LMFDB - Embedded newform 4235.2.a.v.1.3

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			1.3
Root			$0.275377$ 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)

$f(q)$	$=$	$q+0.275377 q^{2} +2.63138 q^{3} -1.92417 q^{4} +1.00000 q^{5} +0.724623 q^{6} -1.00000 q^{7} -1.08063 q^{8} +3.92417 q^{9} +O(q^{10})$	\(q+0.275377 q^{2} +2.63138 q^{3} -1.92417 q^{4} +1.00000 q^{5} +0.724623 q^{6} -1.00000 q^{7} -1.08063 q^{8} +3.92417 q^{9} +0.275377 q^{10} -5.06322 q^{12} +7.06322 q^{13} -0.275377 q^{14} +2.63138 q^{15} +3.55075 q^{16} +3.76771 q^{17} +1.08063 q^{18} -4.83093 q^{19} -1.92417 q^{20} -2.63138 q^{21} -3.35600 q^{23} -2.84354 q^{24} +1.00000 q^{25} +1.94505 q^{26} +2.43184 q^{27} +1.92417 q^{28} +9.81352 q^{29} +0.724623 q^{30} -8.10630 q^{31} +3.13905 q^{32} +1.03754 q^{34} -1.00000 q^{35} -7.55075 q^{36} -9.51726 q^{37} -1.33033 q^{38} +18.5860 q^{39} -1.08063 q^{40} +3.74203 q^{41} -0.724623 q^{42} +10.0680 q^{43} +3.92417 q^{45} -0.924167 q^{46} +5.30105 q^{47} +9.34339 q^{48} +1.00000 q^{49} +0.275377 q^{50} +9.91428 q^{51} -13.5908 q^{52} +11.9068 q^{53} +0.669673 q^{54} +1.08063 q^{56} -12.7120 q^{57} +2.70242 q^{58} -2.02013 q^{59} -5.06322 q^{60} -2.96246 q^{61} -2.23229 q^{62} -3.92417 q^{63} -6.23709 q^{64} +7.06322 q^{65} +12.0680 q^{67} -7.24970 q^{68} -8.83093 q^{69} -0.275377 q^{70} +5.57568 q^{71} -4.24056 q^{72} -7.92896 q^{73} -2.62084 q^{74} +2.63138 q^{75} +9.29551 q^{76} +5.11817 q^{78} -4.37341 q^{79} +3.55075 q^{80} -5.37341 q^{81} +1.03047 q^{82} +15.6694 q^{83} +5.06322 q^{84} +3.76771 q^{85} +2.77250 q^{86} +25.8231 q^{87} -4.79611 q^{89} +1.08063 q^{90} -7.06322 q^{91} +6.45751 q^{92} -21.3308 q^{93} +1.45979 q^{94} -4.83093 q^{95} +8.26004 q^{96} -2.30540 q^{97} +0.275377 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.275377	0.194721	0.0973606	−	0.995249i	$-0.468960\pi$
$2$	0.275377	0.194721	0.0973606	+	0.995249i	$0.468960\pi$
$3$	2.63138	1.51923	0.759614	−	0.650374i	$-0.225388\pi$
$3$	2.63138	1.51923	0.759614	+	0.650374i	$0.225388\pi$
$4$	−1.92417	−0.962084
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.724623	0.295826
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.08063	−0.382059
$9$	3.92417	1.30806
$10$	0.275377	0.0870820
$11$	0	0
$11$	0	0
$12$	−5.06322	−1.46163
$13$	7.06322	1.95898	0.979492	−	0.201483i	$-0.0645760\pi$
$13$	7.06322	1.95898	0.979492	+	0.201483i	$0.0645760\pi$
$14$	−0.275377	−0.0735977
$15$	2.63138	0.679420
$16$	3.55075	0.887689
$17$	3.76771	0.913803	0.456902	−	0.889517i	$-0.348959\pi$
$17$	3.76771	0.913803	0.456902	+	0.889517i	$0.348959\pi$
$18$	1.08063	0.254706
$19$	−4.83093	−1.10829	−0.554145	−	0.832420i	$-0.686955\pi$
$19$	−4.83093	−1.10829	−0.554145	+	0.832420i	$0.686955\pi$
$20$	−1.92417	−0.430257
$21$	−2.63138	−0.574214
$22$	0	0
$23$	−3.35600	−0.699775	−0.349888	−	0.936792i	$-0.613780\pi$
$23$	−3.35600	−0.699775	−0.349888	+	0.936792i	$0.613780\pi$
$24$	−2.84354	−0.580435
$25$	1.00000	0.200000
$26$	1.94505	0.381456
$27$	2.43184	0.468007
$28$	1.92417	0.363633
$29$	9.81352	1.82232	0.911162	−	0.412048i	$-0.135186\pi$
$29$	9.81352	1.82232	0.911162	+	0.412048i	$0.135186\pi$
$30$	0.724623	0.132297
$31$	−8.10630	−1.45594	−0.727968	−	0.685612i	$-0.759535\pi$
$31$	−8.10630	−1.45594	−0.727968	+	0.685612i	$0.759535\pi$
$32$	3.13905	0.554911
$33$	0	0
$34$	1.03754	0.177937
$35$	−1.00000	−0.169031
$36$	−7.55075	−1.25846
$37$	−9.51726	−1.56463	−0.782314	−	0.622885i	$-0.785961\pi$
$37$	−9.51726	−1.56463	−0.782314	+	0.622885i	$0.785961\pi$
$38$	−1.33033	−0.215808
$39$	18.5860	2.97614
$40$	−1.08063	−0.170862
$41$	3.74203	0.584407	0.292204	−	0.956356i	$-0.405612\pi$
$41$	3.74203	0.584407	0.292204	+	0.956356i	$0.405612\pi$
$42$	−0.724623	−0.111812
$43$	10.0680	1.53536	0.767679	−	0.640835i	$-0.221412\pi$
$43$	10.0680	1.53536	0.767679	+	0.640835i	$0.221412\pi$
$44$	0	0
$45$	3.92417	0.584980
$46$	−0.924167	−0.136261
$47$	5.30105	0.773238	0.386619	−	0.922239i	$-0.373643\pi$
$47$	5.30105	0.773238	0.386619	+	0.922239i	$0.373643\pi$
$48$	9.34339	1.34860
$49$	1.00000	0.142857
$50$	0.275377	0.0389442
$51$	9.91428	1.38828
$52$	−13.5908	−1.88471
$53$	11.9068	1.63552	0.817760	−	0.575560i	$-0.195216\pi$
$53$	11.9068	1.63552	0.817760	+	0.575560i	$0.195216\pi$
$54$	0.669673	0.0911309
$55$	0	0
$56$	1.08063	0.144405
$57$	−12.7120	−1.68375
$58$	2.70242	0.354845
$59$	−2.02013	−0.262999	−0.131499	−	0.991316i	$-0.541979\pi$
$59$	−2.02013	−0.262999	−0.131499	+	0.991316i	$0.541979\pi$
$60$	−5.06322	−0.653659
$61$	−2.96246	−0.379304	−0.189652	−	0.981851i	$-0.560736\pi$
$61$	−2.96246	−0.379304	−0.189652	+	0.981851i	$0.560736\pi$
$62$	−2.23229	−0.283501
$63$	−3.92417	−0.494399
$64$	−6.23709	−0.779636
$65$	7.06322	0.876084
$66$	0	0
$67$	12.0680	1.47434	0.737171	−	0.675706i	$-0.236161\pi$
$67$	12.0680	1.47434	0.737171	+	0.675706i	$0.236161\pi$
$68$	−7.24970	−0.879155
$69$	−8.83093	−1.06312
$70$	−0.275377	−0.0329139
$71$	5.57568	0.661712	0.330856	−	0.943681i	$-0.392663\pi$
$71$	5.57568	0.661712	0.330856	+	0.943681i	$0.392663\pi$
$72$	−4.24056	−0.499755
$73$	−7.92896	−0.928015	−0.464007	−	0.885831i	$-0.653589\pi$
$73$	−7.92896	−0.928015	−0.464007	+	0.885831i	$0.653589\pi$
$74$	−2.62084	−0.304666
$75$	2.63138	0.303846
$76$	9.29551	1.06627
$77$	0	0
$78$	5.11817	0.579518
$79$	−4.37341	−0.492047	−0.246024	−	0.969264i	$-0.579124\pi$
