LMFDB - Embedded newform 4205.2.a.m.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4205,2,Mod(1,4205)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4205, 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("4205.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4205 = 5 \cdot 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4205.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$33.5770940499$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.66064384.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 9x^{4} + 13x^{2} - 1 $ x^6 - 9x^4 + 13x^2 - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 145)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$2.68667$ of defining polynomial
Character	$\chi$	$=$	4205.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.68667 q^{2} +2.31446 q^{3} +5.21819 q^{4} -1.00000 q^{5} +6.21819 q^{6} +4.21819 q^{7} +8.64620 q^{8} +2.35673 q^{9} +O(q^{10})$	\(q+2.68667 q^{2} +2.31446 q^{3} +5.21819 q^{4} -1.00000 q^{5} +6.21819 q^{6} +4.21819 q^{7} +8.64620 q^{8} +2.35673 q^{9} -2.68667 q^{10} -2.31446 q^{11} +12.0773 q^{12} +0.643274 q^{13} +11.3329 q^{14} -2.31446 q^{15} +12.7931 q^{16} +0.586195 q^{17} +6.33174 q^{18} -5.95953 q^{19} -5.21819 q^{20} +9.76282 q^{21} -6.21819 q^{22} -5.57491 q^{23} +20.0113 q^{24} +1.00000 q^{25} +1.72826 q^{26} -1.48883 q^{27} +22.0113 q^{28} -6.21819 q^{30} -0.158221 q^{31} +17.0784 q^{32} -5.35673 q^{33} +1.57491 q^{34} -4.21819 q^{35} +12.2978 q^{36} +4.04272 q^{37} -16.0113 q^{38} +1.48883 q^{39} -8.64620 q^{40} -9.76282 q^{41} +26.2295 q^{42} -4.97568 q^{43} -12.0773 q^{44} -2.35673 q^{45} -14.9779 q^{46} +2.31446 q^{47} +29.6091 q^{48} +10.7931 q^{49} +2.68667 q^{50} +1.35673 q^{51} +3.35673 q^{52} +13.0796 q^{53} -4.00000 q^{54} +2.31446 q^{55} +36.4713 q^{56} -13.7931 q^{57} -2.64327 q^{59} -12.0773 q^{60} +0.983848 q^{61} -0.425088 q^{62} +9.94111 q^{63} +20.2978 q^{64} -0.643274 q^{65} -14.3917 q^{66} -1.57491 q^{67} +3.05888 q^{68} -12.9029 q^{69} -11.3329 q^{70} +9.35673 q^{71} +20.3767 q^{72} -9.17663 q^{73} +10.8615 q^{74} +2.31446 q^{75} -31.0980 q^{76} -9.76282 q^{77} +4.00000 q^{78} -4.97568 q^{79} -12.7931 q^{80} -10.5160 q^{81} -26.2295 q^{82} -8.21819 q^{83} +50.9442 q^{84} -0.586195 q^{85} -13.3680 q^{86} -20.0113 q^{88} -7.29014 q^{89} -6.33174 q^{90} +2.71345 q^{91} -29.0909 q^{92} -0.366196 q^{93} +6.21819 q^{94} +5.95953 q^{95} +39.5273 q^{96} +3.05888 q^{97} +28.9975 q^{98} -5.45455 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{4} - 6 q^{5} + 12 q^{6} + 14 q^{9}+O(q^{10}) $ 6 * q + 6 * q^4 - 6 * q^5 + 12 * q^6 + 14 * q^9	$ 6 q + 6 q^{4} - 6 q^{5} + 12 q^{6} + 14 q^{9} + 4 q^{13} + 26 q^{16} - 6 q^{20} - 12 q^{22} - 8 q^{23} + 44 q^{24} + 6 q^{25} + 56 q^{28} - 12 q^{30} - 32 q^{33} - 16 q^{34} - 2 q^{36} - 20 q^{38} + 56 q^{42} - 14 q^{45} + 14 q^{49} + 8 q^{51} + 20 q^{52} + 28 q^{53} - 24 q^{54} - 32 q^{57} - 16 q^{59} - 28 q^{62} - 16 q^{63} + 46 q^{64} - 4 q^{65} + 16 q^{67} + 56 q^{71} + 40 q^{74} + 24 q^{78} - 26 q^{80} + 38 q^{81} - 56 q^{82} - 24 q^{83} - 4 q^{86} - 44 q^{88} + 16 q^{91} - 48 q^{92} + 48 q^{93} + 12 q^{94} + 60 q^{96}+O(q^{100}) $ 6 * q + 6 * q^4 - 6 * q^5 + 12 * q^6 + 14 * q^9 + 4 * q^13 + 26 * q^16 - 6 * q^20 - 12 * q^22 - 8 * q^23 + 44 * q^24 + 6 * q^25 + 56 * q^28 - 12 * q^30 - 32 * q^33 - 16 * q^34 - 2 * q^36 - 20 * q^38 + 56 * q^42 - 14 * q^45 + 14 * q^49 + 8 * q^51 + 20 * q^52 + 28 * q^53 - 24 * q^54 - 32 * q^57 - 16 * q^59 - 28 * q^62 - 16 * q^63 + 46 * q^64 - 4 * q^65 + 16 * q^67 + 56 * q^71 + 40 * q^74 + 24 * q^78 - 26 * q^80 + 38 * q^81 - 56 * q^82 - 24 * q^83 - 4 * q^86 - 44 * q^88 + 16 * q^91 - 48 * q^92 + 48 * q^93 + 12 * q^94 + 60 * q^96

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 $

$2$	2.68667	1.89976	0.949881	−	0.312613i	$-0.101204\pi$
$2$	2.68667	1.89976	0.949881	+	0.312613i	$0.101204\pi$
$3$	2.31446	1.33625	0.668127	−	0.744047i	$-0.267096\pi$
$3$	2.31446	1.33625	0.668127	+	0.744047i	$0.267096\pi$
$4$	5.21819	2.60909
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	6.21819	2.53856
$7$	4.21819	1.59432	0.797162	−	0.603765i	$-0.206333\pi$
$7$	4.21819	1.59432	0.797162	+	0.603765i	$0.206333\pi$
$8$	8.64620	3.05689
$9$	2.35673	0.785575
$10$	−2.68667	−0.849599
$11$	−2.31446	−0.697836	−0.348918	−	0.937153i	$-0.613451\pi$
$11$	−2.31446	−0.697836	−0.348918	+	0.937153i	$0.613451\pi$
$12$	12.0773	3.48641
$13$	0.643274	0.178412	0.0892061	−	0.996013i	$-0.471567\pi$
$13$	0.643274	0.178412	0.0892061	+	0.996013i	$0.471567\pi$
$14$	11.3329	3.02884
$15$	−2.31446	−0.597591
$16$	12.7931	3.19827
$17$	0.586195	0.142173	0.0710866	−	0.997470i	$-0.477353\pi$
$17$	0.586195	0.142173	0.0710866	+	0.997470i	$0.477353\pi$
$18$	6.33174	1.49241
$19$	−5.95953	−1.36721	−0.683605	−	0.729852i	$-0.739589\pi$
$19$	−5.95953	−1.36721	−0.683605	+	0.729852i	$0.739589\pi$
$20$	−5.21819	−1.16682
$21$	9.76282	2.13042
$22$	−6.21819	−1.32572
$23$	−5.57491	−1.16245	−0.581225	−	0.813743i	$-0.697426\pi$
$23$	−5.57491	−1.16245	−0.581225	+	0.813743i	$0.697426\pi$
$24$	20.0113	4.08479
$25$	1.00000	0.200000
$26$	1.72826	0.338941
$27$	−1.48883	−0.286526
$28$	22.0113	4.15974
$29$	0	0
$29$	0	0
$30$	−6.21819	−1.13528
$31$	−0.158221	−0.0284174	−0.0142087	−	0.999899i	$-0.504523\pi$
$31$	−0.158221	−0.0284174	−0.0142087	+	0.999899i	$0.504523\pi$
$32$	17.0784	3.01907
$33$	−5.35673	−0.932486
$34$	1.57491	0.270095
$35$	−4.21819	−0.713004
$36$	12.2978	2.04964
$37$	4.04272	0.664620	0.332310	−	0.943170i	$-0.392172\pi$
$37$	4.04272	0.664620	0.332310	+	0.943170i	$0.392172\pi$
$38$	−16.0113	−2.59737
$39$	1.48883	0.238404
$40$	−8.64620	−1.36708
$41$	−9.76282	−1.52470	−0.762349	−	0.647167i	$-0.775954\pi$
$41$	−9.76282	−1.52470	−0.762349	+	0.647167i	$0.775954\pi$
$42$	26.2295	4.04730
$43$	−4.97568	−0.758785	−0.379392	−	0.925236i	$-0.623867\pi$
$43$	−4.97568	−0.758785	−0.379392	+	0.925236i	$0.623867\pi$
$44$	−12.0773	−1.82072
