LMFDB - Embedded newform 4235.2.a.bn.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4235.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			1.10
Root			$1.36811$ 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)

$f(q)$	$=$	$q+1.36811 q^{2} +3.24763 q^{3} -0.128288 q^{4} -1.00000 q^{5} +4.44310 q^{6} -1.00000 q^{7} -2.91172 q^{8} +7.54712 q^{9} +O(q^{10})$	\(q+1.36811 q^{2} +3.24763 q^{3} -0.128288 q^{4} -1.00000 q^{5} +4.44310 q^{6} -1.00000 q^{7} -2.91172 q^{8} +7.54712 q^{9} -1.36811 q^{10} -0.416632 q^{12} +1.43605 q^{13} -1.36811 q^{14} -3.24763 q^{15} -3.72697 q^{16} +6.36873 q^{17} +10.3253 q^{18} -6.02296 q^{19} +0.128288 q^{20} -3.24763 q^{21} +7.11822 q^{23} -9.45620 q^{24} +1.00000 q^{25} +1.96467 q^{26} +14.7674 q^{27} +0.128288 q^{28} +2.65944 q^{29} -4.44310 q^{30} -1.69505 q^{31} +0.724562 q^{32} +8.71309 q^{34} +1.00000 q^{35} -0.968204 q^{36} +10.0990 q^{37} -8.24005 q^{38} +4.66376 q^{39} +2.91172 q^{40} +2.69234 q^{41} -4.44310 q^{42} +3.80445 q^{43} -7.54712 q^{45} +9.73847 q^{46} -3.73296 q^{47} -12.1038 q^{48} +1.00000 q^{49} +1.36811 q^{50} +20.6833 q^{51} -0.184228 q^{52} +8.24012 q^{53} +20.2033 q^{54} +2.91172 q^{56} -19.5604 q^{57} +3.63839 q^{58} +11.6150 q^{59} +0.416632 q^{60} +3.60327 q^{61} -2.31901 q^{62} -7.54712 q^{63} +8.44521 q^{64} -1.43605 q^{65} -6.52368 q^{67} -0.817031 q^{68} +23.1173 q^{69} +1.36811 q^{70} +2.12829 q^{71} -21.9751 q^{72} -12.3975 q^{73} +13.8164 q^{74} +3.24763 q^{75} +0.772673 q^{76} +6.38051 q^{78} -3.21655 q^{79} +3.72697 q^{80} +25.3176 q^{81} +3.68340 q^{82} -4.90629 q^{83} +0.416632 q^{84} -6.36873 q^{85} +5.20489 q^{86} +8.63688 q^{87} -11.4838 q^{89} -10.3253 q^{90} -1.43605 q^{91} -0.913181 q^{92} -5.50490 q^{93} -5.10708 q^{94} +6.02296 q^{95} +2.35311 q^{96} +4.10287 q^{97} +1.36811 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + q^{2} + 5 q^{3} + 21 q^{4} - 14 q^{5} - q^{6} - 14 q^{7} + 3 q^{8} + 17 q^{9}+O(q^{10}) $ 14 * q + q^2 + 5 * q^3 + 21 * q^4 - 14 * q^5 - q^6 - 14 * q^7 + 3 * q^8 + 17 * q^9	$ 14 q + q^{2} + 5 q^{3} + 21 q^{4} - 14 q^{5} - q^{6} - 14 q^{7} + 3 q^{8} + 17 q^{9} - q^{10} + 15 q^{12} - 10 q^{13} - q^{14} - 5 q^{15} + 31 q^{16} - 11 q^{17} + 21 q^{18} - 21 q^{19} - 21 q^{20} - 5 q^{21} + 8 q^{23} - 22 q^{24} + 14 q^{25} - 18 q^{26} + 26 q^{27} - 21 q^{28} + 4 q^{29} + q^{30} + 6 q^{31} + 42 q^{32} + 16 q^{34} + 14 q^{35} + 28 q^{36} + 48 q^{37} + 35 q^{38} - 6 q^{39} - 3 q^{40} - 13 q^{41} + q^{42} - 17 q^{45} + 31 q^{46} + 11 q^{47} + 59 q^{48} + 14 q^{49} + q^{50} + 33 q^{51} - 52 q^{52} + 31 q^{53} + 57 q^{54} - 3 q^{56} + 4 q^{57} + 52 q^{58} - 4 q^{59} - 15 q^{60} - 17 q^{61} + 27 q^{62} - 17 q^{63} + 43 q^{64} + 10 q^{65} + 45 q^{67} - 14 q^{68} + 20 q^{69} + q^{70} - 6 q^{71} + 14 q^{72} - 11 q^{73} + 33 q^{74} + 5 q^{75} + 5 q^{76} + 52 q^{78} - 30 q^{79} - 31 q^{80} - 6 q^{81} + 26 q^{82} - 23 q^{83} - 15 q^{84} + 11 q^{85} - 23 q^{86} - 23 q^{87} - 15 q^{89} - 21 q^{90} + 10 q^{91} + 44 q^{92} + 29 q^{93} - 49 q^{94} + 21 q^{95} + 52 q^{96} + 44 q^{97} + q^{98}+O(q^{100}) $ 14 * q + q^2 + 5 * q^3 + 21 * q^4 - 14 * q^5 - q^6 - 14 * q^7 + 3 * q^8 + 17 * q^9 - q^10 + 15 * q^12 - 10 * q^13 - q^14 - 5 * q^15 + 31 * q^16 - 11 * q^17 + 21 * q^18 - 21 * q^19 - 21 * q^20 - 5 * q^21 + 8 * q^23 - 22 * q^24 + 14 * q^25 - 18 * q^26 + 26 * q^27 - 21 * q^28 + 4 * q^29 + q^30 + 6 * q^31 + 42 * q^32 + 16 * q^34 + 14 * q^35 + 28 * q^36 + 48 * q^37 + 35 * q^38 - 6 * q^39 - 3 * q^40 - 13 * q^41 + q^42 - 17 * q^45 + 31 * q^46 + 11 * q^47 + 59 * q^48 + 14 * q^49 + q^50 + 33 * q^51 - 52 * q^52 + 31 * q^53 + 57 * q^54 - 3 * q^56 + 4 * q^57 + 52 * q^58 - 4 * q^59 - 15 * q^60 - 17 * q^61 + 27 * q^62 - 17 * q^63 + 43 * q^64 + 10 * q^65 + 45 * q^67 - 14 * q^68 + 20 * q^69 + q^70 - 6 * q^71 + 14 * q^72 - 11 * q^73 + 33 * q^74 + 5 * q^75 + 5 * q^76 + 52 * q^78 - 30 * q^79 - 31 * q^80 - 6 * q^81 + 26 * q^82 - 23 * q^83 - 15 * q^84 + 11 * q^85 - 23 * q^86 - 23 * q^87 - 15 * q^89 - 21 * q^90 + 10 * q^91 + 44 * q^92 + 29 * q^93 - 49 * q^94 + 21 * q^95 + 52 * q^96 + 44 * q^97 + q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.36811	0.967397	0.483698	−	0.875235i	$-0.339293\pi$
$2$	1.36811	0.967397	0.483698	+	0.875235i	$0.339293\pi$
$3$	3.24763	1.87502	0.937511	−	0.347956i	$-0.113124\pi$
$3$	3.24763	1.87502	0.937511	+	0.347956i	$0.113124\pi$
$4$	−0.128288	−0.0641440
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	4.44310	1.81389
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.91172	−1.02945
$9$	7.54712	2.51571
$10$	−1.36811	−0.432633
$11$	0	0
$11$	0	0
$12$	−0.416632	−0.120271
$13$	1.43605	0.398288	0.199144	−	0.979970i	$-0.436184\pi$
$13$	1.43605	0.398288	0.199144	+	0.979970i	$0.436184\pi$
$14$	−1.36811	−0.365642
$15$	−3.24763	−0.838535
$16$	−3.72697	−0.931742
$17$	6.36873	1.54464	0.772321	−	0.635232i	$-0.219095\pi$
$17$	6.36873	1.54464	0.772321	+	0.635232i	$0.219095\pi$
$18$	10.3253	2.43369
$19$	−6.02296	−1.38176	−0.690881	−	0.722968i	$-0.742777\pi$
$19$	−6.02296	−1.38176	−0.690881	+	0.722968i	$0.742777\pi$
$20$	0.128288	0.0286861
$21$	−3.24763	−0.708692
$22$	0	0
$23$	7.11822	1.48425	0.742125	−	0.670261i	$-0.233818\pi$
$23$	7.11822	1.48425	0.742125	+	0.670261i	$0.233818\pi$
$24$	−9.45620	−1.93024
$25$	1.00000	0.200000
$26$	1.96467	0.385303
$27$	14.7674	2.84198
$28$	0.128288	0.0242441
$29$	2.65944	0.493846	0.246923	−	0.969035i	$-0.420581\pi$
$29$	2.65944	0.493846	0.246923	+	0.969035i	$0.420581\pi$
$30$	−4.44310	−0.811196
$31$	−1.69505	−0.304440	−0.152220	−	0.988347i	$-0.548642\pi$
$31$	−1.69505	−0.304440	−0.152220	+	0.988347i	$0.548642\pi$
$32$	0.724562	0.128086
$33$	0	0
$34$	8.71309	1.49428
$35$	1.00000	0.169031
$36$	−0.968204	−0.161367
$37$	10.0990	1.66026	0.830130	−	0.557570i	$-0.188266\pi$
$37$	10.0990	1.66026	0.830130	+	0.557570i	$0.188266\pi$
$38$	−8.24005	−1.33671
$39$	4.66376	0.746799
$40$	2.91172	0.460384
