LMFDB - Embedded newform 315.2.d.e.64.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [315,2,Mod(64,315)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("315.64"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(315, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,0,-10,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			64.4
Root			$0.403032 + 0.403032i$ of defining polynomial
Character	$\chi$	$=$	315.64
Dual form			315.2.d.e.64.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.193937i q^{2} +1.96239 q^{4} +(1.48119 + 1.67513i) q^{5} +1.00000i q^{7} +0.768452i q^{8} +(-0.324869 + 0.287258i) q^{10} -2.00000 q^{11} +1.35026i q^{13} -0.193937 q^{14} +3.77575 q^{16} -3.35026i q^{17} -5.35026 q^{19} +(2.90668 + 3.28726i) q^{20} -0.387873i q^{22} -4.96239i q^{23} +(-0.612127 + 4.96239i) q^{25} -0.261865 q^{26} +1.96239i q^{28} +7.92478 q^{29} +4.57452 q^{31} +2.26916i q^{32} +0.649738 q^{34} +(-1.67513 + 1.48119i) q^{35} +0.775746i q^{37} -1.03761i q^{38} +(-1.28726 + 1.13823i) q^{40} -3.73813 q^{41} -12.6253i q^{43} -3.92478 q^{44} +0.962389 q^{46} +9.92478i q^{47} -1.00000 q^{49} +(-0.962389 - 0.118714i) q^{50} +2.64974i q^{52} -8.57452i q^{53} +(-2.96239 - 3.35026i) q^{55} -0.768452 q^{56} +1.53690i q^{58} -8.62530 q^{59} -8.70052 q^{61} +0.887166i q^{62} +7.11142 q^{64} +(-2.26187 + 2.00000i) q^{65} -9.92478i q^{67} -6.57452i q^{68} +(-0.287258 - 0.324869i) q^{70} -2.00000 q^{71} -9.35026i q^{73} -0.150446 q^{74} -10.4993 q^{76} -2.00000i q^{77} -10.7005 q^{79} +(5.59261 + 6.32487i) q^{80} -0.724961i q^{82} -3.22425i q^{83} +(5.61213 - 4.96239i) q^{85} +2.44851 q^{86} -1.53690i q^{88} +1.03761 q^{89} -1.35026 q^{91} -9.73813i q^{92} -1.92478 q^{94} +(-7.92478 - 8.96239i) q^{95} +18.4993i q^{97} -0.193937i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 10 q^{4} - 2 q^{5} - 12 q^{10} - 12 q^{11} - 2 q^{14} + 26 q^{16} - 12 q^{19} + 30 q^{20} - 2 q^{25} - 20 q^{26} + 4 q^{29} + 4 q^{31} + 24 q^{34} + 4 q^{40} - 4 q^{41} + 20 q^{44} - 16 q^{46} - 6 q^{49}+ \cdots - 4 q^{95}+O(q^{100}) $ 6 * q - 10 * q^4 - 2 * q^5 - 12 * q^10 - 12 * q^11 - 2 * q^14 + 26 * q^16 - 12 * q^19 + 30 * q^20 - 2 * q^25 - 20 * q^26 + 4 * q^29 + 4 * q^31 + 24 * q^34 + 4 * q^40 - 4 * q^41 + 20 * q^44 - 16 * q^46 - 6 * q^49 + 16 * q^50 + 4 * q^55 + 18 * q^56 + 32 * q^59 - 12 * q^61 - 26 * q^64 - 32 * q^65 + 10 * q^70 - 12 * q^71 - 88 * q^74 + 4 * q^76 - 24 * q^79 - 46 * q^80 + 32 * q^85 + 8 * q^86 + 28 * q^89 + 12 * q^91 + 32 * q^94 - 4 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$			0.193937i			0.137134i	0.997647	+	0.0685669i	$0.0218427\pi$
$2$			0.193937i			0.137134i	−0.997647	+	0.0685669i	$0.978157\pi$
$3$		0			0
$3$		0			0
$4$	1.96239			0.981194
$5$	1.48119	+	1.67513i	0.662410	+	0.749141i
$5$	1.48119	+	1.67513i	0.662410	+	0.749141i
$6$		0			0
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$			0.768452i			0.271689i
$9$		0			0
$10$	−0.324869	+	0.287258i	−0.102733	+	0.0908389i
$11$	−2.00000			−0.603023			−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000			−0.603023			−0.301511	+	0.953463i	$0.597491\pi$
$12$		0			0
$13$			1.35026i			0.374495i	0.982313	+	0.187248i	$0.0599567\pi$
$13$			1.35026i			0.374495i	−0.982313	+	0.187248i	$0.940043\pi$
$14$	−0.193937			−0.0518317
$15$		0			0
$16$	3.77575			0.943937
$17$		−	3.35026i		−	0.812558i	−0.913749	−	0.406279i	$-0.866826\pi$
$17$		−	3.35026i		−	0.812558i	0.913749	−	0.406279i	$-0.133174\pi$
$18$		0			0
$19$	−5.35026			−1.22743			−0.613717	−	0.789526i	$-0.710326\pi$
$19$	−5.35026			−1.22743			−0.613717	+	0.789526i	$0.710326\pi$
$20$	2.90668	+	3.28726i	0.649953	+	0.735053i
$21$		0			0
$22$		−	0.387873i		−	0.0826948i
$23$		−	4.96239i		−	1.03473i	−0.855765	−	0.517365i	$-0.826913\pi$
$23$		−	4.96239i		−	1.03473i	0.855765	−	0.517365i	$-0.173087\pi$
$24$		0			0
$25$	−0.612127	+	4.96239i	−0.122425	+	0.992478i
$26$	−0.261865			−0.0513560
$27$		0			0
$28$			1.96239i			0.370857i
$29$	7.92478			1.47159			0.735797	−	0.677202i	$-0.236808\pi$
$29$	7.92478			1.47159			0.735797	+	0.677202i	$0.236808\pi$
$30$		0			0
$31$	4.57452			0.821607			0.410804	−	0.911724i	$-0.365248\pi$
$31$	4.57452			0.821607			0.410804	+	0.911724i	$0.365248\pi$
$32$			2.26916i			0.401134i
$33$		0			0
$34$	0.649738			0.111429
$35$	−1.67513	+	1.48119i	−0.283149	+	0.250368i
$36$		0			0
$37$			0.775746i			0.127532i	0.997965	+	0.0637660i	$0.0203111\pi$
$37$			0.775746i			0.127532i	−0.997965	+	0.0637660i	$0.979689\pi$
$38$		−	1.03761i		−	0.168323i
$39$		0			0
$40$	−1.28726	+	1.13823i	−0.203533	+	0.179969i
$41$	−3.73813			−0.583799			−0.291899	−	0.956449i	$-0.594287\pi$
$41$	−3.73813			−0.583799			−0.291899	+	0.956449i	$0.594287\pi$
$42$		0			0
$43$		−	12.6253i		−	1.92534i	−0.270677	−	0.962670i	$-0.587248\pi$
$43$		−	12.6253i		−	1.92534i	0.270677	−	0.962670i	$-0.412752\pi$
$44$	−3.92478			−0.591682
$45$		0			0
$46$	0.962389			0.141896
$47$			9.92478i			1.44768i	0.689969	+	0.723839i	$0.257624\pi$
$47$			9.92478i			1.44768i	−0.689969	+	0.723839i	$0.742376\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	−0.962389	−	0.118714i	−0.136102	−	0.0167887i
$51$		0			0
$52$			2.64974i			0.367453i
$53$		−	8.57452i		−	1.17780i	−0.808206	−	0.588900i	$-0.799561\pi$
$53$		−	8.57452i		−	1.17780i	0.808206	−	0.588900i	$-0.200439\pi$
$54$		0			0
$55$	−2.96239	−	3.35026i	−0.399448	−	0.451749i
$56$	−0.768452			−0.102689
$57$		0			0
$58$			1.53690i			0.201805i
$59$	−8.62530			−1.12292			−0.561459	−	0.827504i	$-0.689760\pi$
$59$	−8.62530			−1.12292			−0.561459	+	0.827504i	$0.689760\pi$
$60$		0			0
$61$	−8.70052			−1.11399			−0.556994	−	0.830517i	$-0.688045\pi$
$61$	−8.70052			−1.11399			−0.556994	+	0.830517i	$0.688045\pi$
$62$			0.887166i			0.112670i
$63$		0			0
$64$	7.11142			0.888927
$65$	−2.26187	+	2.00000i	−0.280550	+	0.248069i
$66$		0			0
$67$		−	9.92478i		−	1.21250i	−0.795272	−	0.606252i	$-0.792672\pi$
$67$		−	9.92478i		−	1.21250i	0.795272	−	0.606252i	$-0.207328\pi$
$68$		−	6.57452i		−	0.797277i
$69$		0			0
$70$	−0.287258	−	0.324869i	−0.0343339	−	0.0388293i
$71$	−2.00000			−0.237356			−0.118678	−	0.992933i	$-0.537866\pi$
$71$	−2.00000			−0.237356			−0.118678	+	0.992933i	$0.537866\pi$
$72$		0			0
