LMFDB - Embedded newform 3300.2.x.c.1693.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3300,2,Mod(1693,3300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3300, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("3300.1693");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3300 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3300.x (of order $4$, degree $2$, 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:	$26.3506326670$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 660)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1693.11
Character	$\chi$	$=$	3300.1693
Dual form			3300.2.x.c.1957.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{3} +(-1.41964 - 1.41964i) q^{7} +1.00000i q^{9} +O(q^{10})$	$q+(0.707107 + 0.707107i) q^{3} +(-1.41964 - 1.41964i) q^{7} +1.00000i q^{9} +(0.476743 - 3.28218i) q^{11} +(0.145122 - 0.145122i) q^{13} +(3.21300 + 3.21300i) q^{17} -5.69223 q^{19} -2.00767i q^{21} +(0.957657 + 0.957657i) q^{23} +(-0.707107 + 0.707107i) q^{27} -9.39080 q^{29} -2.39625 q^{31} +(2.65796 - 1.98374i) q^{33} +(7.69393 - 7.69393i) q^{37} +0.205234 q^{39} -11.5294i q^{41} +(5.75826 - 5.75826i) q^{43} +(-2.21349 + 2.21349i) q^{47} -2.96927i q^{49} +4.54386i q^{51} +(-2.25736 - 2.25736i) q^{53} +(-4.02502 - 4.02502i) q^{57} +13.4763i q^{59} -6.44414i q^{61} +(1.41964 - 1.41964i) q^{63} +(-6.59960 + 6.59960i) q^{67} +1.35433i q^{69} -6.84581 q^{71} +(-8.61931 + 8.61931i) q^{73} +(-5.33630 + 3.98270i) q^{77} -6.14021 q^{79} -1.00000 q^{81} +(4.69214 - 4.69214i) q^{83} +(-6.64030 - 6.64030i) q^{87} -12.6882i q^{89} -0.412041 q^{91} +(-1.69440 - 1.69440i) q^{93} +(-2.74044 + 2.74044i) q^{97} +(3.28218 + 0.476743i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q + 8 q^{11} - 16 q^{23} + 16 q^{31} + 40 q^{37} - 64 q^{47} - 24 q^{53} - 48 q^{67} - 24 q^{77} - 24 q^{81} - 48 q^{91} - 16 q^{93} + 72 q^{97}+O(q^{100}) $ 24 * q + 8 * q^11 - 16 * q^23 + 16 * q^31 + 40 * q^37 - 64 * q^47 - 24 * q^53 - 48 * q^67 - 24 * q^77 - 24 * q^81 - 48 * q^91 - 16 * q^93 + 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3300\mathbb{Z}\right)^\times$.

$n$	$1201$	$1651$	$2201$	$2377$
$\chi(n)$	$-1$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.41964	−	1.41964i	−0.536572	−	0.536572i	0.385948	−	0.922520i	$-0.373874\pi$
$7$	−1.41964	−	1.41964i	−0.536572	−	0.536572i	−0.922520	+	0.385948i	$0.873874\pi$
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$	0.476743	−	3.28218i	0.143743	−	0.989615i
$11$	0.476743	−	3.28218i	0.143743	−	0.989615i
$12$		0			0
$13$	0.145122	−	0.145122i	0.0402496	−	0.0402496i	−0.686696	−	0.726945i	$-0.740939\pi$
$13$	0.145122	−	0.145122i	0.0402496	−	0.0402496i	0.726945	+	0.686696i	$0.240939\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.21300	+	3.21300i	0.779266	+	0.779266i	0.979706	−	0.200440i	$-0.0642372\pi$
$17$	3.21300	+	3.21300i	0.779266	+	0.779266i	−0.200440	+	0.979706i	$0.564237\pi$
$18$		0			0
$19$	−5.69223			−1.30589			−0.652944	−	0.757406i	$-0.726466\pi$
$19$	−5.69223			−1.30589			−0.652944	+	0.757406i	$0.726466\pi$
$20$		0			0
$21$		−	2.00767i		−	0.438109i
$22$		0			0
$23$	0.957657	+	0.957657i	0.199685	+	0.199685i	0.799865	−	0.600180i	$-0.204904\pi$
$23$	0.957657	+	0.957657i	0.199685	+	0.199685i	−0.600180	+	0.799865i	$0.704904\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$		0			0
$29$	−9.39080			−1.74383			−0.871914	−	0.489659i	$-0.837121\pi$
$29$	−9.39080			−1.74383			−0.871914	+	0.489659i	$0.837121\pi$
$30$		0			0
$31$	−2.39625			−0.430379			−0.215189	−	0.976572i	$-0.569037\pi$
$31$	−2.39625			−0.430379			−0.215189	+	0.976572i	$0.569037\pi$
$32$		0			0
$33$	2.65796	−	1.98374i	0.462692	−	0.345326i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	7.69393	−	7.69393i	1.26487	−	1.26487i	0.316172	−	0.948702i	$-0.397602\pi$
$37$	7.69393	−	7.69393i	1.26487	−	1.26487i	0.948702	−	0.316172i	$-0.102398\pi$
$38$		0			0
$39$	0.205234			0.0328637
$40$		0			0
$41$		−	11.5294i		−	1.80058i	−0.435287	−	0.900292i	$-0.643353\pi$
$41$		−	11.5294i		−	1.80058i	0.435287	−	0.900292i	$-0.356647\pi$
$42$		0			0
$43$	5.75826	−	5.75826i	0.878127	−	0.878127i	−0.115214	−	0.993341i	$-0.536755\pi$
$43$	5.75826	−	5.75826i	0.878127	−	0.878127i	0.993341	+	0.115214i	$0.0367553\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.21349	+	2.21349i	−0.322871	+	0.322871i	−0.849867	−	0.526997i	$-0.823318\pi$
$47$	−2.21349	+	2.21349i	−0.322871	+	0.322871i	0.526997	+	0.849867i	$0.323318\pi$
$48$		0			0
$49$		−	2.96927i		−	0.424181i
$50$		0			0
$51$			4.54386i			0.636268i
$52$		0			0
$53$	−2.25736	−	2.25736i	−0.310072	−	0.310072i	0.534866	−	0.844937i	$-0.320362\pi$
$53$	−2.25736	−	2.25736i	−0.310072	−	0.310072i	−0.844937	+	0.534866i	$0.820362\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−4.02502	−	4.02502i	−0.533126	−	0.533126i
$58$		0			0
$59$			13.4763i			1.75446i	0.480067	+	0.877232i	$0.340612\pi$
$59$			13.4763i			1.75446i	−0.480067	+	0.877232i	$0.659388\pi$
$60$		0			0
$61$		−	6.44414i		−	0.825088i	−0.910938	−	0.412544i	$-0.864640\pi$
$61$		−	6.44414i		−	0.825088i	0.910938	−	0.412544i	$-0.135360\pi$
$62$		0			0
$63$	1.41964	−	1.41964i	0.178857	−	0.178857i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−6.59960	+	6.59960i	−0.806269	+	0.806269i	−0.984067	−	0.177798i	$-0.943103\pi$
$67$	−6.59960	+	6.59960i	−0.806269	+	0.806269i	0.177798	+	0.984067i	$0.443103\pi$
$68$		0			0
$69$			1.35433i			0.163042i
$70$		0			0
$71$	−6.84581			−0.812448			−0.406224	−	0.913774i	$-0.633155\pi$
$71$	−6.84581			−0.812448			−0.406224	+	0.913774i	$0.633155\pi$
$72$		0			0
$73$	−8.61931	+	8.61931i	−1.00881	+	1.00881i	−0.00885306	+	0.999961i	$0.502818\pi$
$73$	−8.61931	+	8.61931i	−1.00881	+	1.00881i	−0.999961	+	0.00885306i	$0.997182\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−5.33630	+	3.98270i	−0.608128	+	0.453871i
$78$		0			0
$79$	−6.14021			−0.690827			−0.345414	−	0.938451i	$-0.612261\pi$
