LMFDB - Embedded newform 4235.2.a.bk.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4235, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4235.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4235 = 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4235.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$33.8166452560$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 14x^{8} + 26x^{7} + 67x^{6} - 110x^{5} - 132x^{4} + 168x^{3} + 94x^{2} - 54x - 11 $ x^10 - 2x^9 - 14x^8 + 26x^7 + 67x^6 - 110x^5 - 132x^4 + 168x^3 + 94x^2 - 54*x - 11
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$1.81029$ 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)

$f(q)$	$=$	$q+1.81029 q^{2} +2.40633 q^{3} +1.27715 q^{4} +1.00000 q^{5} +4.35616 q^{6} -1.00000 q^{7} -1.30857 q^{8} +2.79044 q^{9} +O(q^{10})$	\(q+1.81029 q^{2} +2.40633 q^{3} +1.27715 q^{4} +1.00000 q^{5} +4.35616 q^{6} -1.00000 q^{7} -1.30857 q^{8} +2.79044 q^{9} +1.81029 q^{10} +3.07325 q^{12} +6.34856 q^{13} -1.81029 q^{14} +2.40633 q^{15} -4.92319 q^{16} +2.07927 q^{17} +5.05151 q^{18} +3.10189 q^{19} +1.27715 q^{20} -2.40633 q^{21} +0.122076 q^{23} -3.14885 q^{24} +1.00000 q^{25} +11.4927 q^{26} -0.504265 q^{27} -1.27715 q^{28} +4.67356 q^{29} +4.35616 q^{30} +2.66747 q^{31} -6.29526 q^{32} +3.76409 q^{34} -1.00000 q^{35} +3.56381 q^{36} +6.49112 q^{37} +5.61532 q^{38} +15.2768 q^{39} -1.30857 q^{40} +1.64897 q^{41} -4.35616 q^{42} -7.26481 q^{43} +2.79044 q^{45} +0.220993 q^{46} -8.31293 q^{47} -11.8468 q^{48} +1.00000 q^{49} +1.81029 q^{50} +5.00342 q^{51} +8.10806 q^{52} -4.48011 q^{53} -0.912865 q^{54} +1.30857 q^{56} +7.46418 q^{57} +8.46049 q^{58} +5.00377 q^{59} +3.07325 q^{60} +14.4481 q^{61} +4.82890 q^{62} -2.79044 q^{63} -1.54987 q^{64} +6.34856 q^{65} -10.4595 q^{67} +2.65554 q^{68} +0.293755 q^{69} -1.81029 q^{70} -13.6335 q^{71} -3.65149 q^{72} +5.24386 q^{73} +11.7508 q^{74} +2.40633 q^{75} +3.96157 q^{76} +27.6554 q^{78} -7.08014 q^{79} -4.92319 q^{80} -9.58476 q^{81} +2.98511 q^{82} +12.6211 q^{83} -3.07325 q^{84} +2.07927 q^{85} -13.1514 q^{86} +11.2461 q^{87} +6.09501 q^{89} +5.05151 q^{90} -6.34856 q^{91} +0.155909 q^{92} +6.41883 q^{93} -15.0488 q^{94} +3.10189 q^{95} -15.1485 q^{96} +12.1107 q^{97} +1.81029 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} - 4 q^{3} + 12 q^{4} + 10 q^{5} + 8 q^{6} - 10 q^{7} + 6 q^{8} + 14 q^{9}+O(q^{10}) $ 10 * q + 2 * q^2 - 4 * q^3 + 12 * q^4 + 10 * q^5 + 8 * q^6 - 10 * q^7 + 6 * q^8 + 14 * q^9	$ 10 q + 2 q^{2} - 4 q^{3} + 12 q^{4} + 10 q^{5} + 8 q^{6} - 10 q^{7} + 6 q^{8} + 14 q^{9} + 2 q^{10} - 4 q^{12} + 18 q^{13} - 2 q^{14} - 4 q^{15} + 4 q^{16} + 4 q^{17} + 12 q^{18} + 14 q^{19} + 12 q^{20} + 4 q^{21} - 4 q^{23} + 46 q^{24} + 10 q^{25} + 2 q^{26} - 34 q^{27} - 12 q^{28} + 36 q^{29} + 8 q^{30} - 18 q^{31} + 4 q^{32} - 32 q^{34} - 10 q^{35} + 22 q^{36} + 4 q^{37} + 18 q^{38} + 6 q^{40} + 38 q^{41} - 8 q^{42} + 6 q^{43} + 14 q^{45} + 28 q^{46} - 18 q^{47} + 16 q^{48} + 10 q^{49} + 2 q^{50} - 4 q^{51} + 26 q^{52} - 26 q^{53} + 2 q^{54} - 6 q^{56} + 22 q^{57} + 10 q^{58} - 14 q^{59} - 4 q^{60} + 60 q^{61} + 22 q^{62} - 14 q^{63} + 18 q^{65} - 10 q^{67} + 2 q^{68} - 8 q^{69} - 2 q^{70} - 54 q^{72} + 18 q^{73} - 20 q^{74} - 4 q^{75} + 38 q^{76} + 40 q^{78} + 40 q^{79} + 4 q^{80} + 18 q^{81} - 36 q^{82} + 2 q^{83} + 4 q^{84} + 4 q^{85} + 42 q^{86} - 32 q^{87} + 2 q^{89} + 12 q^{90} - 18 q^{91} - 64 q^{92} + 26 q^{93} - 68 q^{94} + 14 q^{95} + 28 q^{96} + 8 q^{97} + 2 q^{98}+O(q^{100}) $ 10 * q + 2 * q^2 - 4 * q^3 + 12 * q^4 + 10 * q^5 + 8 * q^6 - 10 * q^7 + 6 * q^8 + 14 * q^9 + 2 * q^10 - 4 * q^12 + 18 * q^13 - 2 * q^14 - 4 * q^15 + 4 * q^16 + 4 * q^17 + 12 * q^18 + 14 * q^19 + 12 * q^20 + 4 * q^21 - 4 * q^23 + 46 * q^24 + 10 * q^25 + 2 * q^26 - 34 * q^27 - 12 * q^28 + 36 * q^29 + 8 * q^30 - 18 * q^31 + 4 * q^32 - 32 * q^34 - 10 * q^35 + 22 * q^36 + 4 * q^37 + 18 * q^38 + 6 * q^40 + 38 * q^41 - 8 * q^42 + 6 * q^43 + 14 * q^45 + 28 * q^46 - 18 * q^47 + 16 * q^48 + 10 * q^49 + 2 * q^50 - 4 * q^51 + 26 * q^52 - 26 * q^53 + 2 * q^54 - 6 * q^56 + 22 * q^57 + 10 * q^58 - 14 * q^59 - 4 * q^60 + 60 * q^61 + 22 * q^62 - 14 * q^63 + 18 * q^65 - 10 * q^67 + 2 * q^68 - 8 * q^69 - 2 * q^70 - 54 * q^72 + 18 * q^73 - 20 * q^74 - 4 * q^75 + 38 * q^76 + 40 * q^78 + 40 * q^79 + 4 * q^80 + 18 * q^81 - 36 * q^82 + 2 * q^83 + 4 * q^84 + 4 * q^85 + 42 * q^86 - 32 * q^87 + 2 * q^89 + 12 * q^90 - 18 * q^91 - 64 * q^92 + 26 * q^93 - 68 * q^94 + 14 * q^95 + 28 * q^96 + 8 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.81029	1.28007	0.640034	−	0.768346i	$-0.278920\pi$
$2$	1.81029	1.28007	0.640034	+	0.768346i	$0.278920\pi$
$3$	2.40633	1.38930	0.694649	−	0.719349i	$-0.255560\pi$
$3$	2.40633	1.38930	0.694649	+	0.719349i	$0.255560\pi$
$4$	1.27715	0.638575
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	4.35616	1.77840
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.30857	−0.462649
$9$	2.79044	0.930148
$10$	1.81029	0.572464
$11$	0	0
$11$	0	0
$12$	3.07325	0.887170
$13$	6.34856	1.76077	0.880387	−	0.474256i	$-0.157283\pi$
$13$	6.34856	1.76077	0.880387	+	0.474256i	$0.157283\pi$
$14$	−1.81029	−0.483820
$15$	2.40633	0.621313
$16$	−4.92319	−1.23080
$17$	2.07927	0.504298	0.252149	−	0.967688i	$-0.418863\pi$
$17$	2.07927	0.504298	0.252149	+	0.967688i	$0.418863\pi$
$18$	5.05151	1.19065
$19$	3.10189	0.711622	0.355811	−	0.934558i	$-0.384205\pi$
$19$	3.10189	0.711622	0.355811	+	0.934558i	$0.384205\pi$
$20$	1.27715	0.285579
$21$	−2.40633	−0.525105
$22$	0	0
$23$	0.122076	0.0254546	0.0127273	−	0.999919i	$-0.495949\pi$
$23$	0.122076	0.0254546	0.0127273	+	0.999919i	$0.495949\pi$
$24$	−3.14885	−0.642757
$25$	1.00000	0.200000
$26$	11.4927	2.25391
$27$	−0.504265	−0.0970458
$28$	−1.27715	−0.241359
$29$	4.67356	0.867858	0.433929	−	0.900947i	$-0.357127\pi$
$29$	4.67356	0.867858	0.433929	+	0.900947i	$0.357127\pi$
$30$	4.35616	0.795323
$31$	2.66747	0.479092	0.239546	−	0.970885i	$-0.423001\pi$
