LMFDB - Embedded newform 4235.2.a.bn.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4235,2,Mod(1,4235)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4235, 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("4235.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4235 = 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4235.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:	$33.8166452560$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 24 x^{12} + 22 x^{11} + 223 x^{10} - 190 x^{9} - 1003 x^{8} + 814 x^{7} + 2214 x^{6} + \cdots + 80 $ x^14 - x^13 - 24x^12 + 22x^11 + 223x^10 - 190x^9 - 1003x^8 + 814x^7 + 2214x^6 - 1775x^5 - 2075x^4 + 1750x^3 + 400x^2 - 480x + 80
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 385)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$0.295402$ of defining polynomial
Character	$\chi$	$=$	4235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.295402 q^{2} -2.62617 q^{3} -1.91274 q^{4} -1.00000 q^{5} -0.775775 q^{6} -1.00000 q^{7} -1.15583 q^{8} +3.89676 q^{9} +O(q^{10})$	\(q+0.295402 q^{2} -2.62617 q^{3} -1.91274 q^{4} -1.00000 q^{5} -0.775775 q^{6} -1.00000 q^{7} -1.15583 q^{8} +3.89676 q^{9} -0.295402 q^{10} +5.02317 q^{12} -1.88925 q^{13} -0.295402 q^{14} +2.62617 q^{15} +3.48404 q^{16} -5.47426 q^{17} +1.15111 q^{18} -2.12205 q^{19} +1.91274 q^{20} +2.62617 q^{21} +3.16295 q^{23} +3.03540 q^{24} +1.00000 q^{25} -0.558089 q^{26} -2.35505 q^{27} +1.91274 q^{28} -8.99841 q^{29} +0.775775 q^{30} -7.44014 q^{31} +3.34085 q^{32} -1.61711 q^{34} +1.00000 q^{35} -7.45348 q^{36} -7.77004 q^{37} -0.626859 q^{38} +4.96150 q^{39} +1.15583 q^{40} -10.8636 q^{41} +0.775775 q^{42} -2.10912 q^{43} -3.89676 q^{45} +0.934342 q^{46} -5.08991 q^{47} -9.14968 q^{48} +1.00000 q^{49} +0.295402 q^{50} +14.3763 q^{51} +3.61365 q^{52} +9.78487 q^{53} -0.695685 q^{54} +1.15583 q^{56} +5.57287 q^{57} -2.65815 q^{58} +1.56395 q^{59} -5.02317 q^{60} -8.58140 q^{61} -2.19783 q^{62} -3.89676 q^{63} -5.98119 q^{64} +1.88925 q^{65} -12.4214 q^{67} +10.4708 q^{68} -8.30645 q^{69} +0.295402 q^{70} -14.1724 q^{71} -4.50399 q^{72} +3.03874 q^{73} -2.29528 q^{74} -2.62617 q^{75} +4.05893 q^{76} +1.46564 q^{78} -5.47128 q^{79} -3.48404 q^{80} -5.50553 q^{81} -3.20913 q^{82} -9.54866 q^{83} -5.02317 q^{84} +5.47426 q^{85} -0.623038 q^{86} +23.6313 q^{87} -11.5082 q^{89} -1.15111 q^{90} +1.88925 q^{91} -6.04990 q^{92} +19.5391 q^{93} -1.50357 q^{94} +2.12205 q^{95} -8.77364 q^{96} +1.56596 q^{97} +0.295402 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + q^{2} + 5 q^{3} + 21 q^{4} - 14 q^{5} - q^{6} - 14 q^{7} + 3 q^{8} + 17 q^{9}+O(q^{10}) $ 14 * q + q^2 + 5 * q^3 + 21 * q^4 - 14 * q^5 - q^6 - 14 * q^7 + 3 * q^8 + 17 * q^9	$ 14 q + q^{2} + 5 q^{3} + 21 q^{4} - 14 q^{5} - q^{6} - 14 q^{7} + 3 q^{8} + 17 q^{9} - q^{10} + 15 q^{12} - 10 q^{13} - q^{14} - 5 q^{15} + 31 q^{16} - 11 q^{17} + 21 q^{18} - 21 q^{19} - 21 q^{20} - 5 q^{21} + 8 q^{23} - 22 q^{24} + 14 q^{25} - 18 q^{26} + 26 q^{27} - 21 q^{28} + 4 q^{29} + q^{30} + 6 q^{31} + 42 q^{32} + 16 q^{34} + 14 q^{35} + 28 q^{36} + 48 q^{37} + 35 q^{38} - 6 q^{39} - 3 q^{40} - 13 q^{41} + q^{42} - 17 q^{45} + 31 q^{46} + 11 q^{47} + 59 q^{48} + 14 q^{49} + q^{50} + 33 q^{51} - 52 q^{52} + 31 q^{53} + 57 q^{54} - 3 q^{56} + 4 q^{57} + 52 q^{58} - 4 q^{59} - 15 q^{60} - 17 q^{61} + 27 q^{62} - 17 q^{63} + 43 q^{64} + 10 q^{65} + 45 q^{67} - 14 q^{68} + 20 q^{69} + q^{70} - 6 q^{71} + 14 q^{72} - 11 q^{73} + 33 q^{74} + 5 q^{75} + 5 q^{76} + 52 q^{78} - 30 q^{79} - 31 q^{80} - 6 q^{81} + 26 q^{82} - 23 q^{83} - 15 q^{84} + 11 q^{85} - 23 q^{86} - 23 q^{87} - 15 q^{89} - 21 q^{90} + 10 q^{91} + 44 q^{92} + 29 q^{93} - 49 q^{94} + 21 q^{95} + 52 q^{96} + 44 q^{97} + q^{98}+O(q^{100}) $ 14 * q + q^2 + 5 * q^3 + 21 * q^4 - 14 * q^5 - q^6 - 14 * q^7 + 3 * q^8 + 17 * q^9 - q^10 + 15 * q^12 - 10 * q^13 - q^14 - 5 * q^15 + 31 * q^16 - 11 * q^17 + 21 * q^18 - 21 * q^19 - 21 * q^20 - 5 * q^21 + 8 * q^23 - 22 * q^24 + 14 * q^25 - 18 * q^26 + 26 * q^27 - 21 * q^28 + 4 * q^29 + q^30 + 6 * q^31 + 42 * q^32 + 16 * q^34 + 14 * q^35 + 28 * q^36 + 48 * q^37 + 35 * q^38 - 6 * q^39 - 3 * q^40 - 13 * q^41 + q^42 - 17 * q^45 + 31 * q^46 + 11 * q^47 + 59 * q^48 + 14 * q^49 + q^50 + 33 * q^51 - 52 * q^52 + 31 * q^53 + 57 * q^54 - 3 * q^56 + 4 * q^57 + 52 * q^58 - 4 * q^59 - 15 * q^60 - 17 * q^61 + 27 * q^62 - 17 * q^63 + 43 * q^64 + 10 * q^65 + 45 * q^67 - 14 * q^68 + 20 * q^69 + q^70 - 6 * q^71 + 14 * q^72 - 11 * q^73 + 33 * q^74 + 5 * q^75 + 5 * q^76 + 52 * q^78 - 30 * q^79 - 31 * q^80 - 6 * q^81 + 26 * q^82 - 23 * q^83 - 15 * q^84 + 11 * q^85 - 23 * q^86 - 23 * q^87 - 15 * q^89 - 21 * q^90 + 10 * q^91 + 44 * q^92 + 29 * q^93 - 49 * q^94 + 21 * q^95 + 52 * q^96 + 44 * q^97 + q^98

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 $

$2$	0.295402	0.208881	0.104440	−	0.994531i	$-0.466695\pi$
$2$	0.295402	0.208881	0.104440	+	0.994531i	$0.466695\pi$
$3$	−2.62617	−1.51622	−0.758110	−	0.652127i	$-0.773877\pi$
$3$	−2.62617	−1.51622	−0.758110	+	0.652127i	$0.773877\pi$
$4$	−1.91274	−0.956369
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.775775	−0.316709
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.15583	−0.408648
$9$	3.89676	1.29892
$10$	−0.295402	−0.0934143
$11$	0	0
$11$	0	0
$12$	5.02317	1.45006
$13$	−1.88925	−0.523985	−0.261992	−	0.965070i	$-0.584380\pi$
$13$	−1.88925	−0.523985	−0.261992	+	0.965070i	$0.584380\pi$
$14$	−0.295402	−0.0789495
$15$	2.62617	0.678074
$16$	3.48404	0.871010
$17$	−5.47426	−1.32770	−0.663852	−	0.747864i	$-0.731080\pi$
$17$	−5.47426	−1.32770	−0.663852	+	0.747864i	$0.731080\pi$
$18$	1.15111	0.271319
$19$	−2.12205	−0.486832	−0.243416	−	0.969922i	$-0.578268\pi$
$19$	−2.12205	−0.486832	−0.243416	+	0.969922i	$0.578268\pi$
$20$	1.91274	0.427701
$21$	2.62617	0.573077
$22$	0	0
$23$	3.16295	0.659521	0.329761	−	0.944065i	$-0.393032\pi$
$23$	3.16295	0.659521	0.329761	+	0.944065i	$0.393032\pi$
$24$	3.03540	0.619599
$25$	1.00000	0.200000
$26$	−0.558089	−0.109450
$27$	−2.35505	−0.453229
