LMFDB - Embedded newform 4235.2.a.ba.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4235,2,Mod(1,4235)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4235, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4235.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4235 = 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4235.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$33.8166452560$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.580017.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 7x^{3} - 4x^{2} + 6x + 3 $ x^5 - 7x^3 - 4x^2 + 6*x + 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$2.74137$ of defining polynomial
Character	$\chi$	$=$	4235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.74137 q^{2} -3.04102 q^{3} +5.51511 q^{4} -1.00000 q^{5} -8.33658 q^{6} -1.00000 q^{7} +9.63623 q^{8} +6.24783 q^{9} +O(q^{10})$	\(q+2.74137 q^{2} -3.04102 q^{3} +5.51511 q^{4} -1.00000 q^{5} -8.33658 q^{6} -1.00000 q^{7} +9.63623 q^{8} +6.24783 q^{9} -2.74137 q^{10} -16.7716 q^{12} +6.59521 q^{13} -2.74137 q^{14} +3.04102 q^{15} +15.3863 q^{16} -4.86249 q^{17} +17.1276 q^{18} +0.907153 q^{19} -5.51511 q^{20} +3.04102 q^{21} +3.01425 q^{23} -29.3040 q^{24} +1.00000 q^{25} +18.0799 q^{26} -9.87674 q^{27} -5.51511 q^{28} -0.914310 q^{29} +8.33658 q^{30} -5.33352 q^{31} +22.9070 q^{32} -13.3299 q^{34} +1.00000 q^{35} +34.4575 q^{36} -2.76947 q^{37} +2.48684 q^{38} -20.0562 q^{39} -9.63623 q^{40} -5.06780 q^{41} +8.33658 q^{42} +1.67940 q^{43} -6.24783 q^{45} +8.26318 q^{46} +9.45037 q^{47} -46.7900 q^{48} +1.00000 q^{49} +2.74137 q^{50} +14.7869 q^{51} +36.3733 q^{52} -3.38280 q^{53} -27.0758 q^{54} -9.63623 q^{56} -2.75868 q^{57} -2.50646 q^{58} -1.13751 q^{59} +16.7716 q^{60} +10.4208 q^{61} -14.6212 q^{62} -6.24783 q^{63} +32.0240 q^{64} -6.59521 q^{65} +7.50236 q^{67} -26.8172 q^{68} -9.16641 q^{69} +2.74137 q^{70} +3.74697 q^{71} +60.2056 q^{72} +15.8983 q^{73} -7.59215 q^{74} -3.04102 q^{75} +5.00305 q^{76} -54.9814 q^{78} +13.6658 q^{79} -15.3863 q^{80} +11.2919 q^{81} -13.8927 q^{82} +10.1635 q^{83} +16.7716 q^{84} +4.86249 q^{85} +4.60386 q^{86} +2.78044 q^{87} +7.76964 q^{89} -17.1276 q^{90} -6.59521 q^{91} +16.6239 q^{92} +16.2194 q^{93} +25.9070 q^{94} -0.907153 q^{95} -69.6607 q^{96} +11.3919 q^{97} +2.74137 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 2 q^{3} + 4 q^{4} - 5 q^{5} - 5 q^{6} - 5 q^{7} + 12 q^{8} + 11 q^{9}+O(q^{10}) $ 5 * q - 2 * q^3 + 4 * q^4 - 5 * q^5 - 5 * q^6 - 5 * q^7 + 12 * q^8 + 11 * q^9	$ 5 q - 2 q^{3} + 4 q^{4} - 5 q^{5} - 5 q^{6} - 5 q^{7} + 12 q^{8} + 11 q^{9} - 23 q^{12} + 10 q^{13} + 2 q^{15} + 10 q^{16} + 2 q^{17} + 5 q^{18} - 3 q^{19} - 4 q^{20} + 2 q^{21} + 3 q^{23} - 28 q^{24} + 5 q^{25} + 13 q^{26} - 11 q^{27} - 4 q^{28} + q^{29} + 5 q^{30} - 12 q^{31} + 29 q^{32} - 20 q^{34} + 5 q^{35} + 45 q^{36} + 9 q^{38} - 2 q^{39} - 12 q^{40} - 11 q^{41} + 5 q^{42} + 10 q^{43} - 11 q^{45} + 14 q^{46} + 16 q^{47} - 46 q^{48} + 5 q^{49} + 6 q^{51} + 30 q^{52} + 4 q^{53} - 34 q^{54} - 12 q^{56} + 34 q^{57} - 6 q^{58} - 32 q^{59} + 23 q^{60} + 40 q^{61} + q^{62} - 11 q^{63} + 38 q^{64} - 10 q^{65} + 7 q^{67} - 19 q^{68} - 24 q^{69} + 10 q^{71} + 72 q^{72} + 11 q^{73} - 37 q^{74} - 2 q^{75} + 3 q^{76} - 87 q^{78} + 13 q^{79} - 10 q^{80} + q^{81} + 4 q^{82} + 26 q^{83} + 23 q^{84} - 2 q^{85} - 17 q^{86} + 14 q^{87} + 5 q^{89} - 5 q^{90} - 10 q^{91} + 32 q^{92} + 3 q^{93} + 44 q^{94} + 3 q^{95} - 84 q^{96} - 5 q^{97}+O(q^{100}) $ 5 * q - 2 * q^3 + 4 * q^4 - 5 * q^5 - 5 * q^6 - 5 * q^7 + 12 * q^8 + 11 * q^9 - 23 * q^12 + 10 * q^13 + 2 * q^15 + 10 * q^16 + 2 * q^17 + 5 * q^18 - 3 * q^19 - 4 * q^20 + 2 * q^21 + 3 * q^23 - 28 * q^24 + 5 * q^25 + 13 * q^26 - 11 * q^27 - 4 * q^28 + q^29 + 5 * q^30 - 12 * q^31 + 29 * q^32 - 20 * q^34 + 5 * q^35 + 45 * q^36 + 9 * q^38 - 2 * q^39 - 12 * q^40 - 11 * q^41 + 5 * q^42 + 10 * q^43 - 11 * q^45 + 14 * q^46 + 16 * q^47 - 46 * q^48 + 5 * q^49 + 6 * q^51 + 30 * q^52 + 4 * q^53 - 34 * q^54 - 12 * q^56 + 34 * q^57 - 6 * q^58 - 32 * q^59 + 23 * q^60 + 40 * q^61 + q^62 - 11 * q^63 + 38 * q^64 - 10 * q^65 + 7 * q^67 - 19 * q^68 - 24 * q^69 + 10 * q^71 + 72 * q^72 + 11 * q^73 - 37 * q^74 - 2 * q^75 + 3 * q^76 - 87 * q^78 + 13 * q^79 - 10 * q^80 + q^81 + 4 * q^82 + 26 * q^83 + 23 * q^84 - 2 * q^85 - 17 * q^86 + 14 * q^87 + 5 * q^89 - 5 * q^90 - 10 * q^91 + 32 * q^92 + 3 * q^93 + 44 * q^94 + 3 * q^95 - 84 * q^96 - 5 * q^97

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.74137	1.93844	0.969221	−	0.246193i	$-0.0791795\pi$
$2$	2.74137	1.93844	0.969221	+	0.246193i	$0.0791795\pi$
$3$	−3.04102	−1.75574	−0.877868	−	0.478902i	$-0.841035\pi$
$3$	−3.04102	−1.75574	−0.877868	+	0.478902i	$0.841035\pi$
$4$	5.51511	2.75756
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−8.33658	−3.40339
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	9.63623	3.40692
$9$	6.24783	2.08261
$10$	−2.74137	−0.866898
$11$	0	0
$11$	0	0
$12$	−16.7716	−4.84154
$13$	6.59521	1.82918	0.914591	−	0.404381i	$-0.132513\pi$
$13$	6.59521	1.82918	0.914591	+	0.404381i	$0.132513\pi$
$14$	−2.74137	−0.732662
$15$	3.04102	0.785189
$16$	15.3863	3.84656
$17$	−4.86249	−1.17933	−0.589663	−	0.807649i	$-0.700740\pi$
$17$	−4.86249	−1.17933	−0.589663	+	0.807649i	$0.700740\pi$
$18$	17.1276	4.03702
$19$	0.907153	0.208115	0.104058	−	0.994571i	$-0.466817\pi$
$19$	0.907153	0.208115	0.104058	+	0.994571i	$0.466817\pi$
$20$	−5.51511	−1.23322
$21$	3.04102	0.663606
$22$	0	0
$23$	3.01425	0.628515	0.314257	−	0.949338i	$-0.398245\pi$
$23$	3.01425	0.628515	0.314257	+	0.949338i	$0.398245\pi$
$24$	−29.3040	−5.98166
$25$	1.00000	0.200000
$26$	18.0799	3.54576
$27$	−9.87674	−1.90078
$28$	−5.51511	−1.04226
$29$	−0.914310	−0.169783	−0.0848915	−	0.996390i	$-0.527054\pi$
$29$	−0.914310	−0.169783	−0.0848915	+	0.996390i	$0.527054\pi$
$30$	8.33658	1.52204
$31$	−5.33352	−0.957929	−0.478964	−	0.877834i	$-0.658988\pi$
