LMFDB - Embedded newform 667.2.a.c.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [667,2,Mod(1,667)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(667, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("667.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 667 = 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	667.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$5.32602181482$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 4 x^{12} - 11 x^{11} + 58 x^{10} + 24 x^{9} - 298 x^{8} + 97 x^{7} + 641 x^{6} - 402 x^{5} + \cdots - 40 $ x^13 - 4x^12 - 11x^11 + 58x^10 + 24x^9 - 298x^8 + 97x^7 + 641x^6 - 402x^5 - 547x^4 + 352x^3 + 219x^2 - 88x - 40
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.552582$ of defining polynomial
Character	$\chi$	$=$	667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.552582 q^{2} -2.06764 q^{3} -1.69465 q^{4} +3.05371 q^{5} +1.14254 q^{6} -3.72348 q^{7} +2.04160 q^{8} +1.27512 q^{9} +O(q^{10})$	\(q-0.552582 q^{2} -2.06764 q^{3} -1.69465 q^{4} +3.05371 q^{5} +1.14254 q^{6} -3.72348 q^{7} +2.04160 q^{8} +1.27512 q^{9} -1.68743 q^{10} -2.20629 q^{11} +3.50392 q^{12} +2.13485 q^{13} +2.05753 q^{14} -6.31396 q^{15} +2.26115 q^{16} -1.44746 q^{17} -0.704606 q^{18} -3.68989 q^{19} -5.17498 q^{20} +7.69880 q^{21} +1.21916 q^{22} -1.00000 q^{23} -4.22128 q^{24} +4.32516 q^{25} -1.17968 q^{26} +3.56643 q^{27} +6.31000 q^{28} +1.00000 q^{29} +3.48898 q^{30} +5.48577 q^{31} -5.33267 q^{32} +4.56180 q^{33} +0.799839 q^{34} -11.3704 q^{35} -2.16088 q^{36} +8.63121 q^{37} +2.03897 q^{38} -4.41408 q^{39} +6.23446 q^{40} +9.34872 q^{41} -4.25422 q^{42} +5.07703 q^{43} +3.73890 q^{44} +3.89384 q^{45} +0.552582 q^{46} +7.89286 q^{47} -4.67524 q^{48} +6.86429 q^{49} -2.39001 q^{50} +2.99281 q^{51} -3.61782 q^{52} -4.24428 q^{53} -1.97075 q^{54} -6.73738 q^{55} -7.60185 q^{56} +7.62935 q^{57} -0.552582 q^{58} -10.6564 q^{59} +10.7000 q^{60} +3.09578 q^{61} -3.03134 q^{62} -4.74786 q^{63} -1.57557 q^{64} +6.51921 q^{65} -2.52077 q^{66} +15.3131 q^{67} +2.45294 q^{68} +2.06764 q^{69} +6.28310 q^{70} +8.92059 q^{71} +2.60327 q^{72} -0.542638 q^{73} -4.76945 q^{74} -8.94286 q^{75} +6.25309 q^{76} +8.21508 q^{77} +2.43914 q^{78} +4.51387 q^{79} +6.90492 q^{80} -11.1994 q^{81} -5.16593 q^{82} +14.3983 q^{83} -13.0468 q^{84} -4.42012 q^{85} -2.80548 q^{86} -2.06764 q^{87} -4.50436 q^{88} +4.87686 q^{89} -2.15166 q^{90} -7.94905 q^{91} +1.69465 q^{92} -11.3426 q^{93} -4.36146 q^{94} -11.2679 q^{95} +11.0260 q^{96} -4.94651 q^{97} -3.79309 q^{98} -2.81327 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 4 q^{2} + 3 q^{3} + 12 q^{4} + 16 q^{5} + q^{7} + 6 q^{8} + 14 q^{9}+O(q^{10}) $ 13 * q + 4 * q^2 + 3 * q^3 + 12 * q^4 + 16 * q^5 + q^7 + 6 * q^8 + 14 * q^9	\( 13 q + 4 q^{2} + 3 q^{3} + 12 q^{4} + 16 q^{5} + q^{7} + 6 q^{8} + 14 q^{9} + 10 q^{10} + 10 q^{11} + 3 q^{12} + 7 q^{13} - 12 q^{14} + 8 q^{15} + 2 q^{16} + 26 q^{17} + 7 q^{18} + 25 q^{20} + 11 q^{21} - 15 q^{22} - 13 q^{23} + 10 q^{24} + 19 q^{25} - 15 q^{26} + 12 q^{27} + 5 q^{28} + 13 q^{29} + 7 q^{30} - 6 q^{31} + 16 q^{32} + 3 q^{33} + 11 q^{34} + q^{35} - 22 q^{36} + 15 q^{37} + 8 q^{38} - 4 q^{39} + 14 q^{40} + 9 q^{41} - 34 q^{42} + q^{43} + 29 q^{44} + 16 q^{45} - 4 q^{46} + 15 q^{47} - 15 q^{48} + 4 q^{49} + 31 q^{50} - 14 q^{51} - 8 q^{52} + 43 q^{53} - 35 q^{54} - 3 q^{55} - 5 q^{56} + 6 q^{57} + 4 q^{58} - 9 q^{59} + 3 q^{60} + 20 q^{61} + 11 q^{62} + 21 q^{63} - 16 q^{64} - 25 q^{65} - q^{66} + q^{67} + 21 q^{68} - 3 q^{69} - 2 q^{70} + 17 q^{71} - 59 q^{72} + 26 q^{73} + 11 q^{74} - 43 q^{75} + 8 q^{76} + 17 q^{77} - 10 q^{78} + 5 q^{79} + 10 q^{80} - 3 q^{81} - 25 q^{82} + 4 q^{83} - 78 q^{84} + 20 q^{85} - 13 q^{86} + 3 q^{87} - 32 q^{88} + 48 q^{89} + 17 q^{90} - 9 q^{91} - 12 q^{92} - 8 q^{93} - 65 q^{94} + 8 q^{95} + 8 q^{96} + 30 q^{97} + 2 q^{98} + 4 q^{99}+O(q^{100}) \) 13 * q + 4 * q^2 + 3 * q^3 + 12 * q^4 + 16 * q^5 + q^7 + 6 * q^8 + 14 * q^9 + 10 * q^10 + 10 * q^11 + 3 * q^12 + 7 * q^13 - 12 * q^14 + 8 * q^15 + 2 * q^16 + 26 * q^17 + 7 * q^18 + 25 * q^20 + 11 * q^21 - 15 * q^22 - 13 * q^23 + 10 * q^24 + 19 * q^25 - 15 * q^26 + 12 * q^27 + 5 * q^28 + 13 * q^29 + 7 * q^30 - 6 * q^31 + 16 * q^32 + 3 * q^33 + 11 * q^34 + q^35 - 22 * q^36 + 15 * q^37 + 8 * q^38 - 4 * q^39 + 14 * q^40 + 9 * q^41 - 34 * q^42 + q^43 + 29 * q^44 + 16 * q^45 - 4 * q^46 + 15 * q^47 - 15 * q^48 + 4 * q^49 + 31 * q^50 - 14 * q^51 - 8 * q^52 + 43 * q^53 - 35 * q^54 - 3 * q^55 - 5 * q^56 + 6 * q^57 + 4 * q^58 - 9 * q^59 + 3 * q^60 + 20 * q^61 + 11 * q^62 + 21 * q^63 - 16 * q^64 - 25 * q^65 - q^66 + q^67 + 21 * q^68 - 3 * q^69 - 2 * q^70 + 17 * q^71 - 59 * q^72 + 26 * q^73 + 11 * q^74 - 43 * q^75 + 8 * q^76 + 17 * q^77 - 10 * q^78 + 5 * q^79 + 10 * q^80 - 3 * q^81 - 25 * q^82 + 4 * q^83 - 78 * q^84 + 20 * q^85 - 13 * q^86 + 3 * q^87 - 32 * q^88 + 48 * q^89 + 17 * q^90 - 9 * q^91 - 12 * q^92 - 8 * q^93 - 65 * q^94 + 8 * q^95 + 8 * q^96 + 30 * q^97 + 2 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.552582	−0.390735	−0.195367	−	0.980730i	$-0.562590\pi$
$2$	−0.552582	−0.390735	−0.195367	+	0.980730i	$0.562590\pi$
$3$	−2.06764	−1.19375	−0.596875	−	0.802334i	$-0.703591\pi$
$3$	−2.06764	−1.19375	−0.596875	+	0.802334i	$0.703591\pi$
$4$	−1.69465	−0.847326
$5$	3.05371	1.36566	0.682831	−	0.730576i	$-0.260749\pi$
$5$	3.05371	1.36566	0.682831	+	0.730576i	$0.260749\pi$
$6$	1.14254	0.466439
$7$	−3.72348	−1.40734	−0.703671	−	0.710526i	$-0.748457\pi$
$7$	−3.72348	−1.40734	−0.703671	+	0.710526i	$0.748457\pi$
$8$	2.04160	0.721814
$9$	1.27512	0.425038
$10$	−1.68743	−0.533611
$11$	−2.20629	−0.665222	−0.332611	−	0.943064i	$-0.607930\pi$
$11$	−2.20629	−0.665222	−0.332611	+	0.943064i	$0.607930\pi$
$12$	3.50392	1.01150
$13$	2.13485	0.592100	0.296050	−	0.955173i	$-0.404331\pi$
$13$	2.13485	0.592100	0.296050	+	0.955173i	$0.404331\pi$
$14$	2.05753	0.549898
$15$	−6.31396	−1.63026
$16$	2.26115	0.565289
$17$	−1.44746	−0.351060	−0.175530	−	0.984474i	$-0.556164\pi$
$17$	−1.44746	−0.351060	−0.175530	+	0.984474i	$0.556164\pi$
$18$	−0.704606	−0.166077
$19$	−3.68989	−0.846520	−0.423260	−	0.906008i	$-0.639114\pi$
$19$	−3.68989	−0.846520	−0.423260	+	0.906008i	$0.639114\pi$