$28$	1.91274	0.361473
$29$	−8.99841	−1.67096	−0.835482	−	0.549518i	$-0.814811\pi$
$29$	−8.99841	−1.67096	−0.835482	+	0.549518i	$0.814811\pi$
$30$	0.775775	0.141637
$31$	−7.44014	−1.33629	−0.668145	−	0.744031i	$-0.732911\pi$
$31$	−7.44014	−1.33629	−0.668145	+	0.744031i	$0.732911\pi$
$32$	3.34085	0.590585
$33$	0	0
$34$	−1.61711	−0.277332
$35$	1.00000	0.169031
$36$	−7.45348	−1.24225
$37$	−7.77004	−1.27739	−0.638694	−	0.769461i	$-0.720525\pi$
$37$	−7.77004	−1.27739	−0.638694	+	0.769461i	$0.720525\pi$
$38$	−0.626859	−0.101690
$39$	4.96150	0.794476
$40$	1.15583	0.182753
$41$	−10.8636	−1.69661	−0.848306	−	0.529506i	$-0.822377\pi$
$41$	−10.8636	−1.69661	−0.848306	+	0.529506i	$0.822377\pi$
$42$	0.775775	0.119705
$43$	−2.10912	−0.321638	−0.160819	−	0.986984i	$-0.551414\pi$
$43$	−2.10912	−0.321638	−0.160819	+	0.986984i	$0.551414\pi$
$44$	0	0
$45$	−3.89676	−0.580895
$46$	0.934342	0.137761
$47$	−5.08991	−0.742440	−0.371220	−	0.928545i	$-0.621060\pi$
$47$	−5.08991	−0.742440	−0.371220	+	0.928545i	$0.621060\pi$
$48$	−9.14968	−1.32064
$49$	1.00000	0.142857
$50$	0.295402	0.0417761
$51$	14.3763	2.01309
$52$	3.61365	0.501123
$53$	9.78487	1.34406	0.672028	−	0.740526i	$-0.265424\pi$
$53$	9.78487	1.34406	0.672028	+	0.740526i	$0.265424\pi$
$54$	−0.695685	−0.0946708
$55$	0	0
$56$	1.15583	0.154454
$57$	5.57287	0.738145
$58$	−2.65815	−0.349032
$59$	1.56395	0.203609	0.101804	−	0.994804i	$-0.467538\pi$
$59$	1.56395	0.203609	0.101804	+	0.994804i	$0.467538\pi$
$60$	−5.02317	−0.648489
$61$	−8.58140	−1.09874	−0.549368	−	0.835580i	$-0.685131\pi$
$61$	−8.58140	−1.09874	−0.549368	+	0.835580i	$0.685131\pi$
$62$	−2.19783	−0.279125
$63$	−3.89676	−0.490946
$64$	−5.98119	−0.747649
$65$	1.88925	0.234333
$66$	0	0
$67$	−12.4214	−1.51751	−0.758756	−	0.651375i	$-0.774192\pi$
$67$	−12.4214	−1.51751	−0.758756	+	0.651375i	$0.774192\pi$
$68$	10.4708	1.26977
$69$	−8.30645	−0.999979
$70$	0.295402	0.0353073
$71$	−14.1724	−1.68195	−0.840976	−	0.541072i	$-0.818019\pi$
$71$	−14.1724	−1.68195	−0.840976	+	0.541072i	$0.818019\pi$
$72$	−4.50399	−0.530801
$73$	3.03874	0.355658	0.177829	−	0.984061i	$-0.443093\pi$
$73$	3.03874	0.355658	0.177829	+	0.984061i	$0.443093\pi$
$74$	−2.29528	−0.266821
$75$	−2.62617	−0.303244
$76$	4.05893	0.465591
$77$	0	0
$78$	1.46564	0.165951
$79$	−5.47128	−0.615567	−0.307784	−	0.951456i	$-0.599587\pi$
$79$	−5.47128	−0.615567	−0.307784	+	0.951456i	$0.599587\pi$
$80$	−3.48404	−0.389528
$81$	−5.50553	−0.611726
$82$	−3.20913	−0.354389
$83$	−9.54866	−1.04810	−0.524051	−	0.851687i	$-0.675580\pi$
$83$	−9.54866	−1.04810	−0.524051	+	0.851687i	$0.675580\pi$
$84$	−5.02317	−0.548073
$85$	5.47426	0.593767
$86$	−0.623038	−0.0671839
$87$	23.6313	2.53355
$88$	0	0
$89$	−11.5082	−1.21986	−0.609932	−	0.792454i	$-0.708803\pi$
$89$	−11.5082	−1.21986	−0.609932	+	0.792454i	$0.708803\pi$
$90$	−1.15111	−0.121338
$91$	1.88925	0.198048
$92$	−6.04990	−0.630746
$93$	19.5391	2.02611
$94$	−1.50357	−0.155081
$95$	2.12205	0.217718
$96$	−8.77364	−0.895456
$97$	1.56596	0.159000	0.0794998	−	0.996835i	$-0.474668\pi$
$97$	1.56596	0.159000	0.0794998	+	0.996835i	$0.474668\pi$
$98$	0.295402	0.0298401
$99$	0	0
$100$	−1.91274	−0.191274
$101$	−7.57678	−0.753917	−0.376959	−	0.926230i	$-0.623030\pi$
$101$	−7.57678	−0.753917	−0.376959	+	0.926230i	$0.623030\pi$
$102$	4.24680	0.420496
$103$	5.60393	0.552172	0.276086	−	0.961133i	$-0.410963\pi$
$103$	5.60393	0.552172	0.276086	+	0.961133i	$0.410963\pi$
$104$	2.18366	0.214125
$105$	−2.62617	−0.256288
$106$	2.89047	0.280747
$107$	9.72425	0.940078	0.470039	−	0.882646i	$-0.344240\pi$
$107$	9.72425	0.940078	0.470039	+	0.882646i	$0.344240\pi$
$108$	4.50459	0.433454
$109$	12.7851	1.22459	0.612295	−	0.790630i	$-0.290247\pi$
$109$	12.7851	1.22459	0.612295	+	0.790630i	$0.290247\pi$
$110$	0	0
$111$	20.4054	1.93680
$112$	−3.48404	−0.329211
$113$	10.0801	0.948253	0.474126	−	0.880457i	$-0.342764\pi$
$113$	10.0801	0.948253	0.474126	+	0.880457i	$0.342764\pi$
$114$	1.64624	0.154184
$115$	−3.16295	−0.294947
$116$	17.2116	1.59806
$117$	−7.36197	−0.680614
$118$	0.461994	0.0425300
$119$	5.47426	0.501825
$120$	−3.03540	−0.277093
$121$	0	0
$122$	−2.53496	−0.229505
$123$	28.5297	2.57244
$124$	14.2310	1.27799
$125$	−1.00000	−0.0894427
$126$	−1.15111	−0.102549
$127$	−14.4809	−1.28497	−0.642487	−	0.766296i	$-0.722098\pi$
$127$	−14.4809	−1.28497	−0.642487	+	0.766296i	$0.722098\pi$
$128$	−8.44856	−0.746754
$129$	5.53891	0.487674
$130$	0.558089	0.0489476
$131$	−4.77968	−0.417603	−0.208801	−	0.977958i	$-0.566956\pi$
$131$	−4.77968	−0.417603	−0.208801	+	0.977958i	$0.566956\pi$
$132$	0	0
$133$	2.12205	0.184005
$134$	−3.66929	−0.316979
$135$	2.35505	0.202690
$136$	6.32732	0.542563
$137$	5.93883	0.507389	0.253694	−	0.967284i	$-0.418354\pi$
$137$	5.93883	0.507389	0.253694	+	0.967284i	$0.418354\pi$
$138$	−2.45374	−0.208876
$139$	−0.148326	−0.0125809	−0.00629043	−	0.999980i	$-0.502002\pi$
$139$	−0.148326	−0.0125809	−0.00629043	+	0.999980i	$0.502002\pi$
$140$	−1.91274	−0.161656
$141$	13.3670	1.12570
$142$	−4.18655	−0.351327
$143$	0	0
$144$	13.5765	1.13137
$145$	8.99841	0.747278
$146$	0.897651	0.0742901
$147$	−2.62617	−0.216603
$148$	14.8621	1.22165
$149$	−1.22559	−0.100404	−0.0502020	−	0.998739i	$-0.515987\pi$
$149$	−1.22559	−0.100404	−0.0502020	+	0.998739i	$0.515987\pi$
$150$	−0.775775	−0.0633418
$151$	6.59507	0.536699	0.268350	−	0.963322i	$-0.413522\pi$
$151$	6.59507	0.536699	0.268350	+	0.963322i	$0.413522\pi$
$152$	2.45273	0.198943
$153$	−21.3319	−1.72458
$154$	0	0
$155$	7.44014	0.597607
$156$	−9.49005	−0.759812
$157$	−2.39631	−0.191246	−0.0956231	−	0.995418i	$-0.530484\pi$
$157$	−2.39631	−0.191246	−0.0956231	+	0.995418i	$0.530484\pi$
$158$	−1.61623	−0.128580
$159$	−25.6967	−2.03788
$160$	−3.34085	−0.264118
$161$	−3.16295	−0.249276
$162$	−1.62634	−0.127778
$163$	21.3163	1.66962	0.834809	−	0.550539i	$-0.185578\pi$
$163$	21.3163	1.66962	0.834809	+	0.550539i	$0.185578\pi$
$164$	20.7792	1.62259
$165$	0	0
$166$	−2.82069	−0.218928
$167$	−15.6172	−1.20850	−0.604249	−	0.796796i	$-0.706527\pi$
$167$	−15.6172	−1.20850	−0.604249	+	0.796796i	$0.706527\pi$