$73$		−	9.35026i		−	1.09437i	−0.837013	−	0.547183i	$-0.815700\pi$
$73$		−	9.35026i		−	1.09437i	0.837013	−	0.547183i	$-0.184300\pi$
$74$	−0.150446			−0.0174889
$75$		0			0
$76$	−10.4993			−1.20435
$77$		−	2.00000i		−	0.227921i
$78$		0			0
$79$	−10.7005			−1.20390			−0.601951	−	0.798533i	$-0.705610\pi$
$79$	−10.7005			−1.20390			−0.601951	+	0.798533i	$0.705610\pi$
$80$	5.59261	+	6.32487i	0.625273	+	0.707142i
$81$		0			0
$82$		−	0.724961i		−	0.0800586i
$83$		−	3.22425i		−	0.353908i	−0.984219	−	0.176954i	$-0.943376\pi$
$83$		−	3.22425i		−	0.353908i	0.984219	−	0.176954i	$-0.0566244\pi$
$84$		0			0
$85$	5.61213	−	4.96239i	0.608721	−	0.538247i
$86$	2.44851			0.264029
$87$		0			0
$88$		−	1.53690i		−	0.163835i
$89$	1.03761			0.109987			0.0549933	−	0.998487i	$-0.482486\pi$
$89$	1.03761			0.109987			0.0549933	+	0.998487i	$0.482486\pi$
$90$		0			0
$91$	−1.35026			−0.141546
$92$		−	9.73813i		−	1.01527i
$93$		0			0
$94$	−1.92478			−0.198526
$95$	−7.92478	−	8.96239i	−0.813065	−	0.919522i
$96$		0			0
$97$			18.4993i			1.87832i	0.343482	+	0.939159i	$0.388394\pi$
$97$			18.4993i			1.87832i	−0.343482	+	0.939159i	$0.611606\pi$
$98$		−	0.193937i		−	0.0195906i
$99$		0			0
$100$	−1.20123	+	9.73813i	−0.120123	+	0.973813i
$101$	17.6629			1.75753			0.878763	−	0.477259i	$-0.158370\pi$
$101$	17.6629			1.75753			0.878763	+	0.477259i	$0.158370\pi$
$102$		0			0
$103$			6.70052i			0.660222i	0.943942	+	0.330111i	$0.107086\pi$
$103$			6.70052i			0.660222i	−0.943942	+	0.330111i	$0.892914\pi$
$104$	−1.03761			−0.101746
$105$		0			0
$106$	1.66291			0.161516
$107$			13.7381i			1.32812i	0.747681	+	0.664058i	$0.231167\pi$
$107$			13.7381i			1.32812i	−0.747681	+	0.664058i	$0.768833\pi$
$108$		0			0
$109$	2.77575			0.265868			0.132934	−	0.991125i	$-0.457560\pi$
$109$	2.77575			0.265868			0.132934	+	0.991125i	$0.457560\pi$
$110$	0.649738	−	0.574515i	0.0619501	−	0.0547779i
$111$		0			0
$112$			3.77575i			0.356774i
$113$		−	12.0508i		−	1.13364i	−0.823841	−	0.566821i	$-0.808173\pi$
$113$		−	12.0508i		−	1.13364i	0.823841	−	0.566821i	$-0.191827\pi$
$114$		0			0
$115$	8.31265	−	7.35026i	0.775159	−	0.685415i
$116$	15.5515			1.44392
$117$		0			0
$118$		−	1.67276i		−	0.153990i
$119$	3.35026			0.307118
$120$		0			0
$121$	−7.00000			−0.636364
$122$		−	1.68735i		−	0.152765i
$123$		0			0
$124$	8.97698			0.806156
$125$	−9.21933	+	6.32487i	−0.824602	+	0.565713i
$126$		0			0
$127$		−	2.70052i		−	0.239633i	−0.992796	−	0.119816i	$-0.961769\pi$
$127$		−	2.70052i		−	0.239633i	0.992796	−	0.119816i	$-0.0382306\pi$
$128$			5.91748i			0.523037i
$129$		0			0
$130$	−0.387873	−	0.438658i	−0.0340187	−	0.0384729i
$131$	−20.6253			−1.80204			−0.901020	−	0.433777i	$-0.857181\pi$
$131$	−20.6253			−1.80204			−0.901020	+	0.433777i	$0.857181\pi$
$132$		0			0
$133$		−	5.35026i		−	0.463927i
$134$	1.92478			0.166275
$135$		0			0
$136$	2.57452			0.220763
$137$			22.4993i			1.92224i	0.276124	+	0.961122i	$0.410950\pi$
$137$			22.4993i			1.92224i	−0.276124	+	0.961122i	$0.589050\pi$
$138$		0			0
$139$	3.27504			0.277785			0.138893	−	0.990307i	$-0.455646\pi$
$139$	3.27504			0.277785			0.138893	+	0.990307i	$0.455646\pi$
$140$	−3.28726	+	2.90668i	−0.277824	+	0.245659i
$141$		0			0
$142$		−	0.387873i		−	0.0325496i
$143$		−	2.70052i		−	0.225829i
$144$		0			0
$145$	11.7381	+	13.2750i	0.974799	+	1.10243i
$146$	1.81336			0.150075
$147$		0			0
$148$			1.52232i			0.125134i
$149$	−4.44851			−0.364436			−0.182218	−	0.983258i	$-0.558328\pi$
$149$	−4.44851			−0.364436			−0.182218	+	0.983258i	$0.558328\pi$
$150$		0			0
$151$	1.29948			0.105750			0.0528749	−	0.998601i	$-0.483162\pi$
$151$	1.29948			0.105750			0.0528749	+	0.998601i	$0.483162\pi$
$152$		−	4.11142i		−	0.333480i
$153$		0			0
$154$	0.387873			0.0312557
$155$	6.77575	+	7.66291i	0.544241	+	0.615500i
$156$		0			0
$157$			2.64974i			0.211472i	0.994394	+	0.105736i	$0.0337199\pi$
$157$			2.64974i			0.211472i	−0.994394	+	0.105736i	$0.966280\pi$
$158$		−	2.07522i		−	0.165096i
$159$		0			0
$160$	−3.80114	+	3.36107i	−0.300506	+	0.265716i
$161$	4.96239			0.391091
$162$		0			0
$163$			5.29948i			0.415087i	0.978226	+	0.207544i	$0.0665469\pi$
$163$			5.29948i			0.415087i	−0.978226	+	0.207544i	$0.933453\pi$
$164$	−7.33567			−0.572820
$165$		0			0
$166$	0.625301			0.0485327
$167$		−	14.5501i		−	1.12592i	−0.826485	−	0.562959i	$-0.809663\pi$
$167$		−	14.5501i		−	1.12592i	0.826485	−	0.562959i	$-0.190337\pi$
$168$		0			0
$169$	11.1768			0.859753
$170$	0.962389	+	1.08840i	0.0738118	+	0.0834762i
$171$		0			0
$172$		−	24.7757i		−	1.88913i
$173$			4.49929i			0.342075i	0.985265	+	0.171037i	$0.0547119\pi$
$173$			4.49929i			0.342075i	−0.985265	+	0.171037i	$0.945288\pi$
$174$		0			0
$175$	−4.96239	−	0.612127i	−0.375121	−	0.0462724i
$176$	−7.55149			−0.569215
$177$		0			0
$178$			0.201231i			0.0150829i
$179$	10.0000			0.747435			0.373718	−	0.927543i	$-0.378083\pi$
$179$	10.0000			0.747435			0.373718	+	0.927543i	$0.378083\pi$
$180$		0			0
$181$	10.6253			0.789772			0.394886	−	0.918730i	$-0.370784\pi$
$181$	10.6253			0.789772			0.394886	+	0.918730i	$0.370784\pi$
$182$		−	0.261865i		−	0.0194107i
$183$		0			0
$184$	3.81336			0.281124
$185$	−1.29948	+	1.14903i	−0.0955394	+	0.0844784i
$186$		0			0
$187$			6.70052i			0.489991i
$188$			19.4763i			1.42045i
$189$		0			0
$190$	1.73813	−	1.53690i	0.126098	−	0.111499i
$191$	13.8496			1.00212			0.501059	−	0.865413i	$-0.332944\pi$
$191$	13.8496			1.00212			0.501059	+	0.865413i	$0.332944\pi$
$192$		0			0
$193$			15.3258i			1.10318i	0.834116	+	0.551588i	$0.185978\pi$
$193$			15.3258i			1.10318i	−0.834116	+	0.551588i	$0.814022\pi$
$194$	−3.58769			−0.257581
$195$		0			0
$196$	−1.96239			−0.140171
$197$		−	0.574515i		−	0.0409325i	−0.999791	−	0.0204663i	$-0.993485\pi$
$197$		−	0.574515i		−	0.0409325i	0.999791	−	0.0204663i	$-0.00651507\pi$
$198$		0			0
$199$	0.201231			0.0142649			0.00713244	−	0.999975i	$-0.497730\pi$
$199$	0.201231			0.0142649			0.00713244	+	0.999975i	$0.497730\pi$
$200$	−3.81336	−	0.470390i	−0.269645	−	0.0332616i
$201$		0			0
$202$			3.42548i			0.241016i
$203$			7.92478i			0.556210i
$204$		0			0
$205$	−5.53690	−	6.26187i	−0.386714	−	0.437348i
$206$	−1.29948			−0.0905388
$207$		0			0
$208$			5.09825i			0.353500i
$209$	10.7005			0.740171
