LMFDB - Embedded newform 6026.2.a.j.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, 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("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$0$
Dimension:	$33$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.31184 q^{3} +1.00000 q^{4} -1.83764 q^{5} +2.31184 q^{6} +0.291912 q^{7} -1.00000 q^{8} +2.34459 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.31184 q^{3} +1.00000 q^{4} -1.83764 q^{5} +2.31184 q^{6} +0.291912 q^{7} -1.00000 q^{8} +2.34459 q^{9} +1.83764 q^{10} -0.391390 q^{11} -2.31184 q^{12} +0.600528 q^{13} -0.291912 q^{14} +4.24832 q^{15} +1.00000 q^{16} +8.06571 q^{17} -2.34459 q^{18} -1.02842 q^{19} -1.83764 q^{20} -0.674854 q^{21} +0.391390 q^{22} +1.00000 q^{23} +2.31184 q^{24} -1.62309 q^{25} -0.600528 q^{26} +1.51520 q^{27} +0.291912 q^{28} +6.44707 q^{29} -4.24832 q^{30} +9.49895 q^{31} -1.00000 q^{32} +0.904830 q^{33} -8.06571 q^{34} -0.536429 q^{35} +2.34459 q^{36} +5.12747 q^{37} +1.02842 q^{38} -1.38832 q^{39} +1.83764 q^{40} -5.09126 q^{41} +0.674854 q^{42} -4.74073 q^{43} -0.391390 q^{44} -4.30851 q^{45} -1.00000 q^{46} -1.05671 q^{47} -2.31184 q^{48} -6.91479 q^{49} +1.62309 q^{50} -18.6466 q^{51} +0.600528 q^{52} -4.00089 q^{53} -1.51520 q^{54} +0.719233 q^{55} -0.291912 q^{56} +2.37754 q^{57} -6.44707 q^{58} +9.67887 q^{59} +4.24832 q^{60} +0.715006 q^{61} -9.49895 q^{62} +0.684415 q^{63} +1.00000 q^{64} -1.10355 q^{65} -0.904830 q^{66} +13.1299 q^{67} +8.06571 q^{68} -2.31184 q^{69} +0.536429 q^{70} -5.39996 q^{71} -2.34459 q^{72} -5.19493 q^{73} -5.12747 q^{74} +3.75231 q^{75} -1.02842 q^{76} -0.114252 q^{77} +1.38832 q^{78} +13.6192 q^{79} -1.83764 q^{80} -10.5367 q^{81} +5.09126 q^{82} -15.0036 q^{83} -0.674854 q^{84} -14.8218 q^{85} +4.74073 q^{86} -14.9046 q^{87} +0.391390 q^{88} +3.64262 q^{89} +4.30851 q^{90} +0.175301 q^{91} +1.00000 q^{92} -21.9600 q^{93} +1.05671 q^{94} +1.88986 q^{95} +2.31184 q^{96} +5.12604 q^{97} +6.91479 q^{98} -0.917649 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 33 q - 33 q^{2} + 3 q^{3} + 33 q^{4} - 4 q^{5} - 3 q^{6} + 11 q^{7} - 33 q^{8} + 44 q^{9}+O(q^{10}) $ 33 * q - 33 * q^2 + 3 * q^3 + 33 * q^4 - 4 * q^5 - 3 * q^6 + 11 * q^7 - 33 * q^8 + 44 * q^9	\( 33 q - 33 q^{2} + 3 q^{3} + 33 q^{4} - 4 q^{5} - 3 q^{6} + 11 q^{7} - 33 q^{8} + 44 q^{9} + 4 q^{10} + 5 q^{11} + 3 q^{12} + 15 q^{13} - 11 q^{14} + 16 q^{15} + 33 q^{16} + 2 q^{17} - 44 q^{18} + 32 q^{19} - 4 q^{20} + 8 q^{21} - 5 q^{22} + 33 q^{23} - 3 q^{24} + 49 q^{25} - 15 q^{26} + 15 q^{27} + 11 q^{28} + 20 q^{29} - 16 q^{30} + 25 q^{31} - 33 q^{32} - 6 q^{33} - 2 q^{34} + 15 q^{35} + 44 q^{36} + 6 q^{37} - 32 q^{38} + 25 q^{39} + 4 q^{40} + 2 q^{41} - 8 q^{42} + 31 q^{43} + 5 q^{44} + 2 q^{45} - 33 q^{46} + 4 q^{47} + 3 q^{48} + 72 q^{49} - 49 q^{50} + 26 q^{51} + 15 q^{52} - 65 q^{53} - 15 q^{54} - 4 q^{55} - 11 q^{56} + 12 q^{57} - 20 q^{58} + 8 q^{59} + 16 q^{60} + 23 q^{61} - 25 q^{62} - 14 q^{63} + 33 q^{64} + 5 q^{65} + 6 q^{66} + 31 q^{67} + 2 q^{68} + 3 q^{69} - 15 q^{70} + 20 q^{71} - 44 q^{72} + 22 q^{73} - 6 q^{74} - 32 q^{75} + 32 q^{76} + 2 q^{77} - 25 q^{78} + 53 q^{79} - 4 q^{80} + 17 q^{81} - 2 q^{82} + 45 q^{83} + 8 q^{84} + 60 q^{85} - 31 q^{86} + 11 q^{87} - 5 q^{88} - 54 q^{89} - 2 q^{90} + 38 q^{91} + 33 q^{92} + 63 q^{93} - 4 q^{94} + 44 q^{95} - 3 q^{96} - 72 q^{98} + 43 q^{99}+O(q^{100}) \) 33 * q - 33 * q^2 + 3 * q^3 + 33 * q^4 - 4 * q^5 - 3 * q^6 + 11 * q^7 - 33 * q^8 + 44 * q^9 + 4 * q^10 + 5 * q^11 + 3 * q^12 + 15 * q^13 - 11 * q^14 + 16 * q^15 + 33 * q^16 + 2 * q^17 - 44 * q^18 + 32 * q^19 - 4 * q^20 + 8 * q^21 - 5 * q^22 + 33 * q^23 - 3 * q^24 + 49 * q^25 - 15 * q^26 + 15 * q^27 + 11 * q^28 + 20 * q^29 - 16 * q^30 + 25 * q^31 - 33 * q^32 - 6 * q^33 - 2 * q^34 + 15 * q^35 + 44 * q^36 + 6 * q^37 - 32 * q^38 + 25 * q^39 + 4 * q^40 + 2 * q^41 - 8 * q^42 + 31 * q^43 + 5 * q^44 + 2 * q^45 - 33 * q^46 + 4 * q^47 + 3 * q^48 + 72 * q^49 - 49 * q^50 + 26 * q^51 + 15 * q^52 - 65 * q^53 - 15 * q^54 - 4 * q^55 - 11 * q^56 + 12 * q^57 - 20 * q^58 + 8 * q^59 + 16 * q^60 + 23 * q^61 - 25 * q^62 - 14 * q^63 + 33 * q^64 + 5 * q^65 + 6 * q^66 + 31 * q^67 + 2 * q^68 + 3 * q^69 - 15 * q^70 + 20 * q^71 - 44 * q^72 + 22 * q^73 - 6 * q^74 - 32 * q^75 + 32 * q^76 + 2 * q^77 - 25 * q^78 + 53 * q^79 - 4 * q^80 + 17 * q^81 - 2 * q^82 + 45 * q^83 + 8 * q^84 + 60 * q^85 - 31 * q^86 + 11 * q^87 - 5 * q^88 - 54 * q^89 - 2 * q^90 + 38 * q^91 + 33 * q^92 + 63 * q^93 - 4 * q^94 + 44 * q^95 - 3 * q^96 - 72 * q^98 + 43 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.31184	−1.33474	−0.667370	−	0.744726i	$-0.732580\pi$
$3$	−2.31184	−1.33474	−0.667370	+	0.744726i	$0.732580\pi$
$4$	1.00000	0.500000
$5$	−1.83764	−0.821817	−0.410908	−	0.911677i	$-0.634788\pi$
$5$	−1.83764	−0.821817	−0.410908	+	0.911677i	$0.634788\pi$
$6$	2.31184	0.943803
$7$	0.291912	0.110332	0.0551662	−	0.998477i	$-0.482431\pi$
$7$	0.291912	0.110332	0.0551662	+	0.998477i	$0.482431\pi$
$8$	−1.00000	−0.353553
$9$	2.34459	0.781530
$10$	1.83764	0.581112
$11$	−0.391390	−0.118009	−0.0590043	−	0.998258i	$-0.518793\pi$
$11$	−0.391390	−0.118009	−0.0590043	+	0.998258i	$0.518793\pi$
$12$	−2.31184	−0.667370
$13$	0.600528	0.166556	0.0832782	−	0.996526i	$-0.473461\pi$
$13$	0.600528	0.166556	0.0832782	+	0.996526i	$0.473461\pi$
$14$	−0.291912	−0.0780168
$15$	4.24832	1.09691
$16$	1.00000	0.250000
$17$	8.06571	1.95622	0.978110	−	0.208086i	$-0.0667235\pi$
$17$	8.06571	1.95622	0.978110	+	0.208086i	$0.0667235\pi$
$18$	−2.34459	−0.552625
$19$	−1.02842	−0.235935	−0.117968	−	0.993017i	$-0.537638\pi$
$19$	−1.02842	−0.235935	−0.117968	+	0.993017i	$0.537638\pi$
$20$	−1.83764	−0.410908
$21$	−0.674854	−0.147265
$22$	0.391390	0.0834447
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	2.31184	0.471902
$25$	−1.62309	−0.324617
$26$	−0.600528	−0.117773
$27$	1.51520	0.291600
$28$	0.291912	0.0551662
$29$	6.44707	1.19719	0.598596	−	0.801051i	$-0.295726\pi$
$29$	6.44707	1.19719	0.598596	+	0.801051i	$0.295726\pi$
$30$	−4.24832	−0.775633
$31$	9.49895	1.70606	0.853031	−	0.521861i	$-0.174762\pi$
$31$	9.49895	1.70606	0.853031	+	0.521861i	$0.174762\pi$
$32$	−1.00000	−0.176777
