LMFDB - Embedded newform 1205.2.a.d.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1205,2,Mod(1,1205)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1205, 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("1205.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1205 = 5 \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1205.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:	$9.62197344356$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	1205.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.954311 q^{2} -0.726487 q^{3} -1.08929 q^{4} -1.00000 q^{5} +0.693295 q^{6} -1.92977 q^{7} +2.94814 q^{8} -2.47222 q^{9} +O(q^{10})$	\(q-0.954311 q^{2} -0.726487 q^{3} -1.08929 q^{4} -1.00000 q^{5} +0.693295 q^{6} -1.92977 q^{7} +2.94814 q^{8} -2.47222 q^{9} +0.954311 q^{10} -2.82880 q^{11} +0.791355 q^{12} -6.44491 q^{13} +1.84160 q^{14} +0.726487 q^{15} -0.634866 q^{16} -2.15771 q^{17} +2.35926 q^{18} +1.30556 q^{19} +1.08929 q^{20} +1.40195 q^{21} +2.69956 q^{22} +1.78850 q^{23} -2.14179 q^{24} +1.00000 q^{25} +6.15045 q^{26} +3.97549 q^{27} +2.10208 q^{28} +3.74238 q^{29} -0.693295 q^{30} -8.69196 q^{31} -5.29043 q^{32} +2.05509 q^{33} +2.05912 q^{34} +1.92977 q^{35} +2.69296 q^{36} -5.53981 q^{37} -1.24591 q^{38} +4.68214 q^{39} -2.94814 q^{40} +2.83107 q^{41} -1.33790 q^{42} +4.52447 q^{43} +3.08139 q^{44} +2.47222 q^{45} -1.70679 q^{46} -9.40445 q^{47} +0.461222 q^{48} -3.27600 q^{49} -0.954311 q^{50} +1.56755 q^{51} +7.02038 q^{52} +4.21628 q^{53} -3.79386 q^{54} +2.82880 q^{55} -5.68923 q^{56} -0.948471 q^{57} -3.57139 q^{58} -10.2699 q^{59} -0.791355 q^{60} +12.2459 q^{61} +8.29484 q^{62} +4.77080 q^{63} +6.31845 q^{64} +6.44491 q^{65} -1.96119 q^{66} -11.8281 q^{67} +2.35037 q^{68} -1.29932 q^{69} -1.84160 q^{70} +9.42721 q^{71} -7.28845 q^{72} +16.8357 q^{73} +5.28670 q^{74} -0.726487 q^{75} -1.42213 q^{76} +5.45893 q^{77} -4.46822 q^{78} +16.2958 q^{79} +0.634866 q^{80} +4.52851 q^{81} -2.70172 q^{82} +5.44188 q^{83} -1.52713 q^{84} +2.15771 q^{85} -4.31775 q^{86} -2.71879 q^{87} -8.33971 q^{88} +6.41711 q^{89} -2.35926 q^{90} +12.4372 q^{91} -1.94820 q^{92} +6.31460 q^{93} +8.97477 q^{94} -1.30556 q^{95} +3.84343 q^{96} +3.18370 q^{97} +3.12633 q^{98} +6.99341 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 4 q^{2} + 9 q^{3} + 36 q^{4} - 25 q^{5} + 7 q^{6} + 7 q^{7} - 15 q^{8} + 36 q^{9}+O(q^{10}) $ 25 * q - 4 * q^2 + 9 * q^3 + 36 * q^4 - 25 * q^5 + 7 * q^6 + 7 * q^7 - 15 * q^8 + 36 * q^9	\( 25 q - 4 q^{2} + 9 q^{3} + 36 q^{4} - 25 q^{5} + 7 q^{6} + 7 q^{7} - 15 q^{8} + 36 q^{9} + 4 q^{10} + 10 q^{11} + 22 q^{12} + 10 q^{13} + 13 q^{14} - 9 q^{15} + 54 q^{16} + q^{17} - 13 q^{18} + 50 q^{19} - 36 q^{20} + 9 q^{21} + 11 q^{22} - 31 q^{23} + 22 q^{24} + 25 q^{25} + 8 q^{26} + 42 q^{27} + 14 q^{28} + 4 q^{29} - 7 q^{30} + 34 q^{31} - 44 q^{32} + 28 q^{33} + 33 q^{34} - 7 q^{35} + 83 q^{36} + 14 q^{37} - 10 q^{38} + 23 q^{39} + 15 q^{40} + 11 q^{41} + 23 q^{42} + 49 q^{43} + 20 q^{44} - 36 q^{45} + 27 q^{46} - 28 q^{47} + 30 q^{48} + 66 q^{49} - 4 q^{50} + 49 q^{51} + 39 q^{52} - 16 q^{53} + 5 q^{54} - 10 q^{55} + 51 q^{56} + 10 q^{57} - 8 q^{58} + 30 q^{59} - 22 q^{60} + 35 q^{61} - 18 q^{62} + 73 q^{64} - 10 q^{65} - 13 q^{66} + 37 q^{67} + 11 q^{68} - 4 q^{69} - 13 q^{70} + 12 q^{71} - 90 q^{72} + 36 q^{73} - 12 q^{74} + 9 q^{75} + 57 q^{76} - 31 q^{77} - 9 q^{78} + 16 q^{79} - 54 q^{80} + 65 q^{81} - 11 q^{82} + 43 q^{83} - 62 q^{84} - q^{85} - 9 q^{86} - 22 q^{87} + 20 q^{88} + 38 q^{89} + 13 q^{90} + 86 q^{91} - 119 q^{92} + 10 q^{93} - 18 q^{94} - 50 q^{95} - 34 q^{96} + 17 q^{97} - 32 q^{98} + 26 q^{99}+O(q^{100}) \) 25 * q - 4 * q^2 + 9 * q^3 + 36 * q^4 - 25 * q^5 + 7 * q^6 + 7 * q^7 - 15 * q^8 + 36 * q^9 + 4 * q^10 + 10 * q^11 + 22 * q^12 + 10 * q^13 + 13 * q^14 - 9 * q^15 + 54 * q^16 + q^17 - 13 * q^18 + 50 * q^19 - 36 * q^20 + 9 * q^21 + 11 * q^22 - 31 * q^23 + 22 * q^24 + 25 * q^25 + 8 * q^26 + 42 * q^27 + 14 * q^28 + 4 * q^29 - 7 * q^30 + 34 * q^31 - 44 * q^32 + 28 * q^33 + 33 * q^34 - 7 * q^35 + 83 * q^36 + 14 * q^37 - 10 * q^38 + 23 * q^39 + 15 * q^40 + 11 * q^41 + 23 * q^42 + 49 * q^43 + 20 * q^44 - 36 * q^45 + 27 * q^46 - 28 * q^47 + 30 * q^48 + 66 * q^49 - 4 * q^50 + 49 * q^51 + 39 * q^52 - 16 * q^53 + 5 * q^54 - 10 * q^55 + 51 * q^56 + 10 * q^57 - 8 * q^58 + 30 * q^59 - 22 * q^60 + 35 * q^61 - 18 * q^62 + 73 * q^64 - 10 * q^65 - 13 * q^66 + 37 * q^67 + 11 * q^68 - 4 * q^69 - 13 * q^70 + 12 * q^71 - 90 * q^72 + 36 * q^73 - 12 * q^74 + 9 * q^75 + 57 * q^76 - 31 * q^77 - 9 * q^78 + 16 * q^79 - 54 * q^80 + 65 * q^81 - 11 * q^82 + 43 * q^83 - 62 * q^84 - q^85 - 9 * q^86 - 22 * q^87 + 20 * q^88 + 38 * q^89 + 13 * q^90 + 86 * q^91 - 119 * q^92 + 10 * q^93 - 18 * q^94 - 50 * q^95 - 34 * q^96 + 17 * q^97 - 32 * q^98 + 26 * 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 $

$2$	−0.954311	−0.674800	−0.337400	−	0.941361i	$-0.609547\pi$
$2$	−0.954311	−0.674800	−0.337400	+	0.941361i	$0.609547\pi$
$3$	−0.726487	−0.419437	−0.209719	−	0.977762i	$-0.567255\pi$
$3$	−0.726487	−0.419437	−0.209719	+	0.977762i	$0.567255\pi$
$4$	−1.08929	−0.544645
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.693295	0.283036
$7$	−1.92977	−0.729383	−0.364692	−	0.931128i	$-0.618826\pi$
$7$	−1.92977	−0.729383	−0.364692	+	0.931128i	$0.618826\pi$
$8$	2.94814	1.04233
$9$	−2.47222	−0.824072
$10$	0.954311	0.301780
$11$	−2.82880	−0.852916	−0.426458	−	0.904507i	$-0.640239\pi$
$11$	−2.82880	−0.852916	−0.426458	+	0.904507i	$0.640239\pi$
$12$	0.791355	0.228445
$13$	−6.44491	−1.78750	−0.893748	−	0.448570i	$-0.851934\pi$
$13$	−6.44491	−1.78750	−0.893748	+	0.448570i	$0.851934\pi$
$14$	1.84160	0.492188
$15$	0.726487	0.187578
$16$	−0.634866	−0.158717
$17$	−2.15771	−0.523321	−0.261660	−	0.965160i	$-0.584270\pi$
$17$	−2.15771	−0.523321	−0.261660	+	0.965160i	$0.584270\pi$
$18$	2.35926	0.556084
$19$	1.30556	0.299516	0.149758	−	0.988723i	$-0.452151\pi$
$19$	1.30556	0.299516	0.149758	+	0.988723i	$0.452151\pi$
$20$	1.08929	0.243573
$21$	1.40195	0.305931
$22$	2.69956	0.575547
$23$	1.78850	0.372929	0.186464	−	0.982462i	$-0.440297\pi$
$23$	1.78850	0.372929	0.186464	+	0.982462i	$0.440297\pi$
$24$	−2.14179	−0.437191
$25$	1.00000	0.200000
