LMFDB - Embedded newform 1512.2.cx.a.17.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1512,2,Mod(17,1512)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1512, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1512.17"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.cx (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.16
Character	$\chi$	$=$	1512.17
Dual form			1512.2.cx.a.89.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+1.07485 q^{5} +(-1.26701 - 2.32265i) q^{7} +4.09931i q^{11} +(-3.69867 - 2.13543i) q^{13} +(-0.717607 + 1.24293i) q^{17} +(6.41973 - 3.70644i) q^{19} -6.27615i q^{23} -3.84469 q^{25} +(8.09846 - 4.67565i) q^{29} +(5.96282 - 3.44264i) q^{31} +(-1.36185 - 2.49651i) q^{35} +(-0.453413 - 0.785334i) q^{37} +(-3.88978 + 6.73730i) q^{41} +(-6.32181 - 10.9497i) q^{43} +(4.21764 - 7.30517i) q^{47} +(-3.78938 + 5.88563i) q^{49} +(-1.50593 - 0.869452i) q^{53} +4.40616i q^{55} +(3.05073 + 5.28402i) q^{59} +(-2.36055 - 1.36287i) q^{61} +(-3.97553 - 2.29528i) q^{65} +(-6.01953 - 10.4261i) q^{67} +0.783113i q^{71} +(-1.95868 - 1.13085i) q^{73} +(9.52125 - 5.19386i) q^{77} +(-0.817713 + 1.41632i) q^{79} +(-4.48646 - 7.77077i) q^{83} +(-0.771322 + 1.33597i) q^{85} +(-1.71834 - 2.97625i) q^{89} +(-0.273602 + 11.2963i) q^{91} +(6.90027 - 3.98387i) q^{95} +(5.05015 - 2.91570i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 48 q^{25} - 18 q^{29} + 18 q^{31} + 6 q^{41} - 6 q^{43} - 18 q^{47} - 12 q^{49} + 12 q^{53} + 18 q^{61} + 36 q^{65} + 12 q^{77} + 6 q^{79} + 18 q^{89} + 6 q^{91} + 54 q^{95}+O(q^{100}) $ 48 * q + 48 * q^25 - 18 * q^29 + 18 * q^31 + 6 * q^41 - 6 * q^43 - 18 * q^47 - 12 * q^49 + 12 * q^53 + 18 * q^61 + 36 * q^65 + 12 * q^77 + 6 * q^79 + 18 * q^89 + 6 * q^91 + 54 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.07485			0.480689			0.240345	−	0.970688i	$-0.422740\pi$
$5$	1.07485			0.480689			0.240345	+	0.970688i	$0.422740\pi$
$6$		0			0
$7$	−1.26701	−	2.32265i	−0.478884	−	0.877878i
$7$	−1.26701	−	2.32265i	−0.478884	−	0.877878i
$8$		0			0
$9$		0			0
$10$		0			0
$11$			4.09931i			1.23599i	0.786183	+	0.617994i	$0.212055\pi$
$11$			4.09931i			1.23599i	−0.786183	+	0.617994i	$0.787945\pi$
$12$		0			0
$13$	−3.69867	−	2.13543i	−1.02583	−	0.592262i	−0.110041	−	0.993927i	$-0.535098\pi$
$13$	−3.69867	−	2.13543i	−1.02583	−	0.592262i	−0.915787	+	0.401665i	$0.868432\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.717607	+	1.24293i	−0.174045	+	0.301455i	−0.939830	−	0.341641i	$-0.889017\pi$
$17$	−0.717607	+	1.24293i	−0.174045	+	0.301455i	0.765785	+	0.643096i	$0.222351\pi$
$18$		0			0
$19$	6.41973	−	3.70644i	1.47279	−	0.850315i	0.473257	−	0.880925i	$-0.343078\pi$
$19$	6.41973	−	3.70644i	1.47279	−	0.850315i	0.999531	+	0.0306101i	$0.00974502\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		−	6.27615i		−	1.30867i	−0.756206	−	0.654334i	$-0.772949\pi$
$23$		−	6.27615i		−	1.30867i	0.756206	−	0.654334i	$-0.227051\pi$
$24$		0			0
$25$	−3.84469			−0.768938
$26$		0			0
$27$		0			0
$28$		0			0
$29$	8.09846	−	4.67565i	1.50385	−	0.868246i	0.503856	−	0.863788i	$-0.331914\pi$
$29$	8.09846	−	4.67565i	1.50385	−	0.868246i	0.999990	−	0.00445828i	$-0.00141912\pi$
$30$		0			0
$31$	5.96282	−	3.44264i	1.07095	−	0.618316i	0.142512	−	0.989793i	$-0.454482\pi$
$31$	5.96282	−	3.44264i	1.07095	−	0.618316i	0.928442	+	0.371478i	$0.121149\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.36185	−	2.49651i	−0.230194	−	0.421986i
$36$		0			0
$37$	−0.453413	−	0.785334i	−0.0745406	−	0.129108i	0.826346	−	0.563163i	$-0.190416\pi$
$37$	−0.453413	−	0.785334i	−0.0745406	−	0.129108i	−0.900886	+	0.434055i	$0.857082\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−3.88978	+	6.73730i	−0.607482	+	1.05219i	0.384172	+	0.923262i	$0.374487\pi$
$41$	−3.88978	+	6.73730i	−0.607482	+	1.05219i	−0.991654	+	0.128928i	$0.958846\pi$
$42$		0			0
$43$	−6.32181	−	10.9497i	−0.964067	−	1.66981i	−0.712102	−	0.702076i	$-0.752257\pi$
$43$	−6.32181	−	10.9497i	−0.964067	−	1.66981i	−0.251965	−	0.967736i	$-0.581077\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.21764	−	7.30517i	0.615206	−	1.06557i	−0.375142	−	0.926967i	$-0.622406\pi$
$47$	4.21764	−	7.30517i	0.615206	−	1.06557i	0.990348	−	0.138601i	$-0.0442606\pi$
$48$		0			0
$49$	−3.78938	+	5.88563i	−0.541340	+	0.840804i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−1.50593	−	0.869452i	−0.206856	−	0.119428i	0.392993	−	0.919541i	$-0.371440\pi$
$53$	−1.50593	−	0.869452i	−0.206856	−	0.119428i	−0.599849	+	0.800113i	$0.704773\pi$
$54$		0			0
$55$			4.40616i			0.594126i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.05073	+	5.28402i	0.397171	+	0.687921i	0.993376	−	0.114912i	$-0.0366586\pi$
$59$	3.05073	+	5.28402i	0.397171	+	0.687921i	−0.596205	+	0.802833i	$0.703325\pi$
$60$		0			0
$61$	−2.36055	−	1.36287i	−0.302238	−	0.174497i	0.341210	−	0.939987i	$-0.389163\pi$
$61$	−2.36055	−	1.36287i	−0.302238	−	0.174497i	−0.643448	+	0.765490i	$0.722497\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−3.97553	−	2.29528i	−0.493104	−	0.284694i
$66$		0			0
$67$	−6.01953	−	10.4261i	−0.735403	−	1.27375i	−0.954546	−	0.298062i	$-0.903660\pi$
$67$	−6.01953	−	10.4261i	−0.735403	−	1.27375i	0.219144	−	0.975693i	$-0.429674\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			0.783113i			0.0929385i	0.998920	+	0.0464692i	$0.0147969\pi$
$71$			0.783113i			0.0929385i	−0.998920	+	0.0464692i	$0.985203\pi$
$72$		0			0
$73$	−1.95868	−	1.13085i	−0.229247	−	0.132356i	0.380978	−	0.924584i	$-0.375587\pi$
$73$	−1.95868	−	1.13085i	−0.229247	−	0.132356i	−0.610224	+	0.792229i	$0.708921\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	9.52125	−	5.19386i	1.08505	−	0.591895i
$78$		0			0
$79$	−0.817713	+	1.41632i	−0.0919999	+	0.159348i	−0.908353	−	0.418205i	$-0.862659\pi$
$79$	−0.817713	+	1.41632i	−0.0919999	+	0.159348i	0.816353	+	0.577554i	$0.195993\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−4.48646	−	7.77077i	−0.492452	−	0.852953i	0.507510	−	0.861646i	$-0.330566\pi$