$79$	−6.14021			−0.690827			−0.345414	+	0.938451i	$0.612261\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	4.69214	−	4.69214i	0.515029	−	0.515029i	−0.401034	−	0.916063i	$-0.631349\pi$
$83$	4.69214	−	4.69214i	0.515029	−	0.515029i	0.916063	+	0.401034i	$0.131349\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−6.64030	−	6.64030i	−0.711915	−	0.711915i
$88$		0			0
$89$		−	12.6882i		−	1.34495i	−0.740120	−	0.672475i	$-0.765231\pi$
$89$		−	12.6882i		−	1.34495i	0.740120	−	0.672475i	$-0.234769\pi$
$90$		0			0
$91$	−0.412041			−0.0431936
$92$		0			0
$93$	−1.69440	−	1.69440i	−0.175701	−	0.175701i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−2.74044	+	2.74044i	−0.278250	+	0.278250i	−0.832410	−	0.554160i	$-0.813039\pi$
$97$	−2.74044	+	2.74044i	−0.278250	+	0.278250i	0.554160	+	0.832410i	$0.313039\pi$
$98$		0			0
$99$	3.28218	+	0.476743i	0.329872	+	0.0479145i
$100$		0			0
$101$		−	13.4635i		−	1.33966i	−0.742513	−	0.669832i	$-0.766366\pi$
$101$		−	13.4635i		−	1.33966i	0.742513	−	0.669832i	$-0.233634\pi$
$102$		0			0
$103$	−7.22358	−	7.22358i	−0.711760	−	0.711760i	0.255143	−	0.966903i	$-0.417877\pi$
$103$	−7.22358	−	7.22358i	−0.711760	−	0.711760i	−0.966903	+	0.255143i	$0.917877\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.266335	−	0.266335i	−0.0257475	−	0.0257475i	0.694116	−	0.719863i	$-0.255796\pi$
$107$	−0.266335	−	0.266335i	−0.0257475	−	0.0257475i	−0.719863	+	0.694116i	$0.755796\pi$
$108$		0			0
$109$	5.07239			0.485847			0.242923	−	0.970045i	$-0.421894\pi$
$109$	5.07239			0.485847			0.242923	+	0.970045i	$0.421894\pi$
$110$		0			0
$111$	10.8809			1.03277
$112$		0			0
$113$	−4.00794	−	4.00794i	−0.377035	−	0.377035i	0.492996	−	0.870031i	$-0.335902\pi$
$113$	−4.00794	−	4.00794i	−0.377035	−	0.377035i	−0.870031	+	0.492996i	$0.835902\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.145122	+	0.145122i	0.0134165	+	0.0134165i
$118$		0			0
$119$		−	9.12257i		−	0.836264i
$120$		0			0
$121$	−10.5454	−	3.12952i	−0.958676	−	0.284501i
$122$		0			0
$123$	8.15249	−	8.15249i	0.735085	−	0.735085i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−11.4505	−	11.4505i	−1.01607	−	1.01607i	−0.999869	−	0.0161984i	$-0.994844\pi$
$127$	−11.4505	−	11.4505i	−1.01607	−	1.01607i	−0.0161984	−	0.999869i	$-0.505156\pi$
$128$		0			0
$129$	8.14342			0.716988
$130$		0			0
$131$		−	10.8893i		−	0.951403i	−0.879607	−	0.475701i	$-0.842194\pi$
$131$		−	10.8893i		−	0.951403i	0.879607	−	0.475701i	$-0.157806\pi$
$132$		0			0
$133$	8.08089	+	8.08089i	0.700702	+	0.700702i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	13.0742	−	13.0742i	1.11700	−	1.11700i	0.124822	−	0.992179i	$-0.460164\pi$
$137$	13.0742	−	13.0742i	1.11700	−	1.11700i	0.992179	−	0.124822i	$-0.0398359\pi$
$138$		0			0
$139$	−11.3316			−0.961134			−0.480567	−	0.876958i	$-0.659569\pi$
$139$	−11.3316			−0.961134			−0.480567	+	0.876958i	$0.659569\pi$
$140$		0			0
$141$	−3.13035			−0.263623
$142$		0			0
$143$	−0.407131	−	0.545503i	−0.0340460	−	0.0456172i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	2.09959	−	2.09959i	0.173171	−	0.173171i
$148$		0			0
$149$	5.06586			0.415012			0.207506	−	0.978234i	$-0.433465\pi$
$149$	5.06586			0.415012			0.207506	+	0.978234i	$0.433465\pi$
$150$		0			0
$151$			14.6099i			1.18894i	0.804118	+	0.594470i	$0.202638\pi$
$151$			14.6099i			1.18894i	−0.804118	+	0.594470i	$0.797362\pi$
$152$		0			0
$153$	−3.21300	+	3.21300i	−0.259755	+	0.259755i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−8.77316	+	8.77316i	−0.700174	+	0.700174i	−0.964448	−	0.264273i	$-0.914868\pi$
$157$	−8.77316	+	8.77316i	−0.700174	+	0.700174i	0.264273	+	0.964448i	$0.414868\pi$
$158$		0			0
$159$		−	3.19238i		−	0.253172i
$160$		0			0
$161$		−	2.71905i		−	0.214291i
$162$		0			0
$163$	2.73430	+	2.73430i	0.214167	+	0.214167i	0.806035	−	0.591868i	$-0.201609\pi$
$163$	2.73430	+	2.73430i	0.214167	+	0.214167i	−0.591868	+	0.806035i	$0.701609\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−13.6725	−	13.6725i	−1.05801	−	1.05801i	−0.998211	−	0.0597971i	$-0.980955\pi$
$167$	−13.6725	−	13.6725i	−1.05801	−	1.05801i	−0.0597971	−	0.998211i	$-0.519045\pi$
$168$		0			0
$169$			12.9579i			0.996760i
$170$		0			0
$171$		−	5.69223i		−	0.435296i
$172$		0			0
$173$	4.71150	−	4.71150i	0.358208	−	0.358208i	−0.504944	−	0.863152i	$-0.668487\pi$
$173$	4.71150	−	4.71150i	0.358208	−	0.358208i	0.863152	+	0.504944i	$0.168487\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−9.52917	+	9.52917i	−0.716257	+	0.716257i
$178$		0			0
$179$		−	3.38697i		−	0.253154i	−0.991957	−	0.126577i	$-0.959601\pi$
$179$		−	3.38697i		−	0.253154i	0.991957	−	0.126577i	$-0.0403990\pi$
$180$		0			0
$181$	18.6393			1.38545			0.692723	−	0.721204i	$-0.256411\pi$
$181$	18.6393			1.38545			0.692723	+	0.721204i	$0.256411\pi$
$182$		0			0
$183$	4.55670	−	4.55670i	0.336841	−	0.336841i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	12.0774	−	9.01386i	0.883188	−	0.659159i
$188$		0			0
$189$	2.00767			0.146036
$190$		0			0
$191$	4.01094			0.290222			0.145111	−	0.989415i	$-0.453646\pi$
$191$	4.01094			0.290222			0.145111	+	0.989415i	$0.453646\pi$
$192$		0			0
$193$	0.897030	−	0.897030i	0.0645697	−	0.0645697i	−0.674085	−	0.738654i	$-0.735462\pi$
$193$	0.897030	−	0.897030i	0.0645697	−	0.0645697i	0.738654	+	0.674085i	$0.235462\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	3.10561	+	3.10561i	0.221265	+	0.221265i	0.809031	−	0.587766i	$-0.199992\pi$
$197$	3.10561	+	3.10561i	0.221265	+	0.221265i	−0.587766	+	0.809031i	$0.699992\pi$
$198$		0			0
$199$		−	3.98233i		−	0.282300i	−0.989988	−	0.141150i	$-0.954920\pi$
$199$		−	3.98233i		−	0.282300i	0.989988	−	0.141150i	$-0.0450799\pi$
$200$		0			0
$201$	−9.33324			−0.658316
$202$		0			0
$203$	13.3315	+	13.3315i	0.935689	+	0.935689i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−0.957657	+	0.957657i	−0.0665618	+	0.0665618i
$208$		0			0
