LMFDB - Embedded newform 3630.2.a.bp.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3630,2,Mod(1,3630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3630, 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("3630.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3630.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:	$28.9856959337$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.73205$ of defining polynomial
Character	$\chi$	$=$	3630.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +0.267949 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +0.267949 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +1.00000 q^{12} +3.00000 q^{13} +0.267949 q^{14} +1.00000 q^{15} +1.00000 q^{16} +3.73205 q^{17} +1.00000 q^{18} +2.46410 q^{19} +1.00000 q^{20} +0.267949 q^{21} -1.26795 q^{23} +1.00000 q^{24} +1.00000 q^{25} +3.00000 q^{26} +1.00000 q^{27} +0.267949 q^{28} -3.00000 q^{29} +1.00000 q^{30} -2.19615 q^{31} +1.00000 q^{32} +3.73205 q^{34} +0.267949 q^{35} +1.00000 q^{36} +1.73205 q^{37} +2.46410 q^{38} +3.00000 q^{39} +1.00000 q^{40} +1.26795 q^{41} +0.267949 q^{42} +3.26795 q^{43} +1.00000 q^{45} -1.26795 q^{46} -4.92820 q^{47} +1.00000 q^{48} -6.92820 q^{49} +1.00000 q^{50} +3.73205 q^{51} +3.00000 q^{52} -8.73205 q^{53} +1.00000 q^{54} +0.267949 q^{56} +2.46410 q^{57} -3.00000 q^{58} +6.19615 q^{59} +1.00000 q^{60} +8.19615 q^{61} -2.19615 q^{62} +0.267949 q^{63} +1.00000 q^{64} +3.00000 q^{65} -4.53590 q^{67} +3.73205 q^{68} -1.26795 q^{69} +0.267949 q^{70} +3.92820 q^{71} +1.00000 q^{72} -4.19615 q^{73} +1.73205 q^{74} +1.00000 q^{75} +2.46410 q^{76} +3.00000 q^{78} +7.46410 q^{79} +1.00000 q^{80} +1.00000 q^{81} +1.26795 q^{82} +9.39230 q^{83} +0.267949 q^{84} +3.73205 q^{85} +3.26795 q^{86} -3.00000 q^{87} +4.39230 q^{89} +1.00000 q^{90} +0.803848 q^{91} -1.26795 q^{92} -2.19615 q^{93} -4.92820 q^{94} +2.46410 q^{95} +1.00000 q^{96} -15.2679 q^{97} -6.92820 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} + 4 q^{7} + 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 + 4 * q^7 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} + 4 q^{7} + 2 q^{8} + 2 q^{9} + 2 q^{10} + 2 q^{12} + 6 q^{13} + 4 q^{14} + 2 q^{15} + 2 q^{16} + 4 q^{17} + 2 q^{18} - 2 q^{19} + 2 q^{20} + 4 q^{21} - 6 q^{23} + 2 q^{24} + 2 q^{25} + 6 q^{26} + 2 q^{27} + 4 q^{28} - 6 q^{29} + 2 q^{30} + 6 q^{31} + 2 q^{32} + 4 q^{34} + 4 q^{35} + 2 q^{36} - 2 q^{38} + 6 q^{39} + 2 q^{40} + 6 q^{41} + 4 q^{42} + 10 q^{43} + 2 q^{45} - 6 q^{46} + 4 q^{47} + 2 q^{48} + 2 q^{50} + 4 q^{51} + 6 q^{52} - 14 q^{53} + 2 q^{54} + 4 q^{56} - 2 q^{57} - 6 q^{58} + 2 q^{59} + 2 q^{60} + 6 q^{61} + 6 q^{62} + 4 q^{63} + 2 q^{64} + 6 q^{65} - 16 q^{67} + 4 q^{68} - 6 q^{69} + 4 q^{70} - 6 q^{71} + 2 q^{72} + 2 q^{73} + 2 q^{75} - 2 q^{76} + 6 q^{78} + 8 q^{79} + 2 q^{80} + 2 q^{81} + 6 q^{82} - 2 q^{83} + 4 q^{84} + 4 q^{85} + 10 q^{86} - 6 q^{87} - 12 q^{89} + 2 q^{90} + 12 q^{91} - 6 q^{92} + 6 q^{93} + 4 q^{94} - 2 q^{95} + 2 q^{96} - 34 q^{97}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 + 4 * q^7 + 2 * q^8 + 2 * q^9 + 2 * q^10 + 2 * q^12 + 6 * q^13 + 4 * q^14 + 2 * q^15 + 2 * q^16 + 4 * q^17 + 2 * q^18 - 2 * q^19 + 2 * q^20 + 4 * q^21 - 6 * q^23 + 2 * q^24 + 2 * q^25 + 6 * q^26 + 2 * q^27 + 4 * q^28 - 6 * q^29 + 2 * q^30 + 6 * q^31 + 2 * q^32 + 4 * q^34 + 4 * q^35 + 2 * q^36 - 2 * q^38 + 6 * q^39 + 2 * q^40 + 6 * q^41 + 4 * q^42 + 10 * q^43 + 2 * q^45 - 6 * q^46 + 4 * q^47 + 2 * q^48 + 2 * q^50 + 4 * q^51 + 6 * q^52 - 14 * q^53 + 2 * q^54 + 4 * q^56 - 2 * q^57 - 6 * q^58 + 2 * q^59 + 2 * q^60 + 6 * q^61 + 6 * q^62 + 4 * q^63 + 2 * q^64 + 6 * q^65 - 16 * q^67 + 4 * q^68 - 6 * q^69 + 4 * q^70 - 6 * q^71 + 2 * q^72 + 2 * q^73 + 2 * q^75 - 2 * q^76 + 6 * q^78 + 8 * q^79 + 2 * q^80 + 2 * q^81 + 6 * q^82 - 2 * q^83 + 4 * q^84 + 4 * q^85 + 10 * q^86 - 6 * q^87 - 12 * q^89 + 2 * q^90 + 12 * q^91 - 6 * q^92 + 6 * q^93 + 4 * q^94 - 2 * q^95 + 2 * q^96 - 34 * q^97

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
$5$	1.00000	0.447214
$6$	1.00000	0.408248
$7$	0.267949	0.101275	0.0506376	−	0.998717i	$-0.483875\pi$
$7$	0.267949	0.101275	0.0506376	+	0.998717i	$0.483875\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	0	0
$11$	0	0
$12$	1.00000	0.288675
$13$	3.00000	0.832050	0.416025	−	0.909353i	$-0.363423\pi$
$13$	3.00000	0.832050	0.416025	+	0.909353i	$0.363423\pi$
$14$	0.267949	0.0716124
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	3.73205	0.905155	0.452578	−	0.891725i	$-0.350505\pi$
$17$	3.73205	0.905155	0.452578	+	0.891725i	$0.350505\pi$
$18$	1.00000	0.235702
$19$	2.46410	0.565304	0.282652	−	0.959223i	$-0.408786\pi$
$19$	2.46410	0.565304	0.282652	+	0.959223i	$0.408786\pi$
$20$	1.00000	0.223607
$21$	0.267949	0.0584713
$22$	0	0
$23$	−1.26795	−0.264386	−0.132193	−	0.991224i	$-0.542202\pi$
$23$	−1.26795	−0.264386	−0.132193	+	0.991224i	$0.542202\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	3.00000	0.588348
$27$	1.00000	0.192450
$28$	0.267949	0.0506376
$29$	−3.00000	−0.557086	−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000	−0.557086	−0.278543	+	0.960424i	$0.589851\pi$
$30$	1.00000	0.182574
$31$	−2.19615	−0.394441	−0.197220	−	0.980359i	$-0.563191\pi$
$31$	−2.19615	−0.394441	−0.197220	+	0.980359i	$0.563191\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	3.73205	0.640041
$35$	0.267949	0.0452917
$36$	1.00000	0.166667
$37$	1.73205	0.284747	0.142374	−	0.989813i	$-0.454527\pi$
$37$	1.73205	0.284747	0.142374	+	0.989813i	$0.454527\pi$
$38$	2.46410	0.399730
$39$	3.00000	0.480384
$40$	1.00000	0.158114
$41$	1.26795	0.198020	0.0990102	−	0.995086i	$-0.468432\pi$
$41$	1.26795	0.198020	0.0990102	+	0.995086i	$0.468432\pi$
$42$	0.267949	0.0413455
$43$	3.26795	0.498358	0.249179	−	0.968458i	$-0.419839\pi$
$43$	3.26795	0.498358	0.249179	+	0.968458i	$0.419839\pi$
