LMFDB - Embedded newform 324.6.e.g.109.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,6,Mod(109,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("324.109");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	324.e (of order $3$, degree $2$, not 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:	$51.9643576194$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{41})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 11x^{2} + 10x + 100 $ x^4 - x^3 + 11x^2 + 10x + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			109.2
Root			$-1.35078 + 2.33962i$ of defining polynomial
Character	$\chi$	$=$	324.109
Dual form			324.6.e.g.217.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(28.8141 - 49.9074i) q^{5} +(-78.4422 - 135.866i) q^{7} +O(q^{10})$	$q+(28.8141 - 49.9074i) q^{5} +(-78.4422 - 135.866i) q^{7} +(-109.012 - 188.815i) q^{11} +(293.769 - 508.822i) q^{13} -2124.56 q^{17} +29.7687 q^{19} +(1585.74 - 2746.59i) q^{23} +(-98.0000 - 169.741i) q^{25} +(1821.07 + 3154.18i) q^{29} +(-3165.94 + 5483.57i) q^{31} -9040.95 q^{35} -8435.69 q^{37} +(5073.22 - 8787.07i) q^{41} +(3427.88 + 5937.26i) q^{43} +(12223.9 + 21172.4i) q^{47} +(-3902.85 + 6759.94i) q^{49} +25483.2 q^{53} -12564.4 q^{55} +(-10348.1 + 17923.4i) q^{59} +(-22790.1 - 39473.7i) q^{61} +(-16929.3 - 29322.5i) q^{65} +(-9549.67 + 16540.5i) q^{67} -23055.0 q^{71} -89651.6 q^{73} +(-17102.4 + 29622.1i) q^{77} +(17011.8 + 29465.3i) q^{79} +(-54248.7 - 93961.6i) q^{83} +(-61217.3 + 106031. i) q^{85} +110055. q^{89} -92175.4 q^{91} +(857.757 - 1485.68i) q^{95} +(14416.0 + 24969.2i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 32 q^{7}+O(q^{10}) $ 4 * q + 32 * q^7	$ 4 q + 32 q^{7} + 486 q^{11} - 208 q^{13} - 3888 q^{17} - 1264 q^{19} + 6804 q^{23} - 392 q^{25} + 11664 q^{29} - 3328 q^{31} - 39852 q^{35} - 19912 q^{37} + 13608 q^{41} - 4960 q^{43} + 18468 q^{47} - 26676 q^{49} + 23328 q^{53} - 106272 q^{55} + 1944 q^{59} - 8176 q^{61} - 79704 q^{65} - 90064 q^{67} + 89424 q^{71} - 242428 q^{73} - 167184 q^{77} - 28768 q^{79} - 15066 q^{83} - 132840 q^{85} + 357696 q^{89} - 484880 q^{91} + 39852 q^{95} - 88942 q^{97}+O(q^{100}) $ 4 * q + 32 * q^7 + 486 * q^11 - 208 * q^13 - 3888 * q^17 - 1264 * q^19 + 6804 * q^23 - 392 * q^25 + 11664 * q^29 - 3328 * q^31 - 39852 * q^35 - 19912 * q^37 + 13608 * q^41 - 4960 * q^43 + 18468 * q^47 - 26676 * q^49 + 23328 * q^53 - 106272 * q^55 + 1944 * q^59 - 8176 * q^61 - 79704 * q^65 - 90064 * q^67 + 89424 * q^71 - 242428 * q^73 - 167184 * q^77 - 28768 * q^79 - 15066 * q^83 - 132840 * q^85 + 357696 * q^89 - 484880 * q^91 + 39852 * q^95 - 88942 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	28.8141	−	49.9074i	0.515442	−	0.892771i	−0.484398	−	0.874848i	$-0.660961\pi$
$5$	28.8141	−	49.9074i	0.515442	−	0.892771i	0.999839	−	0.0179231i	$-0.00570541\pi$
$6$		0			0
$7$	−78.4422	−	135.866i	−0.605068	−	1.04801i	−0.992041	−	0.125918i	$-0.959812\pi$
$7$	−78.4422	−	135.866i	−0.605068	−	1.04801i	0.386972	−	0.922091i	$-0.373521\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−109.012	−	188.815i	−0.271640	−	0.470495i	0.697642	−	0.716447i	$-0.254233\pi$
$11$	−109.012	−	188.815i	−0.271640	−	0.470495i	−0.969282	+	0.245952i	$0.920899\pi$
$12$		0			0
$13$	293.769	−	508.822i	0.482111	−	0.835041i	−0.517678	−	0.855576i	$-0.673203\pi$
$13$	293.769	−	508.822i	0.482111	−	0.835041i	0.999789	+	0.0205346i	$0.00653681\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2124.56			−1.78298			−0.891491	−	0.453038i	$-0.850340\pi$
$17$	−2124.56			−1.78298			−0.891491	+	0.453038i	$0.850340\pi$
$18$		0			0
$19$	29.7687			0.0189180			0.00945902	−	0.999955i	$-0.496989\pi$
$19$	29.7687			0.0189180			0.00945902	+	0.999955i	$0.496989\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1585.74	−	2746.59i	0.625048	−	1.08262i	−0.363483	−	0.931601i	$-0.618413\pi$
$23$	1585.74	−	2746.59i	0.625048	−	1.08262i	0.988532	−	0.151014i	$-0.0482540\pi$
$24$		0			0
$25$	−98.0000	−	169.741i	−0.0313600	−	0.0543171i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1821.07	+	3154.18i	0.402097	+	0.696452i	0.993979	−	0.109573i	$-0.0349482\pi$
$29$	1821.07	+	3154.18i	0.402097	+	0.696452i	−0.591882	+	0.806025i	$0.701615\pi$
$30$		0			0
$31$	−3165.94	+	5483.57i	−0.591696	+	1.02485i	0.402309	+	0.915504i	$0.368208\pi$
$31$	−3165.94	+	5483.57i	−0.591696	+	1.02485i	−0.994004	+	0.109343i	$0.965125\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−9040.95			−1.24751
$36$		0			0
$37$	−8435.69			−1.01302			−0.506508	−	0.862235i	$-0.669064\pi$
$37$	−8435.69			−1.01302			−0.506508	+	0.862235i	$0.669064\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	5073.22	−	8787.07i	0.471328	−	0.816365i	−0.528134	−	0.849161i	$-0.677108\pi$
$41$	5073.22	−	8787.07i	0.471328	−	0.816365i	0.999462	+	0.0327965i	$0.0104413\pi$
$42$		0			0
$43$	3427.88	+	5937.26i	0.282718	+	0.489683i	0.972053	−	0.234760i	$-0.0754305\pi$
$43$	3427.88	+	5937.26i	0.282718	+	0.489683i	−0.689335	+	0.724443i	$0.742097\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	12223.9	+	21172.4i	0.807171	+	1.39806i	0.914816	+	0.403872i	$0.132336\pi$
$47$	12223.9	+	21172.4i	0.807171	+	1.39806i	−0.107645	+	0.994189i	$0.534331\pi$
$48$		0			0
$49$	−3902.85	+	6759.94i	−0.232216	+	0.402209i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	25483.2			1.24613			0.623066	−	0.782169i	$-0.285887\pi$
$53$	25483.2			1.24613			0.623066	+	0.782169i	$0.285887\pi$
$54$		0			0
$55$	−12564.4			−0.560059
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−10348.1	+	17923.4i	−0.387017	+	0.670333i	−0.992047	−	0.125870i	$-0.959828\pi$
$59$	−10348.1	+	17923.4i	−0.387017	+	0.670333i	0.605030	+	0.796203i	$0.293161\pi$
$60$		0			0
$61$	−22790.1	−	39473.7i	−0.784191	−	1.35826i	−0.929481	−	0.368870i	$-0.879745\pi$
$61$	−22790.1	−	39473.7i	−0.784191	−	1.35826i	0.145290	−	0.989389i	$-0.453589\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−16929.3	−	29322.5i	−0.497000	−	0.860830i
$66$		0			0
$67$	−9549.67	+	16540.5i	−0.259897	+	0.450155i	−0.966214	−	0.257741i	$-0.917022\pi$
