LMFDB - Embedded newform 503.2.a.f.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [503,2,Mod(1,503)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(503, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("503.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 503 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	503.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:	$4.01647522167$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	503.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.81497 q^{2} +0.577924 q^{3} +1.29413 q^{4} +2.10638 q^{5} +1.04892 q^{6} +1.73516 q^{7} -1.28114 q^{8} -2.66600 q^{9} +O(q^{10})$	\(q+1.81497 q^{2} +0.577924 q^{3} +1.29413 q^{4} +2.10638 q^{5} +1.04892 q^{6} +1.73516 q^{7} -1.28114 q^{8} -2.66600 q^{9} +3.82302 q^{10} +6.36270 q^{11} +0.747908 q^{12} -2.18456 q^{13} +3.14927 q^{14} +1.21733 q^{15} -4.91349 q^{16} -0.631406 q^{17} -4.83873 q^{18} -7.04772 q^{19} +2.72593 q^{20} +1.00279 q^{21} +11.5481 q^{22} +6.00543 q^{23} -0.740398 q^{24} -0.563171 q^{25} -3.96493 q^{26} -3.27452 q^{27} +2.24552 q^{28} +7.71180 q^{29} +2.20941 q^{30} +0.467852 q^{31} -6.35558 q^{32} +3.67716 q^{33} -1.14599 q^{34} +3.65490 q^{35} -3.45016 q^{36} +2.99418 q^{37} -12.7914 q^{38} -1.26251 q^{39} -2.69855 q^{40} -8.67325 q^{41} +1.82004 q^{42} -11.0553 q^{43} +8.23417 q^{44} -5.61561 q^{45} +10.8997 q^{46} +4.33189 q^{47} -2.83962 q^{48} -3.98923 q^{49} -1.02214 q^{50} -0.364905 q^{51} -2.82711 q^{52} -8.09634 q^{53} -5.94316 q^{54} +13.4023 q^{55} -2.22297 q^{56} -4.07304 q^{57} +13.9967 q^{58} +7.20052 q^{59} +1.57538 q^{60} +5.93532 q^{61} +0.849139 q^{62} -4.62594 q^{63} -1.70824 q^{64} -4.60152 q^{65} +6.67394 q^{66} -2.21237 q^{67} -0.817122 q^{68} +3.47068 q^{69} +6.63355 q^{70} -5.83367 q^{71} +3.41551 q^{72} -9.72628 q^{73} +5.43437 q^{74} -0.325470 q^{75} -9.12067 q^{76} +11.0403 q^{77} -2.29142 q^{78} +1.62156 q^{79} -10.3497 q^{80} +6.10559 q^{81} -15.7417 q^{82} +1.72808 q^{83} +1.29774 q^{84} -1.32998 q^{85} -20.0650 q^{86} +4.45683 q^{87} -8.15148 q^{88} -11.1083 q^{89} -10.1922 q^{90} -3.79056 q^{91} +7.77181 q^{92} +0.270383 q^{93} +7.86227 q^{94} -14.8452 q^{95} -3.67304 q^{96} +7.97564 q^{97} -7.24034 q^{98} -16.9630 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q + 4 q^{2} + 4 q^{3} + 36 q^{4} + 9 q^{5} - 4 q^{6} + 11 q^{7} + 18 q^{8} + 42 q^{9}+O(q^{10}) $ 26 * q + 4 * q^2 + 4 * q^3 + 36 * q^4 + 9 * q^5 - 4 * q^6 + 11 * q^7 + 18 * q^8 + 42 * q^9	\( 26 q + 4 q^{2} + 4 q^{3} + 36 q^{4} + 9 q^{5} - 4 q^{6} + 11 q^{7} + 18 q^{8} + 42 q^{9} + 4 q^{10} - 17 q^{11} + 19 q^{12} + 14 q^{13} + q^{14} + 18 q^{15} + 48 q^{16} + 17 q^{17} - 10 q^{18} - 22 q^{19} - 19 q^{20} - 16 q^{21} + 38 q^{22} + 27 q^{23} - 9 q^{24} + 93 q^{25} + q^{26} + 31 q^{27} - 9 q^{28} + 13 q^{29} - 28 q^{30} + 26 q^{31} + 5 q^{32} + 6 q^{33} - 32 q^{34} - 22 q^{35} + 52 q^{36} + 55 q^{37} - 24 q^{38} - 15 q^{39} - 7 q^{40} + 24 q^{41} - 50 q^{42} + 20 q^{43} - 27 q^{44} - 8 q^{45} + 6 q^{46} - 25 q^{47} + 29 q^{48} + 65 q^{49} - 16 q^{50} + 7 q^{51} + 32 q^{52} + 30 q^{53} - 82 q^{54} + 25 q^{55} + 3 q^{56} + 9 q^{57} + 58 q^{58} - 26 q^{59} - 68 q^{60} + 15 q^{61} - 12 q^{62} - 19 q^{63} + 44 q^{64} + 20 q^{65} - 55 q^{66} - 20 q^{67} - 4 q^{68} - 27 q^{69} + 2 q^{70} - 35 q^{71} - 26 q^{72} + 38 q^{73} - 59 q^{74} + 2 q^{75} - 42 q^{76} - 6 q^{77} - 47 q^{78} + 21 q^{79} - 100 q^{80} + 70 q^{81} - 59 q^{82} - 48 q^{83} - 116 q^{84} + 6 q^{85} - 7 q^{86} - 9 q^{87} + 106 q^{88} - 5 q^{89} - 118 q^{90} - 24 q^{91} + 26 q^{92} - 8 q^{93} - 22 q^{94} + 43 q^{95} - 100 q^{96} + 142 q^{97} - 38 q^{98} - 50 q^{99}+O(q^{100}) \) 26 * q + 4 * q^2 + 4 * q^3 + 36 * q^4 + 9 * q^5 - 4 * q^6 + 11 * q^7 + 18 * q^8 + 42 * q^9 + 4 * q^10 - 17 * q^11 + 19 * q^12 + 14 * q^13 + q^14 + 18 * q^15 + 48 * q^16 + 17 * q^17 - 10 * q^18 - 22 * q^19 - 19 * q^20 - 16 * q^21 + 38 * q^22 + 27 * q^23 - 9 * q^24 + 93 * q^25 + q^26 + 31 * q^27 - 9 * q^28 + 13 * q^29 - 28 * q^30 + 26 * q^31 + 5 * q^32 + 6 * q^33 - 32 * q^34 - 22 * q^35 + 52 * q^36 + 55 * q^37 - 24 * q^38 - 15 * q^39 - 7 * q^40 + 24 * q^41 - 50 * q^42 + 20 * q^43 - 27 * q^44 - 8 * q^45 + 6 * q^46 - 25 * q^47 + 29 * q^48 + 65 * q^49 - 16 * q^50 + 7 * q^51 + 32 * q^52 + 30 * q^53 - 82 * q^54 + 25 * q^55 + 3 * q^56 + 9 * q^57 + 58 * q^58 - 26 * q^59 - 68 * q^60 + 15 * q^61 - 12 * q^62 - 19 * q^63 + 44 * q^64 + 20 * q^65 - 55 * q^66 - 20 * q^67 - 4 * q^68 - 27 * q^69 + 2 * q^70 - 35 * q^71 - 26 * q^72 + 38 * q^73 - 59 * q^74 + 2 * q^75 - 42 * q^76 - 6 * q^77 - 47 * q^78 + 21 * q^79 - 100 * q^80 + 70 * q^81 - 59 * q^82 - 48 * q^83 - 116 * q^84 + 6 * q^85 - 7 * q^86 - 9 * q^87 + 106 * q^88 - 5 * q^89 - 118 * q^90 - 24 * q^91 + 26 * q^92 - 8 * q^93 - 22 * q^94 + 43 * q^95 - 100 * q^96 + 142 * q^97 - 38 * q^98 - 50 * 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 $

$2$	1.81497	1.28338	0.641690	−	0.766964i	$-0.278234\pi$
$2$	1.81497	1.28338	0.641690	+	0.766964i	$0.278234\pi$
$3$	0.577924	0.333664	0.166832	−	0.985985i	$-0.446646\pi$
$3$	0.577924	0.333664	0.166832	+	0.985985i	$0.446646\pi$
$4$	1.29413	0.647065
$5$	2.10638	0.942001	0.471000	−	0.882133i	$-0.343893\pi$
$5$	2.10638	0.942001	0.471000	+	0.882133i	$0.343893\pi$
$6$	1.04892	0.428218
$7$	1.73516	0.655828	0.327914	−	0.944708i	$-0.393654\pi$
$7$	1.73516	0.655828	0.327914	+	0.944708i	$0.393654\pi$
$8$	−1.28114	−0.452950
$9$	−2.66600	−0.888668
$10$	3.82302	1.20895
$11$	6.36270	1.91843	0.959213	−	0.282683i	$-0.0912243\pi$
$11$	6.36270	1.91843	0.959213	+	0.282683i	$0.0912243\pi$
$12$	0.747908	0.215903
$13$	−2.18456	−0.605889	−0.302945	−	0.953008i	$-0.597970\pi$
$13$	−2.18456	−0.605889	−0.302945	+	0.953008i	$0.597970\pi$
$14$	3.14927	0.841677
$15$	1.21733	0.314312
$16$	−4.91349	−1.22837
$17$	−0.631406	−0.153139	−0.0765693	−	0.997064i	$-0.524397\pi$
$17$	−0.631406	−0.153139	−0.0765693	+	0.997064i	$0.524397\pi$
$18$	−4.83873	−1.14050
$19$	−7.04772	−1.61686	−0.808429	−	0.588594i	$-0.799682\pi$
$19$	−7.04772	−1.61686	−0.808429	+	0.588594i	$0.799682\pi$
$20$	2.72593	0.609536
$21$	1.00279	0.218826
$22$	11.5481	2.46207
$23$	6.00543	1.25222	0.626109	−	0.779735i	$-0.284646\pi$
$23$	6.00543	1.25222	0.626109	+	0.779735i	$0.284646\pi$
