LMFDB - Embedded newform 3822.2.a.bq.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3822,2,Mod(1,3822)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3822, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3822.1");

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.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$30.5188236525$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.41421$ of defining polynomial
Character	$\chi$	$=$	3822.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -3.58579 q^{11} -1.00000 q^{12} +1.00000 q^{13} -1.00000 q^{15} +1.00000 q^{16} +5.24264 q^{17} +1.00000 q^{18} -6.65685 q^{19} +1.00000 q^{20} -3.58579 q^{22} -7.82843 q^{23} -1.00000 q^{24} -4.00000 q^{25} +1.00000 q^{26} -1.00000 q^{27} -9.48528 q^{29} -1.00000 q^{30} +1.41421 q^{31} +1.00000 q^{32} +3.58579 q^{33} +5.24264 q^{34} +1.00000 q^{36} -5.58579 q^{37} -6.65685 q^{38} -1.00000 q^{39} +1.00000 q^{40} +10.8284 q^{41} +2.65685 q^{43} -3.58579 q^{44} +1.00000 q^{45} -7.82843 q^{46} -6.00000 q^{47} -1.00000 q^{48} -4.00000 q^{50} -5.24264 q^{51} +1.00000 q^{52} +5.65685 q^{53} -1.00000 q^{54} -3.58579 q^{55} +6.65685 q^{57} -9.48528 q^{58} -3.07107 q^{59} -1.00000 q^{60} -7.58579 q^{61} +1.41421 q^{62} +1.00000 q^{64} +1.00000 q^{65} +3.58579 q^{66} +15.5563 q^{67} +5.24264 q^{68} +7.82843 q^{69} -14.2426 q^{71} +1.00000 q^{72} -11.0000 q^{73} -5.58579 q^{74} +4.00000 q^{75} -6.65685 q^{76} -1.00000 q^{78} -6.24264 q^{79} +1.00000 q^{80} +1.00000 q^{81} +10.8284 q^{82} -7.65685 q^{83} +5.24264 q^{85} +2.65685 q^{86} +9.48528 q^{87} -3.58579 q^{88} +5.75736 q^{89} +1.00000 q^{90} -7.82843 q^{92} -1.41421 q^{93} -6.00000 q^{94} -6.65685 q^{95} -1.00000 q^{96} +15.3137 q^{97} -3.58579 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{8} + 2 q^{9} + 2 q^{10} - 10 q^{11} - 2 q^{12} + 2 q^{13} - 2 q^{15} + 2 q^{16} + 2 q^{17} + 2 q^{18} - 2 q^{19} + 2 q^{20} - 10 q^{22} - 10 q^{23} - 2 q^{24} - 8 q^{25} + 2 q^{26} - 2 q^{27} - 2 q^{29} - 2 q^{30} + 2 q^{32} + 10 q^{33} + 2 q^{34} + 2 q^{36} - 14 q^{37} - 2 q^{38} - 2 q^{39} + 2 q^{40} + 16 q^{41} - 6 q^{43} - 10 q^{44} + 2 q^{45} - 10 q^{46} - 12 q^{47} - 2 q^{48} - 8 q^{50} - 2 q^{51} + 2 q^{52} - 2 q^{54} - 10 q^{55} + 2 q^{57} - 2 q^{58} + 8 q^{59} - 2 q^{60} - 18 q^{61} + 2 q^{64} + 2 q^{65} + 10 q^{66} + 2 q^{68} + 10 q^{69} - 20 q^{71} + 2 q^{72} - 22 q^{73} - 14 q^{74} + 8 q^{75} - 2 q^{76} - 2 q^{78} - 4 q^{79} + 2 q^{80} + 2 q^{81} + 16 q^{82} - 4 q^{83} + 2 q^{85} - 6 q^{86} + 2 q^{87} - 10 q^{88} + 20 q^{89} + 2 q^{90} - 10 q^{92} - 12 q^{94} - 2 q^{95} - 2 q^{96} + 8 q^{97} - 10 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^8 + 2 * q^9 + 2 * q^10 - 10 * q^11 - 2 * q^12 + 2 * q^13 - 2 * q^15 + 2 * q^16 + 2 * q^17 + 2 * q^18 - 2 * q^19 + 2 * q^20 - 10 * q^22 - 10 * q^23 - 2 * q^24 - 8 * q^25 + 2 * q^26 - 2 * q^27 - 2 * q^29 - 2 * q^30 + 2 * q^32 + 10 * q^33 + 2 * q^34 + 2 * q^36 - 14 * q^37 - 2 * q^38 - 2 * q^39 + 2 * q^40 + 16 * q^41 - 6 * q^43 - 10 * q^44 + 2 * q^45 - 10 * q^46 - 12 * q^47 - 2 * q^48 - 8 * q^50 - 2 * q^51 + 2 * q^52 - 2 * q^54 - 10 * q^55 + 2 * q^57 - 2 * q^58 + 8 * q^59 - 2 * q^60 - 18 * q^61 + 2 * q^64 + 2 * q^65 + 10 * q^66 + 2 * q^68 + 10 * q^69 - 20 * q^71 + 2 * q^72 - 22 * q^73 - 14 * q^74 + 8 * q^75 - 2 * q^76 - 2 * q^78 - 4 * q^79 + 2 * q^80 + 2 * q^81 + 16 * q^82 - 4 * q^83 + 2 * q^85 - 6 * q^86 + 2 * q^87 - 10 * q^88 + 20 * q^89 + 2 * q^90 - 10 * q^92 - 12 * q^94 - 2 * q^95 - 2 * q^96 + 8 * q^97 - 10 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	1.00000	0.447214	0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000	0.447214	0.223607	+	0.974679i	$0.428217\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	−3.58579	−1.08116	−0.540578	−	0.841294i	$-0.681794\pi$
$11$	−3.58579	−1.08116	−0.540578	+	0.841294i	$0.681794\pi$
$12$	−1.00000	−0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0	0
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	5.24264	1.27153	0.635764	−	0.771884i	$-0.280685\pi$
$17$	5.24264	1.27153	0.635764	+	0.771884i	$0.280685\pi$
$18$	1.00000	0.235702
$19$	−6.65685	−1.52719	−0.763594	−	0.645697i	$-0.776567\pi$
$19$	−6.65685	−1.52719	−0.763594	+	0.645697i	$0.776567\pi$
$20$	1.00000	0.223607
$21$	0	0
$22$	−3.58579	−0.764492
$23$	−7.82843	−1.63234	−0.816170	−	0.577812i	$-0.803907\pi$
$23$	−7.82843	−1.63234	−0.816170	+	0.577812i	$0.803907\pi$
$24$	−1.00000	−0.204124
$25$	−4.00000	−0.800000
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−9.48528	−1.76137	−0.880686	−	0.473700i	$-0.842918\pi$
$29$	−9.48528	−1.76137	−0.880686	+	0.473700i	$0.842918\pi$
$30$	−1.00000	−0.182574
$31$	1.41421	0.254000	0.127000	−	0.991903i	$-0.459465\pi$
$31$	1.41421	0.254000	0.127000	+	0.991903i	$0.459465\pi$
$32$	1.00000	0.176777
$33$	3.58579	0.624205
$34$	5.24264	0.899105
$35$	0	0
$36$	1.00000	0.166667
$37$	−5.58579	−0.918298	−0.459149	−	0.888359i	$-0.651846\pi$
$37$	−5.58579	−0.918298	−0.459149	+	0.888359i	$0.651846\pi$
$38$	−6.65685	−1.07988
$39$	−1.00000	−0.160128
$40$	1.00000	0.158114
$41$	10.8284	1.69112	0.845558	−	0.533883i	$-0.179268\pi$
$41$	10.8284	1.69112	0.845558	+	0.533883i	$0.179268\pi$
$42$	0	0
$43$	2.65685	0.405166	0.202583	−	0.979265i	$-0.435066\pi$
$43$	2.65685	0.405166	0.202583	+	0.979265i	$0.435066\pi$
$44$	−3.58579	−0.540578
$45$	1.00000	0.149071
$46$	−7.82843	−1.15424
$47$	−6.00000	−0.875190	−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000	−0.875190	−0.437595	+	0.899172i	$0.644170\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	−4.00000	−0.565685
$51$	−5.24264	−0.734117