$168$	−3.03540	−0.234187
$169$	−9.43072	−0.725440
$170$	1.61711	0.124027
$171$	−8.26914	−0.632357
$172$	4.03420	0.307604
$173$	13.5899	1.03322	0.516611	−	0.856220i	$-0.327193\pi$
$173$	13.5899	1.03322	0.516611	+	0.856220i	$0.327193\pi$
$174$	6.98074	0.529209
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	−4.10720	−0.308716
$178$	−3.39953	−0.254806
$179$	1.81444	0.135618	0.0678088	−	0.997698i	$-0.478399\pi$
$179$	1.81444	0.135618	0.0678088	+	0.997698i	$0.478399\pi$
$180$	7.45348	0.555550
$181$	−3.12693	−0.232423	−0.116211	−	0.993225i	$-0.537075\pi$
$181$	−3.12693	−0.232423	−0.116211	+	0.993225i	$0.537075\pi$
$182$	0.558089	0.0413683
$183$	22.5362	1.66592
$184$	−3.65584	−0.269512
$185$	7.77004	0.571265
$186$	5.77188	0.423215
$187$	0	0
$188$	9.73567	0.710046
$189$	2.35505	0.171304
$190$	0.626859	0.0454771
$191$	−24.2380	−1.75380	−0.876900	−	0.480672i	$-0.840393\pi$
$191$	−24.2380	−1.75380	−0.876900	+	0.480672i	$0.840393\pi$
$192$	15.7076	1.13360
$193$	−7.70423	−0.554563	−0.277281	−	0.960789i	$-0.589433\pi$
$193$	−7.70423	−0.554563	−0.277281	+	0.960789i	$0.589433\pi$
$194$	0.462589	0.0332120
$195$	−4.96150	−0.355300
$196$	−1.91274	−0.136624
$197$	7.35587	0.524084	0.262042	−	0.965056i	$-0.415604\pi$
$197$	7.35587	0.524084	0.262042	+	0.965056i	$0.415604\pi$
$198$	0	0
$199$	9.48043	0.672050	0.336025	−	0.941853i	$-0.390917\pi$
$199$	9.48043	0.672050	0.336025	+	0.941853i	$0.390917\pi$
$200$	−1.15583	−0.0817295
$201$	32.6206	2.30088
$202$	−2.23819	−0.157479
$203$	8.99841	0.631565
$204$	−27.4982	−1.92526
$205$	10.8636	0.758748
$206$	1.65541	0.115338
$207$	12.3253	0.856666
$208$	−6.58224	−0.456396
$209$	0	0
$210$	−0.775775	−0.0535336
$211$	−22.6124	−1.55670	−0.778352	−	0.627828i	$-0.783944\pi$
$211$	−22.6124	−1.55670	−0.778352	+	0.627828i	$0.783944\pi$
$212$	−18.7159	−1.28541
$213$	37.2191	2.55021
$214$	2.87256	0.196364
$215$	2.10912	0.143841
$216$	2.72203	0.185211
$217$	7.44014	0.505070
$218$	3.77674	0.255793
$219$	−7.98025	−0.539256
$220$	0	0
$221$	10.3423	0.695697
$222$	6.02780	0.404560
$223$	18.7296	1.25423	0.627114	−	0.778927i	$-0.284236\pi$
$223$	18.7296	1.25423	0.627114	+	0.778927i	$0.284236\pi$
$224$	−3.34085	−0.223220
$225$	3.89676	0.259784
$226$	2.97767	0.198072
$227$	5.19308	0.344677	0.172338	−	0.985038i	$-0.444868\pi$
$227$	5.19308	0.344677	0.172338	+	0.985038i	$0.444868\pi$
$228$	−10.6594	−0.705939
$229$	19.8494	1.31168	0.655842	−	0.754898i	$-0.272314\pi$
$229$	19.8494	1.31168	0.655842	+	0.754898i	$0.272314\pi$
$230$	−0.934342	−0.0616087
$231$	0	0
$232$	10.4006	0.682835
$233$	−9.56398	−0.626557	−0.313279	−	0.949661i	$-0.601427\pi$
$233$	−9.56398	−0.626557	−0.313279	+	0.949661i	$0.601427\pi$
$234$	−2.17474	−0.142167
$235$	5.08991	0.332029
$236$	−2.99143	−0.194725
$237$	14.3685	0.933335
$238$	1.61711	0.104822
$239$	16.3283	1.05619	0.528096	−	0.849185i	$-0.322906\pi$
$239$	16.3283	1.05619	0.528096	+	0.849185i	$0.322906\pi$
$240$	9.14968	0.590609
$241$	12.8632	0.828592	0.414296	−	0.910142i	$-0.364028\pi$
$241$	12.8632	0.828592	0.414296	+	0.910142i	$0.364028\pi$
$242$	0	0
$243$	21.5236	1.38074
$244$	16.4140	1.05080
$245$	−1.00000	−0.0638877
$246$	8.42772	0.537332
$247$	4.00910	0.255093
$248$	8.59954	0.546071
$249$	25.0764	1.58915
$250$	−0.295402	−0.0186829
$251$	−27.0388	−1.70667	−0.853336	−	0.521362i	$-0.825424\pi$
$251$	−27.0388	−1.70667	−0.853336	+	0.521362i	$0.825424\pi$
$252$	7.45348	0.469525
$253$	0	0
$254$	−4.27769	−0.268406
$255$	−14.3763	−0.900281
$256$	9.46666	0.591666
$257$	12.5915	0.785435	0.392717	−	0.919659i	$-0.371535\pi$
$257$	12.5915	0.785435	0.392717	+	0.919659i	$0.371535\pi$
$258$	1.63620	0.101866
$259$	7.77004	0.482807
$260$	−3.61365	−0.224109
$261$	−35.0647	−2.17045
$262$	−1.41193	−0.0872291
$263$	17.9541	1.10710	0.553549	−	0.832817i	$-0.313273\pi$
$263$	17.9541	1.10710	0.553549	+	0.832817i	$0.313273\pi$
$264$	0	0
$265$	−9.78487	−0.601080
$266$	0.626859	0.0384352
$267$	30.2224	1.84958
$268$	23.7588	1.45130
$269$	−8.64204	−0.526915	−0.263457	−	0.964671i	$-0.584863\pi$
$269$	−8.64204	−0.526915	−0.263457	+	0.964671i	$0.584863\pi$
$270$	0.695685	0.0423381
$271$	−6.25483	−0.379954	−0.189977	−	0.981789i	$-0.560841\pi$
$271$	−6.25483	−0.379954	−0.189977	+	0.981789i	$0.560841\pi$
$272$	−19.0726	−1.15644
$273$	−4.96150	−0.300284
$274$	1.75434	0.105984
$275$	0	0
$276$	15.8881	0.956349
$277$	−20.2456	−1.21644	−0.608221	−	0.793768i	$-0.708117\pi$
$277$	−20.2456	−1.21644	−0.608221	+	0.793768i	$0.708117\pi$
$278$	−0.0438158	−0.00262790
$279$	−28.9925	−1.73573
$280$	−1.15583	−0.0690741
$281$	19.3005	1.15137	0.575684	−	0.817672i	$-0.304736\pi$
$281$	19.3005	1.15137	0.575684	+	0.817672i	$0.304736\pi$
$282$	3.94863	0.235137
$283$	−6.89332	−0.409765	−0.204883	−	0.978787i	$-0.565681\pi$
$283$	−6.89332	−0.409765	−0.204883	+	0.978787i	$0.565681\pi$
$284$	27.1081	1.60857
$285$	−5.57287	−0.330108
$286$	0	0
$287$	10.8636	0.641259
$288$	13.0185	0.767123
$289$	12.9676	0.762798
$290$	2.65815	0.156092
$291$	−4.11249	−0.241078
$292$	−5.81232	−0.340140
$293$	−20.6826	−1.20829	−0.604144	−	0.796875i	$-0.706485\pi$
$293$	−20.6826	−1.20829	−0.604144	+	0.796875i	$0.706485\pi$
$294$	−0.775775	−0.0452441
$295$	−1.56395	−0.0910567
$296$	8.98085	0.522001
$297$	0	0
$298$	−0.362040	−0.0209724
$299$	−5.97562	−0.345579
$300$	5.02317	0.290013
$301$	2.10912	0.121568
$302$	1.94820	0.112106
$303$	19.8979	1.14310
$304$	−7.39332	−0.424036
$305$	8.58140	0.491370
$306$	−6.30148	−0.360232
$307$	−22.6857	−1.29474	−0.647371	−	0.762175i	$-0.724132\pi$
$307$	−22.6857	−1.29474	−0.647371	+	0.762175i	$0.724132\pi$
$308$	0	0
$309$	−14.7169	−0.837213
$310$	2.19783	0.124828
$311$	3.79174	0.215010	0.107505	−	0.994205i	$-0.465714\pi$
$311$	3.79174	0.215010	0.107505	+	0.994205i	$0.465714\pi$
$312$	−5.73465	−0.324661
$313$	−12.6789	−0.716652	−0.358326	−	0.933597i	$-0.616652\pi$
$313$	−12.6789	−0.716652	−0.358326	+	0.933597i	$0.616652\pi$
$314$	−0.707874	−0.0399476
$315$	3.89676	0.219558
$316$	10.4651	0.588709
$317$	4.01106	0.225284	0.112642	−	0.993636i	$-0.464069\pi$