$31$	2.66747	0.479092	0.239546	+	0.970885i	$0.423001\pi$
$32$	−6.29526	−1.11286
$33$	0	0
$34$	3.76409	0.645536
$35$	−1.00000	−0.169031
$36$	3.56381	0.593969
$37$	6.49112	1.06713	0.533567	−	0.845758i	$-0.320851\pi$
$37$	6.49112	1.06713	0.533567	+	0.845758i	$0.320851\pi$
$38$	5.61532	0.910925
$39$	15.2768	2.44624
$40$	−1.30857	−0.206903
$41$	1.64897	0.257526	0.128763	−	0.991675i	$-0.458899\pi$
$41$	1.64897	0.257526	0.128763	+	0.991675i	$0.458899\pi$
$42$	−4.35616	−0.672170
$43$	−7.26481	−1.10787	−0.553937	−	0.832559i	$-0.686875\pi$
$43$	−7.26481	−1.10787	−0.553937	+	0.832559i	$0.686875\pi$
$44$	0	0
$45$	2.79044	0.415975
$46$	0.220993	0.0325836
$47$	−8.31293	−1.21257	−0.606283	−	0.795249i	$-0.707340\pi$
$47$	−8.31293	−1.21257	−0.606283	+	0.795249i	$0.707340\pi$
$48$	−11.8468	−1.70994
$49$	1.00000	0.142857
$50$	1.81029	0.256014
$51$	5.00342	0.700620
$52$	8.10806	1.12439
$53$	−4.48011	−0.615391	−0.307695	−	0.951485i	$-0.599558\pi$
$53$	−4.48011	−0.615391	−0.307695	+	0.951485i	$0.599558\pi$
$54$	−0.912865	−0.124225
$55$	0	0
$56$	1.30857	0.174865
$57$	7.46418	0.988655
$58$	8.46049	1.11092
$59$	5.00377	0.651435	0.325717	−	0.945467i	$-0.394394\pi$
$59$	5.00377	0.651435	0.325717	+	0.945467i	$0.394394\pi$
$60$	3.07325	0.396755
$61$	14.4481	1.84988	0.924942	−	0.380108i	$-0.124113\pi$
$61$	14.4481	1.84988	0.924942	+	0.380108i	$0.124113\pi$
$62$	4.82890	0.613271
$63$	−2.79044	−0.351563
$64$	−1.54987	−0.193733
$65$	6.34856	0.787442
$66$	0	0
$67$	−10.4595	−1.27784	−0.638919	−	0.769274i	$-0.720618\pi$
$67$	−10.4595	−1.27784	−0.638919	+	0.769274i	$0.720618\pi$
$68$	2.65554	0.322032
$69$	0.293755	0.0353640
$70$	−1.81029	−0.216371
$71$	−13.6335	−1.61800	−0.808999	−	0.587810i	$-0.799990\pi$
$71$	−13.6335	−1.61800	−0.808999	+	0.587810i	$0.799990\pi$
$72$	−3.65149	−0.430332
$73$	5.24386	0.613748	0.306874	−	0.951750i	$-0.400717\pi$
$73$	5.24386	0.613748	0.306874	+	0.951750i	$0.400717\pi$
$74$	11.7508	1.36600
$75$	2.40633	0.277860
$76$	3.96157	0.454424
$77$	0	0
$78$	27.6554	3.13135
$79$	−7.08014	−0.796577	−0.398289	−	0.917260i	$-0.630396\pi$
$79$	−7.08014	−0.796577	−0.398289	+	0.917260i	$0.630396\pi$
$80$	−4.92319	−0.550429
$81$	−9.58476	−1.06497
$82$	2.98511	0.329650
$83$	12.6211	1.38534	0.692672	−	0.721253i	$-0.256434\pi$
$83$	12.6211	1.38534	0.692672	+	0.721253i	$0.256434\pi$
$84$	−3.07325	−0.335319
$85$	2.07927	0.225529
$86$	−13.1514	−1.41815
$87$	11.2461	1.20571
$88$	0	0
$89$	6.09501	0.646069	0.323035	−	0.946387i	$-0.395297\pi$
$89$	6.09501	0.646069	0.323035	+	0.946387i	$0.395297\pi$
$90$	5.05151	0.532476
$91$	−6.34856	−0.665510
$92$	0.155909	0.0162546
$93$	6.41883	0.665602
$94$	−15.0488	−1.55217
$95$	3.10189	0.318247
$96$	−15.1485	−1.54609
$97$	12.1107	1.22965	0.614827	−	0.788662i	$-0.289226\pi$
$97$	12.1107	1.22965	0.614827	+	0.788662i	$0.289226\pi$
$98$	1.81029	0.182867
$99$	0	0
$100$	1.27715	0.127715
$101$	4.95110	0.492653	0.246327	−	0.969187i	$-0.420776\pi$
$101$	4.95110	0.492653	0.246327	+	0.969187i	$0.420776\pi$
$102$	9.05765	0.896841
$103$	−6.20927	−0.611817	−0.305909	−	0.952061i	$-0.598960\pi$
$103$	−6.20927	−0.611817	−0.305909	+	0.952061i	$0.598960\pi$
$104$	−8.30753	−0.814620
$105$	−2.40633	−0.234834
$106$	−8.11030	−0.787742
$107$	−3.18496	−0.307902	−0.153951	−	0.988078i	$-0.549200\pi$
$107$	−3.18496	−0.307902	−0.153951	+	0.988078i	$0.549200\pi$
$108$	−0.644021	−0.0619710
$109$	2.93936	0.281540	0.140770	−	0.990042i	$-0.455042\pi$
$109$	2.93936	0.281540	0.140770	+	0.990042i	$0.455042\pi$
$110$	0	0
$111$	15.6198	1.48257
$112$	4.92319	0.465198
$113$	−11.1702	−1.05081	−0.525404	−	0.850853i	$-0.676086\pi$
$113$	−11.1702	−1.05081	−0.525404	+	0.850853i	$0.676086\pi$
$114$	13.5123	1.26555
$115$	0.122076	0.0113836
$116$	5.96883	0.554192
$117$	17.7153	1.63778
$118$	9.05827	0.833881
$119$	−2.07927	−0.190607
$120$	−3.14885	−0.287450
$121$	0	0
$122$	26.1552	2.36798
$123$	3.96797	0.357780
$124$	3.40676	0.305936
$125$	1.00000	0.0894427
$126$	−5.05151	−0.450024
$127$	−17.6754	−1.56844	−0.784220	−	0.620482i	$-0.786937\pi$
$127$	−17.6754	−1.56844	−0.784220	+	0.620482i	$0.786937\pi$
$128$	9.78481	0.864863
$129$	−17.4816	−1.53917
$130$	11.4927	1.00798
$131$	−16.6426	−1.45407	−0.727034	−	0.686602i	$-0.759102\pi$
$131$	−16.6426	−1.45407	−0.727034	+	0.686602i	$0.759102\pi$
$132$	0	0
$133$	−3.10189	−0.268968
$134$	−18.9348	−1.63572
$135$	−0.504265	−0.0434002
$136$	−2.72087	−0.233313
$137$	−4.64303	−0.396681	−0.198340	−	0.980133i	$-0.563555\pi$
$137$	−4.64303	−0.396681	−0.198340	+	0.980133i	$0.563555\pi$
$138$	0.531782	0.0452683
$139$	22.1077	1.87515	0.937577	−	0.347779i	$-0.113064\pi$
$139$	22.1077	1.87515	0.937577	+	0.347779i	$0.113064\pi$
$140$	−1.27715	−0.107939
$141$	−20.0037	−1.68462
$142$	−24.6806	−2.07115
$143$	0	0
$144$	−13.7379	−1.14482
$145$	4.67356	0.388118
$146$	9.49291	0.785639
$147$	2.40633	0.198471
$148$	8.29013	0.681444
$149$	−22.3934	−1.83454	−0.917268	−	0.398270i	$-0.869611\pi$
$149$	−22.3934	−1.83454	−0.917268	+	0.398270i	$0.869611\pi$
$150$	4.35616	0.355679
$151$	3.78150	0.307734	0.153867	−	0.988092i	$-0.450827\pi$
$151$	3.78150	0.307734	0.153867	+	0.988092i	$0.450827\pi$
$152$	−4.05904	−0.329231
$153$	5.80209	0.469071
$154$	0	0
$155$	2.66747	0.214257
$156$	19.5107	1.56211
$157$	9.19055	0.733486	0.366743	−	0.930322i	$-0.380473\pi$
$157$	9.19055	0.733486	0.366743	+	0.930322i	$0.380473\pi$
$158$	−12.8171	−1.01967
$159$	−10.7806	−0.854961
$160$	−6.29526	−0.497684
$161$	−0.122076	−0.00962092
$162$	−17.3512	−1.36324
$163$	−19.1239	−1.49790	−0.748952	−	0.662625i	$-0.769442\pi$
$163$	−19.1239	−1.49790	−0.748952	+	0.662625i	$0.769442\pi$
$164$	2.10598	0.164449
$165$	0	0
$166$	22.8478	1.77333
$167$	6.80707	0.526747	0.263373	−	0.964694i	$-0.415165\pi$
$167$	6.80707	0.526747	0.263373	+	0.964694i	$0.415165\pi$
$168$	3.14885	0.242939
$169$	27.3042	2.10032
$170$	3.76409	0.288692
$171$	8.65564	0.661914
$172$	−9.27825	−0.707460
$173$	1.83705	0.139668	0.0698341	−	0.997559i	$-0.477753\pi$