$83$	−4.48646	−	7.77077i	−0.492452	−	0.852953i	−0.999962	+	0.00869330i	$0.997233\pi$
$84$		0			0
$85$	−0.771322	+	1.33597i	−0.0836616	+	0.144906i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1.71834	−	2.97625i	−0.182144	−	0.315482i	0.760467	−	0.649377i	$-0.224970\pi$
$89$	−1.71834	−	2.97625i	−0.182144	−	0.315482i	−0.942610	+	0.333895i	$0.891637\pi$
$90$		0			0
$91$	−0.273602	+	11.2963i	−0.0286813	+	1.18418i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	6.90027	−	3.98387i	0.707953	−	0.408737i
$96$		0			0
$97$	5.05015	−	2.91570i	0.512765	−	0.296045i	−0.221205	−	0.975227i	$-0.570999\pi$
$97$	5.05015	−	2.91570i	0.512765	−	0.296045i	0.733969	+	0.679182i	$0.237666\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	4.62440			0.460145			0.230073	−	0.973173i	$-0.426104\pi$
$101$	4.62440			0.460145			0.230073	+	0.973173i	$0.426104\pi$
$102$		0			0
$103$			4.25449i			0.419207i	0.977786	+	0.209604i	$0.0672174\pi$
$103$			4.25449i			0.419207i	−0.977786	+	0.209604i	$0.932783\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	8.73964	−	5.04583i	0.844893	−	0.487799i	−0.0140314	−	0.999902i	$-0.504466\pi$
$107$	8.73964	−	5.04583i	0.844893	−	0.487799i	0.858924	+	0.512102i	$0.171133\pi$
$108$		0			0
$109$	0.548395	−	0.949848i	0.0525267	−	0.0909790i	−0.838567	−	0.544799i	$-0.816606\pi$
$109$	0.548395	−	0.949848i	0.0525267	−	0.0909790i	0.891093	+	0.453820i	$0.149939\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	8.51839	+	4.91809i	0.801343	+	0.462655i	0.843940	−	0.536437i	$-0.180230\pi$
$113$	8.51839	+	4.91809i	0.801343	+	0.462655i	−0.0425979	+	0.999092i	$0.513563\pi$
$114$		0			0
$115$		−	6.74594i		−	0.629062i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	3.79611	+	0.0919433i	0.347988	+	0.00842843i
$120$		0			0
$121$	−5.80435			−0.527668
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−9.50674			−0.850309
$126$		0			0
$127$	15.2201			1.35056			0.675282	−	0.737559i	$-0.264022\pi$
$127$	15.2201			1.35056			0.675282	+	0.737559i	$0.264022\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−8.90882			−0.778367			−0.389184	−	0.921160i	$-0.627243\pi$
$131$	−8.90882			−0.778367			−0.389184	+	0.921160i	$0.627243\pi$
$132$		0			0
$133$	−16.7426	−	10.2147i	−1.45177	−	0.885726i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	11.2738i		−	0.963185i	−0.876395	−	0.481592i	$-0.840059\pi$
$137$		−	11.2738i		−	0.963185i	0.876395	−	0.481592i	$-0.159941\pi$
$138$		0			0
$139$	12.0468	+	6.95522i	1.02180	+	0.589934i	0.914624	−	0.404306i	$-0.132487\pi$
$139$	12.0468	+	6.95522i	1.02180	+	0.589934i	0.107172	+	0.994240i	$0.465820\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	8.75380	−	15.1620i	0.732029	−	1.26791i
$144$		0			0
$145$	8.70466	−	5.02564i	0.722882	−	0.417356i
$146$		0			0
$147$		0			0
$148$		0			0
$149$		−	3.57384i		−	0.292781i	−0.989227	−	0.146390i	$-0.953234\pi$
$149$		−	3.57384i		−	0.292781i	0.989227	−	0.146390i	$-0.0467655\pi$
$150$		0			0
$151$	6.60359			0.537393			0.268696	−	0.963225i	$-0.413407\pi$
$151$	6.60359			0.537393			0.268696	+	0.963225i	$0.413407\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	6.40916	−	3.70033i	0.514796	−	0.297217i
$156$		0			0
$157$	−7.96356	+	4.59777i	−0.635562	+	0.366942i	−0.782903	−	0.622144i	$-0.786262\pi$
$157$	−7.96356	+	4.59777i	−0.635562	+	0.366942i	0.147341	+	0.989086i	$0.452928\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−14.5773	+	7.95193i	−1.14885	+	0.626700i
$162$		0			0
$163$	3.64872	+	6.31976i	0.285790	+	0.495002i	0.972800	−	0.231645i	$-0.0744108\pi$
$163$	3.64872	+	6.31976i	0.285790	+	0.495002i	−0.687011	+	0.726647i	$0.741077\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−7.07118	+	12.2476i	−0.547184	+	0.947751i	0.451282	+	0.892382i	$0.350967\pi$
$167$	−7.07118	+	12.2476i	−0.547184	+	0.947751i	−0.998466	+	0.0553694i	$0.982366\pi$
$168$		0			0
$169$	2.62013	+	4.53820i	0.201549	+	0.349092i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−6.74923	+	11.6900i	−0.513134	+	0.888775i	0.486750	+	0.873542i	$0.338182\pi$
$173$	−6.74923	+	11.6900i	−0.513134	+	0.888775i	−0.999884	+	0.0152333i	$0.995151\pi$
$174$		0			0
$175$	4.87125	+	8.92986i	0.368232	+	0.675034i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	3.97036	+	2.29229i	0.296759	+	0.171334i	0.640986	−	0.767553i	$-0.278526\pi$
$179$	3.97036	+	2.29229i	0.296759	+	0.171334i	−0.344227	+	0.938886i	$0.611859\pi$
$180$		0			0
$181$			2.22901i			0.165681i	0.996563	+	0.0828405i	$0.0263992\pi$
$181$			2.22901i			0.165681i	−0.996563	+	0.0828405i	$0.973601\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.487352	−	0.844118i	−0.0358308	−	0.0620608i
$186$		0			0
$187$	−5.09516	−	2.94169i	−0.372595	−	0.215118i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−18.2169	−	10.5175i	−1.31813	−	0.761022i	−0.334701	−	0.942324i	$-0.608635\pi$
$191$	−18.2169	−	10.5175i	−1.31813	−	0.761022i	−0.983427	+	0.181302i	$0.941969\pi$
$192$		0			0
$193$	5.60213	+	9.70317i	0.403250	+	0.698449i	0.994116	−	0.108320i	$-0.0345472\pi$
$193$	5.60213	+	9.70317i	0.403250	+	0.698449i	−0.590866	+	0.806770i	$0.701214\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			20.8945i			1.48867i	0.667805	+	0.744336i	$0.267234\pi$
$197$			20.8945i			1.48867i	−0.667805	+	0.744336i	$0.732766\pi$
$198$		0			0
$199$	−15.8521	−	9.15222i	−1.12373	−	0.648784i	−0.181377	−	0.983414i	$-0.558055\pi$
$199$	−15.8521	−	9.15222i	−1.12373	−	0.648784i	−0.942350	+	0.334630i	$0.891389\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−21.1207	−	12.8858i	−1.48238	−	0.904405i
$204$		0			0
$205$	−4.18095	+	7.24161i	−0.292010	+	0.505776i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	15.1938	+	26.3165i	1.05098	+	1.82035i
$210$		0			0
$211$	5.93845	−	10.2857i	0.408820	−	0.708096i	−0.585938	−	0.810356i	$-0.699274\pi$