$317$	4.01106	0.225284	0.112642	+	0.993636i	$0.464069\pi$
$318$	−7.59086	−0.425674
$319$	0	0
$320$	5.98119	0.334359
$321$	−25.5375	−1.42536
$322$	−0.934342	−0.0520689
$323$	11.6167	0.646369
$324$	10.5306	0.585036
$325$	−1.88925	−0.104797
$326$	6.29686	0.348751
$327$	−33.5758	−1.85675
$328$	12.5565	0.693316
$329$	5.08991	0.280616
$330$	0	0
$331$	10.5126	0.577826	0.288913	−	0.957355i	$-0.406706\pi$
$331$	10.5126	0.577826	0.288913	+	0.957355i	$0.406706\pi$
$332$	18.2641	1.00237
$333$	−30.2780	−1.65922
$334$	−4.61336	−0.252432
$335$	12.4214	0.678652
$336$	9.14968	0.499156
$337$	−7.57574	−0.412677	−0.206338	−	0.978481i	$-0.566155\pi$
$337$	−7.57574	−0.412677	−0.206338	+	0.978481i	$0.566155\pi$
$338$	−2.78585	−0.151530
$339$	−26.4720	−1.43776
$340$	−10.4708	−0.567861
$341$	0	0
$342$	−2.44272	−0.132087
$343$	−1.00000	−0.0539949
$344$	2.43779	0.131437
$345$	8.30645	0.447204
$346$	4.01449	0.215820
$347$	−7.57214	−0.406494	−0.203247	−	0.979128i	$-0.565149\pi$
$347$	−7.57214	−0.406494	−0.203247	+	0.979128i	$0.565149\pi$
$348$	−45.2006	−2.42301
$349$	28.4864	1.52484	0.762421	−	0.647082i	$-0.224011\pi$
$349$	28.4864	1.52484	0.762421	+	0.647082i	$0.224011\pi$
$350$	−0.295402	−0.0157899
$351$	4.44928	0.237485
$352$	0	0
$353$	−0.944021	−0.0502452	−0.0251226	−	0.999684i	$-0.507998\pi$
$353$	−0.944021	−0.0502452	−0.0251226	+	0.999684i	$0.507998\pi$
$354$	−1.21327	−0.0644848
$355$	14.1724	0.752192
$356$	22.0121	1.16664
$357$	−14.3763	−0.760877
$358$	0.535989	0.0283279
$359$	17.6292	0.930431	0.465216	−	0.885197i	$-0.345977\pi$
$359$	17.6292	0.930431	0.465216	+	0.885197i	$0.345977\pi$
$360$	4.50399	0.237381
$361$	−14.4969	−0.762994
$362$	−0.923700	−0.0485486
$363$	0	0
$364$	−3.61365	−0.189407
$365$	−3.03874	−0.159055
$366$	6.65724	0.347979
$367$	−22.1884	−1.15822	−0.579112	−	0.815248i	$-0.696601\pi$
$367$	−22.1884	−1.15822	−0.579112	+	0.815248i	$0.696601\pi$
$368$	11.0199	0.574450
$369$	−42.3329	−2.20376
$370$	2.29528	0.119326
$371$	−9.78487	−0.508005
$372$	−37.3731	−1.93771
$373$	−7.64036	−0.395603	−0.197801	−	0.980242i	$-0.563380\pi$
$373$	−7.64036	−0.395603	−0.197801	+	0.980242i	$0.563380\pi$
$374$	0	0
$375$	2.62617	0.135615
$376$	5.88307	0.303396
$377$	17.0003	0.875559
$378$	0.695685	0.0357822
$379$	−8.91260	−0.457809	−0.228905	−	0.973449i	$-0.573514\pi$
$379$	−8.91260	−0.457809	−0.228905	+	0.973449i	$0.573514\pi$
$380$	−4.05893	−0.208219
$381$	38.0294	1.94830
$382$	−7.15995	−0.366335
$383$	2.98489	0.152521	0.0762605	−	0.997088i	$-0.475702\pi$
$383$	2.98489	0.152521	0.0762605	+	0.997088i	$0.475702\pi$
$384$	22.1873	1.13224
$385$	0	0
$386$	−2.27585	−0.115837
$387$	−8.21874	−0.417782
$388$	−2.99528	−0.152062
$389$	26.4403	1.34058	0.670288	−	0.742101i	$-0.266170\pi$
$389$	26.4403	1.34058	0.670288	+	0.742101i	$0.266170\pi$
$390$	−1.46564	−0.0742154
$391$	−17.3148	−0.875649
$392$	−1.15583	−0.0583782
$393$	12.5522	0.633177
$394$	2.17294	0.109471
$395$	5.47128	0.275290
$396$	0	0
$397$	24.8044	1.24490	0.622448	−	0.782661i	$-0.286138\pi$
$397$	24.8044	1.24490	0.622448	+	0.782661i	$0.286138\pi$
$398$	2.80054	0.140378
$399$	−5.57287	−0.278992
$400$	3.48404	0.174202
$401$	11.5579	0.577175	0.288588	−	0.957453i	$-0.406814\pi$
$401$	11.5579	0.577175	0.288588	+	0.957453i	$0.406814\pi$
$402$	9.63619	0.480609
$403$	14.0563	0.700195
$404$	14.4924	0.721023
$405$	5.50553	0.273572
$406$	2.65815	0.131922
$407$	0	0
$408$	−16.6166	−0.822645
$409$	−0.174666	−0.00863667	−0.00431834	−	0.999991i	$-0.501375\pi$
$409$	−0.174666	−0.00863667	−0.00431834	+	0.999991i	$0.501375\pi$
$410$	3.20913	0.158488
$411$	−15.5964	−0.769312
$412$	−10.7188	−0.528080
$413$	−1.56395	−0.0769570
$414$	3.64091	0.178941
$415$	9.54866	0.468725
$416$	−6.31172	−0.309457
$417$	0.389529	0.0190753
$418$	0	0
$419$	−11.0698	−0.540793	−0.270397	−	0.962749i	$-0.587155\pi$
$419$	−11.0698	−0.540793	−0.270397	+	0.962749i	$0.587155\pi$
$420$	5.02317	0.245106
$421$	30.2715	1.47534	0.737672	−	0.675159i	$-0.235925\pi$
$421$	30.2715	1.47534	0.737672	+	0.675159i	$0.235925\pi$
$422$	−6.67976	−0.325165
$423$	−19.8342	−0.964370
$424$	−11.3096	−0.549245
$425$	−5.47426	−0.265541
$426$	10.9946	0.532689
$427$	8.58140	0.415283
$428$	−18.5999	−0.899062
$429$	0	0
$430$	0.623038	0.0300456
$431$	−20.0914	−0.967769	−0.483884	−	0.875132i	$-0.660774\pi$
$431$	−20.0914	−0.967769	−0.483884	+	0.875132i	$0.660774\pi$
$432$	−8.20508	−0.394767
$433$	23.2680	1.11819	0.559095	−	0.829103i	$-0.311149\pi$
$433$	23.2680	1.11819	0.559095	+	0.829103i	$0.311149\pi$
$434$	2.19783	0.105499
$435$	−23.6313	−1.13304
$436$	−24.4545	−1.17116
$437$	−6.71196	−0.321076
$438$	−2.35738	−0.112640
$439$	−31.7150	−1.51367	−0.756837	−	0.653603i	$-0.773257\pi$
$439$	−31.7150	−1.51367	−0.756837	+	0.653603i	$0.773257\pi$
$440$	0	0
$441$	3.89676	0.185560
$442$	3.05513	0.145318
$443$	2.28953	0.108779	0.0543894	−	0.998520i	$-0.482679\pi$
$443$	2.28953	0.108779	0.0543894	+	0.998520i	$0.482679\pi$
$444$	−39.0303	−1.85229
$445$	11.5082	0.545539
$446$	5.53277	0.261984
$447$	3.21860	0.152234
$448$	5.98119	0.282585
$449$	−41.7112	−1.96847	−0.984236	−	0.176859i	$-0.943406\pi$
$449$	−41.7112	−1.96847	−0.984236	+	0.176859i	$0.943406\pi$
$450$	1.15111	0.0542639
$451$	0	0
$452$	−19.2805	−0.906880
$453$	−17.3198	−0.813754
$454$	1.53405	0.0719963
$455$	−1.88925	−0.0885696
$456$	−6.44129	−0.301641
$457$	15.3294	0.717078	0.358539	−	0.933515i	$-0.383275\pi$
$457$	15.3294	0.717078	0.358539	+	0.933515i	$0.383275\pi$
$458$	5.86354	0.273985
$459$	12.8922	0.601754
$460$	6.04990	0.282078
$461$	16.2175	0.755324	0.377662	−	0.925943i	$-0.376728\pi$
$461$	16.2175	0.755324	0.377662	+	0.925943i	$0.376728\pi$
$462$	0	0
$463$	−31.2769	−1.45356	−0.726780	−	0.686871i	$-0.758984\pi$
$463$	−31.2769	−1.45356	−0.726780	+	0.686871i	$0.758984\pi$
$464$	−31.3508	−1.45543
$465$	−19.5391	−0.906103
$466$	−2.82522	−0.130876
$467$	−15.3204	−0.708946	−0.354473	−	0.935066i	$-0.615340\pi$
$467$	−15.3204	−0.708946	−0.354473	+	0.935066i	$0.615340\pi$
$468$	14.0815	0.650918
$469$	12.4214	0.573565
$470$	1.50357	0.0693545
$471$	6.29311	0.289971
$472$	−1.80766	−0.0832043