$209$	−2.71373	+	18.6829i	−0.187713	+	1.29233i
$210$		0			0
$211$			5.21688i			0.359145i	0.983745	+	0.179572i	$0.0574714\pi$
$211$			5.21688i			0.359145i	−0.983745	+	0.179572i	$0.942529\pi$
$212$		0			0
$213$	−4.84072	−	4.84072i	−0.331680	−	0.331680i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	3.40180	+	3.40180i	0.230929	+	0.230929i
$218$		0			0
$219$	−12.1895			−0.823693
$220$		0			0
$221$	0.932553			0.0627303
$222$		0			0
$223$	−3.45760	−	3.45760i	−0.231538	−	0.231538i	0.581796	−	0.813335i	$-0.302350\pi$
$223$	−3.45760	−	3.45760i	−0.231538	−	0.231538i	−0.813335	+	0.581796i	$0.802350\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1.54979	+	1.54979i	0.102863	+	0.102863i	0.756665	−	0.653802i	$-0.226827\pi$
$227$	1.54979	+	1.54979i	0.102863	+	0.102863i	−0.653802	+	0.756665i	$0.726827\pi$
$228$		0			0
$229$		−	12.0816i		−	0.798377i	−0.916869	−	0.399189i	$-0.869292\pi$
$229$		−	12.0816i		−	0.798377i	0.916869	−	0.399189i	$-0.130708\pi$
$230$		0			0
$231$	−6.58953	−	0.957142i	−0.433559	−	0.0629753i
$232$		0			0
$233$	13.0324	−	13.0324i	0.853782	−	0.853782i	−0.136815	−	0.990597i	$-0.543687\pi$
$233$	13.0324	−	13.0324i	0.853782	−	0.853782i	0.990597	+	0.136815i	$0.0436865\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−4.34178	−	4.34178i	−0.282029	−	0.282029i
$238$		0			0
$239$	2.82112			0.182483			0.0912416	−	0.995829i	$-0.470916\pi$
$239$	2.82112			0.182483			0.0912416	+	0.995829i	$0.470916\pi$
$240$		0			0
$241$		−	1.09501i		−	0.0705357i	−0.999378	−	0.0352678i	$-0.988772\pi$
$241$		−	1.09501i		−	0.0705357i	0.999378	−	0.0352678i	$-0.0112284\pi$
$242$		0			0
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−0.826068	+	0.826068i	−0.0525615	+	0.0525615i
$248$		0			0
$249$	6.63568			0.420519
$250$		0			0
$251$	11.2736			0.711586			0.355793	−	0.934565i	$-0.384211\pi$
$251$	11.2736			0.711586			0.355793	+	0.934565i	$0.384211\pi$
$252$		0			0
$253$	3.59976	−	2.68665i	0.226315	−	0.168908i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	11.6860	−	11.6860i	0.728953	−	0.728953i	−0.241458	−	0.970411i	$-0.577626\pi$
$257$	11.6860	−	11.6860i	0.728953	−	0.728953i	0.970411	+	0.241458i	$0.0776256\pi$
$258$		0			0
$259$	−21.8451			−1.35739
$260$		0			0
$261$		−	9.39080i		−	0.581276i
$262$		0			0
$263$	9.66997	−	9.66997i	0.596276	−	0.596276i	−0.343044	−	0.939319i	$-0.611458\pi$
$263$	9.66997	−	9.66997i	0.596276	−	0.596276i	0.939319	+	0.343044i	$0.111458\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	8.97194	−	8.97194i	0.549074	−	0.549074i
$268$		0			0
$269$			14.0667i			0.857662i	0.903385	+	0.428831i	$0.141074\pi$
$269$			14.0667i			0.857662i	−0.903385	+	0.428831i	$0.858926\pi$
$270$		0			0
$271$		−	18.9922i		−	1.15369i	−0.816852	−	0.576847i	$-0.804283\pi$
$271$		−	18.9922i		−	1.15369i	0.816852	−	0.576847i	$-0.195717\pi$
$272$		0			0
$273$	−0.291357	−	0.291357i	−0.0176337	−	0.0176337i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	17.6125	+	17.6125i	1.05823	+	1.05823i	0.998196	+	0.0600349i	$0.0191212\pi$
$277$	17.6125	+	17.6125i	1.05823	+	1.05823i	0.0600349	+	0.998196i	$0.480879\pi$
$278$		0			0
$279$		−	2.39625i		−	0.143460i
$280$		0			0
$281$			3.46118i			0.206477i	0.994657	+	0.103238i	$0.0329205\pi$
$281$			3.46118i			0.206477i	−0.994657	+	0.103238i	$0.967080\pi$
$282$		0			0
$283$	−11.7091	+	11.7091i	−0.696033	+	0.696033i	−0.963553	−	0.267519i	$-0.913796\pi$
$283$	−11.7091	+	11.7091i	−0.696033	+	0.696033i	0.267519	+	0.963553i	$0.413796\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−16.3675	+	16.3675i	−0.966143	+	0.966143i
$288$		0			0
$289$			3.64668i			0.214511i
$290$		0			0
$291$	−3.87557			−0.227190
$292$		0			0
$293$	5.64180	−	5.64180i	0.329597	−	0.329597i	−0.522836	−	0.852433i	$-0.675126\pi$
$293$	5.64180	−	5.64180i	0.329597	−	0.329597i	0.852433	+	0.522836i	$0.175126\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	1.98374	+	2.65796i	0.115109	+	0.154231i
$298$		0			0
$299$	0.277954			0.0160745
$300$		0			0
$301$	−16.3493			−0.942356
$302$		0			0
$303$	9.52010	−	9.52010i	0.546915	−	0.546915i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	13.4805	+	13.4805i	0.769375	+	0.769375i	0.977997	−	0.208621i	$-0.0668976\pi$
$307$	13.4805	+	13.4805i	0.769375	+	0.769375i	−0.208621	+	0.977997i	$0.566898\pi$
$308$		0			0
$309$		−	10.2157i		−	0.581150i
$310$		0			0
$311$	−24.9510			−1.41484			−0.707421	−	0.706792i	$-0.750142\pi$
$311$	−24.9510			−1.41484			−0.707421	+	0.706792i	$0.750142\pi$
$312$		0			0
$313$	−5.09323	−	5.09323i	−0.287886	−	0.287886i	0.548358	−	0.836244i	$-0.315253\pi$
$313$	−5.09323	−	5.09323i	−0.287886	−	0.287886i	−0.836244	+	0.548358i	$0.815253\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−16.9245	+	16.9245i	−0.950575	+	0.950575i	−0.998835	−	0.0482601i	$-0.984632\pi$
$317$	−16.9245	+	16.9245i	−0.950575	+	0.950575i	0.0482601	+	0.998835i	$0.484632\pi$
$318$		0			0
$319$	−4.47700	+	30.8223i	−0.250664	+	1.72572i
$320$		0			0
$321$		−	0.376654i		−	0.0210228i
$322$		0			0
$323$	−18.2891	−	18.2891i	−1.01763	−	1.01763i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	3.58672	+	3.58672i	0.198346	+	0.198346i
$328$		0			0
$329$	6.28470			0.346487
$330$		0			0
$331$	9.45326			0.519598			0.259799	−	0.965663i	$-0.416344\pi$
$331$	9.45326			0.519598			0.259799	+	0.965663i	$0.416344\pi$
$332$		0			0
$333$	7.69393	+	7.69393i	0.421625	+	0.421625i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	18.9524	+	18.9524i	1.03240	+	1.03240i	0.999457	+	0.0329454i	$0.0104887\pi$
$337$	18.9524	+	18.9524i	1.03240	+	1.03240i	0.0329454	+	0.999457i	$0.489511\pi$
$338$		0			0
$339$		−	5.66808i		−	0.307848i
$340$		0			0
$341$	−1.14239	+	7.86492i	−0.0618642	+	0.425909i
$342$		0			0
$343$	−14.1527	+	14.1527i	−0.764176	+	0.764176i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−1.52241	−	1.52241i	−0.0817273	−	0.0817273i	0.665061	−	0.746789i	$-0.268405\pi$