$79$	−4.37341	−0.492047	−0.246024	+	0.969264i	$0.579124\pi$
$80$	3.55075	0.396986
$81$	−5.37341	−0.597046
$82$	1.03047	0.113796
$83$	15.6694	1.71994	0.859968	−	0.510347i	$-0.170483\pi$
$83$	15.6694	1.71994	0.859968	+	0.510347i	$0.170483\pi$
$84$	5.06322	0.552442
$85$	3.76771	0.408665
$86$	2.77250	0.298967
$87$	25.8231	2.76853
$88$	0	0
$89$	−4.79611	−0.508386	−0.254193	−	0.967153i	$-0.581810\pi$
$89$	−4.79611	−0.508386	−0.254193	+	0.967153i	$0.581810\pi$
$90$	1.08063	0.113908
$91$	−7.06322	−0.740426
$92$	6.45751	0.673242
$93$	−21.3308	−2.21190
$94$	1.45979	0.150566
$95$	−4.83093	−0.495643
$96$	8.26004	0.843037
$97$	−2.30540	−0.234078	−0.117039	−	0.993127i	$-0.537340\pi$
$97$	−2.30540	−0.234078	−0.117039	+	0.993127i	$0.537340\pi$
$98$	0.275377	0.0278173
$99$	0	0
$100$	−1.92417	−0.192417
$101$	−0.657058	−0.0653797	−0.0326898	−	0.999466i	$-0.510407\pi$
$101$	−0.657058	−0.0653797	−0.0326898	+	0.999466i	$0.510407\pi$
$102$	2.73017	0.270327
$103$	−0.343692	−0.0338650	−0.0169325	−	0.999857i	$-0.505390\pi$
$103$	−0.343692	−0.0338650	−0.0169325	+	0.999857i	$0.505390\pi$
$104$	−7.63270	−0.748448
$105$	−2.63138	−0.256797
$106$	3.27885	0.318470
$107$	−16.5603	−1.60095	−0.800474	−	0.599367i	$-0.795419\pi$
$107$	−16.5603	−1.60095	−0.800474	+	0.599367i	$0.795419\pi$
$108$	−4.67926	−0.450262
$109$	11.5354	1.10489	0.552446	−	0.833549i	$-0.313694\pi$
$109$	11.5354	1.10489	0.552446	+	0.833549i	$0.313694\pi$
$110$	0	0
$111$	−25.0435	−2.37703
$112$	−3.55075	−0.335515
$113$	−2.89849	−0.272667	−0.136334	−	0.990663i	$-0.543532\pi$
$113$	−2.89849	−0.272667	−0.136334	+	0.990663i	$0.543532\pi$
$114$	−3.50060	−0.327861
$115$	−3.35600	−0.312949
$116$	−18.8828	−1.75323
$117$	27.7172	2.56246
$118$	−0.556299	−0.0512114
$119$	−3.76771	−0.345385
$120$	−2.84354	−0.259579
$121$	0	0
$122$	−0.815794	−0.0738585
$123$	9.84671	0.887848
$124$	15.5979	1.40073
$125$	1.00000	0.0894427
$126$	−1.08063	−0.0962699
$127$	6.23784	0.553518	0.276759	−	0.960939i	$-0.410740\pi$
$127$	6.23784	0.553518	0.276759	+	0.960939i	$0.410740\pi$
$128$	−7.99565	−0.706723
$129$	26.4928	2.33256
$130$	1.94505	0.170592
$131$	−1.42402	−0.124417	−0.0622084	−	0.998063i	$-0.519814\pi$
$131$	−1.42402	−0.124417	−0.0622084	+	0.998063i	$0.519814\pi$
$132$	0	0
$133$	4.83093	0.418894
$134$	3.32326	0.287086
$135$	2.43184	0.209299
$136$	−4.07149	−0.349127
$137$	18.5019	1.58073	0.790363	−	0.612639i	$-0.209892\pi$
$137$	18.5019	1.58073	0.790363	+	0.612639i	$0.209892\pi$
$138$	−2.43184	−0.207012
$139$	4.16125	0.352953	0.176476	−	0.984305i	$-0.443530\pi$
$139$	4.16125	0.352953	0.176476	+	0.984305i	$0.443530\pi$
$140$	1.92417	0.162622
$141$	13.9491	1.17473
$142$	1.53542	0.128849
$143$	0	0
$144$	13.9338	1.16115
$145$	9.81352	0.814968
$146$	−2.18346	−0.180704
$147$	2.63138	0.217033
$148$	18.3128	1.50530
$149$	17.1111	1.40180	0.700898	−	0.713262i	$-0.252783\pi$
$149$	17.1111	1.40180	0.700898	+	0.713262i	$0.252783\pi$
$150$	0.724623	0.0591652
$151$	5.90883	0.480854	0.240427	−	0.970667i	$-0.422713\pi$
$151$	5.90883	0.480854	0.240427	+	0.970667i	$0.422713\pi$
$152$	5.22043	0.423433
$153$	14.7851	1.19531
$154$	0	0
$155$	−8.10630	−0.651114
$156$	−35.7626	−2.86330
$157$	5.69460	0.454478	0.227239	−	0.973839i	$-0.427030\pi$
$157$	5.69460	0.454478	0.227239	+	0.973839i	$0.427030\pi$
$158$	−1.20434	−0.0958120
$159$	31.3312	2.48473
$160$	3.13905	0.248164
$161$	3.35600	0.264490
$162$	−1.47972	−0.116257
$163$	−1.23502	−0.0967339	−0.0483669	−	0.998830i	$-0.515402\pi$
$163$	−1.23502	−0.0967339	−0.0483669	+	0.998830i	$0.515402\pi$
$164$	−7.20029	−0.562249
$165$	0	0
$166$	4.31499	0.334908
$167$	1.49158	0.115422	0.0577110	−	0.998333i	$-0.481620\pi$
$167$	1.49158	0.115422	0.0577110	+	0.998333i	$0.481620\pi$
$168$	2.84354	0.219384
$169$	36.8890	2.83762
$170$	1.03754	0.0795758
$171$	−18.9574	−1.44971
$172$	−19.3725	−1.47714
$173$	6.47972	0.492644	0.246322	−	0.969188i	$-0.420778\pi$
$173$	6.47972	0.492644	0.246322	+	0.969188i	$0.420778\pi$
$174$	7.11110	0.539091
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	−5.31574	−0.399555
$178$	−1.32074	−0.0989936
$179$	−14.5255	−1.08569	−0.542844	−	0.839833i	$-0.682653\pi$
$179$	−14.5255	−1.08569	−0.542844	+	0.839833i	$0.682653\pi$
$180$	−7.55075	−0.562800
$181$	−4.30540	−0.320018	−0.160009	−	0.987116i	$-0.551152\pi$
$181$	−4.30540	−0.320018	−0.160009	+	0.987116i	$0.551152\pi$
$182$	−1.94505	−0.144177
$183$	−7.79536	−0.576249
$184$	3.62659	0.267356
$185$	−9.51726	−0.699723
$186$	−5.87401	−0.430703
$187$	0	0
$188$	−10.2001	−0.743920
$189$	−2.43184	−0.176890
$190$	−1.33033	−0.0965121
$191$	−5.05974	−0.366110	−0.183055	−	0.983103i	$-0.558599\pi$
$191$	−5.05974	−0.366110	−0.183055	+	0.983103i	$0.558599\pi$
$192$	−16.4122	−1.18444
$193$	7.28637	0.524484	0.262242	−	0.965002i	$-0.415538\pi$
$193$	7.28637	0.524484	0.262242	+	0.965002i	$0.415538\pi$
$194$	−0.634855	−0.0455799
$195$	18.5860	1.33097
$196$	−1.92417	−0.137441
$197$	−15.8467	−1.12903	−0.564516	−	0.825422i	$-0.690937\pi$
$197$	−15.8467	−1.12903	−0.564516	+	0.825422i	$0.690937\pi$
$198$	0	0
$199$	−4.37689	−0.310269	−0.155135	−	0.987893i	$-0.549581\pi$
$199$	−4.37689	−0.310269	−0.155135	+	0.987893i	$0.549581\pi$
$200$	−1.08063	−0.0764118
$201$	31.7555	2.23986
$202$	−0.180939	−0.0127308
$203$	−9.81352	−0.688774
$204$	−19.0767	−1.33564
$205$	3.74203	0.261355
$206$	−0.0946450	−0.00659423
$207$	−13.1695	−0.915345
$208$	25.0798	1.73897
