LMFDB - Embedded newform 1450.2.b.k.349.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1450,2,Mod(349,1450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1450, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1450.349");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1450 = 2 \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1450.b (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$11.5783082931$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.399424.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 $ x^6 - 2x^5 + 3x^4 - 6x^3 + 6x^2 - 8*x + 8
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			349.5
Root			$0.264658 - 1.38923i$ of defining polynomial
Character	$\chi$	$=$	1450.349
Dual form			1450.2.b.k.349.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +0.470683i q^{3} -1.00000 q^{4} -0.470683 q^{6} +3.30777i q^{7} -1.00000i q^{8} +2.77846 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +0.470683i q^{3} -1.00000 q^{4} -0.470683 q^{6} +3.30777i q^{7} -1.00000i q^{8} +2.77846 q^{9} +4.71982 q^{11} -0.470683i q^{12} +2.24914i q^{13} -3.30777 q^{14} +1.00000 q^{16} -0.719824i q^{17} +2.77846i q^{18} +0.470683 q^{19} -1.55691 q^{21} +4.71982i q^{22} -5.80605i q^{23} +0.470683 q^{24} -2.24914 q^{26} +2.71982i q^{27} -3.30777i q^{28} -1.00000 q^{29} +10.2181 q^{31} +1.00000i q^{32} +2.22154i q^{33} +0.719824 q^{34} -2.77846 q^{36} -1.02760i q^{37} +0.470683i q^{38} -1.05863 q^{39} -0.0275977 q^{41} -1.55691i q^{42} +6.61555i q^{43} -4.71982 q^{44} +5.80605 q^{46} -4.33537i q^{47} +0.470683i q^{48} -3.94137 q^{49} +0.338809 q^{51} -2.24914i q^{52} +10.7474i q^{53} -2.71982 q^{54} +3.30777 q^{56} +0.221543i q^{57} -1.00000i q^{58} -11.0276 q^{59} +1.35342 q^{61} +10.2181i q^{62} +9.19051i q^{63} -1.00000 q^{64} -2.22154 q^{66} +8.80605i q^{67} +0.719824i q^{68} +2.73281 q^{69} -5.80605 q^{71} -2.77846i q^{72} +3.64658i q^{73} +1.02760 q^{74} -0.470683 q^{76} +15.6121i q^{77} -1.05863i q^{78} -16.6707 q^{79} +7.05520 q^{81} -0.0275977i q^{82} -5.21811i q^{83} +1.55691 q^{84} -6.61555 q^{86} -0.470683i q^{87} -4.71982i q^{88} -9.08623 q^{89} -7.43965 q^{91} +5.80605i q^{92} +4.80949i q^{93} +4.33537 q^{94} -0.470683 q^{96} +11.1905i q^{97} -3.94137i q^{98} +13.1138 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} - 2 q^{6}+O(q^{10}) $ 6 * q - 6 * q^4 - 2 * q^6	$ 6 q - 6 q^{4} - 2 q^{6} + 10 q^{11} - 4 q^{14} + 6 q^{16} + 2 q^{19} + 24 q^{21} + 2 q^{24} + 4 q^{26} - 6 q^{29} + 8 q^{31} - 14 q^{34} - 8 q^{39} + 34 q^{41} - 10 q^{44} - 16 q^{46} - 22 q^{49} + 22 q^{51} + 2 q^{54} + 4 q^{56} - 32 q^{59} + 4 q^{61} - 6 q^{64} - 30 q^{66} - 12 q^{69} + 16 q^{71} - 28 q^{74} - 2 q^{76} - 26 q^{81} - 24 q^{84} - 8 q^{86} - 22 q^{89} - 8 q^{91} - 24 q^{94} - 2 q^{96} + 12 q^{99}+O(q^{100}) $ 6 * q - 6 * q^4 - 2 * q^6 + 10 * q^11 - 4 * q^14 + 6 * q^16 + 2 * q^19 + 24 * q^21 + 2 * q^24 + 4 * q^26 - 6 * q^29 + 8 * q^31 - 14 * q^34 - 8 * q^39 + 34 * q^41 - 10 * q^44 - 16 * q^46 - 22 * q^49 + 22 * q^51 + 2 * q^54 + 4 * q^56 - 32 * q^59 + 4 * q^61 - 6 * q^64 - 30 * q^66 - 12 * q^69 + 16 * q^71 - 28 * q^74 - 2 * q^76 - 26 * q^81 - 24 * q^84 - 8 * q^86 - 22 * q^89 - 8 * q^91 - 24 * q^94 - 2 * q^96 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1450\mathbb{Z}\right)^\times$.

$n$	$901$	$1277$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$	1.00000i	0.707107i
$2$	1.00000i	0.707107i
$3$	0.470683i	0.271749i	0.990726	+	0.135875i	$0.0433844\pi$
$3$	0.470683i	0.271749i	−0.990726	+	0.135875i	$0.956616\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−0.470683	−0.192156
$7$	3.30777i	1.25022i	0.780536	+	0.625110i	$0.214946\pi$
$7$	3.30777i	1.25022i	−0.780536	+	0.625110i	$0.785054\pi$
$8$	− 1.00000i	− 0.353553i
$9$	2.77846	0.926152
$10$	0	0
$11$	4.71982	1.42308	0.711540	−	0.702645i	$-0.247998\pi$
$11$	4.71982	1.42308	0.711540	+	0.702645i	$0.247998\pi$
$12$	− 0.470683i	− 0.135875i
$13$	2.24914i	0.623799i	0.950115	+	0.311900i	$0.100965\pi$
$13$	2.24914i	0.623799i	−0.950115	+	0.311900i	$0.899035\pi$
$14$	−3.30777	−0.884040
$15$	0	0
$16$	1.00000	0.250000
$17$	− 0.719824i	− 0.174583i	−0.996183	−	0.0872915i	$-0.972179\pi$
$17$	− 0.719824i	− 0.174583i	0.996183	−	0.0872915i	$-0.0278211\pi$
$18$	2.77846i	0.654889i
$19$	0.470683	0.107982	0.0539911	−	0.998541i	$-0.482806\pi$
$19$	0.470683	0.107982	0.0539911	+	0.998541i	$0.482806\pi$
$20$	0	0
$21$	−1.55691	−0.339747
$22$	4.71982i	1.00627i
$23$	− 5.80605i	− 1.21065i	−0.795980	−	0.605323i	$-0.793044\pi$
$23$	− 5.80605i	− 1.21065i	0.795980	−	0.605323i	$-0.206956\pi$
$24$	0.470683	0.0960779
$25$	0	0
$26$	−2.24914	−0.441093
$27$	2.71982i	0.523430i
$28$	− 3.30777i	− 0.625110i
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	0	0
$31$	10.2181	1.83523	0.917613	−	0.397475i	$-0.130114\pi$
$31$	10.2181	1.83523	0.917613	+	0.397475i	$0.130114\pi$
$32$	1.00000i	0.176777i
$33$	2.22154i	0.386721i
$34$	0.719824	0.123449
$35$	0	0
$36$	−2.77846	−0.463076
$37$	− 1.02760i	− 0.168936i	−0.996426	−	0.0844680i	$-0.973081\pi$
$37$	− 1.02760i	− 0.168936i	0.996426	−	0.0844680i	$-0.0269191\pi$
$38$	0.470683i	0.0763549i
$39$	−1.05863	−0.169517
$40$	0	0
$41$	−0.0275977	−0.00431003	−0.00215501	−	0.999998i	$-0.500686\pi$
$41$	−0.0275977	−0.00431003	−0.00215501	+	0.999998i	$0.500686\pi$
$42$	− 1.55691i	− 0.240237i
$43$	6.61555i	1.00886i	0.863452	+	0.504431i	$0.168298\pi$
$43$	6.61555i	1.00886i	−0.863452	+	0.504431i	$0.831702\pi$
$44$	−4.71982	−0.711540
$45$	0	0
$46$	5.80605	0.856056
$47$	− 4.33537i	− 0.632379i	−0.948696	−	0.316189i	$-0.897596\pi$
$47$	− 4.33537i	− 0.632379i	0.948696	−	0.316189i	$-0.102404\pi$
$48$	0.470683i	0.0679373i
$49$	−3.94137	−0.563052
$50$	0	0
