LMFDB - Embedded newform 2299.2.a.x.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2299,2,Mod(1,2299)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2299, 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("2299.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2299 = 11^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2299.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:	$18.3576074247$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} - 30 x^{18} + 28 x^{17} + 374 x^{16} - 321 x^{15} - 2521 x^{14} + 1965 x^{13} + \cdots + 80 $ x^20 - x^19 - 30x^18 + 28x^17 + 374x^16 - 321x^15 - 2521x^14 + 1965x^13 + 10017x^12 - 7030x^11 - 23999x^10 + 15056x^9 + 34039x^8 - 18683x^7 - 26866x^6 + 11940x^5 + 10535x^4 - 2840x^3 - 1880x^2 + 120x + 80
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 209)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$-0.256781$ of defining polynomial
Character	$\chi$	$=$	2299.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.256781 q^{2} +2.78089 q^{3} -1.93406 q^{4} -2.44163 q^{5} +0.714079 q^{6} +2.92963 q^{7} -1.01019 q^{8} +4.73332 q^{9} -0.626965 q^{10} -5.37841 q^{12} -1.49016 q^{13} +0.752273 q^{14} -6.78990 q^{15} +3.60873 q^{16} +4.19966 q^{17} +1.21543 q^{18} +1.00000 q^{19} +4.72227 q^{20} +8.14695 q^{21} +3.73331 q^{23} -2.80923 q^{24} +0.961568 q^{25} -0.382645 q^{26} +4.82017 q^{27} -5.66608 q^{28} -4.79978 q^{29} -1.74352 q^{30} +1.78497 q^{31} +2.94704 q^{32} +1.07839 q^{34} -7.15307 q^{35} -9.15455 q^{36} +8.45889 q^{37} +0.256781 q^{38} -4.14396 q^{39} +2.46652 q^{40} +2.21446 q^{41} +2.09198 q^{42} -11.0941 q^{43} -11.5570 q^{45} +0.958644 q^{46} +7.54957 q^{47} +10.0355 q^{48} +1.58270 q^{49} +0.246913 q^{50} +11.6788 q^{51} +2.88206 q^{52} +13.9149 q^{53} +1.23773 q^{54} -2.95949 q^{56} +2.78089 q^{57} -1.23249 q^{58} +9.76391 q^{59} +13.1321 q^{60} +12.3223 q^{61} +0.458346 q^{62} +13.8669 q^{63} -6.46071 q^{64} +3.63842 q^{65} +6.65052 q^{67} -8.12242 q^{68} +10.3819 q^{69} -1.83677 q^{70} -10.5453 q^{71} -4.78157 q^{72} +5.11743 q^{73} +2.17208 q^{74} +2.67401 q^{75} -1.93406 q^{76} -1.06409 q^{78} +1.30503 q^{79} -8.81119 q^{80} -0.795627 q^{81} +0.568631 q^{82} -9.16686 q^{83} -15.7567 q^{84} -10.2540 q^{85} -2.84877 q^{86} -13.3476 q^{87} -2.45131 q^{89} -2.96763 q^{90} -4.36561 q^{91} -7.22046 q^{92} +4.96379 q^{93} +1.93859 q^{94} -2.44163 q^{95} +8.19538 q^{96} +4.37412 q^{97} +0.406408 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - q^{2} + 4 q^{3} + 21 q^{4} + 18 q^{5} + 10 q^{6} + 2 q^{7} - 3 q^{8} + 32 q^{9} - 11 q^{10} + 10 q^{12} - q^{13} + 25 q^{14} + 28 q^{15} + 27 q^{16} - 2 q^{17} - 4 q^{18} + 20 q^{19} + 47 q^{20}+ \cdots - 45 q^{98}+O(q^{100}) $ 20 * q - q^2 + 4 * q^3 + 21 * q^4 + 18 * q^5 + 10 * q^6 + 2 * q^7 - 3 * q^8 + 32 * q^9 - 11 * q^10 + 10 * q^12 - q^13 + 25 * q^14 + 28 * q^15 + 27 * q^16 - 2 * q^17 - 4 * q^18 + 20 * q^19 + 47 * q^20 - 11 * q^21 + 8 * q^23 + 36 * q^24 + 36 * q^25 + 8 * q^26 - 2 * q^27 - 28 * q^28 - 17 * q^29 + 10 * q^30 - 9 * q^31 - 2 * q^32 - 19 * q^34 + 20 * q^35 + 17 * q^36 + 29 * q^37 - q^38 - 3 * q^39 - 29 * q^40 - 4 * q^41 - 16 * q^42 - 12 * q^43 + 65 * q^45 + 36 * q^46 + 10 * q^47 + 42 * q^48 + 34 * q^49 - 25 * q^50 + 10 * q^51 + 13 * q^52 + 50 * q^53 + 26 * q^54 + 37 * q^56 + 4 * q^57 + 4 * q^58 + 46 * q^59 - 7 * q^60 - 22 * q^61 + 5 * q^62 + 69 * q^63 + 47 * q^64 - 13 * q^65 + 26 * q^67 + 5 * q^68 + 65 * q^69 + 26 * q^70 + 38 * q^71 - 104 * q^72 + 3 * q^73 + 10 * q^74 + 13 * q^75 + 21 * q^76 - 45 * q^78 - 14 * q^79 + 31 * q^80 + 76 * q^81 - 10 * q^82 - 14 * q^83 + 5 * q^84 - 9 * q^85 + 15 * q^86 - 21 * q^87 + 48 * q^89 + 28 * q^90 + 24 * q^91 + q^92 + 42 * q^93 - 79 * q^94 + 18 * q^95 + 21 * q^96 - 5 * q^97 - 45 * q^98

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 $

$2$	0.256781	0.181572	0.0907859	−	0.995870i	$-0.471062\pi$
$2$	0.256781	0.181572	0.0907859	+	0.995870i	$0.471062\pi$
$3$	2.78089	1.60554	0.802772	−	0.596286i	$-0.203357\pi$
$3$	2.78089	1.60554	0.802772	+	0.596286i	$0.203357\pi$
$4$	−1.93406	−0.967032
$5$	−2.44163	−1.09193	−0.545966	−	0.837808i	$-0.683837\pi$
$5$	−2.44163	−1.09193	−0.545966	+	0.837808i	$0.683837\pi$
$6$	0.714079	0.291522
$7$	2.92963	1.10729	0.553647	−	0.832751i	$-0.313236\pi$
$7$	2.92963	1.10729	0.553647	+	0.832751i	$0.313236\pi$
$8$	−1.01019	−0.357157
$9$	4.73332	1.57777
$10$	−0.626965	−0.198264
$11$	0	0
$11$	0	0
$12$	−5.37841	−1.55261
$13$	−1.49016	−0.413296	−0.206648	−	0.978415i	$-0.566255\pi$
$13$	−1.49016	−0.413296	−0.206648	+	0.978415i	$0.566255\pi$
$14$	0.752273	0.201053
$15$	−6.78990	−1.75314
$16$	3.60873	0.902182
$17$	4.19966	1.01857	0.509284	−	0.860598i	$-0.329910\pi$
$17$	4.19966	1.01857	0.509284	+	0.860598i	$0.329910\pi$
$18$	1.21543	0.286479
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	4.72227	1.05593
$21$	8.14695	1.77781
$22$	0	0
$23$	3.73331	0.778449	0.389225	−	0.921143i	$-0.372743\pi$
$23$	3.73331	0.778449	0.389225	+	0.921143i	$0.372743\pi$
$24$	−2.80923	−0.573432
$25$	0.961568	0.192314
$26$	−0.382645	−0.0750428
$27$	4.82017	0.927642
$28$	−5.66608	−1.07079
$29$	−4.79978	−0.891297	−0.445649	−	0.895208i	$-0.647027\pi$
$29$	−4.79978	−0.891297	−0.445649	+	0.895208i	$0.647027\pi$
$30$	−1.74352	−0.318321
$31$	1.78497	0.320590	0.160295	−	0.987069i	$-0.448755\pi$
$31$	1.78497	0.320590	0.160295	+	0.987069i	$0.448755\pi$
$32$	2.94704	0.520968
$33$	0	0
$34$	1.07839	0.184943
$35$	−7.15307	−1.20909
$36$	−9.15455	−1.52576
$37$	8.45889	1.39063	0.695316	−	0.718704i	$-0.255264\pi$
$37$	8.45889	1.39063	0.695316	+	0.718704i	$0.255264\pi$
$38$	0.256781	0.0416554
$39$	−4.14396	−0.663565
$40$	2.46652	0.389991
$41$	2.21446	0.345840	0.172920	−	0.984936i	$-0.444680\pi$
$41$	2.21446	0.345840	0.172920	+	0.984936i	$0.444680\pi$