$210$		0			0
$211$	6.44851			0.443934			0.221967	−	0.975054i	$-0.428752\pi$
$211$	6.44851			0.443934			0.221967	+	0.975054i	$0.428752\pi$
$212$		−	16.8265i		−	1.15565i
$213$		0			0
$214$	−2.66433			−0.182130
$215$	21.1490	−	18.7005i	1.44235	−	1.27537i
$216$		0			0
$217$			4.57452i			0.310538i
$218$			0.538319i			0.0364595i
$219$		0			0
$220$	−5.81336	−	6.57452i	−0.391936	−	0.443254i
$221$	4.52373			0.304299
$222$		0			0
$223$			1.55149i			0.103896i	0.998650	+	0.0519478i	$0.0165429\pi$
$223$			1.55149i			0.103896i	−0.998650	+	0.0519478i	$0.983457\pi$
$224$	−2.26916			−0.151615
$225$		0			0
$226$	2.33709			0.155461
$227$		−	13.1490i		−	0.872732i	−0.899769	−	0.436366i	$-0.856265\pi$
$227$		−	13.1490i		−	0.872732i	0.899769	−	0.436366i	$-0.143735\pi$
$228$		0			0
$229$	−2.77575			−0.183426			−0.0917132	−	0.995785i	$-0.529234\pi$
$229$	−2.77575			−0.183426			−0.0917132	+	0.995785i	$0.529234\pi$
$230$	1.42548	+	1.61213i	0.0939937	+	0.106300i
$231$		0			0
$232$			6.08981i			0.399816i
$233$			0.0507852i			0.00332705i	0.999999	+	0.00166353i	$0.000529517\pi$
$233$			0.0507852i			0.00332705i	−0.999999	+	0.00166353i	$0.999470\pi$
$234$		0			0
$235$	−16.6253	+	14.7005i	−1.08452	+	0.958956i
$236$	−16.9262			−1.10180
$237$		0			0
$238$			0.649738i			0.0421163i
$239$	5.84955			0.378376			0.189188	−	0.981941i	$-0.439414\pi$
$239$	5.84955			0.378376			0.189188	+	0.981941i	$0.439414\pi$
$240$		0			0
$241$	−0.0752228			−0.00484553			−0.00242276	−	0.999997i	$-0.500771\pi$
$241$	−0.0752228			−0.00484553			−0.00242276	+	0.999997i	$0.500771\pi$
$242$		−	1.35756i		−	0.0872670i
$243$		0			0
$244$	−17.0738			−1.09304
$245$	−1.48119	−	1.67513i	−0.0946300	−	0.107020i
$246$		0			0
$247$		−	7.22425i		−	0.459668i
$248$			3.51530i			0.223222i
$249$		0			0
$250$	−1.22662	−	1.78797i	−0.0775785	−	0.113081i
$251$	−19.2243			−1.21342			−0.606712	−	0.794922i	$-0.707512\pi$
$251$	−19.2243			−1.21342			−0.606712	+	0.794922i	$0.707512\pi$
$252$		0			0
$253$			9.92478i			0.623965i
$254$	0.523730			0.0328618
$255$		0			0
$256$	13.0752			0.817201
$257$			7.35026i			0.458497i	0.973368	+	0.229248i	$0.0736268\pi$
$257$			7.35026i			0.458497i	−0.973368	+	0.229248i	$0.926373\pi$
$258$		0			0
$259$	−0.775746			−0.0482025
$260$	−4.43866	+	3.92478i	−0.275274	+	0.243404i
$261$		0			0
$262$		−	4.00000i		−	0.247121i
$263$			12.9624i			0.799295i	0.916669	+	0.399648i	$0.130867\pi$
$263$			12.9624i			0.799295i	−0.916669	+	0.399648i	$0.869133\pi$
$264$		0			0
$265$	14.3634	−	12.7005i	0.882339	−	0.780187i
$266$	1.03761			0.0636200
$267$		0			0
$268$		−	19.4763i		−	1.18970i
$269$	4.11142			0.250678			0.125339	−	0.992114i	$-0.459998\pi$
$269$	4.11142			0.250678			0.125339	+	0.992114i	$0.459998\pi$
$270$		0			0
$271$	−16.4241			−0.997691			−0.498846	−	0.866691i	$-0.666243\pi$
$271$	−16.4241			−0.997691			−0.498846	+	0.866691i	$0.666243\pi$
$272$		−	12.6497i		−	0.767003i
$273$		0			0
$274$	−4.36344			−0.263605
$275$	1.22425	−	9.92478i	0.0738253	−	0.598487i
$276$		0			0
$277$			11.0738i			0.665361i	0.943040	+	0.332680i	$0.107953\pi$
$277$			11.0738i			0.665361i	−0.943040	+	0.332680i	$0.892047\pi$
$278$			0.635150i			0.0380938i
$279$		0			0
$280$	−1.13823	−	1.28726i	−0.0680221	−	0.0769284i
$281$	−14.3733			−0.857438			−0.428719	−	0.903438i	$-0.641035\pi$
$281$	−14.3733			−0.857438			−0.428719	+	0.903438i	$0.641035\pi$
$282$		0			0
$283$			1.14903i			0.0683028i	0.999417	+	0.0341514i	$0.0108728\pi$
$283$			1.14903i			0.0683028i	−0.999417	+	0.0341514i	$0.989127\pi$
$284$	−3.92478			−0.232893
$285$		0			0
$286$	0.523730			0.0309688
$287$		−	3.73813i		−	0.220655i
$288$		0			0
$289$	5.77575			0.339750
$290$	−2.57452	+	2.27645i	−0.151181	+	0.133678i
$291$		0			0
$292$		−	18.3488i		−	1.07379i
$293$		−	0.649738i		−	0.0379581i	−0.999820	−	0.0189791i	$-0.993958\pi$
$293$		−	0.649738i		−	0.0379581i	0.999820	−	0.0189791i	$-0.00604158\pi$
$294$		0			0
$295$	−12.7757	−	14.4485i	−0.743833	−	0.841225i
$296$	−0.596124			−0.0346490
$297$		0			0
$298$		−	0.862728i		−	0.0499765i
$299$	6.70052			0.387501
$300$		0			0
$301$	12.6253			0.727710
$302$			0.252016i			0.0145019i
$303$		0			0
$304$	−20.2012			−1.15862
$305$	−12.8872	−	14.5745i	−0.737917	−	0.834534i
$306$		0			0
$307$		−	24.1016i		−	1.37555i	−0.725924	−	0.687775i	$-0.758588\pi$
$307$		−	24.1016i		−	1.37555i	0.725924	−	0.687775i	$-0.241412\pi$
$308$		−	3.92478i		−	0.223635i
$309$		0			0
$310$	−1.48612	+	1.31406i	−0.0844059	+	0.0746339i
$311$	−8.25202			−0.467929			−0.233964	−	0.972245i	$-0.575170\pi$
$311$	−8.25202			−0.467929			−0.233964	+	0.972245i	$0.575170\pi$
$312$		0			0
$313$		−	14.9018i		−	0.842297i	−0.906992	−	0.421148i	$-0.861627\pi$
$313$		−	14.9018i		−	0.842297i	0.906992	−	0.421148i	$-0.138373\pi$
$314$	−0.513881			−0.0290000
$315$		0			0
$316$	−20.9986			−1.18126
$317$			10.1260i			0.568733i	0.958716	+	0.284367i	$0.0917833\pi$
$317$			10.1260i			0.568733i	−0.958716	+	0.284367i	$0.908217\pi$
$318$		0			0
$319$	−15.8496			−0.887405
$320$	10.5334	+	11.9126i	0.588835	+	0.665932i
$321$		0			0
$322$			0.962389i			0.0536318i
$323$			17.9248i			0.997361i
$324$		0			0
$325$	−6.70052	−	0.826531i	−0.371678	−	0.0458477i
$326$	−1.02776			−0.0569225
$327$		0			0
$328$		−	2.87258i		−	0.158612i
$329$	−9.92478			−0.547171
$330$		0			0
$331$	27.8496			1.53075			0.765375	−	0.643585i	$-0.222554\pi$
$331$	27.8496			1.53075			0.765375	+	0.643585i	$0.222554\pi$
$332$		−	6.32724i		−	0.347252i
$333$		0			0
$334$	2.82179			0.154402
$335$	16.6253	−	14.7005i	0.908337	−	0.803175i
$336$		0			0
$337$			3.84955i			0.209699i	0.994488	+	0.104849i	$0.0334360\pi$
$337$			3.84955i			0.209699i	−0.994488	+	0.104849i	$0.966564\pi$
$338$			2.16759i			0.117901i
$339$		0			0
$340$	11.0132	−	9.73813i	0.597273	−	0.528125i
$341$	−9.14903			−0.495448
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	9.70194			0.523093
$345$		0			0
$346$	−0.872577			−0.0469101
$347$			9.58769i			0.514694i	0.966319	+	0.257347i	$0.0828484\pi$
$347$			9.58769i			0.514694i	−0.966319	+	0.257347i	$0.917152\pi$
$348$		0			0
$349$	15.1490			0.810909			0.405455	−	0.914115i	$-0.367113\pi$
$349$	15.1490			0.810909			0.405455	+	0.914115i	$0.367113\pi$
$350$	0.118714	−	0.962389i	0.00634552	−	0.0514418i