$33$	0.904830	0.157511
$34$	−8.06571	−1.38326
$35$	−0.536429	−0.0906731
$36$	2.34459	0.390765
$37$	5.12747	0.842951	0.421476	−	0.906840i	$-0.361512\pi$
$37$	5.12747	0.842951	0.421476	+	0.906840i	$0.361512\pi$
$38$	1.02842	0.166831
$39$	−1.38832	−0.222309
$40$	1.83764	0.290556
$41$	−5.09126	−0.795122	−0.397561	−	0.917576i	$-0.630143\pi$
$41$	−5.09126	−0.795122	−0.397561	+	0.917576i	$0.630143\pi$
$42$	0.674854	0.104132
$43$	−4.74073	−0.722954	−0.361477	−	0.932381i	$-0.617727\pi$
$43$	−4.74073	−0.722954	−0.361477	+	0.932381i	$0.617727\pi$
$44$	−0.391390	−0.0590043
$45$	−4.30851	−0.642274
$46$	−1.00000	−0.147442
$47$	−1.05671	−0.154137	−0.0770685	−	0.997026i	$-0.524556\pi$
$47$	−1.05671	−0.154137	−0.0770685	+	0.997026i	$0.524556\pi$
$48$	−2.31184	−0.333685
$49$	−6.91479	−0.987827
$50$	1.62309	0.229539
$51$	−18.6466	−2.61105
$52$	0.600528	0.0832782
$53$	−4.00089	−0.549564	−0.274782	−	0.961507i	$-0.588606\pi$
$53$	−4.00089	−0.549564	−0.274782	+	0.961507i	$0.588606\pi$
$54$	−1.51520	−0.206193
$55$	0.719233	0.0969814
$56$	−0.291912	−0.0390084
$57$	2.37754	0.314912
$58$	−6.44707	−0.846542
$59$	9.67887	1.26008	0.630041	−	0.776562i	$-0.283038\pi$
$59$	9.67887	1.26008	0.630041	+	0.776562i	$0.283038\pi$
$60$	4.24832	0.548456
$61$	0.715006	0.0915471	0.0457736	−	0.998952i	$-0.485425\pi$
$61$	0.715006	0.0915471	0.0457736	+	0.998952i	$0.485425\pi$
$62$	−9.49895	−1.20637
$63$	0.684415	0.0862281
$64$	1.00000	0.125000
$65$	−1.10355	−0.136879
$66$	−0.904830	−0.111377
$67$	13.1299	1.60407	0.802035	−	0.597277i	$-0.203751\pi$
$67$	13.1299	1.60407	0.802035	+	0.597277i	$0.203751\pi$
$68$	8.06571	0.978110
$69$	−2.31184	−0.278312
$70$	0.536429	0.0641155
$71$	−5.39996	−0.640858	−0.320429	−	0.947273i	$-0.603827\pi$
$71$	−5.39996	−0.640858	−0.320429	+	0.947273i	$0.603827\pi$
$72$	−2.34459	−0.276313
$73$	−5.19493	−0.608020	−0.304010	−	0.952669i	$-0.598326\pi$
$73$	−5.19493	−0.608020	−0.304010	+	0.952669i	$0.598326\pi$
$74$	−5.12747	−0.596056
$75$	3.75231	0.433280
$76$	−1.02842	−0.117968
$77$	−0.114252	−0.0130202
$78$	1.38832	0.157197
$79$	13.6192	1.53228	0.766139	−	0.642675i	$-0.222176\pi$
$79$	13.6192	1.53228	0.766139	+	0.642675i	$0.222176\pi$
$80$	−1.83764	−0.205454
$81$	−10.5367	−1.17074
$82$	5.09126	0.562236
$83$	−15.0036	−1.64686	−0.823428	−	0.567421i	$-0.807941\pi$
$83$	−15.0036	−1.64686	−0.823428	+	0.567421i	$0.807941\pi$
$84$	−0.674854	−0.0736326
$85$	−14.8218	−1.60765
$86$	4.74073	0.511206
$87$	−14.9046	−1.59794
$88$	0.391390	0.0417223
$89$	3.64262	0.386117	0.193058	−	0.981187i	$-0.438159\pi$
$89$	3.64262	0.386117	0.193058	+	0.981187i	$0.438159\pi$
$90$	4.30851	0.454157
$91$	0.175301	0.0183766
$92$	1.00000	0.104257
$93$	−21.9600	−2.27715
$94$	1.05671	0.108991
$95$	1.88986	0.193896
$96$	2.31184	0.235951
$97$	5.12604	0.520470	0.260235	−	0.965545i	$-0.416200\pi$
$97$	5.12604	0.520470	0.260235	+	0.965545i	$0.416200\pi$
$98$	6.91479	0.698499
$99$	−0.917649	−0.0922272
$100$	−1.62309	−0.162309
$101$	−9.66843	−0.962044	−0.481022	−	0.876708i	$-0.659734\pi$
$101$	−9.66843	−0.962044	−0.481022	+	0.876708i	$0.659734\pi$
$102$	18.6466	1.84629
$103$	−10.9862	−1.08251	−0.541253	−	0.840860i	$-0.682050\pi$
$103$	−10.9862	−1.08251	−0.541253	+	0.840860i	$0.682050\pi$
$104$	−0.600528	−0.0588866
$105$	1.24014	0.121025
$106$	4.00089	0.388600
$107$	14.1778	1.37062	0.685309	−	0.728253i	$-0.259667\pi$
$107$	14.1778	1.37062	0.685309	+	0.728253i	$0.259667\pi$
$108$	1.51520	0.145800
$109$	19.1852	1.83761	0.918805	−	0.394711i	$-0.129155\pi$
$109$	19.1852	1.83761	0.918805	+	0.394711i	$0.129155\pi$
$110$	−0.719233	−0.0685762
$111$	−11.8539	−1.12512
$112$	0.291912	0.0275831
$113$	−7.68528	−0.722970	−0.361485	−	0.932378i	$-0.617730\pi$
$113$	−7.68528	−0.722970	−0.361485	+	0.932378i	$0.617730\pi$
$114$	−2.37754	−0.222677
$115$	−1.83764	−0.171361
$116$	6.44707	0.598596
$117$	1.40799	0.130169
$118$	−9.67887	−0.891013
$119$	2.35448	0.215835
$120$	−4.24832	−0.387817
$121$	−10.8468	−0.986074
$122$	−0.715006	−0.0647336
$123$	11.7702	1.06128
$124$	9.49895	0.853031
$125$	12.1708	1.08859
$126$	−0.684415	−0.0609725
$127$	−4.61410	−0.409436	−0.204718	−	0.978821i	$-0.565628\pi$
$127$	−4.61410	−0.409436	−0.204718	+	0.978821i	$0.565628\pi$
$128$	−1.00000	−0.0883883
$129$	10.9598	0.964956
$130$	1.10355	0.0967879
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	0.904830	0.0787554
$133$	−0.300208	−0.0260313
$134$	−13.1299	−1.13425
$135$	−2.78439	−0.239642
$136$	−8.06571	−0.691629
$137$	−6.11296	−0.522265	−0.261133	−	0.965303i	$-0.584096\pi$
$137$	−6.11296	−0.522265	−0.261133	+	0.965303i	$0.584096\pi$
$138$	2.31184	0.196797
$139$	14.7533	1.25136	0.625679	−	0.780080i	$-0.284822\pi$
$139$	14.7533	1.25136	0.625679	+	0.780080i	$0.284822\pi$
$140$	−0.536429	−0.0453365
$141$	2.44294	0.205733
$142$	5.39996	0.453155
$143$	−0.235041	−0.0196551
$144$	2.34459	0.195383
$145$	−11.8474	−0.983872
$146$	5.19493	0.429935
$147$	15.9859	1.31849
$148$	5.12747	0.421476
$149$	−2.61721	−0.214410	−0.107205	−	0.994237i	$-0.534190\pi$
$149$	−2.61721	−0.214410	−0.107205	+	0.994237i	$0.534190\pi$
$150$	−3.75231	−0.306375
$151$	−22.7375	−1.85035	−0.925175	−	0.379542i	$-0.876082\pi$
$151$	−22.7375	−1.85035	−0.925175	+	0.379542i	$0.876082\pi$
$152$	1.02842	0.0834157
$153$	18.9108	1.52885
$154$	0.114252	0.00920666
$155$	−17.4556	−1.40207
$156$	−1.38832	−0.111155
$157$	−5.75420	−0.459235	−0.229618	−	0.973281i	$-0.573748\pi$
$157$	−5.75420	−0.459235	−0.229618	+	0.973281i	$0.573748\pi$
$158$	−13.6192	−1.08348
$159$	9.24939	0.733525
$160$	1.83764	0.145278
$161$	0.291912	0.0230059
$162$	10.5367	0.827839
$163$	17.6530	1.38269	0.691346	−	0.722524i	$-0.257018\pi$
$163$	17.6530	1.38269	0.691346	+	0.722524i	$0.257018\pi$
$164$	−5.09126	−0.397561
$165$	−1.66275	−0.129445
$166$	15.0036	1.16450
$167$	−3.15337	−0.244015	−0.122008	−	0.992529i	$-0.538933\pi$
$167$	−3.15337	−0.244015	−0.122008	+	0.992529i	$0.538933\pi$
$168$	0.674854	0.0520661
$169$	−12.6394	−0.972259
$170$	14.8218	1.13678
$171$	−2.41122	−0.184391
$172$	−4.74073	−0.361477
$173$	−0.767044	−0.0583172	−0.0291586	−	0.999575i	$-0.509283\pi$
$173$	−0.767044	−0.0583172	−0.0291586	+	0.999575i	$0.509283\pi$
$174$	14.9046	1.12991
$175$	−0.473799	−0.0358159
