LMFDB - Embedded newform 2031.2.a.i.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2031,2,Mod(1,2031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2031, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("2031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2031 = 3 \cdot 677 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2031.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:	$16.2176166505$
Analytic rank:	$0$
Dimension:	$38$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	2031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00518 q^{2} -1.00000 q^{3} -0.989621 q^{4} -2.22514 q^{5} +1.00518 q^{6} +1.19593 q^{7} +3.00510 q^{8} +1.00000 q^{9} +2.23666 q^{10} +0.183081 q^{11} +0.989621 q^{12} -0.922175 q^{13} -1.20213 q^{14} +2.22514 q^{15} -1.04141 q^{16} -3.54231 q^{17} -1.00518 q^{18} -1.94600 q^{19} +2.20204 q^{20} -1.19593 q^{21} -0.184029 q^{22} +1.99867 q^{23} -3.00510 q^{24} -0.0487581 q^{25} +0.926948 q^{26} -1.00000 q^{27} -1.18352 q^{28} -0.968676 q^{29} -2.23666 q^{30} +7.58204 q^{31} -4.96339 q^{32} -0.183081 q^{33} +3.56064 q^{34} -2.66112 q^{35} -0.989621 q^{36} -6.75267 q^{37} +1.95607 q^{38} +0.922175 q^{39} -6.68675 q^{40} -5.79638 q^{41} +1.20213 q^{42} +8.50133 q^{43} -0.181181 q^{44} -2.22514 q^{45} -2.00902 q^{46} +2.05890 q^{47} +1.04141 q^{48} -5.56974 q^{49} +0.0490105 q^{50} +3.54231 q^{51} +0.912604 q^{52} -10.6422 q^{53} +1.00518 q^{54} -0.407381 q^{55} +3.59390 q^{56} +1.94600 q^{57} +0.973690 q^{58} -11.4822 q^{59} -2.20204 q^{60} +8.14270 q^{61} -7.62128 q^{62} +1.19593 q^{63} +7.07190 q^{64} +2.05197 q^{65} +0.184029 q^{66} -11.6167 q^{67} +3.50554 q^{68} -1.99867 q^{69} +2.67490 q^{70} -0.764133 q^{71} +3.00510 q^{72} +0.600213 q^{73} +6.78762 q^{74} +0.0487581 q^{75} +1.92580 q^{76} +0.218953 q^{77} -0.926948 q^{78} +4.72022 q^{79} +2.31728 q^{80} +1.00000 q^{81} +5.82638 q^{82} +4.37640 q^{83} +1.18352 q^{84} +7.88213 q^{85} -8.54533 q^{86} +0.968676 q^{87} +0.550176 q^{88} +6.54432 q^{89} +2.23666 q^{90} -1.10286 q^{91} -1.97793 q^{92} -7.58204 q^{93} -2.06956 q^{94} +4.33012 q^{95} +4.96339 q^{96} +10.5115 q^{97} +5.59857 q^{98} +0.183081 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 3 q^{2} - 38 q^{3} + 49 q^{4} + 3 q^{5} + 3 q^{6} + 7 q^{7} - 12 q^{8} + 38 q^{9} + 14 q^{10} - 12 q^{11} - 49 q^{12} + 24 q^{13} + q^{14} - 3 q^{15} + 71 q^{16} + 12 q^{17} - 3 q^{18} + 16 q^{19}+ \cdots - 12 q^{99}+O(q^{100}) $ 38 * q - 3 * q^2 - 38 * q^3 + 49 * q^4 + 3 * q^5 + 3 * q^6 + 7 * q^7 - 12 * q^8 + 38 * q^9 + 14 * q^10 - 12 * q^11 - 49 * q^12 + 24 * q^13 + q^14 - 3 * q^15 + 71 * q^16 + 12 * q^17 - 3 * q^18 + 16 * q^19 + 6 * q^20 - 7 * q^21 + 20 * q^22 - 35 * q^23 + 12 * q^24 + 85 * q^25 + 33 * q^26 - 38 * q^27 + 23 * q^28 + 13 * q^29 - 14 * q^30 + 27 * q^31 - 22 * q^32 + 12 * q^33 + 45 * q^34 - 23 * q^35 + 49 * q^36 + 28 * q^37 + 16 * q^38 - 24 * q^39 + 52 * q^40 + 53 * q^41 - q^42 + 17 * q^43 - 8 * q^44 + 3 * q^45 + 28 * q^46 - 13 * q^47 - 71 * q^48 + 135 * q^49 - 7 * q^50 - 12 * q^51 + 68 * q^52 + 6 * q^53 + 3 * q^54 + 49 * q^55 + 13 * q^56 - 16 * q^57 + 26 * q^58 + 17 * q^59 - 6 * q^60 + 63 * q^61 + 13 * q^62 + 7 * q^63 + 100 * q^64 + 29 * q^65 - 20 * q^66 + 28 * q^67 - 17 * q^68 + 35 * q^69 + 44 * q^70 - 2 * q^71 - 12 * q^72 + 55 * q^73 - 13 * q^74 - 85 * q^75 + 53 * q^76 - 23 * q^77 - 33 * q^78 + 30 * q^79 + 19 * q^80 + 38 * q^81 + 55 * q^82 - 19 * q^83 - 23 * q^84 + 45 * q^85 + 12 * q^86 - 13 * q^87 + 47 * q^88 + 126 * q^89 + 14 * q^90 + 66 * q^91 - 77 * q^92 - 27 * q^93 + 52 * q^94 - 53 * q^95 + 22 * q^96 + 80 * q^97 + 4 * q^98 - 12 * q^99

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 $

$2$	−1.00518	−0.710767	−0.355383	−	0.934721i	$-0.615650\pi$
$2$	−1.00518	−0.710767	−0.355383	+	0.934721i	$0.615650\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.989621	−0.494811
$5$	−2.22514	−0.995112	−0.497556	−	0.867432i	$-0.665769\pi$
$5$	−2.22514	−0.995112	−0.497556	+	0.867432i	$0.665769\pi$
$6$	1.00518	0.410361
$7$	1.19593	0.452021	0.226010	−	0.974125i	$-0.427432\pi$
$7$	1.19593	0.452021	0.226010	+	0.974125i	$0.427432\pi$
$8$	3.00510	1.06246
$9$	1.00000	0.333333
$10$	2.23666	0.707293
$11$	0.183081	0.0552010	0.0276005	−	0.999619i	$-0.491213\pi$
$11$	0.183081	0.0552010	0.0276005	+	0.999619i	$0.491213\pi$
$12$	0.989621	0.285679
$13$	−0.922175	−0.255765	−0.127883	−	0.991789i	$-0.540818\pi$
$13$	−0.922175	−0.255765	−0.127883	+	0.991789i	$0.540818\pi$
$14$	−1.20213	−0.321281
$15$	2.22514	0.574528
$16$	−1.04141	−0.260352
$17$	−3.54231	−0.859136	−0.429568	−	0.903034i	$-0.641334\pi$
$17$	−3.54231	−0.859136	−0.429568	+	0.903034i	$0.641334\pi$
$18$	−1.00518	−0.236922
$19$	−1.94600	−0.446443	−0.223221	−	0.974768i	$-0.571657\pi$
$19$	−1.94600	−0.446443	−0.223221	+	0.974768i	$0.571657\pi$
$20$	2.20204	0.492392
$21$	−1.19593	−0.260974
$22$	−0.184029	−0.0392351
$23$	1.99867	0.416752	0.208376	−	0.978049i	$-0.433182\pi$
$23$	1.99867	0.416752	0.208376	+	0.978049i	$0.433182\pi$
$24$	−3.00510	−0.613413
$25$	−0.0487581	−0.00975163
$26$	0.926948	0.181789
$27$	−1.00000	−0.192450
$28$	−1.18352	−0.223665
$29$	−0.968676	−0.179879	−0.0899393	−	0.995947i	$-0.528667\pi$
$29$	−0.968676	−0.179879	−0.0899393	+	0.995947i	$0.528667\pi$
$30$	−2.23666	−0.408356
$31$	7.58204	1.36177	0.680887	−	0.732388i	$-0.261594\pi$
$31$	7.58204	1.36177	0.680887	+	0.732388i	$0.261594\pi$
$32$	−4.96339	−0.877412
$33$	−0.183081	−0.0318703
$34$	3.56064	0.610645
$35$	−2.66112	−0.449812
$36$	−0.989621	−0.164937
$37$	−6.75267	−1.11013	−0.555066	−	0.831806i	$-0.687307\pi$
$37$	−6.75267	−1.11013	−0.555066	+	0.831806i	$0.687307\pi$
$38$	1.95607	0.317317
$39$	0.922175	0.147666
$40$	−6.68675	−1.05727
$41$	−5.79638	−0.905243	−0.452621	−	0.891703i	$-0.649511\pi$
$41$	−5.79638	−0.905243	−0.452621	+	0.891703i	$0.649511\pi$
$42$	1.20213	0.185492
$43$	8.50133	1.29644	0.648220	−	0.761453i	$-0.275514\pi$
$43$	8.50133	1.29644	0.648220	+	0.761453i	$0.275514\pi$
$44$	−0.181181	−0.0273141