$42$	2.09198	0.322800
$43$	−11.0941	−1.69184	−0.845920	−	0.533310i	$-0.820948\pi$
$43$	−11.0941	−1.69184	−0.845920	+	0.533310i	$0.820948\pi$
$44$	0	0
$45$	−11.5570	−1.72282
$46$	0.958644	0.141344
$47$	7.54957	1.10122	0.550609	−	0.834763i	$-0.314395\pi$
$47$	7.54957	1.10122	0.550609	+	0.834763i	$0.314395\pi$
$48$	10.0355	1.44849
$49$	1.58270	0.226100
$50$	0.246913	0.0349187
$51$	11.6788	1.63536
$52$	2.88206	0.399670
$53$	13.9149	1.91135	0.955677	−	0.294418i	$-0.0951257\pi$
$53$	13.9149	1.91135	0.955677	+	0.294418i	$0.0951257\pi$
$54$	1.23773	0.168434
$55$	0	0
$56$	−2.95949	−0.395478
$57$	2.78089	0.368337
$58$	−1.23249	−0.161834
$59$	9.76391	1.27115	0.635576	−	0.772038i	$-0.280763\pi$
$59$	9.76391	1.27115	0.635576	+	0.772038i	$0.280763\pi$
$60$	13.1321	1.69535
$61$	12.3223	1.57771	0.788857	−	0.614577i	$-0.210673\pi$
$61$	12.3223	1.57771	0.788857	+	0.614577i	$0.210673\pi$
$62$	0.458346	0.0582100
$63$	13.8669	1.74706
$64$	−6.46071	−0.807589
$65$	3.63842	0.451290
$66$	0	0
$67$	6.65052	0.812491	0.406245	−	0.913764i	$-0.366838\pi$
$67$	6.65052	0.812491	0.406245	+	0.913764i	$0.366838\pi$
$68$	−8.12242	−0.984988
$69$	10.3819	1.24983
$70$	−1.83677	−0.219536
$71$	−10.5453	−1.25149	−0.625747	−	0.780026i	$-0.715206\pi$
$71$	−10.5453	−1.25149	−0.625747	+	0.780026i	$0.715206\pi$
$72$	−4.78157	−0.563514
$73$	5.11743	0.598950	0.299475	−	0.954104i	$-0.403188\pi$
$73$	5.11743	0.598950	0.299475	+	0.954104i	$0.403188\pi$
$74$	2.17208	0.252499
$75$	2.67401	0.308768
$76$	−1.93406	−0.221852
$77$	0	0
$78$	−1.06409	−0.120485
$79$	1.30503	0.146828	0.0734138	−	0.997302i	$-0.476611\pi$
$79$	1.30503	0.146828	0.0734138	+	0.997302i	$0.476611\pi$
$80$	−8.81119	−0.985121
$81$	−0.795627	−0.0884030
$82$	0.568631	0.0627947
$83$	−9.16686	−1.00619	−0.503097	−	0.864230i	$-0.667806\pi$
$83$	−9.16686	−1.00619	−0.503097	+	0.864230i	$0.667806\pi$
$84$	−15.7567	−1.71920
$85$	−10.2540	−1.11221
$86$	−2.84877	−0.307190
$87$	−13.3476	−1.43102
$88$	0	0
$89$	−2.45131	−0.259838	−0.129919	−	0.991525i	$-0.541472\pi$
$89$	−2.45131	−0.259838	−0.129919	+	0.991525i	$0.541472\pi$
$90$	−2.96763	−0.312816
$91$	−4.36561	−0.457640
$92$	−7.22046	−0.752785
$93$	4.96379	0.514721
$94$	1.93859	0.199950
$95$	−2.44163	−0.250506
$96$	8.19538	0.836438
$97$	4.37412	0.444125	0.222062	−	0.975032i	$-0.428721\pi$
$97$	4.37412	0.444125	0.222062	+	0.975032i	$0.428721\pi$
$98$	0.406408	0.0410534
$99$	0	0
$100$	−1.85973	−0.185973
$101$	4.82056	0.479664	0.239832	−	0.970814i	$-0.422908\pi$
$101$	4.82056	0.479664	0.239832	+	0.970814i	$0.422908\pi$
$102$	2.99889	0.296935
$103$	10.9871	1.08259	0.541297	−	0.840831i	$-0.317933\pi$
$103$	10.9871	1.08259	0.541297	+	0.840831i	$0.317933\pi$
$104$	1.50535	0.147612
$105$	−19.8919	−1.94125
$106$	3.57308	0.347048
$107$	15.4551	1.49410	0.747049	−	0.664769i	$-0.231470\pi$
$107$	15.4551	1.49410	0.747049	+	0.664769i	$0.231470\pi$
$108$	−9.32252	−0.897059
$109$	−10.5781	−1.01320	−0.506599	−	0.862182i	$-0.669098\pi$
$109$	−10.5781	−1.01320	−0.506599	+	0.862182i	$0.669098\pi$
$110$	0	0
$111$	23.5232	2.23272
$112$	10.5722	0.998981
$113$	9.00938	0.847531	0.423765	−	0.905772i	$-0.360708\pi$
$113$	9.00938	0.847531	0.423765	+	0.905772i	$0.360708\pi$
$114$	0.714079	0.0668796
$115$	−9.11537	−0.850013
$116$	9.28309	0.861913
$117$	−7.05340	−0.652087
$118$	2.50719	0.230805
$119$	12.3034	1.12785
$120$	6.85911	0.626148
$121$	0	0
$122$	3.16414	0.286468
$123$	6.15815	0.555261
$124$	−3.45224	−0.310020
$125$	9.86037	0.881938
$126$	3.56075	0.317217
$127$	−20.0203	−1.77652	−0.888259	−	0.459343i	$-0.848085\pi$
$127$	−20.0203	−1.77652	−0.888259	+	0.459343i	$0.848085\pi$
$128$	−7.55307	−0.667603
$129$	−30.8515	−2.71632
$130$	0.934278	0.0819416
$131$	−8.41811	−0.735493	−0.367747	−	0.929926i	$-0.619871\pi$
$131$	−8.41811	−0.735493	−0.367747	+	0.929926i	$0.619871\pi$
$132$	0	0
$133$	2.92963	0.254031
$134$	1.70773	0.147525
$135$	−11.7691	−1.01292
$136$	−4.24247	−0.363789
$137$	13.5074	1.15401	0.577006	−	0.816740i	$-0.304221\pi$
$137$	13.5074	1.15401	0.577006	+	0.816740i	$0.304221\pi$
$138$	2.66588	0.226935
$139$	12.4161	1.05312	0.526561	−	0.850138i	$-0.323481\pi$
$139$	12.4161	1.05312	0.526561	+	0.850138i	$0.323481\pi$
$140$	13.8345	1.16923
$141$	20.9945	1.76806
$142$	−2.70783	−0.227236
$143$	0	0
$144$	17.0813	1.42344
$145$	11.7193	0.973235
$146$	1.31406	0.108752
$147$	4.40132	0.363014
$148$	−16.3600	−1.34479
$149$	2.98473	0.244519	0.122259	−	0.992498i	$-0.460986\pi$
$149$	2.98473	0.244519	0.122259	+	0.992498i	$0.460986\pi$
$150$	0.686636	0.0560636
$151$	−19.3984	−1.57862	−0.789309	−	0.613997i	$-0.789561\pi$
$151$	−19.3984	−1.57862	−0.789309	+	0.613997i	$0.789561\pi$
$152$	−1.01019	−0.0819375
$153$	19.8784	1.60707
$154$	0	0
$155$	−4.35824	−0.350062
$156$	8.01468	0.641688
$157$	−17.9657	−1.43382	−0.716911	−	0.697165i	$-0.754445\pi$
$157$	−17.9657	−1.43382	−0.716911	+	0.697165i	$0.754445\pi$
$158$	0.335108	0.0266597
$159$	38.6956	3.06876
$160$	−7.19559	−0.568861
$161$	10.9372	0.861972
$162$	−0.204302	−0.0160515
$163$	−3.07101	−0.240540	−0.120270	−	0.992741i	$-0.538376\pi$
$163$	−3.07101	−0.240540	−0.120270	+	0.992741i	$0.538376\pi$
$164$	−4.28290	−0.334438
$165$	0	0
$166$	−2.35388	−0.182696
$167$	−5.43104	−0.420266	−0.210133	−	0.977673i	$-0.567390\pi$
$167$	−5.43104	−0.420266	−0.210133	+	0.977673i	$0.567390\pi$
$168$	−8.23000	−0.634958
$169$	−10.7794	−0.829187
$170$	−2.63304	−0.201945
$171$	4.73332	0.361966
$172$	21.4568	1.63606
$173$	15.3064	1.16372	0.581861	−	0.813288i	$-0.302325\pi$
$173$	15.3064	1.16372	0.581861	+	0.813288i	$0.302325\pi$
$174$	−3.42742	−0.259832
$175$	2.81703	0.212948
$176$	0	0
$177$	27.1523	2.04089
$178$	−0.629449	−0.0471792
$179$	−14.0209	−1.04797	−0.523985	−	0.851728i	$-0.675555\pi$
$179$	−14.0209	−1.04797	−0.523985	+	0.851728i	$0.675555\pi$
$180$	22.3520	1.66602