$173$	1.83705	0.139668	0.0698341	+	0.997559i	$0.477753\pi$
$174$	20.3588	1.54339
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	12.0407	0.905037
$178$	11.0337	0.827013
$179$	12.3430	0.922561	0.461280	−	0.887254i	$-0.347390\pi$
$179$	12.3430	0.922561	0.461280	+	0.887254i	$0.347390\pi$
$180$	3.56381	0.265631
$181$	−26.6139	−1.97820	−0.989098	−	0.147258i	$-0.952955\pi$
$181$	−26.6139	−1.97820	−0.989098	+	0.147258i	$0.952955\pi$
$182$	−11.4927	−0.851898
$183$	34.7668	2.57004
$184$	−0.159745	−0.0117765
$185$	6.49112	0.477237
$186$	11.6199	0.852016
$187$	0	0
$188$	−10.6169	−0.774314
$189$	0.504265	0.0366799
$190$	5.61532	0.407378
$191$	10.7397	0.777095	0.388547	−	0.921429i	$-0.372977\pi$
$191$	10.7397	0.777095	0.388547	+	0.921429i	$0.372977\pi$
$192$	−3.72950	−0.269153
$193$	7.83033	0.563639	0.281820	−	0.959467i	$-0.409062\pi$
$193$	7.83033	0.563639	0.281820	+	0.959467i	$0.409062\pi$
$194$	21.9239	1.57404
$195$	15.2768	1.09399
$196$	1.27715	0.0912250
$197$	6.93478	0.494082	0.247041	−	0.969005i	$-0.420542\pi$
$197$	6.93478	0.494082	0.247041	+	0.969005i	$0.420542\pi$
$198$	0	0
$199$	−11.4627	−0.812567	−0.406283	−	0.913747i	$-0.633175\pi$
$199$	−11.4627	−0.812567	−0.406283	+	0.913747i	$0.633175\pi$
$200$	−1.30857	−0.0925298
$201$	−25.1692	−1.77530
$202$	8.96293	0.630630
$203$	−4.67356	−0.328019
$204$	6.39012	0.447398
$205$	1.64897	0.115169
$206$	−11.2406	−0.783168
$207$	0.340645	0.0236765
$208$	−31.2552	−2.16716
$209$	0	0
$210$	−4.35616	−0.300604
$211$	−15.7013	−1.08092	−0.540461	−	0.841369i	$-0.681750\pi$
$211$	−15.7013	−1.08092	−0.540461	+	0.841369i	$0.681750\pi$
$212$	−5.72177	−0.392973
$213$	−32.8067	−2.24788
$214$	−5.76570	−0.394135
$215$	−7.26481	−0.495456
$216$	0.659865	0.0448981
$217$	−2.66747	−0.181080
$218$	5.32110	0.360390
$219$	12.6185	0.852678
$220$	0	0
$221$	13.2004	0.887954
$222$	28.2764	1.89779
$223$	−22.4331	−1.50223	−0.751115	−	0.660171i	$-0.770484\pi$
$223$	−22.4331	−1.50223	−0.751115	+	0.660171i	$0.770484\pi$
$224$	6.29526	0.420620
$225$	2.79044	0.186030
$226$	−20.2214	−1.34511
$227$	−13.5879	−0.901861	−0.450931	−	0.892559i	$-0.648908\pi$
$227$	−13.5879	−0.901861	−0.450931	+	0.892559i	$0.648908\pi$
$228$	9.53287	0.631330
$229$	4.17758	0.276062	0.138031	−	0.990428i	$-0.455923\pi$
$229$	4.17758	0.276062	0.138031	+	0.990428i	$0.455923\pi$
$230$	0.220993	0.0145718
$231$	0	0
$232$	−6.11567	−0.401514
$233$	−19.2373	−1.26028	−0.630140	−	0.776481i	$-0.717003\pi$
$233$	−19.2373	−1.26028	−0.630140	+	0.776481i	$0.717003\pi$
$234$	32.0698	2.09647
$235$	−8.31293	−0.542276
$236$	6.39056	0.415990
$237$	−17.0372	−1.10668
$238$	−3.76409	−0.243989
$239$	4.52900	0.292957	0.146478	−	0.989214i	$-0.453206\pi$
$239$	4.52900	0.292957	0.146478	+	0.989214i	$0.453206\pi$
$240$	−11.8468	−0.764710
$241$	28.4542	1.83290	0.916449	−	0.400151i	$-0.131042\pi$
$241$	28.4542	1.83290	0.916449	+	0.400151i	$0.131042\pi$
$242$	0	0
$243$	−21.5513	−1.38252
$244$	18.4523	1.18129
$245$	1.00000	0.0638877
$246$	7.18317	0.457982
$247$	19.6925	1.25301
$248$	−3.49057	−0.221652
$249$	30.3705	1.92465
$250$	1.81029	0.114493
$251$	0.856950	0.0540902	0.0270451	−	0.999634i	$-0.491390\pi$
$251$	0.856950	0.0540902	0.0270451	+	0.999634i	$0.491390\pi$
$252$	−3.56381	−0.224499
$253$	0	0
$254$	−31.9977	−2.00771
$255$	5.00342	0.313327
$256$	20.8131	1.30082
$257$	5.20123	0.324444	0.162222	−	0.986754i	$-0.448134\pi$
$257$	5.20123	0.324444	0.162222	+	0.986754i	$0.448134\pi$
$258$	−31.6467	−1.97024
$259$	−6.49112	−0.403339
$260$	8.10806	0.502841
$261$	13.0413	0.807236
$262$	−30.1279	−1.86131
$263$	−17.0908	−1.05386	−0.526932	−	0.849908i	$-0.676658\pi$
$263$	−17.0908	−1.05386	−0.526932	+	0.849908i	$0.676658\pi$
$264$	0	0
$265$	−4.48011	−0.275211
$266$	−5.61532	−0.344297
$267$	14.6666	0.897583
$268$	−13.3584	−0.815995
$269$	−17.8670	−1.08937	−0.544686	−	0.838640i	$-0.683351\pi$
$269$	−17.8670	−1.08937	−0.544686	+	0.838640i	$0.683351\pi$
$270$	−0.912865	−0.0555552
$271$	15.8215	0.961087	0.480543	−	0.876971i	$-0.340440\pi$
$271$	15.8215	0.961087	0.480543	+	0.876971i	$0.340440\pi$
$272$	−10.2367	−0.620688
$273$	−15.2768	−0.924591
$274$	−8.40523	−0.507778
$275$	0	0
$276$	0.375169	0.0225825
$277$	8.22407	0.494137	0.247068	−	0.968998i	$-0.420533\pi$
$277$	8.22407	0.494137	0.247068	+	0.968998i	$0.420533\pi$
$278$	40.0214	2.40032
$279$	7.44343	0.445627
$280$	1.30857	0.0782020
$281$	−31.6434	−1.88769	−0.943844	−	0.330391i	$-0.892819\pi$
$281$	−31.6434	−1.88769	−0.943844	+	0.330391i	$0.892819\pi$
$282$	−36.2125	−2.15642
$283$	−19.6965	−1.17083	−0.585416	−	0.810733i	$-0.699069\pi$
$283$	−19.6965	−1.17083	−0.585416	+	0.810733i	$0.699069\pi$
$284$	−17.4120	−1.03321
$285$	7.46418	0.442140
$286$	0	0
$287$	−1.64897	−0.0973355
$288$	−17.5666	−1.03512
$289$	−12.6766	−0.745684
$290$	8.46049	0.496817
$291$	29.1424	1.70836
$292$	6.69720	0.391924
$293$	−30.8051	−1.79965	−0.899826	−	0.436250i	$-0.856306\pi$
$293$	−30.8051	−1.79965	−0.899826	+	0.436250i	$0.856306\pi$
$294$	4.35616	0.254057
$295$	5.00377	0.291331
$296$	−8.49408	−0.493708
$297$	0	0
$298$	−40.5385	−2.34833
$299$	0.775005	0.0448197
$300$	3.07325	0.177434
$301$	7.26481	0.418737
$302$	6.84561	0.393921
$303$	11.9140	0.684442
$304$	−15.2712	−0.875862
$305$	14.4481	0.827293
$306$	10.5035	0.600443
$307$	18.0949	1.03273	0.516365	−	0.856369i	$-0.327285\pi$
$307$	18.0949	1.03273	0.516365	+	0.856369i	$0.327285\pi$
$308$	0	0
$309$	−14.9416	−0.849996
$310$	4.82890	0.274263
$311$	−30.3205	−1.71932	−0.859660	−	0.510867i	$-0.829324\pi$
$311$	−30.3205	−1.71932	−0.859660	+	0.510867i	$0.829324\pi$
$312$	−19.9907	−1.13175
$313$	22.8295	1.29040	0.645201	−	0.764013i	$-0.276774\pi$
$313$	22.8295	1.29040	0.645201	+	0.764013i	$0.276774\pi$
$314$	16.6376	0.938912
$315$	−2.79044	−0.157224
$316$	−9.04239	−0.508674
$317$	16.7644	0.941583	0.470791	−	0.882245i	$-0.343968\pi$
$317$	16.7644	0.941583	0.470791	+	0.882245i	$0.343968\pi$
$318$	−19.5161	−1.09441
$319$	0	0
$320$	−1.54987	−0.0866402
