LMFDB - Embedded newform 4334.2.a.d.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, 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("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$1$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 7 x^{16} - 7 x^{15} + 137 x^{14} - 98 x^{13} - 1048 x^{12} + 1313 x^{11} + 4085 x^{10} + \cdots - 400 $ x^17 - 7x^16 - 7x^15 + 137x^14 - 98x^13 - 1048x^12 + 1313x^11 + 4085x^10 - 6021x^9 - 8879x^8 + 13530x^7 + 11150x^6 - 15676x^5 - 8037x^4 + 8646x^3 + 3040x^2 - 1640x - 400
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Root			$-2.06015$ of defining polynomial
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +2.06015 q^{3} +1.00000 q^{4} -2.29448 q^{5} +2.06015 q^{6} +0.0148240 q^{7} +1.00000 q^{8} +1.24422 q^{9} -2.29448 q^{10} -1.00000 q^{11} +2.06015 q^{12} -6.98107 q^{13} +0.0148240 q^{14} -4.72697 q^{15} +1.00000 q^{16} +2.20528 q^{17} +1.24422 q^{18} +3.95053 q^{19} -2.29448 q^{20} +0.0305397 q^{21} -1.00000 q^{22} -2.46813 q^{23} +2.06015 q^{24} +0.264638 q^{25} -6.98107 q^{26} -3.61717 q^{27} +0.0148240 q^{28} -0.400196 q^{29} -4.72697 q^{30} -6.37837 q^{31} +1.00000 q^{32} -2.06015 q^{33} +2.20528 q^{34} -0.0340134 q^{35} +1.24422 q^{36} -0.740568 q^{37} +3.95053 q^{38} -14.3821 q^{39} -2.29448 q^{40} -5.81975 q^{41} +0.0305397 q^{42} -5.23891 q^{43} -1.00000 q^{44} -2.85483 q^{45} -2.46813 q^{46} +7.82007 q^{47} +2.06015 q^{48} -6.99978 q^{49} +0.264638 q^{50} +4.54322 q^{51} -6.98107 q^{52} -8.40347 q^{53} -3.61717 q^{54} +2.29448 q^{55} +0.0148240 q^{56} +8.13868 q^{57} -0.400196 q^{58} +2.80923 q^{59} -4.72697 q^{60} -1.47967 q^{61} -6.37837 q^{62} +0.0184443 q^{63} +1.00000 q^{64} +16.0179 q^{65} -2.06015 q^{66} +6.49105 q^{67} +2.20528 q^{68} -5.08472 q^{69} -0.0340134 q^{70} -7.19610 q^{71} +1.24422 q^{72} +15.6550 q^{73} -0.740568 q^{74} +0.545195 q^{75} +3.95053 q^{76} -0.0148240 q^{77} -14.3821 q^{78} +10.2082 q^{79} -2.29448 q^{80} -11.1846 q^{81} -5.81975 q^{82} -17.4554 q^{83} +0.0305397 q^{84} -5.05998 q^{85} -5.23891 q^{86} -0.824465 q^{87} -1.00000 q^{88} +5.80344 q^{89} -2.85483 q^{90} -0.103487 q^{91} -2.46813 q^{92} -13.1404 q^{93} +7.82007 q^{94} -9.06440 q^{95} +2.06015 q^{96} -3.44632 q^{97} -6.99978 q^{98} -1.24422 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 17 q^{2} - 7 q^{3} + 17 q^{4} - 4 q^{5} - 7 q^{6} - 5 q^{7} + 17 q^{8} + 12 q^{9} - 4 q^{10} - 17 q^{11} - 7 q^{12} - 18 q^{13} - 5 q^{14} - 16 q^{15} + 17 q^{16} - 10 q^{17} + 12 q^{18} - 31 q^{19}+ \cdots - 12 q^{99}+O(q^{100}) $ 17 * q + 17 * q^2 - 7 * q^3 + 17 * q^4 - 4 * q^5 - 7 * q^6 - 5 * q^7 + 17 * q^8 + 12 * q^9 - 4 * q^10 - 17 * q^11 - 7 * q^12 - 18 * q^13 - 5 * q^14 - 16 * q^15 + 17 * q^16 - 10 * q^17 + 12 * q^18 - 31 * q^19 - 4 * q^20 - 13 * q^21 - 17 * q^22 - 6 * q^23 - 7 * q^24 + 3 * q^25 - 18 * q^26 - 37 * q^27 - 5 * q^28 - 16 * q^29 - 16 * q^30 - 30 * q^31 + 17 * q^32 + 7 * q^33 - 10 * q^34 - 36 * q^35 + 12 * q^36 - 23 * q^37 - 31 * q^38 - 15 * q^39 - 4 * q^40 - 7 * q^41 - 13 * q^42 - 23 * q^43 - 17 * q^44 - 19 * q^45 - 6 * q^46 - 19 * q^47 - 7 * q^48 - 8 * q^49 + 3 * q^50 - 18 * q^51 - 18 * q^52 - 30 * q^53 - 37 * q^54 + 4 * q^55 - 5 * q^56 + 10 * q^57 - 16 * q^58 - 28 * q^59 - 16 * q^60 - 19 * q^61 - 30 * q^62 + 2 * q^63 + 17 * q^64 + 23 * q^65 + 7 * q^66 - 35 * q^67 - 10 * q^68 + q^69 - 36 * q^70 + q^71 + 12 * q^72 - 10 * q^73 - 23 * q^74 - 33 * q^75 - 31 * q^76 + 5 * q^77 - 15 * q^78 - 27 * q^79 - 4 * q^80 + 13 * q^81 - 7 * q^82 - 40 * q^83 - 13 * q^84 - 11 * q^85 - 23 * q^86 - 6 * q^87 - 17 * q^88 - 17 * q^89 - 19 * q^90 - 19 * q^91 - 6 * q^92 + 10 * q^93 - 19 * q^94 - 27 * q^95 - 7 * q^96 - 34 * q^97 - 8 * q^98 - 12 * q^99

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	2.06015	1.18943	0.594714	−	0.803937i	$-0.297265\pi$
$3$	2.06015	1.18943	0.594714	+	0.803937i	$0.297265\pi$
$4$	1.00000	0.500000
$5$	−2.29448	−1.02612	−0.513061	−	0.858352i	$-0.671489\pi$
$5$	−2.29448	−1.02612	−0.513061	+	0.858352i	$0.671489\pi$
$6$	2.06015	0.841053
$7$	0.0148240	0.00560295	0.00280147	−	0.999996i	$-0.499108\pi$
$7$	0.0148240	0.00560295	0.00280147	+	0.999996i	$0.499108\pi$
$8$	1.00000	0.353553
$9$	1.24422	0.414739
$10$	−2.29448	−0.725578
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	2.06015	0.594714
$13$	−6.98107	−1.93620	−0.968100	−	0.250563i	$-0.919384\pi$
$13$	−6.98107	−1.93620	−0.968100	+	0.250563i	$0.919384\pi$
$14$	0.0148240	0.00396188
$15$	−4.72697	−1.22050
$16$	1.00000	0.250000
$17$	2.20528	0.534860	0.267430	−	0.963577i	$-0.413826\pi$
$17$	2.20528	0.534860	0.267430	+	0.963577i	$0.413826\pi$
$18$	1.24422	0.293265
$19$	3.95053	0.906313	0.453156	−	0.891431i	$-0.350298\pi$
$19$	3.95053	0.906313	0.453156	+	0.891431i	$0.350298\pi$
$20$	−2.29448	−0.513061
$21$	0.0305397	0.00666430
$22$	−1.00000	−0.213201
$23$	−2.46813	−0.514641	−0.257320	−	0.966326i	$-0.582840\pi$
$23$	−2.46813	−0.514641	−0.257320	+	0.966326i	$0.582840\pi$
$24$	2.06015	0.420526
$25$	0.264638	0.0529277
$26$	−6.98107	−1.36910
$27$	−3.61717	−0.696125
$28$	0.0148240	0.00280147
$29$	−0.400196	−0.0743146	−0.0371573	−	0.999309i	$-0.511830\pi$
$29$	−0.400196	−0.0743146	−0.0371573	+	0.999309i	$0.511830\pi$
$30$	−4.72697	−0.863023
$31$	−6.37837	−1.14559	−0.572794	−	0.819699i	$-0.694141\pi$
$31$	−6.37837	−1.14559	−0.572794	+	0.819699i	$0.694141\pi$
$32$	1.00000	0.176777
$33$	−2.06015	−0.358626
$34$	2.20528	0.378203
$35$	−0.0340134	−0.00574931
$36$	1.24422	0.207370
$37$	−0.740568	−0.121749	−0.0608743	−	0.998145i	$-0.519389\pi$
$37$	−0.740568	−0.121749	−0.0608743	+	0.998145i	$0.519389\pi$
$38$	3.95053	0.640860
$39$	−14.3821	−2.30297
$40$	−2.29448	−0.362789
$41$	−5.81975	−0.908893	−0.454446	−	0.890774i	$-0.650163\pi$
$41$	−5.81975	−0.908893	−0.454446	+	0.890774i	$0.650163\pi$
$42$	0.0305397	0.00471237
$43$	−5.23891	−0.798926	−0.399463	−	0.916749i	$-0.630803\pi$
$43$	−5.23891	−0.798926	−0.399463	+	0.916749i	$0.630803\pi$
$44$	−1.00000	−0.150756
$45$	−2.85483	−0.425574
$46$	−2.46813	−0.363906