$211$	5.93845	−	10.2857i	0.408820	−	0.708096i	0.994758	+	0.102260i	$0.0326072\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−6.79502	−	11.7693i	−0.463416	−	0.802660i
$216$		0			0
$217$	−15.5510	−	9.48768i	−1.05567	−	0.644066i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	5.30839	−	3.06480i	0.357081	−	0.206161i
$222$		0			0
$223$	4.19957	−	2.42462i	0.281224	−	0.162365i	−0.352754	−	0.935716i	$-0.614755\pi$
$223$	4.19957	−	2.42462i	0.281224	−	0.162365i	0.633977	+	0.773352i	$0.281421\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−2.87291			−0.190682			−0.0953408	−	0.995445i	$-0.530394\pi$
$227$	−2.87291			−0.190682			−0.0953408	+	0.995445i	$0.530394\pi$
$228$		0			0
$229$		−	4.32820i		−	0.286015i	−0.989722	−	0.143008i	$-0.954323\pi$
$229$		−	4.32820i		−	0.286015i	0.989722	−	0.143008i	$-0.0456774\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	11.9136	−	6.87834i	0.780488	−	0.450615i	−0.0561154	−	0.998424i	$-0.517871\pi$
$233$	11.9136	−	6.87834i	0.780488	−	0.450615i	0.836603	+	0.547809i	$0.184538\pi$
$234$		0			0
$235$	4.53335	−	7.85198i	0.295723	−	0.512207i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	15.6571	+	9.03963i	1.01277	+	0.584725i	0.912003	−	0.410184i	$-0.134536\pi$
$239$	15.6571	+	9.03963i	1.01277	+	0.584725i	0.100771	+	0.994910i	$0.467869\pi$
$240$		0			0
$241$		−	5.97741i		−	0.385039i	−0.981293	−	0.192520i	$-0.938334\pi$
$241$		−	5.97741i		−	0.385039i	0.981293	−	0.192520i	$-0.0616659\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−4.07303	+	6.32618i	−0.260216	+	0.404165i
$246$		0			0
$247$	−31.6593			−2.01444
$248$		0			0
$249$		0			0
$250$		0			0
$251$	11.0004			0.694337			0.347169	−	0.937803i	$-0.387143\pi$
$251$	11.0004			0.694337			0.347169	+	0.937803i	$0.387143\pi$
$252$		0			0
$253$	25.7279			1.61750
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−9.48559			−0.591695			−0.295848	−	0.955235i	$-0.595602\pi$
$257$	−9.48559			−0.591695			−0.295848	+	0.955235i	$0.595602\pi$
$258$		0			0
$259$	−1.24958	+	2.04814i	−0.0776448	+	0.127265i
$260$		0			0
$261$		0			0
$262$		0			0
$263$			18.8494i			1.16230i	0.813795	+	0.581152i	$0.197398\pi$
$263$			18.8494i			1.16230i	−0.813795	+	0.581152i	$0.802602\pi$
$264$		0			0
$265$	−1.61866	−	0.934533i	−0.0994334	−	0.0574079i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−10.0233	+	17.3609i	−0.611133	+	1.05851i	0.379916	+	0.925021i	$0.375953\pi$
$269$	−10.0233	+	17.3609i	−0.611133	+	1.05851i	−0.991050	+	0.133493i	$0.957381\pi$
$270$		0			0
$271$	17.3369	−	10.0095i	1.05314	−	0.608032i	0.129615	−	0.991564i	$-0.458626\pi$
$271$	17.3369	−	10.0095i	1.05314	−	0.608032i	0.923528	+	0.383532i	$0.125292\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		−	15.7606i		−	0.950399i
$276$		0			0
$277$	−3.40744			−0.204733			−0.102367	−	0.994747i	$-0.532642\pi$
$277$	−3.40744			−0.204733			−0.102367	+	0.994747i	$0.532642\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−16.0313	+	9.25568i	−0.956347	+	0.552147i	−0.895047	−	0.445972i	$-0.852858\pi$
$281$	−16.0313	+	9.25568i	−0.956347	+	0.552147i	−0.0613004	+	0.998119i	$0.519525\pi$
$282$		0			0
$283$	−21.7473	+	12.5558i	−1.29274	+	0.746366i	−0.979140	−	0.203187i	$-0.934870\pi$
$283$	−21.7473	+	12.5558i	−1.29274	+	0.746366i	−0.313605	+	0.949554i	$0.601537\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	20.5768	+	0.498378i	1.21461	+	0.0294183i
$288$		0			0
$289$	7.47008	+	12.9386i	0.439417	+	0.761092i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−1.11299	+	1.92775i	−0.0650214	+	0.112620i	−0.896703	−	0.442632i	$-0.854045\pi$
$293$	−1.11299	+	1.92775i	−0.0650214	+	0.112620i	0.831682	+	0.555252i	$0.187378\pi$
$294$		0			0
$295$	3.27909	+	5.67955i	0.190916	+	0.330676i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−13.4023	+	23.2134i	−0.775074	+	1.34247i
$300$		0			0
$301$	−17.4225	+	28.5567i	−1.00422	+	1.64598i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−2.53725	−	1.46488i	−0.145282	−	0.0838788i
$306$		0			0
$307$			24.2535i			1.38422i	0.721791	+	0.692111i	$0.243319\pi$
$307$			24.2535i			1.38422i	−0.721791	+	0.692111i	$0.756681\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	9.81502	+	17.0001i	0.556559	+	0.963988i	0.997780	+	0.0665901i	$0.0212120\pi$
$311$	9.81502	+	17.0001i	0.556559	+	0.963988i	−0.441221	+	0.897398i	$0.645455\pi$
$312$		0			0
$313$	14.8564	+	8.57737i	0.839736	+	0.484822i	0.857174	−	0.515026i	$-0.172218\pi$
$313$	14.8564	+	8.57737i	0.839736	+	0.484822i	−0.0174387	+	0.999848i	$0.505551\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	10.7826	+	6.22534i	0.605611	+	0.349650i	0.771246	−	0.636537i	$-0.219634\pi$
$317$	10.7826	+	6.22534i	0.605611	+	0.349650i	−0.165635	+	0.986187i	$0.552967\pi$
$318$		0			0
$319$	19.1669	+	33.1981i	1.07314	+	1.85874i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			10.6391i			0.591973i
$324$		0			0
$325$	14.2203	+	8.21007i	0.788798	+	0.455413i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−22.3111	−	0.540385i	−1.23005	−	0.0297924i
$330$		0			0
$331$	15.4588	−	26.7754i	0.849691	−	1.47171i	−0.0317938	−	0.999494i	$-0.510122\pi$
$331$	15.4588	−	26.7754i	0.849691	−	1.47171i	0.881484	−	0.472213i	$-0.156545\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−6.47011	−	11.2066i	−0.353500	−	0.612280i
$336$		0			0
$337$	−1.06492	+	1.84450i	−0.0580099	+	0.100476i	−0.893572	−	0.448920i	$-0.851809\pi$
$337$	−1.06492	+	1.84450i	−0.0580099	+	0.100476i	0.835562	+	0.549396i	$0.185142\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	14.1124	+	24.4434i	0.764231	+	1.32369i
$342$		0			0
$343$	18.4714	+	1.34426i	0.997362	+	0.0725832i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−19.9209	+	11.5013i	−1.06941	+	0.617423i	−0.928020	−	0.372531i	$-0.878490\pi$
$347$	−19.9209	+	11.5013i	−1.06941	+	0.617423i	−0.141388	+	0.989954i	$0.545157\pi$
$348$		0			0
$349$	21.3306	−	12.3152i	1.14180	−	0.659219i	0.194925	−	0.980818i	$-0.437554\pi$