$176$	−0.391390	−0.0295021
$177$	−22.3760	−1.68188
$178$	−3.64262	−0.273026
$179$	−19.8829	−1.48612	−0.743060	−	0.669225i	$-0.766626\pi$
$179$	−19.8829	−1.48612	−0.743060	+	0.669225i	$0.766626\pi$
$180$	−4.30851	−0.321137
$181$	12.8264	0.953377	0.476689	−	0.879072i	$-0.341837\pi$
$181$	12.8264	0.953377	0.476689	+	0.879072i	$0.341837\pi$
$182$	−0.175301	−0.0129942
$183$	−1.65298	−0.122192
$184$	−1.00000	−0.0737210
$185$	−9.42244	−0.692751
$186$	21.9600	1.61019
$187$	−3.15684	−0.230851
$188$	−1.05671	−0.0770685
$189$	0.442306	0.0321730
$190$	−1.88986	−0.137105
$191$	7.81875	0.565745	0.282872	−	0.959158i	$-0.408713\pi$
$191$	7.81875	0.565745	0.282872	+	0.959158i	$0.408713\pi$
$192$	−2.31184	−0.166842
$193$	−21.0531	−1.51544	−0.757719	−	0.652581i	$-0.773686\pi$
$193$	−21.0531	−1.51544	−0.757719	+	0.652581i	$0.773686\pi$
$194$	−5.12604	−0.368028
$195$	2.55123	0.182698
$196$	−6.91479	−0.493913
$197$	−10.5148	−0.749147	−0.374574	−	0.927197i	$-0.622211\pi$
$197$	−10.5148	−0.749147	−0.374574	+	0.927197i	$0.622211\pi$
$198$	0.917649	0.0652145
$199$	0.438705	0.0310990	0.0155495	−	0.999879i	$-0.495050\pi$
$199$	0.438705	0.0310990	0.0155495	+	0.999879i	$0.495050\pi$
$200$	1.62309	0.114770
$201$	−30.3541	−2.14102
$202$	9.66843	0.680268
$203$	1.88198	0.132089
$204$	−18.6466	−1.30552
$205$	9.35590	0.653444
$206$	10.9862	0.765447
$207$	2.34459	0.162960
$208$	0.600528	0.0416391
$209$	0.402513	0.0278424
$210$	−1.24014	−0.0855776
$211$	4.87649	0.335712	0.167856	−	0.985812i	$-0.446316\pi$
$211$	4.87649	0.335712	0.167856	+	0.985812i	$0.446316\pi$
$212$	−4.00089	−0.274782
$213$	12.4838	0.855378
$214$	−14.1778	−0.969173
$215$	8.71174	0.594136
$216$	−1.51520	−0.103096
$217$	2.77286	0.188234
$218$	−19.1852	−1.29939
$219$	12.0098	0.811549
$220$	0.719233	0.0484907
$221$	4.84368	0.325821
$222$	11.8539	0.795580
$223$	16.8305	1.12705	0.563525	−	0.826099i	$-0.309445\pi$
$223$	16.8305	1.12705	0.563525	+	0.826099i	$0.309445\pi$
$224$	−0.291912	−0.0195042
$225$	−3.80547	−0.253698
$226$	7.68528	0.511217
$227$	5.58864	0.370931	0.185465	−	0.982651i	$-0.440621\pi$
$227$	5.58864	0.370931	0.185465	+	0.982651i	$0.440621\pi$
$228$	2.37754	0.157456
$229$	−9.85633	−0.651324	−0.325662	−	0.945486i	$-0.605587\pi$
$229$	−9.85633	−0.651324	−0.325662	+	0.945486i	$0.605587\pi$
$230$	1.83764	0.121170
$231$	0.264131	0.0173785
$232$	−6.44707	−0.423271
$233$	−2.48199	−0.162600	−0.0813002	−	0.996690i	$-0.525907\pi$
$233$	−2.48199	−0.162600	−0.0813002	+	0.996690i	$0.525907\pi$
$234$	−1.40799	−0.0920433
$235$	1.94185	0.126672
$236$	9.67887	0.630041
$237$	−31.4853	−2.04519
$238$	−2.35448	−0.152618
$239$	−16.0896	−1.04075	−0.520375	−	0.853938i	$-0.674208\pi$
$239$	−16.0896	−1.04075	−0.520375	+	0.853938i	$0.674208\pi$
$240$	4.24832	0.274228
$241$	14.8127	0.954170	0.477085	−	0.878857i	$-0.341693\pi$
$241$	14.8127	0.954170	0.477085	+	0.878857i	$0.341693\pi$
$242$	10.8468	0.697260
$243$	19.8135	1.27103
$244$	0.715006	0.0457736
$245$	12.7069	0.811812
$246$	−11.7702	−0.750438
$247$	−0.617594	−0.0392965
$248$	−9.49895	−0.603184
$249$	34.6858	2.19812
$250$	−12.1708	−0.769751
$251$	−5.88435	−0.371417	−0.185708	−	0.982605i	$-0.559458\pi$
$251$	−5.88435	−0.371417	−0.185708	+	0.982605i	$0.559458\pi$
$252$	0.684415	0.0431141
$253$	−0.391390	−0.0246065
$254$	4.61410	0.289515
$255$	34.2657	2.14580
$256$	1.00000	0.0625000
$257$	−7.44280	−0.464269	−0.232134	−	0.972684i	$-0.574571\pi$
$257$	−7.44280	−0.464269	−0.232134	+	0.972684i	$0.574571\pi$
$258$	−10.9598	−0.682327
$259$	1.49677	0.0930049
$260$	−1.10355	−0.0684394
$261$	15.1157	0.935641
$262$	1.00000	0.0617802
$263$	9.52011	0.587035	0.293518	−	0.955954i	$-0.405174\pi$
$263$	9.52011	0.587035	0.293518	+	0.955954i	$0.405174\pi$
$264$	−0.904830	−0.0556884
$265$	7.35218	0.451641
$266$	0.300208	0.0184069
$267$	−8.42114	−0.515365
$268$	13.1299	0.802035
$269$	4.97658	0.303428	0.151714	−	0.988424i	$-0.451521\pi$
$269$	4.97658	0.303428	0.151714	+	0.988424i	$0.451521\pi$
$270$	2.78439	0.169453
$271$	26.6826	1.62085	0.810427	−	0.585839i	$-0.199235\pi$
$271$	26.6826	1.62085	0.810427	+	0.585839i	$0.199235\pi$
$272$	8.06571	0.489055
$273$	−0.405268	−0.0245280
$274$	6.11296	0.369297
$275$	0.635260	0.0383076
$276$	−2.31184	−0.139156
$277$	25.2453	1.51685	0.758423	−	0.651763i	$-0.225970\pi$
$277$	25.2453	1.51685	0.758423	+	0.651763i	$0.225970\pi$
$278$	−14.7533	−0.884844
$279$	22.2711	1.33334
$280$	0.536429	0.0320578
$281$	5.15622	0.307595	0.153797	−	0.988102i	$-0.450850\pi$
$281$	5.15622	0.307595	0.153797	+	0.988102i	$0.450850\pi$
$282$	−2.44294	−0.145475
$283$	6.09035	0.362033	0.181017	−	0.983480i	$-0.442061\pi$
$283$	6.09035	0.362033	0.181017	+	0.983480i	$0.442061\pi$
$284$	−5.39996	−0.320429
$285$	−4.36905	−0.258800
$286$	0.235041	0.0138982
$287$	−1.48620	−0.0877277
$288$	−2.34459	−0.138156
$289$	48.0556	2.82680
$290$	11.8474	0.695702
$291$	−11.8506	−0.694692
$292$	−5.19493	−0.304010
$293$	8.93691	0.522100	0.261050	−	0.965325i	$-0.415931\pi$
$293$	8.93691	0.522100	0.261050	+	0.965325i	$0.415931\pi$
$294$	−15.9859	−0.932314
$295$	−17.7863	−1.03556
$296$	−5.12747	−0.298028
$297$	−0.593034	−0.0344114
$298$	2.61721	0.151611
$299$	0.600528	0.0347294
$300$	3.75231	0.216640
$301$	−1.38388	−0.0797653
$302$	22.7375	1.30839
$303$	22.3518	1.28408
$304$	−1.02842	−0.0589838
$305$	−1.31392	−0.0752350
$306$	−18.9108	−1.08106
$307$	5.29939	0.302452	0.151226	−	0.988499i	$-0.451678\pi$
$307$	5.29939	0.302452	0.151226	+	0.988499i	$0.451678\pi$
$308$	−0.114252	−0.00651009
$309$	25.3984	1.44486
$310$	17.4556	0.991413
$311$	10.2093	0.578917	0.289458	−	0.957191i	$-0.406525\pi$
$311$	10.2093	0.578917	0.289458	+	0.957191i	$0.406525\pi$
$312$	1.38832	0.0785983
$313$	−16.6678	−0.942122	−0.471061	−	0.882101i	$-0.656129\pi$
$313$	−16.6678	−0.942122	−0.471061	+	0.882101i	$0.656129\pi$
$314$	5.75420	0.324728
$315$	−1.25771	−0.0708637
$316$	13.6192	0.766139
$317$	22.1664	1.24499	0.622493	−	0.782625i	$-0.286120\pi$
$317$	22.1664	1.24499	0.622493	+	0.782625i	$0.286120\pi$
$318$	−9.24939	−0.518680
$319$	−2.52332	−0.141279
$320$	−1.83764	−0.102727
$321$	−32.7767	−1.82942
$322$	−0.291912	−0.0162676
$323$	−8.29492	−0.461542
$324$	−10.5367	−0.585370
$325$	−0.974709	−0.0540671