$47$	7.82007	1.14067	0.570337	−	0.821411i	$-0.306813\pi$
$47$	7.82007	1.14067	0.570337	+	0.821411i	$0.306813\pi$
$48$	2.06015	0.297357
$49$	−6.99978	−0.999969
$50$	0.264638	0.0374255
$51$	4.54322	0.636177
$52$	−6.98107	−0.968100
$53$	−8.40347	−1.15431	−0.577153	−	0.816636i	$-0.695836\pi$
$53$	−8.40347	−1.15431	−0.577153	+	0.816636i	$0.695836\pi$
$54$	−3.61717	−0.492235
$55$	2.29448	0.309388
$56$	0.0148240	0.00198094
$57$	8.13868	1.07799
$58$	−0.400196	−0.0525484
$59$	2.80923	0.365731	0.182865	−	0.983138i	$-0.441463\pi$
$59$	2.80923	0.365731	0.182865	+	0.983138i	$0.441463\pi$
$60$	−4.72697	−0.610250
$61$	−1.47967	−0.189452	−0.0947259	−	0.995503i	$-0.530197\pi$
$61$	−1.47967	−0.189452	−0.0947259	+	0.995503i	$0.530197\pi$
$62$	−6.37837	−0.810054
$63$	0.0184443	0.00232376
$64$	1.00000	0.125000
$65$	16.0179	1.98678
$66$	−2.06015	−0.253587
$67$	6.49105	0.793008	0.396504	−	0.918033i	$-0.370223\pi$
$67$	6.49105	0.793008	0.396504	+	0.918033i	$0.370223\pi$
$68$	2.20528	0.267430
$69$	−5.08472	−0.612128
$70$	−0.0340134	−0.00406538
$71$	−7.19610	−0.854020	−0.427010	−	0.904247i	$-0.640433\pi$
$71$	−7.19610	−0.854020	−0.427010	+	0.904247i	$0.640433\pi$
$72$	1.24422	0.146633
$73$	15.6550	1.83228	0.916139	−	0.400861i	$-0.131289\pi$
$73$	15.6550	1.83228	0.916139	+	0.400861i	$0.131289\pi$
$74$	−0.740568	−0.0860893
$75$	0.545195	0.0629536
$76$	3.95053	0.453156
$77$	−0.0148240	−0.00168935
$78$	−14.3821	−1.62845
$79$	10.2082	1.14851	0.574255	−	0.818677i	$-0.305292\pi$
$79$	10.2082	1.14851	0.574255	+	0.818677i	$0.305292\pi$
$80$	−2.29448	−0.256531
$81$	−11.1846	−1.24273
$82$	−5.81975	−0.642684
$83$	−17.4554	−1.91598	−0.957991	−	0.286799i	$-0.907409\pi$
$83$	−17.4554	−1.91598	−0.957991	+	0.286799i	$0.907409\pi$
$84$	0.0305397	0.00333215
$85$	−5.05998	−0.548832
$86$	−5.23891	−0.564926
$87$	−0.824465	−0.0883919
$88$	−1.00000	−0.106600
$89$	5.80344	0.615164	0.307582	−	0.951522i	$-0.400480\pi$
$89$	5.80344	0.615164	0.307582	+	0.951522i	$0.400480\pi$
$90$	−2.85483	−0.300926
$91$	−0.103487	−0.0108484
$92$	−2.46813	−0.257320
$93$	−13.1404	−1.36260
$94$	7.82007	0.806579
$95$	−9.06440	−0.929988
$96$	2.06015	0.210263
$97$	−3.44632	−0.349921	−0.174960	−	0.984575i	$-0.555980\pi$
$97$	−3.44632	−0.349921	−0.174960	+	0.984575i	$0.555980\pi$
$98$	−6.99978	−0.707085
$99$	−1.24422	−0.125049
$100$	0.264638	0.0264638
$101$	−6.57626	−0.654362	−0.327181	−	0.944962i	$-0.606099\pi$
$101$	−6.57626	−0.654362	−0.327181	+	0.944962i	$0.606099\pi$
$102$	4.54322	0.449845
$103$	−8.64190	−0.851511	−0.425756	−	0.904838i	$-0.639992\pi$
$103$	−8.64190	−0.851511	−0.425756	+	0.904838i	$0.639992\pi$
$104$	−6.98107	−0.684550
$105$	−0.0700727	−0.00683839
$106$	−8.40347	−0.816217
$107$	−5.09834	−0.492875	−0.246437	−	0.969159i	$-0.579260\pi$
$107$	−5.09834	−0.492875	−0.246437	+	0.969159i	$0.579260\pi$
$108$	−3.61717	−0.348063
$109$	−11.2870	−1.08110	−0.540548	−	0.841313i	$-0.681783\pi$
$109$	−11.2870	−1.08110	−0.540548	+	0.841313i	$0.681783\pi$
$110$	2.29448	0.218770
$111$	−1.52568	−0.144811