$67$	−9549.67	+	16540.5i	−0.259897	+	0.450155i	0.706317	+	0.707896i	$0.250355\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−23055.0			−0.542773			−0.271387	−	0.962470i	$-0.587482\pi$
$71$	−23055.0			−0.542773			−0.271387	+	0.962470i	$0.587482\pi$
$72$		0			0
$73$	−89651.6			−1.96902			−0.984511	−	0.175320i	$-0.943904\pi$
$73$	−89651.6			−1.96902			−0.984511	+	0.175320i	$0.943904\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−17102.4	+	29622.1i	−0.328722	+	0.569364i
$78$		0			0
$79$	17011.8	+	29465.3i	0.306678	+	0.531182i	0.977634	−	0.210316i	$-0.0674492\pi$
$79$	17011.8	+	29465.3i	0.306678	+	0.531182i	−0.670955	+	0.741498i	$0.734116\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−54248.7	−	93961.6i	−0.864359	−	1.49711i	−0.867682	−	0.497120i	$-0.834391\pi$
$83$	−54248.7	−	93961.6i	−0.864359	−	1.49711i	0.00332246	−	0.999994i	$-0.498942\pi$
$84$		0			0
$85$	−61217.3	+	106031.i	−0.919023	+	1.59180i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	110055.			1.47277			0.736384	−	0.676564i	$-0.236532\pi$
$89$	110055.			1.47277			0.736384	+	0.676564i	$0.236532\pi$
$90$		0			0
$91$	−92175.4			−1.16684
$92$		0			0
$93$		0			0
$94$		0			0
$95$	857.757	−	1485.68i	0.00975114	−	0.0168895i
$96$		0			0
$97$	14416.0	+	24969.2i	0.155566	+	0.269448i	0.933265	−	0.359189i	$-0.116947\pi$
$97$	14416.0	+	24969.2i	0.155566	+	0.269448i	−0.777699	+	0.628637i	$0.783613\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−20145.2	−	34892.5i	−0.196502	−	0.340352i	0.750890	−	0.660428i	$-0.229625\pi$
$101$	−20145.2	−	34892.5i	−0.196502	−	0.340352i	−0.947392	+	0.320076i	$0.896292\pi$
$102$		0			0
$103$	−102274.	+	177143.i	−0.949885	+	1.64525i	−0.204223	+	0.978924i	$0.565467\pi$
$103$	−102274.	+	177143.i	−0.949885	+	1.64525i	−0.745662	+	0.666324i	$0.767867\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−164042.			−1.38515			−0.692573	−	0.721348i	$-0.743523\pi$
$107$	−164042.			−1.38515			−0.692573	+	0.721348i	$0.743523\pi$
$108$		0			0
$109$	−131554.			−1.06057			−0.530285	−	0.847819i	$-0.677915\pi$
$109$	−131554.			−1.06057			−0.530285	+	0.847819i	$0.677915\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−47161.0	+	81685.2i	−0.347446	+	0.601793i	−0.985795	−	0.167953i	$-0.946284\pi$
$113$	−47161.0	+	81685.2i	−0.347446	+	0.601793i	0.638349	+	0.769747i	$0.279618\pi$
$114$		0			0
$115$	−91383.4	−	158281.i	−0.644352	−	1.11605i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	166655.	+	288655.i	1.07883	+	1.86858i
$120$		0			0
$121$	56758.1	−	98307.8i	0.352423	−	0.610414i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	168793.			0.966226
$126$		0			0
$127$	−303144.			−1.66778			−0.833891	−	0.551929i	$-0.813892\pi$
$127$	−303144.			−1.66778			−0.833891	+	0.551929i	$0.813892\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	158286.	−	274160.i	0.805871	−	1.39581i	−0.109830	−	0.993950i	$-0.535031\pi$
$131$	158286.	−	274160.i	0.805871	−	1.39581i	0.915701	−	0.401859i	$-0.131636\pi$
$132$		0			0
$133$	−2335.12	−	4044.55i	−0.0114467	−	0.0198263i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−491.479	−	851.266i	−0.00223719	−	0.00387493i	0.864905	−	0.501936i	$-0.167379\pi$
$137$	−491.479	−	851.266i	−0.00223719	−	0.00387493i	−0.867142	+	0.498061i	$0.834045\pi$
$138$		0			0
$139$	−38766.9	+	67146.3i	−0.170186	+	0.294771i	−0.938485	−	0.345320i	$-0.887770\pi$
$139$	−38766.9	+	67146.3i	−0.170186	+	0.294771i	0.768299	+	0.640091i	$0.221104\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−128098.			−0.523844
$144$		0			0
$145$	209889.			0.829030
$146$		0			0
$147$		0			0
$148$		0			0
$149$	59604.6	−	103238.i	0.219945	−	0.380956i	−0.734846	−	0.678234i	$-0.762745\pi$
$149$	59604.6	−	103238.i	0.219945	−	0.380956i	0.954791	+	0.297278i	$0.0960788\pi$
$150$		0			0
$151$	29784.4	+	51588.1i	0.106303	+	0.184123i	0.914270	−	0.405105i	$-0.132765\pi$
$151$	29784.4	+	51588.1i	0.106303	+	0.184123i	−0.807967	+	0.589228i	$0.799432\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	182447.	+	316008.i	0.609969	+	1.05650i
$156$		0			0
$157$	−148781.	+	257696.i	−0.481723	+	0.834368i	−0.999780	−	0.0209776i	$-0.993322\pi$
$157$	−148781.	+	257696.i	−0.481723	+	0.834368i	0.518057	+	0.855346i	$0.326655\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−497557.			−1.51279
$162$		0			0
$163$	−98681.9			−0.290917			−0.145458	−	0.989364i	$-0.546466\pi$
$163$	−98681.9			−0.290917			−0.145458	+	0.989364i	$0.546466\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−9276.51	+	16067.4i	−0.0257391	+	0.0445814i	−0.878608	−	0.477544i	$-0.841527\pi$
$167$	−9276.51	+	16067.4i	−0.0257391	+	0.0445814i	0.852869	+	0.522125i	$0.174861\pi$
$168$		0			0
$169$	13046.4	+	22597.0i	0.0351377	+	0.0608603i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−248326.	−	430113.i	−0.630822	−	1.09262i	−0.987384	−	0.158345i	$-0.949384\pi$
$173$	−248326.	−	430113.i	−0.630822	−	1.09262i	0.356561	−	0.934272i	$-0.383949\pi$
$174$		0			0
$175$	−15374.7	+	26629.7i	−0.0379499	+	0.0657311i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	150072.			0.350080			0.175040	−	0.984561i	$-0.443995\pi$
$179$	150072.			0.350080			0.175040	+	0.984561i	$0.443995\pi$
$180$		0			0
$181$	−73515.6			−0.166795			−0.0833976	−	0.996516i	$-0.526577\pi$
$181$	−73515.6			−0.166795			−0.0833976	+	0.996516i	$0.526577\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−243066.	+	421003.i	−0.522150	+	0.904391i
$186$		0			0
$187$	231604.	+	401150.i	0.484330	+	0.838885i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−299659.	−	519025.i	−0.594353	−	1.02945i	−0.993638	−	0.112622i	$-0.964075\pi$
$191$	−299659.	−	519025.i	−0.594353	−	1.02945i	0.399285	−	0.916827i	$-0.369258\pi$
$192$		0			0
$193$	361873.	−	626783.i	0.699299	−	1.21122i	−0.269411	−	0.963025i	$-0.586829\pi$
$193$	361873.	−	626783.i	0.699299	−	1.21122i	0.968710	−	0.248196i	$-0.0798378\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	416589.			0.764790			0.382395	−	0.923999i	$-0.375099\pi$
$197$	416589.			0.764790			0.382395	+	0.923999i	$0.375099\pi$
$198$		0			0