$31$	−5.33352	−0.957929	−0.478964	+	0.877834i	$0.658988\pi$
$32$	22.9070	4.04942
$33$	0	0
$34$	−13.3299	−2.28606
$35$	1.00000	0.169031
$36$	34.4575	5.74292
$37$	−2.76947	−0.455299	−0.227649	−	0.973743i	$-0.573104\pi$
$37$	−2.76947	−0.455299	−0.227649	+	0.973743i	$0.573104\pi$
$38$	2.48684	0.403419
$39$	−20.0562	−3.21156
$40$	−9.63623	−1.52362
$41$	−5.06780	−0.791457	−0.395729	−	0.918368i	$-0.629508\pi$
$41$	−5.06780	−0.791457	−0.395729	+	0.918368i	$0.629508\pi$
$42$	8.33658	1.28636
$43$	1.67940	0.256106	0.128053	−	0.991767i	$-0.459127\pi$
$43$	1.67940	0.256106	0.128053	+	0.991767i	$0.459127\pi$
$44$	0	0
$45$	−6.24783	−0.931372
$46$	8.26318	1.21834
$47$	9.45037	1.37848	0.689239	−	0.724534i	$-0.257945\pi$
$47$	9.45037	1.37848	0.689239	+	0.724534i	$0.257945\pi$
$48$	−46.7900	−6.75355
$49$	1.00000	0.142857
$50$	2.74137	0.387688
$51$	14.7869	2.07059
$52$	36.3733	5.04407
$53$	−3.38280	−0.464663	−0.232332	−	0.972637i	$-0.574635\pi$
$53$	−3.38280	−0.464663	−0.232332	+	0.972637i	$0.574635\pi$
$54$	−27.0758	−3.68455
$55$	0	0
$56$	−9.63623	−1.28770
$57$	−2.75868	−0.365396
$58$	−2.50646	−0.329115
$59$	−1.13751	−0.148091	−0.0740457	−	0.997255i	$-0.523591\pi$
$59$	−1.13751	−0.148091	−0.0740457	+	0.997255i	$0.523591\pi$
$60$	16.7716	2.16520
$61$	10.4208	1.33424	0.667122	−	0.744949i	$-0.267526\pi$
$61$	10.4208	1.33424	0.667122	+	0.744949i	$0.267526\pi$
$62$	−14.6212	−1.85689
$63$	−6.24783	−0.787153
$64$	32.0240	4.00300
$65$	−6.59521	−0.818035
$66$	0	0
$67$	7.50236	0.916559	0.458280	−	0.888808i	$-0.348466\pi$
$67$	7.50236	0.916559	0.458280	+	0.888808i	$0.348466\pi$
$68$	−26.8172	−3.25206
$69$	−9.16641	−1.10351
$70$	2.74137	0.327656
$71$	3.74697	0.444683	0.222342	−	0.974969i	$-0.428630\pi$
$71$	3.74697	0.444683	0.222342	+	0.974969i	$0.428630\pi$
$72$	60.2056	7.09529
$73$	15.8983	1.86076	0.930378	−	0.366600i	$-0.119478\pi$
$73$	15.8983	1.86076	0.930378	+	0.366600i	$0.119478\pi$
$74$	−7.59215	−0.882570
$75$	−3.04102	−0.351147
$76$	5.00305	0.573890
$77$	0	0
$78$	−54.9814	−6.22542
$79$	13.6658	1.53753	0.768763	−	0.639534i	$-0.220873\pi$
$79$	13.6658	1.53753	0.768763	+	0.639534i	$0.220873\pi$
$80$	−15.3863	−1.72024
$81$	11.2919	1.25466
$82$	−13.8927	−1.53419
$83$	10.1635	1.11559	0.557793	−	0.829980i	$-0.311648\pi$
$83$	10.1635	1.11559	0.557793	+	0.829980i	$0.311648\pi$
$84$	16.7716	1.82993
$85$	4.86249	0.527411
$86$	4.60386	0.496447
$87$	2.78044	0.298094
$88$	0	0
$89$	7.76964	0.823580	0.411790	−	0.911279i	$-0.364904\pi$
$89$	7.76964	0.823580	0.411790	+	0.911279i	$0.364904\pi$
$90$	−17.1276	−1.80541
$91$	−6.59521	−0.691365
$92$	16.6239	1.73317
$93$	16.2194	1.68187
$94$	25.9070	2.67210
$95$	−0.907153	−0.0930720
$96$	−69.6607	−7.10971
$97$	11.3919	1.15667	0.578334	−	0.815800i	$-0.303703\pi$
$97$	11.3919	1.15667	0.578334	+	0.815800i	$0.303703\pi$
$98$	2.74137	0.276920
$99$	0	0
$100$	5.51511	0.551511
$101$	1.17248	0.116666	0.0583329	−	0.998297i	$-0.481422\pi$
$101$	1.17248	0.116666	0.0583329	+	0.998297i	$0.481422\pi$
$102$	40.5365	4.01371
$103$	−8.97905	−0.884732	−0.442366	−	0.896834i	$-0.645861\pi$
$103$	−8.97905	−0.884732	−0.442366	+	0.896834i	$0.645861\pi$
$104$	63.5529	6.23188
$105$	−3.04102	−0.296774
$106$	−9.27351	−0.900723
$107$	−6.26036	−0.605211	−0.302606	−	0.953116i	$-0.597857\pi$
$107$	−6.26036	−0.605211	−0.302606	+	0.953116i	$0.597857\pi$
$108$	−54.4713	−5.24151
$109$	−1.70340	−0.163156	−0.0815781	−	0.996667i	$-0.525996\pi$
$109$	−1.70340	−0.163156	−0.0815781	+	0.996667i	$0.525996\pi$
$110$	0	0
$111$	8.42204	0.799384
$112$	−15.3863	−1.45386
$113$	−0.107727	−0.0101341	−0.00506706	−	0.999987i	$-0.501613\pi$
$113$	−0.107727	−0.0101341	−0.00506706	+	0.999987i	$0.501613\pi$
$114$	−7.56255	−0.708298
$115$	−3.01425	−0.281080
$116$	−5.04252	−0.468186
$117$	41.2057	3.80947
$118$	−3.11834	−0.287067
$119$	4.86249	0.445744
$120$	29.3040	2.67508
$121$	0	0
$122$	28.5672	2.58635
$123$	15.4113	1.38959
$124$	−29.4150	−2.64154
$125$	−1.00000	−0.0894427
$126$	−17.1276	−1.52585
$127$	−14.1131	−1.25234	−0.626170	−	0.779687i	$-0.715378\pi$
$127$	−14.1131	−1.25234	−0.626170	+	0.779687i	$0.715378\pi$
$128$	41.9757	3.71016
$129$	−5.10710	−0.449655
$130$	−18.0799	−1.58571
$131$	−10.3314	−0.902662	−0.451331	−	0.892357i	$-0.649051\pi$
$131$	−10.3314	−0.902662	−0.451331	+	0.892357i	$0.649051\pi$
$132$	0	0
$133$	−0.907153	−0.0786602
$134$	20.5667	1.77670
$135$	9.87674	0.850054
$136$	−46.8561	−4.01787
$137$	21.6579	1.85036	0.925180	−	0.379528i	$-0.123913\pi$
$137$	21.6579	1.85036	0.925180	+	0.379528i	$0.123913\pi$
$138$	−25.1285	−2.13908
$139$	−14.7057	−1.24732	−0.623660	−	0.781695i	$-0.714355\pi$
$139$	−14.7057	−1.24732	−0.623660	+	0.781695i	$0.714355\pi$
$140$	5.51511	0.466112
$141$	−28.7388	−2.42024
$142$	10.2718	0.861993
$143$	0	0
$144$	96.1307	8.01089
$145$	0.914310	0.0759293
$146$	43.5832	3.60697
$147$	−3.04102	−0.250820
$148$	−15.2740	−1.25551
$149$	4.62867	0.379196	0.189598	−	0.981862i	$-0.439282\pi$
$149$	4.62867	0.379196	0.189598	+	0.981862i	$0.439282\pi$
$150$	−8.33658	−0.680679
$151$	7.04541	0.573347	0.286674	−	0.958028i	$-0.407450\pi$
$151$	7.04541	0.573347	0.286674	+	0.958028i	$0.407450\pi$
$152$	8.74154	0.709032
$153$	−30.3800	−2.45608
$154$	0	0
$155$	5.33352	0.428399
$156$	−110.612	−8.85606
$157$	6.56589	0.524015	0.262007	−	0.965066i	$-0.415615\pi$
$157$	6.56589	0.524015	0.262007	+	0.965066i	$0.415615\pi$
$158$	37.4631	2.98040
$159$	10.2872	0.815826
$160$	−22.9070	−1.81095
$161$	−3.01425	−0.237556
$162$	30.9553	2.43208
$163$	12.3470	0.967088	0.483544	−	0.875320i	$-0.339349\pi$
$163$	12.3470	0.967088	0.483544	+	0.875320i	$0.339349\pi$
$164$	−27.9495	−2.18249
$165$	0	0
$166$	27.8618	2.16250
$167$	3.90433	0.302126	0.151063	−	0.988524i	$-0.451730\pi$
$167$	3.90433	0.302126	0.151063	+	0.988524i	$0.451730\pi$
$168$	29.3040	2.26085
$169$	30.4967	2.34590
$170$	13.3299	1.02236
$171$	5.66774	0.433423
$172$	9.26208	0.706227
