LMFDB - Embedded newform 3822.2.c.k.883.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3822,2,Mod(883,3822)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3822, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 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("3822.883"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3822.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,6,-6,0,0,0,0,6,0,0,-6,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$30.5188236525$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.9144576.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 12x^{4} + 36x^{2} + 4 $ x^6 + 12x^4 + 36x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			883.1
Root			$-2.60168i$ of defining polynomial
Character	$\chi$	$=$	3822.883
Dual form			3822.2.c.k.883.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} -2.60168i q^{5} -1.00000i q^{6} +1.00000i q^{8} +1.00000 q^{9} -2.60168 q^{10} +3.60168i q^{11} -1.00000 q^{12} +(3.60168 - 0.167055i) q^{13} -2.60168i q^{15} +1.00000 q^{16} -2.83294 q^{17} -1.00000i q^{18} +1.33411i q^{19} +2.60168i q^{20} +3.60168 q^{22} +2.93579 q^{23} +1.00000i q^{24} -1.76873 q^{25} +(-0.167055 - 3.60168i) q^{26} +1.00000 q^{27} +8.97209 q^{29} -2.60168 q^{30} -4.00000i q^{31} -1.00000i q^{32} +3.60168i q^{33} +2.83294i q^{34} -1.00000 q^{36} +0.167055i q^{37} +1.33411 q^{38} +(3.60168 - 0.167055i) q^{39} +2.60168 q^{40} -3.03630i q^{41} +2.33411 q^{43} -3.60168i q^{44} -2.60168i q^{45} -2.93579i q^{46} +9.74083i q^{47} +1.00000 q^{48} +1.76873i q^{50} -2.83294 q^{51} +(-3.60168 + 0.167055i) q^{52} +3.00000 q^{53} -1.00000i q^{54} +9.37041 q^{55} +1.33411i q^{57} -8.97209i q^{58} -11.5738i q^{59} +2.60168i q^{60} +4.03630 q^{61} -4.00000 q^{62} -1.00000 q^{64} +(-0.434624 - 9.37041i) q^{65} +3.60168 q^{66} +11.7408i q^{67} +2.83294 q^{68} +2.93579 q^{69} -5.76873i q^{71} +1.00000i q^{72} -11.4709i q^{73} +0.167055 q^{74} -1.76873 q^{75} -1.33411i q^{76} +(-0.167055 - 3.60168i) q^{78} +6.74083 q^{79} -2.60168i q^{80} +1.00000 q^{81} -3.03630 q^{82} -8.10051i q^{83} +7.37041i q^{85} -2.33411i q^{86} +8.97209 q^{87} -3.60168 q^{88} +8.16706i q^{89} -2.60168 q^{90} -2.93579 q^{92} -4.00000i q^{93} +9.74083 q^{94} +3.47093 q^{95} -1.00000i q^{96} +0.139148i q^{97} +3.60168i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{3} - 6 q^{4} + 6 q^{9} - 6 q^{12} + 6 q^{13} + 6 q^{16} - 18 q^{17} + 6 q^{22} + 6 q^{25} + 6 q^{27} + 6 q^{29} - 6 q^{36} + 6 q^{38} + 6 q^{39} + 12 q^{43} + 6 q^{48} - 18 q^{51} - 6 q^{52}+ \cdots - 24 q^{95}+O(q^{100}) $ 6 * q + 6 * q^3 - 6 * q^4 + 6 * q^9 - 6 * q^12 + 6 * q^13 + 6 * q^16 - 18 * q^17 + 6 * q^22 + 6 * q^25 + 6 * q^27 + 6 * q^29 - 6 * q^36 + 6 * q^38 + 6 * q^39 + 12 * q^43 + 6 * q^48 - 18 * q^51 - 6 * q^52 + 18 * q^53 + 24 * q^55 - 6 * q^61 - 24 * q^62 - 6 * q^64 + 12 * q^65 + 6 * q^66 + 18 * q^68 + 6 * q^75 - 24 * q^79 + 6 * q^81 + 12 * q^82 + 6 * q^87 - 6 * q^88 - 6 * q^94 - 24 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3822\mathbb{Z}\right)^\times$.

$n$	$1471$	$2549$	$3433$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−1.00000			−0.500000
$5$		−	2.60168i		−	1.16351i	−0.813365	−	0.581753i	$-0.802367\pi$
$5$		−	2.60168i		−	1.16351i	0.813365	−	0.581753i	$-0.197633\pi$
$6$		−	1.00000i		−	0.408248i
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	1.00000			0.333333
$10$	−2.60168			−0.822723
$11$			3.60168i			1.08595i	0.839750	+	0.542974i	$0.182702\pi$
$11$			3.60168i			1.08595i	−0.839750	+	0.542974i	$0.817298\pi$
$12$	−1.00000			−0.288675
$13$	3.60168	−	0.167055i	0.998926	−	0.0463328i
$13$	3.60168	−	0.167055i	0.998926	−	0.0463328i
$14$		0			0
$15$		−	2.60168i		−	0.671751i
$16$	1.00000			0.250000
$17$	−2.83294			−0.687090			−0.343545	−	0.939136i	$-0.611628\pi$
$17$	−2.83294			−0.687090			−0.343545	+	0.939136i	$0.611628\pi$
$18$		−	1.00000i		−	0.235702i
$19$			1.33411i			0.306066i	0.988221	+	0.153033i	$0.0489041\pi$
$19$			1.33411i			0.306066i	−0.988221	+	0.153033i	$0.951096\pi$
$20$			2.60168i			0.581753i
$21$		0			0
$22$	3.60168			0.767881
$23$	2.93579			0.612154			0.306077	−	0.952007i	$-0.400983\pi$
$23$	2.93579			0.612154			0.306077	+	0.952007i	$0.400983\pi$
$24$			1.00000i			0.204124i
$25$	−1.76873			−0.353747
$26$	−0.167055	−	3.60168i	−0.0327622	−	0.706347i
$27$	1.00000			0.192450
$28$		0			0
$29$	8.97209			1.66608			0.833038	−	0.553216i	$-0.186600\pi$
$29$	8.97209			1.66608			0.833038	+	0.553216i	$0.186600\pi$
$30$	−2.60168			−0.474999
$31$		−	4.00000i		−	0.718421i	−0.933257	−	0.359211i	$-0.883046\pi$
$31$		−	4.00000i		−	0.718421i	0.933257	−	0.359211i	$-0.116954\pi$
$32$		−	1.00000i		−	0.176777i
$33$			3.60168i			0.626972i
$34$			2.83294i			0.485846i
$35$		0			0
$36$	−1.00000			−0.166667
$37$			0.167055i			0.0274637i	0.999906	+	0.0137319i	$0.00437112\pi$
$37$			0.167055i			0.0274637i	−0.999906	+	0.0137319i	$0.995629\pi$
$38$	1.33411			0.216421
$39$	3.60168	−	0.167055i	0.576730	−	0.0267502i
$40$	2.60168			0.411362
$41$		−	3.03630i		−	0.474191i	−0.971486	−	0.237095i	$-0.923805\pi$
$41$		−	3.03630i		−	0.474191i	0.971486	−	0.237095i	$-0.0761954\pi$
$42$		0			0
$43$	2.33411			0.355948			0.177974	−	0.984035i	$-0.443046\pi$
$43$	2.33411			0.355948			0.177974	+	0.984035i	$0.443046\pi$
$44$		−	3.60168i		−	0.542974i
$45$		−	2.60168i		−	0.387835i
$46$		−	2.93579i		−	0.432859i
$47$			9.74083i			1.42085i	0.703775	+	0.710423i	$0.251496\pi$
$47$			9.74083i			1.42085i	−0.703775	+	0.710423i	$0.748504\pi$
$48$	1.00000			0.144338
$49$		0			0
$50$			1.76873i			0.250137i
$51$	−2.83294			−0.396692
$52$	−3.60168	+	0.167055i	−0.499463	+	0.0231664i
$53$	3.00000			0.412082			0.206041	−	0.978543i	$-0.433942\pi$
$53$	3.00000			0.412082			0.206041	+	0.978543i	$0.433942\pi$
$54$		−	1.00000i		−	0.136083i
$55$	9.37041			1.26351
$56$		0			0
$57$			1.33411i			0.176707i
$58$		−	8.97209i		−	1.17809i
$59$		−	11.5738i		−	1.50678i	−0.657576	−	0.753388i	$-0.728418\pi$
$59$		−	11.5738i		−	1.50678i	0.657576	−	0.753388i	$-0.271582\pi$
$60$			2.60168i			0.335875i
$61$	4.03630			0.516796			0.258398	−	0.966039i	$-0.416805\pi$
$61$	4.03630			0.516796			0.258398	+	0.966039i	$0.416805\pi$
$62$	−4.00000			−0.508001
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−0.434624	−	9.37041i	−0.0539085	−	1.16226i
$66$	3.60168			0.443336
$67$			11.7408i			1.43437i	0.696883	+	0.717185i	$0.254570\pi$
