LMFDB - Embedded newform 3450.2.d.ba.2899.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3450,2,Mod(2899,3450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3450, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("3450.2899");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3450.d (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:	$27.5483886973$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.181494784.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 12x^{3} + 49x^{2} - 14x + 2 $ x^6 - 2x^5 + 2x^4 + 12x^3 + 49x^2 - 14*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2899.3
Root			$-1.51966 - 1.51966i$ of defining polynomial
Character	$\chi$	$=$	3450.2899
Dual form			3450.2.d.ba.2899.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} +4.03932i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} +4.03932i q^{7} +1.00000i q^{8} -1.00000 q^{9} -5.69736 q^{11} +1.00000i q^{12} -0.381275i q^{13} +4.03932 q^{14} +1.00000 q^{16} -3.65804i q^{17} +1.00000i q^{18} -0.381275 q^{19} +4.03932 q^{21} +5.69736i q^{22} +1.00000i q^{23} +1.00000 q^{24} -0.381275 q^{26} +1.00000i q^{27} -4.03932i q^{28} +1.00000 q^{29} +6.00000 q^{31} -1.00000i q^{32} +5.69736i q^{33} -3.65804 q^{34} +1.00000 q^{36} +3.65804i q^{37} +0.381275i q^{38} -0.381275 q^{39} +5.61873 q^{41} -4.03932i q^{42} -3.61873i q^{43} +5.69736 q^{44} +1.00000 q^{46} -3.38127i q^{47} -1.00000i q^{48} -9.31608 q^{49} -3.65804 q^{51} +0.381275i q^{52} -9.31608i q^{53} +1.00000 q^{54} -4.03932 q^{56} +0.381275i q^{57} -1.00000i q^{58} -13.3947 q^{59} +14.0786 q^{61} -6.00000i q^{62} -4.03932i q^{63} -1.00000 q^{64} +5.69736 q^{66} -2.76255i q^{67} +3.65804i q^{68} +1.00000 q^{69} +10.6974 q^{71} -1.00000i q^{72} +7.07863i q^{73} +3.65804 q^{74} +0.381275 q^{76} -23.0134i q^{77} +0.381275i q^{78} -5.69736 q^{79} +1.00000 q^{81} -5.61873i q^{82} -16.1180i q^{83} -4.03932 q^{84} -3.61873 q^{86} -1.00000i q^{87} -5.69736i q^{88} -5.65804 q^{89} +1.54009 q^{91} -1.00000i q^{92} -6.00000i q^{93} -3.38127 q^{94} -1.00000 q^{96} -4.07863i q^{97} +9.31608i q^{98} +5.69736 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} - 6 q^{6} - 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^4 - 6 * q^6 - 6 * q^9	$ 6 q - 6 q^{4} - 6 q^{6} - 6 q^{9} + 6 q^{11} + 2 q^{14} + 6 q^{16} + 2 q^{19} + 2 q^{21} + 6 q^{24} + 2 q^{26} + 6 q^{29} + 36 q^{31} - 4 q^{34} + 6 q^{36} + 2 q^{39} + 38 q^{41} - 6 q^{44} + 6 q^{46} - 20 q^{49} - 4 q^{51} + 6 q^{54} - 2 q^{56} + 40 q^{61} - 6 q^{64} - 6 q^{66} + 6 q^{69} + 24 q^{71} + 4 q^{74} - 2 q^{76} + 6 q^{79} + 6 q^{81} - 2 q^{84} - 26 q^{86} - 16 q^{89} + 58 q^{91} - 16 q^{94} - 6 q^{96} - 6 q^{99}+O(q^{100}) $ 6 * q - 6 * q^4 - 6 * q^6 - 6 * q^9 + 6 * q^11 + 2 * q^14 + 6 * q^16 + 2 * q^19 + 2 * q^21 + 6 * q^24 + 2 * q^26 + 6 * q^29 + 36 * q^31 - 4 * q^34 + 6 * q^36 + 2 * q^39 + 38 * q^41 - 6 * q^44 + 6 * q^46 - 20 * q^49 - 4 * q^51 + 6 * q^54 - 2 * q^56 + 40 * q^61 - 6 * q^64 - 6 * q^66 + 6 * q^69 + 24 * q^71 + 4 * q^74 - 2 * q^76 + 6 * q^79 + 6 * q^81 - 2 * q^84 - 26 * q^86 - 16 * q^89 + 58 * q^91 - 16 * q^94 - 6 * q^96 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3450\mathbb{Z}\right)^\times$.

$n$	$277$	$1151$	$1201$
$\chi(n)$	$-1$	$1$	$1$

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
$3$	− 1.00000i	− 0.577350i
$3$	− 1.00000i	− 0.577350i
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−1.00000	−0.408248
$7$	4.03932i	1.52672i	0.645974	+	0.763359i	$0.276451\pi$
$7$	4.03932i	1.52672i	−0.645974	+	0.763359i	$0.723549\pi$
$8$	1.00000i	0.353553i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	−5.69736	−1.71782	−0.858909	−	0.512128i	$-0.828857\pi$
$11$	−5.69736	−1.71782	−0.858909	+	0.512128i	$0.828857\pi$
$12$	1.00000i	0.288675i
$13$	− 0.381275i	− 0.105747i	−0.998601	−	0.0528733i	$-0.983162\pi$
$13$	− 0.381275i	− 0.105747i	0.998601	−	0.0528733i	$-0.0168380\pi$
$14$	4.03932	1.07955
$15$	0	0
$16$	1.00000	0.250000
$17$	− 3.65804i	− 0.887206i	−0.896223	−	0.443603i	$-0.853700\pi$
$17$	− 3.65804i	− 0.887206i	0.896223	−	0.443603i	$-0.146300\pi$
$18$	1.00000i	0.235702i
$19$	−0.381275	−0.0874705	−0.0437352	−	0.999043i	$-0.513926\pi$
$19$	−0.381275	−0.0874705	−0.0437352	+	0.999043i	$0.513926\pi$
$20$	0	0
$21$	4.03932	0.881451
$22$	5.69736i	1.21468i
$23$	1.00000i	0.208514i
$23$	1.00000i	0.208514i
$24$	1.00000	0.204124
$25$	0	0
$26$	−0.381275	−0.0747742
$27$	1.00000i	0.192450i
$28$	− 4.03932i	− 0.763359i
$29$	1.00000	0.185695	0.0928477	−	0.995680i	$-0.470403\pi$
$29$	1.00000	0.185695	0.0928477	+	0.995680i	$0.470403\pi$
$30$	0	0
$31$	6.00000	1.07763	0.538816	−	0.842424i	$-0.318872\pi$
$31$	6.00000	1.07763	0.538816	+	0.842424i	$0.318872\pi$
$32$	− 1.00000i	− 0.176777i
$33$	5.69736i	0.991783i
$34$	−3.65804	−0.627349
$35$	0	0
$36$	1.00000	0.166667
$37$	3.65804i	0.601378i	0.953722	+	0.300689i	$0.0972167\pi$
$37$	3.65804i	0.601378i	−0.953722	+	0.300689i	$0.902783\pi$
$38$	0.381275i	0.0618510i
$39$	−0.381275	−0.0610528
$40$	0	0
$41$	5.61873	0.877497	0.438749	−	0.898610i	$-0.355422\pi$
$41$	5.61873	0.877497	0.438749	+	0.898610i	$0.355422\pi$
$42$	− 4.03932i	− 0.623280i
$43$	− 3.61873i	− 0.551850i	−0.961179	−	0.275925i	$-0.911016\pi$
$43$	− 3.61873i	− 0.551850i	0.961179	−	0.275925i	$-0.0889842\pi$
$44$	5.69736	0.858909
$45$	0	0
$46$	1.00000	0.147442
$47$	− 3.38127i	− 0.493210i	−0.969116	−	0.246605i	$-0.920685\pi$
$47$	− 3.38127i	− 0.493210i	0.969116	−	0.246605i	$-0.0793150\pi$
$48$	− 1.00000i	− 0.144338i
$49$	−9.31608	−1.33087
$50$	0	0
$51$	−3.65804	−0.512228
$52$	0.381275i	0.0528733i
$53$	− 9.31608i	− 1.27966i	−0.768515	−	0.639831i	$-0.779004\pi$