$112$	0.0148240	0.00140074
$113$	−8.72312	−0.820602	−0.410301	−	0.911950i	$-0.634576\pi$
$113$	−8.72312	−0.820602	−0.410301	+	0.911950i	$0.634576\pi$
$114$	8.13868	0.762257
$115$	5.66308	0.528085
$116$	−0.400196	−0.0371573
$117$	−8.68598	−0.803019
$118$	2.80923	0.258611
$119$	0.0326911	0.00299679
$120$	−4.72697	−0.431512
$121$	1.00000	0.0909091
$122$	−1.47967	−0.133963
$123$	−11.9896	−1.08106
$124$	−6.37837	−0.572794
$125$	10.8652	0.971812
$126$	0.0184443	0.00164315
$127$	17.9539	1.59315	0.796574	−	0.604542i	$-0.206644\pi$
$127$	17.9539	1.59315	0.796574	+	0.604542i	$0.206644\pi$
$128$	1.00000	0.0883883
$129$	−10.7929	−0.950265
$130$	16.0179	1.40487
$131$	19.1598	1.67400	0.836999	−	0.547205i	$-0.184308\pi$
$131$	19.1598	1.67400	0.836999	+	0.547205i	$0.184308\pi$
$132$	−2.06015	−0.179313
$133$	0.0585626	0.00507802
$134$	6.49105	0.560742
$135$	8.29953	0.714310
$136$	2.20528	0.189102
$137$	−3.50614	−0.299550	−0.149775	−	0.988720i	$-0.547855\pi$
$137$	−3.50614	−0.299550	−0.149775	+	0.988720i	$0.547855\pi$
$138$	−5.08472	−0.432840
$139$	−5.24228	−0.444644	−0.222322	−	0.974973i	$-0.571364\pi$
$139$	−5.24228	−0.444644	−0.222322	+	0.974973i	$0.571364\pi$
$140$	−0.0340134	−0.00287466
$141$	16.1105	1.35675
$142$	−7.19610	−0.603883
$143$	6.98107	0.583786
$144$	1.24422	0.103685
$145$	0.918243	0.0762559
$146$	15.6550	1.29562
$147$	−14.4206	−1.18939
$148$	−0.740568	−0.0608743
$149$	−2.71387	−0.222329	−0.111165	−	0.993802i	$-0.535458\pi$
$149$	−2.71387	−0.222329	−0.111165	+	0.993802i	$0.535458\pi$
$150$	0.545195	0.0445149
$151$	−19.3982	−1.57860	−0.789301	−	0.614007i	$-0.789557\pi$
$151$	−19.3982	−1.57860	−0.789301	+	0.614007i	$0.789557\pi$
$152$	3.95053	0.320430
$153$	2.74385	0.221827
$154$	−0.0148240	−0.00119455
$155$	14.6350	1.17551
$156$	−14.3821	−1.15149
$157$	−17.2270	−1.37486	−0.687431	−	0.726250i	$-0.741261\pi$
$157$	−17.2270	−1.37486	−0.687431	+	0.726250i	$0.741261\pi$
$158$	10.2082	0.812119
$159$	−17.3124	−1.37296
$160$	−2.29448	−0.181395
$161$	−0.0365876	−0.00288351
$162$	−11.1846	−0.878743
$163$	19.8683	1.55621	0.778103	−	0.628137i	$-0.216182\pi$
$163$	19.8683	1.55621	0.778103	+	0.628137i	$0.216182\pi$
$164$	−5.81975	−0.454446
$165$	4.72697	0.367994
$166$	−17.4554	−1.35480
$167$	−5.78116	−0.447359	−0.223680	−	0.974663i	$-0.571807\pi$
$167$	−5.78116	−0.447359	−0.223680	+	0.974663i	$0.571807\pi$
$168$	0.0305397	0.00235619
$169$	35.7354	2.74887
$170$	−5.05998	−0.388083
$171$	4.91532	0.375884
$172$	−5.23891	−0.399463
$173$	−15.7914	−1.20060	−0.600301	−	0.799774i	$-0.704952\pi$
$173$	−15.7914	−1.20060	−0.600301	+	0.799774i	$0.704952\pi$
$174$	−0.824465	−0.0625025
$175$	0.00392300	0.000296551 0
$176$	−1.00000	−0.0753778
$177$	5.78744	0.435010
$178$	5.80344	0.434986
$179$	−6.22412	−0.465212	−0.232606	−	0.972571i	$-0.574725\pi$
$179$	−6.22412	−0.465212	−0.232606	+	0.972571i	$0.574725\pi$
$180$	−2.85483	−0.212787
$181$	−8.48768	−0.630884	−0.315442	−	0.948945i	$-0.602153\pi$
$181$	−8.48768	−0.630884	−0.315442	+	0.948945i	$0.602153\pi$