$45$	−2.35673	−0.351320
$46$	−14.9779	−2.20838
$47$	2.31446	0.337599	0.168799	−	0.985650i	$-0.446011\pi$
$47$	2.31446	0.337599	0.168799	+	0.985650i	$0.446011\pi$
$48$	29.6091	4.27371
$49$	10.7931	1.54187
$50$	2.68667	0.379952
$51$	1.35673	0.189980
$52$	3.35673	0.465494
$53$	13.0796	1.79663	0.898314	−	0.439354i	$-0.144793\pi$
$53$	13.0796	1.79663	0.898314	+	0.439354i	$0.144793\pi$
$54$	−4.00000	−0.544331
$55$	2.31446	0.312082
$56$	36.4713	4.87368
$57$	−13.7931	−1.82694
$58$	0	0
$59$	−2.64327	−0.344125	−0.172063	−	0.985086i	$-0.555043\pi$
$59$	−2.64327	−0.344125	−0.172063	+	0.985086i	$0.555043\pi$
$60$	−12.0773	−1.55917
$61$	0.983848	0.125969	0.0629844	−	0.998015i	$-0.479938\pi$
$61$	0.983848	0.125969	0.0629844	+	0.998015i	$0.479938\pi$
$62$	−0.425088	−0.0539862
$63$	9.94111	1.25246
$64$	20.2978	2.53723
$65$	−0.643274	−0.0797884
$66$	−14.3917	−1.77150
$67$	−1.57491	−0.192406	−0.0962031	−	0.995362i	$-0.530670\pi$
$67$	−1.57491	−0.192406	−0.0962031	+	0.995362i	$0.530670\pi$
$68$	3.05888	0.370943
$69$	−12.9029	−1.55333
$70$	−11.3329	−1.35454
$71$	9.35673	1.11044	0.555220	−	0.831704i	$-0.312634\pi$
$71$	9.35673	1.11044	0.555220	+	0.831704i	$0.312634\pi$
$72$	20.3767	2.40142
$73$	−9.17663	−1.07404	−0.537022	−	0.843568i	$-0.680451\pi$
$73$	−9.17663	−1.07404	−0.537022	+	0.843568i	$0.680451\pi$
$74$	10.8615	1.26262
$75$	2.31446	0.267251
$76$	−31.0980	−3.56718
$77$	−9.76282	−1.11258
$78$	4.00000	0.452911
$79$	−4.97568	−0.559808	−0.279904	−	0.960028i	$-0.590303\pi$
$79$	−4.97568	−0.559808	−0.279904	+	0.960028i	$0.590303\pi$
$80$	−12.7931	−1.43031
$81$	−10.5160	−1.16845
$82$	−26.2295	−2.89656
$83$	−8.21819	−0.902063	−0.451032	−	0.892508i	$-0.648944\pi$
$83$	−8.21819	−0.902063	−0.451032	+	0.892508i	$0.648944\pi$
$84$	50.9442	5.55847
$85$	−0.586195	−0.0635818
$86$	−13.3680	−1.44151
$87$	0	0
$88$	−20.0113	−2.13321
$89$	−7.29014	−0.772754	−0.386377	−	0.922341i	$-0.626274\pi$
$89$	−7.29014	−0.772754	−0.386377	+	0.922341i	$0.626274\pi$
$90$	−6.33174	−0.667424
$91$	2.71345	0.284447
$92$	−29.0909	−3.03294
$93$	−0.366196	−0.0379728
$94$	6.21819	0.641357
$95$	5.95953	0.611435
$96$	39.5273	4.03424
$97$	3.05888	0.310582	0.155291	−	0.987869i	$-0.450369\pi$
$97$	3.05888	0.310582	0.155291	+	0.987869i	$0.450369\pi$
$98$	28.9975	2.92919
$99$	−5.45455	−0.548203
$100$	5.21819	0.521819
$101$	−1.48883	−0.148144	−0.0740722	−	0.997253i	$-0.523600\pi$
$101$	−1.48883	−0.148144	−0.0740722	+	0.997253i	$0.523600\pi$
$102$	3.64507	0.360916
$103$	11.2978	1.11321	0.556604	−	0.830778i	$-0.312104\pi$
$103$	11.2978	1.11321	0.556604	+	0.830778i	$0.312104\pi$
$104$	5.56188	0.545387
$105$	−9.76282	−0.952754
$106$	35.1407	3.41316
$107$	−2.93164	−0.283412	−0.141706	−	0.989909i	$-0.545259\pi$
$107$	−2.93164	−0.283412	−0.141706	+	0.989909i	$0.545259\pi$
$108$	−7.76901	−0.747573
$109$	17.0796	1.63593	0.817967	−	0.575265i	$-0.195101\pi$
$109$	17.0796	1.63593	0.817967	+	0.575265i	$0.195101\pi$
$110$	6.21819	0.592881
$111$	9.35673	0.888101
$112$	53.9637	5.09909
$113$	−13.4891	−1.26895	−0.634474	−	0.772944i	$-0.718783\pi$
$113$	−13.4891	−1.26895	−0.634474	+	0.772944i	$0.718783\pi$
$114$	−37.0575	−3.47075
$115$	5.57491	0.519863
$116$	0	0
$117$	1.51602	0.140156
$118$	−7.10160	−0.653755
$119$	2.47268	0.226670
$120$	−20.0113	−1.82677
$121$	−5.64327	−0.513025
$122$	2.64327	0.239311
$123$	−22.5957	−2.03738
$124$	−0.825627	−0.0741435
$125$	−1.00000	−0.0894427
$126$	26.7085	2.37938
$127$	11.0934	0.984383	0.492192	−	0.870487i	$-0.336196\pi$
$127$	11.0934	0.984383	0.492192	+	0.870487i	$0.336196\pi$
$128$	20.3767	1.80106
$129$	−11.5160	−1.01393
$130$	−1.72826	−0.151579
$131$	7.13192	0.623119	0.311559	−	0.950227i	$-0.399149\pi$
$131$	7.13192	0.623119	0.311559	+	0.950227i	$0.399149\pi$
$132$	−27.9524	−2.43294
$133$	−25.1384	−2.17978
$134$	−4.23127	−0.365526
$135$	1.48883	0.128138
$136$	5.06836	0.434608
$137$	14.7894	1.26354	0.631772	−	0.775154i	$-0.282328\pi$
$137$	14.7894	1.26354	0.631772	+	0.775154i	$0.282328\pi$
$138$	−34.6658	−2.95095
$139$	3.56363	0.302263	0.151131	−	0.988514i	$-0.451708\pi$
$139$	3.56363	0.302263	0.151131	+	0.988514i	$0.451708\pi$
$140$	−22.0113	−1.86029
$141$	5.35673	0.451118
$142$	25.1384	2.10957
$143$	−1.48883	−0.124502
$144$	30.1498	2.51249
$145$	0	0
$146$	−24.6546	−2.04043
$147$	24.9802	2.06033
$148$	21.0957	1.73406
$149$	−6.00000	−0.491539	−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000	−0.491539	−0.245770	+	0.969328i	$0.579041\pi$
$150$	6.21819	0.507713
$151$	−4.50655	−0.366738	−0.183369	−	0.983044i	$-0.558700\pi$
$151$	−4.50655	−0.366738	−0.183369	+	0.983044i	$0.558700\pi$
$152$	−51.5273	−4.17942
$153$	1.38150	0.111688
$154$	−26.2295	−2.11363
$155$	0.158221	0.0127086
$156$	7.76901	0.622018
$157$	16.9456	1.35241	0.676205	−	0.736714i	$-0.263624\pi$
$157$	16.9456	1.35241	0.676205	+	0.736714i	$0.263624\pi$
$158$	−13.3680	−1.06350
$159$	30.2723	2.40075
$160$	−17.0784	−1.35017
$161$	−23.5160	−1.85332
$162$	−28.2531	−2.21977
$163$	11.0934	0.868905	0.434453	−	0.900695i	$-0.356942\pi$
$163$	11.0934	0.868905	0.434453	+	0.900695i	$0.356942\pi$
$164$	−50.9442	−3.97808
$165$	5.35673	0.417021
$166$	−22.0795	−1.71370
$167$	5.57491	0.431400	0.215700	−	0.976460i	$-0.430797\pi$
$167$	5.57491	0.431400	0.215700	+	0.976460i	$0.430797\pi$
$168$	84.4113	6.51248
$169$	−12.5862	−0.968169
$170$	−1.57491	−0.120790
$171$	−14.0450	−1.07405
$172$	−25.9640	−1.97974
$173$	−7.79310	−0.592498	−0.296249	−	0.955111i	$-0.595736\pi$
$173$	−7.79310	−0.592498	−0.296249	+	0.955111i	$0.595736\pi$
$174$	0	0
$175$	4.21819	0.318865
$176$	−29.6091	−2.23187
$177$	−6.11775	−0.459838
$178$	−19.5862	−1.46805
$179$	4.43637	0.331590	0.165795	−	0.986160i	$-0.446981\pi$
$179$	4.43637	0.331590	0.165795	+	0.986160i	$0.446981\pi$
$180$	−12.2978	−0.916626
$181$	13.5160	1.00464	0.502319	−	0.864682i	$-0.332480\pi$
$181$	13.5160	1.00464	0.502319	+	0.864682i	$0.332480\pi$
$182$	7.29014	0.540381
$183$	2.27708	0.168326
$184$	−48.2018	−3.55348