$53$	− 9.31608i	− 1.27966i	0.768515	−	0.639831i	$-0.220996\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	−4.03932	−0.539776
$57$	0.381275i	0.0505011i
$58$	− 1.00000i	− 0.131306i
$59$	−13.3947	−1.74384	−0.871922	−	0.489645i	$-0.837126\pi$
$59$	−13.3947	−1.74384	−0.871922	+	0.489645i	$0.837126\pi$
$60$	0	0
$61$	14.0786	1.80258	0.901292	−	0.433212i	$-0.142620\pi$
$61$	14.0786	1.80258	0.901292	+	0.433212i	$0.142620\pi$
$62$	− 6.00000i	− 0.762001i
$63$	− 4.03932i	− 0.508906i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	5.69736	0.701297
$67$	− 2.76255i	− 0.337499i	−0.985659	−	0.168750i	$-0.946027\pi$
$67$	− 2.76255i	− 0.337499i	0.985659	−	0.168750i	$-0.0539729\pi$
$68$	3.65804i	0.443603i
$69$	1.00000	0.120386
$70$	0	0
$71$	10.6974	1.26954	0.634772	−	0.772700i	$-0.281094\pi$
$71$	10.6974	1.26954	0.634772	+	0.772700i	$0.281094\pi$
$72$	− 1.00000i	− 0.117851i
$73$	7.07863i	0.828492i	0.910165	+	0.414246i	$0.135955\pi$
$73$	7.07863i	0.828492i	−0.910165	+	0.414246i	$0.864045\pi$
$74$	3.65804	0.425239
$75$	0	0
$76$	0.381275	0.0437352
$77$	− 23.0134i	− 2.62263i
$78$	0.381275i	0.0431709i
$79$	−5.69736	−0.641003	−0.320502	−	0.947248i	$-0.603851\pi$
$79$	−5.69736	−0.641003	−0.320502	+	0.947248i	$0.603851\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	− 5.61873i	− 0.620484i
$83$	− 16.1180i	− 1.76918i	−0.466374	−	0.884588i	$-0.654440\pi$
$83$	− 16.1180i	− 1.76918i	0.466374	−	0.884588i	$-0.345560\pi$
$84$	−4.03932	−0.440726
$85$	0	0
$86$	−3.61873	−0.390217
$87$	− 1.00000i	− 0.107211i
$88$	− 5.69736i	− 0.607341i
$89$	−5.65804	−0.599751	−0.299876	−	0.953978i	$-0.596945\pi$
$89$	−5.65804	−0.599751	−0.299876	+	0.953978i	$0.596945\pi$
$90$	0	0
$91$	1.54009	0.161445
$92$	− 1.00000i	− 0.104257i
$93$	− 6.00000i	− 0.622171i
$94$	−3.38127	−0.348752
$95$	0	0
$96$	−1.00000	−0.102062
$97$	− 4.07863i	− 0.414123i	−0.978328	−	0.207061i	$-0.933610\pi$
$97$	− 4.07863i	− 0.414123i	0.978328	−	0.207061i	$-0.0663900\pi$
$98$	9.31608i	0.941067i
$99$	5.69736	0.572606
$100$	0	0
$101$	16.7760	1.66927	0.834637	−	0.550801i	$-0.185677\pi$
$101$	16.7760	1.66927	0.834637	+	0.550801i	$0.185677\pi$
$102$	3.65804i	0.362200i
$103$	− 13.3554i	− 1.31595i	−0.753041	−	0.657973i	$-0.771414\pi$
$103$	− 13.3554i	− 1.31595i	0.753041	−	0.657973i	$-0.228586\pi$
$104$	0.381275	0.0373871
$105$	0	0
$106$	−9.31608	−0.904858
$107$	− 6.76255i	− 0.653760i	−0.945066	−	0.326880i	$-0.894003\pi$
$107$	− 6.76255i	− 0.653760i	0.945066	−	0.326880i	$-0.105997\pi$
$108$	− 1.00000i	− 0.0962250i
$109$	13.0528	1.25023	0.625114	−	0.780534i	$-0.285052\pi$
$109$	13.0528	1.25023	0.625114	+	0.780534i	$0.285052\pi$
$110$	0	0
$111$	3.65804	0.347206
$112$	4.03932i	0.381680i
$113$	1.65804i	0.155976i	0.996954	+	0.0779878i	$0.0248495\pi$
$113$	1.65804i	0.155976i	−0.996954	+	0.0779878i	$0.975150\pi$
$114$	0.381275	0.0357097
$115$	0	0
$116$	−1.00000	−0.0928477
$117$	0.381275i	0.0352489i
$118$	13.3947i	1.23308i
$119$	14.7760	1.35451
$120$	0	0
$121$	21.4599	1.95090
$122$	− 14.0786i	− 1.27462i
$123$	− 5.61873i	− 0.506623i
$124$	−6.00000	−0.538816
$125$	0	0
$126$	−4.03932	−0.359851
$127$	− 18.6322i	− 1.65334i	−0.562689	−	0.826669i	$-0.690233\pi$
$127$	− 18.6322i	− 1.65334i	0.562689	−	0.826669i	$-0.309767\pi$
$128$	1.00000i	0.0883883i
$129$	−3.61873	−0.318611
$130$	0	0
$131$	−17.4734	−1.52665	−0.763327	−	0.646012i	$-0.776435\pi$
$131$	−17.4734	−1.52665	−0.763327	+	0.646012i	$0.776435\pi$
$132$	− 5.69736i	− 0.495892i
$133$	− 1.54009i	− 0.133543i
$134$	−2.76255	−0.238648
$135$	0	0
$136$	3.65804	0.313675
$137$	− 14.3420i	− 1.22532i	−0.790348	−	0.612658i	$-0.790100\pi$
$137$	− 14.3420i	− 1.22532i	0.790348	−	0.612658i	$-0.209900\pi$
$138$	− 1.00000i	− 0.0851257i
$139$	8.01344	0.679692	0.339846	−	0.940481i	$-0.389625\pi$
$139$	8.01344	0.679692	0.339846	+	0.940481i	$0.389625\pi$
$140$	0	0
$141$	−3.38127	−0.284755
$142$	− 10.6974i	− 0.897702i
$143$	2.17226i	0.181654i
$144$	−1.00000	−0.0833333
$145$	0	0
$146$	7.07863	0.585832
$147$	9.31608i	0.768378i
$148$	− 3.65804i	− 0.300689i
$149$	−3.23745	−0.265222	−0.132611	−	0.991168i	$-0.542336\pi$
$149$	−3.23745	−0.265222	−0.132611	+	0.991168i	$0.542336\pi$
$150$	0	0
$151$	−9.31608	−0.758132	−0.379066	−	0.925370i	$-0.623755\pi$
$151$	−9.31608	−0.758132	−0.379066	+	0.925370i	$0.623755\pi$
$152$	− 0.381275i	− 0.0309255i
$153$	3.65804i	0.295735i
$154$	−23.0134	−1.85448
$155$	0	0
$156$	0.381275	0.0305264
$157$	− 6.84118i	− 0.545986i	−0.962016	−	0.272993i	$-0.911986\pi$
$157$	− 6.84118i	− 0.545986i	0.962016	−	0.272993i	$-0.0880136\pi$
$158$	5.69736i	0.453258i
$159$	−9.31608	−0.738814
$160$	0	0
$161$	−4.03932	−0.318343
$162$	− 1.00000i	− 0.0785674i
$163$	− 4.76255i	− 0.373032i	−0.982452	−	0.186516i	$-0.940280\pi$
$163$	− 4.76255i	− 0.373032i	0.982452	−	0.186516i	$-0.0597196\pi$
$164$	−5.61873	−0.438749
$165$	0	0
$166$	−16.1180	−1.25100
$167$	14.8546i	1.14949i	0.818334	+	0.574743i	$0.194898\pi$
$167$	14.8546i	1.14949i	−0.818334	+	0.574743i	$0.805102\pi$
$168$	4.03932i	0.311640i
$169$	12.8546	0.988818
$170$	0	0
$171$	0.381275	0.0291568
$172$	3.61873i	0.275925i
$173$	− 9.69736i	− 0.737277i	−0.929573	−	0.368638i	$-0.879824\pi$
$173$	− 9.69736i	− 0.737277i	0.929573	−	0.368638i	$-0.120176\pi$
$174$	−1.00000	−0.0758098
$175$	0	0
$176$	−5.69736	−0.429455
$177$	13.3947i	1.00681i
$178$	5.65804i	0.424088i
$179$	5.31608	0.397343	0.198671	−	0.980066i	$-0.436337\pi$
$179$	5.31608	0.397343	0.198671	+	0.980066i	$0.436337\pi$
$180$	0	0
$181$	24.3688	1.81132	0.905661	−	0.424002i	$-0.139375\pi$
$181$	24.3688	1.81132	0.905661	+	0.424002i	$0.139375\pi$
$182$	− 1.54009i	− 0.114159i
$183$	− 14.0786i	− 1.04072i
$184$	−1.00000	−0.0737210
$185$	0	0
$186$	−6.00000	−0.439941