$51$	0.338809	0.0474428
$52$	− 2.24914i	− 0.311900i
$53$	10.7474i	1.47627i	0.674652	+	0.738136i	$0.264294\pi$
$53$	10.7474i	1.47627i	−0.674652	+	0.738136i	$0.735706\pi$
$54$	−2.71982	−0.370121
$55$	0	0
$56$	3.30777	0.442020
$57$	0.221543i	0.0293441i
$58$	− 1.00000i	− 0.131306i
$59$	−11.0276	−1.43567	−0.717835	−	0.696213i	$-0.754867\pi$
$59$	−11.0276	−1.43567	−0.717835	+	0.696213i	$0.754867\pi$
$60$	0	0
$61$	1.35342	0.173287	0.0866437	−	0.996239i	$-0.472386\pi$
$61$	1.35342	0.173287	0.0866437	+	0.996239i	$0.472386\pi$
$62$	10.2181i	1.29770i
$63$	9.19051i	1.15790i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−2.22154	−0.273453
$67$	8.80605i	1.07583i	0.842999	+	0.537915i	$0.180788\pi$
$67$	8.80605i	1.07583i	−0.842999	+	0.537915i	$0.819212\pi$
$68$	0.719824i	0.0872915i
$69$	2.73281	0.328992
$70$	0	0
$71$	−5.80605	−0.689052	−0.344526	−	0.938777i	$-0.611960\pi$
$71$	−5.80605	−0.689052	−0.344526	+	0.938777i	$0.611960\pi$
$72$	− 2.77846i	− 0.327444i
$73$	3.64658i	0.426800i	0.976965	+	0.213400i	$0.0684538\pi$
$73$	3.64658i	0.426800i	−0.976965	+	0.213400i	$0.931546\pi$
$74$	1.02760	0.119456
$75$	0	0
$76$	−0.470683	−0.0539911
$77$	15.6121i	1.77917i
$78$	− 1.05863i	− 0.119867i
$79$	−16.6707	−1.87561	−0.937803	−	0.347169i	$-0.887143\pi$
$79$	−16.6707	−1.87561	−0.937803	+	0.347169i	$0.887143\pi$
$80$	0	0
$81$	7.05520	0.783911
$82$	− 0.0275977i	− 0.00304765i
$83$	− 5.21811i	− 0.572761i	−0.958116	−	0.286381i	$-0.907548\pi$
$83$	− 5.21811i	− 0.572761i	0.958116	−	0.286381i	$-0.0924522\pi$
$84$	1.55691	0.169873
$85$	0	0
$86$	−6.61555	−0.713373
$87$	− 0.470683i	− 0.0504626i
$88$	− 4.71982i	− 0.503135i
$89$	−9.08623	−0.963139	−0.481569	−	0.876408i	$-0.659933\pi$
$89$	−9.08623	−0.963139	−0.481569	+	0.876408i	$0.659933\pi$
$90$	0	0
$91$	−7.43965	−0.779887
$92$	5.80605i	0.605323i
$93$	4.80949i	0.498721i
$94$	4.33537	0.447159
$95$	0	0
$96$	−0.470683	−0.0480389
$97$	11.1905i	1.13622i	0.822951	+	0.568112i	$0.192326\pi$
$97$	11.1905i	1.13622i	−0.822951	+	0.568112i	$0.807674\pi$
$98$	− 3.94137i	− 0.398138i
$99$	13.1138	1.31799
$100$	0	0
$101$	−3.02760	−0.301257	−0.150629	−	0.988590i	$-0.548130\pi$
$101$	−3.02760	−0.301257	−0.150629	+	0.988590i	$0.548130\pi$
$102$	0.338809i	0.0335471i
$103$	− 6.01461i	− 0.592637i	−0.955089	−	0.296318i	$-0.904241\pi$
$103$	− 6.01461i	− 0.592637i	0.955089	−	0.296318i	$-0.0957590\pi$
$104$	2.24914	0.220546
$105$	0	0
$106$	−10.7474	−1.04388
$107$	− 11.7474i	− 1.13567i	−0.823144	−	0.567833i	$-0.807782\pi$
$107$	− 11.7474i	− 1.13567i	0.823144	−	0.567833i	$-0.192218\pi$
$108$	− 2.71982i	− 0.261715i
$109$	9.92332	0.950482	0.475241	−	0.879856i	$-0.342361\pi$
$109$	9.92332	0.950482	0.475241	+	0.879856i	$0.342361\pi$
$110$	0	0
$111$	0.483673	0.0459082
$112$	3.30777i	0.312555i
$113$	14.0276i	1.31961i	0.751439	+	0.659803i	$0.229360\pi$
$113$	14.0276i	1.31961i	−0.751439	+	0.659803i	$0.770640\pi$
$114$	−0.221543	−0.0207494
$115$	0	0
$116$	1.00000	0.0928477
$117$	6.24914i	0.577733i
$118$	− 11.0276i	− 1.01517i
$119$	2.38101	0.218267
$120$	0	0
$121$	11.2767	1.02516
$122$	1.35342i	0.122533i
$123$	− 0.0129898i	− 0.00117125i
$124$	−10.2181	−0.917613
$125$	0	0
$126$	−9.19051	−0.818755
$127$	− 16.2181i	− 1.43912i	−0.694428	−	0.719562i	$-0.744343\pi$
$127$	− 16.2181i	− 1.43912i	0.694428	−	0.719562i	$-0.255657\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	−3.11383	−0.274157
$130$	0	0
$131$	21.3630	1.86649	0.933246	−	0.359239i	$-0.116964\pi$
$131$	21.3630	1.86649	0.933246	+	0.359239i	$0.116964\pi$
$132$	− 2.22154i	− 0.193360i
$133$	1.55691i	0.135002i
$134$	−8.80605	−0.760727
$135$	0	0
$136$	−0.719824	−0.0617244
$137$	− 9.54392i	− 0.815392i	−0.913118	−	0.407696i	$-0.866332\pi$
$137$	− 9.54392i	− 0.815392i	0.913118	−	0.407696i	$-0.133668\pi$
$138$	2.73281i	0.232633i
$139$	3.74742	0.317852	0.158926	−	0.987290i	$-0.449197\pi$
$139$	3.74742	0.317852	0.158926	+	0.987290i	$0.449197\pi$
$140$	0	0
$141$	2.04059	0.171848
$142$	− 5.80605i	− 0.487233i
$143$	10.6155i	0.887717i
$144$	2.77846	0.231538
$145$	0	0
$146$	−3.64658	−0.301793
$147$	− 1.85514i	− 0.153009i
$148$	1.02760i	0.0844680i
$149$	−2.00000	−0.163846	−0.0819232	−	0.996639i	$-0.526106\pi$
$149$	−2.00000	−0.163846	−0.0819232	+	0.996639i	$0.526106\pi$
$150$	0	0
$151$	−14.2491	−1.15958	−0.579789	−	0.814766i	$-0.696865\pi$
$151$	−14.2491	−1.15958	−0.579789	+	0.814766i	$0.696865\pi$
$152$	− 0.470683i	− 0.0381775i
$153$	− 2.00000i	− 0.161690i
$154$	−15.6121	−1.25806
$155$	0	0
$156$	1.05863	0.0847585
$157$	− 12.2035i	− 0.973945i	−0.873417	−	0.486973i	$-0.838101\pi$
$157$	− 12.2035i	− 0.973945i	0.873417	−	0.486973i	$-0.161899\pi$
$158$	− 16.6707i	− 1.32625i
$159$	−5.05863	−0.401176
$160$	0	0
$161$	19.2051	1.51358
$162$	7.05520i	0.554308i
$163$	17.5845i	1.37733i	0.725082	+	0.688663i	$0.241802\pi$
$163$	17.5845i	1.37733i	−0.725082	+	0.688663i	$0.758198\pi$
$164$	0.0275977	0.00215501
$165$	0	0
$166$	5.21811	0.405003
$167$	− 11.7914i	− 0.912450i	−0.889865	−	0.456225i	$-0.849201\pi$
$167$	− 11.7914i	− 0.912450i	0.889865	−	0.456225i	$-0.150799\pi$
$168$	1.55691i	0.120119i
$169$	7.94137	0.610874
$170$	0	0
$171$	1.30777	0.100008
$172$	− 6.61555i	− 0.504431i
$173$	− 20.7880i	− 1.58048i	−0.612795	−	0.790242i	$-0.709955\pi$
$173$	− 20.7880i	− 1.58048i	0.612795	−	0.790242i	$-0.290045\pi$
$174$	0.470683	0.0356824
$175$	0	0
$176$	4.71982	0.355770
$177$	− 5.19051i	− 0.390142i
$178$	− 9.08623i	− 0.681042i
$179$	7.74742	0.579069	0.289535	−	0.957168i	$-0.406499\pi$
$179$	7.74742	0.579069	0.289535	+	0.957168i	$0.406499\pi$
$180$	0	0
$181$	−19.7440	−1.46756	−0.733779	−	0.679388i	$-0.762245\pi$
$181$	−19.7440	−1.46756	−0.733779	+	0.679388i	$0.762245\pi$
$182$	− 7.43965i	− 0.551463i
$183$	0.637031i	0.0470907i