$20$	−5.17498	−1.15716
$21$	7.69880	1.68001
$22$	1.21916	0.259925
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−4.22128	−0.861666
$25$	4.32516	0.865033
$26$	−1.17968	−0.231354
$27$	3.56643	0.686360
$28$	6.31000	1.19248
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	3.48898	0.636999
$31$	5.48577	0.985273	0.492637	−	0.870235i	$-0.336033\pi$
$31$	5.48577	0.985273	0.492637	+	0.870235i	$0.336033\pi$
$32$	−5.33267	−0.942692
$33$	4.56180	0.794108
$34$	0.799839	0.137171
$35$	−11.3704	−1.92195
$36$	−2.16088	−0.360146
$37$	8.63121	1.41896	0.709481	−	0.704725i	$-0.248929\pi$
$37$	8.63121	1.41896	0.709481	+	0.704725i	$0.248929\pi$
$38$	2.03897	0.330765
$39$	−4.41408	−0.706819
$40$	6.23446	0.985755
$41$	9.34872	1.46002	0.730012	−	0.683434i	$-0.239514\pi$
$41$	9.34872	1.46002	0.730012	+	0.683434i	$0.239514\pi$
$42$	−4.25422	−0.656440
$43$	5.07703	0.774240	0.387120	−	0.922029i	$-0.373470\pi$
$43$	5.07703	0.774240	0.387120	+	0.922029i	$0.373470\pi$
$44$	3.73890	0.563660
$45$	3.89384	0.580459
$46$	0.552582	0.0814738
$47$	7.89286	1.15129	0.575646	−	0.817699i	$-0.304751\pi$
$47$	7.89286	1.15129	0.575646	+	0.817699i	$0.304751\pi$
$48$	−4.67524	−0.674813
$49$	6.86429	0.980613
$50$	−2.39001	−0.337998
$51$	2.99281	0.419078
$52$	−3.61782	−0.501702
$53$	−4.24428	−0.582997	−0.291499	−	0.956571i	$-0.594154\pi$
$53$	−4.24428	−0.582997	−0.291499	+	0.956571i	$0.594154\pi$
$54$	−1.97075	−0.268185
$55$	−6.73738	−0.908468
$56$	−7.60185	−1.01584
$57$	7.62935	1.01053
$58$	−0.552582	−0.0725576
$59$	−10.6564	−1.38734	−0.693669	−	0.720294i	$-0.744007\pi$
$59$	−10.6564	−1.38734	−0.693669	+	0.720294i	$0.744007\pi$
$60$	10.7000	1.38136
$61$	3.09578	0.396374	0.198187	−	0.980164i	$-0.436495\pi$
$61$	3.09578	0.396374	0.198187	+	0.980164i	$0.436495\pi$
$62$	−3.03134	−0.384980
$63$	−4.74786	−0.598175
$64$	−1.57557	−0.196946
$65$	6.51921	0.808608
$66$	−2.52077	−0.310286
$67$	15.3131	1.87079	0.935396	−	0.353603i	$-0.115044\pi$
$67$	15.3131	1.87079	0.935396	+	0.353603i	$0.115044\pi$
$68$	2.45294	0.297462
$69$	2.06764	0.248914
$70$	6.28310	0.750974
$71$	8.92059	1.05868	0.529340	−	0.848410i	$-0.322440\pi$
$71$	8.92059	1.05868	0.529340	+	0.848410i	$0.322440\pi$
$72$	2.60327	0.306799
$73$	−0.542638	−0.0635109	−0.0317555	−	0.999496i	$-0.510110\pi$
$73$	−0.542638	−0.0635109	−0.0317555	+	0.999496i	$0.510110\pi$
$74$	−4.76945	−0.554438
$75$	−8.94286	−1.03263
$76$	6.25309	0.717278
$77$	8.21508	0.936195
$78$	2.43914	0.276179
$79$	4.51387	0.507851	0.253925	−	0.967224i	$-0.418278\pi$
$79$	4.51387	0.507851	0.253925	+	0.967224i	$0.418278\pi$
$80$	6.90492	0.771993
$81$	−11.1994	−1.24438
$82$	−5.16593	−0.570482
$83$	14.3983	1.58042	0.790208	−	0.612839i	$-0.209973\pi$
$83$	14.3983	1.58042	0.790208	+	0.612839i	$0.209973\pi$
$84$	−13.0468	−1.42352
$85$	−4.42012	−0.479429
$86$	−2.80548	−0.302522
$87$	−2.06764	−0.221674
$88$	−4.50436	−0.480167
$89$	4.87686	0.516946	0.258473	−	0.966018i	$-0.416781\pi$
$89$	4.87686	0.516946	0.258473	+	0.966018i	$0.416781\pi$
$90$	−2.15166	−0.226805
$91$	−7.94905	−0.833287
$92$	1.69465	0.176680
$93$	−11.3426	−1.17617
$94$	−4.36146	−0.449850
$95$	−11.2679	−1.15606
$96$	11.0260	1.12534
$97$	−4.94651	−0.502242	−0.251121	−	0.967956i	$-0.580799\pi$
$97$	−4.94651	−0.502242	−0.251121	+	0.967956i	$0.580799\pi$
$98$	−3.79309	−0.383160
$99$	−2.81327	−0.282745
$100$	−7.32965	−0.732965
$101$	−15.8608	−1.57820	−0.789102	−	0.614262i	$-0.789454\pi$
$101$	−15.8608	−1.57820	−0.789102	+	0.614262i	$0.789454\pi$
$102$	−1.65378	−0.163748
$103$	−7.50304	−0.739296	−0.369648	−	0.929172i	$-0.620522\pi$
$103$	−7.50304	−0.739296	−0.369648	+	0.929172i	$0.620522\pi$
$104$	4.35850	0.427386
$105$	23.5099	2.29433
$106$	2.34532	0.227797
$107$	−8.86777	−0.857280	−0.428640	−	0.903475i	$-0.641007\pi$
$107$	−8.86777	−0.857280	−0.428640	+	0.903475i	$0.641007\pi$
$108$	−6.04386	−0.581571
$109$	2.85144	0.273118	0.136559	−	0.990632i	$-0.456396\pi$
$109$	2.85144	0.273118	0.136559	+	0.990632i	$0.456396\pi$
$110$	3.72296	0.354970
$111$	−17.8462	−1.69389
$112$	−8.41936	−0.795555
$113$	12.8542	1.20923	0.604613	−	0.796519i	$-0.293328\pi$
$113$	12.8542	1.20923	0.604613	+	0.796519i	$0.293328\pi$
$114$	−4.21585	−0.394850
$115$	−3.05371	−0.284760
$116$	−1.69465	−0.157345
$117$	2.72217	0.251665
$118$	5.88851	0.542081
$119$	5.38958	0.494062
$120$	−12.8906	−1.17674
$121$	−6.13228	−0.557480
$122$	−1.71067	−0.154877
$123$	−19.3297	−1.74290
$124$	−9.29647	−0.834848
$125$	−2.06076	−0.184320
$126$	2.62359	0.233728
$127$	−17.9824	−1.59568	−0.797839	−	0.602870i	$-0.794024\pi$
$127$	−17.9824	−1.59568	−0.797839	+	0.602870i	$0.794024\pi$
$128$	11.5360	1.01965
$129$	−10.4975	−0.924249
$130$	−3.60240	−0.315951
$131$	−0.197886	−0.0172894	−0.00864471	−	0.999963i	$-0.502752\pi$
$131$	−0.197886	−0.0172894	−0.00864471	+	0.999963i	$0.502752\pi$
$132$	−7.73067	−0.672869
$133$	13.7392	1.19134
$134$	−8.46174	−0.730983
$135$	10.8909	0.937336
$136$	−2.95513	−0.253400
$137$	4.46451	0.381428	0.190714	−	0.981646i	$-0.438920\pi$
$137$	4.46451	0.381428	0.190714	+	0.981646i	$0.438920\pi$
$138$	−1.14254	−0.0972593
$139$	−10.8793	−0.922766	−0.461383	−	0.887201i	$-0.652647\pi$
$139$	−10.8793	−0.922766	−0.461383	+	0.887201i	$0.652647\pi$
$140$	19.2689	1.62852
$141$	−16.3196	−1.37435
$142$	−4.92936	−0.413663
$143$	−4.71009	−0.393877
$144$	2.88323	0.240269
$145$	3.05371	0.253597
$146$	0.299852	0.0248159
$147$	−14.1929	−1.17061
$148$	−14.6269	−1.20232
$149$	6.52247	0.534342	0.267171	−	0.963649i	$-0.413911\pi$
$149$	6.52247	0.534342	0.267171	+	0.963649i	$0.413911\pi$
$150$	4.94167	0.403485
$151$	1.64570	0.133925	0.0669627	−	0.997755i	$-0.478669\pi$
$151$	1.64570	0.133925	0.0669627	+	0.997755i	$0.478669\pi$
$152$	−7.53328	−0.611030
$153$	−1.84568	−0.149214
$154$	−4.53950	−0.365804
$155$	16.7520	1.34555
$156$	7.48034	0.598906
$157$	1.65807	0.132328	0.0661642	−	0.997809i	$-0.478924\pi$
$157$	1.65807	0.132328	0.0661642	+	0.997809i	$0.478924\pi$
$158$	−2.49429	−0.198435
$159$	8.77563	0.695953
$160$	−16.2845	−1.28740
$161$	3.72348	0.293451
$162$	6.18860	0.486223
$163$	23.0927	1.80876	0.904379	−	0.426731i	$-0.140335\pi$
$163$	23.0927	1.80876	0.904379	+	0.426731i	$0.140335\pi$
$164$	−15.8428	−1.23712
$165$	13.9304	1.08448