$26$	6.15045	1.20620
$27$	3.97549	0.765084
$28$	2.10208	0.397255
$29$	3.74238	0.694943	0.347471	−	0.937691i	$-0.387040\pi$
$29$	3.74238	0.694943	0.347471	+	0.937691i	$0.387040\pi$
$30$	−0.693295	−0.126578
$31$	−8.69196	−1.56112	−0.780561	−	0.625079i	$-0.785067\pi$
$31$	−8.69196	−1.56112	−0.780561	+	0.625079i	$0.785067\pi$
$32$	−5.29043	−0.935224
$33$	2.05509	0.357745
$34$	2.05912	0.353137
$35$	1.92977	0.326190
$36$	2.69296	0.448827
$37$	−5.53981	−0.910740	−0.455370	−	0.890302i	$-0.650493\pi$
$37$	−5.53981	−0.910740	−0.455370	+	0.890302i	$0.650493\pi$
$38$	−1.24591	−0.202113
$39$	4.68214	0.749743
$40$	−2.94814	−0.466143
$41$	2.83107	0.442139	0.221069	−	0.975258i	$-0.429045\pi$
$41$	2.83107	0.442139	0.221069	+	0.975258i	$0.429045\pi$
$42$	−1.33790	−0.206442
$43$	4.52447	0.689975	0.344987	−	0.938607i	$-0.387883\pi$
$43$	4.52447	0.689975	0.344987	+	0.938607i	$0.387883\pi$
$44$	3.08139	0.464536
$45$	2.47222	0.368536
$46$	−1.70679	−0.251652
$47$	−9.40445	−1.37178	−0.685890	−	0.727705i	$-0.740587\pi$
$47$	−9.40445	−1.37178	−0.685890	+	0.727705i	$0.740587\pi$
$48$	0.461222	0.0665717
$49$	−3.27600	−0.468000
$50$	−0.954311	−0.134960
$51$	1.56755	0.219500
$52$	7.02038	0.973551
$53$	4.21628	0.579151	0.289576	−	0.957155i	$-0.406486\pi$
$53$	4.21628	0.579151	0.289576	+	0.957155i	$0.406486\pi$
$54$	−3.79386	−0.516279
$55$	2.82880	0.381436
$56$	−5.68923	−0.760255
$57$	−0.948471	−0.125628
$58$	−3.57139	−0.468947
$59$	−10.2699	−1.33702	−0.668512	−	0.743702i	$-0.733068\pi$
$59$	−10.2699	−1.33702	−0.668512	+	0.743702i	$0.733068\pi$
$60$	−0.791355	−0.102164
$61$	12.2459	1.56792	0.783962	−	0.620808i	$-0.213195\pi$
$61$	12.2459	1.56792	0.783962	+	0.620808i	$0.213195\pi$
$62$	8.29484	1.05345
$63$	4.77080	0.601064
$64$	6.31845	0.789806
$65$	6.44491	0.799392
$66$	−1.96119	−0.241406
$67$	−11.8281	−1.44503	−0.722514	−	0.691356i	$-0.757014\pi$
$67$	−11.8281	−1.44503	−0.722514	+	0.691356i	$0.757014\pi$
$68$	2.35037	0.285024
$69$	−1.29932	−0.156420
$70$	−1.84160	−0.220113
$71$	9.42721	1.11880	0.559402	−	0.828897i	$-0.311031\pi$
$71$	9.42721	1.11880	0.559402	+	0.828897i	$0.311031\pi$
$72$	−7.28845	−0.858952
$73$	16.8357	1.97047	0.985237	−	0.171198i	$-0.0547637\pi$
$73$	16.8357	1.97047	0.985237	+	0.171198i	$0.0547637\pi$
$74$	5.28670	0.614567
$75$	−0.726487	−0.0838875
$76$	−1.42213	−0.163130
$77$	5.45893	0.622102
$78$	−4.46822	−0.505926
$79$	16.2958	1.83342	0.916712	−	0.399548i	$-0.130833\pi$
$79$	16.2958	1.83342	0.916712	+	0.399548i	$0.130833\pi$
$80$	0.634866	0.0709802
$81$	4.52851	0.503167
$82$	−2.70172	−0.298355
$83$	5.44188	0.597324	0.298662	−	0.954359i	$-0.403460\pi$
$83$	5.44188	0.597324	0.298662	+	0.954359i	$0.403460\pi$
$84$	−1.52713	−0.166624
$85$	2.15771	0.234036
$86$	−4.31775	−0.465595
$87$	−2.71879	−0.291485
$88$	−8.33971	−0.889017
$89$	6.41711	0.680212	0.340106	−	0.940387i	$-0.389537\pi$
$89$	6.41711	0.680212	0.340106	+	0.940387i	$0.389537\pi$
$90$	−2.35926	−0.248688
$91$	12.4372	1.30377
$92$	−1.94820	−0.203114
$93$	6.31460	0.654793
$94$	8.97477	0.925677
$95$	−1.30556	−0.133947
$96$	3.84343	0.392268
$97$	3.18370	0.323256	0.161628	−	0.986852i	$-0.448326\pi$
$97$	3.18370	0.323256	0.161628	+	0.986852i	$0.448326\pi$
$98$	3.12633	0.315807
$99$	6.99341	0.702864
$100$	−1.08929	−0.108929
$101$	11.1222	1.10670	0.553349	−	0.832949i	$-0.313349\pi$
$101$	11.1222	1.10670	0.553349	+	0.832949i	$0.313349\pi$
$102$	−1.49593	−0.148119
$103$	1.41993	0.139910	0.0699551	−	0.997550i	$-0.477714\pi$
$103$	1.41993	0.139910	0.0699551	+	0.997550i	$0.477714\pi$
$104$	−19.0005	−1.86315
$105$	−1.40195	−0.136816
$106$	−4.02365	−0.390811
$107$	−7.03950	−0.680534	−0.340267	−	0.940329i	$-0.610518\pi$
$107$	−7.03950	−0.680534	−0.340267	+	0.940329i	$0.610518\pi$
$108$	−4.33047	−0.416699
$109$	−8.60893	−0.824586	−0.412293	−	0.911051i	$-0.635272\pi$
$109$	−8.60893	−0.824586	−0.412293	+	0.911051i	$0.635272\pi$
$110$	−2.69956	−0.257393
$111$	4.02460	0.381998
$112$	1.22514	0.115765
$113$	−16.1383	−1.51816	−0.759081	−	0.650996i	$-0.774351\pi$
$113$	−16.1383	−1.51816	−0.759081	+	0.650996i	$0.774351\pi$
$114$	0.905136	0.0847738
$115$	−1.78850	−0.166779
$116$	−4.07654	−0.378497
$117$	15.9332	1.47303
$118$	9.80065	0.902223
$119$	4.16387	0.381701
$120$	2.14179	0.195518
$121$	−2.99788	−0.272535
$122$	−11.6864	−1.05804
$123$	−2.05673	−0.185449
$124$	9.46807	0.850258
$125$	−1.00000	−0.0894427
$126$	−4.55283	−0.405598
$127$	−8.33841	−0.739914	−0.369957	−	0.929049i	$-0.620628\pi$
$127$	−8.33841	−0.739914	−0.369957	+	0.929049i	$0.620628\pi$
$128$	4.55109	0.402264
$129$	−3.28697	−0.289401
$130$	−6.15045	−0.539430
$131$	18.8414	1.64618	0.823088	−	0.567914i	$-0.192249\pi$
$131$	18.8414	1.64618	0.823088	+	0.567914i	$0.192249\pi$
$132$	−2.23859	−0.194844
$133$	−2.51942	−0.218462
$134$	11.2877	0.975105
$135$	−3.97549	−0.342156
$136$	−6.36123	−0.545471
$137$	−19.0380	−1.62653	−0.813263	−	0.581896i	$-0.802311\pi$
$137$	−19.0380	−1.62653	−0.813263	+	0.581896i	$0.802311\pi$
$138$	1.23996	0.105552
$139$	19.8989	1.68780	0.843902	−	0.536497i	$-0.180253\pi$
$139$	19.8989	1.68780	0.843902	+	0.536497i	$0.180253\pi$
$140$	−2.10208	−0.177658
$141$	6.83221	0.575376
$142$	−8.99649	−0.754969
$143$	18.2314	1.52458
$144$	1.56953	0.130794
$145$	−3.74238	−0.310788
$146$	−16.0665	−1.32968
$147$	2.37997	0.196297
$148$	6.03446	0.496030
$149$	−19.4986	−1.59739	−0.798695	−	0.601736i	$-0.794476\pi$
$149$	−19.4986	−1.59739	−0.798695	+	0.601736i	$0.794476\pi$
$150$	0.693295	0.0566073
$151$	−7.24829	−0.589858	−0.294929	−	0.955519i	$-0.595296\pi$
$151$	−7.24829	−0.589858	−0.294929	+	0.955519i	$0.595296\pi$
$152$	3.84897	0.312193
$153$	5.33432	0.431254
$154$	−5.20951	−0.419795
$155$	8.69196	0.698155
$156$	−5.10021	−0.408344
$157$	5.22604	0.417083	0.208542	−	0.978014i	$-0.433128\pi$
$157$	5.22604	0.417083	0.208542	+	0.978014i	$0.433128\pi$
$158$	−15.5513	−1.23719
$159$	−3.06308	−0.242918
$160$	5.29043	0.418245
$161$	−3.45139	−0.272008
$162$	−4.32160	−0.339537
$163$	−5.26431	−0.412332	−0.206166	−	0.978517i	$-0.566099\pi$
$163$	−5.26431	−0.412332	−0.206166	+	0.978517i	$0.566099\pi$
$164$	−3.08386	−0.240809
$165$	−2.05509	−0.159988
$166$	−5.19325	−0.403074
$167$	−2.09327	−0.161982	−0.0809912	−	0.996715i	$-0.525809\pi$
