LMFDB - Embedded newform 950.2.a.n.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(1,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, 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("950.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.568.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 6x - 2 $ x^3 - x^2 - 6*x - 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.363328$ of defining polynomial
Character	$\chi$	$=$	950.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.36333 q^{3} +1.00000 q^{4} +1.36333 q^{6} +0.636672 q^{7} +1.00000 q^{8} -1.14134 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.36333 q^{3} +1.00000 q^{4} +1.36333 q^{6} +0.636672 q^{7} +1.00000 q^{8} -1.14134 q^{9} +3.50466 q^{11} +1.36333 q^{12} -0.141336 q^{13} +0.636672 q^{14} +1.00000 q^{16} +2.14134 q^{17} -1.14134 q^{18} +1.00000 q^{19} +0.867993 q^{21} +3.50466 q^{22} +4.91934 q^{23} +1.36333 q^{24} -0.141336 q^{26} -5.64600 q^{27} +0.636672 q^{28} +7.15066 q^{29} -7.78734 q^{31} +1.00000 q^{32} +4.77801 q^{33} +2.14134 q^{34} -1.14134 q^{36} +3.27334 q^{37} +1.00000 q^{38} -0.192688 q^{39} -4.23132 q^{41} +0.867993 q^{42} +2.49534 q^{43} +3.50466 q^{44} +4.91934 q^{46} -10.2827 q^{47} +1.36333 q^{48} -6.59465 q^{49} +2.91934 q^{51} -0.141336 q^{52} +8.14134 q^{53} -5.64600 q^{54} +0.636672 q^{56} +1.36333 q^{57} +7.15066 q^{58} -5.64600 q^{59} -6.49534 q^{61} -7.78734 q^{62} -0.726656 q^{63} +1.00000 q^{64} +4.77801 q^{66} +8.37266 q^{67} +2.14134 q^{68} +6.70668 q^{69} -8.95798 q^{71} -1.14134 q^{72} -3.69735 q^{73} +3.27334 q^{74} +1.00000 q^{76} +2.23132 q^{77} -0.192688 q^{78} -4.17997 q^{79} -4.27334 q^{81} -4.23132 q^{82} -9.00933 q^{83} +0.867993 q^{84} +2.49534 q^{86} +9.74870 q^{87} +3.50466 q^{88} -6.77801 q^{89} -0.0899847 q^{91} +4.91934 q^{92} -10.6167 q^{93} -10.2827 q^{94} +1.36333 q^{96} +14.5653 q^{97} -6.59465 q^{98} -4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 2 q^{6} + 4 q^{7} + 3 q^{8} + 5 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 2 * q^6 + 4 * q^7 + 3 * q^8 + 5 * q^9	$ 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 2 q^{6} + 4 q^{7} + 3 q^{8} + 5 q^{9} + 2 q^{12} + 8 q^{13} + 4 q^{14} + 3 q^{16} - 2 q^{17} + 5 q^{18} + 3 q^{19} - 10 q^{21} + 2 q^{24} + 8 q^{26} + 2 q^{27} + 4 q^{28} - 8 q^{29} + 4 q^{31} + 3 q^{32} + 8 q^{33} - 2 q^{34} + 5 q^{36} + 14 q^{37} + 3 q^{38} + 10 q^{39} + 2 q^{41} - 10 q^{42} + 18 q^{43} - 14 q^{47} + 2 q^{48} - 3 q^{49} - 6 q^{51} + 8 q^{52} + 16 q^{53} + 2 q^{54} + 4 q^{56} + 2 q^{57} - 8 q^{58} + 2 q^{59} - 30 q^{61} + 4 q^{62} + 2 q^{63} + 3 q^{64} + 8 q^{66} + 2 q^{67} - 2 q^{68} - 22 q^{69} - 8 q^{71} + 5 q^{72} + 10 q^{73} + 14 q^{74} + 3 q^{76} - 8 q^{77} + 10 q^{78} - 17 q^{81} + 2 q^{82} - 6 q^{83} - 10 q^{84} + 18 q^{86} + 6 q^{87} - 14 q^{89} + 6 q^{91} + 4 q^{93} - 14 q^{94} + 2 q^{96} + 10 q^{97} - 3 q^{98} - 12 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 2 * q^6 + 4 * q^7 + 3 * q^8 + 5 * q^9 + 2 * q^12 + 8 * q^13 + 4 * q^14 + 3 * q^16 - 2 * q^17 + 5 * q^18 + 3 * q^19 - 10 * q^21 + 2 * q^24 + 8 * q^26 + 2 * q^27 + 4 * q^28 - 8 * q^29 + 4 * q^31 + 3 * q^32 + 8 * q^33 - 2 * q^34 + 5 * q^36 + 14 * q^37 + 3 * q^38 + 10 * q^39 + 2 * q^41 - 10 * q^42 + 18 * q^43 - 14 * q^47 + 2 * q^48 - 3 * q^49 - 6 * q^51 + 8 * q^52 + 16 * q^53 + 2 * q^54 + 4 * q^56 + 2 * q^57 - 8 * q^58 + 2 * q^59 - 30 * q^61 + 4 * q^62 + 2 * q^63 + 3 * q^64 + 8 * q^66 + 2 * q^67 - 2 * q^68 - 22 * q^69 - 8 * q^71 + 5 * q^72 + 10 * q^73 + 14 * q^74 + 3 * q^76 - 8 * q^77 + 10 * q^78 - 17 * q^81 + 2 * q^82 - 6 * q^83 - 10 * q^84 + 18 * q^86 + 6 * q^87 - 14 * q^89 + 6 * q^91 + 4 * q^93 - 14 * q^94 + 2 * q^96 + 10 * q^97 - 3 * q^98 - 12 * q^99

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.36333	0.787118	0.393559	−	0.919299i	$-0.371244\pi$
$3$	1.36333	0.787118	0.393559	+	0.919299i	$0.371244\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	1.36333	0.556576
$7$	0.636672	0.240639	0.120320	−	0.992735i	$-0.461608\pi$
$7$	0.636672	0.240639	0.120320	+	0.992735i	$0.461608\pi$
$8$	1.00000	0.353553
$9$	−1.14134	−0.380445
$10$	0	0
$11$	3.50466	1.05670	0.528348	−	0.849028i	$-0.322812\pi$
$11$	3.50466	1.05670	0.528348	+	0.849028i	$0.322812\pi$
$12$	1.36333	0.393559
$13$	−0.141336	−0.0391996	−0.0195998	−	0.999808i	$-0.506239\pi$
$13$	−0.141336	−0.0391996	−0.0195998	+	0.999808i	$0.506239\pi$
$14$	0.636672	0.170158
$15$	0	0
$16$	1.00000	0.250000
$17$	2.14134	0.519350	0.259675	−	0.965696i	$-0.416385\pi$
$17$	2.14134	0.519350	0.259675	+	0.965696i	$0.416385\pi$
$18$	−1.14134	−0.269016
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0	0
$21$	0.867993	0.189412
$22$	3.50466	0.747197
$23$	4.91934	1.02575	0.512877	−	0.858462i	$-0.328580\pi$
$23$	4.91934	1.02575	0.512877	+	0.858462i	$0.328580\pi$
$24$	1.36333	0.278288
$25$	0	0
$26$	−0.141336	−0.0277183
$27$	−5.64600	−1.08657
$28$	0.636672	0.120320
$29$	7.15066	1.32785	0.663923	−	0.747801i	$-0.268890\pi$
$29$	7.15066	1.32785	0.663923	+	0.747801i	$0.268890\pi$
$30$	0	0
$31$	−7.78734	−1.39865	−0.699323	−	0.714805i	$-0.746515\pi$
$31$	−7.78734	−1.39865	−0.699323	+	0.714805i	$0.746515\pi$
$32$	1.00000	0.176777
$33$	4.77801	0.831744
$34$	2.14134	0.367236
$35$	0	0
$36$	−1.14134	−0.190223
$37$	3.27334	0.538134	0.269067	−	0.963121i	$-0.413285\pi$
$37$	3.27334	0.538134	0.269067	+	0.963121i	$0.413285\pi$
$38$	1.00000	0.162221
$39$	−0.192688	−0.0308547
$40$	0	0
$41$	−4.23132	−0.660821	−0.330411	−	0.943837i	$-0.607187\pi$
$41$	−4.23132	−0.660821	−0.330411	+	0.943837i	$0.607187\pi$
$42$	0.867993	0.133934
$43$	2.49534	0.380535	0.190268	−	0.981732i	$-0.439064\pi$