$166$	−7.95623	−0.617523
$167$	16.4340	1.27170	0.635851	−	0.771812i	$-0.280649\pi$
$167$	16.4340	1.27170	0.635851	+	0.771812i	$0.280649\pi$
$168$	15.7179	1.21266
$169$	−8.44244	−0.649418
$170$	2.44248	0.187330
$171$	−4.70504	−0.359803
$172$	−8.60381	−0.656034
$173$	−3.10259	−0.235885	−0.117943	−	0.993020i	$-0.537630\pi$
$173$	−3.10259	−0.235885	−0.117943	+	0.993020i	$0.537630\pi$
$174$	1.14254	0.0866156
$175$	−16.1047	−1.21740
$176$	−4.98876	−0.376042
$177$	22.0334	1.65614
$178$	−2.69487	−0.201989
$179$	−5.99479	−0.448072	−0.224036	−	0.974581i	$-0.571923\pi$
$179$	−5.99479	−0.448072	−0.224036	+	0.974581i	$0.571923\pi$
$180$	−6.59870	−0.491838
$181$	6.81903	0.506855	0.253427	−	0.967354i	$-0.418442\pi$
$181$	6.81903	0.506855	0.253427	+	0.967354i	$0.418442\pi$
$182$	4.39250	0.325594
$183$	−6.40095	−0.473172
$184$	−2.04160	−0.150509
$185$	26.3572	1.93782
$186$	6.26770	0.459570
$187$	3.19351	0.233533
$188$	−13.3757	−0.975520
$189$	−13.2795	−0.965944
$190$	6.22643	0.451713
$191$	19.8292	1.43479	0.717394	−	0.696668i	$-0.245335\pi$
$191$	19.8292	1.43479	0.717394	+	0.696668i	$0.245335\pi$
$192$	3.25770	0.235104
$193$	7.83330	0.563853	0.281927	−	0.959436i	$-0.409026\pi$
$193$	7.83330	0.563853	0.281927	+	0.959436i	$0.409026\pi$
$194$	2.73335	0.196243
$195$	−13.4793	−0.965275
$196$	−11.6326	−0.830900
$197$	−15.8865	−1.13187	−0.565934	−	0.824451i	$-0.691484\pi$
$197$	−15.8865	−1.13187	−0.565934	+	0.824451i	$0.691484\pi$
$198$	1.55457	0.110478
$199$	−5.62353	−0.398641	−0.199321	−	0.979934i	$-0.563874\pi$
$199$	−5.62353	−0.398641	−0.199321	+	0.979934i	$0.563874\pi$
$200$	8.83025	0.624393
$201$	−31.6619	−2.23326
$202$	8.76437	0.616659
$203$	−3.72348	−0.261337
$204$	−5.07178	−0.355096
$205$	28.5483	1.99390
$206$	4.14605	0.288869
$207$	−1.27512	−0.0886266
$208$	4.82721	0.334707
$209$	8.14098	0.563123
$210$	−12.9912	−0.896475
$211$	1.58877	0.109375	0.0546877	−	0.998504i	$-0.482584\pi$
$211$	1.58877	0.109375	0.0546877	+	0.998504i	$0.482584\pi$
$212$	7.19259	0.493989
$213$	−18.4445	−1.26380
$214$	4.90017	0.334969
$215$	15.5038	1.05735
$216$	7.28123	0.495425
$217$	−20.4261	−1.38662
$218$	−1.57565	−0.106717
$219$	1.12198	0.0758162
$220$	11.4175	0.769769
$221$	−3.09010	−0.207863
$222$	9.86149	0.661860
$223$	21.1993	1.41961	0.709806	−	0.704397i	$-0.248782\pi$
$223$	21.1993	1.41961	0.709806	+	0.704397i	$0.248782\pi$
$224$	19.8561	1.32669
$225$	5.51508	0.367672
$226$	−7.10303	−0.472486
$227$	19.2280	1.27621	0.638103	−	0.769951i	$-0.279719\pi$
$227$	19.2280	1.27621	0.638103	+	0.769951i	$0.279719\pi$
$228$	−12.9291	−0.856251
$229$	−21.1059	−1.39472	−0.697358	−	0.716723i	$-0.745641\pi$
$229$	−21.1059	−1.39472	−0.697358	+	0.716723i	$0.745641\pi$
$230$	1.68743	0.111266
$231$	−16.9858	−1.11758
$232$	2.04160	0.134038
$233$	14.7370	0.965452	0.482726	−	0.875771i	$-0.339647\pi$
$233$	14.7370	0.965452	0.482726	+	0.875771i	$0.339647\pi$
$234$	−1.50423	−0.0983343
$235$	24.1025	1.57228
$236$	18.0588	1.17553
$237$	−9.33305	−0.606246
$238$	−2.97818	−0.193047
$239$	−7.23214	−0.467808	−0.233904	−	0.972260i	$-0.575150\pi$
$239$	−7.23214	−0.467808	−0.233904	+	0.972260i	$0.575150\pi$
$240$	−14.2768	−0.921567
$241$	15.1694	0.977147	0.488574	−	0.872523i	$-0.337517\pi$
$241$	15.1694	0.977147	0.488574	+	0.872523i	$0.337517\pi$
$242$	3.38859	0.217827
$243$	12.4570	0.799119
$244$	−5.24628	−0.335859
$245$	20.9616	1.33919
$246$	10.6813	0.681013
$247$	−7.87735	−0.501224
$248$	11.1997	0.711184
$249$	−29.7704	−1.88662
$250$	1.13874	0.0720201
$251$	−19.7720	−1.24800	−0.623998	−	0.781426i	$-0.714493\pi$
$251$	−19.7720	−1.24800	−0.623998	+	0.781426i	$0.714493\pi$
$252$	8.04598	0.506849
$253$	2.20629	0.138708
$254$	9.93674	0.623487
$255$	9.13920	0.572319
$256$	−3.22344	−0.201465
$257$	26.2581	1.63793	0.818967	−	0.573840i	$-0.194547\pi$
$257$	26.2581	1.63793	0.818967	+	0.573840i	$0.194547\pi$
$258$	5.80071	0.361136
$259$	−32.1381	−1.99697
$260$	−11.0478	−0.685155
$261$	1.27512	0.0789277
$262$	0.109348	0.00675557
$263$	3.21753	0.198401	0.0992007	−	0.995067i	$-0.468371\pi$
$263$	3.21753	0.198401	0.0992007	+	0.995067i	$0.468371\pi$
$264$	9.31338	0.573199
$265$	−12.9608	−0.796177
$266$	−7.59206	−0.465499
$267$	−10.0836	−0.617104
$268$	−25.9504	−1.58517
$269$	9.08997	0.554226	0.277113	−	0.960837i	$-0.410622\pi$
$269$	9.08997	0.554226	0.277113	+	0.960837i	$0.410622\pi$
$270$	−6.01810	−0.366250
$271$	2.02480	0.122998	0.0614988	−	0.998107i	$-0.480412\pi$
$271$	2.02480	0.122998	0.0614988	+	0.998107i	$0.480412\pi$
$272$	−3.27292	−0.198450
$273$	16.4357	0.994736
$274$	−2.46701	−0.149037
$275$	−9.54257	−0.575438
$276$	−3.50392	−0.210911
$277$	−4.85414	−0.291657	−0.145829	−	0.989310i	$-0.546585\pi$
$277$	−4.85414	−0.291657	−0.145829	+	0.989310i	$0.546585\pi$
$278$	6.01168	0.360557
$279$	6.99499	0.418779
$280$	−23.2139	−1.38729
$281$	8.16942	0.487347	0.243673	−	0.969857i	$-0.421648\pi$
$281$	8.16942	0.487347	0.243673	+	0.969857i	$0.421648\pi$
$282$	9.01790	0.537008
$283$	−20.6081	−1.22502	−0.612511	−	0.790462i	$-0.709841\pi$
$283$	−20.6081	−1.22502	−0.612511	+	0.790462i	$0.709841\pi$
$284$	−15.1173	−0.897047
$285$	23.2979	1.38005
$286$	2.60271	0.153902
$287$	−34.8097	−2.05475
$288$	−6.79977	−0.400680
$289$	−14.9049	−0.876757
$290$	−1.68743	−0.0990892
$291$	10.2276	0.599551
$292$	0.919582	0.0538145
$293$	16.7084	0.976118	0.488059	−	0.872811i	$-0.337705\pi$
$293$	16.7084	0.976118	0.488059	+	0.872811i	$0.337705\pi$
$294$	7.84272	0.457397
$295$	−32.5414	−1.89464
$296$	17.6215	1.02423
$297$	−7.86859	−0.456582
$298$	−3.60420	−0.208786
$299$	−2.13485	−0.123461
$300$	15.1550	0.874977
$301$	−18.9042	−1.08962
$302$	−0.909386	−0.0523293
$303$	32.7943	1.88398
$304$	−8.34342	−0.478528
$305$	9.45363	0.541314
$306$	1.01989	0.0583031
$307$	0.924479	0.0527628	0.0263814	−	0.999652i	$-0.491602\pi$
$307$	0.924479	0.0527628	0.0263814	+	0.999652i	$0.491602\pi$
$308$	−13.9217	−0.793263
$309$	15.5135	0.882535
$310$	−9.25684	−0.525753
$311$	18.2768	1.03638	0.518190	−	0.855266i	$-0.326606\pi$
$311$	18.2768	1.03638	0.518190	+	0.855266i	$0.326606\pi$
$312$	−9.01179	−0.510192
$313$	−3.24200	−0.183248	−0.0916242	−	0.995794i	$-0.529206\pi$
$313$	−3.24200	−0.183248	−0.0916242	+	0.995794i	$0.529206\pi$
$314$	−0.916220	−0.0517053