$209$	0	0
$210$	−0.724623	−0.0500037
$211$	−16.6868	−1.14877	−0.574383	−	0.818587i	$-0.694758\pi$
$211$	−16.6868	−1.14877	−0.574383	+	0.818587i	$0.694758\pi$
$212$	−22.9106	−1.57351
$213$	14.6717	1.00529
$214$	−4.56034	−0.311739
$215$	10.0680	0.686633
$216$	−2.62791	−0.178806
$217$	8.10630	0.550292
$218$	3.17659	0.215146
$219$	−20.8641	−1.40987
$220$	0	0
$221$	26.6121	1.79013
$222$	−6.89642	−0.462857
$223$	−6.70796	−0.449198	−0.224599	−	0.974451i	$-0.572107\pi$
$223$	−6.70796	−0.449198	−0.224599	+	0.974451i	$0.572107\pi$
$224$	−3.13905	−0.209737
$225$	3.92417	0.261611
$226$	−0.798179	−0.0530940
$227$	25.0360	1.66170	0.830849	−	0.556497i	$-0.187855\pi$
$227$	25.0360	1.66170	0.830849	+	0.556497i	$0.187855\pi$
$228$	24.4600	1.61991
$229$	2.04027	0.134825	0.0674123	−	0.997725i	$-0.478526\pi$
$229$	2.04027	0.134825	0.0674123	+	0.997725i	$0.478526\pi$
$230$	−0.924167	−0.0609378
$231$	0	0
$232$	−10.6047	−0.696236
$233$	9.36559	0.613560	0.306780	−	0.951780i	$-0.400748\pi$
$233$	9.36559	0.613560	0.306780	+	0.951780i	$0.400748\pi$
$234$	7.63270	0.498965
$235$	5.30105	0.345803
$236$	3.88707	0.253027
$237$	−11.5081	−0.747532
$238$	−1.03754	−0.0672538
$239$	−5.41443	−0.350230	−0.175115	−	0.984548i	$-0.556030\pi$
$239$	−5.41443	−0.350230	−0.175115	+	0.984548i	$0.556030\pi$
$240$	9.34339	0.603113
$241$	−25.4703	−1.64068	−0.820342	−	0.571873i	$-0.806217\pi$
$241$	−25.4703	−1.64068	−0.820342	+	0.571873i	$0.806217\pi$
$242$	0	0
$243$	−21.4350	−1.37506
$244$	5.70027	0.364922
$245$	1.00000	0.0638877
$246$	2.71156	0.172883
$247$	−34.1219	−2.17112
$248$	8.75989	0.556253
$249$	41.2321	2.61298
$250$	0.275377	0.0174164
$251$	−7.12164	−0.449514	−0.224757	−	0.974415i	$-0.572159\pi$
$251$	−7.12164	−0.449514	−0.224757	+	0.974415i	$0.572159\pi$
$252$	7.55075	0.475653
$253$	0	0
$254$	1.71776	0.107782
$255$	9.91428	0.620856
$256$	10.2724	0.642022
$257$	15.4733	0.965198	0.482599	−	0.875841i	$-0.339693\pi$
$257$	15.4733	0.965198	0.482599	+	0.875841i	$0.339693\pi$
$258$	7.29551	0.454199
$259$	9.51726	0.591374
$260$	−13.5908	−0.842866
$261$	38.5099	2.38370
$262$	−0.392142	−0.0242266
$263$	14.6772	0.905034	0.452517	−	0.891756i	$-0.350526\pi$
$263$	14.6772	0.905034	0.452517	+	0.891756i	$0.350526\pi$
$264$	0	0
$265$	11.9068	0.731426
$266$	1.33033	0.0815676
$267$	−12.6204	−0.772355
$268$	−23.2209	−1.41844
$269$	−14.1244	−0.861178	−0.430589	−	0.902548i	$-0.641694\pi$
$269$	−14.1244	−0.861178	−0.430589	+	0.902548i	$0.641694\pi$
$270$	0.669673	0.0407550
$271$	−16.0958	−0.977748	−0.488874	−	0.872354i	$-0.662592\pi$
$271$	−16.0958	−0.977748	−0.488874	+	0.872354i	$0.662592\pi$
$272$	13.3782	0.811173
$273$	−18.5860	−1.12488
$274$	5.09501	0.307801
$275$	0	0
$276$	16.9922	1.02281
$277$	−15.4059	−0.925648	−0.462824	−	0.886450i	$-0.653164\pi$
$277$	−15.4059	−0.925648	−0.462824	+	0.886450i	$0.653164\pi$
$278$	1.14591	0.0687274
$279$	−31.8105	−1.90444
$280$	1.08063	0.0645798
$281$	−5.51019	−0.328710	−0.164355	−	0.986401i	$-0.552554\pi$
$281$	−5.51019	−0.328710	−0.164355	+	0.986401i	$0.552554\pi$
$282$	3.84126	0.228744
$283$	4.27810	0.254307	0.127153	−	0.991883i	$-0.459416\pi$
$283$	4.27810	0.254307	0.127153	+	0.991883i	$0.459416\pi$
$284$	−10.7285	−0.636622
$285$	−12.7120	−0.752994
$286$	0	0
$287$	−3.74203	−0.220885
$288$	12.3182	0.725855
$289$	−2.80438	−0.164963
$290$	2.70242	0.158692
$291$	−6.06639	−0.355618
$292$	15.2566	0.892828
$293$	−7.27375	−0.424937	−0.212469	−	0.977168i	$-0.568150\pi$
$293$	−7.27375	−0.424937	−0.212469	+	0.977168i	$0.568150\pi$
$294$	0.724623	0.0422609
$295$	−2.02013	−0.117617
$296$	10.2846	0.597780
$297$	0	0
$298$	4.71201	0.272959
$299$	−23.7042	−1.37085
$300$	−5.06322	−0.292325
$301$	−10.0680	−0.580311
$302$	1.62716	0.0936324
$303$	−1.72897	−0.0993267
$304$	−17.1534	−0.983817
$305$	−2.96246	−0.169630
$306$	4.07149	0.232751
$307$	−9.23546	−0.527096	−0.263548	−	0.964646i	$-0.584893\pi$
$307$	−9.23546	−0.527096	−0.263548	+	0.964646i	$0.584893\pi$
$308$	0	0
$309$	−0.904385	−0.0514487
$310$	−2.23229	−0.126786
$311$	−13.2153	−0.749373	−0.374686	−	0.927152i	$-0.622250\pi$
$311$	−13.2153	−0.749373	−0.374686	+	0.927152i	$0.622250\pi$
$312$	−20.0845	−1.13706
$313$	26.5351	1.49985	0.749927	−	0.661521i	$-0.230089\pi$
$313$	26.5351	1.49985	0.749927	+	0.661521i	$0.230089\pi$
$314$	1.56816	0.0884966
$315$	−3.92417	−0.221102
$316$	8.41518	0.473391
$317$	15.7315	0.883568	0.441784	−	0.897121i	$-0.354346\pi$
$317$	15.7315	0.883568	0.441784	+	0.897121i	$0.354346\pi$
$318$	8.62791	0.483829
$319$	0	0
$320$	−6.23709	−0.348664
$321$	−43.5766	−2.43221
$322$	0.924167	0.0515018
$323$	−18.2015	−1.01276
$324$	10.3393	0.574408
$325$	7.06322	0.391797
$326$	−0.340095	−0.0188361
$327$	30.3541	1.67858
$328$	−4.04374	−0.223278
$329$	−5.30105	−0.292257
$330$	0	0
$331$	1.53128	0.0841665	0.0420833	−	0.999114i	$-0.486601\pi$
$331$	1.53128	0.0841665	0.0420833	+	0.999114i	$0.486601\pi$
$332$	−30.1505	−1.65472
$333$	−37.3473	−2.04662
$334$	0.410747	0.0224751
$335$	12.0680	0.659346
$336$	−9.34339	−0.509724
$337$	0.770432	0.0419681	0.0209840	−	0.999780i	$-0.493320\pi$
$337$	0.770432	0.0419681	0.0209840	+	0.999780i	$0.493320\pi$
$338$	10.1584	0.552544
$339$	−7.62703	−0.414244
$340$	−7.24970	−0.393170
$341$	0	0
$342$	−5.22043	−0.282288
$343$	−1.00000	−0.0539949
$344$	−10.8798	−0.586597
$345$	−8.83093	−0.475441
$346$	1.78437	0.0959282