$67$			11.7408i			1.43437i	−0.696883	+	0.717185i	$0.745430\pi$
$68$	2.83294			0.343545
$69$	2.93579			0.353428
$70$		0			0
$71$		−	5.76873i		−	0.684623i	−0.939587	−	0.342311i	$-0.888790\pi$
$71$		−	5.76873i		−	0.684623i	0.939587	−	0.342311i	$-0.111210\pi$
$72$			1.00000i			0.117851i
$73$		−	11.4709i		−	1.34257i	−0.741199	−	0.671285i	$-0.765743\pi$
$73$		−	11.4709i		−	1.34257i	0.741199	−	0.671285i	$-0.234257\pi$
$74$	0.167055			0.0194198
$75$	−1.76873			−0.204236
$76$		−	1.33411i		−	0.153033i
$77$		0			0
$78$	−0.167055	−	3.60168i	−0.0189153	−	0.407810i
$79$	6.74083			0.758402			0.379201	−	0.925314i	$-0.376199\pi$
$79$	6.74083			0.758402			0.379201	+	0.925314i	$0.376199\pi$
$80$		−	2.60168i		−	0.290877i
$81$	1.00000			0.111111
$82$	−3.03630			−0.335304
$83$		−	8.10051i		−	0.889147i	−0.895742	−	0.444573i	$-0.853355\pi$
$83$		−	8.10051i		−	0.889147i	0.895742	−	0.444573i	$-0.146645\pi$
$84$		0			0
$85$			7.37041i			0.799434i
$86$		−	2.33411i		−	0.251694i
$87$	8.97209			0.961909
$88$	−3.60168			−0.383940
$89$			8.16706i			0.865706i	0.901464	+	0.432853i	$0.142493\pi$
$89$			8.16706i			0.865706i	−0.901464	+	0.432853i	$0.857507\pi$
$90$	−2.60168			−0.274241
$91$		0			0
$92$	−2.93579			−0.306077
$93$		−	4.00000i		−	0.414781i
$94$	9.74083			1.00469
$95$	3.47093			0.356110
$96$		−	1.00000i		−	0.102062i
$97$			0.139148i			0.0141283i	0.999975	+	0.00706416i	$0.00224861\pi$
$97$			0.139148i			0.0141283i	−0.999975	+	0.00706416i	$0.997751\pi$
$98$		0			0
$99$			3.60168i			0.361982i
$100$	1.76873			0.176873
$101$	3.56538			0.354768			0.177384	−	0.984142i	$-0.443237\pi$
$101$	3.56538			0.354768			0.177384	+	0.984142i	$0.443237\pi$
$102$			2.83294i			0.280503i
$103$	19.0749			1.87951			0.939755	−	0.341850i	$-0.111053\pi$
$103$	19.0749			1.87951			0.939755	+	0.341850i	$0.111053\pi$
$104$	0.167055	+	3.60168i	0.0163811	+	0.353174i
$105$		0			0
$106$		−	3.00000i		−	0.291386i
$107$	−8.07261			−0.780408			−0.390204	−	0.920728i	$-0.627596\pi$
$107$	−8.07261			−0.780408			−0.390204	+	0.920728i	$0.627596\pi$
$108$	−1.00000			−0.0962250
$109$		−	12.8692i		−	1.23265i	−0.787492	−	0.616325i	$-0.788621\pi$
$109$		−	12.8692i		−	1.23265i	0.787492	−	0.616325i	$-0.211379\pi$
$110$		−	9.37041i		−	0.893434i
$111$			0.167055i			0.0158562i
$112$		0			0
$113$	−19.8800			−1.87015			−0.935075	−	0.354449i	$-0.884668\pi$
$113$	−19.8800			−1.87015			−0.935075	+	0.354449i	$0.884668\pi$
$114$	1.33411			0.124951
$115$		−	7.63798i		−	0.712246i
$116$	−8.97209			−0.833038
$117$	3.60168	−	0.167055i	0.332975	−	0.0154443i
$118$	−11.5738			−1.06545
$119$		0			0
$120$	2.60168			0.237500
$121$	−1.97209			−0.179281
$122$		−	4.03630i		−	0.365430i
$123$		−	3.03630i		−	0.273774i
$124$			4.00000i			0.359211i
$125$		−	8.40672i		−	0.751920i
$126$		0			0
$127$	−10.0386			−0.890785			−0.445392	−	0.895335i	$-0.646936\pi$
$127$	−10.0386			−0.890785			−0.445392	+	0.895335i	$0.646936\pi$
$128$			1.00000i			0.0883883i
$129$	2.33411			0.205507
$130$	−9.37041	+	0.434624i	−0.821840	+	0.0381190i
$131$	8.11124			0.708682			0.354341	−	0.935116i	$-0.384705\pi$
$131$	8.11124			0.708682			0.354341	+	0.935116i	$0.384705\pi$
$132$		−	3.60168i		−	0.313486i
$133$		0			0
$134$	11.7408			1.01425
$135$		−	2.60168i		−	0.223917i
$136$		−	2.83294i		−	0.242923i
$137$			4.62959i			0.395532i	0.980249	+	0.197766i	$0.0633687\pi$
$137$			4.62959i			0.395532i	−0.980249	+	0.197766i	$0.936631\pi$
$138$		−	2.93579i		−	0.249911i
$139$	−0.935789			−0.0793726			−0.0396863	−	0.999212i	$-0.512636\pi$
$139$	−0.935789			−0.0793726			−0.0396863	+	0.999212i	$0.512636\pi$
$140$		0			0
$141$			9.74083i			0.820326i
$142$	−5.76873			−0.484101
$143$	0.601679	+	12.9721i	0.0503149	+	1.08478i
$144$	1.00000			0.0833333
$145$		−	23.3425i		−	1.93849i
$146$	−11.4709			−0.949341
$147$		0			0
$148$		−	0.167055i		−	0.0137319i
$149$		−	8.13915i		−	0.666785i	−0.942788	−	0.333392i	$-0.891807\pi$
$149$		−	8.13915i		−	0.666785i	0.942788	−	0.333392i	$-0.108193\pi$
$150$			1.76873i			0.144417i
$151$			20.0084i			1.62826i	0.580683	+	0.814130i	$0.302786\pi$
$151$			20.0084i			1.62826i	−0.580683	+	0.814130i	$0.697214\pi$
$152$	−1.33411			−0.108211
$153$	−2.83294			−0.229030
$154$		0			0
$155$	−10.4067			−0.835888
$156$	−3.60168	+	0.167055i	−0.288365	+	0.0133751i
$157$	21.3448			1.70350			0.851752	−	0.523946i	$-0.175540\pi$
$157$	21.3448			1.70350			0.851752	+	0.523946i	$0.175540\pi$
$158$		−	6.74083i		−	0.536271i
$159$	3.00000			0.237915
$160$	−2.60168			−0.205681
$161$		0			0
$162$		−	1.00000i		−	0.0785674i
$163$			1.02791i			0.0805119i	0.999189	+	0.0402560i	$0.0128173\pi$
$163$			1.02791i			0.0805119i	−0.999189	+	0.0402560i	$0.987183\pi$
$164$			3.03630i			0.237095i
$165$	9.37041			0.729486
$166$	−8.10051			−0.628722
$167$		−	5.96976i		−	0.461954i	−0.972959	−	0.230977i	$-0.925808\pi$
$167$		−	5.96976i		−	0.461954i	0.972959	−	0.230977i	$-0.0741922\pi$
$168$		0			0
$169$	12.9442	−	1.20336i	0.995707	−	0.0925660i
$170$	7.37041			0.565285
$171$			1.33411i			0.102022i
$172$	−2.33411			−0.177974
$173$	−16.5822			−1.26072			−0.630359	−	0.776303i	$-0.717092\pi$
$173$	−16.5822			−1.26072			−0.630359	+	0.776303i	$0.717092\pi$
$174$		−	8.97209i		−	0.680173i
$175$		0			0
$176$			3.60168i			0.271487i
$177$		−	11.5738i		−	0.869938i
$178$	8.16706			0.612147
$179$	−18.7408			−1.40076			−0.700378	−	0.713773i	$-0.746985\pi$
$179$	−18.7408			−1.40076			−0.700378	+	0.713773i	$0.746985\pi$
$180$			2.60168i			0.193918i
$181$	−0.426228			−0.0316813			−0.0158406	−	0.999875i	$-0.505042\pi$
$181$	−0.426228			−0.0316813			−0.0158406	+	0.999875i	$0.505042\pi$
$182$		0			0
$183$	4.03630			0.298372
$184$			2.93579i			0.216429i
$185$	0.434624			0.0319542
$186$	−4.00000			−0.293294
$187$		−	10.2034i		−	0.746143i
$188$		−	9.74083i		−	0.710423i
$189$		0			0
$190$		−	3.47093i		−	0.251808i
$191$	−8.86925			−0.641756			−0.320878	−	0.947120i	$-0.603978\pi$
$191$	−8.86925			−0.641756			−0.320878	+	0.947120i	$0.603978\pi$
$192$	−1.00000			−0.0721688
$193$		−	7.00840i		−	0.504475i	−0.967665	−	0.252238i	$-0.918834\pi$
$193$		−	7.00840i		−	0.504475i	0.967665	−	0.252238i	$-0.0811665\pi$
$194$	0.139148			0.00999023
$195$	−0.434624	−	9.37041i	−0.0311241	−	0.671029i
$196$		0			0
$197$			17.8050i			1.26856i	0.773105	+	0.634278i	$0.218703\pi$
$197$			17.8050i			1.26856i	−0.773105	+	0.634278i	$0.781297\pi$
$198$	3.60168			0.255960
