LMFDB - Embedded newform 1450.2.b.k.349.6

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			349.6
Root			$-0.671462 + 1.24464i$ of defining polynomial
Character	$\chi$	$=$	1450.349
Dual form			1450.2.b.k.349.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +2.34292i q^{3} -1.00000 q^{4} -2.34292 q^{6} -3.83221i q^{7} -1.00000i q^{8} -2.48929 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +2.34292i q^{3} -1.00000 q^{4} -2.34292 q^{6} -3.83221i q^{7} -1.00000i q^{8} -2.48929 q^{9} +3.19656 q^{11} -2.34292i q^{12} -1.14637i q^{13} +3.83221 q^{14} +1.00000 q^{16} +0.803442i q^{17} -2.48929i q^{18} +2.34292 q^{19} +8.97858 q^{21} +3.19656i q^{22} +8.12494i q^{23} +2.34292 q^{24} +1.14637 q^{26} +1.19656i q^{27} +3.83221i q^{28} -1.00000 q^{29} +1.90383 q^{31} +1.00000i q^{32} +7.48929i q^{33} -0.803442 q^{34} +2.48929 q^{36} +7.63565i q^{37} +2.34292i q^{38} +2.68585 q^{39} +8.63565 q^{41} +8.97858i q^{42} -7.66442i q^{43} -3.19656 q^{44} -8.12494 q^{46} +11.4679i q^{47} +2.34292i q^{48} -7.68585 q^{49} -1.88240 q^{51} +1.14637i q^{52} +0.560904i q^{53} -1.19656 q^{54} -3.83221 q^{56} +5.48929i q^{57} -1.00000i q^{58} -2.36435 q^{59} +10.7146 q^{61} +1.90383i q^{62} +9.53948i q^{63} -1.00000 q^{64} -7.48929 q^{66} -5.12494i q^{67} -0.803442i q^{68} -19.0361 q^{69} +8.12494 q^{71} +2.48929i q^{72} -5.71462i q^{73} -7.63565 q^{74} -2.34292 q^{76} -12.2499i q^{77} +2.68585i q^{78} +14.9357 q^{79} -10.2713 q^{81} +8.63565i q^{82} +3.09617i q^{83} -8.97858 q^{84} +7.66442 q^{86} -2.34292i q^{87} -3.19656i q^{88} +3.32150 q^{89} -4.39312 q^{91} -8.12494i q^{92} +4.46052i q^{93} -11.4679 q^{94} -2.34292 q^{96} +11.5395i q^{97} -7.68585i q^{98} -7.95715 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	2.34292i	1.35269i	0.736586	+	0.676344i	$0.236437\pi$
$3$	2.34292i	1.35269i	−0.736586	+	0.676344i	$0.763563\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−2.34292	−0.956494
$7$	− 3.83221i	− 1.44844i	−0.689569	−	0.724220i	$-0.742200\pi$
$7$	− 3.83221i	− 1.44844i	0.689569	−	0.724220i	$-0.257800\pi$
$8$	− 1.00000i	− 0.353553i
$9$	−2.48929	−0.829763
$10$	0	0
$11$	3.19656	0.963798	0.481899	−	0.876227i	$-0.339947\pi$
$11$	3.19656	0.963798	0.481899	+	0.876227i	$0.339947\pi$
$12$	− 2.34292i	− 0.676344i
$13$	− 1.14637i	− 0.317945i	−0.987283	−	0.158972i	$-0.949182\pi$
$13$	− 1.14637i	− 0.317945i	0.987283	−	0.158972i	$-0.0508181\pi$
$14$	3.83221	1.02420
$15$	0	0
$16$	1.00000	0.250000
$17$	0.803442i	0.194863i	0.995242	+	0.0974317i	$0.0310628\pi$
$17$	0.803442i	0.194863i	−0.995242	+	0.0974317i	$0.968937\pi$
$18$	− 2.48929i	− 0.586731i
$19$	2.34292	0.537503	0.268752	−	0.963209i	$-0.413389\pi$
$19$	2.34292	0.537503	0.268752	+	0.963209i	$0.413389\pi$
$20$	0	0
$21$	8.97858	1.95929
$22$	3.19656i	0.681508i
$23$	8.12494i	1.69417i	0.531459	+	0.847084i	$0.321644\pi$
$23$	8.12494i	1.69417i	−0.531459	+	0.847084i	$0.678356\pi$
$24$	2.34292	0.478247
$25$	0	0
$26$	1.14637	0.224821
$27$	1.19656i	0.230278i
$28$	3.83221i	0.724220i
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	0	0
$31$	1.90383	0.341937	0.170969	−	0.985276i	$-0.445310\pi$
$31$	1.90383	0.341937	0.170969	+	0.985276i	$0.445310\pi$
$32$	1.00000i	0.176777i
$33$	7.48929i	1.30372i
$34$	−0.803442	−0.137789
$35$	0	0
$36$	2.48929	0.414881
$37$	7.63565i	1.25529i	0.778498	+	0.627647i	$0.215982\pi$
$37$	7.63565i	1.25529i	−0.778498	+	0.627647i	$0.784018\pi$
$38$	2.34292i	0.380072i
$39$	2.68585	0.430080
$40$	0	0
$41$	8.63565	1.34866	0.674331	−	0.738429i	$-0.264432\pi$
$41$	8.63565	1.34866	0.674331	+	0.738429i	$0.264432\pi$
$42$	8.97858i	1.38542i
$43$	− 7.66442i	− 1.16881i	−0.811461	−	0.584407i	$-0.801327\pi$
$43$	− 7.66442i	− 1.16881i	0.811461	−	0.584407i	$-0.198673\pi$
$44$	−3.19656	−0.481899
$45$	0	0
$46$	−8.12494	−1.19796
$47$	11.4679i	1.67276i	0.548150	+	0.836380i	$0.315332\pi$
$47$	11.4679i	1.67276i	−0.548150	+	0.836380i	$0.684668\pi$
$48$	2.34292i	0.338172i
$49$	−7.68585	−1.09798
$50$	0	0
$51$	−1.88240	−0.263589
$52$	1.14637i	0.158972i
$53$	0.560904i	0.0770460i	0.999258	+	0.0385230i	$0.0122653\pi$
$53$	0.560904i	0.0770460i	−0.999258	+	0.0385230i	$0.987735\pi$
$54$	−1.19656	−0.162831
$55$	0	0
$56$	−3.83221	−0.512101
$57$	5.48929i	0.727074i
$58$	− 1.00000i	− 0.131306i
$59$	−2.36435	−0.307812	−0.153906	−	0.988086i	$-0.549185\pi$
$59$	−2.36435	−0.307812	−0.153906	+	0.988086i	$0.549185\pi$
$60$	0	0
$61$	10.7146	1.37187	0.685933	−	0.727665i	$-0.259394\pi$
$61$	10.7146	1.37187	0.685933	+	0.727665i	$0.259394\pi$
$62$	1.90383i	0.241786i
$63$	9.53948i	1.20186i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−7.48929	−0.921868
$67$	− 5.12494i	− 0.626111i	−0.949735	−	0.313056i	$-0.898647\pi$
$67$	− 5.12494i	− 0.626111i	0.949735	−	0.313056i	$-0.101353\pi$
$68$	− 0.803442i	− 0.0974317i
$69$	−19.0361	−2.29168
$70$	0	0
$71$	8.12494	0.964253	0.482127	−	0.876102i	$-0.339865\pi$
$71$	8.12494	0.964253	0.482127	+	0.876102i	$0.339865\pi$
$72$	2.48929i	0.293365i
$73$	− 5.71462i	− 0.668845i	−0.942423	−	0.334423i	$-0.891459\pi$
$73$	− 5.71462i	− 0.668845i	0.942423	−	0.334423i	$-0.108541\pi$
$74$	−7.63565	−0.887627
$75$	0	0
$76$	−2.34292	−0.268752
$77$	− 12.2499i	− 1.39600i
$78$	2.68585i	0.304112i
$79$	14.9357	1.68040	0.840201	−	0.542276i	$-0.182437\pi$
$79$	14.9357	1.68040	0.840201	+	0.542276i	$0.182437\pi$
$80$	0	0
