LMFDB - Embedded newform 4235.2.a.v.1.2

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:	$4$
Coefficient field:	4.4.15952.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 6x^{2} - 2x + 1 $ x^4 - 6x^2 - 2x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.637875$ 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)

$f(q)$	$=$	$q-0.637875 q^{2} -2.56771 q^{3} -1.59312 q^{4} +1.00000 q^{5} +1.63787 q^{6} -1.00000 q^{7} +2.29196 q^{8} +3.59312 q^{9} +O(q^{10})$	\(q-0.637875 q^{2} -2.56771 q^{3} -1.59312 q^{4} +1.00000 q^{5} +1.63787 q^{6} -1.00000 q^{7} +2.29196 q^{8} +3.59312 q^{9} -0.637875 q^{10} +4.09065 q^{12} -2.09065 q^{13} +0.637875 q^{14} -2.56771 q^{15} +1.72425 q^{16} +6.47819 q^{17} -2.29196 q^{18} +1.61246 q^{19} -1.59312 q^{20} +2.56771 q^{21} +0.929832 q^{23} -5.88507 q^{24} +1.00000 q^{25} +1.33358 q^{26} -1.52295 q^{27} +1.59312 q^{28} -2.41116 q^{29} +1.63787 q^{30} -0.749661 q^{31} -5.68377 q^{32} -4.13227 q^{34} -1.00000 q^{35} -5.72425 q^{36} +1.51375 q^{37} -1.02855 q^{38} +5.36819 q^{39} +2.29196 q^{40} +10.4366 q^{41} -1.63787 q^{42} -2.78950 q^{43} +3.59312 q^{45} -0.593116 q^{46} +0.403743 q^{47} -4.42737 q^{48} +1.00000 q^{49} -0.637875 q^{50} -16.6341 q^{51} +3.33065 q^{52} +5.79442 q^{53} +0.971450 q^{54} -2.29196 q^{56} -4.14034 q^{57} +1.53802 q^{58} +8.93097 q^{59} +4.09065 q^{60} -8.13227 q^{61} +0.478189 q^{62} -3.59312 q^{63} +0.177031 q^{64} -2.09065 q^{65} -0.789495 q^{67} -10.3205 q^{68} -2.38754 q^{69} +0.637875 q^{70} -10.9056 q^{71} +8.23527 q^{72} -3.89427 q^{73} -0.965580 q^{74} -2.56771 q^{75} -2.56884 q^{76} -3.42423 q^{78} -5.86887 q^{79} +1.72425 q^{80} -6.86887 q^{81} -6.65722 q^{82} -17.6534 q^{83} -4.09065 q^{84} +6.47819 q^{85} +1.77935 q^{86} +6.19116 q^{87} +13.2099 q^{89} -2.29196 q^{90} +2.09065 q^{91} -1.48133 q^{92} +1.92491 q^{93} -0.257538 q^{94} +1.61246 q^{95} +14.5943 q^{96} -16.6584 q^{97} -0.637875 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 4 q^{4} + 4 q^{5} + 4 q^{6} - 4 q^{7} + 6 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 + 4 * q^4 + 4 * q^5 + 4 * q^6 - 4 * q^7 + 6 * q^8 + 4 * q^9	$ 4 q - 2 q^{3} + 4 q^{4} + 4 q^{5} + 4 q^{6} - 4 q^{7} + 6 q^{8} + 4 q^{9} - 8 q^{12} + 16 q^{13} - 2 q^{15} + 12 q^{16} + 2 q^{17} - 6 q^{18} + 6 q^{19} + 4 q^{20} + 2 q^{21} - 2 q^{23} - 10 q^{24} + 4 q^{25} + 2 q^{26} + 10 q^{27} - 4 q^{28} + 12 q^{29} + 4 q^{30} - 6 q^{31} + 12 q^{32} + 8 q^{34} - 4 q^{35} - 28 q^{36} - 6 q^{37} - 10 q^{38} + 12 q^{39} + 6 q^{40} + 18 q^{41} - 4 q^{42} + 6 q^{43} + 4 q^{45} + 8 q^{46} + 4 q^{47} + 2 q^{48} + 4 q^{49} + 4 q^{51} + 30 q^{52} + 34 q^{53} - 2 q^{54} - 6 q^{56} - 28 q^{57} + 32 q^{58} - 10 q^{59} - 8 q^{60} - 8 q^{61} - 22 q^{62} - 4 q^{63} - 16 q^{64} + 16 q^{65} + 14 q^{67} - 44 q^{68} - 10 q^{69} - 12 q^{72} + 2 q^{73} + 48 q^{74} - 2 q^{75} + 38 q^{76} + 14 q^{78} - 8 q^{79} + 12 q^{80} - 12 q^{81} - 34 q^{82} - 10 q^{83} + 8 q^{84} + 2 q^{85} - 24 q^{86} + 32 q^{87} + 10 q^{89} - 6 q^{90} - 16 q^{91} + 10 q^{92} - 26 q^{93} + 54 q^{94} + 6 q^{95} + 8 q^{96} - 34 q^{97}+O(q^{100}) $ 4 * q - 2 * q^3 + 4 * q^4 + 4 * q^5 + 4 * q^6 - 4 * q^7 + 6 * q^8 + 4 * q^9 - 8 * q^12 + 16 * q^13 - 2 * q^15 + 12 * q^16 + 2 * q^17 - 6 * q^18 + 6 * q^19 + 4 * q^20 + 2 * q^21 - 2 * q^23 - 10 * q^24 + 4 * q^25 + 2 * q^26 + 10 * q^27 - 4 * q^28 + 12 * q^29 + 4 * q^30 - 6 * q^31 + 12 * q^32 + 8 * q^34 - 4 * q^35 - 28 * q^36 - 6 * q^37 - 10 * q^38 + 12 * q^39 + 6 * q^40 + 18 * q^41 - 4 * q^42 + 6 * q^43 + 4 * q^45 + 8 * q^46 + 4 * q^47 + 2 * q^48 + 4 * q^49 + 4 * q^51 + 30 * q^52 + 34 * q^53 - 2 * q^54 - 6 * q^56 - 28 * q^57 + 32 * q^58 - 10 * q^59 - 8 * q^60 - 8 * q^61 - 22 * q^62 - 4 * q^63 - 16 * q^64 + 16 * q^65 + 14 * q^67 - 44 * q^68 - 10 * q^69 - 12 * q^72 + 2 * q^73 + 48 * q^74 - 2 * q^75 + 38 * q^76 + 14 * q^78 - 8 * q^79 + 12 * q^80 - 12 * q^81 - 34 * q^82 - 10 * q^83 + 8 * q^84 + 2 * q^85 - 24 * q^86 + 32 * q^87 + 10 * q^89 - 6 * q^90 - 16 * q^91 + 10 * q^92 - 26 * q^93 + 54 * q^94 + 6 * q^95 + 8 * 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 $

$2$	−0.637875	−0.451045	−0.225523	−	0.974238i	$-0.572409\pi$
$2$	−0.637875	−0.451045	−0.225523	+	0.974238i	$0.572409\pi$
$3$	−2.56771	−1.48247	−0.741233	−	0.671248i	$-0.765759\pi$
$3$	−2.56771	−1.48247	−0.741233	+	0.671248i	$0.765759\pi$
$4$	−1.59312	−0.796558
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.63787	0.668659
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.29196	0.810329
$9$	3.59312	1.19771
$10$	−0.637875	−0.201714
$11$	0	0
$11$	0	0
$12$	4.09065	1.18087
$13$	−2.09065	−0.579843	−0.289922	−	0.957050i	$-0.593629\pi$
$13$	−2.09065	−0.579843	−0.289922	+	0.957050i	$0.593629\pi$
$14$	0.637875	0.170479
$15$	−2.56771	−0.662979
$16$	1.72425	0.431063
$17$	6.47819	1.57119	0.785596	−	0.618740i	$-0.212357\pi$
$17$	6.47819	1.57119	0.785596	+	0.618740i	$0.212357\pi$
$18$	−2.29196	−0.540220
$19$	1.61246	0.369925	0.184962	−	0.982746i	$-0.440784\pi$
$19$	1.61246	0.369925	0.184962	+	0.982746i	$0.440784\pi$
$20$	−1.59312	−0.356232
$21$	2.56771	0.560319
$22$	0	0
$23$	0.929832	0.193883	0.0969417	−	0.995290i	$-0.469094\pi$
$23$	0.929832	0.193883	0.0969417	+	0.995290i	$0.469094\pi$
$24$	−5.88507	−1.20129
$25$	1.00000	0.200000
$26$	1.33358	0.261536
$27$	−1.52295	−0.293091
$28$	1.59312	0.301071
$29$	−2.41116	−0.447742	−0.223871	−	0.974619i	$-0.571869\pi$
$29$	−2.41116	−0.447742	−0.223871	+	0.974619i	$0.571869\pi$
$30$	1.63787	0.299034
$31$	−0.749661	−0.134643	−0.0673215	−	0.997731i	$-0.521445\pi$
$31$	−0.749661	−0.134643	−0.0673215	+	0.997731i	$0.521445\pi$
$32$	−5.68377	−1.00476
$33$	0	0
$34$	−4.13227	−0.708679
$35$	−1.00000	−0.169031
$36$	−5.72425	−0.954042
$37$	1.51375	0.248858	0.124429	−	0.992228i	$-0.460290\pi$
$37$	1.51375	0.248858	0.124429	+	0.992228i	$0.460290\pi$
$38$	−1.02855	−0.166853
$39$	5.36819	0.859598
$40$	2.29196	0.362390