$199$	−27.1089			−1.92170			−0.960850	−	0.277070i	$-0.910637\pi$
$199$	−27.1089			−1.92170			−0.960850	+	0.277070i	$0.910637\pi$
$200$		−	1.76873i		−	0.125068i
$201$			11.7408i			0.828134i
$202$		−	3.56538i		−	0.250859i
$203$		0			0
$204$	2.83294			0.198346
$205$	−7.89949			−0.551724
$206$		−	19.0749i		−	1.32901i
$207$	2.93579			0.204051
$208$	3.60168	−	0.167055i	0.249732	−	0.0115832i
$209$	−4.80504			−0.332371
$210$		0			0
$211$	22.6743			1.56096			0.780481	−	0.625179i	$-0.214974\pi$
$211$	22.6743			1.56096			0.780481	+	0.625179i	$0.214974\pi$
$212$	−3.00000			−0.206041
$213$		−	5.76873i		−	0.395267i
$214$			8.07261i			0.551832i
$215$		−	6.07261i		−	0.414148i
$216$			1.00000i			0.0680414i
$217$		0			0
$218$	−12.8692			−0.871615
$219$		−	11.4709i		−	0.775133i
$220$	−9.37041			−0.631753
$221$	−10.2034	+	0.473258i	−0.686352	+	0.0318348i
$222$	0.167055			0.0112120
$223$			9.19496i			0.615740i	0.951428	+	0.307870i	$0.0996162\pi$
$223$			9.19496i			0.615740i	−0.951428	+	0.307870i	$0.900384\pi$
$224$		0			0
$225$	−1.76873			−0.117916
$226$			19.8800i			1.32240i
$227$		−	13.5375i		−	0.898513i	−0.893403	−	0.449257i	$-0.851689\pi$
$227$		−	13.5375i		−	0.898513i	0.893403	−	0.449257i	$-0.148311\pi$
$228$		−	1.33411i		−	0.0883536i
$229$		−	18.4067i		−	1.21635i	−0.793803	−	0.608175i	$-0.791902\pi$
$229$		−	18.4067i		−	1.21635i	0.793803	−	0.608175i	$-0.208098\pi$
$230$	−7.63798			−0.503634
$231$		0			0
$232$			8.97209i			0.589047i
$233$	−11.7301			−0.768464			−0.384232	−	0.923236i	$-0.625534\pi$
$233$	−11.7301			−0.768464			−0.384232	+	0.923236i	$0.625534\pi$
$234$	−0.167055	−	3.60168i	−0.0109207	−	0.235449i
$235$	25.3425			1.65316
$236$			11.5738i			0.753388i
$237$	6.74083			0.437864
$238$		0			0
$239$			11.1731i			0.722729i	0.932425	+	0.361365i	$0.117689\pi$
$239$			11.1731i			0.722729i	−0.932425	+	0.361365i	$0.882311\pi$
$240$		−	2.60168i		−	0.167938i
$241$		−	14.7408i		−	0.949540i	−0.880110	−	0.474770i	$-0.842531\pi$
$241$		−	14.7408i		−	0.949540i	0.880110	−	0.474770i	$-0.157469\pi$
$242$			1.97209i			0.126771i
$243$	1.00000			0.0641500
$244$	−4.03630			−0.258398
$245$		0			0
$246$	−3.03630			−0.193588
$247$	0.222870	+	4.80504i	0.0141809	+	0.305737i
$248$	4.00000			0.254000
$249$		−	8.10051i		−	0.513349i
$250$	−8.40672			−0.531687
$251$	22.9465			1.44837			0.724186	−	0.689605i	$-0.242216\pi$
$251$	22.9465			1.44837			0.724186	+	0.689605i	$0.242216\pi$
$252$		0			0
$253$			10.5738i			0.664767i
$254$			10.0386i			0.629880i
$255$			7.37041i			0.461553i
$256$	1.00000			0.0625000
$257$	−0.740827			−0.0462115			−0.0231058	−	0.999733i	$-0.507355\pi$
$257$	−0.740827			−0.0462115			−0.0231058	+	0.999733i	$0.507355\pi$
$258$		−	2.33411i		−	0.145315i
$259$		0			0
$260$	0.434624	+	9.37041i	0.0269542	+	0.581128i
$261$	8.97209			0.555359
$262$		−	8.11124i		−	0.501114i
$263$	−21.0084			−1.29543			−0.647717	−	0.761881i	$-0.724276\pi$
$263$	−21.0084			−1.29543			−0.647717	+	0.761881i	$0.724276\pi$
$264$	−3.60168			−0.221668
$265$		−	7.80504i		−	0.479460i
$266$		0			0
$267$			8.16706i			0.499816i
$268$		−	11.7408i		−	0.717185i
$269$	−31.1173			−1.89726			−0.948628	−	0.316394i	$-0.897528\pi$
$269$	−31.1173			−1.89726			−0.948628	+	0.316394i	$0.897528\pi$
$270$	−2.60168			−0.158333
$271$		−	2.00840i		−	0.122001i	−0.998138	−	0.0610007i	$-0.980571\pi$
$271$		−	2.00840i		−	0.122001i	0.998138	−	0.0610007i	$-0.0194292\pi$
$272$	−2.83294			−0.171773
$273$		0			0
$274$	4.62959			0.279684
$275$		−	6.37041i		−	0.384150i
$276$	−2.93579			−0.176714
$277$	15.3681			0.923379			0.461689	−	0.887042i	$-0.347244\pi$
$277$	15.3681			0.923379			0.461689	+	0.887042i	$0.347244\pi$
$278$			0.935789i			0.0561249i
$279$		−	4.00000i		−	0.239474i
$280$		0			0
$281$		−	16.6682i		−	0.994343i	−0.867652	−	0.497171i	$-0.834372\pi$
$281$		−	16.6682i		−	0.994343i	0.867652	−	0.497171i	$-0.165628\pi$
$282$	9.74083			0.580058
$283$	17.8050			1.05840			0.529200	−	0.848497i	$-0.322492\pi$
$283$	17.8050			1.05840			0.529200	+	0.848497i	$0.322492\pi$
$284$			5.76873i			0.342311i
$285$	3.47093			0.205600
$286$	12.9721	−	0.601679i	0.767056	−	0.0355780i
$287$		0			0
$288$		−	1.00000i		−	0.0589256i
$289$	−8.97442			−0.527907
$290$	−23.3425			−1.37072
$291$			0.139148i			0.00815699i
$292$			11.4709i			0.671285i
$293$		−	26.4733i		−	1.54658i	−0.634050	−	0.773292i	$-0.718609\pi$
$293$		−	26.4733i		−	1.54658i	0.634050	−	0.773292i	$-0.281391\pi$
$294$		0			0
$295$	−30.1112			−1.75314
$296$	−0.167055			−0.00970988
$297$			3.60168i			0.208991i
$298$	−8.13915			−0.471488
$299$	10.5738	−	0.490439i	0.611497	−	0.0283628i
$300$	1.76873			0.102118
$301$		0			0
$302$	20.0084			1.15135
$303$	3.56538			0.204826
$304$			1.33411i			0.0765165i
$305$		−	10.5012i		−	0.601295i
$306$			2.83294i			0.161949i
$307$			23.2783i			1.32856i	0.747483	+	0.664281i	$0.231262\pi$
$307$			23.2783i			1.32856i	−0.747483	+	0.664281i	$0.768738\pi$
$308$		0			0
$309$	19.0749			1.08514
$310$			10.4067i			0.591062i
$311$	16.5459			0.938230			0.469115	−	0.883137i	$-0.344573\pi$
$311$	16.5459			0.938230			0.469115	+	0.883137i	$0.344573\pi$
$312$	0.167055	+	3.60168i	0.00945764	+	0.203905i
$313$	−10.0279			−0.566811			−0.283405	−	0.959000i	$-0.591464\pi$
$313$	−10.0279			−0.566811			−0.283405	+	0.959000i	$0.591464\pi$
$314$		−	21.3448i		−	1.20456i
$315$		0			0
$316$	−6.74083			−0.379201
$317$		−	21.4090i		−	1.20245i	−0.799079	−	0.601226i	$-0.794679\pi$
$317$		−	21.4090i		−	1.20245i	0.799079	−	0.601226i	$-0.205321\pi$
$318$		−	3.00000i		−	0.168232i
$319$			32.3146i			1.80927i
$320$			2.60168i			0.145438i
$321$	−8.07261			−0.450569
$322$		0			0
$323$		−	3.77946i		−	0.210295i
$324$	−1.00000			−0.0555556
$325$	−6.37041	+	0.295476i	−0.353367	+	0.0163901i
$326$	1.02791			0.0569305
$327$		−	12.8692i		−	0.711671i
$328$	3.03630			0.167652
$329$		0			0
$330$		−	9.37041i		−	0.515824i
$331$			35.8605i			1.97107i	0.169474	+	0.985535i	$0.445793\pi$
$331$			35.8605i			1.97107i	−0.169474	+	0.985535i	$0.554207\pi$
$332$			8.10051i			0.444573i
$333$			0.167055i			0.00915457i
$334$	−5.96976			−0.326651
$335$	30.5459			1.66890
$336$		0			0
$337$	6.73850			0.367069			0.183535	−	0.983013i	$-0.441246\pi$
$337$	6.73850			0.367069			0.183535	+	0.983013i	$0.441246\pi$
$338$	−1.20336	−	12.9442i	−0.0654541	−	0.704071i
$339$	−19.8800			−1.07973
$340$		−	7.37041i		−	0.399717i
$341$	14.4067			0.780167