$43$	2.49534	0.380535	0.190268	+	0.981732i	$0.439064\pi$
$44$	3.50466	0.528348
$45$	0	0
$46$	4.91934	0.725318
$47$	−10.2827	−1.49988	−0.749941	−	0.661505i	$-0.769918\pi$
$47$	−10.2827	−1.49988	−0.749941	+	0.661505i	$0.769918\pi$
$48$	1.36333	0.196779
$49$	−6.59465	−0.942093
$50$	0	0
$51$	2.91934	0.408790
$52$	−0.141336	−0.0195998
$53$	8.14134	1.11830	0.559149	−	0.829067i	$-0.311128\pi$
$53$	8.14134	1.11830	0.559149	+	0.829067i	$0.311128\pi$
$54$	−5.64600	−0.768323
$55$	0	0
$56$	0.636672	0.0850788
$57$	1.36333	0.180577
$58$	7.15066	0.938928
$59$	−5.64600	−0.735047	−0.367523	−	0.930014i	$-0.619794\pi$
$59$	−5.64600	−0.735047	−0.367523	+	0.930014i	$0.619794\pi$
$60$	0	0
$61$	−6.49534	−0.831643	−0.415821	−	0.909446i	$-0.636506\pi$
$61$	−6.49534	−0.831643	−0.415821	+	0.909446i	$0.636506\pi$
$62$	−7.78734	−0.988993
$63$	−0.726656	−0.0915501
$64$	1.00000	0.125000
$65$	0	0
$66$	4.77801	0.588132
$67$	8.37266	1.02288	0.511441	−	0.859318i	$-0.329112\pi$
$67$	8.37266	1.02288	0.511441	+	0.859318i	$0.329112\pi$
$68$	2.14134	0.259675
$69$	6.70668	0.807389
$70$	0	0
$71$	−8.95798	−1.06312	−0.531558	−	0.847022i	$-0.678393\pi$
$71$	−8.95798	−1.06312	−0.531558	+	0.847022i	$0.678393\pi$
$72$	−1.14134	−0.134508
$73$	−3.69735	−0.432742	−0.216371	−	0.976311i	$-0.569422\pi$
$73$	−3.69735	−0.432742	−0.216371	+	0.976311i	$0.569422\pi$
$74$	3.27334	0.380518
$75$	0	0
$76$	1.00000	0.114708
$77$	2.23132	0.254283
$78$	−0.192688	−0.0218176
$79$	−4.17997	−0.470283	−0.235142	−	0.971961i	$-0.575555\pi$
$79$	−4.17997	−0.470283	−0.235142	+	0.971961i	$0.575555\pi$
$80$	0	0
$81$	−4.27334	−0.474816
$82$	−4.23132	−0.467271
$83$	−9.00933	−0.988902	−0.494451	−	0.869205i	$-0.664631\pi$
$83$	−9.00933	−0.988902	−0.494451	+	0.869205i	$0.664631\pi$
$84$	0.867993	0.0947058
$85$	0	0
$86$	2.49534	0.269079
$87$	9.74870	1.04517
$88$	3.50466	0.373598
$89$	−6.77801	−0.718467	−0.359234	−	0.933248i	$-0.616962\pi$
$89$	−6.77801	−0.718467	−0.359234	+	0.933248i	$0.616962\pi$
$90$	0	0
$91$	−0.0899847	−0.00943296
$92$	4.91934	0.512877
$93$	−10.6167	−1.10090
$94$	−10.2827	−1.06058
$95$	0	0
$96$	1.36333	0.139144
$97$	14.5653	1.47889	0.739443	−	0.673219i	$-0.235089\pi$
$97$	14.5653	1.47889	0.739443	+	0.673219i	$0.235089\pi$
$98$	−6.59465	−0.666160
$99$	−4.00000	−0.402015
$100$	0	0
$101$	−16.6167	−1.65342	−0.826712	−	0.562626i	$-0.809791\pi$
$101$	−16.6167	−1.65342	−0.826712	+	0.562626i	$0.809791\pi$
$102$	2.91934	0.289058
$103$	9.06068	0.892775	0.446388	−	0.894840i	$-0.352710\pi$
$103$	9.06068	0.892775	0.446388	+	0.894840i	$0.352710\pi$
$104$	−0.141336	−0.0138591
$105$	0	0
$106$	8.14134	0.790756
$107$	0.0899847	0.00869915	0.00434958	−	0.999991i	$-0.498615\pi$
$107$	0.0899847	0.00869915	0.00434958	+	0.999991i	$0.498615\pi$
$108$	−5.64600	−0.543287
$109$	−13.5946	−1.30213	−0.651066	−	0.759021i	$-0.725678\pi$
$109$	−13.5946	−1.30213	−0.651066	+	0.759021i	$0.725678\pi$
$110$	0	0
$111$	4.46264	0.423575
$112$	0.636672	0.0601598
$113$	11.5233	1.08402	0.542011	−	0.840371i	$-0.317663\pi$
$113$	11.5233	1.08402	0.542011	+	0.840371i	$0.317663\pi$
$114$	1.36333	0.127687
$115$	0	0
$116$	7.15066	0.663923
$117$	0.161312	0.0149133
$118$	−5.64600	−0.519756
$119$	1.36333	0.124976
$120$	0	0
$121$	1.28267	0.116607
$122$	−6.49534	−0.588060
$123$	−5.76868	−0.520144
$124$	−7.78734	−0.699323
$125$	0	0
$126$	−0.726656	−0.0647357
$127$	−3.29200	−0.292118	−0.146059	−	0.989276i	$-0.546659\pi$
$127$	−3.29200	−0.292118	−0.146059	+	0.989276i	$0.546659\pi$
$128$	1.00000	0.0883883
$129$	3.40196	0.299526
$130$	0	0
$131$	18.0187	1.57430	0.787149	−	0.616763i	$-0.211556\pi$
$131$	18.0187	1.57430	0.787149	+	0.616763i	$0.211556\pi$
$132$	4.77801	0.415872
$133$	0.636672	0.0552064
$134$	8.37266	0.723287
$135$	0	0
$136$	2.14134	0.183618
$137$	−14.4240	−1.23233	−0.616163	−	0.787619i	$-0.711314\pi$
$137$	−14.4240	−1.23233	−0.616163	+	0.787619i	$0.711314\pi$
$138$	6.70668	0.570911
$139$	15.4720	1.31232	0.656158	−	0.754624i	$-0.272181\pi$
$139$	15.4720	1.31232	0.656158	+	0.754624i	$0.272181\pi$
$140$	0	0
$141$	−14.0187	−1.18058
$142$	−8.95798	−0.751737
$143$	−0.495336	−0.0414220
$144$	−1.14134	−0.0951113
$145$	0	0
$146$	−3.69735	−0.305995
$147$	−8.99067	−0.741538
$148$	3.27334	0.269067
$149$	−17.1893	−1.40820	−0.704101	−	0.710100i	$-0.748650\pi$
$149$	−17.1893	−1.40820	−0.704101	+	0.710100i	$0.748650\pi$
$150$	0	0
$151$	3.29200	0.267899	0.133950	−	0.990988i	$-0.457234\pi$
$151$	3.29200	0.267899	0.133950	+	0.990988i	$0.457234\pi$
$152$	1.00000	0.0811107
$153$	−2.44398	−0.197584
$154$	2.23132	0.179805
$155$	0	0
$156$	−0.192688	−0.0154273
$157$	15.1893	1.21224	0.606119	−	0.795374i	$-0.292726\pi$
$157$	15.1893	1.21224	0.606119	+	0.795374i	$0.292726\pi$
$158$	−4.17997	−0.332541
$159$	11.0993	0.880233
$160$	0	0
$161$	3.13201	0.246837
$162$	−4.27334	−0.335746
$163$	−14.0700	−1.10205	−0.551024	−	0.834489i	$-0.685763\pi$
$163$	−14.0700	−1.10205	−0.551024	+	0.834489i	$0.685763\pi$
$164$	−4.23132	−0.330411
$165$	0	0
$166$	−9.00933	−0.699260
$167$	−14.7967	−1.14500	−0.572500	−	0.819905i	$-0.694026\pi$
$167$	−14.7967	−1.14500	−0.572500	+	0.819905i	$0.694026\pi$
$168$	0.867993	0.0669671
$169$	−12.9800	−0.998463
$170$	0	0
$171$	−1.14134	−0.0872802
$172$	2.49534	0.190268
$173$	−17.2920	−1.31469	−0.657343	−	0.753591i	$-0.728320\pi$
$173$	−17.2920	−1.31469	−0.657343	+	0.753591i	$0.728320\pi$
$174$	9.74870	0.739047
$175$	0	0
$176$	3.50466	0.264174
$177$	−7.69735	−0.578568
$178$	−6.77801	−0.508033
$179$	17.7360	1.32565	0.662825	−	0.748774i	$-0.269357\pi$
$179$	17.7360	1.32565	0.662825	+	0.748774i	$0.269357\pi$
$180$	0	0
$181$	6.17997	0.459354	0.229677	−	0.973267i	$-0.426233\pi$
$181$	6.17997	0.459354	0.229677	+	0.973267i	$0.426233\pi$