$45$	−2.22514	−0.331704
$46$	−2.00902	−0.296213
$47$	2.05890	0.300322	0.150161	−	0.988662i	$-0.452021\pi$
$47$	2.05890	0.300322	0.150161	+	0.988662i	$0.452021\pi$
$48$	1.04141	0.150314
$49$	−5.56974	−0.795677
$50$	0.0490105	0.00693113
$51$	3.54231	0.496022
$52$	0.912604	0.126555
$53$	−10.6422	−1.46182	−0.730910	−	0.682473i	$-0.760904\pi$
$53$	−10.6422	−1.46182	−0.730910	+	0.682473i	$0.760904\pi$
$54$	1.00518	0.136787
$55$	−0.407381	−0.0549312
$56$	3.59390	0.480255
$57$	1.94600	0.257754
$58$	0.973690	0.127852
$59$	−11.4822	−1.49485	−0.747426	−	0.664345i	$-0.768711\pi$
$59$	−11.4822	−1.49485	−0.747426	+	0.664345i	$0.768711\pi$
$60$	−2.20204	−0.284283
$61$	8.14270	1.04257	0.521283	−	0.853384i	$-0.325454\pi$
$61$	8.14270	1.04257	0.521283	+	0.853384i	$0.325454\pi$
$62$	−7.62128	−0.967904
$63$	1.19593	0.150674
$64$	7.07190	0.883987
$65$	2.05197	0.254515
$66$	0.184029	0.0226524
$67$	−11.6167	−1.41920	−0.709602	−	0.704603i	$-0.751125\pi$
$67$	−11.6167	−1.41920	−0.709602	+	0.704603i	$0.751125\pi$
$68$	3.50554	0.425110
$69$	−1.99867	−0.240612
$70$	2.67490	0.319711
$71$	−0.764133	−0.0906859	−0.0453429	−	0.998971i	$-0.514438\pi$
$71$	−0.764133	−0.0906859	−0.0453429	+	0.998971i	$0.514438\pi$
$72$	3.00510	0.354154
$73$	0.600213	0.0702496	0.0351248	−	0.999383i	$-0.488817\pi$
$73$	0.600213	0.0702496	0.0351248	+	0.999383i	$0.488817\pi$
$74$	6.78762	0.789045
$75$	0.0487581	0.00563010
$76$	1.92580	0.220905
$77$	0.218953	0.0249520
$78$	−0.926948	−0.104956
$79$	4.72022	0.531066	0.265533	−	0.964102i	$-0.414452\pi$
$79$	4.72022	0.531066	0.265533	+	0.964102i	$0.414452\pi$
$80$	2.31728	0.259079
$81$	1.00000	0.111111
$82$	5.82638	0.643417
$83$	4.37640	0.480372	0.240186	−	0.970727i	$-0.422791\pi$
$83$	4.37640	0.480372	0.240186	+	0.970727i	$0.422791\pi$
$84$	1.18352	0.129133
$85$	7.88213	0.854937
$86$	−8.54533	−0.921467
$87$	0.968676	0.103853
$88$	0.550176	0.0586490
$89$	6.54432	0.693697	0.346848	−	0.937921i	$-0.387252\pi$
$89$	6.54432	0.693697	0.346848	+	0.937921i	$0.387252\pi$
$90$	2.23666	0.235764
$91$	−1.10286	−0.115611
$92$	−1.97793	−0.206213
$93$	−7.58204	−0.786221
$94$	−2.06956	−0.213459
$95$	4.33012	0.444261
$96$	4.96339	0.506574
$97$	10.5115	1.06728	0.533641	−	0.845711i	$-0.320823\pi$
$97$	10.5115	1.06728	0.533641	+	0.845711i	$0.320823\pi$
$98$	5.59857	0.565541
$99$	0.183081	0.0184003
$100$	0.0482521	0.00482521
$101$	−6.87142	−0.683732	−0.341866	−	0.939749i	$-0.611059\pi$
$101$	−6.87142	−0.683732	−0.341866	+	0.939749i	$0.611059\pi$
$102$	−3.56064	−0.352556
$103$	16.7629	1.65170	0.825849	−	0.563891i	$-0.190696\pi$
$103$	16.7629	1.65170	0.825849	+	0.563891i	$0.190696\pi$
$104$	−2.77122	−0.271741
$105$	2.66112	0.259699
$106$	10.6973	1.03901
$107$	2.02402	0.195669	0.0978345	−	0.995203i	$-0.468808\pi$
$107$	2.02402	0.195669	0.0978345	+	0.995203i	$0.468808\pi$
$108$	0.989621	0.0952263
$109$	17.9319	1.71757	0.858784	−	0.512338i	$-0.171220\pi$
$109$	17.9319	1.71757	0.858784	+	0.512338i	$0.171220\pi$
$110$	0.409489	0.0390433
$111$	6.75267	0.640935
$112$	−1.24546	−0.117684
$113$	15.0236	1.41330	0.706652	−	0.707562i	$-0.250205\pi$
$113$	15.0236	1.41330	0.706652	+	0.707562i	$0.250205\pi$
$114$	−1.95607	−0.183203
$115$	−4.44732	−0.414715
$116$	0.958623	0.0890059
$117$	−0.922175	−0.0852551
$118$	11.5416	1.06249
$119$	−4.23637	−0.388348
$120$	6.68675	0.610414
$121$	−10.9665	−0.996953
$122$	−8.18485	−0.741021
$123$	5.79638	0.522642
$124$	−7.50335	−0.673821
$125$	11.2342	1.00482
$126$	−1.20213	−0.107094
$127$	15.5680	1.38144	0.690718	−	0.723124i	$-0.257295\pi$
$127$	15.5680	1.38144	0.690718	+	0.723124i	$0.257295\pi$
$128$	2.81828	0.249103
$129$	−8.50133	−0.748500
$130$	−2.06259	−0.180901
$131$	19.0765	1.66672	0.833361	−	0.552730i	$-0.186414\pi$
$131$	19.0765	1.66672	0.833361	+	0.552730i	$0.186414\pi$
$132$	0.181181	0.0157698
$133$	−2.32729	−0.201802
$134$	11.6768	1.00872
$135$	2.22514	0.191509
$136$	−10.6450	−0.912799
$137$	−0.898816	−0.0767910	−0.0383955	−	0.999263i	$-0.512225\pi$
$137$	−0.898816	−0.0767910	−0.0383955	+	0.999263i	$0.512225\pi$
$138$	2.00902	0.171019
$139$	19.9534	1.69243	0.846213	−	0.532845i	$-0.178877\pi$
$139$	19.9534	1.69243	0.846213	+	0.532845i	$0.178877\pi$
$140$	2.63350	0.222572
$141$	−2.05890	−0.173391
$142$	0.768088	0.0644565
$143$	−0.168833	−0.0141185
$144$	−1.04141	−0.0867840
$145$	2.15544	0.178999
$146$	−0.603319	−0.0499311
$147$	5.56974	0.459384
$148$	6.68259	0.549305
$149$	0.254994	0.0208899	0.0104449	−	0.999945i	$-0.496675\pi$
$149$	0.254994	0.0208899	0.0104449	+	0.999945i	$0.496675\pi$
$150$	−0.0490105	−0.00400169
$151$	15.5680	1.26690	0.633452	−	0.773782i	$-0.281637\pi$
$151$	15.5680	1.26690	0.633452	+	0.773782i	$0.281637\pi$
$152$	−5.84791	−0.474329
$153$	−3.54231	−0.286379
$154$	−0.220086	−0.0177351
$155$	−16.8711	−1.35512
$156$	−0.912604	−0.0730668
$157$	15.7071	1.25356	0.626782	−	0.779195i	$-0.284372\pi$
$157$	15.7071	1.25356	0.626782	+	0.779195i	$0.284372\pi$
$158$	−4.74465	−0.377464
$159$	10.6422	0.843983
$160$	11.0442	0.873124
$161$	2.39028	0.188380
$162$	−1.00518	−0.0789741
$163$	−21.4186	−1.67763	−0.838816	−	0.544415i	$-0.816752\pi$
$163$	−21.4186	−1.67763	−0.838816	+	0.544415i	$0.816752\pi$
$164$	5.73622	0.447924
$165$	0.407381	0.0317146
$166$	−4.39905	−0.341433
$167$	−23.6367	−1.82906	−0.914530	−	0.404517i	$-0.867440\pi$
$167$	−23.6367	−1.82906	−0.914530	+	0.404517i	$0.867440\pi$
$168$	−3.59390	−0.277275
$169$	−12.1496	−0.934584
$170$	−7.92293	−0.607661
$171$	−1.94600	−0.148814
$172$	−8.41309	−0.641492
$173$	−3.89164	−0.295876	−0.147938	−	0.988997i	$-0.547264\pi$
$173$	−3.89164	−0.295876	−0.147938	+	0.988997i	$0.547264\pi$
$174$	−0.973690	−0.0738153
$175$	−0.0583116	−0.00440794
$176$	−0.190662	−0.0143717
$177$	11.4822	0.863054
$178$	−6.57820	−0.493057
$179$	11.6125	0.867957	0.433978	−	0.900923i	$-0.357109\pi$
$179$	11.6125	0.867957	0.433978	+	0.900923i	$0.357109\pi$
$180$	2.20204	0.164131
$181$	−3.76916	−0.280160	−0.140080	−	0.990140i	$-0.544736\pi$
$181$	−3.76916	−0.280160	−0.140080	+	0.990140i	$0.544736\pi$