$41$	2.69234	0.420473	0.210236	−	0.977651i	$-0.432577\pi$
$41$	2.69234	0.420473	0.210236	+	0.977651i	$0.432577\pi$
$42$	−4.44310	−0.685586
$43$	3.80445	0.580174	0.290087	−	0.957000i	$-0.406316\pi$
$43$	3.80445	0.580174	0.290087	+	0.957000i	$0.406316\pi$
$44$	0	0
$45$	−7.54712	−1.12506
$46$	9.73847	1.43586
$47$	−3.73296	−0.544508	−0.272254	−	0.962225i	$-0.587769\pi$
$47$	−3.73296	−0.544508	−0.272254	+	0.962225i	$0.587769\pi$
$48$	−12.1038	−1.74704
$49$	1.00000	0.142857
$50$	1.36811	0.193479
$51$	20.6833	2.89624
$52$	−0.184228	−0.0255478
$53$	8.24012	1.13187	0.565934	−	0.824451i	$-0.308516\pi$
$53$	8.24012	1.13187	0.565934	+	0.824451i	$0.308516\pi$
$54$	20.2033	2.74932
$55$	0	0
$56$	2.91172	0.389095
$57$	−19.5604	−2.59083
$58$	3.63839	0.477744
$59$	11.6150	1.51215	0.756073	−	0.654487i	$-0.227115\pi$
$59$	11.6150	1.51215	0.756073	+	0.654487i	$0.227115\pi$
$60$	0.416632	0.0537870
$61$	3.60327	0.461351	0.230676	−	0.973031i	$-0.425906\pi$
$61$	3.60327	0.461351	0.230676	+	0.973031i	$0.425906\pi$
$62$	−2.31901	−0.294514
$63$	−7.54712	−0.950847
$64$	8.44521	1.05565
$65$	−1.43605	−0.178120
$66$	0	0
$67$	−6.52368	−0.796994	−0.398497	−	0.917170i	$-0.630468\pi$
$67$	−6.52368	−0.796994	−0.398497	+	0.917170i	$0.630468\pi$
$68$	−0.817031	−0.0990795
$69$	23.1173	2.78300
$70$	1.36811	0.163520
$71$	2.12829	0.252582	0.126291	−	0.991993i	$-0.459693\pi$
$71$	2.12829	0.252582	0.126291	+	0.991993i	$0.459693\pi$
$72$	−21.9751	−2.58979
$73$	−12.3975	−1.45102	−0.725509	−	0.688212i	$-0.758396\pi$
$73$	−12.3975	−1.45102	−0.725509	+	0.688212i	$0.758396\pi$
$74$	13.8164	1.60613
$75$	3.24763	0.375004
$76$	0.772673	0.0886317
$77$	0	0
$78$	6.38051	0.722451
$79$	−3.21655	−0.361890	−0.180945	−	0.983493i	$-0.557916\pi$
$79$	−3.21655	−0.361890	−0.180945	+	0.983493i	$0.557916\pi$
$80$	3.72697	0.416688
$81$	25.3176	2.81307
$82$	3.68340	0.406764
$83$	−4.90629	−0.538535	−0.269267	−	0.963065i	$-0.586782\pi$
$83$	−4.90629	−0.538535	−0.269267	+	0.963065i	$0.586782\pi$
$84$	0.416632	0.0454583
$85$	−6.36873	−0.690785
$86$	5.20489	0.561258
$87$	8.63688	0.925971
$88$	0	0
$89$	−11.4838	−1.21728	−0.608639	−	0.793447i	$-0.708284\pi$
$89$	−11.4838	−1.21728	−0.608639	+	0.793447i	$0.708284\pi$
$90$	−10.3253	−1.08838
$91$	−1.43605	−0.150539
$92$	−0.913181	−0.0952057
$93$	−5.50490	−0.570832
$94$	−5.10708	−0.526755
$95$	6.02296	0.617943
$96$	2.35311	0.240163
$97$	4.10287	0.416583	0.208291	−	0.978067i	$-0.433210\pi$
$97$	4.10287	0.416583	0.208291	+	0.978067i	$0.433210\pi$
$98$	1.36811	0.138200
$99$	0	0
$100$	−0.128288	−0.0128288
$101$	4.35775	0.433612	0.216806	−	0.976215i	$-0.430436\pi$
$101$	4.35775	0.433612	0.216806	+	0.976215i	$0.430436\pi$
$102$	28.2969	2.80181
$103$	−5.04313	−0.496914	−0.248457	−	0.968643i	$-0.579924\pi$
$103$	−5.04313	−0.496914	−0.248457	+	0.968643i	$0.579924\pi$
$104$	−4.18138	−0.410018
$105$	3.24763	0.316936
$106$	11.2734	1.09497
$107$	−5.19139	−0.501871	−0.250935	−	0.968004i	$-0.580738\pi$
$107$	−5.19139	−0.501871	−0.250935	+	0.968004i	$0.580738\pi$
$108$	−1.89448	−0.182296
$109$	−14.5475	−1.39340	−0.696698	−	0.717365i	$-0.745348\pi$
$109$	−14.5475	−1.39340	−0.696698	+	0.717365i	$0.745348\pi$
$110$	0	0
$111$	32.7977	3.11302
$112$	3.72697	0.352165
$113$	−7.99659	−0.752256	−0.376128	−	0.926568i	$-0.622745\pi$
$113$	−7.99659	−0.752256	−0.376128	+	0.926568i	$0.622745\pi$
$114$	−26.7606	−2.50636
$115$	−7.11822	−0.663777
$116$	−0.341174	−0.0316772
$117$	10.8380	1.00198
$118$	15.8906	1.46285
$119$	−6.36873	−0.583820
$120$	9.45620	0.863229
$121$	0	0
$122$	4.92965	0.446310
$123$	8.74373	0.788396
$124$	0.217455	0.0195280
$125$	−1.00000	−0.0894427
$126$	−10.3253	−0.919846
$127$	−4.41049	−0.391368	−0.195684	−	0.980667i	$-0.562693\pi$
$127$	−4.41049	−0.391368	−0.195684	+	0.980667i	$0.562693\pi$
$128$	10.1048	0.893148
$129$	12.3555	1.08784
$130$	−1.96467	−0.172313
$131$	0.657753	0.0574682	0.0287341	−	0.999587i	$-0.490852\pi$
$131$	0.657753	0.0574682	0.0287341	+	0.999587i	$0.490852\pi$
$132$	0	0
$133$	6.02296	0.522257
$134$	−8.92508	−0.771009
$135$	−14.7674	−1.27097
$136$	−18.5440	−1.59013
$137$	−2.37085	−0.202556	−0.101278	−	0.994858i	$-0.532293\pi$
$137$	−2.37085	−0.202556	−0.101278	+	0.994858i	$0.532293\pi$
$138$	31.6270	2.69227
$139$	−11.1745	−0.947807	−0.473903	−	0.880577i	$-0.657155\pi$
$139$	−11.1745	−0.947807	−0.473903	+	0.880577i	$0.657155\pi$
$140$	−0.128288	−0.0108423
$141$	−12.1233	−1.02096
$142$	2.91173	0.244347
$143$	0	0
$144$	−28.1279	−2.34399
$145$	−2.65944	−0.220854
$146$	−16.9611	−1.40371
$147$	3.24763	0.267860
$148$	−1.29558	−0.106496
$149$	10.4464	0.855804	0.427902	−	0.903825i	$-0.359253\pi$
$149$	10.4464	0.855804	0.427902	+	0.903825i	$0.359253\pi$
$150$	4.44310	0.362778
$151$	−18.9002	−1.53807	−0.769037	−	0.639204i	$-0.779264\pi$
$151$	−18.9002	−1.53807	−0.769037	+	0.639204i	$0.779264\pi$
$152$	17.5372	1.42245
$153$	48.0655	3.88587
$154$	0	0
$155$	1.69505	0.136150
$156$	−0.598304	−0.0479027
$157$	−13.2332	−1.05612	−0.528061	−	0.849206i	$-0.677081\pi$
$157$	−13.2332	−1.05612	−0.528061	+	0.849206i	$0.677081\pi$
$158$	−4.40058	−0.350092
$159$	26.7609	2.12228
$160$	−0.724562	−0.0572816
$161$	−7.11822	−0.560994
$162$	34.6372	2.72135
$163$	−14.1082	−1.10504	−0.552520	−	0.833500i	$-0.686334\pi$
$163$	−14.1082	−1.10504	−0.552520	+	0.833500i	$0.686334\pi$
$164$	−0.345395	−0.0269708
$165$	0	0
$166$	−6.71232	−0.520977
$167$	−14.7445	−1.14096	−0.570482	−	0.821310i	$-0.693244\pi$
$167$	−14.7445	−1.14096	−0.570482	+	0.821310i	$0.693244\pi$
$168$	9.45620	0.729562
$169$	−10.9378	−0.841366
$170$	−8.71309	−0.668263
$171$	−45.4560	−3.47611
$172$	−0.488065	−0.0372146
$173$	−13.8062	−1.04966	−0.524832	−	0.851206i	$-0.675872\pi$
$173$	−13.8062	−1.04966	−0.524832	+	0.851206i	$0.675872\pi$
$174$	11.8162	0.895781
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	37.7213	2.83531
$178$	−15.7110	−1.17759
$179$	−8.73736	−0.653061	−0.326530	−	0.945187i	$-0.605880\pi$
$179$	−8.73736	−0.653061	−0.326530	+	0.945187i	$0.605880\pi$
