LMFDB - Embedded newform 855.2.c.e.514.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [855,2,Mod(514,855)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(855, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("855.514"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,0,-2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 285)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			514.5
Root			$0.403032 + 0.403032i$ of defining polynomial
Character	$\chi$	$=$	855.514
Dual form			855.2.c.e.514.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.48119i q^{2} -0.193937 q^{4} +(-1.67513 + 1.48119i) q^{5} +4.48119i q^{7} +2.67513i q^{8} +(-2.19394 - 2.48119i) q^{10} -3.67513 q^{11} -2.86907i q^{13} -6.63752 q^{14} -4.35026 q^{16} -6.15633i q^{17} +1.00000 q^{19} +(0.324869 - 0.287258i) q^{20} -5.44358i q^{22} +8.15633i q^{23} +(0.612127 - 4.96239i) q^{25} +4.24965 q^{26} -0.869067i q^{28} +4.63752 q^{29} -2.80606 q^{31} -1.09332i q^{32} +9.11871 q^{34} +(-6.63752 - 7.50659i) q^{35} -3.44358i q^{37} +1.48119i q^{38} +(-3.96239 - 4.48119i) q^{40} +5.59991 q^{41} +10.1441i q^{43} +0.712742 q^{44} -12.0811 q^{46} -3.84367i q^{47} -13.0811 q^{49} +(7.35026 + 0.906679i) q^{50} +0.556417i q^{52} -3.89446i q^{53} +(6.15633 - 5.44358i) q^{55} -11.9878 q^{56} +6.86907i q^{58} -9.53690 q^{59} -9.89446 q^{61} -4.15633i q^{62} -7.08110 q^{64} +(4.24965 + 4.80606i) q^{65} +8.70052i q^{67} +1.19394i q^{68} +(11.1187 - 9.83146i) q^{70} +2.00000 q^{71} +3.08840i q^{73} +5.10062 q^{74} -0.193937 q^{76} -16.4690i q^{77} -4.96239 q^{79} +(7.28726 - 6.44358i) q^{80} +8.29455i q^{82} +6.73084i q^{83} +(9.11871 + 10.3127i) q^{85} -15.0254 q^{86} -9.83146i q^{88} +11.4739 q^{89} +12.8568 q^{91} -1.58181i q^{92} +5.69323 q^{94} +(-1.67513 + 1.48119i) q^{95} +9.63023i q^{97} -19.3757i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{4} - 14 q^{10} - 12 q^{11} - 8 q^{14} - 6 q^{16} + 6 q^{19} + 12 q^{20} + 2 q^{25} - 8 q^{26} - 4 q^{29} - 16 q^{31} + 12 q^{34} - 8 q^{35} - 2 q^{40} - 20 q^{41} + 16 q^{44} - 8 q^{46} - 14 q^{49}+ \cdots - 32 q^{94}+O(q^{100}) $ 6 * q - 2 * q^4 - 14 * q^10 - 12 * q^11 - 8 * q^14 - 6 * q^16 + 6 * q^19 + 12 * q^20 + 2 * q^25 - 8 * q^26 - 4 * q^29 - 16 * q^31 + 12 * q^34 - 8 * q^35 - 2 * q^40 - 20 * q^41 + 16 * q^44 - 8 * q^46 - 14 * q^49 + 24 * q^50 + 16 * q^55 - 20 * q^56 - 12 * q^59 - 20 * q^61 + 22 * q^64 - 8 * q^65 + 24 * q^70 + 12 * q^71 + 44 * q^74 - 2 * q^76 - 8 * q^79 + 32 * q^80 + 12 * q^85 - 60 * q^86 + 32 * q^89 + 16 * q^91 - 32 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$			1.48119i			1.04736i	0.851914	+	0.523681i	$0.175442\pi$
$2$			1.48119i			1.04736i	−0.851914	+	0.523681i	$0.824558\pi$
$3$		0			0
$3$		0			0
$4$	−0.193937			−0.0969683
$5$	−1.67513	+	1.48119i	−0.749141	+	0.662410i
$5$	−1.67513	+	1.48119i	−0.749141	+	0.662410i
$6$		0			0
$7$			4.48119i			1.69373i	0.531806	+	0.846866i	$0.321514\pi$
$7$			4.48119i			1.69373i	−0.531806	+	0.846866i	$0.678486\pi$
$8$			2.67513i			0.945802i
$9$		0			0
$10$	−2.19394	−	2.48119i	−0.693784	−	0.784623i
$11$	−3.67513			−1.10809			−0.554047	−	0.832486i	$-0.686917\pi$
$11$	−3.67513			−1.10809			−0.554047	+	0.832486i	$0.686917\pi$
$12$		0			0
$13$		−	2.86907i		−	0.795736i	−0.917443	−	0.397868i	$-0.869750\pi$
$13$		−	2.86907i		−	0.795736i	0.917443	−	0.397868i	$-0.130250\pi$
$14$	−6.63752			−1.77395
$15$		0			0
$16$	−4.35026			−1.08757
$17$		−	6.15633i		−	1.49313i	−0.665314	−	0.746564i	$-0.731702\pi$
$17$		−	6.15633i		−	1.49313i	0.665314	−	0.746564i	$-0.268298\pi$
$18$		0			0
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	0.324869	−	0.287258i	0.0726429	−	0.0642328i
$21$		0			0
$22$		−	5.44358i		−	1.16058i
$23$			8.15633i			1.70071i	0.526208	+	0.850356i	$0.323613\pi$
$23$			8.15633i			1.70071i	−0.526208	+	0.850356i	$0.676387\pi$
$24$		0			0
$25$	0.612127	−	4.96239i	0.122425	−	0.992478i
$26$	4.24965			0.833424
$27$		0			0
$28$		−	0.869067i		−	0.164238i
$29$	4.63752			0.861166			0.430583	−	0.902551i	$-0.358308\pi$
$29$	4.63752			0.861166			0.430583	+	0.902551i	$0.358308\pi$
$30$		0			0
$31$	−2.80606			−0.503984			−0.251992	−	0.967729i	$-0.581086\pi$
$31$	−2.80606			−0.503984			−0.251992	+	0.967729i	$0.581086\pi$
$32$		−	1.09332i		−	0.193274i
$33$		0			0
$34$	9.11871			1.56385
$35$	−6.63752	−	7.50659i	−1.12195	−	1.26884i
$36$		0			0
$37$		−	3.44358i		−	0.566122i	−0.959102	−	0.283061i	$-0.908650\pi$
$37$		−	3.44358i		−	0.566122i	0.959102	−	0.283061i	$-0.0913498\pi$
$38$			1.48119i			0.240281i
$39$		0			0
$40$	−3.96239	−	4.48119i	−0.626509	−	0.708539i
$41$	5.59991			0.874559			0.437279	−	0.899326i	$-0.355942\pi$
$41$	5.59991			0.874559			0.437279	+	0.899326i	$0.355942\pi$
$42$		0			0
$43$			10.1441i			1.54696i	0.633820	+	0.773481i	$0.281486\pi$
$43$			10.1441i			1.54696i	−0.633820	+	0.773481i	$0.718514\pi$
$44$	0.712742			0.107450
$45$		0			0
$46$	−12.0811			−1.78126
$47$		−	3.84367i		−	0.560658i	−0.959904	−	0.280329i	$-0.909557\pi$
$47$		−	3.84367i		−	0.560658i	0.959904	−	0.280329i	$-0.0904435\pi$
$48$		0			0
$49$	−13.0811			−1.86873
$50$	7.35026	+	0.906679i	1.03948	+	0.128224i
$51$		0			0
$52$			0.556417i			0.0771612i
$53$		−	3.89446i		−	0.534945i	−0.963565	−	0.267473i	$-0.913812\pi$
$53$		−	3.89446i		−	0.534945i	0.963565	−	0.267473i	$-0.0861885\pi$
$54$		0			0
$55$	6.15633	−	5.44358i	0.830119	−	0.734013i
$56$	−11.9878			−1.60193
$57$		0			0
$58$			6.86907i			0.901953i
$59$	−9.53690			−1.24160			−0.620800	−	0.783969i	$-0.713192\pi$
$59$	−9.53690			−1.24160			−0.620800	+	0.783969i	$0.713192\pi$
$60$		0			0
$61$	−9.89446			−1.26686			−0.633428	−	0.773802i	$-0.718353\pi$
$61$	−9.89446			−1.26686			−0.633428	+	0.773802i	$0.718353\pi$
$62$		−	4.15633i		−	0.527854i
$63$		0			0
$64$	−7.08110			−0.885138
$65$	4.24965	+	4.80606i	0.527104	+	0.596119i
$66$		0			0
$67$			8.70052i			1.06294i	0.847078	+	0.531469i	$0.178360\pi$
$67$			8.70052i			1.06294i	−0.847078	+	0.531469i	$0.821640\pi$
$68$			1.19394i			0.144786i
$69$		0			0