$41$	10.4366	1.62992	0.814959	−	0.579518i	$-0.196759\pi$
$41$	10.4366	1.62992	0.814959	+	0.579518i	$0.196759\pi$
$42$	−1.63787	−0.252730
$43$	−2.78950	−0.425394	−0.212697	−	0.977118i	$-0.568225\pi$
$43$	−2.78950	−0.425394	−0.212697	+	0.977118i	$0.568225\pi$
$44$	0	0
$45$	3.59312	0.535630
$46$	−0.593116	−0.0874502
$47$	0.403743	0.0588920	0.0294460	−	0.999566i	$-0.490626\pi$
$47$	0.403743	0.0588920	0.0294460	+	0.999566i	$0.490626\pi$
$48$	−4.42737	−0.639036
$49$	1.00000	0.142857
$50$	−0.637875	−0.0902091
$51$	−16.6341	−2.32924
$52$	3.33065	0.461879
$53$	5.79442	0.795925	0.397962	−	0.917402i	$-0.369717\pi$
$53$	5.79442	0.795925	0.397962	+	0.917402i	$0.369717\pi$
$54$	0.971450	0.132198
$55$	0	0
$56$	−2.29196	−0.306276
$57$	−4.14034	−0.548401
$58$	1.53802	0.201952
$59$	8.93097	1.16271	0.581357	−	0.813649i	$-0.302522\pi$
$59$	8.93097	1.16271	0.581357	+	0.813649i	$0.302522\pi$
$60$	4.09065	0.528101
$61$	−8.13227	−1.04123	−0.520615	−	0.853791i	$-0.674297\pi$
$61$	−8.13227	−1.04123	−0.520615	+	0.853791i	$0.674297\pi$
$62$	0.478189	0.0607301
$63$	−3.59312	−0.452690
$64$	0.177031	0.0221288
$65$	−2.09065	−0.259314
$66$	0	0
$67$	−0.789495	−0.0964522	−0.0482261	−	0.998836i	$-0.515357\pi$
$67$	−0.789495	−0.0964522	−0.0482261	+	0.998836i	$0.515357\pi$
$68$	−10.3205	−1.25155
$69$	−2.38754	−0.287425
$70$	0.637875	0.0762406
$71$	−10.9056	−1.29425	−0.647126	−	0.762383i	$-0.724029\pi$
$71$	−10.9056	−1.29425	−0.647126	+	0.762383i	$0.724029\pi$
$72$	8.23527	0.970536
$73$	−3.89427	−0.455790	−0.227895	−	0.973686i	$-0.573184\pi$
$73$	−3.89427	−0.455790	−0.227895	+	0.973686i	$0.573184\pi$
$74$	−0.965580	−0.112246
$75$	−2.56771	−0.296493
$76$	−2.56884	−0.294667
$77$	0	0
$78$	−3.42423	−0.387718
$79$	−5.86887	−0.660299	−0.330149	−	0.943929i	$-0.607099\pi$
$79$	−5.86887	−0.660299	−0.330149	+	0.943929i	$0.607099\pi$
$80$	1.72425	0.192777
$81$	−6.86887	−0.763207
$82$	−6.65722	−0.735167
$83$	−17.6534	−1.93772	−0.968858	−	0.247616i	$-0.920353\pi$
$83$	−17.6534	−1.93772	−0.968858	+	0.247616i	$0.920353\pi$
$84$	−4.09065	−0.446327
$85$	6.47819	0.702658
$86$	1.77935	0.191872
$87$	6.19116	0.663762
$88$	0	0
$89$	13.2099	1.40024	0.700121	−	0.714024i	$-0.253129\pi$
$89$	13.2099	1.40024	0.700121	+	0.714024i	$0.253129\pi$
$90$	−2.29196	−0.241594
$91$	2.09065	0.219160
$92$	−1.48133	−0.154439
$93$	1.92491	0.199604
$94$	−0.257538	−0.0265630
$95$	1.61246	0.165435
$96$	14.5943	1.48952
$97$	−16.6584	−1.69140	−0.845700	−	0.533658i	$-0.820817\pi$
$97$	−16.6584	−1.69140	−0.845700	+	0.533658i	$0.820817\pi$
$98$	−0.637875	−0.0644351
$99$	0	0
$100$	−1.59312	−0.159312
$101$	8.52609	0.848378	0.424189	−	0.905574i	$-0.360559\pi$
$101$	8.52609	0.848378	0.424189	+	0.905574i	$0.360559\pi$
$102$	10.6105	1.05059
$103$	−20.1975	−1.99012	−0.995060	−	0.0992731i	$-0.968348\pi$
$103$	−20.1975	−1.99012	−0.995060	+	0.0992731i	$0.968348\pi$
$104$	−4.79169	−0.469864
$105$	2.56771	0.250582
$106$	−3.69611	−0.358998
$107$	−7.32657	−0.708286	−0.354143	−	0.935191i	$-0.615227\pi$
$107$	−7.32657	−0.708286	−0.354143	+	0.935191i	$0.615227\pi$
$108$	2.42623	0.233464
$109$	16.9564	1.62413	0.812063	−	0.583569i	$-0.198344\pi$
$109$	16.9564	1.62413	0.812063	+	0.583569i	$0.198344\pi$
$110$	0	0
$111$	−3.88686	−0.368924
$112$	−1.72425	−0.162926
$113$	−6.55150	−0.616313	−0.308157	−	0.951336i	$-0.599712\pi$
$113$	−6.55150	−0.616313	−0.308157	+	0.951336i	$0.599712\pi$
$114$	2.64102	0.247354
$115$	0.929832	0.0867073
$116$	3.84126	0.356652
$117$	−7.51196	−0.694481
$118$	−5.69684	−0.524436
$119$	−6.47819	−0.593855
$120$	−5.88507	−0.537231
$121$	0	0
$122$	5.18737	0.469642
$123$	−26.7981	−2.41630
$124$	1.19430	0.107251
$125$	1.00000	0.0894427
$126$	2.29196	0.204184
$127$	10.4944	0.931227	0.465614	−	0.884988i	$-0.345834\pi$
$127$	10.4944	0.931227	0.465614	+	0.884988i	$0.345834\pi$
$128$	11.2546	0.994777
$129$	7.16261	0.630632
$130$	1.33358	0.116962
$131$	15.7193	1.37340	0.686702	−	0.726939i	$-0.259058\pi$
$131$	15.7193	1.37340	0.686702	+	0.726939i	$0.259058\pi$
$132$	0	0
$133$	−1.61246	−0.139818
$134$	0.503599	0.0435043
$135$	−1.52295	−0.131074
$136$	14.8477	1.27318
$137$	14.7184	1.25748	0.628738	−	0.777617i	$-0.283572\pi$
$137$	14.7184	1.25748	0.628738	+	0.777617i	$0.283572\pi$
$138$	1.52295	0.129642
$139$	−2.58391	−0.219165	−0.109582	−	0.993978i	$-0.534951\pi$
$139$	−2.58391	−0.219165	−0.109582	+	0.993978i	$0.534951\pi$
$140$	1.59312	0.134643
$141$	−1.03669	−0.0873054
$142$	6.95638	0.583766
$143$	0	0
$144$	6.19543	0.516286
$145$	−2.41116	−0.200236
$146$	2.48406	0.205582
$147$	−2.56771	−0.211781
$148$	−2.41157	−0.198230
$149$	6.05082	0.495702	0.247851	−	0.968798i	$-0.420276\pi$
$149$	6.05082	0.495702	0.247851	+	0.968798i	$0.420276\pi$
$150$	1.63787	0.133732
$151$	12.8252	1.04370	0.521852	−	0.853036i	$-0.325241\pi$
$151$	12.8252	1.04370	0.521852	+	0.853036i	$0.325241\pi$
$152$	3.69570	0.299761
$153$	23.2769	1.88182
$154$	0	0
$155$	−0.749661	−0.0602142
$156$	−8.55214	−0.684720
$157$	−8.65836	−0.691012	−0.345506	−	0.938416i	$-0.612293\pi$
$157$	−8.65836	−0.691012	−0.345506	+	0.938416i	$0.612293\pi$
$158$	3.74360	0.297825
$159$	−14.8784	−1.17993
$160$	−5.68377	−0.449341
$161$	−0.929832	−0.0732810
$162$	4.38147	0.344241
$163$	18.2079	1.42615	0.713075	−	0.701088i	$-0.247302\pi$
$163$	18.2079	1.42615	0.713075	+	0.701088i	$0.247302\pi$
$164$	−16.6267	−1.29832
$165$	0	0
$166$	11.2607	0.873998
$167$	−5.55536	−0.429887	−0.214943	−	0.976626i	$-0.568957\pi$
$167$	−5.55536	−0.429887	−0.214943	+	0.976626i	$0.568957\pi$
$168$	5.88507	0.454043
$169$	−8.62916	−0.663782
$170$	−4.13227	−0.316931
$171$	5.79377	0.443061
$172$	4.44399	0.338851
$173$	0.618526	0.0470256	0.0235128	−	0.999724i	$-0.492515\pi$
$173$	0.618526	0.0470256	0.0235128	+	0.999724i	$0.492515\pi$
$174$	−3.94918	−0.299387
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	−22.9321	−1.72368
$178$	−8.42623	−0.631573
$179$	6.27083	0.468704	0.234352	−	0.972152i	$-0.424703\pi$