$185$	−4.04272	−0.297227
$186$	−0.983848	−0.0721393
$187$	−1.35673	−0.0992136
$188$	12.0773	0.880827
$189$	−6.28017	−0.456816
$190$	16.0113	1.16158
$191$	11.5723	0.837342	0.418671	−	0.908138i	$-0.362496\pi$
$191$	11.5723	0.837342	0.418671	+	0.908138i	$0.362496\pi$
$192$	46.9785	3.39038
$193$	9.84404	0.708589	0.354295	−	0.935134i	$-0.384721\pi$
$193$	9.84404	0.708589	0.354295	+	0.935134i	$0.384721\pi$
$194$	8.21819	0.590031
$195$	−1.48883	−0.106618
$196$	56.3204	4.02289
$197$	−5.14982	−0.366910	−0.183455	−	0.983028i	$-0.558728\pi$
$197$	−5.14982	−0.366910	−0.183455	+	0.983028i	$0.558728\pi$
$198$	−14.6546	−1.04145
$199$	−17.7931	−1.26132	−0.630660	−	0.776060i	$-0.717216\pi$
$199$	−17.7931	−1.26132	−0.630660	+	0.776060i	$0.717216\pi$
$200$	8.64620	0.611379
$201$	−3.64507	−0.257104
$202$	−4.00000	−0.281439
$203$	0	0
$204$	7.07965	0.495674
$205$	9.76282	0.681865
$206$	30.3535	2.11483
$207$	−13.1385	−0.913192
$208$	8.22947	0.570611
$209$	13.7931	0.954089
$210$	−26.2295	−1.81001
$211$	18.8624	1.29854	0.649272	−	0.760556i	$-0.275074\pi$
$211$	18.8624	1.29854	0.649272	+	0.760556i	$0.275074\pi$
$212$	68.2520	4.68757
$213$	21.6558	1.48383
$214$	−7.87634	−0.538415
$215$	4.97568	0.339339
$216$	−12.8727	−0.875879
$217$	−0.667406	−0.0453065
$218$	45.8873	3.10788
$219$	−21.2389	−1.43519
$220$	12.0773	0.814250
$221$	0.377084	0.0253654
$222$	25.1384	1.68718
$223$	13.5749	0.909043	0.454522	−	0.890736i	$-0.349810\pi$
$223$	13.5749	0.909043	0.454522	+	0.890736i	$0.349810\pi$
$224$	72.0399	4.81337
$225$	2.35673	0.157115
$226$	−36.2408	−2.41070
$227$	7.00181	0.464727	0.232363	−	0.972629i	$-0.425354\pi$
$227$	7.00181	0.464727	0.232363	+	0.972629i	$0.425354\pi$
$228$	−71.9750	−4.76666
$229$	−24.1546	−1.59618	−0.798089	−	0.602539i	$-0.794156\pi$
$229$	−24.1546	−1.59618	−0.798089	+	0.602539i	$0.794156\pi$
$230$	14.9779	0.987616
$231$	−22.5957	−1.48669
$232$	0	0
$233$	5.14982	0.337376	0.168688	−	0.985669i	$-0.446047\pi$
$233$	5.14982	0.337376	0.168688	+	0.985669i	$0.446047\pi$
$234$	4.07305	0.266263
$235$	−2.31446	−0.150979
$236$	−13.7931	−0.897854
$237$	−11.5160	−0.748046
$238$	6.64327	0.430620
$239$	14.6433	0.947195	0.473597	−	0.880741i	$-0.342955\pi$
$239$	14.6433	0.947195	0.473597	+	0.880741i	$0.342955\pi$
$240$	−29.6091	−1.91126
$241$	−2.00000	−0.128831	−0.0644157	−	0.997923i	$-0.520518\pi$
$241$	−2.00000	−0.128831	−0.0644157	+	0.997923i	$0.520518\pi$
$242$	−15.1616	−0.974625
$243$	−19.8724	−1.27482
$244$	5.13390	0.328665
$245$	−10.7931	−0.689546
$246$	−60.7071	−3.87054
$247$	−3.83361	−0.243927
$248$	−1.36801	−0.0868688
$249$	−19.0207	−1.20539
$250$	−2.68667	−0.169920
$251$	−22.6354	−1.42873	−0.714367	−	0.699771i	$-0.753285\pi$
$251$	−22.6354	−1.42873	−0.714367	+	0.699771i	$0.753285\pi$
$252$	51.8746	3.26779
$253$	12.9029	0.811199
$254$	29.8044	1.87009
$255$	−1.35673	−0.0849615
$256$	14.1498	0.884364
$257$	10.9204	0.681193	0.340596	−	0.940210i	$-0.389371\pi$
$257$	10.9204	0.681193	0.340596	+	0.940210i	$0.389371\pi$
$258$	−30.9397	−1.92622
$259$	17.0530	1.05962
$260$	−3.35673	−0.208175
$261$	0	0
$262$	19.1611	1.18378
$263$	9.92105	0.611758	0.305879	−	0.952070i	$-0.401050\pi$
$263$	9.92105	0.611758	0.305879	+	0.952070i	$0.401050\pi$
$264$	−46.3153	−2.85051
$265$	−13.0796	−0.803476
$266$	−67.5386	−4.14106
$267$	−16.8727	−1.03260
$268$	−8.21819	−0.502006
$269$	12.4240	0.757508	0.378754	−	0.925497i	$-0.376353\pi$
$269$	12.4240	0.757508	0.378754	+	0.925497i	$0.376353\pi$
$270$	4.00000	0.243432
$271$	27.2643	1.65619	0.828095	−	0.560587i	$-0.189425\pi$
$271$	27.2643	1.65619	0.828095	+	0.560587i	$0.189425\pi$
$272$	7.49925	0.454709
$273$	6.28017	0.380093
$274$	39.7342	2.40043
$275$	−2.31446	−0.139567
$276$	−67.3298	−4.05278
$277$	−2.92035	−0.175467	−0.0877335	−	0.996144i	$-0.527962\pi$
$277$	−2.92035	−0.175467	−0.0877335	+	0.996144i	$0.527962\pi$
$278$	9.57428	0.574227
$279$	−0.372884	−0.0223240
$280$	−36.4713	−2.17958
$281$	−18.3662	−1.09564	−0.547818	−	0.836598i	$-0.684541\pi$
$281$	−18.3662	−1.09564	−0.547818	+	0.836598i	$0.684541\pi$
$282$	14.3917	0.857016
$283$	14.8615	0.883422	0.441711	−	0.897157i	$-0.354372\pi$
$283$	14.8615	0.883422	0.441711	+	0.897157i	$0.354372\pi$
$284$	48.8251	2.89724
$285$	13.7931	0.817033
$286$	−4.00000	−0.236525
$287$	−41.1814	−2.43086
$288$	40.2491	2.37170
$289$	−16.6564	−0.979787
$290$	0	0
$291$	7.07965	0.415016
$292$	−47.8854	−2.80228
$293$	1.57004	0.0917229	0.0458615	−	0.998948i	$-0.485397\pi$
$293$	1.57004	0.0917229	0.0458615	+	0.998948i	$0.485397\pi$
$294$	67.1135	3.91414
$295$	2.64327	0.153897
$296$	34.9542	2.03167
$297$	3.44584	0.199948
$298$	−16.1200	−0.933807
$299$	−3.58620	−0.207395
$300$	12.0773	0.697282
$301$	−20.9884	−1.20975
$302$	−12.1076	−0.696714
$303$	−3.44584	−0.197959
$304$	−76.2409	−4.37271
$305$	−0.983848	−0.0563350
$306$	3.71164	0.212180
$307$	4.65924	0.265917	0.132958	−	0.991122i	$-0.457552\pi$
$307$	4.65924	0.265917	0.132958	+	0.991122i	$0.457552\pi$
$308$	−50.9442	−2.90282
$309$	26.1484	1.48753
$310$	0.425088	0.0241434
$311$	−21.6516	−1.22775	−0.613874	−	0.789404i	$-0.710390\pi$
$311$	−21.6516	−1.22775	−0.613874	+	0.789404i	$0.710390\pi$
$312$	12.8727	0.728776
$313$	11.3567	0.641920	0.320960	−	0.947093i	$-0.395994\pi$
$313$	11.3567	0.641920	0.320960	+	0.947093i	$0.395994\pi$
$314$	45.5273	2.56925
$315$	−9.94111	−0.560118
$316$	−25.9640	−1.46059
$317$	9.36517	0.526000	0.263000	−	0.964796i	$-0.415288\pi$
$317$	9.36517	0.526000	0.263000	+	0.964796i	$0.415288\pi$
$318$	81.3317	4.56085
$319$	0	0
$320$	−20.2978	−1.13468
$321$	−6.78516	−0.378711
$322$	−63.1797	−3.52087
$323$	−3.49345	−0.194381
$324$	−54.8746	−3.04859
$325$	0.643274	0.0356824
$326$	29.8044	1.65071
$327$	39.5302	2.18602
$328$	−84.4113	−4.66084
$329$	9.76282	0.538242
$330$	14.3917	0.792239
$331$	−18.5115	−1.01748	−0.508741	−	0.860919i	$-0.669889\pi$
$331$	−18.5115	−1.01748	−0.508741	+	0.860919i	$0.669889\pi$
$332$	−42.8840	−2.35357
$333$	9.52759	0.522109