$315$	−14.4986	−0.816904
$316$	−7.64945	−0.430315
$317$	8.19765	0.460426	0.230213	−	0.973140i	$-0.426058\pi$
$317$	8.19765	0.460426	0.230213	+	0.973140i	$0.426058\pi$
$318$	−4.84926	−0.271933
$319$	−2.20629	−0.123529
$320$	−4.81133	−0.268962
$321$	18.3353	1.02338
$322$	−2.05753	−0.114662
$323$	5.34096	0.297179
$324$	18.9791	1.05440
$325$	9.23356	0.512185
$326$	−12.7606	−0.706744
$327$	−5.89573	−0.326035
$328$	19.0863	1.05387
$329$	−29.3889	−1.62026
$330$	−7.69771	−0.423745
$331$	25.0079	1.37456	0.687280	−	0.726393i	$-0.258805\pi$
$331$	25.0079	1.37456	0.687280	+	0.726393i	$0.258805\pi$
$332$	−24.4001	−1.33913
$333$	11.0058	0.603113
$334$	−9.08114	−0.496898
$335$	46.7618	2.55487
$336$	17.4082	0.949693
$337$	2.10087	0.114442	0.0572208	−	0.998362i	$-0.481776\pi$
$337$	2.10087	0.114442	0.0572208	+	0.998362i	$0.481776\pi$
$338$	4.66514	0.253750
$339$	−26.5779	−1.44351
$340$	7.49057	0.406233
$341$	−12.1032	−0.655425
$342$	2.59992	0.140588
$343$	0.505304	0.0272838
$344$	10.3653	0.558858
$345$	6.31396	0.339932
$346$	1.71443	0.0921685
$347$	−18.7585	−1.00701	−0.503505	−	0.863992i	$-0.667956\pi$
$347$	−18.7585	−1.00701	−0.503505	+	0.863992i	$0.667956\pi$
$348$	3.50392	0.187830
$349$	−34.3513	−1.83878	−0.919391	−	0.393345i	$-0.871318\pi$
$349$	−34.3513	−1.83878	−0.919391	+	0.393345i	$0.871318\pi$
$350$	8.89915	0.475679
$351$	7.61378	0.406394
$352$	11.7654	0.627099
$353$	−9.58843	−0.510341	−0.255170	−	0.966896i	$-0.582132\pi$
$353$	−9.58843	−0.510341	−0.255170	+	0.966896i	$0.582132\pi$
$354$	−12.1753	−0.647109
$355$	27.2409	1.44580
$356$	−8.26458	−0.438022
$357$	−11.1437	−0.589786
$358$	3.31262	0.175077
$359$	−12.1565	−0.641597	−0.320799	−	0.947147i	$-0.603951\pi$
$359$	−12.1565	−0.641597	−0.320799	+	0.947147i	$0.603951\pi$
$360$	7.94965	0.418984
$361$	−5.38469	−0.283405
$362$	−3.76808	−0.198046
$363$	12.6793	0.665492
$364$	13.4709	0.706066
$365$	−1.65706	−0.0867345
$366$	3.53705	0.184885
$367$	18.4847	0.964894	0.482447	−	0.875925i	$-0.339748\pi$
$367$	18.4847	0.964894	0.482447	+	0.875925i	$0.339748\pi$
$368$	−2.26115	−0.117871
$369$	11.9207	0.620566
$370$	−14.5645	−0.757174
$371$	15.8035	0.820477
$372$	19.2217	0.996600
$373$	31.7697	1.64497	0.822487	−	0.568784i	$-0.192586\pi$
$373$	31.7697	1.64497	0.822487	+	0.568784i	$0.192586\pi$
$374$	−1.76468	−0.0912493
$375$	4.26089	0.220032
$376$	16.1141	0.831019
$377$	2.13485	0.109950
$378$	7.33803	0.377428
$379$	32.7667	1.68311	0.841555	−	0.540172i	$-0.181641\pi$
$379$	32.7667	1.68311	0.841555	+	0.540172i	$0.181641\pi$
$380$	19.0951	0.979560
$381$	37.1810	1.90484
$382$	−10.9572	−0.560621
$383$	−17.5363	−0.896062	−0.448031	−	0.894018i	$-0.647875\pi$
$383$	−17.5363	−0.896062	−0.448031	+	0.894018i	$0.647875\pi$
$384$	−23.8522	−1.21720
$385$	25.0865	1.27853
$386$	−4.32854	−0.220317
$387$	6.47380	0.329082
$388$	8.38262	0.425563
$389$	16.0290	0.812705	0.406353	−	0.913716i	$-0.366800\pi$
$389$	16.0290	0.812705	0.406353	+	0.913716i	$0.366800\pi$
$390$	7.44844	0.377167
$391$	1.44746	0.0732011
$392$	14.0141	0.707821
$393$	0.409157	0.0206392
$394$	8.77861	0.442260
$395$	13.7841	0.693552
$396$	4.76752	0.239577
$397$	−37.7189	−1.89306	−0.946528	−	0.322622i	$-0.895436\pi$
$397$	−37.7189	−1.89306	−0.946528	+	0.322622i	$0.895436\pi$
$398$	3.10746	0.155763
$399$	−28.4077	−1.42217
$400$	9.77986	0.488993
$401$	−11.8874	−0.593629	−0.296814	−	0.954935i	$-0.595924\pi$
$401$	−11.8874	−0.593629	−0.296814	+	0.954935i	$0.595924\pi$
$402$	17.4958	0.872611
$403$	11.7113	0.583380
$404$	26.8785	1.33725
$405$	−34.1998	−1.69940
$406$	2.05753	0.102113
$407$	−19.0430	−0.943924
$408$	6.11013	0.302496
$409$	−5.38261	−0.266153	−0.133076	−	0.991106i	$-0.542486\pi$
$409$	−5.38261	−0.266153	−0.133076	+	0.991106i	$0.542486\pi$
$410$	−15.7753	−0.779086
$411$	−9.23097	−0.455330
$412$	12.7150	0.626425
$413$	39.6787	1.95246
$414$	0.704606	0.0346295
$415$	43.9682	2.15831
$416$	−11.3844	−0.558168
$417$	22.4943	1.10155
$418$	−4.49856	−0.220032
$419$	13.8668	0.677439	0.338719	−	0.940887i	$-0.390006\pi$
$419$	13.8668	0.677439	0.338719	+	0.940887i	$0.390006\pi$
$420$	−39.8411	−1.94405
$421$	1.34987	0.0657885	0.0328942	−	0.999459i	$-0.489528\pi$
$421$	1.34987	0.0657885	0.0328942	+	0.999459i	$0.489528\pi$
$422$	−0.877926	−0.0427368
$423$	10.0643	0.489344
$424$	−8.66513	−0.420816
$425$	−6.26049	−0.303678
$426$	10.1921	0.493810
$427$	−11.5271	−0.557835
$428$	15.0278	0.726396
$429$	9.73875	0.470191
$430$	−8.56713	−0.413143
$431$	−17.6075	−0.848121	−0.424061	−	0.905634i	$-0.639396\pi$
$431$	−17.6075	−0.848121	−0.424061	+	0.905634i	$0.639396\pi$
$432$	8.06425	0.387992
$433$	35.5611	1.70896	0.854479	−	0.519486i	$-0.173877\pi$
$433$	35.5611	1.70896	0.854479	+	0.519486i	$0.173877\pi$
$434$	11.2871	0.541799
$435$	−6.31396	−0.302731
$436$	−4.83220	−0.231420
$437$	3.68989	0.176512
$438$	−0.619984	−0.0296240
$439$	−31.5384	−1.50525	−0.752623	−	0.658451i	$-0.771212\pi$
$439$	−31.5384	−1.50525	−0.752623	+	0.658451i	$0.771212\pi$
$440$	−13.7550	−0.655745
$441$	8.75276	0.416798
$442$	1.70753	0.0812191
$443$	20.0382	0.952045	0.476022	−	0.879433i	$-0.342078\pi$
$443$	20.0382	0.952045	0.476022	+	0.879433i	$0.342078\pi$
$444$	30.2431	1.43527
$445$	14.8925	0.705974
$446$	−11.7144	−0.554692
$447$	−13.4861	−0.637870
$448$	5.86659	0.277171
$449$	−18.8325	−0.888761	−0.444380	−	0.895838i	$-0.646576\pi$
$449$	−18.8325	−0.888761	−0.444380	+	0.895838i	$0.646576\pi$
$450$	−3.04754	−0.143662
$451$	−20.6260	−0.971240
$452$	−21.7835	−1.02461
$453$	−3.40271	−0.159873
$454$	−10.6250	−0.498658
$455$	−24.2741	−1.13799
$456$	15.5761	0.729417
$457$	20.8871	0.977058	0.488529	−	0.872548i	$-0.337534\pi$
$457$	20.8871	0.977058	0.488529	+	0.872548i	$0.337534\pi$
$458$	11.6627	0.544964
$459$	−5.16226	−0.240954
$460$	5.17498	0.241285
$461$	−10.8855	−0.506989	−0.253494	−	0.967337i	$-0.581580\pi$
$461$	−10.8855	−0.506989	−0.253494	+	0.967337i	$0.581580\pi$
$462$	9.38604	0.436678
$463$	−23.6055	−1.09704	−0.548520	−	0.836138i	$-0.684808\pi$
$463$	−23.6055	−1.09704	−0.548520	+	0.836138i	$0.684808\pi$
$464$	2.26115	0.104971
$465$	−34.6370	−1.60625
$466$	−8.14339	−0.377235
$467$	−33.7872	−1.56349	−0.781743	−	0.623601i	$-0.785669\pi$
$467$	−33.7872	−1.56349	−0.781743	+	0.623601i	$0.785669\pi$
$468$	−4.61314	−0.213242