$179$	6.27083	0.468704	0.234352	+	0.972152i	$0.424703\pi$
$180$	−5.72425	−0.426660
$181$	−18.6584	−1.38687	−0.693433	−	0.720522i	$-0.743902\pi$
$181$	−18.6584	−1.38687	−0.693433	+	0.720522i	$0.743902\pi$
$182$	−1.33358	−0.0988512
$183$	20.8813	1.54359
$184$	2.13113	0.157109
$185$	1.51375	0.111293
$186$	−1.22785	−0.0900303
$187$	0	0
$188$	−0.643210	−0.0469109
$189$	1.52295	0.110778
$190$	−1.02855	−0.0746189
$191$	−1.96758	−0.142369	−0.0711847	−	0.997463i	$-0.522678\pi$
$191$	−1.96758	−0.142369	−0.0711847	+	0.997463i	$0.522678\pi$
$192$	−0.454563	−0.0328052
$193$	−20.1246	−1.44860	−0.724301	−	0.689484i	$-0.757837\pi$
$193$	−20.1246	−1.44860	−0.724301	+	0.689484i	$0.757837\pi$
$194$	10.6259	0.762898
$195$	5.36819	0.384424
$196$	−1.59312	−0.113794
$197$	20.7981	1.48180	0.740900	−	0.671615i	$-0.234399\pi$
$197$	20.7981	1.48180	0.740900	+	0.671615i	$0.234399\pi$
$198$	0	0
$199$	0.189373	0.0134243	0.00671214	−	0.999977i	$-0.497863\pi$
$199$	0.189373	0.0134243	0.00671214	+	0.999977i	$0.497863\pi$
$200$	2.29196	0.162066
$201$	2.02719	0.142987
$202$	−5.43857	−0.382657
$203$	2.41116	0.169230
$204$	26.5000	1.85537
$205$	10.4366	0.728922
$206$	12.8835	0.897635
$207$	3.34099	0.232215
$208$	−3.60481	−0.249949
$209$	0	0
$210$	−1.63787	−0.113024
$211$	10.8547	0.747271	0.373636	−	0.927576i	$-0.378111\pi$
$211$	10.8547	0.747271	0.373636	+	0.927576i	$0.378111\pi$
$212$	−9.23118	−0.634000
$213$	28.0023	1.91868
$214$	4.67343	0.319469
$215$	−2.78950	−0.190242
$216$	−3.49053	−0.237501
$217$	0.749661	0.0508903
$218$	−10.8160	−0.732555
$219$	9.99935	0.675694
$220$	0	0
$221$	−13.5437	−0.911045
$222$	2.47933	0.166402
$223$	−12.5106	−0.837772	−0.418886	−	0.908039i	$-0.637579\pi$
$223$	−12.5106	−0.837772	−0.418886	+	0.908039i	$0.637579\pi$
$224$	5.68377	0.379763
$225$	3.59312	0.239541
$226$	4.17903	0.277985
$227$	24.3154	1.61387	0.806934	−	0.590642i	$-0.201125\pi$
$227$	24.3154	1.61387	0.806934	+	0.590642i	$0.201125\pi$
$228$	6.59604	0.436833
$229$	−19.8619	−1.31251	−0.656257	−	0.754538i	$-0.727861\pi$
$229$	−19.8619	−1.31251	−0.656257	+	0.754538i	$0.727861\pi$
$230$	−0.593116	−0.0391089
$231$	0	0
$232$	−5.52628	−0.362818
$233$	−2.32751	−0.152481	−0.0762403	−	0.997089i	$-0.524292\pi$
$233$	−2.32751	−0.152481	−0.0762403	+	0.997089i	$0.524292\pi$
$234$	4.79169	0.313243
$235$	0.403743	0.0263373
$236$	−14.2281	−0.926168
$237$	15.0695	0.978871
$238$	4.13227	0.267855
$239$	4.32164	0.279544	0.139772	−	0.990184i	$-0.455363\pi$
$239$	4.32164	0.279544	0.139772	+	0.990184i	$0.455363\pi$
$240$	−4.42737	−0.285786
$241$	29.5621	1.90426	0.952132	−	0.305686i	$-0.0988858\pi$
$241$	29.5621	1.90426	0.952132	+	0.305686i	$0.0988858\pi$
$242$	0	0
$243$	22.2061	1.42452
$244$	12.9557	0.829401
$245$	1.00000	0.0638877
$246$	17.0938	1.08986
$247$	−3.37111	−0.214498
$248$	−1.71819	−0.109105
$249$	45.3288	2.87260
$250$	−0.637875	−0.0403427
$251$	7.48247	0.472289	0.236145	−	0.971718i	$-0.424116\pi$
$251$	7.48247	0.472289	0.236145	+	0.971718i	$0.424116\pi$
$252$	5.72425	0.360594
$253$	0	0
$254$	−6.69411	−0.420026
$255$	−16.6341	−1.04167
$256$	−7.53310	−0.470818
$257$	−22.6669	−1.41392	−0.706962	−	0.707252i	$-0.749935\pi$
$257$	−22.6669	−1.41392	−0.706962	+	0.707252i	$0.749935\pi$
$258$	−4.56884	−0.284444
$259$	−1.51375	−0.0940596
$260$	3.33065	0.206558
$261$	−8.66358	−0.536262
$262$	−10.0270	−0.619468
$263$	−5.45706	−0.336497	−0.168248	−	0.985745i	$-0.553811\pi$
$263$	−5.45706	−0.336497	−0.168248	+	0.985745i	$0.553811\pi$
$264$	0	0
$265$	5.79442	0.355948
$266$	1.02855	0.0630645
$267$	−33.9190	−2.07581
$268$	1.25776	0.0768298
$269$	17.2121	1.04944	0.524721	−	0.851274i	$-0.324170\pi$
$269$	17.2121	1.04944	0.524721	+	0.851274i	$0.324170\pi$
$270$	0.971450	0.0591205
$271$	−12.2829	−0.746136	−0.373068	−	0.927804i	$-0.621694\pi$
$271$	−12.2829	−0.746136	−0.373068	+	0.927804i	$0.621694\pi$
$272$	11.1700	0.677282
$273$	−5.36819	−0.324897
$274$	−9.38848	−0.567179
$275$	0	0
$276$	3.80362	0.228951
$277$	18.1895	1.09290	0.546449	−	0.837492i	$-0.315979\pi$
$277$	18.1895	1.09290	0.546449	+	0.837492i	$0.315979\pi$
$278$	1.64821	0.0988533
$279$	−2.69362	−0.161263
$280$	−2.29196	−0.136971
$281$	8.03870	0.479548	0.239774	−	0.970829i	$-0.422927\pi$
$281$	8.03870	0.479548	0.239774	+	0.970829i	$0.422927\pi$
$282$	0.661281	0.0393787
$283$	−13.3675	−0.794618	−0.397309	−	0.917685i	$-0.630056\pi$
$283$	−13.3675	−0.794618	−0.397309	+	0.917685i	$0.630056\pi$
$284$	17.3738	1.03095
$285$	−4.14034	−0.245252
$286$	0	0
$287$	−10.4366	−0.616051
$288$	−20.4224	−1.20340
$289$	24.9669	1.46864
$290$	1.53802	0.0903156
$291$	42.7738	2.50744
$292$	6.20403	0.363063
$293$	29.6222	1.73054	0.865272	−	0.501302i	$-0.167145\pi$
$293$	29.6222	1.73054	0.865272	+	0.501302i	$0.167145\pi$
$294$	1.63787	0.0955228
$295$	8.93097	0.519981
$296$	3.46944	0.201657
$297$	0	0
$298$	−3.85966	−0.223584
$299$	−1.94396	−0.112422
$300$	4.09065	0.236174
$301$	2.78950	0.160784
$302$	−8.18090	−0.470758
$303$	−21.8925	−1.25769
$304$	2.78029	0.159461
$305$	−8.13227	−0.465653
$306$	−14.8477	−0.848788
$307$	33.1613	1.89262	0.946308	−	0.323266i	$-0.104781\pi$
$307$	33.1613	1.89262	0.946308	+	0.323266i	$0.104781\pi$
$308$	0	0
$309$	51.8613	2.95029
$310$	0.478189	0.0271593
$311$	18.2303	1.03375	0.516874	−	0.856061i	$-0.327096\pi$
$311$	18.2303	1.03375	0.516874	+	0.856061i	$0.327096\pi$
$312$	12.3037	0.696557
$313$	−1.66851	−0.0943096	−0.0471548	−	0.998888i	$-0.515015\pi$
$313$	−1.66851	−0.0943096	−0.0471548	+	0.998888i	$0.515015\pi$
$314$	5.52295	0.311678
$315$	−3.59312	−0.202449
$316$	9.34978	0.525966
$317$	25.9699	1.45861	0.729306	−	0.684187i	$-0.239843\pi$
$317$	25.9699	1.45861	0.729306	+	0.684187i	$0.239843\pi$
$318$	9.49053	0.532203
$319$	0	0
$320$	0.177031	0.00989631
$321$	18.8125	1.05001
$322$	0.593116	0.0330531
$323$	10.4459	0.581223
$324$	10.9429	0.607939
$325$	−2.09065	−0.115969
$326$	−11.6143	−0.643258
$327$	−43.5390	−2.40771
$328$	23.9202	1.32077