$184$	−5.80605	−0.428028
$185$	0	0
$186$	−4.80949	−0.352649
$187$	− 3.39744i	− 0.248446i
$188$	4.33537i	0.316189i
$189$	−8.99656	−0.654404
$190$	0	0
$191$	0.397442	0.0287579	0.0143790	−	0.999897i	$-0.495423\pi$
$191$	0.397442	0.0287579	0.0143790	+	0.999897i	$0.495423\pi$
$192$	− 0.470683i	− 0.0339686i
$193$	4.35342i	0.313366i	0.987649	+	0.156683i	$0.0500801\pi$
$193$	4.35342i	0.313366i	−0.987649	+	0.156683i	$0.949920\pi$
$194$	−11.1905	−0.803432
$195$	0	0
$196$	3.94137	0.281526
$197$	6.70683i	0.477842i	0.971039	+	0.238921i	$0.0767937\pi$
$197$	6.70683i	0.477842i	−0.971039	+	0.238921i	$0.923206\pi$
$198$	13.1138i	0.931959i
$199$	9.36297	0.663723	0.331862	−	0.943328i	$-0.392323\pi$
$199$	9.36297	0.663723	0.331862	+	0.943328i	$0.392323\pi$
$200$	0	0
$201$	−4.14486	−0.292356
$202$	− 3.02760i	− 0.213021i
$203$	− 3.30777i	− 0.232160i
$204$	−0.338809	−0.0237214
$205$	0	0
$206$	6.01461	0.419058
$207$	− 16.1319i	− 1.12124i
$208$	2.24914i	0.155950i
$209$	2.22154	0.153667
$210$	0	0
$211$	−24.5665	−1.69123	−0.845613	−	0.533797i	$-0.820765\pi$
$211$	−24.5665	−1.69123	−0.845613	+	0.533797i	$0.820765\pi$
$212$	− 10.7474i	− 0.738136i
$213$	− 2.73281i	− 0.187249i
$214$	11.7474	0.803037
$215$	0	0
$216$	2.71982	0.185061
$217$	33.7992i	2.29444i
$218$	9.92332i	0.672092i
$219$	−1.71639	−0.115983
$220$	0	0
$221$	1.61899	0.108905
$222$	0.483673i	0.0324620i
$223$	− 2.11727i	− 0.141783i	−0.997484	−	0.0708913i	$-0.977416\pi$
$223$	− 2.11727i	− 0.141783i	0.997484	−	0.0708913i	$-0.0225844\pi$
$224$	−3.30777	−0.221010
$225$	0	0
$226$	−14.0276	−0.933102
$227$	− 15.9138i	− 1.05623i	−0.849172	−	0.528117i	$-0.822898\pi$
$227$	− 15.9138i	− 1.05623i	0.849172	−	0.528117i	$-0.177102\pi$
$228$	− 0.221543i	− 0.0146720i
$229$	22.2897	1.47295	0.736473	−	0.676467i	$-0.236490\pi$
$229$	22.2897	1.47295	0.736473	+	0.676467i	$0.236490\pi$
$230$	0	0
$231$	−7.34836	−0.483487
$232$	1.00000i	0.0656532i
$233$	23.3871i	1.53214i	0.642756	+	0.766071i	$0.277791\pi$
$233$	23.3871i	1.53214i	−0.642756	+	0.766071i	$0.722209\pi$
$234$	−6.24914	−0.408519
$235$	0	0
$236$	11.0276	0.717835
$237$	− 7.84664i	− 0.509694i
$238$	2.38101i	0.154338i
$239$	−20.2277	−1.30842	−0.654209	−	0.756314i	$-0.726998\pi$
$239$	−20.2277	−1.30842	−0.654209	+	0.756314i	$0.726998\pi$
$240$	0	0
$241$	1.26375	0.0814052	0.0407026	−	0.999171i	$-0.487040\pi$
$241$	1.26375	0.0814052	0.0407026	+	0.999171i	$0.487040\pi$
$242$	11.2767i	0.724896i
$243$	11.4802i	0.736457i
$244$	−1.35342	−0.0866437
$245$	0	0
$246$	0.0129898	0.000828197 0
$247$	1.05863i	0.0673592i
$248$	− 10.2181i	− 0.648850i
$249$	2.45608	0.155647
$250$	0	0
$251$	9.63971	0.608453	0.304226	−	0.952600i	$-0.401602\pi$
$251$	9.63971	0.608453	0.304226	+	0.952600i	$0.401602\pi$
$252$	− 9.19051i	− 0.578948i
$253$	− 27.4036i	− 1.72285i
$254$	16.2181	1.01761
$255$	0	0
$256$	1.00000	0.0625000
$257$	− 9.43965i	− 0.588829i	−0.955678	−	0.294415i	$-0.904875\pi$
$257$	− 9.43965i	− 0.588829i	0.955678	−	0.294415i	$-0.0951246\pi$
$258$	− 3.11383i	− 0.193858i
$259$	3.39906	0.211207
$260$	0	0
$261$	−2.77846	−0.171982
$262$	21.3630i	1.31981i
$263$	− 11.6646i	− 0.719272i	−0.933093	−	0.359636i	$-0.882901\pi$
$263$	− 11.6646i	− 0.719272i	0.933093	−	0.359636i	$-0.117099\pi$
$264$	2.22154	0.136727
$265$	0	0
$266$	−1.55691	−0.0954605
$267$	− 4.27674i	− 0.261732i
$268$	− 8.80605i	− 0.537915i
$269$	20.1414	1.22804	0.614022	−	0.789289i	$-0.289551\pi$
$269$	20.1414	1.22804	0.614022	+	0.789289i	$0.289551\pi$
$270$	0	0
$271$	−27.0422	−1.64270	−0.821349	−	0.570427i	$-0.806778\pi$
$271$	−27.0422	−1.64270	−0.821349	+	0.570427i	$0.806778\pi$
$272$	− 0.719824i	− 0.0436457i
$273$	− 3.50172i	− 0.211934i
$274$	9.54392	0.576570
$275$	0	0
$276$	−2.73281	−0.164496
$277$	− 12.4216i	− 0.746342i	−0.927763	−	0.373171i	$-0.878271\pi$
$277$	− 12.4216i	− 0.746342i	0.927763	−	0.373171i	$-0.121729\pi$
$278$	3.74742i	0.224755i
$279$	28.3906	1.69970
$280$	0	0
$281$	24.8957	1.48515	0.742577	−	0.669761i	$-0.233603\pi$
$281$	24.8957	1.48515	0.742577	+	0.669761i	$0.233603\pi$
$282$	2.04059i	0.121515i
$283$	4.83709i	0.287535i	0.989611	+	0.143768i	$0.0459218\pi$
$283$	4.83709i	0.287535i	−0.989611	+	0.143768i	$0.954078\pi$
$284$	5.80605	0.344526
$285$	0	0
$286$	−10.6155	−0.627710
$287$	− 0.0912868i	− 0.00538849i
$288$	2.77846i	0.163722i
$289$	16.4819	0.969521
$290$	0	0
$291$	−5.26719	−0.308768
$292$	− 3.64658i	− 0.213400i
$293$	− 33.5190i	− 1.95820i	−0.203377	−	0.979101i	$-0.565192\pi$
$293$	− 33.5190i	− 1.95820i	0.203377	−	0.979101i	$-0.434808\pi$
$294$	1.85514	0.108194
$295$	0	0
$296$	−1.02760	−0.0597279
$297$	12.8371i	0.744884i
$298$	− 2.00000i	− 0.115857i
$299$	13.0586	0.755200
$300$	0	0
$301$	−21.8827	−1.26130
$302$	− 14.2491i	− 0.819946i
$303$	− 1.42504i	− 0.0818664i
$304$	0.470683	0.0269955
$305$	0	0
$306$	2.00000	0.114332
$307$	− 12.3680i	− 0.705880i	−0.935646	−	0.352940i	$-0.885182\pi$
$307$	− 12.3680i	− 0.705880i	0.935646	−	0.352940i	$-0.114818\pi$
$308$	− 15.6121i	− 0.889583i
$309$	2.83098	0.161049
$310$	0	0
$311$	15.3224	0.868853	0.434426	−	0.900707i	$-0.356951\pi$
$311$	15.3224	0.868853	0.434426	+	0.900707i	$0.356951\pi$
$312$	1.05863i	0.0599333i
$313$	− 22.1268i	− 1.25068i	−0.780352	−	0.625341i	$-0.784960\pi$
$313$	− 22.1268i	− 1.25068i	0.780352	−	0.625341i	$-0.215040\pi$
$314$	12.2035	0.688683
$315$	0	0
$316$	16.6707	0.937803
$317$	10.1775i	0.571626i	0.958285	+	0.285813i	$0.0922637\pi$
$317$	10.1775i	0.571626i	−0.958285	+	0.285813i	$0.907736\pi$
$318$	− 5.05863i	− 0.283674i
$319$	−4.71982	−0.264259
$320$	0	0
$321$	5.52932	0.308616
$322$	19.2051i	1.07026i
$323$	− 0.338809i	− 0.0188518i
$324$	−7.05520	−0.391955
$325$	0	0
$326$	−17.5845	−0.973916
$327$	4.67074i	0.258293i