$469$	−57.0179	−2.63284
$470$	−13.3186	−0.614343
$471$	−3.42828	−0.157967
$472$	−21.7560	−1.00140
$473$	−11.2014	−0.515041
$474$	5.15728	0.236881
$475$	−15.9594	−0.732267
$476$	−9.13346	−0.418632
$477$	−5.41195	−0.247796
$478$	3.99635	0.182789
$479$	24.1772	1.10468	0.552342	−	0.833618i	$-0.313734\pi$
$479$	24.1772	1.10468	0.552342	+	0.833618i	$0.313734\pi$
$480$	33.6703	1.53683
$481$	18.4263	0.840167
$482$	−8.38234	−0.381805
$483$	−7.69880	−0.350307
$484$	10.3921	0.472368
$485$	−15.1052	−0.685893
$486$	−6.88353	−0.312243
$487$	−22.6754	−1.02752	−0.513759	−	0.857934i	$-0.671748\pi$
$487$	−22.6754	−1.02752	−0.513759	+	0.857934i	$0.671748\pi$
$488$	6.32035	0.286109
$489$	−47.7472	−2.15920
$490$	−11.5830	−0.523266
$491$	−18.6114	−0.839922	−0.419961	−	0.907542i	$-0.637956\pi$
$491$	−18.6114	−0.839922	−0.419961	+	0.907542i	$0.637956\pi$
$492$	32.7572	1.47681
$493$	−1.44746	−0.0651902
$494$	4.35288	0.195846
$495$	−8.59093	−0.386134
$496$	12.4042	0.556964
$497$	−33.2156	−1.48992
$498$	16.4506	0.737168
$499$	9.98915	0.447176	0.223588	−	0.974684i	$-0.428223\pi$
$499$	9.98915	0.447176	0.223588	+	0.974684i	$0.428223\pi$
$500$	3.49227	0.156179
$501$	−33.9795	−1.51809
$502$	10.9256	0.487636
$503$	−26.9940	−1.20360	−0.601802	−	0.798645i	$-0.705550\pi$
$503$	−26.9940	−1.20360	−0.601802	+	0.798645i	$0.705550\pi$
$504$	−9.69324	−0.431771
$505$	−48.4342	−2.15529
$506$	−1.21916	−0.0541981
$507$	17.4559	0.775243
$508$	30.4739	1.35206
$509$	34.8200	1.54337	0.771685	−	0.636004i	$-0.219414\pi$
$509$	34.8200	1.54337	0.771685	+	0.636004i	$0.219414\pi$
$510$	−5.05016	−0.223625
$511$	2.02050	0.0893816
$512$	−21.2907	−0.940927
$513$	−13.1598	−0.581017
$514$	−14.5098	−0.639998
$515$	−22.9121	−1.00963
$516$	17.7895	0.783141
$517$	−17.4139	−0.765865
$518$	17.7590	0.780284
$519$	6.41502	0.281588
$520$	13.3096	0.583665
$521$	−24.1498	−1.05802	−0.529011	−	0.848615i	$-0.677437\pi$
$521$	−24.1498	−1.05802	−0.529011	+	0.848615i	$0.677437\pi$
$522$	−0.704606	−0.0308398
$523$	29.8195	1.30391	0.651957	−	0.758256i	$-0.273948\pi$
$523$	29.8195	1.30391	0.651957	+	0.758256i	$0.273948\pi$
$524$	0.335349	0.0146498
$525$	33.2985	1.45327
$526$	−1.77795	−0.0775223
$527$	−7.94042	−0.345890
$528$	10.3149	0.448900
$529$	1.00000	0.0434783
$530$	7.16192	0.311094
$531$	−13.5881	−0.589672
$532$	−23.2832	−1.00946
$533$	19.9581	0.864480
$534$	5.57200	0.241124
$535$	−27.0796	−1.17075
$536$	31.2632	1.35036
$537$	12.3950	0.534886
$538$	−5.02296	−0.216555
$539$	−15.1446	−0.652325
$540$	−18.4562	−0.794230
$541$	26.3402	1.13245	0.566226	−	0.824250i	$-0.308403\pi$
$541$	26.3402	1.13245	0.566226	+	0.824250i	$0.308403\pi$
$542$	−1.11887	−0.0480594
$543$	−14.0993	−0.605058
$544$	7.71882	0.330942
$545$	8.70747	0.372987
$546$	−9.08210	−0.388678
$547$	30.9998	1.32546	0.662729	−	0.748859i	$-0.269398\pi$
$547$	30.9998	1.32546	0.662729	+	0.748859i	$0.269398\pi$
$548$	−7.56579	−0.323194
$549$	3.94748	0.168474
$550$	5.27305	0.224844
$551$	−3.68989	−0.157195
$552$	4.22128	0.179670
$553$	−16.8073	−0.714720
$554$	2.68231	0.113961
$555$	−54.4971	−2.31328
$556$	18.4366	0.781884
$557$	37.7148	1.59803	0.799014	−	0.601313i	$-0.205355\pi$
$557$	37.7148	1.59803	0.799014	+	0.601313i	$0.205355\pi$
$558$	−3.86531	−0.163631
$559$	10.8387	0.458427
$560$	−25.7103	−1.08646
$561$	−6.60302	−0.278780
$562$	−4.51428	−0.190423
$563$	44.3729	1.87009	0.935047	−	0.354525i	$-0.115357\pi$
$563$	44.3729	1.87009	0.935047	+	0.354525i	$0.115357\pi$
$564$	27.6560	1.16453
$565$	39.2532	1.65139
$566$	11.3877	0.478659
$567$	41.7008	1.75127
$568$	18.2123	0.764170
$569$	−24.4018	−1.02298	−0.511489	−	0.859290i	$-0.670906\pi$
$569$	−24.4018	−1.02298	−0.511489	+	0.859290i	$0.670906\pi$
$570$	−12.8740	−0.539232
$571$	−14.5931	−0.610701	−0.305351	−	0.952240i	$-0.598774\pi$
$571$	−14.5931	−0.610701	−0.305351	+	0.952240i	$0.598774\pi$
$572$	7.98197	0.333743
$573$	−40.9995	−1.71278
$574$	19.2352	0.802864
$575$	−4.32516	−0.180372
$576$	−2.00903	−0.0837096
$577$	23.2073	0.966134	0.483067	−	0.875584i	$-0.339523\pi$
$577$	23.2073	0.966134	0.483067	+	0.875584i	$0.339523\pi$
$578$	8.23616	0.342579
$579$	−16.1964	−0.673100
$580$	−5.17498	−0.214880
$581$	−53.6116	−2.22419
$582$	−5.65158	−0.234265
$583$	9.36412	0.387822
$584$	−1.10785	−0.0458431
$585$	8.31274	0.343689
$586$	−9.23279	−0.381403
$587$	36.7706	1.51768	0.758842	−	0.651275i	$-0.225765\pi$
$587$	36.7706	1.51768	0.758842	+	0.651275i	$0.225765\pi$
$588$	24.0520	0.991886
$589$	−20.2419	−0.834053
$590$	17.9818	0.740300
$591$	32.8475	1.35117
$592$	19.5165	0.802123
$593$	−38.1366	−1.56608	−0.783040	−	0.621971i	$-0.786332\pi$
$593$	−38.1366	−1.56608	−0.783040	+	0.621971i	$0.786332\pi$
$594$	4.34804	0.178402
$595$	16.4582	0.674721
$596$	−11.0533	−0.452762
$597$	11.6274	0.475878
$598$	1.17968	0.0482406
$599$	9.80754	0.400725	0.200363	−	0.979722i	$-0.435788\pi$
$599$	9.80754	0.400725	0.200363	+	0.979722i	$0.435788\pi$
$600$	−18.2577	−0.745369
$601$	−10.3686	−0.422943	−0.211471	−	0.977384i	$-0.567826\pi$
$601$	−10.3686	−0.422943	−0.211471	+	0.977384i	$0.567826\pi$
$602$	10.4461	0.425753
$603$	19.5260	0.795158
$604$	−2.78889	−0.113478
$605$	−18.7262	−0.761329
$606$	−18.1215	−0.736136
$607$	−46.3266	−1.88034	−0.940169	−	0.340709i	$-0.889333\pi$
$607$	−46.3266	−1.88034	−0.940169	+	0.340709i	$0.889333\pi$
$608$	19.6770	0.798007
$609$	7.69880	0.311971
$610$	−5.22391	−0.211510
$611$	16.8500	0.681680
$612$	3.12778	0.126433
$613$	−12.0079	−0.484993	−0.242496	−	0.970152i	$-0.577966\pi$
$613$	−12.0079	−0.484993	−0.242496	+	0.970152i	$0.577966\pi$
$614$	−0.510851	−0.0206163
$615$	−59.0275	−2.38022
$616$	16.7719	0.675759
$617$	−13.6319	−0.548801	−0.274400	−	0.961616i	$-0.588479\pi$
$617$	−13.6319	−0.548801	−0.274400	+	0.961616i	$0.588479\pi$
$618$	−8.57251	−0.344837
$619$	−14.0875	−0.566223	−0.283112	−	0.959087i	$-0.591367\pi$
$619$	−14.0875	−0.566223	−0.283112	+	0.959087i	$0.591367\pi$
$620$	−28.3888	−1.14012
$621$	−3.56643	−0.143116
$622$	−10.0994	−0.404950
$623$	−18.1589	−0.727520
$624$	−9.98092	−0.399557
$625$	−27.9188	−1.11675
$626$	1.79147	0.0716015
$627$	−16.8326	−0.672228
$628$	−2.80985	−0.112125
$629$	−12.4933	−0.498141
$630$	8.01168	0.319193
$631$	−19.5710	−0.779108	−0.389554	−	0.921004i	$-0.627371\pi$