$199$	688177.			1.23188			0.615938	−	0.787794i	$-0.288777\pi$
$199$	688177.			1.23188			0.615938	+	0.787794i	$0.288777\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	285697.	−	494841.i	0.486592	−	0.842802i
$204$		0			0
$205$	−292360.	−	506382.i	−0.485885	−	0.841577i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−3245.16	−	5620.78i	−0.00513890	−	0.00890084i
$210$		0			0
$211$	160937.	−	278751.i	0.248857	−	0.431033i	−0.714352	−	0.699787i	$-0.753278\pi$
$211$	160937.	−	278751.i	0.248857	−	0.431033i	0.963209	+	0.268753i	$0.0866117\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	395084.			0.582899
$216$		0			0
$217$	993373.			1.43207
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−624130.	+	1.08102e6i	−0.859596	+	1.48886i
$222$		0			0
$223$	177237.	+	306983.i	0.238667	+	0.413383i	0.960332	−	0.278859i	$-0.0899563\pi$
$223$	177237.	+	306983.i	0.238667	+	0.413383i	−0.721665	+	0.692242i	$0.756623\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−113261.	−	196174.i	−0.145887	−	0.252684i	0.783816	−	0.620993i	$-0.213270\pi$
$227$	−113261.	−	196174.i	−0.145887	−	0.252684i	−0.929704	+	0.368309i	$0.879937\pi$
$228$		0			0
$229$	727154.	−	1.25947e6i	0.916299	−	1.58708i	0.111312	−	0.993786i	$-0.464495\pi$
$229$	727154.	−	1.25947e6i	0.916299	−	1.58708i	0.804988	−	0.593292i	$-0.202172\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	423642.			0.511221			0.255611	−	0.966780i	$-0.417723\pi$
$233$	423642.			0.511221			0.255611	+	0.966780i	$0.417723\pi$
$234$		0			0
$235$	1.40888e6			1.66420
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−373526.	+	646966.i	−0.422986	+	0.732633i	−0.996230	−	0.0867515i	$-0.972351\pi$
$239$	−373526.	+	646966.i	−0.422986	+	0.732633i	0.573244	+	0.819385i	$0.305685\pi$
$240$		0			0
$241$	−305937.	−	529899.i	−0.339305	−	0.587693i	0.644998	−	0.764185i	$-0.276858\pi$
$241$	−305937.	−	529899.i	−0.339305	−	0.587693i	−0.984302	+	0.176492i	$0.943525\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	224914.	+	389562.i	0.239387	+	0.414631i
$246$		0			0
$247$	8745.12	−	15147.0i	0.00912059	−	0.0157973i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	985152.			0.987004			0.493502	−	0.869745i	$-0.335717\pi$
$251$	985152.			0.987004			0.493502	+	0.869745i	$0.335717\pi$
$252$		0			0
$253$	−691463.			−0.679153
$254$		0			0
$255$		0			0
$256$		0			0
$257$	693891.	−	1.20185e6i	0.655327	−	1.13506i	−0.326485	−	0.945203i	$-0.605864\pi$
$257$	693891.	−	1.20185e6i	0.655327	−	1.13506i	0.981812	−	0.189857i	$-0.0608026\pi$
$258$		0			0
$259$	661714.	+	1.14612e6i	0.612944	+	1.06165i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	438768.	+	759968.i	0.391152	+	0.677495i	0.992602	−	0.121415i	$-0.0387433\pi$
$263$	438768.	+	759968.i	0.391152	+	0.677495i	−0.601450	+	0.798911i	$0.705410\pi$
$264$		0			0
$265$	734274.	−	1.27180e6i	0.642308	−	1.11251i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−911089.			−0.767680			−0.383840	−	0.923400i	$-0.625399\pi$
$269$	−911089.			−0.767680			−0.383840	+	0.923400i	$0.625399\pi$
$270$		0			0
$271$	620129.			0.512931			0.256465	−	0.966553i	$-0.417442\pi$
$271$	620129.			0.512931			0.256465	+	0.966553i	$0.417442\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−21366.4	+	37007.8i	−0.0170373	+	0.0295095i
$276$		0			0
$277$	118364.	+	205012.i	0.0926871	+	0.160539i	0.908641	−	0.417578i	$-0.137121\pi$
$277$	118364.	+	205012.i	0.0926871	+	0.160539i	−0.815954	+	0.578117i	$0.803788\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	538457.	+	932636.i	0.406804	+	0.704606i	0.994530	−	0.104455i	$-0.0333097\pi$
$281$	538457.	+	932636.i	0.406804	+	0.704606i	−0.587725	+	0.809061i	$0.699976\pi$
$282$		0			0
$283$	−1.02658e6	+	1.77809e6i	−0.761953	+	1.31974i	0.179890	+	0.983687i	$0.442426\pi$
$283$	−1.02658e6	+	1.77809e6i	−0.761953	+	1.31974i	−0.941843	+	0.336054i	$0.890908\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−1.59182e6			−1.14074
$288$		0			0
$289$	3.09391e6			2.17903
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.06433e6	−	1.84347e6i	0.724280	−	1.25449i	−0.234990	−	0.971998i	$-0.575506\pi$
$293$	1.06433e6	−	1.84347e6i	0.724280	−	1.25449i	0.959270	−	0.282492i	$-0.0911610\pi$
$294$		0			0
$295$	596341.	+	1.03289e6i	0.398969	+	0.691035i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−931684.	−	1.61372e6i	−0.602685	−	1.04388i
$300$		0			0
$301$	537780.	−	931463.i	0.342128	−	0.592583i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−2.62670e6			−1.61682
$306$		0			0
$307$	−1.54154e6			−0.933489			−0.466744	−	0.884392i	$-0.654573\pi$
$307$	−1.54154e6			−0.933489			−0.466744	+	0.884392i	$0.654573\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−868197.	+	1.50376e6i	−0.508999	+	0.881612i	0.490946	+	0.871190i	$0.336651\pi$
$311$	−868197.	+	1.50376e6i	−0.508999	+	0.881612i	−0.999946	+	0.0104227i	$0.996682\pi$
$312$		0			0
$313$	−1.13707e6	−	1.96946e6i	−0.656034	−	1.13628i	−0.981634	−	0.190776i	$-0.938900\pi$
$313$	−1.13707e6	−	1.96946e6i	−0.656034	−	1.13628i	0.325600	−	0.945508i	$-0.394434\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−158418.	−	274388.i	−0.0885435	−	0.153362i	0.818352	−	0.574717i	$-0.194888\pi$
$317$	−158418.	−	274388.i	−0.0885435	−	0.153362i	−0.906896	+	0.421355i	$0.861555\pi$
$318$		0			0
$319$	397038.	−	687690.i	0.218452	−	0.378369i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−63245.5			−0.0337305
$324$		0			0
$325$	−115157.			−0.0604760
$326$		0			0
$327$		0			0
$328$		0			0
$329$	1.91774e6	−	3.32162e6i	0.976787	−	1.69185i
$330$		0			0
$331$	224396.	+	388664.i	0.112576	+	0.194987i	0.916808	−	0.399328i	$-0.130757\pi$
$331$	224396.	+	388664.i	0.112576	+	0.194987i	−0.804232	+	0.594315i	$0.797423\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	550330.	+	953199.i	0.267924	+	0.464057i
$336$		0			0
$337$	929347.	−	1.60968e6i	0.445762	−	0.772083i	−0.552343	−	0.833617i	$-0.686266\pi$
$337$	929347.	−	1.60968e6i	0.445762	−	0.772083i	0.998105	+	0.0615344i	$0.0195994\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	1.38051e6			0.642914
$342$		0			0