$328$	0.0275977i	0.00152383i
$329$	14.3404	0.790613
$330$	0	0
$331$	8.69834	0.478104	0.239052	−	0.971007i	$-0.423163\pi$
$331$	8.69834	0.478104	0.239052	+	0.971007i	$0.423163\pi$
$332$	5.21811i	0.286381i
$333$	− 2.85514i	− 0.156460i
$334$	11.7914	0.645199
$335$	0	0
$336$	−1.55691	−0.0849366
$337$	16.7198i	0.910787i	0.890290	+	0.455393i	$0.150501\pi$
$337$	16.7198i	0.910787i	−0.890290	+	0.455393i	$0.849499\pi$
$338$	7.94137i	0.431953i
$339$	−6.60256	−0.358602
$340$	0	0
$341$	48.2277	2.61167
$342$	1.30777i	0.0707163i
$343$	10.1173i	0.546281i
$344$	6.61555	0.356686
$345$	0	0
$346$	20.7880	1.11757
$347$	6.74398i	0.362036i	0.983480	+	0.181018i	$0.0579392\pi$
$347$	6.74398i	0.362036i	−0.983480	+	0.181018i	$0.942061\pi$
$348$	0.470683i	0.0252313i
$349$	−7.42504	−0.397453	−0.198727	−	0.980055i	$-0.563681\pi$
$349$	−7.42504	−0.397453	−0.198727	+	0.980055i	$0.563681\pi$
$350$	0	0
$351$	−6.11727	−0.326516
$352$	4.71982i	0.251567i
$353$	− 3.36802i	− 0.179262i	−0.995975	−	0.0896309i	$-0.971431\pi$
$353$	− 3.36802i	− 0.179262i	0.995975	−	0.0896309i	$-0.0285688\pi$
$354$	5.19051	0.275872
$355$	0	0
$356$	9.08623	0.481569
$357$	1.12070i	0.0593140i
$358$	7.74742i	0.409464i
$359$	−1.81111	−0.0955868	−0.0477934	−	0.998857i	$-0.515219\pi$
$359$	−1.81111	−0.0955868	−0.0477934	+	0.998857i	$0.515219\pi$
$360$	0	0
$361$	−18.7785	−0.988340
$362$	− 19.7440i	− 1.03772i
$363$	5.30777i	0.278586i
$364$	7.43965	0.389944
$365$	0	0
$366$	−0.637031	−0.0332981
$367$	− 30.8268i	− 1.60914i	−0.593855	−	0.804572i	$-0.702395\pi$
$367$	− 30.8268i	− 1.60914i	0.593855	−	0.804572i	$-0.297605\pi$
$368$	− 5.80605i	− 0.302662i
$369$	−0.0766789	−0.00399174
$370$	0	0
$371$	−35.5500	−1.84567
$372$	− 4.80949i	− 0.249361i
$373$	− 2.06207i	− 0.106770i	−0.998574	−	0.0533850i	$-0.982999\pi$
$373$	− 2.06207i	− 0.106770i	0.998574	−	0.0533850i	$-0.0170011\pi$
$374$	3.39744	0.175678
$375$	0	0
$376$	−4.33537	−0.223580
$377$	− 2.24914i	− 0.115837i
$378$	− 8.99656i	− 0.462733i
$379$	7.29478	0.374708	0.187354	−	0.982292i	$-0.440009\pi$
$379$	7.29478	0.374708	0.187354	+	0.982292i	$0.440009\pi$
$380$	0	0
$381$	7.63359	0.391081
$382$	0.397442i	0.0203349i
$383$	15.7846i	0.806554i	0.915078	+	0.403277i	$0.132129\pi$
$383$	15.7846i	0.806554i	−0.915078	+	0.403277i	$0.867871\pi$
$384$	0.470683	0.0240195
$385$	0	0
$386$	−4.35342	−0.221583
$387$	18.3810i	0.934359i
$388$	− 11.1905i	− 0.568112i
$389$	13.3534	0.677045	0.338523	−	0.940958i	$-0.390073\pi$
$389$	13.3534	0.677045	0.338523	+	0.940958i	$0.390073\pi$
$390$	0	0
$391$	−4.17934	−0.211358
$392$	3.94137i	0.199069i
$393$	10.0552i	0.507218i
$394$	−6.70683	−0.337885
$395$	0	0
$396$	−13.1138	−0.658995
$397$	20.2130i	1.01446i	0.861810	+	0.507232i	$0.169331\pi$
$397$	20.2130i	1.01446i	−0.861810	+	0.507232i	$0.830669\pi$
$398$	9.36297i	0.469323i
$399$	−0.732814	−0.0366866
$400$	0	0
$401$	15.2897	0.763533	0.381766	−	0.924259i	$-0.375316\pi$
$401$	15.2897	0.763533	0.381766	+	0.924259i	$0.375316\pi$
$402$	− 4.14486i	− 0.206727i
$403$	22.9820i	1.14481i
$404$	3.02760	0.150629
$405$	0	0
$406$	3.30777	0.164162
$407$	− 4.85008i	− 0.240410i
$408$	− 0.338809i	− 0.0167736i
$409$	−14.8302	−0.733307	−0.366653	−	0.930358i	$-0.619497\pi$
$409$	−14.8302	−0.733307	−0.366653	+	0.930358i	$0.619497\pi$
$410$	0	0
$411$	4.49217	0.221582
$412$	6.01461i	0.296318i
$413$	− 36.4768i	− 1.79491i
$414$	16.1319	0.792838
$415$	0	0
$416$	−2.24914	−0.110273
$417$	1.76385i	0.0863761i
$418$	2.22154i	0.108659i
$419$	13.8647	0.677334	0.338667	−	0.940906i	$-0.390024\pi$
$419$	13.8647	0.677334	0.338667	+	0.940906i	$0.390024\pi$
$420$	0	0
$421$	2.70178	0.131677	0.0658383	−	0.997830i	$-0.479028\pi$
$421$	2.70178	0.131677	0.0658383	+	0.997830i	$0.479028\pi$
$422$	− 24.5665i	− 1.19588i
$423$	− 12.0456i	− 0.585679i
$424$	10.7474	0.521941
$425$	0	0
$426$	2.73281	0.132405
$427$	4.47680i	0.216647i
$428$	11.7474i	0.567833i
$429$	−4.99656	−0.241236
$430$	0	0
$431$	−27.3009	−1.31504	−0.657519	−	0.753438i	$-0.728394\pi$
$431$	−27.3009	−1.31504	−0.657519	+	0.753438i	$0.728394\pi$
$432$	2.71982i	0.130858i
$433$	0.262130i	0.0125972i	0.999980	+	0.00629859i	$0.00200492\pi$
$433$	0.262130i	0.0125972i	−0.999980	+	0.00629859i	$0.997995\pi$
$434$	−33.7992	−1.62241
$435$	0	0
$436$	−9.92332	−0.475241
$437$	− 2.73281i	− 0.130728i
$438$	− 1.71639i	− 0.0820121i
$439$	−20.4983	−0.978330	−0.489165	−	0.872191i	$-0.662698\pi$
$439$	−20.4983	−0.978330	−0.489165	+	0.872191i	$0.662698\pi$
$440$	0	0
$441$	−10.9509	−0.521472
$442$	1.61899i	0.0770073i
$443$	0.456076i	0.0216688i	0.999941	+	0.0108344i	$0.00344876\pi$
$443$	0.456076i	0.0216688i	−0.999941	+	0.0108344i	$0.996551\pi$
$444$	−0.483673	−0.0229541
$445$	0	0
$446$	2.11727	0.100255
$447$	− 0.941367i	− 0.0445251i
$448$	− 3.30777i	− 0.156278i
$449$	8.62854	0.407206	0.203603	−	0.979054i	$-0.434735\pi$
$449$	8.62854	0.407206	0.203603	+	0.979054i	$0.434735\pi$
$450$	0	0
$451$	−0.130256	−0.00613352
$452$	− 14.0276i	− 0.659803i
$453$	− 6.70683i	− 0.315115i
$454$	15.9138	0.746870
$455$	0	0
$456$	0.221543	0.0103747
$457$	− 11.6872i	− 0.546703i	−0.961914	−	0.273351i	$-0.911868\pi$
$457$	− 11.6872i	− 0.546703i	0.961914	−	0.273351i	$-0.0881322\pi$
$458$	22.2897i	1.04153i
$459$	1.95779	0.0913820
$460$	0	0
$461$	−1.82066	−0.0847967	−0.0423984	−	0.999101i	$-0.513500\pi$
$461$	−1.82066	−0.0847967	−0.0423984	+	0.999101i	$0.513500\pi$
$462$	− 7.34836i	− 0.341877i
$463$	− 26.8241i	− 1.24662i	−0.781974	−	0.623311i	$-0.785787\pi$
$463$	− 26.8241i	− 1.24662i	0.781974	−	0.623311i	$-0.214213\pi$
$464$	−1.00000	−0.0464238
$465$	0	0
$466$	−23.3871	−1.08339
$467$	− 0.366407i	− 0.0169553i	−0.999964	−	0.00847764i	$-0.997301\pi$
$467$	− 0.366407i	− 0.0169553i	0.999964	−	0.00847764i	$-0.00269855\pi$