$180$	0.968204	0.0721657
$181$	20.7379	1.54143	0.770716	−	0.637178i	$-0.219899\pi$
$181$	20.7379	1.54143	0.770716	+	0.637178i	$0.219899\pi$
$182$	−1.96467	−0.145631
$183$	11.7021	0.865044
$184$	−20.7263	−1.52796
$185$	−10.0990	−0.742491
$186$	−7.53128	−0.552220
$187$	0	0
$188$	0.478894	0.0349269
$189$	−14.7674	−1.07417
$190$	8.24005	0.597796
$191$	18.7345	1.35558	0.677792	−	0.735254i	$-0.262937\pi$
$191$	18.7345	1.35558	0.677792	+	0.735254i	$0.262937\pi$
$192$	27.4269	1.97937
$193$	−3.24247	−0.233398	−0.116699	−	0.993167i	$-0.537231\pi$
$193$	−3.24247	−0.233398	−0.116699	+	0.993167i	$0.537231\pi$
$194$	5.61315	0.403001
$195$	−4.66376	−0.333979
$196$	−0.128288	−0.00916342
$197$	22.0459	1.57071	0.785354	−	0.619047i	$-0.212481\pi$
$197$	22.0459	1.57071	0.785354	+	0.619047i	$0.212481\pi$
$198$	0	0
$199$	10.0832	0.714778	0.357389	−	0.933956i	$-0.383667\pi$
$199$	10.0832	0.714778	0.357389	+	0.933956i	$0.383667\pi$
$200$	−2.91172	−0.205890
$201$	−21.1865	−1.49438
$202$	5.96186	0.419475
$203$	−2.65944	−0.186656
$204$	−2.65342	−0.185776
$205$	−2.69234	−0.188041
$206$	−6.89953	−0.480713
$207$	53.7220	3.73394
$208$	−5.35211	−0.371102
$209$	0	0
$210$	4.44310	0.306603
$211$	23.0149	1.58441	0.792207	−	0.610253i	$-0.208932\pi$
$211$	23.0149	1.58441	0.792207	+	0.610253i	$0.208932\pi$
$212$	−1.05711	−0.0726025
$213$	6.91192	0.473597
$214$	−7.10237	−0.485508
$215$	−3.80445	−0.259462
$216$	−42.9985	−2.92568
$217$	1.69505	0.115068
$218$	−19.9025	−1.34797
$219$	−40.2626	−2.72069
$220$	0	0
$221$	9.14580	0.615213
$222$	44.8707	3.01153
$223$	−7.94222	−0.531850	−0.265925	−	0.963994i	$-0.585677\pi$
$223$	−7.94222	−0.531850	−0.265925	+	0.963994i	$0.585677\pi$
$224$	−0.724562	−0.0484118
$225$	7.54712	0.503141
$226$	−10.9402	−0.727730
$227$	−15.3060	−1.01590	−0.507948	−	0.861388i	$-0.669596\pi$
$227$	−15.3060	−1.01590	−0.507948	+	0.861388i	$0.669596\pi$
$228$	2.50936	0.166186
$229$	3.03477	0.200543	0.100272	−	0.994960i	$-0.468029\pi$
$229$	3.03477	0.200543	0.100272	+	0.994960i	$0.468029\pi$
$230$	−9.73847	−0.642136
$231$	0	0
$232$	−7.74355	−0.508389
$233$	18.9165	1.23926	0.619631	−	0.784893i	$-0.287282\pi$
$233$	18.9165	1.23926	0.619631	+	0.784893i	$0.287282\pi$
$234$	14.8276	0.969308
$235$	3.73296	0.243511
$236$	−1.49007	−0.0969951
$237$	−10.4462	−0.678552
$238$	−8.71309	−0.564786
$239$	−3.13151	−0.202560	−0.101280	−	0.994858i	$-0.532294\pi$
$239$	−3.13151	−0.202560	−0.101280	+	0.994858i	$0.532294\pi$
$240$	12.1038	0.781298
$241$	0.274745	0.0176979	0.00884894	−	0.999961i	$-0.497183\pi$
$241$	0.274745	0.0176979	0.00884894	+	0.999961i	$0.497183\pi$
$242$	0	0
$243$	37.9203	2.43259
$244$	−0.462256	−0.0295929
$245$	−1.00000	−0.0638877
$246$	11.9623	0.762691
$247$	−8.64927	−0.550340
$248$	4.93551	0.313406
$249$	−15.9338	−1.00976
$250$	−1.36811	−0.0865266
$251$	21.7552	1.37318	0.686589	−	0.727046i	$-0.259107\pi$
$251$	21.7552	1.37318	0.686589	+	0.727046i	$0.259107\pi$
$252$	0.968204	0.0609911
$253$	0	0
$254$	−6.03402	−0.378608
$255$	−20.6833	−1.29524
$256$	−3.06597	−0.191623
$257$	8.16269	0.509175	0.254587	−	0.967050i	$-0.418060\pi$
$257$	8.16269	0.509175	0.254587	+	0.967050i	$0.418060\pi$
$258$	16.9036	1.05237
$259$	−10.0990	−0.627519
$260$	0.184228	0.0114253
$261$	20.0711	1.24237
$262$	0.899876	0.0555945
$263$	14.0620	0.867098	0.433549	−	0.901130i	$-0.357261\pi$
$263$	14.0620	0.867098	0.433549	+	0.901130i	$0.357261\pi$
$264$	0	0
$265$	−8.24012	−0.506187
$266$	8.24005	0.505230
$267$	−37.2951	−2.28242
$268$	0.836909	0.0511224
$269$	3.47526	0.211890	0.105945	−	0.994372i	$-0.466213\pi$
$269$	3.47526	0.211890	0.105945	+	0.994372i	$0.466213\pi$
$270$	−20.2033	−1.22953
$271$	10.2728	0.624026	0.312013	−	0.950078i	$-0.398997\pi$
$271$	10.2728	0.624026	0.312013	+	0.950078i	$0.398997\pi$
$272$	−23.7360	−1.43921
$273$	−4.66376	−0.282264
$274$	−3.24358	−0.195952
$275$	0	0
$276$	−2.96568	−0.178513
$277$	0.842797	0.0506388	0.0253194	−	0.999679i	$-0.491940\pi$
$277$	0.842797	0.0506388	0.0253194	+	0.999679i	$0.491940\pi$
$278$	−15.2879	−0.916905
$279$	−12.7927	−0.765881
$280$	−2.91172	−0.174009
$281$	15.9904	0.953910	0.476955	−	0.878928i	$-0.341741\pi$
$281$	15.9904	0.953910	0.476955	+	0.878928i	$0.341741\pi$
$282$	−16.5859	−0.987677
$283$	−14.3764	−0.854589	−0.427295	−	0.904112i	$-0.640533\pi$
$283$	−14.3764	−0.854589	−0.427295	+	0.904112i	$0.640533\pi$
$284$	−0.273034	−0.0162016
$285$	19.5604	1.15866
$286$	0	0
$287$	−2.69234	−0.158924
$288$	5.46835	0.322226
$289$	23.5607	1.38592
$290$	−3.63839	−0.213654
$291$	13.3246	0.781102
$292$	1.59045	0.0930741
$293$	8.59671	0.502225	0.251113	−	0.967958i	$-0.419204\pi$
$293$	8.59671	0.502225	0.251113	+	0.967958i	$0.419204\pi$
$294$	4.44310	0.259127
$295$	−11.6150	−0.676252
$296$	−29.4054	−1.70915
$297$	0	0
$298$	14.2918	0.827902
$299$	10.2221	0.591160
$300$	−0.416632	−0.0240543
$301$	−3.80445	−0.219285
$302$	−25.8574	−1.48793
$303$	14.1524	0.813033
$304$	22.4474	1.28745
$305$	−3.60327	−0.206323
$306$	65.7587	3.75917
$307$	−34.5475	−1.97173	−0.985865	−	0.167541i	$-0.946417\pi$
$307$	−34.5475	−1.97173	−0.985865	+	0.167541i	$0.946417\pi$
$308$	0	0
$309$	−16.3782	−0.931725
$310$	2.31901	0.131711
$311$	19.7973	1.12260	0.561300	−	0.827612i	$-0.310301\pi$
$311$	19.7973	1.12260	0.561300	+	0.827612i	$0.310301\pi$
$312$	−13.5796	−0.768792
$313$	3.55310	0.200833	0.100417	−	0.994945i	$-0.467982\pi$
$313$	3.55310	0.200833	0.100417	+	0.994945i	$0.467982\pi$
$314$	−18.1044	−1.02169
$315$	7.54712	0.425232
$316$	0.412645	0.0232131
$317$	−22.6511	−1.27221	−0.636106	−	0.771601i	$-0.719456\pi$
$317$	−22.6511	−1.27221	−0.636106	+	0.771601i	$0.719456\pi$
$318$	36.6117	2.05308
$319$	0	0
$320$	−8.44521	−0.472102
$321$	−16.8597	−0.941019
$322$	−9.73847	−0.542704
$323$	−38.3586	−2.13433
$324$	−3.24795	−0.180441
$325$	1.43605	0.0796577
$326$	−19.3015	−1.06901
$327$	−47.2448	−2.61265
$328$	−7.83935	−0.432855
$329$	3.73296	0.205805
$330$	0	0