$70$	11.1187	−	9.83146i	1.32894	−	1.17508i
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$		0			0
$73$			3.08840i			0.361469i	0.983532	+	0.180735i	$0.0578476\pi$
$73$			3.08840i			0.361469i	−0.983532	+	0.180735i	$0.942152\pi$
$74$	5.10062			0.592934
$75$		0			0
$76$	−0.193937			−0.0222460
$77$		−	16.4690i		−	1.87681i
$78$		0			0
$79$	−4.96239			−0.558312			−0.279156	−	0.960246i	$-0.590055\pi$
$79$	−4.96239			−0.558312			−0.279156	+	0.960246i	$0.590055\pi$
$80$	7.28726	−	6.44358i	0.814740	−	0.720414i
$81$		0			0
$82$			8.29455i			0.915980i
$83$			6.73084i			0.738806i	0.929269	+	0.369403i	$0.120438\pi$
$83$			6.73084i			0.738806i	−0.929269	+	0.369403i	$0.879562\pi$
$84$		0			0
$85$	9.11871	+	10.3127i	0.989063	+	1.11856i
$86$	−15.0254			−1.62023
$87$		0			0
$88$		−	9.83146i		−	1.04804i
$89$	11.4739			1.21623			0.608115	−	0.793849i	$-0.291926\pi$
$89$	11.4739			1.21623			0.608115	+	0.793849i	$0.291926\pi$
$90$		0			0
$91$	12.8568			1.34776
$92$		−	1.58181i		−	0.164915i
$93$		0			0
$94$	5.69323			0.587212
$95$	−1.67513	+	1.48119i	−0.171865	+	0.151967i
$96$		0			0
$97$			9.63023i			0.977801i	0.872339	+	0.488901i	$0.162602\pi$
$97$			9.63023i			0.977801i	−0.872339	+	0.488901i	$0.837398\pi$
$98$		−	19.3757i		−	1.95724i
$99$		0			0
$100$	−0.118714	+	0.962389i	−0.0118714	+	0.0962389i
$101$	−5.61213			−0.558427			−0.279214	−	0.960229i	$-0.590074\pi$
$101$	−5.61213			−0.558427			−0.279214	+	0.960229i	$0.590074\pi$
$102$		0			0
$103$			3.53690i			0.348502i	0.984701	+	0.174251i	$0.0557503\pi$
$103$			3.53690i			0.348502i	−0.984701	+	0.174251i	$0.944250\pi$
$104$	7.67513			0.752609
$105$		0			0
$106$	5.76845			0.560282
$107$			16.4387i			1.58919i	0.607143	+	0.794593i	$0.292315\pi$
$107$			16.4387i			1.58919i	−0.607143	+	0.794593i	$0.707685\pi$
$108$		0			0
$109$	12.3879			1.18654			0.593272	−	0.805002i	$-0.297836\pi$
$109$	12.3879			1.18654			0.593272	+	0.805002i	$0.297836\pi$
$110$	8.06300	+	9.11871i	0.768777	+	0.869435i
$111$		0			0
$112$		−	19.4944i		−	1.84204i
$113$			11.2447i			1.05781i	0.848680	+	0.528907i	$0.177398\pi$
$113$			11.2447i			1.05781i	−0.848680	+	0.528907i	$0.822602\pi$
$114$		0			0
$115$	−12.0811	−	13.6629i	−1.12657	−	1.27407i
$116$	−0.899385			−0.0835058
$117$		0			0
$118$		−	14.1260i		−	1.30040i
$119$	27.5877			2.52896
$120$		0			0
$121$	2.50659			0.227872
$122$		−	14.6556i		−	1.32686i
$123$		0			0
$124$	0.544198			0.0488705
$125$	6.32487	+	9.21933i	0.565713	+	0.824602i
$126$		0			0
$127$		−	11.8641i		−	1.05277i	−0.850246	−	0.526386i	$-0.823547\pi$
$127$		−	11.8641i		−	1.05277i	0.850246	−	0.526386i	$-0.176453\pi$
$128$		−	12.6751i		−	1.12033i
$129$		0			0
$130$	−7.11871	+	6.29455i	−0.624353	+	0.552069i
$131$	−1.54912			−0.135347			−0.0676737	−	0.997708i	$-0.521558\pi$
$131$	−1.54912			−0.135347			−0.0676737	+	0.997708i	$0.521558\pi$
$132$		0			0
$133$			4.48119i			0.388569i
$134$	−12.8872			−1.11328
$135$		0			0
$136$	16.4690			1.41220
$137$			17.0738i			1.45871i	0.684133	+	0.729357i	$0.260181\pi$
$137$			17.0738i			1.45871i	−0.684133	+	0.729357i	$0.739819\pi$
$138$		0			0
$139$	−5.61213			−0.476014			−0.238007	−	0.971263i	$-0.576494\pi$
$139$	−5.61213			−0.476014			−0.238007	+	0.971263i	$0.576494\pi$
$140$	1.28726	+	1.45580i	0.108793	+	0.123038i
$141$		0			0
$142$			2.96239i			0.248598i
$143$			10.5442i			0.881750i
$144$		0			0
$145$	−7.76845	+	6.86907i	−0.645135	+	0.570445i
$146$	−4.57452			−0.378590
$147$		0			0
$148$			0.667837i			0.0548958i
$149$	5.53690			0.453601			0.226800	−	0.973941i	$-0.427173\pi$
$149$	5.53690			0.453601			0.226800	+	0.973941i	$0.427173\pi$
$150$		0			0
$151$	0.0811024			0.00660002			0.00330001	−	0.999995i	$-0.498950\pi$
$151$	0.0811024			0.00660002			0.00330001	+	0.999995i	$0.498950\pi$
$152$			2.67513i			0.216982i
$153$		0			0
$154$	24.3938			1.96570
$155$	4.70052	−	4.15633i	0.377555	−	0.333844i
$156$		0			0
$157$		−	2.64974i		−	0.211472i	−0.994394	−	0.105736i	$-0.966280\pi$
$157$		−	2.64974i		−	0.211472i	0.994394	−	0.105736i	$-0.0337199\pi$
$158$		−	7.35026i		−	0.584755i
$159$		0			0
$160$	1.61942	+	1.83146i	0.128026	+	0.144789i
$161$	−36.5501			−2.88055
$162$		0			0
$163$			0.667837i			0.0523090i	0.999658	+	0.0261545i	$0.00832619\pi$
$163$			0.667837i			0.0523090i	−0.999658	+	0.0261545i	$0.991674\pi$
$164$	−1.08603			−0.0848045
$165$		0			0
$166$	−9.96968			−0.773797
$167$		−	10.4182i		−	0.806184i	−0.915160	−	0.403092i	$-0.867936\pi$
$167$		−	10.4182i		−	0.806184i	0.915160	−	0.403092i	$-0.132064\pi$
$168$		0			0
$169$	4.76845			0.366804
$170$	−15.2750	+	13.5066i	−1.17154	+	1.03591i
$171$		0			0
$172$		−	1.96731i		−	0.150006i
$173$			4.54420i			0.345489i	0.984967	+	0.172744i	$0.0552635\pi$
$173$			4.54420i			0.345489i	−0.984967	+	0.172744i	$0.944737\pi$
$174$		0			0
$175$	22.2374	+	2.74306i	1.68099	+	0.207356i
$176$	15.9878			1.20512
$177$		0			0
$178$			16.9951i			1.27383i
$179$	−15.0884			−1.12776			−0.563880	−	0.825857i	$-0.690692\pi$
$179$	−15.0884			−1.12776			−0.563880	+	0.825857i	$0.690692\pi$
$180$		0			0
$181$	−8.44851			−0.627973			−0.313986	−	0.949428i	$-0.601665\pi$
$181$	−8.44851			−0.627973			−0.313986	+	0.949428i	$0.601665\pi$
$182$			19.0435i			1.41160i
$183$		0			0
$184$	−21.8192			−1.60854
$185$	5.10062	+	5.76845i	0.375005	+	0.424105i
$186$		0			0
$187$			22.6253i			1.65453i
$188$			0.745429i			0.0543660i
$189$		0			0
$190$	−2.19394	−	2.48119i	−0.159165	−	0.180005i
$191$	13.5393			0.979667			0.489834	−	0.871816i	$-0.337057\pi$
$191$	13.5393			0.979667			0.489834	+	0.871816i	$0.337057\pi$
$192$		0			0
$193$			11.1817i			0.804878i	0.915447	+	0.402439i	$0.131837\pi$
$193$			11.1817i			0.804878i	−0.915447	+	0.402439i	$0.868163\pi$
$194$	−14.2642			−1.02411
$195$		0			0
$196$	2.53690			0.181207
$197$		−	7.24472i		−	0.516165i	−0.966123	−	0.258083i	$-0.916909\pi$
$197$		−	7.24472i		−	0.516165i	0.966123	−	0.258083i	$-0.0830906\pi$
$198$		0			0
$199$	26.8627			1.90425			0.952124	−	0.305712i	$-0.0988943\pi$
$199$	26.8627			1.90425			0.952124	+	0.305712i	$0.0988943\pi$