$173$	5.70167	0.433490	0.216745	−	0.976228i	$-0.430456\pi$
$173$	5.70167	0.433490	0.216745	+	0.976228i	$0.430456\pi$
$174$	7.62221	0.577838
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	3.45920	0.260010
$178$	21.2995	1.59646
$179$	−19.6283	−1.46708	−0.733542	−	0.679644i	$-0.762134\pi$
$179$	−19.6283	−1.46708	−0.733542	+	0.679644i	$0.762134\pi$
$180$	−34.4575	−2.56831
$181$	15.4408	1.14770	0.573852	−	0.818959i	$-0.305448\pi$
$181$	15.4408	1.14770	0.573852	+	0.818959i	$0.305448\pi$
$182$	−18.0799	−1.34017
$183$	−31.6898	−2.34258
$184$	29.0460	2.14130
$185$	2.76947	0.203616
$186$	44.4633	3.26021
$187$	0	0
$188$	52.1199	3.80123
$189$	9.87674	0.718427
$190$	−2.48684	−0.180415
$191$	−6.21529	−0.449723	−0.224861	−	0.974391i	$-0.572193\pi$
$191$	−6.21529	−0.449723	−0.224861	+	0.974391i	$0.572193\pi$
$192$	−97.3857	−7.02821
$193$	−21.9778	−1.58200	−0.790999	−	0.611817i	$-0.790439\pi$
$193$	−21.9778	−1.58200	−0.790999	+	0.611817i	$0.790439\pi$
$194$	31.2293	2.24213
$195$	20.0562	1.43625
$196$	5.51511	0.393937
$197$	−2.95573	−0.210587	−0.105294	−	0.994441i	$-0.533578\pi$
$197$	−2.95573	−0.210587	−0.105294	+	0.994441i	$0.533578\pi$
$198$	0	0
$199$	−11.6335	−0.824674	−0.412337	−	0.911031i	$-0.635287\pi$
$199$	−11.6335	−0.824674	−0.412337	+	0.911031i	$0.635287\pi$
$200$	9.63623	0.681384
$201$	−22.8149	−1.60924
$202$	3.21420	0.226150
$203$	0.914310	0.0641719
$204$	81.5517	5.70976
$205$	5.06780	0.353950
$206$	−24.6149	−1.71500
$207$	18.8325	1.30895
$208$	101.476	7.03606
$209$	0	0
$210$	−8.33658	−0.575278
$211$	−26.2090	−1.80430	−0.902152	−	0.431419i	$-0.858013\pi$
$211$	−26.2090	−1.80430	−0.902152	+	0.431419i	$0.858013\pi$
$212$	−18.6565	−1.28134
$213$	−11.3946	−0.780747
$214$	−17.1620	−1.17317
$215$	−1.67940	−0.114534
$216$	−95.1745	−6.47581
$217$	5.33352	0.362063
$218$	−4.66965	−0.316269
$219$	−48.3472	−3.26700
$220$	0	0
$221$	−32.0691	−2.15720
$222$	23.0879	1.54956
$223$	4.57357	0.306269	0.153134	−	0.988205i	$-0.451063\pi$
$223$	4.57357	0.306269	0.153134	+	0.988205i	$0.451063\pi$
$224$	−22.9070	−1.53054
$225$	6.24783	0.416522
$226$	−0.295320	−0.0196444
$227$	−8.22365	−0.545823	−0.272911	−	0.962039i	$-0.587987\pi$
$227$	−8.22365	−0.545823	−0.272911	+	0.962039i	$0.587987\pi$
$228$	−15.2144	−1.00760
$229$	−1.84824	−0.122135	−0.0610675	−	0.998134i	$-0.519450\pi$
$229$	−1.84824	−0.122135	−0.0610675	+	0.998134i	$0.519450\pi$
$230$	−8.26318	−0.544858
$231$	0	0
$232$	−8.81050	−0.578438
$233$	23.2023	1.52003	0.760016	−	0.649904i	$-0.225191\pi$
$233$	23.2023	1.52003	0.760016	+	0.649904i	$0.225191\pi$
$234$	112.960	7.38444
$235$	−9.45037	−0.616474
$236$	−6.27351	−0.408371
$237$	−41.5581	−2.69949
$238$	13.3299	0.864048
$239$	−26.4737	−1.71244	−0.856222	−	0.516608i	$-0.827194\pi$
$239$	−26.4737	−1.71244	−0.856222	+	0.516608i	$0.827194\pi$
$240$	46.7900	3.02028
$241$	10.7031	0.689449	0.344724	−	0.938704i	$-0.387972\pi$
$241$	10.7031	0.689449	0.344724	+	0.938704i	$0.387972\pi$
$242$	0	0
$243$	−4.70877	−0.302068
$244$	57.4717	3.67925
$245$	−1.00000	−0.0638877
$246$	42.2481	2.69364
$247$	5.98286	0.380680
$248$	−51.3951	−3.26359
$249$	−30.9074	−1.95867
$250$	−2.74137	−0.173380
$251$	−16.9313	−1.06870	−0.534348	−	0.845265i	$-0.679443\pi$
$251$	−16.9313	−1.06870	−0.534348	+	0.845265i	$0.679443\pi$
$252$	−34.4575	−2.17062
$253$	0	0
$254$	−38.6894	−2.42759
$255$	−14.7869	−0.925994
$256$	51.0229	3.18893
$257$	−12.5126	−0.780513	−0.390256	−	0.920706i	$-0.627614\pi$
$257$	−12.5126	−0.780513	−0.390256	+	0.920706i	$0.627614\pi$
$258$	−14.0004	−0.871630
$259$	2.76947	0.172087
$260$	−36.3733	−2.25578
$261$	−5.71245	−0.353592
$262$	−28.3223	−1.74976
$263$	−22.4525	−1.38448	−0.692240	−	0.721667i	$-0.743376\pi$
$263$	−22.4525	−1.38448	−0.692240	+	0.721667i	$0.743376\pi$
$264$	0	0
$265$	3.38280	0.207804
$266$	−2.48684	−0.152478
$267$	−23.6277	−1.44599
$268$	41.3764	2.52746
$269$	−13.7295	−0.837101	−0.418551	−	0.908194i	$-0.637462\pi$
$269$	−13.7295	−0.837101	−0.418551	+	0.908194i	$0.637462\pi$
$270$	27.0758	1.64778
$271$	−1.95141	−0.118540	−0.0592700	−	0.998242i	$-0.518877\pi$
$271$	−1.95141	−0.118540	−0.0592700	+	0.998242i	$0.518877\pi$
$272$	−74.8155	−4.53635
$273$	20.0562	1.21386
$274$	59.3724	3.58682
$275$	0	0
$276$	−50.5538	−3.04298
$277$	6.52545	0.392076	0.196038	−	0.980596i	$-0.437192\pi$
$277$	6.52545	0.392076	0.196038	+	0.980596i	$0.437192\pi$
$278$	−40.3138	−2.41786
$279$	−33.3230	−1.99499
$280$	9.63623	0.575875
$281$	−2.41881	−0.144294	−0.0721472	−	0.997394i	$-0.522985\pi$
$281$	−2.41881	−0.144294	−0.0721472	+	0.997394i	$0.522985\pi$
$282$	−78.7837	−4.69150
$283$	−0.799239	−0.0475099	−0.0237549	−	0.999718i	$-0.507562\pi$
$283$	−0.799239	−0.0475099	−0.0237549	+	0.999718i	$0.507562\pi$
$284$	20.6650	1.22624
$285$	2.75868	0.163410
$286$	0	0
$287$	5.06780	0.299143
$288$	143.119	8.43336
$289$	6.64379	0.390811
$290$	2.50646	0.147184
$291$	−34.6429	−2.03080
$292$	87.6810	5.13114
$293$	23.9733	1.40053	0.700267	−	0.713881i	$-0.253064\pi$
$293$	23.9733	1.40053	0.700267	+	0.713881i	$0.253064\pi$
$294$	−8.33658	−0.486199
$295$	1.13751	0.0662285
$296$	−26.6873	−1.55117
$297$	0	0
$298$	12.6889	0.735049
$299$	19.8796	1.14967
$300$	−16.7716	−0.968309
$301$	−1.67940	−0.0967990
$302$	19.3141	1.11140
$303$	−3.56553	−0.204835
$304$	13.9577	0.800529
$305$	−10.4208	−0.596692
$306$	−83.2829	−4.76096
$307$	−19.0748	−1.08865	−0.544327	−	0.838873i	$-0.683215\pi$
$307$	−19.0748	−1.08865	−0.544327	+	0.838873i	$0.683215\pi$
$308$	0	0
$309$	27.3055	1.55336
$310$	14.6212	0.830426
$311$	9.18049	0.520578	0.260289	−	0.965531i	$-0.416182\pi$
$311$	9.18049	0.520578	0.260289	+	0.965531i	$0.416182\pi$
$312$	−193.266	−10.9415
$313$	−13.7670	−0.778160	−0.389080	−	0.921204i	$-0.627207\pi$
$313$	−13.7670	−0.778160	−0.389080	+	0.921204i	$0.627207\pi$
$314$	17.9995	1.01577
$315$	6.24783	0.352025
$316$	75.3686	4.23982
$317$	22.9456	1.28875	0.644376	−	0.764709i	$-0.277117\pi$
$317$	22.9456	1.28875	0.644376	+	0.764709i	$0.277117\pi$