$351$		0			0
$352$		−	4.53832i		−	0.241893i
$353$			20.3488i			1.08306i	0.840681	+	0.541530i	$0.182155\pi$
$353$			20.3488i			1.08306i	−0.840681	+	0.541530i	$0.817845\pi$
$354$		0			0
$355$	−2.96239	−	3.35026i	−0.157227	−	0.177813i
$356$	2.03620			0.107918
$357$		0			0
$358$			1.93937i			0.102499i
$359$	−31.4010			−1.65728			−0.828642	−	0.559779i	$-0.810886\pi$
$359$	−31.4010			−1.65728			−0.828642	+	0.559779i	$0.810886\pi$
$360$		0			0
$361$	9.62530			0.506595
$362$			2.06063i			0.108305i
$363$		0			0
$364$	−2.64974			−0.138884
$365$	15.6629	−	13.8496i	0.819834	−	0.724919i
$366$		0			0
$367$			29.4010i			1.53472i	0.641215	+	0.767361i	$0.278431\pi$
$367$			29.4010i			1.53472i	−0.641215	+	0.767361i	$0.721569\pi$
$368$		−	18.7367i		−	0.976719i
$369$		0			0
$370$	−0.222839	−	0.252016i	−0.0115849	−	0.0131017i
$371$	8.57452			0.445167
$372$		0			0
$373$			16.0000i			0.828449i	0.910175	+	0.414224i	$0.135947\pi$
$373$			16.0000i			0.828449i	−0.910175	+	0.414224i	$0.864053\pi$
$374$	−1.29948			−0.0671943
$375$		0			0
$376$	−7.62672			−0.393318
$377$			10.7005i			0.551105i
$378$		0			0
$379$	−10.7005			−0.549649			−0.274824	−	0.961494i	$-0.588620\pi$
$379$	−10.7005			−0.549649			−0.274824	+	0.961494i	$0.588620\pi$
$380$	−15.5515	−	17.5877i	−0.797775	−	0.902229i
$381$		0			0
$382$			2.68594i			0.137424i
$383$			16.7757i			0.857201i	0.903494	+	0.428600i	$0.140993\pi$
$383$			16.7757i			0.857201i	−0.903494	+	0.428600i	$0.859007\pi$
$384$		0			0
$385$	3.35026	−	2.96239i	0.170745	−	0.150977i
$386$	−2.97224			−0.151283
$387$		0			0
$388$			36.3028i			1.84300i
$389$	−29.3258			−1.48688			−0.743439	−	0.668804i	$-0.766807\pi$
$389$	−29.3258			−1.48688			−0.743439	+	0.668804i	$0.766807\pi$
$390$		0			0
$391$	−16.6253			−0.840778
$392$		−	0.768452i		−	0.0388127i
$393$		0			0
$394$	0.111420			0.00561324
$395$	−15.8496	−	17.9248i	−0.797478	−	0.901893i
$396$		0			0
$397$		−	18.3488i		−	0.920902i	−0.887685	−	0.460451i	$-0.847688\pi$
$397$		−	18.3488i		−	0.920902i	0.887685	−	0.460451i	$-0.152312\pi$
$398$			0.0390260i			0.00195620i
$399$		0			0
$400$	−2.31124	+	18.7367i	−0.115562	+	0.936836i
$401$	37.3258			1.86396			0.931981	−	0.362506i	$-0.118079\pi$
$401$	37.3258			1.86396			0.931981	+	0.362506i	$0.118079\pi$
$402$		0			0
$403$			6.17679i			0.307688i
$404$	34.6615			1.72447
$405$		0			0
$406$	−1.53690			−0.0762753
$407$		−	1.55149i		−	0.0769046i
$408$		0			0
$409$	22.3733			1.10629			0.553144	−	0.833086i	$-0.313428\pi$
$409$	22.3733			1.10629			0.553144	+	0.833086i	$0.313428\pi$
$410$	1.21440	−	1.07381i	0.0599752	−	0.0530316i
$411$		0			0
$412$			13.1490i			0.647806i
$413$		−	8.62530i		−	0.424423i
$414$		0			0
$415$	5.40105	−	4.77575i	0.265127	−	0.234432i
$416$	−3.06396			−0.150223
$417$		0			0
$418$			2.07522i			0.101502i
$419$	23.4763			1.14689			0.573445	−	0.819244i	$-0.305606\pi$
$419$	23.4763			1.14689			0.573445	+	0.819244i	$0.305606\pi$
$420$		0			0
$421$	−25.2243			−1.22935			−0.614677	−	0.788779i	$-0.710714\pi$
$421$	−25.2243			−1.22935			−0.614677	+	0.788779i	$0.710714\pi$
$422$			1.25060i			0.0608783i
$423$		0			0
$424$	6.58910			0.319995
$425$	16.6253	+	2.05079i	0.806446	+	0.0994777i
$426$		0			0
$427$		−	8.70052i		−	0.421048i
$428$			26.9596i			1.30314i
$429$		0			0
$430$	3.62672	+	4.10157i	0.174896	+	0.197795i
$431$	19.4010			0.934516			0.467258	−	0.884121i	$-0.345242\pi$
$431$	19.4010			0.934516			0.467258	+	0.884121i	$0.345242\pi$
$432$		0			0
$433$			6.49929i			0.312336i	0.987731	+	0.156168i	$0.0499141\pi$
$433$			6.49929i			0.312336i	−0.987731	+	0.156168i	$0.950086\pi$
$434$	−0.887166			−0.0425853
$435$		0			0
$436$	5.44709			0.260868
$437$			26.5501i			1.27006i
$438$		0			0
$439$	14.6497			0.699194			0.349597	−	0.936900i	$-0.386319\pi$
$439$	14.6497			0.699194			0.349597	+	0.936900i	$0.386319\pi$
$440$	2.57452	−	2.27645i	0.122735	−	0.108526i
$441$		0			0
$442$			0.877317i			0.0417297i
$443$		−	19.1392i		−	0.909330i	−0.890663	−	0.454665i	$-0.849759\pi$
$443$		−	19.1392i		−	0.909330i	0.890663	−	0.454665i	$-0.150241\pi$
$444$		0			0
$445$	1.53690	+	1.73813i	0.0728562	+	0.0823955i
$446$	−0.300891			−0.0142476
$447$		0			0
$448$			7.11142i			0.335983i
$449$	−32.8021			−1.54803			−0.774013	−	0.633169i	$-0.781754\pi$
$449$	−32.8021			−1.54803			−0.774013	+	0.633169i	$0.781754\pi$
$450$		0			0
$451$	7.47627			0.352044
$452$		−	23.6483i		−	1.11232i
$453$		0			0
$454$	2.55008			0.119681
$455$	−2.00000	−	2.26187i	−0.0937614	−	0.106038i
$456$		0			0
$457$			18.7005i			0.874774i	0.899273	+	0.437387i	$0.144096\pi$
$457$			18.7005i			0.874774i	−0.899273	+	0.437387i	$0.855904\pi$
$458$		−	0.538319i		−	0.0251540i
$459$		0			0
$460$	16.3127	−	14.4241i	0.760581	−	0.672526i
$461$	6.96239			0.324271			0.162135	−	0.986769i	$-0.448162\pi$
$461$	6.96239			0.324271			0.162135	+	0.986769i	$0.448162\pi$
$462$		0			0
$463$			5.29948i			0.246288i	0.992389	+	0.123144i	$0.0392976\pi$
$463$			5.29948i			0.246288i	−0.992389	+	0.123144i	$0.960702\pi$
$464$	29.9219			1.38909
$465$		0			0
$466$	−0.00984911			−0.000456251
$467$		−	13.1490i		−	0.608465i	−0.952598	−	0.304232i	$-0.901600\pi$
$467$		−	13.1490i		−	0.608465i	0.952598	−	0.304232i	$-0.0983999\pi$
$468$		0			0
$469$	9.92478			0.458284
$470$	−2.85097	−	3.22425i	−0.131505	−	0.148724i
$471$		0			0
$472$		−	6.62813i		−	0.305084i
$473$			25.2506i			1.16102i
$474$		0			0
$475$	3.27504	−	26.5501i	0.150269	−	1.21820i
$476$	6.57452			0.301342
$477$		0			0
$478$			1.13444i			0.0518882i
$479$	5.14903			0.235265			0.117633	−	0.993057i	$-0.462469\pi$
$479$	5.14903			0.235265			0.117633	+	0.993057i	$0.462469\pi$
$480$		0			0
$481$	−1.04746			−0.0477601
$482$		−	0.0145884i		−	0.000664486i
$483$		0			0
$484$	−13.7367			−0.624396
$485$	−30.9887	+	27.4010i	−1.40713	+	1.24422i
$486$		0			0
$487$			22.1768i			1.00493i	0.864599	+	0.502463i	$0.167573\pi$
$487$			22.1768i			1.00493i	−0.864599	+	0.502463i	$0.832427\pi$
$488$		−	6.68594i		−	0.302658i
$489$		0			0
$490$	0.324869	−	0.287258i	0.0146761	−	0.0129770i
$491$	−2.00000			−0.0902587			−0.0451294	−	0.998981i	$-0.514370\pi$
$491$	−2.00000			−0.0902587			−0.0451294	+	0.998981i	$0.514370\pi$
$492$		0			0
$493$		−	26.5501i		−	1.19576i