$473$	0	0
$474$	4.24448	0.194956
$475$	−2.12205	−0.0973665
$476$	−10.4708	−0.479930
$477$	38.1293	1.74582
$478$	4.82342	0.220618
$479$	−32.5356	−1.48659	−0.743294	−	0.668965i	$-0.766738\pi$
$479$	−32.5356	−1.48659	−0.743294	+	0.668965i	$0.766738\pi$
$480$	8.77364	0.400460
$481$	14.6796	0.669331
$482$	3.79982	0.173077
$483$	8.30645	0.377957
$484$	0	0
$485$	−1.56596	−0.0711068
$486$	6.35811	0.288410
$487$	−35.1588	−1.59320	−0.796600	−	0.604507i	$-0.793370\pi$
$487$	−35.1588	−1.59320	−0.796600	+	0.604507i	$0.793370\pi$
$488$	9.91864	0.448996
$489$	−55.9801	−2.53151
$490$	−0.295402	−0.0133449
$491$	12.5127	0.564692	0.282346	−	0.959313i	$-0.408887\pi$
$491$	12.5127	0.564692	0.282346	+	0.959313i	$0.408887\pi$
$492$	−54.5698	−2.46020
$493$	49.2597	2.21854
$494$	1.18429	0.0532839
$495$	0	0
$496$	−25.9218	−1.16392
$497$	14.1724	0.635718
$498$	7.40761	0.331943
$499$	−29.0987	−1.30263	−0.651317	−	0.758805i	$-0.725783\pi$
$499$	−29.0987	−1.30263	−0.651317	+	0.758805i	$0.725783\pi$
$500$	1.91274	0.0855402
$501$	41.0135	1.83235
$502$	−7.98730	−0.356491
$503$	−35.0649	−1.56346	−0.781732	−	0.623614i	$-0.785664\pi$
$503$	−35.0649	−1.56346	−0.781732	+	0.623614i	$0.785664\pi$
$504$	4.50399	0.200624
$505$	7.57678	0.337162
$506$	0	0
$507$	24.7667	1.09993
$508$	27.6982	1.22891
$509$	33.4298	1.48175	0.740875	−	0.671643i	$-0.234411\pi$
$509$	33.4298	1.48175	0.740875	+	0.671643i	$0.234411\pi$
$510$	−4.24680	−0.188051
$511$	−3.03874	−0.134426
$512$	19.6936	0.870342
$513$	4.99754	0.220647
$514$	3.71955	0.164062
$515$	−5.60393	−0.246939
$516$	−10.5945	−0.466396
$517$	0	0
$518$	2.29528	0.100849
$519$	−35.6894	−1.56659
$520$	−2.18366	−0.0957596
$521$	2.65686	0.116399	0.0581995	−	0.998305i	$-0.481464\pi$
$521$	2.65686	0.116399	0.0581995	+	0.998305i	$0.481464\pi$
$522$	−10.3582	−0.453365
$523$	−38.7475	−1.69431	−0.847156	−	0.531344i	$-0.821687\pi$
$523$	−38.7475	−1.69431	−0.847156	+	0.531344i	$0.821687\pi$
$524$	9.14227	0.399382
$525$	2.62617	0.114615
$526$	5.30368	0.231251
$527$	40.7293	1.77420
$528$	0	0
$529$	−12.9957	−0.565031
$530$	−2.89047	−0.125554
$531$	6.09434	0.264472
$532$	−4.05893	−0.175977
$533$	20.5241	0.888999
$534$	8.92775	0.386341
$535$	−9.72425	−0.420416
$536$	14.3570	0.620127
$537$	−4.76502	−0.205626
$538$	−2.55288	−0.110062
$539$	0	0
$540$	−4.50459	−0.193847
$541$	22.4073	0.963365	0.481682	−	0.876346i	$-0.340026\pi$
$541$	22.4073	0.963365	0.481682	+	0.876346i	$0.340026\pi$
$542$	−1.84769	−0.0793651
$543$	8.21184	0.352404
$544$	−18.2887	−0.784122
$545$	−12.7851	−0.547653
$546$	−1.46564	−0.0627234
$547$	38.7371	1.65628	0.828140	−	0.560521i	$-0.189399\pi$
$547$	38.7371	1.65628	0.828140	+	0.560521i	$0.189399\pi$
$548$	−11.3594	−0.485251
$549$	−33.4397	−1.42717
$550$	0	0
$551$	19.0951	0.813479
$552$	9.60084	0.408639
$553$	5.47128	0.232663
$554$	−5.98060	−0.254091
$555$	−20.4054	−0.866163
$556$	0.283709	0.0120319
$557$	−7.09183	−0.300490	−0.150245	−	0.988649i	$-0.548006\pi$
$557$	−7.09183	−0.300490	−0.150245	+	0.988649i	$0.548006\pi$
$558$	−8.56443	−0.362561
$559$	3.98466	0.168533
$560$	3.48404	0.147228
$561$	0	0
$562$	5.70139	0.240499
$563$	30.3982	1.28113	0.640566	−	0.767903i	$-0.278700\pi$
$563$	30.3982	1.28113	0.640566	+	0.767903i	$0.278700\pi$
$564$	−25.5675	−1.07659
$565$	−10.0801	−0.424072
$566$	−2.03630	−0.0855920
$567$	5.50553	0.231211
$568$	16.3809	0.687326
$569$	−9.12391	−0.382494	−0.191247	−	0.981542i	$-0.561253\pi$
$569$	−9.12391	−0.382494	−0.191247	+	0.981542i	$0.561253\pi$
$570$	−1.64624	−0.0689532
$571$	26.2759	1.09961	0.549805	−	0.835293i	$-0.314702\pi$
$571$	26.2759	1.09961	0.549805	+	0.835293i	$0.314702\pi$
$572$	0	0
$573$	63.6531	2.65915
$574$	3.20913	0.133947
$575$	3.16295	0.131904
$576$	−23.3073	−0.971136
$577$	25.6209	1.06661	0.533307	−	0.845922i	$-0.320949\pi$
$577$	25.6209	1.06661	0.533307	+	0.845922i	$0.320949\pi$
$578$	3.83064	0.159334
$579$	20.2326	0.840839
$580$	−17.2116	−0.714673
$581$	9.54866	0.396145
$582$	−1.21484	−0.0503566
$583$	0	0
$584$	−3.51227	−0.145339
$585$	7.36197	0.304380
$586$	−6.10967	−0.252388
$587$	−33.7865	−1.39452	−0.697259	−	0.716820i	$-0.745597\pi$
$587$	−33.7865	−1.39452	−0.697259	+	0.716820i	$0.745597\pi$
$588$	5.02317	0.207152
$589$	15.7884	0.650549
$590$	−0.461994	−0.0190200
$591$	−19.3178	−0.794626
$592$	−27.0711	−1.11262
$593$	−34.0412	−1.39790	−0.698952	−	0.715169i	$-0.746350\pi$
$593$	−34.0412	−1.39790	−0.698952	+	0.715169i	$0.746350\pi$
$594$	0	0
$595$	−5.47426	−0.224423
$596$	2.34422	0.0960232
$597$	−24.8972	−1.01897
$598$	−1.76521	−0.0721848
$599$	−0.258526	−0.0105631	−0.00528154	−	0.999986i	$-0.501681\pi$
$599$	−0.258526	−0.0105631	−0.00528154	+	0.999986i	$0.501681\pi$
$600$	3.03540	0.123920
$601$	−28.3595	−1.15681	−0.578405	−	0.815750i	$-0.696325\pi$
$601$	−28.3595	−1.15681	−0.578405	+	0.815750i	$0.696325\pi$
$602$	0.623038	0.0253931
$603$	−48.4031	−1.97113
$604$	−12.6146	−0.513283
$605$	0	0
$606$	5.87787	0.238772
$607$	23.0735	0.936523	0.468262	−	0.883590i	$-0.344881\pi$
$607$	23.0735	0.936523	0.468262	+	0.883590i	$0.344881\pi$
$608$	−7.08947	−0.287516
$609$	−23.6313	−0.957591
$610$	2.53496	0.102638
$611$	9.61613	0.389027
$612$	40.8023	1.64934
$613$	8.14255	0.328874	0.164437	−	0.986388i	$-0.447419\pi$
$613$	8.14255	0.328874	0.164437	+	0.986388i	$0.447419\pi$
$614$	−6.70140	−0.270447
$615$	−28.5297	−1.15043
$616$	0	0
$617$	−13.3652	−0.538063	−0.269031	−	0.963131i	$-0.586704\pi$
$617$	−13.3652	−0.538063	−0.269031	+	0.963131i	$0.586704\pi$
$618$	−4.34739	−0.174878
$619$	−25.5796	−1.02813	−0.514065	−	0.857751i	$-0.671861\pi$
$619$	−25.5796	−1.02813	−0.514065	+	0.857751i	$0.671861\pi$
$620$	−14.2310	−0.571532
$621$	−7.44891	−0.298914
$622$	1.12009	0.0449114
$623$	11.5082	0.461065
$624$	17.2861	0.691996
$625$	1.00000	0.0400000
$626$	−3.74536	−0.149695
$627$	0	0
$628$	4.58351	0.182902
$629$	42.5353	1.69599
$630$	1.15111	0.0458613
$631$	26.7595	1.06528	0.532640	−	0.846342i	$-0.321200\pi$
$631$	26.7595	1.06528	0.532640	+	0.846342i	$0.321200\pi$
$632$	6.32387	0.251550
$633$	59.3841	2.36031
$634$	1.18487	0.0470574