$200$	13.2750	+	1.63752i	0.938687	+	0.115790i
$201$		0			0
$202$		−	8.31265i		−	0.584876i
$203$			20.7816i			1.45858i
$204$		0			0
$205$	−9.38058	+	8.29455i	−0.655168	+	0.579317i
$206$	−5.23884			−0.365007
$207$		0			0
$208$			12.4812i			0.865415i
$209$	−3.67513			−0.254214
$210$		0			0
$211$	4.43866			0.305570			0.152785	−	0.988259i	$-0.451176\pi$
$211$	4.43866			0.305570			0.152785	+	0.988259i	$0.451176\pi$
$212$			0.755278i			0.0518727i
$213$		0			0
$214$	−24.3488			−1.66445
$215$	−15.0254	−	16.9927i	−1.02472	−	1.15889i
$216$		0			0
$217$		−	12.5745i		−	0.853614i
$218$			18.3488i			1.24274i
$219$		0			0
$220$	−1.19394	+	1.05571i	−0.0804952	+	0.0711759i
$221$	−17.6629			−1.18814
$222$		0			0
$223$		−	9.08840i		−	0.608604i	−0.952576	−	0.304302i	$-0.901577\pi$
$223$		−	9.08840i		−	0.608604i	0.952576	−	0.304302i	$-0.0984232\pi$
$224$	4.89938			0.327354
$225$		0			0
$226$	−16.6556			−1.10792
$227$		−	11.1939i		−	0.742968i	−0.928439	−	0.371484i	$-0.878849\pi$
$227$		−	11.1939i		−	0.742968i	0.928439	−	0.371484i	$-0.121151\pi$
$228$		0			0
$229$	23.6932			1.56569			0.782846	−	0.622215i	$-0.213767\pi$
$229$	23.6932			1.56569			0.782846	+	0.622215i	$0.213767\pi$
$230$	20.2374	−	17.8945i	1.33442	−	1.17993i
$231$		0			0
$232$			12.4060i			0.814492i
$233$		−	12.0508i		−	0.789473i	−0.918794	−	0.394737i	$-0.870836\pi$
$233$		−	12.0508i		−	0.789473i	0.918794	−	0.394737i	$-0.129164\pi$
$234$		0			0
$235$	5.69323	+	6.43866i	0.371385	+	0.420012i
$236$	1.84955			0.120396
$237$		0			0
$238$			40.8627i			2.64874i
$239$	13.9878			0.904794			0.452397	−	0.891817i	$-0.350569\pi$
$239$	13.9878			0.904794			0.452397	+	0.891817i	$0.350569\pi$
$240$		0			0
$241$	23.7743			1.53144			0.765720	−	0.643174i	$-0.222383\pi$
$241$	23.7743			1.53144			0.765720	+	0.643174i	$0.222383\pi$
$242$			3.71274i			0.238664i
$243$		0			0
$244$	1.91890			0.122845
$245$	21.9126	−	19.3757i	1.39994	−	1.23787i
$246$		0			0
$247$		−	2.86907i		−	0.182554i
$248$		−	7.50659i		−	0.476669i
$249$		0			0
$250$	−13.6556	+	9.36836i	−0.863657	+	0.592507i
$251$	−6.76353			−0.426910			−0.213455	−	0.976953i	$-0.568472\pi$
$251$	−6.76353			−0.426910			−0.213455	+	0.976953i	$0.568472\pi$
$252$		0			0
$253$		−	29.9756i		−	1.88455i
$254$	17.5731			1.10263
$255$		0			0
$256$	4.61213			0.288258
$257$			19.9551i			1.24476i	0.782713	+	0.622382i	$0.213835\pi$
$257$			19.9551i			1.24476i	−0.782713	+	0.622382i	$0.786165\pi$
$258$		0			0
$259$	15.4314			0.958858
$260$	−0.824162	−	0.932071i	−0.0511123	−	0.0578046i
$261$		0			0
$262$		−	2.29455i		−	0.141758i
$263$			5.14315i			0.317140i	0.987348	+	0.158570i	$0.0506884\pi$
$263$			5.14315i			0.317140i	−0.987348	+	0.158570i	$0.949312\pi$
$264$		0			0
$265$	5.76845	+	6.52373i	0.354353	+	0.400750i
$266$	−6.63752			−0.406972
$267$		0			0
$268$		−	1.68735i		−	0.103071i
$269$	−11.1368			−0.679023			−0.339512	−	0.940602i	$-0.610262\pi$
$269$	−11.1368			−0.679023			−0.339512	+	0.940602i	$0.610262\pi$
$270$		0			0
$271$	15.4763			0.940116			0.470058	−	0.882635i	$-0.344233\pi$
$271$	15.4763			0.940116			0.470058	+	0.882635i	$0.344233\pi$
$272$			26.7816i			1.62387i
$273$		0			0
$274$	−25.2896			−1.52780
$275$	−2.24965	+	18.2374i	−0.135659	+	1.09976i
$276$		0			0
$277$			12.6253i			0.758581i	0.925278	+	0.379290i	$0.123832\pi$
$277$			12.6253i			0.758581i	−0.925278	+	0.379290i	$0.876168\pi$
$278$		−	8.31265i		−	0.498560i
$279$		0			0
$280$	20.0811	−	17.7562i	1.20008	−	1.06114i
$281$	−2.66196			−0.158799			−0.0793995	−	0.996843i	$-0.525300\pi$
$281$	−2.66196			−0.158799			−0.0793995	+	0.996843i	$0.525300\pi$
$282$		0			0
$283$		−	1.63023i		−	0.0969068i	−0.998825	−	0.0484534i	$-0.984571\pi$
$283$		−	1.63023i		−	0.0969068i	0.998825	−	0.0484534i	$-0.0154292\pi$
$284$	−0.387873			−0.0230160
$285$		0			0
$286$	−15.6180			−0.923512
$287$			25.0943i			1.48127i
$288$		0			0
$289$	−20.9003			−1.22943
$290$	−10.1744	−	11.5066i	−0.597463	−	0.675690i
$291$		0			0
$292$		−	0.598953i		−	0.0350511i
$293$		−	15.3707i		−	0.897968i	−0.893540	−	0.448984i	$-0.851786\pi$
$293$		−	15.3707i		−	0.897968i	0.893540	−	0.448984i	$-0.148214\pi$
$294$		0			0
$295$	15.9756	−	14.1260i	0.930133	−	0.822448i
$296$	9.21203			0.535439
$297$		0			0
$298$			8.20123i			0.475085i
$299$	23.4010			1.35332
$300$		0			0
$301$	−45.4577			−2.62014
$302$			0.120128i			0.00691261i
$303$		0			0
$304$	−4.35026			−0.249505
$305$	16.5745	−	14.6556i	0.949054	−	0.839178i
$306$		0			0
$307$			18.3634i			1.04806i	0.851701	+	0.524028i	$0.175571\pi$
$307$			18.3634i			1.04806i	−0.851701	+	0.524028i	$0.824429\pi$
$308$			3.19394i			0.181991i
$309$		0			0
$310$	6.15633	+	6.96239i	0.349656	+	0.395437i
$311$	−11.4739			−0.650625			−0.325313	−	0.945607i	$-0.605470\pi$
$311$	−11.4739			−0.650625			−0.325313	+	0.945607i	$0.605470\pi$
$312$		0			0
$313$			4.57452i			0.258567i	0.991608	+	0.129283i	$0.0412677\pi$
$313$			4.57452i			0.258567i	−0.991608	+	0.129283i	$0.958732\pi$
$314$	3.92478			0.221488
$315$		0			0
$316$	0.962389			0.0541386
$317$			22.4083i			1.25858i	0.777171	+	0.629289i	$0.216654\pi$
$317$			22.4083i			1.25858i	−0.777171	+	0.629289i	$0.783346\pi$
$318$		0			0
$319$	−17.0435			−0.954252
$320$	11.8618	−	10.4885i	0.663093	−	0.586324i
$321$		0			0
$322$		−	54.1378i		−	3.01698i
$323$		−	6.15633i		−	0.342547i
$324$		0			0
$325$	−14.2374	−	1.75623i	−0.789750	−	0.0974183i
$326$	−0.989196			−0.0547865
$327$		0			0
$328$			14.9805i			0.827159i
$329$	17.2243			0.949604
$330$		0			0
$331$	−31.8700			−1.75173			−0.875867	−	0.482552i	$-0.839710\pi$
$331$	−31.8700			−1.75173			−0.875867	+	0.482552i	$0.839710\pi$
$332$		−	1.30536i		−	0.0716407i
$333$		0			0
$334$	15.4314			0.844367
$335$	−12.8872	−	14.5745i	−0.704101	−	0.796291i
$336$		0			0
$337$			12.3815i			0.674465i	0.941421	+	0.337233i	$0.109491\pi$
$337$			12.3815i			0.674465i	−0.941421	+	0.337233i	$0.890509\pi$
$338$			7.06300i			0.384177i
$339$		0			0
$340$	−1.76845	−	2.00000i	−0.0959078	−	0.108465i
$341$	10.3127			0.558461
$342$		0			0