$182$	−0.0899847	−0.00667011
$183$	−8.85527	−0.654601
$184$	4.91934	0.362659
$185$	0	0
$186$	−10.6167	−0.778454
$187$	7.50466	0.548795
$188$	−10.2827	−0.749941
$189$	−3.59465	−0.261472
$190$	0	0
$191$	14.6367	1.05907	0.529536	−	0.848287i	$-0.322366\pi$
$191$	14.6367	1.05907	0.529536	+	0.848287i	$0.322366\pi$
$192$	1.36333	0.0983897
$193$	20.0187	1.44097	0.720487	−	0.693468i	$-0.243918\pi$
$193$	20.0187	1.44097	0.720487	+	0.693468i	$0.243918\pi$
$194$	14.5653	1.04573
$195$	0	0
$196$	−6.59465	−0.471046
$197$	−9.94865	−0.708812	−0.354406	−	0.935092i	$-0.615317\pi$
$197$	−9.94865	−0.708812	−0.354406	+	0.935092i	$0.615317\pi$
$198$	−4.00000	−0.284268
$199$	9.74870	0.691067	0.345534	−	0.938406i	$-0.387698\pi$
$199$	9.74870	0.691067	0.345534	+	0.938406i	$0.387698\pi$
$200$	0	0
$201$	11.4147	0.805129
$202$	−16.6167	−1.16915
$203$	4.55263	0.319532
$204$	2.91934	0.204395
$205$	0	0
$206$	9.06068	0.631287
$207$	−5.61462	−0.390243
$208$	−0.141336	−0.00979990
$209$	3.50466	0.242423
$210$	0	0
$211$	−20.7580	−1.42904	−0.714521	−	0.699614i	$-0.753355\pi$
$211$	−20.7580	−1.42904	−0.714521	+	0.699614i	$0.753355\pi$
$212$	8.14134	0.559149
$213$	−12.2127	−0.836798
$214$	0.0899847	0.00615123
$215$	0	0
$216$	−5.64600	−0.384162
$217$	−4.95798	−0.336569
$218$	−13.5946	−0.920746
$219$	−5.04070	−0.340619
$220$	0	0
$221$	−0.302648	−0.0203583
$222$	4.46264	0.299513
$223$	−10.7267	−0.718310	−0.359155	−	0.933278i	$-0.616935\pi$
$223$	−10.7267	−0.718310	−0.359155	+	0.933278i	$0.616935\pi$
$224$	0.636672	0.0425394
$225$	0	0
$226$	11.5233	0.766520
$227$	12.5526	0.833147	0.416574	−	0.909102i	$-0.363231\pi$
$227$	12.5526	0.833147	0.416574	+	0.909102i	$0.363231\pi$
$228$	1.36333	0.0902886
$229$	25.4720	1.68324	0.841618	−	0.540074i	$-0.181604\pi$
$229$	25.4720	1.68324	0.841618	+	0.540074i	$0.181604\pi$
$230$	0	0
$231$	3.04202	0.200150
$232$	7.15066	0.469464
$233$	−3.11203	−0.203876	−0.101938	−	0.994791i	$-0.532504\pi$
$233$	−3.11203	−0.203876	−0.101938	+	0.994791i	$0.532504\pi$
$234$	0.161312	0.0105453
$235$	0	0
$236$	−5.64600	−0.367523
$237$	−5.69867	−0.370168
$238$	1.36333	0.0883714
$239$	−1.54330	−0.0998276	−0.0499138	−	0.998754i	$-0.515895\pi$
$239$	−1.54330	−0.0998276	−0.0499138	+	0.998754i	$0.515895\pi$
$240$	0	0
$241$	10.2827	0.662365	0.331183	−	0.943567i	$-0.392552\pi$
$241$	10.2827	0.662365	0.331183	+	0.943567i	$0.392552\pi$
$242$	1.28267	0.0824533
$243$	11.1120	0.712837
$244$	−6.49534	−0.415821
$245$	0	0
$246$	−5.76868	−0.367798
$247$	−0.141336	−0.00899300
$248$	−7.78734	−0.494496
$249$	−12.2827	−0.778383
$250$	0	0
$251$	−2.51399	−0.158682	−0.0793409	−	0.996848i	$-0.525282\pi$
$251$	−2.51399	−0.158682	−0.0793409	+	0.996848i	$0.525282\pi$
$252$	−0.726656	−0.0457751
$253$	17.2406	1.08391
$254$	−3.29200	−0.206559
$255$	0	0
$256$	1.00000	0.0625000
$257$	−24.7967	−1.54677	−0.773387	−	0.633934i	$-0.781439\pi$
$257$	−24.7967	−1.54677	−0.773387	+	0.633934i	$0.781439\pi$
$258$	3.40196	0.211797
$259$	2.08405	0.129496
$260$	0	0
$261$	−8.16131	−0.505173
$262$	18.0187	1.11320
$263$	−22.5653	−1.39144	−0.695719	−	0.718314i	$-0.744914\pi$
$263$	−22.5653	−1.39144	−0.695719	+	0.718314i	$0.744914\pi$
$264$	4.77801	0.294066
$265$	0	0
$266$	0.636672	0.0390369
$267$	−9.24065	−0.565519
$268$	8.37266	0.511441
$269$	−26.5653	−1.61972	−0.809859	−	0.586625i	$-0.800456\pi$
$269$	−26.5653	−1.61972	−0.809859	+	0.586625i	$0.800456\pi$
$270$	0	0
$271$	−24.9380	−1.51488	−0.757438	−	0.652907i	$-0.773549\pi$
$271$	−24.9380	−1.51488	−0.757438	+	0.652907i	$0.773549\pi$
$272$	2.14134	0.129838
$273$	−0.122679	−0.00742485
$274$	−14.4240	−0.871386
$275$	0	0
$276$	6.70668	0.403695
$277$	18.5467	1.11436	0.557181	−	0.830391i	$-0.311883\pi$
$277$	18.5467	1.11436	0.557181	+	0.830391i	$0.311883\pi$
$278$	15.4720	0.927947
$279$	8.88797	0.532109
$280$	0	0
$281$	24.7967	1.47925	0.739623	−	0.673022i	$-0.235004\pi$
$281$	24.7967	1.47925	0.739623	+	0.673022i	$0.235004\pi$
$282$	−14.0187	−0.834799
$283$	13.5747	0.806931	0.403465	−	0.914995i	$-0.367806\pi$
$283$	13.5747	0.806931	0.403465	+	0.914995i	$0.367806\pi$
$284$	−8.95798	−0.531558
$285$	0	0
$286$	−0.495336	−0.0292898
$287$	−2.69396	−0.159020
$288$	−1.14134	−0.0672539
$289$	−12.4147	−0.730275
$290$	0	0
$291$	19.8573	1.16406
$292$	−3.69735	−0.216371
$293$	−15.6133	−0.912139	−0.456070	−	0.889944i	$-0.650743\pi$
$293$	−15.6133	−0.912139	−0.456070	+	0.889944i	$0.650743\pi$
$294$	−8.99067	−0.524347
$295$	0	0
$296$	3.27334	0.190259
$297$	−19.7873	−1.14818
$298$	−17.1893	−0.995749
$299$	−0.695281	−0.0402091
$300$	0	0
$301$	1.58871	0.0915717
$302$	3.29200	0.189433
$303$	−22.6540	−1.30144
$304$	1.00000	0.0573539
$305$	0	0
$306$	−2.44398	−0.139713
$307$	34.0187	1.94155	0.970774	−	0.239997i	$-0.0771464\pi$
$307$	34.0187	1.94155	0.970774	+	0.239997i	$0.0771464\pi$
$308$	2.23132	0.127141
$309$	12.3527	0.702719
$310$	0	0
$311$	8.93800	0.506828	0.253414	−	0.967358i	$-0.418447\pi$
$311$	8.93800	0.506828	0.253414	+	0.967358i	$0.418447\pi$
$312$	−0.192688	−0.0109088
$313$	−18.4240	−1.04139	−0.520693	−	0.853744i	$-0.674326\pi$
$313$	−18.4240	−1.04139	−0.520693	+	0.853744i	$0.674326\pi$
$314$	15.1893	0.857182
$315$	0	0
$316$	−4.17997	−0.235142
$317$	33.5547	1.88462	0.942310	−	0.334742i	$-0.108649\pi$
$317$	33.5547	1.88462	0.942310	+	0.334742i	$0.108649\pi$
$318$	11.0993	0.622419
$319$	25.0607	1.40313
$320$	0	0
$321$	0.122679	0.00684726
$322$	3.13201	0.174540
$323$	2.14134	0.119147
$324$	−4.27334	−0.237408
$325$	0	0
$326$	−14.0700	−0.779266
$327$	−18.5340	−1.02493
$328$	−4.23132	−0.233636
$329$	−6.54669	−0.360931
$330$	0	0
$331$	2.25130	0.123742	0.0618712	−	0.998084i	$-0.480293\pi$
$331$	2.25130	0.123742	0.0618712	+	0.998084i	$0.480293\pi$
$332$	−9.00933	−0.494451