$468$	− 6.24914i	− 0.288867i
$469$	−29.1284	−1.34503
$470$	0	0
$471$	5.74398	0.264669
$472$	11.0276i	0.507586i
$473$	31.2242i	1.43569i
$474$	7.84664	0.360408
$475$	0	0
$476$	−2.38101	−0.109134
$477$	29.8613i	1.36725i
$478$	− 20.2277i	− 0.925191i
$479$	−13.7363	−0.627625	−0.313813	−	0.949485i	$-0.601606\pi$
$479$	−13.7363	−0.627625	−0.313813	+	0.949485i	$0.601606\pi$
$480$	0	0
$481$	2.31121	0.105382
$482$	1.26375i	0.0575622i
$483$	9.03953i	0.411313i
$484$	−11.2767	−0.512579
$485$	0	0
$486$	−11.4802	−0.520754
$487$	22.9414i	1.03957i	0.854296	+	0.519786i	$0.173988\pi$
$487$	22.9414i	1.03957i	−0.854296	+	0.519786i	$0.826012\pi$
$488$	− 1.35342i	− 0.0612663i
$489$	−8.27674	−0.374287
$490$	0	0
$491$	12.8241	0.578744	0.289372	−	0.957217i	$-0.406554\pi$
$491$	12.8241	0.578744	0.289372	+	0.957217i	$0.406554\pi$
$492$	0.0129898i	0 0.000585624i
$493$	0.719824i	0.0324192i
$494$	−1.05863	−0.0476302
$495$	0	0
$496$	10.2181	0.458806
$497$	− 19.2051i	− 0.861467i
$498$	2.45608i	0.110059i
$499$	0.349979	0.0156672	0.00783361	−	0.999969i	$-0.497506\pi$
$499$	0.349979	0.0156672	0.00783361	+	0.999969i	$0.497506\pi$
$500$	0	0
$501$	5.55004	0.247957
$502$	9.63971i	0.430241i
$503$	− 34.1629i	− 1.52325i	−0.648019	−	0.761624i	$-0.724402\pi$
$503$	− 34.1629i	− 1.52325i	0.648019	−	0.761624i	$-0.275598\pi$
$504$	9.19051	0.409378
$505$	0	0
$506$	27.4036	1.21824
$507$	3.73787i	0.166005i
$508$	16.2181i	0.719562i
$509$	33.7586	1.49632	0.748162	−	0.663517i	$-0.230937\pi$
$509$	33.7586	1.49632	0.748162	+	0.663517i	$0.230937\pi$
$510$	0	0
$511$	−12.0621	−0.533595
$512$	1.00000i	0.0441942i
$513$	1.28018i	0.0565212i
$514$	9.43965	0.416365
$515$	0	0
$516$	3.11383	0.137079
$517$	− 20.4622i	− 0.899926i
$518$	3.39906i	0.149346i
$519$	9.78457	0.429495
$520$	0	0
$521$	31.3810	1.37483	0.687414	−	0.726266i	$-0.258746\pi$
$521$	31.3810	1.37483	0.687414	+	0.726266i	$0.258746\pi$
$522$	− 2.77846i	− 0.121610i
$523$	− 38.0303i	− 1.66295i	−0.555564	−	0.831474i	$-0.687498\pi$
$523$	− 38.0303i	− 1.66295i	0.555564	−	0.831474i	$-0.312502\pi$
$524$	−21.3630	−0.933246
$525$	0	0
$526$	11.6646	0.508602
$527$	− 7.35524i	− 0.320399i
$528$	2.22154i	0.0966802i
$529$	−10.7103	−0.465664
$530$	0	0
$531$	−30.6397	−1.32965
$532$	− 1.55691i	− 0.0675008i
$533$	− 0.0620710i	− 0.00268859i
$534$	4.27674	0.185073
$535$	0	0
$536$	8.80605	0.380364
$537$	3.64658i	0.157362i
$538$	20.1414i	0.868359i
$539$	−18.6026	−0.801269
$540$	0	0
$541$	−42.7862	−1.83952	−0.919761	−	0.392479i	$-0.871618\pi$
$541$	−42.7862	−1.83952	−0.919761	+	0.392479i	$0.871618\pi$
$542$	− 27.0422i	− 1.16156i
$543$	− 9.29317i	− 0.398808i
$544$	0.719824	0.0308622
$545$	0	0
$546$	3.50172	0.149860
$547$	− 28.0974i	− 1.20136i	−0.799490	−	0.600679i	$-0.794897\pi$
$547$	− 28.0974i	− 1.20136i	0.799490	−	0.600679i	$-0.205103\pi$
$548$	9.54392i	0.407696i
$549$	3.76041	0.160490
$550$	0	0
$551$	−0.470683	−0.0200518
$552$	− 2.73281i	− 0.116316i
$553$	− 55.1430i	− 2.34492i
$554$	12.4216	0.527743
$555$	0	0
$556$	−3.74742	−0.158926
$557$	12.6155i	0.534538i	0.963622	+	0.267269i	$0.0861212\pi$
$557$	12.6155i	0.534538i	−0.963622	+	0.267269i	$0.913879\pi$
$558$	28.3906i	1.20187i
$559$	−14.8793	−0.629327
$560$	0	0
$561$	1.59912	0.0675149
$562$	24.8957i	1.05016i
$563$	− 33.7586i	− 1.42276i	−0.702810	−	0.711378i	$-0.748072\pi$
$563$	− 33.7586i	− 1.42276i	0.702810	−	0.711378i	$-0.251928\pi$
$564$	−2.04059	−0.0859242
$565$	0	0
$566$	−4.83709	−0.203318
$567$	23.3370i	0.980061i
$568$	5.80605i	0.243617i
$569$	−5.66119	−0.237329	−0.118665	−	0.992934i	$-0.537861\pi$
$569$	−5.66119	−0.237329	−0.118665	+	0.992934i	$0.537861\pi$
$570$	0	0
$571$	30.6105	1.28101	0.640505	−	0.767954i	$-0.278725\pi$
$571$	30.6105	1.28101	0.640505	+	0.767954i	$0.278725\pi$
$572$	− 10.6155i	− 0.443858i
$573$	0.187070i	0.00781494i
$574$	0.0912868	0.00381024
$575$	0	0
$576$	−2.77846	−0.115769
$577$	− 2.94298i	− 0.122518i	−0.998122	−	0.0612590i	$-0.980488\pi$
$577$	− 2.94298i	− 0.122518i	0.998122	−	0.0612590i	$-0.0195116\pi$
$578$	16.4819i	0.685555i
$579$	−2.04908	−0.0851569
$580$	0	0
$581$	17.2603	0.716078
$582$	− 5.26719i	− 0.218332i
$583$	50.7259i	2.10085i
$584$	3.64658	0.150897
$585$	0	0
$586$	33.5190	1.38466
$587$	− 14.5715i	− 0.601431i	−0.953714	−	0.300716i	$-0.902775\pi$
$587$	− 14.5715i	− 0.601431i	0.953714	−	0.300716i	$-0.0972255\pi$
$588$	1.85514i	0.0765045i
$589$	4.80949	0.198172
$590$	0	0
$591$	−3.15680	−0.129853
$592$	− 1.02760i	− 0.0422340i
$593$	19.0552i	0.782503i	0.920284	+	0.391252i	$0.127958\pi$
$593$	19.0552i	0.782503i	−0.920284	+	0.391252i	$0.872042\pi$
$594$	−12.8371	−0.526712
$595$	0	0
$596$	2.00000	0.0819232
$597$	4.40699i	0.180366i
$598$	13.0586i	0.534007i
$599$	−5.86631	−0.239691	−0.119845	−	0.992793i	$-0.538240\pi$
$599$	−5.86631	−0.239691	−0.119845	+	0.992793i	$0.538240\pi$
$600$	0	0
$601$	−31.3285	−1.27792	−0.638958	−	0.769242i	$-0.720634\pi$
$601$	−31.3285	−1.27792	−0.638958	+	0.769242i	$0.720634\pi$
$602$	− 21.8827i	− 0.891874i
$603$	24.4672i	0.996383i
$604$	14.2491	0.579789
$605$	0	0
$606$	1.42504	0.0578883
$607$	11.0061i	0.446724i	0.974736	+	0.223362i	$0.0717033\pi$
$607$	11.0061i	0.446724i	−0.974736	+	0.223362i	$0.928297\pi$
$608$	0.470683i	0.0190887i
$609$	1.55691	0.0630893
$610$	0	0
$611$	9.75086	0.394478
$612$	2.00000i	0.0808452i
$613$	14.7068i	0.594003i	0.954877	+	0.297002i	$0.0959867\pi$
$613$	14.7068i	0.594003i	−0.954877	+	0.297002i	$0.904013\pi$
$614$	12.3680	0.499133
$615$	0	0
$616$	15.6121	0.629030
$617$	20.1579i	0.811525i	0.913979	+	0.405762i	$0.132994\pi$
$617$	20.1579i	0.811525i	−0.913979	+	0.405762i	$0.867006\pi$
$618$	2.83098i	0.113879i
$619$	−39.9379	−1.60524	−0.802620	−	0.596490i	$-0.796562\pi$
$619$	−39.9379	−1.60524	−0.802620	+	0.596490i	$0.796562\pi$