$494$	1.40105			0.0630361
$495$		0			0
$496$	17.2722			0.775545
$497$		−	2.00000i		−	0.0897123i
$498$		0			0
$499$	6.55008			0.293222			0.146611	−	0.989194i	$-0.453163\pi$
$499$	6.55008			0.293222			0.146611	+	0.989194i	$0.453163\pi$
$500$	−18.0919	+	12.4119i	−0.809095	+	0.555075i
$501$		0			0
$502$		−	3.72829i		−	0.166402i
$503$		−	8.77575i		−	0.391291i	−0.980675	−	0.195646i	$-0.937320\pi$
$503$		−	8.77575i		−	0.391291i	0.980675	−	0.195646i	$-0.0626802\pi$
$504$		0			0
$505$	26.1622	+	29.5877i	1.16420	+	1.31663i
$506$	−1.92478			−0.0855668
$507$		0			0
$508$		−	5.29948i		−	0.235126i
$509$	13.1392			0.582384			0.291192	−	0.956665i	$-0.405948\pi$
$509$	13.1392			0.582384			0.291192	+	0.956665i	$0.405948\pi$
$510$		0			0
$511$	9.35026			0.413631
$512$			14.3707i			0.635103i
$513$		0			0
$514$	−1.42548			−0.0628754
$515$	−11.2243	+	9.92478i	−0.494600	+	0.437338i
$516$		0			0
$517$		−	19.8496i		−	0.872982i
$518$		−	0.150446i		−	0.00661020i
$519$		0			0
$520$	−1.53690	−	1.73813i	−0.0673977	−	0.0762223i
$521$	37.6629			1.65004			0.825021	−	0.565102i	$-0.191163\pi$
$521$	37.6629			1.65004			0.825021	+	0.565102i	$0.191163\pi$
$522$		0			0
$523$		−	4.00000i		−	0.174908i	−0.996169	−	0.0874539i	$-0.972127\pi$
$523$		−	4.00000i		−	0.174908i	0.996169	−	0.0874539i	$-0.0278730\pi$
$524$	−40.4749			−1.76815
$525$		0			0
$526$	−2.51388			−0.109610
$527$		−	15.3258i		−	0.667603i
$528$		0			0
$529$	−1.62530			−0.0706652
$530$	2.46310	+	2.78560i	0.106990	+	0.120999i
$531$		0			0
$532$		−	10.4993i		−	0.455202i
$533$		−	5.04746i		−	0.218630i
$534$		0			0
$535$	−23.0132	+	20.3488i	−0.994946	+	0.879757i
$536$	7.62672			0.329424
$537$		0			0
$538$			0.797355i			0.0343764i
$539$	2.00000			0.0861461
$540$		0			0
$541$	−22.4749			−0.966269			−0.483135	−	0.875546i	$-0.660502\pi$
$541$	−22.4749			−0.966269			−0.483135	+	0.875546i	$0.660502\pi$
$542$		−	3.18523i		−	0.136817i
$543$		0			0
$544$	7.60228			0.325945
$545$	4.11142	+	4.64974i	0.176114	+	0.199173i
$546$		0			0
$547$			25.9248i			1.10846i	0.832362	+	0.554232i	$0.186988\pi$
$547$			25.9248i			1.10846i	−0.832362	+	0.554232i	$0.813012\pi$
$548$			44.1524i			1.88610i
$549$		0			0
$550$	1.92478	+	0.237428i	0.0820728	+	0.0101239i
$551$	−42.3996			−1.80629
$552$		0			0
$553$		−	10.7005i		−	0.455033i
$554$	−2.14762			−0.0912435
$555$		0			0
$556$	6.42690			0.272561
$557$		−	28.5256i		−	1.20867i	−0.796730	−	0.604335i	$-0.793439\pi$
$557$		−	28.5256i		−	1.20867i	0.796730	−	0.604335i	$-0.206561\pi$
$558$		0			0
$559$	17.0475			0.721031
$560$	−6.32487	+	5.59261i	−0.267275	+	0.236331i
$561$		0			0
$562$		−	2.78751i		−	0.117584i
$563$			11.6267i			0.490008i	0.969522	+	0.245004i	$0.0787892\pi$
$563$			11.6267i			0.490008i	−0.969522	+	0.245004i	$0.921211\pi$
$564$		0			0
$565$	20.1866	−	17.8496i	0.849258	−	0.750936i
$566$	−0.222839			−0.00936663
$567$		0			0
$568$		−	1.53690i		−	0.0644871i
$569$	9.32582			0.390959			0.195479	−	0.980708i	$-0.437374\pi$
$569$	9.32582			0.390959			0.195479	+	0.980708i	$0.437374\pi$
$570$		0			0
$571$	−19.6991			−0.824382			−0.412191	−	0.911097i	$-0.635236\pi$
$571$	−19.6991			−0.824382			−0.412191	+	0.911097i	$0.635236\pi$
$572$		−	5.29948i		−	0.221582i
$573$		0			0
$574$	0.724961			0.0302593
$575$	24.6253	+	3.03761i	1.02695	+	0.126677i
$576$		0			0
$577$		−	32.7974i		−	1.36537i	−0.730712	−	0.682686i	$-0.760812\pi$
$577$		−	32.7974i		−	1.36537i	0.730712	−	0.682686i	$-0.239188\pi$
$578$			1.12013i			0.0465912i
$579$		0			0
$580$	23.0348	+	26.0508i	0.956467	+	1.08170i
$581$	3.22425			0.133765
$582$		0			0
$583$			17.1490i			0.710240i
$584$	7.18523			0.297327
$585$		0			0
$586$	0.126008			0.00520534
$587$			18.8218i			0.776859i	0.921479	+	0.388429i	$0.126982\pi$
$587$			18.8218i			0.776859i	−0.921479	+	0.388429i	$0.873018\pi$
$588$		0			0
$589$	−24.4749			−1.00847
$590$	2.80209	−	2.47768i	0.115360	−	0.102005i
$591$		0			0
$592$			2.92902i			0.120382i
$593$		−	33.7499i		−	1.38594i	−0.720965	−	0.692971i	$-0.756301\pi$
$593$		−	33.7499i		−	1.38594i	0.720965	−	0.692971i	$-0.243699\pi$
$594$		0			0
$595$	4.96239	+	5.61213i	0.203438	+	0.230075i
$596$	−8.72970			−0.357582
$597$		0			0
$598$			1.29948i			0.0531395i
$599$	−20.2981			−0.829356			−0.414678	−	0.909968i	$-0.636106\pi$
$599$	−20.2981			−0.829356			−0.414678	+	0.909968i	$0.636106\pi$
$600$		0			0
$601$	−13.8496			−0.564935			−0.282468	−	0.959277i	$-0.591153\pi$
$601$	−13.8496			−0.564935			−0.282468	+	0.959277i	$0.591153\pi$
$602$			2.44851i			0.0997937i
$603$		0			0
$604$	2.55008			0.103761
$605$	−10.3684	−	11.7259i	−0.421534	−	0.476726i
$606$		0			0
$607$			25.2506i			1.02489i	0.858720	+	0.512445i	$0.171260\pi$
$607$			25.2506i			1.02489i	−0.858720	+	0.512445i	$0.828740\pi$
$608$		−	12.1406i		−	0.492366i
$609$		0			0
$610$	2.82653	−	2.49929i	0.114443	−	0.101193i
$611$	−13.4010			−0.542148
$612$		0			0
$613$		−	9.14903i		−	0.369526i	−0.982783	−	0.184763i	$-0.940848\pi$
$613$		−	9.14903i		−	0.369526i	0.982783	−	0.184763i	$-0.0591517\pi$
$614$	4.67418			0.188634
$615$		0			0
$616$	1.53690			0.0619236
$617$			15.9492i			0.642091i	0.947064	+	0.321046i	$0.104034\pi$
$617$			15.9492i			0.642091i	−0.947064	+	0.321046i	$0.895966\pi$
$618$		0			0
$619$	−11.1735			−0.449100			−0.224550	−	0.974463i	$-0.572091\pi$
$619$	−11.1735			−0.449100			−0.224550	+	0.974463i	$0.572091\pi$
$620$	13.2966	+	15.0376i	0.534006	+	0.603925i
$621$		0			0
$622$		−	1.60037i		−	0.0641689i
$623$			1.03761i			0.0415710i
$624$		0			0
$625$	−24.2506	−	6.07522i	−0.970024	−	0.243009i
$626$	2.89000			0.115507
$627$		0			0
$628$			5.19982i			0.207495i
$629$	2.59895			0.103627
$630$		0			0
$631$	−14.5501			−0.579229			−0.289615	−	0.957143i	$-0.593527\pi$
$631$	−14.5501			−0.579229			−0.289615	+	0.957143i	$0.593527\pi$
$632$		−	8.22284i		−	0.327087i
$633$		0			0
$634$	−1.96380			−0.0779926
$635$	4.52373	−	4.00000i	0.179519	−	0.158735i
$636$		0			0
$637$		−	1.35026i		−	0.0534993i
$638$		−	3.07381i		−	0.121693i
$639$		0			0
$640$	−9.91256	+	8.76494i	−0.391828	+	0.346465i
$641$	38.7269			1.52962			0.764810	−	0.644256i	$-0.222833\pi$
$641$	38.7269			1.52962			0.764810	+	0.644256i	$0.222833\pi$
$642$		0			0
$643$		−	11.9511i		−	0.471306i	−0.971837	−	0.235653i	$-0.924277\pi$