$347$	−1.52241	−	1.52241i	−0.0817273	−	0.0817273i	−0.746789	+	0.665061i	$0.768405\pi$
$348$		0			0
$349$	−30.5386			−1.63469			−0.817346	−	0.576147i	$-0.804556\pi$
$349$	−30.5386			−1.63469			−0.817346	+	0.576147i	$0.804556\pi$
$350$		0			0
$351$			0.205234i			0.0109546i
$352$		0			0
$353$	11.8541	+	11.8541i	0.630930	+	0.630930i	0.948301	−	0.317371i	$-0.102800\pi$
$353$	11.8541	+	11.8541i	0.630930	+	0.630930i	−0.317371	+	0.948301i	$0.602800\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	6.45063	−	6.45063i	0.341403	−	0.341403i
$358$		0			0
$359$	8.44992			0.445970			0.222985	−	0.974822i	$-0.428420\pi$
$359$	8.44992			0.445970			0.222985	+	0.974822i	$0.428420\pi$
$360$		0			0
$361$	13.4015			0.705342
$362$		0			0
$363$	−5.24384	−	9.66965i	−0.275230	−	0.507525i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	13.8240	−	13.8240i	0.721608	−	0.721608i	−0.247324	−	0.968933i	$-0.579551\pi$
$367$	13.8240	−	13.8240i	0.721608	−	0.721608i	0.968933	+	0.247324i	$0.0795513\pi$
$368$		0			0
$369$	11.5294			0.600195
$370$		0			0
$371$			6.40924i			0.332751i
$372$		0			0
$373$	−18.0741	+	18.0741i	−0.935844	+	0.935844i	−0.998063	−	0.0622190i	$-0.980182\pi$
$373$	−18.0741	+	18.0741i	−0.935844	+	0.935844i	0.0622190	+	0.998063i	$0.480182\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−1.36281	+	1.36281i	−0.0701884	+	0.0701884i
$378$		0			0
$379$		−	12.9668i		−	0.666057i	−0.942917	−	0.333029i	$-0.891929\pi$
$379$		−	12.9668i		−	0.666057i	0.942917	−	0.333029i	$-0.108071\pi$
$380$		0			0
$381$		−	16.1934i		−	0.829615i
$382$		0			0
$383$	−6.34581	−	6.34581i	−0.324256	−	0.324256i	0.526142	−	0.850397i	$-0.323638\pi$
$383$	−6.34581	−	6.34581i	−0.324256	−	0.324256i	−0.850397	+	0.526142i	$0.823638\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	5.75826	+	5.75826i	0.292709	+	0.292709i
$388$		0			0
$389$		−	24.1883i		−	1.22639i	−0.789930	−	0.613197i	$-0.789883\pi$
$389$		−	24.1883i		−	1.22639i	0.789930	−	0.613197i	$-0.210117\pi$
$390$		0			0
$391$			6.15390i			0.311216i
$392$		0			0
$393$	7.69990	−	7.69990i	0.388409	−	0.388409i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	9.80413	−	9.80413i	0.492055	−	0.492055i	−0.416898	−	0.908953i	$-0.636883\pi$
$397$	9.80413	−	9.80413i	0.492055	−	0.492055i	0.908953	+	0.416898i	$0.136883\pi$
$398$		0			0
$399$			11.4281i			0.572121i
$400$		0			0
$401$	7.66805			0.382924			0.191462	−	0.981500i	$-0.438677\pi$
$401$	7.66805			0.382924			0.191462	+	0.981500i	$0.438677\pi$
$402$		0			0
$403$	−0.347748	+	0.347748i	−0.0173226	+	0.0173226i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−21.5848	−	28.9209i	−1.06992	−	1.43356i
$408$		0			0
$409$	4.63333			0.229104			0.114552	−	0.993417i	$-0.463457\pi$
$409$	4.63333			0.229104			0.114552	+	0.993417i	$0.463457\pi$
$410$		0			0
$411$	18.4897			0.912027
$412$		0			0
$413$	19.1314	−	19.1314i	0.941396	−	0.941396i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−8.01266	−	8.01266i	−0.392381	−	0.392381i
$418$		0			0
$419$		−	25.0447i		−	1.22352i	−0.791045	−	0.611758i	$-0.790463\pi$
$419$		−	25.0447i		−	1.22352i	0.791045	−	0.611758i	$-0.209537\pi$
$420$		0			0
$421$	13.6388			0.664715			0.332357	−	0.943153i	$-0.392156\pi$
$421$	13.6388			0.664715			0.332357	+	0.943153i	$0.392156\pi$
$422$		0			0
$423$	−2.21349	−	2.21349i	−0.107624	−	0.107624i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−9.14833	+	9.14833i	−0.442719	+	0.442719i
$428$		0			0
$429$	0.0978437	−	0.673614i	0.00472394	−	0.0325224i
$430$		0			0
$431$		−	5.00629i		−	0.241145i	−0.992705	−	0.120572i	$-0.961527\pi$
$431$		−	5.00629i		−	0.241145i	0.992705	−	0.120572i	$-0.0384730\pi$
$432$		0			0
$433$	22.4842	+	22.4842i	1.08052	+	1.08052i	0.996461	+	0.0840597i	$0.0267887\pi$
$433$	22.4842	+	22.4842i	1.08052	+	1.08052i	0.0840597	+	0.996461i	$0.473211\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−5.45121	−	5.45121i	−0.260767	−	0.260767i
$438$		0			0
$439$	−33.1102			−1.58026			−0.790132	−	0.612937i	$-0.789988\pi$
$439$	−33.1102			−1.58026			−0.790132	+	0.612937i	$0.789988\pi$
$440$		0			0
$441$	2.96927			0.141394
$442$		0			0
$443$	1.72992	+	1.72992i	0.0821909	+	0.0821909i	0.747007	−	0.664816i	$-0.231490\pi$
$443$	1.72992	+	1.72992i	0.0821909	+	0.0821909i	−0.664816	+	0.747007i	$0.731490\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	3.58211	+	3.58211i	0.169428	+	0.169428i
$448$		0			0
$449$		−	6.22627i		−	0.293836i	−0.989149	−	0.146918i	$-0.953065\pi$
$449$		−	6.22627i		−	0.293836i	0.989149	−	0.146918i	$-0.0469353\pi$
$450$		0			0
$451$	−37.8415	−	5.49654i	−1.78188	−	0.258822i
$452$		0			0
$453$	−10.3308	+	10.3308i	−0.485383	+	0.485383i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	15.7357	+	15.7357i	0.736085	+	0.736085i	0.971818	−	0.235733i	$-0.0757490\pi$
$457$	15.7357	+	15.7357i	0.736085	+	0.736085i	−0.235733	+	0.971818i	$0.575749\pi$
$458$		0			0
$459$	−4.54386			−0.212089
$460$		0			0
$461$			17.9297i			0.835069i	0.908661	+	0.417534i	$0.137106\pi$
$461$			17.9297i			0.835069i	−0.908661	+	0.417534i	$0.862894\pi$
$462$		0			0
$463$	24.8279	+	24.8279i	1.15385	+	1.15385i	0.985774	+	0.168078i	$0.0537560\pi$
$463$	24.8279	+	24.8279i	1.15385	+	1.15385i	0.168078	+	0.985774i	$0.446244\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	19.9139	−	19.9139i	0.921507	−	0.921507i	−0.0756289	−	0.997136i	$-0.524096\pi$
$467$	19.9139	−	19.9139i	0.921507	−	0.921507i	0.997136	+	0.0756289i	$0.0240964\pi$
$468$		0			0
$469$	18.7381			0.865243
$470$		0			0
$471$	−12.4071			−0.571690
$472$		0			0
$473$	−16.1545	−	21.6449i	−0.742783	−	0.995233i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	2.25736	−	2.25736i	0.103357	−	0.103357i
$478$		0			0
$479$	19.8344			0.906256			0.453128	−	0.891445i	$-0.350308\pi$
$479$	19.8344			0.906256			0.453128	+	0.891445i	$0.350308\pi$
$480$		0			0
$481$		−	2.23312i		−	0.101821i
$482$		0			0
$483$	1.92266	−	1.92266i	0.0874839	−	0.0874839i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−26.4609	+	26.4609i	−1.19906	+	1.19906i	−0.224611	+	0.974448i	$0.572111\pi$