$343$	−1.41216e6			−0.648111
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−111822.	+	193681.i	−0.0498542	+	0.0863500i	−0.889876	−	0.456203i	$-0.849209\pi$
$347$	−111822.	+	193681.i	−0.0498542	+	0.0863500i	0.840021	+	0.542553i	$0.182542\pi$
$348$		0			0
$349$	−669904.	−	1.16031e6i	−0.294407	−	0.509929i	0.680439	−	0.732804i	$-0.261789\pi$
$349$	−669904.	−	1.16031e6i	−0.294407	−	0.509929i	−0.974847	+	0.222876i	$0.928456\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	1.69842e6	+	2.94174e6i	0.725449	+	1.25652i	0.958789	+	0.284120i	$0.0917013\pi$
$353$	1.69842e6	+	2.94174e6i	0.725449	+	1.25652i	−0.233339	+	0.972395i	$0.574965\pi$
$354$		0			0
$355$	−664307.	+	1.15061e6i	−0.279768	+	0.484572i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	761965.			0.312032			0.156016	−	0.987755i	$-0.450135\pi$
$359$	761965.			0.312032			0.156016	+	0.987755i	$0.450135\pi$
$360$		0			0
$361$	−2.47521e6			−0.999642
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−2.58323e6	+	4.47428e6i	−1.01492	+	1.75789i
$366$		0			0
$367$	−698558.	−	1.20994e6i	−0.270730	−	0.468919i	0.698319	−	0.715787i	$-0.253932\pi$
$367$	−698558.	−	1.20994e6i	−0.270730	−	0.468919i	−0.969049	+	0.246868i	$0.920599\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−1.99896e6	−	3.46229e6i	−0.753995	−	1.30596i
$372$		0			0
$373$	−1.62621e6	+	2.81668e6i	−0.605209	+	1.04825i	0.386809	+	0.922160i	$0.373577\pi$
$373$	−1.62621e6	+	2.81668e6i	−0.605209	+	1.04825i	−0.992018	+	0.126093i	$0.959756\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	2.13989e6			0.775421
$378$		0			0
$379$	−700188.			−0.250390			−0.125195	−	0.992132i	$-0.539956\pi$
$379$	−700188.			−0.250390			−0.125195	+	0.992132i	$0.539956\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−1.15361e6	+	1.99810e6i	−0.401847	+	0.696019i	−0.993949	−	0.109844i	$-0.964965\pi$
$383$	−1.15361e6	+	1.99810e6i	−0.401847	+	0.696019i	0.592102	+	0.805863i	$0.298298\pi$
$384$		0			0
$385$	985576.	+	1.70707e6i	0.338874	+	0.586947i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−1.00563e6	−	1.74180e6i	−0.336950	−	0.583614i	0.646908	−	0.762568i	$-0.276062\pi$
$389$	−1.00563e6	−	1.74180e6i	−0.336950	−	0.583614i	−0.983857	+	0.178955i	$0.942729\pi$
$390$		0			0
$391$	−3.36901e6	+	5.83530e6i	−1.11445	+	1.93028i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	1.96072e6			0.632299
$396$		0			0
$397$	−165619.			−0.0527392			−0.0263696	−	0.999652i	$-0.508395\pi$
$397$	−165619.			−0.0527392			−0.0263696	+	0.999652i	$0.508395\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	547270.	−	947900.i	0.169958	−	0.294375i	−0.768447	−	0.639913i	$-0.778970\pi$
$401$	547270.	−	947900.i	0.169958	−	0.294375i	0.938405	+	0.345538i	$0.112304\pi$
$402$		0			0
$403$	1.86011e6	+	3.22180e6i	0.570526	+	0.988180i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	919595.	+	1.59279e6i	0.275176	+	0.476619i
$408$		0			0
$409$	536465.	−	929184.i	0.158574	−	0.274659i	−0.775780	−	0.631003i	$-0.782644\pi$
$409$	536465.	−	929184.i	0.158574	−	0.274659i	0.934355	+	0.356344i	$0.115977\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	3.24691e6			0.936687
$414$		0			0
$415$	−6.25250e6			−1.78211
$416$		0			0
$417$		0			0
$418$		0			0
$419$	426090.	−	738010.i	0.118568	−	0.205365i	−0.800633	−	0.599156i	$-0.795503\pi$
$419$	426090.	−	738010.i	0.118568	−	0.205365i	0.919200	+	0.393790i	$0.128836\pi$
$420$		0			0
$421$	−1.59392e6	−	2.76075e6i	−0.438290	−	0.759140i	0.559268	−	0.828987i	$-0.311082\pi$
$421$	−1.59392e6	−	2.76075e6i	−0.438290	−	0.759140i	−0.997558	+	0.0698468i	$0.977749\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	208207.	+	360625.i	0.0559143	+	0.0968465i
$426$		0			0
$427$	−3.57541e6	+	6.19280e6i	−0.948979	+	1.64368i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	4.54409e6			1.17829			0.589147	−	0.808026i	$-0.299464\pi$
$431$	4.54409e6			1.17829			0.589147	+	0.808026i	$0.299464\pi$
$432$		0			0
$433$	−6.16131e6			−1.57926			−0.789629	−	0.613585i	$-0.789727\pi$
$433$	−6.16131e6			−1.57926			−0.789629	+	0.613585i	$0.789727\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	47205.5	−	81762.4i	0.0118247	−	0.0204809i
$438$		0			0
$439$	−451417.	−	781877.i	−0.111793	−	0.193632i	0.804700	−	0.593682i	$-0.202326\pi$
$439$	−451417.	−	781877.i	−0.111793	−	0.193632i	−0.916493	+	0.400050i	$0.868993\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−1.84356e6	−	3.19314e6i	−0.446321	−	0.773051i	0.551822	−	0.833962i	$-0.313933\pi$
$443$	−1.84356e6	−	3.19314e6i	−0.446321	−	0.773051i	−0.998143	+	0.0609110i	$0.980599\pi$
$444$		0			0
$445$	3.17113e6	−	5.49255e6i	0.759126	−	1.31484i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−7.71368e6			−1.80570			−0.902851	−	0.429954i	$-0.858530\pi$
$449$	−7.71368e6			−1.80570			−0.902851	+	0.429954i	$0.858530\pi$
$450$		0			0
$451$	−2.21218e6			−0.512128
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−2.65595e6	+	4.60024e6i	−0.601438	+	1.04172i
$456$		0			0
$457$	−1.89634e6	−	3.28455e6i	−0.424742	−	0.735674i	0.571654	−	0.820494i	$-0.306302\pi$
$457$	−1.89634e6	−	3.28455e6i	−0.424742	−	0.735674i	−0.996396	+	0.0848200i	$0.972968\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−2.38949e6	−	4.13871e6i	−0.523664	−	0.907012i	−0.999621	−	0.0275435i	$-0.991232\pi$
$461$	−2.38949e6	−	4.13871e6i	−0.523664	−	0.907012i	0.475957	−	0.879469i	$-0.342102\pi$
$462$		0			0
$463$	−1.27951e6	+	2.21618e6i	−0.277391	+	0.480456i	−0.970736	−	0.240151i	$-0.922803\pi$
$463$	−1.27951e6	+	2.21618e6i	−0.277391	+	0.480456i	0.693344	+	0.720606i	$0.256136\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−8.22563e6			−1.74533			−0.872664	−	0.488321i	$-0.837610\pi$
$467$	−8.22563e6			−1.74533			−0.872664	+	0.488321i	$0.837610\pi$
$468$		0			0
$469$	2.99639e6			0.629022
$470$		0			0
$471$		0			0
$472$		0			0
$473$	747363.	−	1.29447e6i	0.153596	−	0.266035i
$474$		0			0
$475$	−2917.33	−	5052.97i	−0.000593270	−	0.00102757i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	1.27184e6	+	2.20290e6i	0.253277	+	0.438688i	0.964426	−	0.264353i	$-0.0851583\pi$