$631$	−19.5710	−0.779108	−0.389554	+	0.921004i	$0.627371\pi$
$632$	9.21552	0.366574
$633$	−3.28500	−0.130567
$634$	−4.52988	−0.179904
$635$	−54.9130	−2.17916
$636$	−14.8716	−0.589699
$637$	14.6542	0.580621
$638$	1.21916	0.0482669
$639$	11.3748	0.449979
$640$	35.2276	1.39249
$641$	7.03609	0.277909	0.138954	−	0.990299i	$-0.455626\pi$
$641$	7.03609	0.277909	0.138954	+	0.990299i	$0.455626\pi$
$642$	−10.1318	−0.399869
$643$	22.3806	0.882604	0.441302	−	0.897359i	$-0.354517\pi$
$643$	22.3806	0.882604	0.441302	+	0.897359i	$0.354517\pi$
$644$	−6.31000	−0.248649
$645$	−32.0562	−1.26221
$646$	−2.95132	−0.116118
$647$	2.98422	0.117322	0.0586608	−	0.998278i	$-0.481317\pi$
$647$	2.98422	0.117322	0.0586608	+	0.998278i	$0.481317\pi$
$648$	−22.8647	−0.898212
$649$	23.5110	0.922888
$650$	−5.10230	−0.200129
$651$	42.2338	1.65527
$652$	−39.1341	−1.53261
$653$	28.2914	1.10713	0.553565	−	0.832806i	$-0.313267\pi$
$653$	28.2914	1.10713	0.553565	+	0.832806i	$0.313267\pi$
$654$	3.25788	0.127393
$655$	−0.604288	−0.0236115
$656$	21.1389	0.825335
$657$	−0.691926	−0.0269946
$658$	16.2398	0.633093
$659$	35.5017	1.38295	0.691475	−	0.722400i	$-0.256961\pi$
$659$	35.5017	1.38295	0.691475	+	0.722400i	$0.256961\pi$
$660$	−23.6073	−0.918911
$661$	41.2305	1.60368	0.801839	−	0.597540i	$-0.203855\pi$
$661$	41.2305	1.60368	0.801839	+	0.597540i	$0.203855\pi$
$662$	−13.8189	−0.537088
$663$	6.38920	0.248136
$664$	29.3955	1.14077
$665$	41.9557	1.62697
$666$	−6.08160	−0.235657
$667$	−1.00000	−0.0387202
$668$	−27.8499	−1.07755
$669$	−43.8325	−1.69466
$670$	−25.8397	−0.998276
$671$	−6.83020	−0.263677
$672$	−41.0552	−1.58374
$673$	−44.1086	−1.70026	−0.850130	−	0.526573i	$-0.823477\pi$
$673$	−44.1086	−1.70026	−0.850130	+	0.526573i	$0.823477\pi$
$674$	−1.16090	−0.0447163
$675$	15.4254	0.593724
$676$	14.3070	0.550269
$677$	−14.6605	−0.563449	−0.281724	−	0.959495i	$-0.590906\pi$
$677$	−14.6605	−0.563449	−0.281724	+	0.959495i	$0.590906\pi$
$678$	14.6865	0.564031
$679$	18.4182	0.706826
$680$	−9.02412	−0.346059
$681$	−39.7565	−1.52347
$682$	6.68801	0.256097
$683$	−20.7695	−0.794722	−0.397361	−	0.917662i	$-0.630074\pi$
$683$	−20.7695	−0.794722	−0.397361	+	0.917662i	$0.630074\pi$
$684$	7.97341	0.304871
$685$	13.6333	0.520902
$686$	−0.279222	−0.0106607
$687$	43.6393	1.66494
$688$	11.4800	0.437669
$689$	−9.06089	−0.345192
$690$	−3.48898	−0.132823
$691$	36.8525	1.40194	0.700968	−	0.713192i	$-0.252751\pi$
$691$	36.8525	1.40194	0.700968	+	0.713192i	$0.252751\pi$
$692$	5.25781	0.199872
$693$	10.4752	0.397919
$694$	10.3656	0.393474
$695$	−33.2221	−1.26019
$696$	−4.22128	−0.160007
$697$	−13.5319	−0.512556
$698$	18.9819	0.718476
$699$	−30.4707	−1.15251
$700$	27.2918	1.03153
$701$	22.4611	0.848346	0.424173	−	0.905581i	$-0.360565\pi$
$701$	22.4611	0.848346	0.424173	+	0.905581i	$0.360565\pi$
$702$	−4.20724	−0.158792
$703$	−31.8482	−1.20118
$704$	3.47616	0.131013
$705$	−49.8353	−1.87690
$706$	5.29839	0.199408
$707$	59.0572	2.22107
$708$	−37.3390	−1.40329
$709$	−7.91841	−0.297382	−0.148691	−	0.988884i	$-0.547506\pi$
$709$	−7.91841	−0.297382	−0.148691	+	0.988884i	$0.547506\pi$
$710$	−15.0528	−0.564923
$711$	5.75571	0.215856
$712$	9.95659	0.373139
$713$	−5.48577	−0.205444
$714$	6.15780	0.230450
$715$	−14.3833	−0.537903
$716$	10.1591	0.379663
$717$	14.9534	0.558446
$718$	6.71748	0.250694
$719$	51.1146	1.90625	0.953126	−	0.302574i	$-0.0978459\pi$
$719$	51.1146	1.90625	0.953126	+	0.302574i	$0.0978459\pi$
$720$	8.80456	0.328127
$721$	27.9374	1.04044
$722$	2.97548	0.110736
$723$	−31.3648	−1.16647
$724$	−11.5559	−0.429471
$725$	4.32516	0.160633
$726$	−7.00637	−0.260031
$727$	14.0444	0.520878	0.260439	−	0.965490i	$-0.416133\pi$
$727$	14.0444	0.520878	0.260439	+	0.965490i	$0.416133\pi$
$728$	−16.2288	−0.601479
$729$	7.84168	0.290433
$730$	0.915662	0.0338902
$731$	−7.34879	−0.271805
$732$	10.8474	0.400931
$733$	17.0996	0.631589	0.315794	−	0.948828i	$-0.397729\pi$
$733$	17.0996	0.631589	0.315794	+	0.948828i	$0.397729\pi$
$734$	−10.2143	−0.377018
$735$	−43.3409	−1.59865
$736$	5.33267	0.196565
$737$	−33.7851	−1.24449
$738$	−6.58716	−0.242477
$739$	45.3783	1.66927	0.834635	−	0.550804i	$-0.185679\pi$
$739$	45.3783	1.66927	0.834635	+	0.550804i	$0.185679\pi$
$740$	−44.6664	−1.64197
$741$	16.2875	0.598336
$742$	−8.73273	−0.320589
$743$	−24.9718	−0.916128	−0.458064	−	0.888919i	$-0.651457\pi$
$743$	−24.9718	−0.916128	−0.458064	+	0.888919i	$0.651457\pi$
$744$	−23.1570	−0.848976
$745$	19.9178	0.729730
$746$	−17.5554	−0.642748
$747$	18.3595	0.671737
$748$	−5.41189	−0.197878
$749$	33.0190	1.20649
$750$	−2.35449	−0.0859740
$751$	−32.4192	−1.18299	−0.591497	−	0.806307i	$-0.701463\pi$
$751$	−32.4192	−1.18299	−0.591497	+	0.806307i	$0.701463\pi$
$752$	17.8470	0.650812
$753$	40.8813	1.48980
$754$	−1.17968	−0.0429613
$755$	5.02550	0.182897
$756$	22.5042	0.818470
$757$	−38.2840	−1.39146	−0.695729	−	0.718305i	$-0.744918\pi$
$757$	−38.2840	−1.39146	−0.695729	+	0.718305i	$0.744918\pi$
$758$	−18.1063	−0.657649
$759$	−4.56180	−0.165583
$760$	−23.0045	−0.834461
$761$	−1.76024	−0.0638085	−0.0319043	−	0.999491i	$-0.510157\pi$
$761$	−1.76024	−0.0638085	−0.0319043	+	0.999491i	$0.510157\pi$
$762$	−20.5456	−0.744287
$763$	−10.6173	−0.384371
$764$	−33.6035	−1.21573
$765$	−5.63616	−0.203776
$766$	9.69023	0.350122
$767$	−22.7497	−0.821443
$768$	6.66490	0.240499
$769$	11.7432	0.423469	0.211734	−	0.977327i	$-0.432089\pi$
$769$	11.7432	0.423469	0.211734	+	0.977327i	$0.432089\pi$
$770$	−13.8623	−0.499564
$771$	−54.2921	−1.95528
$772$	−13.2747	−0.477768
$773$	35.1598	1.26461	0.632305	−	0.774719i	$-0.282109\pi$
$773$	35.1598	1.26461	0.632305	+	0.774719i	$0.282109\pi$
$774$	−3.57731	−0.128584
$775$	23.7268	0.852294
$776$	−10.0988	−0.362525
$777$	66.4499	2.38388
$778$	−8.85737	−0.317552
$779$	−34.4958	−1.23594
$780$	22.8428	0.817903
$781$	−19.6814	−0.704256
$782$	−0.799839	−0.0286022
$783$	3.56643	0.127454
$784$	15.5212	0.554329
$785$	5.06327	0.180716
$786$	−0.226093	−0.00806446
$787$	−24.2813	−0.865536	−0.432768	−	0.901505i	$-0.642463\pi$
$787$	−24.2813	−0.865536	−0.432768	+	0.901505i	$0.642463\pi$
$788$	26.9221	0.959061
$789$	−6.65268	−0.236842
$790$	−7.61684	−0.270995
$791$	−47.8625	−1.70180
$792$	−5.74358	−0.204089
$793$	6.60902	0.234693