$329$	−0.403743	−0.0222591
$330$	0	0
$331$	−19.1053	−1.05012	−0.525060	−	0.851065i	$-0.675957\pi$
$331$	−19.1053	−1.05012	−0.525060	+	0.851065i	$0.675957\pi$
$332$	28.1240	1.54350
$333$	5.43907	0.298059
$334$	3.54363	0.193899
$335$	−0.789495	−0.0431347
$336$	4.42737	0.241533
$337$	−13.2515	−0.721854	−0.360927	−	0.932594i	$-0.617540\pi$
$337$	−13.2515	−0.721854	−0.360927	+	0.932594i	$0.617540\pi$
$338$	5.50432	0.299396
$339$	16.8223	0.913663
$340$	−10.3205	−0.559708
$341$	0	0
$342$	−3.69570	−0.199841
$343$	−1.00000	−0.0539949
$344$	−6.39340	−0.344709
$345$	−2.38754	−0.128541
$346$	−0.394542	−0.0212107
$347$	−23.2839	−1.24994	−0.624972	−	0.780647i	$-0.714890\pi$
$347$	−23.2839	−1.24994	−0.624972	+	0.780647i	$0.714890\pi$
$348$	−9.86323	−0.528725
$349$	25.6464	1.37282	0.686411	−	0.727214i	$-0.259185\pi$
$349$	25.6464	1.37282	0.686411	+	0.727214i	$0.259185\pi$
$350$	0.637875	0.0340958
$351$	3.18396	0.169947
$352$	0	0
$353$	−9.17638	−0.488410	−0.244205	−	0.969724i	$-0.578527\pi$
$353$	−9.17638	−0.488410	−0.244205	+	0.969724i	$0.578527\pi$
$354$	14.6278	0.777459
$355$	−10.9056	−0.578807
$356$	−21.0448	−1.11537
$357$	16.6341	0.880369
$358$	−4.00000	−0.211407
$359$	29.8203	1.57386	0.786928	−	0.617045i	$-0.211670\pi$
$359$	29.8203	1.57386	0.786928	+	0.617045i	$0.211670\pi$
$360$	8.23527	0.434037
$361$	−16.4000	−0.863156
$362$	11.9017	0.625539
$363$	0	0
$364$	−3.33065	−0.174574
$365$	−3.89427	−0.203836
$366$	−13.3196	−0.696229
$367$	−6.51394	−0.340025	−0.170012	−	0.985442i	$-0.554381\pi$
$367$	−6.51394	−0.340025	−0.170012	+	0.985442i	$0.554381\pi$
$368$	1.60326	0.0835759
$369$	37.4998	1.95216
$370$	−0.965580	−0.0501981
$371$	−5.79442	−0.300831
$372$	−3.06660	−0.158996
$373$	19.0702	0.987416	0.493708	−	0.869628i	$-0.335641\pi$
$373$	19.0702	0.987416	0.493708	+	0.869628i	$0.335641\pi$
$374$	0	0
$375$	−2.56771	−0.132596
$376$	0.925362	0.0477219
$377$	5.04091	0.259620
$378$	−0.971450	−0.0499660
$379$	14.1305	0.725834	0.362917	−	0.931821i	$-0.381781\pi$
$379$	14.1305	0.725834	0.362917	+	0.931821i	$0.381781\pi$
$380$	−2.56884	−0.131779
$381$	−26.9465	−1.38051
$382$	1.25507	0.0642150
$383$	−0.380117	−0.0194231	−0.00971153	−	0.999953i	$-0.503091\pi$
$383$	−0.380117	−0.0194231	−0.00971153	+	0.999953i	$0.503091\pi$
$384$	−28.8986	−1.47472
$385$	0	0
$386$	12.8370	0.653385
$387$	−10.0230	−0.509497
$388$	26.5387	1.34730
$389$	17.1827	0.871196	0.435598	−	0.900141i	$-0.356537\pi$
$389$	17.1827	0.871196	0.435598	+	0.900141i	$0.356537\pi$
$390$	−3.42423	−0.173393
$391$	6.02363	0.304628
$392$	2.29196	0.115761
$393$	−40.3626	−2.03602
$394$	−13.2665	−0.668359
$395$	−5.86887	−0.295295
$396$	0	0
$397$	10.2049	0.512171	0.256086	−	0.966654i	$-0.417567\pi$
$397$	10.2049	0.512171	0.256086	+	0.966654i	$0.417567\pi$
$398$	−0.120796	−0.00605496
$399$	4.14034	0.207276
$400$	1.72425	0.0862125
$401$	16.6636	0.832140	0.416070	−	0.909333i	$-0.363407\pi$
$401$	16.6636	0.832140	0.416070	+	0.909333i	$0.363407\pi$
$402$	−1.29309	−0.0644937
$403$	1.56728	0.0780718
$404$	−13.5830	−0.675782
$405$	−6.86887	−0.341317
$406$	−1.53802	−0.0763306
$407$	0	0
$408$	−38.1246	−1.88745
$409$	25.1844	1.24529	0.622645	−	0.782504i	$-0.286058\pi$
$409$	25.1844	1.24529	0.622645	+	0.782504i	$0.286058\pi$
$410$	−6.65722	−0.328777
$411$	−37.7925	−1.86417
$412$	32.1770	1.58525
$413$	−8.93097	−0.439464
$414$	−2.13113	−0.104740
$415$	−17.6534	−0.866573
$416$	11.8828	0.582602
$417$	6.63473	0.324904
$418$	0	0
$419$	−36.1916	−1.76808	−0.884039	−	0.467413i	$-0.845186\pi$
$419$	−36.1916	−1.76808	−0.884039	+	0.467413i	$0.845186\pi$
$420$	−4.09065	−0.199603
$421$	−15.6327	−0.761893	−0.380946	−	0.924597i	$-0.624402\pi$
$421$	−15.6327	−0.761893	−0.380946	+	0.924597i	$0.624402\pi$
$422$	−6.92396	−0.337053
$423$	1.45070	0.0705353
$424$	13.2806	0.644961
$425$	6.47819	0.314238
$426$	−17.8619	−0.865414
$427$	8.13227	0.393548
$428$	11.6721	0.564191
$429$	0	0
$430$	1.77935	0.0858078
$431$	−20.6525	−0.994795	−0.497398	−	0.867523i	$-0.665711\pi$
$431$	−20.6525	−0.994795	−0.497398	+	0.867523i	$0.665711\pi$
$432$	−2.62594	−0.126341
$433$	−21.0158	−1.00995	−0.504976	−	0.863133i	$-0.668499\pi$
$433$	−21.0158	−1.00995	−0.504976	+	0.863133i	$0.668499\pi$
$434$	−0.478189	−0.0229538
$435$	6.19116	0.296843
$436$	−27.0135	−1.29371
$437$	1.49932	0.0717223
$438$	−6.37833	−0.304769
$439$	7.55642	0.360648	0.180324	−	0.983607i	$-0.442285\pi$
$439$	7.55642	0.360648	0.180324	+	0.983607i	$0.442285\pi$
$440$	0	0
$441$	3.59312	0.171101
$442$	8.63915	0.410923
$443$	28.8876	1.37249	0.686245	−	0.727371i	$-0.259258\pi$
$443$	28.8876	1.37249	0.686245	+	0.727371i	$0.259258\pi$
$444$	6.19221	0.293869
$445$	13.2099	0.626207
$446$	7.98020	0.377873
$447$	−15.5367	−0.734862
$448$	−0.177031	−0.00836391
$449$	30.5594	1.44219	0.721094	−	0.692837i	$-0.243640\pi$
$449$	30.5594	1.44219	0.721094	+	0.692837i	$0.243640\pi$
$450$	−2.29196	−0.108044
$451$	0	0
$452$	10.4373	0.490929
$453$	−32.9315	−1.54725
$454$	−15.5102	−0.727927
$455$	2.09065	0.0980114
$456$	−9.48947	−0.444385
$457$	−14.2177	−0.665076	−0.332538	−	0.943090i	$-0.607905\pi$
$457$	−14.2177	−0.665076	−0.332538	+	0.943090i	$0.607905\pi$
$458$	12.6694	0.592003
$459$	−9.86594	−0.460503
$460$	−1.48133	−0.0690674
$461$	23.9831	1.11701	0.558503	−	0.829502i	$-0.311376\pi$
$461$	23.9831	1.11701	0.558503	+	0.829502i	$0.311376\pi$
$462$	0	0
$463$	33.3680	1.55074	0.775370	−	0.631507i	$-0.217563\pi$
$463$	33.3680	1.55074	0.775370	+	0.631507i	$0.217563\pi$
$464$	−4.15745	−0.193005
$465$	1.92491	0.0892655
$466$	1.48466	0.0687756
$467$	−35.1440	−1.62627	−0.813136	−	0.582073i	$-0.802242\pi$
$467$	−35.1440	−1.62627	−0.813136	+	0.582073i	$0.802242\pi$
$468$	11.9674	0.553195
$469$	0.789495	0.0364555
$470$	−0.257538	−0.0118793
$471$	22.2321	1.02440
$472$	20.4694	0.942180
$473$	0	0
$474$	−9.61246	−0.441515
$475$	1.61246	0.0739850
$476$	10.3205	0.473040
$477$	20.8200	0.953283
$478$	−2.75667	−0.126087