$181$	3.08755	0.229496	0.114748	−	0.993395i	$-0.463394\pi$
$181$	3.08755	0.229496	0.114748	+	0.993395i	$0.463394\pi$
$182$	−1.12101	−0.0830945
$183$	34.2670	2.53309
$184$	−3.77137	−0.278029
$185$	−20.6535	−1.51847
$186$	1.27461	0.0934588
$187$	0	0
$188$	−14.6014	−1.06491
$189$	14.1213	1.02717
$190$	−0.626965	−0.0454848
$191$	−0.0810879	−0.00586731	−0.00293366	−	0.999996i	$-0.500934\pi$
$191$	−0.0810879	−0.00586731	−0.00293366	+	0.999996i	$0.500934\pi$
$192$	−17.9665	−1.29662
$193$	−25.8289	−1.85920	−0.929602	−	0.368564i	$-0.879849\pi$
$193$	−25.8289	−1.85920	−0.929602	+	0.368564i	$0.879849\pi$
$194$	1.12319	0.0806405
$195$	10.1180	0.724567
$196$	−3.06105	−0.218646
$197$	−12.5922	−0.897155	−0.448578	−	0.893744i	$-0.648069\pi$
$197$	−12.5922	−0.897155	−0.448578	+	0.893744i	$0.648069\pi$
$198$	0	0
$199$	−12.4747	−0.884309	−0.442154	−	0.896939i	$-0.645786\pi$
$199$	−12.4747	−0.884309	−0.442154	+	0.896939i	$0.645786\pi$
$200$	−0.971370	−0.0686862
$201$	18.4943	1.30449
$202$	1.23783	0.0870933
$203$	−14.0616	−0.986928
$204$	−22.5875	−1.58144
$205$	−5.40689	−0.377633
$206$	2.82129	0.196569
$207$	17.6710	1.22822
$208$	−5.37758	−0.372868
$209$	0	0
$210$	−5.10785	−0.352475
$211$	2.77766	0.191222	0.0956111	−	0.995419i	$-0.469519\pi$
$211$	2.77766	0.191222	0.0956111	+	0.995419i	$0.469519\pi$
$212$	−26.9122	−1.84834
$213$	−29.3252	−2.00933
$214$	3.96857	0.271286
$215$	27.0878	1.84737
$216$	−4.86930	−0.331314
$217$	5.22929	0.354987
$218$	−2.71626	−0.183968
$219$	14.2310	0.961641
$220$	0	0
$221$	−6.25817	−0.420970
$222$	6.04031	0.405399
$223$	−1.99948	−0.133895	−0.0669474	−	0.997757i	$-0.521326\pi$
$223$	−1.99948	−0.133895	−0.0669474	+	0.997757i	$0.521326\pi$
$224$	8.63372	0.576865
$225$	4.55141	0.303427
$226$	2.31344	0.153888
$227$	13.6361	0.905057	0.452528	−	0.891750i	$-0.350522\pi$
$227$	13.6361	0.905057	0.452528	+	0.891750i	$0.350522\pi$
$228$	−5.37841	−0.356194
$229$	8.29561	0.548189	0.274095	−	0.961703i	$-0.411622\pi$
$229$	8.29561	0.548189	0.274095	+	0.961703i	$0.411622\pi$
$230$	−2.34066	−0.154338
$231$	0	0
$232$	4.84871	0.318333
$233$	−28.8658	−1.89106	−0.945532	−	0.325529i	$-0.894458\pi$
$233$	−28.8658	−1.89106	−0.945532	+	0.325529i	$0.894458\pi$
$234$	−1.81118	−0.118401
$235$	−18.4333	−1.20245
$236$	−18.8840	−1.22924
$237$	3.62915	0.235738
$238$	3.15929	0.204786
$239$	5.05315	0.326861	0.163431	−	0.986555i	$-0.447744\pi$
$239$	5.05315	0.326861	0.163431	+	0.986555i	$0.447744\pi$
$240$	−24.5029	−1.58166
$241$	6.28489	0.404846	0.202423	−	0.979298i	$-0.435118\pi$
$241$	6.28489	0.404846	0.202423	+	0.979298i	$0.435118\pi$
$242$	0	0
$243$	−16.6731	−1.06958
$244$	−23.8322	−1.52570
$245$	−3.86438	−0.246886
$246$	1.58130	0.100820
$247$	−1.49016	−0.0948165
$248$	−1.80316	−0.114501
$249$	−25.4920	−1.61549
$250$	2.53196	0.160135
$251$	−14.9127	−0.941284	−0.470642	−	0.882324i	$-0.655978\pi$
$251$	−14.9127	−0.941284	−0.470642	+	0.882324i	$0.655978\pi$
$252$	−26.8194	−1.68946
$253$	0	0
$254$	−5.14085	−0.322565
$255$	−28.5153	−1.78570
$256$	10.9819	0.686371
$257$	−2.09159	−0.130470	−0.0652348	−	0.997870i	$-0.520780\pi$
$257$	−2.09159	−0.130470	−0.0652348	+	0.997870i	$0.520780\pi$
$258$	−7.92209	−0.493208
$259$	24.7814	1.53984
$260$	−7.03693	−0.436412
$261$	−22.7189	−1.40627
$262$	−2.16161	−0.133545
$263$	0.765101	0.0471781	0.0235891	−	0.999722i	$-0.492491\pi$
$263$	0.765101	0.0471781	0.0235891	+	0.999722i	$0.492491\pi$
$264$	0	0
$265$	−33.9750	−2.08707
$266$	0.752273	0.0461248
$267$	−6.81680	−0.417181
$268$	−12.8625	−0.785704
$269$	6.11922	0.373095	0.186548	−	0.982446i	$-0.440270\pi$
$269$	6.11922	0.373095	0.186548	+	0.982446i	$0.440270\pi$
$270$	−3.02208	−0.183918
$271$	−28.4534	−1.72842	−0.864211	−	0.503130i	$-0.832182\pi$
$271$	−28.4534	−1.72842	−0.864211	+	0.503130i	$0.832182\pi$
$272$	15.1554	0.918934
$273$	−12.1403	−0.734761
$274$	3.46844	0.209536
$275$	0	0
$276$	−20.0793	−1.20863
$277$	21.2552	1.27710	0.638550	−	0.769580i	$-0.279534\pi$
$277$	21.2552	1.27710	0.638550	+	0.769580i	$0.279534\pi$
$278$	3.18823	0.191217
$279$	8.44883	0.505818
$280$	7.22598	0.431835
$281$	−8.38783	−0.500376	−0.250188	−	0.968197i	$-0.580492\pi$
$281$	−8.38783	−0.500376	−0.250188	+	0.968197i	$0.580492\pi$
$282$	5.39099	0.321029
$283$	19.2757	1.14582	0.572911	−	0.819618i	$-0.305814\pi$
$283$	19.2757	1.14582	0.572911	+	0.819618i	$0.305814\pi$
$284$	20.3952	1.21024
$285$	−6.78990	−0.402199
$286$	0	0
$287$	6.48752	0.382946
$288$	13.9493	0.821970
$289$	0.637175	0.0374809
$290$	3.00930	0.176712
$291$	12.1639	0.713063
$292$	−9.89744	−0.579204
$293$	−0.969687	−0.0566497	−0.0283249	−	0.999599i	$-0.509017\pi$
$293$	−0.969687	−0.0566497	−0.0283249	+	0.999599i	$0.509017\pi$
$294$	1.13017	0.0659131
$295$	−23.8399	−1.38801
$296$	−8.54511	−0.496674
$297$	0	0
$298$	0.766422	0.0443977
$299$	−5.56323	−0.321730
$300$	−5.17171	−0.298589
$301$	−32.5017	−1.87336
$302$	−4.98114	−0.286632
$303$	13.4054	0.770121
$304$	3.60873	0.206975
$305$	−30.0866	−1.72275
$306$	5.10439	0.291799
$307$	−7.68745	−0.438746	−0.219373	−	0.975641i	$-0.570401\pi$
$307$	−7.68745	−0.438746	−0.219373	+	0.975641i	$0.570401\pi$
$308$	0	0
$309$	30.5540	1.73815
$310$	−1.11911	−0.0635613
$311$	21.9520	1.24478	0.622391	−	0.782706i	$-0.286161\pi$
$311$	21.9520	1.24478	0.622391	+	0.782706i	$0.286161\pi$
$312$	4.18620	0.236997
$313$	−29.0973	−1.64467	−0.822337	−	0.569000i	$-0.807330\pi$
$313$	−29.0973	−1.64467	−0.822337	+	0.569000i	$0.807330\pi$
$314$	−4.61326	−0.260342
$315$	−33.8578	−1.90767
$316$	−2.52402	−0.141987
$317$	1.54378	0.0867075	0.0433537	−	0.999060i	$-0.486196\pi$
$317$	1.54378	0.0867075	0.0433537	+	0.999060i	$0.486196\pi$
$318$	9.93631	0.557201
$319$	0	0
$320$	15.7747	0.881832
$321$	42.9788	2.39884
$322$	2.80847	0.156510
$323$	4.19966	0.233676
$324$	1.53879	0.0854885