$347$	−6.16982	−0.331214	−0.165607	−	0.986192i	$-0.552958\pi$
$347$	−6.16982	−0.331214	−0.165607	+	0.986192i	$0.552958\pi$
$348$	−49.6880	−2.66356
$349$	0.945923	0.0506341	0.0253171	−	0.999679i	$-0.491940\pi$
$349$	0.945923	0.0506341	0.0253171	+	0.999679i	$0.491940\pi$
$350$	−0.275377	−0.0147195
$351$	17.1766	0.916819
$352$	0	0
$353$	28.1012	1.49568	0.747838	−	0.663881i	$-0.231092\pi$
$353$	28.1012	1.49568	0.747838	+	0.663881i	$0.231092\pi$
$354$	−1.46383	−0.0778019
$355$	5.57568	0.295926
$356$	9.22852	0.489110
$357$	−9.91428	−0.524719
$358$	−4.00000	−0.211407
$359$	3.93406	0.207632	0.103816	−	0.994597i	$-0.466895\pi$
$359$	3.93406	0.207632	0.103816	+	0.994597i	$0.466895\pi$
$360$	−4.24056	−0.223497
$361$	4.33785	0.228308
$362$	−1.18561	−0.0623143
$363$	0	0
$364$	13.5908	0.712352
$365$	−7.92896	−0.415021
$366$	−2.14666	−0.112208
$367$	−9.74455	−0.508661	−0.254331	−	0.967117i	$-0.581855\pi$
$367$	−9.74455	−0.508661	−0.254331	+	0.967117i	$0.581855\pi$
$368$	−11.9163	−0.621183
$369$	14.6844	0.764437
$370$	−2.62084	−0.136251
$371$	−11.9068	−0.618168
$372$	41.0440	2.12803
$373$	23.3560	1.20933	0.604664	−	0.796481i	$-0.293307\pi$
$373$	23.3560	1.20933	0.604664	+	0.796481i	$0.293307\pi$
$374$	0	0
$375$	2.63138	0.135884
$376$	−5.72846	−0.295423
$377$	69.3150	3.56990
$378$	−0.669673	−0.0344442
$379$	−15.2375	−0.782699	−0.391350	−	0.920242i	$-0.627992\pi$
$379$	−15.2375	−0.782699	−0.391350	+	0.920242i	$0.627992\pi$
$380$	9.29551	0.476850
$381$	16.4141	0.840921
$382$	−1.39334	−0.0712894
$383$	−23.9455	−1.22356	−0.611779	−	0.791029i	$-0.709546\pi$
$383$	−23.9455	−1.22356	−0.611779	+	0.791029i	$0.709546\pi$
$384$	−21.0396	−1.07367
$385$	0	0
$386$	2.00650	0.102128
$387$	39.5086	2.00833
$388$	4.43598	0.225203
$389$	−30.5516	−1.54903	−0.774515	−	0.632555i	$-0.782006\pi$
$389$	−30.5516	−1.54903	−0.774515	+	0.632555i	$0.782006\pi$
$390$	5.11817	0.259169
$391$	−12.6444	−0.639457
$392$	−1.08063	−0.0545799
$393$	−3.74713	−0.189018
$394$	−4.36382	−0.219846
$395$	−4.37341	−0.220050
$396$	0	0
$397$	−26.7709	−1.34359	−0.671796	−	0.740736i	$-0.734477\pi$
$397$	−26.7709	−1.34359	−0.671796	+	0.740736i	$0.734477\pi$
$398$	−1.20530	−0.0604160
$399$	12.7120	0.636396
$400$	3.55075	0.177538
$401$	−30.5099	−1.52359	−0.761795	−	0.647818i	$-0.775682\pi$
$401$	−30.5099	−1.52359	−0.761795	+	0.647818i	$0.775682\pi$
$402$	8.74476	0.436149
$403$	−57.2566	−2.85215
$404$	1.26429	0.0629007
$405$	−5.37341	−0.267007
$406$	−2.70242	−0.134119
$407$	0	0
$408$	−10.7136	−0.530404
$409$	1.64834	0.0815053	0.0407527	−	0.999169i	$-0.487024\pi$
$409$	1.64834	0.0815053	0.0407527	+	0.999169i	$0.487024\pi$
$410$	1.03047	0.0508913
$411$	48.6856	2.40148
$412$	0.661321	0.0325810
$413$	2.02013	0.0994042
$414$	−3.62659	−0.178237
$415$	15.6694	0.769179
$416$	22.1718	1.08706
$417$	10.9498	0.536216
$418$	0	0
$419$	−18.2949	−0.893762	−0.446881	−	0.894593i	$-0.647465\pi$
$419$	−18.2949	−0.893762	−0.446881	+	0.894593i	$0.647465\pi$
$420$	5.06322	0.247060
$421$	−18.5109	−0.902168	−0.451084	−	0.892482i	$-0.648962\pi$
$421$	−18.5109	−0.902168	−0.451084	+	0.892482i	$0.648962\pi$
$422$	−4.59516	−0.223689
$423$	20.8022	1.01144
$424$	−12.8668	−0.624865
$425$	3.76771	0.182761
$426$	4.04027	0.195751
$427$	2.96246	0.143363
$428$	31.8649	1.54025
$429$	0	0
$430$	2.77250	0.133702
$431$	−8.25656	−0.397705	−0.198852	−	0.980029i	$-0.563721\pi$
$431$	−8.25656	−0.397705	−0.198852	+	0.980029i	$0.563721\pi$
$432$	8.63486	0.415445
$433$	−2.86781	−0.137818	−0.0689092	−	0.997623i	$-0.521952\pi$
$433$	−2.86781	−0.137818	−0.0689092	+	0.997623i	$0.521952\pi$
$434$	2.23229	0.107153
$435$	25.8231	1.23812
$436$	−22.1961	−1.06300
$437$	16.2126	0.775554
$438$	−5.74551	−0.274531
$439$	22.8733	1.09168	0.545841	−	0.837889i	$-0.316210\pi$
$439$	22.8733	1.09168	0.545841	+	0.837889i	$0.316210\pi$
$440$	0	0
$441$	3.92417	0.186865
$442$	7.32838	0.348576
$443$	−10.2458	−0.486793	−0.243396	−	0.969927i	$-0.578262\pi$
$443$	−10.2458	−0.486793	−0.243396	+	0.969927i	$0.578262\pi$
$444$	48.1879	2.28690
$445$	−4.79611	−0.227357
$446$	−1.84722	−0.0874685
$447$	45.0258	2.12965
$448$	6.23709	0.294675
$449$	−27.7443	−1.30934	−0.654668	−	0.755917i	$-0.727192\pi$
$449$	−27.7443	−1.30934	−0.654668	+	0.755917i	$0.727192\pi$
$450$	1.08063	0.0509412
$451$	0	0
$452$	5.57718	0.262329
$453$	15.5484	0.730527
$454$	6.89435	0.323568
$455$	−7.06322	−0.331129
$456$	13.7369	0.643291
$457$	−32.7145	−1.53032	−0.765160	−	0.643840i	$-0.777340\pi$
$457$	−32.7145	−1.53032	−0.765160	+	0.643840i	$0.777340\pi$
$458$	0.561843	0.0262532
$459$	9.16245	0.427667
$460$	6.45751	0.301083
$461$	−5.33425	−0.248441	−0.124220	−	0.992255i	$-0.539643\pi$
$461$	−5.33425	−0.248441	−0.124220	+	0.992255i	$0.539643\pi$
$462$	0	0
$463$	7.22262	0.335664	0.167832	−	0.985816i	$-0.446323\pi$
$463$	7.22262	0.335664	0.167832	+	0.985816i	$0.446323\pi$
$464$	34.8454	1.61766
$465$	−21.3308	−0.989191
$466$	2.57907	0.119473
$467$	28.0704	1.29894	0.649472	−	0.760385i	$-0.274990\pi$
$467$	28.0704	1.29894	0.649472	+	0.760385i	$0.274990\pi$
$468$	−53.3326	−2.46530
$469$	−12.0680	−0.557249
$470$	1.45979	0.0673351
$471$	14.9847	0.690457
$472$	2.18301	0.100481
$473$	0	0
$474$	−3.16907	−0.145560
$475$	−4.83093	−0.221658
$476$	7.24970	0.332289
$477$	46.7241	2.13935
$478$	−1.49101	−0.0681972
$479$	17.2744	0.789288	0.394644	−	0.918834i	$-0.370868\pi$
$479$	17.2744	0.789288	0.394644	+	0.918834i	$0.370868\pi$