$326$	−17.6530	−0.977711
$327$	−44.3531	−2.45273
$328$	5.09126	0.281118
$329$	−0.308466	−0.0170063
$330$	1.66275	0.0915314
$331$	13.0179	0.715529	0.357764	−	0.933812i	$-0.383539\pi$
$331$	13.0179	0.715529	0.357764	+	0.933812i	$0.383539\pi$
$332$	−15.0036	−0.823428
$333$	12.0218	0.658792
$334$	3.15337	0.172545
$335$	−24.1280	−1.31825
$336$	−0.674854	−0.0368163
$337$	−18.7061	−1.01898	−0.509492	−	0.860475i	$-0.670167\pi$
$337$	−18.7061	−1.01898	−0.509492	+	0.860475i	$0.670167\pi$
$338$	12.6394	0.687491
$339$	17.7671	0.964977
$340$	−14.8218	−0.803827
$341$	−3.71779	−0.201330
$342$	2.41122	0.130384
$343$	−4.06190	−0.219322
$344$	4.74073	0.255603
$345$	4.24832	0.228722
$346$	0.767044	0.0412365
$347$	−2.90742	−0.156078	−0.0780392	−	0.996950i	$-0.524866\pi$
$347$	−2.90742	−0.156078	−0.0780392	+	0.996950i	$0.524866\pi$
$348$	−14.9046	−0.798969
$349$	9.23019	0.494081	0.247040	−	0.969005i	$-0.420542\pi$
$349$	9.23019	0.494081	0.247040	+	0.969005i	$0.420542\pi$
$350$	0.473799	0.0253256
$351$	0.909920	0.0485679
$352$	0.391390	0.0208612
$353$	−20.2316	−1.07682	−0.538411	−	0.842682i	$-0.680975\pi$
$353$	−20.2316	−1.07682	−0.538411	+	0.842682i	$0.680975\pi$
$354$	22.3760	1.18927
$355$	9.92318	0.526667
$356$	3.64262	0.193058
$357$	−5.44317	−0.288083
$358$	19.8829	1.05085
$359$	−18.7728	−0.990792	−0.495396	−	0.868667i	$-0.664977\pi$
$359$	−18.7728	−0.990792	−0.495396	+	0.868667i	$0.664977\pi$
$360$	4.30851	0.227078
$361$	−17.9424	−0.944335
$362$	−12.8264	−0.674139
$363$	25.0761	1.31615
$364$	0.175301	0.00918829
$365$	9.54639	0.499681
$366$	1.65298	0.0864025
$367$	4.38357	0.228821	0.114410	−	0.993434i	$-0.463502\pi$
$367$	4.38357	0.228821	0.114410	+	0.993434i	$0.463502\pi$
$368$	1.00000	0.0521286
$369$	−11.9369	−0.621411
$370$	9.42244	0.489849
$371$	−1.16791	−0.0606347
$372$	−21.9600	−1.13857
$373$	18.6895	0.967707	0.483853	−	0.875149i	$-0.339237\pi$
$373$	18.6895	0.967707	0.483853	+	0.875149i	$0.339237\pi$
$374$	3.15684	0.163236
$375$	−28.1370	−1.45299
$376$	1.05671	0.0544956
$377$	3.87165	0.199400
$378$	−0.442306	−0.0227497
$379$	−0.781344	−0.0401350	−0.0200675	−	0.999799i	$-0.506388\pi$
$379$	−0.781344	−0.0401350	−0.0200675	+	0.999799i	$0.506388\pi$
$380$	1.88986	0.0969478
$381$	10.6671	0.546490
$382$	−7.81875	−0.400042
$383$	−12.2150	−0.624158	−0.312079	−	0.950056i	$-0.601025\pi$
$383$	−12.2150	−0.624158	−0.312079	+	0.950056i	$0.601025\pi$
$384$	2.31184	0.117975
$385$	0.209953	0.0107002
$386$	21.0531	1.07158
$387$	−11.1151	−0.565011
$388$	5.12604	0.260235
$389$	15.2089	0.771122	0.385561	−	0.922682i	$-0.374008\pi$
$389$	15.2089	0.771122	0.385561	+	0.922682i	$0.374008\pi$
$390$	−2.55123	−0.129187
$391$	8.06571	0.407900
$392$	6.91479	0.349249
$393$	2.31184	0.116617
$394$	10.5148	0.529727
$395$	−25.0271	−1.25925
$396$	−0.917649	−0.0461136
$397$	−9.52792	−0.478193	−0.239096	−	0.970996i	$-0.576851\pi$
$397$	−9.52792	−0.478193	−0.239096	+	0.970996i	$0.576851\pi$
$398$	−0.438705	−0.0219903
$399$	0.694032	0.0347450
$400$	−1.62309	−0.0811544
$401$	−22.6444	−1.13081	−0.565404	−	0.824814i	$-0.691280\pi$
$401$	−22.6444	−1.13081	−0.565404	+	0.824814i	$0.691280\pi$
$402$	30.3541	1.51393
$403$	5.70438	0.284155
$404$	−9.66843	−0.481022
$405$	19.3626	0.962134
$406$	−1.88198	−0.0934011
$407$	−2.00684	−0.0994755
$408$	18.6466	0.923144
$409$	20.8266	1.02981	0.514905	−	0.857247i	$-0.327827\pi$
$409$	20.8266	1.02981	0.514905	+	0.857247i	$0.327827\pi$
$410$	−9.35590	−0.462055
$411$	14.1322	0.697088
$412$	−10.9862	−0.541253
$413$	2.82538	0.139028
$414$	−2.34459	−0.115230
$415$	27.5711	1.35341
$416$	−0.600528	−0.0294433
$417$	−34.1072	−1.67024
$418$	−0.402513	−0.0196875
$419$	−2.15454	−0.105256	−0.0526281	−	0.998614i	$-0.516760\pi$
$419$	−2.15454	−0.105256	−0.0526281	+	0.998614i	$0.516760\pi$
$420$	1.24014	0.0605125
$421$	33.6833	1.64162	0.820812	−	0.571198i	$-0.193521\pi$
$421$	33.6833	1.64162	0.820812	+	0.571198i	$0.193521\pi$
$422$	−4.87649	−0.237384
$423$	−2.47755	−0.120463
$424$	4.00089	0.194300
$425$	−13.0913	−0.635024
$426$	−12.4838	−0.604844
$427$	0.208719	0.0101006
$428$	14.1778	0.685309
$429$	0.543376	0.0262344
$430$	−8.71174	−0.420117
$431$	12.9361	0.623112	0.311556	−	0.950228i	$-0.399150\pi$
$431$	12.9361	0.623112	0.311556	+	0.950228i	$0.399150\pi$
$432$	1.51520	0.0729001
$433$	−12.2226	−0.587379	−0.293690	−	0.955901i	$-0.594883\pi$
$433$	−12.2226	−0.587379	−0.293690	+	0.955901i	$0.594883\pi$
$434$	−2.77286	−0.133102
$435$	27.3892	1.31321
$436$	19.1852	0.918805
$437$	−1.02842	−0.0491959
$438$	−12.0098	−0.573851
$439$	14.0286	0.669549	0.334774	−	0.942298i	$-0.391340\pi$
$439$	14.0286	0.669549	0.334774	+	0.942298i	$0.391340\pi$
$440$	−0.719233	−0.0342881
$441$	−16.2123	−0.772016
$442$	−4.84368	−0.230390
$443$	21.9918	1.04486	0.522432	−	0.852681i	$-0.325025\pi$
$443$	21.9918	1.04486	0.522432	+	0.852681i	$0.325025\pi$
$444$	−11.8539	−0.562560
$445$	−6.69381	−0.317317
$446$	−16.8305	−0.796945
$447$	6.05055	0.286181
$448$	0.291912	0.0137916
$449$	16.9033	0.797718	0.398859	−	0.917012i	$-0.369406\pi$
$449$	16.9033	0.797718	0.398859	+	0.917012i	$0.369406\pi$
$450$	3.80547	0.179392
$451$	1.99267	0.0938311
$452$	−7.68528	−0.361485
$453$	52.5653	2.46973
$454$	−5.58864	−0.262288
$455$	−0.322140	−0.0151022
$456$	−2.37754	−0.111338
$457$	−9.49580	−0.444195	−0.222097	−	0.975024i	$-0.571290\pi$
$457$	−9.49580	−0.444195	−0.222097	+	0.975024i	$0.571290\pi$
$458$	9.85633	0.460556
$459$	12.2212	0.570435
$460$	−1.83764	−0.0856803
$461$	3.13431	0.145979	0.0729897	−	0.997333i	$-0.476746\pi$
$461$	3.13431	0.145979	0.0729897	+	0.997333i	$0.476746\pi$
$462$	−0.264131	−0.0122885
$463$	25.5419	1.18703	0.593516	−	0.804822i	$-0.297739\pi$
$463$	25.5419	1.18703	0.593516	+	0.804822i	$0.297739\pi$
$464$	6.44707	0.299298
$465$	40.3546	1.87140
$466$	2.48199	0.114976
$467$	11.3457	0.525018	0.262509	−	0.964930i	$-0.415450\pi$
$467$	11.3457	0.525018	0.262509	+	0.964930i	$0.415450\pi$
$468$	1.40799	0.0650844
$469$	3.83277	0.176981
$470$	−1.94185	−0.0895708
$471$	13.3028	0.612960
$472$	−9.67887	−0.445506
$473$	1.85547	0.0853148
$474$	31.4853	1.44617
$475$	1.66921	0.0765887
$476$	2.35448	0.107917
$477$	−9.38044	−0.429501
$478$	16.0896	0.735922
$479$	−17.2723	−0.789190	−0.394595	−	0.918855i	$-0.629115\pi$