$24$	−0.740398	−0.151133
$25$	−0.563171	−0.112634
$26$	−3.96493	−0.777586
$27$	−3.27452	−0.630181
$28$	2.24552	0.424364
$29$	7.71180	1.43205	0.716023	−	0.698077i	$-0.245961\pi$
$29$	7.71180	1.43205	0.716023	+	0.698077i	$0.245961\pi$
$30$	2.20941	0.403382
$31$	0.467852	0.0840286	0.0420143	−	0.999117i	$-0.486622\pi$
$31$	0.467852	0.0840286	0.0420143	+	0.999117i	$0.486622\pi$
$32$	−6.35558	−1.12352
$33$	3.67716	0.640111
$34$	−1.14599	−0.196535
$35$	3.65490	0.617791
$36$	−3.45016	−0.575026
$37$	2.99418	0.492241	0.246120	−	0.969239i	$-0.420844\pi$
$37$	2.99418	0.492241	0.246120	+	0.969239i	$0.420844\pi$
$38$	−12.7914	−2.07504
$39$	−1.26251	−0.202164
$40$	−2.69855	−0.426679
$41$	−8.67325	−1.35453	−0.677267	−	0.735738i	$-0.736836\pi$
$41$	−8.67325	−1.35453	−0.677267	+	0.735738i	$0.736836\pi$
$42$	1.82004	0.280838
$43$	−11.0553	−1.68591	−0.842956	−	0.537983i	$-0.819186\pi$
$43$	−11.0553	−1.68591	−0.842956	+	0.537983i	$0.819186\pi$
$44$	8.23417	1.24135
$45$	−5.61561	−0.837126
$46$	10.8997	1.60707
$47$	4.33189	0.631871	0.315936	−	0.948781i	$-0.397682\pi$
$47$	4.33189	0.631871	0.315936	+	0.948781i	$0.397682\pi$
$48$	−2.83962	−0.409864
$49$	−3.98923	−0.569889
$50$	−1.02214	−0.144553
$51$	−0.364905	−0.0510969
$52$	−2.82711	−0.392050
$53$	−8.09634	−1.11212	−0.556059	−	0.831143i	$-0.687687\pi$
$53$	−8.09634	−1.11212	−0.556059	+	0.831143i	$0.687687\pi$
$54$	−5.94316	−0.808762
$55$	13.4023	1.80716
$56$	−2.22297	−0.297057
$57$	−4.07304	−0.539488
$58$	13.9967	1.83786
$59$	7.20052	0.937428	0.468714	−	0.883350i	$-0.344718\pi$
$59$	7.20052	0.937428	0.468714	+	0.883350i	$0.344718\pi$
$60$	1.57538	0.203380
$61$	5.93532	0.759940	0.379970	−	0.924999i	$-0.375934\pi$
$61$	5.93532	0.759940	0.379970	+	0.924999i	$0.375934\pi$
$62$	0.849139	0.107841
$63$	−4.62594	−0.582814
$64$	−1.70824	−0.213530
$65$	−4.60152	−0.570748
$66$	6.67394	0.821505
$67$	−2.21237	−0.270283	−0.135142	−	0.990826i	$-0.543149\pi$
$67$	−2.21237	−0.270283	−0.135142	+	0.990826i	$0.543149\pi$
$68$	−0.817122	−0.0990906
$69$	3.47068	0.417821
$70$	6.63355	0.792861
$71$	−5.83367	−0.692330	−0.346165	−	0.938174i	$-0.612516\pi$
$71$	−5.83367	−0.692330	−0.346165	+	0.938174i	$0.612516\pi$
$72$	3.41551	0.402522
$73$	−9.72628	−1.13837	−0.569187	−	0.822208i	$-0.692742\pi$
$73$	−9.72628	−1.13837	−0.569187	+	0.822208i	$0.692742\pi$
$74$	5.43437	0.631732
$75$	−0.325470	−0.0375820
$76$	−9.12067	−1.04621
$77$	11.0403	1.25816
$78$	−2.29142	−0.259453
$79$	1.62156	0.182439	0.0912197	−	0.995831i	$-0.470923\pi$
$79$	1.62156	0.182439	0.0912197	+	0.995831i	$0.470923\pi$
$80$	−10.3497	−1.15713
$81$	6.10559	0.678399
$82$	−15.7417	−1.73838
$83$	1.72808	0.189682	0.0948409	−	0.995492i	$-0.469766\pi$
$83$	1.72808	0.189682	0.0948409	+	0.995492i	$0.469766\pi$
$84$	1.29774	0.141595
$85$	−1.32998	−0.144257
$86$	−20.0650	−2.16367
$87$	4.45683	0.477823
$88$	−8.15148	−0.868951
$89$	−11.1083	−1.17748	−0.588740	−	0.808322i	$-0.700376\pi$
$89$	−11.1083	−1.17748	−0.588740	+	0.808322i	$0.700376\pi$
$90$	−10.1922	−1.07435
$91$	−3.79056	−0.397359
$92$	7.77181	0.810267
$93$	0.270383	0.0280374
$94$	7.86227	0.810931
$95$	−14.8452	−1.52308
$96$	−3.67304	−0.374878
$97$	7.97564	0.809803	0.404902	−	0.914360i	$-0.367306\pi$
$97$	7.97564	0.809803	0.404902	+	0.914360i	$0.367306\pi$
$98$	−7.24034	−0.731385
$99$	−16.9630	−1.70484
$100$	−0.728817	−0.0728817
$101$	−5.37750	−0.535081	−0.267541	−	0.963547i	$-0.586211\pi$
$101$	−5.37750	−0.535081	−0.267541	+	0.963547i	$0.586211\pi$
$102$	−0.662292	−0.0655767
$103$	5.38662	0.530759	0.265380	−	0.964144i	$-0.414503\pi$
$103$	5.38662	0.530759	0.265380	+	0.964144i	$0.414503\pi$
$104$	2.79872	0.274437
$105$	2.11225	0.206135
$106$	−14.6946	−1.42727
$107$	15.8750	1.53470	0.767348	−	0.641231i	$-0.221576\pi$
$107$	15.8750	1.53470	0.767348	+	0.641231i	$0.221576\pi$
$108$	−4.23765	−0.407768
$109$	−0.871591	−0.0834832	−0.0417416	−	0.999128i	$-0.513291\pi$
$109$	−0.871591	−0.0834832	−0.0417416	+	0.999128i	$0.513291\pi$
$110$	24.3247	2.31927
$111$	1.73041	0.164243
$112$	−8.52568	−0.805601
$113$	12.6631	1.19125	0.595624	−	0.803264i	$-0.296905\pi$
$113$	12.6631	1.19125	0.595624	+	0.803264i	$0.296905\pi$
$114$	−7.39247	−0.692368
$115$	12.6497	1.17959
$116$	9.98008	0.926627
$117$	5.82406	0.538434
$118$	13.0688	1.20308
$119$	−1.09559	−0.100433
$120$	−1.55956	−0.142368
$121$	29.4840	2.68036
$122$	10.7725	0.975293
$123$	−5.01247	−0.451960
$124$	0.605461	0.0543720
$125$	−11.7181	−1.04810
$126$	−8.39596	−0.747972
$127$	−14.0605	−1.24767	−0.623835	−	0.781556i	$-0.714426\pi$
$127$	−14.0605	−1.24767	−0.623835	+	0.781556i	$0.714426\pi$
$128$	9.61075	0.849479
$129$	−6.38910	−0.562528
$130$	−8.35163	−0.732487
$131$	−7.90255	−0.690449	−0.345224	−	0.938520i	$-0.612197\pi$
$131$	−7.90255	−0.690449	−0.345224	+	0.938520i	$0.612197\pi$
$132$	4.75872	0.414193
$133$	−12.2289	−1.06038
$134$	−4.01538	−0.346876
$135$	−6.89737	−0.593631
$136$	0.808917	0.0693640
$137$	11.2138	0.958057	0.479029	−	0.877799i	$-0.340989\pi$
$137$	11.2138	0.958057	0.479029	+	0.877799i	$0.340989\pi$
$138$	6.29919	0.536223
$139$	−8.13599	−0.690086	−0.345043	−	0.938587i	$-0.612136\pi$
$139$	−8.13599	−0.690086	−0.345043	+	0.938587i	$0.612136\pi$
$140$	4.72992	0.399751
$141$	2.50350	0.210833
$142$	−10.5880	−0.888522
$143$	−13.8997	−1.16235
$144$	13.0994	1.09161
$145$	16.2440	1.34899
$146$	−17.6529	−1.46097
$147$	−2.30547	−0.190152
$148$	3.87486	0.318512
$149$	15.4639	1.26686	0.633428	−	0.773802i	$-0.281647\pi$
$149$	15.4639	1.26686	0.633428	+	0.773802i	$0.281647\pi$
$150$	−0.590719	−0.0482320
$151$	−13.8861	−1.13003	−0.565015	−	0.825080i	$-0.691130\pi$
$151$	−13.8861	−1.13003	−0.565015	+	0.825080i	$0.691130\pi$
$152$	9.02908	0.732355
$153$	1.68333	0.136089
$154$	20.0379	1.61470
$155$	0.985473	0.0791551
$156$	−1.63385	−0.130813
$157$	15.0454	1.20075	0.600377	−	0.799717i	$-0.295017\pi$
$157$	15.0454	1.20075	0.600377	+	0.799717i	$0.295017\pi$
$158$	2.94308	0.234139
$159$	−4.67907	−0.371074
$160$	−13.3873	−1.05836
$161$	10.4204	0.821240
$162$	11.0815	0.870644
$163$	−14.6205	−1.14517	−0.572584	−	0.819846i	$-0.694059\pi$
$163$	−14.6205	−1.14517	−0.572584	+	0.819846i	$0.694059\pi$
$164$	−11.2243	−0.876471
$165$	7.74548	0.602985
$166$	3.13643	0.243434
$167$	4.21559	0.326212	0.163106	−	0.986609i	$-0.447849\pi$