$480$	8.26004	0.377017
$481$	−67.2225	−3.06508
$482$	−7.01393	−0.319476
$483$	8.83093	0.401821
$484$	0	0
$485$	−2.30540	−0.104683
$486$	−5.90271	−0.267753
$487$	−22.5587	−1.02223	−0.511117	−	0.859511i	$-0.670768\pi$
$487$	−22.5587	−1.02223	−0.511117	+	0.859511i	$0.670768\pi$
$488$	3.20131	0.144917
$489$	−3.24980	−0.146961
$490$	0.275377	0.0124403
$491$	−20.6959	−0.933994	−0.466997	−	0.884259i	$-0.654664\pi$
$491$	−20.6959	−0.933994	−0.466997	+	0.884259i	$0.654664\pi$
$492$	−18.9467	−0.854184
$493$	36.9745	1.66525
$494$	−9.39639	−0.422764
$495$	0	0
$496$	−28.7835	−1.29242
$497$	−5.57568	−0.250103
$498$	11.3544	0.508802
$499$	0.781643	0.0349911	0.0174956	−	0.999847i	$-0.494431\pi$
$499$	0.781643	0.0349911	0.0174956	+	0.999847i	$0.494431\pi$
$500$	−1.92417	−0.0860514
$501$	3.92492	0.175352
$502$	−1.96114	−0.0875299
$503$	−38.4066	−1.71247	−0.856233	−	0.516590i	$-0.827201\pi$
$503$	−38.4066	−1.71247	−0.856233	+	0.516590i	$0.827201\pi$
$504$	4.24056	0.188890
$505$	−0.657058	−0.0292387
$506$	0	0
$507$	97.0691	4.31099
$508$	−12.0026	−0.532531
$509$	23.5450	1.04361	0.521807	−	0.853064i	$-0.325258\pi$
$509$	23.5450	1.04361	0.521807	+	0.853064i	$0.325258\pi$
$510$	2.73017	0.120894
$511$	7.92896	0.350757
$512$	18.8201	0.831738
$513$	−11.7480	−0.518688
$514$	4.26100	0.187944
$515$	−0.343692	−0.0151449
$516$	−50.9765	−2.24412
$517$	0	0
$518$	2.62084	0.115153
$519$	17.0506	0.748438
$520$	−7.63270	−0.334716
$521$	−10.4832	−0.459277	−0.229638	−	0.973276i	$-0.573754\pi$
$521$	−10.4832	−0.459277	−0.229638	+	0.973276i	$0.573754\pi$
$522$	10.6047	0.464157
$523$	16.3979	0.717031	0.358515	−	0.933524i	$-0.383283\pi$
$523$	16.3979	0.717031	0.358515	+	0.933524i	$0.383283\pi$
$524$	2.74004	0.119699
$525$	−2.63138	−0.114843
$526$	4.04177	0.176229
$527$	−30.5422	−1.33044
$528$	0	0
$529$	−11.7372	−0.510315
$530$	3.27885	0.142424
$531$	−7.92734	−0.344017
$532$	−9.29551	−0.403011
$533$	26.4308	1.14484
$534$	−3.47537	−0.150394
$535$	−16.5603	−0.715966
$536$	−13.0410	−0.563286
$537$	−38.2222	−1.64941
$538$	−3.88953	−0.167690
$539$	0	0
$540$	−4.67926	−0.201363
$541$	−14.8898	−0.640162	−0.320081	−	0.947390i	$-0.603710\pi$
$541$	−14.8898	−0.640162	−0.320081	+	0.947390i	$0.603710\pi$
$542$	−4.43241	−0.190388
$543$	−11.3292	−0.486180
$544$	11.8270	0.507080
$545$	11.5354	0.494123
$546$	−5.11817	−0.219037
$547$	−25.0012	−1.06897	−0.534487	−	0.845177i	$-0.679495\pi$
$547$	−25.0012	−1.06897	−0.534487	+	0.845177i	$0.679495\pi$
$548$	−35.6008	−1.52079
$549$	−11.6252	−0.496151
$550$	0	0
$551$	−47.4084	−2.01966
$552$	9.54293	0.406174
$553$	4.37341	0.185976
$554$	−4.24242	−0.180243
$555$	−25.0435	−1.06304
$556$	−8.00695	−0.339570
$557$	38.3557	1.62518	0.812592	−	0.582833i	$-0.198056\pi$
$557$	38.3557	1.62518	0.812592	+	0.582833i	$0.198056\pi$
$558$	−8.75989	−0.370836
$559$	71.1126	3.00774
$560$	−3.55075	−0.150047
$561$	0	0
$562$	−1.51738	−0.0640068
$563$	10.7886	0.454685	0.227342	−	0.973815i	$-0.426996\pi$
$563$	10.7886	0.454685	0.227342	+	0.973815i	$0.426996\pi$
$564$	−26.8404	−1.13018
$565$	−2.89849	−0.121940
$566$	1.17809	0.0495189
$567$	5.37341	0.225662
$568$	−6.02523	−0.252813
$569$	−31.9757	−1.34049	−0.670245	−	0.742140i	$-0.733811\pi$
$569$	−31.9757	−1.34049	−0.670245	+	0.742140i	$0.733811\pi$
$570$	−3.50060	−0.146624
$571$	−18.8384	−0.788364	−0.394182	−	0.919032i	$-0.628972\pi$
$571$	−18.8384	−0.788364	−0.394182	+	0.919032i	$0.628972\pi$
$572$	0	0
$573$	−13.3141	−0.556205
$574$	−1.03047	−0.0430110
$575$	−3.35600	−0.139955
$576$	−24.4754	−1.01981
$577$	−26.0946	−1.08633	−0.543166	−	0.839625i	$-0.682775\pi$
$577$	−26.0946	−1.08633	−0.543166	+	0.839625i	$0.682775\pi$
$578$	−0.772262	−0.0321218
$579$	19.1732	0.796812
$580$	−18.8828	−0.784068
$581$	−15.6694	−0.650075
$582$	−1.67055	−0.0692464
$583$	0	0
$584$	8.56825	0.354557
$585$	27.7172	1.14597
$586$	−2.00303	−0.0827443
$587$	8.40313	0.346834	0.173417	−	0.984848i	$-0.444519\pi$
$587$	8.40313	0.346834	0.173417	+	0.984848i	$0.444519\pi$
$588$	−5.06322	−0.208804
$589$	39.1610	1.61360
$590$	−0.556299	−0.0229025
$591$	−41.6987	−1.71526
$592$	−33.7934	−1.38890
$593$	−22.8365	−0.937781	−0.468891	−	0.883256i	$-0.655346\pi$
$593$	−22.8365	−0.937781	−0.468891	+	0.883256i	$0.655346\pi$
$594$	0	0
$595$	−3.76771	−0.154461
$596$	−32.9246	−1.34864
$597$	−11.5173	−0.471370
$598$	−6.52760	−0.266933
$599$	−23.9330	−0.977876	−0.488938	−	0.872319i	$-0.662616\pi$
$599$	−23.9330	−0.977876	−0.488938	+	0.872319i	$0.662616\pi$
$600$	−2.84354	−0.116087
$601$	21.6637	0.883681	0.441840	−	0.897094i	$-0.354326\pi$
$601$	21.6637	0.883681	0.441840	+	0.897094i	$0.354326\pi$
$602$	−2.77250	−0.112999
$603$	47.3569	1.92852
$604$	−11.3696	−0.462621
$605$	0	0
$606$	−0.476119	−0.0193410
$607$	25.6790	1.04228	0.521138	−	0.853472i	$-0.325508\pi$
$607$	25.6790	1.04228	0.521138	+	0.853472i	$0.325508\pi$
$608$	−15.1645	−0.615003
$609$	−25.8231	−1.04641
$610$	−0.815794	−0.0330305
$611$	37.4425	1.51476
$612$	−28.4490	−1.14998
$613$	−30.4680	−1.23059	−0.615295	−	0.788297i	$-0.710963\pi$
$613$	−30.4680	−1.23059	−0.615295	+	0.788297i	$0.710963\pi$
$614$	−2.54324	−0.102637
$615$	9.84671	0.397058
$616$	0	0
$617$	−24.9619	−1.00493	−0.502465	−	0.864597i	$-0.667573\pi$
$617$	−24.9619	−1.00493	−0.502465	+	0.864597i	$0.667573\pi$
$618$	−0.249047	−0.0100181
$619$	−18.7301	−0.752825	−0.376413	−	0.926452i	$-0.622842\pi$