$479$	12.4977	0.571036	0.285518	−	0.958373i	$-0.407834\pi$
$479$	12.4977	0.571036	0.285518	+	0.958373i	$0.407834\pi$
$480$	14.5943	0.666133
$481$	−3.16472	−0.144299
$482$	−18.8569	−0.858910
$483$	2.38754	0.108637
$484$	0	0
$485$	−16.6584	−0.756417
$486$	−14.1647	−0.642523
$487$	22.6577	1.02672	0.513360	−	0.858174i	$-0.328401\pi$
$487$	22.6577	1.02672	0.513360	+	0.858174i	$0.328401\pi$
$488$	−18.6388	−0.843740
$489$	−46.7524	−2.11422
$490$	−0.637875	−0.0288162
$491$	−8.70104	−0.392672	−0.196336	−	0.980537i	$-0.562904\pi$
$491$	−8.70104	−0.392672	−0.196336	+	0.980537i	$0.562904\pi$
$492$	42.6924	1.92472
$493$	−15.6200	−0.703488
$494$	2.15034	0.0967485
$495$	0	0
$496$	−1.29260	−0.0580396
$497$	10.9056	0.489181
$498$	−28.9141	−1.29567
$499$	15.3351	0.686494	0.343247	−	0.939245i	$-0.388473\pi$
$499$	15.3351	0.686494	0.343247	+	0.939245i	$0.388473\pi$
$500$	−1.59312	−0.0712463
$501$	14.2645	0.637293
$502$	−4.77288	−0.213024
$503$	−15.4820	−0.690307	−0.345154	−	0.938546i	$-0.612173\pi$
$503$	−15.4820	−0.690307	−0.345154	+	0.938546i	$0.612173\pi$
$504$	−8.23527	−0.366828
$505$	8.52609	0.379406
$506$	0	0
$507$	22.1572	0.984034
$508$	−16.7188	−0.741777
$509$	21.5587	0.955572	0.477786	−	0.878476i	$-0.341439\pi$
$509$	21.5587	0.955572	0.477786	+	0.878476i	$0.341439\pi$
$510$	10.6105	0.469839
$511$	3.89427	0.172273
$512$	−17.7041	−0.782417
$513$	−2.45570	−0.108422
$514$	14.4586	0.637744
$515$	−20.1975	−0.890009
$516$	−11.4109	−0.502335
$517$	0	0
$518$	0.965580	0.0424252
$519$	−1.58819	−0.0697139
$520$	−4.79169	−0.210130
$521$	1.43971	0.0630749	0.0315375	−	0.999503i	$-0.489960\pi$
$521$	1.43971	0.0630749	0.0315375	+	0.999503i	$0.489960\pi$
$522$	5.52628	0.241879
$523$	−45.0273	−1.96890	−0.984452	−	0.175652i	$-0.943797\pi$
$523$	−45.0273	−1.96890	−0.984452	+	0.175652i	$0.943797\pi$
$524$	−25.0427	−1.09400
$525$	2.56771	0.112064
$526$	3.48092	0.151775
$527$	−4.85644	−0.211550
$528$	0	0
$529$	−22.1354	−0.962409
$530$	−3.69611	−0.160549
$531$	32.0900	1.39259
$532$	2.56884	0.111373
$533$	−21.8193	−0.945097
$534$	21.6361	0.936285
$535$	−7.32657	−0.316755
$536$	−1.80949	−0.0781581
$537$	−16.1016	−0.694837
$538$	−10.9792	−0.473346
$539$	0	0
$540$	2.42623	0.104408
$541$	19.9577	0.858050	0.429025	−	0.903293i	$-0.358857\pi$
$541$	19.9577	0.858050	0.429025	+	0.903293i	$0.358857\pi$
$542$	7.83498	0.336541
$543$	47.9092	2.05598
$544$	−36.8205	−1.57867
$545$	16.9564	0.726331
$546$	3.42423	0.146543
$547$	−12.7180	−0.543781	−0.271891	−	0.962328i	$-0.587649\pi$
$547$	−12.7180	−0.543781	−0.271891	+	0.962328i	$0.587649\pi$
$548$	−23.4481	−1.00165
$549$	−29.2202	−1.24709
$550$	0	0
$551$	−3.88791	−0.165631
$552$	−5.47213	−0.232909
$553$	5.86887	0.249570
$554$	−11.6026	−0.492947
$555$	−3.88686	−0.164988
$556$	4.11648	0.174577
$557$	0.445281	0.0188672	0.00943359	−	0.999956i	$-0.496997\pi$
$557$	0.445281	0.0188672	0.00943359	+	0.999956i	$0.496997\pi$
$558$	1.71819	0.0727368
$559$	5.83187	0.246662
$560$	−1.72425	−0.0728629
$561$	0	0
$562$	−5.12768	−0.216298
$563$	13.2186	0.557100	0.278550	−	0.960422i	$-0.410146\pi$
$563$	13.2186	0.557100	0.278550	+	0.960422i	$0.410146\pi$
$564$	1.65157	0.0695438
$565$	−6.55150	−0.275624
$566$	8.52681	0.358409
$567$	6.86887	0.288465
$568$	−24.9951	−1.04877
$569$	32.9020	1.37932	0.689662	−	0.724132i	$-0.257759\pi$
$569$	32.9020	1.37932	0.689662	+	0.724132i	$0.257759\pi$
$570$	2.64102	0.110620
$571$	8.04097	0.336504	0.168252	−	0.985744i	$-0.446188\pi$
$571$	8.04097	0.336504	0.168252	+	0.985744i	$0.446188\pi$
$572$	0	0
$573$	5.05218	0.211058
$574$	6.65722	0.277867
$575$	0.929832	0.0387767
$576$	0.636092	0.0265038
$577$	36.6548	1.52596	0.762980	−	0.646423i	$-0.223736\pi$
$577$	36.6548	1.52596	0.762980	+	0.646423i	$0.223736\pi$
$578$	−15.9258	−0.662425
$579$	51.6741	2.14750
$580$	3.84126	0.159500
$581$	17.6534	0.732388
$582$	−27.2843	−1.13097
$583$	0	0
$584$	−8.92551	−0.369340
$585$	−7.51196	−0.310581
$586$	−18.8952	−0.780554
$587$	−8.45979	−0.349173	−0.174586	−	0.984642i	$-0.555859\pi$
$587$	−8.45979	−0.349173	−0.174586	+	0.984642i	$0.555859\pi$
$588$	4.09065	0.168696
$589$	−1.20880	−0.0498078
$590$	−5.69684	−0.234535
$591$	−53.4033	−2.19672
$592$	2.61008	0.107274
$593$	−23.3601	−0.959285	−0.479643	−	0.877464i	$-0.659234\pi$
$593$	−23.3601	−0.959285	−0.479643	+	0.877464i	$0.659234\pi$
$594$	0	0
$595$	−6.47819	−0.265580
$596$	−9.63966	−0.394856
$597$	−0.486254	−0.0199010
$598$	1.24000	0.0507074
$599$	−5.52401	−0.225705	−0.112852	−	0.993612i	$-0.535999\pi$
$599$	−5.52401	−0.225705	−0.112852	+	0.993612i	$0.535999\pi$
$600$	−5.88507	−0.240257
$601$	−33.2675	−1.35701	−0.678504	−	0.734597i	$-0.737371\pi$
$601$	−33.2675	−1.35701	−0.678504	+	0.734597i	$0.737371\pi$
$602$	−1.77935	−0.0725208
$603$	−2.83675	−0.115521
$604$	−20.4321	−0.831370
$605$	0	0
$606$	13.9647	0.567276
$607$	−15.0511	−0.610906	−0.305453	−	0.952207i	$-0.598808\pi$
$607$	−15.0511	−0.610906	−0.305453	+	0.952207i	$0.598808\pi$
$608$	−9.16488	−0.371685
$609$	−6.19116	−0.250878
$610$	5.18737	0.210030
$611$	−0.844088	−0.0341481
$612$	−37.0828	−1.49898
$613$	30.7859	1.24343	0.621716	−	0.783243i	$-0.286436\pi$
$613$	30.7859	1.24343	0.621716	+	0.783243i	$0.286436\pi$
$614$	−21.1528	−0.853656
$615$	−26.7981	−1.08060
$616$	0	0
$617$	−3.31442	−0.133433	−0.0667167	−	0.997772i	$-0.521252\pi$
$617$	−3.31442	−0.133433	−0.0667167	+	0.997772i	$0.521252\pi$
$618$	−33.0810	−1.33071
$619$	13.8215	0.555531	0.277766	−	0.960649i	$-0.410406\pi$
$619$	13.8215	0.555531	0.277766	+	0.960649i	$0.410406\pi$
$620$	1.19430	0.0479641
$621$	−1.41609	−0.0568256
$622$	−11.6287	−0.466267
$623$	−13.2099	−0.529242
$624$	9.25610	0.370541
$625$	1.00000	0.0400000
$626$	1.06430	0.0425379
$627$	0	0
$628$	13.7938	0.550431
$629$	9.80634	0.391004
$630$	2.29196	0.0913138
$631$	29.6806	1.18157	0.590784	−	0.806830i	$-0.298819\pi$
$631$	29.6806	1.18157	0.590784	+	0.806830i	$0.298819\pi$
$632$	−13.4512	−0.535060