$81$	−10.2713	−1.14126
$82$	8.63565i	0.953648i
$83$	3.09617i	0.339849i	0.985457	+	0.169925i	$0.0543524\pi$
$83$	3.09617i	0.339849i	−0.985457	+	0.169925i	$0.945648\pi$
$84$	−8.97858	−0.979643
$85$	0	0
$86$	7.66442	0.826476
$87$	− 2.34292i	− 0.251188i
$88$	− 3.19656i	− 0.340754i
$89$	3.32150	0.352078	0.176039	−	0.984383i	$-0.443671\pi$
$89$	3.32150	0.352078	0.176039	+	0.984383i	$0.443671\pi$
$90$	0	0
$91$	−4.39312	−0.460524
$92$	− 8.12494i	− 0.847084i
$93$	4.46052i	0.462534i
$94$	−11.4679	−1.18282
$95$	0	0
$96$	−2.34292	−0.239124
$97$	11.5395i	1.17166i	0.810435	+	0.585828i	$0.199231\pi$
$97$	11.5395i	1.17166i	−0.810435	+	0.585828i	$0.800769\pi$
$98$	− 7.68585i	− 0.776388i
$99$	−7.95715	−0.799724
$100$	0	0
$101$	5.63565	0.560769	0.280384	−	0.959888i	$-0.409538\pi$
$101$	5.63565	0.560769	0.280384	+	0.959888i	$0.409538\pi$
$102$	− 1.88240i	− 0.186386i
$103$	− 17.5970i	− 1.73389i	−0.498407	−	0.866943i	$-0.666082\pi$
$103$	− 17.5970i	− 1.73389i	0.498407	−	0.866943i	$-0.333918\pi$
$104$	−1.14637	−0.112410
$105$	0	0
$106$	−0.560904	−0.0544798
$107$	− 1.56090i	− 0.150898i	−0.997150	−	0.0754491i	$-0.975961\pi$
$107$	− 1.56090i	− 0.150898i	0.997150	−	0.0754491i	$-0.0240390\pi$
$108$	− 1.19656i	− 0.115139i
$109$	−11.4966	−1.10118	−0.550589	−	0.834776i	$-0.685597\pi$
$109$	−11.4966	−1.10118	−0.550589	+	0.834776i	$0.685597\pi$
$110$	0	0
$111$	−17.8898	−1.69802
$112$	− 3.83221i	− 0.362110i
$113$	5.36435i	0.504635i	0.967644	+	0.252318i	$0.0811928\pi$
$113$	5.36435i	0.504635i	−0.967644	+	0.252318i	$0.918807\pi$
$114$	−5.48929	−0.514119
$115$	0	0
$116$	1.00000	0.0928477
$117$	2.85363i	0.263819i
$118$	− 2.36435i	− 0.217656i
$119$	3.07896	0.282248
$120$	0	0
$121$	−0.782020	−0.0710927
$122$	10.7146i	0.970056i
$123$	20.2327i	1.82432i
$124$	−1.90383	−0.170969
$125$	0	0
$126$	−9.53948	−0.849844
$127$	− 7.90383i	− 0.701351i	−0.936497	−	0.350676i	$-0.885952\pi$
$127$	− 7.90383i	− 0.701351i	0.936497	−	0.350676i	$-0.114048\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	17.9572	1.58104
$130$	0	0
$131$	−3.10352	−0.271156	−0.135578	−	0.990767i	$-0.543289\pi$
$131$	−3.10352	−0.271156	−0.135578	+	0.990767i	$0.543289\pi$
$132$	− 7.48929i	− 0.651859i
$133$	− 8.97858i	− 0.778541i
$134$	5.12494	0.442728
$135$	0	0
$136$	0.803442	0.0688946
$137$	− 19.2541i	− 1.64499i	−0.568773	−	0.822494i	$-0.692582\pi$
$137$	− 19.2541i	− 1.64499i	0.568773	−	0.822494i	$-0.307418\pi$
$138$	− 19.0361i	− 1.62046i
$139$	−6.43910	−0.546157	−0.273079	−	0.961992i	$-0.588042\pi$
$139$	−6.43910	−0.546157	−0.273079	+	0.961992i	$0.588042\pi$
$140$	0	0
$141$	−26.8683	−2.26272
$142$	8.12494i	0.681830i
$143$	− 3.66442i	− 0.306434i
$144$	−2.48929	−0.207441
$145$	0	0
$146$	5.71462	0.472945
$147$	− 18.0073i	− 1.48522i
$148$	− 7.63565i	− 0.627647i
$149$	−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
$151$	−10.8536	−0.883256	−0.441628	−	0.897198i	$-0.645599\pi$
$151$	−10.8536	−0.883256	−0.441628	+	0.897198i	$0.645599\pi$
$152$	− 2.34292i	− 0.190036i
$153$	− 2.00000i	− 0.161690i
$154$	12.2499	0.987124
$155$	0	0
$156$	−2.68585	−0.215040
$157$	7.69319i	0.613984i	0.951712	+	0.306992i	$0.0993224\pi$
$157$	7.69319i	0.613984i	−0.951712	+	0.306992i	$0.900678\pi$
$158$	14.9357i	1.18822i
$159$	−1.31415	−0.104219
$160$	0	0
$161$	31.1365	2.45390
$162$	− 10.2713i	− 0.806990i
$163$	− 1.61423i	− 0.126436i	−0.998000	−	0.0632182i	$-0.979864\pi$
$163$	− 1.61423i	− 0.126436i	0.998000	−	0.0632182i	$-0.0201364\pi$
$164$	−8.63565	−0.674331
$165$	0	0
$166$	−3.09617	−0.240310
$167$	13.7220i	1.06184i	0.847423	+	0.530919i	$0.178153\pi$
$167$	13.7220i	1.06184i	−0.847423	+	0.530919i	$0.821847\pi$
$168$	− 8.97858i	− 0.692712i
$169$	11.6858	0.898911
$170$	0	0
$171$	−5.83221	−0.446000
$172$	7.66442i	0.584407i
$173$	18.3074i	1.39189i	0.718096	+	0.695944i	$0.245014\pi$
$173$	18.3074i	1.39189i	−0.718096	+	0.695944i	$0.754986\pi$
$174$	2.34292	0.177617
$175$	0	0
$176$	3.19656	0.240950
$177$	− 5.53948i	− 0.416373i
$178$	3.32150i	0.248957i
$179$	−2.43910	−0.182307	−0.0911533	−	0.995837i	$-0.529055\pi$
$179$	−2.43910	−0.182307	−0.0911533	+	0.995837i	$0.529055\pi$
$180$	0	0
$181$	4.02456	0.299143	0.149572	−	0.988751i	$-0.452211\pi$
$181$	4.02456	0.299143	0.149572	+	0.988751i	$0.452211\pi$
$182$	− 4.39312i	− 0.325639i
$183$	25.1035i	1.85571i
$184$	8.12494	0.598979
$185$	0	0
$186$	−4.46052	−0.327061
$187$	2.56825i	0.187809i
$188$	− 11.4679i	− 0.836380i
$189$	4.58546	0.333543
$190$	0	0
$191$	−5.56825	−0.402904	−0.201452	−	0.979498i	$-0.564566\pi$
$191$	−5.56825	−0.402904	−0.201452	+	0.979498i	$0.564566\pi$
$192$	− 2.34292i	− 0.169086i
$193$	13.7146i	0.987200i	0.869689	+	0.493600i	$0.164319\pi$
$193$	13.7146i	0.987200i	−0.869689	+	0.493600i	$0.835681\pi$
$194$	−11.5395	−0.828486
$195$	0	0
$196$	7.68585	0.548989
$197$	25.4292i	1.81176i	0.423537	+	0.905879i	$0.360788\pi$
$197$	25.4292i	1.81176i	−0.423537	+	0.905879i	$0.639212\pi$
$198$	− 7.95715i	− 0.565490i
$199$	−15.1035	−1.07066	−0.535330	−	0.844643i	$-0.679813\pi$
$199$	−15.1035	−1.07066	−0.535330	+	0.844643i	$0.679813\pi$
$200$	0	0
$201$	12.0073	0.846933
$202$	5.63565i	0.396523i
$203$	3.83221i	0.268969i
$204$	1.88240	0.131795
$205$	0	0
$206$	17.5970	1.22604
$207$	− 20.2253i	− 1.40576i
$208$	− 1.14637i	− 0.0794861i
$209$	7.48929	0.518045
$210$	0	0
$211$	19.7967	1.36286	0.681431	−	0.731882i	$-0.261358\pi$