$182$	1.10857	0.0821726
$183$	−8.14270	−0.601926
$184$	6.00620	0.442783
$185$	15.0256	1.10471
$186$	7.62128	0.558820
$187$	−0.648530	−0.0474252
$188$	−2.03753	−0.148602
$189$	−1.19593	−0.0869915
$190$	−4.35253	−0.315766
$191$	15.5790	1.12726	0.563630	−	0.826027i	$-0.309404\pi$
$191$	15.5790	1.12726	0.563630	+	0.826027i	$0.309404\pi$
$192$	−7.07190	−0.510370
$193$	25.5855	1.84168	0.920842	−	0.389937i	$-0.127503\pi$
$193$	25.5855	1.84168	0.920842	+	0.389937i	$0.127503\pi$
$194$	−10.5659	−0.758589
$195$	−2.05197	−0.146944
$196$	5.51193	0.393709
$197$	−11.1257	−0.792671	−0.396336	−	0.918106i	$-0.629718\pi$
$197$	−11.1257	−0.792671	−0.396336	+	0.918106i	$0.629718\pi$
$198$	−0.184029	−0.0130784
$199$	−7.16923	−0.508213	−0.254107	−	0.967176i	$-0.581781\pi$
$199$	−7.16923	−0.508213	−0.254107	+	0.967176i	$0.581781\pi$
$200$	−0.146523	−0.0103607
$201$	11.6167	0.819378
$202$	6.90699	0.485974
$203$	−1.15847	−0.0813089
$204$	−3.50554	−0.245437
$205$	12.8978	0.900818
$206$	−16.8497	−1.17397
$207$	1.99867	0.138917
$208$	0.960360	0.0665890
$209$	−0.356276	−0.0246441
$210$	−2.67490	−0.184585
$211$	−21.3863	−1.47230	−0.736148	−	0.676821i	$-0.763357\pi$
$211$	−21.3863	−1.47230	−0.736148	+	0.676821i	$0.763357\pi$
$212$	10.5318	0.723324
$213$	0.764133	0.0523575
$214$	−2.03449	−0.139075
$215$	−18.9166	−1.29010
$216$	−3.00510	−0.204471
$217$	9.06763	0.615551
$218$	−18.0248	−1.22079
$219$	−0.600213	−0.0405586
$220$	0.403153	0.0271805
$221$	3.26663	0.219737
$222$	−6.78762	−0.455556
$223$	−5.21201	−0.349022	−0.174511	−	0.984655i	$-0.555834\pi$
$223$	−5.21201	−0.349022	−0.174511	+	0.984655i	$0.555834\pi$
$224$	−5.93590	−0.396609
$225$	−0.0487581	−0.00325054
$226$	−15.1014	−1.00453
$227$	−11.8389	−0.785773	−0.392886	−	0.919587i	$-0.628523\pi$
$227$	−11.8389	−0.785773	−0.392886	+	0.919587i	$0.628523\pi$
$228$	−1.92580	−0.127539
$229$	12.1901	0.805543	0.402771	−	0.915301i	$-0.368047\pi$
$229$	12.1901	0.805543	0.402771	+	0.915301i	$0.368047\pi$
$230$	4.47034	0.294765
$231$	−0.218953	−0.0144061
$232$	−2.91096	−0.191114
$233$	9.22288	0.604211	0.302105	−	0.953275i	$-0.402311\pi$
$233$	9.22288	0.604211	0.302105	+	0.953275i	$0.402311\pi$
$234$	0.926948	0.0605965
$235$	−4.58134	−0.298854
$236$	11.3630	0.739669
$237$	−4.72022	−0.306611
$238$	4.25830	0.276024
$239$	0.925473	0.0598639	0.0299319	−	0.999552i	$-0.490471\pi$
$239$	0.925473	0.0598639	0.0299319	+	0.999552i	$0.490471\pi$
$240$	−2.31728	−0.149580
$241$	−4.24397	−0.273378	−0.136689	−	0.990614i	$-0.543646\pi$
$241$	−4.24397	−0.273378	−0.136689	+	0.990614i	$0.543646\pi$
$242$	11.0232	0.708601
$243$	−1.00000	−0.0641500
$244$	−8.05819	−0.515873
$245$	12.3934	0.791788
$246$	−5.82638	−0.371477
$247$	1.79455	0.114185
$248$	22.7848	1.44683
$249$	−4.37640	−0.277343
$250$	−11.2923	−0.714190
$251$	−18.3525	−1.15840	−0.579199	−	0.815186i	$-0.696635\pi$
$251$	−18.3525	−1.15840	−0.579199	+	0.815186i	$0.696635\pi$
$252$	−1.18352	−0.0745549
$253$	0.365919	0.0230051
$254$	−15.6486	−0.981878
$255$	−7.88213	−0.493598
$256$	−16.9767	−1.06104
$257$	16.7036	1.04194	0.520971	−	0.853574i	$-0.325570\pi$
$257$	16.7036	1.04194	0.520971	+	0.853574i	$0.325570\pi$
$258$	8.54533	0.532009
$259$	−8.07576	−0.501803
$260$	−2.03067	−0.125937
$261$	−0.968676	−0.0599596
$262$	−19.1752	−1.18465
$263$	−23.8638	−1.47150	−0.735752	−	0.677251i	$-0.763171\pi$
$263$	−23.8638	−1.47150	−0.735752	+	0.677251i	$0.763171\pi$
$264$	−0.550176	−0.0338610
$265$	23.6804	1.45468
$266$	2.33934	0.143434
$267$	−6.54432	−0.400506
$268$	11.4961	0.702237
$269$	−4.91838	−0.299879	−0.149939	−	0.988695i	$-0.547908\pi$
$269$	−4.91838	−0.299879	−0.149939	+	0.988695i	$0.547908\pi$
$270$	−2.23666	−0.136119
$271$	28.5715	1.73560	0.867798	−	0.496917i	$-0.165535\pi$
$271$	28.5715	1.73560	0.867798	+	0.496917i	$0.165535\pi$
$272$	3.68899	0.223678
$273$	1.10286	0.0667482
$274$	0.903468	0.0545805
$275$	−0.00892669	−0.000538300 0
$276$	1.97793	0.119057
$277$	−1.72049	−0.103374	−0.0516870	−	0.998663i	$-0.516460\pi$
$277$	−1.72049	−0.103374	−0.0516870	+	0.998663i	$0.516460\pi$
$278$	−20.0567	−1.20292
$279$	7.58204	0.453925
$280$	−7.99692	−0.477908
$281$	−21.5399	−1.28496	−0.642482	−	0.766301i	$-0.722095\pi$
$281$	−21.5399	−1.28496	−0.642482	+	0.766301i	$0.722095\pi$
$282$	2.06956	0.123240
$283$	29.5818	1.75846	0.879228	−	0.476401i	$-0.158059\pi$
$283$	29.5818	1.75846	0.879228	+	0.476401i	$0.158059\pi$
$284$	0.756202	0.0448723
$285$	−4.33012	−0.256494
$286$	0.169707	0.0100350
$287$	−6.93210	−0.409189
$288$	−4.96339	−0.292471
$289$	−4.45205	−0.261885
$290$	−2.16660	−0.127227
$291$	−10.5115	−0.616196
$292$	−0.593983	−0.0347602
$293$	0.784142	0.0458101	0.0229050	−	0.999738i	$-0.492708\pi$
$293$	0.784142	0.0458101	0.0229050	+	0.999738i	$0.492708\pi$
$294$	−5.59857	−0.326515
$295$	25.5494	1.48755
$296$	−20.2924	−1.17947
$297$	−0.183081	−0.0106234
$298$	−0.256314	−0.0148478
$299$	−1.84312	−0.106591
$300$	−0.0482521	−0.00278584
$301$	10.1670	0.586018
$302$	−15.6486	−0.900473
$303$	6.87142	0.394753
$304$	2.02658	0.116232
$305$	−18.1186	−1.03747
$306$	3.56064	0.203548
$307$	12.2895	0.701396	0.350698	−	0.936489i	$-0.385944\pi$
$307$	12.2895	0.701396	0.350698	+	0.936489i	$0.385944\pi$
$308$	−0.216681	−0.0123465
$309$	−16.7629	−0.953608
$310$	16.9584	0.963173
$311$	17.0854	0.968824	0.484412	−	0.874840i	$-0.339034\pi$
$311$	17.0854	0.968824	0.484412	+	0.874840i	$0.339034\pi$
$312$	2.77122	0.156890
$313$	−0.845851	−0.0478103	−0.0239052	−	0.999714i	$-0.507610\pi$
$313$	−0.845851	−0.0478103	−0.0239052	+	0.999714i	$0.507610\pi$
$314$	−15.7884	−0.890991
$315$	−2.66112	−0.149937
$316$	−4.67123	−0.262777
$317$	2.22653	0.125054	0.0625272	−	0.998043i	$-0.480084\pi$
$317$	2.22653	0.125054	0.0625272	+	0.998043i	$0.480084\pi$
$318$	−10.6973	−0.599875
$319$	−0.177346	−0.00992949
$320$	−15.7360	−0.879667
$321$	−2.02402	−0.112970
$322$	−2.40265	−0.133895
$323$	6.89333	0.383555
$324$	−0.989621	−0.0549790
$325$	0.0449635	0.00249413
$326$	21.5294	1.19241
$327$	−17.9319	−0.991638