$343$		−	27.2506i		−	1.47139i
$344$	−27.1368			−1.46312
$345$		0			0
$346$	−6.73084			−0.361852
$347$		−	29.7440i		−	1.59674i	−0.602166	−	0.798371i	$-0.705695\pi$
$347$		−	29.7440i		−	1.59674i	0.602166	−	0.798371i	$-0.294305\pi$
$348$		0			0
$349$	3.42548			0.183362			0.0916810	−	0.995788i	$-0.470776\pi$
$349$	3.42548			0.183362			0.0916810	+	0.995788i	$0.470776\pi$
$350$	−4.06300	+	32.9380i	−0.217177	+	1.76061i
$351$		0			0
$352$			4.01810i			0.214165i
$353$		−	7.48612i		−	0.398446i	−0.979954	−	0.199223i	$-0.936158\pi$
$353$		−	7.48612i		−	0.398446i	0.979954	−	0.199223i	$-0.0638418\pi$
$354$		0			0
$355$	−3.35026	+	2.96239i	−0.177813	+	0.157227i
$356$	−2.22521			−0.117936
$357$		0			0
$358$		−	22.3488i		−	1.18117i
$359$	−35.1632			−1.85584			−0.927920	−	0.372779i	$-0.878405\pi$
$359$	−35.1632			−1.85584			−0.927920	+	0.372779i	$0.878405\pi$
$360$		0			0
$361$	1.00000			0.0526316
$362$		−	12.5139i		−	0.657715i
$363$		0			0
$364$	−2.49341			−0.130690
$365$	−4.57452	−	5.17347i	−0.239441	−	0.270792i
$366$		0			0
$367$		−	2.14411i		−	0.111921i	−0.998433	−	0.0559607i	$-0.982178\pi$
$367$		−	2.14411i		−	0.111921i	0.998433	−	0.0559607i	$-0.0178222\pi$
$368$		−	35.4821i		−	1.84963i
$369$		0			0
$370$	−8.54420	+	7.55500i	−0.444192	+	0.392766i
$371$	17.4518			0.906054
$372$		0			0
$373$		−	36.4930i		−	1.88953i	−0.327743	−	0.944767i	$-0.606288\pi$
$373$		−	36.4930i		−	1.88953i	0.327743	−	0.944767i	$-0.393712\pi$
$374$	−33.5125			−1.73289
$375$		0			0
$376$	10.2823			0.530271
$377$		−	13.3054i		−	0.685261i
$378$		0			0
$379$	−2.00588			−0.103035			−0.0515176	−	0.998672i	$-0.516406\pi$
$379$	−2.00588			−0.103035			−0.0515176	+	0.998672i	$0.516406\pi$
$380$	0.324869	−	0.287258i	0.0166654	−	0.0147360i
$381$		0			0
$382$			20.0543i			1.02607i
$383$			18.2374i			0.931889i	0.884814	+	0.465945i	$0.154285\pi$
$383$			18.2374i			0.931889i	−0.884814	+	0.465945i	$0.845715\pi$
$384$		0			0
$385$	24.3938	+	27.5877i	1.24322	+	1.40600i
$386$	−16.5623			−0.842999
$387$		0			0
$388$		−	1.86765i		−	0.0948157i
$389$	13.2144			0.669997			0.334998	−	0.942219i	$-0.391264\pi$
$389$	13.2144			0.669997			0.334998	+	0.942219i	$0.391264\pi$
$390$		0			0
$391$	50.2130			2.53938
$392$		−	34.9937i		−	1.76745i
$393$		0			0
$394$	10.7308			0.540612
$395$	8.31265	−	7.35026i	0.418255	−	0.369832i
$396$		0			0
$397$		−	9.46168i		−	0.474868i	−0.971404	−	0.237434i	$-0.923694\pi$
$397$		−	9.46168i		−	0.474868i	0.971404	−	0.237434i	$-0.0763064\pi$
$398$			39.7889i			1.99444i
$399$		0			0
$400$	−2.66291	+	21.5877i	−0.133146	+	1.07938i
$401$	28.0240			1.39945			0.699725	−	0.714412i	$-0.253306\pi$
$401$	28.0240			1.39945			0.699725	+	0.714412i	$0.253306\pi$
$402$		0			0
$403$			8.05079i			0.401038i
$404$	1.08840			0.0541498
$405$		0			0
$406$	−30.7816			−1.52767
$407$			12.6556i			0.627316i
$408$		0			0
$409$	17.9756			0.888834			0.444417	−	0.895820i	$-0.353411\pi$
$409$	17.9756			0.888834			0.444417	+	0.895820i	$0.353411\pi$
$410$	−12.2858	−	13.8945i	−0.606755	−	0.686198i
$411$		0			0
$412$		−	0.685935i		−	0.0337936i
$413$		−	42.7367i		−	2.10294i
$414$		0			0
$415$	−9.96968	−	11.2750i	−0.489392	−	0.553470i
$416$	−3.13681			−0.153795
$417$		0			0
$418$		−	5.44358i		−	0.266254i
$419$	13.4377			0.656475			0.328237	−	0.944595i	$-0.393545\pi$
$419$	13.4377			0.656475			0.328237	+	0.944595i	$0.393545\pi$
$420$		0			0
$421$	−24.3634			−1.18740			−0.593701	−	0.804686i	$-0.702334\pi$
$421$	−24.3634			−1.18740			−0.593701	+	0.804686i	$0.702334\pi$
$422$			6.57452i			0.320042i
$423$		0			0
$424$	10.4182			0.505952
$425$	−30.5501	−	3.76845i	−1.48190	−	0.182797i
$426$		0			0
$427$		−	44.3390i		−	2.14571i
$428$		−	3.18806i		−	0.154101i
$429$		0			0
$430$	25.1695	−	22.2555i	1.21378	−	1.07326i
$431$	1.42548			0.0686632			0.0343316	−	0.999410i	$-0.489070\pi$
$431$	1.42548			0.0686632			0.0343316	+	0.999410i	$0.489070\pi$
$432$		0			0
$433$		−	1.65466i		−	0.0795180i	−0.999209	−	0.0397590i	$-0.987341\pi$
$433$		−	1.65466i		−	0.0795180i	0.999209	−	0.0397590i	$-0.0126590\pi$
$434$	18.6253			0.894043
$435$		0			0
$436$	−2.40246			−0.115057
$437$			8.15633i			0.390170i
$438$		0			0
$439$	26.3996			1.25999			0.629993	−	0.776601i	$-0.283058\pi$
$439$	26.3996			1.25999			0.629993	+	0.776601i	$0.283058\pi$
$440$	14.5623	+	16.4690i	0.694230	+	0.785128i
$441$		0			0
$442$		−	26.1622i		−	1.24441i
$443$		−	3.35614i		−	0.159455i	−0.996817	−	0.0797275i	$-0.974595\pi$
$443$		−	3.35614i		−	0.159455i	0.996817	−	0.0797275i	$-0.0254050\pi$
$444$		0			0
$445$	−19.2203	+	16.9951i	−0.911129	+	0.805644i
$446$	13.4617			0.637429
$447$		0			0
$448$		−	31.7318i		−	1.49919i
$449$	12.0122			0.566892			0.283446	−	0.958988i	$-0.408522\pi$
$449$	12.0122			0.566892			0.283446	+	0.958988i	$0.408522\pi$
$450$		0			0
$451$	−20.5804			−0.969093
$452$		−	2.18076i		−	0.102574i
$453$		0			0
$454$	16.5804			0.778156
$455$	−21.5369	+	19.0435i	−1.00967	+	0.892773i
$456$		0			0
$457$		−	31.5877i		−	1.47761i	−0.673919	−	0.738805i	$-0.735391\pi$
$457$		−	31.5877i		−	1.47761i	0.673919	−	0.738805i	$-0.264609\pi$
$458$			35.0943i			1.63985i
$459$		0			0
$460$	2.34297	+	2.64974i	0.109241	+	0.123545i
$461$	−5.07381			−0.236311			−0.118155	−	0.992995i	$-0.537698\pi$
$461$	−5.07381			−0.236311			−0.118155	+	0.992995i	$0.537698\pi$
$462$		0			0
$463$		−	14.2701i		−	0.663188i	−0.943422	−	0.331594i	$-0.892414\pi$
$463$		−	14.2701i		−	0.663188i	0.943422	−	0.331594i	$-0.107586\pi$
$464$	−20.1744			−0.936574
$465$		0			0
$466$	17.8496			0.826865
$467$		−	32.3839i		−	1.49855i	−0.662260	−	0.749274i	$-0.730403\pi$
$467$		−	32.3839i		−	1.49855i	0.662260	−	0.749274i	$-0.269597\pi$
$468$		0			0
$469$	−38.9887			−1.80033
$470$	−9.53690	+	8.43278i	−0.439905	+	0.388975i
$471$		0			0
$472$		−	25.5125i		−	1.17431i
$473$		−	37.2809i		−	1.71418i
$474$		0			0
$475$	0.612127	−	4.96239i	0.0280863	−	0.227690i
$476$	−5.35026			−0.245229
$477$		0			0
$478$			20.7186i			0.947648i
$479$	−7.28726			−0.332963			−0.166482	−	0.986045i	$-0.553241\pi$