$167$	4.21559	0.326212	0.163106	+	0.986609i	$0.447849\pi$
$168$	−1.28471	−0.0991174
$169$	−8.22768	−0.632898
$170$	−2.41388	−0.185136
$171$	18.7892	1.43685
$172$	−14.3069	−1.09089
$173$	19.3646	1.47226	0.736132	−	0.676838i	$-0.236650\pi$
$173$	19.3646	1.47226	0.736132	+	0.676838i	$0.236650\pi$
$174$	8.08904	0.613228
$175$	−0.977191	−0.0738687
$176$	−31.2631	−2.35654
$177$	4.16135	0.312786
$178$	−20.1613	−1.51116
$179$	2.65395	0.198366	0.0991829	−	0.995069i	$-0.468377\pi$
$179$	2.65395	0.198366	0.0991829	+	0.995069i	$0.468377\pi$
$180$	−7.26734	−0.541675
$181$	19.7622	1.46891	0.734457	−	0.678656i	$-0.237437\pi$
$181$	19.7622	1.46891	0.734457	+	0.678656i	$0.237437\pi$
$182$	−6.87978	−0.509963
$183$	3.43016	0.253565
$184$	−7.69376	−0.567192
$185$	6.30688	0.463691
$186$	0.490737	0.0359826
$187$	−4.01745	−0.293785
$188$	5.60603	0.408862
$189$	−5.68181	−0.413291
$190$	−26.9436	−1.95469
$191$	11.4647	0.829557	0.414779	−	0.909922i	$-0.363859\pi$
$191$	11.4647	0.829557	0.414779	+	0.909922i	$0.363859\pi$
$192$	−0.987232	−0.0712473
$193$	20.2977	1.46106	0.730531	−	0.682880i	$-0.239273\pi$
$193$	20.2977	1.46106	0.730531	+	0.682880i	$0.239273\pi$
$194$	14.4756	1.03929
$195$	−2.65933	−0.190438
$196$	−5.16258	−0.368756
$197$	−2.51938	−0.179498	−0.0897490	−	0.995964i	$-0.528606\pi$
$197$	−2.51938	−0.179498	−0.0897490	+	0.995964i	$0.528606\pi$
$198$	−30.7874	−2.18796
$199$	2.93963	0.208385	0.104193	−	0.994557i	$-0.466774\pi$
$199$	2.93963	0.208385	0.104193	+	0.994557i	$0.466774\pi$
$200$	0.721498	0.0510176
$201$	−1.27858	−0.0901839
$202$	−9.76002	−0.686713
$203$	13.3812	0.939176
$204$	−0.472234	−0.0330630
$205$	−18.2691	−1.27597
$206$	9.77657	0.681166
$207$	−16.0105	−1.11281
$208$	10.7338	0.744257
$209$	−44.8425	−3.10182
$210$	3.83368	0.264549
$211$	13.6787	0.941679	0.470840	−	0.882219i	$-0.343951\pi$
$211$	13.6787	0.941679	0.470840	+	0.882219i	$0.343951\pi$
$212$	−10.4777	−0.719613
$213$	−3.37142	−0.231006
$214$	28.8127	1.96960
$215$	−23.2866	−1.58813
$216$	4.19510	0.285440
$217$	0.811797	0.0551084
$218$	−1.58191	−0.107141
$219$	−5.62105	−0.379835
$220$	17.3443	1.16935
$221$	1.37935	0.0927849
$222$	3.14065	0.210786
$223$	2.06965	0.138594	0.0692969	−	0.997596i	$-0.477924\pi$
$223$	2.06965	0.138594	0.0692969	+	0.997596i	$0.477924\pi$
$224$	−11.0279	−0.736835
$225$	1.50142	0.100094
$226$	22.9833	1.52882
$227$	−16.1707	−1.07328	−0.536642	−	0.843810i	$-0.680307\pi$
$227$	−16.1707	−1.07328	−0.536642	+	0.843810i	$0.680307\pi$
$228$	−5.27105	−0.349084
$229$	24.1008	1.59262	0.796312	−	0.604886i	$-0.206781\pi$
$229$	24.1008	1.59262	0.796312	+	0.604886i	$0.206781\pi$
$230$	22.9589	1.51386
$231$	6.38045	0.419803
$232$	−9.87986	−0.648645
$233$	−5.26985	−0.345240	−0.172620	−	0.984989i	$-0.555223\pi$
$233$	−5.26985	−0.345240	−0.172620	+	0.984989i	$0.555223\pi$
$234$	10.5705	0.691016
$235$	9.12460	0.595223
$236$	9.31841	0.606577
$237$	0.937136	0.0608735
$238$	−1.98847	−0.128893
$239$	5.69129	0.368139	0.184069	−	0.982913i	$-0.441073\pi$
$239$	5.69129	0.368139	0.184069	+	0.982913i	$0.441073\pi$
$240$	−5.98131	−0.386092
$241$	23.7241	1.52820	0.764100	−	0.645097i	$-0.223183\pi$
$241$	23.7241	1.52820	0.764100	+	0.645097i	$0.223183\pi$
$242$	53.5127	3.43992
$243$	13.3521	0.856539
$244$	7.68108	0.491731
$245$	−8.40282	−0.536836
$246$	−9.09751	−0.580036
$247$	15.3962	0.979636
$248$	−0.599381	−0.0380607
$249$	0.998701	0.0632901
$250$	−21.2681	−1.34511
$251$	24.6823	1.55793	0.778966	−	0.627066i	$-0.215744\pi$
$251$	24.6823	1.55793	0.778966	+	0.627066i	$0.215744\pi$
$252$	−5.98657	−0.377118
$253$	38.2107	2.40229
$254$	−25.5195	−1.60123
$255$	−0.768627	−0.0481333
$256$	20.8597	1.30373
$257$	−12.5279	−0.781466	−0.390733	−	0.920504i	$-0.627778\pi$
$257$	−12.5279	−0.781466	−0.390733	+	0.920504i	$0.627778\pi$
$258$	−11.5960	−0.721938
$259$	5.19538	0.322825
$260$	−5.95496	−0.369311
$261$	−20.5597	−1.27261
$262$	−14.3429	−0.886108
$263$	−27.6584	−1.70549	−0.852745	−	0.522327i	$-0.825064\pi$
$263$	−27.6584	−1.70549	−0.852745	+	0.522327i	$0.825064\pi$
$264$	−4.71093	−0.289938
$265$	−17.0540	−1.04762
$266$	−22.1951	−1.36087
$267$	−6.41977	−0.392883
$268$	−2.86309	−0.174891
$269$	−1.14164	−0.0696069	−0.0348034	−	0.999394i	$-0.511081\pi$
$269$	−1.14164	−0.0696069	−0.0348034	+	0.999394i	$0.511081\pi$
$270$	−12.5186	−0.761855
$271$	−14.2437	−0.865241	−0.432621	−	0.901576i	$-0.642411\pi$
$271$	−14.2437	−0.865241	−0.432621	+	0.901576i	$0.642411\pi$
$272$	3.10241	0.188111
$273$	−2.19066	−0.132585
$274$	20.3527	1.22955
$275$	−3.58329	−0.216080
$276$	4.49151	0.270357
$277$	9.26397	0.556618	0.278309	−	0.960492i	$-0.410226\pi$
$277$	9.26397	0.556618	0.278309	+	0.960492i	$0.410226\pi$
$278$	−14.7666	−0.885643
$279$	−1.24729	−0.0746736
$280$	−4.68242	−0.279828
$281$	19.7177	1.17626	0.588128	−	0.808768i	$-0.299865\pi$
$281$	19.7177	1.17626	0.588128	+	0.808768i	$0.299865\pi$
$282$	4.54379	0.270579
$283$	−8.14971	−0.484450	−0.242225	−	0.970220i	$-0.577877\pi$
$283$	−8.14971	−0.484450	−0.242225	+	0.970220i	$0.577877\pi$
$284$	−7.54953	−0.447982
$285$	−8.57937	−0.508198
$286$	−25.2276	−1.49174
$287$	−15.0495	−0.888341
$288$	16.9440	0.998435
$289$	−16.6013	−0.976549
$290$	29.4824	1.73127
$291$	4.60931	0.270203
$292$	−12.5871	−0.736603
$293$	7.02797	0.410579	0.205289	−	0.978701i	$-0.434186\pi$
$293$	7.02797	0.410579	0.205289	+	0.978701i	$0.434186\pi$
$294$	−4.18436	−0.244037
$295$	15.1670	0.883058
$296$	−3.83595	−0.222960
$297$	−20.8348	−1.20896
$298$	28.0666	1.62586
$299$	−13.1192	−0.758705
$300$	−0.421200	−0.0243180
$301$	−19.1826	−1.10567
$302$	−25.2028	−1.45026
$303$	−3.10778	−0.178537
$304$	34.6289	1.98610
$305$	12.5020	0.715865
$306$	3.05520	0.174654
$307$	−9.82004	−0.560459	−0.280230	−	0.959933i	$-0.590411\pi$
$307$	−9.82004	−0.560459	−0.280230	+	0.959933i	$0.590411\pi$
$308$	14.2876	0.814111
$309$	3.11305	0.177095
$310$	1.78861	0.101586
$311$	2.70208	0.153221	0.0766105	−	0.997061i	$-0.475590\pi$
$311$	2.70208	0.153221	0.0766105	+	0.997061i	$0.475590\pi$
$312$	1.61745	0.0915699
$313$	−10.9934	−0.621386	−0.310693	−	0.950510i	$-0.600561\pi$
$313$	−10.9934	−0.621386	−0.310693	+	0.950510i	$0.600561\pi$
$314$	27.3070	1.54102
$315$	−9.74398	−0.549011
$316$	2.09851	0.118050
$317$	23.7918	1.33628	0.668140	−	0.744036i	$-0.267091\pi$