$328$	−17.4187	−0.961786
$329$	2.46231	0.135752
$330$	−0.409489	−0.0225417
$331$	−2.11349	−0.116168	−0.0580841	−	0.998312i	$-0.518499\pi$
$331$	−2.11349	−0.116168	−0.0580841	+	0.998312i	$0.518499\pi$
$332$	−4.33098	−0.237693
$333$	−6.75267	−0.370044
$334$	23.7590	1.30004
$335$	25.8487	1.41227
$336$	1.24546	0.0679452
$337$	21.8277	1.18903	0.594515	−	0.804085i	$-0.297344\pi$
$337$	21.8277	1.18903	0.594515	+	0.804085i	$0.297344\pi$
$338$	12.2125	0.664271
$339$	−15.0236	−0.815971
$340$	−7.80032	−0.423032
$341$	1.38813	0.0751714
$342$	1.95607	0.105772
$343$	−15.0326	−0.811684
$344$	25.5473	1.37742
$345$	4.44732	0.239436
$346$	3.91179	0.210299
$347$	−0.256758	−0.0137835	−0.00689174	−	0.999976i	$-0.502194\pi$
$347$	−0.256758	−0.0137835	−0.00689174	+	0.999976i	$0.502194\pi$
$348$	−0.958623	−0.0513876
$349$	−14.2588	−0.763254	−0.381627	−	0.924316i	$-0.624636\pi$
$349$	−14.2588	−0.763254	−0.381627	+	0.924316i	$0.624636\pi$
$350$	0.0586134	0.00313302
$351$	0.922175	0.0492221
$352$	−0.908703	−0.0484341
$353$	15.1733	0.807592	0.403796	−	0.914849i	$-0.367690\pi$
$353$	15.1733	0.807592	0.403796	+	0.914849i	$0.367690\pi$
$354$	−11.5416	−0.613430
$355$	1.70030	0.0902426
$356$	−6.47640	−0.343249
$357$	4.23637	0.224213
$358$	−11.6726	−0.616915
$359$	8.42784	0.444804	0.222402	−	0.974955i	$-0.428610\pi$
$359$	8.42784	0.444804	0.222402	+	0.974955i	$0.428610\pi$
$360$	−6.68675	−0.352423
$361$	−15.2131	−0.800689
$362$	3.78867	0.199128
$363$	10.9665	0.575591
$364$	1.09141	0.0572057
$365$	−1.33556	−0.0699062
$366$	8.18485	0.427829
$367$	−8.87584	−0.463315	−0.231657	−	0.972797i	$-0.574415\pi$
$367$	−8.87584	−0.463315	−0.231657	+	0.972797i	$0.574415\pi$
$368$	−2.08143	−0.108502
$369$	−5.79638	−0.301748
$370$	−15.1034	−0.785189
$371$	−12.7274	−0.660774
$372$	7.50335	0.389030
$373$	−19.1125	−0.989609	−0.494805	−	0.869004i	$-0.664760\pi$
$373$	−19.1125	−0.989609	−0.494805	+	0.869004i	$0.664760\pi$
$374$	0.651887	0.0337083
$375$	−11.2342	−0.580131
$376$	6.18719	0.319080
$377$	0.893289	0.0460067
$378$	1.20213	0.0618306
$379$	35.5569	1.82643	0.913217	−	0.407474i	$-0.133590\pi$
$379$	35.5569	1.82643	0.913217	+	0.407474i	$0.133590\pi$
$380$	−4.28518	−0.219825
$381$	−15.5680	−0.797572
$382$	−15.6597	−0.801219
$383$	15.0541	0.769231	0.384615	−	0.923077i	$-0.374334\pi$
$383$	15.0541	0.769231	0.384615	+	0.923077i	$0.374334\pi$
$384$	−2.81828	−0.143820
$385$	−0.487201	−0.0248301
$386$	−25.7179	−1.30901
$387$	8.50133	0.432147
$388$	−10.4024	−0.528103
$389$	18.5223	0.939118	0.469559	−	0.882901i	$-0.344413\pi$
$389$	18.5223	0.939118	0.469559	+	0.882901i	$0.344413\pi$
$390$	2.06259	0.104443
$391$	−7.07991	−0.358046
$392$	−16.7376	−0.845376
$393$	−19.0765	−0.962282
$394$	11.1833	0.563405
$395$	−10.5031	−0.528470
$396$	−0.181181	−0.00910468
$397$	0.823661	0.0413384	0.0206692	−	0.999786i	$-0.493420\pi$
$397$	0.823661	0.0413384	0.0206692	+	0.999786i	$0.493420\pi$
$398$	7.20634	0.361221
$399$	2.32729	0.116510
$400$	0.0507771	0.00253885
$401$	−1.28410	−0.0641249	−0.0320625	−	0.999486i	$-0.510208\pi$
$401$	−1.28410	−0.0641249	−0.0320625	+	0.999486i	$0.510208\pi$
$402$	−11.6768	−0.582386
$403$	−6.99197	−0.348295
$404$	6.80011	0.338318
$405$	−2.22514	−0.110568
$406$	1.16447	0.0577917
$407$	−1.23629	−0.0612805
$408$	10.6450	0.527005
$409$	15.5447	0.768636	0.384318	−	0.923201i	$-0.374437\pi$
$409$	15.5447	0.768636	0.384318	+	0.923201i	$0.374437\pi$
$410$	−12.9645	−0.640272
$411$	0.898816	0.0443353
$412$	−16.5889	−0.817278
$413$	−13.7319	−0.675705
$414$	−2.00902	−0.0987377
$415$	−9.73810	−0.478025
$416$	4.57712	0.224412
$417$	−19.9534	−0.977122
$418$	0.358120	0.0175162
$419$	17.6572	0.862609	0.431305	−	0.902206i	$-0.358053\pi$
$419$	17.6572	0.862609	0.431305	+	0.902206i	$0.358053\pi$
$420$	−2.63350	−0.128502
$421$	38.0435	1.85413	0.927063	−	0.374906i	$-0.122325\pi$
$421$	38.0435	1.85413	0.927063	+	0.374906i	$0.122325\pi$
$422$	21.4970	1.04646
$423$	2.05890	0.100107
$424$	−31.9809	−1.55313
$425$	0.172716	0.00837797
$426$	−0.768088	−0.0372140
$427$	9.73814	0.471262
$428$	−2.00301	−0.0968191
$429$	0.168833	0.00815132
$430$	19.0145	0.916963
$431$	1.34886	0.0649722	0.0324861	−	0.999472i	$-0.489658\pi$
$431$	1.34886	0.0649722	0.0324861	+	0.999472i	$0.489658\pi$
$432$	1.04141	0.0501047
$433$	−10.0279	−0.481910	−0.240955	−	0.970536i	$-0.577461\pi$
$433$	−10.0279	−0.481910	−0.240955	+	0.970536i	$0.577461\pi$
$434$	−9.11456	−0.437513
$435$	−2.15544	−0.103345
$436$	−17.7458	−0.849871
$437$	−3.88941	−0.186056
$438$	0.603319	0.0288277
$439$	34.2333	1.63387	0.816933	−	0.576732i	$-0.195672\pi$
$439$	34.2333	1.63387	0.816933	+	0.576732i	$0.195672\pi$
$440$	−1.22422	−0.0583623
$441$	−5.56974	−0.265226
$442$	−3.28354	−0.156182
$443$	14.9489	0.710246	0.355123	−	0.934820i	$-0.384439\pi$
$443$	14.9489	0.710246	0.355123	+	0.934820i	$0.384439\pi$
$444$	−6.68259	−0.317142
$445$	−14.5620	−0.690306
$446$	5.23898	0.248073
$447$	−0.254994	−0.0120608
$448$	8.45753	0.399581
$449$	24.7561	1.16831	0.584155	−	0.811642i	$-0.301426\pi$
$449$	24.7561	1.16831	0.584155	+	0.811642i	$0.301426\pi$
$450$	0.0490105	0.00231038
$451$	−1.06121	−0.0499703
$452$	−14.8677	−0.699317
$453$	−15.5680	−0.731448
$454$	11.9001	0.558501
$455$	2.45402	0.115046
$456$	5.84791	0.273854
$457$	7.70270	0.360317	0.180159	−	0.983638i	$-0.442339\pi$
$457$	7.70270	0.360317	0.180159	+	0.983638i	$0.442339\pi$
$458$	−12.2532	−0.572553
$459$	3.54231	0.165341
$460$	4.40116	0.205205
$461$	36.7743	1.71275	0.856376	−	0.516353i	$-0.172711\pi$
$461$	36.7743	1.71275	0.856376	+	0.516353i	$0.172711\pi$
$462$	0.220086	0.0102393
$463$	−28.7933	−1.33814	−0.669070	−	0.743200i	$-0.733307\pi$
$463$	−28.7933	−1.33814	−0.669070	+	0.743200i	$0.733307\pi$
$464$	1.00879	0.0468317
$465$	16.8711	0.782378
$466$	−9.27061	−0.429453
$467$	−22.9695	−1.06290	−0.531450	−	0.847090i	$-0.678353\pi$
$467$	−22.9695	−1.06290	−0.531450	+	0.847090i	$0.678353\pi$
$468$	0.912604	0.0421851
$469$	−13.8928	−0.641510
$470$	4.60505	0.212415
$471$	−15.7071	−0.723745