$479$	1.27184e6	+	2.20290e6i	0.253277	+	0.438688i	−0.711149	+	0.703041i	$0.751825\pi$
$480$		0			0
$481$	−2.47814e6	+	4.29227e6i	−0.488386	+	0.845910i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1.66153e6			0.320741
$486$		0			0
$487$	1.25686e6			0.240139			0.120070	−	0.992765i	$-0.461688\pi$
$487$	1.25686e6			0.240139			0.120070	+	0.992765i	$0.461688\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	4.94983e6	−	8.57336e6i	0.926588	−	1.60490i	0.137601	−	0.990488i	$-0.456061\pi$
$491$	4.94983e6	−	8.57336e6i	0.926588	−	1.60490i	0.788987	−	0.614410i	$-0.210606\pi$
$492$		0			0
$493$	−3.86897e6	−	6.70125e6i	−0.716932	−	1.24176i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.80848e6	+	3.13238e6i	0.328415	+	0.568831i
$498$		0			0
$499$	1.52076e6	−	2.63403e6i	0.273406	−	0.473553i	−0.696326	−	0.717726i	$-0.745183\pi$
$499$	1.52076e6	−	2.63403e6i	0.273406	−	0.473553i	0.969732	+	0.244173i	$0.0785164\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−2.75985e6			−0.486368			−0.243184	−	0.969980i	$-0.578192\pi$
$503$	−2.75985e6			−0.486368			−0.243184	+	0.969980i	$0.578192\pi$
$504$		0			0
$505$	−2.32186e6			−0.405142
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−722539.	+	1.25147e6i	−0.123614	+	0.214105i	−0.921190	−	0.389113i	$-0.872782\pi$
$509$	−722539.	+	1.25147e6i	−0.123614	+	0.214105i	0.797577	+	0.603218i	$0.206115\pi$
$510$		0			0
$511$	7.03246e6	+	1.21806e7i	1.19139	+	2.06355i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	5.89384e6	+	1.02084e7i	0.979220	+	1.69606i
$516$		0			0
$517$	2.66512e6	−	4.61612e6i	0.438521	−	0.759540i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−1.28492e6			−0.207388			−0.103694	−	0.994609i	$-0.533066\pi$
$521$	−1.28492e6			−0.207388			−0.103694	+	0.994609i	$0.533066\pi$
$522$		0			0
$523$	−2.38275e6			−0.380912			−0.190456	−	0.981696i	$-0.560997\pi$
$523$	−2.38275e6			−0.380912			−0.190456	+	0.981696i	$0.560997\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	6.72623e6	−	1.16502e7i	1.05498	−	1.82728i
$528$		0			0
$529$	−1.81100e6	−	3.13674e6i	−0.281370	−	0.487347i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−2.98070e6	−	5.16273e6i	−0.454465	−	0.787157i
$534$		0			0
$535$	−4.72671e6	+	8.18691e6i	−0.713961	+	1.23662i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	1.70184e6			0.252317
$540$		0			0
$541$	2.22158e6			0.326339			0.163170	−	0.986598i	$-0.447828\pi$
$541$	2.22158e6			0.326339			0.163170	+	0.986598i	$0.447828\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−3.79062e6	+	6.56554e6i	−0.546662	+	0.946846i
$546$		0			0
$547$	908447.	+	1.57348e6i	0.129817	+	0.224850i	0.923606	−	0.383344i	$-0.125228\pi$
$547$	908447.	+	1.57348e6i	0.129817	+	0.224850i	−0.793789	+	0.608194i	$0.791894\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	54210.8	+	93895.8i	0.00760688	+	0.0131755i
$552$		0			0
$553$	2.66889e6	−	4.62265e6i	0.371123	−	0.642803i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	3.53109e6			0.482248			0.241124	−	0.970494i	$-0.422484\pi$
$557$	3.53109e6			0.482248			0.241124	+	0.970494i	$0.422484\pi$
$558$		0			0
$559$	4.02801e6			0.545207
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−163728.	+	283585.i	−0.0217697	+	0.0377062i	−0.876705	−	0.481028i	$-0.840263\pi$
$563$	−163728.	+	283585.i	−0.0217697	+	0.0377062i	0.854935	+	0.518735i	$0.173597\pi$
$564$		0			0
$565$	2.71780e6	+	4.70737e6i	0.358176	+	0.620379i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	4.03386e6	+	6.98686e6i	0.522325	+	0.904693i	0.999663	+	0.0259731i	$0.00826842\pi$
$569$	4.03386e6	+	6.98686e6i	0.522325	+	0.904693i	−0.477338	+	0.878720i	$0.658398\pi$
$570$		0			0
$571$	105674.	−	183033.i	0.0135637	−	0.0234931i	−0.859164	−	0.511701i	$-0.829016\pi$
$571$	105674.	−	183033.i	0.0135637	−	0.0234931i	0.872728	+	0.488207i	$0.162349\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−621612.			−0.0784060
$576$		0			0
$577$	−1.60363e6			−0.200523			−0.100261	−	0.994961i	$-0.531968\pi$
$577$	−1.60363e6			−0.200523			−0.100261	+	0.994961i	$0.531968\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−8.51078e6	+	1.47411e7i	−1.04599	+	1.81171i
$582$		0			0
$583$	−2.77799e6	−	4.81161e6i	−0.338500	−	0.586299i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	4.96240e6	+	8.59513e6i	0.594424	+	1.02957i	0.993628	+	0.112711i	$0.0359534\pi$
$587$	4.96240e6	+	8.59513e6i	0.594424	+	1.02957i	−0.399203	+	0.916862i	$0.630713\pi$
$588$		0			0
$589$	−94245.9	+	163239.i	−0.0111937	+	0.0193881i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−5.74316e6			−0.670678			−0.335339	−	0.942098i	$-0.608851\pi$
$593$	−5.74316e6			−0.670678			−0.335339	+	0.942098i	$0.608851\pi$
$594$		0			0
$595$	1.92081e7			2.22429
$596$		0			0
$597$		0			0
$598$		0			0
$599$	2.63787e6	−	4.56892e6i	0.300391	−	0.520292i	−0.675834	−	0.737054i	$-0.736216\pi$
$599$	2.63787e6	−	4.56892e6i	0.300391	−	0.520292i	0.976224	+	0.216762i	$0.0695496\pi$
$600$		0			0
$601$	−2.07476e6	−	3.59359e6i	−0.234305	−	0.405828i	0.724765	−	0.688996i	$-0.241948\pi$
$601$	−2.07476e6	−	3.59359e6i	−0.234305	−	0.405828i	−0.959070	+	0.283167i	$0.908615\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−3.27086e6	−	5.66530e6i	−0.363307	−	0.629266i
$606$		0			0
$607$	7.92504e6	−	1.37266e7i	0.873031	−	1.51213i	0.0141852	−	0.999899i	$-0.495485\pi$
$607$	7.92504e6	−	1.37266e7i	0.873031	−	1.51213i	0.858846	−	0.512234i	$-0.171182\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1.43640e7			1.55658
$612$		0			0
$613$	1.48963e7			1.60113			0.800565	−	0.599246i	$-0.204533\pi$
$613$	1.48963e7			1.60113			0.800565	+	0.599246i	$0.204533\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	7.23952e6	−	1.25392e7i	0.765591	−	1.32604i	−0.174343	−	0.984685i	$-0.555780\pi$
$617$	7.23952e6	−	1.25392e7i	0.765591	−	1.32604i	0.939934	−	0.341357i	$-0.110887\pi$
$618$		0			0
$619$	5.29461e6	+	9.17053e6i	0.555402	+	0.961984i	0.997872	+	0.0652007i	$0.0207688\pi$
$619$	5.29461e6	+	9.17053e6i	0.555402	+	0.961984i	−0.442471	+	0.896783i	$0.645898\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−8.63294e6	−	1.49527e7i	−0.891125	−	1.54347i