$479$	−17.2723	−0.789190	−0.394595	+	0.918855i	$0.629115\pi$
$480$	−4.24832	−0.193908
$481$	3.07919	0.140399
$482$	−14.8127	−0.674700
$483$	−0.674854	−0.0307069
$484$	−10.8468	−0.493037
$485$	−9.41980	−0.427731
$486$	−19.8135	−0.898757
$487$	5.31269	0.240741	0.120370	−	0.992729i	$-0.461592\pi$
$487$	5.31269	0.240741	0.120370	+	0.992729i	$0.461592\pi$
$488$	−0.715006	−0.0323668
$489$	−40.8109	−1.84553
$490$	−12.7069	−0.574038
$491$	−3.50231	−0.158057	−0.0790284	−	0.996872i	$-0.525182\pi$
$491$	−3.50231	−0.158057	−0.0790284	+	0.996872i	$0.525182\pi$
$492$	11.7702	0.530640
$493$	52.0002	2.34197
$494$	0.617594	0.0277868
$495$	1.68631	0.0757939
$496$	9.49895	0.426515
$497$	−1.57632	−0.0707074
$498$	−34.6858	−1.55431
$499$	33.8963	1.51741	0.758703	−	0.651437i	$-0.225833\pi$
$499$	33.8963	1.51741	0.758703	+	0.651437i	$0.225833\pi$
$500$	12.1708	0.544296
$501$	7.29008	0.325697
$502$	5.88435	0.262631
$503$	21.6035	0.963251	0.481625	−	0.876377i	$-0.340047\pi$
$503$	21.6035	0.963251	0.481625	+	0.876377i	$0.340047\pi$
$504$	−0.684415	−0.0304863
$505$	17.7671	0.790624
$506$	0.391390	0.0173994
$507$	29.2202	1.29771
$508$	−4.61410	−0.204718
$509$	−38.3094	−1.69803	−0.849017	−	0.528365i	$-0.822805\pi$
$509$	−38.3094	−1.69803	−0.849017	+	0.528365i	$0.822805\pi$
$510$	−34.2657	−1.51731
$511$	−1.51646	−0.0670844
$512$	−1.00000	−0.0441942
$513$	−1.55826	−0.0687988
$514$	7.44280	0.328288
$515$	20.1887	0.889621
$516$	10.9598	0.482478
$517$	0.413586	0.0181895
$518$	−1.49677	−0.0657644
$519$	1.77328	0.0778383
$520$	1.10355	0.0483940
$521$	4.61837	0.202335	0.101167	−	0.994869i	$-0.467742\pi$
$521$	4.61837	0.202335	0.101167	+	0.994869i	$0.467742\pi$
$522$	−15.1157	−0.661598
$523$	1.47740	0.0646021	0.0323010	−	0.999478i	$-0.489716\pi$
$523$	1.47740	0.0646021	0.0323010	+	0.999478i	$0.489716\pi$
$524$	−1.00000	−0.0436852
$525$	1.09535	0.0478048
$526$	−9.52011	−0.415096
$527$	76.6157	3.33743
$528$	0.904830	0.0393777
$529$	1.00000	0.0434783
$530$	−7.35218	−0.319358
$531$	22.6930	0.984792
$532$	−0.300208	−0.0130157
$533$	−3.05744	−0.132433
$534$	8.42114	0.364418
$535$	−26.0536	−1.12640
$536$	−13.1299	−0.567125
$537$	45.9661	1.98358
$538$	−4.97658	−0.214556
$539$	2.70638	0.116572
$540$	−2.78439	−0.119821
$541$	37.6086	1.61692	0.808461	−	0.588550i	$-0.200301\pi$
$541$	37.6086	1.61692	0.808461	+	0.588550i	$0.200301\pi$
$542$	−26.6826	−1.14612
$543$	−29.6525	−1.27251
$544$	−8.06571	−0.345814
$545$	−35.2555	−1.51018
$546$	0.405268	0.0173439
$547$	11.6975	0.500150	0.250075	−	0.968226i	$-0.419545\pi$
$547$	11.6975	0.500150	0.250075	+	0.968226i	$0.419545\pi$
$548$	−6.11296	−0.261133
$549$	1.67640	0.0715468
$550$	−0.635260	−0.0270876
$551$	−6.63029	−0.282460
$552$	2.31184	0.0983983
$553$	3.97561	0.169060
$554$	−25.2453	−1.07257
$555$	21.7831	0.924643
$556$	14.7533	0.625679
$557$	−40.8947	−1.73276	−0.866382	−	0.499382i	$-0.833560\pi$
$557$	−40.8947	−1.73276	−0.866382	+	0.499382i	$0.833560\pi$
$558$	−22.2711	−0.942813
$559$	−2.84694	−0.120413
$560$	−0.536429	−0.0226683
$561$	7.29809	0.308126
$562$	−5.15622	−0.217502
$563$	−25.1196	−1.05866	−0.529332	−	0.848415i	$-0.677557\pi$
$563$	−25.1196	−1.05866	−0.529332	+	0.848415i	$0.677557\pi$
$564$	2.44294	0.102866
$565$	14.1228	0.594149
$566$	−6.09035	−0.255996
$567$	−3.07578	−0.129171
$568$	5.39996	0.226577
$569$	40.4073	1.69396	0.846981	−	0.531623i	$-0.178418\pi$
$569$	40.4073	1.69396	0.846981	+	0.531623i	$0.178418\pi$
$570$	4.36905	0.182999
$571$	13.6070	0.569435	0.284718	−	0.958611i	$-0.408100\pi$
$571$	13.6070	0.569435	0.284718	+	0.958611i	$0.408100\pi$
$572$	−0.235041	−0.00982754
$573$	−18.0757	−0.755122
$574$	1.48620	0.0620329
$575$	−1.62309	−0.0676874
$576$	2.34459	0.0976913
$577$	−6.04962	−0.251849	−0.125924	−	0.992040i	$-0.540190\pi$
$577$	−6.04962	−0.251849	−0.125924	+	0.992040i	$0.540190\pi$
$578$	−48.0556	−1.99885
$579$	48.6714	2.02272
$580$	−11.8474	−0.491936
$581$	−4.37973	−0.181702
$582$	11.8506	0.491222
$583$	1.56591	0.0648532
$584$	5.19493	0.214968
$585$	−2.58738	−0.106975
$586$	−8.93691	−0.369180
$587$	−27.0011	−1.11445	−0.557227	−	0.830360i	$-0.688135\pi$
$587$	−27.0011	−1.11445	−0.557227	+	0.830360i	$0.688135\pi$
$588$	15.9859	0.659246
$589$	−9.76889	−0.402520
$590$	17.7863	0.732249
$591$	24.3085	0.999917
$592$	5.12747	0.210738
$593$	35.7759	1.46914	0.734569	−	0.678534i	$-0.237384\pi$
$593$	35.7759	1.46914	0.734569	+	0.678534i	$0.237384\pi$
$594$	0.593034	0.0243325
$595$	−4.32668	−0.177377
$596$	−2.61721	−0.107205
$597$	−1.01421	−0.0415090
$598$	−0.600528	−0.0245574
$599$	31.1303	1.27195	0.635975	−	0.771710i	$-0.280598\pi$
$599$	31.1303	1.27195	0.635975	+	0.771710i	$0.280598\pi$
$600$	−3.75231	−0.153188
$601$	2.77336	0.113128	0.0565639	−	0.998399i	$-0.481986\pi$
$601$	2.77336	0.113128	0.0565639	+	0.998399i	$0.481986\pi$
$602$	1.38388	0.0564026
$603$	30.7842	1.25363
$604$	−22.7375	−0.925175
$605$	19.9325	0.810372
$606$	−22.3518	−0.907981
$607$	40.2172	1.63236	0.816182	−	0.577795i	$-0.196087\pi$
$607$	40.2172	1.63236	0.816182	+	0.577795i	$0.196087\pi$
$608$	1.02842	0.0417079
$609$	−4.35083	−0.176305
$610$	1.31392	0.0531991
$611$	−0.634583	−0.0256725
$612$	18.9108	0.764423
$613$	6.97330	0.281649	0.140824	−	0.990035i	$-0.455025\pi$
$613$	6.97330	0.281649	0.140824	+	0.990035i	$0.455025\pi$
$614$	−5.29939	−0.213866
$615$	−21.6293	−0.872178
$616$	0.114252	0.00460333
$617$	−21.0336	−0.846781	−0.423390	−	0.905947i	$-0.639160\pi$
$617$	−21.0336	−0.846781	−0.423390	+	0.905947i	$0.639160\pi$
$618$	−25.3984	−1.02167
$619$	9.93695	0.399400	0.199700	−	0.979857i	$-0.436003\pi$
$619$	9.93695	0.399400	0.199700	+	0.979857i	$0.436003\pi$
$620$	−17.4556	−0.701035
$621$	1.51520	0.0608029
$622$	−10.2093	−0.409356
$623$	1.06333	0.0426012
$624$	−1.38832	−0.0555774
$625$	−14.2502	−0.570006
$626$	16.6678	0.666181
$627$	−0.930544	−0.0371623
$628$	−5.75420	−0.229618
$629$	41.3567	1.64900
$630$	1.25771	0.0501082
$631$	37.3336	1.48623	0.743113	−	0.669166i	$-0.233348\pi$
$631$	37.3336	1.48623	0.743113	+	0.669166i	$0.233348\pi$
$632$	−13.6192	−0.541742
$633$	−11.2737	−0.448088
$634$	−22.1664	−0.880338
$635$	8.47905	0.336481
$636$	9.24939	0.366762
$637$	−4.15252	−0.164529
$638$	2.52332	0.0998992