$325$	−1.43289	−0.0794824
$326$	−0.788577	−0.0436752
$327$	−29.4165	−1.62674
$328$	−2.23703	−0.123519
$329$	22.1174	1.21937
$330$	0	0
$331$	−16.3308	−0.897621	−0.448810	−	0.893627i	$-0.648152\pi$
$331$	−16.3308	−0.897621	−0.448810	+	0.893627i	$0.648152\pi$
$332$	17.7293	0.973021
$333$	40.0386	2.19410
$334$	−1.39459	−0.0763085
$335$	−16.2381	−0.887184
$336$	29.4001	1.60391
$337$	6.11074	0.332873	0.166437	−	0.986052i	$-0.446774\pi$
$337$	6.11074	0.332873	0.166437	+	0.986052i	$0.446774\pi$
$338$	−2.76795	−0.150557
$339$	25.0540	1.36075
$340$	19.8320	1.07554
$341$	0	0
$342$	1.21543	0.0657228
$343$	−15.8706	−0.856935
$344$	11.2072	0.604253
$345$	−25.3488	−1.36473
$346$	3.93039	0.211299
$347$	−17.4753	−0.938121	−0.469061	−	0.883166i	$-0.655407\pi$
$347$	−17.4753	−0.938121	−0.469061	+	0.883166i	$0.655407\pi$
$348$	25.8152	1.38384
$349$	−18.8505	−1.00904	−0.504522	−	0.863399i	$-0.668331\pi$
$349$	−18.8505	−1.00904	−0.504522	+	0.863399i	$0.668331\pi$
$350$	0.723361	0.0386653
$351$	−7.18282	−0.383391
$352$	0	0
$353$	−22.3648	−1.19036	−0.595180	−	0.803592i	$-0.702919\pi$
$353$	−22.3648	−1.19036	−0.595180	+	0.803592i	$0.702919\pi$
$354$	6.97220	0.370568
$355$	25.7477	1.36655
$356$	4.74098	0.251271
$357$	34.2145	1.81082
$358$	−3.60030	−0.190282
$359$	3.85510	0.203464	0.101732	−	0.994812i	$-0.467562\pi$
$359$	3.85510	0.203464	0.101732	+	0.994812i	$0.467562\pi$
$360$	11.6748	0.615318
$361$	1.00000	0.0526316
$362$	0.792825	0.0416700
$363$	0	0
$364$	8.44336	0.442552
$365$	−12.4949	−0.654012
$366$	8.79912	0.459937
$367$	10.6739	0.557172	0.278586	−	0.960411i	$-0.410134\pi$
$367$	10.6739	0.557172	0.278586	+	0.960411i	$0.410134\pi$
$368$	13.4725	0.702303
$369$	10.4817	0.545657
$370$	−5.30343	−0.275712
$371$	40.7653	2.11643
$372$	−9.60029	−0.497752
$373$	23.2599	1.20435	0.602177	−	0.798363i	$-0.294300\pi$
$373$	23.2599	1.20435	0.602177	+	0.798363i	$0.294300\pi$
$374$	0	0
$375$	27.4205	1.41599
$376$	−7.62653	−0.393308
$377$	7.15244	0.368369
$378$	3.62608	0.186506
$379$	−32.6378	−1.67649	−0.838245	−	0.545293i	$-0.816418\pi$
$379$	−32.6378	−1.67649	−0.838245	+	0.545293i	$0.816418\pi$
$380$	4.72227	0.242247
$381$	−55.6743	−2.85228
$382$	−0.0208218	−0.00106534
$383$	5.05499	0.258298	0.129149	−	0.991625i	$-0.458775\pi$
$383$	5.05499	0.258298	0.129149	+	0.991625i	$0.458775\pi$
$384$	−21.0042	−1.07187
$385$	0	0
$386$	−6.63237	−0.337579
$387$	−52.5121	−2.66934
$388$	−8.45983	−0.429483
$389$	26.8157	1.35961	0.679806	−	0.733392i	$-0.262064\pi$
$389$	26.8157	1.35961	0.679806	+	0.733392i	$0.262064\pi$
$390$	2.59812	0.131561
$391$	15.6786	0.792903
$392$	−1.59884	−0.0807534
$393$	−23.4098	−1.18087
$394$	−3.23343	−0.162898
$395$	−3.18641	−0.160326
$396$	0	0
$397$	11.6677	0.585583	0.292791	−	0.956176i	$-0.405416\pi$
$397$	11.6677	0.585583	0.292791	+	0.956176i	$0.405416\pi$
$398$	−3.20327	−0.160565
$399$	8.14695	0.407858
$400$	3.47004	0.173502
$401$	−6.70200	−0.334682	−0.167341	−	0.985899i	$-0.553518\pi$
$401$	−6.70200	−0.334682	−0.167341	+	0.985899i	$0.553518\pi$
$402$	4.74900	0.236859
$403$	−2.65989	−0.132498
$404$	−9.32327	−0.463850
$405$	1.94263	0.0965299
$406$	−3.61075	−0.179198
$407$	0	0
$408$	−11.7978	−0.584080
$409$	−19.5470	−0.966535	−0.483268	−	0.875473i	$-0.660550\pi$
$409$	−19.5470	−0.966535	−0.483268	+	0.875473i	$0.660550\pi$
$410$	−1.38839	−0.0685675
$411$	37.5624	1.85282
$412$	−21.2498	−1.04690
$413$	28.6046	1.40754
$414$	4.53757	0.223009
$415$	22.3821	1.09869
$416$	−4.39156	−0.215314
$417$	34.5278	1.69083
$418$	0	0
$419$	15.0965	0.737511	0.368755	−	0.929526i	$-0.379784\pi$
$419$	15.0965	0.737511	0.368755	+	0.929526i	$0.379784\pi$
$420$	38.4721	1.87725
$421$	−15.9915	−0.779379	−0.389690	−	0.920946i	$-0.627418\pi$
$421$	−15.9915	−0.779379	−0.389690	+	0.920946i	$0.627418\pi$
$422$	0.713251	0.0347205
$423$	35.7346	1.73747
$424$	−14.0567	−0.682654
$425$	4.03826	0.195885
$426$	−7.53016	−0.364838
$427$	36.0998	1.74699
$428$	−29.8911	−1.44484
$429$	0	0
$430$	6.95564	0.335431
$431$	−3.87143	−0.186480	−0.0932401	−	0.995644i	$-0.529722\pi$
$431$	−3.87143	−0.186480	−0.0932401	+	0.995644i	$0.529722\pi$
$432$	17.3947	0.836902
$433$	−30.7123	−1.47594	−0.737970	−	0.674833i	$-0.764216\pi$
$433$	−30.7123	−1.47594	−0.737970	+	0.674833i	$0.764216\pi$
$434$	1.34278	0.0644556
$435$	32.5900	1.56257
$436$	20.4587	0.979795
$437$	3.73331	0.178588
$438$	3.65425	0.174607
$439$	−9.99876	−0.477215	−0.238607	−	0.971116i	$-0.576691\pi$
$439$	−9.99876	−0.477215	−0.238607	+	0.971116i	$0.576691\pi$
$440$	0	0
$441$	7.49144	0.356735
$442$	−1.60698	−0.0764362
$443$	14.5072	0.689258	0.344629	−	0.938739i	$-0.388005\pi$
$443$	14.5072	0.689258	0.344629	+	0.938739i	$0.388005\pi$
$444$	−45.4953	−2.15911
$445$	5.98519	0.283725
$446$	−0.513428	−0.0243115
$447$	8.30019	0.392586
$448$	−18.9275	−0.894239
$449$	12.6360	0.596330	0.298165	−	0.954514i	$-0.403625\pi$
$449$	12.6360	0.596330	0.298165	+	0.954514i	$0.403625\pi$
$450$	1.16872	0.0550938
$451$	0	0
$452$	−17.4247	−0.819589
$453$	−53.9446	−2.53454
$454$	3.50148	0.164333
$455$	10.6592	0.499711
$456$	−2.80923	−0.131554
$457$	4.67021	0.218463	0.109232	−	0.994016i	$-0.465161\pi$
$457$	4.67021	0.218463	0.109232	+	0.994016i	$0.465161\pi$
$458$	2.13016	0.0995356
$459$	20.2431	0.944867
$460$	17.6297	0.821989
$461$	−1.86934	−0.0870639	−0.0435320	−	0.999052i	$-0.513861\pi$
$461$	−1.86934	−0.0870639	−0.0435320	+	0.999052i	$0.513861\pi$
$462$	0	0
$463$	21.3757	0.993414	0.496707	−	0.867918i	$-0.334542\pi$
$463$	21.3757	0.993414	0.496707	+	0.867918i	$0.334542\pi$
$464$	−17.3211	−0.804113
$465$	−12.1198	−0.562040
$466$	−7.41220	−0.343364
$467$	−1.31534	−0.0608668	−0.0304334	−	0.999537i	$-0.509689\pi$
$467$	−1.31534	−0.0608668	−0.0304334	+	0.999537i	$0.509689\pi$
$468$	13.6417	0.630589
$469$	19.4835	0.899666
$470$	−4.73332	−0.218332