$187$	20.8412i	1.52406i
$188$	3.38127i	0.246605i
$189$	−4.03932	−0.293817
$190$	0	0
$191$	10.4599	0.756853	0.378426	−	0.925631i	$-0.376465\pi$
$191$	10.4599	0.756853	0.378426	+	0.925631i	$0.376465\pi$
$192$	1.00000i	0.0721688i
$193$	14.0134i	1.00871i	0.863496	+	0.504355i	$0.168270\pi$
$193$	14.0134i	1.00871i	−0.863496	+	0.504355i	$0.831730\pi$
$194$	−4.07863	−0.292829
$195$	0	0
$196$	9.31608	0.665435
$197$	8.47335i	0.603702i	0.953355	+	0.301851i	$0.0976044\pi$
$197$	8.47335i	0.603702i	−0.953355	+	0.301851i	$0.902396\pi$
$198$	− 5.69736i	− 0.404894i
$199$	−1.19813	−0.0849334	−0.0424667	−	0.999098i	$-0.513522\pi$
$199$	−1.19813	−0.0849334	−0.0424667	+	0.999098i	$0.513522\pi$
$200$	0	0
$201$	−2.76255	−0.194855
$202$	− 16.7760i	− 1.18035i
$203$	4.03932i	0.283505i
$204$	3.65804	0.256114
$205$	0	0
$206$	−13.3554	−0.930515
$207$	− 1.00000i	− 0.0695048i
$208$	− 0.381275i	− 0.0264367i
$209$	2.17226	0.150258
$210$	0	0
$211$	−16.2225	−1.11680	−0.558400	−	0.829572i	$-0.688585\pi$
$211$	−16.2225	−1.11680	−0.558400	+	0.829572i	$0.688585\pi$
$212$	9.31608i	0.639831i
$213$	− 10.6974i	− 0.732971i
$214$	−6.76255	−0.462278
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	24.2359i	1.64524i
$218$	− 13.0528i	− 0.884045i
$219$	7.07863	0.478330
$220$	0	0
$221$	−1.39472	−0.0938190
$222$	− 3.65804i	− 0.245512i
$223$	13.6037i	0.910973i	0.890243	+	0.455487i	$0.150535\pi$
$223$	13.6037i	0.910973i	−0.890243	+	0.455487i	$0.849465\pi$
$224$	4.03932	0.269888
$225$	0	0
$226$	1.65804	0.110291
$227$	− 12.4992i	− 0.829603i	−0.909912	−	0.414801i	$-0.863851\pi$
$227$	− 12.4992i	− 0.829603i	0.909912	−	0.414801i	$-0.136149\pi$
$228$	− 0.381275i	− 0.0252505i
$229$	−21.4734	−1.41900	−0.709500	−	0.704706i	$-0.751079\pi$
$229$	−21.4734	−1.41900	−0.709500	+	0.704706i	$0.751079\pi$
$230$	0	0
$231$	−23.0134	−1.51417
$232$	1.00000i	0.0656532i
$233$	11.1438i	0.730056i	0.930996	+	0.365028i	$0.118941\pi$
$233$	11.1438i	0.730056i	−0.930996	+	0.365028i	$0.881059\pi$
$234$	0.381275	0.0249247
$235$	0	0
$236$	13.3947	0.871922
$237$	5.69736i	0.370083i
$238$	− 14.7760i	− 0.957785i
$239$	−22.1707	−1.43410	−0.717052	−	0.697020i	$-0.754509\pi$
$239$	−22.1707	−1.43410	−0.717052	+	0.697020i	$0.754509\pi$
$240$	0	0
$241$	−13.8696	−0.893421	−0.446710	−	0.894679i	$-0.647405\pi$
$241$	−13.8696	−0.893421	−0.446710	+	0.894679i	$0.647405\pi$
$242$	− 21.4599i	− 1.37950i
$243$	− 1.00000i	− 0.0641500i
$244$	−14.0786	−0.901292
$245$	0	0
$246$	−5.61873	−0.358237
$247$	0.145371i	0.00924971i
$248$	6.00000i	0.381000i
$249$	−16.1180	−1.02143
$250$	0	0
$251$	5.73668	0.362096	0.181048	−	0.983474i	$-0.442051\pi$
$251$	5.73668	0.362096	0.181048	+	0.983474i	$0.442051\pi$
$252$	4.03932i	0.254453i
$253$	− 5.69736i	− 0.358190i
$254$	−18.6322	−1.16909
$255$	0	0
$256$	1.00000	0.0625000
$257$	− 20.6322i	− 1.28700i	−0.765446	−	0.643500i	$-0.777482\pi$
$257$	− 20.6322i	− 1.28700i	0.765446	−	0.643500i	$-0.222518\pi$
$258$	3.61873i	0.225292i
$259$	−14.7760	−0.918136
$260$	0	0
$261$	−1.00000	−0.0618984
$262$	17.4734i	1.07951i
$263$	− 19.8696i	− 1.22521i	−0.790388	−	0.612607i	$-0.790121\pi$
$263$	− 19.8696i	− 1.22521i	0.790388	−	0.612607i	$-0.209879\pi$
$264$	−5.69736	−0.350648
$265$	0	0
$266$	−1.54009	−0.0944290
$267$	5.65804i	0.346267i
$268$	2.76255i	0.168750i
$269$	8.17226	0.498272	0.249136	−	0.968469i	$-0.419853\pi$
$269$	8.17226	0.498272	0.249136	+	0.968469i	$0.419853\pi$
$270$	0	0
$271$	−11.3947	−0.692180	−0.346090	−	0.938201i	$-0.612491\pi$
$271$	−11.3947	−0.692180	−0.346090	+	0.938201i	$0.612491\pi$
$272$	− 3.65804i	− 0.221801i
$273$	− 1.54009i	− 0.0932105i
$274$	−14.3420	−0.866429
$275$	0	0
$276$	−1.00000	−0.0601929
$277$	− 4.93481i	− 0.296504i	−0.988950	−	0.148252i	$-0.952635\pi$
$277$	− 4.93481i	− 0.296504i	0.988950	−	0.148252i	$-0.0473647\pi$
$278$	− 8.01344i	− 0.480614i
$279$	−6.00000	−0.359211
$280$	0	0
$281$	14.8955	0.888591	0.444295	−	0.895880i	$-0.353454\pi$
$281$	14.8955	0.888591	0.444295	+	0.895880i	$0.353454\pi$
$282$	3.38127i	0.201352i
$283$	14.6322i	0.869792i	0.900481	+	0.434896i	$0.143215\pi$
$283$	14.6322i	0.869792i	−0.900481	+	0.434896i	$0.856785\pi$
$284$	−10.6974	−0.634772
$285$	0	0
$286$	2.17226	0.128448
$287$	22.6958i	1.33969i
$288$	1.00000i	0.0589256i
$289$	3.61873	0.212866
$290$	0	0
$291$	−4.07863	−0.239094
$292$	− 7.07863i	− 0.414246i
$293$	9.39472i	0.548845i	0.961609	+	0.274423i	$0.0884867\pi$
$293$	9.39472i	0.548845i	−0.961609	+	0.274423i	$0.911513\pi$
$294$	9.31608	0.543325
$295$	0	0
$296$	−3.65804	−0.212619
$297$	− 5.69736i	− 0.330594i
$298$	3.23745i	0.187540i
$299$	0.381275	0.0220497
$300$	0	0
$301$	14.6172	0.842520
$302$	9.31608i	0.536080i
$303$	− 16.7760i	− 0.963756i
$304$	−0.381275	−0.0218676
$305$	0	0
$306$	3.65804	0.209116
$307$	9.22401i	0.526442i	0.964736	+	0.263221i	$0.0847848\pi$
$307$	9.22401i	0.526442i	−0.964736	+	0.263221i	$0.915215\pi$
$308$	23.0134i	1.31131i
$309$	−13.3554	−0.759762
$310$	0	0
$311$	11.3295	0.642439	0.321219	−	0.947005i	$-0.395907\pi$
$311$	11.3295	0.642439	0.321219	+	0.947005i	$0.395907\pi$
$312$	− 0.381275i	− 0.0215854i
$313$	− 15.6037i	− 0.881975i	−0.897513	−	0.440988i	$-0.854628\pi$
$313$	− 15.6037i	− 0.881975i	0.897513	−	0.440988i	$-0.145372\pi$
$314$	−6.84118	−0.386070
$315$	0	0
$316$	5.69736	0.320502
$317$	− 11.0000i	− 0.617822i	−0.951091	−	0.308911i	$-0.900036\pi$
$317$	− 11.0000i	− 0.617822i	0.951091	−	0.308911i	$-0.0999645\pi$
$318$	9.31608i	0.522420i
$319$	−5.69736	−0.318991
$320$	0	0
$321$	−6.76255	−0.377449
$322$	4.03932i	0.225102i
$323$	1.39472i	0.0776043i
$324$	−1.00000	−0.0555556
$325$	0	0
$326$	−4.76255	−0.263773
$327$	− 13.0528i	− 0.721819i
$328$	5.61873i	0.310242i
$329$	13.6580	0.752992
$330$	0	0