$52$	1.00000	0.138675
$53$	5.65685	0.777029	0.388514	−	0.921443i	$-0.372988\pi$
$53$	5.65685	0.777029	0.388514	+	0.921443i	$0.372988\pi$
$54$	−1.00000	−0.136083
$55$	−3.58579	−0.483507
$56$	0	0
$57$	6.65685	0.881722
$58$	−9.48528	−1.24548
$59$	−3.07107	−0.399819	−0.199909	−	0.979814i	$-0.564065\pi$
$59$	−3.07107	−0.399819	−0.199909	+	0.979814i	$0.564065\pi$
$60$	−1.00000	−0.129099
$61$	−7.58579	−0.971260	−0.485630	−	0.874164i	$-0.661410\pi$
$61$	−7.58579	−0.971260	−0.485630	+	0.874164i	$0.661410\pi$
$62$	1.41421	0.179605
$63$	0	0
$64$	1.00000	0.125000
$65$	1.00000	0.124035
$66$	3.58579	0.441380
$67$	15.5563	1.90051	0.950255	−	0.311472i	$-0.100822\pi$
$67$	15.5563	1.90051	0.950255	+	0.311472i	$0.100822\pi$
$68$	5.24264	0.635764
$69$	7.82843	0.942432
$70$	0	0
$71$	−14.2426	−1.69029	−0.845145	−	0.534537i	$-0.820486\pi$
$71$	−14.2426	−1.69029	−0.845145	+	0.534537i	$0.820486\pi$
$72$	1.00000	0.117851
$73$	−11.0000	−1.28745	−0.643726	−	0.765256i	$-0.722612\pi$
$73$	−11.0000	−1.28745	−0.643726	+	0.765256i	$0.722612\pi$
$74$	−5.58579	−0.649334
$75$	4.00000	0.461880
$76$	−6.65685	−0.763594
$77$	0	0
$78$	−1.00000	−0.113228
$79$	−6.24264	−0.702352	−0.351176	−	0.936309i	$-0.614218\pi$
$79$	−6.24264	−0.702352	−0.351176	+	0.936309i	$0.614218\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	10.8284	1.19580
$83$	−7.65685	−0.840449	−0.420224	−	0.907420i	$-0.638049\pi$
$83$	−7.65685	−0.840449	−0.420224	+	0.907420i	$0.638049\pi$
$84$	0	0
$85$	5.24264	0.568644
$86$	2.65685	0.286496
$87$	9.48528	1.01693
$88$	−3.58579	−0.382246
$89$	5.75736	0.610279	0.305139	−	0.952308i	$-0.401297\pi$
$89$	5.75736	0.610279	0.305139	+	0.952308i	$0.401297\pi$
$90$	1.00000	0.105409
$91$	0	0
$92$	−7.82843	−0.816170
$93$	−1.41421	−0.146647
$94$	−6.00000	−0.618853
$95$	−6.65685	−0.682979
$96$	−1.00000	−0.102062
$97$	15.3137	1.55487	0.777436	−	0.628962i	$-0.216520\pi$
$97$	15.3137	1.55487	0.777436	+	0.628962i	$0.216520\pi$
$98$	0	0
$99$	−3.58579	−0.360385
$100$	−4.00000	−0.400000
$101$	15.4142	1.53377	0.766886	−	0.641784i	$-0.221805\pi$
$101$	15.4142	1.53377	0.766886	+	0.641784i	$0.221805\pi$
$102$	−5.24264	−0.519099
$103$	−4.41421	−0.434945	−0.217473	−	0.976066i	$-0.569781\pi$
$103$	−4.41421	−0.434945	−0.217473	+	0.976066i	$0.569781\pi$
$104$	1.00000	0.0980581
$105$	0	0
$106$	5.65685	0.549442
$107$	13.5563	1.31054	0.655271	−	0.755394i	$-0.272554\pi$
$107$	13.5563	1.31054	0.655271	+	0.755394i	$0.272554\pi$
$108$	−1.00000	−0.0962250
$109$	−18.8995	−1.81024	−0.905122	−	0.425153i	$-0.860220\pi$
$109$	−18.8995	−1.81024	−0.905122	+	0.425153i	$0.860220\pi$
$110$	−3.58579	−0.341891
$111$	5.58579	0.530179
$112$	0	0
$113$	7.41421	0.697471	0.348735	−	0.937221i	$-0.386611\pi$
$113$	7.41421	0.697471	0.348735	+	0.937221i	$0.386611\pi$
$114$	6.65685	0.623472
$115$	−7.82843	−0.730005
$116$	−9.48528	−0.880686
$117$	1.00000	0.0924500
$118$	−3.07107	−0.282715
$119$	0	0
$120$	−1.00000	−0.0912871
$121$	1.85786	0.168897
$122$	−7.58579	−0.686785
$123$	−10.8284	−0.976366
$124$	1.41421	0.127000
$125$	−9.00000	−0.804984
$126$	0	0
$127$	−18.7279	−1.66183	−0.830917	−	0.556396i	$-0.812184\pi$
$127$	−18.7279	−1.66183	−0.830917	+	0.556396i	$0.812184\pi$
$128$	1.00000	0.0883883
$129$	−2.65685	−0.233923
$130$	1.00000	0.0877058
$131$	−19.7279	−1.72364	−0.861818	−	0.507217i	$-0.830674\pi$
$131$	−19.7279	−1.72364	−0.861818	+	0.507217i	$0.830674\pi$
$132$	3.58579	0.312103
$133$	0	0
$134$	15.5563	1.34386
$135$	−1.00000	−0.0860663
$136$	5.24264	0.449553
$137$	−3.58579	−0.306354	−0.153177	−	0.988199i	$-0.548951\pi$
$137$	−3.58579	−0.306354	−0.153177	+	0.988199i	$0.548951\pi$
$138$	7.82843	0.666400
$139$	19.7990	1.67933	0.839664	−	0.543106i	$-0.182752\pi$
$139$	19.7990	1.67933	0.839664	+	0.543106i	$0.182752\pi$
$140$	0	0
$141$	6.00000	0.505291
$142$	−14.2426	−1.19522
$143$	−3.58579	−0.299859
$144$	1.00000	0.0833333
$145$	−9.48528	−0.787710
$146$	−11.0000	−0.910366
$147$	0	0
$148$	−5.58579	−0.459149
$149$	−8.48528	−0.695141	−0.347571	−	0.937654i	$-0.612993\pi$
$149$	−8.48528	−0.695141	−0.347571	+	0.937654i	$0.612993\pi$
$150$	4.00000	0.326599
$151$	−3.58579	−0.291807	−0.145904	−	0.989299i	$-0.546609\pi$
$151$	−3.58579	−0.291807	−0.145904	+	0.989299i	$0.546609\pi$
$152$	−6.65685	−0.539942
$153$	5.24264	0.423842
$154$	0	0
$155$	1.41421	0.113592
$156$	−1.00000	−0.0800641
$157$	−5.58579	−0.445794	−0.222897	−	0.974842i	$-0.571551\pi$
$157$	−5.58579	−0.445794	−0.222897	+	0.974842i	$0.571551\pi$
$158$	−6.24264	−0.496638
$159$	−5.65685	−0.448618
$160$	1.00000	0.0790569
$161$	0	0
$162$	1.00000	0.0785674
$163$	−11.6569	−0.913035	−0.456518	−	0.889714i	$-0.650903\pi$
$163$	−11.6569	−0.913035	−0.456518	+	0.889714i	$0.650903\pi$
$164$	10.8284	0.845558
$165$	3.58579	0.279153
$166$	−7.65685	−0.594287
$167$	5.14214	0.397910	0.198955	−	0.980009i	$-0.436245\pi$
$167$	5.14214	0.397910	0.198955	+	0.980009i	$0.436245\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	5.24264	0.402092
$171$	−6.65685	−0.509062
$172$	2.65685	0.202583
$173$	−1.89949	−0.144416	−0.0722080	−	0.997390i	$-0.523005\pi$
$173$	−1.89949	−0.144416	−0.0722080	+	0.997390i	$0.523005\pi$
$174$	9.48528	0.719077
$175$	0	0
$176$	−3.58579	−0.270289
$177$	3.07107	0.230836
$178$	5.75736	0.431532
$179$	−25.8995	−1.93582	−0.967910	−	0.251299i	$-0.919142\pi$
$179$	−25.8995	−1.93582	−0.967910	+	0.251299i	$0.919142\pi$
$180$	1.00000	0.0745356
$181$	−17.1716	−1.27635	−0.638176	−	0.769890i	$-0.720311\pi$
$181$	−17.1716	−1.27635	−0.638176	+	0.769890i	$0.720311\pi$
$182$	0	0
$183$	7.58579	0.560757
$184$	−7.82843	−0.577119
$185$	−5.58579	−0.410675
$186$	−1.41421	−0.103695
$187$	−18.7990	−1.37472