$479$	−7.28726			−0.332963			−0.166482	+	0.986045i	$0.553241\pi$
$480$		0			0
$481$	−9.87987			−0.450483
$482$			35.2144i			1.60397i
$483$		0			0
$484$	−0.486119			−0.0220963
$485$	−14.2642	−	16.1319i	−0.647706	−	0.732511i
$486$		0			0
$487$			37.5731i			1.70260i	0.524679	+	0.851300i	$0.324185\pi$
$487$			37.5731i			1.70260i	−0.524679	+	0.851300i	$0.675815\pi$
$488$		−	26.4690i		−	1.19819i
$489$		0			0
$490$	28.6991	+	32.4568i	1.29649	+	1.46625i
$491$	−23.5901			−1.06460			−0.532302	−	0.846554i	$-0.678673\pi$
$491$	−23.5901			−1.06460			−0.532302	+	0.846554i	$0.678673\pi$
$492$		0			0
$493$		−	28.5501i		−	1.28583i
$494$	4.24965			0.191201
$495$		0			0
$496$	12.2071			0.548115
$497$			8.96239i			0.402018i
$498$		0			0
$499$	25.7137			1.15110			0.575552	−	0.817765i	$-0.304787\pi$
$499$	25.7137			1.15110			0.575552	+	0.817765i	$0.304787\pi$
$500$	−1.22662	−	1.78797i	−0.0548563	−	0.0799602i
$501$		0			0
$502$		−	10.0181i		−	0.447130i
$503$			0.0956908i			0.00426664i	0.999998	+	0.00213332i	$0.000679058\pi$
$503$			0.0956908i			0.00426664i	−0.999998	+	0.00213332i	$0.999321\pi$
$504$		0			0
$505$	9.40105	−	8.31265i	0.418341	−	0.369908i
$506$	44.3996			1.97380
$507$		0			0
$508$			2.30089i			0.102086i
$509$	23.0010			1.01950			0.509750	−	0.860323i	$-0.329738\pi$
$509$	23.0010			1.01950			0.509750	+	0.860323i	$0.329738\pi$
$510$		0			0
$511$	−13.8397			−0.612233
$512$		−	18.5188i		−	0.818423i
$513$		0			0
$514$	−29.5574			−1.30372
$515$	−5.23884	−	5.92478i	−0.230851	−	0.261077i
$516$		0			0
$517$			14.1260i			0.621261i
$518$			22.8568i			1.00427i
$519$		0			0
$520$	−12.8568	+	11.3684i	−0.563810	+	0.498536i
$521$	−14.2398			−0.623857			−0.311928	−	0.950106i	$-0.600975\pi$
$521$	−14.2398			−0.623857			−0.311928	+	0.950106i	$0.600975\pi$
$522$		0			0
$523$			17.9756i			0.786016i	0.919535	+	0.393008i	$0.128566\pi$
$523$			17.9756i			0.786016i	−0.919535	+	0.393008i	$0.871434\pi$
$524$	0.300432			0.0131244
$525$		0			0
$526$	−7.61801			−0.332161
$527$			17.2750i			0.752513i
$528$		0			0
$529$	−43.5256			−1.89242
$530$	−9.66291	+	8.54420i	−0.419730	+	0.371136i
$531$		0			0
$532$		−	0.869067i		−	0.0376789i
$533$		−	16.0665i		−	0.695918i
$534$		0			0
$535$	−24.3488	−	27.5369i	−1.05269	−	1.19052i
$536$	−23.2750			−1.00533
$537$		0			0
$538$		−	16.4958i		−	0.711184i
$539$	48.0748			2.07073
$540$		0			0
$541$	−27.1490			−1.16723			−0.583614	−	0.812031i	$-0.698362\pi$
$541$	−27.1490			−1.16723			−0.583614	+	0.812031i	$0.698362\pi$
$542$			22.9234i			0.984643i
$543$		0			0
$544$	−6.73084			−0.288582
$545$	−20.7513	+	18.3488i	−0.888888	+	0.785978i
$546$		0			0
$547$			34.5256i			1.47621i	0.674686	+	0.738105i	$0.264279\pi$
$547$			34.5256i			1.47621i	−0.674686	+	0.738105i	$0.735721\pi$
$548$		−	3.31124i		−	0.141449i
$549$		0			0
$550$	−27.0132	−	3.33216i	−1.15185	−	0.142084i
$551$	4.63752			0.197565
$552$		0			0
$553$		−	22.2374i		−	0.945632i
$554$	−18.7005			−0.794509
$555$		0			0
$556$	1.08840			0.0461583
$557$			21.6873i			0.918922i	0.888198	+	0.459461i	$0.151957\pi$
$557$			21.6873i			0.918922i	−0.888198	+	0.459461i	$0.848043\pi$
$558$		0			0
$559$	29.1041			1.23097
$560$	28.8749	+	32.6556i	1.22019	+	1.37995i
$561$		0			0
$562$		−	3.94288i		−	0.166320i
$563$		−	8.80606i		−	0.371131i	−0.982632	−	0.185566i	$-0.940588\pi$
$563$		−	8.80606i		−	0.371131i	0.982632	−	0.185566i	$-0.0594117\pi$
$564$		0			0
$565$	−16.6556	−	18.8364i	−0.700707	−	0.792452i
$566$	2.41468			0.101497
$567$		0			0
$568$			5.35026i			0.224492i
$569$	−26.5379			−1.11252			−0.556262	−	0.831007i	$-0.687765\pi$
$569$	−26.5379			−1.11252			−0.556262	+	0.831007i	$0.687765\pi$
$570$		0			0
$571$	31.0376			1.29888			0.649442	−	0.760411i	$-0.275003\pi$
$571$	31.0376			1.29888			0.649442	+	0.760411i	$0.275003\pi$
$572$		−	2.04491i		−	0.0855018i
$573$		0			0
$574$	−37.1695			−1.55142
$575$	40.4749	+	4.99271i	1.68792	+	0.208210i
$576$		0			0
$577$			23.3357i			0.971477i	0.874104	+	0.485738i	$0.161449\pi$
$577$			23.3357i			0.971477i	−0.874104	+	0.485738i	$0.838551\pi$
$578$		−	30.9575i		−	1.28766i
$579$		0			0
$580$	1.50659	−	1.33216i	0.0625576	−	0.0553151i
$581$	−30.1622			−1.25134
$582$		0			0
$583$			14.3127i			0.592769i
$584$	−8.26187			−0.341878
$585$		0			0
$586$	22.7670			0.940498
$587$			19.4168i			0.801416i	0.916206	+	0.400708i	$0.131236\pi$
$587$			19.4168i			0.801416i	−0.916206	+	0.400708i	$0.868764\pi$
$588$		0			0
$589$	−2.80606			−0.115622
$590$	20.9234	+	23.6629i	0.861401	+	0.974187i
$591$		0			0
$592$			14.9805i			0.615694i
$593$			6.21108i			0.255058i	0.991835	+	0.127529i	$0.0407047\pi$
$593$			6.21108i			0.255058i	−0.991835	+	0.127529i	$0.959295\pi$
$594$		0			0
$595$	−46.2130	+	40.8627i	−1.89455	+	1.67521i
$596$	−1.07381			−0.0439849
$597$		0			0
$598$			34.6615i			1.41741i
$599$	30.4993			1.24617			0.623084	−	0.782155i	$-0.285880\pi$
$599$	30.4993			1.24617			0.623084	+	0.782155i	$0.285880\pi$
$600$		0			0
$601$	16.8218			0.686175			0.343088	−	0.939303i	$-0.388527\pi$
$601$	16.8218			0.686175			0.343088	+	0.939303i	$0.388527\pi$
$602$		−	67.3317i		−	2.74424i
$603$		0			0
$604$	−0.0157287			−0.000639993
$605$	−4.19886	+	3.71274i	−0.170708	+	0.150944i
$606$		0			0
$607$			37.7645i			1.53281i	0.642356	+	0.766407i	$0.277957\pi$
$607$			37.7645i			1.53281i	−0.642356	+	0.766407i	$0.722043\pi$
$608$		−	1.09332i		−	0.0443400i
$609$		0			0
$610$	21.7078	+	24.5501i	0.878924	+	0.994004i
$611$	−11.0278			−0.446136
$612$		0			0
$613$		−	25.7235i		−	1.03896i	−0.854481	−	0.519482i	$-0.826125\pi$
$613$		−	25.7235i		−	1.03896i	0.854481	−	0.519482i	$-0.173875\pi$
$614$	−27.1998			−1.09770
$615$		0			0
$616$	44.0567			1.77509
$617$			9.31994i			0.375207i	0.982245	+	0.187603i	$0.0600720\pi$
$617$			9.31994i			0.375207i	−0.982245	+	0.187603i	$0.939928\pi$
$618$		0			0
$619$	−33.9610			−1.36501			−0.682503	−	0.730882i	$-0.739109\pi$
$619$	−33.9610			−1.36501			−0.682503	+	0.730882i	$0.739109\pi$
$620$	−0.911603	+	0.806063i	−0.0366109	+	0.0323723i
$621$		0			0
$622$		−	16.9951i		−	0.681440i