$211$	19.7967	1.36286	0.681431	+	0.731882i	$0.261358\pi$
$212$	− 0.560904i	− 0.0385230i
$213$	19.0361i	1.30433i
$214$	1.56090	0.106701
$215$	0	0
$216$	1.19656	0.0814154
$217$	− 7.29587i	− 0.495276i
$218$	− 11.4966i	− 0.778650i
$219$	13.3889	0.904738
$220$	0	0
$221$	0.921039	0.0619558
$222$	− 17.8898i	− 1.20068i
$223$	5.37169i	0.359715i	0.983693	+	0.179858i	$0.0575637\pi$
$223$	5.37169i	0.359715i	−0.983693	+	0.179858i	$0.942436\pi$
$224$	3.83221	0.256050
$225$	0	0
$226$	−5.36435	−0.356831
$227$	− 28.3215i	− 1.87976i	−0.341499	−	0.939882i	$-0.610935\pi$
$227$	− 28.3215i	− 1.87976i	0.341499	−	0.939882i	$-0.389065\pi$
$228$	− 5.48929i	− 0.363537i
$229$	−10.0147	−0.661790	−0.330895	−	0.943668i	$-0.607351\pi$
$229$	−10.0147	−0.661790	−0.330895	+	0.943668i	$0.607351\pi$
$230$	0	0
$231$	28.7005	1.88836
$232$	1.00000i	0.0656532i
$233$	− 23.3246i	− 1.52805i	−0.645188	−	0.764024i	$-0.723221\pi$
$233$	− 23.3246i	− 1.52805i	0.645188	−	0.764024i	$-0.276779\pi$
$234$	−2.85363	−0.186548
$235$	0	0
$236$	2.36435	0.153906
$237$	34.9933i	2.27306i
$238$	3.07896i	0.199579i
$239$	21.9143	1.41752	0.708759	−	0.705450i	$-0.249255\pi$
$239$	21.9143	1.41752	0.708759	+	0.705450i	$0.249255\pi$
$240$	0	0
$241$	9.45065	0.608770	0.304385	−	0.952549i	$-0.401549\pi$
$241$	9.45065	0.608770	0.304385	+	0.952549i	$0.401549\pi$
$242$	− 0.782020i	− 0.0502701i
$243$	− 20.4752i	− 1.31349i
$244$	−10.7146	−0.685933
$245$	0	0
$246$	−20.2327	−1.28999
$247$	− 2.68585i	− 0.170896i
$248$	− 1.90383i	− 0.120893i
$249$	−7.25410	−0.459710
$250$	0	0
$251$	−26.8855	−1.69700	−0.848500	−	0.529195i	$-0.822494\pi$
$251$	−26.8855	−1.69700	−0.848500	+	0.529195i	$0.822494\pi$
$252$	− 9.53948i	− 0.600931i
$253$	25.9718i	1.63284i
$254$	7.90383	0.495930
$255$	0	0
$256$	1.00000	0.0625000
$257$	− 6.39312i	− 0.398792i	−0.979919	−	0.199396i	$-0.936102\pi$
$257$	− 6.39312i	− 0.398792i	0.979919	−	0.199396i	$-0.0638979\pi$
$258$	17.9572i	1.11796i
$259$	29.2614	1.81822
$260$	0	0
$261$	2.48929	0.154083
$262$	− 3.10352i	− 0.191736i
$263$	− 27.4679i	− 1.69374i	−0.531799	−	0.846871i	$-0.678484\pi$
$263$	− 27.4679i	− 1.69374i	0.531799	−	0.846871i	$-0.321516\pi$
$264$	7.48929	0.460934
$265$	0	0
$266$	8.97858	0.550512
$267$	7.78202i	0.476252i
$268$	5.12494i	0.313056i
$269$	−9.59281	−0.584884	−0.292442	−	0.956283i	$-0.594468\pi$
$269$	−9.59281	−0.584884	−0.292442	+	0.956283i	$0.594468\pi$
$270$	0	0
$271$	−29.9614	−1.82002	−0.910012	−	0.414583i	$-0.863928\pi$
$271$	−29.9614	−1.82002	−0.910012	+	0.414583i	$0.863928\pi$
$272$	0.803442i	0.0487159i
$273$	− 10.2927i	− 0.622944i
$274$	19.2541	1.16318
$275$	0	0
$276$	19.0361	1.14584
$277$	15.7894i	0.948691i	0.880339	+	0.474346i	$0.157315\pi$
$277$	15.7894i	0.948691i	−0.880339	+	0.474346i	$0.842685\pi$
$278$	− 6.43910i	− 0.386191i
$279$	−4.73917	−0.283727
$280$	0	0
$281$	12.1390	0.724153	0.362077	−	0.932148i	$-0.382068\pi$
$281$	12.1390	0.724153	0.362077	+	0.932148i	$0.382068\pi$
$282$	− 26.8683i	− 1.59999i
$283$	− 4.17513i	− 0.248186i	−0.992271	−	0.124093i	$-0.960398\pi$
$283$	− 4.17513i	− 0.248186i	0.992271	−	0.124093i	$-0.0396021\pi$
$284$	−8.12494	−0.482127
$285$	0	0
$286$	3.66442	0.216682
$287$	− 33.0937i	− 1.95346i
$288$	− 2.48929i	− 0.146683i
$289$	16.3545	0.962028
$290$	0	0
$291$	−27.0361	−1.58489
$292$	5.71462i	0.334423i
$293$	9.09931i	0.531587i	0.964030	+	0.265794i	$0.0856340\pi$
$293$	9.09931i	0.531587i	−0.964030	+	0.265794i	$0.914366\pi$
$294$	18.0073	1.05021
$295$	0	0
$296$	7.63565	0.443813
$297$	3.82487i	0.221941i
$298$	− 2.00000i	− 0.115857i
$299$	9.31415	0.538651
$300$	0	0
$301$	−29.3717	−1.69296
$302$	− 10.8536i	− 0.624556i
$303$	13.2039i	0.758544i
$304$	2.34292	0.134376
$305$	0	0
$306$	2.00000	0.114332
$307$	− 33.3116i	− 1.90120i	−0.310426	−	0.950598i	$-0.600472\pi$
$307$	− 33.3116i	− 1.90120i	0.310426	−	0.950598i	$-0.399528\pi$
$308$	12.2499i	0.698002i
$309$	41.2285	2.34541
$310$	0	0
$311$	19.7648	1.12076	0.560380	−	0.828236i	$-0.310655\pi$
$311$	19.7648	1.12076	0.560380	+	0.828236i	$0.310655\pi$
$312$	− 2.68585i	− 0.152056i
$313$	19.1898i	1.08467i	0.840161	+	0.542337i	$0.182460\pi$
$313$	19.1898i	1.08467i	−0.840161	+	0.542337i	$0.817540\pi$
$314$	−7.69319	−0.434152
$315$	0	0
$316$	−14.9357	−0.840201
$317$	30.7722i	1.72834i	0.503203	+	0.864168i	$0.332155\pi$
$317$	30.7722i	1.72834i	−0.503203	+	0.864168i	$0.667845\pi$
$318$	− 1.31415i	− 0.0736941i
$319$	−3.19656	−0.178973
$320$	0	0
$321$	3.65708	0.204118
$322$	31.1365i	1.73517i
$323$	1.88240i	0.104740i
$324$	10.2713	0.570628
$325$	0	0
$326$	1.61423	0.0894040
$327$	− 26.9357i	− 1.48955i
$328$	− 8.63565i	− 0.476824i
$329$	43.9473	2.42289
$330$	0	0
$331$	−31.5714	−1.73532	−0.867660	−	0.497158i	$-0.834377\pi$
$331$	−31.5714	−1.73532	−0.867660	+	0.497158i	$0.834377\pi$
$332$	− 3.09617i	− 0.169925i
$333$	− 19.0073i	− 1.04160i
$334$	−13.7220	−0.750832
$335$	0	0
$336$	8.97858	0.489822
$337$	15.1966i	0.827809i	0.910320	+	0.413905i	$0.135835\pi$
$337$	15.1966i	0.827809i	−0.910320	+	0.413905i	$0.864165\pi$
$338$	11.6858i	0.635626i
$339$	−12.5682	−0.682614
$340$	0	0
$341$	6.08569	0.329559
$342$	− 5.83221i	− 0.315370i
$343$	2.62831i	0.141915i
$344$	−7.66442	−0.413238
$345$	0	0
$346$	−18.3074	−0.984213
$347$	− 17.0246i	− 0.913926i	−0.889486	−	0.456963i	$-0.848937\pi$
$347$	− 17.0246i	− 0.913926i	0.889486	−	0.456963i	$-0.151063\pi$