$639$	−12.6607	−0.500850
$640$	1.83764	0.0726390
$641$	45.1693	1.78408	0.892040	−	0.451957i	$-0.149274\pi$
$641$	45.1693	1.78408	0.892040	+	0.451957i	$0.149274\pi$
$642$	32.7767	1.29359
$643$	−36.1403	−1.42523	−0.712617	−	0.701554i	$-0.752490\pi$
$643$	−36.1403	−1.42523	−0.712617	+	0.701554i	$0.752490\pi$
$644$	0.291912	0.0115030
$645$	−20.1401	−0.793017
$646$	8.29492	0.326359
$647$	−19.5308	−0.767837	−0.383918	−	0.923367i	$-0.625426\pi$
$647$	−19.5308	−0.767837	−0.383918	+	0.923367i	$0.625426\pi$
$648$	10.5367	0.413919
$649$	−3.78822	−0.148700
$650$	0.974709	0.0382312
$651$	−6.41040	−0.251243
$652$	17.6530	0.691346
$653$	−8.93254	−0.349557	−0.174779	−	0.984608i	$-0.555921\pi$
$653$	−8.93254	−0.349557	−0.174779	+	0.984608i	$0.555921\pi$
$654$	44.3531	1.73434
$655$	1.83764	0.0718024
$656$	−5.09126	−0.198780
$657$	−12.1800	−0.475186
$658$	0.308466	0.0120253
$659$	33.5200	1.30576	0.652878	−	0.757463i	$-0.273562\pi$
$659$	33.5200	1.30576	0.652878	+	0.757463i	$0.273562\pi$
$660$	−1.66275	−0.0647225
$661$	0.510953	0.0198738	0.00993688	−	0.999951i	$-0.496837\pi$
$661$	0.510953	0.0198738	0.00993688	+	0.999951i	$0.496837\pi$
$662$	−13.0179	−0.505955
$663$	−11.1978	−0.434886
$664$	15.0036	0.582251
$665$	0.551673	0.0213930
$666$	−12.0218	−0.465836
$667$	6.44707	0.249632
$668$	−3.15337	−0.122008
$669$	−38.9093	−1.50432
$670$	24.1280	0.932145
$671$	−0.279846	−0.0108033
$672$	0.674854	0.0260330
$673$	−2.79126	−0.107595	−0.0537976	−	0.998552i	$-0.517133\pi$
$673$	−2.79126	−0.107595	−0.0537976	+	0.998552i	$0.517133\pi$
$674$	18.7061	0.720531
$675$	−2.45930	−0.0946586
$676$	−12.6394	−0.486129
$677$	2.47139	0.0949832	0.0474916	−	0.998872i	$-0.484877\pi$
$677$	2.47139	0.0949832	0.0474916	+	0.998872i	$0.484877\pi$
$678$	−17.7671	−0.682342
$679$	1.49635	0.0574248
$680$	14.8218	0.568392
$681$	−12.9200	−0.495096
$682$	3.71779	0.142362
$683$	−42.9761	−1.64443	−0.822217	−	0.569174i	$-0.807263\pi$
$683$	−42.9761	−1.64443	−0.822217	+	0.569174i	$0.807263\pi$
$684$	−2.41122	−0.0921953
$685$	11.2334	0.429206
$686$	4.06190	0.155084
$687$	22.7862	0.869349
$688$	−4.74073	−0.180739
$689$	−2.40264	−0.0915334
$690$	−4.24832	−0.161731
$691$	−6.68098	−0.254157	−0.127078	−	0.991893i	$-0.540560\pi$
$691$	−6.68098	−0.254157	−0.127078	+	0.991893i	$0.540560\pi$
$692$	−0.767044	−0.0291586
$693$	−0.267873	−0.0101757
$694$	2.90742	0.110364
$695$	−27.1112	−1.02839
$696$	14.9046	0.564957
$697$	−41.0646	−1.55543
$698$	−9.23019	−0.349368
$699$	5.73795	0.217029
$700$	−0.473799	−0.0179079
$701$	−15.7800	−0.596001	−0.298000	−	0.954566i	$-0.596320\pi$
$701$	−15.7800	−0.596001	−0.298000	+	0.954566i	$0.596320\pi$
$702$	−0.909920	−0.0343427
$703$	−5.27319	−0.198882
$704$	−0.391390	−0.0147511
$705$	−4.48924	−0.169075
$706$	20.2316	0.761428
$707$	−2.82233	−0.106145
$708$	−22.3760	−0.840941
$709$	−10.9250	−0.410297	−0.205148	−	0.978731i	$-0.565768\pi$
$709$	−10.9250	−0.410297	−0.205148	+	0.978731i	$0.565768\pi$
$710$	−9.92318	−0.372410
$711$	31.9314	1.19752
$712$	−3.64262	−0.136513
$713$	9.49895	0.355738
$714$	5.44317	0.203706
$715$	0.431919	0.0161529
$716$	−19.8829	−0.743060
$717$	37.1966	1.38913
$718$	18.7728	0.700596
$719$	7.16778	0.267313	0.133657	−	0.991028i	$-0.457328\pi$
$719$	7.16778	0.267313	0.133657	+	0.991028i	$0.457328\pi$
$720$	−4.30851	−0.160569
$721$	−3.20701	−0.119435
$722$	17.9424	0.667745
$723$	−34.2445	−1.27357
$724$	12.8264	0.476689
$725$	−10.4642	−0.388629
$726$	−25.0761	−0.930660
$727$	11.0765	0.410806	0.205403	−	0.978677i	$-0.434149\pi$
$727$	11.0765	0.410806	0.205403	+	0.978677i	$0.434149\pi$
$728$	−0.175301	−0.00649710
$729$	−14.1955	−0.525758
$730$	−9.54639	−0.353328
$731$	−38.2373	−1.41426
$732$	−1.65298	−0.0610958
$733$	−22.0414	−0.814116	−0.407058	−	0.913402i	$-0.633445\pi$
$733$	−22.0414	−0.814116	−0.407058	+	0.913402i	$0.633445\pi$
$734$	−4.38357	−0.161801
$735$	−29.3762	−1.08356
$736$	−1.00000	−0.0368605
$737$	−5.13891	−0.189294
$738$	11.9369	0.439404
$739$	−2.11263	−0.0777143	−0.0388572	−	0.999245i	$-0.512372\pi$
$739$	−2.11263	−0.0777143	−0.0388572	+	0.999245i	$0.512372\pi$
$740$	−9.42244	−0.346376
$741$	1.42778	0.0524507
$742$	1.16791	0.0428752
$743$	−44.9082	−1.64752	−0.823761	−	0.566937i	$-0.808128\pi$
$743$	−44.9082	−1.64752	−0.823761	+	0.566937i	$0.808128\pi$
$744$	21.9600	0.805093
$745$	4.80948	0.176206
$746$	−18.6895	−0.684272
$747$	−35.1772	−1.28707
$748$	−3.15684	−0.115425
$749$	4.13867	0.151224
$750$	28.1370	1.02742
$751$	28.6291	1.04469	0.522345	−	0.852734i	$-0.325057\pi$
$751$	28.6291	1.04469	0.522345	+	0.852734i	$0.325057\pi$
$752$	−1.05671	−0.0385342
$753$	13.6037	0.495745
$754$	−3.87165	−0.140997
$755$	41.7832	1.52065
$756$	0.442306	0.0160865
$757$	−12.1385	−0.441183	−0.220591	−	0.975366i	$-0.570799\pi$
$757$	−12.1385	−0.441183	−0.220591	+	0.975366i	$0.570799\pi$
$758$	0.781344	0.0283797
$759$	0.904830	0.0328433
$760$	−1.88986	−0.0685524
$761$	46.0156	1.66807	0.834033	−	0.551715i	$-0.186026\pi$
$761$	46.0156	1.66807	0.834033	+	0.551715i	$0.186026\pi$
$762$	−10.6671	−0.386427
$763$	5.60040	0.202748
$764$	7.81875	0.282872
$765$	−34.7512	−1.25643
$766$	12.2150	0.441346
$767$	5.81243	0.209875
$768$	−2.31184	−0.0834212
$769$	22.2253	0.801466	0.400733	−	0.916195i	$-0.368755\pi$
$769$	22.2253	0.801466	0.400733	+	0.916195i	$0.368755\pi$
$770$	−0.209953	−0.00756618
$771$	17.2065	0.619678
$772$	−21.0531	−0.757719
$773$	−3.83845	−0.138059	−0.0690297	−	0.997615i	$-0.521990\pi$
$773$	−3.83845	−0.138059	−0.0690297	+	0.997615i	$0.521990\pi$
$774$	11.1151	0.399523
$775$	−15.4176	−0.553817
$776$	−5.12604	−0.184014
$777$	−3.46029	−0.124137
$778$	−15.2089	−0.545266
$779$	5.23595	0.187597
$780$	2.55123	0.0913488
$781$	2.11349	0.0756267
$782$	−8.06571	−0.288429
$783$	9.76861	0.349102
$784$	−6.91479	−0.246957
$785$	10.5741	0.377407
$786$	−2.31184	−0.0824605
$787$	52.5794	1.87425	0.937127	−	0.348988i	$-0.113475\pi$
$787$	52.5794	1.87425	0.937127	+	0.348988i	$0.113475\pi$
$788$	−10.5148	−0.374574
$789$	−22.0089	−0.783539
$790$	25.0271	0.890425
$791$	−2.24343	−0.0797671
$792$	0.917649	0.0326073
$793$	0.429381	0.0152478
$794$	9.52792	0.338133
$795$	−16.9970	−0.602823
$796$	0.438705	0.0155495
$797$	36.5466	1.29455	0.647274	−	0.762258i	$-0.275909\pi$