$635$	14.4809	0.574658
$636$	49.1511	1.94897
$637$	−1.88925	−0.0748549
$638$	0	0
$639$	−55.2264	−2.18472
$640$	8.44856	0.333959
$641$	−24.6975	−0.975493	−0.487746	−	0.872985i	$-0.662181\pi$
$641$	−24.6975	−0.975493	−0.487746	+	0.872985i	$0.662181\pi$
$642$	−7.54383	−0.297731
$643$	23.2394	0.916472	0.458236	−	0.888831i	$-0.348481\pi$
$643$	23.2394	0.916472	0.458236	+	0.888831i	$0.348481\pi$
$644$	6.04990	0.238399
$645$	−5.53891	−0.218094
$646$	3.43159	0.135014
$647$	1.69325	0.0665685	0.0332843	−	0.999446i	$-0.489403\pi$
$647$	1.69325	0.0665685	0.0332843	+	0.999446i	$0.489403\pi$
$648$	6.36346	0.249980
$649$	0	0
$650$	−0.558089	−0.0218901
$651$	−19.5391	−0.765797
$652$	−40.7724	−1.59677
$653$	−2.16400	−0.0846839	−0.0423419	−	0.999103i	$-0.513482\pi$
$653$	−2.16400	−0.0846839	−0.0423419	+	0.999103i	$0.513482\pi$
$654$	−9.91835	−0.387838
$655$	4.77968	0.186758
$656$	−37.8493	−1.47777
$657$	11.8413	0.461972
$658$	1.50357	0.0586152
$659$	−5.25913	−0.204867	−0.102433	−	0.994740i	$-0.532663\pi$
$659$	−5.25913	−0.204867	−0.102433	+	0.994740i	$0.532663\pi$
$660$	0	0
$661$	−18.9704	−0.737865	−0.368932	−	0.929456i	$-0.620277\pi$
$661$	−18.9704	−0.737865	−0.368932	+	0.929456i	$0.620277\pi$
$662$	3.10545	0.120697
$663$	−27.1606	−1.05483
$664$	11.0366	0.428304
$665$	−2.12205	−0.0822897
$666$	−8.94418	−0.346580
$667$	−28.4616	−1.10204
$668$	29.8717	1.15577
$669$	−49.1872	−1.90169
$670$	3.66929	0.141757
$671$	0	0
$672$	8.77364	0.338451
$673$	24.1297	0.930130	0.465065	−	0.885276i	$-0.346031\pi$
$673$	24.1297	0.930130	0.465065	+	0.885276i	$0.346031\pi$
$674$	−2.23789	−0.0862002
$675$	−2.35505	−0.0906458
$676$	18.0385	0.693788
$677$	−32.6539	−1.25499	−0.627496	−	0.778620i	$-0.715920\pi$
$677$	−32.6539	−1.25499	−0.627496	+	0.778620i	$0.715920\pi$
$678$	−7.81987	−0.300320
$679$	−1.56596	−0.0600962
$680$	−6.32732	−0.242642
$681$	−13.6379	−0.522606
$682$	0	0
$683$	30.1315	1.15295	0.576475	−	0.817115i	$-0.304428\pi$
$683$	30.1315	1.15295	0.576475	+	0.817115i	$0.304428\pi$
$684$	15.8167	0.604766
$685$	−5.93883	−0.226911
$686$	−0.295402	−0.0112785
$687$	−52.1278	−1.98880
$688$	−7.34826	−0.280150
$689$	−18.4861	−0.704264
$690$	2.45374	0.0934123
$691$	−8.71325	−0.331467	−0.165734	−	0.986171i	$-0.552999\pi$
$691$	−8.71325	−0.331467	−0.165734	+	0.986171i	$0.552999\pi$
$692$	−25.9939	−0.988141
$693$	0	0
$694$	−2.23682	−0.0849087
$695$	0.148326	0.00562633
$696$	−27.3138	−1.03533
$697$	59.4703	2.25260
$698$	8.41493	0.318510
$699$	25.1166	0.949998
$700$	1.91274	0.0722947
$701$	−22.9582	−0.867119	−0.433560	−	0.901125i	$-0.642743\pi$
$701$	−22.9582	−0.867119	−0.433560	+	0.901125i	$0.642743\pi$
$702$	1.31433	0.0496060
$703$	16.4884	0.621873
$704$	0	0
$705$	−13.3670	−0.503429
$706$	−0.278865	−0.0104952
$707$	7.57678	0.284954
$708$	7.85599	0.295246
$709$	0.0807320	0.00303195	0.00151598	−	0.999999i	$-0.499517\pi$
$709$	0.0807320	0.00303195	0.00151598	+	0.999999i	$0.499517\pi$
$710$	4.18655	0.157118
$711$	−21.3203	−0.799573
$712$	13.3015	0.498494
$713$	−23.5328	−0.881311
$714$	−4.24680	−0.158932
$715$	0	0
$716$	−3.47055	−0.129700
$717$	−42.8809	−1.60142
$718$	5.20769	0.194349
$719$	−5.36177	−0.199960	−0.0999801	−	0.994989i	$-0.531878\pi$
$719$	−5.36177	−0.199960	−0.0999801	+	0.994989i	$0.531878\pi$
$720$	−13.5765	−0.505965
$721$	−5.60393	−0.208701
$722$	−4.28241	−0.159375
$723$	−33.7810	−1.25633
$724$	5.98099	0.222282
$725$	−8.99841	−0.334193
$726$	0	0
$727$	−42.3431	−1.57042	−0.785209	−	0.619231i	$-0.787444\pi$
$727$	−42.3431	−1.57042	−0.785209	+	0.619231i	$0.787444\pi$
$728$	−2.18366	−0.0809317
$729$	−40.0080	−1.48178
$730$	−0.897651	−0.0332235
$731$	11.5459	0.427040
$732$	−43.1059	−1.59324
$733$	−48.3957	−1.78754	−0.893768	−	0.448529i	$-0.851948\pi$
$733$	−48.3957	−1.78754	−0.893768	+	0.448529i	$0.851948\pi$
$734$	−6.55449	−0.241931
$735$	2.62617	0.0968677
$736$	10.5670	0.389503
$737$	0	0
$738$	−12.5052	−0.460324
$739$	−50.6271	−1.86235	−0.931174	−	0.364576i	$-0.881214\pi$
$739$	−50.6271	−1.86235	−0.931174	+	0.364576i	$0.881214\pi$
$740$	−14.8621	−0.546340
$741$	−10.5286	−0.386776
$742$	−2.89047	−0.106112
$743$	6.05149	0.222008	0.111004	−	0.993820i	$-0.464593\pi$
$743$	6.05149	0.222008	0.111004	+	0.993820i	$0.464593\pi$
$744$	−22.5838	−0.827964
$745$	1.22559	0.0449020
$746$	−2.25698	−0.0826337
$747$	−37.2088	−1.36140
$748$	0	0
$749$	−9.72425	−0.355316
$750$	0.775775	0.0283273
$751$	12.3331	0.450042	0.225021	−	0.974354i	$-0.427755\pi$
$751$	12.3331	0.450042	0.225021	+	0.974354i	$0.427755\pi$
$752$	−17.7335	−0.646673
$753$	71.0084	2.58769
$754$	5.02192	0.182887
$755$	−6.59507	−0.240019
$756$	−4.50459	−0.163830
$757$	25.5843	0.929878	0.464939	−	0.885343i	$-0.346076\pi$
$757$	25.5843	0.929878	0.464939	+	0.885343i	$0.346076\pi$
$758$	−2.63280	−0.0956275
$759$	0	0
$760$	−2.45273	−0.0889700
$761$	33.2867	1.20664	0.603320	−	0.797499i	$-0.293844\pi$
$761$	33.2867	1.20664	0.603320	+	0.797499i	$0.293844\pi$
$762$	11.2339	0.406963
$763$	−12.7851	−0.462851
$764$	46.3609	1.67728
$765$	21.3319	0.771257
$766$	0.881743	0.0318587
$767$	−2.95470	−0.106688
$768$	−24.8610	−0.897095
$769$	−18.1003	−0.652714	−0.326357	−	0.945247i	$-0.605821\pi$
$769$	−18.1003	−0.652714	−0.326357	+	0.945247i	$0.605821\pi$
$770$	0	0
$771$	−33.0673	−1.19089
$772$	14.7362	0.530367
$773$	8.45527	0.304115	0.152057	−	0.988372i	$-0.451410\pi$
$773$	8.45527	0.304115	0.152057	+	0.988372i	$0.451410\pi$
$774$	−2.42783	−0.0872666
$775$	−7.44014	−0.267258
$776$	−1.80999	−0.0649748
$777$	−20.4054	−0.732041
$778$	7.81051	0.280021
$779$	23.0532	0.825966
$780$	9.49005	0.339798
$781$	0	0
$782$	−5.11484	−0.182906
$783$	21.1917	0.757329
$784$	3.48404	0.124430
$785$	2.39631	0.0855279
$786$	3.70796	0.132258
$787$	45.1369	1.60896	0.804479	−	0.593981i	$-0.202445\pi$
$787$	45.1369	1.60896	0.804479	+	0.593981i	$0.202445\pi$
$788$	−14.0699	−0.501218
$789$	−47.1505	−1.67860
$790$	1.61623	0.0575028
$791$	−10.0801	−0.358406
$792$	0	0
$793$	16.2124	0.575721
$794$	7.32726	0.260035
$795$	25.6967	0.911369
$796$	−18.1336	−0.642727
$797$	40.3820	1.43040	0.715201	−	0.698919i	$-0.246335\pi$