$331$	−15.8396	−0.870624	−0.435312	−	0.900280i	$-0.643362\pi$
$331$	−15.8396	−0.870624	−0.435312	+	0.900280i	$0.643362\pi$
$332$	0.629417	0.0345438
$333$	76.2181	4.17672
$334$	−20.1721	−1.10377
$335$	6.52368	0.356427
$336$	12.1038	0.660317
$337$	2.28458	0.124449	0.0622245	−	0.998062i	$-0.480181\pi$
$337$	2.28458	0.124449	0.0622245	+	0.998062i	$0.480181\pi$
$338$	−14.9640	−0.813935
$339$	−25.9700	−1.41050
$340$	0.817031	0.0443097
$341$	0	0
$342$	−62.1886	−3.36277
$343$	−1.00000	−0.0539949
$344$	−11.0775	−0.597259
$345$	−23.1173	−1.24460
$346$	−18.8883	−1.01544
$347$	−18.2179	−0.977990	−0.488995	−	0.872287i	$-0.662636\pi$
$347$	−18.2179	−0.977990	−0.488995	+	0.872287i	$0.662636\pi$
$348$	−1.10801	−0.0593955
$349$	9.84933	0.527222	0.263611	−	0.964629i	$-0.415086\pi$
$349$	9.84933	0.527222	0.263611	+	0.964629i	$0.415086\pi$
$350$	−1.36811	−0.0731283
$351$	21.2067	1.13193
$352$	0	0
$353$	22.2698	1.18530	0.592650	−	0.805460i	$-0.298082\pi$
$353$	22.2698	1.18530	0.592650	+	0.805460i	$0.298082\pi$
$354$	51.6067	2.74287
$355$	−2.12829	−0.112958
$356$	1.47323	0.0780811
$357$	−20.6833	−1.09468
$358$	−11.9536	−0.631769
$359$	−22.3793	−1.18113	−0.590567	−	0.806989i	$-0.701096\pi$
$359$	−22.3793	−1.18113	−0.590567	+	0.806989i	$0.701096\pi$
$360$	21.9751	1.15819
$361$	17.2761	0.909267
$362$	28.3716	1.49118
$363$	0	0
$364$	0.184228	0.00965616
$365$	12.3975	0.648915
$366$	16.0097	0.836840
$367$	27.1983	1.41974	0.709870	−	0.704332i	$-0.248753\pi$
$367$	27.1983	1.41974	0.709870	+	0.704332i	$0.248753\pi$
$368$	−26.5294	−1.38294
$369$	20.3194	1.05779
$370$	−13.8164	−0.718283
$371$	−8.24012	−0.427806
$372$	0.706212	0.0366154
$373$	4.23267	0.219159	0.109580	−	0.993978i	$-0.465050\pi$
$373$	4.23267	0.219159	0.109580	+	0.993978i	$0.465050\pi$
$374$	0	0
$375$	−3.24763	−0.167707
$376$	10.8693	0.560543
$377$	3.81909	0.196693
$378$	−20.2033	−1.03915
$379$	−18.9308	−0.972410	−0.486205	−	0.873845i	$-0.661619\pi$
$379$	−18.9308	−0.972410	−0.486205	+	0.873845i	$0.661619\pi$
$380$	−0.772673	−0.0396373
$381$	−14.3237	−0.733824
$382$	25.6308	1.31139
$383$	21.9857	1.12342	0.561710	−	0.827334i	$-0.310144\pi$
$383$	21.9857	1.12342	0.561710	+	0.827334i	$0.310144\pi$
$384$	32.8167	1.67467
$385$	0	0
$386$	−4.43604	−0.225788
$387$	28.7127	1.45955
$388$	−0.526348	−0.0267213
$389$	−28.2801	−1.43386	−0.716929	−	0.697146i	$-0.754453\pi$
$389$	−28.2801	−1.43386	−0.716929	+	0.697146i	$0.754453\pi$
$390$	−6.38051	−0.323090
$391$	45.3340	2.29264
$392$	−2.91172	−0.147064
$393$	2.13614	0.107754
$394$	30.1611	1.51950
$395$	3.21655	0.161842
$396$	0	0
$397$	17.7794	0.892320	0.446160	−	0.894953i	$-0.352791\pi$
$397$	17.7794	0.892320	0.446160	+	0.894953i	$0.352791\pi$
$398$	13.7949	0.691474
$399$	19.5604	0.979243
$400$	−3.72697	−0.186348
$401$	−12.5767	−0.628052	−0.314026	−	0.949414i	$-0.601678\pi$
$401$	−12.5767	−0.628052	−0.314026	+	0.949414i	$0.601678\pi$
$402$	−28.9854	−1.44566
$403$	−2.43417	−0.121255
$404$	−0.559047	−0.0278136
$405$	−25.3176	−1.25804
$406$	−3.63839	−0.180570
$407$	0	0
$408$	−60.2240	−2.98153
$409$	3.85082	0.190411	0.0952055	−	0.995458i	$-0.469649\pi$
$409$	3.85082	0.190411	0.0952055	+	0.995458i	$0.469649\pi$
$410$	−3.68340	−0.181910
$411$	−7.69966	−0.379796
$412$	0.646973	0.0318741
$413$	−11.6150	−0.571538
$414$	73.4974	3.61220
$415$	4.90629	0.240840
$416$	1.04051	0.0510150
$417$	−36.2906	−1.77716
$418$	0	0
$419$	−4.65871	−0.227593	−0.113797	−	0.993504i	$-0.536301\pi$
$419$	−4.65871	−0.227593	−0.113797	+	0.993504i	$0.536301\pi$
$420$	−0.416632	−0.0203296
$421$	11.7825	0.574245	0.287123	−	0.957894i	$-0.407301\pi$
$421$	11.7825	0.574245	0.287123	+	0.957894i	$0.407301\pi$
$422$	31.4869	1.53276
$423$	−28.1731	−1.36982
$424$	−23.9929	−1.16520
$425$	6.36873	0.308929
$426$	9.45623	0.458156
$427$	−3.60327	−0.174374
$428$	0.665993	0.0321920
$429$	0	0
$430$	−5.20489	−0.251002
$431$	4.13030	0.198950	0.0994749	−	0.995040i	$-0.468284\pi$
$431$	4.13030	0.198950	0.0994749	+	0.995040i	$0.468284\pi$
$432$	−55.0375	−2.64799
$433$	−20.0422	−0.963169	−0.481584	−	0.876400i	$-0.659939\pi$
$433$	−20.0422	−0.963169	−0.481584	+	0.876400i	$0.659939\pi$
$434$	2.31901	0.111316
$435$	−8.63688	−0.414107
$436$	1.86627	0.0893779
$437$	−42.8727	−2.05088
$438$	−55.0834	−2.63199
$439$	−34.6581	−1.65414	−0.827071	−	0.562097i	$-0.809995\pi$
$439$	−34.6581	−1.65414	−0.827071	+	0.562097i	$0.809995\pi$
$440$	0	0
$441$	7.54712	0.359387
$442$	12.5124	0.595155
$443$	−27.0554	−1.28544	−0.642719	−	0.766102i	$-0.722194\pi$
$443$	−27.0554	−1.28544	−0.642719	+	0.766102i	$0.722194\pi$
$444$	−4.20755	−0.199682
$445$	11.4838	0.544384
$446$	−10.8658	−0.514510
$447$	33.9261	1.60465
$448$	−8.44521	−0.398999
$449$	−12.5630	−0.592885	−0.296443	−	0.955051i	$-0.595800\pi$
$449$	−12.5630	−0.592885	−0.296443	+	0.955051i	$0.595800\pi$
$450$	10.3253	0.486737
$451$	0	0
$452$	1.02587	0.0482527
$453$	−61.3808	−2.88392
$454$	−20.9402	−0.982774
$455$	1.43605	0.0673230
$456$	56.9544	2.66713
$457$	16.9653	0.793604	0.396802	−	0.917904i	$-0.370120\pi$
$457$	16.9653	0.793604	0.396802	+	0.917904i	$0.370120\pi$
$458$	4.15189	0.194005
$459$	94.0493	4.38985
$460$	0.913181	0.0425773
$461$	11.5722	0.538970	0.269485	−	0.963005i	$-0.413147\pi$
$461$	11.5722	0.538970	0.269485	+	0.963005i	$0.413147\pi$
$462$	0	0
$463$	0.798933	0.0371296	0.0185648	−	0.999828i	$-0.494090\pi$
$463$	0.798933	0.0371296	0.0185648	+	0.999828i	$0.494090\pi$
$464$	−9.91164	−0.460136
$465$	5.50490	0.255284
$466$	25.8798	1.19886
$467$	−29.8979	−1.38351	−0.691756	−	0.722132i	$-0.743162\pi$
$467$	−29.8979	−1.38351	−0.691756	+	0.722132i	$0.743162\pi$
$468$	−1.39039	−0.0642707
$469$	6.52368	0.301235
$470$	5.10708	0.235572
$471$	−42.9765	−1.98025
$472$	−33.8197	−1.55668
$473$	0	0
$474$	−14.2915	−0.656429
$475$	−6.02296	−0.276352
$476$	0.817031	0.0374485
$477$	62.1892	2.84745
$478$	−4.28423	−0.195956
$479$	−12.7505	−0.582585	−0.291293	−	0.956634i	$-0.594085\pi$
$479$	−12.7505	−0.582585	−0.291293	+	0.956634i	$0.594085\pi$