$44$	0	0
$45$	1.00000	0.149071
$46$	−1.26795	−0.186949
$47$	−4.92820	−0.718852	−0.359426	−	0.933174i	$-0.617028\pi$
$47$	−4.92820	−0.718852	−0.359426	+	0.933174i	$0.617028\pi$
$48$	1.00000	0.144338
$49$	−6.92820	−0.989743
$50$	1.00000	0.141421
$51$	3.73205	0.522592
$52$	3.00000	0.416025
$53$	−8.73205	−1.19944	−0.599720	−	0.800210i	$-0.704721\pi$
$53$	−8.73205	−1.19944	−0.599720	+	0.800210i	$0.704721\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	0.267949	0.0358062
$57$	2.46410	0.326378
$58$	−3.00000	−0.393919
$59$	6.19615	0.806670	0.403335	−	0.915052i	$-0.367851\pi$
$59$	6.19615	0.806670	0.403335	+	0.915052i	$0.367851\pi$
$60$	1.00000	0.129099
$61$	8.19615	1.04941	0.524705	−	0.851284i	$-0.324176\pi$
$61$	8.19615	1.04941	0.524705	+	0.851284i	$0.324176\pi$
$62$	−2.19615	−0.278912
$63$	0.267949	0.0337584
$64$	1.00000	0.125000
$65$	3.00000	0.372104
$66$	0	0
$67$	−4.53590	−0.554148	−0.277074	−	0.960849i	$-0.589365\pi$
$67$	−4.53590	−0.554148	−0.277074	+	0.960849i	$0.589365\pi$
$68$	3.73205	0.452578
$69$	−1.26795	−0.152643
$70$	0.267949	0.0320261
$71$	3.92820	0.466192	0.233096	−	0.972454i	$-0.425114\pi$
$71$	3.92820	0.466192	0.233096	+	0.972454i	$0.425114\pi$
$72$	1.00000	0.117851
$73$	−4.19615	−0.491122	−0.245561	−	0.969381i	$-0.578972\pi$
$73$	−4.19615	−0.491122	−0.245561	+	0.969381i	$0.578972\pi$
$74$	1.73205	0.201347
$75$	1.00000	0.115470
$76$	2.46410	0.282652
$77$	0	0
$78$	3.00000	0.339683
$79$	7.46410	0.839777	0.419889	−	0.907576i	$-0.362069\pi$
$79$	7.46410	0.839777	0.419889	+	0.907576i	$0.362069\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	1.26795	0.140022
$83$	9.39230	1.03094	0.515470	−	0.856908i	$-0.327617\pi$
$83$	9.39230	1.03094	0.515470	+	0.856908i	$0.327617\pi$
$84$	0.267949	0.0292357
$85$	3.73205	0.404798
$86$	3.26795	0.352392
$87$	−3.00000	−0.321634
$88$	0	0
$89$	4.39230	0.465583	0.232792	−	0.972527i	$-0.425214\pi$
$89$	4.39230	0.465583	0.232792	+	0.972527i	$0.425214\pi$
$90$	1.00000	0.105409
$91$	0.803848	0.0842661
$92$	−1.26795	−0.132193
$93$	−2.19615	−0.227730
$94$	−4.92820	−0.508305
$95$	2.46410	0.252811
$96$	1.00000	0.102062
$97$	−15.2679	−1.55023	−0.775113	−	0.631823i	$-0.782307\pi$
$97$	−15.2679	−1.55023	−0.775113	+	0.631823i	$0.782307\pi$
$98$	−6.92820	−0.699854
$99$	0	0
$100$	1.00000	0.100000
$101$	−12.4641	−1.24022	−0.620112	−	0.784513i	$-0.712913\pi$
$101$	−12.4641	−1.24022	−0.620112	+	0.784513i	$0.712913\pi$
$102$	3.73205	0.369528
$103$	16.3205	1.60811	0.804054	−	0.594557i	$-0.202672\pi$
$103$	16.3205	1.60811	0.804054	+	0.594557i	$0.202672\pi$
$104$	3.00000	0.294174
$105$	0.267949	0.0261492
$106$	−8.73205	−0.848132
$107$	4.53590	0.438502	0.219251	−	0.975669i	$-0.429639\pi$
$107$	4.53590	0.438502	0.219251	+	0.975669i	$0.429639\pi$
$108$	1.00000	0.0962250
$109$	6.53590	0.626026	0.313013	−	0.949749i	$-0.398662\pi$
$109$	6.53590	0.626026	0.313013	+	0.949749i	$0.398662\pi$
$110$	0	0
$111$	1.73205	0.164399
$112$	0.267949	0.0253188
$113$	−13.8564	−1.30350	−0.651751	−	0.758433i	$-0.725965\pi$
$113$	−13.8564	−1.30350	−0.651751	+	0.758433i	$0.725965\pi$
$114$	2.46410	0.230784
$115$	−1.26795	−0.118237
$116$	−3.00000	−0.278543
$117$	3.00000	0.277350
$118$	6.19615	0.570402
$119$	1.00000	0.0916698
$120$	1.00000	0.0912871
$121$	0	0
$122$	8.19615	0.742045
$123$	1.26795	0.114327
$124$	−2.19615	−0.197220
$125$	1.00000	0.0894427
$126$	0.267949	0.0238708
$127$	20.3923	1.80952	0.904762	−	0.425917i	$-0.140048\pi$
$127$	20.3923	1.80952	0.904762	+	0.425917i	$0.140048\pi$
$128$	1.00000	0.0883883
$129$	3.26795	0.287727
$130$	3.00000	0.263117
$131$	−5.66025	−0.494539	−0.247269	−	0.968947i	$-0.579533\pi$
$131$	−5.66025	−0.494539	−0.247269	+	0.968947i	$0.579533\pi$
$132$	0	0
$133$	0.660254	0.0572513
$134$	−4.53590	−0.391842
$135$	1.00000	0.0860663
$136$	3.73205	0.320021
$137$	21.7846	1.86118	0.930592	−	0.366057i	$-0.119293\pi$
$137$	21.7846	1.86118	0.930592	+	0.366057i	$0.119293\pi$
$138$	−1.26795	−0.107935
$139$	−14.3205	−1.21465	−0.607325	−	0.794454i	$-0.707757\pi$
$139$	−14.3205	−1.21465	−0.607325	+	0.794454i	$0.707757\pi$
$140$	0.267949	0.0226458
$141$	−4.92820	−0.415030
$142$	3.92820	0.329647
$143$	0	0
$144$	1.00000	0.0833333
$145$	−3.00000	−0.249136
$146$	−4.19615	−0.347276
$147$	−6.92820	−0.571429
$148$	1.73205	0.142374
$149$	20.3923	1.67060	0.835301	−	0.549792i	$-0.185293\pi$
$149$	20.3923	1.67060	0.835301	+	0.549792i	$0.185293\pi$
$150$	1.00000	0.0816497
$151$	16.7321	1.36163	0.680817	−	0.732453i	$-0.261625\pi$
$151$	16.7321	1.36163	0.680817	+	0.732453i	$0.261625\pi$
$152$	2.46410	0.199865
$153$	3.73205	0.301718
$154$	0	0
$155$	−2.19615	−0.176399
$156$	3.00000	0.240192
$157$	2.80385	0.223771	0.111886	−	0.993721i	$-0.464311\pi$
$157$	2.80385	0.223771	0.111886	+	0.993721i	$0.464311\pi$
$158$	7.46410	0.593812
$159$	−8.73205	−0.692497
$160$	1.00000	0.0790569
$161$	−0.339746	−0.0267757
$162$	1.00000	0.0785674
$163$	−20.0526	−1.57064	−0.785319	−	0.619092i	$-0.787501\pi$
$163$	−20.0526	−1.57064	−0.785319	+	0.619092i	$0.787501\pi$
$164$	1.26795	0.0990102
$165$	0	0
$166$	9.39230	0.728984
$167$	−14.5359	−1.12482	−0.562411	−	0.826858i	$-0.690126\pi$
$167$	−14.5359	−1.12482	−0.562411	+	0.826858i	$0.690126\pi$
$168$	0.267949	0.0206727
$169$	−4.00000	−0.307692
$170$	3.73205	0.286235
$171$	2.46410	0.188435
$172$	3.26795	0.249179
$173$	−16.5885	−1.26120	−0.630599	−	0.776109i	$-0.717191\pi$
$173$	−16.5885	−1.26120	−0.630599	+	0.776109i	$0.717191\pi$
$174$	−3.00000	−0.227429
$175$	0.267949	0.0202551
$176$	0	0
$177$	6.19615	0.465731
$178$	4.39230	0.329217
$179$	−17.1244	−1.27993	−0.639967	−	0.768402i	$-0.721052\pi$
$179$	−17.1244	−1.27993	−0.639967	+	0.768402i	$0.721052\pi$
$180$	1.00000	0.0745356
$181$	−6.19615	−0.460556	−0.230278	−	0.973125i	$-0.573964\pi$
$181$	−6.19615	−0.460556	−0.230278	+	0.973125i	$0.573964\pi$
$182$	0.803848	0.0595851
$183$	8.19615	0.605877