$334$	14.9779	0.819556
$335$	1.57491	0.0860467
$336$	124.897	6.81368
$337$	−18.8116	−1.02473	−0.512365	−	0.858768i	$-0.671231\pi$
$337$	−18.8116	−1.02473	−0.512365	+	0.858768i	$0.671231\pi$
$338$	−33.8149	−1.83929
$339$	−31.2200	−1.69564
$340$	−3.05888	−0.165891
$341$	0.366196	0.0198306
$342$	−37.7342	−2.04043
$343$	16.0000	0.863919
$344$	−43.0208	−2.31952
$345$	12.9029	0.694669
$346$	−20.9375	−1.12561
$347$	25.2313	1.35449	0.677243	−	0.735759i	$-0.263174\pi$
$347$	25.2313	1.35449	0.677243	+	0.735759i	$0.263174\pi$
$348$	0	0
$349$	2.85018	0.152566	0.0762832	−	0.997086i	$-0.475695\pi$
$349$	2.85018	0.152566	0.0762832	+	0.997086i	$0.475695\pi$
$350$	11.3329	0.605767
$351$	−0.957728	−0.0511197
$352$	−39.5273	−2.10681
$353$	30.0927	1.60168	0.800838	−	0.598881i	$-0.204388\pi$
$353$	30.0927	1.60168	0.800838	+	0.598881i	$0.204388\pi$
$354$	−16.4364	−0.873583
$355$	−9.35673	−0.496603
$356$	−38.0413	−2.01619
$357$	5.72292	0.302889
$358$	11.9191	0.629942
$359$	−23.6193	−1.24658	−0.623289	−	0.781992i	$-0.714204\pi$
$359$	−23.6193	−1.24658	−0.623289	+	0.781992i	$0.714204\pi$
$360$	−20.3767	−1.07395
$361$	16.5160	0.869264
$362$	36.3131	1.90857
$363$	−13.0611	−0.685532
$364$	14.1593	0.742149
$365$	9.17663	0.480327
$366$	6.11775	0.319780
$367$	17.2112	0.898417	0.449208	−	0.893427i	$-0.351706\pi$
$367$	17.2112	0.898417	0.449208	+	0.893427i	$0.351706\pi$
$368$	−71.3204	−3.71783
$369$	−23.0083	−1.19776
$370$	−10.8615	−0.564660
$371$	55.1724	2.86441
$372$	−1.91088	−0.0990746
$373$	22.8727	1.18431	0.592153	−	0.805826i	$-0.298278\pi$
$373$	22.8727	1.18431	0.592153	+	0.805826i	$0.298278\pi$
$374$	−3.64507	−0.188482
$375$	−2.31446	−0.119518
$376$	20.0113	1.03200
$377$	0	0
$378$	−16.8727	−0.867840
$379$	27.2643	1.40047	0.700237	−	0.713910i	$-0.253077\pi$
$379$	27.2643	1.40047	0.700237	+	0.713910i	$0.253077\pi$
$380$	31.0980	1.59529
$381$	25.6753	1.31539
$382$	31.0909	1.59075
$383$	−37.2313	−1.90243	−0.951215	−	0.308529i	$-0.900163\pi$
$383$	−37.2313	−1.90243	−0.951215	+	0.308529i	$0.900163\pi$
$384$	47.1611	2.40668
$385$	9.76282	0.497560
$386$	26.4477	1.34615
$387$	−11.7263	−0.596082
$388$	15.9618	0.810337
$389$	−23.6496	−1.19908	−0.599541	−	0.800344i	$-0.704650\pi$
$389$	−23.6496	−1.19908	−0.599541	+	0.800344i	$0.704650\pi$
$390$	−4.00000	−0.202548
$391$	−3.26799	−0.165269
$392$	93.3193	4.71334
$393$	16.5066	0.832645
$394$	−13.8359	−0.697041
$395$	4.97568	0.250354
$396$	−28.4628	−1.43031
$397$	−30.0226	−1.50679	−0.753395	−	0.657568i	$-0.771585\pi$
$397$	−30.0226	−1.50679	−0.753395	+	0.657568i	$0.771585\pi$
$398$	−47.8042	−2.39621
$399$	−58.1819	−2.91274
$400$	12.7931	0.639655
$401$	−32.3698	−1.61647	−0.808236	−	0.588859i	$-0.799577\pi$
$401$	−32.3698	−1.61647	−0.808236	+	0.588859i	$0.799577\pi$
$402$	−9.79310	−0.488435
$403$	−0.101780	−0.00507000
$404$	−7.76901	−0.386523
$405$	10.5160	0.522545
$406$	0	0
$407$	−9.35673	−0.463796
$408$	11.7305	0.580747
$409$	24.5055	1.21172	0.605860	−	0.795571i	$-0.292829\pi$
$409$	24.5055	1.21172	0.605860	+	0.795571i	$0.292829\pi$
$410$	26.2295	1.29538
$411$	34.2295	1.68842
$412$	58.9542	2.90447
$413$	−11.1498	−0.548647
$414$	−35.2989	−1.73485
$415$	8.21819	0.403415
$416$	10.9861	0.538638
$417$	8.24787	0.403900
$418$	37.0575	1.81254
$419$	−6.22947	−0.304330	−0.152165	−	0.988355i	$-0.548624\pi$
$419$	−6.22947	−0.304330	−0.152165	+	0.988355i	$0.548624\pi$
$420$	−50.9442	−2.48582
$421$	−32.9074	−1.60381	−0.801905	−	0.597452i	$-0.796180\pi$
$421$	−32.9074	−1.60381	−0.801905	+	0.597452i	$0.796180\pi$
$422$	50.6771	2.46692
$423$	5.45455	0.265209
$424$	113.089	5.49210
$425$	0.586195	0.0284346
$426$	58.1819	2.81892
$427$	4.15006	0.200835
$428$	−15.2978	−0.739449
$429$	−3.44584	−0.166367
$430$	13.3680	0.644663
$431$	3.00947	0.144961	0.0724806	−	0.997370i	$-0.476908\pi$
$431$	3.00947	0.144961	0.0724806	+	0.997370i	$0.476908\pi$
$432$	−19.0468	−0.916389
$433$	−34.3150	−1.64908	−0.824538	−	0.565807i	$-0.808565\pi$
$433$	−34.3150	−1.64908	−0.824538	+	0.565807i	$0.808565\pi$
$434$	−1.79310	−0.0860715
$435$	0	0
$436$	89.1248	4.26830
$437$	33.2239	1.58931
$438$	−57.0620	−2.72653
$439$	−29.8157	−1.42302	−0.711512	−	0.702674i	$-0.751989\pi$
$439$	−29.8157	−1.42302	−0.711512	+	0.702674i	$0.751989\pi$
$440$	20.0113	0.954001
$441$	25.4364	1.21126
$442$	1.01310	0.0481883
$443$	−27.9579	−1.32832	−0.664159	−	0.747591i	$-0.731210\pi$
$443$	−27.9579	−1.32832	−0.664159	+	0.747591i	$0.731210\pi$
$444$	48.8251	2.31714
$445$	7.29014	0.345586
$446$	36.4713	1.72697
$447$	−13.8868	−0.656821
$448$	85.6201	4.04517
$449$	4.27796	0.201889	0.100945	−	0.994892i	$-0.467814\pi$
$449$	4.27796	0.201889	0.100945	+	0.994892i	$0.467814\pi$
$450$	6.33174	0.298481
$451$	22.5957	1.06399
$452$	−70.3887	−3.31081
$453$	−10.4302	−0.490055
$454$	18.8116	0.882870
$455$	−2.71345	−0.127209
$456$	−119.258	−5.58476
$457$	10.3662	0.484910	0.242455	−	0.970163i	$-0.422047\pi$
$457$	10.3662	0.484910	0.242455	+	0.970163i	$0.422047\pi$
$458$	−64.8953	−3.03236
$459$	−0.872747	−0.0407363
$460$	29.0909	1.35637
$461$	13.0915	0.609730	0.304865	−	0.952396i	$-0.401389\pi$
$461$	13.0915	0.609730	0.304865	+	0.952396i	$0.401389\pi$
$462$	−60.7071	−2.82435
$463$	33.4571	1.55488	0.777442	−	0.628954i	$-0.216517\pi$
$463$	33.4571	1.55488	0.777442	+	0.628954i	$0.216517\pi$
$464$	0	0
$465$	0.366196	0.0169820
$466$	13.8359	0.640934
$467$	−32.5868	−1.50794	−0.753968	−	0.656911i	$-0.771863\pi$
$467$	−32.5868	−1.50794	−0.753968	+	0.656911i	$0.771863\pi$
$468$	7.91088	0.365681
$469$	−6.64327	−0.306758
$470$	−6.21819	−0.286824
$471$	39.2200	1.80716
$472$	−22.8543	−1.05195
$473$	11.5160	0.529507
$474$	−30.9397	−1.42111
$475$	−5.95953	−0.273442
$476$	12.9029	0.591404
$477$	30.8251	1.41139
$478$	39.3416	1.79944
$479$	36.5222	1.66874	0.834370	−	0.551204i	$-0.185831\pi$
$479$	36.5222	1.66874	0.834370	+	0.551204i	$0.185831\pi$
$480$	−39.5273	−1.80417
$481$	2.60058	0.118576
$482$	−5.37334	−0.244749
$483$	−54.4269	−2.47651
$484$	−29.4477	−1.33853