$480$	−2.35311	−0.107404
$481$	14.5026	0.661262
$482$	0.375880	0.0171209
$483$	−23.1173	−1.05188
$484$	0	0
$485$	−4.10287	−0.186302
$486$	51.8789	2.35327
$487$	−3.55214	−0.160963	−0.0804813	−	0.996756i	$-0.525646\pi$
$487$	−3.55214	−0.160963	−0.0804813	+	0.996756i	$0.525646\pi$
$488$	−10.4917	−0.474938
$489$	−45.8182	−2.07197
$490$	−1.36811	−0.0618047
$491$	2.28809	0.103260	0.0516300	−	0.998666i	$-0.483558\pi$
$491$	2.28809	0.103260	0.0516300	+	0.998666i	$0.483558\pi$
$492$	−1.12172	−0.0505708
$493$	16.9372	0.762815
$494$	−11.8331	−0.532397
$495$	0	0
$496$	6.31739	0.283659
$497$	−2.12829	−0.0954670
$498$	−21.7991	−0.976843
$499$	6.76079	0.302655	0.151327	−	0.988484i	$-0.451645\pi$
$499$	6.76079	0.302655	0.151327	+	0.988484i	$0.451645\pi$
$500$	0.128288	0.00573721
$501$	−47.8848	−2.13933
$502$	29.7634	1.32841
$503$	−3.56457	−0.158936	−0.0794682	−	0.996837i	$-0.525322\pi$
$503$	−3.56457	−0.158936	−0.0794682	+	0.996837i	$0.525322\pi$
$504$	21.9751	0.978849
$505$	−4.35775	−0.193917
$506$	0	0
$507$	−35.5218	−1.57758
$508$	0.565813	0.0251039
$509$	−23.5397	−1.04338	−0.521691	−	0.853135i	$-0.674698\pi$
$509$	−23.5397	−1.04338	−0.521691	+	0.853135i	$0.674698\pi$
$510$	−28.2969	−1.25301
$511$	12.3975	0.548434
$512$	−24.4042	−1.07852
$513$	−88.9433	−3.92694
$514$	11.1674	0.492574
$515$	5.04313	0.222227
$516$	−1.58506	−0.0697783
$517$	0	0
$518$	−13.8164	−0.607060
$519$	−44.8374	−1.96814
$520$	4.18138	0.183365
$521$	−24.5613	−1.07605	−0.538025	−	0.842929i	$-0.680830\pi$
$521$	−24.5613	−1.07605	−0.538025	+	0.842929i	$0.680830\pi$
$522$	27.4594	1.20186
$523$	19.7224	0.862400	0.431200	−	0.902256i	$-0.358090\pi$
$523$	19.7224	0.862400	0.431200	+	0.902256i	$0.358090\pi$
$524$	−0.0843818	−0.00368624
$525$	−3.24763	−0.141738
$526$	19.2383	0.838828
$527$	−10.7953	−0.470251
$528$	0	0
$529$	27.6690	1.20300
$530$	−11.2734	−0.489683
$531$	87.6599	3.80412
$532$	−0.772673	−0.0334996
$533$	3.86633	0.167469
$534$	−51.0236	−2.20801
$535$	5.19139	0.224443
$536$	18.9951	0.820465
$537$	−28.3757	−1.22450
$538$	4.75452	0.204982
$539$	0	0
$540$	1.89448	0.0815252
$541$	−11.5031	−0.494557	−0.247279	−	0.968944i	$-0.579536\pi$
$541$	−11.5031	−0.494557	−0.247279	+	0.968944i	$0.579536\pi$
$542$	14.0542	0.603680
$543$	67.3489	2.89022
$544$	4.61453	0.197847
$545$	14.5475	0.623145
$546$	−6.38051	−0.273061
$547$	1.30290	0.0557080	0.0278540	−	0.999612i	$-0.491133\pi$
$547$	1.30290	0.0557080	0.0278540	+	0.999612i	$0.491133\pi$
$548$	0.304152	0.0129927
$549$	27.1943	1.16062
$550$	0	0
$551$	−16.0177	−0.682377
$552$	−67.3113	−2.86496
$553$	3.21655	0.136782
$554$	1.15303	0.0489878
$555$	−32.7977	−1.39219
$556$	1.43355	0.0607961
$557$	−6.15881	−0.260957	−0.130479	−	0.991451i	$-0.541651\pi$
$557$	−6.15881	−0.260957	−0.130479	+	0.991451i	$0.541651\pi$
$558$	−17.5018	−0.740911
$559$	5.46338	0.231076
$560$	−3.72697	−0.157493
$561$	0	0
$562$	21.8766	0.922809
$563$	−23.9408	−1.00899	−0.504493	−	0.863416i	$-0.668321\pi$
$563$	−23.9408	−1.00899	−0.504493	+	0.863416i	$0.668321\pi$
$564$	1.55527	0.0654887
$565$	7.99659	0.336419
$566$	−19.6684	−0.826727
$567$	−25.3176	−1.06324
$568$	−6.19700	−0.260020
$569$	4.54520	0.190545	0.0952724	−	0.995451i	$-0.469628\pi$
$569$	4.54520	0.190545	0.0952724	+	0.995451i	$0.469628\pi$
$570$	26.7606	1.12088
$571$	−31.6174	−1.32315	−0.661574	−	0.749880i	$-0.730111\pi$
$571$	−31.6174	−1.32315	−0.661574	+	0.749880i	$0.730111\pi$
$572$	0	0
$573$	60.8429	2.54175
$574$	−3.68340	−0.153742
$575$	7.11822	0.296850
$576$	63.7370	2.65571
$577$	32.1478	1.33833	0.669165	−	0.743114i	$-0.266652\pi$
$577$	32.1478	1.33833	0.669165	+	0.743114i	$0.266652\pi$
$578$	32.2335	1.34074
$579$	−10.5303	−0.437626
$580$	0.341174	0.0141665
$581$	4.90629	0.203547
$582$	18.2295	0.755635
$583$	0	0
$584$	36.0981	1.49375
$585$	−10.8380	−0.448097
$586$	11.7612	0.485851
$587$	−46.3053	−1.91122	−0.955612	−	0.294629i	$-0.904804\pi$
$587$	−46.3053	−1.91122	−0.955612	+	0.294629i	$0.904804\pi$
$588$	−0.416632	−0.0171816
$589$	10.2092	0.420664
$590$	−15.8906	−0.654204
$591$	71.5971	2.94511
$592$	−37.6385	−1.54693
$593$	11.2766	0.463073	0.231536	−	0.972826i	$-0.425625\pi$
$593$	11.2766	0.463073	0.231536	+	0.972826i	$0.425625\pi$
$594$	0	0
$595$	6.36873	0.261092
$596$	−1.34015	−0.0548947
$597$	32.7465	1.34022
$598$	13.9849	0.571886
$599$	−35.1767	−1.43728	−0.718641	−	0.695381i	$-0.755235\pi$
$599$	−35.1767	−1.43728	−0.718641	+	0.695381i	$0.755235\pi$
$600$	−9.45620	−0.386048
$601$	26.3131	1.07334	0.536668	−	0.843794i	$-0.319683\pi$
$601$	26.3131	1.07334	0.536668	+	0.843794i	$0.319683\pi$
$602$	−5.20489	−0.212136
$603$	−49.2350	−2.00500
$604$	2.42466	0.0986582
$605$	0	0
$606$	19.3619	0.786525
$607$	−18.3351	−0.744197	−0.372098	−	0.928193i	$-0.621362\pi$
$607$	−18.3351	−0.744197	−0.372098	+	0.928193i	$0.621362\pi$
$608$	−4.36401	−0.176984
$609$	−8.63688	−0.349984
$610$	−4.92965	−0.199596
$611$	−5.36071	−0.216871
$612$	−6.16623	−0.249255
$613$	−8.33703	−0.336729	−0.168365	−	0.985725i	$-0.553849\pi$
$613$	−8.33703	−0.336729	−0.168365	+	0.985725i	$0.553849\pi$
$614$	−47.2646	−1.90744
$615$	−8.74373	−0.352581
$616$	0	0
$617$	24.0304	0.967429	0.483714	−	0.875226i	$-0.339287\pi$
$617$	24.0304	0.967429	0.483714	+	0.875226i	$0.339287\pi$
$618$	−22.4071	−0.901348
$619$	−20.2292	−0.813082	−0.406541	−	0.913633i	$-0.633265\pi$
$619$	−20.2292	−0.813082	−0.406541	+	0.913633i	$0.633265\pi$
$620$	−0.217455	−0.00873318
$621$	105.117	4.21821
$622$	27.0847	1.08600
$623$	11.4838	0.460088
$624$	−17.3817	−0.695824
$625$	1.00000	0.0400000
$626$	4.86102	0.194285
$627$	0	0
$628$	1.69766	0.0677439
$629$	64.3175	2.56451
$630$	10.3253	0.411368
$631$	35.9642	1.43171	0.715856	−	0.698248i	$-0.246037\pi$
$631$	35.9642	1.43171	0.715856	+	0.698248i	$0.246037\pi$
$632$	9.36571	0.372548
$633$	74.7441	2.97081
$634$	−30.9891	−1.23073
$635$	4.41049	0.175025
$636$	−3.43310	−0.136131
$637$	1.43605	0.0568983
$638$	0	0
$639$	16.0625	0.635422