$184$	−1.26795	−0.0934745
$185$	1.73205	0.127343
$186$	−2.19615	−0.161030
$187$	0	0
$188$	−4.92820	−0.359426
$189$	0.267949	0.0194904
$190$	2.46410	0.178765
$191$	11.5359	0.834708	0.417354	−	0.908744i	$-0.362957\pi$
$191$	11.5359	0.834708	0.417354	+	0.908744i	$0.362957\pi$
$192$	1.00000	0.0721688
$193$	2.53590	0.182538	0.0912690	−	0.995826i	$-0.470908\pi$
$193$	2.53590	0.182538	0.0912690	+	0.995826i	$0.470908\pi$
$194$	−15.2679	−1.09617
$195$	3.00000	0.214834
$196$	−6.92820	−0.494872
$197$	−6.53590	−0.465663	−0.232832	−	0.972517i	$-0.574799\pi$
$197$	−6.53590	−0.465663	−0.232832	+	0.972517i	$0.574799\pi$
$198$	0	0
$199$	4.39230	0.311362	0.155681	−	0.987807i	$-0.450243\pi$
$199$	4.39230	0.311362	0.155681	+	0.987807i	$0.450243\pi$
$200$	1.00000	0.0707107
$201$	−4.53590	−0.319938
$202$	−12.4641	−0.876971
$203$	−0.803848	−0.0564190
$204$	3.73205	0.261296
$205$	1.26795	0.0885574
$206$	16.3205	1.13710
$207$	−1.26795	−0.0881286
$208$	3.00000	0.208013
$209$	0	0
$210$	0.267949	0.0184903
$211$	−23.7846	−1.63740	−0.818700	−	0.574221i	$-0.805305\pi$
$211$	−23.7846	−1.63740	−0.818700	+	0.574221i	$0.805305\pi$
$212$	−8.73205	−0.599720
$213$	3.92820	0.269156
$214$	4.53590	0.310068
$215$	3.26795	0.222872
$216$	1.00000	0.0680414
$217$	−0.588457	−0.0399471
$218$	6.53590	0.442667
$219$	−4.19615	−0.283550
$220$	0	0
$221$	11.1962	0.753135
$222$	1.73205	0.116248
$223$	−0.464102	−0.0310785	−0.0155393	−	0.999879i	$-0.504947\pi$
$223$	−0.464102	−0.0310785	−0.0155393	+	0.999879i	$0.504947\pi$
$224$	0.267949	0.0179031
$225$	1.00000	0.0666667
$226$	−13.8564	−0.921714
$227$	10.3923	0.689761	0.344881	−	0.938647i	$-0.387919\pi$
$227$	10.3923	0.689761	0.344881	+	0.938647i	$0.387919\pi$
$228$	2.46410	0.163189
$229$	−12.0000	−0.792982	−0.396491	−	0.918039i	$-0.629772\pi$
$229$	−12.0000	−0.792982	−0.396491	+	0.918039i	$0.629772\pi$
$230$	−1.26795	−0.0836061
$231$	0	0
$232$	−3.00000	−0.196960
$233$	−25.8564	−1.69391	−0.846955	−	0.531665i	$-0.821567\pi$
$233$	−25.8564	−1.69391	−0.846955	+	0.531665i	$0.821567\pi$
$234$	3.00000	0.196116
$235$	−4.92820	−0.321481
$236$	6.19615	0.403335
$237$	7.46410	0.484846
$238$	1.00000	0.0648204
$239$	−9.73205	−0.629514	−0.314757	−	0.949172i	$-0.601923\pi$
$239$	−9.73205	−0.629514	−0.314757	+	0.949172i	$0.601923\pi$
$240$	1.00000	0.0645497
$241$	−5.33975	−0.343963	−0.171982	−	0.985100i	$-0.555017\pi$
$241$	−5.33975	−0.343963	−0.171982	+	0.985100i	$0.555017\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	8.19615	0.524705
$245$	−6.92820	−0.442627
$246$	1.26795	0.0808415
$247$	7.39230	0.470361
$248$	−2.19615	−0.139456
$249$	9.39230	0.595213
$250$	1.00000	0.0632456
$251$	25.4641	1.60728	0.803640	−	0.595116i	$-0.202894\pi$
$251$	25.4641	1.60728	0.803640	+	0.595116i	$0.202894\pi$
$252$	0.267949	0.0168792
$253$	0	0
$254$	20.3923	1.27953
$255$	3.73205	0.233710
$256$	1.00000	0.0625000
$257$	−28.3205	−1.76658	−0.883292	−	0.468823i	$-0.844678\pi$
$257$	−28.3205	−1.76658	−0.883292	+	0.468823i	$0.844678\pi$
$258$	3.26795	0.203454
$259$	0.464102	0.0288379
$260$	3.00000	0.186052
$261$	−3.00000	−0.185695
$262$	−5.66025	−0.349692
$263$	−0.875644	−0.0539945	−0.0269973	−	0.999636i	$-0.508595\pi$
$263$	−0.875644	−0.0539945	−0.0269973	+	0.999636i	$0.508595\pi$
$264$	0	0
$265$	−8.73205	−0.536406
$266$	0.660254	0.0404828
$267$	4.39230	0.268805
$268$	−4.53590	−0.277074
$269$	−19.5885	−1.19433	−0.597165	−	0.802119i	$-0.703706\pi$
$269$	−19.5885	−1.19433	−0.597165	+	0.802119i	$0.703706\pi$
$270$	1.00000	0.0608581
$271$	3.85641	0.234260	0.117130	−	0.993117i	$-0.462631\pi$
$271$	3.85641	0.234260	0.117130	+	0.993117i	$0.462631\pi$
$272$	3.73205	0.226289
$273$	0.803848	0.0486511
$274$	21.7846	1.31606
$275$	0	0
$276$	−1.26795	−0.0763216
$277$	5.07180	0.304735	0.152367	−	0.988324i	$-0.451310\pi$
$277$	5.07180	0.304735	0.152367	+	0.988324i	$0.451310\pi$
$278$	−14.3205	−0.858887
$279$	−2.19615	−0.131480
$280$	0.267949	0.0160130
$281$	−12.0526	−0.718995	−0.359498	−	0.933146i	$-0.617052\pi$
$281$	−12.0526	−0.718995	−0.359498	+	0.933146i	$0.617052\pi$
$282$	−4.92820	−0.293470
$283$	18.2487	1.08477	0.542387	−	0.840129i	$-0.317521\pi$
$283$	18.2487	1.08477	0.542387	+	0.840129i	$0.317521\pi$
$284$	3.92820	0.233096
$285$	2.46410	0.145961
$286$	0	0
$287$	0.339746	0.0200546
$288$	1.00000	0.0589256
$289$	−3.07180	−0.180694
$290$	−3.00000	−0.176166
$291$	−15.2679	−0.895023
$292$	−4.19615	−0.245561
$293$	−5.07180	−0.296298	−0.148149	−	0.988965i	$-0.547331\pi$
$293$	−5.07180	−0.296298	−0.148149	+	0.988965i	$0.547331\pi$
$294$	−6.92820	−0.404061
$295$	6.19615	0.360754
$296$	1.73205	0.100673
$297$	0	0
$298$	20.3923	1.18129
$299$	−3.80385	−0.219982
$300$	1.00000	0.0577350
$301$	0.875644	0.0504713
$302$	16.7321	0.962821
$303$	−12.4641	−0.716044
$304$	2.46410	0.141326
$305$	8.19615	0.469310
$306$	3.73205	0.213347
$307$	3.26795	0.186512	0.0932559	−	0.995642i	$-0.470273\pi$
$307$	3.26795	0.186512	0.0932559	+	0.995642i	$0.470273\pi$
$308$	0	0
$309$	16.3205	0.928441
$310$	−2.19615	−0.124733
$311$	−13.8564	−0.785725	−0.392862	−	0.919597i	$-0.628515\pi$
$311$	−13.8564	−0.785725	−0.392862	+	0.919597i	$0.628515\pi$
$312$	3.00000	0.169842
$313$	5.12436	0.289646	0.144823	−	0.989458i	$-0.453739\pi$
$313$	5.12436	0.289646	0.144823	+	0.989458i	$0.453739\pi$
$314$	2.80385	0.158230
$315$	0.267949	0.0150972
$316$	7.46410	0.419889
$317$	9.12436	0.512475	0.256237	−	0.966614i	$-0.417517\pi$
$317$	9.12436	0.512475	0.256237	+	0.966614i	$0.417517\pi$
$318$	−8.73205	−0.489669
$319$	0	0
$320$	1.00000	0.0559017
$321$	4.53590	0.253169
$322$	−0.339746	−0.0189333
$323$	9.19615	0.511688
$324$	1.00000	0.0555556
$325$	3.00000	0.166410
$326$	−20.0526	−1.11061
$327$	6.53590	0.361436
$328$	1.26795	0.0700108
$329$	−1.32051	−0.0728020
$330$	0	0
$331$	14.5167	0.797908	0.398954	−	0.916971i	$-0.369373\pi$
$331$	14.5167	0.797908	0.398954	+	0.916971i	$0.369373\pi$