$643$		−	11.9511i		−	0.471306i	0.971837	−	0.235653i	$-0.0757229\pi$
$644$	9.73813			0.383736
$645$		0			0
$646$	−3.47627			−0.136772
$647$		−	14.5501i		−	0.572023i	−0.958226	−	0.286011i	$-0.907671\pi$
$647$		−	14.5501i		−	0.572023i	0.958226	−	0.286011i	$-0.0923295\pi$
$648$		0			0
$649$	17.2506			0.677145
$650$	0.160295	−	1.29948i	0.00628727	−	0.0509697i
$651$		0			0
$652$			10.3996i			0.407281i
$653$		−	49.9756i		−	1.95569i	−0.209319	−	0.977847i	$-0.567125\pi$
$653$		−	49.9756i		−	1.95569i	0.209319	−	0.977847i	$-0.432875\pi$
$654$		0			0
$655$	−30.5501	−	34.5501i	−1.19369	−	1.34998i
$656$	−14.1142			−0.551069
$657$		0			0
$658$		−	1.92478i		−	0.0750356i
$659$	−16.9525			−0.660377			−0.330189	−	0.943915i	$-0.607112\pi$
$659$	−16.9525			−0.660377			−0.330189	+	0.943915i	$0.607112\pi$
$660$		0			0
$661$	−15.6531			−0.608834			−0.304417	−	0.952539i	$-0.598462\pi$
$661$	−15.6531			−0.608834			−0.304417	+	0.952539i	$0.598462\pi$
$662$			5.40105i			0.209918i
$663$		0			0
$664$	2.47768			0.0961528
$665$	8.96239	−	7.92478i	0.347547	−	0.307310i
$666$		0			0
$667$		−	39.3258i		−	1.52270i
$668$		−	28.5529i		−	1.10475i
$669$		0			0
$670$	2.85097	+	3.22425i	0.110143	+	0.124564i
$671$	17.4010			0.671760
$672$		0			0
$673$			26.0263i			1.00324i	0.865088	+	0.501621i	$0.167263\pi$
$673$			26.0263i			1.00324i	−0.865088	+	0.501621i	$0.832737\pi$
$674$	−0.746569			−0.0287568
$675$		0			0
$676$	21.9332			0.843585
$677$		−	35.4518i		−	1.36252i	−0.732039	−	0.681262i	$-0.761431\pi$
$677$		−	35.4518i		−	1.36252i	0.732039	−	0.681262i	$-0.238569\pi$
$678$		0			0
$679$	−18.4993			−0.709938
$680$	3.81336	+	4.31265i	0.146236	+	0.165383i
$681$		0			0
$682$		−	1.77433i		−	0.0679427i
$683$			23.6629i			0.905436i	0.891654	+	0.452718i	$0.149546\pi$
$683$			23.6629i			0.905436i	−0.891654	+	0.452718i	$0.850454\pi$
$684$		0			0
$685$	−37.6893	+	33.3258i	−1.44003	+	1.27331i
$686$	0.193937			0.00740453
$687$		0			0
$688$		−	47.6699i		−	1.81740i
$689$	11.5778			0.441081
$690$		0			0
$691$	−0.574515			−0.0218556			−0.0109278	−	0.999940i	$-0.503478\pi$
$691$	−0.574515			−0.0218556			−0.0109278	+	0.999940i	$0.503478\pi$
$692$			8.82936i			0.335642i
$693$		0			0
$694$	−1.85940			−0.0705820
$695$	4.85097	+	5.48612i	0.184008	+	0.208100i
$696$		0			0
$697$			12.5237i			0.474370i
$698$			2.93795i			0.111203i
$699$		0			0
$700$	−9.73813	−	1.20123i	−0.368067	−	0.0454023i
$701$	−42.7269			−1.61377			−0.806886	−	0.590707i	$-0.798849\pi$
$701$	−42.7269			−1.61377			−0.806886	+	0.590707i	$0.798849\pi$
$702$		0			0
$703$		−	4.15045i		−	0.156537i
$704$	−14.2228			−0.536043
$705$		0			0
$706$	−3.94639			−0.148524
$707$			17.6629i			0.664282i
$708$		0			0
$709$	−27.2506			−1.02342			−0.511709	−	0.859159i	$-0.670987\pi$
$709$	−27.2506			−1.02342			−0.511709	+	0.859159i	$0.670987\pi$
$710$	0.649738	−	0.574515i	0.0243842	−	0.0215612i
$711$		0			0
$712$			0.797355i			0.0298821i
$713$		−	22.7005i		−	0.850141i
$714$		0			0
$715$	4.52373	−	4.00000i	0.169178	−	0.149592i
$716$	19.6239			0.733379
$717$		0			0
$718$		−	6.08981i		−	0.227270i
$719$	−10.7005			−0.399062			−0.199531	−	0.979891i	$-0.563942\pi$
$719$	−10.7005			−0.399062			−0.199531	+	0.979891i	$0.563942\pi$
$720$		0			0
$721$	−6.70052			−0.249541
$722$			1.86670i			0.0694713i
$723$		0			0
$724$	20.8510			0.774920
$725$	−4.85097	+	39.3258i	−0.180160	+	1.46052i
$726$		0			0
$727$		−	39.9511i		−	1.48171i	−0.671668	−	0.740853i	$-0.734422\pi$
$727$		−	39.9511i		−	1.48171i	0.671668	−	0.740853i	$-0.265578\pi$
$728$		−	1.03761i		−	0.0384564i
$729$		0			0
$730$	2.68594	+	3.03761i	0.0994109	+	0.112427i
$731$	−42.2981			−1.56445
$732$		0			0
$733$		−	30.3488i		−	1.12096i	−0.828168	−	0.560480i	$-0.810617\pi$
$733$		−	30.3488i		−	1.12096i	0.828168	−	0.560480i	$-0.189383\pi$
$734$	−5.70194			−0.210462
$735$		0			0
$736$	11.2605			0.415066
$737$			19.8496i			0.731168i
$738$		0			0
$739$	−37.2506			−1.37029			−0.685143	−	0.728409i	$-0.740260\pi$
$739$	−37.2506			−1.37029			−0.685143	+	0.728409i	$0.740260\pi$
$740$	−2.55008	+	2.25485i	−0.0937427	+	0.0828898i
$741$		0			0
$742$			1.66291i			0.0610474i
$743$		−	26.3634i		−	0.967181i	−0.875294	−	0.483590i	$-0.839332\pi$
$743$		−	26.3634i		−	0.967181i	0.875294	−	0.483590i	$-0.160668\pi$
$744$		0			0
$745$	−6.58910	−	7.45183i	−0.241406	−	0.273014i
$746$	−3.10299			−0.113608
$747$		0			0
$748$			13.1490i			0.480776i
$749$	−13.7381			−0.501981
$750$		0			0
$751$	50.6516			1.84830			0.924152	−	0.382024i	$-0.124773\pi$
$751$	50.6516			1.84830			0.924152	+	0.382024i	$0.124773\pi$
$752$			37.4734i			1.36652i
$753$		0			0
$754$	−2.07522			−0.0755752
$755$	1.92478	+	2.17679i	0.0700498	+	0.0792216i
$756$		0			0
$757$		−	38.9525i		−	1.41575i	−0.706336	−	0.707877i	$-0.749653\pi$
$757$		−	38.9525i		−	1.41575i	0.706336	−	0.707877i	$-0.250347\pi$
$758$		−	2.07522i		−	0.0753755i
$759$		0			0
$760$	6.88717	−	6.08981i	0.249824	−	0.220901i
$761$	−48.2130			−1.74772			−0.873860	−	0.486178i	$-0.838391\pi$
$761$	−48.2130			−1.74772			−0.873860	+	0.486178i	$0.838391\pi$
$762$		0			0
$763$			2.77575i			0.100489i
$764$	27.1782			0.983273
$765$		0			0
$766$	−3.25343			−0.117551
$767$		−	11.6464i		−	0.420528i
$768$		0			0
$769$	−4.44851			−0.160417			−0.0802086	−	0.996778i	$-0.525559\pi$
$769$	−4.44851			−0.160417			−0.0802086	+	0.996778i	$0.525559\pi$
$770$	0.574515	+	0.649738i	0.0207041	+	0.0234149i
$771$		0			0
$772$			30.0752i			1.08243i
$773$		−	39.3014i		−	1.41357i	−0.707427	−	0.706786i	$-0.750144\pi$
$773$		−	39.3014i		−	1.41357i	0.707427	−	0.706786i	$-0.249856\pi$
$774$		0			0
$775$	−2.80018	+	22.7005i	−0.100586	+	0.815427i
$776$	−14.2158			−0.510318
$777$		0			0
$778$		−	5.68735i		−	0.203901i
$779$	20.0000			0.716574
$780$		0			0
$781$	4.00000			0.143131
$782$		−	3.22425i		−	0.115299i
$783$		0			0
$784$	−3.77575			−0.134848
$785$	−4.43866	+	3.92478i	−0.158423	+	0.140081i
$786$		0			0
$787$		−	0.897015i		−	0.0319751i	−0.999872	−	0.0159876i	$-0.994911\pi$
$787$		−	0.897015i		−	0.0319751i	0.999872	−	0.0159876i	$-0.00508922\pi$
$788$		−	1.12742i		−	0.0401628i
$789$		0			0
$790$	3.47627	−	3.07381i	0.123680	−	0.109361i
$791$	12.0508			0.428477
$792$		0			0
$793$		−	11.7480i		−	0.417183i
$794$	3.55851			0.126287