$624$		0			0
$625$	5.16985e6	−	8.95445e6i	0.529393	−	0.916936i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	1.79221e7			1.80619
$630$		0			0
$631$	−4.93118e6			−0.493035			−0.246517	−	0.969138i	$-0.579286\pi$
$631$	−4.93118e6			−0.493035			−0.246517	+	0.969138i	$0.579286\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−8.73480e6	+	1.51291e7i	−0.859644	+	1.48895i
$636$		0			0
$637$	2.29307e6	+	3.97171e6i	0.223908	+	0.387819i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−9.50299e6	−	1.64597e7i	−0.913514	−	1.58225i	−0.809062	−	0.587723i	$-0.800025\pi$
$641$	−9.50299e6	−	1.64597e7i	−0.913514	−	1.58225i	−0.104452	−	0.994530i	$-0.533309\pi$
$642$		0			0
$643$	3.34869e6	−	5.80010e6i	0.319409	−	0.553233i	−0.660956	−	0.750425i	$-0.729849\pi$
$643$	3.34869e6	−	5.80010e6i	0.319409	−	0.553233i	0.980365	+	0.197192i	$0.0631822\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.62821e7			−1.52915			−0.764574	−	0.644536i	$-0.777051\pi$
$647$	−1.62821e7			−1.52915			−0.764574	+	0.644536i	$0.777051\pi$
$648$		0			0
$649$	4.51228e6			0.420518
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−2.76043e6	+	4.78121e6i	−0.253334	+	0.438788i	−0.964442	−	0.264296i	$-0.914861\pi$
$653$	−2.76043e6	+	4.78121e6i	−0.253334	+	0.438788i	0.711108	+	0.703083i	$0.248194\pi$
$654$		0			0
$655$	−9.12175e6	−	1.57993e7i	−0.830759	−	1.43892i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	69588.1	+	120530.i	0.00624197	+	0.0108114i	0.869130	−	0.494585i	$-0.164680\pi$
$659$	69588.1	+	120530.i	0.00624197	+	0.0108114i	−0.862888	+	0.505396i	$0.831346\pi$
$660$		0			0
$661$	9.72751e6	−	1.68485e7i	0.865960	−	1.49989i	−0.000129981	−	1.00000i	$-0.500041\pi$
$661$	9.72751e6	−	1.68485e7i	0.865960	−	1.49989i	0.866090	−	0.499887i	$-0.166625\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−269137.			−0.0236004
$666$		0			0
$667$	1.15510e7			1.00532
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−4.96882e6	+	8.60624e6i	−0.426036	+	0.737916i
$672$		0			0
$673$	4.57506e6	+	7.92423e6i	0.389367	+	0.674403i	0.992364	−	0.123340i	$-0.0393605\pi$
$673$	4.57506e6	+	7.92423e6i	0.389367	+	0.674403i	−0.602998	+	0.797743i	$0.706027\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−4.96358e6	−	8.59717e6i	−0.416220	−	0.720915i	0.579335	−	0.815089i	$-0.303312\pi$
$677$	−4.96358e6	−	8.59717e6i	−0.416220	−	0.720915i	−0.995556	+	0.0941744i	$0.969979\pi$
$678$		0			0
$679$	2.26164e6	−	3.91728e6i	0.188256	−	0.326069i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−1.27969e7			−1.04967			−0.524835	−	0.851204i	$-0.675873\pi$
$683$	−1.27969e7			−1.04967			−0.524835	+	0.851204i	$0.675873\pi$
$684$		0			0
$685$	−56646.0			−0.00461257
$686$		0			0
$687$		0			0
$688$		0			0
$689$	7.48616e6	−	1.29664e7i	0.600774	−	1.04057i
$690$		0			0
$691$	−4.02846e6	−	6.97749e6i	−0.320955	−	0.555910i	0.659731	−	0.751502i	$-0.270670\pi$
$691$	−4.02846e6	−	6.97749e6i	−0.320955	−	0.555910i	−0.980685	+	0.195592i	$0.937337\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	2.23406e6	+	3.86951e6i	0.175442	+	0.303874i
$696$		0			0
$697$	−1.07784e7	+	1.86687e7i	−0.840371	+	1.45556i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	1.05658e7			0.812100			0.406050	−	0.913851i	$-0.366906\pi$
$701$	1.05658e7			0.812100			0.406050	+	0.913851i	$0.366906\pi$
$702$		0			0
$703$	−251120.			−0.0191643
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−3.16046e6	+	5.47408e6i	−0.237795	+	0.411872i
$708$		0			0
$709$	7.59109e6	+	1.31482e7i	0.567138	+	0.982312i	0.996847	+	0.0793445i	$0.0252827\pi$
$709$	7.59109e6	+	1.31482e7i	0.567138	+	0.982312i	−0.429709	+	0.902967i	$0.641384\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	1.00407e7	+	1.73911e7i	0.739676	+	1.28116i
$714$		0			0
$715$	−3.69102e6	+	6.39303e6i	−0.270011	+	0.467672i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−2.93525e6			−0.211750			−0.105875	−	0.994379i	$-0.533764\pi$
$719$	−2.93525e6			−0.211750			−0.105875	+	0.994379i	$0.533764\pi$
$720$		0			0
$721$	3.20903e7			2.29898
$722$		0			0
$723$		0			0
$724$		0			0
$725$	356929.	−	618219.i	0.0252195	−	0.0436815i
$726$		0			0
$727$	4.66682e6	+	8.08316e6i	0.327480	+	0.567212i	0.982011	−	0.188823i	$-0.0604673\pi$
$727$	4.66682e6	+	8.08316e6i	0.327480	+	0.567212i	−0.654531	+	0.756035i	$0.727134\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−7.28274e6	−	1.26141e7i	−0.504082	−	0.873096i
$732$		0			0
$733$	2.36625e6	−	4.09846e6i	0.162667	−	0.281748i	−0.773157	−	0.634215i	$-0.781324\pi$
$733$	2.36625e6	−	4.09846e6i	0.162667	−	0.281748i	0.935824	+	0.352466i	$0.114657\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	4.16413e6			0.282394
$738$		0			0
$739$	−2.42162e7			−1.63115			−0.815575	−	0.578651i	$-0.803579\pi$
$739$	−2.42162e7			−1.63115			−0.815575	+	0.578651i	$0.803579\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	1.23724e7	−	2.14296e7i	0.822207	−	1.42410i	−0.0818282	−	0.996646i	$-0.526076\pi$
$743$	1.23724e7	−	2.14296e7i	0.822207	−	1.42410i	0.904035	−	0.427458i	$-0.140591\pi$
$744$		0			0
$745$	−3.43490e6	−	5.94943e6i	−0.226738	−	0.392721i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1.28678e7	+	2.22877e7i	0.838108	+	1.45165i
$750$		0			0
$751$	2.78532e6	−	4.82432e6i	0.180209	−	0.312131i	−0.761743	−	0.647880i	$-0.775656\pi$
$751$	2.78532e6	−	4.82432e6i	0.180209	−	0.312131i	0.941952	+	0.335749i	$0.108989\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	3.43284e6			0.219173
$756$		0			0
$757$	−2.72203e6			−0.172645			−0.0863224	−	0.996267i	$-0.527511\pi$
$757$	−2.72203e6			−0.172645			−0.0863224	+	0.996267i	$0.527511\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−7.53087e6	+	1.30438e7i	−0.471393	+	0.816477i	−0.999464	−	0.0327230i	$-0.989582\pi$
$761$	−7.53087e6	+	1.30438e7i	−0.471393	+	0.816477i	0.528071	+	0.849200i	$0.322915\pi$
$762$		0			0
$763$	1.03194e7	+	1.78738e7i	0.641718	+	1.11149i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	6.07989e6	+	1.05307e7i	0.373170	+	0.646350i