$342$	1.33411			0.0721404
$343$		0			0
$344$			2.33411i			0.125847i
$345$		−	7.63798i		−	0.411215i
$346$			16.5822i			0.891463i
$347$	34.5738			1.85602			0.928009	−	0.372559i	$-0.121519\pi$
$347$	34.5738			1.85602			0.928009	+	0.372559i	$0.121519\pi$
$348$	−8.97209			−0.480955
$349$			21.7771i			1.16570i	0.812579	+	0.582852i	$0.198063\pi$
$349$			21.7771i			1.16570i	−0.812579	+	0.582852i	$0.801937\pi$
$350$		0			0
$351$	3.60168	−	0.167055i	0.192243	−	0.00891675i
$352$	3.60168			0.191970
$353$			20.3509i			1.08317i	0.840646	+	0.541585i	$0.182175\pi$
$353$			20.3509i			1.08317i	−0.840646	+	0.541585i	$0.817825\pi$
$354$	−11.5738			−0.615139
$355$	−15.0084			−0.796563
$356$		−	8.16706i		−	0.432853i
$357$		0			0
$358$			18.7408i			0.990483i
$359$		−	1.43229i		−	0.0755935i	−0.999285	−	0.0377968i	$-0.987966\pi$
$359$		−	1.43229i		−	0.0755935i	0.999285	−	0.0377968i	$-0.0120340\pi$
$360$	2.60168			0.137121
$361$	17.2201			0.906324
$362$			0.426228i			0.0224021i
$363$	−1.97209			−0.103508
$364$		0			0
$365$	−29.8437			−1.56209
$366$		−	4.03630i		−	0.210981i
$367$	24.3509			1.27111			0.635553	−	0.772057i	$-0.280772\pi$
$367$	24.3509			1.27111			0.635553	+	0.772057i	$0.280772\pi$
$368$	2.93579			0.153039
$369$		−	3.03630i		−	0.158064i
$370$		−	0.434624i		−	0.0225950i
$371$		0			0
$372$			4.00000i			0.207390i
$373$	31.9526			1.65444			0.827221	−	0.561877i	$-0.189920\pi$
$373$	31.9526			1.65444			0.827221	+	0.561877i	$0.189920\pi$
$374$	−10.2034			−0.527603
$375$		−	8.40672i		−	0.434121i
$376$	−9.74083			−0.502345
$377$	32.3146	−	1.49883i	1.66429	−	0.0771939i
$378$		0			0
$379$		−	2.79664i		−	0.143654i	−0.997417	−	0.0718269i	$-0.977117\pi$
$379$		−	2.79664i		−	0.143654i	0.997417	−	0.0718269i	$-0.0228829\pi$
$380$	−3.47093			−0.178055
$381$	−10.0386			−0.514295
$382$			8.86925i			0.453790i
$383$		−	9.84367i		−	0.502988i	−0.967859	−	0.251494i	$-0.919078\pi$
$383$		−	9.84367i		−	0.502988i	0.967859	−	0.251494i	$-0.0809219\pi$
$384$			1.00000i			0.0510310i
$385$		0			0
$386$	−7.00840			−0.356718
$387$	2.33411			0.118649
$388$		−	0.139148i		−	0.00706416i
$389$	16.3811			0.830557			0.415278	−	0.909694i	$-0.363684\pi$
$389$	16.3811			0.830557			0.415278	+	0.909694i	$0.363684\pi$
$390$	−9.37041	+	0.434624i	−0.474489	+	0.0220080i
$391$	−8.31693			−0.420605
$392$		0			0
$393$	8.11124			0.409158
$394$	17.8050			0.897005
$395$		−	17.5375i		−	0.882406i
$396$		−	3.60168i		−	0.180991i
$397$			5.44302i			0.273177i	0.990628	+	0.136589i	$0.0436139\pi$
$397$			5.44302i			0.273177i	−0.990628	+	0.136589i	$0.956386\pi$
$398$			27.1089i			1.35885i
$399$		0			0
$400$	−1.76873			−0.0884367
$401$		−	17.5761i		−	0.877709i	−0.898558	−	0.438854i	$-0.855384\pi$
$401$		−	17.5761i		−	0.877709i	0.898558	−	0.438854i	$-0.144616\pi$
$402$	11.7408			0.585579
$403$	−0.668221	−	14.4067i	−0.0332864	−	0.717650i
$404$	−3.56538			−0.177384
$405$		−	2.60168i		−	0.129278i
$406$		0			0
$407$	−0.601679			−0.0298241
$408$		−	2.83294i		−	0.140252i
$409$		−	19.0084i		−	0.939905i	−0.882692	−	0.469952i	$-0.844271\pi$
$409$		−	19.0084i		−	0.939905i	0.882692	−	0.469952i	$-0.155729\pi$
$410$			7.89949i			0.390128i
$411$			4.62959i			0.228361i
$412$	−19.0749			−0.939755
$413$		0			0
$414$		−	2.93579i		−	0.144286i
$415$	−21.0749			−1.03453
$416$	−0.167055	−	3.60168i	−0.00819055	−	0.176587i
$417$	−0.935789			−0.0458258
$418$			4.80504i			0.235022i
$419$	5.48165			0.267796			0.133898	−	0.990995i	$-0.457250\pi$
$419$	5.48165			0.267796			0.133898	+	0.990995i	$0.457250\pi$
$420$		0			0
$421$		−	3.16472i		−	0.154239i	−0.997022	−	0.0771196i	$-0.975428\pi$
$421$		−	3.16472i		−	0.154239i	0.997022	−	0.0771196i	$-0.0245723\pi$
$422$		−	22.6743i		−	1.10377i
$423$			9.74083i			0.473615i
$424$			3.00000i			0.145693i
$425$	5.01073			0.243056
$426$	−5.76873			−0.279496
$427$		0			0
$428$	8.07261			0.390204
$429$	0.601679	+	12.9721i	0.0290493	+	0.626299i
$430$	−6.07261			−0.292847
$431$		−	15.4370i		−	0.743572i	−0.928318	−	0.371786i	$-0.878746\pi$
$431$		−	15.4370i		−	0.743572i	0.928318	−	0.371786i	$-0.121254\pi$
$432$	1.00000			0.0481125
$433$	13.9419			0.670003			0.335001	−	0.942218i	$-0.391263\pi$
$433$	13.9419			0.670003			0.335001	+	0.942218i	$0.391263\pi$
$434$		0			0
$435$		−	23.3425i		−	1.11919i
$436$			12.8692i			0.616325i
$437$			3.91667i			0.187360i
$438$	−11.4709			−0.548102
$439$	−27.3872			−1.30712			−0.653560	−	0.756875i	$-0.726725\pi$
$439$	−27.3872			−1.30712			−0.653560	+	0.756875i	$0.726725\pi$
$440$			9.37041i			0.446717i
$441$		0			0
$442$	0.473258	+	10.2034i	0.0225106	+	0.485324i
$443$	24.1112			1.14556			0.572780	−	0.819709i	$-0.305865\pi$
$443$	24.1112			1.14556			0.572780	+	0.819709i	$0.305865\pi$
$444$		−	0.167055i		−	0.00792809i
$445$	21.2481			1.00725
$446$	9.19496			0.435394
$447$		−	8.13915i		−	0.384968i
$448$		0			0
$449$			2.59095i			0.122275i	0.998129	+	0.0611373i	$0.0194728\pi$
$449$			2.59095i			0.122275i	−0.998129	+	0.0611373i	$0.980527\pi$
$450$			1.76873i			0.0833789i
$451$	10.9358			0.514946
$452$	19.8800			0.935075
$453$			20.0084i			0.940076i
$454$	−13.5375			−0.635345
$455$		0			0
$456$	−1.33411			−0.0624754
$457$			10.4686i			0.489700i	0.969561	+	0.244850i	$0.0787388\pi$
$457$			10.4686i			0.489700i	−0.969561	+	0.244850i	$0.921261\pi$
$458$	−18.4067			−0.860089
$459$	−2.83294			−0.132231
$460$			7.63798i			0.356123i
$461$			30.0168i			1.39802i	0.715111	+	0.699011i	$0.246376\pi$
$461$			30.0168i			1.39802i	−0.715111	+	0.699011i	$0.753624\pi$
$462$		0			0
$463$		−	19.4649i		−	0.904609i	−0.891864	−	0.452304i	$-0.850602\pi$
$463$		−	19.4649i		−	0.904609i	0.891864	−	0.452304i	$-0.149398\pi$
$464$	8.97209			0.416519
$465$	−10.4067			−0.482600
$466$			11.7301i			0.543386i
$467$	−0.300138			−0.0138887			−0.00694437	−	0.999976i	$-0.502210\pi$
$467$	−0.300138			−0.0138887			−0.00694437	+	0.999976i	$0.502210\pi$
$468$	−3.60168	+	0.167055i	−0.166488	+	0.00772213i
$469$		0			0
$470$		−	25.3425i		−	1.16896i
$471$	21.3448			0.983518
$472$	11.5738			0.532726
$473$			8.40672i			0.386541i
$474$		−	6.74083i		−	0.309616i
$475$		−	2.35969i		−	0.108270i
$476$		0			0
$477$	3.00000			0.137361
$478$	11.1731			0.511047
$479$			23.5845i			1.07760i	0.842433	+	0.538802i	$0.181123\pi$
$479$			23.5845i			1.07760i	−0.842433	+	0.538802i	$0.818877\pi$
$480$	−2.60168			−0.118750
$481$	0.0279074	+	0.601679i	0.00127247	+	0.0274342i