$317$	23.7918	1.33628	0.668140	+	0.744036i	$0.267091\pi$
$318$	−8.49238	−0.476229
$319$	49.0679	2.74728
$320$	−3.59820	−0.201145
$321$	9.17454	0.512073
$322$	18.9127	1.05396
$323$	4.44997	0.247603
$324$	7.90143	0.438968
$325$	1.23028	0.0682438
$326$	−26.5359	−1.46969
$327$	−0.503713	−0.0278554
$328$	11.1116	0.613535
$329$	7.51652	0.414399
$330$	14.0578	0.773859
$331$	−11.6897	−0.642523	−0.321261	−	0.946991i	$-0.604107\pi$
$331$	−11.6897	−0.642523	−0.321261	+	0.946991i	$0.604107\pi$
$332$	2.23637	0.122737
$333$	−7.98251	−0.437439
$334$	7.65119	0.418654
$335$	−4.66008	−0.254607
$336$	−4.92719	−0.268800
$337$	1.78759	0.0973762	0.0486881	−	0.998814i	$-0.484496\pi$
$337$	1.78759	0.0973762	0.0486881	+	0.998814i	$0.484496\pi$
$338$	−14.9330	−0.812250
$339$	7.31832	0.397477
$340$	−1.72117	−0.0933434
$341$	2.97680	0.161203
$342$	34.1020	1.84402
$343$	−19.0680	−1.02958
$344$	14.1633	0.763633
$345$	7.31056	0.393587
$346$	35.1463	1.88948
$347$	11.9985	0.644116	0.322058	−	0.946720i	$-0.395625\pi$
$347$	11.9985	0.644116	0.322058	+	0.946720i	$0.395625\pi$
$348$	5.76772	0.309182
$349$	−14.2527	−0.762928	−0.381464	−	0.924384i	$-0.624580\pi$
$349$	−14.2527	−0.762928	−0.381464	+	0.924384i	$0.624580\pi$
$350$	−1.77358	−0.0948016
$351$	7.15339	0.381820
$352$	−40.4387	−2.15539
$353$	−27.6920	−1.47390	−0.736948	−	0.675950i	$-0.763734\pi$
$353$	−27.6920	−1.47390	−0.736948	+	0.675950i	$0.763734\pi$
$354$	7.55274	0.401424
$355$	−12.2879	−0.652175
$356$	−14.3756	−0.761907
$357$	−0.633167	−0.0335108
$358$	4.81686	0.254579
$359$	−23.2691	−1.22809	−0.614047	−	0.789270i	$-0.710459\pi$
$359$	−23.2691	−1.22809	−0.614047	+	0.789270i	$0.710459\pi$
$360$	7.19436	0.379176
$361$	30.6703	1.61423
$362$	35.8679	1.88517
$363$	17.0395	0.894341
$364$	−4.90548	−0.257117
$365$	−20.4872	−1.07235
$366$	6.22566	0.325420
$367$	28.3461	1.47965	0.739827	−	0.672797i	$-0.234907\pi$
$367$	28.3461	1.47965	0.739827	+	0.672797i	$0.234907\pi$
$368$	−29.5076	−1.53819
$369$	23.1229	1.20373
$370$	11.4468	0.595092
$371$	−14.0484	−0.729358
$372$	0.349910	0.0181420
$373$	17.8836	0.925980	0.462990	−	0.886363i	$-0.346777\pi$
$373$	17.8836	0.925980	0.462990	+	0.886363i	$0.346777\pi$
$374$	−7.29157	−0.377038
$375$	−6.77219	−0.349714
$376$	−5.54974	−0.286206
$377$	−16.8469	−0.867661
$378$	−10.3123	−0.530409
$379$	21.7991	1.11974	0.559872	−	0.828579i	$-0.310850\pi$
$379$	21.7991	1.11974	0.559872	+	0.828579i	$0.310850\pi$
$380$	−19.2116	−0.985533
$381$	−8.12591	−0.416303
$382$	20.8081	1.06464
$383$	−35.4957	−1.81375	−0.906874	−	0.421402i	$-0.861538\pi$
$383$	−35.4957	−1.81375	−0.906874	+	0.421402i	$0.861538\pi$
$384$	5.55428	0.283441
$385$	23.2550	1.18519
$386$	36.8398	1.87510
$387$	29.4734	1.49822
$388$	10.3215	0.523996
$389$	−12.2599	−0.621602	−0.310801	−	0.950475i	$-0.600597\pi$
$389$	−12.2599	−0.621602	−0.310801	+	0.950475i	$0.600597\pi$
$390$	−4.82661	−0.244405
$391$	−3.79186	−0.191763
$392$	5.11074	0.258131
$393$	−4.56707	−0.230378
$394$	−4.57260	−0.230364
$395$	3.41561	0.171858
$396$	−21.9523	−1.10315
$397$	−36.3867	−1.82620	−0.913098	−	0.407740i	$-0.866317\pi$
$397$	−36.3867	−1.82620	−0.913098	+	0.407740i	$0.866317\pi$
$398$	5.33536	0.267437
$399$	−7.06737	−0.353811
$400$	2.76713	0.138357
$401$	30.2605	1.51114	0.755568	−	0.655070i	$-0.227361\pi$
$401$	30.2605	1.51114	0.755568	+	0.655070i	$0.227361\pi$
$402$	−2.32059	−0.115740
$403$	−1.02205	−0.0509120
$404$	−6.95918	−0.346232
$405$	12.8607	0.639053
$406$	24.2865	1.20532
$407$	19.0511	0.944328
$408$	0.467492	0.0231443
$409$	−28.7574	−1.42196	−0.710982	−	0.703210i	$-0.751749\pi$
$409$	−28.7574	−1.42196	−0.710982	+	0.703210i	$0.751749\pi$
$410$	−33.1580	−1.63756
$411$	6.48070	0.319670
$412$	6.97099	0.343436
$413$	12.4940	0.614791
$414$	−29.0586	−1.42815
$415$	3.64000	0.178681
$416$	13.8842	0.680728
$417$	−4.70198	−0.230257
$418$	−81.3880	−3.98082
$419$	−20.0041	−0.977264	−0.488632	−	0.872490i	$-0.662504\pi$
$419$	−20.0041	−0.977264	−0.488632	+	0.872490i	$0.662504\pi$
$420$	2.73353	0.133383
$421$	−21.9536	−1.06995	−0.534976	−	0.844867i	$-0.679679\pi$
$421$	−21.9536	−1.06995	−0.534976	+	0.844867i	$0.679679\pi$
$422$	24.8264	1.20853
$423$	−11.5488	−0.561524
$424$	10.3725	0.503733
$425$	0.355590	0.0172486
$426$	−6.11904	−0.296468
$427$	10.2987	0.498390
$428$	20.5443	0.993048
$429$	−8.03298	−0.387836
$430$	−42.2645	−2.03817
$431$	−25.5771	−1.23200	−0.616002	−	0.787745i	$-0.711249\pi$
$431$	−25.5771	−1.23200	−0.616002	+	0.787745i	$0.711249\pi$
$432$	16.0893	0.774097
$433$	−2.27003	−0.109091	−0.0545454	−	0.998511i	$-0.517371\pi$
$433$	−2.27003	−0.109091	−0.0545454	+	0.998511i	$0.517371\pi$
$434$	1.47339	0.0707250
$435$	9.38778	0.450109
$436$	−1.12795	−0.0540191
$437$	−42.3246	−2.02466
$438$	−10.2021	−0.487473
$439$	−16.9124	−0.807187	−0.403593	−	0.914938i	$-0.632239\pi$
$439$	−16.9124	−0.807187	−0.403593	+	0.914938i	$0.632239\pi$
$440$	−17.1701	−0.818552
$441$	10.6353	0.506442
$442$	2.50348	0.119078
$443$	34.5988	1.64384	0.821920	−	0.569603i	$-0.192903\pi$
$443$	34.5988	1.64384	0.821920	+	0.569603i	$0.192903\pi$
$444$	2.23938	0.106276
$445$	−23.3983	−1.10919
$446$	3.75635	0.177869
$447$	8.93698	0.422704
$448$	−2.96407	−0.140039
$449$	13.0996	0.618208	0.309104	−	0.951028i	$-0.399971\pi$
$449$	13.0996	0.618208	0.309104	+	0.951028i	$0.399971\pi$
$450$	2.72503	0.128459
$451$	−55.1853	−2.59857
$452$	16.3877	0.770815
$453$	−8.02508	−0.377051
$454$	−29.3493	−1.37743
$455$	−7.98436	−0.374313
$456$	5.21812	0.244361
$457$	8.01557	0.374952	0.187476	−	0.982269i	$-0.439969\pi$
$457$	8.01557	0.374952	0.187476	+	0.982269i	$0.439969\pi$
$458$	43.7423	2.04394
$459$	2.06755	0.0965050
$460$	16.3704	0.763272
$461$	−15.1868	−0.707320	−0.353660	−	0.935374i	$-0.615063\pi$
$461$	−15.1868	−0.707320	−0.353660	+	0.935374i	$0.615063\pi$
$462$	11.5803	0.538766
$463$	34.6450	1.61009	0.805046	−	0.593212i	$-0.202141\pi$
$463$	34.6450	1.61009	0.805046	+	0.593212i	$0.202141\pi$
$464$	−37.8919	−1.75909
$465$	0.569528	0.0264112
$466$	−9.56464	−0.443074
$467$	−37.1749	−1.72025	−0.860125	−	0.510083i	$-0.829615\pi$
$467$	−37.1749	−1.72025	−0.860125	+	0.510083i	$0.829615\pi$
$468$	7.53709	0.348402
$469$	−3.83880	−0.177259
$470$	16.5609	0.763898
$471$	8.69510	0.400649
$472$	−9.22483	−0.424607
$473$	−70.3413	−3.23430