$318$	28.2010	1.58143
$319$	0	0
$320$	−32.0240	−1.79019
$321$	19.0379	1.06259
$322$	−8.26318	−0.460489
$323$	−4.41102	−0.245436
$324$	62.2762	3.45979
$325$	6.59521	0.365836
$326$	33.8476	1.87464
$327$	5.18008	0.286459
$328$	−48.8345	−2.69643
$329$	−9.45037	−0.521016
$330$	0	0
$331$	−3.44016	−0.189088	−0.0945441	−	0.995521i	$-0.530139\pi$
$331$	−3.44016	−0.189088	−0.0945441	+	0.995521i	$0.530139\pi$
$332$	56.0527	3.07629
$333$	−17.3032	−0.948210
$334$	10.7032	0.585654
$335$	−7.50236	−0.409898
$336$	46.7900	2.55260
$337$	30.2961	1.65033	0.825166	−	0.564891i	$-0.191082\pi$
$337$	30.2961	1.65033	0.825166	+	0.564891i	$0.191082\pi$
$338$	83.6029	4.54740
$339$	0.327601	0.0177929
$340$	26.8172	1.45437
$341$	0	0
$342$	15.5374	0.840165
$343$	−1.00000	−0.0539949
$344$	16.1831	0.872534
$345$	9.16641	0.493503
$346$	15.6304	0.840296
$347$	3.88350	0.208477	0.104239	−	0.994552i	$-0.466759\pi$
$347$	3.88350	0.208477	0.104239	+	0.994552i	$0.466759\pi$
$348$	15.3344	0.822012
$349$	19.2489	1.03037	0.515184	−	0.857080i	$-0.327724\pi$
$349$	19.2489	1.03037	0.515184	+	0.857080i	$0.327724\pi$
$350$	−2.74137	−0.146532
$351$	−65.1391	−3.47687
$352$	0	0
$353$	−26.3031	−1.39997	−0.699986	−	0.714156i	$-0.746811\pi$
$353$	−26.3031	−1.39997	−0.699986	+	0.714156i	$0.746811\pi$
$354$	9.48296	0.504014
$355$	−3.74697	−0.198868
$356$	42.8505	2.27107
$357$	−14.7869	−0.782608
$358$	−53.8083	−2.84386
$359$	−21.4912	−1.13426	−0.567131	−	0.823627i	$-0.691947\pi$
$359$	−21.4912	−1.13426	−0.567131	+	0.823627i	$0.691947\pi$
$360$	−60.2056	−3.17311
$361$	−18.1771	−0.956688
$362$	42.3289	2.22476
$363$	0	0
$364$	−36.3733	−1.90648
$365$	−15.8983	−0.832156
$366$	−86.8736	−4.54095
$367$	−5.20635	−0.271769	−0.135885	−	0.990725i	$-0.543388\pi$
$367$	−5.20635	−0.271769	−0.135885	+	0.990725i	$0.543388\pi$
$368$	46.3780	2.41762
$369$	−31.6628	−1.64830
$370$	7.59215	0.394697
$371$	3.38280	0.175626
$372$	89.4517	4.63785
$373$	15.6505	0.810354	0.405177	−	0.914238i	$-0.367210\pi$
$373$	15.6505	0.810354	0.405177	+	0.914238i	$0.367210\pi$
$374$	0	0
$375$	3.04102	0.157038
$376$	91.0659	4.69637
$377$	−6.03006	−0.310564
$378$	27.0758	1.39263
$379$	19.0890	0.980537	0.490269	−	0.871571i	$-0.336899\pi$
$379$	19.0890	0.980537	0.490269	+	0.871571i	$0.336899\pi$
$380$	−5.00305	−0.256651
$381$	42.9184	2.19878
$382$	−17.0384	−0.871761
$383$	23.3917	1.19526	0.597629	−	0.801773i	$-0.296110\pi$
$383$	23.3917	1.19526	0.597629	+	0.801773i	$0.296110\pi$
$384$	−127.649	−6.51406
$385$	0	0
$386$	−60.2494	−3.06661
$387$	10.4926	0.533369
$388$	62.8274	3.18958
$389$	11.3746	0.576715	0.288358	−	0.957523i	$-0.406891\pi$
$389$	11.3746	0.576715	0.288358	+	0.957523i	$0.406891\pi$
$390$	54.9814	2.78409
$391$	−14.6568	−0.741224
$392$	9.63623	0.486703
$393$	31.4182	1.58484
$394$	−8.10276	−0.408211
$395$	−13.6658	−0.687602
$396$	0	0
$397$	−15.2708	−0.766418	−0.383209	−	0.923662i	$-0.625181\pi$
$397$	−15.2708	−0.766418	−0.383209	+	0.923662i	$0.625181\pi$
$398$	−31.8916	−1.59858
$399$	2.75868	0.138107
$400$	15.3863	0.769313
$401$	9.66663	0.482728	0.241364	−	0.970435i	$-0.422405\pi$
$401$	9.66663	0.482728	0.241364	+	0.970435i	$0.422405\pi$
$402$	−62.5440	−3.11941
$403$	−35.1757	−1.75223
$404$	6.46635	0.321713
$405$	−11.2919	−0.561100
$406$	2.50646	0.124394
$407$	0	0
$408$	142.490	7.05433
$409$	14.2142	0.702849	0.351425	−	0.936216i	$-0.385697\pi$
$409$	14.2142	0.702849	0.351425	+	0.936216i	$0.385697\pi$
$410$	13.8927	0.686112
$411$	−65.8623	−3.24875
$412$	−49.5205	−2.43970
$413$	1.13751	0.0559733
$414$	51.6270	2.53733
$415$	−10.1635	−0.498905
$416$	151.076	7.40712
$417$	44.7204	2.18997
$418$	0	0
$419$	15.2832	0.746633	0.373317	−	0.927704i	$-0.378221\pi$
$419$	15.2832	0.746633	0.373317	+	0.927704i	$0.378221\pi$
$420$	−16.7716	−0.818370
$421$	8.10283	0.394908	0.197454	−	0.980312i	$-0.436733\pi$
$421$	8.10283	0.394908	0.197454	+	0.980312i	$0.436733\pi$
$422$	−71.8487	−3.49754
$423$	59.0443	2.87083
$424$	−32.5974	−1.58307
$425$	−4.86249	−0.235865
$426$	−31.2369	−1.51343
$427$	−10.4208	−0.504296
$428$	−34.5266	−1.66890
$429$	0	0
$430$	−4.60386	−0.222018
$431$	−16.6282	−0.800953	−0.400476	−	0.916307i	$-0.631155\pi$
$431$	−16.6282	−0.800953	−0.400476	+	0.916307i	$0.631155\pi$
$432$	−151.966	−7.31147
$433$	35.0842	1.68604	0.843019	−	0.537884i	$-0.180776\pi$
$433$	35.0842	1.68604	0.843019	+	0.537884i	$0.180776\pi$
$434$	14.6212	0.701838
$435$	−2.78044	−0.133312
$436$	−9.39445	−0.449912
$437$	2.73439	0.130804
$438$	−132.538	−6.33289
$439$	24.3254	1.16099	0.580493	−	0.814265i	$-0.302860\pi$
$439$	24.3254	1.16099	0.580493	+	0.814265i	$0.302860\pi$
$440$	0	0
$441$	6.24783	0.297516
$442$	−87.9133	−4.18161
$443$	5.08137	0.241423	0.120712	−	0.992688i	$-0.461482\pi$
$443$	5.08137	0.241423	0.120712	+	0.992688i	$0.461482\pi$
$444$	46.4485	2.20435
$445$	−7.76964	−0.368316
$446$	12.5378	0.593684
$447$	−14.0759	−0.665768
$448$	−32.0240	−1.51299
$449$	−31.8906	−1.50501	−0.752504	−	0.658588i	$-0.771154\pi$
$449$	−31.8906	−1.50501	−0.752504	+	0.658588i	$0.771154\pi$
$450$	17.1276	0.807404
$451$	0	0
$452$	−0.594128	−0.0279454
$453$	−21.4253	−1.00665
$454$	−22.5441	−1.05805
$455$	6.59521	0.309188
$456$	−26.5832	−1.24487
$457$	−6.92579	−0.323975	−0.161987	−	0.986793i	$-0.551790\pi$
$457$	−6.92579	−0.323975	−0.161987	+	0.986793i	$0.551790\pi$
$458$	−5.06671	−0.236752
$459$	48.0255	2.24164
$460$	−16.6239	−0.775095
$461$	−26.9670	−1.25598	−0.627989	−	0.778222i	$-0.716122\pi$
$461$	−26.9670	−1.25598	−0.627989	+	0.778222i	$0.716122\pi$
$462$	0	0
$463$	−35.4519	−1.64759	−0.823795	−	0.566888i	$-0.808147\pi$
$463$	−35.4519	−1.64759	−0.823795	+	0.566888i	$0.808147\pi$
$464$	−14.0678	−0.653081
$465$	−16.2194	−0.752156
$466$	63.6061	2.94649
$467$	−32.4914	−1.50352	−0.751762	−	0.659434i	$-0.770796\pi$
$467$	−32.4914	−1.50352	−0.751762	+	0.659434i	$0.770796\pi$
$468$	227.254	10.5048
$469$	−7.50236	−0.346427
$470$	−25.9070	−1.19500