$321$	−7.66408	−0.427767
$322$	−0.220993	−0.0123154
$323$	6.44967	0.358869
$324$	−12.2412	−0.680065
$325$	6.34856	0.352155
$326$	−34.6199	−1.91742
$327$	7.07309	0.391143
$328$	−2.15779	−0.119144
$329$	8.31293	0.458307
$330$	0	0
$331$	−24.3704	−1.33952	−0.669759	−	0.742579i	$-0.733602\pi$
$331$	−24.3704	−1.33952	−0.669759	+	0.742579i	$0.733602\pi$
$332$	16.1190	0.884645
$333$	18.1131	0.992592
$334$	12.3228	0.674272
$335$	−10.4595	−0.571466
$336$	11.8468	0.646298
$337$	−17.2360	−0.938907	−0.469453	−	0.882957i	$-0.655549\pi$
$337$	−17.2360	−0.938907	−0.469453	+	0.882957i	$0.655549\pi$
$338$	49.4285	2.68856
$339$	−26.8793	−1.45989
$340$	2.65554	0.144017
$341$	0	0
$342$	15.6692	0.847294
$343$	−1.00000	−0.0539949
$344$	9.50651	0.512557
$345$	0.293755	0.0158152
$346$	3.32559	0.178785
$347$	−10.1968	−0.547392	−0.273696	−	0.961816i	$-0.588246\pi$
$347$	−10.1968	−0.547392	−0.273696	+	0.961816i	$0.588246\pi$
$348$	14.3630	0.769937
$349$	−24.3277	−1.30223	−0.651115	−	0.758979i	$-0.725699\pi$
$349$	−24.3277	−1.30223	−0.651115	+	0.758979i	$0.725699\pi$
$350$	−1.81029	−0.0967641
$351$	−3.20135	−0.170876
$352$	0	0
$353$	−16.4334	−0.874660	−0.437330	−	0.899301i	$-0.644076\pi$
$353$	−16.4334	−0.874660	−0.437330	+	0.899301i	$0.644076\pi$
$354$	21.7972	1.15851
$355$	−13.6335	−0.723591
$356$	7.78423	0.412564
$357$	−5.00342	−0.264809
$358$	22.3444	1.18094
$359$	−9.26599	−0.489040	−0.244520	−	0.969644i	$-0.578630\pi$
$359$	−9.26599	−0.489040	−0.244520	+	0.969644i	$0.578630\pi$
$360$	−3.65149	−0.192450
$361$	−9.37829	−0.493594
$362$	−48.1789	−2.53223
$363$	0	0
$364$	−8.10806	−0.424978
$365$	5.24386	0.274476
$366$	62.9381	3.28983
$367$	−20.0932	−1.04886	−0.524429	−	0.851454i	$-0.675721\pi$
$367$	−20.0932	−1.04886	−0.524429	+	0.851454i	$0.675721\pi$
$368$	−0.601002	−0.0313294
$369$	4.60135	0.239537
$370$	11.7508	0.610895
$371$	4.48011	0.232596
$372$	8.19781	0.425037
$373$	14.8177	0.767230	0.383615	−	0.923493i	$-0.374679\pi$
$373$	14.8177	0.767230	0.383615	+	0.923493i	$0.374679\pi$
$374$	0	0
$375$	2.40633	0.124263
$376$	10.8780	0.560993
$377$	29.6704	1.52810
$378$	0.912865	0.0469527
$379$	27.8280	1.42943	0.714713	−	0.699417i	$-0.246557\pi$
$379$	27.8280	1.42943	0.714713	+	0.699417i	$0.246557\pi$
$380$	3.96157	0.203225
$381$	−42.5330	−2.17903
$382$	19.4419	0.994735
$383$	0.742326	0.0379311	0.0189656	−	0.999820i	$-0.493963\pi$
$383$	0.742326	0.0379311	0.0189656	+	0.999820i	$0.493963\pi$
$384$	23.5455	1.20155
$385$	0	0
$386$	14.1752	0.721497
$387$	−20.2720	−1.03049
$388$	15.4672	0.785226
$389$	16.1081	0.816711	0.408355	−	0.912823i	$-0.366102\pi$
$389$	16.1081	0.816711	0.408355	+	0.912823i	$0.366102\pi$
$390$	27.6554	1.40038
$391$	0.253829	0.0128367
$392$	−1.30857	−0.0660927
$393$	−40.0476	−2.02013
$394$	12.5540	0.632459
$395$	−7.08014	−0.356240
$396$	0	0
$397$	23.0476	1.15673	0.578364	−	0.815779i	$-0.303691\pi$
$397$	23.0476	1.15673	0.578364	+	0.815779i	$0.303691\pi$
$398$	−20.7507	−1.04014
$399$	−7.46418	−0.373676
$400$	−4.92319	−0.246159
$401$	−11.6330	−0.580925	−0.290463	−	0.956886i	$-0.593809\pi$
$401$	−11.6330	−0.580925	−0.290463	+	0.956886i	$0.593809\pi$
$402$	−45.5635	−2.27250
$403$	16.9346	0.843574
$404$	6.32330	0.314596
$405$	−9.58476	−0.476270
$406$	−8.46049	−0.419887
$407$	0	0
$408$	−6.54733	−0.324141
$409$	17.7527	0.877812	0.438906	−	0.898533i	$-0.355366\pi$
$409$	17.7527	0.877812	0.438906	+	0.898533i	$0.355366\pi$
$410$	2.98511	0.147424
$411$	−11.1727	−0.551108
$412$	−7.93016	−0.390691
$413$	−5.00377	−0.246219
$414$	0.616667	0.0303075
$415$	12.6211	0.619544
$416$	−39.9658	−1.95949
$417$	53.1986	2.60515
$418$	0	0
$419$	−1.44062	−0.0703791	−0.0351896	−	0.999381i	$-0.511203\pi$
$419$	−1.44062	−0.0703791	−0.0351896	+	0.999381i	$0.511203\pi$
$420$	−3.07325	−0.149959
$421$	1.60098	0.0780272	0.0390136	−	0.999239i	$-0.487578\pi$
$421$	1.60098	0.0780272	0.0390136	+	0.999239i	$0.487578\pi$
$422$	−28.4239	−1.38365
$423$	−23.1968	−1.12787
$424$	5.86253	0.284710
$425$	2.07927	0.100860
$426$	−59.3897	−2.87744
$427$	−14.4481	−0.699190
$428$	−4.06767	−0.196618
$429$	0	0
$430$	−13.1514	−0.634218
$431$	−0.688505	−0.0331641	−0.0165821	−	0.999863i	$-0.505278\pi$
$431$	−0.688505	−0.0331641	−0.0165821	+	0.999863i	$0.505278\pi$
$432$	2.48259	0.119444
$433$	11.1280	0.534777	0.267388	−	0.963589i	$-0.413839\pi$
$433$	11.1280	0.534777	0.267388	+	0.963589i	$0.413839\pi$
$434$	−4.82890	−0.231795
$435$	11.2461	0.539211
$436$	3.75401	0.179784
$437$	0.378665	0.0181140
$438$	22.8431	1.09149
$439$	−13.3926	−0.639193	−0.319596	−	0.947554i	$-0.603547\pi$
$439$	−13.3926	−0.639193	−0.319596	+	0.947554i	$0.603547\pi$
$440$	0	0
$441$	2.79044	0.132878
$442$	23.8965	1.13664
$443$	−23.8591	−1.13358	−0.566789	−	0.823863i	$-0.691815\pi$
$443$	−23.8591	−1.13358	−0.566789	+	0.823863i	$0.691815\pi$
$444$	19.9488	0.946729
$445$	6.09501	0.288931
$446$	−40.6104	−1.92296
$447$	−53.8859	−2.54872
$448$	1.54987	0.0732244
$449$	0.374398	0.0176689	0.00883446	−	0.999961i	$-0.497188\pi$
$449$	0.374398	0.0176689	0.00883446	+	0.999961i	$0.497188\pi$
$450$	5.05151	0.238130
$451$	0	0
$452$	−14.2661	−0.671020
$453$	9.09955	0.427534
$454$	−24.5981	−1.15444
$455$	−6.34856	−0.297625
$456$	−9.76740	−0.457400
$457$	−25.4667	−1.19128	−0.595640	−	0.803251i	$-0.703102\pi$
$457$	−25.4667	−1.19128	−0.595640	+	0.803251i	$0.703102\pi$
$458$	7.56263	0.353379
$459$	−1.04850	−0.0489400
$460$	0.155909	0.00726929
$461$	−14.4063	−0.670966	−0.335483	−	0.942046i	$-0.608900\pi$
$461$	−14.4063	−0.670966	−0.335483	+	0.942046i	$0.608900\pi$
$462$	0	0
$463$	8.64612	0.401819	0.200910	−	0.979610i	$-0.435610\pi$
$463$	8.64612	0.401819	0.200910	+	0.979610i	$0.435610\pi$
$464$	−23.0088	−1.06816
$465$	6.41883	0.297666
$466$	−34.8252	−1.61324
$467$	−4.98818	−0.230825	−0.115413	−	0.993318i	$-0.536819\pi$
$467$	−4.98818	−0.230825	−0.115413	+	0.993318i	$0.536819\pi$
$468$	22.6251	1.04584
$469$	10.4595	0.482977
$470$	−15.0488	−0.694150
$471$	22.1155	1.01903