$348$	2.34292i	0.125594i
$349$	7.20390	0.385616	0.192808	−	0.981236i	$-0.438241\pi$
$349$	7.20390	0.385616	0.192808	+	0.981236i	$0.438241\pi$
$350$	0	0
$351$	1.37169	0.0732155
$352$	3.19656i	0.170377i
$353$	− 24.3116i	− 1.29398i	−0.762499	−	0.646989i	$-0.776028\pi$
$353$	− 24.3116i	− 1.29398i	0.762499	−	0.646989i	$-0.223972\pi$
$354$	5.53948	0.294420
$355$	0	0
$356$	−3.32150	−0.176039
$357$	7.21377i	0.381793i
$358$	− 2.43910i	− 0.128910i
$359$	−33.2902	−1.75699	−0.878495	−	0.477751i	$-0.841452\pi$
$359$	−33.2902	−1.75699	−0.878495	+	0.477751i	$0.841452\pi$
$360$	0	0
$361$	−13.5107	−0.711090
$362$	4.02456i	0.211526i
$363$	− 1.83221i	− 0.0961662i
$364$	4.39312	0.230262
$365$	0	0
$366$	−25.1035	−1.31218
$367$	18.9315i	0.988217i	0.869400	+	0.494109i	$0.164506\pi$
$367$	18.9315i	0.988217i	−0.869400	+	0.494109i	$0.835494\pi$
$368$	8.12494i	0.423542i
$369$	−21.4966	−1.11907
$370$	0	0
$371$	2.14950	0.111597
$372$	− 4.46052i	− 0.231267i
$373$	− 11.8996i	− 0.616139i	−0.951364	−	0.308069i	$-0.900317\pi$
$373$	− 11.8996i	− 0.616139i	0.951364	−	0.308069i	$-0.0996829\pi$
$374$	−2.56825	−0.132801
$375$	0	0
$376$	11.4679	0.591410
$377$	1.14637i	0.0590408i
$378$	4.58546i	0.235851i
$379$	20.4005	1.04790	0.523951	−	0.851749i	$-0.324458\pi$
$379$	20.4005	1.04790	0.523951	+	0.851749i	$0.324458\pi$
$380$	0	0
$381$	18.5181	0.948709
$382$	− 5.56825i	− 0.284896i
$383$	− 36.8929i	− 1.88514i	−0.334011	−	0.942569i	$-0.608402\pi$
$383$	− 36.8929i	− 1.88514i	0.334011	−	0.942569i	$-0.391598\pi$
$384$	2.34292	0.119562
$385$	0	0
$386$	−13.7146	−0.698056
$387$	19.0790i	0.969838i
$388$	− 11.5395i	− 0.585828i
$389$	22.7146	1.15168	0.575838	−	0.817564i	$-0.304676\pi$
$389$	22.7146	1.15168	0.575838	+	0.817564i	$0.304676\pi$
$390$	0	0
$391$	−6.52792	−0.330131
$392$	7.68585i	0.388194i
$393$	− 7.27131i	− 0.366789i
$394$	−25.4292	−1.28111
$395$	0	0
$396$	7.95715	0.399862
$397$	− 33.5113i	− 1.68189i	−0.541124	−	0.840943i	$-0.682001\pi$
$397$	− 33.5113i	− 1.68189i	0.541124	−	0.840943i	$-0.317999\pi$
$398$	− 15.1035i	− 0.757071i
$399$	21.0361	1.05312
$400$	0	0
$401$	−17.0147	−0.849673	−0.424837	−	0.905270i	$-0.639668\pi$
$401$	−17.0147	−0.849673	−0.424837	+	0.905270i	$0.639668\pi$
$402$	12.0073i	0.598872i
$403$	− 2.18248i	− 0.108717i
$404$	−5.63565	−0.280384
$405$	0	0
$406$	−3.83221	−0.190189
$407$	24.4078i	1.20985i
$408$	1.88240i	0.0931929i
$409$	21.3461	1.05549	0.527747	−	0.849401i	$-0.323037\pi$
$409$	21.3461	1.05549	0.527747	+	0.849401i	$0.323037\pi$
$410$	0	0
$411$	45.1109	2.22515
$412$	17.5970i	0.866943i
$413$	9.06067i	0.445847i
$414$	20.2253	0.994021
$415$	0	0
$416$	1.14637	0.0562052
$417$	− 15.0863i	− 0.738780i
$418$	7.48929i	0.366313i
$419$	−3.81079	−0.186169	−0.0930846	−	0.995658i	$-0.529673\pi$
$419$	−3.81079	−0.186169	−0.0930846	+	0.995658i	$0.529673\pi$
$420$	0	0
$421$	−23.9859	−1.16900	−0.584501	−	0.811393i	$-0.698710\pi$
$421$	−23.9859	−1.16900	−0.584501	+	0.811393i	$0.698710\pi$
$422$	19.7967i	0.963689i
$423$	− 28.5468i	− 1.38799i
$424$	0.560904	0.0272399
$425$	0	0
$426$	−19.0361	−0.922303
$427$	− 41.0607i	− 1.98707i
$428$	1.56090i	0.0754491i
$429$	8.58546	0.414510
$430$	0	0
$431$	7.00314	0.337329	0.168665	−	0.985674i	$-0.446055\pi$
$431$	7.00314	0.337329	0.168665	+	0.985674i	$0.446055\pi$
$432$	1.19656i	0.0575694i
$433$	− 23.3790i	− 1.12352i	−0.827299	−	0.561762i	$-0.810123\pi$
$433$	− 23.3790i	− 1.12352i	0.827299	−	0.561762i	$-0.189877\pi$
$434$	7.29587	0.350213
$435$	0	0
$436$	11.4966	0.550589
$437$	19.0361i	0.910621i
$438$	13.3889i	0.639747i
$439$	−13.7073	−0.654212	−0.327106	−	0.944988i	$-0.606073\pi$
$439$	−13.7073	−0.654212	−0.327106	+	0.944988i	$0.606073\pi$
$440$	0	0
$441$	19.1323	0.911061
$442$	0.921039i	0.0438093i
$443$	− 9.25410i	− 0.439675i	−0.975536	−	0.219838i	$-0.929447\pi$
$443$	− 9.25410i	− 0.439675i	0.975536	−	0.219838i	$-0.0705528\pi$
$444$	17.8898	0.849010
$445$	0	0
$446$	−5.37169	−0.254357
$447$	− 4.68585i	− 0.221633i
$448$	3.83221i	0.181055i
$449$	−25.8971	−1.22216	−0.611080	−	0.791569i	$-0.709265\pi$
$449$	−25.8971	−1.22216	−0.611080	+	0.791569i	$0.709265\pi$
$450$	0	0
$451$	27.6044	1.29984
$452$	− 5.36435i	− 0.252318i
$453$	− 25.4292i	− 1.19477i
$454$	28.3215	1.32919
$455$	0	0
$456$	5.48929	0.257059
$457$	26.5829i	1.24350i	0.783217	+	0.621749i	$0.213578\pi$
$457$	26.5829i	1.24350i	−0.783217	+	0.621749i	$0.786422\pi$
$458$	− 10.0147i	− 0.467956i
$459$	−0.961365	−0.0448727
$460$	0	0
$461$	0.527923	0.0245878	0.0122939	−	0.999924i	$-0.496087\pi$
$461$	0.527923	0.0245878	0.0122939	+	0.999924i	$0.496087\pi$
$462$	28.7005i	1.33527i
$463$	− 38.0575i	− 1.76868i	−0.466840	−	0.884342i	$-0.654608\pi$
$463$	− 38.0575i	− 1.76868i	0.466840	−	0.884342i	$-0.345392\pi$
$464$	−1.00000	−0.0464238
$465$	0	0
$466$	23.3246	1.08049
$467$	10.5181i	0.486718i	0.969936	+	0.243359i	$0.0782493\pi$
$467$	10.5181i	0.486718i	−0.969936	+	0.243359i	$0.921751\pi$
$468$	− 2.85363i	− 0.131909i
$469$	−19.6399	−0.906885
$470$	0	0
$471$	−18.0246	−0.830528
$472$	2.36435i	0.108828i
$473$	− 24.4998i	− 1.12650i
$474$	−34.9933	−1.60729
$475$	0	0
$476$	−3.07896	−0.141124
$477$	− 1.39625i	− 0.0639299i
$478$	21.9143i	1.00234i
$479$	−5.54935	−0.253556	−0.126778	−	0.991931i	$-0.540464\pi$
$479$	−5.54935	−0.253556	−0.126778	+	0.991931i	$0.540464\pi$
$480$	0	0
$481$	8.75325	0.399114
$482$	9.45065i	0.430465i