$188$	−6.00000	−0.437595
$189$	0	0
$190$	−6.65685	−0.482939
$191$	11.9706	0.866160	0.433080	−	0.901356i	$-0.357427\pi$
$191$	11.9706	0.866160	0.433080	+	0.901356i	$0.357427\pi$
$192$	−1.00000	−0.0721688
$193$	14.2426	1.02521	0.512604	−	0.858625i	$-0.328681\pi$
$193$	14.2426	1.02521	0.512604	+	0.858625i	$0.328681\pi$
$194$	15.3137	1.09946
$195$	−1.00000	−0.0716115
$196$	0	0
$197$	7.41421	0.528241	0.264120	−	0.964490i	$-0.414918\pi$
$197$	7.41421	0.528241	0.264120	+	0.964490i	$0.414918\pi$
$198$	−3.58579	−0.254831
$199$	−14.5563	−1.03187	−0.515936	−	0.856627i	$-0.672556\pi$
$199$	−14.5563	−1.03187	−0.515936	+	0.856627i	$0.672556\pi$
$200$	−4.00000	−0.282843
$201$	−15.5563	−1.09726
$202$	15.4142	1.08454
$203$	0	0
$204$	−5.24264	−0.367058
$205$	10.8284	0.756290
$206$	−4.41421	−0.307553
$207$	−7.82843	−0.544113
$208$	1.00000	0.0693375
$209$	23.8701	1.65113
$210$	0	0
$211$	1.34315	0.0924660	0.0462330	−	0.998931i	$-0.485278\pi$
$211$	1.34315	0.0924660	0.0462330	+	0.998931i	$0.485278\pi$
$212$	5.65685	0.388514
$213$	14.2426	0.975890
$214$	13.5563	0.926693
$215$	2.65685	0.181196
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	−18.8995	−1.28004
$219$	11.0000	0.743311
$220$	−3.58579	−0.241754
$221$	5.24264	0.352658
$222$	5.58579	0.374893
$223$	14.0000	0.937509	0.468755	−	0.883328i	$-0.344703\pi$
$223$	14.0000	0.937509	0.468755	+	0.883328i	$0.344703\pi$
$224$	0	0
$225$	−4.00000	−0.266667
$226$	7.41421	0.493186
$227$	9.07107	0.602068	0.301034	−	0.953613i	$-0.402668\pi$
$227$	9.07107	0.602068	0.301034	+	0.953613i	$0.402668\pi$
$228$	6.65685	0.440861
$229$	−15.8995	−1.05067	−0.525334	−	0.850896i	$-0.676060\pi$
$229$	−15.8995	−1.05067	−0.525334	+	0.850896i	$0.676060\pi$
$230$	−7.82843	−0.516191
$231$	0	0
$232$	−9.48528	−0.622739
$233$	22.1421	1.45058	0.725290	−	0.688444i	$-0.241706\pi$
$233$	22.1421	1.45058	0.725290	+	0.688444i	$0.241706\pi$
$234$	1.00000	0.0653720
$235$	−6.00000	−0.391397
$236$	−3.07107	−0.199909
$237$	6.24264	0.405503
$238$	0	0
$239$	16.3848	1.05984	0.529922	−	0.848047i	$-0.322221\pi$
$239$	16.3848	1.05984	0.529922	+	0.848047i	$0.322221\pi$
$240$	−1.00000	−0.0645497
$241$	18.9706	1.22200	0.611001	−	0.791630i	$-0.290767\pi$
$241$	18.9706	1.22200	0.611001	+	0.791630i	$0.290767\pi$
$242$	1.85786	0.119428
$243$	−1.00000	−0.0641500
$244$	−7.58579	−0.485630
$245$	0	0
$246$	−10.8284	−0.690395
$247$	−6.65685	−0.423565
$248$	1.41421	0.0898027
$249$	7.65685	0.485233
$250$	−9.00000	−0.569210
$251$	24.5563	1.54998	0.774992	−	0.631972i	$-0.217754\pi$
$251$	24.5563	1.54998	0.774992	+	0.631972i	$0.217754\pi$
$252$	0	0
$253$	28.0711	1.76481
$254$	−18.7279	−1.17509
$255$	−5.24264	−0.328307
$256$	1.00000	0.0625000
$257$	−2.82843	−0.176432	−0.0882162	−	0.996101i	$-0.528117\pi$
$257$	−2.82843	−0.176432	−0.0882162	+	0.996101i	$0.528117\pi$
$258$	−2.65685	−0.165409
$259$	0	0
$260$	1.00000	0.0620174
$261$	−9.48528	−0.587124
$262$	−19.7279	−1.21880
$263$	−18.6274	−1.14862	−0.574308	−	0.818639i	$-0.694729\pi$
$263$	−18.6274	−1.14862	−0.574308	+	0.818639i	$0.694729\pi$
$264$	3.58579	0.220690
$265$	5.65685	0.347498
$266$	0	0
$267$	−5.75736	−0.352345
$268$	15.5563	0.950255
$269$	−29.2132	−1.78116	−0.890580	−	0.454826i	$-0.849701\pi$
$269$	−29.2132	−1.78116	−0.890580	+	0.454826i	$0.849701\pi$
$270$	−1.00000	−0.0608581
$271$	8.38478	0.509339	0.254669	−	0.967028i	$-0.418033\pi$
$271$	8.38478	0.509339	0.254669	+	0.967028i	$0.418033\pi$
$272$	5.24264	0.317882
$273$	0	0
$274$	−3.58579	−0.216625
$275$	14.3431	0.864924
$276$	7.82843	0.471216
$277$	−7.41421	−0.445477	−0.222738	−	0.974878i	$-0.571500\pi$
$277$	−7.41421	−0.445477	−0.222738	+	0.974878i	$0.571500\pi$
$278$	19.7990	1.18746
$279$	1.41421	0.0846668
$280$	0	0
$281$	−6.97056	−0.415829	−0.207914	−	0.978147i	$-0.566668\pi$
$281$	−6.97056	−0.415829	−0.207914	+	0.978147i	$0.566668\pi$
$282$	6.00000	0.357295
$283$	−8.48528	−0.504398	−0.252199	−	0.967675i	$-0.581154\pi$
$283$	−8.48528	−0.504398	−0.252199	+	0.967675i	$0.581154\pi$
$284$	−14.2426	−0.845145
$285$	6.65685	0.394318
$286$	−3.58579	−0.212032
$287$	0	0
$288$	1.00000	0.0589256
$289$	10.4853	0.616781
$290$	−9.48528	−0.556995
$291$	−15.3137	−0.897705
$292$	−11.0000	−0.643726
$293$	−19.7990	−1.15667	−0.578335	−	0.815800i	$-0.696297\pi$
$293$	−19.7990	−1.15667	−0.578335	+	0.815800i	$0.696297\pi$
$294$	0	0
$295$	−3.07107	−0.178804
$296$	−5.58579	−0.324667
$297$	3.58579	0.208068
$298$	−8.48528	−0.491539
$299$	−7.82843	−0.452730
$300$	4.00000	0.230940
$301$	0	0
$302$	−3.58579	−0.206339
$303$	−15.4142	−0.885523
$304$	−6.65685	−0.381797
$305$	−7.58579	−0.434361
$306$	5.24264	0.299702
$307$	1.31371	0.0749773	0.0374887	−	0.999297i	$-0.488064\pi$
$307$	1.31371	0.0749773	0.0374887	+	0.999297i	$0.488064\pi$
$308$	0	0
$309$	4.41421	0.251116
$310$	1.41421	0.0803219
$311$	−7.17157	−0.406663	−0.203331	−	0.979110i	$-0.565177\pi$
$311$	−7.17157	−0.406663	−0.203331	+	0.979110i	$0.565177\pi$
$312$	−1.00000	−0.0566139
$313$	3.89949	0.220412	0.110206	−	0.993909i	$-0.464849\pi$
$313$	3.89949	0.220412	0.110206	+	0.993909i	$0.464849\pi$
$314$	−5.58579	−0.315224
$315$	0	0
$316$	−6.24264	−0.351176
$317$	−12.5858	−0.706888	−0.353444	−	0.935456i	$-0.614990\pi$
$317$	−12.5858	−0.706888	−0.353444	+	0.935456i	$0.614990\pi$
$318$	−5.65685	−0.317221
$319$	34.0122	1.90432
$320$	1.00000	0.0559017
$321$	−13.5563	−0.756642
$322$	0	0
$323$	−34.8995	−1.94186
$324$	1.00000	0.0555556
$325$	−4.00000	−0.221880
$326$	−11.6569	−0.645613
$327$	18.8995	1.04514
$328$	10.8284	0.597900
$329$	0	0
$330$	3.58579	0.197391
$331$	12.2426	0.672916	0.336458	−	0.941698i	$-0.390771\pi$