$485$	−3.05888	−0.138896
$486$	−53.3906	−2.42185
$487$	25.9411	1.17550	0.587752	−	0.809041i	$-0.300013\pi$
$487$	25.9411	1.17550	0.587752	+	0.809041i	$0.300013\pi$
$488$	8.50655	0.385073
$489$	25.6753	1.16108
$490$	−28.9975	−1.30997
$491$	−26.3411	−1.18876	−0.594379	−	0.804185i	$-0.702602\pi$
$491$	−26.3411	−1.18876	−0.594379	+	0.804185i	$0.702602\pi$
$492$	−117.908	−5.31572
$493$	0	0
$494$	−10.2996	−0.463403
$495$	5.45455	0.245164
$496$	−2.02414	−0.0908865
$497$	39.4684	1.77040
$498$	−51.1022	−2.28995
$499$	21.0131	0.940676	0.470338	−	0.882486i	$-0.344132\pi$
$499$	21.0131	0.940676	0.470338	+	0.882486i	$0.344132\pi$
$500$	−5.21819	−0.233364
$501$	12.9029	0.576460
$502$	−60.8139	−2.71426
$503$	14.5500	0.648751	0.324375	−	0.945928i	$-0.394846\pi$
$503$	14.5500	0.648751	0.324375	+	0.945928i	$0.394846\pi$
$504$	85.9528	3.82864
$505$	1.48883	0.0662522
$506$	34.6658	1.54108
$507$	−29.1303	−1.29372
$508$	57.8876	2.56835
$509$	−12.2295	−0.542062	−0.271031	−	0.962571i	$-0.587365\pi$
$509$	−12.2295	−0.542062	−0.271031	+	0.962571i	$0.587365\pi$
$510$	−3.64507	−0.161406
$511$	−38.7087	−1.71237
$512$	−2.73756	−0.120984
$513$	8.87275	0.391741
$514$	29.3394	1.29410
$515$	−11.2978	−0.497842
$516$	−60.0927	−2.64544
$517$	−5.35673	−0.235589
$518$	45.8157	2.01302
$519$	−18.0368	−0.791728
$520$	−5.56188	−0.243905
$521$	−17.5160	−0.767391	−0.383695	−	0.923460i	$-0.625349\pi$
$521$	−17.5160	−0.767391	−0.383695	+	0.923460i	$0.625349\pi$
$522$	0	0
$523$	−10.8840	−0.475926	−0.237963	−	0.971274i	$-0.576480\pi$
$523$	−10.8840	−0.475926	−0.237963	+	0.971274i	$0.576480\pi$
$524$	37.2157	1.62578
$525$	9.76282	0.426085
$526$	26.6546	1.16219
$527$	−0.0927485	−0.00404019
$528$	−68.5291	−2.98235
$529$	8.07965	0.351289
$530$	−35.1407	−1.52641
$531$	−6.22947	−0.270336
$532$	−131.177	−5.68724
$533$	−6.28017	−0.272025
$534$	−45.3315	−1.96168
$535$	2.93164	0.126746
$536$	−13.6170	−0.588165
$537$	10.2678	0.443089
$538$	33.3793	1.43908
$539$	−24.9802	−1.07597
$540$	7.76901	0.334325
$541$	−35.7572	−1.53732	−0.768661	−	0.639657i	$-0.779077\pi$
$541$	−35.7572	−1.53732	−0.768661	+	0.639657i	$0.779077\pi$
$542$	73.2502	3.14637
$543$	31.2823	1.34245
$544$	10.0113	0.429230
$545$	−17.0796	−0.731612
$546$	16.8727	0.722087
$547$	12.6320	0.540105	0.270052	−	0.962846i	$-0.412959\pi$
$547$	12.6320	0.540105	0.270052	+	0.962846i	$0.412959\pi$
$548$	77.1738	3.29670
$549$	2.31866	0.0989580
$550$	−6.21819	−0.265144
$551$	0	0
$552$	−111.561	−4.74836
$553$	−20.9884	−0.892516
$554$	−7.84602	−0.333345
$555$	−9.35673	−0.397171
$556$	18.5957	0.788632
$557$	21.0095	0.890200	0.445100	−	0.895481i	$-0.353168\pi$
$557$	21.0095	0.890200	0.445100	+	0.895481i	$0.353168\pi$
$558$	−1.00181	−0.0424102
$559$	−3.20073	−0.135376
$560$	−53.9637	−2.28038
$561$	−3.14009	−0.132575
$562$	−49.3439	−2.08145
$563$	−45.6782	−1.92511	−0.962554	−	0.271090i	$-0.912616\pi$
$563$	−45.6782	−1.92511	−0.962554	+	0.271090i	$0.912616\pi$
$564$	27.9524	1.17701
$565$	13.4891	0.567491
$566$	39.9278	1.67829
$567$	−44.3585	−1.86288
$568$	80.9001	3.39449
$569$	38.5463	1.61595	0.807973	−	0.589220i	$-0.200565\pi$
$569$	38.5463	1.61595	0.807973	+	0.589220i	$0.200565\pi$
$570$	37.0575	1.55217
$571$	−25.7229	−1.07647	−0.538235	−	0.842795i	$-0.680909\pi$
$571$	−25.7229	−1.07647	−0.538235	+	0.842795i	$0.680909\pi$
$572$	−7.76901	−0.324839
$573$	26.7836	1.11890
$574$	−110.641	−4.61806
$575$	−5.57491	−0.232490
$576$	47.8364	1.99318
$577$	31.7145	1.32029	0.660145	−	0.751138i	$-0.270495\pi$
$577$	31.7145	1.32029	0.660145	+	0.751138i	$0.270495\pi$
$578$	−44.7502	−1.86136
$579$	22.7836	0.946855
$580$	0	0
$581$	−34.6658	−1.43818
$582$	19.0207	0.788432
$583$	−30.2723	−1.25375
$584$	−79.3430	−3.28324
$585$	−1.51602	−0.0626798
$586$	4.21819	0.174252
$587$	37.5975	1.55181	0.775907	−	0.630847i	$-0.217293\pi$
$587$	37.5975	1.55181	0.775907	+	0.630847i	$0.217293\pi$
$588$	130.351	5.37560
$589$	0.942924	0.0388525
$590$	7.10160	0.292368
$591$	−11.9191	−0.490285
$592$	51.7190	2.12564
$593$	−36.2295	−1.48777	−0.743883	−	0.668310i	$-0.767018\pi$
$593$	−36.2295	−1.48777	−0.743883	+	0.668310i	$0.767018\pi$
$594$	9.25784	0.379854
$595$	−2.47268	−0.101370
$596$	−31.3091	−1.28247
$597$	−41.1814	−1.68544
$598$	−9.63492	−0.394001
$599$	3.48685	0.142469	0.0712344	−	0.997460i	$-0.477306\pi$
$599$	3.48685	0.142469	0.0712344	+	0.997460i	$0.477306\pi$
$600$	20.0113	0.816957
$601$	4.81746	0.196508	0.0982542	−	0.995161i	$-0.468674\pi$
$601$	4.81746	0.196508	0.0982542	+	0.995161i	$0.468674\pi$
$602$	−56.3888	−2.29823
$603$	−3.71164	−0.151150
$604$	−23.5160	−0.956853
$605$	5.64327	0.229432
$606$	−9.25784	−0.376074
$607$	−7.57626	−0.307511	−0.153756	−	0.988109i	$-0.549137\pi$
$607$	−7.57626	−0.307511	−0.153756	+	0.988109i	$0.549137\pi$
$608$	−101.779	−4.12770
$609$	0	0
$610$	−2.64327	−0.107023
$611$	1.48883	0.0602317
$612$	7.20893	0.291404
$613$	−4.15930	−0.167992	−0.0839962	−	0.996466i	$-0.526768\pi$
$613$	−4.15930	−0.167992	−0.0839962	+	0.996466i	$0.526768\pi$
$614$	12.5178	0.505179
$615$	22.5957	0.911145
$616$	−84.4113	−3.40103
$617$	−25.7246	−1.03563	−0.517817	−	0.855491i	$-0.673255\pi$
$617$	−25.7246	−1.03563	−0.517817	+	0.855491i	$0.673255\pi$
$618$	70.2520	2.82595
$619$	−31.1997	−1.25402	−0.627012	−	0.779010i	$-0.715722\pi$
$619$	−31.1997	−1.25402	−0.627012	+	0.779010i	$0.715722\pi$
$620$	0.825627	0.0331580
$621$	8.30011	0.333072
$622$	−58.1706	−2.33243
$623$	−30.7512	−1.23202
$624$	19.0468	0.762482
$625$	1.00000	0.0400000
$626$	30.5118	1.21949
$627$	31.9236	1.27490
$628$	88.4255	3.52856
$629$	2.36983	0.0944912
$630$	−26.7085	−1.06409
$631$	−22.1593	−0.882148	−0.441074	−	0.897471i	$-0.645402\pi$
$631$	−22.1593	−0.882148	−0.441074	+	0.897471i	$0.645402\pi$
$632$	−43.0208	−1.71127
$633$	43.6564	1.73519
$634$	25.1611	0.999275
$635$	−11.0934	−0.440230
$636$	157.967	6.26378
$637$	6.94292	0.275089
$638$	0	0
$639$	22.0512	0.872333
$640$	−20.3767	−0.805461