$182$	−0.103487	−0.00767100
$183$	−3.04833	−0.225339
$184$	−2.46813	−0.181953
$185$	1.69922	0.124929
$186$	−13.1404	−0.963501
$187$	−2.20528	−0.161266
$188$	7.82007	0.570337
$189$	−0.0536210	−0.00390035
$190$	−9.06440	−0.657601
$191$	18.4055	1.33177	0.665886	−	0.746053i	$-0.268054\pi$
$191$	18.4055	1.33177	0.665886	+	0.746053i	$0.268054\pi$
$192$	2.06015	0.148679
$193$	4.94993	0.356304	0.178152	−	0.984003i	$-0.442988\pi$
$193$	4.94993	0.356304	0.178152	+	0.984003i	$0.442988\pi$
$194$	−3.44632	−0.247431
$195$	32.9993	2.36313
$196$	−6.99978	−0.499984
$197$	1.00000	0.0712470
$197$	1.00000	0.0712470
$198$	−1.24422	−0.0884227
$199$	19.9783	1.41623	0.708113	−	0.706099i	$-0.249547\pi$
$199$	19.9783	1.41623	0.708113	+	0.706099i	$0.249547\pi$
$200$	0.264638	0.0187128
$201$	13.3725	0.943227
$202$	−6.57626	−0.462704
$203$	−0.00593251	−0.000416381 0
$204$	4.54322	0.318089
$205$	13.3533	0.932635
$206$	−8.64190	−0.602109
$207$	−3.07089	−0.213442
$208$	−6.98107	−0.484050
$209$	−3.95053	−0.273264
$210$	−0.0700727	−0.00483547
$211$	−1.24344	−0.0856022	−0.0428011	−	0.999084i	$-0.513628\pi$
$211$	−1.24344	−0.0856022	−0.0428011	+	0.999084i	$0.513628\pi$
$212$	−8.40347	−0.577153
$213$	−14.8250	−1.01580
$214$	−5.09834	−0.348515
$215$	12.0206	0.819796
$216$	−3.61717	−0.246118
$217$	−0.0945530	−0.00641867
$218$	−11.2870	−0.764451
$219$	32.2516	2.17936
$220$	2.29448	0.154694
$221$	−15.3952	−1.03560
$222$	−1.52568	−0.102397
$223$	−11.7810	−0.788911	−0.394456	−	0.918915i	$-0.629067\pi$
$223$	−11.7810	−0.788911	−0.394456	+	0.918915i	$0.629067\pi$
$224$	0.0148240	0.000990470 0
$225$	0.329268	0.0219512
$226$	−8.72312	−0.580253
$227$	28.4151	1.88598	0.942989	−	0.332823i	$-0.108001\pi$
$227$	28.4151	1.88598	0.942989	+	0.332823i	$0.108001\pi$
$228$	8.13868	0.538997
$229$	19.6624	1.29933	0.649665	−	0.760220i	$-0.274909\pi$
$229$	19.6624	1.29933	0.649665	+	0.760220i	$0.274909\pi$
$230$	5.66308	0.373412
$231$	−0.0305397	−0.00200936
$232$	−0.400196	−0.0262742
$233$	−12.9353	−0.847421	−0.423711	−	0.905798i	$-0.639273\pi$
$233$	−12.9353	−0.847421	−0.423711	+	0.905798i	$0.639273\pi$
$234$	−8.68598	−0.567820
$235$	−17.9430	−1.17047
$236$	2.80923	0.182865
$237$	21.0304	1.36607
$238$	0.0326911	0.00211905
$239$	−1.68758	−0.109160	−0.0545801	−	0.998509i	$-0.517382\pi$
$239$	−1.68758	−0.109160	−0.0545801	+	0.998509i	$0.517382\pi$
$240$	−4.72697	−0.305125
$241$	−12.9567	−0.834613	−0.417306	−	0.908766i	$-0.637026\pi$
$241$	−12.9567	−0.834613	−0.417306	+	0.908766i	$0.637026\pi$
$242$	1.00000	0.0642824
$243$	−12.1904	−0.782013
$244$	−1.47967	−0.0947259
$245$	16.0609	1.02609
$246$	−11.9896	−0.764427
$247$	−27.5789	−1.75480
$248$	−6.37837	−0.405027
$249$	−35.9608	−2.27892
$250$	10.8652	0.687175
$251$	9.04731	0.571061	0.285530	−	0.958370i	$-0.407830\pi$
$251$	9.04731	0.571061	0.285530	+	0.958370i	$0.407830\pi$
$252$	0.0184443	0.00116188
$253$	2.46813	0.155170
$254$	17.9539	1.12653
$255$	−10.4243	−0.652796
$256$	1.00000	0.0625000