$331$	12.2426	0.672916	0.336458	+	0.941698i	$0.390771\pi$
$332$	−7.65685	−0.420224
$333$	−5.58579	−0.306099
$334$	5.14214	0.281365
$335$	15.5563	0.849934
$336$	0	0
$337$	−22.1716	−1.20776	−0.603881	−	0.797074i	$-0.706380\pi$
$337$	−22.1716	−1.20776	−0.603881	+	0.797074i	$0.706380\pi$
$338$	1.00000	0.0543928
$339$	−7.41421	−0.402685
$340$	5.24264	0.284322
$341$	−5.07107	−0.274614
$342$	−6.65685	−0.359961
$343$	0	0
$344$	2.65685	0.143248
$345$	7.82843	0.421468
$346$	−1.89949	−0.102117
$347$	−10.5858	−0.568275	−0.284137	−	0.958784i	$-0.591707\pi$
$347$	−10.5858	−0.568275	−0.284137	+	0.958784i	$0.591707\pi$
$348$	9.48528	0.508464
$349$	4.10051	0.219495	0.109748	−	0.993959i	$-0.464996\pi$
$349$	4.10051	0.219495	0.109748	+	0.993959i	$0.464996\pi$
$350$	0	0
$351$	−1.00000	−0.0533761
$352$	−3.58579	−0.191123
$353$	20.8284	1.10859	0.554293	−	0.832322i	$-0.312989\pi$
$353$	20.8284	1.10859	0.554293	+	0.832322i	$0.312989\pi$
$354$	3.07107	0.163225
$355$	−14.2426	−0.755921
$356$	5.75736	0.305139
$357$	0	0
$358$	−25.8995	−1.36883
$359$	22.1421	1.16862	0.584309	−	0.811532i	$-0.301366\pi$
$359$	22.1421	1.16862	0.584309	+	0.811532i	$0.301366\pi$
$360$	1.00000	0.0527046
$361$	25.3137	1.33230
$362$	−17.1716	−0.902518
$363$	−1.85786	−0.0975126
$364$	0	0
$365$	−11.0000	−0.575766
$366$	7.58579	0.396515
$367$	17.6569	0.921680	0.460840	−	0.887483i	$-0.347548\pi$
$367$	17.6569	0.921680	0.460840	+	0.887483i	$0.347548\pi$
$368$	−7.82843	−0.408085
$369$	10.8284	0.563705
$370$	−5.58579	−0.290391
$371$	0	0
$372$	−1.41421	−0.0733236
$373$	−22.8701	−1.18417	−0.592083	−	0.805877i	$-0.701694\pi$
$373$	−22.8701	−1.18417	−0.592083	+	0.805877i	$0.701694\pi$
$374$	−18.7990	−0.972073
$375$	9.00000	0.464758
$376$	−6.00000	−0.309426
$377$	−9.48528	−0.488517
$378$	0	0
$379$	−7.89949	−0.405770	−0.202885	−	0.979203i	$-0.565032\pi$
$379$	−7.89949	−0.405770	−0.202885	+	0.979203i	$0.565032\pi$
$380$	−6.65685	−0.341489
$381$	18.7279	0.959461
$382$	11.9706	0.612467
$383$	−0.313708	−0.0160298	−0.00801488	−	0.999968i	$-0.502551\pi$
$383$	−0.313708	−0.0160298	−0.00801488	+	0.999968i	$0.502551\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	14.2426	0.724931
$387$	2.65685	0.135055
$388$	15.3137	0.777436
$389$	18.3431	0.930034	0.465017	−	0.885302i	$-0.346048\pi$
$389$	18.3431	0.930034	0.465017	+	0.885302i	$0.346048\pi$
$390$	−1.00000	−0.0506370
$391$	−41.0416	−2.07556
$392$	0	0
$393$	19.7279	0.995142
$394$	7.41421	0.373523
$395$	−6.24264	−0.314101
$396$	−3.58579	−0.180193
$397$	0.343146	0.0172220	0.00861100	−	0.999963i	$-0.497259\pi$
$397$	0.343146	0.0172220	0.00861100	+	0.999963i	$0.497259\pi$
$398$	−14.5563	−0.729644
$399$	0	0
$400$	−4.00000	−0.200000
$401$	15.7990	0.788964	0.394482	−	0.918904i	$-0.370924\pi$
$401$	15.7990	0.788964	0.394482	+	0.918904i	$0.370924\pi$
$402$	−15.5563	−0.775880
$403$	1.41421	0.0704470
$404$	15.4142	0.766886
$405$	1.00000	0.0496904
$406$	0	0
$407$	20.0294	0.992822
$408$	−5.24264	−0.259549
$409$	−30.7990	−1.52291	−0.761456	−	0.648217i	$-0.775515\pi$
$409$	−30.7990	−1.52291	−0.761456	+	0.648217i	$0.775515\pi$
$410$	10.8284	0.534778
$411$	3.58579	0.176874
$412$	−4.41421	−0.217473
$413$	0	0
$414$	−7.82843	−0.384746
$415$	−7.65685	−0.375860
$416$	1.00000	0.0490290
$417$	−19.7990	−0.969561
$418$	23.8701	1.16752
$419$	−7.92893	−0.387354	−0.193677	−	0.981065i	$-0.562041\pi$
$419$	−7.92893	−0.387354	−0.193677	+	0.981065i	$0.562041\pi$
$420$	0	0
$421$	15.4558	0.753272	0.376636	−	0.926361i	$-0.377081\pi$
$421$	15.4558	0.753272	0.376636	+	0.926361i	$0.377081\pi$
$422$	1.34315	0.0653833
$423$	−6.00000	−0.291730
$424$	5.65685	0.274721
$425$	−20.9706	−1.01722
$426$	14.2426	0.690058
$427$	0	0
$428$	13.5563	0.655271
$429$	3.58579	0.173123
$430$	2.65685	0.128125
$431$	30.4853	1.46842	0.734212	−	0.678920i	$-0.237552\pi$
$431$	30.4853	1.46842	0.734212	+	0.678920i	$0.237552\pi$
$432$	−1.00000	−0.0481125
$433$	0	0		−	1.00000i	$-0.5\pi$
$433$	0	0			1.00000i	$0.5\pi$
$434$	0	0
$435$	9.48528	0.454784
$436$	−18.8995	−0.905122
$437$	52.1127	2.49289
$438$	11.0000	0.525600
$439$	−12.0711	−0.576121	−0.288060	−	0.957612i	$-0.593010\pi$
$439$	−12.0711	−0.576121	−0.288060	+	0.957612i	$0.593010\pi$
$440$	−3.58579	−0.170946
$441$	0	0
$442$	5.24264	0.249367
$443$	29.7990	1.41579	0.707896	−	0.706316i	$-0.249644\pi$
$443$	29.7990	1.41579	0.707896	+	0.706316i	$0.249644\pi$
$444$	5.58579	0.265090
$445$	5.75736	0.272925
$446$	14.0000	0.662919
$447$	8.48528	0.401340
$448$	0	0
$449$	−27.0416	−1.27617	−0.638087	−	0.769965i	$-0.720274\pi$
$449$	−27.0416	−1.27617	−0.638087	+	0.769965i	$0.720274\pi$
$450$	−4.00000	−0.188562
$451$	−38.8284	−1.82836
$452$	7.41421	0.348735
$453$	3.58579	0.168475
$454$	9.07107	0.425726
$455$	0	0
$456$	6.65685	0.311736
$457$	−19.6985	−0.921456	−0.460728	−	0.887541i	$-0.652412\pi$
$457$	−19.6985	−0.921456	−0.460728	+	0.887541i	$0.652412\pi$
$458$	−15.8995	−0.742935
$459$	−5.24264	−0.244706
$460$	−7.82843	−0.365002
$461$	16.5147	0.769167	0.384584	−	0.923090i	$-0.374345\pi$
$461$	16.5147	0.769167	0.384584	+	0.923090i	$0.374345\pi$
$462$	0	0
$463$	9.92893	0.461437	0.230718	−	0.973021i	$-0.425892\pi$
$463$	9.92893	0.461437	0.230718	+	0.973021i	$0.425892\pi$
$464$	−9.48528	−0.440343
$465$	−1.41421	−0.0655826
$466$	22.1421	1.02571
$467$	−7.58579	−0.351028	−0.175514	−	0.984477i	$-0.556159\pi$
$467$	−7.58579	−0.351028	−0.175514	+	0.984477i	$0.556159\pi$
$468$	1.00000	0.0462250
$469$	0	0
$470$	−6.00000	−0.276759
$471$	5.58579	0.257379
$472$	−3.07107	−0.141357
$473$	−9.52691	−0.438048
$474$	6.24264	0.286734
$475$	26.6274	1.22175
$476$	0	0
$477$	5.65685	0.259010
$478$	16.3848	0.749422