$167$	−2.09327	−0.161982	−0.0809912	+	0.996715i	$0.525809\pi$
$168$	4.13315	0.318879
$169$	28.5368	2.19514
$170$	−2.05912	−0.157928
$171$	−3.22762	−0.246822
$172$	−4.92846	−0.375791
$173$	−15.6587	−1.19051	−0.595254	−	0.803538i	$-0.702949\pi$
$173$	−15.6587	−1.19051	−0.595254	+	0.803538i	$0.702949\pi$
$174$	2.59457	0.196694
$175$	−1.92977	−0.145877
$176$	1.79591	0.135372
$177$	7.46093	0.560798
$178$	−6.12392	−0.459007
$179$	15.6924	1.17291	0.586453	−	0.809983i	$-0.300524\pi$
$179$	15.6924	1.17291	0.586453	+	0.809983i	$0.300524\pi$
$180$	−2.69296	−0.200722
$181$	−25.3735	−1.88600	−0.942999	−	0.332795i	$-0.892008\pi$
$181$	−25.3735	−1.88600	−0.942999	+	0.332795i	$0.892008\pi$
$182$	−11.8689	−0.879783
$183$	−8.89648	−0.657646
$184$	5.27276	0.388713
$185$	5.53981	0.407295
$186$	−6.02609	−0.441854
$187$	6.10373	0.446349
$188$	10.2442	0.747133
$189$	−7.67177	−0.558039
$190$	1.24591	0.0903877
$191$	3.11508	0.225399	0.112700	−	0.993629i	$-0.464050\pi$
$191$	3.11508	0.225399	0.112700	+	0.993629i	$0.464050\pi$
$192$	−4.59027	−0.331274
$193$	−1.60613	−0.115612	−0.0578058	−	0.998328i	$-0.518410\pi$
$193$	−1.60613	−0.115612	−0.0578058	+	0.998328i	$0.518410\pi$
$194$	−3.03824	−0.218133
$195$	−4.68214	−0.335295
$196$	3.56852	0.254894
$197$	−15.2199	−1.08437	−0.542187	−	0.840258i	$-0.682404\pi$
$197$	−15.2199	−1.08437	−0.542187	+	0.840258i	$0.682404\pi$
$198$	−6.67389	−0.474293
$199$	3.89119	0.275839	0.137920	−	0.990443i	$-0.455958\pi$
$199$	3.89119	0.275839	0.137920	+	0.990443i	$0.455958\pi$
$200$	2.94814	0.208465
$201$	8.59293	0.606099
$202$	−10.6140	−0.746800
$203$	−7.22192	−0.506879
$204$	−1.70751	−0.119550
$205$	−2.83107	−0.197730
$206$	−1.35506	−0.0944114
$207$	−4.42157	−0.307320
$208$	4.09165	0.283705
$209$	−3.69317	−0.255462
$210$	1.33790	0.0923236
$211$	23.3482	1.60735	0.803677	−	0.595066i	$-0.202874\pi$
$211$	23.3482	1.60735	0.803677	+	0.595066i	$0.202874\pi$
$212$	−4.59276	−0.315432
$213$	−6.84874	−0.469268
$214$	6.71788	0.459225
$215$	−4.52447	−0.308566
$216$	11.7203	0.797467
$217$	16.7735	1.13866
$218$	8.21560	0.556431
$219$	−12.2309	−0.826490
$220$	−3.08139	−0.207747
$221$	13.9062	0.935434
$222$	−3.84072	−0.257772
$223$	−24.7633	−1.65827	−0.829135	−	0.559048i	$-0.811167\pi$
$223$	−24.7633	−1.65827	−0.829135	+	0.559048i	$0.811167\pi$
$224$	10.2093	0.682137
$225$	−2.47222	−0.164814
$226$	15.4009	1.02446
$227$	4.59488	0.304973	0.152486	−	0.988306i	$-0.451272\pi$
$227$	4.59488	0.304973	0.152486	+	0.988306i	$0.451272\pi$
$228$	1.03316	0.0684227
$229$	8.91085	0.588846	0.294423	−	0.955675i	$-0.404873\pi$
$229$	8.91085	0.588846	0.294423	+	0.955675i	$0.404873\pi$
$230$	1.70679	0.112542
$231$	−3.96584	−0.260933
$232$	11.0331	0.724357
$233$	−11.1866	−0.732858	−0.366429	−	0.930446i	$-0.619420\pi$
$233$	−11.1866	−0.732858	−0.366429	+	0.930446i	$0.619420\pi$
$234$	−15.2052	−0.993998
$235$	9.40445	0.613479
$236$	11.1869	0.728203
$237$	−11.8387	−0.769007
$238$	−3.97363	−0.257572
$239$	9.02136	0.583543	0.291771	−	0.956488i	$-0.405755\pi$
$239$	9.02136	0.583543	0.291771	+	0.956488i	$0.405755\pi$
$240$	−0.461222	−0.0297718
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	2.86091	0.183906
$243$	−15.2164	−0.976131
$244$	−13.3393	−0.853963
$245$	3.27600	0.209296
$246$	1.96276	0.125141
$247$	−8.41420	−0.535383
$248$	−25.6252	−1.62720
$249$	−3.95346	−0.250540
$250$	0.954311	0.0603559
$251$	0.292167	0.0184414	0.00922072	−	0.999957i	$-0.497065\pi$
$251$	0.292167	0.0184414	0.00922072	+	0.999957i	$0.497065\pi$
$252$	−5.19679	−0.327367
$253$	−5.05932	−0.318077
$254$	7.95744	0.499294
$255$	−1.56755	−0.0981636
$256$	−16.9801	−1.06125
$257$	1.33623	0.0833516	0.0416758	−	0.999131i	$-0.486730\pi$
$257$	1.33623	0.0833516	0.0416758	+	0.999131i	$0.486730\pi$
$258$	3.13679	0.195288
$259$	10.6905	0.664278
$260$	−7.02038	−0.435385
$261$	−9.25197	−0.572683
$262$	−17.9805	−1.11084
$263$	−0.261451	−0.0161218	−0.00806089	−	0.999968i	$-0.502566\pi$
$263$	−0.261451	−0.0161218	−0.00806089	+	0.999968i	$0.502566\pi$
$264$	6.05869	0.372887
$265$	−4.21628	−0.259004
$266$	2.40431	0.147418
$267$	−4.66195	−0.285306
$268$	12.8842	0.787027
$269$	−31.1244	−1.89769	−0.948843	−	0.315748i	$-0.897744\pi$
$269$	−31.1244	−1.89769	−0.948843	+	0.315748i	$0.897744\pi$
$270$	3.79386	0.230887
$271$	6.21072	0.377274	0.188637	−	0.982047i	$-0.439593\pi$
$271$	6.21072	0.377274	0.188637	+	0.982047i	$0.439593\pi$
$272$	1.36986	0.0830597
$273$	−9.03544	−0.546850
$274$	18.1682	1.09758
$275$	−2.82880	−0.170583
$276$	1.41534	0.0851935
$277$	31.1724	1.87297	0.936483	−	0.350712i	$-0.114060\pi$
$277$	31.1724	1.87297	0.936483	+	0.350712i	$0.114060\pi$
$278$	−18.9898	−1.13893
$279$	21.4884	1.28648
$280$	5.68923	0.339996
$281$	−30.3646	−1.81140	−0.905701	−	0.423916i	$-0.860655\pi$
$281$	−30.3646	−1.81140	−0.905701	+	0.423916i	$0.860655\pi$
$282$	−6.52006	−0.388264
$283$	32.8954	1.95543	0.977715	−	0.209937i	$-0.0673260\pi$
$283$	32.8954	1.95543	0.977715	+	0.209937i	$0.0673260\pi$
$284$	−10.2690	−0.609351
$285$	0.948471	0.0561826
$286$	−17.3984	−1.02879
$287$	−5.46330	−0.322488
$288$	13.0791	0.770692
$289$	−12.3443	−0.726135
$290$	3.57139	0.209720
$291$	−2.31292	−0.135586
$292$	−18.3390	−1.07321
$293$	−10.8629	−0.634616	−0.317308	−	0.948323i	$-0.602779\pi$
$293$	−10.8629	−0.634616	−0.317308	+	0.948323i	$0.602779\pi$
$294$	−2.27123	−0.132461
$295$	10.2699	0.597935
$296$	−16.3322	−0.949288
$297$	−11.2459	−0.652552
$298$	18.6078	1.07792
$299$	−11.5267	−0.666608
$300$	0.791355	0.0456889
$301$	−8.73117	−0.503256
$302$	6.91713	0.398036
$303$	−8.08012	−0.464191
$304$	−0.828855	−0.0475381
$305$	−12.2459	−0.701197
$306$	−5.09060	−0.291010
$307$	−15.4972	−0.884472	−0.442236	−	0.896899i	$-0.645815\pi$
$307$	−15.4972	−0.884472	−0.442236	+	0.896899i	$0.645815\pi$
$308$	−5.94635	−0.338825
$309$	−1.03156	−0.0586836
$310$	−8.29484	−0.471115
$311$	10.0955	0.572465	0.286232	−	0.958160i	$-0.407597\pi$
$311$	10.0955	0.572465	0.286232	+	0.958160i	$0.407597\pi$
$312$	13.8036	0.781477
$313$	24.5157	1.38571	0.692854	−	0.721078i	$-0.256353\pi$
$313$	24.5157	1.38571	0.692854	+	0.721078i	$0.256353\pi$
$314$	−4.98726	−0.281448
$315$	−4.77080	−0.268804
$316$	−17.7509	−0.998566
$317$	−21.3367	−1.19839	−0.599195	−	0.800603i	$-0.704513\pi$
$317$	−21.3367	−1.19839	−0.599195	+	0.800603i	$0.704513\pi$