$257$	22.9705	1.43286	0.716430	−	0.697659i	$-0.245775\pi$
$257$	22.9705	1.43286	0.716430	+	0.697659i	$0.245775\pi$
$258$	−10.7929	−0.671939
$259$	−0.0109782	−0.000682151 0
$260$	16.0179	0.993390
$261$	−0.497932	−0.0308212
$262$	19.1598	1.18369
$263$	25.2751	1.55853	0.779265	−	0.626694i	$-0.215592\pi$
$263$	25.2751	1.55853	0.779265	+	0.626694i	$0.215592\pi$
$264$	−2.06015	−0.126793
$265$	19.2816	1.18446
$266$	0.0585626	0.00359070
$267$	11.9560	0.731693
$268$	6.49105	0.396504
$269$	2.36398	0.144134	0.0720672	−	0.997400i	$-0.477040\pi$
$269$	2.36398	0.144134	0.0720672	+	0.997400i	$0.477040\pi$
$270$	8.29953	0.505093
$271$	3.42840	0.208261	0.104130	−	0.994564i	$-0.466794\pi$
$271$	3.42840	0.208261	0.104130	+	0.994564i	$0.466794\pi$
$272$	2.20528	0.133715
$273$	−0.213200	−0.0129034
$274$	−3.50614	−0.211814
$275$	−0.264638	−0.0159583
$276$	−5.08472	−0.306064
$277$	−11.1458	−0.669686	−0.334843	−	0.942274i	$-0.608683\pi$
$277$	−11.1458	−0.669686	−0.334843	+	0.942274i	$0.608683\pi$
$278$	−5.24228	−0.314411
$279$	−7.93608	−0.475121
$280$	−0.0340134	−0.00203269
$281$	0.927280	0.0553169	0.0276584	−	0.999617i	$-0.491195\pi$
$281$	0.927280	0.0553169	0.0276584	+	0.999617i	$0.491195\pi$
$282$	16.1105	0.959367
$283$	−27.6861	−1.64577	−0.822883	−	0.568211i	$-0.807636\pi$
$283$	−27.6861	−1.64577	−0.822883	+	0.568211i	$0.807636\pi$
$284$	−7.19610	−0.427010
$285$	−18.6740	−1.10615
$286$	6.98107	0.412799
$287$	−0.0862720	−0.00509248
$288$	1.24422	0.0733163
$289$	−12.1367	−0.713925
$290$	0.918243	0.0539211
$291$	−7.09993	−0.416205
$292$	15.6550	0.916139
$293$	−14.8290	−0.866321	−0.433161	−	0.901317i	$-0.642602\pi$
$293$	−14.8290	−0.866321	−0.433161	+	0.901317i	$0.642602\pi$
$294$	−14.4206	−0.841026
$295$	−6.44572	−0.375284
$296$	−0.740568	−0.0430447
$297$	3.61717	0.209890
$298$	−2.71387	−0.157210
$299$	17.2302	0.996448
$300$	0.545195	0.0314768
$301$	−0.0776616	−0.00447634
$302$	−19.3982	−1.11624
$303$	−13.5481	−0.778316
$304$	3.95053	0.226578
$305$	3.39506	0.194401
$306$	2.74385	0.156856
$307$	29.8585	1.70411	0.852057	−	0.523448i	$-0.175355\pi$
$307$	29.8585	1.70411	0.852057	+	0.523448i	$0.175355\pi$
$308$	−0.0148240	−0.000844676 0
$309$	−17.8036	−1.01281
$310$	14.6350	0.831214
$311$	14.9065	0.845267	0.422634	−	0.906301i	$-0.361106\pi$
$311$	14.9065	0.845267	0.422634	+	0.906301i	$0.361106\pi$
$312$	−14.3821	−0.814223
$313$	3.00386	0.169788	0.0848940	−	0.996390i	$-0.472945\pi$
$313$	3.00386	0.169788	0.0848940	+	0.996390i	$0.472945\pi$
$314$	−17.2270	−0.972174
$315$	−0.0423201	−0.00238447
$316$	10.2082	0.574255
$317$	−4.38038	−0.246027	−0.123013	−	0.992405i	$-0.539256\pi$
$317$	−4.38038	−0.246027	−0.123013	+	0.992405i	$0.539256\pi$
$318$	−17.3124	−0.970832
$319$	0.400196	0.0224067
$320$	−2.29448	−0.128265
$321$	−10.5033	−0.586239
$322$	−0.0365876	−0.00203895
$323$	8.71203	0.484750
$324$	−11.1846	−0.621365
$325$	−1.84746	−0.102479
$326$	19.8683	1.10040
$327$	−23.2529	−1.28589
$328$	−5.81975	−0.321342
$329$	0.115925	0.00639114
$330$	4.72697	0.260211