$633$	−27.8718	−1.10780
$634$	−16.5655	−0.657901
$635$	10.4944	0.416457
$636$	23.7030	0.939884
$637$	−2.09065	−0.0828347
$638$	0	0
$639$	−39.1849	−1.55013
$640$	11.2546	0.444878
$641$	−45.7358	−1.80646	−0.903228	−	0.429162i	$-0.858809\pi$
$641$	−45.7358	−1.80646	−0.903228	+	0.429162i	$0.858809\pi$
$642$	−12.0000	−0.473602
$643$	−11.4658	−0.452166	−0.226083	−	0.974108i	$-0.572592\pi$
$643$	−11.4658	−0.452166	−0.226083	+	0.974108i	$0.572592\pi$
$644$	1.48133	0.0583726
$645$	7.16261	0.282027
$646$	−6.66314	−0.262158
$647$	−31.5824	−1.24163	−0.620816	−	0.783956i	$-0.713199\pi$
$647$	−31.5824	−1.24163	−0.620816	+	0.783956i	$0.713199\pi$
$648$	−15.7431	−0.618449
$649$	0	0
$650$	1.33358	0.0523071
$651$	−1.92491	−0.0754431
$652$	−29.0072	−1.13601
$653$	3.60724	0.141162	0.0705811	−	0.997506i	$-0.477515\pi$
$653$	3.60724	0.141162	0.0705811	+	0.997506i	$0.477515\pi$
$654$	27.7724	1.08599
$655$	15.7193	0.614205
$656$	17.9953	0.702597
$657$	−13.9926	−0.545903
$658$	0.257538	0.0100399
$659$	−19.0672	−0.742753	−0.371377	−	0.928482i	$-0.621114\pi$
$659$	−19.0672	−0.742753	−0.371377	+	0.928482i	$0.621114\pi$
$660$	0	0
$661$	0.139279	0.00541732	0.00270866	−	0.999996i	$-0.499138\pi$
$661$	0.139279	0.00541732	0.00270866	+	0.999996i	$0.499138\pi$
$662$	12.1868	0.473652
$663$	34.7761	1.35059
$664$	−40.4609	−1.57019
$665$	−1.61246	−0.0625287
$666$	−3.46944	−0.134438
$667$	−2.24198	−0.0868096
$668$	8.85034	0.342430
$669$	32.1236	1.24197
$670$	0.503599	0.0194557
$671$	0	0
$672$	−14.5943	−0.562986
$673$	30.8673	1.18985	0.594923	−	0.803783i	$-0.297183\pi$
$673$	30.8673	1.18985	0.594923	+	0.803783i	$0.297183\pi$
$674$	8.45278	0.325589
$675$	−1.52295	−0.0586183
$676$	13.7473	0.528741
$677$	20.0624	0.771061	0.385530	−	0.922695i	$-0.374018\pi$
$677$	20.0624	0.771061	0.385530	+	0.922695i	$0.374018\pi$
$678$	−10.7305	−0.412104
$679$	16.6584	0.639289
$680$	14.8477	0.569385
$681$	−62.4347	−2.39250
$682$	0	0
$683$	−39.1013	−1.49617	−0.748085	−	0.663603i	$-0.769026\pi$
$683$	−39.1013	−1.49617	−0.748085	+	0.663603i	$0.769026\pi$
$684$	−9.23015	−0.352924
$685$	14.7184	0.562360
$686$	0.637875	0.0243542
$687$	50.9996	1.94576
$688$	−4.80979	−0.183372
$689$	−12.1141	−0.461511
$690$	1.52295	0.0579776
$691$	−47.0562	−1.79010	−0.895052	−	0.445962i	$-0.852862\pi$
$691$	−47.0562	−1.79010	−0.895052	+	0.445962i	$0.852862\pi$
$692$	−0.985383	−0.0374587
$693$	0	0
$694$	14.8522	0.563782
$695$	−2.58391	−0.0980135
$696$	14.1899	0.537865
$697$	67.6101	2.56091
$698$	−16.3592	−0.619205
$699$	5.97637	0.226047
$700$	1.59312	0.0602141
$701$	12.7715	0.482373	0.241187	−	0.970479i	$-0.422463\pi$
$701$	12.7715	0.482373	0.241187	+	0.970479i	$0.422463\pi$
$702$	−2.03097	−0.0766539
$703$	2.44086	0.0920589
$704$	0	0
$705$	−1.03669	−0.0390442
$706$	5.85338	0.220295
$707$	−8.52609	−0.320657
$708$	36.5335	1.37301
$709$	−14.2137	−0.533808	−0.266904	−	0.963723i	$-0.586001\pi$
$709$	−14.2137	−0.533808	−0.266904	+	0.963723i	$0.586001\pi$
$710$	6.95638	0.261068
$711$	−21.0875	−0.790844
$712$	30.2764	1.13466
$713$	−0.697058	−0.0261050
$714$	−10.6105	−0.397087
$715$	0	0
$716$	−9.99015	−0.373350
$717$	−11.0967	−0.414414
$718$	−19.0216	−0.709881
$719$	−6.32971	−0.236058	−0.118029	−	0.993010i	$-0.537658\pi$
$719$	−6.32971	−0.236058	−0.118029	+	0.993010i	$0.537658\pi$
$720$	6.19543	0.230890
$721$	20.1975	0.752195
$722$	10.4611	0.389322
$723$	−75.9069	−2.82301
$724$	29.7249	1.10472
$725$	−2.41116	−0.0895483
$726$	0	0
$727$	27.5329	1.02114	0.510569	−	0.859837i	$-0.329435\pi$
$727$	27.5329	1.02114	0.510569	+	0.859837i	$0.329435\pi$
$728$	4.79169	0.177592
$729$	−36.4121	−1.34860
$730$	2.48406	0.0919391
$731$	−18.0709	−0.668376
$732$	−33.2663	−1.22956
$733$	−23.4494	−0.866124	−0.433062	−	0.901364i	$-0.642567\pi$
$733$	−23.4494	−0.866124	−0.433062	+	0.901364i	$0.642567\pi$
$734$	4.15508	0.153367
$735$	−2.56771	−0.0947113
$736$	−5.28495	−0.194806
$737$	0	0
$738$	−23.9202	−0.880514
$739$	5.55014	0.204165	0.102083	−	0.994776i	$-0.467449\pi$
$739$	5.55014	0.204165	0.102083	+	0.994776i	$0.467449\pi$
$740$	−2.41157	−0.0886512
$741$	8.65601	0.317987
$742$	3.69611	0.135689
$743$	−46.9974	−1.72417	−0.862083	−	0.506767i	$-0.830840\pi$
$743$	−46.9974	−1.72417	−0.862083	+	0.506767i	$0.830840\pi$
$744$	4.41181	0.161745
$745$	6.05082	0.221685
$746$	−12.1644	−0.445369
$747$	−63.4308	−2.32081
$748$	0	0
$749$	7.32657	0.267707
$750$	1.63787	0.0598067
$751$	47.1787	1.72157	0.860787	−	0.508966i	$-0.169972\pi$
$751$	47.1787	1.72157	0.860787	+	0.508966i	$0.169972\pi$
$752$	0.696155	0.0253862
$753$	−19.2128	−0.700153
$754$	−3.21547	−0.117100
$755$	12.8252	0.466758
$756$	−2.42623	−0.0882412
$757$	48.2852	1.75496	0.877478	−	0.479617i	$-0.159224\pi$
$757$	48.2852	1.75496	0.877478	+	0.479617i	$0.159224\pi$
$758$	−9.01348	−0.327384
$759$	0	0
$760$	3.69570	0.134057
$761$	42.2057	1.52995	0.764977	−	0.644058i	$-0.222750\pi$
$761$	42.2057	1.52995	0.764977	+	0.644058i	$0.222750\pi$
$762$	17.1885	0.622674
$763$	−16.9564	−0.613862
$764$	3.13459	0.113405
$765$	23.2769	0.841578
$766$	0.242467	0.00876068
$767$	−18.6716	−0.674191
$768$	19.3428	0.697972
$769$	−24.6277	−0.888099	−0.444049	−	0.896002i	$-0.646458\pi$
$769$	−24.6277	−0.888099	−0.444049	+	0.896002i	$0.646458\pi$
$770$	0	0
$771$	58.2020	2.09609
$772$	32.0609	1.15390
$773$	−44.9737	−1.61759	−0.808796	−	0.588089i	$-0.799880\pi$
$773$	−44.9737	−1.61759	−0.808796	+	0.588089i	$0.799880\pi$
$774$	6.39340	0.229806
$775$	−0.749661	−0.0269286
$776$	−38.1803	−1.37059
$777$	3.88686	0.139440
$778$	−10.9604	−0.392949
$779$	16.8286	0.602947
$780$	−8.55214	−0.306216
$781$	0	0
$782$	−3.84232	−0.137401
$783$	3.67207	0.131229
$784$	1.72425	0.0615804
$785$	−8.65836	−0.309030
$786$	25.7463	0.918340
$787$	1.51416	0.0539739	0.0269870	−	0.999636i	$-0.491409\pi$
$787$	1.51416	0.0539739	0.0269870	+	0.999636i	$0.491409\pi$
$788$	−33.1337	−1.18034
$789$	14.0121	0.498845
$790$	3.74360	0.133191
$791$	6.55150	0.232944