$795$		0			0
$796$	0.394893			0.0139966
$797$			3.19982i			0.113343i	0.998393	+	0.0566717i	$0.0180488\pi$
$797$			3.19982i			0.113343i	−0.998393	+	0.0566717i	$0.981951\pi$
$798$		0			0
$799$	33.2506			1.17632
$800$	−11.2605	−	1.38901i	−0.398117	−	0.0491090i
$801$		0			0
$802$			7.23884i			0.255612i
$803$			18.7005i			0.659927i
$804$		0			0
$805$	7.35026	+	8.31265i	0.259063	+	0.292982i
$806$	−1.19791			−0.0421944
$807$		0			0
$808$			13.5731i			0.477500i
$809$	4.44851			0.156401			0.0782006	−	0.996938i	$-0.475083\pi$
$809$	4.44851			0.156401			0.0782006	+	0.996938i	$0.475083\pi$
$810$		0			0
$811$	37.6747			1.32294			0.661468	−	0.749973i	$-0.269934\pi$
$811$	37.6747			1.32294			0.661468	+	0.749973i	$0.269934\pi$
$812$			15.5515i			0.545750i
$813$		0			0
$814$	0.300891			0.0105462
$815$	−8.87732	+	7.84955i	−0.310959	+	0.274958i
$816$		0			0
$817$			67.5487i			2.36323i
$818$			4.33900i			0.151710i
$819$		0			0
$820$	−10.8656	−	12.2882i	−0.379442	−	0.429123i
$821$	0.749399			0.0261542			0.0130771	−	0.999914i	$-0.495837\pi$
$821$	0.749399			0.0261542			0.0130771	+	0.999914i	$0.495837\pi$
$822$		0			0
$823$		−	26.3996i		−	0.920233i	−0.887858	−	0.460117i	$-0.847808\pi$
$823$		−	26.3996i		−	0.920233i	0.887858	−	0.460117i	$-0.152192\pi$
$824$	−5.14903			−0.179375
$825$		0			0
$826$	1.67276			0.0582028
$827$			5.43724i			0.189071i	0.995521	+	0.0945357i	$0.0301367\pi$
$827$			5.43724i			0.189071i	−0.995521	+	0.0945357i	$0.969863\pi$
$828$		0			0
$829$	−22.7757			−0.791034			−0.395517	−	0.918459i	$-0.629435\pi$
$829$	−22.7757			−0.791034			−0.395517	+	0.918459i	$0.629435\pi$
$830$	0.926192	+	1.04746i	0.0321486	+	0.0363579i
$831$		0			0
$832$			9.60228i			0.332899i
$833$			3.35026i			0.116080i
$834$		0			0
$835$	24.3733	−	21.5515i	0.843472	−	0.745820i
$836$	20.9986			0.726251
$837$		0			0
$838$			4.55291i			0.157278i
$839$	15.8496			0.547187			0.273594	−	0.961845i	$-0.411788\pi$
$839$	15.8496			0.547187			0.273594	+	0.961845i	$0.411788\pi$
$840$		0			0
$841$	33.8021			1.16559
$842$		−	4.89191i		−	0.168586i
$843$		0			0
$844$	12.6545			0.435585
$845$	16.5550	+	18.7226i	0.569509	+	0.644077i
$846$		0			0
$847$		−	7.00000i		−	0.240523i
$848$		−	32.3752i		−	1.11177i
$849$		0			0
$850$	−0.397722	+	3.22425i	−0.0136418	+	0.110591i
$851$	3.84955			0.131961
$852$		0			0
$853$		−	21.0494i		−	0.720717i	−0.932814	−	0.360358i	$-0.882654\pi$
$853$		−	21.0494i		−	0.720717i	0.932814	−	0.360358i	$-0.117346\pi$
$854$	1.68735			0.0577399
$855$		0			0
$856$	−10.5571			−0.360834
$857$			50.1524i			1.71317i	0.516004	+	0.856586i	$0.327419\pi$
$857$			50.1524i			1.71317i	−0.516004	+	0.856586i	$0.672581\pi$
$858$		0			0
$859$	5.35026			0.182549			0.0912743	−	0.995826i	$-0.470906\pi$
$859$	5.35026			0.182549			0.0912743	+	0.995826i	$0.470906\pi$
$860$	41.5026	−	36.6977i	1.41523	−	1.25138i
$861$		0			0
$862$			3.76257i			0.128154i
$863$			33.6893i			1.14680i	0.819277	+	0.573398i	$0.194375\pi$
$863$			33.6893i			1.14680i	−0.819277	+	0.573398i	$0.805625\pi$
$864$		0			0
$865$	−7.53690	+	6.66433i	−0.256262	+	0.226594i
$866$	−1.26045			−0.0428319
$867$		0			0
$868$			8.97698i			0.304698i
$869$	21.4010			0.725981
$870$		0			0
$871$	13.4010			0.454077
$872$			2.13303i			0.0722334i
$873$		0			0
$874$	−5.14903			−0.174169
$875$	−6.32487	−	9.21933i	−0.213820	−	0.311670i
$876$		0			0
$877$			21.5026i			0.726092i	0.931771	+	0.363046i	$0.118263\pi$
$877$			21.5026i			0.726092i	−0.931771	+	0.363046i	$0.881737\pi$
$878$			2.84112i			0.0958832i
$879$		0			0
$880$	−11.1852	−	12.6497i	−0.377054	−	0.426423i
$881$	−32.3634			−1.09035			−0.545176	−	0.838322i	$-0.683537\pi$
$881$	−32.3634			−1.09035			−0.545176	+	0.838322i	$0.683537\pi$
$882$		0			0
$883$		−	2.59895i		−	0.0874617i	−0.999043	−	0.0437309i	$-0.986076\pi$
$883$		−	2.59895i		−	0.0874617i	0.999043	−	0.0437309i	$-0.0139244\pi$
$884$	8.87732			0.298576
$885$		0			0
$886$	3.71179			0.124700
$887$			38.2784i			1.28526i	0.766176	+	0.642631i	$0.222157\pi$
$887$			38.2784i			1.28526i	−0.766176	+	0.642631i	$0.777843\pi$
$888$		0			0
$889$	2.70052			0.0905727
$890$	−0.337088	+	0.298062i	−0.0112992	+	0.00999106i
$891$		0			0
$892$			3.04463i			0.101942i
$893$		−	53.1002i		−	1.77693i
$894$		0			0
$895$	14.8119	+	16.7513i	0.495109	+	0.559934i
$896$	−5.91748			−0.197689
$897$		0			0
$898$		−	6.36153i		−	0.212287i
$899$	36.2520			1.20907
$900$		0			0
$901$	−28.7269			−0.957031
$902$			1.44992i			0.0482771i
$903$		0			0
$904$	9.26045			0.307998
$905$	15.7381	+	17.7988i	0.523153	+	0.591651i
$906$		0			0
$907$			49.9972i			1.66013i	0.557668	+	0.830064i	$0.311696\pi$
$907$			49.9972i			1.66013i	−0.557668	+	0.830064i	$0.688304\pi$
$908$		−	25.8035i		−	0.856320i
$909$		0			0
$910$	0.438658	−	0.387873i	0.0145414	−	0.0128579i
$911$	24.9525			0.826715			0.413357	−	0.910569i	$-0.364356\pi$
$911$	24.9525			0.826715			0.413357	+	0.910569i	$0.364356\pi$
$912$		0			0
$913$			6.44851i			0.213414i
$914$	−3.62672			−0.119961
$915$		0			0
$916$	−5.44709			−0.179977
$917$		−	20.6253i		−	0.681107i
$918$		0			0
$919$	11.6991			0.385918			0.192959	−	0.981207i	$-0.438192\pi$
$919$	11.6991			0.385918			0.192959	+	0.981207i	$0.438192\pi$
$920$	5.64832	+	6.38787i	0.186220	+	0.210602i
$921$		0			0
$922$			1.35026i			0.0444685i
$923$		−	2.70052i		−	0.0888888i
$924$		0			0
$925$	−3.84955	−	0.474855i	−0.126573	−	0.0156131i
$926$	−1.02776			−0.0337744
$927$		0			0
$928$			17.9826i			0.590307i
$929$	23.7090			0.777866			0.388933	−	0.921266i	$-0.372844\pi$
$929$	23.7090			0.777866			0.388933	+	0.921266i	$0.372844\pi$
$930$		0			0
$931$	5.35026			0.175348
$932$			0.0996603i			0.00326448i
$933$		0			0
$934$	2.55008			0.0834411
$935$	−11.2243	+	9.92478i	−0.367072	+	0.324575i
$936$		0			0
$937$			19.9003i			0.650116i	0.945694	+	0.325058i	$0.105384\pi$
$937$			19.9003i			0.650116i	−0.945694	+	0.325058i	$0.894616\pi$
$938$			1.92478i			0.0628462i
$939$		0			0
$940$	−32.6253	+	28.8481i	−1.06412	+	0.940923i
$941$	6.28821			0.204990			0.102495	−	0.994734i	$-0.467317\pi$
$941$	6.28821			0.204990			0.102495	+	0.994734i	$0.467317\pi$
$942$		0			0
$943$			18.5501i			0.604074i
$944$	−32.5669			−1.05996
$945$		0			0
$946$	−4.89701			−0.159216