$332$	9.39230	0.515470
$333$	1.73205	0.0949158
$334$	−14.5359	−0.795369
$335$	−4.53590	−0.247823
$336$	0.267949	0.0146178
$337$	26.7321	1.45619	0.728094	−	0.685478i	$-0.240407\pi$
$337$	26.7321	1.45619	0.728094	+	0.685478i	$0.240407\pi$
$338$	−4.00000	−0.217571
$339$	−13.8564	−0.752577
$340$	3.73205	0.202399
$341$	0	0
$342$	2.46410	0.133243
$343$	−3.73205	−0.201512
$344$	3.26795	0.176196
$345$	−1.26795	−0.0682641
$346$	−16.5885	−0.891801
$347$	4.60770	0.247354	0.123677	−	0.992323i	$-0.460531\pi$
$347$	4.60770	0.247354	0.123677	+	0.992323i	$0.460531\pi$
$348$	−3.00000	−0.160817
$349$	−19.8564	−1.06289	−0.531445	−	0.847093i	$-0.678351\pi$
$349$	−19.8564	−1.06289	−0.531445	+	0.847093i	$0.678351\pi$
$350$	0.267949	0.0143225
$351$	3.00000	0.160128
$352$	0	0
$353$	−6.92820	−0.368751	−0.184376	−	0.982856i	$-0.559026\pi$
$353$	−6.92820	−0.368751	−0.184376	+	0.982856i	$0.559026\pi$
$354$	6.19615	0.329322
$355$	3.92820	0.208487
$356$	4.39230	0.232792
$357$	1.00000	0.0529256
$358$	−17.1244	−0.905050
$359$	−20.5359	−1.08384	−0.541922	−	0.840429i	$-0.682303\pi$
$359$	−20.5359	−1.08384	−0.541922	+	0.840429i	$0.682303\pi$
$360$	1.00000	0.0527046
$361$	−12.9282	−0.680432
$362$	−6.19615	−0.325663
$363$	0	0
$364$	0.803848	0.0421331
$365$	−4.19615	−0.219637
$366$	8.19615	0.428420
$367$	−12.8564	−0.671099	−0.335549	−	0.942023i	$-0.608922\pi$
$367$	−12.8564	−0.671099	−0.335549	+	0.942023i	$0.608922\pi$
$368$	−1.26795	−0.0660964
$369$	1.26795	0.0660068
$370$	1.73205	0.0900450
$371$	−2.33975	−0.121474
$372$	−2.19615	−0.113865
$373$	19.9282	1.03184	0.515922	−	0.856636i	$-0.327450\pi$
$373$	19.9282	1.03184	0.515922	+	0.856636i	$0.327450\pi$
$374$	0	0
$375$	1.00000	0.0516398
$376$	−4.92820	−0.254153
$377$	−9.00000	−0.463524
$378$	0.267949	0.0137818
$379$	−37.4449	−1.92341	−0.961707	−	0.274081i	$-0.911626\pi$
$379$	−37.4449	−1.92341	−0.961707	+	0.274081i	$0.911626\pi$
$380$	2.46410	0.126406
$381$	20.3923	1.04473
$382$	11.5359	0.590228
$383$	−3.07180	−0.156961	−0.0784807	−	0.996916i	$-0.525007\pi$
$383$	−3.07180	−0.156961	−0.0784807	+	0.996916i	$0.525007\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	2.53590	0.129074
$387$	3.26795	0.166119
$388$	−15.2679	−0.775113
$389$	−10.1436	−0.514301	−0.257150	−	0.966371i	$-0.582784\pi$
$389$	−10.1436	−0.514301	−0.257150	+	0.966371i	$0.582784\pi$
$390$	3.00000	0.151911
$391$	−4.73205	−0.239310
$392$	−6.92820	−0.349927
$393$	−5.66025	−0.285522
$394$	−6.53590	−0.329274
$395$	7.46410	0.375560
$396$	0	0
$397$	−25.9808	−1.30394	−0.651969	−	0.758246i	$-0.726057\pi$
$397$	−25.9808	−1.30394	−0.651969	+	0.758246i	$0.726057\pi$
$398$	4.39230	0.220166
$399$	0.660254	0.0330540
$400$	1.00000	0.0500000
$401$	0.339746	0.0169661	0.00848305	−	0.999964i	$-0.497300\pi$
$401$	0.339746	0.0169661	0.00848305	+	0.999964i	$0.497300\pi$
$402$	−4.53590	−0.226230
$403$	−6.58846	−0.328194
$404$	−12.4641	−0.620112
$405$	1.00000	0.0496904
$406$	−0.803848	−0.0398943
$407$	0	0
$408$	3.73205	0.184764
$409$	14.0000	0.692255	0.346128	−	0.938187i	$-0.387496\pi$
$409$	14.0000	0.692255	0.346128	+	0.938187i	$0.387496\pi$
$410$	1.26795	0.0626195
$411$	21.7846	1.07456
$412$	16.3205	0.804054
$413$	1.66025	0.0816958
$414$	−1.26795	−0.0623163
$415$	9.39230	0.461050
$416$	3.00000	0.147087
$417$	−14.3205	−0.701278
$418$	0	0
$419$	−4.53590	−0.221593	−0.110797	−	0.993843i	$-0.535340\pi$
$419$	−4.53590	−0.221593	−0.110797	+	0.993843i	$0.535340\pi$
$420$	0.267949	0.0130746
$421$	34.0526	1.65962	0.829810	−	0.558046i	$-0.188449\pi$
$421$	34.0526	1.65962	0.829810	+	0.558046i	$0.188449\pi$
$422$	−23.7846	−1.15782
$423$	−4.92820	−0.239617
$424$	−8.73205	−0.424066
$425$	3.73205	0.181031
$426$	3.92820	0.190322
$427$	2.19615	0.106279
$428$	4.53590	0.219251
$429$	0	0
$430$	3.26795	0.157595
$431$	−18.1244	−0.873019	−0.436510	−	0.899700i	$-0.643786\pi$
$431$	−18.1244	−0.873019	−0.436510	+	0.899700i	$0.643786\pi$
$432$	1.00000	0.0481125
$433$	2.92820	0.140720	0.0703602	−	0.997522i	$-0.477585\pi$
$433$	2.92820	0.140720	0.0703602	+	0.997522i	$0.477585\pi$
$434$	−0.588457	−0.0282469
$435$	−3.00000	−0.143839
$436$	6.53590	0.313013
$437$	−3.12436	−0.149458
$438$	−4.19615	−0.200500
$439$	−8.92820	−0.426120	−0.213060	−	0.977039i	$-0.568343\pi$
$439$	−8.92820	−0.426120	−0.213060	+	0.977039i	$0.568343\pi$
$440$	0	0
$441$	−6.92820	−0.329914
$442$	11.1962	0.532547
$443$	5.19615	0.246877	0.123438	−	0.992352i	$-0.460608\pi$
$443$	5.19615	0.246877	0.123438	+	0.992352i	$0.460608\pi$
$444$	1.73205	0.0821995
$445$	4.39230	0.208215
$446$	−0.464102	−0.0219758
$447$	20.3923	0.964523
$448$	0.267949	0.0126594
$449$	3.46410	0.163481	0.0817405	−	0.996654i	$-0.473952\pi$
$449$	3.46410	0.163481	0.0817405	+	0.996654i	$0.473952\pi$
$450$	1.00000	0.0471405
$451$	0	0
$452$	−13.8564	−0.651751
$453$	16.7321	0.786140
$454$	10.3923	0.487735
$455$	0.803848	0.0376850
$456$	2.46410	0.115392
$457$	28.4449	1.33059	0.665297	−	0.746579i	$-0.268305\pi$
$457$	28.4449	1.33059	0.665297	+	0.746579i	$0.268305\pi$
$458$	−12.0000	−0.560723
$459$	3.73205	0.174197
$460$	−1.26795	−0.0591184
$461$	31.2487	1.45540	0.727699	−	0.685897i	$-0.240590\pi$
$461$	31.2487	1.45540	0.727699	+	0.685897i	$0.240590\pi$
$462$	0	0
$463$	−4.53590	−0.210801	−0.105401	−	0.994430i	$-0.533612\pi$
$463$	−4.53590	−0.210801	−0.105401	+	0.994430i	$0.533612\pi$
$464$	−3.00000	−0.139272
$465$	−2.19615	−0.101844
$466$	−25.8564	−1.19777
$467$	−5.87564	−0.271892	−0.135946	−	0.990716i	$-0.543407\pi$
$467$	−5.87564	−0.271892	−0.135946	+	0.990716i	$0.543407\pi$
$468$	3.00000	0.138675
$469$	−1.21539	−0.0561215
$470$	−4.92820	−0.227321
$471$	2.80385	0.129194
$472$	6.19615	0.285201
$473$	0	0
$474$	7.46410	0.342838
$475$	2.46410	0.113061
$476$	1.00000	0.0458349
$477$	−8.73205	−0.399813
$478$	−9.73205	−0.445134
$479$	−11.7321	−0.536051	−0.268026	−	0.963412i	$-0.586371\pi$