$623$			51.4168i			2.05997i
$624$		0			0
$625$	−24.2506	−	6.07522i	−0.970024	−	0.243009i
$626$	−6.77575			−0.270813
$627$		0			0
$628$			0.513881i			0.0205061i
$629$	−21.1998			−0.845292
$630$		0			0
$631$	31.3620			1.24850			0.624251	−	0.781224i	$-0.285404\pi$
$631$	31.3620			1.24850			0.624251	+	0.781224i	$0.285404\pi$
$632$		−	13.2750i		−	0.528053i
$633$		0			0
$634$	−33.1911			−1.31819
$635$	17.5731	+	19.8740i	0.697367	+	0.788675i
$636$		0			0
$637$			37.5306i			1.48702i
$638$		−	25.2447i		−	0.999448i
$639$		0			0
$640$	18.7743	+	21.2325i	0.742121	+	0.839288i
$641$	13.5853			0.536588			0.268294	−	0.963337i	$-0.413540\pi$
$641$	13.5853			0.536588			0.268294	+	0.963337i	$0.413540\pi$
$642$		0			0
$643$		−	41.0557i		−	1.61908i	−0.587065	−	0.809540i	$-0.699717\pi$
$643$		−	41.0557i		−	1.61908i	0.587065	−	0.809540i	$-0.300283\pi$
$644$	7.08840			0.279322
$645$		0			0
$646$	9.11871			0.358771
$647$		−	16.2170i		−	0.637554i	−0.947830	−	0.318777i	$-0.896728\pi$
$647$		−	16.2170i		−	0.637554i	0.947830	−	0.318777i	$-0.103272\pi$
$648$		0			0
$649$	35.0494			1.37581
$650$	2.60132	−	21.0884i	0.102032	−	0.827155i
$651$		0			0
$652$		−	0.129518i		−	0.00507231i
$653$		−	8.44263i		−	0.330386i	−0.986261	−	0.165193i	$-0.947175\pi$
$653$		−	8.44263i		−	0.330386i	0.986261	−	0.165193i	$-0.0528246\pi$
$654$		0			0
$655$	2.59498	−	2.29455i	0.101394	−	0.0896556i
$656$	−24.3611			−0.951140
$657$		0			0
$658$			25.5125i			0.994579i
$659$	−5.71179			−0.222500			−0.111250	−	0.993792i	$-0.535485\pi$
$659$	−5.71179			−0.222500			−0.111250	+	0.993792i	$0.535485\pi$
$660$		0			0
$661$	−12.5139			−0.486734			−0.243367	−	0.969934i	$-0.578252\pi$
$661$	−12.5139			−0.486734			−0.243367	+	0.969934i	$0.578252\pi$
$662$		−	47.2057i		−	1.83470i
$663$		0			0
$664$	−18.0059			−0.698764
$665$	−6.63752	−	7.50659i	−0.257392	−	0.291093i
$666$		0			0
$667$			37.8251i			1.46459i
$668$			2.02047i			0.0781743i
$669$		0			0
$670$	21.5877	−	19.0884i	0.834005	−	0.737449i
$671$	36.3634			1.40379
$672$		0			0
$673$			27.7807i			1.07087i	0.844578	+	0.535433i	$0.179852\pi$
$673$			27.7807i			1.07087i	−0.844578	+	0.535433i	$0.820148\pi$
$674$	−18.3395			−0.706410
$675$		0			0
$676$	−0.924777			−0.0355684
$677$			41.3923i			1.59084i	0.606061	+	0.795418i	$0.292749\pi$
$677$			41.3923i			1.59084i	−0.606061	+	0.795418i	$0.707251\pi$
$678$		0			0
$679$	−43.1549			−1.65613
$680$	−27.5877	+	24.3938i	−1.05794	+	0.935458i
$681$		0			0
$682$			15.2750i			0.584911i
$683$		−	13.9902i		−	0.535318i	−0.963514	−	0.267659i	$-0.913750\pi$
$683$		−	13.9902i		−	0.535318i	0.963514	−	0.267659i	$-0.0862501\pi$
$684$		0			0
$685$	−25.2896	−	28.6009i	−0.966267	−	1.09278i
$686$	40.3634			1.54108
$687$		0			0
$688$		−	44.1295i		−	1.68242i
$689$	−11.1735			−0.425675
$690$		0			0
$691$	25.0640			0.953478			0.476739	−	0.879045i	$-0.341819\pi$
$691$	25.0640			0.953478			0.476739	+	0.879045i	$0.341819\pi$
$692$		−	0.881286i		−	0.0335015i
$693$		0			0
$694$	44.0567			1.67237
$695$	9.40105	−	8.31265i	0.356602	−	0.315317i
$696$		0			0
$697$		−	34.4749i		−	1.30583i
$698$			5.07381i			0.192046i
$699$		0			0
$700$	−4.31265	−	0.531980i	−0.163003	−	0.0201069i
$701$	−5.62672			−0.212518			−0.106259	−	0.994338i	$-0.533887\pi$
$701$	−5.62672			−0.212518			−0.106259	+	0.994338i	$0.533887\pi$
$702$		0			0
$703$		−	3.44358i		−	0.129877i
$704$	26.0240			0.980816
$705$		0			0
$706$	11.0884			0.417317
$707$		−	25.1490i		−	0.945827i
$708$		0			0
$709$	37.8653			1.42206			0.711030	−	0.703161i	$-0.248229\pi$
$709$	37.8653			1.42206			0.711030	+	0.703161i	$0.248229\pi$
$710$	−4.38787	−	4.96239i	−0.164674	−	0.186235i
$711$		0			0
$712$			30.6942i			1.15031i
$713$		−	22.8872i		−	0.857131i
$714$		0			0
$715$	−15.6180	−	17.6629i	−0.584080	−	0.660555i
$716$	2.92619			0.109357
$717$		0			0
$718$		−	52.0835i		−	1.94374i
$719$	−20.8749			−0.778504			−0.389252	−	0.921131i	$-0.627266\pi$
$719$	−20.8749			−0.778504			−0.389252	+	0.921131i	$0.627266\pi$
$720$		0			0
$721$	−15.8496			−0.590268
$722$			1.48119i			0.0551243i
$723$		0			0
$724$	1.63847			0.0608934
$725$	2.83875	−	23.0132i	0.105429	−	0.854688i
$726$		0			0
$727$		−	3.34392i		−	0.124019i	−0.998076	−	0.0620096i	$-0.980249\pi$
$727$		−	3.34392i		−	0.124019i	0.998076	−	0.0620096i	$-0.0197509\pi$
$728$			34.3938i			1.27472i
$729$		0			0
$730$	7.66291	−	6.77575i	0.283617	−	0.250782i
$731$	62.4504			2.30981
$732$		0			0
$733$			31.0884i			1.14828i	0.818759	+	0.574138i	$0.194663\pi$
$733$			31.0884i			1.14828i	−0.818759	+	0.574138i	$0.805337\pi$
$734$	3.17584			0.117222
$735$		0			0
$736$	8.91748			0.328703
$737$		−	31.9756i		−	1.17783i
$738$		0			0
$739$	−3.13918			−0.115477			−0.0577383	−	0.998332i	$-0.518389\pi$
$739$	−3.13918			−0.115477			−0.0577383	+	0.998332i	$0.518389\pi$
$740$	−0.989196	−	1.11871i	−0.0363636	−	0.0411247i
$741$		0			0
$742$			25.8496i			0.948967i
$743$		−	6.48944i		−	0.238075i	−0.992890	−	0.119037i	$-0.962019\pi$
$743$		−	6.48944i		−	0.238075i	0.992890	−	0.119037i	$-0.0379808\pi$
$744$		0			0
$745$	−9.27504	+	8.20123i	−0.339811	+	0.300470i
$746$	54.0532			1.97903
$747$		0			0
$748$		−	4.38787i		−	0.160437i
$749$	−73.6648			−2.69165
$750$		0			0
$751$	24.6458			0.899337			0.449668	−	0.893196i	$-0.351542\pi$
$751$	24.6458			0.899337			0.449668	+	0.893196i	$0.351542\pi$
$752$			16.7210i			0.609752i
$753$		0			0
$754$	19.7078			0.717716
$755$	−0.135857	+	0.120128i	−0.00494435	+	0.00437192i
$756$		0			0
$757$		−	37.3766i		−	1.35848i	−0.733918	−	0.679238i	$-0.762310\pi$
$757$		−	37.3766i		−	1.35848i	0.733918	−	0.679238i	$-0.237690\pi$
$758$		−	2.97110i		−	0.107915i
$759$		0			0
$760$	−3.96239	−	4.48119i	−0.143731	−	0.162550i
$761$	−5.64832			−0.204752			−0.102376	−	0.994746i	$-0.532644\pi$
$761$	−5.64832			−0.204752			−0.102376	+	0.994746i	$0.532644\pi$
$762$		0			0
$763$			55.5125i			2.00969i
$764$	−2.62576			−0.0949967
$765$		0			0
$766$	−27.0132			−0.976026
$767$			27.3620i			0.987985i
$768$		0			0
$769$	10.2520			0.369697			0.184849	−	0.982767i	$-0.440821\pi$