$620$	0	0
$621$	15.7914	0.633689
$622$	15.3224i	0.614372i
$623$	− 30.0552i	− 1.20414i
$624$	−1.05863	−0.0423792
$625$	0	0
$626$	22.1268	0.884366
$627$	1.04564i	0.0417590i
$628$	12.2035i	0.486973i
$629$	−0.739689	−0.0294933
$630$	0	0
$631$	40.3189	1.60507	0.802536	−	0.596604i	$-0.203484\pi$
$631$	40.3189	1.60507	0.802536	+	0.596604i	$0.203484\pi$
$632$	16.6707i	0.663127i
$633$	− 11.5630i	− 0.459589i
$634$	−10.1775	−0.404201
$635$	0	0
$636$	5.05863	0.200588
$637$	− 8.86469i	− 0.351232i
$638$	− 4.71982i	− 0.186860i
$639$	−16.1319	−0.638167
$640$	0	0
$641$	−35.7992	−1.41398	−0.706991	−	0.707222i	$-0.749948\pi$
$641$	−35.7992	−1.41398	−0.706991	+	0.707222i	$0.749948\pi$
$642$	5.52932i	0.218225i
$643$	21.1741i	0.835024i	0.908671	+	0.417512i	$0.137098\pi$
$643$	21.1741i	0.835024i	−0.908671	+	0.417512i	$0.862902\pi$
$644$	−19.2051	−0.756788
$645$	0	0
$646$	0.338809	0.0133303
$647$	33.6742i	1.32387i	0.749562	+	0.661934i	$0.230264\pi$
$647$	33.6742i	1.32387i	−0.749562	+	0.661934i	$0.769736\pi$
$648$	− 7.05520i	− 0.277154i
$649$	−52.0483	−2.04308
$650$	0	0
$651$	−15.9087	−0.623512
$652$	− 17.5845i	− 0.688663i
$653$	28.3500i	1.10942i	0.832044	+	0.554710i	$0.187171\pi$
$653$	28.3500i	1.10942i	−0.832044	+	0.554710i	$0.812829\pi$
$654$	−4.67074	−0.182640
$655$	0	0
$656$	−0.0275977	−0.00107751
$657$	10.1319i	0.395282i
$658$	14.3404i	0.559048i
$659$	13.1268	0.511348	0.255674	−	0.966763i	$-0.417703\pi$
$659$	13.1268	0.511348	0.255674	+	0.966763i	$0.417703\pi$
$660$	0	0
$661$	−23.3078	−0.906567	−0.453284	−	0.891366i	$-0.649748\pi$
$661$	−23.3078	−0.906567	−0.453284	+	0.891366i	$0.649748\pi$
$662$	8.69834i	0.338071i
$663$	0.762030i	0.0295948i
$664$	−5.21811	−0.202502
$665$	0	0
$666$	2.85514	0.110634
$667$	5.80605i	0.224811i
$668$	11.7914i	0.456225i
$669$	0.996562	0.0385293
$670$	0	0
$671$	6.38789	0.246602
$672$	− 1.55691i	− 0.0600593i
$673$	− 27.4784i	− 1.05922i	−0.848243	−	0.529608i	$-0.822339\pi$
$673$	− 27.4784i	− 1.05922i	0.848243	−	0.529608i	$-0.177661\pi$
$674$	−16.7198	−0.644024
$675$	0	0
$676$	−7.94137	−0.305437
$677$	− 35.6363i	− 1.36961i	−0.728725	−	0.684807i	$-0.759887\pi$
$677$	− 35.6363i	− 1.36961i	0.728725	−	0.684807i	$-0.240113\pi$
$678$	− 6.60256i	− 0.253570i
$679$	−37.0157	−1.42053
$680$	0	0
$681$	7.49035	0.287031
$682$	48.2277i	1.84673i
$683$	− 10.3319i	− 0.395340i	−0.980269	−	0.197670i	$-0.936662\pi$
$683$	− 10.3319i	− 0.395340i	0.980269	−	0.197670i	$-0.0633375\pi$
$684$	−1.30777	−0.0500040
$685$	0	0
$686$	−10.1173	−0.386279
$687$	10.4914i	0.400272i
$688$	6.61555i	0.252215i
$689$	−24.1725	−0.920897
$690$	0	0
$691$	3.02148	0.114943	0.0574713	−	0.998347i	$-0.481696\pi$
$691$	3.02148	0.114943	0.0574713	+	0.998347i	$0.481696\pi$
$692$	20.7880i	0.790242i
$693$	43.3776i	1.64778i
$694$	−6.74398	−0.255998
$695$	0	0
$696$	−0.470683	−0.0178412
$697$	0.0198655i	0 0.000752458i
$698$	− 7.42504i	− 0.281042i
$699$	−11.0079	−0.416358
$700$	0	0
$701$	37.5500	1.41825	0.709123	−	0.705085i	$-0.249091\pi$
$701$	37.5500	1.41825	0.709123	+	0.705085i	$0.249091\pi$
$702$	− 6.11727i	− 0.230881i
$703$	− 0.483673i	− 0.0182421i
$704$	−4.71982	−0.177885
$705$	0	0
$706$	3.36802	0.126757
$707$	− 10.0146i	− 0.376638i
$708$	5.19051i	0.195071i
$709$	23.7586	0.892273	0.446136	−	0.894965i	$-0.352800\pi$
$709$	23.7586	0.892273	0.446136	+	0.894965i	$0.352800\pi$
$710$	0	0
$711$	−46.3189	−1.73710
$712$	9.08623i	0.340521i
$713$	− 59.3269i	− 2.22181i
$714$	−1.12070	−0.0419413
$715$	0	0
$716$	−7.74742	−0.289535
$717$	− 9.52082i	− 0.355562i
$718$	− 1.81111i	− 0.0675901i
$719$	−48.4768	−1.80788	−0.903940	−	0.427660i	$-0.859338\pi$
$719$	−48.4768	−1.80788	−0.903940	+	0.427660i	$0.859338\pi$
$720$	0	0
$721$	19.8950	0.740927
$722$	− 18.7785i	− 0.698862i
$723$	0.594825i	0.0221218i
$724$	19.7440	0.733779
$725$	0	0
$726$	−5.30777	−0.196990
$727$	− 31.5208i	− 1.16904i	−0.811378	−	0.584521i	$-0.801282\pi$
$727$	− 31.5208i	− 1.16904i	0.811378	−	0.584521i	$-0.198718\pi$
$728$	7.43965i	0.275732i
$729$	15.7620	0.583779
$730$	0	0
$731$	4.76203	0.176130
$732$	− 0.637031i	− 0.0235453i
$733$	21.5017i	0.794184i	0.917779	+	0.397092i	$0.129981\pi$
$733$	21.5017i	0.794184i	−0.917779	+	0.397092i	$0.870019\pi$
$734$	30.8268	1.13784
$735$	0	0
$736$	5.80605	0.214014
$737$	41.5630i	1.53099i
$738$	− 0.0766789i	− 0.00282259i
$739$	−12.5604	−0.462040	−0.231020	−	0.972949i	$-0.574206\pi$
$739$	−12.5604	−0.462040	−0.231020	+	0.972949i	$0.574206\pi$
$740$	0	0
$741$	−0.498281	−0.0183048
$742$	− 35.5500i	− 1.30508i
$743$	26.5275i	0.973199i	0.873625	+	0.486600i	$0.161763\pi$
$743$	26.5275i	0.973199i	−0.873625	+	0.486600i	$0.838237\pi$
$744$	4.80949	0.176325
$745$	0	0
$746$	2.06207	0.0754978
$747$	− 14.4983i	− 0.530464i
$748$	3.39744i	0.124223i
$749$	38.8578	1.41983
$750$	0	0
$751$	−37.4232	−1.36559	−0.682796	−	0.730609i	$-0.739236\pi$
$751$	−37.4232	−1.36559	−0.682796	+	0.730609i	$0.739236\pi$
$752$	− 4.33537i	− 0.158095i
$753$	4.53725i	0.165347i
$754$	2.24914	0.0819089
$755$	0	0
$756$	8.99656	0.327202
$757$	30.0844i	1.09344i	0.837317	+	0.546718i	$0.184123\pi$
$757$	30.0844i	1.09344i	−0.837317	+	0.546718i	$0.815877\pi$
$758$	7.29478i	0.264958i
$759$	12.8984	0.468182
$760$	0	0
$761$	42.1690	1.52863	0.764313	−	0.644845i	$-0.223078\pi$
$761$	42.1690	1.52863	0.764313	+	0.644845i	$0.223078\pi$
$762$	7.63359i	0.276536i
$763$	32.8241i	1.18831i
$764$	−0.397442	−0.0143790
$765$	0	0
$766$	−15.7846	−0.570320
$767$	− 24.8026i	− 0.895571i
$768$	0.470683i	0.0169843i
$769$	29.9587	1.08034	0.540168	−	0.841557i	$-0.318361\pi$
$769$	29.9587	1.08034	0.540168	+	0.841557i	$0.318361\pi$
$770$	0	0
$771$	4.44309	0.160014
$772$	− 4.35342i	− 0.156683i
$773$	50.1966i	1.80545i	0.430221	+	0.902723i	$0.358436\pi$