$487$	−26.4609	+	26.4609i	−1.19906	+	1.19906i	−0.974448	+	0.224611i	$0.927889\pi$
$488$		0			0
$489$			3.86689i			0.174867i
$490$		0			0
$491$			39.2359i			1.77069i	0.464933	+	0.885346i	$0.346078\pi$
$491$			39.2359i			1.77069i	−0.464933	+	0.885346i	$0.653922\pi$
$492$		0			0
$493$	−30.1726	−	30.1726i	−1.35891	−	1.35891i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	9.71855	+	9.71855i	0.435937	+	0.435937i
$498$		0			0
$499$			32.5595i			1.45756i	0.684747	+	0.728781i	$0.259913\pi$
$499$			32.5595i			1.45756i	−0.684747	+	0.728781i	$0.740087\pi$
$500$		0			0
$501$		−	19.3358i		−	0.863860i
$502$		0			0
$503$	−11.0832	+	11.0832i	−0.494177	+	0.494177i	−0.909619	−	0.415443i	$-0.863627\pi$
$503$	−11.0832	+	11.0832i	−0.494177	+	0.494177i	0.415443	+	0.909619i	$0.363627\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−9.16260	+	9.16260i	−0.406926	+	0.406926i
$508$		0			0
$509$			13.4112i			0.594440i	0.954809	+	0.297220i	$0.0960595\pi$
$509$			13.4112i			0.594440i	−0.954809	+	0.297220i	$0.903941\pi$
$510$		0			0
$511$	24.4726			1.08260
$512$		0			0
$513$	4.02502	−	4.02502i	0.177709	−	0.177709i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	6.20981	+	8.32034i	0.273107	+	0.365928i
$518$		0			0
$519$	6.66306			0.292476
$520$		0			0
$521$	−10.0696			−0.441155			−0.220578	−	0.975369i	$-0.570794\pi$
$521$	−10.0696			−0.441155			−0.220578	+	0.975369i	$0.570794\pi$
$522$		0			0
$523$	−32.2051	+	32.2051i	−1.40823	+	1.40823i	−0.639141	+	0.769090i	$0.720710\pi$
$523$	−32.2051	+	32.2051i	−1.40823	+	1.40823i	−0.769090	+	0.639141i	$0.779290\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−7.69914	−	7.69914i	−0.335380	−	0.335380i
$528$		0			0
$529$		−	21.1658i		−	0.920252i
$530$		0			0
$531$	−13.4763			−0.584821
$532$		0			0
$533$	−1.67316	−	1.67316i	−0.0724728	−	0.0724728i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	2.39495	−	2.39495i	0.103350	−	0.103350i
$538$		0			0
$539$	−9.74568	−	1.41558i	−0.419776	−	0.0609733i
$540$		0			0
$541$			17.7894i			0.764828i	0.923991	+	0.382414i	$0.124907\pi$
$541$			17.7894i			0.764828i	−0.923991	+	0.382414i	$0.875093\pi$
$542$		0			0
$543$	13.1800	+	13.1800i	0.565606	+	0.565606i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−2.25426	−	2.25426i	−0.0963852	−	0.0963852i	0.657270	−	0.753655i	$-0.271711\pi$
$547$	−2.25426	−	2.25426i	−0.0963852	−	0.0963852i	−0.753655	+	0.657270i	$0.771711\pi$
$548$		0			0
$549$	6.44414			0.275029
$550$		0			0
$551$	53.4546			2.27724
$552$		0			0
$553$	8.71686	+	8.71686i	0.370678	+	0.370678i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−25.8844	−	25.8844i	−1.09676	−	1.09676i	−0.994788	−	0.101970i	$-0.967486\pi$
$557$	−25.8844	−	25.8844i	−1.09676	−	1.09676i	−0.101970	−	0.994788i	$-0.532514\pi$
$558$		0			0
$559$		−	1.67130i		−	0.0706885i
$560$		0			0
$561$	14.9138	+	2.16626i	0.629660	+	0.0914594i
$562$		0			0
$563$	−20.9843	+	20.9843i	−0.884382	+	0.884382i	−0.993976	−	0.109594i	$-0.965045\pi$
$563$	−20.9843	+	20.9843i	−0.884382	+	0.884382i	0.109594	+	0.993976i	$0.465045\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	1.41964	+	1.41964i	0.0596191	+	0.0596191i
$568$		0			0
$569$	6.26435			0.262615			0.131308	−	0.991342i	$-0.458082\pi$
$569$	6.26435			0.262615			0.131308	+	0.991342i	$0.458082\pi$
$570$		0			0
$571$			20.9444i			0.876497i	0.898854	+	0.438249i	$0.144401\pi$
$571$			20.9444i			0.876497i	−0.898854	+	0.438249i	$0.855599\pi$
$572$		0			0
$573$	2.83617	+	2.83617i	0.118483	+	0.118483i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−4.53489	+	4.53489i	−0.188790	+	0.188790i	−0.795173	−	0.606383i	$-0.792620\pi$
$577$	−4.53489	+	4.53489i	−0.188790	+	0.188790i	0.606383	+	0.795173i	$0.292620\pi$
$578$		0			0
$579$	1.26859			0.0527209
$580$		0			0
$581$	−13.3223			−0.552700
$582$		0			0
$583$	−8.48523	+	6.33287i	−0.351422	+	0.262281i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	1.98863	−	1.98863i	0.0820795	−	0.0820795i	−0.664875	−	0.746955i	$-0.731515\pi$
$587$	1.98863	−	1.98863i	0.0820795	−	0.0820795i	0.746955	+	0.664875i	$0.231515\pi$
$588$		0			0
$589$	13.6400			0.562026
$590$		0			0
$591$			4.39199i			0.180662i
$592$		0			0
$593$	5.13480	−	5.13480i	0.210861	−	0.210861i	−0.593772	−	0.804633i	$-0.702362\pi$
$593$	5.13480	−	5.13480i	0.210861	−	0.210861i	0.804633	+	0.593772i	$0.202362\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	2.81593	−	2.81593i	0.115248	−	0.115248i
$598$		0			0
$599$		−	9.94504i		−	0.406343i	−0.979143	−	0.203172i	$-0.934875\pi$
$599$		−	9.94504i		−	0.406343i	0.979143	−	0.203172i	$-0.0651249\pi$
$600$		0			0
$601$			39.3997i			1.60715i	0.595206	+	0.803573i	$0.297070\pi$
$601$			39.3997i			1.60715i	−0.595206	+	0.803573i	$0.702930\pi$
$602$		0			0
$603$	−6.59960	−	6.59960i	−0.268756	−	0.268756i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−19.6389	−	19.6389i	−0.797118	−	0.797118i	0.185522	−	0.982640i	$-0.440602\pi$
$607$	−19.6389	−	19.6389i	−0.797118	−	0.797118i	−0.982640	+	0.185522i	$0.940602\pi$
$608$		0			0
$609$			18.8536i			0.763987i
$610$		0			0
$611$			0.642452i			0.0259908i
$612$		0			0
$613$	−20.4336	+	20.4336i	−0.825305	+	0.825305i	−0.986863	−	0.161558i	$-0.948348\pi$
$613$	−20.4336	+	20.4336i	−0.825305	+	0.825305i	0.161558	+	0.986863i	$0.448348\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−28.8165	+	28.8165i	−1.16011	+	1.16011i	−0.175659	+	0.984451i	$0.556206\pi$
$617$	−28.8165	+	28.8165i	−1.16011	+	1.16011i	−0.984451	+	0.175659i	$0.943794\pi$
$618$		0			0
$619$		−	14.4468i		−	0.580665i	−0.956926	−	0.290333i	$-0.906234\pi$
$619$		−	14.4468i		−	0.580665i	0.956926	−	0.290333i	$-0.0937660\pi$
$620$		0			0
$621$	−1.35433			−0.0543475
$622$		0			0
$623$	−18.0127	+	18.0127i	−0.721662	+	0.721662i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−15.1297	+	11.2919i	−0.604223	+	0.450956i