$482$	−14.7408			−0.671426
$483$		0			0
$484$	1.97209			0.0896406
$485$	0.362018			0.0164384
$486$		−	1.00000i		−	0.0453609i
$487$			34.2420i			1.55165i	0.630946	+	0.775826i	$0.282667\pi$
$487$			34.2420i			1.55165i	−0.630946	+	0.775826i	$0.717333\pi$
$488$			4.03630i			0.182715i
$489$			1.02791i			0.0464836i
$490$		0			0
$491$	−39.7553			−1.79413			−0.897065	−	0.441898i	$-0.854305\pi$
$491$	−39.7553			−1.79413			−0.897065	+	0.441898i	$0.854305\pi$
$492$			3.03630i			0.136887i
$493$	−25.4174			−1.14474
$494$	4.80504	−	0.222870i	0.216189	−	0.0100274i
$495$	9.37041			0.421169
$496$		−	4.00000i		−	0.179605i
$497$		0			0
$498$	−8.10051			−0.362993
$499$		−	12.2504i		−	0.548403i	−0.961672	−	0.274201i	$-0.911587\pi$
$499$		−	12.2504i		−	0.548403i	0.961672	−	0.274201i	$-0.0884135\pi$
$500$			8.40672i			0.375960i
$501$		−	5.96976i		−	0.266709i
$502$		−	22.9465i		−	1.02415i
$503$	2.12842			0.0949016			0.0474508	−	0.998874i	$-0.484890\pi$
$503$	2.12842			0.0949016			0.0474508	+	0.998874i	$0.484890\pi$
$504$		0			0
$505$		−	9.27596i		−	0.412775i
$506$	10.5738			0.470061
$507$	12.9442	−	1.20336i	0.574871	−	0.0534430i
$508$	10.0386			0.445392
$509$		−	33.6873i		−	1.49317i	−0.665293	−	0.746583i	$-0.731693\pi$
$509$		−	33.6873i		−	1.49317i	0.665293	−	0.746583i	$-0.268307\pi$
$510$	7.37041			0.326367
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$			1.33411i			0.0589024i
$514$			0.740827i			0.0326765i
$515$		−	49.6269i		−	2.18682i
$516$	−2.33411			−0.102753
$517$	−35.0833			−1.54296
$518$		0			0
$519$	−16.5822			−0.727876
$520$	9.37041	−	0.434624i	0.410920	−	0.0190595i
$521$	−0.261504			−0.0114567			−0.00572835	−	0.999984i	$-0.501823\pi$
$521$	−0.261504			−0.0114567			−0.00572835	+	0.999984i	$0.501823\pi$
$522$		−	8.97209i		−	0.392698i
$523$	10.4793			0.458229			0.229114	−	0.973400i	$-0.426417\pi$
$523$	10.4793			0.458229			0.229114	+	0.973400i	$0.426417\pi$
$524$	−8.11124			−0.354341
$525$		0			0
$526$			21.0084i			0.916010i
$527$			11.3318i			0.493620i
$528$			3.60168i			0.156743i
$529$	−14.3811			−0.625267
$530$	−7.80504			−0.339029
$531$		−	11.5738i		−	0.502259i
$532$		0			0
$533$	−0.507230	−	10.9358i	−0.0219706	−	0.473682i
$534$	8.16706			0.353423
$535$			21.0023i			0.908010i
$536$	−11.7408			−0.507126
$537$	−18.7408			−0.808726
$538$			31.1173i			1.34156i
$539$		0			0
$540$			2.60168i			0.111958i
$541$			21.7213i			0.933872i	0.884291	+	0.466936i	$0.154642\pi$
$541$			21.7213i			0.933872i	−0.884291	+	0.466936i	$0.845358\pi$
$542$	−2.00840			−0.0862680
$543$	−0.426228			−0.0182912
$544$			2.83294i			0.121462i
$545$	−33.4817			−1.43420
$546$		0			0
$547$	−33.3593			−1.42634			−0.713170	−	0.700991i	$-0.752741\pi$
$547$	−33.3593			−1.42634			−0.713170	+	0.700991i	$0.752741\pi$
$548$		−	4.62959i		−	0.197766i
$549$	4.03630			0.172265
$550$	−6.37041			−0.271635
$551$			11.9698i			0.509929i
$552$			2.93579i			0.124955i
$553$		0			0
$554$		−	15.3681i		−	0.652927i
$555$	0.434624			0.0184488
$556$	0.935789			0.0396863
$557$			38.4067i			1.62734i	0.581324	+	0.813672i	$0.302535\pi$
$557$			38.4067i			1.62734i	−0.581324	+	0.813672i	$0.697465\pi$
$558$	−4.00000			−0.169334
$559$	8.40672	−	0.389925i	0.355566	−	0.0164921i
$560$		0			0
$561$		−	10.2034i		−	0.430786i
$562$	−16.6682			−0.703106
$563$	3.86692			0.162971			0.0814856	−	0.996675i	$-0.474034\pi$
$563$	3.86692			0.162971			0.0814856	+	0.996675i	$0.474034\pi$
$564$		−	9.74083i		−	0.410163i
$565$			51.7213i			2.17593i
$566$		−	17.8050i		−	0.748402i
$567$		0			0
$568$	5.76873			0.242051
$569$	−27.6743			−1.16017			−0.580083	−	0.814557i	$-0.696980\pi$
$569$	−27.6743			−1.16017			−0.580083	+	0.814557i	$0.696980\pi$
$570$		−	3.47093i		−	0.145381i
$571$	−40.0941			−1.67788			−0.838942	−	0.544221i	$-0.816825\pi$
$571$	−40.0941			−1.67788			−0.838942	+	0.544221i	$0.816825\pi$
$572$	−0.601679	−	12.9721i	−0.0251575	−	0.542390i
$573$	−8.86925			−0.370518
$574$		0			0
$575$	−5.19263			−0.216548
$576$	−1.00000			−0.0416667
$577$			0.406717i			0.0169318i	0.999964	+	0.00846592i	$0.00269482\pi$
$577$			0.406717i			0.0169318i	−0.999964	+	0.00846592i	$0.997305\pi$
$578$			8.97442i			0.373287i
$579$		−	7.00840i		−	0.291259i
$580$			23.3425i			0.969245i
$581$		0			0
$582$	0.139148			0.00576786
$583$			10.8050i			0.447499i
$584$	11.4709			0.474670
$585$	−0.434624	−	9.37041i	−0.0179695	−	0.387419i
$586$	−26.4733			−1.09360
$587$			22.0131i			0.908576i	0.890855	+	0.454288i	$0.150106\pi$
$587$			22.0131i			0.908576i	−0.890855	+	0.454288i	$0.849894\pi$
$588$		0			0
$589$	5.33644			0.219884
$590$			30.1112i			1.23966i
$591$			17.8050i			0.732401i
$592$			0.167055i			0.00686593i
$593$			31.1862i			1.28066i	0.768099	+	0.640331i	$0.221203\pi$
$593$			31.1862i			1.28066i	−0.768099	+	0.640331i	$0.778797\pi$
$594$	3.60168			0.147779
$595$		0			0
$596$			8.13915i			0.333392i
$597$	−27.1089			−1.10949
$598$	−0.490439	−	10.5738i	−0.0200555	−	0.432394i
$599$	−6.34017			−0.259053			−0.129526	−	0.991576i	$-0.541346\pi$
$599$	−6.34017			−0.259053			−0.129526	+	0.991576i	$0.541346\pi$
$600$		−	1.76873i		−	0.0722083i
$601$	−23.5566			−0.960893			−0.480447	−	0.877024i	$-0.659525\pi$
$601$	−23.5566			−0.960893			−0.480447	+	0.877024i	$0.659525\pi$
$602$		0			0
$603$			11.7408i			0.478123i
$604$		−	20.0084i		−	0.814130i
$605$			5.13075i			0.208595i
$606$		−	3.56538i		−	0.144834i
$607$	16.0386			0.650988			0.325494	−	0.945544i	$-0.394469\pi$
$607$	16.0386			0.650988			0.325494	+	0.945544i	$0.394469\pi$
$608$	1.33411			0.0541053
$609$		0			0
$610$	−10.5012			−0.425180
$611$	1.62726	+	35.0833i	0.0658317	+	1.41932i
$612$	2.83294			0.114515
$613$		−	8.51835i		−	0.344053i	−0.985092	−	0.172026i	$-0.944969\pi$
$613$		−	8.51835i		−	0.344053i	0.985092	−	0.172026i	$-0.0550314\pi$
$614$	23.2783			0.939436
$615$	−7.89949			−0.318538
$616$		0			0
$617$			1.40905i			0.0567261i	0.999598	+	0.0283631i	$0.00902945\pi$
$617$			1.40905i			0.0567261i	−0.999598	+	0.0283631i	$0.990971\pi$
$618$		−	19.0749i		−	0.767307i
$619$		−	45.4537i		−	1.82694i	−0.406906	−	0.913470i	$-0.633392\pi$
$619$		−	45.4537i		−	1.82694i	0.406906	−	0.913470i	$-0.366608\pi$
$620$	10.4067			0.417944
$621$	2.93579			0.117809
$622$		−	16.5459i		−	0.663429i
$623$		0			0
$624$	3.60168	−	0.167055i	0.144183	−	0.00668756i
$625$	−30.7153			−1.22861
$626$			10.0279i			0.400796i
$627$	−4.80504			−0.191895
$628$	−21.3448			−0.851752