$479$	4.85786	0.221961	0.110981	−	0.993823i	$-0.464601\pi$
$479$	4.85786	0.221961	0.110981	+	0.993823i	$0.464601\pi$
$480$	−1.00000	−0.0456435
$481$	−5.58579	−0.254690
$482$	18.9706	0.864085
$483$	0	0
$484$	1.85786	0.0844484
$485$	15.3137	0.695360
$486$	−1.00000	−0.0453609
$487$	19.6569	0.890737	0.445369	−	0.895347i	$-0.353073\pi$
$487$	19.6569	0.890737	0.445369	+	0.895347i	$0.353073\pi$
$488$	−7.58579	−0.343392
$489$	11.6569	0.527141
$490$	0	0
$491$	19.1716	0.865201	0.432600	−	0.901586i	$-0.357596\pi$
$491$	19.1716	0.865201	0.432600	+	0.901586i	$0.357596\pi$
$492$	−10.8284	−0.488183
$493$	−49.7279	−2.23963
$494$	−6.65685	−0.299506
$495$	−3.58579	−0.161169
$496$	1.41421	0.0635001
$497$	0	0
$498$	7.65685	0.343112
$499$	−26.0416	−1.16578	−0.582892	−	0.812550i	$-0.698079\pi$
$499$	−26.0416	−1.16578	−0.582892	+	0.812550i	$0.698079\pi$
$500$	−9.00000	−0.402492
$501$	−5.14214	−0.229734
$502$	24.5563	1.09600
$503$	14.3848	0.641385	0.320693	−	0.947183i	$-0.396084\pi$
$503$	14.3848	0.641385	0.320693	+	0.947183i	$0.396084\pi$
$504$	0	0
$505$	15.4142	0.685924
$506$	28.0711	1.24791
$507$	−1.00000	−0.0444116
$508$	−18.7279	−0.830917
$509$	20.7990	0.921899	0.460950	−	0.887426i	$-0.347509\pi$
$509$	20.7990	0.921899	0.460950	+	0.887426i	$0.347509\pi$
$510$	−5.24264	−0.232148
$511$	0	0
$512$	1.00000	0.0441942
$513$	6.65685	0.293907
$514$	−2.82843	−0.124757
$515$	−4.41421	−0.194513
$516$	−2.65685	−0.116961
$517$	21.5147	0.946216
$518$	0	0
$519$	1.89949	0.0833786
$520$	1.00000	0.0438529
$521$	0.757359	0.0331805	0.0165903	−	0.999862i	$-0.494719\pi$
$521$	0.757359	0.0331805	0.0165903	+	0.999862i	$0.494719\pi$
$522$	−9.48528	−0.415159
$523$	−22.2426	−0.972603	−0.486301	−	0.873791i	$-0.661654\pi$
$523$	−22.2426	−0.972603	−0.486301	+	0.873791i	$0.661654\pi$
$524$	−19.7279	−0.861818
$525$	0	0
$526$	−18.6274	−0.812194
$527$	7.41421	0.322968
$528$	3.58579	0.156051
$529$	38.2843	1.66453
$530$	5.65685	0.245718
$531$	−3.07107	−0.133273
$532$	0	0
$533$	10.8284	0.469031
$534$	−5.75736	−0.249145
$535$	13.5563	0.586092
$536$	15.5563	0.671932
$537$	25.8995	1.11765
$538$	−29.2132	−1.25947
$539$	0	0
$540$	−1.00000	−0.0430331
$541$	−25.3848	−1.09138	−0.545688	−	0.837988i	$-0.683732\pi$
$541$	−25.3848	−1.09138	−0.545688	+	0.837988i	$0.683732\pi$
$542$	8.38478	0.360157
$543$	17.1716	0.736903
$544$	5.24264	0.224776
$545$	−18.8995	−0.809565
$546$	0	0
$547$	34.4853	1.47448	0.737242	−	0.675629i	$-0.236128\pi$
$547$	34.4853	1.47448	0.737242	+	0.675629i	$0.236128\pi$
$548$	−3.58579	−0.153177
$549$	−7.58579	−0.323753
$550$	14.3431	0.611594
$551$	63.1421	2.68995
$552$	7.82843	0.333200
$553$	0	0
$554$	−7.41421	−0.315000
$555$	5.58579	0.237103
$556$	19.7990	0.839664
$557$	−11.5147	−0.487894	−0.243947	−	0.969789i	$-0.578442\pi$
$557$	−11.5147	−0.487894	−0.243947	+	0.969789i	$0.578442\pi$
$558$	1.41421	0.0598684
$559$	2.65685	0.112373
$560$	0	0
$561$	18.7990	0.793694
$562$	−6.97056	−0.294035
$563$	14.7574	0.621949	0.310974	−	0.950418i	$-0.399345\pi$
$563$	14.7574	0.621949	0.310974	+	0.950418i	$0.399345\pi$
$564$	6.00000	0.252646
$565$	7.41421	0.311918
$566$	−8.48528	−0.356663
$567$	0	0
$568$	−14.2426	−0.597608
$569$	29.7990	1.24924	0.624619	−	0.780929i	$-0.285254\pi$
$569$	29.7990	1.24924	0.624619	+	0.780929i	$0.285254\pi$
$570$	6.65685	0.278825
$571$	0.627417	0.0262566	0.0131283	−	0.999914i	$-0.495821\pi$
$571$	0.627417	0.0262566	0.0131283	+	0.999914i	$0.495821\pi$
$572$	−3.58579	−0.149929
$573$	−11.9706	−0.500077
$574$	0	0
$575$	31.3137	1.30587
$576$	1.00000	0.0416667
$577$	22.1421	0.921789	0.460895	−	0.887455i	$-0.347529\pi$
$577$	22.1421	0.921789	0.460895	+	0.887455i	$0.347529\pi$
$578$	10.4853	0.436130
$579$	−14.2426	−0.591904
$580$	−9.48528	−0.393855
$581$	0	0
$582$	−15.3137	−0.634774
$583$	−20.2843	−0.840089
$584$	−11.0000	−0.455183
$585$	1.00000	0.0413449
$586$	−19.7990	−0.817889
$587$	−3.17157	−0.130905	−0.0654524	−	0.997856i	$-0.520849\pi$
$587$	−3.17157	−0.130905	−0.0654524	+	0.997856i	$0.520849\pi$
$588$	0	0
$589$	−9.41421	−0.387906
$590$	−3.07107	−0.126434
$591$	−7.41421	−0.304980
$592$	−5.58579	−0.229574
$593$	3.89949	0.160133	0.0800665	−	0.996790i	$-0.474487\pi$
$593$	3.89949	0.160133	0.0800665	+	0.996790i	$0.474487\pi$
$594$	3.58579	0.147127
$595$	0	0
$596$	−8.48528	−0.347571
$597$	14.5563	0.595752
$598$	−7.82843	−0.320128
$599$	−24.3137	−0.993431	−0.496716	−	0.867913i	$-0.665461\pi$
$599$	−24.3137	−0.993431	−0.496716	+	0.867913i	$0.665461\pi$
$600$	4.00000	0.163299
$601$	−41.4558	−1.69102	−0.845510	−	0.533960i	$-0.820703\pi$
$601$	−41.4558	−1.69102	−0.845510	+	0.533960i	$0.820703\pi$
$602$	0	0
$603$	15.5563	0.633504
$604$	−3.58579	−0.145904
$605$	1.85786	0.0755329
$606$	−15.4142	−0.626160
$607$	−5.72792	−0.232489	−0.116245	−	0.993221i	$-0.537086\pi$
$607$	−5.72792	−0.232489	−0.116245	+	0.993221i	$0.537086\pi$
$608$	−6.65685	−0.269971
$609$	0	0
$610$	−7.58579	−0.307140
$611$	−6.00000	−0.242734
$612$	5.24264	0.211921
$613$	−27.8701	−1.12566	−0.562831	−	0.826572i	$-0.690288\pi$
$613$	−27.8701	−1.12566	−0.562831	+	0.826572i	$0.690288\pi$
$614$	1.31371	0.0530170
$615$	−10.8284	−0.436644
$616$	0	0
$617$	6.75736	0.272041	0.136021	−	0.990706i	$-0.456569\pi$
$617$	6.75736	0.272041	0.136021	+	0.990706i	$0.456569\pi$
$618$	4.41421	0.177566
$619$	20.1716	0.810764	0.405382	−	0.914147i	$-0.367139\pi$
$619$	20.1716	0.810764	0.405382	+	0.914147i	$0.367139\pi$
$620$	1.41421	0.0567962
$621$	7.82843	0.314144
$622$	−7.17157	−0.287554
$623$	0	0
$624$	−1.00000	−0.0400320
$625$	11.0000	0.440000
$626$	3.89949	0.155855
$627$	−23.8701	−0.953278
$628$	−5.58579	−0.222897
$629$	−29.2843	−1.16764
$630$	0	0