$641$	−22.3754	−0.883776	−0.441888	−	0.897070i	$-0.645691\pi$
$641$	−22.3754	−0.883776	−0.441888	+	0.897070i	$0.645691\pi$
$642$	−18.2295	−0.719460
$643$	20.1480	0.794560	0.397280	−	0.917697i	$-0.369954\pi$
$643$	20.1480	0.794560	0.397280	+	0.917697i	$0.369954\pi$
$644$	−122.711	−4.83549
$645$	11.5160	0.453443
$646$	−9.38574	−0.369277
$647$	−34.9542	−1.37419	−0.687096	−	0.726567i	$-0.741115\pi$
$647$	−34.9542	−1.37419	−0.687096	+	0.726567i	$0.741115\pi$
$648$	−90.9236	−3.57182
$649$	6.11775	0.240143
$650$	1.72826	0.0677881
$651$	−1.54468	−0.0605410
$652$	57.8876	2.26705
$653$	−17.3227	−0.677890	−0.338945	−	0.940806i	$-0.610070\pi$
$653$	−17.3227	−0.677890	−0.338945	+	0.940806i	$0.610070\pi$
$654$	106.204	4.15292
$655$	−7.13192	−0.278667
$656$	−124.897	−4.87640
$657$	−21.6268	−0.843742
$658$	26.2295	1.02253
$659$	−17.1851	−0.669435	−0.334718	−	0.942318i	$-0.608641\pi$
$659$	−17.1851	−0.669435	−0.334718	+	0.942318i	$0.608641\pi$
$660$	27.9524	1.08805
$661$	24.0891	0.936958	0.468479	−	0.883475i	$-0.344802\pi$
$661$	24.0891	0.936958	0.468479	+	0.883475i	$0.344802\pi$
$662$	−49.7342	−1.93297
$663$	0.872747	0.0338947
$664$	−71.0561	−2.75751
$665$	25.1384	0.974826
$666$	25.5975	0.991882
$667$	0	0
$668$	29.0909	1.12556
$669$	31.4186	1.21471
$670$	4.23127	0.163468
$671$	−2.27708	−0.0879056
$672$	166.734	6.43189
$673$	31.4495	1.21229	0.606144	−	0.795355i	$-0.292715\pi$
$673$	31.4495	1.21229	0.606144	+	0.795355i	$0.292715\pi$
$674$	−50.5404	−1.94674
$675$	−1.48883	−0.0573052
$676$	−65.6771	−2.52604
$677$	29.0187	1.11528	0.557640	−	0.830083i	$-0.311707\pi$
$677$	29.0187	1.11528	0.557640	+	0.830083i	$0.311707\pi$
$678$	−83.8778	−3.22131
$679$	12.9029	0.495168
$680$	−5.06836	−0.194363
$681$	16.2054	0.620993
$682$	0.983848	0.0376735
$683$	12.2884	0.470201	0.235101	−	0.971971i	$-0.424458\pi$
$683$	12.2884	0.470201	0.235101	+	0.971971i	$0.424458\pi$
$684$	−73.2893	−2.80229
$685$	−14.7894	−0.565074
$686$	42.9867	1.64124
$687$	−55.9048	−2.13290
$688$	−63.6544	−2.42680
$689$	8.41380	0.320540
$690$	34.6658	1.31971
$691$	−41.6753	−1.58540	−0.792702	−	0.609609i	$-0.791326\pi$
$691$	−41.6753	−1.58540	−0.792702	+	0.609609i	$0.791326\pi$
$692$	−40.6658	−1.54588
$693$	−23.0083	−0.874013
$694$	67.7881	2.57320
$695$	−3.56363	−0.135176
$696$	0	0
$697$	−5.72292	−0.216771
$698$	7.65748	0.289840
$699$	11.9191	0.450820
$700$	22.0113	0.831948
$701$	−27.8157	−1.05058	−0.525292	−	0.850922i	$-0.676044\pi$
$701$	−27.8157	−1.05058	−0.525292	+	0.850922i	$0.676044\pi$
$702$	−2.57310	−0.0971153
$703$	−24.0927	−0.908675
$704$	−46.9785	−1.77057
$705$	−5.35673	−0.201746
$706$	80.8492	3.04280
$707$	−6.28017	−0.236190
$708$	−31.9236	−1.19976
$709$	0.643274	0.0241587	0.0120793	−	0.999927i	$-0.496155\pi$
$709$	0.643274	0.0241587	0.0120793	+	0.999927i	$0.496155\pi$
$710$	−25.1384	−0.943428
$711$	−11.7263	−0.439771
$712$	−63.0320	−2.36223
$713$	0.882069	0.0330337
$714$	15.3756	0.575417
$715$	1.48883	0.0556792
$716$	23.1498	0.865150
$717$	33.8913	1.26569
$718$	−63.4571	−2.36820
$719$	21.2389	0.792079	0.396039	−	0.918233i	$-0.370384\pi$
$719$	21.2389	0.792079	0.396039	+	0.918233i	$0.370384\pi$
$720$	−30.1498	−1.12362
$721$	47.6564	1.77482
$722$	44.3731	1.65139
$723$	−4.62892	−0.172151
$724$	70.5291	2.62119
$725$	0	0
$726$	−35.0909	−1.30235
$727$	−19.0771	−0.707531	−0.353765	−	0.935334i	$-0.615099\pi$
$727$	−19.0771	−0.707531	−0.353765	+	0.935334i	$0.615099\pi$
$728$	23.4610	0.869524
$729$	−14.4458	−0.535031
$730$	24.6546	0.912506
$731$	−2.91672	−0.107879
$732$	11.8822	0.439179
$733$	39.4835	1.45836	0.729178	−	0.684324i	$-0.239903\pi$
$733$	39.4835	1.45836	0.729178	+	0.684324i	$0.239903\pi$
$734$	46.2408	1.70678
$735$	−24.9802	−0.921408
$736$	−95.2107	−3.50951
$737$	3.64507	0.134268
$738$	−61.8157	−2.27547
$739$	−5.95953	−0.219225	−0.109612	−	0.993974i	$-0.534961\pi$
$739$	−5.95953	−0.219225	−0.109612	+	0.993974i	$0.534961\pi$
$740$	−21.0957	−0.775493
$741$	−8.87275	−0.325948
$742$	148.230	5.44169
$743$	−18.0065	−0.660594	−0.330297	−	0.943877i	$-0.607149\pi$
$743$	−18.0065	−0.660594	−0.330297	+	0.943877i	$0.607149\pi$
$744$	−3.16621	−0.116079
$745$	6.00000	0.219823
$746$	61.4515	2.24990
$747$	−19.3680	−0.708638
$748$	−7.07965	−0.258858
$749$	−12.3662	−0.451851
$750$	−6.21819	−0.227056
$751$	−25.8623	−0.943727	−0.471864	−	0.881671i	$-0.656419\pi$
$751$	−25.8623	−0.943727	−0.471864	+	0.881671i	$0.656419\pi$
$752$	29.6091	1.07973
$753$	−52.3888	−1.90915
$754$	0	0
$755$	4.50655	0.164010
$756$	−32.7711	−1.19187
$757$	53.0193	1.92702	0.963509	−	0.267676i	$-0.0862555\pi$
$757$	53.0193	1.92702	0.963509	+	0.267676i	$0.0862555\pi$
$758$	73.2502	2.66057
$759$	29.8633	1.08397
$760$	51.5273	1.86909
$761$	−34.8953	−1.26495	−0.632477	−	0.774579i	$-0.717962\pi$
$761$	−34.8953	−1.26495	−0.632477	+	0.774579i	$0.717962\pi$
$762$	68.9811	2.49892
$763$	72.0451	2.60821
$764$	60.3864	2.18470
$765$	−1.38150	−0.0499483
$766$	−100.028	−3.61416
$767$	−1.70035	−0.0613961
$768$	32.7492	1.18174
$769$	−30.5888	−1.10306	−0.551530	−	0.834155i	$-0.685956\pi$
$769$	−30.5888	−1.10306	−0.551530	+	0.834155i	$0.685956\pi$
$770$	26.2295	0.945245
$771$	25.2747	0.910247
$772$	51.3680	1.84878
$773$	−11.9658	−0.430378	−0.215189	−	0.976572i	$-0.569037\pi$
$773$	−11.9658	−0.430378	−0.215189	+	0.976572i	$0.569037\pi$
$774$	−31.5047	−1.13241
$775$	−0.158221	−0.00568347
$776$	26.4477	0.949416
$777$	39.4684	1.41592
$778$	−63.5386	−2.27797
$779$	58.1819	2.08458
$780$	−7.76901	−0.278175
$781$	−21.6558	−0.774904
$782$	−8.78000	−0.313972
$783$	0	0
$784$	138.077	4.93133
$785$	−16.9456	−0.604816
$786$	44.3476	1.58183
$787$	21.2087	0.756009	0.378005	−	0.925804i	$-0.376610\pi$
$787$	21.2087	0.756009	0.378005	+	0.925804i	$0.376610\pi$
$788$	−26.8727	−0.957302
$789$	22.9619	0.817464
$790$	13.3680	0.475613
$791$	−56.8996	−2.02312
$792$	−47.1611	−1.67580
$793$	0.632884	0.0224744
$794$	−80.6607	−2.86254
$795$	−30.2723	−1.07365
$796$	−92.8477	−3.29090
$797$	8.32068	0.294734	0.147367	−	0.989082i	$-0.452920\pi$
