	+	0.716766i	$0.745621\pi$
$888$		0			0
$889$	−9902.92			−0.373603
$890$	−29951.3	−	4056.29i	−1.12806	−	0.152772i
$891$		0			0
$892$			12772.9i			0.479449i
$893$			4750.15i			0.178004i
$894$		0			0
$895$	5526.86	−	40809.9i	0.206416	−	1.52416i
$896$	706.385			0.0263378
$897$		0			0
$898$		−	16489.6i		−	0.612767i
$899$	4762.69			0.176690
$900$		0			0
$901$	33654.6			1.24439
$902$		−	54088.8i		−	1.99663i
$903$		0			0
$904$	−51110.1			−1.88042
$905$	4700.38	−	34707.3i	0.172647	−	1.27482i
$906$		0			0
$907$			11717.5i			0.428968i	0.976728	+	0.214484i	$0.0688070\pi$
$907$			11717.5i			0.428968i	−0.976728	+	0.214484i	$0.931193\pi$
$908$			2917.66i			0.106636i
$909$		0			0
$910$	−6657.64	−	901.639i	−0.242526	−	0.0328451i
$911$	15909.2			0.578589			0.289294	−	0.957240i	$-0.406579\pi$
$911$	15909.2			0.578589			0.289294	+	0.957240i	$0.406579\pi$
$912$		0			0
$913$			28775.4i			1.04308i
$914$	24304.9			0.879578
$915$		0			0
$916$	4606.92			0.166176
$917$		−	17307.6i		−	0.623279i
$918$		0			0
$919$	32933.3			1.18212			0.591060	−	0.806628i	$-0.298710\pi$
$919$	32933.3			1.18212			0.591060	+	0.806628i	$0.298710\pi$
$920$	4811.75	−	35529.6i	0.172433	−	1.27324i
$921$		0			0
$922$			17531.2i			0.626203i
$923$		−	4045.47i		−	0.144267i
$924$		0			0
$925$	−5565.35	+	20170.2i	−0.197824	+	0.716965i
$926$	−16830.7			−0.597292
$927$		0			0
$928$		−	10307.5i		−	0.364612i
$929$	−30912.6			−1.09172			−0.545861	−	0.837876i	$-0.683797\pi$
$929$	−30912.6			−1.09172			−0.545861	+	0.837876i	$0.683797\pi$
$930$		0			0
$931$	−637.219			−0.0224318
$932$		−	7761.09i		−	0.272771i
$933$		0			0
$934$	−7247.29			−0.253896
$935$	74297.3	+	10062.0i	2.59870	+	0.351940i
$936$		0			0
$937$		−	45737.6i		−	1.59465i	−0.603553	−	0.797323i	$-0.706249\pi$
$937$		−	45737.6i		−	1.59465i	0.603553	−	0.797323i	$-0.293751\pi$
$938$			6104.97i			0.212510i
$939$		0			0
$940$	12669.5	+	1715.82i	0.439609	+	0.0595359i
$941$	2137.79			0.0740595			0.0370297	−	0.999314i	$-0.488210\pi$
$941$	2137.79			0.0740595			0.0370297	+	0.999314i	$0.488210\pi$
$942$		0			0
$943$		−	56944.8i		−	1.96647i
$944$	−12094.2			−0.416984
$945$		0			0
$946$	48742.1			1.67520
$947$		−	42513.2i		−	1.45881i	−0.684082	−	0.729405i	$-0.739797\pi$
$947$		−	42513.2i		−	1.45881i	0.684082	−	0.729405i	$-0.260203\pi$
$948$		0			0
$949$	4980.53			0.170363
$950$	−954.085	+	3457.84i	−0.0325838	+	0.118092i
$951$		0			0
$952$			20515.2i			0.698425i
$953$		−	9012.85i		−	0.306353i	−0.988199	−	0.153177i	$-0.951050\pi$
$953$		−	9012.85i		−	0.306353i	0.988199	−	0.153177i	$-0.0489504\pi$
$954$		0			0
$955$	−2381.10	+	17581.9i	−0.0806813	+	0.595745i
$956$	−2986.86			−0.101048
$957$		0			0
$958$			6420.15i			0.216520i
$959$	−1500.74			−0.0505332
$960$		0			0
$961$	−26061.9			−0.874826
$962$		−	14369.7i		−	0.481598i
$963$		0			0
$964$	−16583.1			−0.554053
$965$	−57379.1	−	7770.81i	−1.91409	−	0.259224i
$966$		0			0
$967$			29024.2i			0.965207i	0.875839	+	0.482604i	$0.160309\pi$
$967$			29024.2i			0.965207i	−0.875839	+	0.482604i	$0.839691\pi$
$968$		−	44887.4i		−	1.49043i
$969$		0			0
$970$	−618.358	+	4565.91i	−0.0204683	+	0.151137i
$971$	−12874.4			−0.425498			−0.212749	−	0.977107i	$-0.568242\pi$
$971$	−12874.4			−0.425498			−0.212749	+	0.977107i	$0.568242\pi$
$972$		0			0
$973$			6599.42i			0.217438i