$619$	−18.7301	−0.752825	−0.376413	+	0.926452i	$0.622842\pi$
$620$	15.5979	0.626426
$621$	−8.16125	−0.327500
$622$	−3.63920	−0.145919
$623$	4.79611	0.192152
$624$	65.9944	2.64189
$625$	1.00000	0.0400000
$626$	7.30717	0.292053
$627$	0	0
$628$	−10.9574	−0.437246
$629$	−35.8582	−1.42976
$630$	−1.08063	−0.0430532
$631$	26.0862	1.03847	0.519237	−	0.854630i	$-0.326216\pi$
$631$	26.0862	1.03847	0.519237	+	0.854630i	$0.326216\pi$
$632$	4.72603	0.187991
$633$	−43.9093	−1.74524
$634$	4.33209	0.172049
$635$	6.23784	0.247541
$636$	−60.2865	−2.39052
$637$	7.06322	0.279855
$638$	0	0
$639$	21.8799	0.865556
$640$	−7.99565	−0.316056
$641$	49.8455	1.96878	0.984390	−	0.176000i	$-0.0563159\pi$
$641$	49.8455	1.96878	0.984390	+	0.176000i	$0.0563159\pi$
$642$	−12.0000	−0.473602
$643$	−35.9365	−1.41720	−0.708598	−	0.705612i	$-0.750672\pi$
$643$	−35.9365	−1.41720	−0.708598	+	0.705612i	$0.750672\pi$
$644$	−6.45751	−0.254462
$645$	26.4928	1.04315
$646$	−5.01229	−0.197206
$647$	14.1284	0.555445	0.277723	−	0.960661i	$-0.410420\pi$
$647$	14.1284	0.555445	0.277723	+	0.960661i	$0.410420\pi$
$648$	5.80665	0.228107
$649$	0	0
$650$	1.94505	0.0762911
$651$	21.3308	0.836019
$652$	2.37638	0.0930661
$653$	29.9844	1.17338	0.586689	−	0.809812i	$-0.300431\pi$
$653$	29.9844	1.17338	0.586689	+	0.809812i	$0.300431\pi$
$654$	8.35882	0.326856
$655$	−1.42402	−0.0556409
$656$	13.2870	0.518772
$657$	−31.1146	−1.21390
$658$	−1.45979	−0.0569085
$659$	−42.8430	−1.66893	−0.834464	−	0.551063i	$-0.814222\pi$
$659$	−42.8430	−1.66893	−0.834464	+	0.551063i	$0.814222\pi$
$660$	0	0
$661$	−13.6528	−0.531034	−0.265517	−	0.964106i	$-0.585543\pi$
$661$	−13.6528	−0.531034	−0.265517	+	0.964106i	$0.585543\pi$
$662$	0.421679	0.0163890
$663$	70.0267	2.71961
$664$	−16.9327	−0.657118
$665$	4.83093	0.187335
$666$	−10.2846	−0.398520
$667$	−32.9342	−1.27522
$668$	−2.87005	−0.111046
$669$	−17.6512	−0.682435
$670$	3.32326	0.128389
$671$	0	0
$672$	−8.26004	−0.318638
$673$	19.4352	0.749173	0.374586	−	0.927192i	$-0.377785\pi$
$673$	19.4352	0.749173	0.374586	+	0.927192i	$0.377785\pi$
$674$	0.212159	0.00817208
$675$	2.43184	0.0936014
$676$	−70.9807	−2.73003
$677$	−41.1836	−1.58281	−0.791407	−	0.611289i	$-0.790651\pi$
$677$	−41.1836	−1.58281	−0.791407	+	0.611289i	$0.790651\pi$
$678$	−2.10031	−0.0806620
$679$	2.30540	0.0884732
$680$	−4.07149	−0.156134
$681$	65.8793	2.52450
$682$	0	0
$683$	21.4320	0.820072	0.410036	−	0.912069i	$-0.365516\pi$
$683$	21.4320	0.820072	0.410036	+	0.912069i	$0.365516\pi$
$684$	36.4771	1.39474
$685$	18.5019	0.706922
$686$	−0.275377	−0.0105140
$687$	5.36872	0.204829
$688$	35.7490	1.36292
$689$	84.1000	3.20396
$690$	−2.43184	−0.0925784
$691$	−39.5576	−1.50484	−0.752421	−	0.658682i	$-0.771114\pi$
$691$	−39.5576	−1.50484	−0.752421	+	0.658682i	$0.771114\pi$
$692$	−12.4681	−0.473964
$693$	0	0
$694$	−1.69903	−0.0644943
$695$	4.16125	0.157845
$696$	−27.9051	−1.05774
$697$	14.0989	0.534033
$698$	0.260486	0.00985953
$699$	24.6444	0.932138
$700$	1.92417	0.0727267
$701$	−22.7381	−0.858807	−0.429404	−	0.903113i	$-0.641276\pi$
$701$	−22.7381	−0.858807	−0.429404	+	0.903113i	$0.641276\pi$
$702$	4.73004	0.178524
$703$	45.9772	1.73406
$704$	0	0
$705$	13.9491	0.525353
$706$	7.73843	0.291240
$707$	0.657058	0.0247112
$708$	10.2284	0.384406
$709$	7.18618	0.269883	0.134941	−	0.990854i	$-0.456915\pi$
$709$	7.18618	0.269883	0.134941	+	0.990854i	$0.456915\pi$
$710$	1.53542	0.0576231
$711$	−17.1620	−0.643625
$712$	5.18280	0.194234
$713$	27.2048	1.01883
$714$	−2.73017	−0.102174
$715$	0	0
$716$	27.9495	1.04452
$717$	−14.2474	−0.532080
$718$	1.08335	0.0404303
$719$	−10.3351	−0.385435	−0.192717	−	0.981254i	$-0.561730\pi$
$719$	−10.3351	−0.385435	−0.192717	+	0.981254i	$0.561730\pi$
$720$	13.9338	0.519280
$721$	0.343692	0.0127998
$722$	1.19454	0.0444563
$723$	−67.0220	−2.49257
$724$	8.28431	0.307884
$725$	9.81352	0.364465
$726$	0	0
$727$	32.4887	1.20494	0.602470	−	0.798141i	$-0.294183\pi$
$727$	32.4887	1.20494	0.602470	+	0.798141i	$0.294183\pi$
$728$	7.63270	0.282887
$729$	−40.2834	−1.49198
$730$	−2.18346	−0.0808133
$731$	37.9333	1.40301
$732$	14.9996	0.554400
$733$	18.9260	0.699048	0.349524	−	0.936927i	$-0.386343\pi$
$733$	18.9260	0.699048	0.349524	+	0.936927i	$0.386343\pi$
$734$	−2.68343	−0.0990471
$735$	2.63138	0.0970600
$736$	−10.5347	−0.388313
$737$	0	0
$738$	4.04374	0.148852
$739$	31.3237	1.15226	0.576131	−	0.817358i	$-0.304562\pi$
$739$	31.3237	1.15226	0.576131	+	0.817358i	$0.304562\pi$
$740$	18.3128	0.673192
$741$	−89.7877	−3.29843
$742$	−3.27885	−0.120370
$743$	−14.6970	−0.539180	−0.269590	−	0.962975i	$-0.586888\pi$
$743$	−14.6970	−0.539180	−0.269590	+	0.962975i	$0.586888\pi$
$744$	23.0506	0.845076
$745$	17.1111	0.626902
$746$	6.43171	0.235482
$747$	61.4892	2.24977
$748$	0	0
$749$	16.5603	0.605102
$750$	0.724623	0.0264595
$751$	−3.42946	−0.125143	−0.0625714	−	0.998040i	$-0.519930\pi$
$751$	−3.42946	−0.125143	−0.0625714	+	0.998040i	$0.519930\pi$
$752$	18.8227	0.686395
$753$	−18.7398	−0.682915
$754$	19.0878	0.695136
$755$	5.90883	0.215044
$756$	4.67926	0.170183
$757$	38.7675	1.40903	0.704514	−	0.709690i	$-0.251165\pi$
$757$	38.7675	1.40903	0.704514	+	0.709690i	$0.251165\pi$
$758$	−4.19607	−0.152408
$759$	0	0
$760$	5.22043	0.189365
$761$	7.06427	0.256080	0.128040	−	0.991769i	$-0.459131\pi$
$761$	7.06427	0.256080	0.128040	+	0.991769i	$0.459131\pi$