$472$	−6.54777	−0.301386
$473$	0	0
$474$	−30.8422	−1.41663
$475$	3.10189	0.142324
$476$	−2.65554	−0.121717
$477$	−12.5015	−0.572404
$478$	8.19880	0.375005
$479$	29.2426	1.33613	0.668063	−	0.744104i	$-0.267124\pi$
$479$	29.2426	1.33613	0.668063	+	0.744104i	$0.267124\pi$
$480$	−15.1485	−0.691431
$481$	41.2093	1.87898
$482$	51.5104	2.34623
$483$	−0.293755	−0.0133663
$484$	0	0
$485$	12.1107	0.549918
$486$	−39.0142	−1.76972
$487$	10.1079	0.458032	0.229016	−	0.973423i	$-0.426449\pi$
$487$	10.1079	0.458032	0.229016	+	0.973423i	$0.426449\pi$
$488$	−18.9063	−0.855847
$489$	−46.0186	−2.08103
$490$	1.81029	0.0817806
$491$	29.7852	1.34419	0.672095	−	0.740465i	$-0.265395\pi$
$491$	29.7852	1.34419	0.672095	+	0.740465i	$0.265395\pi$
$492$	5.06769	0.228469
$493$	9.71760	0.437659
$494$	35.6492	1.60393
$495$	0	0
$496$	−13.1325	−0.589666
$497$	13.6335	0.611546
$498$	54.9795	2.46369
$499$	−19.4081	−0.868828	−0.434414	−	0.900713i	$-0.643044\pi$
$499$	−19.4081	−0.868828	−0.434414	+	0.900713i	$0.643044\pi$
$500$	1.27715	0.0571159
$501$	16.3801	0.731808
$502$	1.55133	0.0692391
$503$	33.8575	1.50963	0.754815	−	0.655938i	$-0.227727\pi$
$503$	33.8575	1.50963	0.754815	+	0.655938i	$0.227727\pi$
$504$	3.65149	0.162650
$505$	4.95110	0.220321
$506$	0	0
$507$	65.7031	2.91798
$508$	−22.5742	−1.00157
$509$	−25.0359	−1.10969	−0.554847	−	0.831952i	$-0.687223\pi$
$509$	−25.0359	−1.10969	−0.554847	+	0.831952i	$0.687223\pi$
$510$	9.05765	0.401079
$511$	−5.24386	−0.231975
$512$	18.1081	0.800272
$513$	−1.56417	−0.0690599
$514$	9.41573	0.415310
$515$	−6.20927	−0.273613
$516$	−22.3266	−0.982872
$517$	0	0
$518$	−11.7508	−0.516301
$519$	4.42055	0.194041
$520$	−8.30753	−0.364309
$521$	41.2581	1.80755	0.903776	−	0.428006i	$-0.140784\pi$
$521$	41.2581	1.80755	0.903776	+	0.428006i	$0.140784\pi$
$522$	23.6085	1.03332
$523$	27.0821	1.18422	0.592110	−	0.805857i	$-0.298295\pi$
$523$	27.0821	1.18422	0.592110	+	0.805857i	$0.298295\pi$
$524$	−21.2550	−0.928531
$525$	−2.40633	−0.105021
$526$	−30.9393	−1.34902
$527$	5.54641	0.241605
$528$	0	0
$529$	−22.9851	−0.999352
$530$	−8.11030	−0.352289
$531$	13.9627	0.605931
$532$	−3.96157	−0.171756
$533$	10.4686	0.453444
$534$	26.5508	1.14897
$535$	−3.18496	−0.137698
$536$	13.6870	0.591190
$537$	29.7014	1.28171
$538$	−32.3445	−1.39447
$539$	0	0
$540$	−0.644021	−0.0277143
$541$	43.9866	1.89113	0.945565	−	0.325433i	$-0.105510\pi$
$541$	43.9866	1.89113	0.945565	+	0.325433i	$0.105510\pi$
$542$	28.6415	1.23026
$543$	−64.0420	−2.74830
$544$	−13.0896	−0.561210
$545$	2.93936	0.125909
$546$	−27.6554	−1.18354
$547$	−0.564038	−0.0241165	−0.0120583	−	0.999927i	$-0.503838\pi$
$547$	−0.564038	−0.0241165	−0.0120583	+	0.999927i	$0.503838\pi$
$548$	−5.92984	−0.253310
$549$	40.3165	1.72067
$550$	0	0
$551$	14.4969	0.617587
$552$	−0.384399	−0.0163611
$553$	7.08014	0.301078
$554$	14.8880	0.632528
$555$	15.6198	0.663024
$556$	28.2349	1.19743
$557$	25.3769	1.07526	0.537628	−	0.843182i	$-0.319321\pi$
$557$	25.3769	1.07526	0.537628	+	0.843182i	$0.319321\pi$
$558$	13.4748	0.570433
$559$	−46.1211	−1.95071
$560$	4.92319	0.208043
$561$	0	0
$562$	−57.2838	−2.41637
$563$	−41.9065	−1.76615	−0.883074	−	0.469234i	$-0.844530\pi$
$563$	−41.9065	−1.76615	−0.883074	+	0.469234i	$0.844530\pi$
$564$	−25.5477	−1.07575
$565$	−11.1702	−0.469936
$566$	−35.6563	−1.49875
$567$	9.58476	0.402522
$568$	17.8404	0.748565
$569$	31.1835	1.30728	0.653641	−	0.756805i	$-0.273241\pi$
$569$	31.1835	1.30728	0.653641	+	0.756805i	$0.273241\pi$
$570$	13.5123	0.565969
$571$	13.9570	0.584084	0.292042	−	0.956405i	$-0.405665\pi$
$571$	13.9570	0.584084	0.292042	+	0.956405i	$0.405665\pi$
$572$	0	0
$573$	25.8432	1.07962
$574$	−2.98511	−0.124596
$575$	0.122076	0.00509091
$576$	−4.32482	−0.180201
$577$	−6.85282	−0.285287	−0.142643	−	0.989774i	$-0.545560\pi$
$577$	−6.85282	−0.285287	−0.142643	+	0.989774i	$0.545560\pi$
$578$	−22.9484	−0.954526
$579$	18.8424	0.783063
$580$	5.96883	0.247842
$581$	−12.6211	−0.523611
$582$	52.7562	2.18681
$583$	0	0
$584$	−6.86196	−0.283950
$585$	17.7153	0.732437
$586$	−55.7661	−2.30368
$587$	39.3326	1.62343	0.811715	−	0.584053i	$-0.198534\pi$
$587$	39.3326	1.62343	0.811715	+	0.584053i	$0.198534\pi$
$588$	3.07325	0.126739
$589$	8.27421	0.340933
$590$	9.05827	0.372923
$591$	16.6874	0.686427
$592$	−31.9570	−1.31342
$593$	−1.47206	−0.0604502	−0.0302251	−	0.999543i	$-0.509622\pi$
$593$	−1.47206	−0.0604502	−0.0302251	+	0.999543i	$0.509622\pi$
$594$	0	0
$595$	−2.07927	−0.0852419
$596$	−28.5997	−1.17149
$597$	−27.5830	−1.12890
$598$	1.40298	0.0573723
$599$	31.5752	1.29013	0.645065	−	0.764128i	$-0.276830\pi$
$599$	31.5752	1.29013	0.645065	+	0.764128i	$0.276830\pi$
$600$	−3.14885	−0.128551
$601$	6.85556	0.279644	0.139822	−	0.990177i	$-0.455347\pi$
$601$	6.85556	0.279644	0.139822	+	0.990177i	$0.455347\pi$
$602$	13.1514	0.536012
$603$	−29.1868	−1.18858
$604$	4.82954	0.196511
$605$	0	0
$606$	21.5678	0.876132
$607$	8.59258	0.348762	0.174381	−	0.984678i	$-0.444208\pi$
$607$	8.59258	0.348762	0.174381	+	0.984678i	$0.444208\pi$
$608$	−19.5272	−0.791932
$609$	−11.2461	−0.455717
$610$	26.1552	1.05899
$611$	−52.7752	−2.13505
$612$	7.41014	0.299537
$613$	3.17722	0.128327	0.0641634	−	0.997939i	$-0.479562\pi$
$613$	3.17722	0.128327	0.0641634	+	0.997939i	$0.479562\pi$
$614$	32.7570	1.32197
$615$	3.96797	0.160004
$616$	0	0
$617$	43.4292	1.74840	0.874198	−	0.485570i	$-0.161388\pi$
$617$	43.4292	1.74840	0.874198	+	0.485570i	$0.161388\pi$
$618$	−27.0486	−1.08805
$619$	−36.8799	−1.48233	−0.741164	−	0.671324i	$-0.765726\pi$
$619$	−36.8799	−1.48233	−0.741164	+	0.671324i	$0.765726\pi$
$620$	3.40676	0.136819
$621$	−0.0615585	−0.00247026
$622$	−54.8889	−2.20085
$623$	−6.09501	−0.244191
$624$	−75.2103	−3.01082
$625$	1.00000	0.0400000
$626$	41.3281	1.65180
$627$	0	0
$628$	11.7377	0.468386
$629$	13.4968	0.538153
$630$	−5.05151	−0.201257
$631$	−22.4909	−0.895348	−0.447674	−	0.894197i	$-0.647747\pi$
$631$	−22.4909	−0.895348	−0.447674	+	0.894197i	$0.647747\pi$
$632$	9.26485	0.368536