$333$	−3.73599	−0.204731
$334$	−14.7967	−0.809638
$335$	0	0
$336$	0.867993	0.0473529
$337$	−21.3620	−1.16366	−0.581831	−	0.813309i	$-0.697664\pi$
$337$	−21.3620	−1.16366	−0.581831	+	0.813309i	$0.697664\pi$
$338$	−12.9800	−0.706020
$339$	15.7101	0.853254
$340$	0	0
$341$	−27.2920	−1.47794
$342$	−1.14134	−0.0617164
$343$	−8.65533	−0.467344
$344$	2.49534	0.134539
$345$	0	0
$346$	−17.2920	−0.929624
$347$	11.5560	0.620359	0.310180	−	0.950678i	$-0.399611\pi$
$347$	11.5560	0.620359	0.310180	+	0.950678i	$0.399611\pi$
$348$	9.74870	0.522585
$349$	−17.1120	−0.915986	−0.457993	−	0.888956i	$-0.651432\pi$
$349$	−17.1120	−0.915986	−0.457993	+	0.888956i	$0.651432\pi$
$350$	0	0
$351$	0.797984	0.0425932
$352$	3.50466	0.186799
$353$	11.6974	0.622587	0.311294	−	0.950314i	$-0.399238\pi$
$353$	11.6974	0.622587	0.311294	+	0.950314i	$0.399238\pi$
$354$	−7.69735	−0.409110
$355$	0	0
$356$	−6.77801	−0.359234
$357$	1.85866	0.0983709
$358$	17.7360	0.937376
$359$	−4.47536	−0.236200	−0.118100	−	0.993002i	$-0.537680\pi$
$359$	−4.47536	−0.236200	−0.118100	+	0.993002i	$0.537680\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	6.17997	0.324812
$363$	1.74870	0.0917831
$364$	−0.0899847	−0.00471648
$365$	0	0
$366$	−8.85527	−0.462873
$367$	18.7453	0.978497	0.489249	−	0.872144i	$-0.337271\pi$
$367$	18.7453	0.978497	0.489249	+	0.872144i	$0.337271\pi$
$368$	4.91934	0.256439
$369$	4.82936	0.251406
$370$	0	0
$371$	5.18336	0.269107
$372$	−10.6167	−0.550450
$373$	1.69735	0.0878855	0.0439428	−	0.999034i	$-0.486008\pi$
$373$	1.69735	0.0878855	0.0439428	+	0.999034i	$0.486008\pi$
$374$	7.50466	0.388057
$375$	0	0
$376$	−10.2827	−0.530288
$377$	−1.01065	−0.0520510
$378$	−3.59465	−0.184889
$379$	2.63667	0.135437	0.0677184	−	0.997704i	$-0.478428\pi$
$379$	2.63667	0.135437	0.0677184	+	0.997704i	$0.478428\pi$
$380$	0	0
$381$	−4.48808	−0.229931
$382$	14.6367	0.748877
$383$	12.4953	0.638482	0.319241	−	0.947674i	$-0.396572\pi$
$383$	12.4953	0.638482	0.319241	+	0.947674i	$0.396572\pi$
$384$	1.36333	0.0695721
$385$	0	0
$386$	20.0187	1.01892
$387$	−2.84802	−0.144773
$388$	14.5653	0.739443
$389$	−4.51399	−0.228869	−0.114434	−	0.993431i	$-0.536506\pi$
$389$	−4.51399	−0.228869	−0.114434	+	0.993431i	$0.536506\pi$
$390$	0	0
$391$	10.5340	0.532726
$392$	−6.59465	−0.333080
$393$	24.5653	1.23916
$394$	−9.94865	−0.501206
$395$	0	0
$396$	−4.00000	−0.201008
$397$	−35.6774	−1.79060	−0.895298	−	0.445468i	$-0.853037\pi$
$397$	−35.6774	−1.79060	−0.895298	+	0.445468i	$0.853037\pi$
$398$	9.74870	0.488658
$399$	0.867993	0.0434540
$400$	0	0
$401$	15.3434	0.766210	0.383105	−	0.923705i	$-0.374855\pi$
$401$	15.3434	0.766210	0.383105	+	0.923705i	$0.374855\pi$
$402$	11.4147	0.569312
$403$	1.10063	0.0548264
$404$	−16.6167	−0.826712
$405$	0	0
$406$	4.55263	0.225943
$407$	11.4720	0.568644
$408$	2.91934	0.144529
$409$	29.3620	1.45186	0.725929	−	0.687770i	$-0.241410\pi$
$409$	29.3620	1.45186	0.725929	+	0.687770i	$0.241410\pi$
$410$	0	0
$411$	−19.6647	−0.969986
$412$	9.06068	0.446388
$413$	−3.59465	−0.176881
$414$	−5.61462	−0.275944
$415$	0	0
$416$	−0.141336	−0.00692957
$417$	21.0934	1.03295
$418$	3.50466	0.171419
$419$	25.1379	1.22807	0.614035	−	0.789279i	$-0.289546\pi$
$419$	25.1379	1.22807	0.614035	+	0.789279i	$0.289546\pi$
$420$	0	0
$421$	14.5454	0.708898	0.354449	−	0.935075i	$-0.384668\pi$
$421$	14.5454	0.708898	0.354449	+	0.935075i	$0.384668\pi$
$422$	−20.7580	−1.01049
$423$	11.7360	0.570623
$424$	8.14134	0.395378
$425$	0	0
$426$	−12.2127	−0.591705
$427$	−4.13540	−0.200126
$428$	0.0899847	0.00434958
$429$	−0.675305	−0.0326040
$430$	0	0
$431$	19.4020	0.934560	0.467280	−	0.884109i	$-0.345234\pi$
$431$	19.4020	0.934560	0.467280	+	0.884109i	$0.345234\pi$
$432$	−5.64600	−0.271643
$433$	5.50466	0.264537	0.132269	−	0.991214i	$-0.457774\pi$
$433$	5.50466	0.264537	0.132269	+	0.991214i	$0.457774\pi$
$434$	−4.95798	−0.237991
$435$	0	0
$436$	−13.5946	−0.651066
$437$	4.91934	0.235324
$438$	−5.04070	−0.240854
$439$	12.2500	0.584660	0.292330	−	0.956318i	$-0.405570\pi$
$439$	12.2500	0.584660	0.292330	+	0.956318i	$0.405570\pi$
$440$	0	0
$441$	7.52671	0.358415
$442$	−0.302648	−0.0143955
$443$	31.6006	1.50139	0.750695	−	0.660649i	$-0.229719\pi$
$443$	31.6006	1.50139	0.750695	+	0.660649i	$0.229719\pi$
$444$	4.46264	0.211788
$445$	0	0
$446$	−10.7267	−0.507922
$447$	−23.4347	−1.10842
$448$	0.636672	0.0300799
$449$	−36.0187	−1.69983	−0.849913	−	0.526923i	$-0.823345\pi$
$449$	−36.0187	−1.69983	−0.849913	+	0.526923i	$0.823345\pi$
$450$	0	0
$451$	−14.8294	−0.698287
$452$	11.5233	0.542011
$453$	4.48808	0.210868
$454$	12.5526	0.589124
$455$	0	0
$456$	1.36333	0.0638437
$457$	22.1413	1.03573	0.517864	−	0.855463i	$-0.326727\pi$
$457$	22.1413	1.03573	0.517864	+	0.855463i	$0.326727\pi$
$458$	25.4720	1.19023
$459$	−12.0900	−0.564312
$460$	0	0
$461$	−2.31537	−0.107837	−0.0539187	−	0.998545i	$-0.517171\pi$
$461$	−2.31537	−0.107837	−0.0539187	+	0.998545i	$0.517171\pi$
$462$	3.04202	0.141528
$463$	15.8387	0.736086	0.368043	−	0.929809i	$-0.380028\pi$
$463$	15.8387	0.736086	0.368043	+	0.929809i	$0.380028\pi$
$464$	7.15066	0.331961
$465$	0	0
$466$	−3.11203	−0.144162
$467$	23.1379	1.07070	0.535348	−	0.844631i	$-0.320180\pi$
$467$	23.1379	1.07070	0.535348	+	0.844631i	$0.320180\pi$
$468$	0.161312	0.00745665
$469$	5.33063	0.246146
$470$	0	0
$471$	20.7080	0.954174
$472$	−5.64600	−0.259878
$473$	8.74531	0.402110
$474$	−5.69867	−0.261749
$475$	0	0
$476$	1.36333	0.0624880
$477$	−9.29200	−0.425451
$478$	−1.54330	−0.0705888
$479$	−10.1214	−0.462457	−0.231228	−	0.972900i	$-0.574274\pi$
$479$	−10.1214	−0.462457	−0.231228	+	0.972900i	$0.574274\pi$
$480$	0	0
$481$	−0.462642	−0.0210946
$482$	10.2827	0.468363