$974$	4858.70			0.159839
$975$		0			0
$976$	16437.0			0.539072
$977$			15195.8i			0.497600i	0.968555	+	0.248800i	$0.0800362\pi$
$977$			15195.8i			0.497600i	−0.968555	+	0.248800i	$0.919964\pi$
$978$		0			0
$979$	−68851.9			−2.24772
$980$	−230.172	+	1699.57i	−0.00750262	+	0.0553988i
$981$		0			0
$982$		−	26099.5i		−	0.848134i
$983$			12042.2i			0.390728i	0.980731	+	0.195364i	$0.0625888\pi$
$983$			12042.2i			0.390728i	−0.980731	+	0.195364i	$0.937411\pi$
$984$		0			0
$985$	10013.4	+	1356.10i	0.323911	+	0.0438670i
$986$	−20535.7			−0.663275
$987$		0			0
$988$			1583.82i			0.0510001i
$989$	51315.8			1.64990
$990$		0			0
$991$	11490.7			0.368330			0.184165	−	0.982895i	$-0.441042\pi$
$991$	11490.7			0.368330			0.184165	+	0.982895i	$0.441042\pi$
$992$		−	8070.49i		−	0.258305i
$993$		0			0
$994$	1606.29			0.0512560
$995$	1757.79	−	12979.4i	0.0560057	−	0.413542i
$996$		0			0
$997$			4076.85i			0.129504i	0.997901	+	0.0647518i	$0.0206256\pi$
$997$			4076.85i			0.129504i	−0.997901	+	0.0647518i	$0.979374\pi$
$998$			3108.44i			0.0985931i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.4.d.b.64.4		10
3.2	odd	2		105.4.d.b.64.7	yes	10
5.2	odd	4		1575.4.a.bo.1.4		5
5.3	odd	4		1575.4.a.bp.1.2		5
5.4	even	2	inner	315.4.d.b.64.7		10
15.2	even	4		525.4.a.x.1.2		5
15.8	even	4		525.4.a.w.1.4		5
15.14	odd	2		105.4.d.b.64.4	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.d.b.64.4	✓	10	15.14	odd	2
105.4.d.b.64.7	yes	10	3.2	odd	2
315.4.d.b.64.4		10	1.1	even	1	trivial
315.4.d.b.64.7		10	5.4	even	2	inner
525.4.a.w.1.4		5	15.8	even	4
525.4.a.x.1.2		5	15.2	even	4
1575.4.a.bo.1.4		5	5.2	odd	4
1575.4.a.bp.1.2		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)

\(f(q)\)	\(=\)	\(q-2.20666i q^{2} +3.13065 q^{4} +(1.50045 - 11.0792i) q^{5} -7.00000i q^{7} -24.5616i q^{8} +O(q^{10})\)	\(q-2.20666i q^{2} +3.13065 q^{4} +(1.50045 - 11.0792i) q^{5} -7.00000i q^{7} -24.5616i q^{8} +(-24.4480 - 3.31098i) q^{10} -56.2010 q^{11} +38.9026i q^{13} -15.4466 q^{14} -29.1538 q^{16} -119.322i q^{17} +13.0045 q^{19} +(4.69738 - 34.6851i) q^{20} +124.016i q^{22} +130.565i q^{23} +(-120.497 - 33.2475i) q^{25} +85.8448 q^{26} -21.9146i q^{28} +77.9925 q^{29} +61.0660 q^{31} -132.160i q^{32} -263.303 q^{34} +(-77.5544 - 10.5031i) q^{35} -167.391i q^{37} -28.6964i q^{38} +(-272.122 - 36.8533i) q^{40} -436.142 q^{41} -393.030i q^{43} -175.946 q^{44} +288.112 q^{46} +365.271i q^{47} -49.0000 q^{49} +(-73.3659 + 265.897i) q^{50} +121.791i q^{52} +282.048i q^{53} +(-84.3266 + 622.662i) q^{55} -171.931 q^{56} -172.103i q^{58} +414.842 q^{59} -563.802 q^{61} -134.752i q^{62} -524.862 q^{64} +(431.009 + 58.3713i) q^{65} -395.230i q^{67} -373.556i q^{68} +(-23.1768 + 171.136i) q^{70} -103.990 q^{71} -128.026i q^{73} -369.376 q^{74} +40.7125 q^{76} +393.407i q^{77} +641.999 q^{79} +(-43.7437 + 323.000i) q^{80} +962.417i q^{82} -512.010i q^{83} +(-1321.99 - 179.037i) q^{85} -867.283 q^{86} +1380.38i q^{88} +1225.10 q^{89} +272.318 q^{91} +408.753i q^{92} +806.028 q^{94} +(19.5125 - 144.079i) q^{95} -186.760i q^{97} +108.126i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 54 q^{4} + 14 q^{5}+O(q^{10}) \) 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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