$474$	1.70088	0.0781239
$475$	3.96907	0.182113
$476$	−1.41784	−0.0649864
$477$	21.5849	0.988304
$478$	10.3295	0.472462
$479$	28.4871	1.30161	0.650805	−	0.759245i	$-0.274431\pi$
$479$	28.4871	1.30161	0.650805	+	0.759245i	$0.274431\pi$
$480$	−7.73681	−0.353136
$481$	−6.54099	−0.298243
$482$	43.0585	1.96126
$483$	6.02218	0.274019
$484$	38.1561	1.73437
$485$	16.7997	0.762836
$486$	24.2337	1.09927
$487$	14.9167	0.675941	0.337971	−	0.941157i	$-0.390260\pi$
$487$	14.9167	0.675941	0.337971	+	0.941157i	$0.390260\pi$
$488$	−7.60395	−0.344215
$489$	−8.44954	−0.382102
$490$	−15.2509	−0.688965
$491$	−33.6713	−1.51956	−0.759782	−	0.650178i	$-0.774694\pi$
$491$	−33.6713	−1.51956	−0.759782	+	0.650178i	$0.774694\pi$
$492$	−6.48679	−0.292447
$493$	−4.86928	−0.219301
$494$	27.9437	1.25725
$495$	−35.7305	−1.60597
$496$	−2.29878	−0.103218
$497$	−10.1223	−0.454049
$498$	1.81262	0.0812253
$499$	−21.4249	−0.959112	−0.479556	−	0.877511i	$-0.659202\pi$
$499$	−21.4249	−0.959112	−0.479556	+	0.877511i	$0.659202\pi$
$500$	−15.1648	−0.678191
$501$	2.43629	0.108845
$502$	44.7977	1.99942
$503$	1.00000	0.0445878
$503$	1.00000	0.0445878
$504$	5.92645	0.263985
$505$	−11.3270	−0.504047
$506$	69.3515	3.08305
$507$	−4.75497	−0.211176
$508$	−18.1962	−0.807324
$509$	−20.3267	−0.900965	−0.450482	−	0.892785i	$-0.648748\pi$
$509$	−20.3267	−0.900965	−0.450482	+	0.892785i	$0.648748\pi$
$510$	−1.39504	−0.0617733
$511$	−16.8766	−0.746578
$512$	18.6384	0.823708
$513$	23.0779	1.01891
$514$	−22.7377	−1.00292
$515$	11.3463	0.499976
$516$	−8.26832	−0.363993
$517$	27.5625	1.21220
$518$	9.42948	0.414308
$519$	11.1913	0.491242
$520$	5.89517	0.258520
$521$	−18.4511	−0.808359	−0.404179	−	0.914680i	$-0.632443\pi$
$521$	−18.4511	−0.808359	−0.404179	+	0.914680i	$0.632443\pi$
$522$	−37.3153	−1.63325
$523$	−9.91110	−0.433382	−0.216691	−	0.976240i	$-0.569526\pi$
$523$	−9.91110	−0.433382	−0.216691	+	0.976240i	$0.569526\pi$
$524$	−10.2269	−0.446765
$525$	−0.564742	−0.0246473
$526$	−50.1993	−2.18879
$527$	−0.295404	−0.0128680
$528$	−18.0677	−0.786294
$529$	13.0652	0.568050
$530$	−30.9525	−1.34449
$531$	−19.1966	−0.833062
$532$	−15.8258	−0.686135
$533$	18.9473	0.820697
$534$	−11.6517	−0.504219
$535$	33.4388	1.44568
$536$	2.83434	0.122425
$537$	1.53378	0.0661876
$538$	−2.07204	−0.0893321
$539$	−25.3823	−1.09329
$540$	−8.92610	−0.384118
$541$	−7.37029	−0.316874	−0.158437	−	0.987369i	$-0.550645\pi$
$541$	−7.37029	−0.316874	−0.158437	+	0.987369i	$0.550645\pi$
$542$	−25.8519	−1.11043
$543$	11.4210	0.490124
$544$	4.01295	0.172054
$545$	−1.83590	−0.0786413
$546$	−3.97598	−0.170156
$547$	16.8670	0.721179	0.360590	−	0.932725i	$-0.382575\pi$
$547$	16.8670	0.721179	0.360590	+	0.932725i	$0.382575\pi$
$548$	14.5121	0.619925
$549$	−15.8236	−0.675335
$550$	−6.50358	−0.277313
$551$	−54.3506	−2.31541
$552$	−4.44641	−0.189252
$553$	2.81366	0.119649
$554$	16.8139	0.714353
$555$	3.64490	0.154717
$556$	−10.5290	−0.446531
$557$	−21.6892	−0.919002	−0.459501	−	0.888177i	$-0.651972\pi$
$557$	−21.6892	−0.919002	−0.459501	+	0.888177i	$0.651972\pi$
$558$	−2.26381	−0.0958346
$559$	24.1509	1.02148
$560$	−17.9583	−0.758877
$561$	−2.32178	−0.0980256
$562$	35.7870	1.50958
$563$	22.2548	0.937929	0.468964	−	0.883217i	$-0.344627\pi$
$563$	22.2548	0.937929	0.468964	+	0.883217i	$0.344627\pi$
$564$	3.23986	0.136423
$565$	26.6733	1.12216
$566$	−14.7915	−0.621734
$567$	10.5942	0.444913
$568$	7.47372	0.313591
$569$	11.2599	0.472039	0.236020	−	0.971748i	$-0.424157\pi$
$569$	11.2599	0.472039	0.236020	+	0.971748i	$0.424157\pi$
$570$	−15.5713	−0.652211
$571$	−31.1893	−1.30523	−0.652616	−	0.757689i	$-0.726328\pi$
$571$	−31.1893	−1.30523	−0.652616	+	0.757689i	$0.726328\pi$
$572$	−17.9881	−0.752119
$573$	6.62572	0.276794
$574$	−27.3144	−1.14008
$575$	−3.38208	−0.141043
$576$	4.55417	0.189757
$577$	2.51403	0.104660	0.0523302	−	0.998630i	$-0.483335\pi$
$577$	2.51403	0.104660	0.0523302	+	0.998630i	$0.483335\pi$
$578$	−30.1310	−1.25328
$579$	11.7305	0.487504
$580$	21.0218	0.872884
$581$	2.99850	0.124399
$582$	8.36578	0.346773
$583$	−51.5146	−2.13352
$584$	12.4607	0.515626
$585$	12.2677	0.507206
$586$	12.7556	0.526929
$587$	−16.1608	−0.667026	−0.333513	−	0.942746i	$-0.608234\pi$
$587$	−16.1608	−0.667026	−0.333513	+	0.942746i	$0.608234\pi$
$588$	−2.98358	−0.123041
$589$	−3.29729	−0.135862
$590$	27.5277	1.13330
$591$	−1.45601	−0.0598921
$592$	−14.7119	−0.604655
$593$	−11.4918	−0.471912	−0.235956	−	0.971764i	$-0.575822\pi$
$593$	−11.4918	−0.471912	−0.235956	+	0.971764i	$0.575822\pi$
$594$	−37.8146	−1.55155
$595$	−2.30773	−0.0946076
$596$	20.0124	0.819738
$597$	1.69888	0.0695307
$598$	−23.8111	−0.973707
$599$	−24.5532	−1.00322	−0.501608	−	0.865095i	$-0.667258\pi$
$599$	−24.5532	−1.00322	−0.501608	+	0.865095i	$0.667258\pi$
$600$	0.416971	0.0170228
$601$	−46.5706	−1.89965	−0.949827	−	0.312777i	$-0.898741\pi$
$601$	−46.5706	−1.89965	−0.949827	+	0.312777i	$0.898741\pi$
$602$	−34.8160	−1.41899
$603$	5.89817	0.240192
$604$	−17.9704	−0.731204
$605$	62.1044	2.52490
$606$	−5.64055	−0.229132
$607$	−27.3430	−1.10982	−0.554909	−	0.831911i	$-0.687247\pi$
$607$	−27.3430	−1.10982	−0.554909	+	0.831911i	$0.687247\pi$
$608$	44.7923	1.81657
$609$	7.73331	0.313370
$610$	22.6909	0.918727
$611$	−9.46329	−0.382844
$612$	2.17845	0.0880586
$613$	37.3092	1.50691	0.753453	−	0.657502i	$-0.228387\pi$
$613$	37.3092	1.50691	0.753453	+	0.657502i	$0.228387\pi$
$614$	−17.8231	−0.719282
$615$	−10.5582	−0.425746
$616$	−14.1441	−0.569882
$617$	36.4668	1.46810	0.734049	−	0.679096i	$-0.237628\pi$
$617$	36.4668	1.46810	0.734049	+	0.679096i	$0.237628\pi$
$618$	5.65011	0.227281
$619$	43.5639	1.75098	0.875491	−	0.483234i	$-0.160538\pi$
$619$	43.5639	1.75098	0.875491	+	0.483234i	$0.160538\pi$
$620$	1.27533	0.0512185
$621$	−19.6649	−0.789124
$622$	4.90421	0.196641
$623$	−19.2747	−0.772225
$624$	6.20333	0.248332
$625$	−21.8670	−0.874679
$626$	−19.9528	−0.797474
$627$	−25.9156	−1.03497
$628$	19.4707	0.776967
$629$	−1.89055	−0.0753810
$630$	−17.6851	−0.704590
$631$	42.4843	1.69127	0.845637	−	0.533759i	$-0.179221\pi$
$631$	42.4843	1.69127	0.845637	+	0.533759i	$0.179221\pi$
$632$	−2.07743	−0.0826358
$633$	7.90523	0.314205
$634$	43.1815	1.71496
$635$	−29.6168	−1.17531
$636$	−6.05532	−0.240109
$637$	8.71472	0.345290