$483$	4.26995	0.194290
$484$	1.28267	0.0583033
$485$	0	0
$486$	11.1120	0.504052
$487$	20.3854	0.923750	0.461875	−	0.886945i	$-0.347177\pi$
$487$	20.3854	0.923750	0.461875	+	0.886945i	$0.347177\pi$
$488$	−6.49534	−0.294030
$489$	−19.1820	−0.867442
$490$	0	0
$491$	−7.78734	−0.351438	−0.175719	−	0.984440i	$-0.556225\pi$
$491$	−7.78734	−0.351438	−0.175719	+	0.984440i	$0.556225\pi$
$492$	−5.76868	−0.260072
$493$	15.3120	0.689617
$494$	−0.141336	−0.00635901
$495$	0	0
$496$	−7.78734	−0.349662
$497$	−5.70329	−0.255828
$498$	−12.2827	−0.550400
$499$	4.31537	0.193182	0.0965912	−	0.995324i	$-0.469206\pi$
$499$	4.31537	0.193182	0.0965912	+	0.995324i	$0.469206\pi$
$500$	0	0
$501$	−20.1727	−0.901250
$502$	−2.51399	−0.112205
$503$	18.5526	0.827221	0.413610	−	0.910454i	$-0.364268\pi$
$503$	18.5526	0.827221	0.413610	+	0.910454i	$0.364268\pi$
$504$	−0.726656	−0.0323679
$505$	0	0
$506$	17.2406	0.766440
$507$	−17.6960	−0.785908
$508$	−3.29200	−0.146059
$509$	−7.73599	−0.342892	−0.171446	−	0.985194i	$-0.554844\pi$
$509$	−7.73599	−0.342892	−0.171446	+	0.985194i	$0.554844\pi$
$510$	0	0
$511$	−2.35400	−0.104135
$512$	1.00000	0.0441942
$513$	−5.64600	−0.249277
$514$	−24.7967	−1.09373
$515$	0	0
$516$	3.40196	0.149763
$517$	−36.0373	−1.58492
$518$	2.08405	0.0915677
$519$	−23.5747	−1.03481
$520$	0	0
$521$	15.2080	0.666273	0.333136	−	0.942879i	$-0.391893\pi$
$521$	15.2080	0.666273	0.333136	+	0.942879i	$0.391893\pi$
$522$	−8.16131	−0.357211
$523$	−18.2113	−0.796327	−0.398163	−	0.917315i	$-0.630352\pi$
$523$	−18.2113	−0.796327	−0.398163	+	0.917315i	$0.630352\pi$
$524$	18.0187	0.787149
$525$	0	0
$526$	−22.5653	−0.983896
$527$	−16.6753	−0.726388
$528$	4.77801	0.207936
$529$	1.19995	0.0521715
$530$	0	0
$531$	6.44398	0.279645
$532$	0.636672	0.0276032
$533$	0.598038	0.0259039
$534$	−9.24065	−0.399882
$535$	0	0
$536$	8.37266	0.361644
$537$	24.1800	1.04344
$538$	−26.5653	−1.14531
$539$	−23.1120	−0.995506
$540$	0	0
$541$	16.5140	0.709992	0.354996	−	0.934868i	$-0.384482\pi$
$541$	16.5140	0.709992	0.354996	+	0.934868i	$0.384482\pi$
$542$	−24.9380	−1.07118
$543$	8.42533	0.361565
$544$	2.14134	0.0918090
$545$	0	0
$546$	−0.122679	−0.00525016
$547$	16.2827	0.696197	0.348098	−	0.937458i	$-0.386828\pi$
$547$	16.2827	0.696197	0.348098	+	0.937458i	$0.386828\pi$
$548$	−14.4240	−0.616163
$549$	7.41336	0.316395
$550$	0	0
$551$	7.15066	0.304629
$552$	6.70668	0.285455
$553$	−2.66127	−0.113169
$554$	18.5467	0.787973
$555$	0	0
$556$	15.4720	0.656158
$557$	37.4533	1.58695	0.793474	−	0.608604i	$-0.208270\pi$
$557$	37.4533	1.58695	0.793474	+	0.608604i	$0.208270\pi$
$558$	8.88797	0.376258
$559$	−0.352681	−0.0149168
$560$	0	0
$561$	10.2313	0.431967
$562$	24.7967	1.04598
$563$	−29.1307	−1.22771	−0.613856	−	0.789418i	$-0.710382\pi$
$563$	−29.1307	−1.22771	−0.613856	+	0.789418i	$0.710382\pi$
$564$	−14.0187	−0.590292
$565$	0	0
$566$	13.5747	0.570586
$567$	−2.72072	−0.114259
$568$	−8.95798	−0.375868
$569$	14.8480	0.622461	0.311231	−	0.950334i	$-0.399259\pi$
$569$	14.8480	0.622461	0.311231	+	0.950334i	$0.399259\pi$
$570$	0	0
$571$	41.9087	1.75382	0.876912	−	0.480651i	$-0.159599\pi$
$571$	41.9087	1.75382	0.876912	+	0.480651i	$0.159599\pi$
$572$	−0.495336	−0.0207110
$573$	19.9546	0.833615
$574$	−2.69396	−0.112444
$575$	0	0
$576$	−1.14134	−0.0475557
$577$	16.4427	0.684517	0.342259	−	0.939606i	$-0.388808\pi$
$577$	16.4427	0.684517	0.342259	+	0.939606i	$0.388808\pi$
$578$	−12.4147	−0.516383
$579$	27.2920	1.13422
$580$	0	0
$581$	−5.73599	−0.237969
$582$	19.8573	0.823113
$583$	28.5327	1.18170
$584$	−3.69735	−0.152998
$585$	0	0
$586$	−15.6133	−0.644980
$587$	−42.5327	−1.75551	−0.877755	−	0.479109i	$-0.840960\pi$
$587$	−42.5327	−1.75551	−0.877755	+	0.479109i	$0.840960\pi$
$588$	−8.99067	−0.370769
$589$	−7.78734	−0.320872
$590$	0	0
$591$	−13.5633	−0.557919
$592$	3.27334	0.134534
$593$	3.92273	0.161087	0.0805437	−	0.996751i	$-0.474334\pi$
$593$	3.92273	0.161087	0.0805437	+	0.996751i	$0.474334\pi$
$594$	−19.7873	−0.811884
$595$	0	0
$596$	−17.1893	−0.704101
$597$	13.2907	0.543951
$598$	−0.695281	−0.0284322
$599$	−10.7594	−0.439615	−0.219808	−	0.975543i	$-0.570543\pi$
$599$	−10.7594	−0.439615	−0.219808	+	0.975543i	$0.570543\pi$
$600$	0	0
$601$	25.2220	1.02883	0.514413	−	0.857542i	$-0.328010\pi$
$601$	25.2220	1.02883	0.514413	+	0.857542i	$0.328010\pi$
$602$	1.58871	0.0647510
$603$	−9.55602	−0.389151
$604$	3.29200	0.133950
$605$	0	0
$606$	−22.6540	−0.920256
$607$	39.2920	1.59481	0.797407	−	0.603442i	$-0.206205\pi$
$607$	39.2920	1.59481	0.797407	+	0.603442i	$0.206205\pi$
$608$	1.00000	0.0405554
$609$	6.20672	0.251509
$610$	0	0
$611$	1.45331	0.0587947
$612$	−2.44398	−0.0987922
$613$	9.80599	0.396060	0.198030	−	0.980196i	$-0.436546\pi$
$613$	9.80599	0.396060	0.198030	+	0.980196i	$0.436546\pi$
$614$	34.0187	1.37288
$615$	0	0
$616$	2.23132	0.0899025
$617$	−35.0093	−1.40942	−0.704711	−	0.709494i	$-0.748923\pi$
$617$	−35.0093	−1.40942	−0.704711	+	0.709494i	$0.748923\pi$
$618$	12.3527	0.496898
$619$	13.4206	0.539420	0.269710	−	0.962942i	$-0.413072\pi$
$619$	13.4206	0.539420	0.269710	+	0.962942i	$0.413072\pi$
$620$	0	0
$621$	−27.7746	−1.11456
$622$	8.93800	0.358381
$623$	−4.31537	−0.172891
$624$	−0.192688	−0.00771367
$625$	0	0
$626$	−18.4240	−0.736371
$627$	4.77801	0.190815
$628$	15.1893	0.606119
$629$	7.00933	0.279480
$630$	0	0
$631$	40.5254	1.61329	0.806645	−	0.591036i	$-0.201281\pi$
$631$	40.5254	1.61329	0.806645	+	0.591036i	$0.201281\pi$
$632$	−4.17997	−0.166270
$633$	−28.3000	−1.12482
$634$	33.5547	1.33263
$635$	0	0
$636$	11.0993	0.440116
$637$	0.932062	0.0369296
$638$	25.0607	0.992162
$639$	10.2241	0.404458
$640$	0	0
$641$	−26.0700	−1.02970	−0.514852	−	0.857279i	$-0.672153\pi$