$318$	2.92313	0.163921
$319$	−10.5865	−0.592727
$320$	−6.31845	−0.353212
$321$	5.11411	0.285442
$322$	3.29370	0.183551
$323$	−2.81701	−0.156743
$324$	−4.93286	−0.274048
$325$	−6.44491	−0.357499
$326$	5.02379	0.278242
$327$	6.25428	0.345862
$328$	8.34640	0.460853
$329$	18.1484	1.00055
$330$	1.96119	0.107960
$331$	18.3486	1.00853	0.504266	−	0.863548i	$-0.331763\pi$
$331$	18.3486	1.00853	0.504266	+	0.863548i	$0.331763\pi$
$332$	−5.92779	−0.325330
$333$	13.6956	0.750515
$334$	1.99763	0.109306
$335$	11.8281	0.646236
$336$	−0.890051	−0.0485562
$337$	23.5672	1.28379	0.641893	−	0.766794i	$-0.278149\pi$
$337$	23.5672	1.28379	0.641893	+	0.766794i	$0.278149\pi$
$338$	−27.2330	−1.48128
$339$	11.7243	0.636774
$340$	−2.35037	−0.127467
$341$	24.5878	1.33151
$342$	3.08016	0.166556
$343$	19.8303	1.07073
$344$	13.3388	0.719179
$345$	1.29932	0.0699532
$346$	14.9433	0.803355
$347$	−29.9357	−1.60703	−0.803516	−	0.595284i	$-0.797040\pi$
$347$	−29.9357	−1.60703	−0.803516	+	0.595284i	$0.797040\pi$
$348$	2.96155	0.158756
$349$	−14.2722	−0.763973	−0.381987	−	0.924168i	$-0.624760\pi$
$349$	−14.2722	−0.763973	−0.381987	+	0.924168i	$0.624760\pi$
$350$	1.84160	0.0984375
$351$	−25.6217	−1.36758
$352$	14.9656	0.797668
$353$	−7.32451	−0.389844	−0.194922	−	0.980819i	$-0.562445\pi$
$353$	−7.32451	−0.389844	−0.194922	+	0.980819i	$0.562445\pi$
$354$	−7.12005	−0.378426
$355$	−9.42721	−0.500344
$356$	−6.99009	−0.370474
$357$	−3.02500	−0.160100
$358$	−14.9755	−0.791477
$359$	1.92275	0.101479	0.0507394	−	0.998712i	$-0.483842\pi$
$359$	1.92275	0.101479	0.0507394	+	0.998712i	$0.483842\pi$
$360$	7.28845	0.384135
$361$	−17.2955	−0.910290
$362$	24.2142	1.27267
$363$	2.17792	0.114311
$364$	−13.5477	−0.710092
$365$	−16.8357	−0.881223
$366$	8.49001	0.443780
$367$	10.6190	0.554305	0.277153	−	0.960826i	$-0.410609\pi$
$367$	10.6190	0.554305	0.277153	+	0.960826i	$0.410609\pi$
$368$	−1.13546	−0.0591899
$369$	−6.99901	−0.364354
$370$	−5.28670	−0.274843
$371$	−8.13644	−0.422423
$372$	−6.87843	−0.356630
$373$	21.9835	1.13826	0.569132	−	0.822246i	$-0.307279\pi$
$373$	21.9835	1.13826	0.569132	+	0.822246i	$0.307279\pi$
$374$	−5.82485	−0.301196
$375$	0.726487	0.0375156
$376$	−27.7257	−1.42984
$377$	−24.1193	−1.24221
$378$	7.32126	0.376565
$379$	11.7937	0.605801	0.302901	−	0.953022i	$-0.402045\pi$
$379$	11.7937	0.605801	0.302901	+	0.953022i	$0.402045\pi$
$380$	1.42213	0.0729538
$381$	6.05775	0.310348
$382$	−2.97275	−0.152099
$383$	3.77603	0.192946	0.0964731	−	0.995336i	$-0.469244\pi$
$383$	3.77603	0.192946	0.0964731	+	0.995336i	$0.469244\pi$
$384$	−3.30631	−0.168724
$385$	−5.45893	−0.278213
$386$	1.53275	0.0780147
$387$	−11.1855	−0.568589
$388$	−3.46798	−0.176060
$389$	−5.79768	−0.293954	−0.146977	−	0.989140i	$-0.546954\pi$
$389$	−5.79768	−0.293954	−0.146977	+	0.989140i	$0.546954\pi$
$390$	4.46822	0.226257
$391$	−3.85907	−0.195161
$392$	−9.65813	−0.487809
$393$	−13.6880	−0.690468
$394$	14.5245	0.731735
$395$	−16.2958	−0.819932
$396$	−7.61785	−0.382812
$397$	10.3725	0.520583	0.260291	−	0.965530i	$-0.416181\pi$
$397$	10.3725	0.520583	0.260291	+	0.965530i	$0.416181\pi$
$398$	−3.71341	−0.186136
$399$	1.83033	0.0916310
$400$	−0.634866	−0.0317433
$401$	14.1753	0.707880	0.353940	−	0.935268i	$-0.384842\pi$
$401$	14.1753	0.707880	0.353940	+	0.935268i	$0.384842\pi$
$402$	−8.20033	−0.408995
$403$	56.0189	2.79050
$404$	−12.1153	−0.602758
$405$	−4.52851	−0.225023
$406$	6.89196	0.342042
$407$	15.6710	0.776784
$408$	4.62135	0.228791
$409$	−36.9371	−1.82642	−0.913212	−	0.407485i	$-0.866406\pi$
$409$	−36.9371	−1.82642	−0.913212	+	0.407485i	$0.866406\pi$
$410$	2.70172	0.133428
$411$	13.8309	0.682226
$412$	−1.54672	−0.0762014
$413$	19.8185	0.975202
$414$	4.21955	0.207380
$415$	−5.44188	−0.267132
$416$	34.0963	1.67171
$417$	−14.4563	−0.707928
$418$	3.52443	0.172385
$419$	23.1100	1.12899	0.564497	−	0.825435i	$-0.309070\pi$
$419$	23.1100	1.12899	0.564497	+	0.825435i	$0.309070\pi$
$420$	1.52713	0.0745163
$421$	−18.5538	−0.904255	−0.452127	−	0.891953i	$-0.649335\pi$
$421$	−18.5538	−0.904255	−0.452127	+	0.891953i	$0.649335\pi$
$422$	−22.2814	−1.08464
$423$	23.2498	1.13045
$424$	12.4302	0.603664
$425$	−2.15771	−0.104664
$426$	6.53583	0.316662
$427$	−23.6317	−1.14362
$428$	7.66806	0.370650
$429$	−13.2448	−0.639467
$430$	4.31775	0.208220
$431$	−9.98236	−0.480833	−0.240417	−	0.970670i	$-0.577284\pi$
$431$	−9.98236	−0.480833	−0.240417	+	0.970670i	$0.577284\pi$
$432$	−2.52391	−0.121432
$433$	15.6993	0.754459	0.377230	−	0.926120i	$-0.376877\pi$
$433$	15.6993	0.754459	0.377230	+	0.926120i	$0.376877\pi$
$434$	−16.0071	−0.768365
$435$	2.71879	0.130356
$436$	9.37763	0.449107
$437$	2.33499	0.111698
$438$	11.6721	0.557716
$439$	3.10402	0.148147	0.0740733	−	0.997253i	$-0.476400\pi$
$439$	3.10402	0.148147	0.0740733	+	0.997253i	$0.476400\pi$
$440$	8.33971	0.397580
$441$	8.09899	0.385666
$442$	−13.2709	−0.631231
$443$	1.81863	0.0864058	0.0432029	−	0.999066i	$-0.486244\pi$
$443$	1.81863	0.0864058	0.0432029	+	0.999066i	$0.486244\pi$
$444$	−4.38396	−0.208053
$445$	−6.41711	−0.304200
$446$	23.6318	1.11900
$447$	14.1655	0.670005
$448$	−12.1931	−0.576071
$449$	−8.38120	−0.395533	−0.197767	−	0.980249i	$-0.563369\pi$
$449$	−8.38120	−0.395533	−0.197767	+	0.980249i	$0.563369\pi$
$450$	2.35926	0.111217
$451$	−8.00853	−0.377107
$452$	17.5793	0.826859
$453$	5.26579	0.247408
$454$	−4.38494	−0.205796
$455$	−12.4372	−0.583063
$456$	−2.79623	−0.130945
$457$	−34.0456	−1.59259	−0.796294	−	0.604910i	$-0.793209\pi$
$457$	−34.0456	−1.59259	−0.796294	+	0.604910i	$0.793209\pi$
$458$	−8.50372	−0.397353
$459$	−8.57795	−0.400385
$460$	1.94820	0.0908352
$461$	37.0441	1.72532	0.862659	−	0.505786i	$-0.168797\pi$
$461$	37.0441	1.72532	0.862659	+	0.505786i	$0.168797\pi$
$462$	3.78464	0.176078
$463$	17.9429	0.833876	0.416938	−	0.908935i	$-0.363103\pi$
$463$	17.9429	0.833876	0.416938	+	0.908935i	$0.363103\pi$
$464$	−2.37591	−0.110299
$465$	−6.31460	−0.292832
$466$	10.6755	0.494532
$467$	22.5460	1.04330	0.521652	−	0.853158i	$-0.325316\pi$
$467$	22.5460	1.04330	0.521652	+	0.853158i	$0.325316\pi$
$468$	−17.3559	−0.802276
$469$	22.8254	1.05398
$470$	−8.97477	−0.413975
$471$	−3.79665	−0.174940
$472$	−30.2771	−1.39361
$473$	−12.7988	−0.588490
$474$	11.2978	0.518926