$633$	−37.7826	−1.50172
$634$	30.3484	1.20529
$635$	−17.6754	−0.701428
$636$	−13.7685	−0.545956
$637$	6.34856	0.251539
$638$	0	0
$639$	−38.0435	−1.50498
$640$	9.78481	0.386779
$641$	−33.6984	−1.33101	−0.665504	−	0.746395i	$-0.731783\pi$
$641$	−33.6984	−1.33101	−0.665504	+	0.746395i	$0.731783\pi$
$642$	−13.8742	−0.547571
$643$	29.1195	1.14836	0.574180	−	0.818729i	$-0.305321\pi$
$643$	29.1195	1.14836	0.574180	+	0.818729i	$0.305321\pi$
$644$	−0.155909	−0.00614368
$645$	−17.4816	−0.688336
$646$	11.6758	0.459377
$647$	42.2721	1.66189	0.830943	−	0.556358i	$-0.187802\pi$
$647$	42.2721	1.66189	0.830943	+	0.556358i	$0.187802\pi$
$648$	12.5423	0.492709
$649$	0	0
$650$	11.4927	0.450782
$651$	−6.41883	−0.251574
$652$	−24.4241	−0.956523
$653$	16.6330	0.650898	0.325449	−	0.945560i	$-0.394485\pi$
$653$	16.6330	0.650898	0.325449	+	0.945560i	$0.394485\pi$
$654$	12.8043	0.500689
$655$	−16.6426	−0.650279
$656$	−8.11818	−0.316962
$657$	14.6327	0.570876
$658$	15.0488	0.586664
$659$	27.7195	1.07980	0.539899	−	0.841729i	$-0.318462\pi$
$659$	27.7195	1.07980	0.539899	+	0.841729i	$0.318462\pi$
$660$	0	0
$661$	−20.2302	−0.786865	−0.393433	−	0.919353i	$-0.628713\pi$
$661$	−20.2302	−0.786865	−0.393433	+	0.919353i	$0.628713\pi$
$662$	−44.1174	−1.71467
$663$	31.7645	1.23363
$664$	−16.5156	−0.640928
$665$	−3.10189	−0.120286
$666$	32.7900	1.27058
$667$	0.570528	0.0220909
$668$	8.69365	0.336367
$669$	−53.9815	−2.08705
$670$	−18.9348	−0.731516
$671$	0	0
$672$	15.1485	0.584366
$673$	−28.1029	−1.08329	−0.541644	−	0.840608i	$-0.682198\pi$
$673$	−28.1029	−1.08329	−0.541644	+	0.840608i	$0.682198\pi$
$674$	−31.2022	−1.20186
$675$	−0.504265	−0.0194092
$676$	34.8716	1.34121
$677$	−0.590270	−0.0226859	−0.0113430	−	0.999936i	$-0.503611\pi$
$677$	−0.590270	−0.0226859	−0.0113430	+	0.999936i	$0.503611\pi$
$678$	−48.6594	−1.86875
$679$	−12.1107	−0.464766
$680$	−2.72087	−0.104341
$681$	−32.6970	−1.25295
$682$	0	0
$683$	−7.81455	−0.299015	−0.149508	−	0.988761i	$-0.547769\pi$
$683$	−7.81455	−0.299015	−0.149508	+	0.988761i	$0.547769\pi$
$684$	11.0545	0.422681
$685$	−4.64303	−0.177401
$686$	−1.81029	−0.0691172
$687$	10.0527	0.383533
$688$	35.7660	1.36357
$689$	−28.4423	−1.08356
$690$	0.531782	0.0202446
$691$	22.2992	0.848303	0.424151	−	0.905591i	$-0.360572\pi$
$691$	22.2992	0.848303	0.424151	+	0.905591i	$0.360572\pi$
$692$	2.34618	0.0891885
$693$	0	0
$694$	−18.4591	−0.700699
$695$	22.1077	0.838594
$696$	−14.7163	−0.557822
$697$	3.42865	0.129870
$698$	−44.0401	−1.66694
$699$	−46.2915	−1.75090
$700$	−1.27715	−0.0482717
$701$	−1.61931	−0.0611604	−0.0305802	−	0.999532i	$-0.509736\pi$
$701$	−1.61931	−0.0611604	−0.0305802	+	0.999532i	$0.509736\pi$
$702$	−5.79538	−0.218732
$703$	20.1347	0.759396
$704$	0	0
$705$	−20.0037	−0.753383
$706$	−29.7492	−1.11962
$707$	−4.95110	−0.186205
$708$	15.3778	0.577934
$709$	25.6577	0.963595	0.481798	−	0.876282i	$-0.339984\pi$
$709$	25.6577	0.963595	0.481798	+	0.876282i	$0.339984\pi$
$710$	−24.6806	−0.926246
$711$	−19.7567	−0.740935
$712$	−7.97574	−0.298903
$713$	0.325634	0.0121951
$714$	−9.05765	−0.338974
$715$	0	0
$716$	15.7639	0.589124
$717$	10.8983	0.407004
$718$	−16.7741	−0.626005
$719$	−21.0932	−0.786644	−0.393322	−	0.919401i	$-0.628674\pi$
$719$	−21.0932	−0.786644	−0.393322	+	0.919401i	$0.628674\pi$
$720$	−13.7379	−0.511980
$721$	6.20927	0.231245
$722$	−16.9774	−0.631834
$723$	68.4704	2.54644
$724$	−33.9899	−1.26323
$725$	4.67356	0.173572
$726$	0	0
$727$	33.4904	1.24209	0.621045	−	0.783775i	$-0.286708\pi$
$727$	33.4904	1.24209	0.621045	+	0.783775i	$0.286708\pi$
$728$	8.30753	0.307898
$729$	−23.1054	−0.855757
$730$	9.49291	0.351348
$731$	−15.1055	−0.558698
$732$	44.4025	1.64116
$733$	15.4755	0.571601	0.285800	−	0.958289i	$-0.407741\pi$
$733$	15.4755	0.571601	0.285800	+	0.958289i	$0.407741\pi$
$734$	−36.3746	−1.34261
$735$	2.40633	0.0887590
$736$	−0.768499	−0.0283272
$737$	0	0
$738$	8.32978	0.306623
$739$	−1.63149	−0.0600154	−0.0300077	−	0.999550i	$-0.509553\pi$
$739$	−1.63149	−0.0600154	−0.0300077	+	0.999550i	$0.509553\pi$
$740$	8.29013	0.304751
$741$	47.3868	1.74080
$742$	8.11030	0.297738
$743$	−28.9222	−1.06105	−0.530527	−	0.847668i	$-0.678006\pi$
$743$	−28.9222	−1.06105	−0.530527	+	0.847668i	$0.678006\pi$
$744$	−8.39949	−0.307940
$745$	−22.3934	−0.820430
$746$	26.8243	0.982106
$747$	35.2184	1.28857
$748$	0	0
$749$	3.18496	0.116376
$750$	4.35616	0.159065
$751$	−0.839533	−0.0306350	−0.0153175	−	0.999883i	$-0.504876\pi$
$751$	−0.839533	−0.0306350	−0.0153175	+	0.999883i	$0.504876\pi$
$752$	40.9261	1.49242
$753$	2.06211	0.0751474
$754$	53.7119	1.95607
$755$	3.78150	0.137623
$756$	0.644021	0.0234228
$757$	−11.9540	−0.434474	−0.217237	−	0.976119i	$-0.569705\pi$
$757$	−11.9540	−0.434474	−0.217237	+	0.976119i	$0.569705\pi$
$758$	50.3767	1.82976
$759$	0	0
$760$	−4.05904	−0.147237
$761$	−28.5362	−1.03444	−0.517219	−	0.855853i	$-0.673033\pi$
$761$	−28.5362	−1.03444	−0.517219	+	0.855853i	$0.673033\pi$
$762$	−76.9970	−2.78931
$763$	−2.93936	−0.106412
$764$	13.7162	0.496233
$765$	5.80209	0.209775
$766$	1.34383	0.0485544
$767$	31.7667	1.14703
$768$	50.0832	1.80722
$769$	−30.7242	−1.10794	−0.553972	−	0.832535i	$-0.686889\pi$
$769$	−30.7242	−1.10794	−0.553972	+	0.832535i	$0.686889\pi$
$770$	0	0
$771$	12.5159	0.450749
$772$	10.0005	0.359926
$773$	−12.2591	−0.440929	−0.220465	−	0.975395i	$-0.570757\pi$
$773$	−12.2591	−0.440929	−0.220465	+	0.975395i	$0.570757\pi$
$774$	−36.6983	−1.31909
$775$	2.66747	0.0958185
$776$	−15.8477	−0.568899
$777$	−15.6198	−0.560357
$778$	29.1603	1.04545
$779$	5.11492	0.183261
$780$	19.5107	0.698595
$781$	0	0
$782$	0.459504	0.0164318
$783$	−2.35671	−0.0842219
$784$	−4.92319	−0.175828
$785$	9.19055	0.328025
$786$	−72.4977	−2.58591
$787$	45.3109	1.61516	0.807579	−	0.589759i	$-0.200777\pi$
$787$	45.3109	1.61516	0.807579	+	0.589759i	$0.200777\pi$
$788$	8.85675	0.315508
$789$	−41.1262	−1.46413
$790$	−12.8171	−0.456012
$791$	11.1702	0.397168
$792$	0	0
$793$	91.7244	3.25723