$349$	21.3306	−	12.3152i	1.14180	−	0.659219i	0.946876	+	0.321599i	$0.104220\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−3.24379			−0.172650			−0.0863248	−	0.996267i	$-0.527512\pi$
$353$	−3.24379			−0.172650			−0.0863248	+	0.996267i	$0.527512\pi$
$354$		0			0
$355$			0.841732i			0.0446745i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	4.88399	−	2.81977i	0.257767	−	0.148822i	−0.365548	−	0.930792i	$-0.619119\pi$
$359$	4.88399	−	2.81977i	0.257767	−	0.148822i	0.623316	+	0.781970i	$0.285785\pi$
$360$		0			0
$361$	17.9753	−	31.1342i	0.946070	−	1.63864i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−2.10530	−	1.21549i	−0.110196	−	0.0636219i
$366$		0			0
$367$			12.5479i			0.654996i	0.944852	+	0.327498i	$0.106205\pi$
$367$			12.5479i			0.654996i	−0.944852	+	0.327498i	$0.893795\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.111398	+	4.59936i	−0.00578352	+	0.238787i
$372$		0			0
$373$	−13.1754			−0.682196			−0.341098	−	0.940028i	$-0.610799\pi$
$373$	−13.1754			−0.682196			−0.341098	+	0.940028i	$0.610799\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−39.9381			−2.05692
$378$		0			0
$379$	−6.80285			−0.349439			−0.174720	−	0.984618i	$-0.555902\pi$
$379$	−6.80285			−0.349439			−0.174720	+	0.984618i	$0.555902\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	19.6596			1.00456			0.502280	−	0.864705i	$-0.332495\pi$
$383$	19.6596			1.00456			0.502280	+	0.864705i	$0.332495\pi$
$384$		0			0
$385$	10.2340	−	5.58264i	0.521570	−	0.284518i
$386$		0			0
$387$		0			0
$388$		0			0
$389$		−	18.2599i		−	0.925813i	−0.886407	−	0.462907i	$-0.846806\pi$
$389$		−	18.2599i		−	0.925813i	0.886407	−	0.462907i	$-0.153194\pi$
$390$		0			0
$391$	7.80082	+	4.50381i	0.394504	+	0.227767i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−0.878921	+	1.52234i	−0.0442233	+	0.0765970i
$396$		0			0
$397$	−31.8395	+	18.3825i	−1.59798	+	0.922593i	−0.606101	+	0.795387i	$0.707267\pi$
$397$	−31.8395	+	18.3825i	−1.59798	+	0.922593i	−0.991876	+	0.127206i	$0.959399\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		−	15.9551i		−	0.796757i	−0.917221	−	0.398379i	$-0.869573\pi$
$401$		−	15.9551i		−	0.796757i	0.917221	−	0.398379i	$-0.130427\pi$
$402$		0			0
$403$	−29.4060			−1.46482
$404$		0			0
$405$		0			0
$406$		0			0
$407$	3.21933	−	1.85868i	0.159576	−	0.0921313i
$408$		0			0
$409$	8.52864	−	4.92401i	0.421714	−	0.243477i	−0.274096	−	0.961702i	$-0.588379\pi$
$409$	8.52864	−	4.92401i	0.421714	−	0.243477i	0.695810	+	0.718225i	$0.255045\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	8.40761	−	13.7807i	0.413712	−	0.678102i
$414$		0			0
$415$	−4.82228	−	8.35244i	−0.236716	−	0.410005i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−19.4482	+	33.6853i	−0.950106	+	1.64563i	−0.204917	+	0.978779i	$0.565692\pi$
$419$	−19.4482	+	33.6853i	−0.950106	+	1.64563i	−0.745189	+	0.666853i	$0.767641\pi$
$420$		0			0
$421$	−8.99598	−	15.5815i	−0.438437	−	0.759396i	0.559132	−	0.829079i	$-0.311135\pi$
$421$	−8.99598	−	15.5815i	−0.438437	−	0.759396i	−0.997569	+	0.0696829i	$0.977801\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	2.75898	−	4.77869i	0.133830	−	0.231800i
$426$		0			0
$427$	−0.174617	+	7.20949i	−0.00845031	+	0.348892i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	6.23236	+	3.59826i	0.300202	+	0.173322i	0.642534	−	0.766257i	$-0.277883\pi$
$431$	6.23236	+	3.59826i	0.300202	+	0.173322i	−0.342331	+	0.939579i	$0.611217\pi$
$432$		0			0
$433$			26.5567i			1.27623i	0.769939	+	0.638117i	$0.220286\pi$
$433$			26.5567i			1.27623i	−0.769939	+	0.638117i	$0.779714\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−23.2621	−	40.2912i	−1.11278	−	1.92739i
$438$		0			0
$439$	23.1077	+	13.3413i	1.10287	+	0.636744i	0.936974	−	0.349399i	$-0.113614\pi$
$439$	23.1077	+	13.3413i	1.10287	+	0.636744i	0.165898	+	0.986143i	$0.446948\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−33.0102	−	19.0584i	−1.56836	−	0.905494i	−0.996360	−	0.0852408i	$-0.972834\pi$
$443$	−33.0102	−	19.0584i	−1.56836	−	0.905494i	−0.572001	−	0.820253i	$-0.693833\pi$
$444$		0			0
$445$	−1.84696	−	3.19903i	−0.0875544	−	0.151649i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	21.5864i		−	1.01872i	−0.860552	−	0.509362i	$-0.829881\pi$
$449$		−	21.5864i		−	1.01872i	0.860552	−	0.509362i	$-0.170119\pi$
$450$		0			0
$451$	−27.6183	−	15.9454i	−1.30049	−	0.750841i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.294082	+	12.1419i	−0.0137868	+	0.569221i
$456$		0			0
$457$	−1.42761	+	2.47270i	−0.0667809	+	0.115668i	−0.897483	−	0.441050i	$-0.854606\pi$
$457$	−1.42761	+	2.47270i	−0.0667809	+	0.115668i	0.830702	+	0.556718i	$0.187940\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	13.3315	+	23.0909i	0.620911	+	1.07545i	0.989316	+	0.145784i	$0.0465706\pi$
$461$	13.3315	+	23.0909i	0.620911	+	1.07545i	−0.368405	+	0.929665i	$0.620096\pi$
$462$		0			0
$463$	−3.63687	+	6.29925i	−0.169020	+	0.292751i	−0.938076	−	0.346431i	$-0.887394\pi$
$463$	−3.63687	+	6.29925i	−0.169020	+	0.292751i	0.769056	+	0.639182i	$0.220727\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	2.37755	+	4.11804i	0.110020	+	0.190560i	0.915778	−	0.401685i	$-0.131575\pi$
$467$	2.37755	+	4.11804i	0.110020	+	0.190560i	−0.805758	+	0.592245i	$0.798242\pi$
$468$		0			0
$469$	−16.5894	+	27.1912i	−0.766029	+	1.25557i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	44.8862	−	25.9151i	2.06387	−	1.19158i
$474$		0			0
$475$	−24.6819	+	14.2501i	−1.13248	+	0.653839i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−19.8019			−0.904774			−0.452387	−	0.891822i	$-0.649427\pi$
$479$	−19.8019			−0.904774			−0.452387	+	0.891822i	$0.649427\pi$
$480$		0			0
$481$			3.87292i			0.176590i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	5.42817	−	3.13395i	0.246480	−	0.142306i
$486$		0			0
$487$	17.0806	−	29.5845i	0.773996	−	1.34060i	−0.161362	−	0.986895i	$-0.551589\pi$