$641$	−26.0700	−1.02970	−0.514852	+	0.857279i	$0.672153\pi$
$642$	0.122679	0.00484174
$643$	30.1400	1.18861	0.594303	−	0.804241i	$-0.297428\pi$
$643$	30.1400	1.18861	0.594303	+	0.804241i	$0.297428\pi$
$644$	3.13201	0.123418
$645$	0	0
$646$	2.14134	0.0842497
$647$	−20.1086	−0.790552	−0.395276	−	0.918562i	$-0.629351\pi$
$647$	−20.1086	−0.790552	−0.395276	+	0.918562i	$0.629351\pi$
$648$	−4.27334	−0.167873
$649$	−19.7873	−0.776721
$650$	0	0
$651$	−6.75935	−0.264920
$652$	−14.0700	−0.551024
$653$	−28.0373	−1.09718	−0.548592	−	0.836090i	$-0.684836\pi$
$653$	−28.0373	−1.09718	−0.548592	+	0.836090i	$0.684836\pi$
$654$	−18.5340	−0.724736
$655$	0	0
$656$	−4.23132	−0.165205
$657$	4.21992	0.164635
$658$	−6.54669	−0.255216
$659$	4.90069	0.190904	0.0954518	−	0.995434i	$-0.469570\pi$
$659$	4.90069	0.190904	0.0954518	+	0.995434i	$0.469570\pi$
$660$	0	0
$661$	−8.03863	−0.312667	−0.156333	−	0.987704i	$-0.549967\pi$
$661$	−8.03863	−0.312667	−0.156333	+	0.987704i	$0.549967\pi$
$662$	2.25130	0.0874991
$663$	−0.412609	−0.0160244
$664$	−9.00933	−0.349630
$665$	0	0
$666$	−3.73599	−0.144766
$667$	35.1766	1.36204
$668$	−14.7967	−0.572500
$669$	−14.6240	−0.565395
$670$	0	0
$671$	−22.7640	−0.878793
$672$	0.867993	0.0334835
$673$	−4.82936	−0.186158	−0.0930791	−	0.995659i	$-0.529671\pi$
$673$	−4.82936	−0.186158	−0.0930791	+	0.995659i	$0.529671\pi$
$674$	−21.3620	−0.822834
$675$	0	0
$676$	−12.9800	−0.499232
$677$	12.8094	0.492305	0.246152	−	0.969231i	$-0.420834\pi$
$677$	12.8094	0.492305	0.246152	+	0.969231i	$0.420834\pi$
$678$	15.7101	0.603342
$679$	9.27334	0.355878
$680$	0	0
$681$	17.1133	0.655785
$682$	−27.2920	−1.04506
$683$	37.1307	1.42077	0.710383	−	0.703815i	$-0.248522\pi$
$683$	37.1307	1.42077	0.710383	+	0.703815i	$0.248522\pi$
$684$	−1.14134	−0.0436401
$685$	0	0
$686$	−8.65533	−0.330462
$687$	34.7267	1.32490
$688$	2.49534	0.0951338
$689$	−1.15066	−0.0438368
$690$	0	0
$691$	−18.1986	−0.692308	−0.346154	−	0.938178i	$-0.612513\pi$
$691$	−18.1986	−0.692308	−0.346154	+	0.938178i	$0.612513\pi$
$692$	−17.2920	−0.657343
$693$	−2.54669	−0.0967406
$694$	11.5560	0.438660
$695$	0	0
$696$	9.74870	0.369524
$697$	−9.06068	−0.343198
$698$	−17.1120	−0.647700
$699$	−4.24272	−0.160474
$700$	0	0
$701$	−26.2827	−0.992683	−0.496341	−	0.868127i	$-0.665324\pi$
$701$	−26.2827	−0.992683	−0.496341	+	0.868127i	$0.665324\pi$
$702$	0.797984	0.0301180
$703$	3.27334	0.123456
$704$	3.50466	0.132087
$705$	0	0
$706$	11.6974	0.440236
$707$	−10.5794	−0.397879
$708$	−7.69735	−0.289284
$709$	−14.9253	−0.560531	−0.280265	−	0.959923i	$-0.590422\pi$
$709$	−14.9253	−0.560531	−0.280265	+	0.959923i	$0.590422\pi$
$710$	0	0
$711$	4.77075	0.178917
$712$	−6.77801	−0.254017
$713$	−38.3086	−1.43467
$714$	1.85866	0.0695587
$715$	0	0
$716$	17.7360	0.662825
$717$	−2.10402	−0.0785761
$718$	−4.47536	−0.167019
$719$	32.3327	1.20581	0.602903	−	0.797814i	$-0.294011\pi$
$719$	32.3327	1.20581	0.602903	+	0.797814i	$0.294011\pi$
$720$	0	0
$721$	5.76868	0.214837
$722$	1.00000	0.0372161
$723$	14.0187	0.521359
$724$	6.17997	0.229677
$725$	0	0
$726$	1.74870	0.0649005
$727$	−42.0246	−1.55861	−0.779303	−	0.626647i	$-0.784427\pi$
$727$	−42.0246	−1.55861	−0.779303	+	0.626647i	$0.784427\pi$
$728$	−0.0899847	−0.00333506
$729$	27.9694	1.03590
$730$	0	0
$731$	5.34335	0.197631
$732$	−8.85527	−0.327300
$733$	26.5840	0.981903	0.490951	−	0.871187i	$-0.336649\pi$
$733$	26.5840	0.981903	0.490951	+	0.871187i	$0.336649\pi$
$734$	18.7453	0.691902
$735$	0	0
$736$	4.91934	0.181329
$737$	29.3434	1.08088
$738$	4.82936	0.177771
$739$	8.14728	0.299702	0.149851	−	0.988709i	$-0.452121\pi$
$739$	8.14728	0.299702	0.149851	+	0.988709i	$0.452121\pi$
$740$	0	0
$741$	−0.192688	−0.00707855
$742$	5.18336	0.190287
$743$	35.8247	1.31428	0.657139	−	0.753769i	$-0.271766\pi$
$743$	35.8247	1.31428	0.657139	+	0.753769i	$0.271766\pi$
$744$	−10.6167	−0.389227
$745$	0	0
$746$	1.69735	0.0621445
$747$	10.2827	0.376223
$748$	7.50466	0.274398
$749$	0.0572907	0.00209336
$750$	0	0
$751$	−14.8994	−0.543686	−0.271843	−	0.962342i	$-0.587633\pi$
$751$	−14.8994	−0.543686	−0.271843	+	0.962342i	$0.587633\pi$
$752$	−10.2827	−0.374970
$753$	−3.42740	−0.124901
$754$	−1.01065	−0.0368056
$755$	0	0
$756$	−3.59465	−0.130736
$757$	−47.7920	−1.73703	−0.868514	−	0.495664i	$-0.834925\pi$
$757$	−47.7920	−1.73703	−0.868514	+	0.495664i	$0.834925\pi$
$758$	2.63667	0.0957682
$759$	23.5047	0.853165
$760$	0	0
$761$	−38.9053	−1.41032	−0.705158	−	0.709050i	$-0.749124\pi$
$761$	−38.9053	−1.41032	−0.705158	+	0.709050i	$0.749124\pi$
$762$	−4.48808	−0.162586
$763$	−8.65533	−0.313344
$764$	14.6367	0.529536
$765$	0	0
$766$	12.4953	0.451475
$767$	0.797984	0.0288135
$768$	1.36333	0.0491949
$769$	8.74663	0.315412	0.157706	−	0.987486i	$-0.449590\pi$
$769$	8.74663	0.315412	0.157706	+	0.987486i	$0.449590\pi$
$770$	0	0
$771$	−33.8060	−1.21749
$772$	20.0187	0.720487
$773$	−23.4707	−0.844181	−0.422090	−	0.906554i	$-0.638703\pi$
$773$	−23.4707	−0.844181	−0.422090	+	0.906554i	$0.638703\pi$
$774$	−2.84802	−0.102370
$775$	0	0
$776$	14.5653	0.522865
$777$	2.84124	0.101929
$778$	−4.51399	−0.161834
$779$	−4.23132	−0.151603
$780$	0	0
$781$	−31.3947	−1.12339
$782$	10.5340	0.376694
$783$	−40.3727	−1.44280
$784$	−6.59465	−0.235523
$785$	0	0
$786$	24.5653	0.876217
$787$	1.26063	0.0449364	0.0224682	−	0.999748i	$-0.492848\pi$
$787$	1.26063	0.0449364	0.0224682	+	0.999748i	$0.492848\pi$
$788$	−9.94865	−0.354406
$789$	−30.7640	−1.09523
$790$	0	0
$791$	7.33657	0.260859
$792$	−4.00000	−0.142134
$793$	0.918026	0.0326000
$794$	−35.6774	−1.26614
$795$	0	0
$796$	9.74870	0.345534
$797$	−38.6481	−1.36898	−0.684492	−	0.729020i	$-0.739976\pi$
$797$	−38.6481	−1.36898	−0.684492	+	0.729020i	$0.739976\pi$