$638$	89.0570	3.52580
$639$	15.5526	0.615251
$640$	20.2439	0.800210
$641$	−7.90513	−0.312234	−0.156117	−	0.987739i	$-0.549898\pi$
$641$	−7.90513	−0.312234	−0.156117	+	0.987739i	$0.549898\pi$
$642$	16.6516	0.657185
$643$	−36.7190	−1.44806	−0.724028	−	0.689771i	$-0.757711\pi$
$643$	−36.7190	−1.44806	−0.724028	+	0.689771i	$0.757711\pi$
$644$	13.4853	0.531396
$645$	−13.4579	−0.529902
$646$	8.07659	0.317769
$647$	−37.2473	−1.46434	−0.732172	−	0.681120i	$-0.761493\pi$
$647$	−37.2473	−1.46434	−0.732172	+	0.681120i	$0.761493\pi$
$648$	−7.82209	−0.307281
$649$	45.8147	1.79839
$650$	2.23293	0.0875828
$651$	0.469157	0.0183877
$652$	−18.9209	−0.740998
$653$	−8.25286	−0.322959	−0.161480	−	0.986876i	$-0.551627\pi$
$653$	−8.25286	−0.322959	−0.161480	+	0.986876i	$0.551627\pi$
$654$	−0.914226	−0.0357490
$655$	−16.6458	−0.650403
$656$	42.6159	1.66387
$657$	25.9303	1.01164
$658$	13.6423	0.531831
$659$	−1.05840	−0.0412295	−0.0206147	−	0.999787i	$-0.506562\pi$
$659$	−1.05840	−0.0412295	−0.0206147	+	0.999787i	$0.506562\pi$
$660$	10.0237	0.390171
$661$	17.5566	0.682872	0.341436	−	0.939905i	$-0.389087\pi$
$661$	17.5566	0.682872	0.341436	+	0.939905i	$0.389087\pi$
$662$	−21.2165	−0.824601
$663$	0.797157	0.0309590
$664$	−2.21391	−0.0859163
$665$	−25.7587	−0.998880
$666$	−14.4880	−0.561400
$667$	46.3127	1.79323
$668$	5.45552	0.211081
$669$	1.19610	0.0462438
$670$	−8.45792	−0.326758
$671$	37.7647	1.45789
$672$	−6.37331	−0.245856
$673$	8.97715	0.346044	0.173022	−	0.984918i	$-0.444647\pi$
$673$	8.97715	0.346044	0.173022	+	0.984918i	$0.444647\pi$
$674$	3.24443	0.124971
$675$	1.84411	0.0709799
$676$	−10.6477	−0.409527
$677$	1.53938	0.0591633	0.0295817	−	0.999562i	$-0.490582\pi$
$677$	1.53938	0.0591633	0.0295817	+	0.999562i	$0.490582\pi$
$678$	13.2826	0.510114
$679$	13.8390	0.531092
$680$	1.70388	0.0653410
$681$	−9.34540	−0.358117
$682$	5.40282	0.206885
$683$	−23.4907	−0.898848	−0.449424	−	0.893319i	$-0.648371\pi$
$683$	−23.4907	−0.898848	−0.449424	+	0.893319i	$0.648371\pi$
$684$	24.3157	0.929735
$685$	23.6204	0.902491
$686$	−34.6080	−1.32134
$687$	13.9284	0.531402
$688$	54.3199	2.07093
$689$	17.6870	0.673820
$690$	13.2685	0.505122
$691$	−8.94518	−0.340291	−0.170145	−	0.985419i	$-0.554424\pi$
$691$	−8.94518	−0.340291	−0.170145	+	0.985419i	$0.554424\pi$
$692$	25.0603	0.952651
$693$	−29.4335	−1.11809
$694$	21.7770	0.826645
$695$	−17.1375	−0.650062
$696$	−5.70981	−0.216430
$697$	5.47634	0.207431
$698$	−25.8682	−0.979126
$699$	−3.04557	−0.115194
$700$	−1.26461	−0.0477978
$701$	2.19846	0.0830347	0.0415174	−	0.999138i	$-0.486781\pi$
$701$	2.19846	0.0830347	0.0415174	+	0.999138i	$0.486781\pi$
$702$	12.9832	0.490020
$703$	−21.1022	−0.795883
$704$	−10.8690	−0.409642
$705$	5.27332	0.198605
$706$	−50.2602	−1.89157
$707$	−9.33081	−0.350921
$708$	5.38533	0.202393
$709$	−33.8056	−1.26960	−0.634799	−	0.772677i	$-0.718917\pi$
$709$	−33.8056	−1.26960	−0.634799	+	0.772677i	$0.718917\pi$
$710$	−22.3023	−0.836989
$711$	−4.32308	−0.162128
$712$	14.2313	0.533339
$713$	2.80965	0.105222
$714$	−1.14918	−0.0430071
$715$	−29.2781	−1.09494
$716$	3.43456	0.128356
$717$	3.28913	0.122835
$718$	−42.2327	−1.57611
$719$	15.9502	0.594843	0.297422	−	0.954746i	$-0.403873\pi$
$719$	15.9502	0.594843	0.297422	+	0.954746i	$0.403873\pi$
$720$	27.5922	1.02830
$721$	9.34664	0.348087
$722$	55.6658	2.07167
$723$	13.7107	0.509906
$724$	25.5749	0.950483
$725$	−4.34306	−0.161297
$726$	30.9262	1.14778
$727$	8.83593	0.327707	0.163853	−	0.986485i	$-0.447608\pi$
$727$	8.83593	0.327707	0.163853	+	0.986485i	$0.447608\pi$
$728$	4.85622	0.179984
$729$	−10.6003	−0.392603
$730$	−37.1838	−1.37623
$731$	6.98036	0.258178
$732$	4.43908	0.164073
$733$	1.49567	0.0552437	0.0276219	−	0.999618i	$-0.491207\pi$
$733$	1.49567	0.0552437	0.0276219	+	0.999618i	$0.491207\pi$
$734$	51.4474	1.89896
$735$	−4.85619	−0.179123
$736$	−38.1680	−1.40689
$737$	−14.0766	−0.518519
$738$	41.9675	1.54484
$739$	−2.77630	−0.102128	−0.0510639	−	0.998695i	$-0.516261\pi$
$739$	−2.77630	−0.102128	−0.0510639	+	0.998695i	$0.516261\pi$
$740$	8.16193	0.300038
$741$	8.89782	0.326870
$742$	−25.4975	−0.936044
$743$	44.6921	1.63959	0.819797	−	0.572654i	$-0.194086\pi$
$743$	44.6921	1.63959	0.819797	+	0.572654i	$0.194086\pi$
$744$	−0.346397	−0.0126995
$745$	32.5729	1.19338
$746$	32.4584	1.18838
$747$	−4.60708	−0.168564
$748$	−5.19910	−0.190098
$749$	27.5457	1.00650
$750$	−12.2913	−0.448817
$751$	−0.221622	−0.00808710	−0.00404355	−	0.999992i	$-0.501287\pi$
$751$	−0.221622	−0.00808710	−0.00404355	+	0.999992i	$0.501287\pi$
$752$	−21.2847	−0.776173
$753$	14.2645	0.519826
$754$	−30.5767	−1.11354
$755$	−29.2493	−1.06449
$756$	−7.35300	−0.267426
$757$	−4.76369	−0.173139	−0.0865696	−	0.996246i	$-0.527590\pi$
$757$	−4.76369	−0.173139	−0.0865696	+	0.996246i	$0.527590\pi$
$758$	39.5648	1.43706
$759$	22.0829	0.801558
$760$	19.0187	0.689879
$761$	12.3929	0.449243	0.224621	−	0.974446i	$-0.427885\pi$
$761$	12.3929	0.449243	0.224621	+	0.974446i	$0.427885\pi$
$762$	−14.7483	−0.534275
$763$	−1.51235	−0.0547507
$764$	14.8368	0.536777
$765$	3.54573	0.128196
$766$	−64.4239	−2.32773
$767$	−15.7300	−0.567977
$768$	12.0553	0.435010
$769$	49.4167	1.78201	0.891005	−	0.453993i	$-0.150001\pi$
$769$	49.4167	1.78201	0.891005	+	0.453993i	$0.150001\pi$
$770$	42.2073	1.52105
$771$	−7.24014	−0.260747
$772$	26.2679	0.945402
$773$	4.87037	0.175175	0.0875876	−	0.996157i	$-0.472084\pi$
$773$	4.87037	0.175175	0.0875876	+	0.996157i	$0.472084\pi$
$774$	53.4934	1.92278
$775$	−0.263480	−0.00946450
$776$	−10.2179	−0.366800
$777$	3.00253	0.107715
$778$	−22.2514	−0.797752
$779$	61.1266	2.19009
$780$	−3.44151	−0.123226
$781$	−37.1179	−1.32818
$782$	−6.88213	−0.246105
$783$	−25.2524	−0.902449
$784$	19.6010	0.700036
$785$	31.6913	1.13111
$786$	−8.28911	−0.295663
$787$	15.7824	0.562582	0.281291	−	0.959622i	$-0.409237\pi$
$787$	15.7824	0.562582	0.281291	+	0.959622i	$0.409237\pi$
$788$	−3.26040	−0.116147
$789$	−15.9844	−0.569061
$790$	6.19924	0.220559
$791$	21.9725	0.781253
$792$	21.7319	0.772209
$793$	−12.9661	−0.460440
$794$	−66.0409	−2.34370
$795$	−9.85588	−0.349552
$796$	3.80427	0.134839
$797$	19.4658	0.689515	0.344757	−	0.938692i	$-0.387961\pi$
$797$	19.4658	0.689515	0.344757	+	0.938692i	$0.387961\pi$
$798$	−12.8271	−0.454074