$797$	8.32068	0.294734	0.147367	+	0.989082i	$0.452920\pi$
$798$	−156.315	−5.53350
$799$	1.35673	0.0479975
$800$	17.0784	0.603813
$801$	−17.1809	−0.607056
$802$	−86.9670	−3.07091
$803$	21.2389	0.749506
$804$	−19.0207	−0.670807
$805$	23.5160	0.828831
$806$	−0.273448	−0.00963179
$807$	28.7550	1.01222
$808$	−12.8727	−0.452862
$809$	23.4610	0.824846	0.412423	−	0.910992i	$-0.364683\pi$
$809$	23.4610	0.824846	0.412423	+	0.910992i	$0.364683\pi$
$810$	28.2531	0.992711
$811$	7.00947	0.246136	0.123068	−	0.992398i	$-0.460727\pi$
$811$	7.00947	0.246136	0.123068	+	0.992398i	$0.460727\pi$
$812$	0	0
$813$	63.1022	2.21309
$814$	−25.1384	−0.881101
$815$	−11.0934	−0.388586
$816$	17.3567	0.607607
$817$	29.6527	1.03742
$818$	65.8382	2.30198
$819$	6.39486	0.223455
$820$	50.9442	1.77905
$821$	−1.44584	−0.0504603	−0.0252302	−	0.999682i	$-0.508032\pi$
$821$	−1.44584	−0.0504603	−0.0252302	+	0.999682i	$0.508032\pi$
$822$	91.9632	3.20759
$823$	47.1671	1.64414	0.822070	−	0.569386i	$-0.192819\pi$
$823$	47.1671	1.64414	0.822070	+	0.569386i	$0.192819\pi$
$824$	97.6833	3.40296
$825$	−5.35673	−0.186497
$826$	−29.9559	−1.04230
$827$	20.1366	0.700219	0.350109	−	0.936709i	$-0.386144\pi$
$827$	20.1366	0.700219	0.350109	+	0.936709i	$0.386144\pi$
$828$	−68.5593	−2.38260
$829$	12.8011	0.444602	0.222301	−	0.974978i	$-0.428643\pi$
$829$	12.8011	0.444602	0.222301	+	0.974978i	$0.428643\pi$
$830$	22.0795	0.766392
$831$	−6.75904	−0.234468
$832$	13.0571	0.452673
$833$	6.32686	0.219213
$834$	22.1593	0.767314
$835$	−5.57491	−0.192928
$836$	71.9750	2.48931
$837$	0.235565	0.00814231
$838$	−16.7365	−0.578154
$839$	16.8341	0.581178	0.290589	−	0.956848i	$-0.406149\pi$
$839$	16.8341	0.581178	0.290589	+	0.956848i	$0.406149\pi$
$840$	−84.4113	−2.91247
$841$	0	0
$842$	−88.4113	−3.04686
$843$	−42.5078	−1.46405
$844$	98.4278	3.38802
$845$	12.5862	0.432978
$846$	14.6546	0.503834
$847$	−23.8044	−0.817928
$848$	167.329	5.74611
$849$	34.3963	1.18048
$850$	1.57491	0.0540190
$851$	−22.5378	−0.772587
$852$	113.004	3.87145
$853$	40.1164	1.37356	0.686779	−	0.726866i	$-0.259024\pi$
$853$	40.1164	1.37356	0.686779	+	0.726866i	$0.259024\pi$
$854$	11.1498	0.381539
$855$	14.0450	0.480328
$856$	−25.3475	−0.866361
$857$	15.2389	0.520552	0.260276	−	0.965534i	$-0.416186\pi$
$857$	15.2389	0.520552	0.260276	+	0.965534i	$0.416186\pi$
$858$	−9.25784	−0.316057
$859$	10.7770	0.367706	0.183853	−	0.982954i	$-0.441143\pi$
$859$	10.7770	0.367706	0.183853	+	0.982954i	$0.441143\pi$
$860$	25.9640	0.885367
$861$	−95.3128	−3.24825
$862$	8.08545	0.275392
$863$	32.1004	1.09271	0.546355	−	0.837554i	$-0.316015\pi$
$863$	32.1004	1.09271	0.546355	+	0.837554i	$0.316015\pi$
$864$	−25.4269	−0.865041
$865$	7.79310	0.264973
$866$	−92.1932	−3.13285
$867$	−38.5505	−1.30924
$868$	−3.48265	−0.118209
$869$	11.5160	0.390654
$870$	0	0
$871$	−1.01310	−0.0343276
$872$	147.674	5.00087
$873$	7.20893	0.243985
$874$	89.2615	3.01932
$875$	−4.21819	−0.142601
$876$	−110.829	−3.74456
$877$	28.2520	0.954004	0.477002	−	0.878902i	$-0.341723\pi$
$877$	28.2520	0.954004	0.477002	+	0.878902i	$0.341723\pi$
$878$	−80.1048	−2.70341
$879$	3.63380	0.122565
$880$	29.6091	0.998123
$881$	−8.59043	−0.289419	−0.144710	−	0.989474i	$-0.546225\pi$
$881$	−8.59043	−0.289419	−0.144710	+	0.989474i	$0.546225\pi$
$882$	68.3391	2.30110
$883$	34.7913	1.17082	0.585410	−	0.810737i	$-0.300934\pi$
$883$	34.7913	1.17082	0.585410	+	0.810737i	$0.300934\pi$
$884$	1.96770	0.0661808
$885$	6.11775	0.205646
$886$	−75.1135	−2.52349
$887$	−40.3558	−1.35501	−0.677507	−	0.735516i	$-0.736940\pi$
$887$	−40.3558	−1.35501	−0.677507	+	0.735516i	$0.736940\pi$
$888$	80.9001	2.71483
$889$	46.7942	1.56943
$890$	19.5862	0.656531
$891$	24.3389	0.815384
$892$	70.8364	2.37178
$893$	−13.7931	−0.461568
$894$	−37.3091	−1.24780
$895$	−4.43637	−0.148292
$896$	85.9528	2.87148
$897$	−8.30011	−0.277133
$898$	11.4934	0.383541
$899$	0	0
$900$	12.2978	0.409928
$901$	7.66723	0.255432
$902$	60.7071	2.02132
$903$	−48.5767	−1.61653
$904$	−116.630	−3.87904
$905$	−13.5160	−0.449288
$906$	−28.0226	−0.930988
$907$	−8.59463	−0.285380	−0.142690	−	0.989767i	$-0.545575\pi$
$907$	−8.59463	−0.285380	−0.142690	+	0.989767i	$0.545575\pi$
$908$	36.5368	1.21252
$909$	−3.50877	−0.116379
$910$	−7.29014	−0.241666
$911$	12.9332	0.428497	0.214249	−	0.976779i	$-0.431270\pi$
$911$	12.9332	0.428497	0.214249	+	0.976779i	$0.431270\pi$
$912$	−176.456	−5.84306
$913$	19.0207	0.629492
$914$	27.8505	0.921214
$915$	−2.27708	−0.0752779
$916$	−126.043	−4.16458
$917$	30.0838	0.993454
$918$	−2.34478	−0.0773893
$919$	52.1153	1.71913	0.859563	−	0.511030i	$-0.170736\pi$
$919$	52.1153	1.71913	0.859563	+	0.511030i	$0.170736\pi$
$920$	48.2018	1.58917
$921$	10.7836	0.355333
$922$	35.1724	1.15834
$923$	6.01894	0.198116
$924$	−117.908	−3.87890
$925$	4.04272	0.132924
$926$	89.8882	2.95391
$927$	26.6259	0.874509
$928$	0	0
$929$	−26.5993	−0.872695	−0.436347	−	0.899778i	$-0.643728\pi$
$929$	−26.5993	−0.872695	−0.436347	+	0.899778i	$0.643728\pi$
$930$	0.983848	0.0322617
$931$	−64.3218	−2.10806
$932$	26.8727	0.880246
$933$	−50.1117	−1.64058
$934$	−87.5499	−2.86472
$935$	1.35673	0.0443697
$936$	13.1078	0.428443
$937$	14.5291	0.474646	0.237323	−	0.971431i	$-0.423730\pi$
$937$	14.5291	0.474646	0.237323	+	0.971431i	$0.423730\pi$
$938$	−17.8483	−0.582767
$939$	26.2847	0.857768
$940$	−12.0773	−0.393918
$941$	−3.14619	−0.102563	−0.0512815	−	0.998684i	$-0.516331\pi$
$941$	−3.14619	−0.102563	−0.0512815	+	0.998684i	$0.516331\pi$
$942$	105.371	3.43318
$943$	54.4269	1.77238
$944$	−33.8157	−1.10061
$945$	6.28017	0.204294
$946$	30.9397	1.00594
$947$	51.7960	1.68314	0.841572	−	0.540145i	$-0.181631\pi$
$947$	51.7960	1.68314	0.841572	+	0.540145i	$0.181631\pi$
$948$	−60.0927	−1.95172
$949$	−5.90309	−0.191622
$950$	−16.0113	−0.519475
$951$	21.6753	0.702870
$952$	21.3793	0.692907
$953$	−10.5542	−0.341883	−0.170941	−	0.985281i	$-0.554681\pi$
$953$	−10.5542	−0.341883	−0.170941	+	0.985281i	$0.554681\pi$