$773$	50.1966i	1.80545i	−0.430221	+	0.902723i	$0.641564\pi$
$774$	−18.3810	−0.660692
$775$	0	0
$776$	11.1905	0.401716
$777$	1.59988i	0.0573954i
$778$	13.3534i	0.478743i
$779$	−0.0129898	−0.000465406 0
$780$	0	0
$781$	−27.4036	−0.980576
$782$	− 4.17934i	− 0.149453i
$783$	− 2.71982i	− 0.0971986i
$784$	−3.94137	−0.140763
$785$	0	0
$786$	−10.0552	−0.358657
$787$	− 44.5845i	− 1.58927i	−0.607090	−	0.794633i	$-0.707663\pi$
$787$	− 44.5845i	− 1.58927i	0.607090	−	0.794633i	$-0.292337\pi$
$788$	− 6.70683i	− 0.238921i
$789$	5.49035	0.195462
$790$	0	0
$791$	−46.4001	−1.64980
$792$	− 13.1138i	− 0.465980i
$793$	3.04403i	0.108097i
$794$	−20.2130	−0.717334
$795$	0	0
$796$	−9.36297	−0.331862
$797$	− 23.3155i	− 0.825878i	−0.910759	−	0.412939i	$-0.864502\pi$
$797$	− 23.3155i	− 0.825878i	0.910759	−	0.412939i	$-0.135498\pi$
$798$	− 0.732814i	− 0.0259413i
$799$	−3.12070	−0.110403
$800$	0	0
$801$	−25.2457	−0.892013
$802$	15.2897i	0.539899i
$803$	17.2112i	0.607371i
$804$	4.14486	0.146178
$805$	0	0
$806$	−22.9820	−0.809505
$807$	9.48024i	0.333720i
$808$	3.02760i	0.106511i
$809$	−50.6570	−1.78100	−0.890502	−	0.454978i	$-0.849647\pi$
$809$	−50.6570	−1.78100	−0.890502	+	0.454978i	$0.849647\pi$
$810$	0	0
$811$	40.6949	1.42899	0.714496	−	0.699640i	$-0.246656\pi$
$811$	40.6949	1.42899	0.714496	+	0.699640i	$0.246656\pi$
$812$	3.30777i	0.116080i
$813$	− 12.7283i	− 0.446402i
$814$	4.85008	0.169995
$815$	0	0
$816$	0.338809	0.0118607
$817$	3.11383i	0.108939i
$818$	− 14.8302i	− 0.518526i
$819$	−20.6707	−0.722294
$820$	0	0
$821$	−11.8421	−0.413294	−0.206647	−	0.978416i	$-0.566255\pi$
$821$	−11.8421	−0.413294	−0.206647	+	0.978416i	$0.566255\pi$
$822$	4.49217i	0.156682i
$823$	− 14.5243i	− 0.506284i	−0.967429	−	0.253142i	$-0.918536\pi$
$823$	− 14.5243i	− 0.506284i	0.967429	−	0.253142i	$-0.0814640\pi$
$824$	−6.01461	−0.209529
$825$	0	0
$826$	36.4768	1.26919
$827$	− 30.9183i	− 1.07513i	−0.843221	−	0.537567i	$-0.819344\pi$
$827$	− 30.9183i	− 1.07513i	0.843221	−	0.537567i	$-0.180656\pi$
$828$	16.1319i	0.560621i
$829$	−1.26719	−0.0440112	−0.0220056	−	0.999758i	$-0.507005\pi$
$829$	−1.26719	−0.0440112	−0.0220056	+	0.999758i	$0.507005\pi$
$830$	0	0
$831$	5.84664	0.202818
$832$	− 2.24914i	− 0.0779749i
$833$	2.83709i	0.0982994i
$834$	−1.76385	−0.0610771
$835$	0	0
$836$	−2.22154	−0.0768337
$837$	27.7914i	0.960613i
$838$	13.8647i	0.478948i
$839$	−33.1855	−1.14569	−0.572845	−	0.819664i	$-0.694160\pi$
$839$	−33.1855	−1.14569	−0.572845	+	0.819664i	$0.694160\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	2.70178i	0.0931094i
$843$	11.7180i	0.403590i
$844$	24.5665	0.845613
$845$	0	0
$846$	12.0456	0.414138
$847$	37.3009i	1.28167i
$848$	10.7474i	0.369068i
$849$	−2.27674	−0.0781375
$850$	0	0
$851$	−5.96629	−0.204522
$852$	2.73281i	0.0936247i
$853$	42.7743i	1.46456i	0.681002	+	0.732281i	$0.261544\pi$
$853$	42.7743i	1.46456i	−0.681002	+	0.732281i	$0.738456\pi$
$854$	−4.47680	−0.153193
$855$	0	0
$856$	−11.7474	−0.401519
$857$	44.7061i	1.52713i	0.645731	+	0.763565i	$0.276553\pi$
$857$	44.7061i	1.52713i	−0.645731	+	0.763565i	$0.723447\pi$
$858$	− 4.99656i	− 0.170580i
$859$	7.01643	0.239397	0.119699	−	0.992810i	$-0.461807\pi$
$859$	7.01643	0.239397	0.119699	+	0.992810i	$0.461807\pi$
$860$	0	0
$861$	0.0429672	0.00146432
$862$	− 27.3009i	− 0.929872i
$863$	− 40.4768i	− 1.37785i	−0.724834	−	0.688923i	$-0.758084\pi$
$863$	− 40.4768i	− 1.37785i	0.724834	−	0.688923i	$-0.241916\pi$
$864$	−2.71982	−0.0925303
$865$	0	0
$866$	−0.262130	−0.00890755
$867$	7.75774i	0.263466i
$868$	− 33.7992i	− 1.14722i
$869$	−78.6830	−2.66914
$870$	0	0
$871$	−19.8061	−0.671103
$872$	− 9.92332i	− 0.336046i
$873$	31.0923i	1.05232i
$874$	2.73281	0.0924388
$875$	0	0
$876$	1.71639	0.0579913
$877$	6.14325i	0.207443i	0.994606	+	0.103721i	$0.0330750\pi$
$877$	6.14325i	0.207443i	−0.994606	+	0.103721i	$0.966925\pi$
$878$	− 20.4983i	− 0.691783i
$879$	15.7768	0.532140
$880$	0	0
$881$	−56.6639	−1.90905	−0.954527	−	0.298124i	$-0.903639\pi$
$881$	−56.6639	−1.90905	−0.954527	+	0.298124i	$0.903639\pi$
$882$	− 10.9509i	− 0.368737i
$883$	49.5389i	1.66712i	0.552432	+	0.833558i	$0.313700\pi$
$883$	49.5389i	1.66712i	−0.552432	+	0.833558i	$0.686300\pi$
$884$	−1.61899	−0.0544524
$885$	0	0
$886$	−0.456076	−0.0153222
$887$	− 1.03265i	− 0.0346731i	−0.999850	−	0.0173366i	$-0.994481\pi$
$887$	− 1.03265i	− 0.0346731i	0.999850	−	0.0173366i	$-0.00551867\pi$
$888$	− 0.483673i	− 0.0162310i
$889$	53.6458	1.79922
$890$	0	0
$891$	33.2993	1.11557
$892$	2.11727i	0.0708913i
$893$	− 2.04059i	− 0.0682857i
$894$	0.941367	0.0314840
$895$	0	0
$896$	3.30777	0.110505
$897$	6.14648i	0.205225i
$898$	8.62854i	0.287938i
$899$	−10.2181	−0.340793
$900$	0	0
$901$	7.73625	0.257732
$902$	− 0.130256i	− 0.00433705i
$903$	− 10.2998i	− 0.342757i
$904$	14.0276	0.466551
$905$	0	0
$906$	6.70683	0.222820
$907$	− 8.04059i	− 0.266983i	−0.991050	−	0.133492i	$-0.957381\pi$
$907$	− 8.04059i	− 0.266983i	0.991050	−	0.133492i	$-0.0426189\pi$
$908$	15.9138i	0.528117i
$909$	−8.41205	−0.279010
$910$	0	0
$911$	14.0456	0.465353	0.232676	−	0.972554i	$-0.425252\pi$
$911$	14.0456	0.465353	0.232676	+	0.972554i	$0.425252\pi$
$912$	0.221543i	0.00733602i
$913$	− 24.6285i	− 0.815086i
$914$	11.6872	0.386577
$915$	0	0
$916$	−22.2897	−0.736473
$917$	70.6639i	2.33353i
$918$	1.95779i	0.0646168i
$919$	−15.5163	−0.511836	−0.255918	−	0.966698i	$-0.582378\pi$
$919$	−15.5163	−0.511836	−0.255918	+	0.966698i	$0.582378\pi$
$920$	0	0
$921$	5.82142	0.191822
$922$	− 1.82066i	− 0.0599603i
$923$	− 13.0586i	− 0.429830i
$924$	7.34836	0.241743
$925$	0	0
$926$	26.8241	0.881495
$927$	− 16.7113i	− 0.548872i
$928$	− 1.00000i	− 0.0328266i
$929$	−6.93181	−0.227425	−0.113713	−	0.993514i	$-0.536274\pi$