$472$	−34.5051	−1.58822
$473$	1.55643	0.0715648
$474$	4.74465	0.217929
$475$	0.0948833	0.00435354
$476$	4.19240	0.192158
$477$	−10.6422	−0.487274
$478$	−0.930264	−0.0425493
$479$	−15.9554	−0.729021	−0.364511	−	0.931199i	$-0.618764\pi$
$479$	−15.9554	−0.729021	−0.364511	+	0.931199i	$0.618764\pi$
$480$	−11.0442	−0.504098
$481$	6.22715	0.283933
$482$	4.26594	0.194308
$483$	−2.39028	−0.108762
$484$	10.8527	0.493303
$485$	−23.3896	−1.06207
$486$	1.00518	0.0455957
$487$	9.13415	0.413908	0.206954	−	0.978351i	$-0.433645\pi$
$487$	9.13415	0.413908	0.206954	+	0.978351i	$0.433645\pi$
$488$	24.4696	1.10769
$489$	21.4186	0.968582
$490$	−12.4576	−0.562777
$491$	−19.0617	−0.860241	−0.430121	−	0.902771i	$-0.641529\pi$
$491$	−19.0617	−0.860241	−0.430121	+	0.902771i	$0.641529\pi$
$492$	−5.73622	−0.258609
$493$	3.43135	0.154540
$494$	−1.80384	−0.0811586
$495$	−0.407381	−0.0183104
$496$	−7.89599	−0.354541
$497$	−0.913853	−0.0409919
$498$	4.39905	0.197126
$499$	−16.3552	−0.732159	−0.366080	−	0.930583i	$-0.619300\pi$
$499$	−16.3552	−0.732159	−0.366080	+	0.930583i	$0.619300\pi$
$500$	−11.1176	−0.497194
$501$	23.6367	1.05601
$502$	18.4475	0.823351
$503$	23.2252	1.03556	0.517780	−	0.855514i	$-0.326758\pi$
$503$	23.2252	1.03556	0.517780	+	0.855514i	$0.326758\pi$
$504$	3.59390	0.160085
$505$	15.2899	0.680390
$506$	−0.367813	−0.0163513
$507$	12.1496	0.539582
$508$	−15.4064	−0.683549
$509$	23.4098	1.03762	0.518811	−	0.854889i	$-0.326375\pi$
$509$	23.4098	1.03762	0.518811	+	0.854889i	$0.326375\pi$
$510$	7.92293	0.350833
$511$	0.717815	0.0317543
$512$	11.4280	0.505050
$513$	1.94600	0.0859180
$514$	−16.7901	−0.740578
$515$	−37.2998	−1.64363
$516$	8.41309	0.370366
$517$	0.376946	0.0165781
$518$	8.11756	0.356665
$519$	3.89164	0.170824
$520$	6.16636	0.270413
$521$	−33.6346	−1.47356	−0.736780	−	0.676133i	$-0.763655\pi$
$521$	−33.6346	−1.47356	−0.736780	+	0.676133i	$0.763655\pi$
$522$	0.973690	0.0426173
$523$	2.54007	0.111070	0.0555348	−	0.998457i	$-0.482314\pi$
$523$	2.54007	0.111070	0.0555348	+	0.998457i	$0.482314\pi$
$524$	−18.8785	−0.824711
$525$	0.0583116	0.00254492
$526$	23.9873	1.04590
$527$	−26.8579	−1.16995
$528$	0.190662	0.00829750
$529$	−19.0053	−0.826318
$530$	−23.8030	−1.03394
$531$	−11.4822	−0.498284
$532$	2.30313	0.0998535
$533$	5.34528	0.231530
$534$	6.57820	0.284666
$535$	−4.50372	−0.194713
$536$	−34.9092	−1.50785
$537$	−11.6125	−0.501115
$538$	4.94384	0.213144
$539$	−1.01971	−0.0439222
$540$	−2.20204	−0.0947609
$541$	−0.644430	−0.0277062	−0.0138531	−	0.999904i	$-0.504410\pi$
$541$	−0.644430	−0.0277062	−0.0138531	+	0.999904i	$0.504410\pi$
$542$	−28.7194	−1.23360
$543$	3.76916	0.161750
$544$	17.5819	0.753817
$545$	−39.9010	−1.70917
$546$	−1.10857	−0.0474424
$547$	−31.4714	−1.34562	−0.672809	−	0.739816i	$-0.734913\pi$
$547$	−31.4714	−1.34562	−0.672809	+	0.739816i	$0.734913\pi$
$548$	0.889488	0.0379970
$549$	8.14270	0.347522
$550$	0.00897290	0.000382606 0
$551$	1.88504	0.0803056
$552$	−6.00620	−0.255641
$553$	5.64507	0.240053
$554$	1.72939	0.0734748
$555$	−15.0256	−0.637803
$556$	−19.7463	−0.837430
$557$	−15.7215	−0.666140	−0.333070	−	0.942902i	$-0.608084\pi$
$557$	−15.7215	−0.666140	−0.333070	+	0.942902i	$0.608084\pi$
$558$	−7.62128	−0.322635
$559$	−7.83971	−0.331584
$560$	2.77131	0.117109
$561$	0.648530	0.0273809
$562$	21.6514	0.913310
$563$	38.9763	1.64266	0.821328	−	0.570456i	$-0.193233\pi$
$563$	38.9763	1.64266	0.821328	+	0.570456i	$0.193233\pi$
$564$	2.03753	0.0857956
$565$	−33.4296	−1.40640
$566$	−29.7349	−1.24985
$567$	1.19593	0.0502245
$568$	−2.29629	−0.0963503
$569$	31.9292	1.33854	0.669271	−	0.743019i	$-0.266607\pi$
$569$	31.9292	1.33854	0.669271	+	0.743019i	$0.266607\pi$
$570$	4.35253	0.182307
$571$	40.6078	1.69938	0.849692	−	0.527279i	$-0.176788\pi$
$571$	40.6078	1.69938	0.849692	+	0.527279i	$0.176788\pi$
$572$	0.167081	0.00698599
$573$	−15.5790	−0.650824
$574$	6.96798	0.290838
$575$	−0.0974514	−0.00406401
$576$	7.07190	0.294662
$577$	−2.21788	−0.0923314	−0.0461657	−	0.998934i	$-0.514700\pi$
$577$	−2.21788	−0.0923314	−0.0461657	+	0.998934i	$0.514700\pi$
$578$	4.47509	0.186139
$579$	−25.5855	−1.06330
$580$	−2.13307	−0.0885708
$581$	5.23389	0.217138
$582$	10.5659	0.437972
$583$	−1.94839	−0.0806940
$584$	1.80370	0.0746375
$585$	2.05197	0.0848384
$586$	−0.788201	−0.0325603
$587$	−11.1965	−0.462131	−0.231065	−	0.972938i	$-0.574221\pi$
$587$	−11.1965	−0.462131	−0.231065	+	0.972938i	$0.574221\pi$
$588$	−5.51193	−0.227308
$589$	−14.7546	−0.607955
$590$	−25.6817	−1.05730
$591$	11.1257	0.457649
$592$	7.03228	0.289025
$593$	−22.5170	−0.924663	−0.462331	−	0.886707i	$-0.652987\pi$
$593$	−22.5170	−0.924663	−0.462331	+	0.886707i	$0.652987\pi$
$594$	0.184029	0.00755079
$595$	9.42651	0.386449
$596$	−0.252347	−0.0103365
$597$	7.16923	0.293417
$598$	1.85266	0.0757611
$599$	−21.9993	−0.898868	−0.449434	−	0.893314i	$-0.648374\pi$
$599$	−21.9993	−0.898868	−0.449434	+	0.893314i	$0.648374\pi$
$600$	0.146523	0.00598177
$601$	31.0130	1.26505	0.632523	−	0.774542i	$-0.282019\pi$
$601$	31.0130	1.26505	0.632523	+	0.774542i	$0.282019\pi$
$602$	−10.2197	−0.416522
$603$	−11.6167	−0.473068
$604$	−15.4064	−0.626878
$605$	24.4019	0.992080
$606$	−6.90699	−0.280577
$607$	20.4663	0.830700	0.415350	−	0.909662i	$-0.363659\pi$
$607$	20.4663	0.830700	0.415350	+	0.909662i	$0.363659\pi$
$608$	9.65876	0.391714
$609$	1.15847	0.0469437
$610$	18.2124	0.737399
$611$	−1.89867	−0.0768118
$612$	3.50554	0.141703
$613$	−32.9463	−1.33069	−0.665343	−	0.746538i	$-0.731715\pi$
$613$	−32.9463	−1.33069	−0.665343	+	0.746538i	$0.731715\pi$
$614$	−12.3531	−0.498529
$615$	−12.8978	−0.520088
$616$	0.657975	0.0265106
$617$	3.34521	0.134673	0.0673365	−	0.997730i	$-0.478550\pi$
$617$	3.34521	0.134673	0.0673365	+	0.997730i	$0.478550\pi$
$618$	16.8497	0.677793
$619$	−21.1538	−0.850244	−0.425122	−	0.905136i	$-0.639769\pi$
$619$	−21.1538	−0.850244	−0.425122	+	0.905136i	$0.639769\pi$
$620$	16.6960	0.670527
$621$	−1.99867	−0.0802039
$622$	−17.1738	−0.688608
$623$	7.82658	0.313565