$794$	41.7229	1.48069
$795$	−10.7806	−0.382350
$796$	−14.6395	−0.518885
$797$	29.2762	1.03702	0.518508	−	0.855073i	$-0.326488\pi$
$797$	29.2762	1.03702	0.518508	+	0.855073i	$0.326488\pi$
$798$	−13.5123	−0.478331
$799$	−17.2849	−0.611494
$800$	−6.29526	−0.222571
$801$	17.0078	0.600940
$802$	−21.0591	−0.743624
$803$	0	0
$804$	−32.1448	−1.13366
$805$	−0.122076	−0.00430261
$806$	30.6566	1.07983
$807$	−42.9940	−1.51346
$808$	−6.47886	−0.227926
$809$	56.6925	1.99320	0.996601	−	0.0823766i	$-0.0262510\pi$
$809$	56.6925	1.99320	0.996601	+	0.0823766i	$0.0262510\pi$
$810$	−17.3512	−0.609659
$811$	3.01900	0.106012	0.0530058	−	0.998594i	$-0.483120\pi$
$811$	3.01900	0.106012	0.0530058	+	0.998594i	$0.483120\pi$
$812$	−5.96883	−0.209465
$813$	38.0718	1.33524
$814$	0	0
$815$	−19.1239	−0.669883
$816$	−24.6328	−0.862321
$817$	−22.5346	−0.788387
$818$	32.1374	1.12366
$819$	−17.7153	−0.619022
$820$	2.10598	0.0735440
$821$	18.2397	0.636568	0.318284	−	0.947995i	$-0.396893\pi$
$821$	18.2397	0.636568	0.318284	+	0.947995i	$0.396893\pi$
$822$	−20.2258	−0.705455
$823$	19.0710	0.664773	0.332386	−	0.943143i	$-0.392146\pi$
$823$	19.0710	0.664773	0.332386	+	0.943143i	$0.392146\pi$
$824$	8.12525	0.283057
$825$	0	0
$826$	−9.05827	−0.315177
$827$	−20.9934	−0.730013	−0.365006	−	0.931005i	$-0.618933\pi$
$827$	−20.9934	−0.730013	−0.365006	+	0.931005i	$0.618933\pi$
$828$	0.435055	0.0151192
$829$	−11.1353	−0.386744	−0.193372	−	0.981125i	$-0.561942\pi$
$829$	−11.1353	−0.386744	−0.193372	+	0.981125i	$0.561942\pi$
$830$	22.8478	0.793059
$831$	19.7899	0.686503
$832$	−9.83943	−0.341121
$833$	2.07927	0.0720425
$834$	96.3049	3.33476
$835$	6.80707	0.235568
$836$	0	0
$837$	−1.34511	−0.0464939
$838$	−2.60795	−0.0900901
$839$	22.5684	0.779148	0.389574	−	0.920995i	$-0.372622\pi$
$839$	22.5684	0.779148	0.389574	+	0.920995i	$0.372622\pi$
$840$	3.14885	0.108646
$841$	−7.15787	−0.246823
$842$	2.89825	0.0998801
$843$	−76.1446	−2.62256
$844$	−20.0529	−0.690250
$845$	27.3042	0.939294
$846$	−41.9929	−1.44374
$847$	0	0
$848$	22.0564	0.757421
$849$	−47.3962	−1.62663
$850$	3.76409	0.129107
$851$	0.792408	0.0271634
$852$	−41.8991	−1.43544
$853$	33.7762	1.15648	0.578238	−	0.815868i	$-0.303741\pi$
$853$	33.7762	1.15648	0.578238	+	0.815868i	$0.303741\pi$
$854$	−26.1552	−0.895012
$855$	8.65564	0.296017
$856$	4.16774	0.142451
$857$	−20.1698	−0.688989	−0.344494	−	0.938788i	$-0.611950\pi$
$857$	−20.1698	−0.688989	−0.344494	+	0.938788i	$0.611950\pi$
$858$	0	0
$859$	2.76965	0.0944992	0.0472496	−	0.998883i	$-0.484954\pi$
$859$	2.76965	0.0944992	0.0472496	+	0.998883i	$0.484954\pi$
$860$	−9.27825	−0.316386
$861$	−3.96797	−0.135228
$862$	−1.24639	−0.0424523
$863$	−0.619281	−0.0210806	−0.0105403	−	0.999944i	$-0.503355\pi$
$863$	−0.619281	−0.0210806	−0.0105403	+	0.999944i	$0.503355\pi$
$864$	3.17448	0.107998
$865$	1.83705	0.0624615
$866$	20.1449	0.684551
$867$	−30.5042	−1.03598
$868$	−3.40676	−0.115633
$869$	0	0
$870$	20.3588	0.690227
$871$	−66.4031	−2.24998
$872$	−3.84636	−0.130254
$873$	33.7942	1.14376
$874$	0.685494	0.0231872
$875$	−1.00000	−0.0338062
$876$	16.1157	0.544499
$877$	−37.7474	−1.27464	−0.637320	−	0.770599i	$-0.719957\pi$
$877$	−37.7474	−1.27464	−0.637320	+	0.770599i	$0.719957\pi$
$878$	−24.2444	−0.818210
$879$	−74.1273	−2.50025
$880$	0	0
$881$	−17.1719	−0.578538	−0.289269	−	0.957248i	$-0.593412\pi$
$881$	−17.1719	−0.578538	−0.289269	+	0.957248i	$0.593412\pi$
$882$	5.05151	0.170093
$883$	0.243161	0.00818301	0.00409150	−	0.999992i	$-0.498698\pi$
$883$	0.243161	0.00818301	0.00409150	+	0.999992i	$0.498698\pi$
$884$	16.8589	0.567025
$885$	12.0407	0.404745
$886$	−43.1918	−1.45106
$887$	36.7485	1.23389	0.616946	−	0.787005i	$-0.288370\pi$
$887$	36.7485	1.23389	0.616946	+	0.787005i	$0.288370\pi$
$888$	−20.4396	−0.685908
$889$	17.6754	0.592815
$890$	11.0337	0.369851
$891$	0	0
$892$	−28.6504	−0.959287
$893$	−25.7858	−0.862889
$894$	−97.5492	−3.26253
$895$	12.3430	0.412582
$896$	−9.78481	−0.326888
$897$	1.86492	0.0622679
$898$	0.677768	0.0226174
$899$	12.4666	0.415784
$900$	3.56381	0.118794
$901$	−9.31537	−0.310340
$902$	0	0
$903$	17.4816	0.581750
$904$	14.6170	0.486156
$905$	−26.6139	−0.884676
$906$	16.4728	0.547273
$907$	24.7745	0.822625	0.411312	−	0.911494i	$-0.365071\pi$
$907$	24.7745	0.822625	0.411312	+	0.911494i	$0.365071\pi$
$908$	−17.3538	−0.575906
$909$	13.8158	0.458240
$910$	−11.4927	−0.380980
$911$	50.2534	1.66497	0.832485	−	0.554047i	$-0.186917\pi$
$911$	50.2534	1.66497	0.832485	+	0.554047i	$0.186917\pi$
$912$	−36.7476	−1.21683
$913$	0	0
$914$	−46.1021	−1.52492
$915$	34.7668	1.14936
$916$	5.33539	0.176286
$917$	16.6426	0.549586
$918$	−1.89810	−0.0626465
$919$	24.8305	0.819081	0.409541	−	0.912292i	$-0.365689\pi$
$919$	24.8305	0.819081	0.409541	+	0.912292i	$0.365689\pi$
$920$	−0.159745	−0.00526662
$921$	43.5424	1.43477
$922$	−26.0795	−0.858883
$923$	−86.5531	−2.84893
$924$	0	0
$925$	6.49112	0.213427
$926$	15.6520	0.514356
$927$	−17.3266	−0.569080
$928$	−29.4213	−0.965800
$929$	−10.1544	−0.333156	−0.166578	−	0.986028i	$-0.553272\pi$
$929$	−10.1544	−0.333156	−0.166578	+	0.986028i	$0.553272\pi$
$930$	11.6199	0.381033
$931$	3.10189	0.101660
$932$	−24.5690	−0.804783
$933$	−72.9613	−2.38865
$934$	−9.03005	−0.295472
$935$	0	0
$936$	−23.1817	−0.757717
$937$	−8.92555	−0.291585	−0.145792	−	0.989315i	$-0.546573\pi$
$937$	−8.92555	−0.291585	−0.145792	+	0.989315i	$0.546573\pi$
$938$	18.9348	0.618244
$939$	54.9355	1.79275
$940$	−10.6169	−0.346284
$941$	31.3159	1.02087	0.510434	−	0.859917i	$-0.329485\pi$
$941$	31.3159	1.02087	0.510434	+	0.859917i	$0.329485\pi$
$942$	40.0355	1.30443
$943$	0.201299	0.00655520
$944$	−24.6345	−0.801784
$945$	0.504265	0.0164037
$946$	0	0
$947$	−24.8196	−0.806530	−0.403265	−	0.915083i	$-0.632125\pi$
$947$	−24.8196	−0.806530	−0.403265	+	0.915083i	$0.632125\pi$
$948$	−21.7590	−0.706700
$949$	33.2910	1.08067
$950$	5.61532	0.182185
$951$	40.3408	1.30814
$952$	2.72087	0.0881840
$953$	−3.61264	−0.117025	−0.0585124	−	0.998287i	$-0.518636\pi$