$792$	0	0
$793$	17.0018	0.603751
$794$	−6.50947	−0.231012
$795$	−14.8784	−0.527681
$796$	−0.301693	−0.0106932
$797$	31.3462	1.11034	0.555169	−	0.831737i	$-0.312653\pi$
$797$	31.3462	1.11034	0.555169	+	0.831737i	$0.312653\pi$
$798$	−2.64102	−0.0934909
$799$	2.61553	0.0925306
$800$	−5.68377	−0.200952
$801$	47.4646	1.67708
$802$	−10.6293	−0.375333
$803$	0	0
$804$	−3.22955	−0.113898
$805$	−0.929832	−0.0327723
$806$	−0.999729	−0.0352139
$807$	−44.1957	−1.55576
$808$	19.5414	0.687465
$809$	−9.70948	−0.341367	−0.170684	−	0.985326i	$-0.554598\pi$
$809$	−9.70948	−0.341367	−0.170684	+	0.985326i	$0.554598\pi$
$810$	4.38147	0.153949
$811$	23.3079	0.818452	0.409226	−	0.912433i	$-0.365799\pi$
$811$	23.3079	0.818452	0.409226	+	0.912433i	$0.365799\pi$
$812$	−3.84126	−0.134802
$813$	31.5390	1.10612
$814$	0	0
$815$	18.2079	0.637793
$816$	−28.6813	−1.00405
$817$	−4.49796	−0.157364
$818$	−16.0645	−0.561683
$819$	7.51196	0.262489
$820$	−16.6267	−0.580628
$821$	3.74985	0.130871	0.0654354	−	0.997857i	$-0.479156\pi$
$821$	3.74985	0.130871	0.0654354	+	0.997857i	$0.479156\pi$
$822$	24.1069	0.840823
$823$	−31.1092	−1.08440	−0.542200	−	0.840249i	$-0.682409\pi$
$823$	−31.1092	−1.08440	−0.542200	+	0.840249i	$0.682409\pi$
$824$	−46.2918	−1.61265
$825$	0	0
$826$	5.69684	0.198218
$827$	−15.3613	−0.534164	−0.267082	−	0.963674i	$-0.586060\pi$
$827$	−15.3613	−0.534164	−0.267082	+	0.963674i	$0.586060\pi$
$828$	−5.32259	−0.184973
$829$	−5.22493	−0.181469	−0.0907347	−	0.995875i	$-0.528922\pi$
$829$	−5.22493	−0.181469	−0.0907347	+	0.995875i	$0.528922\pi$
$830$	11.2607	0.390864
$831$	−46.7052	−1.62018
$832$	−0.370110	−0.0128313
$833$	6.47819	0.224456
$834$	−4.23213	−0.146547
$835$	−5.55536	−0.192251
$836$	0	0
$837$	1.14169	0.0394627
$838$	23.0857	0.797483
$839$	−52.4526	−1.81087	−0.905433	−	0.424489i	$-0.860454\pi$
$839$	−52.4526	−1.81087	−0.905433	+	0.424489i	$0.860454\pi$
$840$	5.88507	0.203054
$841$	−23.1863	−0.799528
$842$	9.97172	0.343648
$843$	−20.6410	−0.710914
$844$	−17.2929	−0.595245
$845$	−8.62916	−0.296852
$846$	−0.925362	−0.0318146
$847$	0	0
$848$	9.99103	0.343093
$849$	34.3239	1.17799
$850$	−4.13227	−0.141736
$851$	1.40753	0.0482495
$852$	−44.6109	−1.52834
$853$	35.1937	1.20501	0.602504	−	0.798116i	$-0.294170\pi$
$853$	35.1937	1.20501	0.602504	+	0.798116i	$0.294170\pi$
$854$	−5.18737	−0.177508
$855$	5.79377	0.198143
$856$	−16.7922	−0.573945
$857$	−54.5011	−1.86172	−0.930862	−	0.365372i	$-0.880942\pi$
$857$	−54.5011	−1.86172	−0.930862	+	0.365372i	$0.880942\pi$
$858$	0	0
$859$	11.5923	0.395523	0.197762	−	0.980250i	$-0.436633\pi$
$859$	11.5923	0.395523	0.197762	+	0.980250i	$0.436633\pi$
$860$	4.44399	0.151539
$861$	26.7981	0.913275
$862$	13.1737	0.448698
$863$	26.6514	0.907225	0.453613	−	0.891199i	$-0.350135\pi$
$863$	26.6514	0.907225	0.453613	+	0.891199i	$0.350135\pi$
$864$	8.65609	0.294486
$865$	0.618526	0.0210305
$866$	13.4054	0.455535
$867$	−64.1078	−2.17721
$868$	−1.19430	−0.0405371
$869$	0	0
$870$	−3.94918	−0.133890
$871$	1.65056	0.0559272
$872$	38.8633	1.31608
$873$	−59.8554	−2.02580
$874$	−0.956379	−0.0323500
$875$	−1.00000	−0.0338062
$876$	−15.9301	−0.538229
$877$	12.0449	0.406729	0.203365	−	0.979103i	$-0.434812\pi$
$877$	12.0449	0.406729	0.203365	+	0.979103i	$0.434812\pi$
$878$	−4.82005	−0.162669
$879$	−76.0610	−2.56547
$880$	0	0
$881$	−6.11314	−0.205957	−0.102979	−	0.994684i	$-0.532837\pi$
$881$	−6.11314	−0.205957	−0.102979	+	0.994684i	$0.532837\pi$
$882$	−2.29196	−0.0771742
$883$	11.5321	0.388088	0.194044	−	0.980993i	$-0.437840\pi$
$883$	11.5321	0.388088	0.194044	+	0.980993i	$0.437840\pi$
$884$	21.5766	0.725700
$885$	−22.9321	−0.770854
$886$	−18.4266	−0.619055
$887$	19.6325	0.659196	0.329598	−	0.944121i	$-0.393087\pi$
$887$	19.6325	0.659196	0.329598	+	0.944121i	$0.393087\pi$
$888$	−8.90851	−0.298950
$889$	−10.4944	−0.351971
$890$	−8.42623	−0.282448
$891$	0	0
$892$	19.9308	0.667334
$893$	0.651022	0.0217856
$894$	9.91048	0.331456
$895$	6.27083	0.209611
$896$	−11.2546	−0.375990
$897$	4.99151	0.166662
$898$	−19.4931	−0.650492
$899$	1.80755	0.0602853
$900$	−5.72425	−0.190808
$901$	37.5373	1.25055
$902$	0	0
$903$	−7.16261	−0.238357
$904$	−15.0158	−0.499417
$905$	−18.6584	−0.620225
$906$	21.0061	0.697882
$907$	−30.3586	−1.00804	−0.504021	−	0.863691i	$-0.668147\pi$
$907$	−30.3586	−1.00804	−0.504021	+	0.863691i	$0.668147\pi$
$908$	−38.7372	−1.28554
$909$	30.6352	1.01611
$910$	−1.33358	−0.0442076
$911$	14.7391	0.488328	0.244164	−	0.969734i	$-0.421487\pi$
$911$	14.7391	0.488328	0.244164	+	0.969734i	$0.421487\pi$
$912$	−7.13898	−0.236395
$913$	0	0
$914$	9.06911	0.299980
$915$	20.8813	0.690314
$916$	31.6424	1.04549
$917$	−15.7193	−0.519098
$918$	6.29324	0.207708
$919$	−4.78135	−0.157722	−0.0788611	−	0.996886i	$-0.525128\pi$
$919$	−4.78135	−0.157722	−0.0788611	+	0.996886i	$0.525128\pi$
$920$	2.13113	0.0702614
$921$	−85.1485	−2.80574
$922$	−15.2982	−0.503821
$923$	22.7998	0.750463
$924$	0	0
$925$	1.51375	0.0497717
$926$	−21.2846	−0.699454
$927$	−72.5720	−2.38358
$928$	13.7045	0.449872
$929$	1.68714	0.0553534	0.0276767	−	0.999617i	$-0.491189\pi$
$929$	1.68714	0.0553534	0.0276767	+	0.999617i	$0.491189\pi$
$930$	−1.22785	−0.0402628
$931$	1.61246	0.0528464
$932$	3.70800	0.121460
$933$	−46.8102	−1.53250
$934$	22.4175	0.733523
$935$	0	0
$936$	−17.2171	−0.562758
$937$	22.1923	0.724991	0.362495	−	0.931986i	$-0.381925\pi$
$937$	22.1923	0.724991	0.362495	+	0.931986i	$0.381925\pi$
$938$	−0.503599	−0.0164431
$939$	4.28424	0.139811
$940$	−0.643210	−0.0209792
$941$	15.0418	0.490350	0.245175	−	0.969479i	$-0.421155\pi$
$941$	15.0418	0.490350	0.245175	+	0.969479i	$0.421155\pi$
$942$	−14.1813	−0.462052
$943$	9.70426	0.316014
$944$	15.3992	0.501202
$945$	1.52295	0.0495415
$946$	0	0
$947$	10.7171	0.348259	0.174129	−	0.984723i	$-0.444289\pi$
$947$	10.7171	0.348259	0.174129	+	0.984723i	$0.444289\pi$
$948$	−24.0075	−0.779727
$949$	8.14158	0.264287
$950$	−1.02855	−0.0333706