$631$	−41.0416	−1.63384	−0.816921	−	0.576750i	$-0.804321\pi$
$631$	−41.0416	−1.63384	−0.816921	+	0.576750i	$0.804321\pi$
$632$	−6.24264	−0.248319
$633$	−1.34315	−0.0533853
$634$	−12.5858	−0.499845
$635$	−18.7279	−0.743195
$636$	−5.65685	−0.224309
$637$	0	0
$638$	34.0122	1.34656
$639$	−14.2426	−0.563430
$640$	1.00000	0.0395285
$641$	9.75736	0.385393	0.192696	−	0.981258i	$-0.438277\pi$
$641$	9.75736	0.385393	0.192696	+	0.981258i	$0.438277\pi$
$642$	−13.5563	−0.535026
$643$	28.1127	1.10866	0.554328	−	0.832298i	$-0.312975\pi$
$643$	28.1127	1.10866	0.554328	+	0.832298i	$0.312975\pi$
$644$	0	0
$645$	−2.65685	−0.104614
$646$	−34.8995	−1.37310
$647$	39.3137	1.54558	0.772791	−	0.634661i	$-0.218860\pi$
$647$	39.3137	1.54558	0.772791	+	0.634661i	$0.218860\pi$
$648$	1.00000	0.0392837
$649$	11.0122	0.432266
$650$	−4.00000	−0.156893
$651$	0	0
$652$	−11.6569	−0.456518
$653$	17.0000	0.665261	0.332631	−	0.943057i	$-0.392064\pi$
$653$	17.0000	0.665261	0.332631	+	0.943057i	$0.392064\pi$
$654$	18.8995	0.739029
$655$	−19.7279	−0.770834
$656$	10.8284	0.422779
$657$	−11.0000	−0.429151
$658$	0	0
$659$	−6.20101	−0.241557	−0.120779	−	0.992679i	$-0.538539\pi$
$659$	−6.20101	−0.241557	−0.120779	+	0.992679i	$0.538539\pi$
$660$	3.58579	0.139577
$661$	−11.6569	−0.453399	−0.226700	−	0.973965i	$-0.572794\pi$
$661$	−11.6569	−0.453399	−0.226700	+	0.973965i	$0.572794\pi$
$662$	12.2426	0.475824
$663$	−5.24264	−0.203607
$664$	−7.65685	−0.297144
$665$	0	0
$666$	−5.58579	−0.216445
$667$	74.2548	2.87516
$668$	5.14214	0.198955
$669$	−14.0000	−0.541271
$670$	15.5563	0.600994
$671$	27.2010	1.05008
$672$	0	0
$673$	−9.48528	−0.365631	−0.182815	−	0.983147i	$-0.558521\pi$
$673$	−9.48528	−0.365631	−0.182815	+	0.983147i	$0.558521\pi$
$674$	−22.1716	−0.854017
$675$	4.00000	0.153960
$676$	1.00000	0.0384615
$677$	26.4853	1.01791	0.508956	−	0.860793i	$-0.330032\pi$
$677$	26.4853	1.01791	0.508956	+	0.860793i	$0.330032\pi$
$678$	−7.41421	−0.284741
$679$	0	0
$680$	5.24264	0.201046
$681$	−9.07107	−0.347604
$682$	−5.07107	−0.194181
$683$	7.24264	0.277132	0.138566	−	0.990353i	$-0.455751\pi$
$683$	7.24264	0.277132	0.138566	+	0.990353i	$0.455751\pi$
$684$	−6.65685	−0.254531
$685$	−3.58579	−0.137006
$686$	0	0
$687$	15.8995	0.606604
$688$	2.65685	0.101292
$689$	5.65685	0.215509
$690$	7.82843	0.298023
$691$	−4.14214	−0.157574	−0.0787871	−	0.996891i	$-0.525105\pi$
$691$	−4.14214	−0.157574	−0.0787871	+	0.996891i	$0.525105\pi$
$692$	−1.89949	−0.0722080
$693$	0	0
$694$	−10.5858	−0.401831
$695$	19.7990	0.751018
$696$	9.48528	0.359539
$697$	56.7696	2.15030
$698$	4.10051	0.155206
$699$	−22.1421	−0.837492
$700$	0	0
$701$	48.4853	1.83126	0.915632	−	0.402018i	$-0.131691\pi$
$701$	48.4853	1.83126	0.915632	+	0.402018i	$0.131691\pi$
$702$	−1.00000	−0.0377426
$703$	37.1838	1.40241
$704$	−3.58579	−0.135144
$705$	6.00000	0.225973
$706$	20.8284	0.783888
$707$	0	0
$708$	3.07107	0.115418
$709$	−19.8579	−0.745778	−0.372889	−	0.927876i	$-0.621633\pi$
$709$	−19.8579	−0.745778	−0.372889	+	0.927876i	$0.621633\pi$
$710$	−14.2426	−0.534517
$711$	−6.24264	−0.234117
$712$	5.75736	0.215766
$713$	−11.0711	−0.414615
$714$	0	0
$715$	−3.58579	−0.134101
$716$	−25.8995	−0.967910
$717$	−16.3848	−0.611901
$718$	22.1421	0.826337
$719$	−38.8701	−1.44961	−0.724804	−	0.688955i	$-0.758070\pi$
$719$	−38.8701	−1.44961	−0.724804	+	0.688955i	$0.758070\pi$
$720$	1.00000	0.0372678
$721$	0	0
$722$	25.3137	0.942079
$723$	−18.9706	−0.705523
$724$	−17.1716	−0.638176
$725$	37.9411	1.40910
$726$	−1.85786	−0.0689518
$727$	−11.8701	−0.440236	−0.220118	−	0.975473i	$-0.570644\pi$
$727$	−11.8701	−0.440236	−0.220118	+	0.975473i	$0.570644\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−11.0000	−0.407128
$731$	13.9289	0.515180
$732$	7.58579	0.280379
$733$	39.5563	1.46105	0.730524	−	0.682888i	$-0.239276\pi$
$733$	39.5563	1.46105	0.730524	+	0.682888i	$0.239276\pi$
$734$	17.6569	0.651726
$735$	0	0
$736$	−7.82843	−0.288560
$737$	−55.7817	−2.05475
$738$	10.8284	0.398600
$739$	19.6569	0.723089	0.361545	−	0.932355i	$-0.382250\pi$
$739$	19.6569	0.723089	0.361545	+	0.932355i	$0.382250\pi$
$740$	−5.58579	−0.205338
$741$	6.65685	0.244546
$742$	0	0
$743$	−22.2843	−0.817531	−0.408765	−	0.912640i	$-0.634041\pi$
$743$	−22.2843	−0.817531	−0.408765	+	0.912640i	$0.634041\pi$
$744$	−1.41421	−0.0518476
$745$	−8.48528	−0.310877
$746$	−22.8701	−0.837332
$747$	−7.65685	−0.280150
$748$	−18.7990	−0.687359
$749$	0	0
$750$	9.00000	0.328634
$751$	21.2132	0.774081	0.387040	−	0.922063i	$-0.373497\pi$
$751$	21.2132	0.774081	0.387040	+	0.922063i	$0.373497\pi$
$752$	−6.00000	−0.218797
$753$	−24.5563	−0.894883
$754$	−9.48528	−0.345434
$755$	−3.58579	−0.130500
$756$	0	0
$757$	−5.27208	−0.191617	−0.0958085	−	0.995400i	$-0.530544\pi$
$757$	−5.27208	−0.191617	−0.0958085	+	0.995400i	$0.530544\pi$
$758$	−7.89949	−0.286923
$759$	−28.0711	−1.01892
$760$	−6.65685	−0.241469
$761$	52.0833	1.88802	0.944008	−	0.329922i	$-0.107022\pi$
$761$	52.0833	1.88802	0.944008	+	0.329922i	$0.107022\pi$
$762$	18.7279	0.678441
$763$	0	0
$764$	11.9706	0.433080
$765$	5.24264	0.189548
$766$	−0.313708	−0.0113347
$767$	−3.07107	−0.110890
$768$	−1.00000	−0.0360844
$769$	−38.9411	−1.40425	−0.702126	−	0.712052i	$-0.747766\pi$
$769$	−38.9411	−1.40425	−0.702126	+	0.712052i	$0.747766\pi$
$770$	0	0
$771$	2.82843	0.101863
$772$	14.2426	0.512604
$773$	36.2548	1.30400	0.651998	−	0.758221i	$-0.273931\pi$
$773$	36.2548	1.30400	0.651998	+	0.758221i	$0.273931\pi$
$774$	2.65685	0.0954987
$775$	−5.65685	−0.203200
$776$	15.3137	0.549730
$777$	0	0
$778$	18.3431	0.657634
$779$	−72.0833	−2.58265
$780$	−1.00000	−0.0358057
$781$	51.0711	1.82747