$797$	36.5466	1.29455	0.647274	+	0.762258i	$0.275909\pi$
$798$	−0.694032	−0.0245685
$799$	−8.52311	−0.301526
$800$	1.62309	0.0573848
$801$	8.54045	0.301762
$802$	22.6444	0.799602
$803$	2.03324	0.0717516
$804$	−30.3541	−1.07051
$805$	−0.536429	−0.0189066
$806$	−5.70438	−0.200928
$807$	−11.5050	−0.404997
$808$	9.66843	0.340134
$809$	−5.97613	−0.210110	−0.105055	−	0.994466i	$-0.533502\pi$
$809$	−5.97613	−0.210110	−0.105055	+	0.994466i	$0.533502\pi$
$810$	−19.3626	−0.680332
$811$	1.09223	0.0383535	0.0191767	−	0.999816i	$-0.493895\pi$
$811$	1.09223	0.0383535	0.0191767	+	0.999816i	$0.493895\pi$
$812$	1.88198	0.0660445
$813$	−61.6859	−2.16342
$814$	2.00684	0.0703398
$815$	−32.4399	−1.13632
$816$	−18.6466	−0.652761
$817$	4.87545	0.170570
$818$	−20.8266	−0.728185
$819$	0.411010	0.0143619
$820$	9.35590	0.326722
$821$	−43.3201	−1.51188	−0.755941	−	0.654640i	$-0.772820\pi$
$821$	−43.3201	−1.51188	−0.755941	+	0.654640i	$0.772820\pi$
$822$	−14.1322	−0.492916
$823$	−36.4413	−1.27026	−0.635132	−	0.772403i	$-0.719054\pi$
$823$	−36.4413	−1.27026	−0.635132	+	0.772403i	$0.719054\pi$
$824$	10.9862	0.382723
$825$	−1.46862	−0.0511307
$826$	−2.82538	−0.0983076
$827$	52.9344	1.84071	0.920355	−	0.391084i	$-0.127900\pi$
$827$	52.9344	1.84071	0.920355	+	0.391084i	$0.127900\pi$
$828$	2.34459	0.0814801
$829$	−25.8646	−0.898314	−0.449157	−	0.893453i	$-0.648276\pi$
$829$	−25.8646	−0.898314	−0.449157	+	0.893453i	$0.648276\pi$
$830$	−27.5711	−0.957008
$831$	−58.3631	−2.02459
$832$	0.600528	0.0208196
$833$	−55.7726	−1.93241
$834$	34.1072	1.18104
$835$	5.79476	0.200536
$836$	0.402513	0.0139212
$837$	14.3928	0.497488
$838$	2.15454	0.0744274
$839$	26.3222	0.908742	0.454371	−	0.890813i	$-0.349864\pi$
$839$	26.3222	0.908742	0.454371	+	0.890813i	$0.349864\pi$
$840$	−1.24014	−0.0427888
$841$	12.5648	0.433267
$842$	−33.6833	−1.16080
$843$	−11.9203	−0.410559
$844$	4.87649	0.167856
$845$	23.2266	0.799019
$846$	2.47755	0.0851799
$847$	−3.16632	−0.108796
$848$	−4.00089	−0.137391
$849$	−14.0799	−0.483220
$850$	13.0913	0.449029
$851$	5.12747	0.175767
$852$	12.4838	0.427689
$853$	−41.5731	−1.42344	−0.711719	−	0.702465i	$-0.752083\pi$
$853$	−41.5731	−1.42344	−0.711719	+	0.702465i	$0.752083\pi$
$854$	−0.208719	−0.00714222
$855$	4.43095	0.151535
$856$	−14.1778	−0.484586
$857$	−1.93308	−0.0660327	−0.0330164	−	0.999455i	$-0.510511\pi$
$857$	−1.93308	−0.0660327	−0.0330164	+	0.999455i	$0.510511\pi$
$858$	−0.543376	−0.0185505
$859$	37.2019	1.26931	0.634657	−	0.772794i	$-0.281142\pi$
$859$	37.2019	1.26931	0.634657	+	0.772794i	$0.281142\pi$
$860$	8.71174	0.297068
$861$	3.43586	0.117094
$862$	−12.9361	−0.440607
$863$	33.3017	1.13360	0.566801	−	0.823855i	$-0.308181\pi$
$863$	33.3017	1.13360	0.566801	+	0.823855i	$0.308181\pi$
$864$	−1.51520	−0.0515482
$865$	1.40955	0.0479261
$866$	12.2226	0.415340
$867$	−111.097	−3.77304
$868$	2.77286	0.0941170
$869$	−5.33041	−0.180822
$870$	−27.3892	−0.928582
$871$	7.88486	0.267168
$872$	−19.1852	−0.649694
$873$	12.0185	0.406763
$874$	1.02842	0.0347868
$875$	3.55282	0.120107
$876$	12.0098	0.405774
$877$	26.7970	0.904871	0.452435	−	0.891797i	$-0.350555\pi$
$877$	26.7970	0.904871	0.452435	+	0.891797i	$0.350555\pi$
$878$	−14.0286	−0.473442
$879$	−20.6607	−0.696867
$880$	0.719233	0.0242453
$881$	49.3912	1.66403	0.832016	−	0.554751i	$-0.187187\pi$
$881$	49.3912	1.66403	0.832016	+	0.554751i	$0.187187\pi$
$882$	16.2123	0.545898
$883$	−32.3332	−1.08810	−0.544050	−	0.839053i	$-0.683110\pi$
$883$	−32.3332	−1.08810	−0.544050	+	0.839053i	$0.683110\pi$
$884$	4.84368	0.162911
$885$	41.1189	1.38220
$886$	−21.9918	−0.738831
$887$	−48.5609	−1.63052	−0.815258	−	0.579098i	$-0.803405\pi$
$887$	−48.5609	−1.63052	−0.815258	+	0.579098i	$0.803405\pi$
$888$	11.8539	0.397790
$889$	−1.34691	−0.0451740
$890$	6.69381	0.224377
$891$	4.12395	0.138157
$892$	16.8305	0.563525
$893$	1.08674	0.0363663
$894$	−6.05055	−0.202361
$895$	36.5376	1.22132
$896$	−0.291912	−0.00975211
$897$	−1.38832	−0.0463547
$898$	−16.9033	−0.564072
$899$	61.2404	2.04248
$900$	−3.80547	−0.126849
$901$	−32.2700	−1.07507
$902$	−1.99267	−0.0663486
$903$	3.19930	0.106466
$904$	7.68528	0.255608
$905$	−23.5702	−0.783501
$906$	−52.5653	−1.74637
$907$	13.7691	0.457196	0.228598	−	0.973521i	$-0.426586\pi$
$907$	13.7691	0.457196	0.228598	+	0.973521i	$0.426586\pi$
$908$	5.58864	0.185465
$909$	−22.6685	−0.751867
$910$	0.322140	0.0106789
$911$	35.3910	1.17256	0.586279	−	0.810110i	$-0.300592\pi$
$911$	35.3910	1.17256	0.586279	+	0.810110i	$0.300592\pi$
$912$	2.37754	0.0787281
$913$	5.87225	0.194343
$914$	9.49580	0.314093
$915$	3.03757	0.100419
$916$	−9.85633	−0.325662
$917$	−0.291912	−0.00963979
$918$	−12.2212	−0.403358
$919$	−17.4031	−0.574074	−0.287037	−	0.957920i	$-0.592670\pi$
$919$	−17.4031	−0.574074	−0.287037	+	0.957920i	$0.592670\pi$
$920$	1.83764	0.0605851
$921$	−12.2513	−0.403695
$922$	−3.13431	−0.103223
$923$	−3.24283	−0.106739
$924$	0.264131	0.00868927
$925$	−8.32233	−0.273637
$926$	−25.5419	−0.839359
$927$	−25.7582	−0.846010
$928$	−6.44707	−0.211636
$929$	−41.9984	−1.37792	−0.688962	−	0.724797i	$-0.741933\pi$
$929$	−41.9984	−1.37792	−0.688962	+	0.724797i	$0.741933\pi$
$930$	−40.3546	−1.32328
$931$	7.11129	0.233063
$932$	−2.48199	−0.0813002
$933$	−23.6023	−0.772703
$934$	−11.3457	−0.371244
$935$	5.80112	0.189717
$936$	−1.40799	−0.0460216
$937$	−9.45234	−0.308795	−0.154397	−	0.988009i	$-0.549344\pi$
$937$	−9.45234	−0.308795	−0.154397	+	0.988009i	$0.549344\pi$
$938$	−3.83277	−0.125145
$939$	38.5333	1.25749
$940$	1.94185	0.0633361
$941$	−49.2484	−1.60545	−0.802726	−	0.596348i	$-0.796618\pi$
$941$	−49.2484	−1.60545	−0.802726	+	0.596348i	$0.796618\pi$
$942$	−13.3028	−0.433428
$943$	−5.09126	−0.165794
$944$	9.67887	0.315021
$945$	−0.812798	−0.0264403
$946$	−1.85547	−0.0603267
$947$	−19.8431	−0.644815	−0.322408	−	0.946601i	$-0.604492\pi$
$947$	−19.8431	−0.644815	−0.322408	+	0.946601i	$0.604492\pi$
$948$	−31.4853	−1.02260
$949$	−3.11970	−0.101270
$950$	−1.66921	−0.0541564
$951$	−51.2450	−1.66173
$952$	−2.35448	−0.0763091
$953$	−22.0569	−0.714493	−0.357247	−	0.934010i	$-0.616284\pi$
$953$	−22.0569	−0.714493	−0.357247	+	0.934010i	$0.616284\pi$
$954$	9.38044	0.303703
$955$	−14.3680	−0.464939