$628$		0			0
$629$	49.4411			1.97135
$630$		0			0
$631$	17.2681			0.687434			0.343717	−	0.939073i	$-0.388314\pi$
$631$	17.2681			0.687434			0.343717	+	0.939073i	$0.388314\pi$
$632$		0			0
$633$	−3.68889	+	3.68889i	−0.146620	+	0.146620i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−0.430906	−	0.430906i	−0.0170731	−	0.0170731i
$638$		0			0
$639$		−	6.84581i		−	0.270816i
$640$		0			0
$641$	−32.4657			−1.28232			−0.641160	−	0.767407i	$-0.721546\pi$
$641$	−32.4657			−1.28232			−0.641160	+	0.767407i	$0.721546\pi$
$642$		0			0
$643$	1.61548	+	1.61548i	0.0637083	+	0.0637083i	0.738243	−	0.674535i	$-0.235656\pi$
$643$	1.61548	+	1.61548i	0.0637083	+	0.0637083i	−0.674535	+	0.738243i	$0.735656\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	16.0536	−	16.0536i	0.631132	−	0.631132i	−0.317220	−	0.948352i	$-0.602749\pi$
$647$	16.0536	−	16.0536i	0.631132	−	0.631132i	0.948352	+	0.317220i	$0.102749\pi$
$648$		0			0
$649$	44.2316	+	6.42473i	1.73624	+	0.252193i
$650$		0			0
$651$			4.81087i			0.188553i
$652$		0			0
$653$	−1.62087	−	1.62087i	−0.0634294	−	0.0634294i	0.674681	−	0.738110i	$-0.264281\pi$
$653$	−1.62087	−	1.62087i	−0.0634294	−	0.0634294i	−0.738110	+	0.674681i	$0.764281\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−8.61931	−	8.61931i	−0.336271	−	0.336271i
$658$		0			0
$659$	39.4221			1.53567			0.767833	−	0.640649i	$-0.221335\pi$
$659$	39.4221			1.53567			0.767833	+	0.640649i	$0.221335\pi$
$660$		0			0
$661$	−34.4378			−1.33947			−0.669737	−	0.742598i	$-0.733593\pi$
$661$	−34.4378			−1.33947			−0.669737	+	0.742598i	$0.733593\pi$
$662$		0			0
$663$	0.659414	+	0.659414i	0.0256095	+	0.0256095i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−8.99317	−	8.99317i	−0.348217	−	0.348217i
$668$		0			0
$669$		−	4.88979i		−	0.189050i
$670$		0			0
$671$	−21.1508	−	3.07220i	−0.816519	−	0.118601i
$672$		0			0
$673$	18.8034	−	18.8034i	0.724819	−	0.724819i	−0.244763	−	0.969583i	$-0.578710\pi$
$673$	18.8034	−	18.8034i	0.724819	−	0.724819i	0.969583	+	0.244763i	$0.0787103\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−19.7637	−	19.7637i	−0.759582	−	0.759582i	0.216664	−	0.976246i	$-0.430482\pi$
$677$	−19.7637	−	19.7637i	−0.759582	−	0.759582i	−0.976246	+	0.216664i	$0.930482\pi$
$678$		0			0
$679$	7.78086			0.298602
$680$		0			0
$681$			2.19173i			0.0839874i
$682$		0			0
$683$	7.11481	+	7.11481i	0.272240	+	0.272240i	0.830002	−	0.557761i	$-0.188339\pi$
$683$	7.11481	+	7.11481i	0.272240	+	0.272240i	−0.557761	+	0.830002i	$0.688339\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	8.54301	−	8.54301i	0.325936	−	0.325936i
$688$		0			0
$689$	−0.655184			−0.0249605
$690$		0			0
$691$	−32.5558			−1.23848			−0.619240	−	0.785202i	$-0.712559\pi$
$691$	−32.5558			−1.23848			−0.619240	+	0.785202i	$0.712559\pi$
$692$		0			0
$693$	−3.98270	−	5.33630i	−0.151290	−	0.202709i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	37.0438	−	37.0438i	1.40313	−	1.40313i
$698$		0			0
$699$	18.4306			0.697110
$700$		0			0
$701$			28.0136i			1.05806i	0.848604	+	0.529029i	$0.177444\pi$
$701$			28.0136i			1.05806i	−0.848604	+	0.529029i	$0.822556\pi$
$702$		0			0
$703$	−43.7956	+	43.7956i	−1.65178	+	1.65178i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−19.1132	+	19.1132i	−0.718826	+	0.718826i
$708$		0			0
$709$		−	6.43629i		−	0.241720i	−0.992670	−	0.120860i	$-0.961435\pi$
$709$		−	6.43629i		−	0.241720i	0.992670	−	0.120860i	$-0.0385652\pi$
$710$		0			0
$711$		−	6.14021i		−	0.230276i
$712$		0			0
$713$	−2.29478	−	2.29478i	−0.0859403	−	0.0859403i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	1.99483	+	1.99483i	0.0744985	+	0.0744985i
$718$		0			0
$719$		−	7.33610i		−	0.273590i	−0.990599	−	0.136795i	$-0.956320\pi$
$719$		−	7.33610i		−	0.273590i	0.990599	−	0.136795i	$-0.0436802\pi$
$720$		0			0
$721$			20.5097i			0.763821i
$722$		0			0
$723$	0.774288	−	0.774288i	0.0287961	−	0.0287961i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	32.8750	−	32.8750i	1.21927	−	1.21927i	0.251375	−	0.967890i	$-0.419117\pi$
$727$	32.8750	−	32.8750i	1.21927	−	1.21927i	0.967890	−	0.251375i	$-0.0808829\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	37.0026			1.36859
$732$		0			0
$733$	−9.39670	+	9.39670i	−0.347075	+	0.347075i	−0.859019	−	0.511944i	$-0.828926\pi$
$733$	−9.39670	+	9.39670i	−0.347075	+	0.347075i	0.511944	+	0.859019i	$0.328926\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	18.5148	+	24.8074i	0.682000	+	0.913792i
$738$		0			0
$739$	−30.5118			−1.12240			−0.561198	−	0.827682i	$-0.689659\pi$
$739$	−30.5118			−1.12240			−0.561198	+	0.827682i	$0.689659\pi$
$740$		0			0
$741$	−1.16824			−0.0429163
$742$		0			0
$743$	−2.01757	+	2.01757i	−0.0740175	+	0.0740175i	−0.743146	−	0.669129i	$-0.766667\pi$
$743$	−2.01757	+	2.01757i	−0.0740175	+	0.0740175i	0.669129	+	0.743146i	$0.266667\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	4.69214	+	4.69214i	0.171676	+	0.171676i
$748$		0			0
$749$			0.756196i			0.0276308i
$750$		0			0
$751$	37.7271			1.37668			0.688340	−	0.725388i	$-0.258340\pi$
$751$	37.7271			1.37668			0.688340	+	0.725388i	$0.258340\pi$
$752$		0			0
$753$	7.97167	+	7.97167i	0.290504	+	0.290504i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	9.84866	−	9.84866i	0.357956	−	0.357956i	−0.505103	−	0.863059i	$-0.668546\pi$
$757$	9.84866	−	9.84866i	0.357956	−	0.357956i	0.863059	+	0.505103i	$0.168546\pi$
$758$		0			0
$759$	4.44516	+	0.645668i	0.161349	+	0.0234363i
$760$		0			0
$761$			5.64635i			0.204680i	0.994749	+	0.102340i	$0.0326330\pi$
$761$			5.64635i			0.204680i	−0.994749	+	0.102340i	$0.967367\pi$
$762$		0			0
$763$	−7.20094	−	7.20094i	−0.260692	−	0.260692i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1.95571	+	1.95571i	0.0706165	+	0.0706165i
$768$		0			0
$769$	−5.11155			−0.184327			−0.0921637	−	0.995744i	$-0.529378\pi$
$769$	−5.11155			−0.184327			−0.0921637	+	0.995744i	$0.529378\pi$
$770$		0			0
$771$	16.5265			0.595188