$797$	40.3820	1.43040	0.715201	+	0.698919i	$0.246335\pi$
$798$	−1.64624	−0.0582761
$799$	27.8635	0.985740
$800$	3.34085	0.118117
$801$	−44.8446	−1.58451
$802$	3.41423	0.120561
$803$	0	0
$804$	−62.3947	−2.20049
$805$	3.16295	0.111479
$806$	4.15226	0.146257
$807$	22.6955	0.798918
$808$	8.75746	0.308087
$809$	−4.59071	−0.161401	−0.0807004	−	0.996738i	$-0.525716\pi$
$809$	−4.59071	−0.161401	−0.0807004	+	0.996738i	$0.525716\pi$
$810$	1.62634	0.0571439
$811$	−39.1499	−1.37474	−0.687370	−	0.726308i	$-0.741235\pi$
$811$	−39.1499	−1.37474	−0.687370	+	0.726308i	$0.741235\pi$
$812$	−17.2116	−0.604009
$813$	16.4262	0.576094
$814$	0	0
$815$	−21.3163	−0.746676
$816$	50.0878	1.75342
$817$	4.47567	0.156584
$818$	−0.0515966	−0.00180403
$819$	7.36197	0.257248
$820$	−20.7792	−0.725643
$821$	−27.8612	−0.972364	−0.486182	−	0.873858i	$-0.661611\pi$
$821$	−27.8612	−0.972364	−0.486182	+	0.873858i	$0.661611\pi$
$822$	−4.60720	−0.160694
$823$	17.9532	0.625811	0.312905	−	0.949784i	$-0.398698\pi$
$823$	17.9532	0.625811	0.312905	+	0.949784i	$0.398698\pi$
$824$	−6.47719	−0.225644
$825$	0	0
$826$	−0.461994	−0.0160748
$827$	35.9863	1.25137	0.625683	−	0.780078i	$-0.284820\pi$
$827$	35.9863	1.25137	0.625683	+	0.780078i	$0.284820\pi$
$828$	−23.5750	−0.819289
$829$	53.4462	1.85626	0.928132	−	0.372251i	$-0.121414\pi$
$829$	53.4462	1.85626	0.928132	+	0.372251i	$0.121414\pi$
$830$	2.82069	0.0979076
$831$	53.1685	1.84439
$832$	11.3000	0.391756
$833$	−5.47426	−0.189672
$834$	0.115068	0.00398447
$835$	15.6172	0.540456
$836$	0	0
$837$	17.5219	0.605645
$838$	−3.27003	−0.112961
$839$	18.9458	0.654081	0.327041	−	0.945010i	$-0.393949\pi$
$839$	18.9458	0.654081	0.327041	+	0.945010i	$0.393949\pi$
$840$	3.03540	0.104731
$841$	51.9714	1.79212
$842$	8.94226	0.308171
$843$	−50.6863	−1.74573
$844$	43.2517	1.48878
$845$	9.43072	0.324427
$846$	−5.85905	−0.201438
$847$	0	0
$848$	34.0909	1.17069
$849$	18.1030	0.621294
$850$	−1.61711	−0.0554663
$851$	−24.5763	−0.842464
$852$	−71.1903	−2.43894
$853$	22.9048	0.784247	0.392124	−	0.919913i	$-0.371741\pi$
$853$	22.9048	0.784247	0.392124	+	0.919913i	$0.371741\pi$
$854$	2.53496	0.0867446
$855$	8.26914	0.282798
$856$	−11.2396	−0.384161
$857$	16.2264	0.554283	0.277142	−	0.960829i	$-0.410613\pi$
$857$	16.2264	0.554283	0.277142	+	0.960829i	$0.410613\pi$
$858$	0	0
$859$	−33.6931	−1.14959	−0.574797	−	0.818296i	$-0.694919\pi$
$859$	−33.6931	−1.14959	−0.574797	+	0.818296i	$0.694919\pi$
$860$	−4.03420	−0.137565
$861$	−28.5297	−0.972289
$862$	−5.93504	−0.202148
$863$	−41.3895	−1.40892	−0.704458	−	0.709746i	$-0.748810\pi$
$863$	−41.3895	−1.40892	−0.704458	+	0.709746i	$0.748810\pi$
$864$	−7.86787	−0.267670
$865$	−13.5899	−0.462071
$866$	6.87342	0.233568
$867$	−34.0550	−1.15657
$868$	−14.2310	−0.483033
$869$	0	0
$870$	−6.98074	−0.236669
$871$	23.4671	0.795153
$872$	−14.7774	−0.500425
$873$	6.10219	0.206528
$874$	−1.98272	−0.0670667
$875$	1.00000	0.0338062
$876$	15.2641	0.515727
$877$	35.2896	1.19164	0.595822	−	0.803116i	$-0.296826\pi$
$877$	35.2896	1.19164	0.595822	+	0.803116i	$0.296826\pi$
$878$	−9.36867	−0.316177
$879$	54.3159	1.83203
$880$	0	0
$881$	−16.2994	−0.549142	−0.274571	−	0.961567i	$-0.588536\pi$
$881$	−16.2994	−0.549142	−0.274571	+	0.961567i	$0.588536\pi$
$882$	1.15111	0.0387599
$883$	−0.845626	−0.0284576	−0.0142288	−	0.999899i	$-0.504529\pi$
$883$	−0.845626	−0.0284576	−0.0142288	+	0.999899i	$0.504529\pi$
$884$	−19.7821	−0.665343
$885$	4.10720	0.138062
$886$	0.676331	0.0227218
$887$	15.4635	0.519214	0.259607	−	0.965714i	$-0.416407\pi$
$887$	15.4635	0.519214	0.259607	+	0.965714i	$0.416407\pi$
$888$	−23.5852	−0.791468
$889$	14.4809	0.485675
$890$	3.39953	0.113953
$891$	0	0
$892$	−35.8249	−1.19951
$893$	10.8011	0.361444
$894$	0.950779	0.0317988
$895$	−1.81444	−0.0606500
$896$	8.44856	0.282247
$897$	15.6930	0.523974
$898$	−12.3216	−0.411176
$899$	66.9495	2.23289
$900$	−7.45348	−0.248449
$901$	−53.5650	−1.78451
$902$	0	0
$903$	−5.53891	−0.184323
$904$	−11.6508	−0.387501
$905$	3.12693	0.103943
$906$	−5.11629	−0.169977
$907$	55.9138	1.85659	0.928294	−	0.371847i	$-0.121275\pi$
$907$	55.9138	1.85659	0.928294	+	0.371847i	$0.121275\pi$
$908$	−9.93300	−0.329638
$909$	−29.5249	−0.979279
$910$	−0.558089	−0.0185005
$911$	−38.7952	−1.28534	−0.642672	−	0.766141i	$-0.722174\pi$
$911$	−38.7952	−1.28534	−0.642672	+	0.766141i	$0.722174\pi$
$912$	19.4161	0.642932
$913$	0	0
$914$	4.52833	0.149784
$915$	−22.5362	−0.745024
$916$	−37.9666	−1.25445
$917$	4.77968	0.157839
$918$	3.80837	0.125695
$919$	−22.1477	−0.730585	−0.365292	−	0.930893i	$-0.619031\pi$
$919$	−22.1477	−0.730585	−0.365292	+	0.930893i	$0.619031\pi$
$920$	3.65584	0.120529
$921$	59.5765	1.96311
$922$	4.79068	0.157773
$923$	26.7752	0.881317
$924$	0	0
$925$	−7.77004	−0.255477
$926$	−9.23924	−0.303620
$927$	21.8372	0.717227
$928$	−30.0624	−0.986846
$929$	5.20214	0.170677	0.0853383	−	0.996352i	$-0.472803\pi$
$929$	5.20214	0.170677	0.0853383	+	0.996352i	$0.472803\pi$
$930$	−5.77188	−0.189267
$931$	−2.12205	−0.0695475
$932$	18.2934	0.599220
$933$	−9.95776	−0.326002
$934$	−4.52569	−0.148085
$935$	0	0
$936$	8.50919	0.278131
$937$	−23.4000	−0.764444	−0.382222	−	0.924071i	$-0.624841\pi$
$937$	−23.4000	−0.764444	−0.382222	+	0.924071i	$0.624841\pi$
$938$	3.66929	0.119807
$939$	33.2969	1.08660
$940$	−9.73567	−0.317542
$941$	−60.6136	−1.97595	−0.987974	−	0.154619i	$-0.950585\pi$
$941$	−60.6136	−1.97595	−0.987974	+	0.154619i	$0.950585\pi$
$942$	1.85900	0.0605694
$943$	−34.3611	−1.11895
$944$	5.44887	0.177346
$945$	−2.35505	−0.0766097
$946$	0	0
$947$	−8.86142	−0.287957	−0.143979	−	0.989581i	$-0.545990\pi$
$947$	−8.86142	−0.287957	−0.143979	+	0.989581i	$0.545990\pi$
$948$	−27.4832	−0.892612
$949$	−5.74096	−0.186359
$950$	−0.626859	−0.0203380
$951$	−10.5337	−0.341579
$952$	−6.32732	−0.205070
$953$	50.4703	1.63489	0.817447	−	0.576003i	$-0.195389\pi$
$953$	50.4703	1.63489	0.817447	+	0.576003i	$0.195389\pi$
$954$	11.2635	0.364668
$955$	24.2380	0.784323
$956$	−31.2318	−1.01011
$957$	0	0
$958$	−9.61107	−0.310520
$959$	−5.93883	−0.191775