$629$		−	0.473258i		−	0.0188700i
$630$		0			0
$631$			35.2313i			1.40253i	0.712898	+	0.701267i	$0.247382\pi$
$631$			35.2313i			1.40253i	−0.712898	+	0.701267i	$0.752618\pi$
$632$			6.74083i			0.268136i
$633$	22.6743			0.901222
$634$	−21.4090			−0.850262
$635$			26.1173i			1.03643i
$636$	−3.00000			−0.118958
$637$		0			0
$638$	32.3146			1.27935
$639$		−	5.76873i		−	0.228208i
$640$	2.60168			0.102840
$641$	22.2336			0.878174			0.439087	−	0.898444i	$-0.355302\pi$
$641$	22.2336			0.878174			0.439087	+	0.898444i	$0.355302\pi$
$642$			8.07261i			0.318600i
$643$		−	3.64031i		−	0.143560i	−0.997420	−	0.0717800i	$-0.977132\pi$
$643$		−	3.64031i		−	0.143560i	0.997420	−	0.0717800i	$-0.0228679\pi$
$644$		0			0
$645$		−	6.07261i		−	0.239109i
$646$	−3.77946			−0.148701
$647$	14.0558			0.552591			0.276296	−	0.961073i	$-0.410893\pi$
$647$	14.0558			0.552591			0.276296	+	0.961073i	$0.410893\pi$
$648$			1.00000i			0.0392837i
$649$	41.6850			1.63628
$650$	0.295476	+	6.37041i	0.0115895	+	0.249868i
$651$		0			0
$652$		−	1.02791i		−	0.0402560i
$653$	−17.2481			−0.674969			−0.337484	−	0.941331i	$-0.609576\pi$
$653$	−17.2481			−0.674969			−0.337484	+	0.941331i	$0.609576\pi$
$654$	−12.8692			−0.503227
$655$		−	21.1028i		−	0.824556i
$656$		−	3.03630i		−	0.118548i
$657$		−	11.4709i		−	0.447523i
$658$		0			0
$659$	−21.6999			−0.845307			−0.422653	−	0.906291i	$-0.638901\pi$
$659$	−21.6999			−0.845307			−0.422653	+	0.906291i	$0.638901\pi$
$660$	−9.37041			−0.364743
$661$			23.1815i			0.901656i	0.892611	+	0.450828i	$0.148871\pi$
$661$			23.1815i			0.901656i	−0.892611	+	0.450828i	$0.851129\pi$
$662$	35.8605			1.39376
$663$	−10.2034	+	0.473258i	−0.396266	+	0.0183798i
$664$	8.10051			0.314361
$665$		0			0
$666$	0.167055			0.00647326
$667$	26.3402			1.01990
$668$			5.96976i			0.230977i
$669$			9.19496i			0.355498i
$670$		−	30.5459i		−	1.18009i
$671$			14.5375i			0.561213i
$672$		0			0
$673$	7.56538			0.291624			0.145812	−	0.989312i	$-0.453421\pi$
$673$	7.56538			0.291624			0.145812	+	0.989312i	$0.453421\pi$
$674$		−	6.73850i		−	0.259557i
$675$	−1.76873			−0.0680786
$676$	−12.9442	+	1.20336i	−0.497853	+	0.0462830i
$677$	−20.9163			−0.803878			−0.401939	−	0.915666i	$-0.631664\pi$
$677$	−20.9163			−0.803878			−0.401939	+	0.915666i	$0.631664\pi$
$678$			19.8800i			0.763486i
$679$		0			0
$680$	−7.37041			−0.282642
$681$		−	13.5375i		−	0.518757i
$682$		−	14.4067i		−	0.551662i
$683$		−	19.7432i		−	0.755451i	−0.925918	−	0.377725i	$-0.876706\pi$
$683$		−	19.7432i		−	0.755451i	0.925918	−	0.377725i	$-0.123294\pi$
$684$		−	1.33411i		−	0.0510110i
$685$	12.0447			0.460204
$686$		0			0
$687$		−	18.4067i		−	0.702260i
$688$	2.33411			0.0889871
$689$	10.8050	−	0.501166i	0.411639	−	0.0190929i
$690$	−7.63798			−0.290773
$691$			27.0215i			1.02794i	0.857807	+	0.513972i	$0.171827\pi$
$691$			27.0215i			1.02794i	−0.857807	+	0.513972i	$0.828173\pi$
$692$	16.5822			0.630359
$693$		0			0
$694$		−	34.5738i		−	1.31240i
$695$			2.43462i			0.0923506i
$696$			8.97209i			0.340086i
$697$			8.60168i			0.325812i
$698$	21.7771			0.824277
$699$	−11.7301			−0.443673
$700$		0			0
$701$	46.3956			1.75234			0.876169	−	0.482004i	$-0.160091\pi$
$701$	46.3956			1.75234			0.876169	+	0.482004i	$0.160091\pi$
$702$	−0.167055	−	3.60168i	−0.00630509	−	0.135937i
$703$	−0.222870			−0.00840570
$704$		−	3.60168i		−	0.135743i
$705$	25.3425			0.954454
$706$	20.3509			0.765916
$707$		0			0
$708$			11.5738i			0.434969i
$709$			41.3146i			1.55160i	0.630977	+	0.775801i	$0.282654\pi$
$709$			41.3146i			1.55160i	−0.630977	+	0.775801i	$0.717346\pi$
$710$			15.0084i			0.563255i
$711$	6.74083			0.252801
$712$	−8.16706			−0.306073
$713$		−	11.7432i		−	0.439785i
$714$		0			0
$715$	33.7492	−	1.56538i	1.26215	−	0.0585417i
$716$	18.7408			0.700378
$717$			11.1731i			0.417268i
$718$	−1.43229			−0.0534527
$719$	−29.9442			−1.11673			−0.558365	−	0.829596i	$-0.688571\pi$
$719$	−29.9442			−1.11673			−0.558365	+	0.829596i	$0.688571\pi$
$720$		−	2.60168i		−	0.0969589i
$721$		0			0
$722$		−	17.2201i		−	0.640868i
$723$		−	14.7408i		−	0.548217i
$724$	0.426228			0.0158406
$725$	−15.8692			−0.589369
$726$			1.97209i			0.0731912i
$727$	22.8860			0.848796			0.424398	−	0.905476i	$-0.360486\pi$
$727$	22.8860			0.848796			0.424398	+	0.905476i	$0.360486\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$			29.8437i			1.10456i
$731$	−6.61241			−0.244569
$732$	−4.03630			−0.149186
$733$		−	39.0531i		−	1.44246i	−0.692696	−	0.721229i	$-0.743577\pi$
$733$		−	39.0531i		−	1.44246i	0.692696	−	0.721229i	$-0.256423\pi$
$734$		−	24.3509i		−	0.898808i
$735$		0			0
$736$		−	2.93579i		−	0.108215i
$737$	−42.2867			−1.55765
$738$	−3.03630			−0.111768
$739$			49.4537i			1.81919i	0.415501	+	0.909593i	$0.363606\pi$
$739$			49.4537i			1.81919i	−0.415501	+	0.909593i	$0.636394\pi$
$740$	−0.434624			−0.0159771
$741$	0.222870	+	4.80504i	0.00818734	+	0.176517i
$742$		0			0
$743$			0.203358i			0.00746049i	0.999993	+	0.00373025i	$0.00118738\pi$
$743$			0.203358i			0.00746049i	−0.999993	+	0.00373025i	$0.998813\pi$
$744$	4.00000			0.146647
$745$	−21.1755			−0.775808
$746$		−	31.9526i		−	1.16987i
$747$		−	8.10051i		−	0.296382i
$748$			10.2034i			0.373072i
$749$		0			0
$750$	−8.40672			−0.306970
$751$	−42.9465			−1.56714			−0.783570	−	0.621303i	$-0.786604\pi$
$751$	−42.9465			−1.56714			−0.783570	+	0.621303i	$0.786604\pi$
$752$			9.74083i			0.355211i
$753$	22.9465			0.836218
$754$	−1.49883	−	32.3146i	−0.0545843	−	1.17683i
$755$	52.0554			1.89449
$756$		0			0
$757$	−19.5180			−0.709392			−0.354696	−	0.934982i	$-0.615416\pi$
$757$	−19.5180			−0.709392			−0.354696	+	0.934982i	$0.615416\pi$
$758$	−2.79664			−0.101579
$759$			10.5738i			0.383804i
$760$			3.47093i			0.125904i
$761$			42.0168i			1.52311i	0.648102	+	0.761554i	$0.275563\pi$
$761$			42.0168i			1.52311i	−0.648102	+	0.761554i	$0.724437\pi$
$762$			10.0386i			0.363661i
$763$		0			0
$764$	8.86925			0.320878
$765$			7.37041i			0.266478i
$766$	−9.84367			−0.355666
$767$	−1.93346	−	41.6850i	−0.0698131	−	1.50516i
$768$	1.00000			0.0360844
$769$			51.9502i			1.87337i	0.350168	+	0.936687i	$0.386125\pi$
$769$			51.9502i			1.87337i	−0.350168	+	0.936687i	$0.613875\pi$
$770$		0			0
$771$	−0.740827			−0.0266802
$772$			7.00840i			0.252238i
$773$			42.0336i			1.51184i	0.654662	+	0.755921i	$0.272811\pi$
$773$			42.0336i			1.51184i	−0.654662	+	0.755921i	$0.727189\pi$