$331$	−6.09976	−0.335273	−0.167637	−	0.985849i	$-0.553614\pi$
$331$	−6.09976	−0.335273	−0.167637	+	0.985849i	$0.553614\pi$
$332$	−17.4554	−0.957991
$333$	−0.921429	−0.0504940
$334$	−5.78116	−0.316331
$335$	−14.8936	−0.813724
$336$	0.0305397	0.00166608
$337$	−14.2478	−0.776128	−0.388064	−	0.921632i	$-0.626856\pi$
$337$	−14.2478	−0.776128	−0.388064	+	0.921632i	$0.626856\pi$
$338$	35.7354	1.94375
$339$	−17.9709	−0.976047
$340$	−5.05998	−0.274416
$341$	6.37837	0.345408
$342$	4.91532	0.265790
$343$	−0.207533	−0.0112057
$344$	−5.23891	−0.282463
$345$	11.6668	0.628119
$346$	−15.7914	−0.848953
$347$	32.8817	1.76518	0.882591	−	0.470142i	$-0.155797\pi$
$347$	32.8817	1.76518	0.882591	+	0.470142i	$0.155797\pi$
$348$	−0.824465	−0.0441960
$349$	1.05250	0.0563388	0.0281694	−	0.999603i	$-0.491032\pi$
$349$	1.05250	0.0563388	0.0281694	+	0.999603i	$0.491032\pi$
$350$	0.00392300	0.000209693 0
$351$	25.2517	1.34784
$352$	−1.00000	−0.0533002
$353$	−29.2241	−1.55544	−0.777722	−	0.628608i	$-0.783625\pi$
$353$	−29.2241	−1.55544	−0.777722	+	0.628608i	$0.783625\pi$
$354$	5.78744	0.307599
$355$	16.5113	0.876329
$356$	5.80344	0.307582
$357$	0.0673486	0.00356447
$358$	−6.22412	−0.328955
$359$	−21.8626	−1.15386	−0.576931	−	0.816793i	$-0.695750\pi$
$359$	−21.8626	−1.15386	−0.576931	+	0.816793i	$0.695750\pi$
$360$	−2.85483	−0.150463
$361$	−3.39334	−0.178597
$362$	−8.48768	−0.446102
$363$	2.06015	0.108130
$364$	−0.103487	−0.00542421
$365$	−35.9201	−1.88014
$366$	−3.04833	−0.159339
$367$	−32.3002	−1.68606	−0.843029	−	0.537868i	$-0.819230\pi$
$367$	−32.3002	−1.68606	−0.843029	+	0.537868i	$0.819230\pi$
$368$	−2.46813	−0.128660
$369$	−7.24104	−0.376954
$370$	1.69922	0.0883382
$371$	−0.124573	−0.00646751
$372$	−13.1404	−0.681298
$373$	8.61803	0.446225	0.223112	−	0.974793i	$-0.428378\pi$
$373$	8.61803	0.446225	0.223112	+	0.974793i	$0.428378\pi$
$374$	−2.20528	−0.114033
$375$	22.3839	1.15590
$376$	7.82007	0.403289
$377$	2.79380	0.143888
$378$	−0.0536210	−0.00275797
$379$	7.63252	0.392056	0.196028	−	0.980598i	$-0.437196\pi$
$379$	7.63252	0.392056	0.196028	+	0.980598i	$0.437196\pi$
$380$	−9.06440	−0.464994
$381$	36.9876	1.89493
$382$	18.4055	0.941705
$383$	9.28159	0.474267	0.237134	−	0.971477i	$-0.423792\pi$
$383$	9.28159	0.474267	0.237134	+	0.971477i	$0.423792\pi$
$384$	2.06015	0.105132
$385$	0.0340134	0.00173348
$386$	4.94993	0.251945
$387$	−6.51834	−0.331346
$388$	−3.44632	−0.174960
$389$	−18.9220	−0.959383	−0.479692	−	0.877437i	$-0.659251\pi$
$389$	−18.9220	−0.959383	−0.479692	+	0.877437i	$0.659251\pi$
$390$	32.9993	1.67099
$391$	−5.44293	−0.275261
$392$	−6.99978	−0.353542
$393$	39.4720	1.99110
$394$	1.00000	0.0503793
$395$	−23.4224	−1.17851
$396$	−1.24422	−0.0625243
$397$	2.41179	0.121044	0.0605222	−	0.998167i	$-0.480723\pi$
$397$	2.41179	0.121044	0.0605222	+	0.998167i	$0.480723\pi$
$398$	19.9783	1.00142
$399$	0.120648	0.00603994
$400$	0.264638	0.0132319
$401$	1.77189	0.0884838	0.0442419	−	0.999021i	$-0.485913\pi$
$401$	1.77189	0.0884838	0.0442419	+	0.999021i	$0.485913\pi$