$953$	−3.61264	−0.117025	−0.0585124	+	0.998287i	$0.518636\pi$
$954$	−22.6313	−0.732716
$955$	10.7397	0.347527
$956$	5.78421	0.187075
$957$	0	0
$958$	52.9375	1.71033
$959$	4.64303	0.149931
$960$	−3.72950	−0.120369
$961$	−23.8846	−0.770470
$962$	74.6007	2.40522
$963$	−8.88745	−0.286394
$964$	36.3403	1.17044
$965$	7.83033	0.252067
$966$	−0.531782	−0.0171098
$967$	19.0005	0.611016	0.305508	−	0.952190i	$-0.401174\pi$
$967$	19.0005	0.611016	0.305508	+	0.952190i	$0.401174\pi$
$968$	0	0
$969$	15.5201	0.498576
$970$	21.9239	0.703933
$971$	24.2957	0.779686	0.389843	−	0.920881i	$-0.372529\pi$
$971$	24.2957	0.779686	0.389843	+	0.920881i	$0.372529\pi$
$972$	−27.5243	−0.882841
$973$	−22.1077	−0.708741
$974$	18.2982	0.586312
$975$	15.2768	0.489248
$976$	−71.1305	−2.27683
$977$	7.98325	0.255407	0.127703	−	0.991812i	$-0.459239\pi$
$977$	7.98325	0.255407	0.127703	+	0.991812i	$0.459239\pi$
$978$	−83.3070	−2.66386
$979$	0	0
$980$	1.27715	0.0407970
$981$	8.20213	0.261874
$982$	53.9199	1.72065
$983$	1.30228	0.0415362	0.0207681	−	0.999784i	$-0.493389\pi$
$983$	1.30228	0.0415362	0.0207681	+	0.999784i	$0.493389\pi$
$984$	−5.19236	−0.165526
$985$	6.93478	0.220960
$986$	17.5917	0.560233
$987$	20.0037	0.636725
$988$	25.1503	0.800138
$989$	−0.886858	−0.0282004
$990$	0	0
$991$	−2.03529	−0.0646532	−0.0323266	−	0.999477i	$-0.510292\pi$
$991$	−2.03529	−0.0646532	−0.0323266	+	0.999477i	$0.510292\pi$
$992$	−16.7924	−0.533161
$993$	−58.6433	−1.86099
$994$	24.6806	0.782820
$995$	−11.4627	−0.363391
$996$	38.7877	1.22904
$997$	−11.7933	−0.373499	−0.186750	−	0.982408i	$-0.559795\pi$
$997$	−11.7933	−0.373499	−0.186750	+	0.982408i	$0.559795\pi$
$998$	−35.1344	−1.11216
$999$	−3.27324	−0.103561

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.bk.1.7	yes	10
11.10	odd	2		4235.2.a.bi.1.4	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4235.2.a.bi.1.4	✓	10	11.10	odd	2
4235.2.a.bk.1.7	yes	10	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)

\(f(q)\)	\(=\)	\(q+1.81029 q^{2} +2.40633 q^{3} +1.27715 q^{4} +1.00000 q^{5} +4.35616 q^{6} -1.00000 q^{7} -1.30857 q^{8} +2.79044 q^{9} +O(q^{10})\)	\(q+1.81029 q^{2} +2.40633 q^{3} +1.27715 q^{4} +1.00000 q^{5} +4.35616 q^{6} -1.00000 q^{7} -1.30857 q^{8} +2.79044 q^{9} +1.81029 q^{10} +3.07325 q^{12} +6.34856 q^{13} -1.81029 q^{14} +2.40633 q^{15} -4.92319 q^{16} +2.07927 q^{17} +5.05151 q^{18} +3.10189 q^{19} +1.27715 q^{20} -2.40633 q^{21} +0.122076 q^{23} -3.14885 q^{24} +1.00000 q^{25} +11.4927 q^{26} -0.504265 q^{27} -1.27715 q^{28} +4.67356 q^{29} +4.35616 q^{30} +2.66747 q^{31} -6.29526 q^{32} +3.76409 q^{34} -1.00000 q^{35} +3.56381 q^{36} +6.49112 q^{37} +5.61532 q^{38} +15.2768 q^{39} -1.30857 q^{40} +1.64897 q^{41} -4.35616 q^{42} -7.26481 q^{43} +2.79044 q^{45} +0.220993 q^{46} -8.31293 q^{47} -11.8468 q^{48} +1.00000 q^{49} +1.81029 q^{50} +5.00342 q^{51} +8.10806 q^{52} -4.48011 q^{53} -0.912865 q^{54} +1.30857 q^{56} +7.46418 q^{57} +8.46049 q^{58} +5.00377 q^{59} +3.07325 q^{60} +14.4481 q^{61} +4.82890 q^{62} -2.79044 q^{63} -1.54987 q^{64} +6.34856 q^{65} -10.4595 q^{67} +2.65554 q^{68} +0.293755 q^{69} -1.81029 q^{70} -13.6335 q^{71} -3.65149 q^{72} +5.24386 q^{73} +11.7508 q^{74} +2.40633 q^{75} +3.96157 q^{76} +27.6554 q^{78} -7.08014 q^{79} -4.92319 q^{80} -9.58476 q^{81} +2.98511 q^{82} +12.6211 q^{83} -3.07325 q^{84} +2.07927 q^{85} -13.1514 q^{86} +11.2461 q^{87} +6.09501 q^{89} +5.05151 q^{90} -6.34856 q^{91} +0.155909 q^{92} +6.41883 q^{93} -15.0488 q^{94} +3.10189 q^{95} -15.1485 q^{96} +12.1107 q^{97} +1.81029 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} - 4 q^{3} + 12 q^{4} + 10 q^{5} + 8 q^{6} - 10 q^{7} + 6 q^{8} + 14 q^{9}+O(q^{10}) \) 10 * q + 2 * q^2 - 4 * q^3 + 12 * q^4 + 10 * q^5 + 8 * q^6 - 10 * q^7 + 6 * q^8 + 14 * q^9	\( 10 q + 2 q^{2} - 4 q^{3} + 12 q^{4} + 10 q^{5} + 8 q^{6} - 10 q^{7} + 6 q^{8} + 14 q^{9} + 2 q^{10} - 4 q^{12} + 18 q^{13} - 2 q^{14} - 4 q^{15} + 4 q^{16} + 4 q^{17} + 12 q^{18} + 14 q^{19} + 12 q^{20} + 4 q^{21} - 4 q^{23} + 46 q^{24} + 10 q^{25} + 2 q^{26} - 34 q^{27} - 12 q^{28} + 36 q^{29} + 8 q^{30} - 18 q^{31} + 4 q^{32} - 32 q^{34} - 10 q^{35} + 22 q^{36} + 4 q^{37} + 18 q^{38} + 6 q^{40} + 38 q^{41} - 8 q^{42} + 6 q^{43} + 14 q^{45} + 28 q^{46} - 18 q^{47} + 16 q^{48} + 10 q^{49} + 2 q^{50} - 4 q^{51} + 26 q^{52} - 26 q^{53} + 2 q^{54} - 6 q^{56} + 22 q^{57} + 10 q^{58} - 14 q^{59} - 4 q^{60} + 60 q^{61} + 22 q^{62} - 14 q^{63} + 18 q^{65} - 10 q^{67} + 2 q^{68} - 8 q^{69} - 2 q^{70} - 54 q^{72} + 18 q^{73} - 20 q^{74} - 4 q^{75} + 38 q^{76} + 40 q^{78} + 40 q^{79} + 4 q^{80} + 18 q^{81} - 36 q^{82} + 2 q^{83} + 4 q^{84} + 4 q^{85} + 42 q^{86} - 32 q^{87} + 2 q^{89} + 12 q^{90} - 18 q^{91} - 64 q^{92} + 26 q^{93} - 68 q^{94} + 14 q^{95} + 28 q^{96} + 8 q^{97} + 2 q^{98}+O(q^{100}) \) 10 * q + 2 * q^2 - 4 * q^3 + 12 * q^4 + 10 * q^5 + 8 * q^6 - 10 * q^7 + 6 * q^8 + 14 * q^9 + 2 * q^10 - 4 * q^12 + 18 * q^13 - 2 * q^14 - 4 * q^15 + 4 * q^16 + 4 * q^17 + 12 * q^18 + 14 * q^19 + 12 * q^20 + 4 * q^21 - 4 * q^23 + 46 * q^24 + 10 * q^25 + 2 * q^26 - 34 * q^27 - 12 * q^28 + 36 * q^29 + 8 * q^30 - 18 * q^31 + 4 * q^32 - 32 * q^34 - 10 * q^35 + 22 * q^36 + 4 * q^37 + 18 * q^38 + 6 * q^40 + 38 * q^41 - 8 * q^42 + 6 * q^43 + 14 * q^45 + 28 * q^46 - 18 * q^47 + 16 * q^48 + 10 * q^49 + 2 * q^50 - 4 * q^51 + 26 * q^52 - 26 * q^53 + 2 * q^54 - 6 * q^56 + 22 * q^57 + 10 * q^58 - 14 * q^59 - 4 * q^60 + 60 * q^61 + 22 * q^62 - 14 * q^63 + 18 * q^65 - 10 * q^67 + 2 * q^68 - 8 * q^69 - 2 * q^70 - 54 * q^72 + 18 * q^73 - 20 * q^74 - 4 * q^75 + 38 * q^76 + 40 * q^78 + 40 * q^79 + 4 * q^80 + 18 * q^81 - 36 * q^82 + 2 * q^83 + 4 * q^84 + 4 * q^85 + 42 * q^86 - 32 * q^87 + 2 * q^89 + 12 * q^90 - 18 * q^91 - 64 * q^92 + 26 * q^93 - 68 * q^94 + 14 * q^95 + 28 * q^96 + 8 * q^97 + 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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