$487$	17.0806	−	29.5845i	0.773996	−	1.34060i	0.935357	−	0.353704i	$-0.115078\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	9.91208	+	5.72274i	0.447326	+	0.258264i	0.706700	−	0.707513i	$-0.250183\pi$
$491$	9.91208	+	5.72274i	0.447326	+	0.258264i	−0.259374	+	0.965777i	$0.583516\pi$
$492$		0			0
$493$			13.4211i			0.604456i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.81890	−	0.992211i	0.0815886	−	0.0445067i
$498$		0			0
$499$	7.76302			0.347521			0.173760	−	0.984788i	$-0.444408\pi$
$499$	7.76302			0.347521			0.173760	+	0.984788i	$0.444408\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	2.92995			0.130640			0.0653200	−	0.997864i	$-0.479193\pi$
$503$	2.92995			0.130640			0.0653200	+	0.997864i	$0.479193\pi$
$504$		0			0
$505$	4.97055			0.221187
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−11.6268			−0.515347			−0.257673	−	0.966232i	$-0.582956\pi$
$509$	−11.6268			−0.515347			−0.257673	+	0.966232i	$0.582956\pi$
$510$		0			0
$511$	−0.144890	+	5.98213i	−0.00640954	+	0.264634i
$512$		0			0
$513$		0			0
$514$		0			0
$515$			4.57295i			0.201508i
$516$		0			0
$517$	29.9462	+	17.2894i	1.31703	+	0.760388i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	12.7515	−	22.0863i	0.558655	−	0.967619i	−0.438954	−	0.898509i	$-0.644651\pi$
$521$	12.7515	−	22.0863i	0.558655	−	0.967619i	0.997609	−	0.0691093i	$-0.0220157\pi$
$522$		0			0
$523$	0.781452	−	0.451172i	0.0341705	−	0.0197284i	−0.482817	−	0.875721i	$-0.660387\pi$
$523$	0.781452	−	0.451172i	0.0341705	−	0.0197284i	0.516988	+	0.855993i	$0.327053\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			9.88183i			0.430459i
$528$		0			0
$529$	−16.3900			−0.712610
$530$		0			0
$531$		0			0
$532$		0			0
$533$	28.7741	−	16.6127i	1.24634	−	0.719577i
$534$		0			0
$535$	9.39383	−	5.42353i	0.406131	−	0.234480i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−24.1270	−	15.5339i	−1.03922	−	0.669090i
$540$		0			0
$541$	−17.2460	−	29.8710i	−0.741464	−	1.28425i	−0.951829	−	0.306630i	$-0.900799\pi$
$541$	−17.2460	−	29.8710i	−0.741464	−	1.28425i	0.210365	−	0.977623i	$-0.432535\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	0.589444	−	1.02095i	0.0252490	−	0.0437326i
$546$		0			0
$547$	3.68664	+	6.38545i	0.157629	+	0.273022i	0.934013	−	0.357238i	$-0.116282\pi$
$547$	3.68664	+	6.38545i	0.157629	+	0.273022i	−0.776384	+	0.630260i	$0.782948\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	34.6600	−	60.0328i	1.47656	−	2.55748i
$552$		0			0
$553$	4.32566	+	0.104769i	0.183946	+	0.00445525i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−18.6335	−	10.7581i	−0.789528	−	0.455834i	0.0502687	−	0.998736i	$-0.483992\pi$
$557$	−18.6335	−	10.7581i	−0.789528	−	0.455834i	−0.839796	+	0.542902i	$0.817326\pi$
$558$		0			0
$559$			53.9991i			2.28392i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−15.7775	−	27.3274i	−0.664942	−	1.15171i	−0.979301	−	0.202409i	$-0.935123\pi$
$563$	−15.7775	−	27.3274i	−0.664942	−	1.15171i	0.314360	−	0.949304i	$-0.398210\pi$
$564$		0			0
$565$	9.15602	+	5.28623i	0.385197	+	0.222393i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	20.4138	+	11.7859i	0.855792	+	0.494092i	0.862601	−	0.505885i	$-0.168834\pi$
$569$	20.4138	+	11.7859i	0.855792	+	0.494092i	−0.00680861	+	0.999977i	$0.502167\pi$
$570$		0			0
$571$	−7.83445	−	13.5697i	−0.327861	−	0.567873i	0.654226	−	0.756299i	$-0.272995\pi$
$571$	−7.83445	−	13.5697i	−0.327861	−	0.567873i	−0.982087	+	0.188427i	$0.939661\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			24.1298i			1.00628i
$576$		0			0
$577$	0.137448	+	0.0793554i	0.00572202	+	0.00330361i	0.502858	−	0.864369i	$-0.332282\pi$
$577$	0.137448	+	0.0793554i	0.00572202	+	0.00330361i	−0.497136	+	0.867672i	$0.665615\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−12.3644	+	20.2661i	−0.512961	+	0.840779i
$582$		0			0
$583$	3.56415	−	6.17329i	0.147612	−	0.255672i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	15.9041	+	27.5467i	0.656432	+	1.13697i	0.981533	+	0.191294i	$0.0612683\pi$
$587$	15.9041	+	27.5467i	0.656432	+	1.13697i	−0.325101	+	0.945679i	$0.605398\pi$
$588$		0			0
$589$	25.5198	−	44.2016i	1.05153	−	1.82130i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	15.8934	+	27.5283i	0.652666	+	1.13045i	0.982474	+	0.186402i	$0.0596827\pi$
$593$	15.8934	+	27.5283i	0.652666	+	1.13045i	−0.329808	+	0.944048i	$0.606984\pi$
$594$		0			0
$595$	4.08026	+	0.0988256i	0.167274	+	0.00405145i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	10.5520	−	6.09222i	0.431144	−	0.248921i	−0.268690	−	0.963227i	$-0.586591\pi$
$599$	10.5520	−	6.09222i	0.431144	−	0.248921i	0.699834	+	0.714306i	$0.253257\pi$
$600$		0			0
$601$	−13.6048	+	7.85473i	−0.554951	+	0.320401i	−0.751117	−	0.660170i	$-0.770484\pi$
$601$	−13.6048	+	7.85473i	−0.554951	+	0.320401i	0.196165	+	0.980571i	$0.437151\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−6.23882			−0.253644
$606$		0			0
$607$		−	12.6280i		−	0.512553i	−0.966604	−	0.256277i	$-0.917504\pi$
$607$		−	12.6280i		−	0.512553i	0.966604	−	0.256277i	$-0.0824958\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−31.1994	+	18.0130i	−1.26219	+	0.728727i
$612$		0			0
$613$	11.3476	−	19.6546i	0.458325	−	0.793842i	−0.540547	−	0.841314i	$-0.681783\pi$
$613$	11.3476	−	19.6546i	0.458325	−	0.793842i	0.998873	+	0.0474711i	$0.0151162\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	32.6259	+	18.8366i	1.31347	+	0.758333i	0.982669	−	0.185368i	$-0.0593476\pi$
$617$	32.6259	+	18.8366i	1.31347	+	0.758333i	0.330801	+	0.943700i	$0.392681\pi$
$618$		0			0
$619$			5.20651i			0.209267i	0.994511	+	0.104634i	$0.0333670\pi$
$619$			5.20651i			0.209267i	−0.994511	+	0.104634i	$0.966633\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−4.73563	+	7.76203i	−0.189729	+	0.310979i
$624$		0			0
$625$	9.00510			0.360204
$626$		0			0
$627$		0			0
$628$		0			0
$629$	1.30149			0.0518937
$630$		0			0