$471$	−49.9607	−2.30207
$472$	−9.86343	−0.454001
$473$	0	0
$474$	0.931896	0.0428034
$475$	0.961568	0.0441198
$476$	−23.7956	−1.09067
$477$	65.8635	3.01568
$478$	1.29755	0.0593487
$479$	37.1620	1.69798	0.848988	−	0.528413i	$-0.177213\pi$
$479$	37.1620	1.69798	0.848988	+	0.528413i	$0.177213\pi$
$480$	−20.0101	−0.913332
$481$	−12.6051	−0.574742
$482$	1.61384	0.0735085
$483$	30.4151	1.38393
$484$	0	0
$485$	−10.6800	−0.484954
$486$	−4.28133	−0.194205
$487$	6.71033	0.304074	0.152037	−	0.988375i	$-0.451417\pi$
$487$	6.71033	0.304074	0.152037	+	0.988375i	$0.451417\pi$
$488$	−12.4479	−0.563492
$489$	−8.54012	−0.386197
$490$	−0.992300	−0.0448275
$491$	−27.8221	−1.25560	−0.627798	−	0.778376i	$-0.716044\pi$
$491$	−27.8221	−1.25560	−0.627798	+	0.778376i	$0.716044\pi$
$492$	−11.9102	−0.536955
$493$	−20.1575	−0.907847
$494$	−0.382645	−0.0172160
$495$	0	0
$496$	6.44146	0.289230
$497$	−30.8937	−1.38577
$498$	−6.54586	−0.293327
$499$	26.1934	1.17258	0.586290	−	0.810101i	$-0.300588\pi$
$499$	26.1934	1.17258	0.586290	+	0.810101i	$0.300588\pi$
$500$	−19.0706	−0.852862
$501$	−15.1031	−0.674757
$502$	−3.82931	−0.170911
$503$	−9.22970	−0.411532	−0.205766	−	0.978601i	$-0.565969\pi$
$503$	−9.22970	−0.411532	−0.205766	+	0.978601i	$0.565969\pi$
$504$	−14.0082	−0.623975
$505$	−11.7700	−0.523760
$506$	0	0
$507$	−29.9763	−1.33130
$508$	38.7206	1.71795
$509$	27.1395	1.20294	0.601468	−	0.798897i	$-0.294583\pi$
$509$	27.1395	1.20294	0.601468	+	0.798897i	$0.294583\pi$
$510$	−7.32219	−0.324232
$511$	14.9922	0.663214
$512$	17.9261	0.792229
$513$	4.82017	0.212816
$514$	−0.537080	−0.0236896
$515$	−26.8265	−1.18212
$516$	59.6688	2.62677
$517$	0	0
$518$	6.36339	0.279591
$519$	42.5653	1.86841
$520$	−3.67551	−0.161182
$521$	−37.7841	−1.65535	−0.827676	−	0.561207i	$-0.810337\pi$
$521$	−37.7841	−1.65535	−0.827676	+	0.561207i	$0.810337\pi$
$522$	−5.83379	−0.255338
$523$	19.2200	0.840434	0.420217	−	0.907424i	$-0.361954\pi$
$523$	19.2200	0.840434	0.420217	+	0.907424i	$0.361954\pi$
$524$	16.2812	0.711246
$525$	7.83385	0.341897
$526$	0.196463	0.00856621
$527$	7.49627	0.326542
$528$	0	0
$529$	−9.06239	−0.394017
$530$	−8.72414	−0.378952
$531$	46.2157	2.00559
$532$	−5.66608	−0.245656
$533$	−3.29989	−0.142934
$534$	−1.75043	−0.0757483
$535$	−37.7356	−1.63145
$536$	−6.71831	−0.290187
$537$	−38.9904	−1.68256
$538$	1.57130	0.0677436
$539$	0	0
$540$	22.7622	0.979527
$541$	11.6378	0.500348	0.250174	−	0.968201i	$-0.419512\pi$
$541$	11.6378	0.500348	0.250174	+	0.968201i	$0.419512\pi$
$542$	−7.30630	−0.313832
$543$	8.58612	0.368466
$544$	12.3766	0.530641
$545$	25.8278	1.10634
$546$	−3.11739	−0.133412
$547$	40.3150	1.72374	0.861872	−	0.507125i	$-0.169292\pi$
$547$	40.3150	1.72374	0.861872	+	0.507125i	$0.169292\pi$
$548$	−26.1241	−1.11597
$549$	58.3256	2.48928
$550$	0	0
$551$	−4.79978	−0.204478
$552$	−10.4877	−0.446388
$553$	3.82326	0.162581
$554$	5.45793	0.231885
$555$	−57.4350	−2.43798
$556$	−24.0136	−1.01840
$557$	−4.44738	−0.188442	−0.0942208	−	0.995551i	$-0.530036\pi$
$557$	−4.44738	−0.188442	−0.0942208	+	0.995551i	$0.530036\pi$
$558$	2.16950	0.0918423
$559$	16.5320	0.699230
$560$	−25.8135	−1.09082
$561$	0	0
$562$	−2.15384	−0.0908541
$563$	13.8633	0.584268	0.292134	−	0.956377i	$-0.405635\pi$
$563$	13.8633	0.584268	0.292134	+	0.956377i	$0.405635\pi$
$564$	−40.6047	−1.70977
$565$	−21.9976	−0.925445
$566$	4.94964	0.208049
$567$	−2.33089	−0.0978881
$568$	10.6528	0.446980
$569$	−28.6839	−1.20249	−0.601246	−	0.799064i	$-0.705329\pi$
$569$	−28.6839	−1.20249	−0.601246	+	0.799064i	$0.705329\pi$
$570$	−1.74352	−0.0730279
$571$	8.27342	0.346232	0.173116	−	0.984901i	$-0.444616\pi$
$571$	8.27342	0.346232	0.173116	+	0.984901i	$0.444616\pi$
$572$	0	0
$573$	−0.225496	−0.00942024
$574$	1.66587	0.0695322
$575$	3.58983	0.149706
$576$	−30.5806	−1.27419
$577$	−9.06405	−0.377341	−0.188671	−	0.982040i	$-0.560418\pi$
$577$	−9.06405	−0.377341	−0.188671	+	0.982040i	$0.560418\pi$
$578$	0.163615	0.00680547
$579$	−71.8272	−2.98504
$580$	−22.6659	−0.941150
$581$	−26.8555	−1.11415
$582$	3.12347	0.129472
$583$	0	0
$584$	−5.16960	−0.213919
$585$	17.2218	0.712034
$586$	−0.248997	−0.0102860
$587$	12.1244	0.500428	0.250214	−	0.968191i	$-0.419499\pi$
$587$	12.1244	0.500428	0.250214	+	0.968191i	$0.419499\pi$
$588$	−8.51242	−0.351046
$589$	1.78497	0.0735483
$590$	−6.12163	−0.252023
$591$	−35.0174	−1.44042
$592$	30.5258	1.25460
$593$	−24.9107	−1.02296	−0.511481	−	0.859295i	$-0.670903\pi$
$593$	−24.9107	−1.02296	−0.511481	+	0.859295i	$0.670903\pi$
$594$	0	0
$595$	−30.0405	−1.23154
$596$	−5.77266	−0.236457
$597$	−34.6907	−1.41980
$598$	−1.42853	−0.0584170
$599$	41.4959	1.69548	0.847739	−	0.530414i	$-0.177963\pi$
$599$	41.4959	1.69548	0.847739	+	0.530414i	$0.177963\pi$
$600$	−2.70127	−0.110279
$601$	−16.2749	−0.663866	−0.331933	−	0.943303i	$-0.607701\pi$
$601$	−16.2749	−0.663866	−0.331933	+	0.943303i	$0.607701\pi$
$602$	−8.34581	−0.340150
$603$	31.4791	1.28193
$604$	37.5177	1.52657
$605$	0	0
$606$	3.44226	0.139832
$607$	44.0021	1.78599	0.892994	−	0.450068i	$-0.148600\pi$
$607$	44.0021	1.78599	0.892994	+	0.450068i	$0.148600\pi$
$608$	2.94704	0.119518
$609$	−39.1036	−1.58456
$610$	−7.72568	−0.312803
$611$	−11.2501	−0.455129
$612$	−38.4460	−1.55409
$613$	2.71623	0.109708	0.0548538	−	0.998494i	$-0.482531\pi$
$613$	2.71623	0.109708	0.0548538	+	0.998494i	$0.482531\pi$
$614$	−1.97399	−0.0796638
$615$	−15.0359	−0.606307
$616$	0	0
$617$	35.6598	1.43561	0.717806	−	0.696244i	$-0.245147\pi$
$617$	35.6598	1.43561	0.717806	+	0.696244i	$0.245147\pi$
$618$	7.84568	0.315600
$619$	−10.9080	−0.438431	−0.219215	−	0.975677i	$-0.570350\pi$
$619$	−10.9080	−0.438431	−0.219215	+	0.975677i	$0.570350\pi$
$620$	8.42910	0.338521
$621$	17.9952	0.722122
$622$	5.63686	0.226017
$623$	−7.18141	−0.287717
$624$	−14.9544	−0.598656
$625$	−28.8832	−1.15533