$475$	1.30556	0.0599031
$476$	−4.53566	−0.207892
$477$	−10.4236	−0.477262
$478$	−8.60918	−0.393775
$479$	−6.58124	−0.300705	−0.150352	−	0.988632i	$-0.548041\pi$
$479$	−6.58124	−0.300705	−0.150352	+	0.988632i	$0.548041\pi$
$480$	−3.84343	−0.175428
$481$	35.7036	1.62794
$482$	−0.954311	−0.0434677
$483$	2.50739	0.114090
$484$	3.26556	0.148435
$485$	−3.18370	−0.144565
$486$	14.5212	0.658693
$487$	30.3973	1.37743	0.688717	−	0.725031i	$-0.258174\pi$
$487$	30.3973	1.37743	0.688717	+	0.725031i	$0.258174\pi$
$488$	36.1026	1.63429
$489$	3.82445	0.172948
$490$	−3.12633	−0.141233
$491$	−6.16398	−0.278176	−0.139088	−	0.990280i	$-0.544417\pi$
$491$	−6.16398	−0.278176	−0.139088	+	0.990280i	$0.544417\pi$
$492$	2.24038	0.101004
$493$	−8.07496	−0.363678
$494$	8.02977	0.361276
$495$	−6.99341	−0.314330
$496$	5.51823	0.247776
$497$	−18.1923	−0.816036
$498$	3.77283	0.169064
$499$	10.2121	0.457157	0.228579	−	0.973525i	$-0.426592\pi$
$499$	10.2121	0.457157	0.228579	+	0.973525i	$0.426592\pi$
$500$	1.08929	0.0487145
$501$	1.52074	0.0679415
$502$	−0.278819	−0.0124443
$503$	−33.2347	−1.48186	−0.740930	−	0.671582i	$-0.765615\pi$
$503$	−33.2347	−1.48186	−0.740930	+	0.671582i	$0.765615\pi$
$504$	14.0650	0.626505
$505$	−11.1222	−0.494931
$506$	4.82816	0.214638
$507$	−20.7316	−0.920724
$508$	9.08295	0.402991
$509$	32.8944	1.45802	0.729009	−	0.684504i	$-0.239981\pi$
$509$	32.8944	1.45802	0.729009	+	0.684504i	$0.239981\pi$
$510$	1.49593	0.0662408
$511$	−32.4890	−1.43723
$512$	7.10207	0.313870
$513$	5.19024	0.229155
$514$	−1.27518	−0.0562457
$515$	−1.41993	−0.0625698
$516$	3.58046	0.157621
$517$	26.6033	1.17001
$518$	−10.2021	−0.448255
$519$	11.3758	0.499344
$520$	19.0005	0.833228
$521$	−16.7379	−0.733302	−0.366651	−	0.930359i	$-0.619496\pi$
$521$	−16.7379	−0.733302	−0.366651	+	0.930359i	$0.619496\pi$
$522$	8.82926	0.386446
$523$	1.77831	0.0777599	0.0388799	−	0.999244i	$-0.487621\pi$
$523$	1.77831	0.0777599	0.0388799	+	0.999244i	$0.487621\pi$
$524$	−20.5237	−0.896582
$525$	1.40195	0.0611861
$526$	0.249506	0.0108790
$527$	18.7547	0.816968
$528$	−1.30471	−0.0567800
$529$	−19.8013	−0.860924
$530$	4.02365	0.174776
$531$	25.3894	1.10180
$532$	2.74438	0.118984
$533$	−18.2460	−0.790321
$534$	4.44895	0.192525
$535$	7.03950	0.304344
$536$	−34.8708	−1.50619
$537$	−11.4003	−0.491961
$538$	29.7023	1.28056
$539$	9.26716	0.399165
$540$	4.33047	0.186354
$541$	16.6472	0.715718	0.357859	−	0.933776i	$-0.383507\pi$
$541$	16.6472	0.715718	0.357859	+	0.933776i	$0.383507\pi$
$542$	−5.92696	−0.254585
$543$	18.4335	0.791058
$544$	11.4152	0.489423
$545$	8.60893	0.368766
$546$	8.62262	0.369014
$547$	19.0159	0.813060	0.406530	−	0.913637i	$-0.366739\pi$
$547$	19.0159	0.813060	0.406530	+	0.913637i	$0.366739\pi$
$548$	20.7379	0.885880
$549$	−30.2745	−1.29208
$550$	2.69956	0.115109
$551$	4.88590	0.208146
$552$	−3.83059	−0.163041
$553$	−31.4472	−1.33727
$554$	−29.7482	−1.26388
$555$	−4.02460	−0.170835
$556$	−21.6757	−0.919254
$557$	20.6747	0.876017	0.438008	−	0.898971i	$-0.355684\pi$
$557$	20.6747	0.876017	0.438008	+	0.898971i	$0.355684\pi$
$558$	−20.5066	−0.868115
$559$	−29.1598	−1.23333
$560$	−1.22514	−0.0517718
$561$	−4.43428	−0.187215
$562$	28.9773	1.22233
$563$	−33.3776	−1.40670	−0.703349	−	0.710845i	$-0.748313\pi$
$563$	−33.3776	−1.40670	−0.703349	+	0.710845i	$0.748313\pi$
$564$	−7.44226	−0.313376
$565$	16.1383	0.678943
$566$	−31.3925	−1.31952
$567$	−8.73896	−0.367002
$568$	27.7928	1.16616
$569$	28.2188	1.18299	0.591496	−	0.806308i	$-0.298538\pi$
$569$	28.2188	1.18299	0.591496	+	0.806308i	$0.298538\pi$
$570$	−0.905136	−0.0379120
$571$	−14.6813	−0.614392	−0.307196	−	0.951646i	$-0.599391\pi$
$571$	−14.6813	−0.614392	−0.307196	+	0.951646i	$0.599391\pi$
$572$	−19.8592	−0.830357
$573$	−2.26306	−0.0945408
$574$	5.21369	0.217615
$575$	1.78850	0.0745857
$576$	−15.6206	−0.650857
$577$	−5.06714	−0.210948	−0.105474	−	0.994422i	$-0.533636\pi$
$577$	−5.06714	−0.210948	−0.105474	+	0.994422i	$0.533636\pi$
$578$	11.7803	0.489996
$579$	1.16683	0.0484918
$580$	4.07654	0.169269
$581$	−10.5016	−0.435678
$582$	2.20724	0.0914932
$583$	−11.9270	−0.493967
$584$	49.6342	2.05388
$585$	−15.9332	−0.658757
$586$	10.3666	0.428239
$587$	37.9278	1.56545	0.782725	−	0.622368i	$-0.213829\pi$
$587$	37.9278	1.56545	0.782725	+	0.622368i	$0.213829\pi$
$588$	−2.59248	−0.106912
$589$	−11.3479	−0.467581
$590$	−9.80065	−0.403487
$591$	11.0571	0.454827
$592$	3.51704	0.144549
$593$	15.7405	0.646385	0.323193	−	0.946333i	$-0.395244\pi$
$593$	15.7405	0.646385	0.323193	+	0.946333i	$0.395244\pi$
$594$	10.7321	0.440342
$595$	−4.16387	−0.170702
$596$	21.2397	0.870011
$597$	−2.82690	−0.115697
$598$	11.0001	0.449827
$599$	−19.7226	−0.805842	−0.402921	−	0.915235i	$-0.632005\pi$
$599$	−19.7226	−0.805842	−0.402921	+	0.915235i	$0.632005\pi$
$600$	−2.14179	−0.0874381
$601$	16.4315	0.670255	0.335127	−	0.942173i	$-0.391221\pi$
$601$	16.4315	0.670255	0.335127	+	0.942173i	$0.391221\pi$
$602$	8.33225	0.339597
$603$	29.2415	1.19081
$604$	7.89550	0.321263
$605$	2.99788	0.121881
$606$	7.71095	0.313236
$607$	3.48612	0.141497	0.0707487	−	0.997494i	$-0.477461\pi$
$607$	3.48612	0.141497	0.0707487	+	0.997494i	$0.477461\pi$
$608$	−6.90696	−0.280114
$609$	5.24663	0.212604
$610$	11.6864	0.473168
$611$	60.6108	2.45205
$612$	−5.81062	−0.234881
$613$	−26.4960	−1.07016	−0.535081	−	0.844801i	$-0.679719\pi$
$613$	−26.4960	−1.07016	−0.535081	+	0.844801i	$0.679719\pi$
$614$	14.7892	0.596842
$615$	2.05673	0.0829355
$616$	16.0937	0.648434
$617$	38.4572	1.54823	0.774115	−	0.633045i	$-0.218195\pi$
$617$	38.4572	1.54823	0.774115	+	0.633045i	$0.218195\pi$
$618$	0.984433	0.0395997
$619$	36.4591	1.46542	0.732708	−	0.680544i	$-0.238256\pi$
$619$	36.4591	1.46542	0.732708	+	0.680544i	$0.238256\pi$
$620$	−9.46807	−0.380247
$621$	7.11018	0.285322
$622$	−9.63427	−0.386299
$623$	−12.3835	−0.496135
$624$	−2.97253	−0.118997
$625$	1.00000	0.0400000
$626$	−23.3956	−0.935076
$627$	2.68304	0.107150
$628$	−5.69267	−0.227162
$629$	11.9533	0.476609
$630$	4.55283	0.181389
$631$	29.7324	1.18363	0.591814	−	0.806074i	$-0.298412\pi$
$631$	29.7324	1.18363	0.591814	+	0.806074i	$0.298412\pi$
$632$	48.0425	1.91103
$633$	−16.9621	−0.674184
$634$	20.3619	0.808674
$635$	8.33841	0.330900
$636$	3.33658	0.132304