$631$	−5.73635			−0.228361			−0.114180	−	0.993460i	$-0.536424\pi$
$631$	−5.73635			−0.228361			−0.114180	+	0.993460i	$0.536424\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	16.3594			0.649202
$636$		0			0
$637$	26.5840	−	13.6771i	1.05330	−	0.541905i
$638$		0			0
$639$		0			0
$640$		0			0
$641$			26.5960i			1.05048i	0.850954	+	0.525240i	$0.176024\pi$
$641$			26.5960i			1.05048i	−0.850954	+	0.525240i	$0.823976\pi$
$642$		0			0
$643$	−22.7885	−	13.1569i	−0.898689	−	0.518858i	−0.0219144	−	0.999760i	$-0.506976\pi$
$643$	−22.7885	−	13.1569i	−0.898689	−	0.518858i	−0.876775	+	0.480901i	$0.840309\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−23.8420	+	41.2955i	−0.937324	+	1.62349i	−0.166888	+	0.985976i	$0.553372\pi$
$647$	−23.8420	+	41.2955i	−0.937324	+	1.62349i	−0.770436	+	0.637517i	$0.779961\pi$
$648$		0			0
$649$	−21.6608	+	12.5059i	−0.850262	+	0.490899i
$650$		0			0
$651$		0			0
$652$		0			0
$653$		−	32.7208i		−	1.28046i	−0.768182	−	0.640231i	$-0.778838\pi$
$653$		−	32.7208i		−	1.28046i	0.768182	−	0.640231i	$-0.221162\pi$
$654$		0			0
$655$	−9.57568			−0.374153
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−26.5499	+	15.3286i	−1.03424	+	0.597118i	−0.918196	−	0.396126i	$-0.870354\pi$
$659$	−26.5499	+	15.3286i	−1.03424	+	0.597118i	−0.116043	+	0.993244i	$0.537021\pi$
$660$		0			0
$661$	9.35521	−	5.40123i	0.363875	−	0.210084i	−0.306904	−	0.951740i	$-0.599293\pi$
$661$	9.35521	−	5.40123i	0.363875	−	0.210084i	0.670779	+	0.741657i	$0.265960\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−17.9958	−	10.9793i	−0.697849	−	0.425759i
$666$		0			0
$667$	−29.3451	−	50.8271i	−1.13624	−	1.96803i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	5.58681	−	9.67663i	0.215676	−	0.373562i
$672$		0			0
$673$	19.4199	+	33.6363i	0.748583	+	1.29658i	0.948502	+	0.316771i	$0.102599\pi$
$673$	19.4199	+	33.6363i	0.748583	+	1.29658i	−0.199919	+	0.979812i	$0.564068\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	9.43192	−	16.3366i	0.362498	−	0.627865i	−0.625873	−	0.779925i	$-0.715257\pi$
$677$	9.43192	−	16.3366i	0.362498	−	0.627865i	0.988371	+	0.152060i	$0.0485906\pi$
$678$		0			0
$679$	−13.1707	−	8.03549i	−0.505446	−	0.308374i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	29.7510	+	17.1768i	1.13839	+	0.657251i	0.946032	−	0.324074i	$-0.105053\pi$
$683$	29.7510	+	17.1768i	1.13839	+	0.657251i	0.192360	+	0.981325i	$0.438386\pi$
$684$		0			0
$685$		−	12.1177i		−	0.462992i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	3.71331	+	6.43164i	0.141466	+	0.245026i
$690$		0			0
$691$	−22.1391	−	12.7820i	−0.842212	−	0.486251i	0.0158037	−	0.999875i	$-0.494969\pi$
$691$	−22.1391	−	12.7820i	−0.842212	−	0.486251i	−0.858015	+	0.513624i	$0.828303\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	12.9485	+	7.47584i	0.491166	+	0.283575i
$696$		0			0
$697$	−5.58267	−	9.66947i	−0.211459	−	0.366257i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	32.3485i		−	1.22178i	−0.791714	−	0.610892i	$-0.790811\pi$
$701$		−	32.3485i		−	1.22178i	0.791714	−	0.610892i	$-0.209189\pi$
$702$		0			0
$703$	−5.82158	−	3.36109i	−0.219565	−	0.126766i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−5.85915	−	10.7409i	−0.220356	−	0.403951i
$708$		0			0
$709$	−1.30119	+	2.25373i	−0.0488672	+	0.0846405i	−0.889424	−	0.457082i	$-0.848894\pi$
$709$	−1.30119	+	2.25373i	−0.0488672	+	0.0846405i	0.840557	+	0.541723i	$0.182228\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−21.6065	−	37.4235i	−0.809169	−	1.40152i
$714$		0			0
$715$	9.40905	−	16.2969i	0.351878	−	0.609471i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−8.42868	−	14.5989i	−0.314337	−	0.544447i	0.664960	−	0.746879i	$-0.268449\pi$
$719$	−8.42868	−	14.5989i	−0.314337	−	0.544447i	−0.979296	+	0.202432i	$0.935115\pi$
$720$		0			0
$721$	9.88168	−	5.39047i	0.368013	−	0.200752i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−31.1361	+	17.9764i	−1.15636	+	0.667627i
$726$		0			0
$727$	36.1005	−	20.8426i	1.33889	−	0.773009i	0.352249	−	0.935906i	$-0.385417\pi$
$727$	36.1005	−	20.8426i	1.33889	−	0.773009i	0.986643	+	0.162897i	$0.0520838\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	18.1463			0.671165
$732$		0			0
$733$		−	36.0421i		−	1.33125i	−0.746288	−	0.665623i	$-0.768166\pi$
$733$		−	36.0421i		−	1.33125i	0.746288	−	0.665623i	$-0.231834\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	42.7400	−	24.6759i	1.57435	−	0.908949i
$738$		0			0
$739$	−14.1322	+	24.4777i	−0.519861	+	0.900426i	0.479872	+	0.877339i	$0.340683\pi$
$739$	−14.1322	+	24.4777i	−0.519861	+	0.900426i	−0.999733	+	0.0230879i	$0.992650\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	28.7161	+	16.5793i	1.05349	+	0.608234i	0.923625	−	0.383298i	$-0.125212\pi$
$743$	28.7161	+	16.5793i	1.05349	+	0.608234i	0.129867	+	0.991531i	$0.458545\pi$
$744$		0			0
$745$		−	3.84136i		−	0.140736i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−22.7929	−	13.9060i	−0.832834	−	0.508114i
$750$		0			0
$751$	−43.2310			−1.57752			−0.788761	−	0.614700i	$-0.789277\pi$
$751$	−43.2310			−1.57752			−0.788761	+	0.614700i	$0.789277\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	7.09789			0.258319
$756$		0			0
$757$	33.2085			1.20698			0.603492	−	0.797369i	$-0.293776\pi$
$757$	33.2085			1.20698			0.603492	+	0.797369i	$0.293776\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	4.31938			0.156577			0.0782887	−	0.996931i	$-0.475054\pi$
$761$	4.31938			0.156577			0.0782887	+	0.996931i	$0.475054\pi$
$762$		0			0
$763$	−2.90098	−	0.0702631i	−0.105023	−	0.00254369i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	26.0585i		−	0.940918i
$768$		0			0
$769$	−16.1845	−	9.34412i	−0.583628	−	0.336958i	0.178946	−	0.983859i	$-0.442731\pi$
$769$	−16.1845	−	9.34412i	−0.583628	−	0.336958i	−0.762574	+	0.646901i	$0.776065\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	4.91482	−	8.51272i	0.176774	−	0.306181i	−0.764000	−	0.645216i	$-0.776767\pi$