$769$	10.2520			0.369697			0.184849	+	0.982767i	$0.440821\pi$
$770$	−40.8627	+	36.1319i	−1.47259	+	1.30210i
$771$		0			0
$772$		−	2.16854i		−	0.0780476i
$773$			13.1939i			0.474553i	0.971442	+	0.237276i	$0.0762547\pi$
$773$			13.1939i			0.474553i	−0.971442	+	0.237276i	$0.923745\pi$
$774$		0			0
$775$	−1.71767	+	13.9248i	−0.0617004	+	0.500193i
$776$	−25.7621			−0.924806
$777$		0			0
$778$			19.5731i			0.701730i
$779$	5.59991			0.200638
$780$		0			0
$781$	−7.35026			−0.263013
$782$			74.3752i			2.65965i
$783$		0			0
$784$	56.9062			2.03236
$785$	3.92478	+	4.43866i	0.140081	+	0.158423i
$786$		0			0
$787$			14.6497i			0.522207i	0.965311	+	0.261103i	$0.0840864\pi$
$787$			14.6497i			0.522207i	−0.965311	+	0.261103i	$0.915914\pi$
$788$			1.40502i			0.0500516i
$789$		0			0
$790$	10.8872	+	12.3127i	0.387348	+	0.438064i
$791$	−50.3898			−1.79165
$792$		0			0
$793$			28.3879i			1.00808i
$794$	14.0146			0.497359
$795$		0			0
$796$	−5.20967			−0.184652
$797$		−	36.7426i		−	1.30149i	−0.759296	−	0.650745i	$-0.774457\pi$
$797$		−	36.7426i		−	1.30149i	0.759296	−	0.650745i	$-0.225543\pi$
$798$		0			0
$799$	−23.6629			−0.837134
$800$	−5.42548	−	0.669251i	−0.191820	−	0.0236616i
$801$		0			0
$802$			41.5090i			1.46573i
$803$		−	11.3503i		−	0.400542i
$804$		0			0
$805$	61.2262	−	54.1378i	2.15794	−	1.90811i
$806$	−11.9248			−0.420032
$807$		0			0
$808$		−	15.0132i		−	0.528162i
$809$	14.3127			0.503206			0.251603	−	0.967831i	$-0.419042\pi$
$809$	14.3127			0.503206			0.251603	+	0.967831i	$0.419042\pi$
$810$		0			0
$811$	0.625301			0.0219573			0.0109786	−	0.999940i	$-0.496505\pi$
$811$	0.625301			0.0219573			0.0109786	+	0.999940i	$0.496505\pi$
$812$		−	4.03032i		−	0.141436i
$813$		0			0
$814$	−18.7454			−0.657027
$815$	−0.989196	−	1.11871i	−0.0346500	−	0.0391868i
$816$		0			0
$817$			10.1441i			0.354897i
$818$			26.6253i			0.930932i
$819$		0			0
$820$	1.81924	−	1.60862i	0.0635305	−	0.0561753i
$821$	14.8510			0.518302			0.259151	−	0.965837i	$-0.416557\pi$
$821$	14.8510			0.518302			0.259151	+	0.965837i	$0.416557\pi$
$822$		0			0
$823$		−	54.0181i		−	1.88295i	−0.337079	−	0.941476i	$-0.609439\pi$
$823$		−	54.0181i		−	1.88295i	0.337079	−	0.941476i	$-0.390561\pi$
$824$	−9.46168			−0.329613
$825$		0			0
$826$	63.3014			2.20254
$827$		−	5.32979i		−	0.185335i	−0.995697	−	0.0926675i	$-0.970461\pi$
$827$		−	5.32979i		−	0.185335i	0.995697	−	0.0926675i	$-0.0295394\pi$
$828$		0			0
$829$	26.5599			0.922464			0.461232	−	0.887279i	$-0.347408\pi$
$829$	26.5599			0.922464			0.461232	+	0.887279i	$0.347408\pi$
$830$	16.7005	−	14.7670i	0.579684	−	0.512571i
$831$		0			0
$832$			20.3162i			0.704336i
$833$			80.5315i			2.79025i
$834$		0			0
$835$	15.4314	+	17.4518i	0.534024	+	0.603946i
$836$	0.712742			0.0246507
$837$		0			0
$838$			19.9038i			0.687567i
$839$	−9.07381			−0.313263			−0.156631	−	0.987657i	$-0.550063\pi$
$839$	−9.07381			−0.313263			−0.156631	+	0.987657i	$0.550063\pi$
$840$		0			0
$841$	−7.49341			−0.258394
$842$		−	36.0870i		−	1.24364i
$843$		0			0
$844$	−0.860818			−0.0296306
$845$	−7.98778	+	7.06300i	−0.274788	+	0.242975i
$846$		0			0
$847$			11.2325i			0.385953i
$848$			16.9419i			0.581788i
$849$		0			0
$850$	5.58181	−	45.2506i	0.191454	−	1.55208i
$851$	28.0870			0.962809
$852$		0			0
$853$		−	7.19982i		−	0.246517i	−0.992375	−	0.123259i	$-0.960666\pi$
$853$		−	7.19982i		−	0.246517i	0.992375	−	0.123259i	$-0.0393344\pi$
$854$	65.6747			2.24734
$855$		0			0
$856$	−43.9756			−1.50305
$857$			25.5066i			0.871288i	0.900119	+	0.435644i	$0.143479\pi$
$857$			25.5066i			0.871288i	−0.900119	+	0.435644i	$0.856521\pi$
$858$		0			0
$859$	−2.47295			−0.0843758			−0.0421879	−	0.999110i	$-0.513433\pi$
$859$	−2.47295			−0.0843758			−0.0421879	+	0.999110i	$0.513433\pi$
$860$	2.91397	+	3.29551i	0.0993657	+	0.112376i
$861$		0			0
$862$			2.11142i			0.0719152i
$863$			47.0903i			1.60297i	0.598013	+	0.801486i	$0.295957\pi$
$863$			47.0903i			1.60297i	−0.598013	+	0.801486i	$0.704043\pi$
$864$		0			0
$865$	−6.73084	−	7.61213i	−0.228855	−	0.258820i
$866$	2.45088			0.0832842
$867$		0			0
$868$			2.43866i			0.0827735i
$869$	18.2374			0.618662
$870$		0			0
$871$	24.9624			0.845818
$872$			33.1392i			1.12223i
$873$		0			0
$874$	−12.0811			−0.408649
$875$	−41.3136	+	28.3430i	−1.39665	+	0.958167i
$876$		0			0
$877$		−	52.2067i		−	1.76289i	−0.472284	−	0.881447i	$-0.656570\pi$
$877$		−	52.2067i		−	1.76289i	0.472284	−	0.881447i	$-0.343430\pi$
$878$			39.1030i			1.31966i
$879$		0			0
$880$	−26.7816	+	23.6810i	−0.902808	+	0.798287i
$881$	2.06537			0.0695842			0.0347921	−	0.999395i	$-0.488923\pi$
$881$	2.06537			0.0695842			0.0347921	+	0.999395i	$0.488923\pi$
$882$		0			0
$883$			42.9053i			1.44388i	0.691957	+	0.721939i	$0.256749\pi$
$883$			42.9053i			1.44388i	−0.691957	+	0.721939i	$0.743251\pi$
$884$	3.42548			0.115212
$885$		0			0
$886$	4.97110			0.167007
$887$		−	22.1768i		−	0.744624i	−0.928108	−	0.372312i	$-0.878565\pi$
$887$		−	22.1768i		−	0.744624i	0.928108	−	0.372312i	$-0.121435\pi$
$888$		0			0
$889$	53.1655			1.78311
$890$	−25.1730	−	28.4690i	−0.843801	−	0.954282i
$891$		0			0
$892$			1.76257i			0.0590153i
$893$		−	3.84367i		−	0.128624i
$894$		0			0
$895$	25.2750	−	22.3488i	0.844851	−	0.747040i
$896$	56.7997			1.89755
$897$		0			0
$898$			17.7924i			0.593741i
$899$	−13.0132			−0.434014
$900$		0			0
$901$	−23.9756			−0.798742
$902$		−	30.4836i		−	1.01499i
$903$		0			0
$904$	−30.0811			−1.00048
$905$	14.1524	−	12.5139i	0.470440	−	0.415975i
$906$		0			0
$907$		−	25.6629i		−	0.852123i	−0.904694	−	0.426062i	$-0.859901\pi$
$907$		−	25.6629i		−	0.852123i	0.904694	−	0.426062i	$-0.140099\pi$
$908$			2.17091i			0.0720443i
$909$		0			0
$910$	−28.2071	−	31.9003i	−0.935057	−	1.05749i
$911$	2.65959			0.0881161			0.0440580	−	0.999029i	$-0.485971\pi$
$911$	2.65959			0.0881161			0.0440580	+	0.999029i	$0.485971\pi$
$912$		0			0
$913$		−	24.7367i		−	0.818666i
$914$	46.7875			1.54759
$915$		0			0
$916$	−4.59498			−0.151823
$917$		−	6.94192i		−	0.229242i
$918$		0			0