$640$	−10.1048	−0.399428
$641$	−43.9633	−1.73644	−0.868222	−	0.496176i	$-0.834737\pi$
$641$	−43.9633	−1.73644	−0.868222	+	0.496176i	$0.834737\pi$
$642$	−23.0659	−0.910338
$643$	−7.86312	−0.310091	−0.155046	−	0.987907i	$-0.549552\pi$
$643$	−7.86312	−0.310091	−0.155046	+	0.987907i	$0.549552\pi$
$644$	0.913181	0.0359844
$645$	−12.3555	−0.486496
$646$	−52.4786	−2.06474
$647$	−11.3107	−0.444670	−0.222335	−	0.974970i	$-0.571368\pi$
$647$	−11.3107	−0.444670	−0.222335	+	0.974970i	$0.571368\pi$
$648$	−73.7179	−2.89591
$649$	0	0
$650$	1.96467	0.0770605
$651$	5.50490	0.215754
$652$	1.80991	0.0708816
$653$	−38.8736	−1.52124	−0.760621	−	0.649197i	$-0.775105\pi$
$653$	−38.8736	−1.52124	−0.760621	+	0.649197i	$0.775105\pi$
$654$	−64.6359	−2.52746
$655$	−0.657753	−0.0257006
$656$	−10.0343	−0.391772
$657$	−93.5655	−3.65034
$658$	5.10708	0.199095
$659$	40.8736	1.59221	0.796105	−	0.605158i	$-0.206890\pi$
$659$	40.8736	1.59221	0.796105	+	0.605158i	$0.206890\pi$
$660$	0	0
$661$	−39.1182	−1.52152	−0.760761	−	0.649032i	$-0.775174\pi$
$661$	−39.1182	−1.52152	−0.760761	+	0.649032i	$0.775174\pi$
$662$	−21.6703	−0.842239
$663$	29.7022	1.15354
$664$	14.2857	0.554394
$665$	−6.02296	−0.233560
$666$	104.274	4.04055
$667$	18.9305	0.732991
$668$	1.89154	0.0731860
$669$	−25.7934	−0.997231
$670$	8.92508	0.344806
$671$	0	0
$672$	−2.35311	−0.0907732
$673$	−37.3959	−1.44151	−0.720753	−	0.693192i	$-0.756204\pi$
$673$	−37.3959	−1.44151	−0.720753	+	0.693192i	$0.756204\pi$
$674$	3.12555	0.120392
$675$	14.7674	0.568396
$676$	1.40318	0.0539686
$677$	6.83242	0.262591	0.131296	−	0.991343i	$-0.458086\pi$
$677$	6.83242	0.262591	0.131296	+	0.991343i	$0.458086\pi$
$678$	−35.5297	−1.36451
$679$	−4.10287	−0.157454
$680$	18.5440	0.711128
$681$	−49.7083	−1.90483
$682$	0	0
$683$	38.6397	1.47851	0.739253	−	0.673428i	$-0.235179\pi$
$683$	38.6397	1.47851	0.739253	+	0.673428i	$0.235179\pi$
$684$	5.83146	0.222971
$685$	2.37085	0.0905857
$686$	−1.36811	−0.0522345
$687$	9.85582	0.376023
$688$	−14.1791	−0.540572
$689$	11.8332	0.450810
$690$	−31.6270	−1.20402
$691$	4.75646	0.180944	0.0904721	−	0.995899i	$-0.471162\pi$
$691$	4.75646	0.180944	0.0904721	+	0.995899i	$0.471162\pi$
$692$	1.77117	0.0673297
$693$	0	0
$694$	−24.9240	−0.946104
$695$	11.1745	0.423872
$696$	−25.1482	−0.953240
$697$	17.1468	0.649480
$698$	13.4749	0.510033
$699$	61.4339	2.32364
$700$	0.128288	0.00484883
$701$	26.9521	1.01797	0.508984	−	0.860776i	$-0.330021\pi$
$701$	26.9521	1.01797	0.508984	+	0.860776i	$0.330021\pi$
$702$	29.0129	1.09502
$703$	−60.8257	−2.29408
$704$	0	0
$705$	12.1233	0.456589
$706$	30.4674	1.14666
$707$	−4.35775	−0.163890
$708$	−4.83919	−0.181868
$709$	11.3605	0.426652	0.213326	−	0.976981i	$-0.431570\pi$
$709$	11.3605	0.426652	0.213326	+	0.976981i	$0.431570\pi$
$710$	−2.91173	−0.109275
$711$	−24.2757	−0.910410
$712$	33.4376	1.25313
$713$	−12.0657	−0.451865
$714$	−28.2969	−1.05899
$715$	0	0
$716$	1.12090	0.0418899
$717$	−10.1700	−0.379805
$718$	−30.6172	−1.14262
$719$	−3.74197	−0.139552	−0.0697760	−	0.997563i	$-0.522228\pi$
$719$	−3.74197	−0.139552	−0.0697760	+	0.997563i	$0.522228\pi$
$720$	28.1279	1.04826
$721$	5.04313	0.187816
$722$	23.6355	0.879622
$723$	0.892271	0.0331839
$724$	−2.66042	−0.0988736
$725$	2.65944	0.0987691
$726$	0	0
$727$	−29.7332	−1.10274	−0.551372	−	0.834259i	$-0.685896\pi$
$727$	−29.7332	−1.10274	−0.551372	+	0.834259i	$0.685896\pi$
$728$	4.18138	0.154972
$729$	47.1982	1.74808
$730$	16.9611	0.627758
$731$	24.2295	0.896161
$732$	−1.50124	−0.0554873
$733$	2.97899	0.110032	0.0550158	−	0.998485i	$-0.482479\pi$
$733$	2.97899	0.110032	0.0550158	+	0.998485i	$0.482479\pi$
$734$	37.2102	1.37345
$735$	−3.24763	−0.119791
$736$	5.15759	0.190111
$737$	0	0
$738$	27.7991	1.02330
$739$	18.5414	0.682056	0.341028	−	0.940053i	$-0.389225\pi$
$739$	18.5414	0.682056	0.341028	+	0.940053i	$0.389225\pi$
$740$	1.29558	0.0476263
$741$	−28.0896	−1.03190
$742$	−11.2734	−0.413858
$743$	29.0196	1.06463	0.532314	−	0.846547i	$-0.321323\pi$
$743$	29.0196	1.06463	0.532314	+	0.846547i	$0.321323\pi$
$744$	16.0287	0.587642
$745$	−10.4464	−0.382727
$746$	5.79074	0.212014
$747$	−37.0283	−1.35480
$748$	0	0
$749$	5.19139	0.189689
$750$	−4.44310	−0.162239
$751$	41.8942	1.52874	0.764371	−	0.644777i	$-0.223050\pi$
$751$	41.8942	1.52874	0.764371	+	0.644777i	$0.223050\pi$
$752$	13.9126	0.507341
$753$	70.6530	2.57474
$754$	5.22491	0.190280
$755$	18.9002	0.687847
$756$	1.89448	0.0689014
$757$	8.81048	0.320222	0.160111	−	0.987099i	$-0.448815\pi$
$757$	8.81048	0.320222	0.160111	+	0.987099i	$0.448815\pi$
$758$	−25.8993	−0.940706
$759$	0	0
$760$	−17.5372	−0.636141
$761$	−7.71070	−0.279513	−0.139756	−	0.990186i	$-0.544632\pi$
$761$	−7.71070	−0.279513	−0.139756	+	0.990186i	$0.544632\pi$
$762$	−19.5963	−0.709898
$763$	14.5475	0.526654
$764$	−2.40341	−0.0869525
$765$	−48.0655	−1.73781
$766$	30.0788	1.08679
$767$	16.6797	0.602270
$768$	−9.95715	−0.359298
$769$	8.85938	0.319477	0.159739	−	0.987159i	$-0.448935\pi$
$769$	8.85938	0.319477	0.159739	+	0.987159i	$0.448935\pi$
$770$	0	0
$771$	26.5094	0.954714
$772$	0.415969	0.0149711
$773$	50.0301	1.79946	0.899730	−	0.436448i	$-0.143764\pi$
$773$	50.0301	1.79946	0.899730	+	0.436448i	$0.143764\pi$
$774$	39.2819	1.41196
$775$	−1.69505	−0.0608880
$776$	−11.9464	−0.428851
$777$	−32.7977	−1.17661
$778$	−38.6902	−1.38711
$779$	−16.2159	−0.580994
$780$	0.598304	0.0214227
$781$	0	0
$782$	62.0216	2.21789
$783$	39.2729	1.40350
$784$	−3.72697	−0.133106
$785$	13.2332	0.472312
$786$	2.92247	0.104241
$787$	−15.2799	−0.544670	−0.272335	−	0.962203i	$-0.587796\pi$
$787$	−15.2799	−0.544670	−0.272335	+	0.962203i	$0.587796\pi$
$788$	−2.82823	−0.100751
$789$	45.6681	1.62583
$790$	4.40058	0.156566
$791$	7.99659	0.284326
$792$	0	0
$793$	5.17447	0.183751
$794$	24.3240	0.863228
$795$	−26.7609	−0.949111
$796$	−1.29355	−0.0458487
$797$	−46.9313	−1.66239	−0.831197	−	0.555979i	$-0.812344\pi$
$797$	−46.9313	−1.66239	−0.831197	+	0.555979i	$0.812344\pi$