$762$	4.52008	0.163745
$763$	−11.5354	−0.417610
$764$	9.73579	0.352229
$765$	14.7851	0.534557
$766$	−6.59405	−0.238253
$767$	−14.2686	−0.515211
$768$	27.0305	0.975378
$769$	−37.5651	−1.35463	−0.677317	−	0.735692i	$-0.736857\pi$
$769$	−37.5651	−1.35463	−0.677317	+	0.735692i	$0.736857\pi$
$770$	0	0
$771$	40.7161	1.46636
$772$	−14.0202	−0.504598
$773$	−31.3414	−1.12727	−0.563636	−	0.826023i	$-0.690598\pi$
$773$	−31.3414	−1.12727	−0.563636	+	0.826023i	$0.690598\pi$
$774$	10.8798	0.391065
$775$	−8.10630	−0.291187
$776$	2.49128	0.0894317
$777$	25.0435	0.898432
$778$	−8.41323	−0.301629
$779$	−18.0775	−0.647693
$780$	−35.7626	−1.28051
$781$	0	0
$782$	−3.48199	−0.124516
$783$	23.8649	0.852861
$784$	3.55075	0.126813
$785$	5.69460	0.203249
$786$	−1.03187	−0.0368057
$787$	−18.0165	−0.642220	−0.321110	−	0.947042i	$-0.604056\pi$
$787$	−18.0165	−0.642220	−0.321110	+	0.947042i	$0.604056\pi$
$788$	30.4917	1.08622
$789$	38.6213	1.37495
$790$	−1.20434	−0.0428484
$791$	2.89849	0.103058
$792$	0	0
$793$	−20.9245	−0.743050
$794$	−7.37209	−0.261626
$795$	31.3312	1.11120
$796$	8.42186	0.298505
$797$	19.0381	0.674364	0.337182	−	0.941440i	$-0.390526\pi$
$797$	19.0381	0.674364	0.337182	+	0.941440i	$0.390526\pi$
$798$	3.50060	0.123920
$799$	19.9728	0.706588
$800$	3.13905	0.110982
$801$	−18.8207	−0.664998
$802$	−8.40173	−0.296675
$803$	0	0
$804$	−61.1030	−2.15494
$805$	3.35600	0.118284
$806$	−15.7672	−0.555375
$807$	−37.1666	−1.30833
$808$	0.710034	0.0249789
$809$	45.3736	1.59525	0.797625	−	0.603154i	$-0.206090\pi$
$809$	45.3736	1.59525	0.797625	+	0.603154i	$0.206090\pi$
$810$	−1.47972	−0.0519919
$811$	−20.9739	−0.736493	−0.368247	−	0.929728i	$-0.620042\pi$
$811$	−20.9739	−0.736493	−0.368247	+	0.929728i	$0.620042\pi$
$812$	18.8828	0.662658
$813$	−42.3541	−1.48542
$814$	0	0
$815$	−1.23502	−0.0432607
$816$	35.2032	1.23236
$817$	−48.6378	−1.70162
$818$	0.453916	0.0158708
$819$	−27.7172	−0.968519
$820$	−7.20029	−0.251445
$821$	25.3681	0.885353	0.442677	−	0.896681i	$-0.354029\pi$
$821$	25.3681	0.885353	0.442677	+	0.896681i	$0.354029\pi$
$822$	13.4069	0.467620
$823$	−50.3694	−1.75577	−0.877884	−	0.478873i	$-0.841045\pi$
$823$	−50.3694	−1.75577	−0.877884	+	0.478873i	$0.841045\pi$
$824$	0.371403	0.0129384
$825$	0	0
$826$	0.556299	0.0193561
$827$	28.8505	1.00323	0.501616	−	0.865090i	$-0.332739\pi$
$827$	28.8505	1.00323	0.501616	+	0.865090i	$0.332739\pi$
$828$	25.3404	0.880638
$829$	7.66185	0.266107	0.133054	−	0.991109i	$-0.457522\pi$
$829$	7.66185	0.266107	0.133054	+	0.991109i	$0.457522\pi$
$830$	4.31499	0.149775
$831$	−40.5387	−1.40627
$832$	−44.0539	−1.52729
$833$	3.76771	0.130543
$834$	3.01534	0.104413
$835$	1.49158	0.0516183
$836$	0	0
$837$	−19.7132	−0.681388
$838$	−5.03799	−0.174034
$839$	24.1802	0.834794	0.417397	−	0.908724i	$-0.362943\pi$
$839$	24.1802	0.834794	0.417397	+	0.908724i	$0.362943\pi$
$840$	2.84354	0.0981115
$841$	67.3051	2.32087
$842$	−5.09749	−0.175671
$843$	−14.4994	−0.499386
$844$	32.1082	1.10521
$845$	36.8890	1.26902
$846$	5.72846	0.196949
$847$	0	0
$848$	42.2780	1.45183
$849$	11.2573	0.386350
$850$	1.03754	0.0355874
$851$	31.9400	1.09489
$852$	−28.2309	−0.967174
$853$	18.7338	0.641432	0.320716	−	0.947175i	$-0.396077\pi$
$853$	18.7338	0.641432	0.320716	+	0.947175i	$0.396077\pi$
$854$	0.815794	0.0279159
$855$	−18.9574	−0.648328
$856$	17.8955	0.611657
$857$	−39.2820	−1.34185	−0.670924	−	0.741526i	$-0.734102\pi$
$857$	−39.2820	−1.34185	−0.670924	+	0.741526i	$0.734102\pi$
$858$	0	0
$859$	−33.2018	−1.13283	−0.566415	−	0.824120i	$-0.691670\pi$
$859$	−33.2018	−1.13283	−0.566415	+	0.824120i	$0.691670\pi$
$860$	−19.3725	−0.660598
$861$	−9.84671	−0.335575
$862$	−2.27367	−0.0774415
$863$	−8.10828	−0.276009	−0.138004	−	0.990432i	$-0.544069\pi$
$863$	−8.10828	−0.276009	−0.138004	+	0.990432i	$0.544069\pi$
$864$	7.63366	0.259702
$865$	6.47972	0.220317
$866$	−0.789731	−0.0268361
$867$	−7.37938	−0.250617
$868$	−15.5979	−0.529427
$869$	0	0
$870$	7.11110	0.241089
$871$	85.2390	2.88821
$872$	−12.4655	−0.422134
$873$	−9.04678	−0.306187
$874$	4.46458	0.151017
$875$	−1.00000	−0.0338062
$876$	40.1461	1.35641
$877$	25.0623	0.846292	0.423146	−	0.906061i	$-0.360926\pi$
$877$	25.0623	0.846292	0.423146	+	0.906061i	$0.360926\pi$
$878$	6.29878	0.212573
$879$	−19.1400	−0.645577
$880$	0	0
$881$	15.0435	0.506829	0.253415	−	0.967358i	$-0.418446\pi$
$881$	15.0435	0.506829	0.253415	+	0.967358i	$0.418446\pi$
$882$	1.08063	0.0363866
$883$	14.6536	0.493132	0.246566	−	0.969126i	$-0.420698\pi$
$883$	14.6536	0.493132	0.246566	+	0.969126i	$0.420698\pi$
$884$	−51.2062	−1.72225
$885$	−5.31574	−0.178687
$886$	−2.82146	−0.0947888
$887$	−53.8754	−1.80896	−0.904479	−	0.426519i	$-0.859740\pi$
$887$	−53.8754	−1.80896	−0.904479	+	0.426519i	$0.859740\pi$
$888$	27.0627	0.908165
$889$	−6.23784	−0.209210
$890$	−1.32074	−0.0442713
$891$	0	0
$892$	12.9072	0.432167
$893$	−25.6090	−0.856972
$894$	12.3991	0.414688
$895$	−14.5255	−0.485535
$896$	7.99565	0.267116
$897$	−62.3748	−2.08263
$898$	−7.64016	−0.254955
$899$	−79.5513	−2.65319
$900$	−7.55075	−0.251692
$901$	44.8612	1.49454
$902$	0	0
$903$	−26.4928	−0.881624
$904$	3.13219	0.104175
$905$	−4.30540	−0.143116
$906$	4.28167	0.142249
$907$	46.1536	1.53250	0.766252	−	0.642540i	$-0.222119\pi$
$907$	46.1536	1.53250	0.766252	+	0.642540i	$0.222119\pi$
$908$	−48.1735	−1.59869
$909$	−2.57840	−0.0855203
$910$	−1.94505	−0.0644778