$951$	−66.6830	−2.16234
$952$	−14.8477	−0.481218
$953$	−31.2924	−1.01366	−0.506831	−	0.862045i	$-0.669183\pi$
$953$	−31.2924	−1.01366	−0.506831	+	0.862045i	$0.669183\pi$
$954$	−13.2806	−0.429974
$955$	−1.96758	−0.0636695
$956$	−6.88488	−0.222673
$957$	0	0
$958$	−7.97198	−0.257563
$959$	−14.7184	−0.475281
$960$	−0.454563	−0.0146709
$961$	−30.4380	−0.981871
$962$	2.01869	0.0650853
$963$	−26.3252	−0.848318
$964$	−47.0959	−1.51686
$965$	−20.1246	−0.647834
$966$	−1.52295	−0.0490000
$967$	30.8263	0.991307	0.495654	−	0.868520i	$-0.334929\pi$
$967$	30.8263	0.991307	0.495654	+	0.868520i	$0.334929\pi$
$968$	0	0
$969$	−26.8219	−0.861643
$970$	10.6259	0.341179
$971$	−27.1359	−0.870833	−0.435416	−	0.900229i	$-0.643399\pi$
$971$	−27.1359	−0.870833	−0.435416	+	0.900229i	$0.643399\pi$
$972$	−35.3769	−1.13471
$973$	2.58391	0.0828365
$974$	−14.4528	−0.463097
$975$	5.36819	0.171920
$976$	−14.0221	−0.448836
$977$	42.5686	1.36189	0.680945	−	0.732334i	$-0.261569\pi$
$977$	42.5686	1.36189	0.680945	+	0.732334i	$0.261569\pi$
$978$	29.8222	0.953608
$979$	0	0
$980$	−1.59312	−0.0508902
$981$	60.9262	1.94523
$982$	5.55017	0.177113
$983$	42.1199	1.34342	0.671708	−	0.740816i	$-0.265561\pi$
$983$	42.1199	1.34342	0.671708	+	0.740816i	$0.265561\pi$
$984$	−61.4200	−1.95800
$985$	20.7981	0.662681
$986$	9.96358	0.317305
$987$	1.03669	0.0329983
$988$	5.37056	0.170860
$989$	−2.59376	−0.0824768
$990$	0	0
$991$	−36.5439	−1.16086	−0.580428	−	0.814312i	$-0.697115\pi$
$991$	−36.5439	−1.16086	−0.580428	+	0.814312i	$0.697115\pi$
$992$	4.26090	0.135284
$993$	49.0567	1.55677
$994$	−6.95638	−0.220643
$995$	0.189373	0.00600352
$996$	−72.2141	−2.28819
$997$	−15.0094	−0.475352	−0.237676	−	0.971344i	$-0.576386\pi$
$997$	−15.0094	−0.475352	−0.237676	+	0.971344i	$0.576386\pi$
$998$	−9.78189	−0.309640
$999$	−2.30536	−0.0729383

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.v.1.2	yes	4
11.10	odd	2		4235.2.a.u.1.3	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4235.2.a.u.1.3	✓	4	11.10	odd	2
4235.2.a.v.1.2	yes	4	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)

\(f(q)\)	\(=\)	\(q-0.637875 q^{2} -2.56771 q^{3} -1.59312 q^{4} +1.00000 q^{5} +1.63787 q^{6} -1.00000 q^{7} +2.29196 q^{8} +3.59312 q^{9} +O(q^{10})\)	\(q-0.637875 q^{2} -2.56771 q^{3} -1.59312 q^{4} +1.00000 q^{5} +1.63787 q^{6} -1.00000 q^{7} +2.29196 q^{8} +3.59312 q^{9} -0.637875 q^{10} +4.09065 q^{12} -2.09065 q^{13} +0.637875 q^{14} -2.56771 q^{15} +1.72425 q^{16} +6.47819 q^{17} -2.29196 q^{18} +1.61246 q^{19} -1.59312 q^{20} +2.56771 q^{21} +0.929832 q^{23} -5.88507 q^{24} +1.00000 q^{25} +1.33358 q^{26} -1.52295 q^{27} +1.59312 q^{28} -2.41116 q^{29} +1.63787 q^{30} -0.749661 q^{31} -5.68377 q^{32} -4.13227 q^{34} -1.00000 q^{35} -5.72425 q^{36} +1.51375 q^{37} -1.02855 q^{38} +5.36819 q^{39} +2.29196 q^{40} +10.4366 q^{41} -1.63787 q^{42} -2.78950 q^{43} +3.59312 q^{45} -0.593116 q^{46} +0.403743 q^{47} -4.42737 q^{48} +1.00000 q^{49} -0.637875 q^{50} -16.6341 q^{51} +3.33065 q^{52} +5.79442 q^{53} +0.971450 q^{54} -2.29196 q^{56} -4.14034 q^{57} +1.53802 q^{58} +8.93097 q^{59} +4.09065 q^{60} -8.13227 q^{61} +0.478189 q^{62} -3.59312 q^{63} +0.177031 q^{64} -2.09065 q^{65} -0.789495 q^{67} -10.3205 q^{68} -2.38754 q^{69} +0.637875 q^{70} -10.9056 q^{71} +8.23527 q^{72} -3.89427 q^{73} -0.965580 q^{74} -2.56771 q^{75} -2.56884 q^{76} -3.42423 q^{78} -5.86887 q^{79} +1.72425 q^{80} -6.86887 q^{81} -6.65722 q^{82} -17.6534 q^{83} -4.09065 q^{84} +6.47819 q^{85} +1.77935 q^{86} +6.19116 q^{87} +13.2099 q^{89} -2.29196 q^{90} +2.09065 q^{91} -1.48133 q^{92} +1.92491 q^{93} -0.257538 q^{94} +1.61246 q^{95} +14.5943 q^{96} -16.6584 q^{97} -0.637875 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 4 q^{4} + 4 q^{5} + 4 q^{6} - 4 q^{7} + 6 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 + 4 * q^4 + 4 * q^5 + 4 * q^6 - 4 * q^7 + 6 * q^8 + 4 * q^9	\( 4 q - 2 q^{3} + 4 q^{4} + 4 q^{5} + 4 q^{6} - 4 q^{7} + 6 q^{8} + 4 q^{9} - 8 q^{12} + 16 q^{13} - 2 q^{15} + 12 q^{16} + 2 q^{17} - 6 q^{18} + 6 q^{19} + 4 q^{20} + 2 q^{21} - 2 q^{23} - 10 q^{24} + 4 q^{25} + 2 q^{26} + 10 q^{27} - 4 q^{28} + 12 q^{29} + 4 q^{30} - 6 q^{31} + 12 q^{32} + 8 q^{34} - 4 q^{35} - 28 q^{36} - 6 q^{37} - 10 q^{38} + 12 q^{39} + 6 q^{40} + 18 q^{41} - 4 q^{42} + 6 q^{43} + 4 q^{45} + 8 q^{46} + 4 q^{47} + 2 q^{48} + 4 q^{49} + 4 q^{51} + 30 q^{52} + 34 q^{53} - 2 q^{54} - 6 q^{56} - 28 q^{57} + 32 q^{58} - 10 q^{59} - 8 q^{60} - 8 q^{61} - 22 q^{62} - 4 q^{63} - 16 q^{64} + 16 q^{65} + 14 q^{67} - 44 q^{68} - 10 q^{69} - 12 q^{72} + 2 q^{73} + 48 q^{74} - 2 q^{75} + 38 q^{76} + 14 q^{78} - 8 q^{79} + 12 q^{80} - 12 q^{81} - 34 q^{82} - 10 q^{83} + 8 q^{84} + 2 q^{85} - 24 q^{86} + 32 q^{87} + 10 q^{89} - 6 q^{90} - 16 q^{91} + 10 q^{92} - 26 q^{93} + 54 q^{94} + 6 q^{95} + 8 q^{96} - 34 q^{97}+O(q^{100}) \) 4 * q - 2 * q^3 + 4 * q^4 + 4 * q^5 + 4 * q^6 - 4 * q^7 + 6 * q^8 + 4 * q^9 - 8 * q^12 + 16 * q^13 - 2 * q^15 + 12 * q^16 + 2 * q^17 - 6 * q^18 + 6 * q^19 + 4 * q^20 + 2 * q^21 - 2 * q^23 - 10 * q^24 + 4 * q^25 + 2 * q^26 + 10 * q^27 - 4 * q^28 + 12 * q^29 + 4 * q^30 - 6 * q^31 + 12 * q^32 + 8 * q^34 - 4 * q^35 - 28 * q^36 - 6 * q^37 - 10 * q^38 + 12 * q^39 + 6 * q^40 + 18 * q^41 - 4 * q^42 + 6 * q^43 + 4 * q^45 + 8 * q^46 + 4 * q^47 + 2 * q^48 + 4 * q^49 + 4 * q^51 + 30 * q^52 + 34 * q^53 - 2 * q^54 - 6 * q^56 - 28 * q^57 + 32 * q^58 - 10 * q^59 - 8 * q^60 - 8 * q^61 - 22 * q^62 - 4 * q^63 - 16 * q^64 + 16 * q^65 + 14 * q^67 - 44 * q^68 - 10 * q^69 - 12 * q^72 + 2 * q^73 + 48 * q^74 - 2 * q^75 + 38 * q^76 + 14 * q^78 - 8 * q^79 + 12 * q^80 - 12 * q^81 - 34 * q^82 - 10 * q^83 + 8 * q^84 + 2 * q^85 - 24 * q^86 + 32 * q^87 + 10 * q^89 - 6 * q^90 - 16 * q^91 + 10 * q^92 - 26 * q^93 + 54 * q^94 + 6 * q^95 + 8 * q^96 - 34 * q^97

Introduction

L-functions

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