$956$	−16.0896	−0.520375
$957$	5.83351	0.188570
$958$	17.2723	0.558041
$959$	−1.78445	−0.0576228
$960$	4.24832	0.137114
$961$	59.2300	1.91065
$962$	−3.07919	−0.0992770
$963$	33.2411	1.07118
$964$	14.8127	0.477085
$965$	38.6881	1.24541
$966$	0.674854	0.0217131
$967$	2.55272	0.0820900	0.0410450	−	0.999157i	$-0.486931\pi$
$967$	2.55272	0.0820900	0.0410450	+	0.999157i	$0.486931\pi$
$968$	10.8468	0.348630
$969$	19.1765	0.616038
$970$	9.41980	0.302452
$971$	−22.1532	−0.710929	−0.355464	−	0.934690i	$-0.615677\pi$
$971$	−22.1532	−0.710929	−0.355464	+	0.934690i	$0.615677\pi$
$972$	19.8135	0.635517
$973$	4.30667	0.138066
$974$	−5.31269	−0.170229
$975$	2.25337	0.0721655
$976$	0.715006	0.0228868
$977$	−58.3425	−1.86654	−0.933271	−	0.359172i	$-0.883059\pi$
$977$	−58.3425	−1.86654	−0.933271	+	0.359172i	$0.883059\pi$
$978$	40.8109	1.30499
$979$	−1.42568	−0.0455651
$980$	12.7069	0.405906
$981$	44.9815	1.43615
$982$	3.50231	0.111763
$983$	−43.5128	−1.38784	−0.693922	−	0.720051i	$-0.744119\pi$
$983$	−43.5128	−1.38784	−0.693922	+	0.720051i	$0.744119\pi$
$984$	−11.7702	−0.375219
$985$	19.3224	0.615662
$986$	−52.0002	−1.65602
$987$	0.713124	0.0226990
$988$	−0.617594	−0.0196483
$989$	−4.74073	−0.150746
$990$	−1.68631	−0.0535944
$991$	−13.6453	−0.433457	−0.216729	−	0.976232i	$-0.569539\pi$
$991$	−13.6453	−0.433457	−0.216729	+	0.976232i	$0.569539\pi$
$992$	−9.49895	−0.301592
$993$	−30.0953	−0.955045
$994$	1.57632	0.0499977
$995$	−0.806181	−0.0255576
$996$	34.6858	1.09906
$997$	−18.2018	−0.576455	−0.288228	−	0.957562i	$-0.593066\pi$
$997$	−18.2018	−0.576455	−0.288228	+	0.957562i	$0.593066\pi$
$998$	−33.8963	−1.07297
$999$	7.76915	0.245805

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.j.1.6	✓	33

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.j.1.6	✓	33	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.31184 q^{3} +1.00000 q^{4} -1.83764 q^{5} +2.31184 q^{6} +0.291912 q^{7} -1.00000 q^{8} +2.34459 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.31184 q^{3} +1.00000 q^{4} -1.83764 q^{5} +2.31184 q^{6} +0.291912 q^{7} -1.00000 q^{8} +2.34459 q^{9} +1.83764 q^{10} -0.391390 q^{11} -2.31184 q^{12} +0.600528 q^{13} -0.291912 q^{14} +4.24832 q^{15} +1.00000 q^{16} +8.06571 q^{17} -2.34459 q^{18} -1.02842 q^{19} -1.83764 q^{20} -0.674854 q^{21} +0.391390 q^{22} +1.00000 q^{23} +2.31184 q^{24} -1.62309 q^{25} -0.600528 q^{26} +1.51520 q^{27} +0.291912 q^{28} +6.44707 q^{29} -4.24832 q^{30} +9.49895 q^{31} -1.00000 q^{32} +0.904830 q^{33} -8.06571 q^{34} -0.536429 q^{35} +2.34459 q^{36} +5.12747 q^{37} +1.02842 q^{38} -1.38832 q^{39} +1.83764 q^{40} -5.09126 q^{41} +0.674854 q^{42} -4.74073 q^{43} -0.391390 q^{44} -4.30851 q^{45} -1.00000 q^{46} -1.05671 q^{47} -2.31184 q^{48} -6.91479 q^{49} +1.62309 q^{50} -18.6466 q^{51} +0.600528 q^{52} -4.00089 q^{53} -1.51520 q^{54} +0.719233 q^{55} -0.291912 q^{56} +2.37754 q^{57} -6.44707 q^{58} +9.67887 q^{59} +4.24832 q^{60} +0.715006 q^{61} -9.49895 q^{62} +0.684415 q^{63} +1.00000 q^{64} -1.10355 q^{65} -0.904830 q^{66} +13.1299 q^{67} +8.06571 q^{68} -2.31184 q^{69} +0.536429 q^{70} -5.39996 q^{71} -2.34459 q^{72} -5.19493 q^{73} -5.12747 q^{74} +3.75231 q^{75} -1.02842 q^{76} -0.114252 q^{77} +1.38832 q^{78} +13.6192 q^{79} -1.83764 q^{80} -10.5367 q^{81} +5.09126 q^{82} -15.0036 q^{83} -0.674854 q^{84} -14.8218 q^{85} +4.74073 q^{86} -14.9046 q^{87} +0.391390 q^{88} +3.64262 q^{89} +4.30851 q^{90} +0.175301 q^{91} +1.00000 q^{92} -21.9600 q^{93} +1.05671 q^{94} +1.88986 q^{95} +2.31184 q^{96} +5.12604 q^{97} +6.91479 q^{98} -0.917649 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 33 q - 33 q^{2} + 3 q^{3} + 33 q^{4} - 4 q^{5} - 3 q^{6} + 11 q^{7} - 33 q^{8} + 44 q^{9}+O(q^{10}) \) 33 * q - 33 * q^2 + 3 * q^3 + 33 * q^4 - 4 * q^5 - 3 * q^6 + 11 * q^7 - 33 * q^8 + 44 * q^9	\( 33 q - 33 q^{2} + 3 q^{3} + 33 q^{4} - 4 q^{5} - 3 q^{6} + 11 q^{7} - 33 q^{8} + 44 q^{9} + 4 q^{10} + 5 q^{11} + 3 q^{12} + 15 q^{13} - 11 q^{14} + 16 q^{15} + 33 q^{16} + 2 q^{17} - 44 q^{18} + 32 q^{19} - 4 q^{20} + 8 q^{21} - 5 q^{22} + 33 q^{23} - 3 q^{24} + 49 q^{25} - 15 q^{26} + 15 q^{27} + 11 q^{28} + 20 q^{29} - 16 q^{30} + 25 q^{31} - 33 q^{32} - 6 q^{33} - 2 q^{34} + 15 q^{35} + 44 q^{36} + 6 q^{37} - 32 q^{38} + 25 q^{39} + 4 q^{40} + 2 q^{41} - 8 q^{42} + 31 q^{43} + 5 q^{44} + 2 q^{45} - 33 q^{46} + 4 q^{47} + 3 q^{48} + 72 q^{49} - 49 q^{50} + 26 q^{51} + 15 q^{52} - 65 q^{53} - 15 q^{54} - 4 q^{55} - 11 q^{56} + 12 q^{57} - 20 q^{58} + 8 q^{59} + 16 q^{60} + 23 q^{61} - 25 q^{62} - 14 q^{63} + 33 q^{64} + 5 q^{65} + 6 q^{66} + 31 q^{67} + 2 q^{68} + 3 q^{69} - 15 q^{70} + 20 q^{71} - 44 q^{72} + 22 q^{73} - 6 q^{74} - 32 q^{75} + 32 q^{76} + 2 q^{77} - 25 q^{78} + 53 q^{79} - 4 q^{80} + 17 q^{81} - 2 q^{82} + 45 q^{83} + 8 q^{84} + 60 q^{85} - 31 q^{86} + 11 q^{87} - 5 q^{88} - 54 q^{89} - 2 q^{90} + 38 q^{91} + 33 q^{92} + 63 q^{93} - 4 q^{94} + 44 q^{95} - 3 q^{96} - 72 q^{98} + 43 q^{99}+O(q^{100}) \) 33 * q - 33 * q^2 + 3 * q^3 + 33 * q^4 - 4 * q^5 - 3 * q^6 + 11 * q^7 - 33 * q^8 + 44 * q^9 + 4 * q^10 + 5 * q^11 + 3 * q^12 + 15 * q^13 - 11 * q^14 + 16 * q^15 + 33 * q^16 + 2 * q^17 - 44 * q^18 + 32 * q^19 - 4 * q^20 + 8 * q^21 - 5 * q^22 + 33 * q^23 - 3 * q^24 + 49 * q^25 - 15 * q^26 + 15 * q^27 + 11 * q^28 + 20 * q^29 - 16 * q^30 + 25 * q^31 - 33 * q^32 - 6 * q^33 - 2 * q^34 + 15 * q^35 + 44 * q^36 + 6 * q^37 - 32 * q^38 + 25 * q^39 + 4 * q^40 + 2 * q^41 - 8 * q^42 + 31 * q^43 + 5 * q^44 + 2 * q^45 - 33 * q^46 + 4 * q^47 + 3 * q^48 + 72 * q^49 - 49 * q^50 + 26 * q^51 + 15 * q^52 - 65 * q^53 - 15 * q^54 - 4 * q^55 - 11 * q^56 + 12 * q^57 - 20 * q^58 + 8 * q^59 + 16 * q^60 + 23 * q^61 - 25 * q^62 - 14 * q^63 + 33 * q^64 + 5 * q^65 + 6 * q^66 + 31 * q^67 + 2 * q^68 + 3 * q^69 - 15 * q^70 + 20 * q^71 - 44 * q^72 + 22 * q^73 - 6 * q^74 - 32 * q^75 + 32 * q^76 + 2 * q^77 - 25 * q^78 + 53 * q^79 - 4 * q^80 + 17 * q^81 - 2 * q^82 + 45 * q^83 + 8 * q^84 + 60 * q^85 - 31 * q^86 + 11 * q^87 - 5 * q^88 - 54 * q^89 - 2 * q^90 + 38 * q^91 + 33 * q^92 + 63 * q^93 - 4 * q^94 + 44 * q^95 - 3 * q^96 - 72 * q^98 + 43 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more