$626$	−7.47163	−0.298626
$627$	0	0
$628$	34.7469	1.38655
$629$	35.5245	1.41645
$630$	−8.69404	−0.346379
$631$	15.1135	0.601658	0.300829	−	0.953678i	$-0.402737\pi$
$631$	15.1135	0.601658	0.300829	+	0.953678i	$0.402737\pi$
$632$	−1.31834	−0.0524406
$633$	7.72436	0.307016
$634$	0.396414	0.0157436
$635$	48.8823	1.93984
$636$	−74.8398	−2.96759
$637$	−2.35848	−0.0934463
$638$	0	0
$639$	−49.9142	−1.97458
$640$	18.4418	0.728977
$641$	−8.52912	−0.336880	−0.168440	−	0.985712i	$-0.553873\pi$
$641$	−8.52912	−0.336880	−0.168440	+	0.985712i	$0.553873\pi$
$642$	11.0361	0.435562
$643$	18.5443	0.731315	0.365658	−	0.930749i	$-0.380844\pi$
$643$	18.5443	0.731315	0.365658	+	0.930749i	$0.380844\pi$
$644$	−21.1532	−0.833554
$645$	75.3281	2.96604
$646$	1.07839	0.0424289
$647$	0.277869	0.0109241	0.00546207	−	0.999985i	$-0.498261\pi$
$647$	0.277869	0.0109241	0.00546207	+	0.999985i	$0.498261\pi$
$648$	0.803737	0.0315738
$649$	0	0
$650$	−0.367939	−0.0144318
$651$	14.5420	0.569948
$652$	5.93952	0.232610
$653$	−13.4968	−0.528172	−0.264086	−	0.964499i	$-0.585070\pi$
$653$	−13.4968	−0.528172	−0.264086	+	0.964499i	$0.585070\pi$
$654$	−7.55360	−0.295369
$655$	20.5539	0.803108
$656$	7.99137	0.312011
$657$	24.2225	0.945008
$658$	5.67934	0.221404
$659$	−34.6157	−1.34843	−0.674217	−	0.738533i	$-0.735519\pi$
$659$	−34.6157	−1.34843	−0.674217	+	0.738533i	$0.735519\pi$
$660$	0	0
$661$	−28.9833	−1.12732	−0.563660	−	0.826007i	$-0.690607\pi$
$661$	−28.9833	−1.12732	−0.563660	+	0.826007i	$0.690607\pi$
$662$	−4.19344	−0.162983
$663$	−17.4032	−0.675886
$664$	9.26030	0.359369
$665$	−7.15307	−0.277384
$666$	10.2812	0.398387
$667$	−17.9191	−0.693830
$668$	10.5040	0.406411
$669$	−5.56032	−0.214974
$670$	−4.16965	−0.161087
$671$	0	0
$672$	24.0094	0.926182
$673$	1.52562	0.0588085	0.0294043	−	0.999568i	$-0.490639\pi$
$673$	1.52562	0.0588085	0.0294043	+	0.999568i	$0.490639\pi$
$674$	1.56912	0.0604403
$675$	4.63492	0.178398
$676$	20.8481	0.801850
$677$	−20.7211	−0.796375	−0.398187	−	0.917304i	$-0.630361\pi$
$677$	−20.7211	−0.796375	−0.398187	+	0.917304i	$0.630361\pi$
$678$	6.43341	0.247074
$679$	12.8145	0.491777
$680$	10.3586	0.397233
$681$	37.9203	1.45311
$682$	0	0
$683$	8.44932	0.323304	0.161652	−	0.986848i	$-0.448318\pi$
$683$	8.44932	0.323304	0.161652	+	0.986848i	$0.448318\pi$
$684$	−9.15455	−0.350033
$685$	−32.9800	−1.26010
$686$	−4.07528	−0.155595
$687$	23.0691	0.880142
$688$	−40.0357	−1.52635
$689$	−20.7354	−0.789954
$690$	−6.50909	−0.247797
$691$	−18.1105	−0.688958	−0.344479	−	0.938794i	$-0.611944\pi$
$691$	−18.1105	−0.688958	−0.344479	+	0.938794i	$0.611944\pi$
$692$	−29.6035	−1.12536
$693$	0	0
$694$	−4.48732	−0.170336
$695$	−30.3156	−1.14994
$696$	13.4837	0.511099
$697$	9.29997	0.352261
$698$	−4.84045	−0.183214
$699$	−80.2726	−3.03619
$700$	−5.44832	−0.205927
$701$	−15.8274	−0.597792	−0.298896	−	0.954286i	$-0.596618\pi$
$701$	−15.8274	−0.597792	−0.298896	+	0.954286i	$0.596618\pi$
$702$	−1.84441	−0.0696129
$703$	8.45889	0.319033
$704$	0	0
$705$	−51.2608	−1.93060
$706$	−5.74287	−0.216136
$707$	14.1224	0.531129
$708$	−52.5143	−1.97361
$709$	−14.1478	−0.531333	−0.265666	−	0.964065i	$-0.585592\pi$
$709$	−14.1478	−0.531333	−0.265666	+	0.964065i	$0.585592\pi$
$710$	6.61152	0.248126
$711$	6.17714	0.231661
$712$	2.47629	0.0928030
$713$	6.66384	0.249563
$714$	8.78563	0.328794
$715$	0	0
$716$	27.1173	1.01342
$717$	14.0522	0.524790
$718$	0.989916	0.0369433
$719$	−14.4890	−0.540348	−0.270174	−	0.962812i	$-0.587081\pi$
$719$	−14.4890	−0.540348	−0.270174	+	0.962812i	$0.587081\pi$
$720$	−41.7062	−1.55430
$721$	32.1882	1.19875
$722$	0.256781	0.00955641
$723$	17.4776	0.649998
$724$	−5.97152	−0.221930
$725$	−4.61532	−0.171409
$726$	0	0
$727$	−5.90862	−0.219139	−0.109569	−	0.993979i	$-0.534947\pi$
$727$	−5.90862	−0.219139	−0.109569	+	0.993979i	$0.534947\pi$
$728$	4.41011	0.163449
$729$	−43.9790	−1.62885
$730$	−3.20845	−0.118750
$731$	−46.5916	−1.72325
$732$	−66.2746	−2.44958
$733$	35.5641	1.31359	0.656796	−	0.754069i	$-0.271911\pi$
$733$	35.5641	1.31359	0.656796	+	0.754069i	$0.271911\pi$
$734$	2.74085	0.101167
$735$	−10.7464	−0.396387
$736$	11.0022	0.405547
$737$	0	0
$738$	2.69151	0.0990759
$739$	−45.1654	−1.66144	−0.830718	−	0.556693i	$-0.812070\pi$
$739$	−45.1654	−1.66144	−0.830718	+	0.556693i	$0.812070\pi$
$740$	39.9452	1.46841
$741$	−4.14396	−0.152232
$742$	10.4678	0.384284
$743$	−26.6110	−0.976262	−0.488131	−	0.872770i	$-0.662321\pi$
$743$	−26.6110	−0.976262	−0.488131	+	0.872770i	$0.662321\pi$
$744$	−5.01439	−0.183836
$745$	−7.28761	−0.266997
$746$	5.97271	0.218676
$747$	−43.3897	−1.58755
$748$	0	0
$749$	45.2776	1.65441
$750$	7.04108	0.257104
$751$	2.45561	0.0896065	0.0448032	−	0.998996i	$-0.485734\pi$
$751$	2.45561	0.0896065	0.0448032	+	0.998996i	$0.485734\pi$
$752$	27.2444	0.993500
$753$	−41.4706	−1.51127
$754$	1.83661	0.0668855
$755$	47.3637	1.72374
$756$	−27.3115	−0.993309
$757$	37.3012	1.35573	0.677867	−	0.735184i	$-0.262904\pi$
$757$	37.3012	1.35573	0.677867	+	0.735184i	$0.262904\pi$
$758$	−8.38077	−0.304403
$759$	0	0
$760$	2.46652	0.0894701
$761$	23.9679	0.868836	0.434418	−	0.900711i	$-0.356954\pi$
$761$	23.9679	0.868836	0.434418	+	0.900711i	$0.356954\pi$
$762$	−14.2961	−0.517893
$763$	−30.9899	−1.12191
$764$	0.156829	0.00567388
$765$	−48.5357	−1.75481
$766$	1.29803	0.0468996
$767$	−14.5498	−0.525362
$768$	30.5395	1.10200
$769$	−10.6655	−0.384609	−0.192305	−	0.981335i	$-0.561596\pi$
$769$	−10.6655	−0.384609	−0.192305	+	0.981335i	$0.561596\pi$
$770$	0	0
$771$	−5.81647	−0.209475
$772$	49.9547	1.79791
$773$	28.2846	1.01733	0.508664	−	0.860965i	$-0.330140\pi$
$773$	28.2846	1.01733	0.508664	+	0.860965i	$0.330140\pi$
$774$	−13.4841	−0.484677
$775$	1.71637	0.0616538
$776$	−4.41871	−0.158622
$777$	68.9141	2.47228
$778$	6.88578	0.246867
$779$	2.21446	0.0793411