$798$	26.7606	0.947317
$799$	−23.7742	−0.841070
$800$	0.724562	0.0256171
$801$	−86.6695	−3.06232
$802$	−17.2063	−0.607575
$803$	0	0
$804$	2.71797	0.0958555
$805$	7.11822	0.250884
$806$	−3.33021	−0.117302
$807$	11.2864	0.397298
$808$	−12.6886	−0.446382
$809$	1.69809	0.0597016	0.0298508	−	0.999554i	$-0.490497\pi$
$809$	1.69809	0.0597016	0.0298508	+	0.999554i	$0.490497\pi$
$810$	−34.6372	−1.21703
$811$	−14.5477	−0.510839	−0.255420	−	0.966830i	$-0.582214\pi$
$811$	−14.5477	−0.510839	−0.255420	+	0.966830i	$0.582214\pi$
$812$	0.341174	0.0119729
$813$	33.3622	1.17006
$814$	0	0
$815$	14.1082	0.494189
$816$	−77.0859	−2.69855
$817$	−22.9141	−0.801662
$818$	5.26833	0.184203
$819$	−10.8380	−0.378711
$820$	0.345395	0.0120617
$821$	32.8114	1.14512	0.572562	−	0.819861i	$-0.305950\pi$
$821$	32.8114	1.14512	0.572562	+	0.819861i	$0.305950\pi$
$822$	−10.5339	−0.367414
$823$	−6.81483	−0.237550	−0.118775	−	0.992921i	$-0.537897\pi$
$823$	−6.81483	−0.237550	−0.118775	+	0.992921i	$0.537897\pi$
$824$	14.6842	0.511548
$825$	0	0
$826$	−15.8906	−0.552903
$827$	56.1439	1.95231	0.976157	−	0.217064i	$-0.0696480\pi$
$827$	56.1439	1.95231	0.976157	+	0.217064i	$0.0696480\pi$
$828$	−6.89189	−0.239510
$829$	1.43846	0.0499597	0.0249798	−	0.999688i	$-0.492048\pi$
$829$	1.43846	0.0499597	0.0249798	+	0.999688i	$0.492048\pi$
$830$	6.71232	0.232988
$831$	2.73709	0.0949487
$832$	12.1277	0.420453
$833$	6.36873	0.220663
$834$	−49.6493	−1.71922
$835$	14.7445	0.510255
$836$	0	0
$837$	−25.0314	−0.865213
$838$	−6.37361	−0.220173
$839$	−8.60383	−0.297037	−0.148519	−	0.988910i	$-0.547451\pi$
$839$	−8.60383	−0.297037	−0.148519	+	0.988910i	$0.547451\pi$
$840$	−9.45620	−0.326270
$841$	−21.9274	−0.756117
$842$	16.1197	0.555523
$843$	51.9311	1.78860
$844$	−2.95254	−0.101631
$845$	10.9378	0.376271
$846$	−38.5437	−1.32516
$847$	0	0
$848$	−30.7107	−1.05461
$849$	−46.6893	−1.60237
$850$	8.71309	0.298856
$851$	71.8866	2.46424
$852$	−0.886716	−0.0303784
$853$	−16.9739	−0.581174	−0.290587	−	0.956849i	$-0.593851\pi$
$853$	−16.9739	−0.581174	−0.290587	+	0.956849i	$0.593851\pi$
$854$	−4.92965	−0.168689
$855$	45.4560	1.55456
$856$	15.1159	0.516651
$857$	−37.9102	−1.29499	−0.647494	−	0.762071i	$-0.724183\pi$
$857$	−37.9102	−1.29499	−0.647494	+	0.762071i	$0.724183\pi$
$858$	0	0
$859$	−21.9095	−0.747542	−0.373771	−	0.927521i	$-0.621935\pi$
$859$	−21.9095	−0.747542	−0.373771	+	0.927521i	$0.621935\pi$
$860$	0.488065	0.0166429
$861$	−8.74373	−0.297986
$862$	5.65069	0.192463
$863$	41.2690	1.40481	0.702407	−	0.711775i	$-0.252109\pi$
$863$	41.2690	1.40481	0.702407	+	0.711775i	$0.252109\pi$
$864$	10.6999	0.364017
$865$	13.8062	0.469424
$866$	−27.4199	−0.931766
$867$	76.5164	2.59863
$868$	−0.217455	−0.00738089
$869$	0	0
$870$	−11.8162	−0.400606
$871$	−9.36832	−0.317433
$872$	42.3582	1.43443
$873$	30.9648	1.04800
$874$	−58.6544	−1.98402
$875$	1.00000	0.0338062
$876$	5.16520	0.174516
$877$	20.2999	0.685480	0.342740	−	0.939430i	$-0.388645\pi$
$877$	20.2999	0.685480	0.342740	+	0.939430i	$0.388645\pi$
$878$	−47.4160	−1.60021
$879$	27.9190	0.941683
$880$	0	0
$881$	−32.7155	−1.10221	−0.551106	−	0.834435i	$-0.685794\pi$
$881$	−32.7155	−1.10221	−0.551106	+	0.834435i	$0.685794\pi$
$882$	10.3253	0.347669
$883$	−5.97420	−0.201048	−0.100524	−	0.994935i	$-0.532052\pi$
$883$	−5.97420	−0.201048	−0.100524	+	0.994935i	$0.532052\pi$
$884$	−1.17330	−0.0394622
$885$	−37.7213	−1.26799
$886$	−37.0146	−1.24353
$887$	−27.2548	−0.915126	−0.457563	−	0.889177i	$-0.651278\pi$
$887$	−27.2548	−0.915126	−0.457563	+	0.889177i	$0.651278\pi$
$888$	−95.4979	−3.20470
$889$	4.41049	0.147923
$890$	15.7110	0.526635
$891$	0	0
$892$	1.01889	0.0341150
$893$	22.4835	0.752381
$894$	46.4145	1.55233
$895$	8.73736	0.292058
$896$	−10.1048	−0.337578
$897$	33.1976	1.10844
$898$	−17.1875	−0.573555
$899$	−4.50788	−0.150346
$900$	−0.968204	−0.0322735
$901$	52.4791	1.74833
$902$	0	0
$903$	−12.3555	−0.411164
$904$	23.2838	0.774409
$905$	−20.7379	−0.689350
$906$	−83.9754	−2.78990
$907$	30.5831	1.01550	0.507748	−	0.861506i	$-0.330478\pi$
$907$	30.5831	1.01550	0.507748	+	0.861506i	$0.330478\pi$
$908$	1.96358	0.0651636
$909$	32.8885	1.09084
$910$	1.96467	0.0651280
$911$	18.8942	0.625991	0.312996	−	0.949755i	$-0.398667\pi$
$911$	18.8942	0.625991	0.312996	+	0.949755i	$0.398667\pi$
$912$	72.9008	2.41399
$913$	0	0
$914$	23.2103	0.767730
$915$	−11.7021	−0.386859
$916$	−0.389324	−0.0128636
$917$	−0.657753	−0.0217209
$918$	128.669	4.24672
$919$	−6.65387	−0.219491	−0.109745	−	0.993960i	$-0.535004\pi$
$919$	−6.65387	−0.219491	−0.109745	+	0.993960i	$0.535004\pi$
$920$	20.7263	0.683325
$921$	−112.198	−3.69704
$922$	15.8319	0.521397
$923$	3.05633	0.100600
$924$	0	0
$925$	10.0990	0.332052
$926$	1.09302	0.0359190
$927$	−38.0611	−1.25009
$928$	1.92693	0.0632545
$929$	−19.3952	−0.636337	−0.318169	−	0.948034i	$-0.603068\pi$
$929$	−19.3952	−0.636337	−0.318169	+	0.948034i	$0.603068\pi$
$930$	7.53128	0.246960
$931$	−6.02296	−0.197395
$932$	−2.42676	−0.0794912
$933$	64.2942	2.10490
$934$	−40.9035	−1.33840
$935$	0	0
$936$	−31.5573	−1.03148
$937$	−50.8996	−1.66282	−0.831408	−	0.555662i	$-0.812465\pi$
$937$	−50.8996	−1.66282	−0.831408	+	0.555662i	$0.812465\pi$
$938$	8.92508	0.291414
$939$	11.5392	0.376567
$940$	−0.478894	−0.0156198
$941$	50.2980	1.63967	0.819835	−	0.572600i	$-0.194065\pi$
$941$	50.2980	1.63967	0.819835	+	0.572600i	$0.194065\pi$
$942$	−58.7964	−1.91569
$943$	19.1647	0.624087
$944$	−43.2888	−1.40893
$945$	14.7674	0.480382
$946$	0	0
$947$	3.58669	0.116552	0.0582758	−	0.998301i	$-0.481440\pi$
$947$	3.58669	0.116552	0.0582758	+	0.998301i	$0.481440\pi$
$948$	1.34012	0.0435250
$949$	−17.8034	−0.577924
$950$	−8.24005	−0.267342
$951$	−73.5625	−2.38543
$952$	18.5440	0.601013
$953$	20.8712	0.676084	0.338042	−	0.941131i	$-0.390235\pi$
$953$	20.8712	0.676084	0.338042	+	0.941131i	$0.390235\pi$
$954$	85.0813	2.75461
$955$	−18.7345	−0.606235
$956$	0.401734	0.0129930
$957$	0	0