$331$	2.69736	0.148260	0.0741302	−	0.997249i	$-0.476382\pi$
$331$	2.69736	0.148260	0.0741302	+	0.997249i	$0.476382\pi$
$332$	16.1180i	0.884588i
$333$	− 3.65804i	− 0.200459i
$334$	14.8546	0.812809
$335$	0	0
$336$	4.03932	0.220363
$337$	− 17.3161i	− 0.943267i	−0.881795	−	0.471634i	$-0.843664\pi$
$337$	− 17.3161i	− 0.943267i	0.881795	−	0.471634i	$-0.156336\pi$
$338$	− 12.8546i	− 0.699200i
$339$	1.65804	0.0900525
$340$	0	0
$341$	−34.1842	−1.85118
$342$	− 0.381275i	− 0.0206170i
$343$	− 9.35540i	− 0.505144i
$344$	3.61873	0.195109
$345$	0	0
$346$	−9.69736	−0.521333
$347$	− 3.47335i	− 0.186459i	−0.995645	−	0.0932297i	$-0.970281\pi$
$347$	− 3.47335i	− 0.186459i	0.995645	−	0.0932297i	$-0.0297191\pi$
$348$	1.00000i	0.0536056i
$349$	13.1438	0.703573	0.351786	−	0.936080i	$-0.385574\pi$
$349$	13.1438	0.703573	0.351786	+	0.936080i	$0.385574\pi$
$350$	0	0
$351$	0.381275	0.0203509
$352$	5.69736i	0.303670i
$353$	13.8546i	0.737408i	0.929547	+	0.368704i	$0.120198\pi$
$353$	13.8546i	0.737408i	−0.929547	+	0.368704i	$0.879802\pi$
$354$	13.3947	0.711921
$355$	0	0
$356$	5.65804	0.299876
$357$	− 14.7760i	− 0.782029i
$358$	− 5.31608i	− 0.280964i
$359$	−14.9348	−0.788229	−0.394115	−	0.919061i	$-0.628949\pi$
$359$	−14.9348	−0.788229	−0.394115	+	0.919061i	$0.628949\pi$
$360$	0	0
$361$	−18.8546	−0.992349
$362$	− 24.3688i	− 1.28080i
$363$	− 21.4599i	− 1.12635i
$364$	−1.54009	−0.0807227
$365$	0	0
$366$	−14.0786	−0.735902
$367$	28.9348i	1.51038i	0.655503	+	0.755192i	$0.272457\pi$
$367$	28.9348i	1.51038i	−0.655503	+	0.755192i	$0.727543\pi$
$368$	1.00000i	0.0521286i
$369$	−5.61873	−0.292499
$370$	0	0
$371$	37.6306	1.95368
$372$	6.00000i	0.311086i
$373$	− 26.4475i	− 1.36940i	−0.728826	−	0.684699i	$-0.759934\pi$
$373$	− 26.4475i	− 1.36940i	0.728826	−	0.684699i	$-0.240066\pi$
$374$	20.8412	1.07767
$375$	0	0
$376$	3.38127	0.174376
$377$	− 0.381275i	− 0.0196367i
$378$	4.03932i	0.207760i
$379$	26.2359	1.34765	0.673824	−	0.738892i	$-0.264651\pi$
$379$	26.2359	1.34765	0.673824	+	0.738892i	$0.264651\pi$
$380$	0	0
$381$	−18.6322	−0.954555
$382$	− 10.4599i	− 0.535176i
$383$	29.7242i	1.51884i	0.650602	+	0.759419i	$0.274517\pi$
$383$	29.7242i	1.51884i	−0.650602	+	0.759419i	$0.725483\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	14.0134	0.713266
$387$	3.61873i	0.183950i
$388$	4.07863i	0.207061i
$389$	−8.47490	−0.429695	−0.214847	−	0.976648i	$-0.568925\pi$
$389$	−8.47490	−0.429695	−0.214847	+	0.976648i	$0.568925\pi$
$390$	0	0
$391$	3.65804	0.184995
$392$	− 9.31608i	− 0.470533i
$393$	17.4734i	0.881414i
$394$	8.47335	0.426881
$395$	0	0
$396$	−5.69736	−0.286303
$397$	21.8696i	1.09760i	0.835952	+	0.548802i	$0.184916\pi$
$397$	21.8696i	1.09760i	−0.835952	+	0.548802i	$0.815084\pi$
$398$	1.19813i	0.0600570i
$399$	−1.54009	−0.0771010
$400$	0	0
$401$	−4.71080	−0.235246	−0.117623	−	0.993058i	$-0.537527\pi$
$401$	−4.71080	−0.235246	−0.117623	+	0.993058i	$0.537527\pi$
$402$	2.76255i	0.137783i
$403$	− 2.28765i	− 0.113956i
$404$	−16.7760	−0.834637
$405$	0	0
$406$	4.03932	0.200468
$407$	− 20.8412i	− 1.03306i
$408$	− 3.65804i	− 0.181100i
$409$	−35.1055	−1.73586	−0.867928	−	0.496690i	$-0.834549\pi$
$409$	−35.1055	−1.73586	−0.867928	+	0.496690i	$0.834549\pi$
$410$	0	0
$411$	−14.3420	−0.707437
$412$	13.3554i	0.657973i
$413$	− 54.1055i	− 2.66236i
$414$	−1.00000	−0.0491473
$415$	0	0
$416$	−0.381275	−0.0186935
$417$	− 8.01344i	− 0.392420i
$418$	− 2.17226i	− 0.106249i
$419$	24.7232	1.20781	0.603904	−	0.797057i	$-0.293611\pi$
$419$	24.7232	1.20781	0.603904	+	0.797057i	$0.293611\pi$
$420$	0	0
$421$	17.4734	0.851599	0.425800	−	0.904817i	$-0.359993\pi$
$421$	17.4734	0.851599	0.425800	+	0.904817i	$0.359993\pi$
$422$	16.2225i	0.789697i
$423$	3.38127i	0.164403i
$424$	9.31608	0.452429
$425$	0	0
$426$	−10.6974	−0.518289
$427$	56.8681i	2.75204i
$428$	6.76255i	0.326880i
$429$	2.17226	0.104878
$430$	0	0
$431$	4.84118	0.233192	0.116596	−	0.993179i	$-0.462802\pi$
$431$	4.84118	0.233192	0.116596	+	0.993179i	$0.462802\pi$
$432$	1.00000i	0.0481125i
$433$	− 16.8412i	− 0.809336i	−0.914464	−	0.404668i	$-0.867387\pi$
$433$	− 16.8412i	− 0.809336i	0.914464	−	0.404668i	$-0.132613\pi$
$434$	24.2359	1.16336
$435$	0	0
$436$	−13.0528	−0.625114
$437$	− 0.381275i	− 0.0182389i
$438$	− 7.07863i	− 0.338230i
$439$	20.7108	0.988473	0.494236	−	0.869328i	$-0.335448\pi$
$439$	20.7108	0.988473	0.494236	+	0.869328i	$0.335448\pi$
$440$	0	0
$441$	9.31608	0.443623
$442$	1.39472i	0.0663401i
$443$	14.8412i	0.705126i	0.935788	+	0.352563i	$0.114690\pi$
$443$	14.8412i	0.705126i	−0.935788	+	0.352563i	$0.885310\pi$
$444$	−3.65804	−0.173603
$445$	0	0
$446$	13.6037	0.644155
$447$	3.23745i	0.153126i
$448$	− 4.03932i	− 0.190840i
$449$	30.1573	1.42321	0.711605	−	0.702580i	$-0.247969\pi$
$449$	30.1573	1.42321	0.711605	+	0.702580i	$0.247969\pi$
$450$	0	0
$451$	−32.0119	−1.50738
$452$	− 1.65804i	− 0.0779878i
$453$	9.31608i	0.437708i
$454$	−12.4992	−0.586618
$455$	0	0
$456$	−0.381275	−0.0178548
$457$	12.7625i	0.597007i	0.954409	+	0.298503i	$0.0964874\pi$
$457$	12.7625i	0.597007i	−0.954409	+	0.298503i	$0.903513\pi$
$458$	21.4734i	1.00338i
$459$	3.65804	0.170743
$460$	0	0
$461$	17.2359	0.802756	0.401378	−	0.915912i	$-0.368531\pi$
$461$	17.2359	0.802756	0.401378	+	0.915912i	$0.368531\pi$
$462$	23.0134i	1.07068i
$463$	12.0000i	0.557687i	0.960337	+	0.278844i	$0.0899511\pi$
$463$	12.0000i	0.557687i	−0.960337	+	0.278844i	$0.910049\pi$
$464$	1.00000	0.0464238
$465$	0	0
$466$	11.1438	0.516228
$467$	− 5.88205i	− 0.272189i	−0.990696	−	0.136094i	$-0.956545\pi$
$467$	− 5.88205i	− 0.272189i	0.990696	−	0.136094i	$-0.0434550\pi$
$468$	− 0.381275i	− 0.0176244i
$469$	11.1588	0.515266
$470$	0	0
$471$	−6.84118	−0.315225