$954$	82.8169	2.68130
$955$	−11.5723	−0.374471
$956$	76.4113	2.47132
$957$	0	0
$958$	98.1230	3.17021
$959$	62.3844	2.01450
$960$	−46.9785	−1.51623
$961$	−30.9750	−0.999192
$962$	6.98690	0.225267
$963$	−6.90907	−0.222642
$964$	−10.4364	−0.336133
$965$	−9.84404	−0.316891
$966$	−146.227	−4.70478
$967$	21.0448	0.676755	0.338378	−	0.941010i	$-0.390122\pi$
$967$	21.0448	0.676755	0.338378	+	0.941010i	$0.390122\pi$
$968$	−48.7929	−1.56826
$969$	−8.08545	−0.259742
$970$	−8.21819	−0.263870
$971$	−1.01417	−0.0325462	−0.0162731	−	0.999868i	$-0.505180\pi$
$971$	−1.01417	−0.0325462	−0.0162731	+	0.999868i	$0.505180\pi$
$972$	−103.698	−3.32611
$973$	15.0320	0.481905
$974$	69.6952	2.23318
$975$	1.48883	0.0476808
$976$	12.5865	0.402883
$977$	9.95239	0.318405	0.159203	−	0.987246i	$-0.449108\pi$
$977$	9.95239	0.318405	0.159203	+	0.987246i	$0.449108\pi$
$978$	68.9811	2.20577
$979$	16.8727	0.539255
$980$	−56.3204	−1.79909
$981$	40.2520	1.28515
$982$	−70.7699	−2.25836
$983$	−15.4059	−0.491372	−0.245686	−	0.969349i	$-0.579013\pi$
$983$	−15.4059	−0.491372	−0.245686	+	0.969349i	$0.579013\pi$
$984$	−195.367	−6.22806
$985$	5.14982	0.164087
$986$	0	0
$987$	22.5957	0.719228
$988$	−20.0045	−0.636428
$989$	27.7390	0.882049
$990$	14.6546	0.465752
$991$	8.92035	0.283364	0.141682	−	0.989912i	$-0.454749\pi$
$991$	8.92035	0.283364	0.141682	+	0.989912i	$0.454749\pi$
$992$	−2.70217	−0.0857938
$993$	−42.8441	−1.35962
$994$	106.039	3.36334
$995$	17.7931	0.564079
$996$	−99.2534	−3.14496
$997$	1.19296	0.0377814	0.0188907	−	0.999822i	$-0.493987\pi$
$997$	1.19296	0.0377814	0.0188907	+	0.999822i	$0.493987\pi$
$998$	56.4552	1.78706
$999$	−6.01894	−0.190431

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4205.2.a.m.1.6		6
29.12	odd	4		145.2.c.b.86.6	yes	6
29.17	odd	4		145.2.c.b.86.1	✓	6
29.28	even	2	inner	4205.2.a.m.1.1		6
87.17	even	4		1305.2.d.b.811.6		6
87.41	even	4		1305.2.d.b.811.1		6
116.75	even	4		2320.2.g.i.1681.5		6
116.99	even	4		2320.2.g.i.1681.2		6
145.12	even	4		725.2.d.c.724.2		12
145.17	even	4		725.2.d.c.724.12		12
145.99	odd	4		725.2.c.e.376.1		6
145.104	odd	4		725.2.c.e.376.6		6
145.128	even	4		725.2.d.c.724.11		12
145.133	even	4		725.2.d.c.724.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.2.c.b.86.1	✓	6	29.17	odd	4
145.2.c.b.86.6	yes	6	29.12	odd	4
725.2.c.e.376.1		6	145.99	odd	4
725.2.c.e.376.6		6	145.104	odd	4
725.2.d.c.724.1		12	145.133	even	4
725.2.d.c.724.2		12	145.12	even	4
725.2.d.c.724.11		12	145.128	even	4
725.2.d.c.724.12		12	145.17	even	4
1305.2.d.b.811.1		6	87.41	even	4
1305.2.d.b.811.6		6	87.17	even	4
2320.2.g.i.1681.2		6	116.99	even	4
2320.2.g.i.1681.5		6	116.75	even	4
4205.2.a.m.1.1		6	29.28	even	2	inner
4205.2.a.m.1.6		6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4205 = 5 \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4205.a (trivial)

\(f(q)\)	\(=\)	\(q+2.68667 q^{2} +2.31446 q^{3} +5.21819 q^{4} -1.00000 q^{5} +6.21819 q^{6} +4.21819 q^{7} +8.64620 q^{8} +2.35673 q^{9} +O(q^{10})\)	\(q+2.68667 q^{2} +2.31446 q^{3} +5.21819 q^{4} -1.00000 q^{5} +6.21819 q^{6} +4.21819 q^{7} +8.64620 q^{8} +2.35673 q^{9} -2.68667 q^{10} -2.31446 q^{11} +12.0773 q^{12} +0.643274 q^{13} +11.3329 q^{14} -2.31446 q^{15} +12.7931 q^{16} +0.586195 q^{17} +6.33174 q^{18} -5.95953 q^{19} -5.21819 q^{20} +9.76282 q^{21} -6.21819 q^{22} -5.57491 q^{23} +20.0113 q^{24} +1.00000 q^{25} +1.72826 q^{26} -1.48883 q^{27} +22.0113 q^{28} -6.21819 q^{30} -0.158221 q^{31} +17.0784 q^{32} -5.35673 q^{33} +1.57491 q^{34} -4.21819 q^{35} +12.2978 q^{36} +4.04272 q^{37} -16.0113 q^{38} +1.48883 q^{39} -8.64620 q^{40} -9.76282 q^{41} +26.2295 q^{42} -4.97568 q^{43} -12.0773 q^{44} -2.35673 q^{45} -14.9779 q^{46} +2.31446 q^{47} +29.6091 q^{48} +10.7931 q^{49} +2.68667 q^{50} +1.35673 q^{51} +3.35673 q^{52} +13.0796 q^{53} -4.00000 q^{54} +2.31446 q^{55} +36.4713 q^{56} -13.7931 q^{57} -2.64327 q^{59} -12.0773 q^{60} +0.983848 q^{61} -0.425088 q^{62} +9.94111 q^{63} +20.2978 q^{64} -0.643274 q^{65} -14.3917 q^{66} -1.57491 q^{67} +3.05888 q^{68} -12.9029 q^{69} -11.3329 q^{70} +9.35673 q^{71} +20.3767 q^{72} -9.17663 q^{73} +10.8615 q^{74} +2.31446 q^{75} -31.0980 q^{76} -9.76282 q^{77} +4.00000 q^{78} -4.97568 q^{79} -12.7931 q^{80} -10.5160 q^{81} -26.2295 q^{82} -8.21819 q^{83} +50.9442 q^{84} -0.586195 q^{85} -13.3680 q^{86} -20.0113 q^{88} -7.29014 q^{89} -6.33174 q^{90} +2.71345 q^{91} -29.0909 q^{92} -0.366196 q^{93} +6.21819 q^{94} +5.95953 q^{95} +39.5273 q^{96} +3.05888 q^{97} +28.9975 q^{98} -5.45455 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{4} - 6 q^{5} + 12 q^{6} + 14 q^{9}+O(q^{10}) \) 6 * q + 6 * q^4 - 6 * q^5 + 12 * q^6 + 14 * q^9	\( 6 q + 6 q^{4} - 6 q^{5} + 12 q^{6} + 14 q^{9} + 4 q^{13} + 26 q^{16} - 6 q^{20} - 12 q^{22} - 8 q^{23} + 44 q^{24} + 6 q^{25} + 56 q^{28} - 12 q^{30} - 32 q^{33} - 16 q^{34} - 2 q^{36} - 20 q^{38} + 56 q^{42} - 14 q^{45} + 14 q^{49} + 8 q^{51} + 20 q^{52} + 28 q^{53} - 24 q^{54} - 32 q^{57} - 16 q^{59} - 28 q^{62} - 16 q^{63} + 46 q^{64} - 4 q^{65} + 16 q^{67} + 56 q^{71} + 40 q^{74} + 24 q^{78} - 26 q^{80} + 38 q^{81} - 56 q^{82} - 24 q^{83} - 4 q^{86} - 44 q^{88} + 16 q^{91} - 48 q^{92} + 48 q^{93} + 12 q^{94} + 60 q^{96}+O(q^{100}) \) 6 * q + 6 * q^4 - 6 * q^5 + 12 * q^6 + 14 * q^9 + 4 * q^13 + 26 * q^16 - 6 * q^20 - 12 * q^22 - 8 * q^23 + 44 * q^24 + 6 * q^25 + 56 * q^28 - 12 * q^30 - 32 * q^33 - 16 * q^34 - 2 * q^36 - 20 * q^38 + 56 * q^42 - 14 * q^45 + 14 * q^49 + 8 * q^51 + 20 * q^52 + 28 * q^53 - 24 * q^54 - 32 * q^57 - 16 * q^59 - 28 * q^62 - 16 * q^63 + 46 * q^64 - 4 * q^65 + 16 * q^67 + 56 * q^71 + 40 * q^74 + 24 * q^78 - 26 * q^80 + 38 * q^81 - 56 * q^82 - 24 * q^83 - 4 * q^86 - 44 * q^88 + 16 * q^91 - 48 * q^92 + 48 * q^93 + 12 * q^94 + 60 * q^96

Introduction

L-functions

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Database

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