$479$	−11.7321	−0.536051	−0.268026	+	0.963412i	$0.586371\pi$
$480$	1.00000	0.0456435
$481$	5.19615	0.236924
$482$	−5.33975	−0.243219
$483$	−0.339746	−0.0154590
$484$	0	0
$485$	−15.2679	−0.693282
$486$	1.00000	0.0453609
$487$	−0.464102	−0.0210305	−0.0105152	−	0.999945i	$-0.503347\pi$
$487$	−0.464102	−0.0210305	−0.0105152	+	0.999945i	$0.503347\pi$
$488$	8.19615	0.371022
$489$	−20.0526	−0.906808
$490$	−6.92820	−0.312984
$491$	4.73205	0.213554	0.106777	−	0.994283i	$-0.465947\pi$
$491$	4.73205	0.213554	0.106777	+	0.994283i	$0.465947\pi$
$492$	1.26795	0.0571636
$493$	−11.1962	−0.504249
$494$	7.39230	0.332596
$495$	0	0
$496$	−2.19615	−0.0986102
$497$	1.05256	0.0472137
$498$	9.39230	0.420879
$499$	37.4449	1.67626	0.838131	−	0.545469i	$-0.183648\pi$
$499$	37.4449	1.67626	0.838131	+	0.545469i	$0.183648\pi$
$500$	1.00000	0.0447214
$501$	−14.5359	−0.649416
$502$	25.4641	1.13652
$503$	−20.7321	−0.924396	−0.462198	−	0.886777i	$-0.652939\pi$
$503$	−20.7321	−0.924396	−0.462198	+	0.886777i	$0.652939\pi$
$504$	0.267949	0.0119354
$505$	−12.4641	−0.554645
$506$	0	0
$507$	−4.00000	−0.177646
$508$	20.3923	0.904762
$509$	−35.8564	−1.58931	−0.794654	−	0.607063i	$-0.792348\pi$
$509$	−35.8564	−1.58931	−0.794654	+	0.607063i	$0.792348\pi$
$510$	3.73205	0.165258
$511$	−1.12436	−0.0497386
$512$	1.00000	0.0441942
$513$	2.46410	0.108793
$514$	−28.3205	−1.24916
$515$	16.3205	0.719168
$516$	3.26795	0.143863
$517$	0	0
$518$	0.464102	0.0203915
$519$	−16.5885	−0.728152
$520$	3.00000	0.131559
$521$	8.58846	0.376267	0.188134	−	0.982143i	$-0.439756\pi$
$521$	8.58846	0.376267	0.188134	+	0.982143i	$0.439756\pi$
$522$	−3.00000	−0.131306
$523$	−22.7321	−0.994003	−0.497002	−	0.867750i	$-0.665566\pi$
$523$	−22.7321	−0.994003	−0.497002	+	0.867750i	$0.665566\pi$
$524$	−5.66025	−0.247269
$525$	0.267949	0.0116943
$526$	−0.875644	−0.0381799
$527$	−8.19615	−0.357030
$528$	0	0
$529$	−21.3923	−0.930100
$530$	−8.73205	−0.379296
$531$	6.19615	0.268890
$532$	0.660254	0.0286256
$533$	3.80385	0.164763
$534$	4.39230	0.190074
$535$	4.53590	0.196104
$536$	−4.53590	−0.195921
$537$	−17.1244	−0.738970
$538$	−19.5885	−0.844518
$539$	0	0
$540$	1.00000	0.0430331
$541$	−22.5885	−0.971154	−0.485577	−	0.874194i	$-0.661390\pi$
$541$	−22.5885	−0.971154	−0.485577	+	0.874194i	$0.661390\pi$
$542$	3.85641	0.165647
$543$	−6.19615	−0.265902
$544$	3.73205	0.160010
$545$	6.53590	0.279967
$546$	0.803848	0.0344015
$547$	28.9282	1.23688	0.618440	−	0.785832i	$-0.287765\pi$
$547$	28.9282	1.23688	0.618440	+	0.785832i	$0.287765\pi$
$548$	21.7846	0.930592
$549$	8.19615	0.349803
$550$	0	0
$551$	−7.39230	−0.314923
$552$	−1.26795	−0.0539675
$553$	2.00000	0.0850487
$554$	5.07180	0.215480
$555$	1.73205	0.0735215
$556$	−14.3205	−0.607325
$557$	10.3923	0.440336	0.220168	−	0.975462i	$-0.429339\pi$
$557$	10.3923	0.440336	0.220168	+	0.975462i	$0.429339\pi$
$558$	−2.19615	−0.0929705
$559$	9.80385	0.414659
$560$	0.267949	0.0113229
$561$	0	0
$562$	−12.0526	−0.508407
$563$	−35.1051	−1.47950	−0.739752	−	0.672879i	$-0.765057\pi$
$563$	−35.1051	−1.47950	−0.739752	+	0.672879i	$0.765057\pi$
$564$	−4.92820	−0.207515
$565$	−13.8564	−0.582943
$566$	18.2487	0.767051
$567$	0.267949	0.0112528
$568$	3.92820	0.164824
$569$	−36.1962	−1.51742	−0.758711	−	0.651428i	$-0.774170\pi$
$569$	−36.1962	−1.51742	−0.758711	+	0.651428i	$0.774170\pi$
$570$	2.46410	0.103210
$571$	−10.6795	−0.446923	−0.223461	−	0.974713i	$-0.571736\pi$
$571$	−10.6795	−0.446923	−0.223461	+	0.974713i	$0.571736\pi$
$572$	0	0
$573$	11.5359	0.481919
$574$	0.339746	0.0141807
$575$	−1.26795	−0.0528771
$576$	1.00000	0.0416667
$577$	17.3205	0.721062	0.360531	−	0.932747i	$-0.382595\pi$
$577$	17.3205	0.721062	0.360531	+	0.932747i	$0.382595\pi$
$578$	−3.07180	−0.127770
$579$	2.53590	0.105388
$580$	−3.00000	−0.124568
$581$	2.51666	0.104409
$582$	−15.2679	−0.632877
$583$	0	0
$584$	−4.19615	−0.173638
$585$	3.00000	0.124035
$586$	−5.07180	−0.209514
$587$	−42.9090	−1.77104	−0.885521	−	0.464599i	$-0.846199\pi$
$587$	−42.9090	−1.77104	−0.885521	+	0.464599i	$0.846199\pi$
$588$	−6.92820	−0.285714
$589$	−5.41154	−0.222979
$590$	6.19615	0.255092
$591$	−6.53590	−0.268851
$592$	1.73205	0.0711868
$593$	8.92820	0.366637	0.183319	−	0.983054i	$-0.441316\pi$
$593$	8.92820	0.366637	0.183319	+	0.983054i	$0.441316\pi$
$594$	0	0
$595$	1.00000	0.0409960
$596$	20.3923	0.835301
$597$	4.39230	0.179765
$598$	−3.80385	−0.155551
$599$	−13.6077	−0.555995	−0.277998	−	0.960582i	$-0.589671\pi$
$599$	−13.6077	−0.555995	−0.277998	+	0.960582i	$0.589671\pi$
$600$	1.00000	0.0408248
$601$	12.1436	0.495348	0.247674	−	0.968843i	$-0.420334\pi$
$601$	12.1436	0.495348	0.247674	+	0.968843i	$0.420334\pi$
$602$	0.875644	0.0356886
$603$	−4.53590	−0.184716
$604$	16.7321	0.680817
$605$	0	0
$606$	−12.4641	−0.506320
$607$	39.5885	1.60685	0.803423	−	0.595409i	$-0.203010\pi$
$607$	39.5885	1.60685	0.803423	+	0.595409i	$0.203010\pi$
$608$	2.46410	0.0999325
$609$	−0.803848	−0.0325735
$610$	8.19615	0.331853
$611$	−14.7846	−0.598121
$612$	3.73205	0.150859
$613$	−35.6410	−1.43953	−0.719764	−	0.694219i	$-0.755750\pi$
$613$	−35.6410	−1.43953	−0.719764	+	0.694219i	$0.755750\pi$
$614$	3.26795	0.131884
$615$	1.26795	0.0511286
$616$	0	0
$617$	−13.7846	−0.554947	−0.277474	−	0.960733i	$-0.589497\pi$
$617$	−13.7846	−0.554947	−0.277474	+	0.960733i	$0.589497\pi$
$618$	16.3205	0.656507
$619$	31.9808	1.28542	0.642708	−	0.766112i	$-0.277811\pi$
$619$	31.9808	1.28542	0.642708	+	0.766112i	$0.277811\pi$
$620$	−2.19615	−0.0881996
$621$	−1.26795	−0.0508810
$622$	−13.8564	−0.555591
$623$	1.17691	0.0471521
$624$	3.00000	0.120096
$625$	1.00000	0.0400000
$626$	5.12436	0.204810
$627$	0	0
$628$	2.80385	0.111886
$629$	6.46410	0.257741
$630$	0.267949	0.0106754
$631$	28.1962	1.12247	0.561236	−	0.827656i	$-0.310326\pi$
$631$	28.1962	1.12247	0.561236	+	0.827656i	$0.310326\pi$
$632$	7.46410	0.296906
$633$	−23.7846	−0.945353
$634$	9.12436	0.362374