$472$	− 13.3947i	− 0.616542i
$473$	20.6172i	0.947979i
$474$	5.69736	0.261688
$475$	0	0
$476$	−14.7760	−0.677257
$477$	9.31608i	0.426554i
$478$	22.1707i	1.01406i
$479$	28.4868	1.30160	0.650798	−	0.759251i	$-0.274435\pi$
$479$	28.4868	1.30160	0.650798	+	0.759251i	$0.274435\pi$
$480$	0	0
$481$	1.39472	0.0635937
$482$	13.8696i	0.631744i
$483$	4.03932i	0.183795i
$484$	−21.4599	−0.975450
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	− 25.6306i	− 1.16143i	−0.814105	−	0.580717i	$-0.802772\pi$
$487$	− 25.6306i	− 1.16143i	0.814105	−	0.580717i	$-0.197228\pi$
$488$	14.0786i	0.637310i
$489$	−4.76255	−0.215370
$490$	0	0
$491$	33.9483	1.53206	0.766032	−	0.642803i	$-0.222229\pi$
$491$	33.9483	1.53206	0.766032	+	0.642803i	$0.222229\pi$
$492$	5.61873i	0.253312i
$493$	− 3.65804i	− 0.164750i
$494$	0.145371	0.00654053
$495$	0	0
$496$	6.00000	0.269408
$497$	43.2100i	1.93823i
$498$	16.1180i	0.722263i
$499$	−18.0134	−0.806393	−0.403196	−	0.915114i	$-0.632101\pi$
$499$	−18.0134	−0.806393	−0.403196	+	0.915114i	$0.632101\pi$
$500$	0	0
$501$	14.8546	0.663656
$502$	− 5.73668i	− 0.256040i
$503$	− 14.3813i	− 0.641229i	−0.947210	−	0.320615i	$-0.896111\pi$
$503$	− 14.3813i	− 0.641229i	0.947210	−	0.320615i	$-0.103889\pi$
$504$	4.03932	0.179925
$505$	0	0
$506$	−5.69736	−0.253279
$507$	− 12.8546i	− 0.570894i
$508$	18.6322i	0.826669i
$509$	−32.3797	−1.43521	−0.717603	−	0.696452i	$-0.754761\pi$
$509$	−32.3797	−1.43521	−0.717603	+	0.696452i	$0.754761\pi$
$510$	0	0
$511$	−28.5929	−1.26487
$512$	− 1.00000i	− 0.0441942i
$513$	− 0.381275i	− 0.0168337i
$514$	−20.6322	−0.910046
$515$	0	0
$516$	3.61873	0.159305
$517$	19.2643i	0.847245i
$518$	14.7760i	0.649220i
$519$	−9.69736	−0.425667
$520$	0	0
$521$	24.3420	1.06644	0.533220	−	0.845976i	$-0.320982\pi$
$521$	24.3420	1.06644	0.533220	+	0.845976i	$0.320982\pi$
$522$	1.00000i	0.0437688i
$523$	− 3.54009i	− 0.154797i	−0.997000	−	0.0773987i	$-0.975339\pi$
$523$	− 3.54009i	− 0.154797i	0.997000	−	0.0773987i	$-0.0246614\pi$
$524$	17.4734	0.763327
$525$	0	0
$526$	−19.8696	−0.866357
$527$	− 21.9483i	− 0.956081i
$528$	5.69736i	0.247946i
$529$	−1.00000	−0.0434783
$530$	0	0
$531$	13.3947	0.581281
$532$	1.54009i	0.0667714i
$533$	− 2.14228i	− 0.0927924i
$534$	5.65804	0.244847
$535$	0	0
$536$	2.76255	0.119324
$537$	− 5.31608i	− 0.229406i
$538$	− 8.17226i	− 0.352331i
$539$	53.0771	2.28619
$540$	0	0
$541$	−23.2493	−0.999568	−0.499784	−	0.866150i	$-0.666587\pi$
$541$	−23.2493	−0.999568	−0.499784	+	0.866150i	$0.666587\pi$
$542$	11.3947i	0.489445i
$543$	− 24.3688i	− 1.04577i
$544$	−3.65804	−0.156837
$545$	0	0
$546$	−1.54009	−0.0659098
$547$	32.2225i	1.37773i	0.724888	+	0.688866i	$0.241891\pi$
$547$	32.2225i	1.37773i	−0.724888	+	0.688866i	$0.758109\pi$
$548$	14.3420i	0.612658i
$549$	−14.0786	−0.600861
$550$	0	0
$551$	−0.381275	−0.0162429
$552$	1.00000i	0.0425628i
$553$	− 23.0134i	− 0.978631i
$554$	−4.93481	−0.209660
$555$	0	0
$556$	−8.01344	−0.339846
$557$	− 44.9985i	− 1.90665i	−0.301953	−	0.953323i	$-0.597639\pi$
$557$	− 44.9985i	− 1.90665i	0.301953	−	0.953323i	$-0.402361\pi$
$558$	6.00000i	0.254000i
$559$	−1.37973	−0.0583563
$560$	0	0
$561$	20.8412	0.879916
$562$	− 14.8955i	− 0.628328i
$563$	13.0921i	0.551765i	0.961191	+	0.275883i	$0.0889701\pi$
$563$	13.0921i	0.551765i	−0.961191	+	0.275883i	$0.911030\pi$
$564$	3.38127	0.142377
$565$	0	0
$566$	14.6322	0.615036
$567$	4.03932i	0.169635i
$568$	10.6974i	0.448851i
$569$	34.0786	1.42865	0.714325	−	0.699814i	$-0.246734\pi$
$569$	34.0786	1.42865	0.714325	+	0.699814i	$0.246734\pi$
$570$	0	0
$571$	23.4734	0.982329	0.491165	−	0.871067i	$-0.336571\pi$
$571$	23.4734	0.982329	0.491165	+	0.871067i	$0.336571\pi$
$572$	− 2.17226i	− 0.0908268i
$573$	− 10.4599i	− 0.436969i
$574$	22.6958	0.947305
$575$	0	0
$576$	1.00000	0.0416667
$577$	24.9348i	1.03805i	0.854759	+	0.519025i	$0.173705\pi$
$577$	24.9348i	1.03805i	−0.854759	+	0.519025i	$0.826295\pi$
$578$	− 3.61873i	− 0.150519i
$579$	14.0134	0.582379
$580$	0	0
$581$	65.1055	2.70103
$582$	4.07863i	0.169065i
$583$	53.0771i	2.19823i
$584$	−7.07863	−0.292916
$585$	0	0
$586$	9.39472	0.388092
$587$	− 30.0786i	− 1.24148i	−0.784017	−	0.620739i	$-0.786833\pi$
$587$	− 30.0786i	− 1.24148i	0.784017	−	0.620739i	$-0.213167\pi$
$588$	− 9.31608i	− 0.384189i
$589$	−2.28765	−0.0942610
$590$	0	0
$591$	8.47335	0.348547
$592$	3.65804i	0.150345i
$593$	− 16.4599i	− 0.675927i	−0.941159	−	0.337964i	$-0.890262\pi$
$593$	− 16.4599i	− 0.675927i	0.941159	−	0.337964i	$-0.109738\pi$
$594$	−5.69736	−0.233766
$595$	0	0
$596$	3.23745	0.132611
$597$	1.19813i	0.0490363i
$598$	− 0.381275i	− 0.0155915i
$599$	26.0269	1.06343	0.531715	−	0.846923i	$-0.321548\pi$
$599$	26.0269	1.06343	0.531715	+	0.846923i	$0.321548\pi$
$600$	0	0
$601$	−30.8546	−1.25859	−0.629293	−	0.777168i	$-0.716656\pi$
$601$	−30.8546	−1.25859	−0.629293	+	0.777168i	$0.716656\pi$
$602$	− 14.6172i	− 0.595752i
$603$	2.76255i	0.112500i
$604$	9.31608	0.379066
$605$	0	0
$606$	−16.7760	−0.681478
$607$	5.05020i	0.204981i	0.994734	+	0.102491i	$0.0326812\pi$
$607$	5.05020i	0.204981i	−0.994734	+	0.102491i	$0.967319\pi$
$608$	0.381275i	0.0154627i
$609$	4.03932	0.163681
$610$	0	0
$611$	−1.28920	−0.0521553
$612$	− 3.65804i	− 0.147868i
$613$	− 48.5261i	− 1.95995i	−0.199117	−	0.979976i	$-0.563807\pi$
$613$	− 48.5261i	− 1.95995i	0.199117	−	0.979976i	$-0.436193\pi$
$614$	9.22401	0.372251
$615$	0	0
$616$	23.0134	0.927238
$617$	− 20.7108i	− 0.833786i	−0.908956	−	0.416893i	$-0.863119\pi$
$617$	− 20.7108i	− 0.833786i	0.908956	−	0.416893i	$-0.136881\pi$
$618$	13.3554i	0.537233i
$619$	−42.2359	−1.69760	−0.848802	−	0.528711i	$-0.822676\pi$
$619$	−42.2359	−1.69760	−0.848802	+	0.528711i	$0.822676\pi$
$620$	0	0