$911$	−17.6784	−0.585711	−0.292856	−	0.956157i	$-0.594606\pi$
$911$	−17.6784	−0.585711	−0.292856	+	0.956157i	$0.594606\pi$
$912$	−45.1372	−1.49464
$913$	0	0
$914$	−9.00884	−0.297986
$915$	−7.79536	−0.257707
$916$	−3.92581	−0.129712
$917$	1.42402	0.0470251
$918$	2.52313	0.0832757
$919$	−7.21141	−0.237882	−0.118941	−	0.992901i	$-0.537950\pi$
$919$	−7.21141	−0.237882	−0.118941	+	0.992901i	$0.537950\pi$
$920$	3.62659	0.119565
$921$	−24.3020	−0.800779
$922$	−1.46893	−0.0483767
$923$	39.3823	1.29628
$924$	0	0
$925$	−9.51726	−0.312925
$926$	1.98895	0.0653608
$927$	−1.34871	−0.0442973
$928$	30.8051	1.01123
$929$	26.9991	0.885813	0.442906	−	0.896568i	$-0.353947\pi$
$929$	26.9991	0.885813	0.442906	+	0.896568i	$0.353947\pi$
$930$	−5.87401	−0.192616
$931$	−4.83093	−0.158327
$932$	−18.0210	−0.590296
$933$	−34.7746	−1.13847
$934$	7.72996	0.252932
$935$	0	0
$936$	−29.9520	−0.979012
$937$	35.1590	1.14859	0.574297	−	0.818647i	$-0.305276\pi$
$937$	35.1590	1.14859	0.574297	+	0.818647i	$0.305276\pi$
$938$	−3.32326	−0.108508
$939$	69.8240	2.27862
$940$	−10.2001	−0.332691
$941$	−3.73541	−0.121771	−0.0608854	−	0.998145i	$-0.519392\pi$
$941$	−3.73541	−0.121771	−0.0608854	+	0.998145i	$0.519392\pi$
$942$	4.12644	0.134447
$943$	−12.5583	−0.408954
$944$	−7.17299	−0.233461
$945$	−2.43184	−0.0791077
$946$	0	0
$947$	−47.2263	−1.53465	−0.767325	−	0.641259i	$-0.778412\pi$
$947$	−47.2263	−1.53465	−0.767325	+	0.641259i	$0.778412\pi$
$948$	22.1435	0.719189
$949$	−56.0040	−1.81797
$950$	−1.33033	−0.0431615
$951$	41.3955	1.34234
$952$	4.07149	0.131958
$953$	9.60888	0.311262	0.155631	−	0.987815i	$-0.450259\pi$
$953$	9.60888	0.311262	0.155631	+	0.987815i	$0.450259\pi$
$954$	12.8668	0.416577
$955$	−5.05974	−0.163729
$956$	10.4183	0.336951
$957$	0	0
$958$	4.75698	0.153691
$959$	−18.5019	−0.597458
$960$	−16.4122	−0.529700
$961$	34.7122	1.11975
$962$	−18.5115	−0.596836
$963$	−64.9856	−2.09413
$964$	49.0091	1.57848
$965$	7.28637	0.234557
$966$	2.43184	0.0782431
$967$	46.2737	1.48806	0.744030	−	0.668146i	$-0.232912\pi$
$967$	46.2737	1.48806	0.744030	+	0.668146i	$0.232912\pi$
$968$	0	0
$969$	−47.8951	−1.53861
$970$	−0.634855	−0.0203840
$971$	20.7910	0.667215	0.333608	−	0.942712i	$-0.391734\pi$
$971$	20.7910	0.667215	0.333608	+	0.942712i	$0.391734\pi$
$972$	41.2445	1.32292
$973$	−4.16125	−0.133404
$974$	−6.21216	−0.199050
$975$	18.5860	0.595229
$976$	−10.5190	−0.336704
$977$	−8.65891	−0.277023	−0.138512	−	0.990361i	$-0.544232\pi$
$977$	−8.65891	−0.277023	−0.138512	+	0.990361i	$0.544232\pi$
$978$	−0.894920	−0.0286164
$979$	0	0
$980$	−1.92417	−0.0614653
$981$	45.2669	1.44526
$982$	−5.69919	−0.181868
$983$	10.0007	0.318972	0.159486	−	0.987200i	$-0.449016\pi$
$983$	10.0007	0.318972	0.159486	+	0.987200i	$0.449016\pi$
$984$	−10.6406	−0.339211
$985$	−15.8467	−0.504918
$986$	10.1819	0.324259
$987$	−13.9491	−0.444005
$988$	65.6562	2.08880
$989$	−33.7883	−1.07441
$990$	0	0
$991$	18.3793	0.583838	0.291919	−	0.956443i	$-0.405706\pi$
$991$	18.3793	0.583838	0.291919	+	0.956443i	$0.405706\pi$
$992$	−25.4461	−0.807914
$993$	4.02937	0.127868
$994$	−1.53542	−0.0487004
$995$	−4.37689	−0.138757
$996$	−79.3374	−2.51390
$997$	−36.3472	−1.15113	−0.575564	−	0.817757i	$-0.695217\pi$
$997$	−36.3472	−1.15113	−0.575564	+	0.817757i	$0.695217\pi$
$998$	0.215247	0.00681352
$999$	−23.1444	−0.732257

Twists

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

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

\(f(q)\)	\(=\)	\(q+0.275377 q^{2} +2.63138 q^{3} -1.92417 q^{4} +1.00000 q^{5} +0.724623 q^{6} -1.00000 q^{7} -1.08063 q^{8} +3.92417 q^{9} +O(q^{10})\)	\(q+0.275377 q^{2} +2.63138 q^{3} -1.92417 q^{4} +1.00000 q^{5} +0.724623 q^{6} -1.00000 q^{7} -1.08063 q^{8} +3.92417 q^{9} +0.275377 q^{10} -5.06322 q^{12} +7.06322 q^{13} -0.275377 q^{14} +2.63138 q^{15} +3.55075 q^{16} +3.76771 q^{17} +1.08063 q^{18} -4.83093 q^{19} -1.92417 q^{20} -2.63138 q^{21} -3.35600 q^{23} -2.84354 q^{24} +1.00000 q^{25} +1.94505 q^{26} +2.43184 q^{27} +1.92417 q^{28} +9.81352 q^{29} +0.724623 q^{30} -8.10630 q^{31} +3.13905 q^{32} +1.03754 q^{34} -1.00000 q^{35} -7.55075 q^{36} -9.51726 q^{37} -1.33033 q^{38} +18.5860 q^{39} -1.08063 q^{40} +3.74203 q^{41} -0.724623 q^{42} +10.0680 q^{43} +3.92417 q^{45} -0.924167 q^{46} +5.30105 q^{47} +9.34339 q^{48} +1.00000 q^{49} +0.275377 q^{50} +9.91428 q^{51} -13.5908 q^{52} +11.9068 q^{53} +0.669673 q^{54} +1.08063 q^{56} -12.7120 q^{57} +2.70242 q^{58} -2.02013 q^{59} -5.06322 q^{60} -2.96246 q^{61} -2.23229 q^{62} -3.92417 q^{63} -6.23709 q^{64} +7.06322 q^{65} +12.0680 q^{67} -7.24970 q^{68} -8.83093 q^{69} -0.275377 q^{70} +5.57568 q^{71} -4.24056 q^{72} -7.92896 q^{73} -2.62084 q^{74} +2.63138 q^{75} +9.29551 q^{76} +5.11817 q^{78} -4.37341 q^{79} +3.55075 q^{80} -5.37341 q^{81} +1.03047 q^{82} +15.6694 q^{83} +5.06322 q^{84} +3.76771 q^{85} +2.77250 q^{86} +25.8231 q^{87} -4.79611 q^{89} +1.08063 q^{90} -7.06322 q^{91} +6.45751 q^{92} -21.3308 q^{93} +1.45979 q^{94} -4.83093 q^{95} +8.26004 q^{96} -2.30540 q^{97} +0.275377 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 4 q^{4} + 4 q^{5} + 4 q^{6} - 4 q^{7} + 6 q^{8} + 4 q^{9}+O(q^{10}) \) 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

Modular forms

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Database

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