$780$	−19.5689	−0.700679
$781$	0	0
$782$	4.02598	0.143969
$783$	−23.1358	−0.826805
$784$	5.71154	0.203984
$785$	43.8657	1.56564
$786$	−6.01119	−0.214412
$787$	28.2203	1.00594	0.502972	−	0.864303i	$-0.332240\pi$
$787$	28.2203	1.00594	0.502972	+	0.864303i	$0.332240\pi$
$788$	24.3541	0.867578
$789$	2.12766	0.0757466
$790$	−0.818210	−0.0291106
$791$	26.3941	0.938466
$792$	0	0
$793$	−18.3622	−0.652062
$794$	2.99603	0.106325
$795$	−94.4805	−3.35088
$796$	24.1269	0.855154
$797$	−1.66168	−0.0588596	−0.0294298	−	0.999567i	$-0.509369\pi$
$797$	−1.66168	−0.0588596	−0.0294298	+	0.999567i	$0.509369\pi$
$798$	2.09198	0.0740554
$799$	31.7057	1.12167
$800$	2.83378	0.100189
$801$	−11.6028	−0.409965
$802$	−1.72095	−0.0607687
$803$	0	0
$804$	−35.7692	−1.26148
$805$	−26.7046	−0.941214
$806$	−0.683009	−0.0240580
$807$	17.0169	0.599021
$808$	−4.86970	−0.171315
$809$	−2.44069	−0.0858101	−0.0429051	−	0.999079i	$-0.513661\pi$
$809$	−2.44069	−0.0858101	−0.0429051	+	0.999079i	$0.513661\pi$
$810$	0.498830	0.0175271
$811$	−43.7575	−1.53654	−0.768268	−	0.640129i	$-0.778881\pi$
$811$	−43.7575	−1.53654	−0.768268	+	0.640129i	$0.778881\pi$
$812$	27.1960	0.954391
$813$	−79.1257	−2.77506
$814$	0	0
$815$	7.49827	0.262653
$816$	42.1456	1.47539
$817$	−11.0941	−0.388135
$818$	−5.01929	−0.175495
$819$	−20.6638	−0.722052
$820$	10.4573	0.365183
$821$	−16.6519	−0.581156	−0.290578	−	0.956851i	$-0.593848\pi$
$821$	−16.6519	−0.581156	−0.290578	+	0.956851i	$0.593848\pi$
$822$	9.64532	0.336419
$823$	−1.89733	−0.0661368	−0.0330684	−	0.999453i	$-0.510528\pi$
$823$	−1.89733	−0.0661368	−0.0330684	+	0.999453i	$0.510528\pi$
$824$	−11.0991	−0.386657
$825$	0	0
$826$	7.34512	0.255569
$827$	19.1547	0.666075	0.333038	−	0.942914i	$-0.391926\pi$
$827$	19.1547	0.666075	0.333038	+	0.942914i	$0.391926\pi$
$828$	−34.1768	−1.18772
$829$	−36.1229	−1.25460	−0.627300	−	0.778778i	$-0.715840\pi$
$829$	−36.1229	−1.25460	−0.627300	+	0.778778i	$0.715840\pi$
$830$	5.74730	0.199492
$831$	59.1082	2.05044
$832$	9.62749	0.333773
$833$	6.64682	0.230299
$834$	8.86609	0.307008
$835$	13.2606	0.458902
$836$	0	0
$837$	8.60385	0.297393
$838$	3.87649	0.133911
$839$	−0.709258	−0.0244863	−0.0122431	−	0.999925i	$-0.503897\pi$
$839$	−0.709258	−0.0244863	−0.0122431	+	0.999925i	$0.503897\pi$
$840$	20.0946	0.693330
$841$	−5.96208	−0.205589
$842$	−4.10632	−0.141513
$843$	−23.3256	−0.803376
$844$	−5.37217	−0.184918
$845$	26.3194	0.905415
$846$	9.17596	0.315476
$847$	0	0
$848$	50.2150	1.72439
$849$	53.6035	1.83967
$850$	1.03695	0.0355671
$851$	31.5796	1.08254
$852$	56.7168	1.94309
$853$	12.0002	0.410879	0.205439	−	0.978670i	$-0.434138\pi$
$853$	12.0002	0.410879	0.205439	+	0.978670i	$0.434138\pi$
$854$	9.26976	0.317205
$855$	−11.5570	−0.395242
$856$	−15.6126	−0.533628
$857$	−24.5032	−0.837013	−0.418506	−	0.908214i	$-0.637446\pi$
$857$	−24.5032	−0.837013	−0.418506	+	0.908214i	$0.637446\pi$
$858$	0	0
$859$	−1.96982	−0.0672093	−0.0336046	−	0.999435i	$-0.510699\pi$
$859$	−1.96982	−0.0672093	−0.0336046	+	0.999435i	$0.510699\pi$
$860$	−52.3895	−1.78647
$861$	18.0411	0.614838
$862$	−0.994110	−0.0338595
$863$	35.5042	1.20858	0.604288	−	0.796766i	$-0.293458\pi$
$863$	35.5042	1.20858	0.604288	+	0.796766i	$0.293458\pi$
$864$	14.2052	0.483272
$865$	−37.3726	−1.27071
$866$	−7.88635	−0.267989
$867$	1.77191	0.0601773
$868$	−10.1138	−0.343284
$869$	0	0
$870$	8.36851	0.283719
$871$	−9.91034	−0.335799
$872$	10.6859	0.361871
$873$	20.7041	0.700729
$874$	0.958644	0.0324266
$875$	28.8872	0.976565
$876$	−27.5236	−0.929938
$877$	−15.1016	−0.509945	−0.254973	−	0.966948i	$-0.582066\pi$
$877$	−15.1016	−0.509945	−0.254973	+	0.966948i	$0.582066\pi$
$878$	−2.56749	−0.0866487
$879$	−2.69659	−0.0909537
$880$	0	0
$881$	26.3321	0.887151	0.443575	−	0.896237i	$-0.353710\pi$
$881$	26.3321	0.887151	0.443575	+	0.896237i	$0.353710\pi$
$882$	1.92366	0.0647731
$883$	4.12801	0.138918	0.0694592	−	0.997585i	$-0.477873\pi$
$883$	4.12801	0.138918	0.0694592	+	0.997585i	$0.477873\pi$
$884$	12.1037	0.407091
$885$	−66.2959	−2.22851
$886$	3.72518	0.125150
$887$	−15.1636	−0.509145	−0.254573	−	0.967054i	$-0.581935\pi$
$887$	−15.1636	−0.509145	−0.254573	+	0.967054i	$0.581935\pi$
$888$	−23.7630	−0.797433
$889$	−58.6521	−1.96713
$890$	1.53688	0.0515164
$891$	0	0
$892$	3.86712	0.129481
$893$	7.54957	0.252637
$894$	2.13133	0.0712824
$895$	34.2338	1.14431
$896$	−22.1277	−0.739233
$897$	−15.4707	−0.516551
$898$	3.24469	0.108277
$899$	−8.56746	−0.285741
$900$	−8.80272	−0.293424
$901$	58.4378	1.94684
$902$	0	0
$903$	−90.3834	−3.00777
$904$	−9.10121	−0.302702
$905$	−7.53866	−0.250594
$906$	−13.8520	−0.460201
$907$	8.67915	0.288186	0.144093	−	0.989564i	$-0.453974\pi$
$907$	8.67915	0.288186	0.144093	+	0.989564i	$0.453974\pi$
$908$	−26.3730	−0.875219
$909$	22.8173	0.756801
$910$	2.73708	0.0907334
$911$	−45.9917	−1.52377	−0.761887	−	0.647710i	$-0.775727\pi$
$911$	−45.9917	−1.52377	−0.761887	+	0.647710i	$0.775727\pi$
$912$	10.0355	0.332307
$913$	0	0
$914$	1.19922	0.0396668
$915$	−83.6674	−2.76596
$916$	−16.0442	−0.530116
$917$	−24.6619	−0.814408
$918$	5.19805	0.171561
$919$	−49.4285	−1.63049	−0.815247	−	0.579113i	$-0.803399\pi$
$919$	−49.4285	−1.63049	−0.815247	+	0.579113i	$0.803399\pi$
$920$	9.20829	0.303588
$921$	−21.3779	−0.704426
$922$	−0.480012	−0.0158083
$923$	15.7141	0.517237
$924$	0	0
$925$	8.13380	0.267438
$926$	5.48888	0.180376
$927$	52.0056	1.70809
$928$	−14.1452	−0.464337
$929$	−50.3985	−1.65352	−0.826760	−	0.562555i	$-0.809818\pi$
$929$	−50.3985	−1.65352	−0.826760	+	0.562555i	$0.809818\pi$
$930$	−3.11212	−0.102051
$931$	1.58270	0.0518710
$932$	55.8284	1.82872
$933$	61.0459	1.99855
$934$	−0.337755	−0.0110517
$935$	0	0
$936$	7.12530	0.232898
$937$	−58.8816	−1.92358	−0.961789	−	0.273792i	$-0.911722\pi$
$937$	−58.8816	−1.92358	−0.961789	+	0.273792i	$0.911722\pi$