$483$	72.9504i	3.31936i
$484$	0.782020	0.0355463
$485$	0	0
$486$	20.4752	0.928774
$487$	26.6858i	1.20925i	0.796510	+	0.604626i	$0.206677\pi$
$487$	26.6858i	1.20925i	−0.796510	+	0.604626i	$0.793323\pi$
$488$	− 10.7146i	− 0.485028i
$489$	3.78202	0.171029
$490$	0	0
$491$	24.0575	1.08570	0.542851	−	0.839829i	$-0.317345\pi$
$491$	24.0575	1.08570	0.542851	+	0.839829i	$0.317345\pi$
$492$	− 20.2327i	− 0.912159i
$493$	− 0.803442i	− 0.0361852i
$494$	2.68585	0.120842
$495$	0	0
$496$	1.90383	0.0854843
$497$	− 31.1365i	− 1.39666i
$498$	− 7.25410i	− 0.325064i
$499$	−3.87085	−0.173283	−0.0866414	−	0.996240i	$-0.527613\pi$
$499$	−3.87085	−0.173283	−0.0866414	+	0.996240i	$0.527613\pi$
$500$	0	0
$501$	−32.1495	−1.43633
$502$	− 26.8855i	− 1.19996i
$503$	− 43.1751i	− 1.92508i	−0.271132	−	0.962542i	$-0.587398\pi$
$503$	− 43.1751i	− 1.92508i	0.271132	−	0.962542i	$-0.412602\pi$
$504$	9.53948	0.424922
$505$	0	0
$506$	−25.9718	−1.15459
$507$	27.3790i	1.21595i
$508$	7.90383i	0.350676i
$509$	21.5725	0.956183	0.478091	−	0.878310i	$-0.341329\pi$
$509$	21.5725	0.956183	0.478091	+	0.878310i	$0.341329\pi$
$510$	0	0
$511$	−21.8996	−0.968782
$512$	1.00000i	0.0441942i
$513$	2.80344i	0.123775i
$514$	6.39312	0.281988
$515$	0	0
$516$	−17.9572	−0.790520
$517$	36.6577i	1.61220i
$518$	29.2614i	1.28567i
$519$	−42.8929	−1.88279
$520$	0	0
$521$	32.0790	1.40540	0.702702	−	0.711484i	$-0.251977\pi$
$521$	32.0790	1.40540	0.702702	+	0.711484i	$0.251977\pi$
$522$	2.48929i	0.108953i
$523$	31.6247i	1.38285i	0.722447	+	0.691426i	$0.243017\pi$
$523$	31.6247i	1.38285i	−0.722447	+	0.691426i	$0.756983\pi$
$524$	3.10352	0.135578
$525$	0	0
$526$	27.4679	1.19766
$527$	1.52962i	0.0666311i
$528$	7.48929i	0.325929i
$529$	−43.0147	−1.87020
$530$	0	0
$531$	5.88554	0.255411
$532$	8.97858i	0.389271i
$533$	− 9.89962i	− 0.428800i
$534$	−7.78202	−0.336761
$535$	0	0
$536$	−5.12494	−0.221364
$537$	− 5.71462i	− 0.246604i
$538$	− 9.59281i	− 0.413575i
$539$	−24.5682	−1.05823
$540$	0	0
$541$	−21.9368	−0.943137	−0.471568	−	0.881829i	$-0.656312\pi$
$541$	−21.9368	−0.943137	−0.471568	+	0.881829i	$0.656312\pi$
$542$	− 29.9614i	− 1.28695i
$543$	9.42923i	0.404647i
$544$	−0.803442	−0.0344473
$545$	0	0
$546$	10.2927	0.440488
$547$	− 13.6901i	− 0.585345i	−0.956213	−	0.292672i	$-0.905456\pi$
$547$	− 13.6901i	− 0.585345i	0.956213	−	0.292672i	$-0.0945445\pi$
$548$	19.2541i	0.822494i
$549$	−26.6718	−1.13832
$550$	0	0
$551$	−2.34292	−0.0998119
$552$	19.0361i	0.810231i
$553$	− 57.2369i	− 2.43396i
$554$	−15.7894	−0.670826
$555$	0	0
$556$	6.43910	0.273079
$557$	− 1.66442i	− 0.0705239i	−0.999378	−	0.0352619i	$-0.988773\pi$
$557$	− 1.66442i	− 0.0705239i	0.999378	−	0.0352619i	$-0.0112266\pi$
$558$	− 4.73917i	− 0.200625i
$559$	−8.78623	−0.371618
$560$	0	0
$561$	−6.01721	−0.254047
$562$	12.1390i	0.512054i
$563$	− 21.5725i	− 0.909171i	−0.890703	−	0.454585i	$-0.849787\pi$
$563$	− 21.5725i	− 0.909171i	0.890703	−	0.454585i	$-0.150213\pi$
$564$	26.8683	1.13136
$565$	0	0
$566$	4.17513	0.175494
$567$	39.3618i	1.65304i
$568$	− 8.12494i	− 0.340915i
$569$	−7.88240	−0.330448	−0.165224	−	0.986256i	$-0.552835\pi$
$569$	−7.88240	−0.330448	−0.165224	+	0.986256i	$0.552835\pi$
$570$	0	0
$571$	−29.0796	−1.21694	−0.608471	−	0.793576i	$-0.708217\pi$
$571$	−29.0796	−1.21694	−0.608471	+	0.793576i	$0.708217\pi$
$572$	3.66442i	0.153217i
$573$	− 13.0460i	− 0.545004i
$574$	33.0937	1.38130
$575$	0	0
$576$	2.48929	0.103720
$577$	− 38.5155i	− 1.60342i	−0.597711	−	0.801711i	$-0.703923\pi$
$577$	− 38.5155i	− 1.60342i	0.597711	−	0.801711i	$-0.296077\pi$
$578$	16.3545i	0.680257i
$579$	−32.1323	−1.33537
$580$	0	0
$581$	11.8652	0.492251
$582$	− 27.0361i	− 1.12068i
$583$	1.79296i	0.0742568i
$584$	−5.71462	−0.236472
$585$	0	0
$586$	−9.09931	−0.375889
$587$	− 15.6184i	− 0.644642i	−0.946630	−	0.322321i	$-0.895537\pi$
$587$	− 15.6184i	− 0.644642i	0.946630	−	0.322321i	$-0.104463\pi$
$588$	18.0073i	0.742610i
$589$	4.46052	0.183792
$590$	0	0
$591$	−59.5787	−2.45074
$592$	7.63565i	0.313823i
$593$	1.72869i	0.0709889i	0.999370	+	0.0354944i	$0.0113006\pi$
$593$	1.72869i	0.0709889i	−0.999370	+	0.0354944i	$0.988699\pi$
$594$	−3.82487	−0.156936
$595$	0	0
$596$	2.00000	0.0819232
$597$	− 35.3864i	− 1.44827i
$598$	9.31415i	0.380884i
$599$	−20.0189	−0.817950	−0.408975	−	0.912546i	$-0.634114\pi$
$599$	−20.0189	−0.817950	−0.408975	+	0.912546i	$0.634114\pi$
$600$	0	0
$601$	11.6388	0.474756	0.237378	−	0.971417i	$-0.423712\pi$
$601$	11.6388	0.474756	0.237378	+	0.971417i	$0.423712\pi$
$602$	− 29.3717i	− 1.19710i
$603$	12.7575i	0.519524i
$604$	10.8536	0.441628
$605$	0	0
$606$	−13.2039	−0.536372
$607$	− 36.4036i	− 1.47758i	−0.673938	−	0.738788i	$-0.735398\pi$
$607$	− 36.4036i	− 1.47758i	0.673938	−	0.738788i	$-0.264602\pi$
$608$	2.34292i	0.0950181i
$609$	−8.97858	−0.363830
$610$	0	0
$611$	13.1464	0.531845
$612$	2.00000i	0.0808452i
$613$	33.4292i	1.35019i	0.737729	+	0.675097i	$0.235898\pi$
$613$	33.4292i	1.35019i	−0.737729	+	0.675097i	$0.764102\pi$
$614$	33.3116	1.34435
$615$	0	0
$616$	−12.2499	−0.493562
$617$	− 16.2400i	− 0.653799i	−0.945059	−	0.326899i	$-0.893996\pi$
$617$	− 16.2400i	− 0.653799i	0.945059	−	0.326899i	$-0.106004\pi$
$618$	41.2285i	1.65845i
$619$	−30.1004	−1.20984	−0.604918	−	0.796288i	$-0.706794\pi$
$619$	−30.1004	−1.20984	−0.604918	+	0.796288i	$0.706794\pi$
$620$	0	0
$621$	−9.72196	−0.390129