$929$	−6.93181	−0.227425	−0.113713	+	0.993514i	$0.536274\pi$
$930$	0	0
$931$	−1.85514	−0.0607996
$932$	− 23.3871i	− 0.766071i
$933$	7.21199i	0.236110i
$934$	0.366407	0.0119892
$935$	0	0
$936$	6.24914	0.204260
$937$	45.3189i	1.48051i	0.672329	+	0.740253i	$0.265294\pi$
$937$	45.3189i	1.48051i	−0.672329	+	0.740253i	$0.734706\pi$
$938$	− 29.1284i	− 0.951077i
$939$	10.4147	0.339872
$940$	0	0
$941$	7.75086	0.252671	0.126335	−	0.991988i	$-0.459678\pi$
$941$	7.75086	0.252671	0.126335	+	0.991988i	$0.459678\pi$
$942$	5.74398i	0.187149i
$943$	0.160234i	0.00521792i
$944$	−11.0276	−0.358918
$945$	0	0
$946$	−31.2242	−1.01519
$947$	11.1544i	0.362470i	0.983440	+	0.181235i	$0.0580094\pi$
$947$	11.1544i	0.362470i	−0.983440	+	0.181235i	$0.941991\pi$
$948$	7.84664i	0.254847i
$949$	−8.20168	−0.266238
$950$	0	0
$951$	−4.79039	−0.155339
$952$	− 2.38101i	− 0.0771691i
$953$	− 55.1492i	− 1.78646i	−0.449604	−	0.893228i	$-0.648435\pi$
$953$	− 55.1492i	− 1.78646i	0.449604	−	0.893228i	$-0.351565\pi$
$954$	−29.8613	−0.966794
$955$	0	0
$956$	20.2277	0.654209
$957$	− 2.22154i	− 0.0718123i
$958$	− 13.7363i	− 0.443798i
$959$	31.5691	1.01942
$960$	0	0
$961$	73.4097	2.36805
$962$	2.31121i	0.0745165i
$963$	− 32.6397i	− 1.05180i
$964$	−1.26375	−0.0407026
$965$	0	0
$966$	−9.03953	−0.290842
$967$	28.8984i	0.929310i	0.885492	+	0.464655i	$0.153822\pi$
$967$	28.8984i	0.929310i	−0.885492	+	0.464655i	$0.846178\pi$
$968$	− 11.2767i	− 0.362448i
$969$	0.159472	0.00512297
$970$	0	0
$971$	−12.1932	−0.391298	−0.195649	−	0.980674i	$-0.562681\pi$
$971$	−12.1932	−0.391298	−0.195649	+	0.980674i	$0.562681\pi$
$972$	− 11.4802i	− 0.368229i
$973$	12.3956i	0.397385i
$974$	−22.9414	−0.735089
$975$	0	0
$976$	1.35342	0.0433218
$977$	− 20.5861i	− 0.658609i	−0.944224	−	0.329304i	$-0.893186\pi$
$977$	− 20.5861i	− 0.658609i	0.944224	−	0.329304i	$-0.106814\pi$
$978$	− 8.27674i	− 0.264661i
$979$	−42.8854	−1.37062
$980$	0	0
$981$	27.5715	0.880291
$982$	12.8241i	0.409233i
$983$	− 19.7681i	− 0.630506i	−0.949008	−	0.315253i	$-0.897911\pi$
$983$	− 19.7681i	− 0.630506i	0.949008	−	0.315253i	$-0.102089\pi$
$984$	−0.0129898	−0.000414098 0
$985$	0	0
$986$	−0.719824	−0.0229239
$987$	6.74980i	0.214849i
$988$	− 1.05863i	− 0.0336796i
$989$	38.4102	1.22137
$990$	0	0
$991$	47.5139	1.50933	0.754665	−	0.656110i	$-0.227799\pi$
$991$	47.5139	1.50933	0.754665	+	0.656110i	$0.227799\pi$
$992$	10.2181i	0.324425i
$993$	4.09416i	0.129924i
$994$	19.2051	0.609149
$995$	0	0
$996$	−2.45608	−0.0778237
$997$	31.7276i	1.00482i	0.864629	+	0.502411i	$0.167554\pi$
$997$	31.7276i	1.00482i	−0.864629	+	0.502411i	$0.832446\pi$
$998$	0.349979i	0.0110784i
$999$	2.79488	0.0884262

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1450.2.b.k.349.5		6
5.2	odd	4		1450.2.a.q.1.2	✓	3
5.3	odd	4		1450.2.a.s.1.2	yes	3
5.4	even	2	inner	1450.2.b.k.349.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1450.2.a.q.1.2	✓	3	5.2	odd	4
1450.2.a.s.1.2	yes	3	5.3	odd	4
1450.2.b.k.349.2		6	5.4	even	2	inner
1450.2.b.k.349.5		6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1450 = 2 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1450.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +0.470683i q^{3} -1.00000 q^{4} -0.470683 q^{6} +3.30777i q^{7} -1.00000i q^{8} +2.77846 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +0.470683i q^{3} -1.00000 q^{4} -0.470683 q^{6} +3.30777i q^{7} -1.00000i q^{8} +2.77846 q^{9} +4.71982 q^{11} -0.470683i q^{12} +2.24914i q^{13} -3.30777 q^{14} +1.00000 q^{16} -0.719824i q^{17} +2.77846i q^{18} +0.470683 q^{19} -1.55691 q^{21} +4.71982i q^{22} -5.80605i q^{23} +0.470683 q^{24} -2.24914 q^{26} +2.71982i q^{27} -3.30777i q^{28} -1.00000 q^{29} +10.2181 q^{31} +1.00000i q^{32} +2.22154i q^{33} +0.719824 q^{34} -2.77846 q^{36} -1.02760i q^{37} +0.470683i q^{38} -1.05863 q^{39} -0.0275977 q^{41} -1.55691i q^{42} +6.61555i q^{43} -4.71982 q^{44} +5.80605 q^{46} -4.33537i q^{47} +0.470683i q^{48} -3.94137 q^{49} +0.338809 q^{51} -2.24914i q^{52} +10.7474i q^{53} -2.71982 q^{54} +3.30777 q^{56} +0.221543i q^{57} -1.00000i q^{58} -11.0276 q^{59} +1.35342 q^{61} +10.2181i q^{62} +9.19051i q^{63} -1.00000 q^{64} -2.22154 q^{66} +8.80605i q^{67} +0.719824i q^{68} +2.73281 q^{69} -5.80605 q^{71} -2.77846i q^{72} +3.64658i q^{73} +1.02760 q^{74} -0.470683 q^{76} +15.6121i q^{77} -1.05863i q^{78} -16.6707 q^{79} +7.05520 q^{81} -0.0275977i q^{82} -5.21811i q^{83} +1.55691 q^{84} -6.61555 q^{86} -0.470683i q^{87} -4.71982i q^{88} -9.08623 q^{89} -7.43965 q^{91} +5.80605i q^{92} +4.80949i q^{93} +4.33537 q^{94} -0.470683 q^{96} +11.1905i q^{97} -3.94137i q^{98} +13.1138 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} - 2 q^{6}+O(q^{10}) \) 6 * q - 6 * q^4 - 2 * q^6	\( 6 q - 6 q^{4} - 2 q^{6} + 10 q^{11} - 4 q^{14} + 6 q^{16} + 2 q^{19} + 24 q^{21} + 2 q^{24} + 4 q^{26} - 6 q^{29} + 8 q^{31} - 14 q^{34} - 8 q^{39} + 34 q^{41} - 10 q^{44} - 16 q^{46} - 22 q^{49} + 22 q^{51} + 2 q^{54} + 4 q^{56} - 32 q^{59} + 4 q^{61} - 6 q^{64} - 30 q^{66} - 12 q^{69} + 16 q^{71} - 28 q^{74} - 2 q^{76} - 26 q^{81} - 24 q^{84} - 8 q^{86} - 22 q^{89} - 8 q^{91} - 24 q^{94} - 2 q^{96} + 12 q^{99}+O(q^{100}) \) 6 * q - 6 * q^4 - 2 * q^6 + 10 * q^11 - 4 * q^14 + 6 * q^16 + 2 * q^19 + 24 * q^21 + 2 * q^24 + 4 * q^26 - 6 * q^29 + 8 * q^31 - 14 * q^34 - 8 * q^39 + 34 * q^41 - 10 * q^44 - 16 * q^46 - 22 * q^49 + 22 * q^51 + 2 * q^54 + 4 * q^56 - 32 * q^59 + 4 * q^61 - 6 * q^64 - 30 * q^66 - 12 * q^69 + 16 * q^71 - 28 * q^74 - 2 * q^76 - 26 * q^81 - 24 * q^84 - 8 * q^86 - 22 * q^89 - 8 * q^91 - 24 * q^94 - 2 * q^96 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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