$960$	−15.7076	−0.506961
$961$	24.3557	0.785669
$962$	4.33637	0.139810
$963$	37.8931	1.22109
$964$	−24.6040	−0.792440
$965$	7.70423	0.248008
$966$	2.45374	0.0789478
$967$	−19.9489	−0.641514	−0.320757	−	0.947161i	$-0.603937\pi$
$967$	−19.9489	−0.641514	−0.320757	+	0.947161i	$0.603937\pi$
$968$	0	0
$969$	−30.5074	−0.980038
$970$	−0.462589	−0.0148528
$971$	10.3865	0.333318	0.166659	−	0.986015i	$-0.446702\pi$
$971$	10.3865	0.333318	0.166659	+	0.986015i	$0.446702\pi$
$972$	−41.1690	−1.32050
$973$	0.148326	0.00475512
$974$	−10.3860	−0.332788
$975$	4.96150	0.158895
$976$	−29.8980	−0.957010
$977$	44.2025	1.41416	0.707081	−	0.707132i	$-0.250011\pi$
$977$	44.2025	1.41416	0.707081	+	0.707132i	$0.250011\pi$
$978$	−16.5366	−0.528783
$979$	0	0
$980$	1.91274	0.0611002
$981$	49.8204	1.59064
$982$	3.69628	0.117953
$983$	−11.5443	−0.368206	−0.184103	−	0.982907i	$-0.558938\pi$
$983$	−11.5443	−0.368206	−0.184103	+	0.982907i	$0.558938\pi$
$984$	−32.9755	−1.05122
$985$	−7.35587	−0.234378
$986$	14.5514	0.463411
$987$	−13.3670	−0.425475
$988$	−7.66835	−0.243963
$989$	−6.67105	−0.212127
$990$	0	0
$991$	35.6962	1.13393	0.566963	−	0.823743i	$-0.308118\pi$
$991$	35.6962	1.13393	0.566963	+	0.823743i	$0.308118\pi$
$992$	−24.8564	−0.789192
$993$	−27.6079	−0.876111
$994$	4.18655	0.132789
$995$	−9.48043	−0.300550
$996$	−47.9645	−1.51981
$997$	23.2458	0.736201	0.368100	−	0.929786i	$-0.380008\pi$
$997$	23.2458	0.736201	0.368100	+	0.929786i	$0.380008\pi$
$998$	−8.59580	−0.272095
$999$	18.2988	0.578949

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.bn.1.7		14
11.7	odd	10		385.2.n.e.71.4	✓	28
11.8	odd	10		385.2.n.e.141.4	yes	28
11.10	odd	2		4235.2.a.bm.1.8		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.n.e.71.4	✓	28	11.7	odd	10
385.2.n.e.141.4	yes	28	11.8	odd	10
4235.2.a.bm.1.8		14	11.10	odd	2
4235.2.a.bn.1.7		14	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:	\( N \)	\(=\)	\( 4235 = 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4235.a (trivial)

\(f(q)\)	\(=\)	\(q+0.295402 q^{2} -2.62617 q^{3} -1.91274 q^{4} -1.00000 q^{5} -0.775775 q^{6} -1.00000 q^{7} -1.15583 q^{8} +3.89676 q^{9} +O(q^{10})\)	\(q+0.295402 q^{2} -2.62617 q^{3} -1.91274 q^{4} -1.00000 q^{5} -0.775775 q^{6} -1.00000 q^{7} -1.15583 q^{8} +3.89676 q^{9} -0.295402 q^{10} +5.02317 q^{12} -1.88925 q^{13} -0.295402 q^{14} +2.62617 q^{15} +3.48404 q^{16} -5.47426 q^{17} +1.15111 q^{18} -2.12205 q^{19} +1.91274 q^{20} +2.62617 q^{21} +3.16295 q^{23} +3.03540 q^{24} +1.00000 q^{25} -0.558089 q^{26} -2.35505 q^{27} +1.91274 q^{28} -8.99841 q^{29} +0.775775 q^{30} -7.44014 q^{31} +3.34085 q^{32} -1.61711 q^{34} +1.00000 q^{35} -7.45348 q^{36} -7.77004 q^{37} -0.626859 q^{38} +4.96150 q^{39} +1.15583 q^{40} -10.8636 q^{41} +0.775775 q^{42} -2.10912 q^{43} -3.89676 q^{45} +0.934342 q^{46} -5.08991 q^{47} -9.14968 q^{48} +1.00000 q^{49} +0.295402 q^{50} +14.3763 q^{51} +3.61365 q^{52} +9.78487 q^{53} -0.695685 q^{54} +1.15583 q^{56} +5.57287 q^{57} -2.65815 q^{58} +1.56395 q^{59} -5.02317 q^{60} -8.58140 q^{61} -2.19783 q^{62} -3.89676 q^{63} -5.98119 q^{64} +1.88925 q^{65} -12.4214 q^{67} +10.4708 q^{68} -8.30645 q^{69} +0.295402 q^{70} -14.1724 q^{71} -4.50399 q^{72} +3.03874 q^{73} -2.29528 q^{74} -2.62617 q^{75} +4.05893 q^{76} +1.46564 q^{78} -5.47128 q^{79} -3.48404 q^{80} -5.50553 q^{81} -3.20913 q^{82} -9.54866 q^{83} -5.02317 q^{84} +5.47426 q^{85} -0.623038 q^{86} +23.6313 q^{87} -11.5082 q^{89} -1.15111 q^{90} +1.88925 q^{91} -6.04990 q^{92} +19.5391 q^{93} -1.50357 q^{94} +2.12205 q^{95} -8.77364 q^{96} +1.56596 q^{97} +0.295402 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + q^{2} + 5 q^{3} + 21 q^{4} - 14 q^{5} - q^{6} - 14 q^{7} + 3 q^{8} + 17 q^{9}+O(q^{10}) \) 14 * q + q^2 + 5 * q^3 + 21 * q^4 - 14 * q^5 - q^6 - 14 * q^7 + 3 * q^8 + 17 * q^9	\( 14 q + q^{2} + 5 q^{3} + 21 q^{4} - 14 q^{5} - q^{6} - 14 q^{7} + 3 q^{8} + 17 q^{9} - q^{10} + 15 q^{12} - 10 q^{13} - q^{14} - 5 q^{15} + 31 q^{16} - 11 q^{17} + 21 q^{18} - 21 q^{19} - 21 q^{20} - 5 q^{21} + 8 q^{23} - 22 q^{24} + 14 q^{25} - 18 q^{26} + 26 q^{27} - 21 q^{28} + 4 q^{29} + q^{30} + 6 q^{31} + 42 q^{32} + 16 q^{34} + 14 q^{35} + 28 q^{36} + 48 q^{37} + 35 q^{38} - 6 q^{39} - 3 q^{40} - 13 q^{41} + q^{42} - 17 q^{45} + 31 q^{46} + 11 q^{47} + 59 q^{48} + 14 q^{49} + q^{50} + 33 q^{51} - 52 q^{52} + 31 q^{53} + 57 q^{54} - 3 q^{56} + 4 q^{57} + 52 q^{58} - 4 q^{59} - 15 q^{60} - 17 q^{61} + 27 q^{62} - 17 q^{63} + 43 q^{64} + 10 q^{65} + 45 q^{67} - 14 q^{68} + 20 q^{69} + q^{70} - 6 q^{71} + 14 q^{72} - 11 q^{73} + 33 q^{74} + 5 q^{75} + 5 q^{76} + 52 q^{78} - 30 q^{79} - 31 q^{80} - 6 q^{81} + 26 q^{82} - 23 q^{83} - 15 q^{84} + 11 q^{85} - 23 q^{86} - 23 q^{87} - 15 q^{89} - 21 q^{90} + 10 q^{91} + 44 q^{92} + 29 q^{93} - 49 q^{94} + 21 q^{95} + 52 q^{96} + 44 q^{97} + q^{98}+O(q^{100}) \) 14 * q + q^2 + 5 * q^3 + 21 * q^4 - 14 * q^5 - q^6 - 14 * q^7 + 3 * q^8 + 17 * q^9 - q^10 + 15 * q^12 - 10 * q^13 - q^14 - 5 * q^15 + 31 * q^16 - 11 * q^17 + 21 * q^18 - 21 * q^19 - 21 * q^20 - 5 * q^21 + 8 * q^23 - 22 * q^24 + 14 * q^25 - 18 * q^26 + 26 * q^27 - 21 * q^28 + 4 * q^29 + q^30 + 6 * q^31 + 42 * q^32 + 16 * q^34 + 14 * q^35 + 28 * q^36 + 48 * q^37 + 35 * q^38 - 6 * q^39 - 3 * q^40 - 13 * q^41 + q^42 - 17 * q^45 + 31 * q^46 + 11 * q^47 + 59 * q^48 + 14 * q^49 + q^50 + 33 * q^51 - 52 * q^52 + 31 * q^53 + 57 * q^54 - 3 * q^56 + 4 * q^57 + 52 * q^58 - 4 * q^59 - 15 * q^60 - 17 * q^61 + 27 * q^62 - 17 * q^63 + 43 * q^64 + 10 * q^65 + 45 * q^67 - 14 * q^68 + 20 * q^69 + q^70 - 6 * q^71 + 14 * q^72 - 11 * q^73 + 33 * q^74 + 5 * q^75 + 5 * q^76 + 52 * q^78 - 30 * q^79 - 31 * q^80 - 6 * q^81 + 26 * q^82 - 23 * q^83 - 15 * q^84 + 11 * q^85 - 23 * q^86 - 23 * q^87 - 15 * q^89 - 21 * q^90 + 10 * q^91 + 44 * q^92 + 29 * q^93 - 49 * q^94 + 21 * q^95 + 52 * q^96 + 44 * q^97 + q^98

Introduction

L-functions

Modular forms

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Groups

Database

Properties

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