$621$	−1.00000	−0.0401286
$622$	− 11.3295i	− 0.454273i
$623$	− 22.8546i	− 0.915651i
$624$	−0.381275	−0.0152632
$625$	0	0
$626$	−15.6037	−0.623651
$627$	− 2.17226i	− 0.0867517i
$628$	6.84118i	0.272993i
$629$	13.3813	0.533546
$630$	0	0
$631$	25.5913	1.01877	0.509387	−	0.860538i	$-0.329872\pi$
$631$	25.5913	1.01877	0.509387	+	0.860538i	$0.329872\pi$
$632$	− 5.69736i	− 0.226629i
$633$	16.2225i	0.644785i
$634$	−11.0000	−0.436866
$635$	0	0
$636$	9.31608	0.369407
$637$	3.55199i	0.140735i
$638$	5.69736i	0.225561i
$639$	−10.6974	−0.423181
$640$	0	0
$641$	−36.6834	−1.44891	−0.724453	−	0.689324i	$-0.757908\pi$
$641$	−36.6834	−1.44891	−0.724453	+	0.689324i	$0.757908\pi$
$642$	6.76255i	0.266897i
$643$	− 13.6974i	− 0.540171i	−0.962836	−	0.270086i	$-0.912948\pi$
$643$	− 13.6974i	− 0.540171i	0.962836	−	0.270086i	$-0.0870520\pi$
$644$	4.03932	0.159171
$645$	0	0
$646$	1.39472	0.0548745
$647$	24.0652i	0.946100i	0.881036	+	0.473050i	$0.156847\pi$
$647$	24.0652i	0.946100i	−0.881036	+	0.473050i	$0.843153\pi$
$648$	1.00000i	0.0392837i
$649$	76.3145	2.99561
$650$	0	0
$651$	24.2359	0.949880
$652$	4.76255i	0.186516i
$653$	14.9214i	0.583918i	0.956431	+	0.291959i	$0.0943071\pi$
$653$	14.9214i	0.583918i	−0.956431	+	0.291959i	$0.905693\pi$
$654$	−13.0528	−0.510403
$655$	0	0
$656$	5.61873	0.219374
$657$	− 7.07863i	− 0.276164i
$658$	− 13.6580i	− 0.532446i
$659$	−40.8288	−1.59046	−0.795231	−	0.606306i	$-0.792651\pi$
$659$	−40.8288	−1.59046	−0.795231	+	0.606306i	$0.792651\pi$
$660$	0	0
$661$	−29.1045	−1.13203	−0.566017	−	0.824394i	$-0.691516\pi$
$661$	−29.1045	−1.13203	−0.566017	+	0.824394i	$0.691516\pi$
$662$	− 2.69736i	− 0.104836i
$663$	1.39472i	0.0541664i
$664$	16.1180	0.625498
$665$	0	0
$666$	−3.65804	−0.141746
$667$	1.00000i	0.0387202i
$668$	− 14.8546i	− 0.574743i
$669$	13.6037	0.525951
$670$	0	0
$671$	−80.2110	−3.09651
$672$	− 4.03932i	− 0.155820i
$673$	41.9198i	1.61589i	0.589258	+	0.807945i	$0.299420\pi$
$673$	41.9198i	1.61589i	−0.589258	+	0.807945i	$0.700580\pi$
$674$	−17.3161	−0.666991
$675$	0	0
$676$	−12.8546	−0.494409
$677$	− 24.3145i	− 0.934484i	−0.884130	−	0.467242i	$-0.845248\pi$
$677$	− 24.3145i	− 0.934484i	0.884130	−	0.467242i	$-0.154752\pi$
$678$	− 1.65804i	− 0.0636767i
$679$	16.4749	0.632249
$680$	0	0
$681$	−12.4992	−0.478971
$682$	34.1842i	1.30898i
$683$	− 44.2628i	− 1.69367i	−0.531857	−	0.846834i	$-0.678506\pi$
$683$	− 44.2628i	− 1.69367i	0.531857	−	0.846834i	$-0.321494\pi$
$684$	−0.381275	−0.0145784
$685$	0	0
$686$	−9.35540	−0.357191
$687$	21.4734i	0.819260i
$688$	− 3.61873i	− 0.137963i
$689$	−3.55199	−0.135320
$690$	0	0
$691$	−37.1423	−1.41296	−0.706479	−	0.707734i	$-0.749718\pi$
$691$	−37.1423	−1.41296	−0.706479	+	0.707734i	$0.749718\pi$
$692$	9.69736i	0.368638i
$693$	23.0134i	0.874208i
$694$	−3.47335	−0.131847
$695$	0	0
$696$	1.00000	0.0379049
$697$	− 20.5535i	− 0.778521i
$698$	− 13.1438i	− 0.497501i
$699$	11.1438	0.421498
$700$	0	0
$701$	−0.130380	−0.00492438	−0.00246219	−	0.999997i	$-0.500784\pi$
$701$	−0.130380	−0.00492438	−0.00246219	+	0.999997i	$0.500784\pi$
$702$	− 0.381275i	− 0.0143903i
$703$	− 1.39472i	− 0.0526029i
$704$	5.69736	0.214727
$705$	0	0
$706$	13.8546	0.521426
$707$	67.7636i	2.54851i
$708$	− 13.3947i	− 0.503404i
$709$	21.2618	0.798503	0.399251	−	0.916841i	$-0.369270\pi$
$709$	21.2618	0.798503	0.399251	+	0.916841i	$0.369270\pi$
$710$	0	0
$711$	5.69736	0.213668
$712$	− 5.65804i	− 0.212044i
$713$	6.00000i	0.224702i
$714$	−14.7760	−0.552978
$715$	0	0
$716$	−5.31608	−0.198671
$717$	22.1707i	0.827981i
$718$	14.9348i	0.557362i
$719$	23.3026	0.869042	0.434521	−	0.900662i	$-0.356918\pi$
$719$	23.3026	0.869042	0.434521	+	0.900662i	$0.356918\pi$
$720$	0	0
$721$	53.9467	2.00908
$722$	18.8546i	0.701697i
$723$	13.8696i	0.515817i
$724$	−24.3688	−0.905661
$725$	0	0
$726$	−21.4599	−0.796452
$727$	14.6053i	0.541680i	0.962624	+	0.270840i	$0.0873014\pi$
$727$	14.6053i	0.541680i	−0.962624	+	0.270840i	$0.912699\pi$
$728$	1.54009i	0.0570795i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	−13.2375	−0.489605
$732$	14.0786i	0.520361i
$733$	− 26.6565i	− 0.984580i	−0.870431	−	0.492290i	$-0.836160\pi$
$733$	− 26.6565i	− 0.984580i	0.870431	−	0.492290i	$-0.163840\pi$
$734$	28.9348	1.06800
$735$	0	0
$736$	1.00000	0.0368605
$737$	15.7392i	0.579762i
$738$	5.61873i	0.206828i
$739$	−49.1992	−1.80982	−0.904910	−	0.425603i	$-0.860062\pi$
$739$	−49.1992	−1.80982	−0.904910	+	0.425603i	$0.860062\pi$
$740$	0	0
$741$	0.145371	0.00534032
$742$	− 37.6306i	− 1.38146i
$743$	17.1438i	0.628946i	0.949266	+	0.314473i	$0.101828\pi$
$743$	17.1438i	0.628946i	−0.949266	+	0.314473i	$0.898172\pi$
$744$	6.00000	0.219971
$745$	0	0
$746$	−26.4475	−0.968311
$747$	16.1180i	0.589725i
$748$	− 20.8412i	− 0.762029i
$749$	27.3161	0.998108
$750$	0	0
$751$	42.2752	1.54264	0.771322	−	0.636445i	$-0.219596\pi$
$751$	42.2752	1.54264	0.771322	+	0.636445i	$0.219596\pi$
$752$	− 3.38127i	− 0.123302i
$753$	− 5.73668i	− 0.209056i
$754$	−0.381275	−0.0138852
$755$	0	0
$756$	4.03932	0.146909
$757$	− 53.8939i	− 1.95881i	−0.201908	−	0.979404i	$-0.564714\pi$
$757$	− 53.8939i	− 1.95881i	0.201908	−	0.979404i	$-0.435286\pi$
$758$	− 26.2359i	− 0.952931i
$759$	−5.69736	−0.206801
$760$	0	0
$761$	−41.6456	−1.50965	−0.754826	−	0.655925i	$-0.772279\pi$
$761$	−41.6456	−1.50965	−0.754826	+	0.655925i	$0.772279\pi$
$762$	18.6322i	0.674972i
$763$	52.7242i	1.90875i
$764$	−10.4599	−0.378426
$765$	0	0
$766$	29.7242	1.07398
$767$	5.10707i	0.184406i
$768$	− 1.00000i	− 0.0360844i
$769$	12.5266	0.451722	0.225861	−	0.974159i	$-0.427480\pi$
$769$	12.5266	0.451722	0.225861	+	0.974159i	$0.427480\pi$
$770$	0	0
$771$	−20.6322	−0.743049
$772$	− 14.0134i	− 0.504355i