$471$	−19.9670	−0.920032
$472$	−10.9613	−0.504536
$473$	0	0
$474$	−113.926	−5.23281
$475$	0.907153	0.0416231
$476$	26.8172	1.22916
$477$	−21.1352	−0.967713
$478$	−72.5743	−3.31947
$479$	20.7343	0.947375	0.473687	−	0.880693i	$-0.342923\pi$
$479$	20.7343	0.947375	0.473687	+	0.880693i	$0.342923\pi$
$480$	69.6607	3.17956
$481$	−18.2652	−0.832823
$482$	29.3412	1.33646
$483$	9.16641	0.417086
$484$	0	0
$485$	−11.3919	−0.517277
$486$	−12.9085	−0.585540
$487$	3.50987	0.159047	0.0795236	−	0.996833i	$-0.474660\pi$
$487$	3.50987	0.159047	0.0795236	+	0.996833i	$0.474660\pi$
$488$	100.417	4.54566
$489$	−37.5474	−1.69795
$490$	−2.74137	−0.123843
$491$	−0.148819	−0.00671611	−0.00335805	−	0.999994i	$-0.501069\pi$
$491$	−0.148819	−0.00671611	−0.00335805	+	0.999994i	$0.501069\pi$
$492$	84.9951	3.83187
$493$	4.44582	0.200230
$494$	16.4012	0.737927
$495$	0	0
$496$	−82.0629	−3.68473
$497$	−3.74697	−0.168075
$498$	−84.7285	−3.79678
$499$	3.48032	0.155800	0.0779002	−	0.996961i	$-0.475178\pi$
$499$	3.48032	0.155800	0.0779002	+	0.996961i	$0.475178\pi$
$500$	−5.51511	−0.246643
$501$	−11.8732	−0.530454
$502$	−46.4150	−2.07160
$503$	−18.0097	−0.803012	−0.401506	−	0.915856i	$-0.631513\pi$
$503$	−18.0097	−0.803012	−0.401506	+	0.915856i	$0.631513\pi$
$504$	−60.2056	−2.68177
$505$	−1.17248	−0.0521746
$506$	0	0
$507$	−92.7414	−4.11879
$508$	−77.8356	−3.45340
$509$	−35.1540	−1.55818	−0.779088	−	0.626915i	$-0.784317\pi$
$509$	−35.1540	−1.55818	−0.779088	+	0.626915i	$0.784317\pi$
$510$	−40.5365	−1.79499
$511$	−15.8983	−0.703300
$512$	55.9214	2.47140
$513$	−8.95972	−0.395581
$514$	−34.3016	−1.51298
$515$	8.97905	0.395664
$516$	−28.1662	−1.23995
$517$	0	0
$518$	7.59215	0.333580
$519$	−17.3389	−0.761095
$520$	−63.5529	−2.78698
$521$	−24.5834	−1.07702	−0.538509	−	0.842620i	$-0.681012\pi$
$521$	−24.5834	−1.07702	−0.538509	+	0.842620i	$0.681012\pi$
$522$	−15.6600	−0.685417
$523$	16.0636	0.702411	0.351205	−	0.936298i	$-0.385772\pi$
$523$	16.0636	0.702411	0.351205	+	0.936298i	$0.385772\pi$
$524$	−56.9791	−2.48914
$525$	3.04102	0.132721
$526$	−61.5506	−2.68373
$527$	25.9342	1.12971
$528$	0	0
$529$	−13.9143	−0.604969
$530$	9.27351	0.402816
$531$	−7.10699	−0.308417
$532$	−5.00305	−0.216910
$533$	−33.4232	−1.44772
$534$	−64.7722	−2.80297
$535$	6.26036	0.270659
$536$	72.2945	3.12265
$537$	59.6900	2.57581
$538$	−37.6376	−1.62267
$539$	0	0
$540$	54.4713	2.34407
$541$	24.6520	1.05987	0.529937	−	0.848037i	$-0.322216\pi$
$541$	24.6520	1.05987	0.529937	+	0.848037i	$0.322216\pi$
$542$	−5.34955	−0.229783
$543$	−46.9558	−2.01507
$544$	−111.385	−4.77559
$545$	1.70340	0.0729656
$546$	54.9814	2.35299
$547$	−24.6864	−1.05552	−0.527758	−	0.849395i	$-0.676967\pi$
$547$	−24.6864	−1.05552	−0.527758	+	0.849395i	$0.676967\pi$
$548$	119.446	5.10248
$549$	65.1072	2.77871
$550$	0	0
$551$	−0.829419	−0.0353344
$552$	−88.3297	−3.75956
$553$	−13.6658	−0.581130
$554$	17.8887	0.760017
$555$	−8.42204	−0.357496
$556$	−81.1036	−3.43956
$557$	20.2912	0.859766	0.429883	−	0.902885i	$-0.358555\pi$
$557$	20.2912	0.859766	0.429883	+	0.902885i	$0.358555\pi$
$558$	−91.3506	−3.86718
$559$	11.0760	0.468464
$560$	15.3863	0.650188
$561$	0	0
$562$	−6.63086	−0.279706
$563$	−11.9397	−0.503200	−0.251600	−	0.967831i	$-0.580957\pi$
$563$	−11.9397	−0.503200	−0.251600	+	0.967831i	$0.580957\pi$
$564$	−158.498	−6.67396
$565$	0.107727	0.00453212
$566$	−2.19101	−0.0920951
$567$	−11.2919	−0.474216
$568$	36.1067	1.51500
$569$	18.0100	0.755017	0.377509	−	0.926006i	$-0.376781\pi$
$569$	18.0100	0.755017	0.377509	+	0.926006i	$0.376781\pi$
$570$	7.56255	0.316761
$571$	0.0419420	0.00175522	0.000877610	−	1.00000i	$-0.499721\pi$
$571$	0.0419420	0.00175522	0.000877610		1.00000i	$0.499721\pi$
$572$	0	0
$573$	18.9009	0.789595
$574$	13.8927	0.579871
$575$	3.01425	0.125703
$576$	200.080	8.33669
$577$	−12.9887	−0.540726	−0.270363	−	0.962758i	$-0.587144\pi$
$577$	−12.9887	−0.540726	−0.270363	+	0.962758i	$0.587144\pi$
$578$	18.2131	0.757564
$579$	66.8351	2.77757
$580$	5.04252	0.209379
$581$	−10.1635	−0.421652
$582$	−94.9691	−3.93659
$583$	0	0
$584$	153.200	6.33945
$585$	−41.2057	−1.70365
$586$	65.7196	2.71485
$587$	4.44817	0.183596	0.0917979	−	0.995778i	$-0.470739\pi$
$587$	4.44817	0.183596	0.0917979	+	0.995778i	$0.470739\pi$
$588$	−16.7716	−0.691649
$589$	−4.83832	−0.199360
$590$	3.11834	0.128380
$591$	8.98846	0.369736
$592$	−42.6118	−1.75133
$593$	−25.1551	−1.03300	−0.516498	−	0.856288i	$-0.672765\pi$
$593$	−25.1551	−1.03300	−0.516498	+	0.856288i	$0.672765\pi$
$594$	0	0
$595$	−4.86249	−0.199343
$596$	25.5277	1.04565
$597$	35.3776	1.44791
$598$	54.4974	2.22856
$599$	−41.3234	−1.68843	−0.844215	−	0.536004i	$-0.819933\pi$
$599$	−41.3234	−1.68843	−0.844215	+	0.536004i	$0.819933\pi$
$600$	−29.3040	−1.19633
$601$	−36.8476	−1.50305	−0.751523	−	0.659707i	$-0.770680\pi$
$601$	−36.8476	−1.50305	−0.751523	+	0.659707i	$0.770680\pi$
$602$	−4.60386	−0.187639
$603$	46.8735	1.90884
$604$	38.8562	1.58104
$605$	0	0
$606$	−9.77445	−0.397060
$607$	9.84153	0.399455	0.199728	−	0.979851i	$-0.435994\pi$
$607$	9.84153	0.399455	0.199728	+	0.979851i	$0.435994\pi$
$608$	20.7801	0.842746
$609$	−2.78044	−0.112669
$610$	−28.5672	−1.15665
$611$	62.3271	2.52149
$612$	−167.549	−6.77278
$613$	27.7360	1.12025	0.560123	−	0.828409i	$-0.310754\pi$
$613$	27.7360	1.12025	0.560123	+	0.828409i	$0.310754\pi$
$614$	−52.2910	−2.11029
$615$	−15.4113	−0.621444
$616$	0	0
$617$	−6.34939	−0.255617	−0.127808	−	0.991799i	$-0.540794\pi$
$617$	−6.34939	−0.255617	−0.127808	+	0.991799i	$0.540794\pi$
$618$	74.8546	3.01109
$619$	21.7248	0.873192	0.436596	−	0.899658i	$-0.356184\pi$
$619$	21.7248	0.873192	0.436596	+	0.899658i	$0.356184\pi$
$620$	29.4150	1.18133
$621$	−29.7710	−1.19467
$622$	25.1671	1.00911
$623$	−7.76964	−0.311284
$624$	−308.590	−12.3535
$625$	1.00000	0.0400000
$626$	−37.7406	−1.50842
$627$	0	0
$628$	36.2116	1.44500
$629$	13.4665	0.536946
$630$	17.1276	0.682381