$782$	−41.0416	−1.46765
$783$	9.48528	0.338976
$784$	0	0
$785$	−5.58579	−0.199365
$786$	19.7279	0.703672
$787$	−19.9706	−0.711874	−0.355937	−	0.934510i	$-0.615838\pi$
$787$	−19.9706	−0.711874	−0.355937	+	0.934510i	$0.615838\pi$
$788$	7.41421	0.264120
$789$	18.6274	0.663154
$790$	−6.24264	−0.222103
$791$	0	0
$792$	−3.58579	−0.127415
$793$	−7.58579	−0.269379
$794$	0.343146	0.0121778
$795$	−5.65685	−0.200628
$796$	−14.5563	−0.515936
$797$	2.24264	0.0794384	0.0397192	−	0.999211i	$-0.487354\pi$
$797$	2.24264	0.0794384	0.0397192	+	0.999211i	$0.487354\pi$
$798$	0	0
$799$	−31.4558	−1.11283
$800$	−4.00000	−0.141421
$801$	5.75736	0.203426
$802$	15.7990	0.557882
$803$	39.4437	1.39194
$804$	−15.5563	−0.548630
$805$	0	0
$806$	1.41421	0.0498135
$807$	29.2132	1.02835
$808$	15.4142	0.542270
$809$	16.1005	0.566064	0.283032	−	0.959111i	$-0.408660\pi$
$809$	16.1005	0.566064	0.283032	+	0.959111i	$0.408660\pi$
$810$	1.00000	0.0351364
$811$	10.1716	0.357172	0.178586	−	0.983924i	$-0.442848\pi$
$811$	10.1716	0.357172	0.178586	+	0.983924i	$0.442848\pi$
$812$	0	0
$813$	−8.38478	−0.294067
$814$	20.0294	0.702031
$815$	−11.6569	−0.408322
$816$	−5.24264	−0.183529
$817$	−17.6863	−0.618765
$818$	−30.7990	−1.07686
$819$	0	0
$820$	10.8284	0.378145
$821$	15.7990	0.551389	0.275694	−	0.961245i	$-0.411092\pi$
$821$	15.7990	0.551389	0.275694	+	0.961245i	$0.411092\pi$
$822$	3.58579	0.125069
$823$	−24.0416	−0.838039	−0.419019	−	0.907977i	$-0.637626\pi$
$823$	−24.0416	−0.838039	−0.419019	+	0.907977i	$0.637626\pi$
$824$	−4.41421	−0.153776
$825$	−14.3431	−0.499364
$826$	0	0
$827$	−33.3848	−1.16090	−0.580451	−	0.814295i	$-0.697124\pi$
$827$	−33.3848	−1.16090	−0.580451	+	0.814295i	$0.697124\pi$
$828$	−7.82843	−0.272057
$829$	45.3848	1.57628	0.788139	−	0.615497i	$-0.211045\pi$
$829$	45.3848	1.57628	0.788139	+	0.615497i	$0.211045\pi$
$830$	−7.65685	−0.265773
$831$	7.41421	0.257196
$832$	1.00000	0.0346688
$833$	0	0
$834$	−19.7990	−0.685583
$835$	5.14214	0.177951
$836$	23.8701	0.825563
$837$	−1.41421	−0.0488824
$838$	−7.92893	−0.273900
$839$	5.02944	0.173635	0.0868177	−	0.996224i	$-0.472330\pi$
$839$	5.02944	0.173635	0.0868177	+	0.996224i	$0.472330\pi$
$840$	0	0
$841$	60.9706	2.10243
$842$	15.4558	0.532644
$843$	6.97056	0.240079
$844$	1.34315	0.0462330
$845$	1.00000	0.0344010
$846$	−6.00000	−0.206284
$847$	0	0
$848$	5.65685	0.194257
$849$	8.48528	0.291214
$850$	−20.9706	−0.719284
$851$	43.7279	1.49897
$852$	14.2426	0.487945
$853$	19.0294	0.651556	0.325778	−	0.945446i	$-0.394374\pi$
$853$	19.0294	0.651556	0.325778	+	0.945446i	$0.394374\pi$
$854$	0	0
$855$	−6.65685	−0.227660
$856$	13.5563	0.463346
$857$	−13.5147	−0.461654	−0.230827	−	0.972995i	$-0.574143\pi$
$857$	−13.5147	−0.461654	−0.230827	+	0.972995i	$0.574143\pi$
$858$	3.58579	0.122417
$859$	−20.0000	−0.682391	−0.341196	−	0.939992i	$-0.610832\pi$
$859$	−20.0000	−0.682391	−0.341196	+	0.939992i	$0.610832\pi$
$860$	2.65685	0.0905980
$861$	0	0
$862$	30.4853	1.03833
$863$	−18.0000	−0.612727	−0.306364	−	0.951915i	$-0.599112\pi$
$863$	−18.0000	−0.612727	−0.306364	+	0.951915i	$0.599112\pi$
$864$	−1.00000	−0.0340207
$865$	−1.89949	−0.0645848
$866$	0	0
$867$	−10.4853	−0.356099
$868$	0	0
$869$	22.3848	0.759352
$870$	9.48528	0.321581
$871$	15.5563	0.527107
$872$	−18.8995	−0.640018
$873$	15.3137	0.518291
$874$	52.1127	1.76274
$875$	0	0
$876$	11.0000	0.371656
$877$	−8.48528	−0.286528	−0.143264	−	0.989685i	$-0.545760\pi$
$877$	−8.48528	−0.286528	−0.143264	+	0.989685i	$0.545760\pi$
$878$	−12.0711	−0.407379
$879$	19.7990	0.667803
$880$	−3.58579	−0.120877
$881$	28.2721	0.952511	0.476255	−	0.879307i	$-0.341994\pi$
$881$	28.2721	0.952511	0.476255	+	0.879307i	$0.341994\pi$
$882$	0	0
$883$	34.5980	1.16431	0.582157	−	0.813076i	$-0.302209\pi$
$883$	34.5980	1.16431	0.582157	+	0.813076i	$0.302209\pi$
$884$	5.24264	0.176329
$885$	3.07107	0.103233
$886$	29.7990	1.00112
$887$	−2.82843	−0.0949693	−0.0474846	−	0.998872i	$-0.515121\pi$
$887$	−2.82843	−0.0949693	−0.0474846	+	0.998872i	$0.515121\pi$
$888$	5.58579	0.187447
$889$	0	0
$890$	5.75736	0.192987
$891$	−3.58579	−0.120128
$892$	14.0000	0.468755
$893$	39.9411	1.33658
$894$	8.48528	0.283790
$895$	−25.8995	−0.865725
$896$	0	0
$897$	7.82843	0.261384
$898$	−27.0416	−0.902391
$899$	−13.4142	−0.447389
$900$	−4.00000	−0.133333
$901$	29.6569	0.988013
$902$	−38.8284	−1.29285
$903$	0	0
$904$	7.41421	0.246593
$905$	−17.1716	−0.570802
$906$	3.58579	0.119130
$907$	−34.4853	−1.14506	−0.572532	−	0.819882i	$-0.694039\pi$
$907$	−34.4853	−1.14506	−0.572532	+	0.819882i	$0.694039\pi$
$908$	9.07107	0.301034
$909$	15.4142	0.511257
$910$	0	0
$911$	−36.1716	−1.19842	−0.599209	−	0.800593i	$-0.704518\pi$
$911$	−36.1716	−1.19842	−0.599209	+	0.800593i	$0.704518\pi$
$912$	6.65685	0.220430
$913$	27.4558	0.908656
$914$	−19.6985	−0.651568
$915$	7.58579	0.250778
$916$	−15.8995	−0.525334
$917$	0	0
$918$	−5.24264	−0.173033
$919$	33.5147	1.10555	0.552774	−	0.833331i	$-0.313569\pi$
$919$	33.5147	1.10555	0.552774	+	0.833331i	$0.313569\pi$
$920$	−7.82843	−0.258096
$921$	−1.31371	−0.0432882
$922$	16.5147	0.543883
$923$	−14.2426	−0.468802
$924$	0	0
$925$	22.3431	0.734638
$926$	9.92893	0.326285
$927$	−4.41421	−0.144982
$928$	−9.48528	−0.311370
$929$	−30.8284	−1.01145	−0.505724	−	0.862695i	$-0.668775\pi$
$929$	−30.8284	−1.01145	−0.505724	+	0.862695i	$0.668775\pi$
$930$	−1.41421	−0.0463739
$931$	0	0
$932$	22.1421	0.725290
$933$	7.17157	0.234787
$934$	−7.58579	−0.248215
$935$	−18.7990	−0.614793
$936$	1.00000	0.0326860
$937$	−25.2132	−0.823679	−0.411840	−	0.911256i	$-0.635114\pi$
$937$	−25.2132	−0.823679	−0.411840	+	0.911256i	$0.635114\pi$
$938$	0	0