$637$	21.1135	0.836549
$638$	10.1028	0.399972
$639$	−23.3061	−0.921975
$640$	−4.55109	−0.179898
$641$	18.7422	0.740274	0.370137	−	0.928977i	$-0.379311\pi$
$641$	18.7422	0.740274	0.370137	+	0.928977i	$0.379311\pi$
$642$	−4.88045	−0.192616
$643$	29.5989	1.16727	0.583633	−	0.812018i	$-0.301631\pi$
$643$	29.5989	1.16727	0.583633	+	0.812018i	$0.301631\pi$
$644$	3.75957	0.148148
$645$	3.28697	0.129424
$646$	2.68831	0.105770
$647$	−37.4655	−1.47292	−0.736460	−	0.676481i	$-0.763504\pi$
$647$	−37.4655	−1.47292	−0.736460	+	0.676481i	$0.763504\pi$
$648$	13.3507	0.524465
$649$	29.0514	1.14037
$650$	6.15045	0.241240
$651$	−12.1857	−0.477595
$652$	5.73436	0.224575
$653$	19.4784	0.762249	0.381124	−	0.924524i	$-0.375537\pi$
$653$	19.4784	0.762249	0.381124	+	0.924524i	$0.375537\pi$
$654$	−5.96853	−0.233388
$655$	−18.8414	−0.736192
$656$	−1.79735	−0.0701747
$657$	−41.6216	−1.62381
$658$	−17.3192	−0.675173
$659$	27.6813	1.07831	0.539155	−	0.842206i	$-0.318744\pi$
$659$	27.6813	1.07831	0.539155	+	0.842206i	$0.318744\pi$
$660$	2.23859	0.0871369
$661$	34.3354	1.33549	0.667745	−	0.744390i	$-0.267260\pi$
$661$	34.3354	1.33549	0.667745	+	0.744390i	$0.267260\pi$
$662$	−17.5103	−0.680558
$663$	−10.1027	−0.392356
$664$	16.0435	0.622607
$665$	2.51942	0.0976990
$666$	−13.0699	−0.506448
$667$	6.69326	0.259164
$668$	2.28018	0.0882229
$669$	17.9902	0.695541
$670$	−11.2877	−0.436080
$671$	−34.6412	−1.33731
$672$	−7.41692	−0.286114
$673$	−11.8998	−0.458702	−0.229351	−	0.973344i	$-0.573660\pi$
$673$	−11.8998	−0.458702	−0.229351	+	0.973344i	$0.573660\pi$
$674$	−22.4904	−0.866299
$675$	3.97549	0.153017
$676$	−31.0849	−1.19557
$677$	22.0197	0.846288	0.423144	−	0.906063i	$-0.360927\pi$
$677$	22.0197	0.846288	0.423144	+	0.906063i	$0.360927\pi$
$678$	−11.1886	−0.429695
$679$	−6.14380	−0.235777
$680$	6.36123	0.243942
$681$	−3.33812	−0.127917
$682$	−23.4645	−0.898500
$683$	−47.4084	−1.81403	−0.907016	−	0.421096i	$-0.861645\pi$
$683$	−47.4084	−1.81403	−0.907016	+	0.421096i	$0.861645\pi$
$684$	3.51582	0.134431
$685$	19.0380	0.727405
$686$	−18.9243	−0.722532
$687$	−6.47362	−0.246984
$688$	−2.87243	−0.109510
$689$	−27.1736	−1.03523
$690$	−1.23996	−0.0472044
$691$	−32.9505	−1.25350	−0.626748	−	0.779222i	$-0.715614\pi$
$691$	−32.9505	−1.25350	−0.626748	+	0.779222i	$0.715614\pi$
$692$	17.0569	0.648404
$693$	−13.4956	−0.512657
$694$	28.5679	1.08442
$695$	−19.8989	−0.754809
$696$	−8.01539	−0.303822
$697$	−6.10862	−0.231380
$698$	13.6201	0.515529
$699$	8.12691	0.307388
$700$	2.10208	0.0794510
$701$	−21.4743	−0.811072	−0.405536	−	0.914079i	$-0.632915\pi$
$701$	−21.4743	−0.811072	−0.405536	+	0.914079i	$0.632915\pi$
$702$	24.4511	0.922846
$703$	−7.23255	−0.272781
$704$	−17.8736	−0.673638
$705$	−6.83221	−0.257316
$706$	6.98986	0.263067
$707$	−21.4632	−0.807207
$708$	−8.12712	−0.305436
$709$	19.2938	0.724593	0.362296	−	0.932063i	$-0.381993\pi$
$709$	19.2938	0.724593	0.362296	+	0.932063i	$0.381993\pi$
$710$	8.99649	0.337632
$711$	−40.2868	−1.51087
$712$	18.9186	0.709003
$713$	−15.5456	−0.582187
$714$	2.88679	0.108035
$715$	−18.2314	−0.681814
$716$	−17.0936	−0.638818
$717$	−6.55390	−0.244760
$718$	−1.83490	−0.0684779
$719$	−2.49526	−0.0930574	−0.0465287	−	0.998917i	$-0.514816\pi$
$719$	−2.49526	−0.0930574	−0.0465287	+	0.998917i	$0.514816\pi$
$720$	−1.56953	−0.0584928
$721$	−2.74014	−0.102048
$722$	16.5053	0.614264
$723$	−0.726487	−0.0270183
$724$	27.6391	1.02720
$725$	3.74238	0.138989
$726$	−2.07842	−0.0771372
$727$	24.6994	0.916048	0.458024	−	0.888940i	$-0.348557\pi$
$727$	24.6994	0.916048	0.458024	+	0.888940i	$0.348557\pi$
$728$	36.6666	1.35895
$729$	−2.53101	−0.0937412
$730$	16.0665	0.594649
$731$	−9.76248	−0.361078
$732$	9.69084	0.358184
$733$	−8.47061	−0.312869	−0.156435	−	0.987688i	$-0.550000\pi$
$733$	−8.47061	−0.312869	−0.156435	+	0.987688i	$0.550000\pi$
$734$	−10.1338	−0.374045
$735$	−2.37997	−0.0877866
$736$	−9.46194	−0.348772
$737$	33.4592	1.23249
$738$	6.67924	0.245866
$739$	25.6575	0.943825	0.471913	−	0.881645i	$-0.343564\pi$
$739$	25.6575	0.943825	0.471913	+	0.881645i	$0.343564\pi$
$740$	−6.03446	−0.221831
$741$	6.11281	0.224560
$742$	7.76470	0.285051
$743$	3.16313	0.116044	0.0580221	−	0.998315i	$-0.481521\pi$
$743$	3.16313	0.116044	0.0580221	+	0.998315i	$0.481521\pi$
$744$	18.6163	0.682508
$745$	19.4986	0.714375
$746$	−20.9791	−0.768100
$747$	−13.4535	−0.492238
$748$	−6.64873	−0.243102
$749$	13.5846	0.496370
$750$	−0.693295	−0.0253155
$751$	−29.3697	−1.07171	−0.535857	−	0.844309i	$-0.680012\pi$
$751$	−29.3697	−1.07171	−0.535857	+	0.844309i	$0.680012\pi$
$752$	5.97057	0.217724
$753$	−0.212256	−0.00773503
$754$	23.0173	0.838241
$755$	7.24829	0.263792
$756$	8.35679	0.303933
$757$	−0.0845371	−0.00307255	−0.00153628	−	0.999999i	$-0.500489\pi$
$757$	−0.0845371	−0.00307255	−0.00153628	+	0.999999i	$0.500489\pi$
$758$	−11.2549	−0.408795
$759$	3.67553	0.133413
$760$	−3.84897	−0.139617
$761$	0.857810	0.0310956	0.0155478	−	0.999879i	$-0.495051\pi$
$761$	0.857810	0.0310956	0.0155478	+	0.999879i	$0.495051\pi$
$762$	−5.78098	−0.209423
$763$	16.6132	0.601439
$764$	−3.39322	−0.122762
$765$	−5.33432	−0.192863
$766$	−3.60351	−0.130200
$767$	66.1884	2.38992
$768$	12.3358	0.445129
$769$	35.8091	1.29131	0.645655	−	0.763629i	$-0.276584\pi$
$769$	35.8091	1.29131	0.645655	+	0.763629i	$0.276584\pi$
$770$	5.20951	0.187738
$771$	−0.970752	−0.0349608
$772$	1.74954	0.0629673
$773$	22.4083	0.805970	0.402985	−	0.915207i	$-0.367973\pi$
$773$	22.4083	0.805970	0.402985	+	0.915207i	$0.367973\pi$
$774$	10.6744	0.383684
$775$	−8.69196	−0.312225
$776$	9.38602	0.336938
$777$	−7.76654	−0.278623
$778$	5.53279	0.198360
$779$	3.69612	0.132427
$780$	5.10021	0.182617
$781$	−26.6677	−0.954245
$782$	3.68275	0.131695
$783$	14.8778	0.531690
$784$	2.07982	0.0742794
$785$	−5.22604	−0.186525
$786$	13.0626	0.465928
$787$	−41.4843	−1.47875	−0.739377	−	0.673291i	$-0.764880\pi$
$787$	−41.4843	−1.47875	−0.739377	+	0.673291i	$0.764880\pi$
$788$	16.5789	0.590599
$789$	0.189941	0.00676208
$790$	15.5513	0.553290
$791$	31.1431	1.10732
$792$	20.6176	0.732614
$793$	−78.9236	−2.80266
$794$	−9.89863	−0.351289
$795$	3.06308	0.108636
$796$	−4.23864	−0.150235
$797$	−14.2759	−0.505679	−0.252840	−	0.967508i	$-0.581364\pi$