$635$	20.3923	0.809244
$636$	−8.73205	−0.346248
$637$	−20.7846	−0.823516
$638$	0	0
$639$	3.92820	0.155397
$640$	1.00000	0.0395285
$641$	−4.92820	−0.194652	−0.0973262	−	0.995253i	$-0.531029\pi$
$641$	−4.92820	−0.194652	−0.0973262	+	0.995253i	$0.531029\pi$
$642$	4.53590	0.179018
$643$	10.1436	0.400024	0.200012	−	0.979793i	$-0.435902\pi$
$643$	10.1436	0.400024	0.200012	+	0.979793i	$0.435902\pi$
$644$	−0.339746	−0.0133879
$645$	3.26795	0.128675
$646$	9.19615	0.361818
$647$	43.3205	1.70310	0.851552	−	0.524269i	$-0.175662\pi$
$647$	43.3205	1.70310	0.851552	+	0.524269i	$0.175662\pi$
$648$	1.00000	0.0392837
$649$	0	0
$650$	3.00000	0.117670
$651$	−0.588457	−0.0230635
$652$	−20.0526	−0.785319
$653$	−15.8038	−0.618452	−0.309226	−	0.950989i	$-0.600070\pi$
$653$	−15.8038	−0.618452	−0.309226	+	0.950989i	$0.600070\pi$
$654$	6.53590	0.255574
$655$	−5.66025	−0.221164
$656$	1.26795	0.0495051
$657$	−4.19615	−0.163707
$658$	−1.32051	−0.0514788
$659$	−2.39230	−0.0931910	−0.0465955	−	0.998914i	$-0.514837\pi$
$659$	−2.39230	−0.0931910	−0.0465955	+	0.998914i	$0.514837\pi$
$660$	0	0
$661$	−7.80385	−0.303534	−0.151767	−	0.988416i	$-0.548496\pi$
$661$	−7.80385	−0.303534	−0.151767	+	0.988416i	$0.548496\pi$
$662$	14.5167	0.564206
$663$	11.1962	0.434823
$664$	9.39230	0.364492
$665$	0.660254	0.0256036
$666$	1.73205	0.0671156
$667$	3.80385	0.147286
$668$	−14.5359	−0.562411
$669$	−0.464102	−0.0179432
$670$	−4.53590	−0.175237
$671$	0	0
$672$	0.267949	0.0103364
$673$	9.85641	0.379937	0.189968	−	0.981790i	$-0.439161\pi$
$673$	9.85641	0.379937	0.189968	+	0.981790i	$0.439161\pi$
$674$	26.7321	1.02968
$675$	1.00000	0.0384900
$676$	−4.00000	−0.153846
$677$	4.05256	0.155752	0.0778762	−	0.996963i	$-0.475186\pi$
$677$	4.05256	0.155752	0.0778762	+	0.996963i	$0.475186\pi$
$678$	−13.8564	−0.532152
$679$	−4.09103	−0.157000
$680$	3.73205	0.143118
$681$	10.3923	0.398234
$682$	0	0
$683$	−30.1244	−1.15268	−0.576338	−	0.817211i	$-0.695519\pi$
$683$	−30.1244	−1.15268	−0.576338	+	0.817211i	$0.695519\pi$
$684$	2.46410	0.0942173
$685$	21.7846	0.832347
$686$	−3.73205	−0.142490
$687$	−12.0000	−0.457829
$688$	3.26795	0.124589
$689$	−26.1962	−0.997994
$690$	−1.26795	−0.0482700
$691$	12.9474	0.492544	0.246272	−	0.969201i	$-0.420794\pi$
$691$	12.9474	0.492544	0.246272	+	0.969201i	$0.420794\pi$
$692$	−16.5885	−0.630599
$693$	0	0
$694$	4.60770	0.174906
$695$	−14.3205	−0.543208
$696$	−3.00000	−0.113715
$697$	4.73205	0.179239
$698$	−19.8564	−0.751576
$699$	−25.8564	−0.977979
$700$	0.267949	0.0101275
$701$	−41.5359	−1.56879	−0.784395	−	0.620262i	$-0.787026\pi$
$701$	−41.5359	−1.56879	−0.784395	+	0.620262i	$0.787026\pi$
$702$	3.00000	0.113228
$703$	4.26795	0.160969
$704$	0	0
$705$	−4.92820	−0.185607
$706$	−6.92820	−0.260746
$707$	−3.33975	−0.125604
$708$	6.19615	0.232866
$709$	−21.6603	−0.813468	−0.406734	−	0.913547i	$-0.633332\pi$
$709$	−21.6603	−0.813468	−0.406734	+	0.913547i	$0.633332\pi$
$710$	3.92820	0.147423
$711$	7.46410	0.279926
$712$	4.39230	0.164609
$713$	2.78461	0.104284
$714$	1.00000	0.0374241
$715$	0	0
$716$	−17.1244	−0.639967
$717$	−9.73205	−0.363450
$718$	−20.5359	−0.766393
$719$	31.4641	1.17341	0.586706	−	0.809800i	$-0.300424\pi$
$719$	31.4641	1.17341	0.586706	+	0.809800i	$0.300424\pi$
$720$	1.00000	0.0372678
$721$	4.37307	0.162862
$722$	−12.9282	−0.481138
$723$	−5.33975	−0.198587
$724$	−6.19615	−0.230278
$725$	−3.00000	−0.111417
$726$	0	0
$727$	−49.4974	−1.83576	−0.917879	−	0.396861i	$-0.870100\pi$
$727$	−49.4974	−1.83576	−0.917879	+	0.396861i	$0.870100\pi$
$728$	0.803848	0.0297926
$729$	1.00000	0.0370370
$730$	−4.19615	−0.155307
$731$	12.1962	0.451091
$732$	8.19615	0.302939
$733$	−9.85641	−0.364055	−0.182027	−	0.983293i	$-0.558266\pi$
$733$	−9.85641	−0.364055	−0.182027	+	0.983293i	$0.558266\pi$
$734$	−12.8564	−0.474539
$735$	−6.92820	−0.255551
$736$	−1.26795	−0.0467372
$737$	0	0
$738$	1.26795	0.0466739
$739$	9.53590	0.350784	0.175392	−	0.984499i	$-0.443881\pi$
$739$	9.53590	0.350784	0.175392	+	0.984499i	$0.443881\pi$
$740$	1.73205	0.0636715
$741$	7.39230	0.271563
$742$	−2.33975	−0.0858948
$743$	4.05256	0.148674	0.0743370	−	0.997233i	$-0.476316\pi$
$743$	4.05256	0.148674	0.0743370	+	0.997233i	$0.476316\pi$
$744$	−2.19615	−0.0805149
$745$	20.3923	0.747116
$746$	19.9282	0.729623
$747$	9.39230	0.343646
$748$	0	0
$749$	1.21539	0.0444094
$750$	1.00000	0.0365148
$751$	38.1962	1.39380	0.696899	−	0.717170i	$-0.254563\pi$
$751$	38.1962	1.39380	0.696899	+	0.717170i	$0.254563\pi$
$752$	−4.92820	−0.179713
$753$	25.4641	0.927963
$754$	−9.00000	−0.327761
$755$	16.7321	0.608942
$756$	0.267949	0.00974522
$757$	3.46410	0.125905	0.0629525	−	0.998017i	$-0.479948\pi$
$757$	3.46410	0.125905	0.0629525	+	0.998017i	$0.479948\pi$
$758$	−37.4449	−1.36006
$759$	0	0
$760$	2.46410	0.0893824
$761$	47.3205	1.71537	0.857684	−	0.514178i	$-0.171903\pi$
$761$	47.3205	1.71537	0.857684	+	0.514178i	$0.171903\pi$
$762$	20.3923	0.738735
$763$	1.75129	0.0634009
$764$	11.5359	0.417354
$765$	3.73205	0.134933
$766$	−3.07180	−0.110989
$767$	18.5885	0.671190
$768$	1.00000	0.0360844
$769$	−34.5167	−1.24470	−0.622351	−	0.782738i	$-0.713822\pi$
$769$	−34.5167	−1.24470	−0.622351	+	0.782738i	$0.713822\pi$
$770$	0	0
$771$	−28.3205	−1.01994
$772$	2.53590	0.0912690
$773$	20.3397	0.731570	0.365785	−	0.930699i	$-0.380801\pi$
$773$	20.3397	0.731570	0.365785	+	0.930699i	$0.380801\pi$
$774$	3.26795	0.117464
$775$	−2.19615	−0.0788881
$776$	−15.2679	−0.548087
$777$	0.464102	0.0166496
$778$	−10.1436	−0.363665
$779$	3.12436	0.111942
$780$	3.00000	0.107417
$781$	0	0
$782$	−4.73205	−0.169218
$783$	−3.00000	−0.107211
$784$	−6.92820	−0.247436
$785$	2.80385	0.100074
$786$	−5.66025	−0.201895
$787$	−20.9808	−0.747883	−0.373942	−	0.927452i	$-0.621994\pi$
$787$	−20.9808	−0.747883	−0.373942	+	0.927452i	$0.621994\pi$
$788$	−6.53590	−0.232832
$789$	−0.875644	−0.0311738
$790$	7.46410	0.265561