$774$		−	2.33411i		−	0.0838979i
$775$			7.07494i			0.254139i
$776$	−0.139148			−0.00499511
$777$		0			0
$778$		−	16.3811i		−	0.587292i
$779$	4.05076			0.145134
$780$	0.434624	+	9.37041i	0.0155620	+	0.335515i
$781$	20.7771			0.743464
$782$			8.31693i			0.297413i
$783$	8.97209			0.320636
$784$		0			0
$785$		−	55.5324i		−	1.98204i
$786$		−	8.11124i		−	0.289318i
$787$		−	8.79431i		−	0.313483i	−0.987640	−	0.156742i	$-0.949901\pi$
$787$		−	8.79431i		−	0.313483i	0.987640	−	0.156742i	$-0.0500990\pi$
$788$		−	17.8050i		−	0.634278i
$789$	−21.0084			−0.747919
$790$	−17.5375			−0.623955
$791$		0			0
$792$	−3.60168			−0.127980
$793$	14.5375	−	0.674285i	0.516241	−	0.0239446i
$794$	5.44302			0.193166
$795$		−	7.80504i		−	0.276816i
$796$	27.1089			0.960850
$797$	−6.25039			−0.221400			−0.110700	−	0.993854i	$-0.535309\pi$
$797$	−6.25039			−0.221400			−0.110700	+	0.993854i	$0.535309\pi$
$798$		0			0
$799$		−	27.5952i		−	0.976249i
$800$			1.76873i			0.0625342i
$801$			8.16706i			0.288569i
$802$	−17.5761			−0.620634
$803$	41.3146			1.45796
$804$		−	11.7408i		−	0.414067i
$805$		0			0
$806$	−14.4067	+	0.668221i	−0.507455	+	0.0235371i
$807$	−31.1173			−1.09538
$808$			3.56538i			0.125429i
$809$	−45.8521			−1.61207			−0.806036	−	0.591866i	$-0.798391\pi$
$809$	−45.8521			−1.61207			−0.806036	+	0.591866i	$0.798391\pi$
$810$	−2.60168			−0.0914137
$811$			29.5096i			1.03622i	0.855314	+	0.518110i	$0.173364\pi$
$811$			29.5096i			1.03622i	−0.855314	+	0.518110i	$0.826636\pi$
$812$		0			0
$813$		−	2.00840i		−	0.0704375i
$814$			0.601679i			0.0210888i
$815$	2.67429			0.0936761
$816$	−2.83294			−0.0991729
$817$			3.11396i			0.108944i
$818$	−19.0084			−0.664613
$819$		0			0
$820$	7.89949			0.275862
$821$		−	24.1559i		−	0.843048i	−0.906817	−	0.421524i	$-0.861495\pi$
$821$		−	24.1559i		−	0.843048i	0.906817	−	0.421524i	$-0.138505\pi$
$822$	4.62959			0.161475
$823$	−30.7022			−1.07021			−0.535106	−	0.844785i	$-0.679728\pi$
$823$	−30.7022			−1.07021			−0.535106	+	0.844785i	$0.679728\pi$
$824$			19.0749i			0.664507i
$825$		−	6.37041i		−	0.221789i
$826$		0			0
$827$		−	3.32338i		−	0.115565i	−0.998329	−	0.0577827i	$-0.981597\pi$
$827$		−	3.32338i		−	0.115565i	0.998329	−	0.0577827i	$-0.0184031\pi$
$828$	−2.93579			−0.102026
$829$	−29.6464			−1.02966			−0.514831	−	0.857292i	$-0.672145\pi$
$829$	−29.6464			−1.02966			−0.514831	+	0.857292i	$0.672145\pi$
$830$			21.0749i			0.731522i
$831$	15.3681			0.533113
$832$	−3.60168	+	0.167055i	−0.124866	+	0.00579160i
$833$		0			0
$834$			0.935789i			0.0324037i
$835$	−15.5314			−0.537486
$836$	4.80504			0.166186
$837$		−	4.00000i		−	0.138260i
$838$		−	5.48165i		−	0.189361i
$839$			5.51189i			0.190292i	0.995463	+	0.0951458i	$0.0303317\pi$
$839$			5.51189i			0.190292i	−0.995463	+	0.0951458i	$0.969668\pi$
$840$		0			0
$841$	51.4984			1.77581
$842$	−3.16472			−0.109064
$843$		−	16.6682i		−	0.574084i
$844$	−22.6743			−0.780481
$845$	−3.13075	−	33.6766i	−0.107701	−	1.15851i
$846$	9.74083			0.334897
$847$		0			0
$848$	3.00000			0.103020
$849$	17.8050			0.611067
$850$		−	5.01073i		−	0.171867i
$851$			0.490439i			0.0168120i
$852$			5.76873i			0.197634i
$853$		−	34.2611i		−	1.17308i	−0.809921	−	0.586539i	$-0.800490\pi$
$853$		−	34.2611i		−	1.17308i	0.809921	−	0.586539i	$-0.199510\pi$
$854$		0			0
$855$	3.47093			0.118703
$856$		−	8.07261i		−	0.275916i
$857$	36.4598			1.24544			0.622722	−	0.782443i	$-0.286027\pi$
$857$	36.4598			1.24544			0.622722	+	0.782443i	$0.286027\pi$
$858$	12.9721	−	0.601679i	0.442860	−	0.0205410i
$859$	43.3486			1.47903			0.739517	−	0.673138i	$-0.235054\pi$
$859$	43.3486			1.47903			0.739517	+	0.673138i	$0.235054\pi$
$860$			6.07261i			0.207074i
$861$		0			0
$862$	−15.4370			−0.525785
$863$			13.6147i			0.463451i	0.972781	+	0.231726i	$0.0744371\pi$
$863$			13.6147i			0.463451i	−0.972781	+	0.231726i	$0.925563\pi$
$864$		−	1.00000i		−	0.0340207i
$865$			43.1415i			1.46685i
$866$		−	13.9419i		−	0.473763i
$867$	−8.97442			−0.304787
$868$		0			0
$869$			24.2783i			0.823585i
$870$	−23.3425			−0.791385
$871$	1.96137	+	42.2867i	0.0664583	+	1.43283i
$872$	12.8692			0.435808
$873$			0.139148i			0.00470944i
$874$	3.91667			0.132483
$875$		0			0
$876$			11.4709i			0.387567i
$877$			27.5156i			0.929137i	0.885537	+	0.464568i	$0.153790\pi$
$877$			27.5156i			0.929137i	−0.885537	+	0.464568i	$0.846210\pi$
$878$			27.3872i			0.924273i
$879$		−	26.4733i		−	0.892921i
$880$	9.37041			0.315877
$881$	−22.3341			−0.752455			−0.376228	−	0.926527i	$-0.622779\pi$
$881$	−22.3341			−0.752455			−0.376228	+	0.926527i	$0.622779\pi$
$882$		0			0
$883$	9.28669			0.312522			0.156261	−	0.987716i	$-0.450056\pi$
$883$	9.28669			0.312522			0.156261	+	0.987716i	$0.450056\pi$
$884$	10.2034	−	0.473258i	0.343176	−	0.0159174i
$885$	−30.1112			−1.01218
$886$		−	24.1112i		−	0.810033i
$887$	−13.9442			−0.468200			−0.234100	−	0.972213i	$-0.575214\pi$
$887$	−13.9442			−0.468200			−0.234100	+	0.972213i	$0.575214\pi$
$888$	−0.167055			−0.00560600
$889$		0			0
$890$		−	21.2481i		−	0.712236i
$891$			3.60168i			0.120661i
$892$		−	9.19496i		−	0.307870i
$893$	−12.9953			−0.434872
$894$	−8.13915			−0.272214
$895$			48.7576i			1.62979i
$896$		0			0
$897$	10.5738	−	0.490439i	0.353048	−	0.0163753i
$898$	2.59095			0.0864612
$899$		−	35.8884i		−	1.19694i
$900$	1.76873			0.0589578
$901$	−8.49883			−0.283137
$902$		−	10.9358i		−	0.364122i
$903$		0			0
$904$		−	19.8800i		−	0.661198i
$905$			1.10891i			0.0368614i
$906$	20.0084			0.664734
$907$	4.13915			0.137438			0.0687191	−	0.997636i	$-0.478109\pi$
$907$	4.13915			0.137438			0.0687191	+	0.997636i	$0.478109\pi$
$908$			13.5375i			0.449257i
$909$	3.56538			0.118256
$910$		0			0
$911$	18.5566			0.614807			0.307404	−	0.951579i	$-0.400540\pi$
$911$	18.5566			0.614807			0.307404	+	0.951579i	$0.400540\pi$
$912$			1.33411i			0.0441768i
$913$	29.1755			0.965566
$914$	10.4686			0.346270
$915$		−	10.5012i		−	0.347158i
$916$			18.4067i			0.608175i
$917$		0			0
$918$			2.83294i			0.0935011i
$919$	51.3486			1.69383			0.846917	−	0.531726i	$-0.178456\pi$
$919$	51.3486			1.69383			0.846917	+	0.531726i	$0.178456\pi$
$920$	7.63798			0.251817
$921$			23.2783i			0.767046i
$922$	30.0168			0.988550
$923$	−0.963697	−	20.7771i	−0.0317205	−	0.683888i
$924$		0			0
$925$		−	0.295476i		−	0.00971520i
$926$	−19.4649			−0.639655
$927$	19.0749			0.626503
$928$		−	8.97209i		−	0.294523i