$797$	−14.2759	−0.505679	−0.252840	+	0.967508i	$0.581364\pi$
$798$	−1.74670	−0.0618326
$799$	20.2921	0.717881
$800$	−5.29043	−0.187045
$801$	−15.8645	−0.560544
$802$	−13.5276	−0.477678
$803$	−47.6249	−1.68065
$804$	−9.36020	−0.330109
$805$	3.45139	0.121646
$806$	−53.4595	−1.88303
$807$	22.6114	0.795961
$808$	32.7898	1.15354
$809$	28.2967	0.994858	0.497429	−	0.867505i	$-0.334277\pi$
$809$	28.2967	0.994858	0.497429	+	0.867505i	$0.334277\pi$
$810$	4.32160	0.151846
$811$	27.7290	0.973696	0.486848	−	0.873487i	$-0.338147\pi$
$811$	27.7290	0.973696	0.486848	+	0.873487i	$0.338147\pi$
$812$	7.86677	0.276069
$813$	−4.51200	−0.158243
$814$	−14.9550	−0.524174
$815$	5.26431	0.184401
$816$	−0.995182	−0.0348384
$817$	5.90696	0.206658
$818$	35.2495	1.23247
$819$	−30.7474	−1.07440
$820$	3.08386	0.107693
$821$	−2.87351	−0.100286	−0.0501431	−	0.998742i	$-0.515968\pi$
$821$	−2.87351	−0.100286	−0.0501431	+	0.998742i	$0.515968\pi$
$822$	−13.1989	−0.460366
$823$	−44.3438	−1.54573	−0.772865	−	0.634571i	$-0.781177\pi$
$823$	−44.3438	−1.54573	−0.772865	+	0.634571i	$0.781177\pi$
$824$	4.18617	0.145832
$825$	2.05509	0.0715490
$826$	−18.9130	−0.658066
$827$	28.5124	0.991474	0.495737	−	0.868473i	$-0.334898\pi$
$827$	28.5124	0.991474	0.495737	+	0.868473i	$0.334898\pi$
$828$	4.81637	0.167380
$829$	−20.2274	−0.702527	−0.351264	−	0.936277i	$-0.614248\pi$
$829$	−20.2274	−0.702527	−0.351264	+	0.936277i	$0.614248\pi$
$830$	5.19325	0.180260
$831$	−22.6463	−0.785592
$832$	−40.7218	−1.41177
$833$	7.06866	0.244914
$834$	13.7958	0.477710
$835$	2.09327	0.0724407
$836$	4.02293	0.139136
$837$	−34.5549	−1.19439
$838$	−22.0541	−0.761846
$839$	−29.7728	−1.02787	−0.513935	−	0.857829i	$-0.671813\pi$
$839$	−29.7728	−1.02787	−0.513935	+	0.857829i	$0.671813\pi$
$840$	−4.13315	−0.142607
$841$	−14.9946	−0.517055
$842$	17.7061	0.610191
$843$	22.0595	0.759770
$844$	−25.4329	−0.875437
$845$	−28.5368	−0.981697
$846$	−22.1876	−0.762825
$847$	5.78521	0.198782
$848$	−2.67678	−0.0919209
$849$	−23.8981	−0.820180
$850$	2.05912	0.0706274
$851$	−9.90797	−0.339641
$852$	7.46027	0.255585
$853$	23.5214	0.805356	0.402678	−	0.915342i	$-0.368079\pi$
$853$	23.5214	0.805356	0.402678	+	0.915342i	$0.368079\pi$
$854$	22.5520	0.771713
$855$	3.22762	0.110382
$856$	−20.7535	−0.709339
$857$	0.198145	0.00676851	0.00338426	−	0.999994i	$-0.498923\pi$
$857$	0.198145	0.00676851	0.00338426	+	0.999994i	$0.498923\pi$
$858$	12.6397	0.431512
$859$	3.33604	0.113824	0.0569121	−	0.998379i	$-0.481875\pi$
$859$	3.33604	0.113824	0.0569121	+	0.998379i	$0.481875\pi$
$860$	4.92846	0.168059
$861$	3.96902	0.135264
$862$	9.52627	0.324466
$863$	38.9081	1.32445	0.662223	−	0.749307i	$-0.269613\pi$
$863$	38.9081	1.32445	0.662223	+	0.749307i	$0.269613\pi$
$864$	−21.0321	−0.715525
$865$	15.6587	0.532411
$866$	−14.9820	−0.509109
$867$	8.96797	0.304568
$868$	−18.2712	−0.620164
$869$	−46.0977	−1.56376
$870$	−2.59457	−0.0879642
$871$	76.2308	2.58298
$872$	−25.3804	−0.859488
$873$	−7.87080	−0.266386
$874$	−2.22831	−0.0753737
$875$	1.92977	0.0652380
$876$	13.3230	0.450144
$877$	29.5938	0.999311	0.499655	−	0.866224i	$-0.333460\pi$
$877$	29.5938	0.999311	0.499655	+	0.866224i	$0.333460\pi$
$878$	−2.96220	−0.0999693
$879$	7.89174	0.266182
$880$	−1.79591	−0.0605401
$881$	−34.5670	−1.16459	−0.582296	−	0.812977i	$-0.697846\pi$
$881$	−34.5670	−1.16459	−0.582296	+	0.812977i	$0.697846\pi$
$882$	−7.72895	−0.260247
$883$	26.9745	0.907765	0.453883	−	0.891061i	$-0.350039\pi$
$883$	26.9745	0.907765	0.453883	+	0.891061i	$0.350039\pi$
$884$	−15.1479	−0.509480
$885$	−7.46093	−0.250796
$886$	−1.73554	−0.0583066
$887$	49.5386	1.66334	0.831672	−	0.555267i	$-0.187384\pi$
$887$	49.5386	1.66334	0.831672	+	0.555267i	$0.187384\pi$
$888$	11.8651	0.398167
$889$	16.0912	0.539681
$890$	6.12392	0.205274
$891$	−12.8102	−0.429159
$892$	26.9744	0.903169
$893$	−12.2781	−0.410870
$894$	−13.5183	−0.452120
$895$	−15.6924	−0.524540
$896$	−8.78254	−0.293404
$897$	8.37402	0.279600
$898$	7.99827	0.266906
$899$	−32.5286	−1.08489
$900$	2.69296	0.0897654
$901$	−9.09751	−0.303082
$902$	7.64263	0.254472
$903$	6.34308	0.211084
$904$	−47.5780	−1.58242
$905$	25.3735	0.843444
$906$	−5.02520	−0.166951
$907$	44.9401	1.49221	0.746106	−	0.665827i	$-0.231921\pi$
$907$	44.9401	1.49221	0.746106	+	0.665827i	$0.231921\pi$
$908$	−5.00516	−0.166102
$909$	−27.4965	−0.912000
$910$	11.8689	0.393451
$911$	0.879323	0.0291333	0.0145666	−	0.999894i	$-0.495363\pi$
$911$	0.879323	0.0291333	0.0145666	+	0.999894i	$0.495363\pi$
$912$	0.602152	0.0199393
$913$	−15.3940	−0.509467
$914$	32.4901	1.07468
$915$	8.89648	0.294108
$916$	−9.70650	−0.320712
$917$	−36.3594	−1.20069
$918$	8.18604	0.270179
$919$	−31.1511	−1.02758	−0.513789	−	0.857916i	$-0.671759\pi$
$919$	−31.1511	−1.02758	−0.513789	+	0.857916i	$0.671759\pi$
$920$	−5.27276	−0.173838
$921$	11.2585	0.370981
$922$	−35.3516	−1.16424
$923$	−60.7575	−1.99986
$924$	4.31995	0.142116
$925$	−5.53981	−0.182148
$926$	−17.1231	−0.562699
$927$	−3.51039	−0.115296
$928$	−19.7988	−0.649927
$929$	−14.7760	−0.484785	−0.242393	−	0.970178i	$-0.577932\pi$
$929$	−14.7760	−0.484785	−0.242393	+	0.970178i	$0.577932\pi$
$930$	6.02609	0.197603
$931$	−4.27701	−0.140173
$932$	12.1854	0.399147
$933$	−7.33427	−0.240113
$934$	−21.5159	−0.704022
$935$	−6.10373	−0.199613
$936$	46.9734	1.53537
$937$	4.98095	0.162720	0.0813602	−	0.996685i	$-0.474074\pi$
$937$	4.98095	0.162720	0.0813602	+	0.996685i	$0.474074\pi$
$938$	−21.7825	−0.711225
$939$	−17.8103	−0.581218
$940$	−10.2442	−0.334128
$941$	−26.6282	−0.868053	−0.434026	−	0.900900i	$-0.642908\pi$
$941$	−26.6282	−0.868053	−0.434026	+	0.900900i	$0.642908\pi$
$942$	3.62318	0.118050
$943$	5.06337	0.164886
$944$	6.52000	0.212208
$945$	7.67177	0.249563
$946$	12.2141	0.397113
$947$	−34.7075	−1.12784	−0.563921	−	0.825829i	$-0.690708\pi$
$947$	−34.7075	−1.12784	−0.563921	+	0.825829i	$0.690708\pi$
$948$	12.8958	0.418836
$949$	−108.505	−3.52221
$950$	−1.24591	−0.0404226
$951$	15.5009	0.502650
$952$	12.2757	0.397857
$953$	7.26177	0.235232	0.117616	−	0.993059i	$-0.462475\pi$
$953$	7.26177	0.235232	0.117616	+	0.993059i	$0.462475\pi$
$954$	9.94733	0.322057
$955$	−3.11508	−0.100802
$956$	−9.82687	−0.317824
$957$	7.69092	0.248612
$958$	6.28055	0.202916
$959$	36.7389	1.18636
$960$	4.59027	0.148150