$768$		0			0
$769$	−4.56946e6	+	7.91454e6i	−0.278644	+	0.482625i	−0.971048	−	0.238885i	$-0.923218\pi$
$769$	−4.56946e6	+	7.91454e6i	−0.278644	+	0.482625i	0.692404	+	0.721510i	$0.256552\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−1.35738e7			−0.817060			−0.408530	−	0.912745i	$-0.633959\pi$
$773$	−1.35738e7			−0.817060			−0.408530	+	0.912745i	$0.633959\pi$
$774$		0			0
$775$	1.24105e6			0.0742223
$776$		0			0
$777$		0			0
$778$		0			0
$779$	151023.	−	261580.i	0.00891661	−	0.0154440i
$780$		0			0
$781$	2.51328e6	+	4.35312e6i	0.147439	+	0.255372i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	8.57395e6	+	1.48505e7i	0.496600	+	0.860136i
$786$		0			0
$787$	1.02146e7	−	1.76922e7i	0.587875	−	1.01823i	−0.406635	−	0.913591i	$-0.633298\pi$
$787$	1.02146e7	−	1.76922e7i	0.587875	−	1.01823i	0.994510	−	0.104639i	$-0.0333686\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	1.47976e7			0.840913
$792$		0			0
$793$	−2.67801e7			−1.51227
$794$		0			0
$795$		0			0
$796$		0			0
$797$	1.51983e7	−	2.63242e7i	0.847518	−	1.46794i	−0.0358980	−	0.999355i	$-0.511429\pi$
$797$	1.51983e7	−	2.63242e7i	0.847518	−	1.46794i	0.883416	−	0.468589i	$-0.155238\pi$
$798$		0			0
$799$	−2.59705e7	−	4.49822e7i	−1.43917	−	2.49272i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	9.77314e6	+	1.69276e7i	0.534866	+	0.926416i
$804$		0			0
$805$	−1.43366e7	+	2.48318e7i	−0.779754	+	1.35057i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−3.50428e7			−1.88247			−0.941234	−	0.337755i	$-0.890333\pi$
$809$	−3.50428e7			−1.88247			−0.941234	+	0.337755i	$0.890333\pi$
$810$		0			0
$811$	1.55069e7			0.827893			0.413946	−	0.910301i	$-0.364150\pi$
$811$	1.55069e7			0.827893			0.413946	+	0.910301i	$0.364150\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−2.84343e6	+	4.92496e6i	−0.149951	+	0.259722i
$816$		0			0
$817$	102043.	+	176745.i	0.00534848	+	0.00926383i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−7.58087e6	−	1.31304e7i	−0.392519	−	0.679863i	0.600262	−	0.799804i	$-0.295063\pi$
$821$	−7.58087e6	−	1.31304e7i	−0.392519	−	0.679863i	−0.992781	+	0.119940i	$0.961730\pi$
$822$		0			0
$823$	6.32661e6	−	1.09580e7i	0.325590	−	0.563939i	−0.656041	−	0.754725i	$-0.727770\pi$
$823$	6.32661e6	−	1.09580e7i	0.325590	−	0.563939i	0.981632	+	0.190786i	$0.0611037\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1.21240e7			−0.616427			−0.308213	−	0.951317i	$-0.599731\pi$
$827$	−1.21240e7			−0.616427			−0.308213	+	0.951317i	$0.599731\pi$
$828$		0			0
$829$	−1.79003e7			−0.904634			−0.452317	−	0.891857i	$-0.649402\pi$
$829$	−1.79003e7			−0.904634			−0.452317	+	0.891857i	$0.649402\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	8.29185e6	−	1.43619e7i	0.414037	−	0.717133i
$834$		0			0
$835$	534588.	+	925933.i	0.0265340	+	0.0459583i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−1.17183e7	−	2.02966e7i	−0.574723	−	0.995449i	−0.996072	−	0.0885507i	$-0.971776\pi$
$839$	−1.17183e7	−	2.02966e7i	−0.574723	−	0.995449i	0.421349	−	0.906899i	$-0.361557\pi$
$840$		0			0
$841$	3.62301e6	−	6.27524e6i	0.176636	−	0.305943i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	1.50368e6			0.0724458
$846$		0			0
$847$	−1.78089e7			−0.852960
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−1.33768e7	+	2.31694e7i	−0.633183	+	1.09671i
$852$		0			0
$853$	−1.44546e7	−	2.50361e7i	−0.680196	−	1.17813i	−0.974921	−	0.222552i	$-0.928561\pi$
$853$	−1.44546e7	−	2.50361e7i	−0.680196	−	1.17813i	0.294725	−	0.955582i	$-0.404772\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	5.34804e6	+	9.26307e6i	0.248738	+	0.430827i	0.963176	−	0.268872i	$-0.0866508\pi$
$857$	5.34804e6	+	9.26307e6i	0.248738	+	0.430827i	−0.714438	+	0.699699i	$0.753318\pi$
$858$		0			0
$859$	−1.84851e7	+	3.20172e7i	−0.854752	+	1.48047i	0.0221237	+	0.999755i	$0.492957\pi$
$859$	−1.84851e7	+	3.20172e7i	−0.854752	+	1.48047i	−0.876875	+	0.480718i	$0.840376\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	3.83720e7			1.75383			0.876914	−	0.480646i	$-0.159598\pi$
$863$	3.83720e7			1.75383			0.876914	+	0.480646i	$0.159598\pi$
$864$		0			0
$865$	−2.86211e7			−1.30061
$866$		0			0
$867$		0			0
$868$		0			0
$869$	3.70900e6	−	6.42417e6i	0.166612	−	0.288581i
$870$		0			0
$871$	5.61079e6	+	9.71817e6i	0.250599	+	0.434050i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−1.32405e7	−	2.29332e7i	−0.584633	−	1.01261i
$876$		0			0
$877$	−1.83104e7	+	3.17146e7i	−0.803895	+	1.39239i	0.113140	+	0.993579i	$0.463909\pi$
$877$	−1.83104e7	+	3.17146e7i	−0.803895	+	1.39239i	−0.917035	+	0.398808i	$0.869424\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1.70223e7			0.738889			0.369445	−	0.929253i	$-0.379548\pi$
$881$	1.70223e7			0.738889			0.369445	+	0.929253i	$0.379548\pi$
$882$		0			0
$883$	3.54409e7			1.52969			0.764844	−	0.644215i	$-0.222816\pi$
$883$	3.54409e7			1.52969			0.764844	+	0.644215i	$0.222816\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−6.00360e6	+	1.03985e7i	−0.256214	+	0.443776i	−0.965225	−	0.261422i	$-0.915809\pi$
$887$	−6.00360e6	+	1.03985e7i	−0.256214	+	0.443776i	0.709011	+	0.705198i	$0.249142\pi$
$888$		0			0
$889$	2.37793e7	+	4.11869e7i	1.00912	+	1.74785i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	363890.	+	630276.i	0.0152701	+	0.0264486i
$894$		0			0
$895$	4.32418e6	−	7.48971e6i	0.180446	−	0.312541i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−2.30615e7			−0.951676
$900$		0			0
$901$	−5.41406e7			−2.22183
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−2.11828e6	+	3.66898e6i	−0.0859731	+	0.148910i
$906$		0			0
$907$	4.21452e6	+	7.29977e6i	0.170110	+	0.294639i	0.938458	−	0.345393i	$-0.112254\pi$
$907$	4.21452e6	+	7.29977e6i	0.170110	+	0.294639i	−0.768348	+	0.640032i	$0.778921\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−1.24424e7	−	2.15508e7i	−0.496715	−	0.860335i	0.503278	−	0.864125i	$-0.332127\pi$
$911$	−1.24424e7	−	2.15508e7i	−0.496715	−	0.860335i	−0.999993	+	0.00378921i	$0.998794\pi$
$912$		0			0
$913$	−1.18276e7	+	2.04860e7i	−0.469590	+	0.813354i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−4.96653e7			−1.95043