$929$		−	6.94185i		−	0.227755i	−0.993495	−	0.113877i	$-0.963673\pi$
$929$		−	6.94185i		−	0.227755i	0.993495	−	0.113877i	$-0.0363271\pi$
$930$			10.4067i			0.341250i
$931$		0			0
$932$	11.7301			0.384232
$933$	16.5459			0.541687
$934$			0.300138i			0.00982083i
$935$	−26.5459			−0.868143
$936$	0.167055	+	3.60168i	0.00546037	+	0.117725i
$937$	37.1005			1.21202			0.606010	−	0.795457i	$-0.292769\pi$
$937$	37.1005			1.21202			0.606010	+	0.795457i	$0.292769\pi$
$938$		0			0
$939$	−10.0279			−0.327248
$940$	−25.3425			−0.826581
$941$			8.41138i			0.274203i	0.990557	+	0.137102i	$0.0437787\pi$
$941$			8.41138i			0.274203i	−0.990557	+	0.137102i	$0.956221\pi$
$942$		−	21.3448i		−	0.695452i
$943$		−	8.91395i		−	0.290278i
$944$		−	11.5738i		−	0.376694i
$945$		0			0
$946$	8.40672			0.273326
$947$		−	25.1671i		−	0.817819i	−0.912575	−	0.408910i	$-0.865909\pi$
$947$		−	25.1671i		−	0.817819i	0.912575	−	0.408910i	$-0.134091\pi$
$948$	−6.74083			−0.218932
$949$	−1.91628	−	41.3146i	−0.0622050	−	1.34113i
$950$	−2.35969			−0.0765583
$951$		−	21.4090i		−	0.694236i
$952$		0			0
$953$	35.3681			1.14568			0.572842	−	0.819666i	$-0.305841\pi$
$953$	35.3681			1.14568			0.572842	+	0.819666i	$0.305841\pi$
$954$		−	3.00000i		−	0.0971286i
$955$			23.0749i			0.746687i
$956$		−	11.1731i		−	0.361365i
$957$			32.3146i			1.04458i
$958$	23.5845			0.761981
$959$		0			0
$960$			2.60168i			0.0839688i
$961$	15.0000			0.483871
$962$	0.601679	−	0.0279074i	0.0193989	−	0.000899772i
$963$	−8.07261			−0.260136
$964$			14.7408i			0.474770i
$965$	−18.2336			−0.586960
$966$		0			0
$967$			17.3123i			0.556725i	0.960476	+	0.278362i	$0.0897917\pi$
$967$			17.3123i			0.556725i	−0.960476	+	0.278362i	$0.910208\pi$
$968$		−	1.97209i		−	0.0633855i
$969$		−	3.77946i		−	0.121414i
$970$		−	0.362018i		−	0.0116237i
$971$	−53.3919			−1.71343			−0.856713	−	0.515793i	$-0.827497\pi$
$971$	−53.3919			−1.71343			−0.856713	+	0.515793i	$0.827497\pi$
$972$	−1.00000			−0.0320750
$973$		0			0
$974$	34.2420			1.09718
$975$	−6.37041	+	0.295476i	−0.204017	+	0.00946281i
$976$	4.03630			0.129199
$977$		−	32.8692i		−	1.05158i	−0.850614	−	0.525790i	$-0.823770\pi$
$977$		−	32.8692i		−	1.05158i	0.850614	−	0.525790i	$-0.176230\pi$
$978$	1.02791			0.0328689
$979$	−29.4151			−0.940111
$980$		0			0
$981$		−	12.8692i		−	0.410883i
$982$			39.7553i			1.26864i
$983$			9.72404i			0.310149i	0.987903	+	0.155074i	$0.0495617\pi$
$983$			9.72404i			0.310149i	−0.987903	+	0.155074i	$0.950438\pi$
$984$	3.03630			0.0967938
$985$	46.3230			1.47597
$986$			25.4174i			0.809456i
$987$		0			0
$988$	−0.222870	−	4.80504i	−0.00709044	−	0.152869i
$989$	6.85246			0.217895
$990$		−	9.37041i		−	0.297811i
$991$	32.4114			1.02958			0.514791	−	0.857316i	$-0.327870\pi$
$991$	32.4114			1.02958			0.514791	+	0.857316i	$0.327870\pi$
$992$	−4.00000			−0.127000
$993$			35.8605i			1.13800i
$994$		0			0
$995$			70.5287i			2.23591i
$996$			8.10051i			0.256675i
$997$	−45.6789			−1.44667			−0.723333	−	0.690499i	$-0.757391\pi$
$997$	−45.6789			−1.44667			−0.723333	+	0.690499i	$0.757391\pi$
$998$	−12.2504			−0.387779
$999$			0.167055i			0.00528539i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3822.2.c.k.883.1		6
7.2	even	3		546.2.bk.b.25.1	✓	12
7.4	even	3		546.2.bk.b.415.6	yes	12
7.6	odd	2		3822.2.c.j.883.3		6
13.12	even	2	inner	3822.2.c.k.883.6		6
21.2	odd	6		1638.2.dm.c.1117.6		12
21.11	odd	6		1638.2.dm.c.415.1		12
91.25	even	6		546.2.bk.b.415.1	yes	12
91.51	even	6		546.2.bk.b.25.6	yes	12
91.90	odd	2		3822.2.c.j.883.4		6
273.116	odd	6		1638.2.dm.c.415.6		12
273.233	odd	6		1638.2.dm.c.1117.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bk.b.25.1	✓	12	7.2	even	3
546.2.bk.b.25.6	yes	12	91.51	even	6
546.2.bk.b.415.1	yes	12	91.25	even	6
546.2.bk.b.415.6	yes	12	7.4	even	3
1638.2.dm.c.415.1		12	21.11	odd	6
1638.2.dm.c.415.6		12	273.116	odd	6
1638.2.dm.c.1117.1		12	273.233	odd	6
1638.2.dm.c.1117.6		12	21.2	odd	6
3822.2.c.j.883.3		6	7.6	odd	2
3822.2.c.j.883.4		6	91.90	odd	2
3822.2.c.k.883.1		6	1.1	even	1	trivial
3822.2.c.k.883.6		6	13.12	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3822.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} -2.60168i q^{5} -1.00000i q^{6} +1.00000i q^{8} +1.00000 q^{9} -2.60168 q^{10} +3.60168i q^{11} -1.00000 q^{12} +(3.60168 - 0.167055i) q^{13} -2.60168i q^{15} +1.00000 q^{16} -2.83294 q^{17} -1.00000i q^{18} +1.33411i q^{19} +2.60168i q^{20} +3.60168 q^{22} +2.93579 q^{23} +1.00000i q^{24} -1.76873 q^{25} +(-0.167055 - 3.60168i) q^{26} +1.00000 q^{27} +8.97209 q^{29} -2.60168 q^{30} -4.00000i q^{31} -1.00000i q^{32} +3.60168i q^{33} +2.83294i q^{34} -1.00000 q^{36} +0.167055i q^{37} +1.33411 q^{38} +(3.60168 - 0.167055i) q^{39} +2.60168 q^{40} -3.03630i q^{41} +2.33411 q^{43} -3.60168i q^{44} -2.60168i q^{45} -2.93579i q^{46} +9.74083i q^{47} +1.00000 q^{48} +1.76873i q^{50} -2.83294 q^{51} +(-3.60168 + 0.167055i) q^{52} +3.00000 q^{53} -1.00000i q^{54} +9.37041 q^{55} +1.33411i q^{57} -8.97209i q^{58} -11.5738i q^{59} +2.60168i q^{60} +4.03630 q^{61} -4.00000 q^{62} -1.00000 q^{64} +(-0.434624 - 9.37041i) q^{65} +3.60168 q^{66} +11.7408i q^{67} +2.83294 q^{68} +2.93579 q^{69} -5.76873i q^{71} +1.00000i q^{72} -11.4709i q^{73} +0.167055 q^{74} -1.76873 q^{75} -1.33411i q^{76} +(-0.167055 - 3.60168i) q^{78} +6.74083 q^{79} -2.60168i q^{80} +1.00000 q^{81} -3.03630 q^{82} -8.10051i q^{83} +7.37041i q^{85} -2.33411i q^{86} +8.97209 q^{87} -3.60168 q^{88} +8.16706i q^{89} -2.60168 q^{90} -2.93579 q^{92} -4.00000i q^{93} +9.74083 q^{94} +3.47093 q^{95} -1.00000i q^{96} +0.139148i q^{97} +3.60168i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{3} - 6 q^{4} + 6 q^{9} - 6 q^{12} + 6 q^{13} + 6 q^{16} - 18 q^{17} + 6 q^{22} + 6 q^{25} + 6 q^{27} + 6 q^{29} - 6 q^{36} + 6 q^{38} + 6 q^{39} + 12 q^{43} + 6 q^{48} - 18 q^{51} - 6 q^{52}+ \cdots - 24 q^{95}+O(q^{100}) \) 6 * q + 6 * q^3 - 6 * q^4 + 6 * q^9 - 6 * q^12 + 6 * q^13 + 6 * q^16 - 18 * q^17 + 6 * q^22 + 6 * q^25 + 6 * q^27 + 6 * q^29 - 6 * q^36 + 6 * q^38 + 6 * q^39 + 12 * q^43 + 6 * q^48 - 18 * q^51 - 6 * q^52 + 18 * q^53 + 24 * q^55 - 6 * q^61 - 24 * q^62 - 6 * q^64 + 12 * q^65 + 6 * q^66 + 18 * q^68 + 6 * q^75 - 24 * q^79 + 6 * q^81 + 12 * q^82 + 6 * q^87 - 6 * q^88 - 6 * q^94 - 24 * q^95

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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