$631$	−46.9428	−1.86876	−0.934382	−	0.356272i	$-0.884048\pi$
$631$	−46.9428	−1.86876	−0.934382	+	0.356272i	$0.884048\pi$
$632$	131.687	5.23823
$633$	79.7023	3.16788
$634$	62.9023	2.49817
$635$	14.1131	0.560063
$636$	56.7350	2.24969
$637$	6.59521	0.261312
$638$	0	0
$639$	23.4104	0.926103
$640$	−41.9757	−1.65923
$641$	−34.5237	−1.36361	−0.681803	−	0.731536i	$-0.738804\pi$
$641$	−34.5237	−1.36361	−0.681803	+	0.731536i	$0.738804\pi$
$642$	52.1899	2.05977
$643$	−0.0386672	−0.00152489	−0.000762443	−	1.00000i	$-0.500243\pi$
$643$	−0.0386672	−0.00152489	−0.000762443		1.00000i	$0.500243\pi$
$644$	−16.6239	−0.655075
$645$	5.10710	0.201092
$646$	−12.0922	−0.475763
$647$	3.77288	0.148327	0.0741636	−	0.997246i	$-0.476371\pi$
$647$	3.77288	0.148327	0.0741636	+	0.997246i	$0.476371\pi$
$648$	108.811	4.27452
$649$	0	0
$650$	18.0799	0.709152
$651$	−16.2194	−0.635687
$652$	68.0949	2.66680
$653$	−47.8327	−1.87184	−0.935918	−	0.352217i	$-0.885428\pi$
$653$	−47.8327	−1.87184	−0.935918	+	0.352217i	$0.885428\pi$
$654$	14.2005	0.555284
$655$	10.3314	0.403683
$656$	−77.9744	−3.04439
$657$	99.3300	3.87523
$658$	−25.9070	−1.00996
$659$	19.7418	0.769030	0.384515	−	0.923119i	$-0.374369\pi$
$659$	19.7418	0.769030	0.384515	+	0.923119i	$0.374369\pi$
$660$	0	0
$661$	−15.6196	−0.607530	−0.303765	−	0.952747i	$-0.598244\pi$
$661$	−15.6196	−0.607530	−0.303765	+	0.952747i	$0.598244\pi$
$662$	−9.43075	−0.366536
$663$	97.5230	3.78748
$664$	97.9375	3.80071
$665$	0.907153	0.0351779
$666$	−47.4345	−1.83805
$667$	−2.75596	−0.106711
$668$	21.5328	0.833130
$669$	−13.9083	−0.537727
$670$	−20.5667	−0.794563
$671$	0	0
$672$	69.6607	2.68722
$673$	−3.27724	−0.126328	−0.0631642	−	0.998003i	$-0.520119\pi$
$673$	−3.27724	−0.126328	−0.0631642	+	0.998003i	$0.520119\pi$
$674$	83.0527	3.19907
$675$	−9.87674	−0.380156
$676$	168.193	6.46896
$677$	31.4726	1.20959	0.604795	−	0.796381i	$-0.293255\pi$
$677$	31.4726	1.20959	0.604795	+	0.796381i	$0.293255\pi$
$678$	0.898076	0.0344904
$679$	−11.3919	−0.437179
$680$	46.8561	1.79685
$681$	25.0083	0.958321
$682$	0	0
$683$	35.0569	1.34142	0.670708	−	0.741721i	$-0.265990\pi$
$683$	35.0569	1.34142	0.670708	+	0.741721i	$0.265990\pi$
$684$	31.2582	1.19519
$685$	−21.6579	−0.827507
$686$	−2.74137	−0.104666
$687$	5.62054	0.214437
$688$	25.8397	0.985128
$689$	−22.3103	−0.849953
$690$	25.1285	0.956627
$691$	36.2261	1.37810	0.689052	−	0.724712i	$-0.258027\pi$
$691$	36.2261	1.37810	0.689052	+	0.724712i	$0.258027\pi$
$692$	31.4454	1.19537
$693$	0	0
$694$	10.6461	0.404121
$695$	14.7057	0.557819
$696$	26.7929	1.01558
$697$	24.6421	0.933386
$698$	52.7683	1.99731
$699$	−70.5587	−2.66878
$700$	−5.51511	−0.208452
$701$	−32.4214	−1.22454	−0.612269	−	0.790649i	$-0.709743\pi$
$701$	−32.4214	−1.22454	−0.612269	+	0.790649i	$0.709743\pi$
$702$	−178.571	−6.73971
$703$	−2.51234	−0.0947546
$704$	0	0
$705$	28.7388	1.08237
$706$	−72.1065	−2.71377
$707$	−1.17248	−0.0440955
$708$	19.0779	0.716991
$709$	38.9574	1.46308	0.731538	−	0.681801i	$-0.238803\pi$
$709$	38.9574	1.46308	0.731538	+	0.681801i	$0.238803\pi$
$710$	−10.2718	−0.385495
$711$	85.3818	3.20207
$712$	74.8701	2.80587
$713$	−16.0766	−0.602073
$714$	−40.5365	−1.51704
$715$	0	0
$716$	−108.252	−4.04557
$717$	80.5073	3.00660
$718$	−58.9154	−2.19870
$719$	−21.0902	−0.786531	−0.393266	−	0.919425i	$-0.628655\pi$
$719$	−21.0902	−0.786531	−0.393266	+	0.919425i	$0.628655\pi$
$720$	−96.1307	−3.58258
$721$	8.97905	0.334397
$722$	−49.8301	−1.85448
$723$	−32.5485	−1.21049
$724$	85.1577	3.16486
$725$	−0.914310	−0.0339566
$726$	0	0
$727$	−48.1383	−1.78535	−0.892675	−	0.450702i	$-0.851174\pi$
$727$	−48.1383	−1.78535	−0.892675	+	0.450702i	$0.851174\pi$
$728$	−63.5529	−2.35543
$729$	−19.5563	−0.724306
$730$	−43.5832	−1.61309
$731$	−8.16606	−0.302033
$732$	−174.773	−6.45980
$733$	−48.4595	−1.78989	−0.894946	−	0.446174i	$-0.852786\pi$
$733$	−48.4595	−1.78989	−0.894946	+	0.446174i	$0.852786\pi$
$734$	−14.2725	−0.526809
$735$	3.04102	0.112170
$736$	69.0473	2.54512
$737$	0	0
$738$	−86.7994	−3.19513
$739$	13.6252	0.501211	0.250606	−	0.968089i	$-0.419370\pi$
$739$	13.6252	0.501211	0.250606	+	0.968089i	$0.419370\pi$
$740$	15.2740	0.561482
$741$	−18.1940	−0.668375
$742$	9.27351	0.340441
$743$	15.5807	0.571602	0.285801	−	0.958289i	$-0.407740\pi$
$743$	15.5807	0.571602	0.285801	+	0.958289i	$0.407740\pi$
$744$	156.294	5.73000
$745$	−4.62867	−0.169582
$746$	42.9039	1.57082
$747$	63.4997	2.32333
$748$	0	0
$749$	6.26036	0.228748
$750$	8.33658	0.304409
$751$	−30.0749	−1.09745	−0.548725	−	0.836003i	$-0.684887\pi$
$751$	−30.0749	−1.09745	−0.548725	+	0.836003i	$0.684887\pi$
$752$	145.406	5.30240
$753$	51.4886	1.87635
$754$	−16.5306	−0.602010
$755$	−7.04541	−0.256409
$756$	54.4713	1.98110
$757$	20.9610	0.761840	0.380920	−	0.924608i	$-0.375607\pi$
$757$	20.9610	0.761840	0.380920	+	0.924608i	$0.375607\pi$
$758$	52.3301	1.90071
$759$	0	0
$760$	−8.74154	−0.317089
$761$	−48.0504	−1.74182	−0.870912	−	0.491439i	$-0.836471\pi$
$761$	−48.0504	−1.74182	−0.870912	+	0.491439i	$0.836471\pi$
$762$	117.655	4.26220
$763$	1.70340	0.0616672
$764$	−34.2780	−1.24014
$765$	30.3800	1.09839
$766$	64.1252	2.31694
$767$	−7.50213	−0.270886
$768$	−155.162	−5.59893
$769$	−22.9234	−0.826638	−0.413319	−	0.910586i	$-0.635630\pi$
$769$	−22.9234	−0.826638	−0.413319	+	0.910586i	$0.635630\pi$
$770$	0	0
$771$	38.0510	1.37037
$772$	−121.210	−4.36245
$773$	−31.4722	−1.13198	−0.565988	−	0.824413i	$-0.691505\pi$
$773$	−31.4722	−1.13198	−0.565988	+	0.824413i	$0.691505\pi$
$774$	28.7641	1.03391
$775$	−5.33352	−0.191586
$776$	109.775	3.94068
$777$	−8.42204	−0.302139
$778$	31.1820	1.11793
$779$	−4.59727	−0.164714
$780$	110.612	3.96055
$781$	0	0
$782$	−40.1796	−1.43682
$783$	9.03040	0.322720
$784$	15.3863	0.549509
$785$	−6.56589	−0.234347
$786$	86.1288	3.07211
$787$	44.9445	1.60210	0.801049	−	0.598598i	$-0.204275\pi$
$787$	44.9445	1.60210	0.801049	+	0.598598i	$0.204275\pi$
$788$	−16.3012	−0.580707
$789$	68.2786	2.43078