$958$	−17.4440	−0.563591
$959$	2.37085	0.0765589
$960$	−27.4269	−0.885201
$961$	−28.1268	−0.907316
$962$	19.8411	0.639702
$963$	−39.1801	−1.26256
$964$	−0.0352465	−0.00113521
$965$	3.24247	0.104379
$966$	−31.6270	−1.01758
$967$	48.7720	1.56840	0.784201	−	0.620506i	$-0.213073\pi$
$967$	48.7720	1.56840	0.784201	+	0.620506i	$0.213073\pi$
$968$	0	0
$969$	−124.575	−4.00191
$970$	−5.61315	−0.180227
$971$	−32.6661	−1.04831	−0.524153	−	0.851624i	$-0.675618\pi$
$971$	−32.6661	−1.04831	−0.524153	+	0.851624i	$0.675618\pi$
$972$	−4.86471	−0.156036
$973$	11.1745	0.358237
$974$	−4.85970	−0.155715
$975$	4.66376	0.149360
$976$	−13.4293	−0.429860
$977$	−44.7108	−1.43042	−0.715212	−	0.698908i	$-0.753670\pi$
$977$	−44.7108	−1.43042	−0.715212	+	0.698908i	$0.753670\pi$
$978$	−62.6842	−2.00442
$979$	0	0
$980$	0.128288	0.00409801
$981$	−109.791	−3.50537
$982$	3.13034	0.0998933
$983$	47.0513	1.50070	0.750352	−	0.661039i	$-0.229884\pi$
$983$	47.0513	1.50070	0.750352	+	0.661039i	$0.229884\pi$
$984$	−25.4593	−0.811613
$985$	−22.0459	−0.702442
$986$	23.1719	0.737945
$987$	12.1233	0.385888
$988$	1.10960	0.0353010
$989$	27.0809	0.861123
$990$	0	0
$991$	−29.7336	−0.944518	−0.472259	−	0.881460i	$-0.656561\pi$
$991$	−29.7336	−0.944518	−0.472259	+	0.881460i	$0.656561\pi$
$992$	−1.22817	−0.0389944
$993$	−51.4413	−1.63244
$994$	−2.91173	−0.0923545
$995$	−10.0832	−0.319658
$996$	2.04412	0.0647703
$997$	21.1390	0.669479	0.334739	−	0.942311i	$-0.391352\pi$
$997$	21.1390	0.669479	0.334739	+	0.942311i	$0.391352\pi$
$998$	9.24947	0.292787
$999$	149.135	4.71843

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.bn.1.10		14
11.7	odd	10		385.2.n.e.71.2	✓	28
11.8	odd	10		385.2.n.e.141.2	yes	28
11.10	odd	2		4235.2.a.bm.1.5		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.n.e.71.2	✓	28	11.7	odd	10
385.2.n.e.141.2	yes	28	11.8	odd	10
4235.2.a.bm.1.5		14	11.10	odd	2
4235.2.a.bn.1.10		14	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+1.36811 q^{2} +3.24763 q^{3} -0.128288 q^{4} -1.00000 q^{5} +4.44310 q^{6} -1.00000 q^{7} -2.91172 q^{8} +7.54712 q^{9} +O(q^{10})\)	\(q+1.36811 q^{2} +3.24763 q^{3} -0.128288 q^{4} -1.00000 q^{5} +4.44310 q^{6} -1.00000 q^{7} -2.91172 q^{8} +7.54712 q^{9} -1.36811 q^{10} -0.416632 q^{12} +1.43605 q^{13} -1.36811 q^{14} -3.24763 q^{15} -3.72697 q^{16} +6.36873 q^{17} +10.3253 q^{18} -6.02296 q^{19} +0.128288 q^{20} -3.24763 q^{21} +7.11822 q^{23} -9.45620 q^{24} +1.00000 q^{25} +1.96467 q^{26} +14.7674 q^{27} +0.128288 q^{28} +2.65944 q^{29} -4.44310 q^{30} -1.69505 q^{31} +0.724562 q^{32} +8.71309 q^{34} +1.00000 q^{35} -0.968204 q^{36} +10.0990 q^{37} -8.24005 q^{38} +4.66376 q^{39} +2.91172 q^{40} +2.69234 q^{41} -4.44310 q^{42} +3.80445 q^{43} -7.54712 q^{45} +9.73847 q^{46} -3.73296 q^{47} -12.1038 q^{48} +1.00000 q^{49} +1.36811 q^{50} +20.6833 q^{51} -0.184228 q^{52} +8.24012 q^{53} +20.2033 q^{54} +2.91172 q^{56} -19.5604 q^{57} +3.63839 q^{58} +11.6150 q^{59} +0.416632 q^{60} +3.60327 q^{61} -2.31901 q^{62} -7.54712 q^{63} +8.44521 q^{64} -1.43605 q^{65} -6.52368 q^{67} -0.817031 q^{68} +23.1173 q^{69} +1.36811 q^{70} +2.12829 q^{71} -21.9751 q^{72} -12.3975 q^{73} +13.8164 q^{74} +3.24763 q^{75} +0.772673 q^{76} +6.38051 q^{78} -3.21655 q^{79} +3.72697 q^{80} +25.3176 q^{81} +3.68340 q^{82} -4.90629 q^{83} +0.416632 q^{84} -6.36873 q^{85} +5.20489 q^{86} +8.63688 q^{87} -11.4838 q^{89} -10.3253 q^{90} -1.43605 q^{91} -0.913181 q^{92} -5.50490 q^{93} -5.10708 q^{94} +6.02296 q^{95} +2.35311 q^{96} +4.10287 q^{97} +1.36811 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + q^{2} + 5 q^{3} + 21 q^{4} - 14 q^{5} - q^{6} - 14 q^{7} + 3 q^{8} + 17 q^{9}+O(q^{10}) \) 14 * q + q^2 + 5 * q^3 + 21 * q^4 - 14 * q^5 - q^6 - 14 * q^7 + 3 * q^8 + 17 * q^9	\( 14 q + q^{2} + 5 q^{3} + 21 q^{4} - 14 q^{5} - q^{6} - 14 q^{7} + 3 q^{8} + 17 q^{9} - q^{10} + 15 q^{12} - 10 q^{13} - q^{14} - 5 q^{15} + 31 q^{16} - 11 q^{17} + 21 q^{18} - 21 q^{19} - 21 q^{20} - 5 q^{21} + 8 q^{23} - 22 q^{24} + 14 q^{25} - 18 q^{26} + 26 q^{27} - 21 q^{28} + 4 q^{29} + q^{30} + 6 q^{31} + 42 q^{32} + 16 q^{34} + 14 q^{35} + 28 q^{36} + 48 q^{37} + 35 q^{38} - 6 q^{39} - 3 q^{40} - 13 q^{41} + q^{42} - 17 q^{45} + 31 q^{46} + 11 q^{47} + 59 q^{48} + 14 q^{49} + q^{50} + 33 q^{51} - 52 q^{52} + 31 q^{53} + 57 q^{54} - 3 q^{56} + 4 q^{57} + 52 q^{58} - 4 q^{59} - 15 q^{60} - 17 q^{61} + 27 q^{62} - 17 q^{63} + 43 q^{64} + 10 q^{65} + 45 q^{67} - 14 q^{68} + 20 q^{69} + q^{70} - 6 q^{71} + 14 q^{72} - 11 q^{73} + 33 q^{74} + 5 q^{75} + 5 q^{76} + 52 q^{78} - 30 q^{79} - 31 q^{80} - 6 q^{81} + 26 q^{82} - 23 q^{83} - 15 q^{84} + 11 q^{85} - 23 q^{86} - 23 q^{87} - 15 q^{89} - 21 q^{90} + 10 q^{91} + 44 q^{92} + 29 q^{93} - 49 q^{94} + 21 q^{95} + 52 q^{96} + 44 q^{97} + q^{98}+O(q^{100}) \) 14 * q + q^2 + 5 * q^3 + 21 * q^4 - 14 * q^5 - q^6 - 14 * q^7 + 3 * q^8 + 17 * q^9 - q^10 + 15 * q^12 - 10 * q^13 - q^14 - 5 * q^15 + 31 * q^16 - 11 * q^17 + 21 * q^18 - 21 * q^19 - 21 * q^20 - 5 * q^21 + 8 * q^23 - 22 * q^24 + 14 * q^25 - 18 * q^26 + 26 * q^27 - 21 * q^28 + 4 * q^29 + q^30 + 6 * q^31 + 42 * q^32 + 16 * q^34 + 14 * q^35 + 28 * q^36 + 48 * q^37 + 35 * q^38 - 6 * q^39 - 3 * q^40 - 13 * q^41 + q^42 - 17 * q^45 + 31 * q^46 + 11 * q^47 + 59 * q^48 + 14 * q^49 + q^50 + 33 * q^51 - 52 * q^52 + 31 * q^53 + 57 * q^54 - 3 * q^56 + 4 * q^57 + 52 * q^58 - 4 * q^59 - 15 * q^60 - 17 * q^61 + 27 * q^62 - 17 * q^63 + 43 * q^64 + 10 * q^65 + 45 * q^67 - 14 * q^68 + 20 * q^69 + q^70 - 6 * q^71 + 14 * q^72 - 11 * q^73 + 33 * q^74 + 5 * q^75 + 5 * q^76 + 52 * q^78 - 30 * q^79 - 31 * q^80 - 6 * q^81 + 26 * q^82 - 23 * q^83 - 15 * q^84 + 11 * q^85 - 23 * q^86 - 23 * q^87 - 15 * q^89 - 21 * q^90 + 10 * q^91 + 44 * q^92 + 29 * q^93 - 49 * q^94 + 21 * q^95 + 52 * q^96 + 44 * q^97 + q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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