$798$	0.867993	0.0307266
$799$	−22.0187	−0.778964
$800$	0	0
$801$	7.73599	0.273338
$802$	15.3434	0.541793
$803$	−12.9580	−0.457277
$804$	11.4147	0.402565
$805$	0	0
$806$	1.10063	0.0387681
$807$	−36.2173	−1.27491
$808$	−16.6167	−0.584573
$809$	51.6506	1.81594	0.907970	−	0.419036i	$-0.137632\pi$
$809$	51.6506	1.81594	0.907970	+	0.419036i	$0.137632\pi$
$810$	0	0
$811$	8.19269	0.287684	0.143842	−	0.989601i	$-0.454054\pi$
$811$	8.19269	0.287684	0.143842	+	0.989601i	$0.454054\pi$
$812$	4.55263	0.159766
$813$	−33.9987	−1.19239
$814$	11.4720	0.402092
$815$	0	0
$816$	2.91934	0.102197
$817$	2.49534	0.0873007
$818$	29.3620	1.02662
$819$	0.102703	0.00358873
$820$	0	0
$821$	−49.9600	−1.74362	−0.871809	−	0.489846i	$-0.837053\pi$
$821$	−49.9600	−1.74362	−0.871809	+	0.489846i	$0.837053\pi$
$822$	−19.6647	−0.685884
$823$	−16.8421	−0.587078	−0.293539	−	0.955947i	$-0.594833\pi$
$823$	−16.8421	−0.587078	−0.293539	+	0.955947i	$0.594833\pi$
$824$	9.06068	0.315644
$825$	0	0
$826$	−3.59465	−0.125074
$827$	−41.7487	−1.45174	−0.725872	−	0.687829i	$-0.758564\pi$
$827$	−41.7487	−1.45174	−0.725872	+	0.687829i	$0.758564\pi$
$828$	−5.61462	−0.195122
$829$	−5.98002	−0.207695	−0.103847	−	0.994593i	$-0.533115\pi$
$829$	−5.98002	−0.207695	−0.103847	+	0.994593i	$0.533115\pi$
$830$	0	0
$831$	25.2852	0.877135
$832$	−0.141336	−0.00489995
$833$	−14.1214	−0.489276
$834$	21.0934	0.730404
$835$	0	0
$836$	3.50466	0.121211
$837$	43.9673	1.51973
$838$	25.1379	0.868376
$839$	32.0373	1.10605	0.553025	−	0.833164i	$-0.313473\pi$
$839$	32.0373	1.10605	0.553025	+	0.833164i	$0.313473\pi$
$840$	0	0
$841$	22.1320	0.763173
$842$	14.5454	0.501267
$843$	33.8060	1.16434
$844$	−20.7580	−0.714521
$845$	0	0
$846$	11.7360	0.403491
$847$	0.816641	0.0280601
$848$	8.14134	0.279575
$849$	18.5067	0.635150
$850$	0	0
$851$	16.1027	0.551994
$852$	−12.2127	−0.418399
$853$	−40.8480	−1.39861	−0.699305	−	0.714824i	$-0.746507\pi$
$853$	−40.8480	−1.39861	−0.699305	+	0.714824i	$0.746507\pi$
$854$	−4.13540	−0.141510
$855$	0	0
$856$	0.0899847	0.00307561
$857$	28.8667	0.986067	0.493033	−	0.870010i	$-0.335888\pi$
$857$	28.8667	0.986067	0.493033	+	0.870010i	$0.335888\pi$
$858$	−0.675305	−0.0230545
$859$	−11.5047	−0.392534	−0.196267	−	0.980550i	$-0.562882\pi$
$859$	−11.5047	−0.392534	−0.196267	+	0.980550i	$0.562882\pi$
$860$	0	0
$861$	−3.67276	−0.125167
$862$	19.4020	0.660833
$863$	−31.6074	−1.07593	−0.537964	−	0.842968i	$-0.680806\pi$
$863$	−31.6074	−1.07593	−0.537964	+	0.842968i	$0.680806\pi$
$864$	−5.64600	−0.192081
$865$	0	0
$866$	5.50466	0.187056
$867$	−16.9253	−0.574813
$868$	−4.95798	−0.168285
$869$	−14.6494	−0.496947
$870$	0	0
$871$	−1.18336	−0.0400966
$872$	−13.5946	−0.460373
$873$	−16.6240	−0.562636
$874$	4.91934	0.166399
$875$	0	0
$876$	−5.04070	−0.170310
$877$	12.0641	0.407375	0.203687	−	0.979036i	$-0.434707\pi$
$877$	12.0641	0.407375	0.203687	+	0.979036i	$0.434707\pi$
$878$	12.2500	0.413417
$879$	−21.2861	−0.717961
$880$	0	0
$881$	−22.8480	−0.769769	−0.384885	−	0.922965i	$-0.625759\pi$
$881$	−22.8480	−0.769769	−0.384885	+	0.922965i	$0.625759\pi$
$882$	7.52671	0.253438
$883$	−34.1773	−1.15016	−0.575079	−	0.818098i	$-0.695029\pi$
$883$	−34.1773	−1.15016	−0.575079	+	0.818098i	$0.695029\pi$
$884$	−0.302648	−0.0101792
$885$	0	0
$886$	31.6006	1.06164
$887$	26.6167	0.893701	0.446851	−	0.894609i	$-0.352546\pi$
$887$	26.6167	0.893701	0.446851	+	0.894609i	$0.352546\pi$
$888$	4.46264	0.149756
$889$	−2.09592	−0.0702950
$890$	0	0
$891$	−14.9766	−0.501736
$892$	−10.7267	−0.359155
$893$	−10.2827	−0.344097
$894$	−23.4347	−0.783772
$895$	0	0
$896$	0.636672	0.0212697
$897$	−0.947896	−0.0316493
$898$	−36.0187	−1.20196
$899$	−55.6846	−1.85719
$900$	0	0
$901$	17.4333	0.580789
$902$	−14.8294	−0.493764
$903$	2.16593	0.0720777
$904$	11.5233	0.383260
$905$	0	0
$906$	4.48808	0.149106
$907$	13.1434	0.436420	0.218210	−	0.975902i	$-0.429978\pi$
$907$	13.1434	0.436420	0.218210	+	0.975902i	$0.429978\pi$
$908$	12.5526	0.416574
$909$	18.9652	0.629037
$910$	0	0
$911$	−32.9253	−1.09086	−0.545432	−	0.838155i	$-0.683634\pi$
$911$	−32.9253	−1.09086	−0.545432	+	0.838155i	$0.683634\pi$
$912$	1.36333	0.0451443
$913$	−31.5747	−1.04497
$914$	22.1413	0.732370
$915$	0	0
$916$	25.4720	0.841618
$917$	11.4720	0.378838
$918$	−12.0900	−0.399029
$919$	−24.1273	−0.795886	−0.397943	−	0.917410i	$-0.630276\pi$
$919$	−24.1273	−0.795886	−0.397943	+	0.917410i	$0.630276\pi$
$920$	0	0
$921$	46.3786	1.52823
$922$	−2.31537	−0.0762525
$923$	1.26609	0.0416737
$924$	3.04202	0.100075
$925$	0	0
$926$	15.8387	0.520492
$927$	−10.3413	−0.339652
$928$	7.15066	0.234732
$929$	−15.9359	−0.522841	−0.261420	−	0.965225i	$-0.584191\pi$
$929$	−15.9359	−0.522841	−0.261420	+	0.965225i	$0.584191\pi$
$930$	0	0
$931$	−6.59465	−0.216131
$932$	−3.11203	−0.101938
$933$	12.1854	0.398933
$934$	23.1379	0.757097
$935$	0	0
$936$	0.161312	0.00527265
$937$	23.5547	0.769498	0.384749	−	0.923021i	$-0.374288\pi$
$937$	23.5547	0.769498	0.384749	+	0.923021i	$0.374288\pi$
$938$	5.33063	0.174051
$939$	−25.1180	−0.819694
$940$	0	0
$941$	−25.6974	−0.837710	−0.418855	−	0.908053i	$-0.637568\pi$
$941$	−25.6974	−0.837710	−0.418855	+	0.908053i	$0.637568\pi$
$942$	20.7080	0.674703
$943$	−20.8153	−0.677840
$944$	−5.64600	−0.183762
$945$	0	0
$946$	8.74531	0.284335
$947$	−16.3013	−0.529722	−0.264861	−	0.964287i	$-0.585326\pi$
$947$	−16.3013	−0.529722	−0.264861	+	0.964287i	$0.585326\pi$
$948$	−5.69867	−0.185084
$949$	0.522569	0.0169633
$950$	0	0
$951$	45.7461	1.48342
$952$	1.36333	0.0441857
$953$	10.2754	0.332853	0.166427	−	0.986054i	$-0.446777\pi$
$953$	10.2754	0.332853	0.166427	+	0.986054i	$0.446777\pi$
$954$	−9.29200	−0.300840
$955$	0	0
$956$	−1.54330	−0.0499138