$938$	5.00301	0.163354
$939$	−80.9162	−2.64060
$940$	35.6511	1.16281
$941$	−5.87601	−0.191553	−0.0957763	−	0.995403i	$-0.530533\pi$
$941$	−5.87601	−0.191553	−0.0957763	+	0.995403i	$0.530533\pi$
$942$	−12.8290	−0.417990
$943$	8.26725	0.269219
$944$	35.2353	1.14681
$945$	−34.4790	−1.12160
$946$	0	0
$947$	40.9791	1.33164	0.665821	−	0.746111i	$-0.268081\pi$
$947$	40.9791	1.33164	0.665821	+	0.746111i	$0.268081\pi$
$948$	−7.01900	−0.227966
$949$	−7.62579	−0.247544
$950$	0.246913	0.00801090
$951$	4.29308	0.139213
$952$	−12.4289	−0.402821
$953$	−6.01629	−0.194887	−0.0974434	−	0.995241i	$-0.531067\pi$
$953$	−6.01629	−0.194887	−0.0974434	+	0.995241i	$0.531067\pi$
$954$	16.9125	0.547563
$955$	0.197987	0.00640670
$956$	−9.77311	−0.316085
$957$	0	0
$958$	9.54250	0.308304
$959$	39.5715	1.27783
$960$	43.8676	1.41582
$961$	−27.8139	−0.897222
$962$	−3.23675	−0.104357
$963$	73.1539	2.35735
$964$	−12.1554	−0.391498
$965$	63.0647	2.03012
$966$	7.81002	0.251283
$967$	15.5956	0.501522	0.250761	−	0.968049i	$-0.419319\pi$
$967$	15.5956	0.501522	0.250761	+	0.968049i	$0.419319\pi$
$968$	0	0
$969$	11.6788	0.375177
$970$	−2.74242	−0.0880539
$971$	−7.25518	−0.232830	−0.116415	−	0.993201i	$-0.537140\pi$
$971$	−7.25518	−0.232830	−0.116415	+	0.993201i	$0.537140\pi$
$972$	32.2468	1.03432
$973$	36.3746	1.16612
$974$	1.72309	0.0552112
$975$	−3.98470	−0.127613
$976$	44.4680	1.42338
$977$	−27.9251	−0.893404	−0.446702	−	0.894683i	$-0.647402\pi$
$977$	−27.9251	−0.893404	−0.446702	+	0.894683i	$0.647402\pi$
$978$	−2.19294	−0.0701225
$979$	0	0
$980$	7.47395	0.238747
$981$	−50.0696	−1.59860
$982$	−7.14420	−0.227981
$983$	9.58015	0.305559	0.152780	−	0.988260i	$-0.451178\pi$
$983$	9.58015	0.305559	0.152780	+	0.988260i	$0.451178\pi$
$984$	−6.22092	−0.198316
$985$	30.7455	0.979632
$986$	−5.17606	−0.164839
$987$	61.5060	1.95776
$988$	2.88206	0.0916906
$989$	−41.4179	−1.31701
$990$	0	0
$991$	−4.40388	−0.139894	−0.0699470	−	0.997551i	$-0.522283\pi$
$991$	−4.40388	−0.139894	−0.0699470	+	0.997551i	$0.522283\pi$
$992$	5.26037	0.167017
$993$	−45.4140	−1.44117
$994$	−7.93293	−0.251617
$995$	30.4586	0.965604
$996$	49.3031	1.56223
$997$	37.7132	1.19439	0.597194	−	0.802097i	$-0.296282\pi$
$997$	37.7132	1.19439	0.597194	+	0.802097i	$0.296282\pi$
$998$	6.72598	0.212907
$999$	40.7733	1.29001

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2299.2.a.x.1.11		20
11.5	even	5		209.2.f.c.58.5	✓	40
11.9	even	5		209.2.f.c.191.5	yes	40
11.10	odd	2		2299.2.a.y.1.10		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
209.2.f.c.58.5	✓	40	11.5	even	5
209.2.f.c.191.5	yes	40	11.9	even	5
2299.2.a.x.1.11		20	1.1	even	1	trivial
2299.2.a.y.1.10		20	11.10	odd	2

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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:	\( N \)	\(=\)	\( 2299 = 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2299.a (trivial)

\(f(q)\)	\(=\)	\(q+0.256781 q^{2} +2.78089 q^{3} -1.93406 q^{4} -2.44163 q^{5} +0.714079 q^{6} +2.92963 q^{7} -1.01019 q^{8} +4.73332 q^{9} -0.626965 q^{10} -5.37841 q^{12} -1.49016 q^{13} +0.752273 q^{14} -6.78990 q^{15} +3.60873 q^{16} +4.19966 q^{17} +1.21543 q^{18} +1.00000 q^{19} +4.72227 q^{20} +8.14695 q^{21} +3.73331 q^{23} -2.80923 q^{24} +0.961568 q^{25} -0.382645 q^{26} +4.82017 q^{27} -5.66608 q^{28} -4.79978 q^{29} -1.74352 q^{30} +1.78497 q^{31} +2.94704 q^{32} +1.07839 q^{34} -7.15307 q^{35} -9.15455 q^{36} +8.45889 q^{37} +0.256781 q^{38} -4.14396 q^{39} +2.46652 q^{40} +2.21446 q^{41} +2.09198 q^{42} -11.0941 q^{43} -11.5570 q^{45} +0.958644 q^{46} +7.54957 q^{47} +10.0355 q^{48} +1.58270 q^{49} +0.246913 q^{50} +11.6788 q^{51} +2.88206 q^{52} +13.9149 q^{53} +1.23773 q^{54} -2.95949 q^{56} +2.78089 q^{57} -1.23249 q^{58} +9.76391 q^{59} +13.1321 q^{60} +12.3223 q^{61} +0.458346 q^{62} +13.8669 q^{63} -6.46071 q^{64} +3.63842 q^{65} +6.65052 q^{67} -8.12242 q^{68} +10.3819 q^{69} -1.83677 q^{70} -10.5453 q^{71} -4.78157 q^{72} +5.11743 q^{73} +2.17208 q^{74} +2.67401 q^{75} -1.93406 q^{76} -1.06409 q^{78} +1.30503 q^{79} -8.81119 q^{80} -0.795627 q^{81} +0.568631 q^{82} -9.16686 q^{83} -15.7567 q^{84} -10.2540 q^{85} -2.84877 q^{86} -13.3476 q^{87} -2.45131 q^{89} -2.96763 q^{90} -4.36561 q^{91} -7.22046 q^{92} +4.96379 q^{93} +1.93859 q^{94} -2.44163 q^{95} +8.19538 q^{96} +4.37412 q^{97} +0.406408 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - q^{2} + 4 q^{3} + 21 q^{4} + 18 q^{5} + 10 q^{6} + 2 q^{7} - 3 q^{8} + 32 q^{9} - 11 q^{10} + 10 q^{12} - q^{13} + 25 q^{14} + 28 q^{15} + 27 q^{16} - 2 q^{17} - 4 q^{18} + 20 q^{19} + 47 q^{20}+ \cdots - 45 q^{98}+O(q^{100}) \) 20 * q - q^2 + 4 * q^3 + 21 * q^4 + 18 * q^5 + 10 * q^6 + 2 * q^7 - 3 * q^8 + 32 * q^9 - 11 * q^10 + 10 * q^12 - q^13 + 25 * q^14 + 28 * q^15 + 27 * q^16 - 2 * q^17 - 4 * q^18 + 20 * q^19 + 47 * q^20 - 11 * q^21 + 8 * q^23 + 36 * q^24 + 36 * q^25 + 8 * q^26 - 2 * q^27 - 28 * q^28 - 17 * q^29 + 10 * q^30 - 9 * q^31 - 2 * q^32 - 19 * q^34 + 20 * q^35 + 17 * q^36 + 29 * q^37 - q^38 - 3 * q^39 - 29 * q^40 - 4 * q^41 - 16 * q^42 - 12 * q^43 + 65 * q^45 + 36 * q^46 + 10 * q^47 + 42 * q^48 + 34 * q^49 - 25 * q^50 + 10 * q^51 + 13 * q^52 + 50 * q^53 + 26 * q^54 + 37 * q^56 + 4 * q^57 + 4 * q^58 + 46 * q^59 - 7 * q^60 - 22 * q^61 + 5 * q^62 + 69 * q^63 + 47 * q^64 - 13 * q^65 + 26 * q^67 + 5 * q^68 + 65 * q^69 + 26 * q^70 + 38 * q^71 - 104 * q^72 + 3 * q^73 + 10 * q^74 + 13 * q^75 + 21 * q^76 - 45 * q^78 - 14 * q^79 + 31 * q^80 + 76 * q^81 - 10 * q^82 - 14 * q^83 + 5 * q^84 - 9 * q^85 + 15 * q^86 - 21 * q^87 + 48 * q^89 + 28 * q^90 + 24 * q^91 + q^92 + 42 * q^93 - 79 * q^94 + 18 * q^95 + 21 * q^96 - 5 * q^97 - 45 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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