$947$		−	40.0362i		−	1.30100i	−0.759506	−	0.650501i	$-0.774559\pi$
$947$		−	40.0362i		−	1.30100i	0.759506	−	0.650501i	$-0.225441\pi$
$948$		0			0
$949$	12.6253			0.409835
$950$	5.14903	+	0.635150i	0.167057	+	0.0206070i
$951$		0			0
$952$			2.57452i			0.0834405i
$953$		−	40.9478i		−	1.32643i	−0.748429	−	0.663215i	$-0.769192\pi$
$953$		−	40.9478i		−	1.32643i	0.748429	−	0.663215i	$-0.230808\pi$
$954$		0			0
$955$	20.5139	+	23.1998i	0.663814	+	0.750728i
$956$	11.4791			0.371261
$957$		0			0
$958$			0.998585i			0.0322628i
$959$	−22.4993			−0.726540
$960$		0			0
$961$	−10.0738			−0.324962
$962$		−	0.203141i		−	0.00654953i
$963$		0			0
$964$	−0.147616			−0.00475440
$965$	−25.6728	+	22.7005i	−0.826435	+	0.730756i
$966$		0			0
$967$		−	38.2784i		−	1.23095i	−0.788157	−	0.615475i	$-0.788964\pi$
$967$		−	38.2784i		−	1.23095i	0.788157	−	0.615475i	$-0.211036\pi$
$968$		−	5.37916i		−	0.172893i
$969$		0			0
$970$	−5.31406	−	6.00985i	−0.170624	−	0.192965i
$971$	28.7269			0.921889			0.460945	−	0.887429i	$-0.347511\pi$
$971$	28.7269			0.921889			0.460945	+	0.887429i	$0.347511\pi$
$972$		0			0
$973$			3.27504i			0.104993i
$974$	−4.30089			−0.137809
$975$		0			0
$976$	−32.8510			−1.05153
$977$		−	41.3014i		−	1.32135i	−0.750673	−	0.660674i	$-0.770270\pi$
$977$		−	41.3014i		−	1.32135i	0.750673	−	0.660674i	$-0.229730\pi$
$978$		0			0
$979$	−2.07522			−0.0663244
$980$	−2.90668	−	3.28726i	−0.0928504	−	0.105008i
$981$		0			0
$982$		−	0.387873i		−	0.0123775i
$983$			24.0000i			0.765481i	0.923856	+	0.382741i	$0.125020\pi$
$983$			24.0000i			0.765481i	−0.923856	+	0.382741i	$0.874980\pi$
$984$		0			0
$985$	0.962389	−	0.850969i	0.0306643	−	0.0271141i
$986$	5.14903			0.163979
$987$		0			0
$988$		−	14.1768i		−	0.451024i
$989$	−62.6516			−1.99221
$990$		0			0
$991$	25.1002			0.797333			0.398666	−	0.917096i	$-0.369473\pi$
$991$	25.1002			0.797333			0.398666	+	0.917096i	$0.369473\pi$
$992$			10.3803i			0.329575i
$993$		0			0
$994$	0.387873			0.0123026
$995$	0.298062	+	0.337088i	0.00944920	+	0.0106864i
$996$		0			0
$997$		−	32.7974i		−	1.03870i	−0.854561	−	0.519351i	$-0.826174\pi$
$997$		−	32.7974i		−	1.03870i	0.854561	−	0.519351i	$-0.173826\pi$
$998$			1.27030i			0.0402106i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.d.e.64.4		6
3.2	odd	2		105.2.d.b.64.3	✓	6
4.3	odd	2		5040.2.t.v.1009.6		6
5.2	odd	4		1575.2.a.w.1.2		3
5.3	odd	4		1575.2.a.x.1.2		3
5.4	even	2	inner	315.2.d.e.64.3		6
7.6	odd	2		2205.2.d.l.1324.4		6
12.11	even	2		1680.2.t.k.1009.4		6
15.2	even	4		525.2.a.k.1.2		3
15.8	even	4		525.2.a.j.1.2		3
15.14	odd	2		105.2.d.b.64.4	yes	6
20.19	odd	2		5040.2.t.v.1009.5		6
21.2	odd	6		735.2.q.e.214.3		12
21.5	even	6		735.2.q.f.214.3		12
21.11	odd	6		735.2.q.e.79.4		12
21.17	even	6		735.2.q.f.79.4		12
21.20	even	2		735.2.d.b.589.3		6
35.34	odd	2		2205.2.d.l.1324.3		6
60.23	odd	4		8400.2.a.dg.1.1		3
60.47	odd	4		8400.2.a.dj.1.3		3
60.59	even	2		1680.2.t.k.1009.1		6
105.44	odd	6		735.2.q.e.214.4		12
105.59	even	6		735.2.q.f.79.3		12
105.62	odd	4		3675.2.a.bj.1.2		3
105.74	odd	6		735.2.q.e.79.3		12
105.83	odd	4		3675.2.a.bi.1.2		3
105.89	even	6		735.2.q.f.214.4		12
105.104	even	2		735.2.d.b.589.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.d.b.64.3	✓	6	3.2	odd	2
105.2.d.b.64.4	yes	6	15.14	odd	2
315.2.d.e.64.3		6	5.4	even	2	inner
315.2.d.e.64.4		6	1.1	even	1	trivial
525.2.a.j.1.2		3	15.8	even	4
525.2.a.k.1.2		3	15.2	even	4
735.2.d.b.589.3		6	21.20	even	2
735.2.d.b.589.4		6	105.104	even	2
735.2.q.e.79.3		12	105.74	odd	6
735.2.q.e.79.4		12	21.11	odd	6
735.2.q.e.214.3		12	21.2	odd	6
735.2.q.e.214.4		12	105.44	odd	6
735.2.q.f.79.3		12	105.59	even	6
735.2.q.f.79.4		12	21.17	even	6
735.2.q.f.214.3		12	21.5	even	6
735.2.q.f.214.4		12	105.89	even	6
1575.2.a.w.1.2		3	5.2	odd	4
1575.2.a.x.1.2		3	5.3	odd	4
1680.2.t.k.1009.1		6	60.59	even	2
1680.2.t.k.1009.4		6	12.11	even	2
2205.2.d.l.1324.3		6	35.34	odd	2
2205.2.d.l.1324.4		6	7.6	odd	2
3675.2.a.bi.1.2		3	105.83	odd	4
3675.2.a.bj.1.2		3	105.62	odd	4
5040.2.t.v.1009.5		6	20.19	odd	2
5040.2.t.v.1009.6		6	4.3	odd	2
8400.2.a.dg.1.1		3	60.23	odd	4
8400.2.a.dj.1.3		3	60.47	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.193937i q^{2} +1.96239 q^{4} +(1.48119 + 1.67513i) q^{5} +1.00000i q^{7} +0.768452i q^{8} +(-0.324869 + 0.287258i) q^{10} -2.00000 q^{11} +1.35026i q^{13} -0.193937 q^{14} +3.77575 q^{16} -3.35026i q^{17} -5.35026 q^{19} +(2.90668 + 3.28726i) q^{20} -0.387873i q^{22} -4.96239i q^{23} +(-0.612127 + 4.96239i) q^{25} -0.261865 q^{26} +1.96239i q^{28} +7.92478 q^{29} +4.57452 q^{31} +2.26916i q^{32} +0.649738 q^{34} +(-1.67513 + 1.48119i) q^{35} +0.775746i q^{37} -1.03761i q^{38} +(-1.28726 + 1.13823i) q^{40} -3.73813 q^{41} -12.6253i q^{43} -3.92478 q^{44} +0.962389 q^{46} +9.92478i q^{47} -1.00000 q^{49} +(-0.962389 - 0.118714i) q^{50} +2.64974i q^{52} -8.57452i q^{53} +(-2.96239 - 3.35026i) q^{55} -0.768452 q^{56} +1.53690i q^{58} -8.62530 q^{59} -8.70052 q^{61} +0.887166i q^{62} +7.11142 q^{64} +(-2.26187 + 2.00000i) q^{65} -9.92478i q^{67} -6.57452i q^{68} +(-0.287258 - 0.324869i) q^{70} -2.00000 q^{71} -9.35026i q^{73} -0.150446 q^{74} -10.4993 q^{76} -2.00000i q^{77} -10.7005 q^{79} +(5.59261 + 6.32487i) q^{80} -0.724961i q^{82} -3.22425i q^{83} +(5.61213 - 4.96239i) q^{85} +2.44851 q^{86} -1.53690i q^{88} +1.03761 q^{89} -1.35026 q^{91} -9.73813i q^{92} -1.92478 q^{94} +(-7.92478 - 8.96239i) q^{95} +18.4993i q^{97} -0.193937i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 10 q^{4} - 2 q^{5} - 12 q^{10} - 12 q^{11} - 2 q^{14} + 26 q^{16} - 12 q^{19} + 30 q^{20} - 2 q^{25} - 20 q^{26} + 4 q^{29} + 4 q^{31} + 24 q^{34} + 4 q^{40} - 4 q^{41} + 20 q^{44} - 16 q^{46} - 6 q^{49}+ \cdots - 4 q^{95}+O(q^{100}) \) 6 * q - 10 * q^4 - 2 * q^5 - 12 * q^10 - 12 * q^11 - 2 * q^14 + 26 * q^16 - 12 * q^19 + 30 * q^20 - 2 * q^25 - 20 * q^26 + 4 * q^29 + 4 * q^31 + 24 * q^34 + 4 * q^40 - 4 * q^41 + 20 * q^44 - 16 * q^46 - 6 * q^49 + 16 * q^50 + 4 * q^55 + 18 * q^56 + 32 * q^59 - 12 * q^61 - 26 * q^64 - 32 * q^65 + 10 * q^70 - 12 * q^71 - 88 * q^74 + 4 * q^76 - 24 * q^79 - 46 * q^80 + 32 * q^85 + 8 * q^86 + 28 * q^89 + 12 * q^91 + 32 * q^94 - 4 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more