$773$	4.91482	−	8.51272i	0.176774	−	0.306181i	0.940774	+	0.339035i	$0.110101\pi$
$774$		0			0
$775$	−22.9252	+	13.2359i	−0.823497	+	0.475446i
$776$		0			0
$777$		0			0
$778$		0			0
$779$			57.6689i			2.06620i
$780$		0			0
$781$	−3.21023			−0.114871
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−8.55966	+	4.94192i	−0.305507	+	0.176385i
$786$		0			0
$787$	39.3412	−	22.7136i	1.40236	−	0.809654i	0.407727	−	0.913104i	$-0.366321\pi$
$787$	39.3412	−	22.7136i	1.40236	−	0.809654i	0.994635	+	0.103450i	$0.0329881\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	0.630130	−	26.0165i	0.0224049	−	0.925039i
$792$		0			0
$793$	5.82061	+	10.0816i	0.206696	+	0.358008i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	7.67140	−	13.2872i	0.271735	−	0.470658i	−0.697571	−	0.716515i	$-0.745736\pi$
$797$	7.67140	−	13.2872i	0.271735	−	0.470658i	0.969306	+	0.245857i	$0.0790693\pi$
$798$		0			0
$799$	6.05322	+	10.4845i	0.214147	+	0.370914i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	4.63569	−	8.02926i	0.163590	−	0.283346i
$804$		0			0
$805$	−15.6684	+	8.54716i	−0.552240	+	0.301248i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.785783	+	0.453672i	0.0276267	+	0.0159503i	0.513750	−	0.857940i	$-0.328256\pi$
$809$	0.785783	+	0.453672i	0.0276267	+	0.0159503i	−0.486123	+	0.873890i	$0.661589\pi$
$810$		0			0
$811$		−	7.95121i		−	0.279205i	−0.990208	−	0.139602i	$-0.955418\pi$
$811$		−	7.95121i		−	0.279205i	0.990208	−	0.139602i	$-0.0445824\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	3.92184	+	6.79282i	0.137376	+	0.237942i
$816$		0			0
$817$	−81.1686	−	46.8627i	−2.83973	−	1.63952i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	40.5906	+	23.4350i	1.41662	+	0.817886i	0.996000	−	0.0893510i	$-0.0284793\pi$
$821$	40.5906	+	23.4350i	1.41662	+	0.817886i	0.420620	+	0.907237i	$0.361813\pi$
$822$		0			0
$823$	−10.4949	−	18.1778i	−0.365831	−	0.633637i	0.623078	−	0.782159i	$-0.285882\pi$
$823$	−10.4949	−	18.1778i	−0.365831	−	0.633637i	−0.988909	+	0.148522i	$0.952548\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	12.6370i		−	0.439430i	−0.975564	−	0.219715i	$-0.929487\pi$
$827$		−	12.6370i		−	0.439430i	0.975564	−	0.219715i	$-0.0705127\pi$
$828$		0			0
$829$	3.12273	+	1.80291i	0.108457	+	0.0626177i	0.553247	−	0.833017i	$-0.313388\pi$
$829$	3.12273	+	1.80291i	0.108457	+	0.0626177i	−0.444790	+	0.895635i	$0.646722\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−4.59614	−	8.93351i	−0.159247	−	0.309528i
$834$		0			0
$835$	−7.60048	+	13.1644i	−0.263025	+	0.455573i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−0.287256	−	0.497541i	−0.00991716	−	0.0171770i	0.861024	−	0.508564i	$-0.169823\pi$
$839$	−0.287256	−	0.497541i	−0.00991716	−	0.0171770i	−0.870941	+	0.491387i	$0.836490\pi$
$840$		0			0
$841$	29.2234	−	50.6163i	1.00770	−	1.74539i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	2.81626	+	4.87790i	0.0968822	+	0.167805i
$846$		0			0
$847$	7.35416	+	13.4815i	0.252692	+	0.463228i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−4.92887	+	2.84568i	−0.168959	+	0.0975488i
$852$		0			0
$853$	−5.62283	+	3.24634i	−0.192522	+	0.111153i	−0.593163	−	0.805083i	$-0.702121\pi$
$853$	−5.62283	+	3.24634i	−0.192522	+	0.111153i	0.400641	+	0.916235i	$0.368788\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	2.31537			0.0790915			0.0395457	−	0.999218i	$-0.487409\pi$
$857$	2.31537			0.0790915			0.0395457	+	0.999218i	$0.487409\pi$
$858$		0			0
$859$		−	55.6555i		−	1.89894i	−0.313855	−	0.949471i	$-0.601621\pi$
$859$		−	55.6555i		−	1.89894i	0.313855	−	0.949471i	$-0.398379\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	7.50527	−	4.33317i	0.255482	−	0.147503i	−0.366790	−	0.930304i	$-0.619543\pi$
$863$	7.50527	−	4.33317i	0.255482	−	0.147503i	0.622272	+	0.782801i	$0.286210\pi$
$864$		0			0
$865$	−7.25443	+	12.5650i	−0.246658	+	0.427224i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−5.80593	−	3.35206i	−0.196953	−	0.113711i
$870$		0			0
$871$			51.4172i			1.74220i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	12.0451	+	22.0808i	0.407199	+	0.746468i
$876$		0			0
$877$	35.6629			1.20425			0.602126	−	0.798401i	$-0.294321\pi$
$877$	35.6629			1.20425			0.602126	+	0.798401i	$0.294321\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−7.57740			−0.255289			−0.127644	−	0.991820i	$-0.540742\pi$
$881$	−7.57740			−0.255289			−0.127644	+	0.991820i	$0.540742\pi$
$882$		0			0
$883$	−5.35854			−0.180329			−0.0901646	−	0.995927i	$-0.528739\pi$
$883$	−5.35854			−0.180329			−0.0901646	+	0.995927i	$0.528739\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	23.5904			0.792090			0.396045	−	0.918231i	$-0.370382\pi$
$887$	23.5904			0.792090			0.396045	+	0.918231i	$0.370382\pi$
$888$		0			0
$889$	−19.2840	−	35.3509i	−0.646764	−	1.18563i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		−	62.5297i		−	2.09248i
$894$		0			0
$895$	4.26755	+	2.46387i	0.142649	+	0.0823582i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	32.1931	−	55.7601i	1.07370	−	1.85970i
$900$		0			0
$901$	2.16134	−	1.24785i	0.0720046	−	0.0415719i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			2.39586i			0.0796410i
$906$		0			0
$907$	−14.2703			−0.473838			−0.236919	−	0.971529i	$-0.576138\pi$
$907$	−14.2703			−0.473838			−0.236919	+	0.971529i	$0.576138\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	40.0156	−	23.1030i	1.32578	−	0.765437i	0.341133	−	0.940015i	$-0.389189\pi$
$911$	40.0156	−	23.1030i	1.32578	−	0.765437i	0.984643	+	0.174578i	$0.0558560\pi$
$912$		0			0
$913$	31.8548	−	18.3914i	1.05424	−	0.608666i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	11.2875	+	20.6920i	0.372748	+	0.683312i
$918$		0			0
$919$	−16.8957	−	29.2643i	−0.557339	−	0.965339i	−0.997717	−	0.0675269i	$-0.978489\pi$