$773$	− 18.3663i	− 0.660589i	−0.943878	−	0.330295i	$-0.892852\pi$
$773$	− 18.3663i	− 0.660589i	0.943878	−	0.330295i	$-0.107148\pi$
$774$	3.61873	0.130072
$775$	0	0
$776$	4.07863	0.146414
$777$	14.7760i	0.530086i
$778$	8.47490i	0.303840i
$779$	−2.14228	−0.0767551
$780$	0	0
$781$	−60.9467	−2.18084
$782$	− 3.65804i	− 0.130811i
$783$	1.00000i	0.0357371i
$784$	−9.31608	−0.332717
$785$	0	0
$786$	17.4734	0.623254
$787$	− 32.6172i	− 1.16268i	−0.813662	−	0.581338i	$-0.802529\pi$
$787$	− 32.6172i	− 1.16268i	0.813662	−	0.581338i	$-0.197471\pi$
$788$	− 8.47335i	− 0.301851i
$789$	−19.8696	−0.707377
$790$	0	0
$791$	−6.69736	−0.238131
$792$	5.69736i	0.202447i
$793$	− 5.36783i	− 0.190617i
$794$	21.8696	0.776124
$795$	0	0
$796$	1.19813	0.0424667
$797$	− 21.7910i	− 0.771876i	−0.922525	−	0.385938i	$-0.873878\pi$
$797$	− 21.7910i	− 0.771876i	0.922525	−	0.385938i	$-0.126122\pi$
$798$	1.54009i	0.0545186i
$799$	−12.3688	−0.437578
$800$	0	0
$801$	5.65804	0.199917
$802$	4.71080i	0.166344i
$803$	− 40.3295i	− 1.42320i
$804$	2.76255	0.0974276
$805$	0	0
$806$	−2.28765	−0.0805790
$807$	− 8.17226i	− 0.287677i
$808$	16.7760i	0.590177i
$809$	−8.17226	−0.287321	−0.143661	−	0.989627i	$-0.545887\pi$
$809$	−8.17226	−0.287321	−0.143661	+	0.989627i	$0.545887\pi$
$810$	0	0
$811$	−29.4216	−1.03313	−0.516566	−	0.856247i	$-0.672790\pi$
$811$	−29.4216	−1.03313	−0.516566	+	0.856247i	$0.672790\pi$
$812$	− 4.03932i	− 0.141752i
$813$	11.3947i	0.399630i
$814$	−20.8412	−0.730483
$815$	0	0
$816$	−3.65804	−0.128057
$817$	1.37973i	0.0482706i
$818$	35.1055i	1.22744i
$819$	−1.54009	−0.0538151
$820$	0	0
$821$	41.6974	1.45525	0.727624	−	0.685976i	$-0.240625\pi$
$821$	41.6974	1.45525	0.727624	+	0.685976i	$0.240625\pi$
$822$	14.3420i	0.500233i
$823$	26.2359i	0.914526i	0.889331	+	0.457263i	$0.151170\pi$
$823$	26.2359i	0.914526i	−0.889331	+	0.457263i	$0.848830\pi$
$824$	13.3554	0.465257
$825$	0	0
$826$	−54.1055	−1.88257
$827$	− 41.9358i	− 1.45825i	−0.684380	−	0.729126i	$-0.739927\pi$
$827$	− 41.9358i	− 1.45825i	0.684380	−	0.729126i	$-0.260073\pi$
$828$	1.00000i	0.0347524i
$829$	27.7760	0.964700	0.482350	−	0.875979i	$-0.339783\pi$
$829$	27.7760	0.964700	0.482350	+	0.875979i	$0.339783\pi$
$830$	0	0
$831$	−4.93481	−0.171187
$832$	0.381275i	0.0132183i
$833$	34.0786i	1.18075i
$834$	−8.01344	−0.277483
$835$	0	0
$836$	−2.17226	−0.0751292
$837$	6.00000i	0.207390i
$838$	− 24.7232i	− 0.854050i
$839$	−31.3011	−1.08063	−0.540317	−	0.841462i	$-0.681696\pi$
$839$	−31.3011	−1.08063	−0.540317	+	0.841462i	$0.681696\pi$
$840$	0	0
$841$	−28.0000	−0.965517
$842$	− 17.4734i	− 0.602172i
$843$	− 14.8955i	− 0.513028i
$844$	16.2225	0.558400
$845$	0	0
$846$	3.38127	0.116251
$847$	86.6834i	2.97848i
$848$	− 9.31608i	− 0.319916i
$849$	14.6322	0.502175
$850$	0	0
$851$	−3.65804	−0.125396
$852$	10.6974i	0.366486i
$853$	20.6172i	0.705919i	0.935639	+	0.352959i	$0.114825\pi$
$853$	20.6172i	0.705919i	−0.935639	+	0.352959i	$0.885175\pi$
$854$	56.8681	1.94599
$855$	0	0
$856$	6.76255	0.231139
$857$	0.235904i	0.00805834i	0.999992	+	0.00402917i	$0.00128253\pi$
$857$	0.235904i	0.00805834i	−0.999992	+	0.00402917i	$0.998717\pi$
$858$	− 2.17226i	− 0.0741597i
$859$	23.7392	0.809972	0.404986	−	0.914323i	$-0.367276\pi$
$859$	23.7392	0.809972	0.404986	+	0.914323i	$0.367276\pi$
$860$	0	0
$861$	22.6958	0.773471
$862$	− 4.84118i	− 0.164891i
$863$	20.2225i	0.688381i	0.938900	+	0.344190i	$0.111847\pi$
$863$	20.2225i	0.688381i	−0.938900	+	0.344190i	$0.888153\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	−16.8412	−0.572287
$867$	− 3.61873i	− 0.122898i
$868$	− 24.2359i	− 0.822620i
$869$	32.4599	1.10113
$870$	0	0
$871$	−1.05329	−0.0356894
$872$	13.0528i	0.442022i
$873$	4.07863i	0.138041i
$874$	−0.381275	−0.0128968
$875$	0	0
$876$	−7.07863	−0.239165
$877$	14.0000i	0.472746i	0.971662	+	0.236373i	$0.0759588\pi$
$877$	14.0000i	0.472746i	−0.971662	+	0.236373i	$0.924041\pi$
$878$	− 20.7108i	− 0.698956i
$879$	9.39472	0.316876
$880$	0	0
$881$	26.0786	0.878612	0.439306	−	0.898338i	$-0.355224\pi$
$881$	26.0786	0.878612	0.439306	+	0.898338i	$0.355224\pi$
$882$	− 9.31608i	− 0.313689i
$883$	− 4.40971i	− 0.148399i	−0.997243	−	0.0741993i	$-0.976360\pi$
$883$	− 4.40971i	− 0.148399i	0.997243	−	0.0741993i	$-0.0236401\pi$
$884$	1.39472	0.0469095
$885$	0	0
$886$	14.8412	0.498599
$887$	22.6456i	0.760365i	0.924911	+	0.380183i	$0.124139\pi$
$887$	22.6456i	0.760365i	−0.924911	+	0.380183i	$0.875861\pi$
$888$	3.65804i	0.122756i
$889$	75.2612	2.52418
$890$	0	0
$891$	−5.69736	−0.190869
$892$	− 13.6037i	− 0.455487i
$893$	1.28920i	0.0431413i
$894$	3.23745	0.108277
$895$	0	0
$896$	−4.03932	−0.134944
$897$	− 0.381275i	− 0.0127304i
$898$	− 30.1573i	− 1.00636i
$899$	6.00000	0.200111
$900$	0	0
$901$	−34.0786	−1.13532
$902$	32.0119i	1.06588i
$903$	− 14.6172i	− 0.486429i
$904$	−1.65804	−0.0551457
$905$	0	0
$906$	9.31608	0.309506
$907$	16.2240i	0.538709i	0.963041	+	0.269355i	$0.0868104\pi$
$907$	16.2240i	0.538709i	−0.963041	+	0.269355i	$0.913190\pi$
$908$	12.4992i	0.414801i
$909$	−16.7760	−0.556425
$910$	0	0
$911$	−1.77599	−0.0588413	−0.0294207	−	0.999567i	$-0.509366\pi$
$911$	−1.77599	−0.0588413	−0.0294207	+	0.999567i	$0.509366\pi$
$912$	0.381275i	0.0126253i
$913$	91.8298i	3.03912i
$914$	12.7625	0.422148
$915$	0	0
$916$	21.4734	0.709500
$917$	− 70.5804i	− 2.33077i
$918$	− 3.65804i	− 0.120733i
$919$	27.6580	0.912355	0.456177	−	0.889889i	$-0.349218\pi$
$919$	27.6580	0.912355	0.456177	+	0.889889i	$0.349218\pi$
$920$	0	0
$921$	9.22401	0.303941
$922$	− 17.2359i	− 0.567634i
$923$	− 4.07863i	− 0.134250i
$924$	23.0134	0.757087
$925$	0	0
$926$	12.0000	0.394344
$927$	13.3554i	0.438649i
$928$	− 1.00000i	− 0.0328266i
$929$	−0.777541	−0.0255103	−0.0127551	−	0.999919i	$-0.504060\pi$