$919$	6.94780			0.229187			0.114593	−	0.993412i	$-0.463443\pi$
$919$	6.94780			0.229187			0.114593	+	0.993412i	$0.463443\pi$
$920$	36.5501	−	32.3185i	1.20502	−	1.06551i
$921$		0			0
$922$		−	7.51530i		−	0.247503i
$923$		−	5.73813i		−	0.188873i
$924$		0			0
$925$	−17.0884	−	2.10791i	−0.561863	−	0.0693076i
$926$	21.1368			0.694599
$927$		0			0
$928$		−	5.07030i		−	0.166441i
$929$	53.3112			1.74908			0.874542	−	0.484949i	$-0.161162\pi$
$929$	53.3112			1.74908			0.874542	+	0.484949i	$0.161162\pi$
$930$		0			0
$931$	−13.0811			−0.428716
$932$			2.33709i			0.0765539i
$933$		0			0
$934$	47.9669			1.56952
$935$	−33.5125	−	37.9003i	−1.09597	−	1.23947i
$936$		0			0
$937$		−	40.9135i		−	1.33659i	−0.743898	−	0.668293i	$-0.767025\pi$
$937$		−	40.9135i		−	1.33659i	0.743898	−	0.668293i	$-0.232975\pi$
$938$		−	57.7499i		−	1.88560i
$939$		0			0
$940$	−1.10413	−	1.24869i	−0.0360126	−	0.0407278i
$941$	27.0762			0.882658			0.441329	−	0.897345i	$-0.354507\pi$
$941$	27.0762			0.882658			0.441329	+	0.897345i	$0.354507\pi$
$942$		0			0
$943$			45.6747i			1.48737i
$944$	41.4880			1.35032
$945$		0			0
$946$	55.2203			1.79537
$947$		−	13.7929i		−	0.448209i	−0.974565	−	0.224104i	$-0.928054\pi$
$947$		−	13.7929i		−	0.448209i	0.974565	−	0.224104i	$-0.0719456\pi$
$948$		0			0
$949$	8.86082			0.287634
$950$	7.35026	+	0.906679i	0.238474	+	0.0294165i
$951$		0			0
$952$			73.8007i			2.39189i
$953$			13.7948i			0.446857i	0.974720	+	0.223429i	$0.0717250\pi$
$953$			13.7948i			0.446857i	−0.974720	+	0.223429i	$0.928275\pi$
$954$		0			0
$955$	−22.6801	+	20.0543i	−0.733909	+	0.648942i
$956$	−2.71274			−0.0877364
$957$		0			0
$958$		−	10.7938i		−	0.348733i
$959$	−76.5111			−2.47067
$960$		0			0
$961$	−23.1260			−0.746000
$962$		−	14.6340i		−	0.471819i
$963$		0			0
$964$	−4.61071			−0.148501
$965$	−16.5623	−	18.7308i	−0.533159	−	0.602967i
$966$		0			0
$967$			20.6072i			0.662683i	0.943511	+	0.331341i	$0.107501\pi$
$967$			20.6072i			0.662683i	−0.943511	+	0.331341i	$0.892499\pi$
$968$			6.70545i			0.215521i
$969$		0			0
$970$	23.8945	−	21.1281i	0.767205	−	0.678383i
$971$	−1.93463			−0.0620851			−0.0310426	−	0.999518i	$-0.509883\pi$
$971$	−1.93463			−0.0620851			−0.0310426	+	0.999518i	$0.509883\pi$
$972$		0			0
$973$		−	25.1490i		−	0.806241i
$974$	−55.6531			−1.78324
$975$		0			0
$976$	43.0435			1.37779
$977$		−	30.6312i		−	0.979978i	−0.871729	−	0.489989i	$-0.837001\pi$
$977$		−	30.6312i		−	0.979978i	0.871729	−	0.489989i	$-0.162999\pi$
$978$		0			0
$979$	−42.1681			−1.34770
$980$	−4.24965	+	3.75765i	−0.135750	+	0.120034i
$981$		0			0
$982$		−	34.9415i		−	1.11503i
$983$		−	51.2663i		−	1.63514i	−0.575828	−	0.817571i	$-0.695320\pi$
$983$		−	51.2663i		−	1.63514i	0.575828	−	0.817571i	$-0.304680\pi$
$984$		0			0
$985$	10.7308	+	12.1359i	0.341913	+	0.386681i
$986$	42.2882			1.34673
$987$		0			0
$988$			0.556417i			0.0177020i
$989$	−82.7386			−2.63094
$990$		0			0
$991$	−31.5778			−1.00310			−0.501552	−	0.865128i	$-0.667237\pi$
$991$	−31.5778			−1.00310			−0.501552	+	0.865128i	$0.667237\pi$
$992$			3.06793i			0.0974068i
$993$		0			0
$994$	−13.2750			−0.421059
$995$	−44.9986	+	39.7889i	−1.42655	+	1.26139i
$996$		0			0
$997$		−	35.7090i		−	1.13091i	−0.824778	−	0.565457i	$-0.808700\pi$
$997$		−	35.7090i		−	1.13091i	0.824778	−	0.565457i	$-0.191300\pi$
$998$			38.0870i			1.20562i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.c.e.514.5		6
3.2	odd	2		285.2.c.a.229.2	✓	6
5.2	odd	4		4275.2.a.bi.1.1		3
5.3	odd	4		4275.2.a.bd.1.3		3
5.4	even	2	inner	855.2.c.e.514.2		6
15.2	even	4		1425.2.a.s.1.3		3
15.8	even	4		1425.2.a.x.1.1		3
15.14	odd	2		285.2.c.a.229.5	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.c.a.229.2	✓	6	3.2	odd	2
285.2.c.a.229.5	yes	6	15.14	odd	2
855.2.c.e.514.2		6	5.4	even	2	inner
855.2.c.e.514.5		6	1.1	even	1	trivial
1425.2.a.s.1.3		3	15.2	even	4
1425.2.a.x.1.1		3	15.8	even	4
4275.2.a.bd.1.3		3	5.3	odd	4
4275.2.a.bi.1.1		3	5.2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.48119i q^{2} -0.193937 q^{4} +(-1.67513 + 1.48119i) q^{5} +4.48119i q^{7} +2.67513i q^{8} +(-2.19394 - 2.48119i) q^{10} -3.67513 q^{11} -2.86907i q^{13} -6.63752 q^{14} -4.35026 q^{16} -6.15633i q^{17} +1.00000 q^{19} +(0.324869 - 0.287258i) q^{20} -5.44358i q^{22} +8.15633i q^{23} +(0.612127 - 4.96239i) q^{25} +4.24965 q^{26} -0.869067i q^{28} +4.63752 q^{29} -2.80606 q^{31} -1.09332i q^{32} +9.11871 q^{34} +(-6.63752 - 7.50659i) q^{35} -3.44358i q^{37} +1.48119i q^{38} +(-3.96239 - 4.48119i) q^{40} +5.59991 q^{41} +10.1441i q^{43} +0.712742 q^{44} -12.0811 q^{46} -3.84367i q^{47} -13.0811 q^{49} +(7.35026 + 0.906679i) q^{50} +0.556417i q^{52} -3.89446i q^{53} +(6.15633 - 5.44358i) q^{55} -11.9878 q^{56} +6.86907i q^{58} -9.53690 q^{59} -9.89446 q^{61} -4.15633i q^{62} -7.08110 q^{64} +(4.24965 + 4.80606i) q^{65} +8.70052i q^{67} +1.19394i q^{68} +(11.1187 - 9.83146i) q^{70} +2.00000 q^{71} +3.08840i q^{73} +5.10062 q^{74} -0.193937 q^{76} -16.4690i q^{77} -4.96239 q^{79} +(7.28726 - 6.44358i) q^{80} +8.29455i q^{82} +6.73084i q^{83} +(9.11871 + 10.3127i) q^{85} -15.0254 q^{86} -9.83146i q^{88} +11.4739 q^{89} +12.8568 q^{91} -1.58181i q^{92} +5.69323 q^{94} +(-1.67513 + 1.48119i) q^{95} +9.63023i q^{97} -19.3757i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{4} - 14 q^{10} - 12 q^{11} - 8 q^{14} - 6 q^{16} + 6 q^{19} + 12 q^{20} + 2 q^{25} - 8 q^{26} - 4 q^{29} - 16 q^{31} + 12 q^{34} - 8 q^{35} - 2 q^{40} - 20 q^{41} + 16 q^{44} - 8 q^{46} - 14 q^{49}+ \cdots - 32 q^{94}+O(q^{100}) \) 6 * q - 2 * q^4 - 14 * q^10 - 12 * q^11 - 8 * q^14 - 6 * q^16 + 6 * q^19 + 12 * q^20 + 2 * q^25 - 8 * q^26 - 4 * q^29 - 16 * q^31 + 12 * q^34 - 8 * q^35 - 2 * q^40 - 20 * q^41 + 16 * q^44 - 8 * q^46 - 14 * q^49 + 24 * q^50 + 16 * q^55 - 20 * q^56 - 12 * q^59 - 20 * q^61 + 22 * q^64 - 8 * q^65 + 24 * q^70 + 12 * q^71 + 44 * q^74 - 2 * q^76 - 8 * q^79 + 32 * q^80 + 12 * q^85 - 60 * q^86 + 32 * q^89 + 16 * q^91 - 32 * q^94

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