$799$	−2.73518	−0.0967638
$800$	3.57928	0.126547
$801$	29.6149	1.04639
$802$	54.9220	1.93936
$803$	−61.8854	−2.18389
$804$	−1.65465	−0.0583549
$805$	21.9492	0.773609
$806$	−1.85500	−0.0653395
$807$	−0.659780	−0.0232253
$808$	6.88930	0.242365
$809$	0.500555	0.0175986	0.00879929	−	0.999961i	$-0.497199\pi$
$809$	0.500555	0.0175986	0.00879929	+	0.999961i	$0.497199\pi$
$810$	23.3418	0.820148
$811$	17.1329	0.601618	0.300809	−	0.953684i	$-0.402743\pi$
$811$	17.1329	0.601618	0.300809	+	0.953684i	$0.402743\pi$
$812$	17.3170	0.607708
$813$	−8.23175	−0.288700
$814$	34.5772	1.21193
$815$	−30.7963	−1.07875
$816$	1.79295	0.0627659
$817$	77.9144	2.72588
$818$	−52.1940	−1.82492
$819$	10.1057	0.353120
$820$	−23.6426	−0.825637
$821$	2.73557	0.0954722	0.0477361	−	0.998860i	$-0.484799\pi$
$821$	2.73557	0.0954722	0.0477361	+	0.998860i	$0.484799\pi$
$822$	11.7623	0.410258
$823$	−12.9005	−0.449683	−0.224841	−	0.974395i	$-0.572186\pi$
$823$	−12.9005	−0.449683	−0.224841	+	0.974395i	$0.572186\pi$
$824$	−6.90099	−0.240407
$825$	−2.07087	−0.0720983
$826$	22.6764	0.789011
$827$	0.345192	0.0120035	0.00600174	−	0.999982i	$-0.498090\pi$
$827$	0.345192	0.0120035	0.00600174	+	0.999982i	$0.498090\pi$
$828$	−20.7197	−0.720058
$829$	−38.8024	−1.34766	−0.673832	−	0.738885i	$-0.735353\pi$
$829$	−38.8024	−1.34766	−0.673832	+	0.738885i	$0.735353\pi$
$830$	6.60650	0.229315
$831$	5.35387	0.185724
$832$	3.73176	0.129375
$833$	2.51882	0.0872720
$834$	−8.53397	−0.295507
$835$	8.87963	0.307292
$836$	−58.0321	−2.00708
$837$	−1.53199	−0.0529533
$838$	−36.3069	−1.25420
$839$	−6.45512	−0.222855	−0.111428	−	0.993773i	$-0.535542\pi$
$839$	−6.45512	−0.222855	−0.111428	+	0.993773i	$0.535542\pi$
$840$	−2.70608	−0.0933687
$841$	30.4719	1.05076
$842$	−39.8452	−1.37316
$843$	11.3953	0.392475
$844$	17.7020	0.609328
$845$	−17.3306	−0.596191
$846$	−20.9608	−0.720649
$847$	51.1594	1.75786
$848$	39.7813	1.36609
$849$	−4.70991	−0.161644
$850$	0.645386	0.0221366
$851$	17.9814	0.616393
$852$	−4.36305	−0.149476
$853$	2.58663	0.0885647	0.0442823	−	0.999019i	$-0.485900\pi$
$853$	2.58663	0.0885647	0.0442823	+	0.999019i	$0.485900\pi$
$854$	18.6919	0.639624
$855$	39.5773	1.35351
$856$	−20.3380	−0.695140
$857$	25.1394	0.858745	0.429373	−	0.903127i	$-0.358735\pi$
$857$	25.1394	0.858745	0.429373	+	0.903127i	$0.358735\pi$
$858$	−14.5797	−0.497741
$859$	−49.8581	−1.70113	−0.850567	−	0.525866i	$-0.823741\pi$
$859$	−49.8581	−1.70113	−0.850567	+	0.525866i	$0.823741\pi$
$860$	−30.1358	−1.02762
$861$	−8.69744	−0.296408
$862$	−46.4217	−1.58113
$863$	29.5886	1.00721	0.503605	−	0.863934i	$-0.332007\pi$
$863$	29.5886	1.00721	0.503605	+	0.863934i	$0.332007\pi$
$864$	20.8115	0.708020
$865$	40.7892	1.38687
$866$	−4.12005	−0.140005
$867$	−9.59430	−0.325839
$868$	1.05057	0.0356587
$869$	10.3175	0.349997
$870$	17.0386	0.577662
$871$	4.83305	0.163762
$872$	1.11663	0.0378137
$873$	−21.2631	−0.719646
$874$	−76.8180	−2.59841
$875$	−20.3328	−0.687375
$876$	−7.27437	−0.245778
$877$	−11.0963	−0.374697	−0.187348	−	0.982294i	$-0.559989\pi$
$877$	−11.0963	−0.374697	−0.187348	+	0.982294i	$0.559989\pi$
$878$	−30.6956	−1.03593
$879$	4.06163	0.136995
$880$	−65.8518	−2.21986
$881$	9.44078	0.318068	0.159034	−	0.987273i	$-0.449162\pi$
$881$	9.44078	0.318068	0.159034	+	0.987273i	$0.449162\pi$
$882$	19.3028	0.649958
$883$	−5.46071	−0.183767	−0.0918837	−	0.995770i	$-0.529289\pi$
$883$	−5.46071	−0.183767	−0.0918837	+	0.995770i	$0.529289\pi$
$884$	1.78506	0.0600379
$885$	8.76537	0.294645
$886$	62.7960	2.10967
$887$	38.6891	1.29905	0.649527	−	0.760338i	$-0.274967\pi$
$887$	38.6891	1.29905	0.649527	+	0.760338i	$0.274967\pi$
$888$	−2.21689	−0.0743939
$889$	−24.3972	−0.818257
$890$	−42.4674	−1.42351
$891$	38.8481	1.30146
$892$	2.67839	0.0896792
$893$	−30.5299	−1.02165
$894$	16.2204	0.542491
$895$	5.59023	0.186861
$896$	16.6762	0.557112
$897$	−7.58192	−0.253153
$898$	23.7754	0.793396
$899$	3.60798	0.120333
$900$	1.94303	0.0647676
$901$	5.11208	0.170308
$902$	−100.160	−3.33496
$903$	−11.0861	−0.368922
$904$	−16.2232	−0.539575
$905$	41.6267	1.38372
$906$	−14.5653	−0.483900
$907$	−7.01063	−0.232784	−0.116392	−	0.993203i	$-0.537133\pi$
$907$	−7.01063	−0.232784	−0.116392	+	0.993203i	$0.537133\pi$
$908$	−20.9269	−0.694485
$909$	14.3364	0.475510
$910$	−14.4914	−0.480386
$911$	−29.9470	−0.992187	−0.496093	−	0.868269i	$-0.665233\pi$
$911$	−29.9470	−0.992187	−0.496093	+	0.868269i	$0.665233\pi$
$912$	20.0128	0.662691
$913$	10.9953	0.363891
$914$	14.5480	0.481207
$915$	7.22522	0.238858
$916$	31.1896	1.03053
$917$	−13.7122	−0.452816
$918$	3.75255	0.123853
$919$	0.754207	0.0248790	0.0124395	−	0.999923i	$-0.496040\pi$
$919$	0.754207	0.0248790	0.0124395	+	0.999923i	$0.496040\pi$
$920$	−16.2060	−0.534295
$921$	−5.67523	−0.187005
$922$	−27.5637	−0.907761
$923$	12.7440	0.419475
$924$	8.25713	0.271640
$925$	−1.68624	−0.0554431
$926$	62.8799	2.06636
$927$	−14.3608	−0.471669
$928$	−49.0130	−1.60893
$929$	24.4277	0.801448	0.400724	−	0.916199i	$-0.368759\pi$
$929$	24.4277	0.801448	0.400724	+	0.916199i	$0.368759\pi$
$930$	1.03368	0.0338956
$931$	28.1149	0.921430
$932$	−6.81988	−0.223392
$933$	1.56160	0.0511244
$934$	−67.4715	−2.20774
$935$	−8.46227	−0.276746
$936$	−7.46140	−0.243884
$937$	44.1224	1.44141	0.720707	−	0.693239i	$-0.243817\pi$
$937$	44.1224	1.44141	0.720707	+	0.693239i	$0.243817\pi$
$938$	−6.96733	−0.227491
$939$	−6.35337	−0.207334
$940$	11.8084	0.385148
$941$	2.98022	0.0971523	0.0485762	−	0.998819i	$-0.484532\pi$
$941$	2.98022	0.0971523	0.0485762	+	0.998819i	$0.484532\pi$
$942$	15.7814	0.514185
$943$	−52.0866	−1.69617
$944$	−35.3797	−1.15151
$945$	−11.9680	−0.389320
$946$	−127.668	−4.15083
$947$	16.6297	0.540394	0.270197	−	0.962805i	$-0.412911\pi$
$947$	16.6297	0.540394	0.270197	+	0.962805i	$0.412911\pi$
$948$	1.21278	0.0393891
$949$	21.2477	0.689729
$950$	7.20376	0.233721
$951$	13.7498	0.445869
$952$	1.40360	0.0454909
$953$	−20.8876	−0.676615	−0.338307	−	0.941036i	$-0.609854\pi$
$953$	−20.8876	−0.676615	−0.338307	+	0.941036i	$0.609854\pi$
$954$	39.1760	1.26837
$955$	24.1490	0.781444
$956$	7.36526	0.238210
$957$	28.3575	0.916668
$958$	51.7034	1.67046
$959$	19.4577	0.628321
$960$	−2.07948	−0.0671151
$961$	−30.7811	−0.992939
$962$	−11.8717	−0.382760
$963$	−42.3229	−1.36383
$964$	30.7020	0.988845