$624$	−0.960360	−0.0384452
$625$	−24.7538	−0.990153
$626$	0.850229	0.0339820
$627$	0.356276	0.0142283
$628$	−15.5441	−0.620276
$629$	23.9201	0.953755
$630$	2.67490	0.106570
$631$	0.527461	0.0209979	0.0104989	−	0.999945i	$-0.496658\pi$
$631$	0.527461	0.0209979	0.0104989	+	0.999945i	$0.496658\pi$
$632$	14.1847	0.564237
$633$	21.3863	0.850030
$634$	−2.23805	−0.0888845
$635$	−34.6409	−1.37468
$636$	−10.5318	−0.417612
$637$	5.13627	0.203507
$638$	0.178264	0.00705755
$639$	−0.764133	−0.0302286
$640$	−6.27107	−0.247886
$641$	35.6179	1.40682	0.703411	−	0.710784i	$-0.251659\pi$
$641$	35.6179	1.40682	0.703411	+	0.710784i	$0.251659\pi$
$642$	2.03449	0.0802950
$643$	27.5620	1.08694	0.543470	−	0.839428i	$-0.317110\pi$
$643$	27.5620	1.08694	0.543470	+	0.839428i	$0.317110\pi$
$644$	−2.36547	−0.0932126
$645$	18.9166	0.744842
$646$	−6.92901	−0.272618
$647$	−40.3509	−1.58636	−0.793179	−	0.608989i	$-0.791575\pi$
$647$	−40.3509	−1.58636	−0.793179	+	0.608989i	$0.791575\pi$
$648$	3.00510	0.118051
$649$	−2.10217	−0.0825174
$650$	−0.0451963	−0.00177274
$651$	−9.06763	−0.355388
$652$	21.1963	0.830110
$653$	16.4009	0.641815	0.320908	−	0.947111i	$-0.396012\pi$
$653$	16.4009	0.641815	0.320908	+	0.947111i	$0.396012\pi$
$654$	18.0248	0.704824
$655$	−42.4479	−1.65857
$656$	6.03640	0.235682
$657$	0.600213	0.0234165
$658$	−2.47506	−0.0964878
$659$	0.592201	0.0230689	0.0115344	−	0.999933i	$-0.496328\pi$
$659$	0.592201	0.0230689	0.0115344	+	0.999933i	$0.496328\pi$
$660$	−0.403153	−0.0156927
$661$	−10.5172	−0.409071	−0.204536	−	0.978859i	$-0.565568\pi$
$661$	−10.5172	−0.409071	−0.204536	+	0.978859i	$0.565568\pi$
$662$	2.12443	0.0825684
$663$	−3.26663	−0.126865
$664$	13.1515	0.510377
$665$	5.17854	0.200815
$666$	6.78762	0.263015
$667$	−1.93606	−0.0749647
$668$	23.3914	0.905039
$669$	5.21201	0.201508
$670$	−25.9825	−1.00379
$671$	1.49077	0.0575507
$672$	5.93590	0.228982
$673$	−21.6045	−0.832791	−0.416396	−	0.909184i	$-0.636707\pi$
$673$	−21.6045	−0.832791	−0.416396	+	0.909184i	$0.636707\pi$
$674$	−21.9407	−0.845122
$675$	0.0487581	0.00187670
$676$	12.0235	0.462442
$677$	1.00000	0.0384331
$677$	1.00000	0.0384331
$678$	15.1014	0.579965
$679$	12.5711	0.482434
$680$	23.6865	0.908338
$681$	11.8389	0.453666
$682$	−1.39531	−0.0534293
$683$	−3.08657	−0.118104	−0.0590521	−	0.998255i	$-0.518808\pi$
$683$	−3.08657	−0.118104	−0.0590521	+	0.998255i	$0.518808\pi$
$684$	1.92580	0.0736349
$685$	1.99999	0.0764157
$686$	15.1104	0.576918
$687$	−12.1901	−0.465080
$688$	−8.85335	−0.337531
$689$	9.81398	0.373883
$690$	−4.47034	−0.170183
$691$	10.0767	0.383334	0.191667	−	0.981460i	$-0.438611\pi$
$691$	10.0767	0.383334	0.191667	+	0.981460i	$0.438611\pi$
$692$	3.85125	0.146403
$693$	0.218953	0.00831734
$694$	0.258087	0.00979683
$695$	−44.3991	−1.68415
$696$	2.91096	0.110340
$697$	20.5326	0.777727
$698$	14.3326	0.542495
$699$	−9.22288	−0.348841
$700$	0.0577064	0.00218110
$701$	12.1646	0.459451	0.229725	−	0.973255i	$-0.426217\pi$
$701$	12.1646	0.459451	0.229725	+	0.973255i	$0.426217\pi$
$702$	−0.926948	−0.0349854
$703$	13.1407	0.495611
$704$	1.29473	0.0487970
$705$	4.58134	0.172543
$706$	−15.2518	−0.574010
$707$	−8.21778	−0.309061
$708$	−11.3630	−0.427048
$709$	−13.7509	−0.516426	−0.258213	−	0.966088i	$-0.583134\pi$
$709$	−13.7509	−0.516426	−0.258213	+	0.966088i	$0.583134\pi$
$710$	−1.70910	−0.0641415
$711$	4.72022	0.177022
$712$	19.6663	0.737026
$713$	15.1540	0.567522
$714$	−4.25830	−0.159363
$715$	0.375676	0.0140495
$716$	−11.4919	−0.429474
$717$	−0.925473	−0.0345624
$718$	−8.47146	−0.316152
$719$	10.1193	0.377385	0.188693	−	0.982036i	$-0.439575\pi$
$719$	10.1193	0.377385	0.188693	+	0.982036i	$0.439575\pi$
$720$	2.31728	0.0863598
$721$	20.0473	0.746602
$722$	15.2918	0.569103
$723$	4.24397	0.157835
$724$	3.73004	0.138626
$725$	0.0472308	0.00175411
$726$	−11.0232	−0.409111
$727$	8.71246	0.323127	0.161564	−	0.986862i	$-0.448346\pi$
$727$	8.71246	0.323127	0.161564	+	0.986862i	$0.448346\pi$
$728$	−3.31420	−0.122833
$729$	1.00000	0.0370370
$730$	1.34247	0.0496870
$731$	−30.1143	−1.11382
$732$	8.05819	0.297839
$733$	12.4062	0.458234	0.229117	−	0.973399i	$-0.426416\pi$
$733$	12.4062	0.458234	0.229117	+	0.973399i	$0.426416\pi$
$734$	8.92178	0.329309
$735$	−12.3934	−0.457139
$736$	−9.92019	−0.365663
$737$	−2.12679	−0.0783415
$738$	5.82638	0.214472
$739$	−47.1488	−1.73440	−0.867198	−	0.497964i	$-0.834081\pi$
$739$	−47.1488	−1.73440	−0.867198	+	0.497964i	$0.834081\pi$
$740$	−14.8697	−0.546621
$741$	−1.79455	−0.0659245
$742$	12.7933	0.469656
$743$	50.1036	1.83812	0.919062	−	0.394113i	$-0.128948\pi$
$743$	50.1036	1.83812	0.919062	+	0.394113i	$0.128948\pi$
$744$	−22.7848	−0.835330
$745$	−0.567396	−0.0207878
$746$	19.2115	0.703381
$747$	4.37640	0.160124
$748$	0.641799	0.0234665
$749$	2.42059	0.0884465
$750$	11.2923	0.412338
$751$	7.48513	0.273136	0.136568	−	0.990631i	$-0.456393\pi$
$751$	7.48513	0.273136	0.136568	+	0.990631i	$0.456393\pi$
$752$	−2.14416	−0.0781893
$753$	18.3525	0.668801
$754$	−0.897913	−0.0327000
$755$	−34.6409	−1.26071
$756$	1.18352	0.0430443
$757$	−35.2872	−1.28254	−0.641268	−	0.767317i	$-0.721591\pi$
$757$	−35.2872	−1.28254	−0.641268	+	0.767317i	$0.721591\pi$
$758$	−35.7409	−1.29817
$759$	−0.365919	−0.0132820
$760$	13.0124	0.472010
$761$	2.88904	0.104728	0.0523639	−	0.998628i	$-0.483324\pi$
$761$	2.88904	0.104728	0.0523639	+	0.998628i	$0.483324\pi$
$762$	15.6486	0.566888
$763$	21.4454	0.776377
$764$	−15.4174	−0.557780
$765$	7.88213	0.284979
$766$	−15.1321	−0.546744
$767$	10.5886	0.382331
$768$	16.9767	0.612593
$769$	48.5105	1.74933	0.874666	−	0.484726i	$-0.161081\pi$
$769$	48.5105	1.74933	0.874666	+	0.484726i	$0.161081\pi$
$770$	0.489723	0.0176484
$771$	−16.7036	−0.601566
$772$	−25.3199	−0.911285
$773$	17.0289	0.612488	0.306244	−	0.951953i	$-0.400928\pi$
$773$	17.0289	0.612488	0.306244	+	0.951953i	$0.400928\pi$
$774$	−8.54533	−0.307156
$775$	−0.369686	−0.0132795
$776$	31.5881	1.13395
$777$	8.07576	0.289716
$778$	−18.6182	−0.667494
$779$	11.2798	0.404139