$622$	19.7648i	0.792497i
$623$	− 12.7287i	− 0.509964i
$624$	2.68585	0.107520
$625$	0	0
$626$	−19.1898	−0.766980
$627$	17.5468i	0.700753i
$628$	− 7.69319i	− 0.306992i
$629$	−6.13481	−0.244611
$630$	0	0
$631$	31.1793	1.24123	0.620615	−	0.784115i	$-0.286883\pi$
$631$	31.1793	1.24123	0.620615	+	0.784115i	$0.286883\pi$
$632$	− 14.9357i	− 0.594111i
$633$	46.3822i	1.84353i
$634$	−30.7722	−1.22212
$635$	0	0
$636$	1.31415	0.0521096
$637$	8.81079i	0.349096i
$638$	− 3.19656i	− 0.126553i
$639$	−20.2253	−0.800102
$640$	0	0
$641$	5.29587	0.209174	0.104587	−	0.994516i	$-0.466648\pi$
$641$	5.29587	0.209174	0.104587	+	0.994516i	$0.466648\pi$
$642$	3.65708i	0.144333i
$643$	28.1867i	1.11157i	0.831325	+	0.555787i	$0.187583\pi$
$643$	28.1867i	1.11157i	−0.831325	+	0.555787i	$0.812417\pi$
$644$	−31.1365	−1.22695
$645$	0	0
$646$	−1.88240	−0.0740622
$647$	15.6497i	0.615254i	0.951507	+	0.307627i	$0.0995350\pi$
$647$	15.6497i	0.615254i	−0.951507	+	0.307627i	$0.900465\pi$
$648$	10.2713i	0.403495i
$649$	−7.55777	−0.296668
$650$	0	0
$651$	17.0937	0.669953
$652$	1.61423i	0.0632182i
$653$	24.1292i	0.944247i	0.881532	+	0.472123i	$0.156512\pi$
$653$	24.1292i	0.944247i	−0.881532	+	0.472123i	$0.843488\pi$
$654$	26.9357	1.05327
$655$	0	0
$656$	8.63565	0.337166
$657$	14.2253i	0.554983i
$658$	43.9473i	1.71324i
$659$	−28.1898	−1.09812	−0.549060	−	0.835783i	$-0.685014\pi$
$659$	−28.1898	−1.09812	−0.549060	+	0.835783i	$0.685014\pi$
$660$	0	0
$661$	−16.1678	−0.628854	−0.314427	−	0.949282i	$-0.601812\pi$
$661$	−16.1678	−0.628854	−0.314427	+	0.949282i	$0.601812\pi$
$662$	− 31.5714i	− 1.22706i
$663$	2.15792i	0.0838068i
$664$	3.09617	0.120155
$665$	0	0
$666$	19.0073	0.736520
$667$	− 8.12494i	− 0.314599i
$668$	− 13.7220i	− 0.530919i
$669$	−12.5855	−0.486582
$670$	0	0
$671$	34.2499	1.32220
$672$	8.97858i	0.346356i
$673$	− 13.7690i	− 0.530757i	−0.964144	−	0.265378i	$-0.914503\pi$
$673$	− 13.7690i	− 0.530757i	0.964144	−	0.265378i	$-0.0854969\pi$
$674$	−15.1966	−0.585350
$675$	0	0
$676$	−11.6858	−0.449456
$677$	14.4710i	0.556166i	0.960557	+	0.278083i	$0.0896990\pi$
$677$	14.4710i	0.556166i	−0.960557	+	0.278083i	$0.910301\pi$
$678$	− 12.5682i	− 0.482681i
$679$	44.2217	1.69707
$680$	0	0
$681$	66.3551	2.54273
$682$	6.08569i	0.233033i
$683$	19.0533i	0.729055i	0.931193	+	0.364528i	$0.118770\pi$
$683$	19.0533i	0.729055i	−0.931193	+	0.364528i	$0.881230\pi$
$684$	5.83221	0.223000
$685$	0	0
$686$	−2.62831	−0.100349
$687$	− 23.4637i	− 0.895194i
$688$	− 7.66442i	− 0.292203i
$689$	0.643000	0.0244964
$690$	0	0
$691$	41.7679	1.58893	0.794464	−	0.607312i	$-0.207752\pi$
$691$	41.7679	1.58893	0.794464	+	0.607312i	$0.207752\pi$
$692$	− 18.3074i	− 0.695944i
$693$	30.4935i	1.15835i
$694$	17.0246	0.646243
$695$	0	0
$696$	−2.34292	−0.0888083
$697$	6.93825i	0.262805i
$698$	7.20390i	0.272672i
$699$	54.6478	2.06697
$700$	0	0
$701$	−0.149501	−0.00564658	−0.00282329	−	0.999996i	$-0.500899\pi$
$701$	−0.149501	−0.00564658	−0.00282329	+	0.999996i	$0.500899\pi$
$702$	1.37169i	0.0517712i
$703$	17.8898i	0.674725i
$704$	−3.19656	−0.120475
$705$	0	0
$706$	24.3116	0.914980
$707$	− 21.5970i	− 0.812240i
$708$	5.53948i	0.208186i
$709$	11.5725	0.434613	0.217306	−	0.976103i	$-0.430273\pi$
$709$	11.5725	0.434613	0.217306	+	0.976103i	$0.430273\pi$
$710$	0	0
$711$	−37.1793	−1.39433
$712$	− 3.32150i	− 0.124478i
$713$	15.4685i	0.579299i
$714$	−7.21377	−0.269969
$715$	0	0
$716$	2.43910	0.0911533
$717$	51.3435i	1.91746i
$718$	− 33.2902i	− 1.24238i
$719$	−2.93933	−0.109618	−0.0548092	−	0.998497i	$-0.517455\pi$
$719$	−2.93933	−0.109618	−0.0548092	+	0.998497i	$0.517455\pi$
$720$	0	0
$721$	−67.4355	−2.51143
$722$	− 13.5107i	− 0.502817i
$723$	22.1422i	0.823476i
$724$	−4.02456	−0.149572
$725$	0	0
$726$	1.83221	0.0679998
$727$	29.3435i	1.08829i	0.838991	+	0.544146i	$0.183146\pi$
$727$	29.3435i	1.08829i	−0.838991	+	0.544146i	$0.816854\pi$
$728$	4.39312i	0.162820i
$729$	17.1579	0.635479
$730$	0	0
$731$	6.15792	0.227759
$732$	− 25.1035i	− 0.927853i
$733$	28.2927i	1.04502i	0.852634	+	0.522508i	$0.175003\pi$
$733$	28.2927i	1.04502i	−0.852634	+	0.522508i	$0.824997\pi$
$734$	−18.9315	−0.698775
$735$	0	0
$736$	−8.12494	−0.299489
$737$	− 16.3822i	− 0.603445i
$738$	− 21.4966i	− 0.791302i
$739$	−15.6069	−0.574109	−0.287054	−	0.957914i	$-0.592676\pi$
$739$	−15.6069	−0.574109	−0.287054	+	0.957914i	$0.592676\pi$
$740$	0	0
$741$	6.29273	0.231169
$742$	2.14950i	0.0789107i
$743$	42.9013i	1.57390i	0.617019	+	0.786948i	$0.288340\pi$
$743$	42.9013i	1.57390i	−0.617019	+	0.786948i	$0.711660\pi$
$744$	4.46052	0.163531
$745$	0	0
$746$	11.8996	0.435676
$747$	− 7.70727i	− 0.281994i
$748$	− 2.56825i	− 0.0939045i
$749$	−5.98171	−0.218567
$750$	0	0
$751$	−41.0403	−1.49758	−0.748791	−	0.662806i	$-0.769366\pi$
$751$	−41.0403	−1.49758	−0.748791	+	0.662806i	$0.769366\pi$
$752$	11.4679i	0.418190i
$753$	− 62.9908i	− 2.29551i
$754$	−1.14637	−0.0417482
$755$	0	0
$756$	−4.58546	−0.166772
$757$	35.9227i	1.30563i	0.757516	+	0.652817i	$0.226413\pi$
$757$	35.9227i	1.30563i	−0.757516	+	0.652817i	$0.773587\pi$
$758$	20.4005i	0.740978i
$759$	−60.8500	−2.20872
$760$	0	0
$761$	3.77154	0.136718	0.0683591	−	0.997661i	$-0.478224\pi$
$761$	3.77154	0.136718	0.0683591	+	0.997661i	$0.478224\pi$
$762$	18.5181i	0.670838i
$763$	44.0575i	1.59499i
$764$	5.56825	0.201452
$765$	0	0
$766$	36.8929	1.33299