$957$	34.1659	1.10443
$958$	−10.1214	−0.327006
$959$	−9.18336	−0.296546
$960$	0	0
$961$	29.6426	0.956213
$962$	−0.462642	−0.0149162
$963$	−0.102703	−0.00330955
$964$	10.2827	0.331183
$965$	0	0
$966$	4.26995	0.137384
$967$	−53.2920	−1.71376	−0.856878	−	0.515520i	$-0.827599\pi$
$967$	−53.2920	−1.71376	−0.856878	+	0.515520i	$0.827599\pi$
$968$	1.28267	0.0412266
$969$	2.91934	0.0937828
$970$	0	0
$971$	2.54669	0.0817271	0.0408635	−	0.999165i	$-0.486989\pi$
$971$	2.54669	0.0817271	0.0408635	+	0.999165i	$0.486989\pi$
$972$	11.1120	0.356419
$973$	9.85057	0.315795
$974$	20.3854	0.653190
$975$	0	0
$976$	−6.49534	−0.207911
$977$	−49.2966	−1.57714	−0.788569	−	0.614946i	$-0.789178\pi$
$977$	−49.2966	−1.57714	−0.788569	+	0.614946i	$0.789178\pi$
$978$	−19.1820	−0.613374
$979$	−23.7546	−0.759202
$980$	0	0
$981$	15.5161	0.495390
$982$	−7.78734	−0.248504
$983$	−36.7453	−1.17199	−0.585997	−	0.810313i	$-0.699297\pi$
$983$	−36.7453	−1.17199	−0.585997	+	0.810313i	$0.699297\pi$
$984$	−5.76868	−0.183899
$985$	0	0
$986$	15.3120	0.487633
$987$	−8.92528	−0.284095
$988$	−0.141336	−0.00449650
$989$	12.2754	0.390335
$990$	0	0
$991$	−35.5674	−1.12984	−0.564918	−	0.825147i	$-0.691092\pi$
$991$	−35.5674	−1.12984	−0.564918	+	0.825147i	$0.691092\pi$
$992$	−7.78734	−0.247248
$993$	3.06926	0.0973999
$994$	−5.70329	−0.180897
$995$	0	0
$996$	−12.2827	−0.389191
$997$	−48.4299	−1.53379	−0.766896	−	0.641771i	$-0.778200\pi$
$997$	−48.4299	−1.53379	−0.766896	+	0.641771i	$0.778200\pi$
$998$	4.31537	0.136601
$999$	−18.4813	−0.584722

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.a.n.1.2		3
3.2	odd	2		8550.2.a.ck.1.2		3
4.3	odd	2		7600.2.a.bi.1.2		3
5.2	odd	4		190.2.b.b.39.5	yes	6
5.3	odd	4		190.2.b.b.39.2	✓	6
5.4	even	2		950.2.a.i.1.2		3
15.2	even	4		1710.2.d.d.1369.2		6
15.8	even	4		1710.2.d.d.1369.5		6
15.14	odd	2		8550.2.a.cl.1.2		3
20.3	even	4		1520.2.d.j.609.3		6
20.7	even	4		1520.2.d.j.609.4		6
20.19	odd	2		7600.2.a.cd.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.b.b.39.2	✓	6	5.3	odd	4
190.2.b.b.39.5	yes	6	5.2	odd	4
950.2.a.i.1.2		3	5.4	even	2
950.2.a.n.1.2		3	1.1	even	1	trivial
1520.2.d.j.609.3		6	20.3	even	4
1520.2.d.j.609.4		6	20.7	even	4
1710.2.d.d.1369.2		6	15.2	even	4
1710.2.d.d.1369.5		6	15.8	even	4
7600.2.a.bi.1.2		3	4.3	odd	2
7600.2.a.cd.1.2		3	20.19	odd	2
8550.2.a.ck.1.2		3	3.2	odd	2
8550.2.a.cl.1.2		3	15.14	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.36333 q^{3} +1.00000 q^{4} +1.36333 q^{6} +0.636672 q^{7} +1.00000 q^{8} -1.14134 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.36333 q^{3} +1.00000 q^{4} +1.36333 q^{6} +0.636672 q^{7} +1.00000 q^{8} -1.14134 q^{9} +3.50466 q^{11} +1.36333 q^{12} -0.141336 q^{13} +0.636672 q^{14} +1.00000 q^{16} +2.14134 q^{17} -1.14134 q^{18} +1.00000 q^{19} +0.867993 q^{21} +3.50466 q^{22} +4.91934 q^{23} +1.36333 q^{24} -0.141336 q^{26} -5.64600 q^{27} +0.636672 q^{28} +7.15066 q^{29} -7.78734 q^{31} +1.00000 q^{32} +4.77801 q^{33} +2.14134 q^{34} -1.14134 q^{36} +3.27334 q^{37} +1.00000 q^{38} -0.192688 q^{39} -4.23132 q^{41} +0.867993 q^{42} +2.49534 q^{43} +3.50466 q^{44} +4.91934 q^{46} -10.2827 q^{47} +1.36333 q^{48} -6.59465 q^{49} +2.91934 q^{51} -0.141336 q^{52} +8.14134 q^{53} -5.64600 q^{54} +0.636672 q^{56} +1.36333 q^{57} +7.15066 q^{58} -5.64600 q^{59} -6.49534 q^{61} -7.78734 q^{62} -0.726656 q^{63} +1.00000 q^{64} +4.77801 q^{66} +8.37266 q^{67} +2.14134 q^{68} +6.70668 q^{69} -8.95798 q^{71} -1.14134 q^{72} -3.69735 q^{73} +3.27334 q^{74} +1.00000 q^{76} +2.23132 q^{77} -0.192688 q^{78} -4.17997 q^{79} -4.27334 q^{81} -4.23132 q^{82} -9.00933 q^{83} +0.867993 q^{84} +2.49534 q^{86} +9.74870 q^{87} +3.50466 q^{88} -6.77801 q^{89} -0.0899847 q^{91} +4.91934 q^{92} -10.6167 q^{93} -10.2827 q^{94} +1.36333 q^{96} +14.5653 q^{97} -6.59465 q^{98} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 2 q^{6} + 4 q^{7} + 3 q^{8} + 5 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 2 * q^6 + 4 * q^7 + 3 * q^8 + 5 * q^9	\( 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 2 q^{6} + 4 q^{7} + 3 q^{8} + 5 q^{9} + 2 q^{12} + 8 q^{13} + 4 q^{14} + 3 q^{16} - 2 q^{17} + 5 q^{18} + 3 q^{19} - 10 q^{21} + 2 q^{24} + 8 q^{26} + 2 q^{27} + 4 q^{28} - 8 q^{29} + 4 q^{31} + 3 q^{32} + 8 q^{33} - 2 q^{34} + 5 q^{36} + 14 q^{37} + 3 q^{38} + 10 q^{39} + 2 q^{41} - 10 q^{42} + 18 q^{43} - 14 q^{47} + 2 q^{48} - 3 q^{49} - 6 q^{51} + 8 q^{52} + 16 q^{53} + 2 q^{54} + 4 q^{56} + 2 q^{57} - 8 q^{58} + 2 q^{59} - 30 q^{61} + 4 q^{62} + 2 q^{63} + 3 q^{64} + 8 q^{66} + 2 q^{67} - 2 q^{68} - 22 q^{69} - 8 q^{71} + 5 q^{72} + 10 q^{73} + 14 q^{74} + 3 q^{76} - 8 q^{77} + 10 q^{78} - 17 q^{81} + 2 q^{82} - 6 q^{83} - 10 q^{84} + 18 q^{86} + 6 q^{87} - 14 q^{89} + 6 q^{91} + 4 q^{93} - 14 q^{94} + 2 q^{96} + 10 q^{97} - 3 q^{98} - 12 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 2 * q^6 + 4 * q^7 + 3 * q^8 + 5 * q^9 + 2 * q^12 + 8 * q^13 + 4 * q^14 + 3 * q^16 - 2 * q^17 + 5 * q^18 + 3 * q^19 - 10 * q^21 + 2 * q^24 + 8 * q^26 + 2 * q^27 + 4 * q^28 - 8 * q^29 + 4 * q^31 + 3 * q^32 + 8 * q^33 - 2 * q^34 + 5 * q^36 + 14 * q^37 + 3 * q^38 + 10 * q^39 + 2 * q^41 - 10 * q^42 + 18 * q^43 - 14 * q^47 + 2 * q^48 - 3 * q^49 - 6 * q^51 + 8 * q^52 + 16 * q^53 + 2 * q^54 + 4 * q^56 + 2 * q^57 - 8 * q^58 + 2 * q^59 - 30 * q^61 + 4 * q^62 + 2 * q^63 + 3 * q^64 + 8 * q^66 + 2 * q^67 - 2 * q^68 - 22 * q^69 - 8 * q^71 + 5 * q^72 + 10 * q^73 + 14 * q^74 + 3 * q^76 - 8 * q^77 + 10 * q^78 - 17 * q^81 + 2 * q^82 - 6 * q^83 - 10 * q^84 + 18 * q^86 + 6 * q^87 - 14 * q^89 + 6 * q^91 + 4 * q^93 - 14 * q^94 + 2 * q^96 + 10 * q^97 - 3 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more