$772$		0			0
$773$	16.1849	+	16.1849i	0.582131	+	0.582131i	0.935489	−	0.353357i	$-0.114960\pi$
$773$	16.1849	+	16.1849i	0.582131	+	0.582131i	−0.353357	+	0.935489i	$0.614960\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−15.4469	−	15.4469i	−0.554153	−	0.554153i
$778$		0			0
$779$			65.6278i			2.35136i
$780$		0			0
$781$	−3.26369	+	22.4692i	−0.116784	+	0.804011i
$782$		0			0
$783$	6.64030	−	6.64030i	0.237305	−	0.237305i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	26.4921	+	26.4921i	0.944342	+	0.944342i	0.998531	−	0.0541891i	$-0.0172574\pi$
$787$	26.4921	+	26.4921i	0.944342	+	0.944342i	−0.0541891	+	0.998531i	$0.517257\pi$
$788$		0			0
$789$	13.6754			0.486857
$790$		0			0
$791$			11.3796i			0.404613i
$792$		0			0
$793$	−0.935187	−	0.935187i	−0.0332095	−	0.0332095i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	15.3289	−	15.3289i	0.542979	−	0.542979i	−0.381422	−	0.924401i	$-0.624566\pi$
$797$	15.3289	−	15.3289i	0.542979	−	0.542979i	0.924401	+	0.381422i	$0.124566\pi$
$798$		0			0
$799$	−14.2239			−0.503204
$800$		0			0
$801$	12.6882			0.448317
$802$		0			0
$803$	24.1809	+	32.3993i	0.853327	+	1.14335i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−9.94666	+	9.94666i	−0.350139	+	0.350139i
$808$		0			0
$809$	−24.2292			−0.851853			−0.425927	−	0.904758i	$-0.640052\pi$
$809$	−24.2292			−0.851853			−0.425927	+	0.904758i	$0.640052\pi$
$810$		0			0
$811$			2.59463i			0.0911099i	0.998962	+	0.0455549i	$0.0145056\pi$
$811$			2.59463i			0.0911099i	−0.998962	+	0.0455549i	$0.985494\pi$
$812$		0			0
$813$	13.4295	−	13.4295i	0.470993	−	0.470993i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−32.7774	+	32.7774i	−1.14674	+	1.14674i
$818$		0			0
$819$		−	0.412041i		−	0.0143979i
$820$		0			0
$821$		−	41.9633i		−	1.46453i	−0.681021	−	0.732264i	$-0.738464\pi$
$821$		−	41.9633i		−	1.46453i	0.681021	−	0.732264i	$-0.261536\pi$
$822$		0			0
$823$	9.78175	+	9.78175i	0.340970	+	0.340970i	0.856732	−	0.515762i	$-0.172491\pi$
$823$	9.78175	+	9.78175i	0.340970	+	0.340970i	−0.515762	+	0.856732i	$0.672491\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	30.2752	+	30.2752i	1.05277	+	1.05277i	0.998528	+	0.0542446i	$0.0172751\pi$
$827$	30.2752	+	30.2752i	1.05277	+	1.05277i	0.0542446	+	0.998528i	$0.482725\pi$
$828$		0			0
$829$		−	45.9706i		−	1.59662i	−0.602245	−	0.798312i	$-0.705727\pi$
$829$		−	45.9706i		−	1.59662i	0.602245	−	0.798312i	$-0.294273\pi$
$830$		0			0
$831$			24.9078i			0.864042i
$832$		0			0
$833$	9.54025	−	9.54025i	0.330550	−	0.330550i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	1.69440	−	1.69440i	0.0585671	−	0.0585671i
$838$		0			0
$839$			1.15601i			0.0399100i	0.999801	+	0.0199550i	$0.00635229\pi$
$839$			1.15601i			0.0399100i	−0.999801	+	0.0199550i	$0.993648\pi$
$840$		0			0
$841$	59.1871			2.04094
$842$		0			0
$843$	−2.44742	+	2.44742i	−0.0842938	+	0.0842938i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	10.5279	+	19.4134i	0.361743	+	0.667054i
$848$		0			0
$849$	−16.5592			−0.568309
$850$		0			0
$851$	14.7363			0.505154
$852$		0			0
$853$	5.35709	−	5.35709i	0.183423	−	0.183423i	−0.609422	−	0.792846i	$-0.708599\pi$
$853$	5.35709	−	5.35709i	0.183423	−	0.183423i	0.792846	+	0.609422i	$0.208599\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	30.8816	+	30.8816i	1.05489	+	1.05489i	0.998403	+	0.0564918i	$0.0179915\pi$
$857$	30.8816	+	30.8816i	1.05489	+	1.05489i	0.0564918	+	0.998403i	$0.482009\pi$
$858$		0			0
$859$		−	22.3650i		−	0.763083i	−0.924352	−	0.381541i	$-0.875393\pi$
$859$		−	22.3650i		−	0.763083i	0.924352	−	0.381541i	$-0.124607\pi$
$860$		0			0
$861$	−23.1471			−0.788852
$862$		0			0
$863$	35.4659	+	35.4659i	1.20727	+	1.20727i	0.971907	+	0.235365i	$0.0756287\pi$
$863$	35.4659	+	35.4659i	1.20727	+	1.20727i	0.235365	+	0.971907i	$0.424371\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−2.57859	+	2.57859i	−0.0875736	+	0.0875736i
$868$		0			0
$869$	−2.92730	+	20.1533i	−0.0993019	+	0.683653i
$870$		0			0
$871$			1.91549i			0.0649041i
$872$		0			0
$873$	−2.74044	−	2.74044i	−0.0927499	−	0.0927499i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	15.6784	+	15.6784i	0.529421	+	0.529421i	0.920400	−	0.390978i	$-0.127863\pi$
$877$	15.6784	+	15.6784i	0.529421	+	0.529421i	−0.390978	+	0.920400i	$0.627863\pi$
$878$		0			0
$879$	7.97871			0.269115
$880$		0			0
$881$	45.1013			1.51950			0.759752	−	0.650214i	$-0.225321\pi$
$881$	45.1013			1.51950			0.759752	+	0.650214i	$0.225321\pi$
$882$		0			0
$883$	−31.2495	−	31.2495i	−1.05163	−	1.05163i	−0.998593	−	0.0530373i	$-0.983110\pi$
$883$	−31.2495	−	31.2495i	−1.05163	−	1.05163i	−0.0530373	−	0.998593i	$-0.516890\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	13.5535	+	13.5535i	0.455081	+	0.455081i	0.897037	−	0.441956i	$-0.145715\pi$
$887$	13.5535	+	13.5535i	0.455081	+	0.455081i	−0.441956	+	0.897037i	$0.645715\pi$
$888$		0			0
$889$			32.5111i			1.09039i
$890$		0			0
$891$	−0.476743	+	3.28218i	−0.0159715	+	0.109957i
$892$		0			0
$893$	12.5997	−	12.5997i	0.421633	−	0.421633i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	0.196543	+	0.196543i	0.00656239	+	0.00656239i
$898$		0			0
$899$	22.5027			0.750507
$900$		0			0
$901$		−	14.5057i		−	0.483256i
$902$		0			0
$903$	−11.5607	−	11.5607i	−0.384715	−	0.384715i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−0.756930	+	0.756930i	−0.0251334	+	0.0251334i	−0.719562	−	0.694428i	$-0.755657\pi$
$907$	−0.756930	+	0.756930i	−0.0251334	+	0.0251334i	0.694428	+	0.719562i	$0.255657\pi$
$908$		0			0
$909$	13.4635			0.446555
$910$		0			0
$911$	−44.1348			−1.46225			−0.731125	−	0.682244i	$-0.761004\pi$
$911$	−44.1348			−1.46225			−0.731125	+	0.682244i	$0.761004\pi$
$912$		0			0
$913$	−13.1635	−	17.6374i	−0.435648	−	0.583712i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−15.4588	+	15.4588i	−0.510496	+	0.510496i
$918$		0			0
$919$	−1.00299			−0.0330855			−0.0165427	−	0.999863i	$-0.505266\pi$