$767$	2.71040i	0.0978670i
$768$	2.34292i	0.0845430i
$769$	−15.7062	−0.566380	−0.283190	−	0.959064i	$-0.591393\pi$
$769$	−15.7062	−0.566380	−0.283190	+	0.959064i	$0.591393\pi$
$770$	0	0
$771$	14.9786	0.539440
$772$	− 13.7146i	− 0.493600i
$773$	3.13588i	0.112790i	0.998409	+	0.0563949i	$0.0179606\pi$
$773$	3.13588i	0.112790i	−0.998409	+	0.0563949i	$0.982039\pi$
$774$	−19.0790	−0.685779
$775$	0	0
$776$	11.5395	0.414243
$777$	68.5573i	2.45948i
$778$	22.7146i	0.814358i
$779$	20.2327	0.724911
$780$	0	0
$781$	25.9718	0.929346
$782$	− 6.52792i	− 0.233438i
$783$	− 1.19656i	− 0.0427615i
$784$	−7.68585	−0.274495
$785$	0	0
$786$	7.27131	0.259359
$787$	− 25.3858i	− 0.904905i	−0.891789	−	0.452452i	$-0.850549\pi$
$787$	− 25.3858i	− 0.904905i	0.891789	−	0.452452i	$-0.149451\pi$
$788$	− 25.4292i	− 0.905879i
$789$	64.3551	2.29110
$790$	0	0
$791$	20.5573	0.730934
$792$	7.95715i	0.282745i
$793$	− 12.2829i	− 0.436177i
$794$	33.5113	1.18927
$795$	0	0
$796$	15.1035	0.535330
$797$	− 0.593884i	− 0.0210364i	−0.999945	−	0.0105182i	$-0.996652\pi$
$797$	− 0.593884i	− 0.0210364i	0.999945	−	0.0105182i	$-0.00334811\pi$
$798$	21.0361i	0.744670i
$799$	−9.21377	−0.325960
$800$	0	0
$801$	−8.26817	−0.292142
$802$	− 17.0147i	− 0.600810i
$803$	− 18.2671i	− 0.644632i
$804$	−12.0073	−0.423466
$805$	0	0
$806$	2.18248	0.0768746
$807$	− 22.4752i	− 0.791165i
$808$	− 5.63565i	− 0.198262i
$809$	35.2776	1.24029	0.620147	−	0.784486i	$-0.287073\pi$
$809$	35.2776	1.24029	0.620147	+	0.784486i	$0.287073\pi$
$810$	0	0
$811$	−13.1568	−0.461999	−0.231000	−	0.972954i	$-0.574200\pi$
$811$	−13.1568	−0.461999	−0.231000	+	0.972954i	$0.574200\pi$
$812$	− 3.83221i	− 0.134484i
$813$	− 70.1972i	− 2.46192i
$814$	−24.4078	−0.855493
$815$	0	0
$816$	−1.88240	−0.0658973
$817$	− 17.9572i	− 0.628241i
$818$	21.3461i	0.746347i
$819$	10.9357	0.382125
$820$	0	0
$821$	−48.2400	−1.68359	−0.841794	−	0.539799i	$-0.818500\pi$
$821$	−48.2400	−1.68359	−0.841794	+	0.539799i	$0.818500\pi$
$822$	45.1109i	1.57342i
$823$	32.7581i	1.14187i	0.820994	+	0.570937i	$0.193420\pi$
$823$	32.7581i	1.14187i	−0.820994	+	0.570937i	$0.806580\pi$
$824$	−17.5970	−0.613021
$825$	0	0
$826$	−9.06067	−0.315261
$827$	35.9118i	1.24878i	0.781115	+	0.624388i	$0.214651\pi$
$827$	35.9118i	1.24878i	−0.781115	+	0.624388i	$0.785349\pi$
$828$	20.2253i	0.702879i
$829$	−23.0361	−0.800077	−0.400039	−	0.916498i	$-0.631003\pi$
$829$	−23.0361	−0.800077	−0.400039	+	0.916498i	$0.631003\pi$
$830$	0	0
$831$	−36.9933	−1.28328
$832$	1.14637i	0.0397431i
$833$	− 6.17513i	− 0.213956i
$834$	15.0863	0.522396
$835$	0	0
$836$	−7.48929	−0.259022
$837$	2.27804i	0.0787405i
$838$	− 3.81079i	− 0.131642i
$839$	11.8757	0.409994	0.204997	−	0.978763i	$-0.434282\pi$
$839$	11.8757	0.409994	0.204997	+	0.978763i	$0.434282\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	− 23.9859i	− 0.826610i
$843$	28.4408i	0.979553i
$844$	−19.7967	−0.681431
$845$	0	0
$846$	28.5468	0.981460
$847$	2.99686i	0.102973i
$848$	0.560904i	0.0192615i
$849$	9.78202	0.335718
$850$	0	0
$851$	−62.0393	−2.12668
$852$	− 19.0361i	− 0.652167i
$853$	− 50.6493i	− 1.73420i	−0.498136	−	0.867099i	$-0.665982\pi$
$853$	− 50.6493i	− 1.73420i	0.498136	−	0.867099i	$-0.334018\pi$
$854$	41.0607	1.40507
$855$	0	0
$856$	−1.56090	−0.0533506
$857$	− 11.1453i	− 0.380716i	−0.981715	−	0.190358i	$-0.939035\pi$
$857$	− 11.1453i	− 0.380716i	0.981715	−	0.190358i	$-0.0609649\pi$
$858$	8.58546i	0.293103i
$859$	0.352789	0.0120370	0.00601850	−	0.999982i	$-0.498084\pi$
$859$	0.352789	0.0120370	0.00601850	+	0.999982i	$0.498084\pi$
$860$	0	0
$861$	77.5359	2.64242
$862$	7.00314i	0.238528i
$863$	5.06067i	0.172267i	0.996284	+	0.0861337i	$0.0274512\pi$
$863$	5.06067i	0.172267i	−0.996284	+	0.0861337i	$0.972549\pi$
$864$	−1.19656	−0.0407077
$865$	0	0
$866$	23.3790	0.794452
$867$	38.3173i	1.30132i
$868$	7.29587i	0.247638i
$869$	47.7429	1.61957
$870$	0	0
$871$	−5.87506	−0.199069
$872$	11.4966i	0.389325i
$873$	− 28.7251i	− 0.972197i
$874$	−19.0361	−0.643906
$875$	0	0
$876$	−13.3889	−0.452369
$877$	− 41.8370i	− 1.41274i	−0.707845	−	0.706368i	$-0.750332\pi$
$877$	− 41.8370i	− 1.41274i	0.707845	−	0.706368i	$-0.249668\pi$
$878$	− 13.7073i	− 0.462598i
$879$	−21.3190	−0.719071
$880$	0	0
$881$	2.10666	0.0709750	0.0354875	−	0.999370i	$-0.488702\pi$
$881$	2.10666	0.0709750	0.0354875	+	0.999370i	$0.488702\pi$
$882$	19.1323i	0.644218i
$883$	13.8389i	0.465717i	0.972511	+	0.232859i	$0.0748080\pi$
$883$	13.8389i	0.465717i	−0.972511	+	0.232859i	$0.925192\pi$
$884$	−0.921039	−0.0309779
$885$	0	0
$886$	9.25410	0.310897
$887$	− 37.7795i	− 1.26851i	−0.773123	−	0.634256i	$-0.781307\pi$
$887$	− 37.7795i	− 1.26851i	0.773123	−	0.634256i	$-0.218693\pi$
$888$	17.8898i	0.600341i
$889$	−30.2891	−1.01587
$890$	0	0
$891$	−32.8328	−1.09994
$892$	− 5.37169i	− 0.179858i
$893$	26.8683i	0.899114i
$894$	4.68585	0.156718
$895$	0	0
$896$	−3.83221	−0.128025
$897$	21.8223i	0.728627i
$898$	− 25.8971i	− 0.864197i
$899$	−1.90383	−0.0634962
$900$	0	0
$901$	−0.450654	−0.0150135
$902$	27.6044i	0.919125i
$903$	− 68.8156i	− 2.29004i
$904$	5.36435	0.178415
$905$	0	0
$906$	25.4292	0.844830
$907$	20.8683i	0.692921i	0.938064	+	0.346461i	$0.112617\pi$
$907$	20.8683i	0.692921i	−0.938064	+	0.346461i	$0.887383\pi$
$908$	28.3215i	0.939882i
$909$	−14.0288	−0.465305
$910$	0	0
$911$	30.5468	1.01206	0.506031	−	0.862515i	$-0.331112\pi$