$961$	44.5502	1.43710
$962$	−34.0723	−1.09854
$963$	17.4032	0.560809
$964$	−1.08929	−0.0350837
$965$	1.60613	0.0517031
$966$	−2.39283	−0.0769881
$967$	8.56893	0.275558	0.137779	−	0.990463i	$-0.456004\pi$
$967$	8.56893	0.275558	0.137779	+	0.990463i	$0.456004\pi$
$968$	−8.83819	−0.284070
$969$	2.04652	0.0657438
$970$	3.03824	0.0975521
$971$	12.8300	0.411733	0.205867	−	0.978580i	$-0.433999\pi$
$971$	12.8300	0.411733	0.205867	+	0.978580i	$0.433999\pi$
$972$	16.5751	0.531645
$973$	−38.4003	−1.23106
$974$	−29.0085	−0.929492
$975$	4.68214	0.149949
$976$	−7.77450	−0.248856
$977$	−11.6047	−0.371267	−0.185633	−	0.982619i	$-0.559434\pi$
$977$	−11.6047	−0.371267	−0.185633	+	0.982619i	$0.559434\pi$
$978$	−3.64972	−0.116705
$979$	−18.1527	−0.580164
$980$	−3.56852	−0.113992
$981$	21.2832	0.679519
$982$	5.88235	0.187713
$983$	15.5809	0.496953	0.248476	−	0.968638i	$-0.420070\pi$
$983$	15.5809	0.496953	0.248476	+	0.968638i	$0.420070\pi$
$984$	−6.06355	−0.193299
$985$	15.2199	0.484947
$986$	7.70603	0.245410
$987$	−13.1846	−0.419670
$988$	9.16551	0.291594
$989$	8.09202	0.257311
$990$	6.67389	0.212110
$991$	−24.9277	−0.791854	−0.395927	−	0.918282i	$-0.629577\pi$
$991$	−24.9277	−0.791854	−0.395927	+	0.918282i	$0.629577\pi$
$992$	45.9842	1.46000
$993$	−13.3300	−0.423016
$994$	17.3611	0.550661
$995$	−3.89119	−0.123359
$996$	4.30646	0.136455
$997$	−11.4849	−0.363730	−0.181865	−	0.983324i	$-0.558213\pi$
$997$	−11.4849	−0.363730	−0.181865	+	0.983324i	$0.558213\pi$
$998$	−9.74554	−0.308490
$999$	−22.0235	−0.696792

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1205.2.a.d.1.11	✓	25
5.4	even	2		6025.2.a.k.1.15		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.d.1.11	✓	25	1.1	even	1	trivial
6025.2.a.k.1.15		25	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1205 = 5 \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1205.a (trivial)

\(f(q)\)	\(=\)	\(q-0.954311 q^{2} -0.726487 q^{3} -1.08929 q^{4} -1.00000 q^{5} +0.693295 q^{6} -1.92977 q^{7} +2.94814 q^{8} -2.47222 q^{9} +O(q^{10})\)	\(q-0.954311 q^{2} -0.726487 q^{3} -1.08929 q^{4} -1.00000 q^{5} +0.693295 q^{6} -1.92977 q^{7} +2.94814 q^{8} -2.47222 q^{9} +0.954311 q^{10} -2.82880 q^{11} +0.791355 q^{12} -6.44491 q^{13} +1.84160 q^{14} +0.726487 q^{15} -0.634866 q^{16} -2.15771 q^{17} +2.35926 q^{18} +1.30556 q^{19} +1.08929 q^{20} +1.40195 q^{21} +2.69956 q^{22} +1.78850 q^{23} -2.14179 q^{24} +1.00000 q^{25} +6.15045 q^{26} +3.97549 q^{27} +2.10208 q^{28} +3.74238 q^{29} -0.693295 q^{30} -8.69196 q^{31} -5.29043 q^{32} +2.05509 q^{33} +2.05912 q^{34} +1.92977 q^{35} +2.69296 q^{36} -5.53981 q^{37} -1.24591 q^{38} +4.68214 q^{39} -2.94814 q^{40} +2.83107 q^{41} -1.33790 q^{42} +4.52447 q^{43} +3.08139 q^{44} +2.47222 q^{45} -1.70679 q^{46} -9.40445 q^{47} +0.461222 q^{48} -3.27600 q^{49} -0.954311 q^{50} +1.56755 q^{51} +7.02038 q^{52} +4.21628 q^{53} -3.79386 q^{54} +2.82880 q^{55} -5.68923 q^{56} -0.948471 q^{57} -3.57139 q^{58} -10.2699 q^{59} -0.791355 q^{60} +12.2459 q^{61} +8.29484 q^{62} +4.77080 q^{63} +6.31845 q^{64} +6.44491 q^{65} -1.96119 q^{66} -11.8281 q^{67} +2.35037 q^{68} -1.29932 q^{69} -1.84160 q^{70} +9.42721 q^{71} -7.28845 q^{72} +16.8357 q^{73} +5.28670 q^{74} -0.726487 q^{75} -1.42213 q^{76} +5.45893 q^{77} -4.46822 q^{78} +16.2958 q^{79} +0.634866 q^{80} +4.52851 q^{81} -2.70172 q^{82} +5.44188 q^{83} -1.52713 q^{84} +2.15771 q^{85} -4.31775 q^{86} -2.71879 q^{87} -8.33971 q^{88} +6.41711 q^{89} -2.35926 q^{90} +12.4372 q^{91} -1.94820 q^{92} +6.31460 q^{93} +8.97477 q^{94} -1.30556 q^{95} +3.84343 q^{96} +3.18370 q^{97} +3.12633 q^{98} +6.99341 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 4 q^{2} + 9 q^{3} + 36 q^{4} - 25 q^{5} + 7 q^{6} + 7 q^{7} - 15 q^{8} + 36 q^{9}+O(q^{10}) \) 25 * q - 4 * q^2 + 9 * q^3 + 36 * q^4 - 25 * q^5 + 7 * q^6 + 7 * q^7 - 15 * q^8 + 36 * q^9	\( 25 q - 4 q^{2} + 9 q^{3} + 36 q^{4} - 25 q^{5} + 7 q^{6} + 7 q^{7} - 15 q^{8} + 36 q^{9} + 4 q^{10} + 10 q^{11} + 22 q^{12} + 10 q^{13} + 13 q^{14} - 9 q^{15} + 54 q^{16} + q^{17} - 13 q^{18} + 50 q^{19} - 36 q^{20} + 9 q^{21} + 11 q^{22} - 31 q^{23} + 22 q^{24} + 25 q^{25} + 8 q^{26} + 42 q^{27} + 14 q^{28} + 4 q^{29} - 7 q^{30} + 34 q^{31} - 44 q^{32} + 28 q^{33} + 33 q^{34} - 7 q^{35} + 83 q^{36} + 14 q^{37} - 10 q^{38} + 23 q^{39} + 15 q^{40} + 11 q^{41} + 23 q^{42} + 49 q^{43} + 20 q^{44} - 36 q^{45} + 27 q^{46} - 28 q^{47} + 30 q^{48} + 66 q^{49} - 4 q^{50} + 49 q^{51} + 39 q^{52} - 16 q^{53} + 5 q^{54} - 10 q^{55} + 51 q^{56} + 10 q^{57} - 8 q^{58} + 30 q^{59} - 22 q^{60} + 35 q^{61} - 18 q^{62} + 73 q^{64} - 10 q^{65} - 13 q^{66} + 37 q^{67} + 11 q^{68} - 4 q^{69} - 13 q^{70} + 12 q^{71} - 90 q^{72} + 36 q^{73} - 12 q^{74} + 9 q^{75} + 57 q^{76} - 31 q^{77} - 9 q^{78} + 16 q^{79} - 54 q^{80} + 65 q^{81} - 11 q^{82} + 43 q^{83} - 62 q^{84} - q^{85} - 9 q^{86} - 22 q^{87} + 20 q^{88} + 38 q^{89} + 13 q^{90} + 86 q^{91} - 119 q^{92} + 10 q^{93} - 18 q^{94} - 50 q^{95} - 34 q^{96} + 17 q^{97} - 32 q^{98} + 26 q^{99}+O(q^{100}) \) 25 * q - 4 * q^2 + 9 * q^3 + 36 * q^4 - 25 * q^5 + 7 * q^6 + 7 * q^7 - 15 * q^8 + 36 * q^9 + 4 * q^10 + 10 * q^11 + 22 * q^12 + 10 * q^13 + 13 * q^14 - 9 * q^15 + 54 * q^16 + q^17 - 13 * q^18 + 50 * q^19 - 36 * q^20 + 9 * q^21 + 11 * q^22 - 31 * q^23 + 22 * q^24 + 25 * q^25 + 8 * q^26 + 42 * q^27 + 14 * q^28 + 4 * q^29 - 7 * q^30 + 34 * q^31 - 44 * q^32 + 28 * q^33 + 33 * q^34 - 7 * q^35 + 83 * q^36 + 14 * q^37 - 10 * q^38 + 23 * q^39 + 15 * q^40 + 11 * q^41 + 23 * q^42 + 49 * q^43 + 20 * q^44 - 36 * q^45 + 27 * q^46 - 28 * q^47 + 30 * q^48 + 66 * q^49 - 4 * q^50 + 49 * q^51 + 39 * q^52 - 16 * q^53 + 5 * q^54 - 10 * q^55 + 51 * q^56 + 10 * q^57 - 8 * q^58 + 30 * q^59 - 22 * q^60 + 35 * q^61 - 18 * q^62 + 73 * q^64 - 10 * q^65 - 13 * q^66 + 37 * q^67 + 11 * q^68 - 4 * q^69 - 13 * q^70 + 12 * q^71 - 90 * q^72 + 36 * q^73 - 12 * q^74 + 9 * q^75 + 57 * q^76 - 31 * q^77 - 9 * q^78 + 16 * q^79 - 54 * q^80 + 65 * q^81 - 11 * q^82 + 43 * q^83 - 62 * q^84 - q^85 - 9 * q^86 - 22 * q^87 + 20 * q^88 + 38 * q^89 + 13 * q^90 + 86 * q^91 - 119 * q^92 + 10 * q^93 - 18 * q^94 - 50 * q^95 - 34 * q^96 + 17 * q^97 - 32 * q^98 + 26 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more