$780$	2.03067	0.0727096
$781$	−0.139898	−0.00500595
$782$	7.11655	0.254487
$783$	0.968676	0.0346177
$784$	5.80037	0.207156
$785$	−34.9505	−1.24744
$786$	19.1752	0.683958
$787$	−4.03480	−0.143825	−0.0719125	−	0.997411i	$-0.522910\pi$
$787$	−4.03480	−0.143825	−0.0719125	+	0.997411i	$0.522910\pi$
$788$	11.0102	0.392222
$789$	23.8638	0.849573
$790$	10.5575	0.375619
$791$	17.9673	0.638843
$792$	0.550176	0.0195497
$793$	−7.50899	−0.266652
$794$	−0.827924	−0.0293819
$795$	−23.6804	−0.839858
$796$	7.09482	0.251469
$797$	−42.5457	−1.50705	−0.753523	−	0.657422i	$-0.771647\pi$
$797$	−42.5457	−1.50705	−0.753523	+	0.657422i	$0.771647\pi$
$798$	−2.33934	−0.0828116
$799$	−7.29326	−0.258017
$800$	0.242006	0.00855620
$801$	6.54432	0.231232
$802$	1.29075	0.0455779
$803$	0.109888	0.00387785
$804$	−11.4961	−0.405437
$805$	−5.31870	−0.187460
$806$	7.02816	0.247556
$807$	4.91838	0.173135
$808$	−20.6493	−0.726439
$809$	42.9029	1.50839	0.754193	−	0.656653i	$-0.228029\pi$
$809$	42.9029	1.50839	0.754193	+	0.656653i	$0.228029\pi$
$810$	2.23666	0.0785881
$811$	−6.96347	−0.244521	−0.122260	−	0.992498i	$-0.539014\pi$
$811$	−6.96347	−0.244521	−0.122260	+	0.992498i	$0.539014\pi$
$812$	1.14645	0.0402325
$813$	−28.5715	−1.00205
$814$	1.24269	0.0435561
$815$	47.6593	1.66943
$816$	−3.68899	−0.129140
$817$	−16.5436	−0.578787
$818$	−15.6252	−0.546321
$819$	−1.10286	−0.0385371
$820$	−12.7639	−0.445734
$821$	37.4378	1.30659	0.653295	−	0.757104i	$-0.273386\pi$
$821$	37.4378	1.30659	0.653295	+	0.757104i	$0.273386\pi$
$822$	−0.903468	−0.0315121
$823$	10.5157	0.366555	0.183277	−	0.983061i	$-0.441329\pi$
$823$	10.5157	0.366555	0.183277	+	0.983061i	$0.441329\pi$
$824$	50.3741	1.75487
$825$	0.00892669	0.000310788 0
$826$	13.8030	0.480269
$827$	−52.9664	−1.84182	−0.920911	−	0.389773i	$-0.872553\pi$
$827$	−52.9664	−1.84182	−0.920911	+	0.389773i	$0.872553\pi$
$828$	−1.97793	−0.0687377
$829$	16.1308	0.560246	0.280123	−	0.959964i	$-0.409625\pi$
$829$	16.1308	0.560246	0.280123	+	0.959964i	$0.409625\pi$
$830$	9.78850	0.339764
$831$	1.72049	0.0596830
$832$	−6.52153	−0.226093
$833$	19.7297	0.683595
$834$	20.0567	0.694506
$835$	52.5949	1.82012
$836$	0.352578	0.0121942
$837$	−7.58204	−0.262074
$838$	−17.7486	−0.613114
$839$	30.5221	1.05374	0.526870	−	0.849946i	$-0.323366\pi$
$839$	30.5221	1.05374	0.526870	+	0.849946i	$0.323366\pi$
$840$	7.99692	0.275920
$841$	−28.0617	−0.967644
$842$	−38.2404	−1.31785
$843$	21.5399	0.741874
$844$	21.1644	0.728507
$845$	27.0345	0.930016
$846$	−2.06956	−0.0711529
$847$	−13.1152	−0.450644
$848$	11.0829	0.380588
$849$	−29.5818	−1.01524
$850$	−0.173610	−0.00595479
$851$	−13.4964	−0.462650
$852$	−0.756202	−0.0259071
$853$	1.14130	0.0390774	0.0195387	−	0.999809i	$-0.493780\pi$
$853$	1.14130	0.0390774	0.0195387	+	0.999809i	$0.493780\pi$
$854$	−9.78854	−0.334957
$855$	4.33012	0.148087
$856$	6.08236	0.207891
$857$	11.2386	0.383904	0.191952	−	0.981404i	$-0.438518\pi$
$857$	11.2386	0.383904	0.191952	+	0.981404i	$0.438518\pi$
$858$	−0.169707	−0.00579369
$859$	14.3081	0.488184	0.244092	−	0.969752i	$-0.421510\pi$
$859$	14.3081	0.488184	0.244092	+	0.969752i	$0.421510\pi$
$860$	18.7203	0.638357
$861$	6.93210	0.236245
$862$	−1.35584	−0.0461801
$863$	−29.4523	−1.00257	−0.501283	−	0.865283i	$-0.667139\pi$
$863$	−29.4523	−1.00257	−0.501283	+	0.865283i	$0.667139\pi$
$864$	4.96339	0.168858
$865$	8.65945	0.294430
$866$	10.0798	0.342526
$867$	4.45205	0.151199
$868$	−8.97352	−0.304581
$869$	0.864182	0.0293154
$870$	2.16660	0.0734545
$871$	10.7126	0.362983
$872$	53.8872	1.82485
$873$	10.5115	0.355761
$874$	3.90954	0.132242
$875$	13.4354	0.454198
$876$	0.593983	0.0200688
$877$	−24.4575	−0.825870	−0.412935	−	0.910760i	$-0.635496\pi$
$877$	−24.4575	−0.825870	−0.412935	+	0.910760i	$0.635496\pi$
$878$	−34.4105	−1.16130
$879$	−0.784142	−0.0264485
$880$	0.424249	0.0143014
$881$	27.3931	0.922898	0.461449	−	0.887167i	$-0.347330\pi$
$881$	27.3931	0.922898	0.461449	+	0.887167i	$0.347330\pi$
$882$	5.59857	0.188514
$883$	−16.6452	−0.560156	−0.280078	−	0.959977i	$-0.590360\pi$
$883$	−16.6452	−0.560156	−0.280078	+	0.959977i	$0.590360\pi$
$884$	−3.23272	−0.108728
$885$	−25.5494	−0.858835
$886$	−15.0263	−0.504819
$887$	−24.5904	−0.825664	−0.412832	−	0.910807i	$-0.635460\pi$
$887$	−24.5904	−0.825664	−0.412832	+	0.910807i	$0.635460\pi$
$888$	20.2924	0.680969
$889$	18.6183	0.624438
$890$	14.6374	0.490647
$891$	0.183081	0.00613345
$892$	5.15791	0.172700
$893$	−4.00662	−0.134076
$894$	0.256314	0.00857241
$895$	−25.8394	−0.863715
$896$	3.37048	0.112600
$897$	1.84312	0.0615401
$898$	−24.8842	−0.830396
$899$	−7.34454	−0.244954
$900$	0.0482521	0.00160840
$901$	37.6980	1.25590
$902$	1.06670	0.0355173
$903$	−10.1670	−0.338338
$904$	45.1474	1.50158
$905$	8.38691	0.278790
$906$	15.6486	0.519889
$907$	−13.1734	−0.437416	−0.218708	−	0.975790i	$-0.570184\pi$
$907$	−13.1734	−0.437416	−0.218708	+	0.975790i	$0.570184\pi$
$908$	11.7160	0.388809
$909$	−6.87142	−0.227911
$910$	−2.46672	−0.0817710
$911$	−5.56149	−0.184260	−0.0921302	−	0.995747i	$-0.529368\pi$
$911$	−5.56149	−0.184260	−0.0921302	+	0.995747i	$0.529368\pi$
$912$	−2.02658	−0.0671067
$913$	0.801236	0.0265171
$914$	−7.74257	−0.256101
$915$	18.1186	0.598984
$916$	−12.0636	−0.398591
$917$	22.8143	0.753393
$918$	−3.56064	−0.117519
$919$	−59.1243	−1.95033	−0.975165	−	0.221481i	$-0.928911\pi$
$919$	−59.1243	−1.95033	−0.975165	+	0.221481i	$0.928911\pi$
$920$	−13.3646	−0.440618
$921$	−12.2895	−0.404951
$922$	−36.9647	−1.21737
$923$	0.704664	0.0231943
$924$	0.216681	0.00712827
$925$	0.329248	0.0108256
$926$	28.9424	0.951105
$927$	16.7629	0.550566
$928$	4.80792	0.157828
$929$	51.6774	1.69548	0.847740	−	0.530412i	$-0.177963\pi$
$929$	51.6774	1.69548	0.847740	+	0.530412i	$0.177963\pi$
$930$	−16.9584	−0.556088
$931$	10.8387	0.355224
$932$	−9.12715	−0.298970
$933$	−17.0854	−0.559351
$934$	23.0884	0.755474
$935$	1.44307	0.0471934
$936$	−2.77122	−0.0905803
$937$	17.8913	0.584482	0.292241	−	0.956345i	$-0.405599\pi$
$937$	17.8913	0.584482	0.292241	+	0.956345i	$0.405599\pi$