$965$	42.7547	1.37632
$966$	10.9301	0.351670
$967$	8.51761	0.273908	0.136954	−	0.990577i	$-0.456269\pi$
$967$	8.51761	0.273908	0.136954	+	0.990577i	$0.456269\pi$
$968$	−37.7730	−1.21407
$969$	2.57174	0.0826163
$970$	30.4910	0.979008
$971$	−5.67027	−0.181968	−0.0909838	−	0.995852i	$-0.529001\pi$
$971$	−5.67027	−0.181968	−0.0909838	+	0.995852i	$0.529001\pi$
$972$	17.2794	0.554236
$973$	−14.1172	−0.452578
$974$	27.0735	0.867490
$975$	0.711010	0.0227705
$976$	−29.1631	−0.933489
$977$	16.0162	0.512404	0.256202	−	0.966623i	$-0.417529\pi$
$977$	16.0162	0.512404	0.256202	+	0.966623i	$0.417529\pi$
$978$	−15.3357	−0.490382
$979$	−70.6790	−2.25891
$980$	−10.8743	−0.347368
$981$	2.32366	0.0741889
$982$	−61.1125	−1.95018
$983$	56.1584	1.79117	0.895587	−	0.444886i	$-0.146756\pi$
$983$	56.1584	1.79117	0.895587	+	0.444886i	$0.146756\pi$
$984$	6.42166	0.204715
$985$	−5.30676	−0.169087
$986$	−8.83762	−0.281447
$987$	4.34397	0.138270
$988$	19.9247	0.633888
$989$	−66.3916	−2.11113
$990$	−64.8499	−2.06106
$991$	4.22053	0.134069	0.0670347	−	0.997751i	$-0.478646\pi$
$991$	4.22053	0.134069	0.0670347	+	0.997751i	$0.478646\pi$
$992$	−2.97347	−0.0944077
$993$	−6.75574	−0.214387
$994$	−18.3718	−0.582718
$995$	6.19198	0.196299
$996$	1.29245	0.0409528
$997$	−7.81561	−0.247523	−0.123761	−	0.992312i	$-0.539496\pi$
$997$	−7.81561	−0.247523	−0.123761	+	0.992312i	$0.539496\pi$
$998$	−38.8857	−1.23091
$999$	−9.80451	−0.310201

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	503.2.a.f.1.19	✓	26
3.2	odd	2		4527.2.a.o.1.8		26
4.3	odd	2		8048.2.a.u.1.12		26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
503.2.a.f.1.19	✓	26	1.1	even	1	trivial
4527.2.a.o.1.8		26	3.2	odd	2
8048.2.a.u.1.12		26	4.3	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:	\( N \)	\(=\)	\( 503 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	503.a (trivial)

\(f(q)\)	\(=\)	\(q+1.81497 q^{2} +0.577924 q^{3} +1.29413 q^{4} +2.10638 q^{5} +1.04892 q^{6} +1.73516 q^{7} -1.28114 q^{8} -2.66600 q^{9} +O(q^{10})\)	\(q+1.81497 q^{2} +0.577924 q^{3} +1.29413 q^{4} +2.10638 q^{5} +1.04892 q^{6} +1.73516 q^{7} -1.28114 q^{8} -2.66600 q^{9} +3.82302 q^{10} +6.36270 q^{11} +0.747908 q^{12} -2.18456 q^{13} +3.14927 q^{14} +1.21733 q^{15} -4.91349 q^{16} -0.631406 q^{17} -4.83873 q^{18} -7.04772 q^{19} +2.72593 q^{20} +1.00279 q^{21} +11.5481 q^{22} +6.00543 q^{23} -0.740398 q^{24} -0.563171 q^{25} -3.96493 q^{26} -3.27452 q^{27} +2.24552 q^{28} +7.71180 q^{29} +2.20941 q^{30} +0.467852 q^{31} -6.35558 q^{32} +3.67716 q^{33} -1.14599 q^{34} +3.65490 q^{35} -3.45016 q^{36} +2.99418 q^{37} -12.7914 q^{38} -1.26251 q^{39} -2.69855 q^{40} -8.67325 q^{41} +1.82004 q^{42} -11.0553 q^{43} +8.23417 q^{44} -5.61561 q^{45} +10.8997 q^{46} +4.33189 q^{47} -2.83962 q^{48} -3.98923 q^{49} -1.02214 q^{50} -0.364905 q^{51} -2.82711 q^{52} -8.09634 q^{53} -5.94316 q^{54} +13.4023 q^{55} -2.22297 q^{56} -4.07304 q^{57} +13.9967 q^{58} +7.20052 q^{59} +1.57538 q^{60} +5.93532 q^{61} +0.849139 q^{62} -4.62594 q^{63} -1.70824 q^{64} -4.60152 q^{65} +6.67394 q^{66} -2.21237 q^{67} -0.817122 q^{68} +3.47068 q^{69} +6.63355 q^{70} -5.83367 q^{71} +3.41551 q^{72} -9.72628 q^{73} +5.43437 q^{74} -0.325470 q^{75} -9.12067 q^{76} +11.0403 q^{77} -2.29142 q^{78} +1.62156 q^{79} -10.3497 q^{80} +6.10559 q^{81} -15.7417 q^{82} +1.72808 q^{83} +1.29774 q^{84} -1.32998 q^{85} -20.0650 q^{86} +4.45683 q^{87} -8.15148 q^{88} -11.1083 q^{89} -10.1922 q^{90} -3.79056 q^{91} +7.77181 q^{92} +0.270383 q^{93} +7.86227 q^{94} -14.8452 q^{95} -3.67304 q^{96} +7.97564 q^{97} -7.24034 q^{98} -16.9630 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + 4 q^{2} + 4 q^{3} + 36 q^{4} + 9 q^{5} - 4 q^{6} + 11 q^{7} + 18 q^{8} + 42 q^{9}+O(q^{10}) \) 26 * q + 4 * q^2 + 4 * q^3 + 36 * q^4 + 9 * q^5 - 4 * q^6 + 11 * q^7 + 18 * q^8 + 42 * q^9	\( 26 q + 4 q^{2} + 4 q^{3} + 36 q^{4} + 9 q^{5} - 4 q^{6} + 11 q^{7} + 18 q^{8} + 42 q^{9} + 4 q^{10} - 17 q^{11} + 19 q^{12} + 14 q^{13} + q^{14} + 18 q^{15} + 48 q^{16} + 17 q^{17} - 10 q^{18} - 22 q^{19} - 19 q^{20} - 16 q^{21} + 38 q^{22} + 27 q^{23} - 9 q^{24} + 93 q^{25} + q^{26} + 31 q^{27} - 9 q^{28} + 13 q^{29} - 28 q^{30} + 26 q^{31} + 5 q^{32} + 6 q^{33} - 32 q^{34} - 22 q^{35} + 52 q^{36} + 55 q^{37} - 24 q^{38} - 15 q^{39} - 7 q^{40} + 24 q^{41} - 50 q^{42} + 20 q^{43} - 27 q^{44} - 8 q^{45} + 6 q^{46} - 25 q^{47} + 29 q^{48} + 65 q^{49} - 16 q^{50} + 7 q^{51} + 32 q^{52} + 30 q^{53} - 82 q^{54} + 25 q^{55} + 3 q^{56} + 9 q^{57} + 58 q^{58} - 26 q^{59} - 68 q^{60} + 15 q^{61} - 12 q^{62} - 19 q^{63} + 44 q^{64} + 20 q^{65} - 55 q^{66} - 20 q^{67} - 4 q^{68} - 27 q^{69} + 2 q^{70} - 35 q^{71} - 26 q^{72} + 38 q^{73} - 59 q^{74} + 2 q^{75} - 42 q^{76} - 6 q^{77} - 47 q^{78} + 21 q^{79} - 100 q^{80} + 70 q^{81} - 59 q^{82} - 48 q^{83} - 116 q^{84} + 6 q^{85} - 7 q^{86} - 9 q^{87} + 106 q^{88} - 5 q^{89} - 118 q^{90} - 24 q^{91} + 26 q^{92} - 8 q^{93} - 22 q^{94} + 43 q^{95} - 100 q^{96} + 142 q^{97} - 38 q^{98} - 50 q^{99}+O(q^{100}) \) 26 * q + 4 * q^2 + 4 * q^3 + 36 * q^4 + 9 * q^5 - 4 * q^6 + 11 * q^7 + 18 * q^8 + 42 * q^9 + 4 * q^10 - 17 * q^11 + 19 * q^12 + 14 * q^13 + q^14 + 18 * q^15 + 48 * q^16 + 17 * q^17 - 10 * q^18 - 22 * q^19 - 19 * q^20 - 16 * q^21 + 38 * q^22 + 27 * q^23 - 9 * q^24 + 93 * q^25 + q^26 + 31 * q^27 - 9 * q^28 + 13 * q^29 - 28 * q^30 + 26 * q^31 + 5 * q^32 + 6 * q^33 - 32 * q^34 - 22 * q^35 + 52 * q^36 + 55 * q^37 - 24 * q^38 - 15 * q^39 - 7 * q^40 + 24 * q^41 - 50 * q^42 + 20 * q^43 - 27 * q^44 - 8 * q^45 + 6 * q^46 - 25 * q^47 + 29 * q^48 + 65 * q^49 - 16 * q^50 + 7 * q^51 + 32 * q^52 + 30 * q^53 - 82 * q^54 + 25 * q^55 + 3 * q^56 + 9 * q^57 + 58 * q^58 - 26 * q^59 - 68 * q^60 + 15 * q^61 - 12 * q^62 - 19 * q^63 + 44 * q^64 + 20 * q^65 - 55 * q^66 - 20 * q^67 - 4 * q^68 - 27 * q^69 + 2 * q^70 - 35 * q^71 - 26 * q^72 + 38 * q^73 - 59 * q^74 + 2 * q^75 - 42 * q^76 - 6 * q^77 - 47 * q^78 + 21 * q^79 - 100 * q^80 + 70 * q^81 - 59 * q^82 - 48 * q^83 - 116 * q^84 + 6 * q^85 - 7 * q^86 - 9 * q^87 + 106 * q^88 - 5 * q^89 - 118 * q^90 - 24 * q^91 + 26 * q^92 - 8 * q^93 - 22 * q^94 + 43 * q^95 - 100 * q^96 + 142 * q^97 - 38 * q^98 - 50 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more