$794$	20.8428	0.739682
$795$	26.7983	0.950436
$796$	9.52992	0.337779
$797$	32.6353	1.15600	0.578001	−	0.816036i	$-0.303833\pi$
$797$	32.6353	1.15600	0.578001	+	0.816036i	$0.303833\pi$
$798$	15.6976	0.555689
$799$	−11.4246	−0.404173
$800$	−23.0647	−0.815460
$801$	6.21856	0.219722
$802$	6.56877	0.231951
$803$	1.19722	0.0422488
$804$	53.6559	1.89230
$805$	11.3704	0.400755
$806$	−6.47144	−0.227947
$807$	−18.7948	−0.661607
$808$	−32.3813	−1.13917
$809$	41.8984	1.47307	0.736535	−	0.676400i	$-0.236461\pi$
$809$	41.8984	1.47307	0.736535	+	0.676400i	$0.236461\pi$
$810$	18.8982	0.664016
$811$	1.34288	0.0471548	0.0235774	−	0.999722i	$-0.492494\pi$
$811$	1.34288	0.0471548	0.0235774	+	0.999722i	$0.492494\pi$
$812$	6.31000	0.221438
$813$	−4.18654	−0.146828
$814$	10.5228	0.368824
$815$	70.5184	2.47015
$816$	6.76721	0.236900
$817$	−18.7337	−0.655410
$818$	2.97433	0.103995
$819$	−10.1360	−0.354179
$820$	−48.3795	−1.68948
$821$	−20.8244	−0.726777	−0.363389	−	0.931638i	$-0.618380\pi$
$821$	−20.8244	−0.726777	−0.363389	+	0.931638i	$0.618380\pi$
$822$	5.10087	0.177913
$823$	−43.1560	−1.50433	−0.752163	−	0.658978i	$-0.770989\pi$
$823$	−43.1560	−1.50433	−0.752163	+	0.658978i	$0.770989\pi$
$824$	−15.3182	−0.533635
$825$	19.7305	0.686930
$826$	−21.9257	−0.762894
$827$	28.7839	1.00092	0.500458	−	0.865761i	$-0.333165\pi$
$827$	28.7839	1.00092	0.500458	+	0.865761i	$0.333165\pi$
$828$	2.16088	0.0750957
$829$	−47.9539	−1.66551	−0.832755	−	0.553642i	$-0.813238\pi$
$829$	−47.9539	−1.66551	−0.832755	+	0.553642i	$0.813238\pi$
$830$	−24.2960	−0.843328
$831$	10.0366	0.348166
$832$	−3.36359	−0.116612
$833$	−9.93577	−0.344254
$834$	−12.4300	−0.430414
$835$	50.1848	1.73672
$836$	−13.7961	−0.477149
$837$	19.5646	0.676252
$838$	−7.66256	−0.264699
$839$	28.7923	0.994020	0.497010	−	0.867745i	$-0.334431\pi$
$839$	28.7923	0.994020	0.497010	+	0.867745i	$0.334431\pi$
$840$	47.9978	1.65608
$841$	1.00000	0.0344828
$842$	−0.745912	−0.0257058
$843$	−16.8914	−0.581770
$844$	−2.69241	−0.0926767
$845$	−25.7808	−0.886886
$846$	−5.56136	−0.191203
$847$	22.8334	0.784566
$848$	−9.59698	−0.329562
$849$	42.6100	1.46237
$850$	3.45944	0.118658
$851$	−8.63121	−0.295874
$852$	31.2571	1.07085
$853$	34.0006	1.16416	0.582079	−	0.813132i	$-0.302240\pi$
$853$	34.0006	1.16416	0.582079	+	0.813132i	$0.302240\pi$
$854$	6.36966	0.217965
$855$	−14.3678	−0.491370
$856$	−18.1044	−0.618797
$857$	46.0328	1.57245	0.786225	−	0.617941i	$-0.212033\pi$
$857$	46.0328	1.57245	0.786225	+	0.617941i	$0.212033\pi$
$858$	−5.38146	−0.183720
$859$	−17.5780	−0.599754	−0.299877	−	0.953978i	$-0.596946\pi$
$859$	−17.5780	−0.599754	−0.299877	+	0.953978i	$0.596946\pi$
$860$	−26.2736	−0.895921
$861$	71.9739	2.45286
$862$	9.72956	0.331390
$863$	6.37579	0.217035	0.108517	−	0.994095i	$-0.465390\pi$
$863$	6.37579	0.217035	0.108517	+	0.994095i	$0.465390\pi$
$864$	−19.0186	−0.647026
$865$	−9.47441	−0.322139
$866$	−19.6504	−0.667749
$867$	30.8178	1.04663
$868$	34.6152	1.17492
$869$	−9.95892	−0.337833
$870$	3.48898	0.118288
$871$	32.6911	1.10769
$872$	5.82149	0.197141
$873$	−6.30737	−0.213472
$874$	−2.03897	−0.0689692
$875$	7.67318	0.259401
$876$	−1.90136	−0.0642410
$877$	−33.0719	−1.11676	−0.558379	−	0.829586i	$-0.688576\pi$
$877$	−33.0719	−1.11676	−0.558379	+	0.829586i	$0.688576\pi$
$878$	17.4276	0.588152
$879$	−34.5470	−1.16524
$880$	−15.2343	−0.513546
$881$	47.8543	1.61225	0.806126	−	0.591744i	$-0.201560\pi$
$881$	47.8543	1.61225	0.806126	+	0.591744i	$0.201560\pi$
$882$	−4.83662	−0.162858
$883$	26.6522	0.896917	0.448458	−	0.893804i	$-0.351973\pi$
$883$	26.6522	0.896917	0.448458	+	0.893804i	$0.351973\pi$
$884$	5.23664	0.176127
$885$	67.2838	2.26172
$886$	−11.0728	−0.371997
$887$	−6.11086	−0.205183	−0.102591	−	0.994724i	$-0.532713\pi$
$887$	−6.11086	−0.205183	−0.102591	+	0.994724i	$0.532713\pi$
$888$	−36.4348	−1.22267
$889$	66.9570	2.24567
$890$	−8.22935	−0.275848
$891$	24.7092	0.827789
$892$	−35.9255	−1.20288
$893$	−29.1238	−0.974592
$894$	7.45218	0.249238
$895$	−18.3064	−0.611915
$896$	−42.9540	−1.43499
$897$	4.41408	0.147382
$898$	10.4065	0.347270
$899$	5.48577	0.182961
$900$	−9.34615	−0.311538
$901$	6.14342	0.204667
$902$	11.3976	0.379497
$903$	39.0870	1.30074
$904$	26.2432	0.872837
$905$	20.8234	0.692192
$906$	1.88028	0.0624681
$907$	−34.4053	−1.14241	−0.571204	−	0.820808i	$-0.693524\pi$
$907$	−34.4053	−1.14241	−0.571204	+	0.820808i	$0.693524\pi$
$908$	−32.5848	−1.08136
$909$	−20.2243	−0.670797
$910$	13.4134	0.444651
$911$	−23.9276	−0.792756	−0.396378	−	0.918087i	$-0.629733\pi$
$911$	−23.9276	−0.792756	−0.396378	+	0.918087i	$0.629733\pi$
$912$	17.2511	0.571242
$913$	−31.7668	−1.05133
$914$	−11.5418	−0.381770
$915$	−19.5467	−0.646193
$916$	35.7672	1.18178
$917$	0.736826	0.0243321
$918$	2.85257	0.0941489
$919$	14.2293	0.469380	0.234690	−	0.972070i	$-0.424592\pi$
$919$	14.2293	0.469380	0.234690	+	0.972070i	$0.424592\pi$
$920$	−6.23446	−0.205544
$921$	−1.91149	−0.0629856
$922$	6.01514	0.198098
$923$	19.0441	0.626843
$924$	28.7850	0.946957
$925$	37.3314	1.22745
$926$	13.0440	0.428651
$927$	−9.56724	−0.314229
$928$	−5.33267	−0.175054
$929$	−21.5875	−0.708264	−0.354132	−	0.935196i	$-0.615224\pi$
$929$	−21.5875	−0.708264	−0.354132	+	0.935196i	$0.615224\pi$
$930$	19.1398	0.627618
$931$	−25.3285	−0.830108
$932$	−24.9741	−0.818053
$933$	−37.7897	−1.23718
$934$	18.6702	0.610908
$935$	9.75207	0.318927
$936$	5.55759	0.181655
$937$	44.9436	1.46824	0.734121	−	0.679018i	$-0.237594\pi$
$937$	44.9436	1.46824	0.734121	+	0.679018i	$0.237594\pi$
$938$	31.5071	1.02874
$939$	6.70327	0.218753
$940$	−40.8454	−1.33223
$941$	31.7462	1.03490	0.517448	−	0.855715i	$-0.326882\pi$
$941$	31.7462	1.03490	0.517448	+	0.855715i	$0.326882\pi$
$942$	1.89441	0.0617231
$943$	−9.34872	−0.304436
$944$	−24.0957	−0.784247
$945$	−40.5519	−1.31915
$946$	6.18970	0.201244
$947$	29.1418	0.946980	0.473490	−	0.880799i	$-0.342994\pi$
$947$	29.1418	0.946980	0.473490	+	0.880799i	$0.342994\pi$
$948$	15.8163	0.513689
$949$	−1.15845	−0.0376048
$950$	8.81888	0.286122
$951$	−16.9498	−0.549634
$952$	11.0034	0.356621
$953$	−28.1259	−0.911088	−0.455544	−	0.890213i	$-0.650555\pi$
$953$	−28.1259	−0.911088	−0.455544	+	0.890213i	$0.650555\pi$
$954$	2.99055	0.0968226
$955$	60.5525	1.95943