$919$	−16.8957	−	29.2643i	−0.557339	−	0.965339i	0.440379	−	0.897812i	$-0.354844\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	1.67228	−	2.89648i	0.0550439	−	0.0953389i
$924$		0			0
$925$	1.74323	+	3.01936i	0.0573171	+	0.0992761i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−17.4684	+	30.2562i	−0.573121	+	0.992674i	0.423123	+	0.906072i	$0.360934\pi$
$929$	−17.4684	+	30.2562i	−0.573121	+	0.992674i	−0.996243	+	0.0866014i	$0.972399\pi$
$930$		0			0
$931$	−2.51213	+	51.8292i	−0.0823317	+	1.69863i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−5.47655	−	3.16189i	−0.179102	−	0.103405i
$936$		0			0
$937$			11.6175i			0.379528i	0.981830	+	0.189764i	$0.0607723\pi$
$937$			11.6175i			0.379528i	−0.981830	+	0.189764i	$0.939228\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	4.77515	+	8.27080i	0.155665	+	0.269620i	0.933301	−	0.359095i	$-0.116914\pi$
$941$	4.77515	+	8.27080i	0.155665	+	0.269620i	−0.777636	+	0.628715i	$0.783581\pi$
$942$		0			0
$943$	42.2843	+	24.4129i	1.37697	+	0.794992i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−31.7721	−	18.3436i	−1.03245	−	0.596088i	−0.114768	−	0.993392i	$-0.536612\pi$
$947$	−31.7721	−	18.3436i	−1.03245	−	0.596088i	−0.917687	+	0.397305i	$0.869946\pi$
$948$		0			0
$949$	4.82969	+	8.36527i	0.156778	+	0.271548i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			17.1813i			0.556556i	0.960501	+	0.278278i	$0.0897636\pi$
$953$			17.1813i			0.556556i	−0.960501	+	0.278278i	$0.910236\pi$
$954$		0			0
$955$	−19.5805	−	11.3048i	−0.633610	−	0.365815i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−26.1850	+	14.2840i	−0.845559	+	0.461254i
$960$		0			0
$961$	8.20347	−	14.2088i	0.264628	−	0.458349i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	6.02146	+	10.4295i	0.193838	+	0.335737i
$966$		0			0
$967$	−2.43550	+	4.21841i	−0.0783204	+	0.135655i	−0.902525	−	0.430637i	$-0.858289\pi$
$967$	−2.43550	+	4.21841i	−0.0783204	+	0.135655i	0.824205	+	0.566292i	$0.191622\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−14.0544	−	24.3429i	−0.451026	−	0.781200i	0.547424	−	0.836855i	$-0.315608\pi$
$971$	−14.0544	−	24.3429i	−0.451026	−	0.781200i	−0.998450	+	0.0556556i	$0.982275\pi$
$972$		0			0
$973$	0.891137	−	36.7928i	0.0285686	−	1.17952i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	26.4642	−	15.2791i	0.846664	−	0.488822i	−0.0128600	−	0.999917i	$-0.504094\pi$
$977$	26.4642	−	15.2791i	0.846664	−	0.488822i	0.859524	+	0.511096i	$0.170760\pi$
$978$		0			0
$979$	12.2006	−	7.04401i	0.389932	−	0.225127i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−11.9711			−0.381820			−0.190910	−	0.981608i	$-0.561144\pi$
$983$	−11.9711			−0.381820			−0.190910	+	0.981608i	$0.561144\pi$
$984$		0			0
$985$			22.4585i			0.715588i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−68.7219	+	39.6766i	−2.18523	+	1.26164i
$990$		0			0
$991$	−3.32513	+	5.75929i	−0.105626	+	0.182950i	−0.913994	−	0.405728i	$-0.867018\pi$
$991$	−3.32513	+	5.75929i	−0.105626	+	0.182950i	0.808368	+	0.588678i	$0.200351\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−17.0387	−	9.83730i	−0.540163	−	0.311863i
$996$		0			0
$997$			55.0505i			1.74347i	0.489982	+	0.871733i	$0.337003\pi$
$997$			55.0505i			1.74347i	−0.489982	+	0.871733i	$0.662997\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.cx.a.17.16		48
3.2	odd	2		504.2.cx.a.185.12	yes	48
4.3	odd	2		3024.2.df.e.17.16		48
7.5	odd	6		1512.2.bs.a.1097.16		48
9.2	odd	6		1512.2.bs.a.521.16		48
9.7	even	3		504.2.bs.a.353.21	yes	48
12.11	even	2		1008.2.df.e.689.13		48
21.5	even	6		504.2.bs.a.257.21	✓	48
28.19	even	6		3024.2.ca.e.2609.16		48
36.7	odd	6		1008.2.ca.e.353.4		48
36.11	even	6		3024.2.ca.e.2033.16		48
63.47	even	6	inner	1512.2.cx.a.89.16		48
63.61	odd	6		504.2.cx.a.425.12	yes	48
84.47	odd	6		1008.2.ca.e.257.4		48
252.47	odd	6		3024.2.df.e.1601.16		48
252.187	even	6		1008.2.df.e.929.13		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.21	✓	48	21.5	even	6
504.2.bs.a.353.21	yes	48	9.7	even	3
504.2.cx.a.185.12	yes	48	3.2	odd	2
504.2.cx.a.425.12	yes	48	63.61	odd	6
1008.2.ca.e.257.4		48	84.47	odd	6
1008.2.ca.e.353.4		48	36.7	odd	6
1008.2.df.e.689.13		48	12.11	even	2
1008.2.df.e.929.13		48	252.187	even	6
1512.2.bs.a.521.16		48	9.2	odd	6
1512.2.bs.a.1097.16		48	7.5	odd	6
1512.2.cx.a.17.16		48	1.1	even	1	trivial
1512.2.cx.a.89.16		48	63.47	even	6	inner
3024.2.ca.e.2033.16		48	36.11	even	6
3024.2.ca.e.2609.16		48	28.19	even	6
3024.2.df.e.17.16		48	4.3	odd	2
3024.2.df.e.1601.16		48	252.47	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.cx (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.07485 q^{5} +(-1.26701 - 2.32265i) q^{7} +4.09931i q^{11} +(-3.69867 - 2.13543i) q^{13} +(-0.717607 + 1.24293i) q^{17} +(6.41973 - 3.70644i) q^{19} -6.27615i q^{23} -3.84469 q^{25} +(8.09846 - 4.67565i) q^{29} +(5.96282 - 3.44264i) q^{31} +(-1.36185 - 2.49651i) q^{35} +(-0.453413 - 0.785334i) q^{37} +(-3.88978 + 6.73730i) q^{41} +(-6.32181 - 10.9497i) q^{43} +(4.21764 - 7.30517i) q^{47} +(-3.78938 + 5.88563i) q^{49} +(-1.50593 - 0.869452i) q^{53} +4.40616i q^{55} +(3.05073 + 5.28402i) q^{59} +(-2.36055 - 1.36287i) q^{61} +(-3.97553 - 2.29528i) q^{65} +(-6.01953 - 10.4261i) q^{67} +0.783113i q^{71} +(-1.95868 - 1.13085i) q^{73} +(9.52125 - 5.19386i) q^{77} +(-0.817713 + 1.41632i) q^{79} +(-4.48646 - 7.77077i) q^{83} +(-0.771322 + 1.33597i) q^{85} +(-1.71834 - 2.97625i) q^{89} +(-0.273602 + 11.2963i) q^{91} +(6.90027 - 3.98387i) q^{95} +(5.05015 - 2.91570i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 48 q^{25} - 18 q^{29} + 18 q^{31} + 6 q^{41} - 6 q^{43} - 18 q^{47} - 12 q^{49} + 12 q^{53} + 18 q^{61} + 36 q^{65} + 12 q^{77} + 6 q^{79} + 18 q^{89} + 6 q^{91} + 54 q^{95}+O(q^{100}) \) 48 * q + 48 * q^25 - 18 * q^29 + 18 * q^31 + 6 * q^41 - 6 * q^43 - 18 * q^47 - 12 * q^49 + 12 * q^53 + 18 * q^61 + 36 * q^65 + 12 * q^77 + 6 * q^79 + 18 * q^89 + 6 * q^91 + 54 * q^95

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