$929$	−0.777541	−0.0255103	−0.0127551	+	0.999919i	$0.504060\pi$
$930$	0	0
$931$	3.55199	0.116412
$932$	− 11.1438i	− 0.365028i
$933$	− 11.3295i	− 0.370912i
$934$	−5.88205	−0.192466
$935$	0	0
$936$	−0.381275	−0.0124624
$937$	7.52510i	0.245834i	0.992417	+	0.122917i	$0.0392249\pi$
$937$	7.52510i	0.245834i	−0.992417	+	0.122917i	$0.960775\pi$
$938$	− 11.1588i	− 0.364348i
$939$	−15.6037	−0.509209
$940$	0	0
$941$	−40.6322	−1.32457	−0.662285	−	0.749252i	$-0.730413\pi$
$941$	−40.6322	−1.32457	−0.662285	+	0.749252i	$0.730413\pi$
$942$	6.84118i	0.222898i
$943$	5.61873i	0.182971i
$944$	−13.3947	−0.435961
$945$	0	0
$946$	20.6172	0.670322
$947$	23.3947i	0.760226i	0.924940	+	0.380113i	$0.124115\pi$
$947$	23.3947i	0.760226i	−0.924940	+	0.380113i	$0.875885\pi$
$948$	− 5.69736i	− 0.185042i
$949$	2.69891	0.0876102
$950$	0	0
$951$	−11.0000	−0.356699
$952$	14.7760i	0.478893i
$953$	34.2902i	1.11077i	0.831594	+	0.555384i	$0.187429\pi$
$953$	34.2902i	1.11077i	−0.831594	+	0.555384i	$0.812571\pi$
$954$	9.31608	0.301619
$955$	0	0
$956$	22.1707	0.717052
$957$	5.69736i	0.184169i
$958$	− 28.4868i	− 0.920367i
$959$	57.9317	1.87071
$960$	0	0
$961$	5.00000	0.161290
$962$	− 1.39472i	− 0.0449676i
$963$	6.76255i	0.217920i
$964$	13.8696	0.446710
$965$	0	0
$966$	4.03932	0.129963
$967$	− 5.39472i	− 0.173482i	−0.996231	−	0.0867412i	$-0.972355\pi$
$967$	− 5.39472i	− 0.173482i	0.996231	−	0.0867412i	$-0.0276453\pi$
$968$	21.4599i	0.689748i
$969$	1.39472	0.0448049
$970$	0	0
$971$	58.3807	1.87353	0.936764	−	0.349963i	$-0.113806\pi$
$971$	58.3807	1.87353	0.936764	+	0.349963i	$0.113806\pi$
$972$	1.00000i	0.0320750i
$973$	32.3688i	1.03770i
$974$	−25.6306	−0.821258
$975$	0	0
$976$	14.0786	0.450646
$977$	− 33.4190i	− 1.06917i	−0.845115	−	0.534585i	$-0.820468\pi$
$977$	− 33.4190i	− 1.06917i	0.845115	−	0.534585i	$-0.179532\pi$
$978$	4.76255i	0.152290i
$979$	32.2359	1.03026
$980$	0	0
$981$	−13.0528	−0.416743
$982$	− 33.9483i	− 1.08333i
$983$	42.4868i	1.35512i	0.735468	+	0.677559i	$0.236962\pi$
$983$	42.4868i	1.35512i	−0.735468	+	0.677559i	$0.763038\pi$
$984$	5.61873	0.179118
$985$	0	0
$986$	−3.65804	−0.116496
$987$	− 13.6580i	− 0.434740i
$988$	− 0.145371i	− 0.00462485i
$989$	3.61873	0.115069
$990$	0	0
$991$	16.7625	0.532480	0.266240	−	0.963907i	$-0.414219\pi$
$991$	16.7625	0.532480	0.266240	+	0.963907i	$0.414219\pi$
$992$	− 6.00000i	− 0.190500i
$993$	− 2.69736i	− 0.0855981i
$994$	43.2100	1.37054
$995$	0	0
$996$	16.1180	0.510717
$997$	15.7760i	0.499631i	0.968293	+	0.249815i	$0.0803699\pi$
$997$	15.7760i	0.499631i	−0.968293	+	0.249815i	$0.919630\pi$
$998$	18.0134i	0.570206i
$999$	−3.65804	−0.115735

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3450.2.d.ba.2899.3		6
5.2	odd	4		3450.2.a.bs.1.1	yes	3
5.3	odd	4		3450.2.a.bp.1.3	✓	3
5.4	even	2	inner	3450.2.d.ba.2899.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3450.2.a.bp.1.3	✓	3	5.3	odd	4
3450.2.a.bs.1.1	yes	3	5.2	odd	4
3450.2.d.ba.2899.3		6	1.1	even	1	trivial
3450.2.d.ba.2899.4		6	5.4	even	2	inner

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:	\( N \)	\(=\)	\( 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3450.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} +4.03932i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} +4.03932i q^{7} +1.00000i q^{8} -1.00000 q^{9} -5.69736 q^{11} +1.00000i q^{12} -0.381275i q^{13} +4.03932 q^{14} +1.00000 q^{16} -3.65804i q^{17} +1.00000i q^{18} -0.381275 q^{19} +4.03932 q^{21} +5.69736i q^{22} +1.00000i q^{23} +1.00000 q^{24} -0.381275 q^{26} +1.00000i q^{27} -4.03932i q^{28} +1.00000 q^{29} +6.00000 q^{31} -1.00000i q^{32} +5.69736i q^{33} -3.65804 q^{34} +1.00000 q^{36} +3.65804i q^{37} +0.381275i q^{38} -0.381275 q^{39} +5.61873 q^{41} -4.03932i q^{42} -3.61873i q^{43} +5.69736 q^{44} +1.00000 q^{46} -3.38127i q^{47} -1.00000i q^{48} -9.31608 q^{49} -3.65804 q^{51} +0.381275i q^{52} -9.31608i q^{53} +1.00000 q^{54} -4.03932 q^{56} +0.381275i q^{57} -1.00000i q^{58} -13.3947 q^{59} +14.0786 q^{61} -6.00000i q^{62} -4.03932i q^{63} -1.00000 q^{64} +5.69736 q^{66} -2.76255i q^{67} +3.65804i q^{68} +1.00000 q^{69} +10.6974 q^{71} -1.00000i q^{72} +7.07863i q^{73} +3.65804 q^{74} +0.381275 q^{76} -23.0134i q^{77} +0.381275i q^{78} -5.69736 q^{79} +1.00000 q^{81} -5.61873i q^{82} -16.1180i q^{83} -4.03932 q^{84} -3.61873 q^{86} -1.00000i q^{87} -5.69736i q^{88} -5.65804 q^{89} +1.54009 q^{91} -1.00000i q^{92} -6.00000i q^{93} -3.38127 q^{94} -1.00000 q^{96} -4.07863i q^{97} +9.31608i q^{98} +5.69736 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} - 6 q^{6} - 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^4 - 6 * q^6 - 6 * q^9	\( 6 q - 6 q^{4} - 6 q^{6} - 6 q^{9} + 6 q^{11} + 2 q^{14} + 6 q^{16} + 2 q^{19} + 2 q^{21} + 6 q^{24} + 2 q^{26} + 6 q^{29} + 36 q^{31} - 4 q^{34} + 6 q^{36} + 2 q^{39} + 38 q^{41} - 6 q^{44} + 6 q^{46} - 20 q^{49} - 4 q^{51} + 6 q^{54} - 2 q^{56} + 40 q^{61} - 6 q^{64} - 6 q^{66} + 6 q^{69} + 24 q^{71} + 4 q^{74} - 2 q^{76} + 6 q^{79} + 6 q^{81} - 2 q^{84} - 26 q^{86} - 16 q^{89} + 58 q^{91} - 16 q^{94} - 6 q^{96} - 6 q^{99}+O(q^{100}) \) 6 * q - 6 * q^4 - 6 * q^6 - 6 * q^9 + 6 * q^11 + 2 * q^14 + 6 * q^16 + 2 * q^19 + 2 * q^21 + 6 * q^24 + 2 * q^26 + 6 * q^29 + 36 * q^31 - 4 * q^34 + 6 * q^36 + 2 * q^39 + 38 * q^41 - 6 * q^44 + 6 * q^46 - 20 * q^49 - 4 * q^51 + 6 * q^54 - 2 * q^56 + 40 * q^61 - 6 * q^64 - 6 * q^66 + 6 * q^69 + 24 * q^71 + 4 * q^74 - 2 * q^76 + 6 * q^79 + 6 * q^81 - 2 * q^84 - 26 * q^86 - 16 * q^89 + 58 * q^91 - 16 * q^94 - 6 * q^96 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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