$919$	−1.00299			−0.0330855			−0.0165427	+	0.999863i	$0.505266\pi$
$920$		0			0
$921$			19.0644i			0.628192i
$922$		0			0
$923$	−0.993478	+	0.993478i	−0.0327007	+	0.0327007i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	7.22358	−	7.22358i	0.237253	−	0.237253i
$928$		0			0
$929$		−	6.85691i		−	0.224968i	−0.993654	−	0.112484i	$-0.964119\pi$
$929$		−	6.85691i		−	0.224968i	0.993654	−	0.112484i	$-0.0358807\pi$
$930$		0			0
$931$			16.9018i			0.553933i
$932$		0			0
$933$	−17.6430	−	17.6430i	−0.577607	−	0.577607i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−6.67134	−	6.67134i	−0.217943	−	0.217943i	0.589688	−	0.807631i	$-0.299251\pi$
$937$	−6.67134	−	6.67134i	−0.217943	−	0.217943i	−0.807631	+	0.589688i	$0.799251\pi$
$938$		0			0
$939$		−	7.20292i		−	0.235058i
$940$		0			0
$941$		−	11.6576i		−	0.380027i	−0.981781	−	0.190014i	$-0.939147\pi$
$941$		−	11.6576i		−	0.380027i	0.981781	−	0.190014i	$-0.0608532\pi$
$942$		0			0
$943$	11.0412	−	11.0412i	0.359550	−	0.359550i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	9.57867	−	9.57867i	0.311265	−	0.311265i	−0.534135	−	0.845399i	$-0.679362\pi$
$947$	9.57867	−	9.57867i	0.311265	−	0.311265i	0.845399	+	0.534135i	$0.179362\pi$
$948$		0			0
$949$			2.50170i			0.0812087i
$950$		0			0
$951$	−23.9349			−0.776141
$952$		0			0
$953$	14.0583	−	14.0583i	0.455392	−	0.455392i	−0.441748	−	0.897139i	$-0.645641\pi$
$953$	14.0583	−	14.0583i	0.455392	−	0.455392i	0.897139	+	0.441748i	$0.145641\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−24.9604	+	18.6290i	−0.806855	+	0.602188i
$958$		0			0
$959$	−37.1211			−1.19870
$960$		0			0
$961$	−25.2580			−0.814774
$962$		0			0
$963$	0.266335	−	0.266335i	0.00858251	−	0.00858251i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−27.3654	−	27.3654i	−0.880014	−	0.880014i	0.113522	−	0.993535i	$-0.463787\pi$
$967$	−27.3654	−	27.3654i	−0.880014	−	0.880014i	−0.993535	+	0.113522i	$0.963787\pi$
$968$		0			0
$969$		−	25.8647i		−	0.830894i
$970$		0			0
$971$	−30.5076			−0.979034			−0.489517	−	0.871994i	$-0.662827\pi$
$971$	−30.5076			−0.979034			−0.489517	+	0.871994i	$0.662827\pi$
$972$		0			0
$973$	16.0868	+	16.0868i	0.515718	+	0.515718i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	22.2577	−	22.2577i	0.712088	−	0.712088i	−0.254884	−	0.966972i	$-0.582037\pi$
$977$	22.2577	−	22.2577i	0.712088	−	0.712088i	0.966972	+	0.254884i	$0.0820373\pi$
$978$		0			0
$979$	−41.6451	−	6.04903i	−1.33098	−	0.193328i
$980$		0			0
$981$			5.07239i			0.161949i
$982$		0			0
$983$	−35.3554	−	35.3554i	−1.12766	−	1.12766i	−0.990556	−	0.137106i	$-0.956220\pi$
$983$	−35.3554	−	35.3554i	−1.12766	−	1.12766i	−0.137106	−	0.990556i	$-0.543780\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	4.44395	+	4.44395i	0.141453	+	0.141453i
$988$		0			0
$989$	11.0289			0.350698
$990$		0			0
$991$	−34.0251			−1.08084			−0.540421	−	0.841394i	$-0.681735\pi$
$991$	−34.0251			−1.08084			−0.540421	+	0.841394i	$0.681735\pi$
$992$		0			0
$993$	6.68446	+	6.68446i	0.212125	+	0.212125i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	40.0954	+	40.0954i	1.26984	+	1.26984i	0.946173	+	0.323662i	$0.104914\pi$
$997$	40.0954	+	40.0954i	1.26984	+	1.26984i	0.323662	+	0.946173i	$0.395086\pi$
$998$		0			0
$999$			10.8809i			0.344255i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3300.2.x.c.1693.11		24
5.2	odd	4	inner	3300.2.x.c.1957.12		24
5.3	odd	4		660.2.x.a.637.1	yes	24
5.4	even	2		660.2.x.a.373.2	yes	24
11.10	odd	2	inner	3300.2.x.c.1693.12		24
15.8	even	4		1980.2.y.c.1297.11		24
15.14	odd	2		1980.2.y.c.1693.12		24
55.32	even	4	inner	3300.2.x.c.1957.11		24
55.43	even	4		660.2.x.a.637.2	yes	24
55.54	odd	2		660.2.x.a.373.1	✓	24
165.98	odd	4		1980.2.y.c.1297.12		24
165.164	even	2		1980.2.y.c.1693.11		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
660.2.x.a.373.1	✓	24	55.54	odd	2
660.2.x.a.373.2	yes	24	5.4	even	2
660.2.x.a.637.1	yes	24	5.3	odd	4
660.2.x.a.637.2	yes	24	55.43	even	4
1980.2.y.c.1297.11		24	15.8	even	4
1980.2.y.c.1297.12		24	165.98	odd	4
1980.2.y.c.1693.11		24	165.164	even	2
1980.2.y.c.1693.12		24	15.14	odd	2
3300.2.x.c.1693.11		24	1.1	even	1	trivial
3300.2.x.c.1693.12		24	11.10	odd	2	inner
3300.2.x.c.1957.11		24	55.32	even	4	inner
3300.2.x.c.1957.12		24	5.2	odd	4	inner

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:	\( N \)	\(=\)	\( 3300 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3300.x (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{3} +(-1.41964 - 1.41964i) q^{7} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{3} +(-1.41964 - 1.41964i) q^{7} +1.00000i q^{9} +(0.476743 - 3.28218i) q^{11} +(0.145122 - 0.145122i) q^{13} +(3.21300 + 3.21300i) q^{17} -5.69223 q^{19} -2.00767i q^{21} +(0.957657 + 0.957657i) q^{23} +(-0.707107 + 0.707107i) q^{27} -9.39080 q^{29} -2.39625 q^{31} +(2.65796 - 1.98374i) q^{33} +(7.69393 - 7.69393i) q^{37} +0.205234 q^{39} -11.5294i q^{41} +(5.75826 - 5.75826i) q^{43} +(-2.21349 + 2.21349i) q^{47} -2.96927i q^{49} +4.54386i q^{51} +(-2.25736 - 2.25736i) q^{53} +(-4.02502 - 4.02502i) q^{57} +13.4763i q^{59} -6.44414i q^{61} +(1.41964 - 1.41964i) q^{63} +(-6.59960 + 6.59960i) q^{67} +1.35433i q^{69} -6.84581 q^{71} +(-8.61931 + 8.61931i) q^{73} +(-5.33630 + 3.98270i) q^{77} -6.14021 q^{79} -1.00000 q^{81} +(4.69214 - 4.69214i) q^{83} +(-6.64030 - 6.64030i) q^{87} -12.6882i q^{89} -0.412041 q^{91} +(-1.69440 - 1.69440i) q^{93} +(-2.74044 + 2.74044i) q^{97} +(3.28218 + 0.476743i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q + 8 q^{11} - 16 q^{23} + 16 q^{31} + 40 q^{37} - 64 q^{47} - 24 q^{53} - 48 q^{67} - 24 q^{77} - 24 q^{81} - 48 q^{91} - 16 q^{93} + 72 q^{97}+O(q^{100}) \) 24 * q + 8 * q^11 - 16 * q^23 + 16 * q^31 + 40 * q^37 - 64 * q^47 - 24 * q^53 - 48 * q^67 - 24 * q^77 - 24 * q^81 - 48 * q^91 - 16 * q^93 + 72 * q^97

Introduction

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