$939$	−3.89949	−0.127255
$940$	−6.00000	−0.195698
$941$	55.9411	1.82363	0.911814	−	0.410603i	$-0.134682\pi$
$941$	55.9411	1.82363	0.911814	+	0.410603i	$0.134682\pi$
$942$	5.58579	0.181995
$943$	−84.7696	−2.76048
$944$	−3.07107	−0.0999547
$945$	0	0
$946$	−9.52691	−0.309747
$947$	−17.7279	−0.576080	−0.288040	−	0.957618i	$-0.593004\pi$
$947$	−17.7279	−0.576080	−0.288040	+	0.957618i	$0.593004\pi$
$948$	6.24264	0.202752
$949$	−11.0000	−0.357075
$950$	26.6274	0.863907
$951$	12.5858	0.408122
$952$	0	0
$953$	33.9411	1.09946	0.549730	−	0.835342i	$-0.314730\pi$
$953$	33.9411	1.09946	0.549730	+	0.835342i	$0.314730\pi$
$954$	5.65685	0.183147
$955$	11.9706	0.387358
$956$	16.3848	0.529922
$957$	−34.0122	−1.09946
$958$	4.85786	0.156950
$959$	0	0
$960$	−1.00000	−0.0322749
$961$	−29.0000	−0.935484
$962$	−5.58579	−0.180093
$963$	13.5563	0.436847
$964$	18.9706	0.611001
$965$	14.2426	0.458487
$966$	0	0
$967$	42.4142	1.36395	0.681975	−	0.731376i	$-0.261121\pi$
$967$	42.4142	1.36395	0.681975	+	0.731376i	$0.261121\pi$
$968$	1.85786	0.0597140
$969$	34.8995	1.12113
$970$	15.3137	0.491694
$971$	27.7990	0.892112	0.446056	−	0.895005i	$-0.352828\pi$
$971$	27.7990	0.892112	0.446056	+	0.895005i	$0.352828\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	19.6569	0.629846
$975$	4.00000	0.128103
$976$	−7.58579	−0.242815
$977$	25.7279	0.823109	0.411555	−	0.911385i	$-0.364986\pi$
$977$	25.7279	0.823109	0.411555	+	0.911385i	$0.364986\pi$
$978$	11.6569	0.372745
$979$	−20.6447	−0.659806
$980$	0	0
$981$	−18.8995	−0.603414
$982$	19.1716	0.611789
$983$	33.6274	1.07255	0.536274	−	0.844044i	$-0.319831\pi$
$983$	33.6274	1.07255	0.536274	+	0.844044i	$0.319831\pi$
$984$	−10.8284	−0.345198
$985$	7.41421	0.236236
$986$	−49.7279	−1.58366
$987$	0	0
$988$	−6.65685	−0.211783
$989$	−20.7990	−0.661369
$990$	−3.58579	−0.113964
$991$	−8.34315	−0.265029	−0.132514	−	0.991181i	$-0.542305\pi$
$991$	−8.34315	−0.265029	−0.132514	+	0.991181i	$0.542305\pi$
$992$	1.41421	0.0449013
$993$	−12.2426	−0.388508
$994$	0	0
$995$	−14.5563	−0.461467
$996$	7.65685	0.242617
$997$	43.2548	1.36989	0.684947	−	0.728593i	$-0.259825\pi$
$997$	43.2548	1.36989	0.684947	+	0.728593i	$0.259825\pi$
$998$	−26.0416	−0.824333
$999$	5.58579	0.176726

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3822.2.a.bq.1.2	✓	2
7.6	odd	2		3822.2.a.br.1.2	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3822.2.a.bq.1.2	✓	2	1.1	even	1	trivial
3822.2.a.br.1.2	yes	2	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3822.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -3.58579 q^{11} -1.00000 q^{12} +1.00000 q^{13} -1.00000 q^{15} +1.00000 q^{16} +5.24264 q^{17} +1.00000 q^{18} -6.65685 q^{19} +1.00000 q^{20} -3.58579 q^{22} -7.82843 q^{23} -1.00000 q^{24} -4.00000 q^{25} +1.00000 q^{26} -1.00000 q^{27} -9.48528 q^{29} -1.00000 q^{30} +1.41421 q^{31} +1.00000 q^{32} +3.58579 q^{33} +5.24264 q^{34} +1.00000 q^{36} -5.58579 q^{37} -6.65685 q^{38} -1.00000 q^{39} +1.00000 q^{40} +10.8284 q^{41} +2.65685 q^{43} -3.58579 q^{44} +1.00000 q^{45} -7.82843 q^{46} -6.00000 q^{47} -1.00000 q^{48} -4.00000 q^{50} -5.24264 q^{51} +1.00000 q^{52} +5.65685 q^{53} -1.00000 q^{54} -3.58579 q^{55} +6.65685 q^{57} -9.48528 q^{58} -3.07107 q^{59} -1.00000 q^{60} -7.58579 q^{61} +1.41421 q^{62} +1.00000 q^{64} +1.00000 q^{65} +3.58579 q^{66} +15.5563 q^{67} +5.24264 q^{68} +7.82843 q^{69} -14.2426 q^{71} +1.00000 q^{72} -11.0000 q^{73} -5.58579 q^{74} +4.00000 q^{75} -6.65685 q^{76} -1.00000 q^{78} -6.24264 q^{79} +1.00000 q^{80} +1.00000 q^{81} +10.8284 q^{82} -7.65685 q^{83} +5.24264 q^{85} +2.65685 q^{86} +9.48528 q^{87} -3.58579 q^{88} +5.75736 q^{89} +1.00000 q^{90} -7.82843 q^{92} -1.41421 q^{93} -6.00000 q^{94} -6.65685 q^{95} -1.00000 q^{96} +15.3137 q^{97} -3.58579 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{8} + 2 q^{9} + 2 q^{10} - 10 q^{11} - 2 q^{12} + 2 q^{13} - 2 q^{15} + 2 q^{16} + 2 q^{17} + 2 q^{18} - 2 q^{19} + 2 q^{20} - 10 q^{22} - 10 q^{23} - 2 q^{24} - 8 q^{25} + 2 q^{26} - 2 q^{27} - 2 q^{29} - 2 q^{30} + 2 q^{32} + 10 q^{33} + 2 q^{34} + 2 q^{36} - 14 q^{37} - 2 q^{38} - 2 q^{39} + 2 q^{40} + 16 q^{41} - 6 q^{43} - 10 q^{44} + 2 q^{45} - 10 q^{46} - 12 q^{47} - 2 q^{48} - 8 q^{50} - 2 q^{51} + 2 q^{52} - 2 q^{54} - 10 q^{55} + 2 q^{57} - 2 q^{58} + 8 q^{59} - 2 q^{60} - 18 q^{61} + 2 q^{64} + 2 q^{65} + 10 q^{66} + 2 q^{68} + 10 q^{69} - 20 q^{71} + 2 q^{72} - 22 q^{73} - 14 q^{74} + 8 q^{75} - 2 q^{76} - 2 q^{78} - 4 q^{79} + 2 q^{80} + 2 q^{81} + 16 q^{82} - 4 q^{83} + 2 q^{85} - 6 q^{86} + 2 q^{87} - 10 q^{88} + 20 q^{89} + 2 q^{90} - 10 q^{92} - 12 q^{94} - 2 q^{95} - 2 q^{96} + 8 q^{97} - 10 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^8 + 2 * q^9 + 2 * q^10 - 10 * q^11 - 2 * q^12 + 2 * q^13 - 2 * q^15 + 2 * q^16 + 2 * q^17 + 2 * q^18 - 2 * q^19 + 2 * q^20 - 10 * q^22 - 10 * q^23 - 2 * q^24 - 8 * q^25 + 2 * q^26 - 2 * q^27 - 2 * q^29 - 2 * q^30 + 2 * q^32 + 10 * q^33 + 2 * q^34 + 2 * q^36 - 14 * q^37 - 2 * q^38 - 2 * q^39 + 2 * q^40 + 16 * q^41 - 6 * q^43 - 10 * q^44 + 2 * q^45 - 10 * q^46 - 12 * q^47 - 2 * q^48 - 8 * q^50 - 2 * q^51 + 2 * q^52 - 2 * q^54 - 10 * q^55 + 2 * q^57 - 2 * q^58 + 8 * q^59 - 2 * q^60 - 18 * q^61 + 2 * q^64 + 2 * q^65 + 10 * q^66 + 2 * q^68 + 10 * q^69 - 20 * q^71 + 2 * q^72 - 22 * q^73 - 14 * q^74 + 8 * q^75 - 2 * q^76 - 2 * q^78 - 4 * q^79 + 2 * q^80 + 2 * q^81 + 16 * q^82 - 4 * q^83 + 2 * q^85 - 6 * q^86 + 2 * q^87 - 10 * q^88 + 20 * q^89 + 2 * q^90 - 10 * q^92 - 12 * q^94 - 2 * q^95 - 2 * q^96 + 8 * q^97 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more