$911$	30.5468	1.01206	0.506031	+	0.862515i	$0.331112\pi$
$912$	5.48929i	0.181769i
$913$	9.89710i	0.327546i
$914$	−26.5829	−0.879286
$915$	0	0
$916$	10.0147	0.330895
$917$	11.8933i	0.392753i
$918$	− 0.961365i	− 0.0317298i
$919$	−33.8898	−1.11792	−0.558960	−	0.829195i	$-0.688799\pi$
$919$	−33.8898	−1.11792	−0.558960	+	0.829195i	$0.688799\pi$
$920$	0	0
$921$	78.0466	2.57172
$922$	0.527923i	0.0173862i
$923$	− 9.31415i	− 0.306579i
$924$	−28.7005	−0.944178
$925$	0	0
$926$	38.0575	1.25065
$927$	43.8041i	1.43871i
$928$	− 1.00000i	− 0.0328266i
$929$	−44.5040	−1.46013	−0.730064	−	0.683379i	$-0.760510\pi$
$929$	−44.5040	−1.46013	−0.730064	+	0.683379i	$0.760510\pi$
$930$	0	0
$931$	−18.0073	−0.590167
$932$	23.3246i	0.764024i
$933$	46.3074i	1.51604i
$934$	−10.5181	−0.344161
$935$	0	0
$936$	2.85363	0.0932740
$937$	36.1793i	1.18193i	0.806698	+	0.590964i	$0.201252\pi$
$937$	36.1793i	1.18193i	−0.806698	+	0.590964i	$0.798748\pi$
$938$	− 19.6399i	− 0.641264i
$939$	−44.9603	−1.46722
$940$	0	0
$941$	11.1464	0.363361	0.181681	−	0.983358i	$-0.441846\pi$
$941$	11.1464	0.363361	0.181681	+	0.983358i	$0.441846\pi$
$942$	− 18.0246i	− 0.587272i
$943$	70.1642i	2.28486i
$944$	−2.36435	−0.0769529
$945$	0	0
$946$	24.4998	0.796556
$947$	− 38.8255i	− 1.26166i	−0.775922	−	0.630829i	$-0.782715\pi$
$947$	− 38.8255i	− 1.26166i	0.775922	−	0.630829i	$-0.217285\pi$
$948$	− 34.9933i	− 1.13653i
$949$	−6.55104	−0.212656
$950$	0	0
$951$	−72.0968	−2.33790
$952$	− 3.07896i	− 0.0997897i
$953$	− 9.83329i	− 0.318531i	−0.987236	−	0.159266i	$-0.949087\pi$
$953$	− 9.83329i	− 0.318531i	0.987236	−	0.159266i	$-0.0509127\pi$
$954$	1.39625	0.0452053
$955$	0	0
$956$	−21.9143	−0.708759
$957$	− 7.48929i	− 0.242094i
$958$	− 5.54935i	− 0.179291i
$959$	−73.7858	−2.38267
$960$	0	0
$961$	−27.3754	−0.883079
$962$	8.75325i	0.282216i
$963$	3.88554i	0.125210i
$964$	−9.45065	−0.304385
$965$	0	0
$966$	−72.9504	−2.34714
$967$	− 44.8500i	− 1.44228i	−0.692789	−	0.721140i	$-0.743618\pi$
$967$	− 44.8500i	− 1.44228i	0.692789	−	0.721140i	$-0.256382\pi$
$968$	0.782020i	0.0251351i
$969$	−4.41033	−0.141680
$970$	0	0
$971$	48.4496	1.55482	0.777410	−	0.628994i	$-0.216533\pi$
$971$	48.4496	1.55482	0.777410	+	0.628994i	$0.216533\pi$
$972$	20.4752i	0.656743i
$973$	24.6760i	0.791076i
$974$	−26.6858	−0.855070
$975$	0	0
$976$	10.7146	0.342966
$977$	− 33.2155i	− 1.06266i	−0.847166	−	0.531328i	$-0.821693\pi$
$977$	− 33.2155i	− 1.06266i	0.847166	−	0.531328i	$-0.178307\pi$
$978$	3.78202i	0.120936i
$979$	10.6174	0.339333
$980$	0	0
$981$	28.6184	0.913717
$982$	24.0575i	0.767707i
$983$	26.2457i	0.837107i	0.908192	+	0.418554i	$0.137463\pi$
$983$	26.2457i	0.837107i	−0.908192	+	0.418554i	$0.862537\pi$
$984$	20.2327	0.644994
$985$	0	0
$986$	0.803442	0.0255868
$987$	102.965i	3.27742i
$988$	2.68585i	0.0854481i
$989$	62.2730	1.98017
$990$	0	0
$991$	−40.5145	−1.28698	−0.643492	−	0.765453i	$-0.722515\pi$
$991$	−40.5145	−1.28698	−0.643492	+	0.765453i	$0.722515\pi$
$992$	1.90383i	0.0604466i
$993$	− 73.9693i	− 2.34735i
$994$	31.1365	0.987590
$995$	0	0
$996$	7.25410	0.229855
$997$	14.6227i	0.463104i	0.972823	+	0.231552i	$0.0743804\pi$
$997$	14.6227i	0.463104i	−0.972823	+	0.231552i	$0.925620\pi$
$998$	− 3.87085i	− 0.122530i
$999$	−9.13650	−0.289066

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1450.2.b.k.349.6		6
5.2	odd	4		1450.2.a.q.1.3	✓	3
5.3	odd	4		1450.2.a.s.1.1	yes	3
5.4	even	2	inner	1450.2.b.k.349.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1450.2.a.q.1.3	✓	3	5.2	odd	4
1450.2.a.s.1.1	yes	3	5.3	odd	4
1450.2.b.k.349.1		6	5.4	even	2	inner
1450.2.b.k.349.6		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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +2.34292i q^{3} -1.00000 q^{4} -2.34292 q^{6} -3.83221i q^{7} -1.00000i q^{8} -2.48929 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +2.34292i q^{3} -1.00000 q^{4} -2.34292 q^{6} -3.83221i q^{7} -1.00000i q^{8} -2.48929 q^{9} +3.19656 q^{11} -2.34292i q^{12} -1.14637i q^{13} +3.83221 q^{14} +1.00000 q^{16} +0.803442i q^{17} -2.48929i q^{18} +2.34292 q^{19} +8.97858 q^{21} +3.19656i q^{22} +8.12494i q^{23} +2.34292 q^{24} +1.14637 q^{26} +1.19656i q^{27} +3.83221i q^{28} -1.00000 q^{29} +1.90383 q^{31} +1.00000i q^{32} +7.48929i q^{33} -0.803442 q^{34} +2.48929 q^{36} +7.63565i q^{37} +2.34292i q^{38} +2.68585 q^{39} +8.63565 q^{41} +8.97858i q^{42} -7.66442i q^{43} -3.19656 q^{44} -8.12494 q^{46} +11.4679i q^{47} +2.34292i q^{48} -7.68585 q^{49} -1.88240 q^{51} +1.14637i q^{52} +0.560904i q^{53} -1.19656 q^{54} -3.83221 q^{56} +5.48929i q^{57} -1.00000i q^{58} -2.36435 q^{59} +10.7146 q^{61} +1.90383i q^{62} +9.53948i q^{63} -1.00000 q^{64} -7.48929 q^{66} -5.12494i q^{67} -0.803442i q^{68} -19.0361 q^{69} +8.12494 q^{71} +2.48929i q^{72} -5.71462i q^{73} -7.63565 q^{74} -2.34292 q^{76} -12.2499i q^{77} +2.68585i q^{78} +14.9357 q^{79} -10.2713 q^{81} +8.63565i q^{82} +3.09617i q^{83} -8.97858 q^{84} +7.66442 q^{86} -2.34292i q^{87} -3.19656i q^{88} +3.32150 q^{89} -4.39312 q^{91} -8.12494i q^{92} +4.46052i q^{93} -11.4679 q^{94} -2.34292 q^{96} +11.5395i q^{97} -7.68585i q^{98} -7.95715 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} - 2 q^{6}+O(q^{10}) \) 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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