$790$	−37.4631	−1.33288
$791$	0.107727	0.00383034
$792$	0	0
$793$	68.7271	2.44057
$794$	−41.8629	−1.48566
$795$	−10.2872	−0.364849
$796$	−64.1598	−2.27409
$797$	29.7898	1.05521	0.527605	−	0.849490i	$-0.323090\pi$
$797$	29.7898	1.05521	0.527605	+	0.849490i	$0.323090\pi$
$798$	7.56255	0.267711
$799$	−45.9523	−1.62568
$800$	22.9070	0.809884
$801$	48.5434	1.71520
$802$	26.4998	0.935741
$803$	0	0
$804$	−125.827	−4.43756
$805$	3.01425	0.106238
$806$	−96.4296	−3.39659
$807$	41.7517	1.46973
$808$	11.2983	0.397471
$809$	−28.3849	−0.997961	−0.498980	−	0.866613i	$-0.666292\pi$
$809$	−28.3849	−0.997961	−0.498980	+	0.866613i	$0.666292\pi$
$810$	−30.9553	−1.08766
$811$	−1.22401	−0.0429807	−0.0214904	−	0.999769i	$-0.506841\pi$
$811$	−1.22401	−0.0429807	−0.0214904	+	0.999769i	$0.506841\pi$
$812$	5.04252	0.176958
$813$	5.93430	0.208125
$814$	0	0
$815$	−12.3470	−0.432495
$816$	227.516	7.96464
$817$	1.52347	0.0532996
$818$	38.9665	1.36243
$819$	−41.2057	−1.43985
$820$	27.9495	0.976038
$821$	−9.87864	−0.344767	−0.172383	−	0.985030i	$-0.555147\pi$
$821$	−9.87864	−0.344767	−0.172383	+	0.985030i	$0.555147\pi$
$822$	−180.553	−6.29751
$823$	13.9342	0.485714	0.242857	−	0.970062i	$-0.421915\pi$
$823$	13.9342	0.485714	0.242857	+	0.970062i	$0.421915\pi$
$824$	−86.5242	−3.01421
$825$	0	0
$826$	3.11834	0.108501
$827$	30.9317	1.07560	0.537801	−	0.843072i	$-0.319255\pi$
$827$	30.9317	1.07560	0.537801	+	0.843072i	$0.319255\pi$
$828$	103.864	3.60951
$829$	−39.1431	−1.35950	−0.679749	−	0.733445i	$-0.737911\pi$
$829$	−39.1431	−1.35950	−0.679749	+	0.733445i	$0.737911\pi$
$830$	−27.8618	−0.967099
$831$	−19.8441	−0.688383
$832$	211.205	7.32221
$833$	−4.86249	−0.168475
$834$	122.595	4.24512
$835$	−3.90433	−0.135115
$836$	0	0
$837$	52.6778	1.82081
$838$	41.8969	1.44730
$839$	8.38642	0.289531	0.144766	−	0.989466i	$-0.453757\pi$
$839$	8.38642	0.289531	0.144766	+	0.989466i	$0.453757\pi$
$840$	−29.3040	−1.01108
$841$	−28.1640	−0.971174
$842$	22.2129	0.765506
$843$	7.35567	0.253343
$844$	−144.546	−4.97547
$845$	−30.4967	−1.04912
$846$	161.862	5.56494
$847$	0	0
$848$	−52.0486	−1.78736
$849$	2.43051	0.0834148
$850$	−13.3299	−0.457211
$851$	−8.34789	−0.286162
$852$	−62.8427	−2.15295
$853$	−6.41870	−0.219772	−0.109886	−	0.993944i	$-0.535049\pi$
$853$	−6.41870	−0.219772	−0.109886	+	0.993944i	$0.535049\pi$
$854$	−28.5672	−0.977549
$855$	−5.66774	−0.193833
$856$	−60.3262	−2.06191
$857$	42.0950	1.43794	0.718968	−	0.695043i	$-0.244615\pi$
$857$	42.0950	1.43794	0.718968	+	0.695043i	$0.244615\pi$
$858$	0	0
$859$	−28.4518	−0.970763	−0.485381	−	0.874303i	$-0.661319\pi$
$859$	−28.4518	−0.970763	−0.485381	+	0.874303i	$0.661319\pi$
$860$	−9.26208	−0.315834
$861$	−15.4113	−0.525216
$862$	−45.5841	−1.55260
$863$	49.5170	1.68558	0.842789	−	0.538245i	$-0.180912\pi$
$863$	49.5170	1.68558	0.842789	+	0.538245i	$0.180912\pi$
$864$	−226.246	−7.69705
$865$	−5.70167	−0.193863
$866$	96.1787	3.26829
$867$	−20.2039	−0.686161
$868$	29.4150	0.998410
$869$	0	0
$870$	−7.62221	−0.258417
$871$	49.4796	1.67655
$872$	−16.4144	−0.555860
$873$	71.1744	2.40889
$874$	7.49597	0.253555
$875$	1.00000	0.0338062
$876$	−266.640	−9.00894
$877$	−30.9398	−1.04476	−0.522381	−	0.852712i	$-0.674956\pi$
$877$	−30.9398	−1.04476	−0.522381	+	0.852712i	$0.674956\pi$
$878$	66.6848	2.25050
$879$	−72.9033	−2.45897
$880$	0	0
$881$	−17.9677	−0.605348	−0.302674	−	0.953094i	$-0.597879\pi$
$881$	−17.9677	−0.605348	−0.302674	+	0.953094i	$0.597879\pi$
$882$	17.1276	0.576717
$883$	4.90553	0.165084	0.0825421	−	0.996588i	$-0.473696\pi$
$883$	4.90553	0.165084	0.0825421	+	0.996588i	$0.473696\pi$
$884$	−176.865	−5.94861
$885$	−3.45920	−0.116280
$886$	13.9299	0.467985
$887$	−24.4188	−0.819902	−0.409951	−	0.912107i	$-0.634454\pi$
$887$	−24.4188	−0.819902	−0.409951	+	0.912107i	$0.634454\pi$
$888$	81.1567	2.72344
$889$	14.1131	0.473340
$890$	−21.2995	−0.713960
$891$	0	0
$892$	25.2238	0.844554
$893$	8.57293	0.286882
$894$	−38.5873	−1.29055
$895$	19.6283	0.656100
$896$	−41.9757	−1.40231
$897$	−60.4544	−2.01851
$898$	−87.4238	−2.91737
$899$	4.87649	0.162640
$900$	34.4575	1.14858
$901$	16.4488	0.547990
$902$	0	0
$903$	5.10710	0.169954
$904$	−1.03808	−0.0345262
$905$	−15.4408	−0.513269
$906$	−58.7346	−1.95133
$907$	−33.4445	−1.11051	−0.555253	−	0.831682i	$-0.687378\pi$
$907$	−33.4445	−1.11051	−0.555253	+	0.831682i	$0.687378\pi$
$908$	−45.3544	−1.50514
$909$	7.32544	0.242970
$910$	18.0799	0.599343
$911$	−20.8102	−0.689474	−0.344737	−	0.938699i	$-0.612032\pi$
$911$	−20.8102	−0.689474	−0.344737	+	0.938699i	$0.612032\pi$
$912$	−42.4457	−1.40552
$913$	0	0
$914$	−18.9861	−0.628006
$915$	31.6898	1.04763
$916$	−10.1932	−0.336794
$917$	10.3314	0.341174
$918$	131.656	4.34529
$919$	−11.8322	−0.390308	−0.195154	−	0.980773i	$-0.562521\pi$
$919$	−11.8322	−0.390308	−0.195154	+	0.980773i	$0.562521\pi$
$920$	−29.0460	−0.957619
$921$	58.0068	1.91139
$922$	−73.9265	−2.43464
$923$	24.7120	0.813407
$924$	0	0
$925$	−2.76947	−0.0910597
$926$	−97.1868	−3.19376
$927$	−56.0996	−1.84255
$928$	−20.9441	−0.687522
$929$	57.2642	1.87878	0.939388	−	0.342855i	$-0.111394\pi$
$929$	57.2642	1.87878	0.939388	+	0.342855i	$0.111394\pi$
$930$	−44.4633	−1.45801
$931$	0.907153	0.0297308
$932$	127.963	4.19158
$933$	−27.9181	−0.913998
$934$	−89.0711	−2.91449
$935$	0	0
$936$	397.068	12.9786
$937$	49.7345	1.62476	0.812378	−	0.583131i	$-0.198173\pi$
$937$	49.7345	1.62476	0.812378	+	0.583131i	$0.198173\pi$
$938$	−20.5667	−0.671528
$939$	41.8659	1.36624
$940$	−52.1199	−1.69996
$941$	47.0701	1.53444	0.767221	−	0.641383i	$-0.221639\pi$
$941$	47.0701	1.53444	0.767221	+	0.641383i	$0.221639\pi$
$942$	−54.7370	−1.78343
$943$	−15.2756	−0.497443
$944$	−17.5021	−0.569643
$945$	−9.87674	−0.321290
$946$	0	0
$947$	16.1208	0.523855	0.261927	−	0.965088i	$-0.415642\pi$
$947$	16.1208	0.523855	0.261927	+	0.965088i	$0.415642\pi$
$948$	−229.198	−7.44400
$949$	104.853	3.40366
$950$	2.48684	0.0806839