$918$		0			0
$919$	−3.68789e7			−1.44042			−0.720210	−	0.693757i	$-0.755954\pi$
$919$	−3.68789e7			−1.44042			−0.720210	+	0.693757i	$0.755954\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−6.77282e6	+	1.17309e7i	−0.261677	+	0.453238i
$924$		0			0
$925$	826697.	+	1.43188e6i	0.0317682	+	0.0550241i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−1.30455e7	−	2.25955e7i	−0.495932	−	0.858979i	0.504057	−	0.863670i	$-0.331840\pi$
$929$	−1.30455e7	−	2.25955e7i	−0.495932	−	0.858979i	−0.999989	+	0.00469142i	$0.998507\pi$
$930$		0			0
$931$	−116183.	+	201235.i	−0.00439307	+	0.00760901i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	2.66938e7			0.998576
$936$		0			0
$937$	7.84259e6			0.291817			0.145908	−	0.989298i	$-0.453390\pi$
$937$	7.84259e6			0.291817			0.145908	+	0.989298i	$0.453390\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1.68082e7	+	2.91127e7i	−0.618796	+	1.07179i	0.370910	+	0.928669i	$0.379046\pi$
$941$	−1.68082e7	+	2.91127e7i	−0.618796	+	1.07179i	−0.989706	+	0.143117i	$0.954287\pi$
$942$		0			0
$943$	−1.60896e7	−	2.78681e7i	−0.589206	−	1.02053i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	7.88767e6	+	1.36619e7i	0.285808	+	0.495034i	0.972805	−	0.231627i	$-0.0744048\pi$
$947$	7.88767e6	+	1.36619e7i	0.285808	+	0.495034i	−0.686997	+	0.726660i	$0.741071\pi$
$948$		0			0
$949$	−2.63368e7	+	4.56167e7i	−0.949288	+	1.64421i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	2.32737e7			0.830104			0.415052	−	0.909798i	$-0.363763\pi$
$953$	2.32737e7			0.830104			0.415052	+	0.909798i	$0.363763\pi$
$954$		0			0
$955$	−3.45376e7			−1.22542
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−77105.3	+	133550.i	−0.00270731	+	0.00468920i
$960$		0			0
$961$	−5.73176e6	−	9.92770e6i	−0.200207	−	0.346769i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−2.08541e7	−	3.61203e7i	−0.720896	−	1.24863i
$966$		0			0
$967$	−9.77148e6	+	1.69247e7i	−0.336043	+	0.582043i	−0.983685	−	0.179902i	$-0.942422\pi$
$967$	−9.77148e6	+	1.69247e7i	−0.336043	+	0.582043i	0.647642	+	0.761945i	$0.275755\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	5.59842e7			1.90554			0.952768	−	0.303700i	$-0.0982220\pi$
$971$	5.59842e7			1.90554			0.952768	+	0.303700i	$0.0982220\pi$
$972$		0			0
$973$	1.21638e7			0.411897
$974$		0			0
$975$		0			0
$976$		0			0
$977$	2.10112e6	−	3.63925e6i	0.0704231	−	0.121976i	−0.828664	−	0.559747i	$-0.810898\pi$
$977$	2.10112e6	−	3.63925e6i	0.0704231	−	0.121976i	0.899087	+	0.437770i	$0.144232\pi$
$978$		0			0
$979$	−1.19974e7	−	2.07800e7i	−0.400063	−	0.692930i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	9.07877e6	+	1.57249e7i	0.299670	+	0.519044i	0.976060	−	0.217500i	$-0.0697901\pi$
$983$	9.07877e6	+	1.57249e7i	0.299670	+	0.519044i	−0.676390	+	0.736543i	$0.736457\pi$
$984$		0			0
$985$	1.20036e7	−	2.07909e7i	0.394205	−	0.682782i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	2.17429e7			0.706851
$990$		0			0
$991$	6.51450e6			0.210716			0.105358	−	0.994434i	$-0.466401\pi$
$991$	6.51450e6			0.210716			0.105358	+	0.994434i	$0.466401\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	1.98292e7	−	3.43451e7i	0.634960	−	1.09978i
$996$		0			0
$997$	1.44585e7	+	2.50428e7i	0.460664	+	0.797894i	0.998994	−	0.0448401i	$-0.0142778\pi$
$997$	1.44585e7	+	2.50428e7i	0.460664	+	0.797894i	−0.538330	+	0.842734i	$0.680944\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.6.e.g.109.2		4
3.2	odd	2		324.6.e.f.109.1		4
9.2	odd	6		324.6.e.f.217.1		4
9.4	even	3		108.6.a.b.1.1	✓	2
9.5	odd	6		108.6.a.c.1.2	yes	2
9.7	even	3	inner	324.6.e.g.217.2		4
36.23	even	6		432.6.a.q.1.2		2
36.31	odd	6		432.6.a.r.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.6.a.b.1.1	✓	2	9.4	even	3
108.6.a.c.1.2	yes	2	9.5	odd	6
324.6.e.f.109.1		4	3.2	odd	2
324.6.e.f.217.1		4	9.2	odd	6
324.6.e.g.109.2		4	1.1	even	1	trivial
324.6.e.g.217.2		4	9.7	even	3	inner
432.6.a.q.1.2		2	36.23	even	6
432.6.a.r.1.1		2	36.31	odd	6

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	324.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(28.8141 - 49.9074i) q^{5} +(-78.4422 - 135.866i) q^{7} +O(q^{10})\)	\(q+(28.8141 - 49.9074i) q^{5} +(-78.4422 - 135.866i) q^{7} +(-109.012 - 188.815i) q^{11} +(293.769 - 508.822i) q^{13} -2124.56 q^{17} +29.7687 q^{19} +(1585.74 - 2746.59i) q^{23} +(-98.0000 - 169.741i) q^{25} +(1821.07 + 3154.18i) q^{29} +(-3165.94 + 5483.57i) q^{31} -9040.95 q^{35} -8435.69 q^{37} +(5073.22 - 8787.07i) q^{41} +(3427.88 + 5937.26i) q^{43} +(12223.9 + 21172.4i) q^{47} +(-3902.85 + 6759.94i) q^{49} +25483.2 q^{53} -12564.4 q^{55} +(-10348.1 + 17923.4i) q^{59} +(-22790.1 - 39473.7i) q^{61} +(-16929.3 - 29322.5i) q^{65} +(-9549.67 + 16540.5i) q^{67} -23055.0 q^{71} -89651.6 q^{73} +(-17102.4 + 29622.1i) q^{77} +(17011.8 + 29465.3i) q^{79} +(-54248.7 - 93961.6i) q^{83} +(-61217.3 + 106031. i) q^{85} +110055. q^{89} -92175.4 q^{91} +(857.757 - 1485.68i) q^{95} +(14416.0 + 24969.2i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 32 q^{7}+O(q^{10}) \) 4 * q + 32 * q^7	\( 4 q + 32 q^{7} + 486 q^{11} - 208 q^{13} - 3888 q^{17} - 1264 q^{19} + 6804 q^{23} - 392 q^{25} + 11664 q^{29} - 3328 q^{31} - 39852 q^{35} - 19912 q^{37} + 13608 q^{41} - 4960 q^{43} + 18468 q^{47} - 26676 q^{49} + 23328 q^{53} - 106272 q^{55} + 1944 q^{59} - 8176 q^{61} - 79704 q^{65} - 90064 q^{67} + 89424 q^{71} - 242428 q^{73} - 167184 q^{77} - 28768 q^{79} - 15066 q^{83} - 132840 q^{85} + 357696 q^{89} - 484880 q^{91} + 39852 q^{95} - 88942 q^{97}+O(q^{100}) \) 4 * q + 32 * q^7 + 486 * q^11 - 208 * q^13 - 3888 * q^17 - 1264 * q^19 + 6804 * q^23 - 392 * q^25 + 11664 * q^29 - 3328 * q^31 - 39852 * q^35 - 19912 * q^37 + 13608 * q^41 - 4960 * q^43 + 18468 * q^47 - 26676 * q^49 + 23328 * q^53 - 106272 * q^55 + 1944 * q^59 - 8176 * q^61 - 79704 * q^65 - 90064 * q^67 + 89424 * q^71 - 242428 * q^73 - 167184 * q^77 - 28768 * q^79 - 15066 * q^83 - 132840 * q^85 + 357696 * q^89 - 484880 * q^91 + 39852 * q^95 - 88942 * q^97

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