$791$	−3.71281	−0.132012
$792$	0	0
$793$	24.5885	0.873162
$794$	−25.9808	−0.922023
$795$	−8.73205	−0.309694
$796$	4.39230	0.155681
$797$	47.3731	1.67804	0.839020	−	0.544100i	$-0.183129\pi$
$797$	47.3731	1.67804	0.839020	+	0.544100i	$0.183129\pi$
$798$	0.660254	0.0233727
$799$	−18.3923	−0.650673
$800$	1.00000	0.0353553
$801$	4.39230	0.155194
$802$	0.339746	0.0119968
$803$	0	0
$804$	−4.53590	−0.159969
$805$	−0.339746	−0.0119745
$806$	−6.58846	−0.232069
$807$	−19.5885	−0.689546
$808$	−12.4641	−0.438486
$809$	−22.7321	−0.799216	−0.399608	−	0.916686i	$-0.630854\pi$
$809$	−22.7321	−0.799216	−0.399608	+	0.916686i	$0.630854\pi$
$810$	1.00000	0.0351364
$811$	−13.0000	−0.456492	−0.228246	−	0.973604i	$-0.573299\pi$
$811$	−13.0000	−0.456492	−0.228246	+	0.973604i	$0.573299\pi$
$812$	−0.803848	−0.0282095
$813$	3.85641	0.135250
$814$	0	0
$815$	−20.0526	−0.702411
$816$	3.73205	0.130648
$817$	8.05256	0.281723
$818$	14.0000	0.489499
$819$	0.803848	0.0280887
$820$	1.26795	0.0442787
$821$	−47.3205	−1.65150	−0.825749	−	0.564038i	$-0.809247\pi$
$821$	−47.3205	−1.65150	−0.825749	+	0.564038i	$0.809247\pi$
$822$	21.7846	0.759826
$823$	1.39230	0.0485327	0.0242663	−	0.999706i	$-0.492275\pi$
$823$	1.39230	0.0485327	0.0242663	+	0.999706i	$0.492275\pi$
$824$	16.3205	0.568552
$825$	0	0
$826$	1.66025	0.0577676
$827$	−28.5692	−0.993449	−0.496725	−	0.867908i	$-0.665464\pi$
$827$	−28.5692	−0.993449	−0.496725	+	0.867908i	$0.665464\pi$
$828$	−1.26795	−0.0440643
$829$	37.1244	1.28938	0.644691	−	0.764443i	$-0.276986\pi$
$829$	37.1244	1.28938	0.644691	+	0.764443i	$0.276986\pi$
$830$	9.39230	0.326012
$831$	5.07180	0.175939
$832$	3.00000	0.104006
$833$	−25.8564	−0.895871
$834$	−14.3205	−0.495879
$835$	−14.5359	−0.503036
$836$	0	0
$837$	−2.19615	−0.0759101
$838$	−4.53590	−0.156690
$839$	−11.7846	−0.406850	−0.203425	−	0.979091i	$-0.565207\pi$
$839$	−11.7846	−0.406850	−0.203425	+	0.979091i	$0.565207\pi$
$840$	0.267949	0.00924513
$841$	−20.0000	−0.689655
$842$	34.0526	1.17353
$843$	−12.0526	−0.415112
$844$	−23.7846	−0.818700
$845$	−4.00000	−0.137604
$846$	−4.92820	−0.169435
$847$	0	0
$848$	−8.73205	−0.299860
$849$	18.2487	0.626294
$850$	3.73205	0.128008
$851$	−2.19615	−0.0752831
$852$	3.92820	0.134578
$853$	40.3205	1.38055	0.690274	−	0.723548i	$-0.257490\pi$
$853$	40.3205	1.38055	0.690274	+	0.723548i	$0.257490\pi$
$854$	2.19615	0.0751508
$855$	2.46410	0.0842705
$856$	4.53590	0.155034
$857$	−27.3397	−0.933908	−0.466954	−	0.884282i	$-0.654649\pi$
$857$	−27.3397	−0.933908	−0.466954	+	0.884282i	$0.654649\pi$
$858$	0	0
$859$	−22.3923	−0.764016	−0.382008	−	0.924159i	$-0.624767\pi$
$859$	−22.3923	−0.764016	−0.382008	+	0.924159i	$0.624767\pi$
$860$	3.26795	0.111436
$861$	0.339746	0.0115785
$862$	−18.1244	−0.617318
$863$	−36.2487	−1.23392	−0.616960	−	0.786994i	$-0.711636\pi$
$863$	−36.2487	−1.23392	−0.616960	+	0.786994i	$0.711636\pi$
$864$	1.00000	0.0340207
$865$	−16.5885	−0.564024
$866$	2.92820	0.0995044
$867$	−3.07180	−0.104324
$868$	−0.588457	−0.0199735
$869$	0	0
$870$	−3.00000	−0.101710
$871$	−13.6077	−0.461079
$872$	6.53590	0.221333
$873$	−15.2679	−0.516742
$874$	−3.12436	−0.105683
$875$	0.267949	0.00905834
$876$	−4.19615	−0.141775
$877$	−35.6410	−1.20351	−0.601756	−	0.798680i	$-0.705532\pi$
$877$	−35.6410	−1.20351	−0.601756	+	0.798680i	$0.705532\pi$
$878$	−8.92820	−0.301312
$879$	−5.07180	−0.171067
$880$	0	0
$881$	−8.44486	−0.284515	−0.142257	−	0.989830i	$-0.545436\pi$
$881$	−8.44486	−0.284515	−0.142257	+	0.989830i	$0.545436\pi$
$882$	−6.92820	−0.233285
$883$	47.1244	1.58586	0.792930	−	0.609312i	$-0.208554\pi$
$883$	47.1244	1.58586	0.792930	+	0.609312i	$0.208554\pi$
$884$	11.1962	0.376567
$885$	6.19615	0.208281
$886$	5.19615	0.174568
$887$	3.21539	0.107962	0.0539811	−	0.998542i	$-0.482809\pi$
$887$	3.21539	0.107962	0.0539811	+	0.998542i	$0.482809\pi$
$888$	1.73205	0.0581238
$889$	5.46410	0.183260
$890$	4.39230	0.147230
$891$	0	0
$892$	−0.464102	−0.0155393
$893$	−12.1436	−0.406370
$894$	20.3923	0.682021
$895$	−17.1244	−0.572404
$896$	0.267949	0.00895155
$897$	−3.80385	−0.127007
$898$	3.46410	0.115599
$899$	6.58846	0.219737
$900$	1.00000	0.0333333
$901$	−32.5885	−1.08568
$902$	0	0
$903$	0.875644	0.0291396
$904$	−13.8564	−0.460857
$905$	−6.19615	−0.205967
$906$	16.7321	0.555885
$907$	54.7846	1.81909	0.909547	−	0.415602i	$-0.136429\pi$
$907$	54.7846	1.81909	0.909547	+	0.415602i	$0.136429\pi$
$908$	10.3923	0.344881
$909$	−12.4641	−0.413408
$910$	0.803848	0.0266473
$911$	52.5692	1.74170	0.870848	−	0.491552i	$-0.163570\pi$
$911$	52.5692	1.74170	0.870848	+	0.491552i	$0.163570\pi$
$912$	2.46410	0.0815946
$913$	0	0
$914$	28.4449	0.940872
$915$	8.19615	0.270956
$916$	−12.0000	−0.396491
$917$	−1.51666	−0.0500845
$918$	3.73205	0.123176
$919$	−31.6603	−1.04438	−0.522188	−	0.852831i	$-0.674884\pi$
$919$	−31.6603	−1.04438	−0.522188	+	0.852831i	$0.674884\pi$
$920$	−1.26795	−0.0418030
$921$	3.26795	0.107683
$922$	31.2487	1.02912
$923$	11.7846	0.387895
$924$	0	0
$925$	1.73205	0.0569495
$926$	−4.53590	−0.149059
$927$	16.3205	0.536036
$928$	−3.00000	−0.0984798
$929$	−15.1244	−0.496214	−0.248107	−	0.968733i	$-0.579808\pi$
$929$	−15.1244	−0.496214	−0.248107	+	0.968733i	$0.579808\pi$
$930$	−2.19615	−0.0720147
$931$	−17.0718	−0.559506
$932$	−25.8564	−0.846955
$933$	−13.8564	−0.453638
$934$	−5.87564	−0.192257
$935$	0	0
$936$	3.00000	0.0980581
$937$	49.7128	1.62405	0.812023	−	0.583625i	$-0.198366\pi$
$937$	49.7128	1.62405	0.812023	+	0.583625i	$0.198366\pi$
$938$	−1.21539	−0.0396839
$939$	5.12436	0.167227
$940$	−4.92820	−0.160740
$941$	−6.07180	−0.197935	−0.0989675	−	0.995091i	$-0.531554\pi$
$941$	−6.07180	−0.197935	−0.0989675	+	0.995091i	$0.531554\pi$
$942$	2.80385	0.0913543
$943$	−1.60770	−0.0523538
$944$	6.19615	0.201668
$945$	0.267949	0.00871639
$946$	0	0
$947$	−18.8038	−0.611043	−0.305521	−	0.952185i	$-0.598831\pi$