$951$	−69.7780	−2.26271
$952$	46.8561	1.51861
$953$	−17.5288	−0.567813	−0.283907	−	0.958852i	$-0.591631\pi$
$953$	−17.5288	−0.567813	−0.283907	+	0.958852i	$0.591631\pi$
$954$	−57.9393	−1.87586
$955$	6.21529	0.201122
$956$	−146.006	−4.72216
$957$	0	0
$958$	56.8404	1.83643
$959$	−21.6579	−0.699371
$960$	97.3857	3.14311
$961$	−2.55354	−0.0823721
$962$	−50.0718	−1.61438
$963$	−39.1136	−1.26042
$964$	59.0289	1.90119
$965$	21.9778	0.707491
$966$	25.1285	0.808497
$967$	11.5858	0.372575	0.186287	−	0.982495i	$-0.440354\pi$
$967$	11.5858	0.372575	0.186287	+	0.982495i	$0.440354\pi$
$968$	0	0
$969$	13.4140	0.430921
$970$	−31.2293	−1.00271
$971$	30.6243	0.982782	0.491391	−	0.870939i	$-0.336489\pi$
$971$	30.6243	0.982782	0.491391	+	0.870939i	$0.336489\pi$
$972$	−25.9694	−0.832968
$973$	14.7057	0.471443
$974$	9.62184	0.308304
$975$	−20.0562	−0.642312
$976$	160.337	5.13225
$977$	1.44818	0.0463314	0.0231657	−	0.999732i	$-0.492625\pi$
$977$	1.44818	0.0463314	0.0231657	+	0.999732i	$0.492625\pi$
$978$	−102.931	−3.29138
$979$	0	0
$980$	−5.51511	−0.176174
$981$	−10.6426	−0.339791
$982$	−0.407968	−0.0130188
$983$	−60.3589	−1.92515	−0.962574	−	0.271018i	$-0.912640\pi$
$983$	−60.3589	−1.92515	−0.962574	+	0.271018i	$0.912640\pi$
$984$	148.507	4.73423
$985$	2.95573	0.0941775
$986$	12.1876	0.388133
$987$	28.7388	0.914766
$988$	32.9962	1.04975
$989$	5.06213	0.160966
$990$	0	0
$991$	27.9689	0.888460	0.444230	−	0.895913i	$-0.353477\pi$
$991$	27.9689	0.888460	0.444230	+	0.895913i	$0.353477\pi$
$992$	−122.175	−3.87905
$993$	10.4616	0.331989
$994$	−10.2718	−0.325803
$995$	11.6335	0.368805
$996$	−170.458	−5.40116
$997$	4.12371	0.130599	0.0652996	−	0.997866i	$-0.479200\pi$
$997$	4.12371	0.130599	0.0652996	+	0.997866i	$0.479200\pi$
$998$	9.54084	0.302010
$999$	27.3534	0.865422

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.ba.1.5	✓	5
11.10	odd	2		4235.2.a.bb.1.1	yes	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4235.2.a.ba.1.5	✓	5	1.1	even	1	trivial
4235.2.a.bb.1.1	yes	5	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4235 = 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4235.a (trivial)

\(f(q)\)	\(=\)	\(q+2.74137 q^{2} -3.04102 q^{3} +5.51511 q^{4} -1.00000 q^{5} -8.33658 q^{6} -1.00000 q^{7} +9.63623 q^{8} +6.24783 q^{9} +O(q^{10})\)	\(q+2.74137 q^{2} -3.04102 q^{3} +5.51511 q^{4} -1.00000 q^{5} -8.33658 q^{6} -1.00000 q^{7} +9.63623 q^{8} +6.24783 q^{9} -2.74137 q^{10} -16.7716 q^{12} +6.59521 q^{13} -2.74137 q^{14} +3.04102 q^{15} +15.3863 q^{16} -4.86249 q^{17} +17.1276 q^{18} +0.907153 q^{19} -5.51511 q^{20} +3.04102 q^{21} +3.01425 q^{23} -29.3040 q^{24} +1.00000 q^{25} +18.0799 q^{26} -9.87674 q^{27} -5.51511 q^{28} -0.914310 q^{29} +8.33658 q^{30} -5.33352 q^{31} +22.9070 q^{32} -13.3299 q^{34} +1.00000 q^{35} +34.4575 q^{36} -2.76947 q^{37} +2.48684 q^{38} -20.0562 q^{39} -9.63623 q^{40} -5.06780 q^{41} +8.33658 q^{42} +1.67940 q^{43} -6.24783 q^{45} +8.26318 q^{46} +9.45037 q^{47} -46.7900 q^{48} +1.00000 q^{49} +2.74137 q^{50} +14.7869 q^{51} +36.3733 q^{52} -3.38280 q^{53} -27.0758 q^{54} -9.63623 q^{56} -2.75868 q^{57} -2.50646 q^{58} -1.13751 q^{59} +16.7716 q^{60} +10.4208 q^{61} -14.6212 q^{62} -6.24783 q^{63} +32.0240 q^{64} -6.59521 q^{65} +7.50236 q^{67} -26.8172 q^{68} -9.16641 q^{69} +2.74137 q^{70} +3.74697 q^{71} +60.2056 q^{72} +15.8983 q^{73} -7.59215 q^{74} -3.04102 q^{75} +5.00305 q^{76} -54.9814 q^{78} +13.6658 q^{79} -15.3863 q^{80} +11.2919 q^{81} -13.8927 q^{82} +10.1635 q^{83} +16.7716 q^{84} +4.86249 q^{85} +4.60386 q^{86} +2.78044 q^{87} +7.76964 q^{89} -17.1276 q^{90} -6.59521 q^{91} +16.6239 q^{92} +16.2194 q^{93} +25.9070 q^{94} -0.907153 q^{95} -69.6607 q^{96} +11.3919 q^{97} +2.74137 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{3} + 4 q^{4} - 5 q^{5} - 5 q^{6} - 5 q^{7} + 12 q^{8} + 11 q^{9}+O(q^{10}) \) 5 * q - 2 * q^3 + 4 * q^4 - 5 * q^5 - 5 * q^6 - 5 * q^7 + 12 * q^8 + 11 * q^9	\( 5 q - 2 q^{3} + 4 q^{4} - 5 q^{5} - 5 q^{6} - 5 q^{7} + 12 q^{8} + 11 q^{9} - 23 q^{12} + 10 q^{13} + 2 q^{15} + 10 q^{16} + 2 q^{17} + 5 q^{18} - 3 q^{19} - 4 q^{20} + 2 q^{21} + 3 q^{23} - 28 q^{24} + 5 q^{25} + 13 q^{26} - 11 q^{27} - 4 q^{28} + q^{29} + 5 q^{30} - 12 q^{31} + 29 q^{32} - 20 q^{34} + 5 q^{35} + 45 q^{36} + 9 q^{38} - 2 q^{39} - 12 q^{40} - 11 q^{41} + 5 q^{42} + 10 q^{43} - 11 q^{45} + 14 q^{46} + 16 q^{47} - 46 q^{48} + 5 q^{49} + 6 q^{51} + 30 q^{52} + 4 q^{53} - 34 q^{54} - 12 q^{56} + 34 q^{57} - 6 q^{58} - 32 q^{59} + 23 q^{60} + 40 q^{61} + q^{62} - 11 q^{63} + 38 q^{64} - 10 q^{65} + 7 q^{67} - 19 q^{68} - 24 q^{69} + 10 q^{71} + 72 q^{72} + 11 q^{73} - 37 q^{74} - 2 q^{75} + 3 q^{76} - 87 q^{78} + 13 q^{79} - 10 q^{80} + q^{81} + 4 q^{82} + 26 q^{83} + 23 q^{84} - 2 q^{85} - 17 q^{86} + 14 q^{87} + 5 q^{89} - 5 q^{90} - 10 q^{91} + 32 q^{92} + 3 q^{93} + 44 q^{94} + 3 q^{95} - 84 q^{96} - 5 q^{97}+O(q^{100}) \) 5 * q - 2 * q^3 + 4 * q^4 - 5 * q^5 - 5 * q^6 - 5 * q^7 + 12 * q^8 + 11 * q^9 - 23 * q^12 + 10 * q^13 + 2 * q^15 + 10 * q^16 + 2 * q^17 + 5 * q^18 - 3 * q^19 - 4 * q^20 + 2 * q^21 + 3 * q^23 - 28 * q^24 + 5 * q^25 + 13 * q^26 - 11 * q^27 - 4 * q^28 + q^29 + 5 * q^30 - 12 * q^31 + 29 * q^32 - 20 * q^34 + 5 * q^35 + 45 * q^36 + 9 * q^38 - 2 * q^39 - 12 * q^40 - 11 * q^41 + 5 * q^42 + 10 * q^43 - 11 * q^45 + 14 * q^46 + 16 * q^47 - 46 * q^48 + 5 * q^49 + 6 * q^51 + 30 * q^52 + 4 * q^53 - 34 * q^54 - 12 * q^56 + 34 * q^57 - 6 * q^58 - 32 * q^59 + 23 * q^60 + 40 * q^61 + q^62 - 11 * q^63 + 38 * q^64 - 10 * q^65 + 7 * q^67 - 19 * q^68 - 24 * q^69 + 10 * q^71 + 72 * q^72 + 11 * q^73 - 37 * q^74 - 2 * q^75 + 3 * q^76 - 87 * q^78 + 13 * q^79 - 10 * q^80 + q^81 + 4 * q^82 + 26 * q^83 + 23 * q^84 - 2 * q^85 - 17 * q^86 + 14 * q^87 + 5 * q^89 - 5 * q^90 - 10 * q^91 + 32 * q^92 + 3 * q^93 + 44 * q^94 + 3 * q^95 - 84 * q^96 - 5 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more