$956$	12.2560	0.396386
$957$	4.56180	0.147462
$958$	−13.3599	−0.431638
$959$	−16.6235	−0.536800
$960$	9.94808	0.321073
$961$	−0.906340	−0.0292368
$962$	−10.1820	−0.328282
$963$	−11.3074	−0.364377
$964$	−25.7069	−0.827963
$965$	23.9207	0.770033
$966$	4.25422	0.136877
$967$	−53.5218	−1.72115	−0.860573	−	0.509328i	$-0.829894\pi$
$967$	−53.5218	−1.72115	−0.860573	+	0.509328i	$0.829894\pi$
$968$	−12.5197	−0.402397
$969$	−11.0432	−0.354758
$970$	8.34688	0.268002
$971$	−10.5182	−0.337546	−0.168773	−	0.985655i	$-0.553980\pi$
$971$	−10.5182	−0.337546	−0.168773	+	0.985655i	$0.553980\pi$
$972$	−21.1103	−0.677115
$973$	40.5087	1.29865
$974$	12.5300	0.401487
$975$	−19.0916	−0.611421
$976$	7.00004	0.224066
$977$	36.2566	1.15995	0.579976	−	0.814633i	$-0.303062\pi$
$977$	36.2566	1.15995	0.579976	+	0.814633i	$0.303062\pi$
$978$	26.3843	0.843676
$979$	−10.7598	−0.343884
$980$	−35.5226	−1.13473
$981$	3.63591	0.116086
$982$	10.2844	0.328187
$983$	10.4594	0.333604	0.166802	−	0.985990i	$-0.446656\pi$
$983$	10.4594	0.333604	0.166802	+	0.985990i	$0.446656\pi$
$984$	−39.4636	−1.25805
$985$	−48.5129	−1.54575
$986$	0.799839	0.0254721
$987$	60.7655	1.93419
$988$	13.3494	0.424700
$989$	−5.07703	−0.161440
$990$	4.74720	0.150876
$991$	21.6294	0.687081	0.343540	−	0.939138i	$-0.388374\pi$
$991$	21.6294	0.687081	0.343540	+	0.939138i	$0.388374\pi$
$992$	−29.2538	−0.928809
$993$	−51.7073	−1.64088
$994$	18.3544	0.582165
$995$	−17.1726	−0.544409
$996$	50.4504	1.59858
$997$	0.386487	0.0122402	0.00612008	−	0.999981i	$-0.498052\pi$
$997$	0.386487	0.0122402	0.00612008	+	0.999981i	$0.498052\pi$
$998$	−5.51983	−0.174727
$999$	30.7826	0.973919

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.2.a.c.1.5	✓	13
3.2	odd	2		6003.2.a.o.1.9		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.2.a.c.1.5	✓	13	1.1	even	1	trivial
6003.2.a.o.1.9		13	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 667 = 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	667.a (trivial)

\(f(q)\)	\(=\)	\(q-0.552582 q^{2} -2.06764 q^{3} -1.69465 q^{4} +3.05371 q^{5} +1.14254 q^{6} -3.72348 q^{7} +2.04160 q^{8} +1.27512 q^{9} +O(q^{10})\)	\(q-0.552582 q^{2} -2.06764 q^{3} -1.69465 q^{4} +3.05371 q^{5} +1.14254 q^{6} -3.72348 q^{7} +2.04160 q^{8} +1.27512 q^{9} -1.68743 q^{10} -2.20629 q^{11} +3.50392 q^{12} +2.13485 q^{13} +2.05753 q^{14} -6.31396 q^{15} +2.26115 q^{16} -1.44746 q^{17} -0.704606 q^{18} -3.68989 q^{19} -5.17498 q^{20} +7.69880 q^{21} +1.21916 q^{22} -1.00000 q^{23} -4.22128 q^{24} +4.32516 q^{25} -1.17968 q^{26} +3.56643 q^{27} +6.31000 q^{28} +1.00000 q^{29} +3.48898 q^{30} +5.48577 q^{31} -5.33267 q^{32} +4.56180 q^{33} +0.799839 q^{34} -11.3704 q^{35} -2.16088 q^{36} +8.63121 q^{37} +2.03897 q^{38} -4.41408 q^{39} +6.23446 q^{40} +9.34872 q^{41} -4.25422 q^{42} +5.07703 q^{43} +3.73890 q^{44} +3.89384 q^{45} +0.552582 q^{46} +7.89286 q^{47} -4.67524 q^{48} +6.86429 q^{49} -2.39001 q^{50} +2.99281 q^{51} -3.61782 q^{52} -4.24428 q^{53} -1.97075 q^{54} -6.73738 q^{55} -7.60185 q^{56} +7.62935 q^{57} -0.552582 q^{58} -10.6564 q^{59} +10.7000 q^{60} +3.09578 q^{61} -3.03134 q^{62} -4.74786 q^{63} -1.57557 q^{64} +6.51921 q^{65} -2.52077 q^{66} +15.3131 q^{67} +2.45294 q^{68} +2.06764 q^{69} +6.28310 q^{70} +8.92059 q^{71} +2.60327 q^{72} -0.542638 q^{73} -4.76945 q^{74} -8.94286 q^{75} +6.25309 q^{76} +8.21508 q^{77} +2.43914 q^{78} +4.51387 q^{79} +6.90492 q^{80} -11.1994 q^{81} -5.16593 q^{82} +14.3983 q^{83} -13.0468 q^{84} -4.42012 q^{85} -2.80548 q^{86} -2.06764 q^{87} -4.50436 q^{88} +4.87686 q^{89} -2.15166 q^{90} -7.94905 q^{91} +1.69465 q^{92} -11.3426 q^{93} -4.36146 q^{94} -11.2679 q^{95} +11.0260 q^{96} -4.94651 q^{97} -3.79309 q^{98} -2.81327 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 4 q^{2} + 3 q^{3} + 12 q^{4} + 16 q^{5} + q^{7} + 6 q^{8} + 14 q^{9}+O(q^{10}) \) 13 * q + 4 * q^2 + 3 * q^3 + 12 * q^4 + 16 * q^5 + q^7 + 6 * q^8 + 14 * q^9	\( 13 q + 4 q^{2} + 3 q^{3} + 12 q^{4} + 16 q^{5} + q^{7} + 6 q^{8} + 14 q^{9} + 10 q^{10} + 10 q^{11} + 3 q^{12} + 7 q^{13} - 12 q^{14} + 8 q^{15} + 2 q^{16} + 26 q^{17} + 7 q^{18} + 25 q^{20} + 11 q^{21} - 15 q^{22} - 13 q^{23} + 10 q^{24} + 19 q^{25} - 15 q^{26} + 12 q^{27} + 5 q^{28} + 13 q^{29} + 7 q^{30} - 6 q^{31} + 16 q^{32} + 3 q^{33} + 11 q^{34} + q^{35} - 22 q^{36} + 15 q^{37} + 8 q^{38} - 4 q^{39} + 14 q^{40} + 9 q^{41} - 34 q^{42} + q^{43} + 29 q^{44} + 16 q^{45} - 4 q^{46} + 15 q^{47} - 15 q^{48} + 4 q^{49} + 31 q^{50} - 14 q^{51} - 8 q^{52} + 43 q^{53} - 35 q^{54} - 3 q^{55} - 5 q^{56} + 6 q^{57} + 4 q^{58} - 9 q^{59} + 3 q^{60} + 20 q^{61} + 11 q^{62} + 21 q^{63} - 16 q^{64} - 25 q^{65} - q^{66} + q^{67} + 21 q^{68} - 3 q^{69} - 2 q^{70} + 17 q^{71} - 59 q^{72} + 26 q^{73} + 11 q^{74} - 43 q^{75} + 8 q^{76} + 17 q^{77} - 10 q^{78} + 5 q^{79} + 10 q^{80} - 3 q^{81} - 25 q^{82} + 4 q^{83} - 78 q^{84} + 20 q^{85} - 13 q^{86} + 3 q^{87} - 32 q^{88} + 48 q^{89} + 17 q^{90} - 9 q^{91} - 12 q^{92} - 8 q^{93} - 65 q^{94} + 8 q^{95} + 8 q^{96} + 30 q^{97} + 2 q^{98} + 4 q^{99}+O(q^{100}) \) 13 * q + 4 * q^2 + 3 * q^3 + 12 * q^4 + 16 * q^5 + q^7 + 6 * q^8 + 14 * q^9 + 10 * q^10 + 10 * q^11 + 3 * q^12 + 7 * q^13 - 12 * q^14 + 8 * q^15 + 2 * q^16 + 26 * q^17 + 7 * q^18 + 25 * q^20 + 11 * q^21 - 15 * q^22 - 13 * q^23 + 10 * q^24 + 19 * q^25 - 15 * q^26 + 12 * q^27 + 5 * q^28 + 13 * q^29 + 7 * q^30 - 6 * q^31 + 16 * q^32 + 3 * q^33 + 11 * q^34 + q^35 - 22 * q^36 + 15 * q^37 + 8 * q^38 - 4 * q^39 + 14 * q^40 + 9 * q^41 - 34 * q^42 + q^43 + 29 * q^44 + 16 * q^45 - 4 * q^46 + 15 * q^47 - 15 * q^48 + 4 * q^49 + 31 * q^50 - 14 * q^51 - 8 * q^52 + 43 * q^53 - 35 * q^54 - 3 * q^55 - 5 * q^56 + 6 * q^57 + 4 * q^58 - 9 * q^59 + 3 * q^60 + 20 * q^61 + 11 * q^62 + 21 * q^63 - 16 * q^64 - 25 * q^65 - q^66 + q^67 + 21 * q^68 - 3 * q^69 - 2 * q^70 + 17 * q^71 - 59 * q^72 + 26 * q^73 + 11 * q^74 - 43 * q^75 + 8 * q^76 + 17 * q^77 - 10 * q^78 + 5 * q^79 + 10 * q^80 - 3 * q^81 - 25 * q^82 + 4 * q^83 - 78 * q^84 + 20 * q^85 - 13 * q^86 + 3 * q^87 - 32 * q^88 + 48 * q^89 + 17 * q^90 - 9 * q^91 - 12 * q^92 - 8 * q^93 - 65 * q^94 + 8 * q^95 + 8 * q^96 + 30 * q^97 + 2 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more