$947$	−18.8038	−0.611043	−0.305521	+	0.952185i	$0.598831\pi$
$948$	7.46410	0.242423
$949$	−12.5885	−0.408639
$950$	2.46410	0.0799460
$951$	9.12436	0.295878
$952$	1.00000	0.0324102
$953$	−31.8564	−1.03193	−0.515965	−	0.856610i	$-0.672567\pi$
$953$	−31.8564	−1.03193	−0.515965	+	0.856610i	$0.672567\pi$
$954$	−8.73205	−0.282711
$955$	11.5359	0.373293
$956$	−9.73205	−0.314757
$957$	0	0
$958$	−11.7321	−0.379045
$959$	5.83717	0.188492
$960$	1.00000	0.0322749
$961$	−26.1769	−0.844417
$962$	5.19615	0.167531
$963$	4.53590	0.146167
$964$	−5.33975	−0.171982
$965$	2.53590	0.0816335
$966$	−0.339746	−0.0109311
$967$	28.5359	0.917653	0.458826	−	0.888526i	$-0.348270\pi$
$967$	28.5359	0.917653	0.458826	+	0.888526i	$0.348270\pi$
$968$	0	0
$969$	9.19615	0.295423
$970$	−15.2679	−0.490224
$971$	−2.53590	−0.0813809	−0.0406904	−	0.999172i	$-0.512956\pi$
$971$	−2.53590	−0.0813809	−0.0406904	+	0.999172i	$0.512956\pi$
$972$	1.00000	0.0320750
$973$	−3.83717	−0.123014
$974$	−0.464102	−0.0148708
$975$	3.00000	0.0960769
$976$	8.19615	0.262352
$977$	10.0000	0.319928	0.159964	−	0.987123i	$-0.448862\pi$
$977$	10.0000	0.319928	0.159964	+	0.987123i	$0.448862\pi$
$978$	−20.0526	−0.641210
$979$	0	0
$980$	−6.92820	−0.221313
$981$	6.53590	0.208675
$982$	4.73205	0.151006
$983$	1.41154	0.0450212	0.0225106	−	0.999747i	$-0.492834\pi$
$983$	1.41154	0.0450212	0.0225106	+	0.999747i	$0.492834\pi$
$984$	1.26795	0.0404207
$985$	−6.53590	−0.208251
$986$	−11.1962	−0.356558
$987$	−1.32051	−0.0420322
$988$	7.39230	0.235181
$989$	−4.14359	−0.131759
$990$	0	0
$991$	50.7846	1.61323	0.806613	−	0.591080i	$-0.201298\pi$
$991$	50.7846	1.61323	0.806613	+	0.591080i	$0.201298\pi$
$992$	−2.19615	−0.0697279
$993$	14.5167	0.460672
$994$	1.05256	0.0333851
$995$	4.39230	0.139245
$996$	9.39230	0.297607
$997$	38.6077	1.22272	0.611359	−	0.791353i	$-0.290623\pi$
$997$	38.6077	1.22272	0.611359	+	0.791353i	$0.290623\pi$
$998$	37.4449	1.18530
$999$	1.73205	0.0547997

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3630.2.a.bp.1.1	yes	2
11.10	odd	2		3630.2.a.bh.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3630.2.a.bh.1.2	✓	2	11.10	odd	2
3630.2.a.bp.1.1	yes	2	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3630.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +0.267949 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +0.267949 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +1.00000 q^{12} +3.00000 q^{13} +0.267949 q^{14} +1.00000 q^{15} +1.00000 q^{16} +3.73205 q^{17} +1.00000 q^{18} +2.46410 q^{19} +1.00000 q^{20} +0.267949 q^{21} -1.26795 q^{23} +1.00000 q^{24} +1.00000 q^{25} +3.00000 q^{26} +1.00000 q^{27} +0.267949 q^{28} -3.00000 q^{29} +1.00000 q^{30} -2.19615 q^{31} +1.00000 q^{32} +3.73205 q^{34} +0.267949 q^{35} +1.00000 q^{36} +1.73205 q^{37} +2.46410 q^{38} +3.00000 q^{39} +1.00000 q^{40} +1.26795 q^{41} +0.267949 q^{42} +3.26795 q^{43} +1.00000 q^{45} -1.26795 q^{46} -4.92820 q^{47} +1.00000 q^{48} -6.92820 q^{49} +1.00000 q^{50} +3.73205 q^{51} +3.00000 q^{52} -8.73205 q^{53} +1.00000 q^{54} +0.267949 q^{56} +2.46410 q^{57} -3.00000 q^{58} +6.19615 q^{59} +1.00000 q^{60} +8.19615 q^{61} -2.19615 q^{62} +0.267949 q^{63} +1.00000 q^{64} +3.00000 q^{65} -4.53590 q^{67} +3.73205 q^{68} -1.26795 q^{69} +0.267949 q^{70} +3.92820 q^{71} +1.00000 q^{72} -4.19615 q^{73} +1.73205 q^{74} +1.00000 q^{75} +2.46410 q^{76} +3.00000 q^{78} +7.46410 q^{79} +1.00000 q^{80} +1.00000 q^{81} +1.26795 q^{82} +9.39230 q^{83} +0.267949 q^{84} +3.73205 q^{85} +3.26795 q^{86} -3.00000 q^{87} +4.39230 q^{89} +1.00000 q^{90} +0.803848 q^{91} -1.26795 q^{92} -2.19615 q^{93} -4.92820 q^{94} +2.46410 q^{95} +1.00000 q^{96} -15.2679 q^{97} -6.92820 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} + 4 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 + 4 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} + 4 q^{7} + 2 q^{8} + 2 q^{9} + 2 q^{10} + 2 q^{12} + 6 q^{13} + 4 q^{14} + 2 q^{15} + 2 q^{16} + 4 q^{17} + 2 q^{18} - 2 q^{19} + 2 q^{20} + 4 q^{21} - 6 q^{23} + 2 q^{24} + 2 q^{25} + 6 q^{26} + 2 q^{27} + 4 q^{28} - 6 q^{29} + 2 q^{30} + 6 q^{31} + 2 q^{32} + 4 q^{34} + 4 q^{35} + 2 q^{36} - 2 q^{38} + 6 q^{39} + 2 q^{40} + 6 q^{41} + 4 q^{42} + 10 q^{43} + 2 q^{45} - 6 q^{46} + 4 q^{47} + 2 q^{48} + 2 q^{50} + 4 q^{51} + 6 q^{52} - 14 q^{53} + 2 q^{54} + 4 q^{56} - 2 q^{57} - 6 q^{58} + 2 q^{59} + 2 q^{60} + 6 q^{61} + 6 q^{62} + 4 q^{63} + 2 q^{64} + 6 q^{65} - 16 q^{67} + 4 q^{68} - 6 q^{69} + 4 q^{70} - 6 q^{71} + 2 q^{72} + 2 q^{73} + 2 q^{75} - 2 q^{76} + 6 q^{78} + 8 q^{79} + 2 q^{80} + 2 q^{81} + 6 q^{82} - 2 q^{83} + 4 q^{84} + 4 q^{85} + 10 q^{86} - 6 q^{87} - 12 q^{89} + 2 q^{90} + 12 q^{91} - 6 q^{92} + 6 q^{93} + 4 q^{94} - 2 q^{95} + 2 q^{96} - 34 q^{97}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 + 4 * q^7 + 2 * q^8 + 2 * q^9 + 2 * q^10 + 2 * q^12 + 6 * q^13 + 4 * q^14 + 2 * q^15 + 2 * q^16 + 4 * q^17 + 2 * q^18 - 2 * q^19 + 2 * q^20 + 4 * q^21 - 6 * q^23 + 2 * q^24 + 2 * q^25 + 6 * q^26 + 2 * q^27 + 4 * q^28 - 6 * q^29 + 2 * q^30 + 6 * q^31 + 2 * q^32 + 4 * q^34 + 4 * q^35 + 2 * q^36 - 2 * q^38 + 6 * q^39 + 2 * q^40 + 6 * q^41 + 4 * q^42 + 10 * q^43 + 2 * q^45 - 6 * q^46 + 4 * q^47 + 2 * q^48 + 2 * q^50 + 4 * q^51 + 6 * q^52 - 14 * q^53 + 2 * q^54 + 4 * q^56 - 2 * q^57 - 6 * q^58 + 2 * q^59 + 2 * q^60 + 6 * q^61 + 6 * q^62 + 4 * q^63 + 2 * q^64 + 6 * q^65 - 16 * q^67 + 4 * q^68 - 6 * q^69 + 4 * q^70 - 6 * q^71 + 2 * q^72 + 2 * q^73 + 2 * q^75 - 2 * q^76 + 6 * q^78 + 8 * q^79 + 2 * q^80 + 2 * q^81 + 6 * q^82 - 2 * q^83 + 4 * q^84 + 4 * q^85 + 10 * q^86 - 6 * q^87 - 12 * q^89 + 2 * q^90 + 12 * q^91 - 6 * q^92 + 6 * q^93 + 4 * q^94 - 2 * q^95 + 2 * q^96 - 34 * q^97

Introduction

L-functions

Modular forms

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Database

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