$938$	13.9647	0.455964
$939$	0.845851	0.0276033
$940$	4.53379	0.147876
$941$	14.0459	0.457885	0.228942	−	0.973440i	$-0.426473\pi$
$941$	14.0459	0.457885	0.228942	+	0.973440i	$0.426473\pi$
$942$	15.7884	0.514414
$943$	−11.5851	−0.377261
$944$	11.9576	0.389188
$945$	2.66112	0.0865663
$946$	−1.56449	−0.0508659
$947$	4.06864	0.132213	0.0661065	−	0.997813i	$-0.478942\pi$
$947$	4.06864	0.132213	0.0661065	+	0.997813i	$0.478942\pi$
$948$	4.67123	0.151714
$949$	−0.553501	−0.0179674
$950$	−0.0953744	−0.00309435
$951$	−2.22653	−0.0722002
$952$	−12.7307	−0.412604
$953$	60.8936	1.97254	0.986269	−	0.165145i	$-0.0528093\pi$
$953$	60.8936	1.97254	0.986269	+	0.165145i	$0.0528093\pi$
$954$	10.6973	0.346338
$955$	−34.6655	−1.12175
$956$	−0.915868	−0.0296213
$957$	0.177346	0.00573279
$958$	16.0380	0.518164
$959$	−1.07493	−0.0347112
$960$	15.7360	0.507876
$961$	26.4873	0.854430
$962$	−6.25938	−0.201810
$963$	2.02402	0.0652230
$964$	4.19993	0.135271
$965$	−56.9312	−1.83268
$966$	2.40265	0.0773041
$967$	23.5431	0.757096	0.378548	−	0.925582i	$-0.376424\pi$
$967$	23.5431	0.757096	0.378548	+	0.925582i	$0.376424\pi$
$968$	−32.9553	−1.05922
$969$	−6.89333	−0.221446
$970$	23.5106	0.754881
$971$	31.6680	1.01627	0.508136	−	0.861277i	$-0.330335\pi$
$971$	31.6680	1.01627	0.508136	+	0.861277i	$0.330335\pi$
$972$	0.989621	0.0317421
$973$	23.8630	0.765012
$974$	−9.18143	−0.294192
$975$	−0.0449635	−0.00143999
$976$	−8.47987	−0.271434
$977$	53.9529	1.72611	0.863053	−	0.505113i	$-0.168549\pi$
$977$	53.9529	1.72611	0.863053	+	0.505113i	$0.168549\pi$
$978$	−21.5294	−0.688436
$979$	1.19814	0.0382928
$980$	−12.2648	−0.391785
$981$	17.9319	0.572523
$982$	19.1603	0.611431
$983$	3.19894	0.102030	0.0510151	−	0.998698i	$-0.483754\pi$
$983$	3.19894	0.102030	0.0510151	+	0.998698i	$0.483754\pi$
$984$	17.4187	0.555287
$985$	24.7562	0.788797
$986$	−3.44911	−0.109842
$987$	−2.46231	−0.0783763
$988$	−1.77593	−0.0564998
$989$	16.9914	0.540294
$990$	0.409489	0.0130144
$991$	−37.9397	−1.20519	−0.602597	−	0.798045i	$-0.705867\pi$
$991$	−37.9397	−1.20519	−0.602597	+	0.798045i	$0.705867\pi$
$992$	−37.6326	−1.19484
$993$	2.11349	0.0670697
$994$	0.918583	0.0291357
$995$	15.9525	0.505729
$996$	4.33098	0.137232
$997$	−42.6680	−1.35131	−0.675654	−	0.737219i	$-0.736139\pi$
$997$	−42.6680	−1.35131	−0.675654	+	0.737219i	$0.736139\pi$
$998$	16.4399	0.520395
$999$	6.75267	0.213645

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2031.2.a.i.1.15	✓	38
3.2	odd	2		6093.2.a.o.1.24		38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2031.2.a.i.1.15	✓	38	1.1	even	1	trivial
6093.2.a.o.1.24		38	3.2	odd	2

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:	\( N \)	\(=\)	\( 2031 = 3 \cdot 677 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2031.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00518 q^{2} -1.00000 q^{3} -0.989621 q^{4} -2.22514 q^{5} +1.00518 q^{6} +1.19593 q^{7} +3.00510 q^{8} +1.00000 q^{9} +2.23666 q^{10} +0.183081 q^{11} +0.989621 q^{12} -0.922175 q^{13} -1.20213 q^{14} +2.22514 q^{15} -1.04141 q^{16} -3.54231 q^{17} -1.00518 q^{18} -1.94600 q^{19} +2.20204 q^{20} -1.19593 q^{21} -0.184029 q^{22} +1.99867 q^{23} -3.00510 q^{24} -0.0487581 q^{25} +0.926948 q^{26} -1.00000 q^{27} -1.18352 q^{28} -0.968676 q^{29} -2.23666 q^{30} +7.58204 q^{31} -4.96339 q^{32} -0.183081 q^{33} +3.56064 q^{34} -2.66112 q^{35} -0.989621 q^{36} -6.75267 q^{37} +1.95607 q^{38} +0.922175 q^{39} -6.68675 q^{40} -5.79638 q^{41} +1.20213 q^{42} +8.50133 q^{43} -0.181181 q^{44} -2.22514 q^{45} -2.00902 q^{46} +2.05890 q^{47} +1.04141 q^{48} -5.56974 q^{49} +0.0490105 q^{50} +3.54231 q^{51} +0.912604 q^{52} -10.6422 q^{53} +1.00518 q^{54} -0.407381 q^{55} +3.59390 q^{56} +1.94600 q^{57} +0.973690 q^{58} -11.4822 q^{59} -2.20204 q^{60} +8.14270 q^{61} -7.62128 q^{62} +1.19593 q^{63} +7.07190 q^{64} +2.05197 q^{65} +0.184029 q^{66} -11.6167 q^{67} +3.50554 q^{68} -1.99867 q^{69} +2.67490 q^{70} -0.764133 q^{71} +3.00510 q^{72} +0.600213 q^{73} +6.78762 q^{74} +0.0487581 q^{75} +1.92580 q^{76} +0.218953 q^{77} -0.926948 q^{78} +4.72022 q^{79} +2.31728 q^{80} +1.00000 q^{81} +5.82638 q^{82} +4.37640 q^{83} +1.18352 q^{84} +7.88213 q^{85} -8.54533 q^{86} +0.968676 q^{87} +0.550176 q^{88} +6.54432 q^{89} +2.23666 q^{90} -1.10286 q^{91} -1.97793 q^{92} -7.58204 q^{93} -2.06956 q^{94} +4.33012 q^{95} +4.96339 q^{96} +10.5115 q^{97} +5.59857 q^{98} +0.183081 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 3 q^{2} - 38 q^{3} + 49 q^{4} + 3 q^{5} + 3 q^{6} + 7 q^{7} - 12 q^{8} + 38 q^{9} + 14 q^{10} - 12 q^{11} - 49 q^{12} + 24 q^{13} + q^{14} - 3 q^{15} + 71 q^{16} + 12 q^{17} - 3 q^{18} + 16 q^{19}+ \cdots - 12 q^{99}+O(q^{100}) \) 38 * q - 3 * q^2 - 38 * q^3 + 49 * q^4 + 3 * q^5 + 3 * q^6 + 7 * q^7 - 12 * q^8 + 38 * q^9 + 14 * q^10 - 12 * q^11 - 49 * q^12 + 24 * q^13 + q^14 - 3 * q^15 + 71 * q^16 + 12 * q^17 - 3 * q^18 + 16 * q^19 + 6 * q^20 - 7 * q^21 + 20 * q^22 - 35 * q^23 + 12 * q^24 + 85 * q^25 + 33 * q^26 - 38 * q^27 + 23 * q^28 + 13 * q^29 - 14 * q^30 + 27 * q^31 - 22 * q^32 + 12 * q^33 + 45 * q^34 - 23 * q^35 + 49 * q^36 + 28 * q^37 + 16 * q^38 - 24 * q^39 + 52 * q^40 + 53 * q^41 - q^42 + 17 * q^43 - 8 * q^44 + 3 * q^45 + 28 * q^46 - 13 * q^47 - 71 * q^48 + 135 * q^49 - 7 * q^50 - 12 * q^51 + 68 * q^52 + 6 * q^53 + 3 * q^54 + 49 * q^55 + 13 * q^56 - 16 * q^57 + 26 * q^58 + 17 * q^59 - 6 * q^60 + 63 * q^61 + 13 * q^62 + 7 * q^63 + 100 * q^64 + 29 * q^65 - 20 * q^66 + 28 * q^67 - 17 * q^68 + 35 * q^69 + 44 * q^70 - 2 * q^71 - 12 * q^72 + 55 * q^73 - 13 * q^74 - 85 * q^75 + 53 * q^76 - 23 * q^77 - 33 * q^78 + 30 * q^79 + 19 * q^80 + 38 * q^81 + 55 * q^82 - 19 * q^83 - 23 * q^84 + 45 * q^85 + 12 * q^86 - 13 * q^87 + 47 * q^88 + 126 * q^89 + 14 * q^90 + 66 * q^91 - 77 * q^92 - 27 * q^93 + 52 * q^94 - 53 * q^95 + 22 * q^96 + 80 * q^97 + 4 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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