$402$	13.3725	0.666962
$403$	44.5279	2.21809
$404$	−6.57626	−0.327181
$405$	25.6628	1.27519
$406$	−0.00593251	−0.000294426 0
$407$	0.740568	0.0367086
$408$	4.54322	0.224923
$409$	−11.6274	−0.574939	−0.287470	−	0.957790i	$-0.592814\pi$
$409$	−11.6274	−0.574939	−0.287470	+	0.957790i	$0.592814\pi$
$410$	13.3533	0.659473
$411$	−7.22318	−0.356293
$412$	−8.64190	−0.425756
$413$	0.0416440	0.00204917
$414$	−3.07089	−0.150926
$415$	40.0511	1.96603
$416$	−6.98107	−0.342275
$417$	−10.7999	−0.528872
$418$	−3.95053	−0.193227
$419$	−34.4452	−1.68276	−0.841379	−	0.540445i	$-0.818256\pi$
$419$	−34.4452	−1.68276	−0.841379	+	0.540445i	$0.818256\pi$
$420$	−0.0700727	−0.00341920
$421$	14.1560	0.689920	0.344960	−	0.938617i	$-0.387892\pi$
$421$	14.1560	0.689920	0.344960	+	0.938617i	$0.387892\pi$
$422$	−1.24344	−0.0605299
$423$	9.72987	0.473083
$424$	−8.40347	−0.408109
$425$	0.583602	0.0283089
$426$	−14.8250	−0.718276
$427$	−0.0219346	−0.00106149
$428$	−5.09834	−0.246437
$429$	14.3821	0.694372
$430$	12.0206	0.579683
$431$	−14.8061	−0.713185	−0.356593	−	0.934260i	$-0.616062\pi$
$431$	−14.8061	−0.713185	−0.356593	+	0.934260i	$0.616062\pi$
$432$	−3.61717	−0.174031
$433$	6.79624	0.326607	0.163303	−	0.986576i	$-0.447785\pi$
$433$	6.79624	0.326607	0.163303	+	0.986576i	$0.447785\pi$
$434$	−0.0945530	−0.00453869
$435$	1.89172	0.0907009
$436$	−11.2870	−0.540548
$437$	−9.75041	−0.466426
$438$	32.2516	1.54104
$439$	−14.5879	−0.696242	−0.348121	−	0.937450i	$-0.613180\pi$
$439$	−14.5879	−0.696242	−0.348121	+	0.937450i	$0.613180\pi$
$440$	2.29448	0.109385
$441$	−8.70925	−0.414726
$442$	−15.3952	−0.732277
$443$	37.8462	1.79813	0.899064	−	0.437817i	$-0.144248\pi$
$443$	37.8462	1.79813	0.899064	+	0.437817i	$0.144248\pi$
$444$	−1.52568	−0.0724057
$445$	−13.3159	−0.631233
$446$	−11.7810	−0.557844
$447$	−5.59099	−0.264445
$448$	0.0148240	0.000700368 0
$449$	34.8467	1.64452	0.822258	−	0.569115i	$-0.192714\pi$
$449$	34.8467	1.64452	0.822258	+	0.569115i	$0.192714\pi$
$450$	0.329268	0.0155218
$451$	5.81975	0.274041
$452$	−8.72312	−0.410301
$453$	−39.9632	−1.87763
$454$	28.4151	1.33359
$455$	0.237450	0.0111318
$456$	8.13868	0.381128
$457$	12.0551	0.563915	0.281958	−	0.959427i	$-0.409016\pi$
$457$	12.0551	0.563915	0.281958	+	0.959427i	$0.409016\pi$
$458$	19.6624	0.918765
$459$	−7.97689	−0.372330
$460$	5.66308	0.264042
$461$	−33.4393	−1.55742	−0.778712	−	0.627381i	$-0.784127\pi$
$461$	−33.4393	−1.55742	−0.778712	+	0.627381i	$0.784127\pi$
$462$	−0.0305397	−0.00142083
$463$	27.7496	1.28963	0.644817	−	0.764337i	$-0.276934\pi$
$463$	27.7496	1.28963	0.644817	+	0.764337i	$0.276934\pi$
$464$	−0.400196	−0.0185787
$465$	30.1504	1.39819
$466$	−12.9353	−0.599217
$467$	36.9712	1.71082	0.855412	−	0.517948i	$-0.173304\pi$
$467$	36.9712	1.71082	0.855412	+	0.517948i	$0.173304\pi$
$468$	−8.68598	−0.401509
$469$	0.0962234	0.00444318
$470$	−17.9430	−0.827649
$471$	−35.4901	−1.63530
$472$	2.80923	0.129305
$473$	5.23891	0.240885
$474$	21.0304	0.965957
$475$	1.04546	0.0479690
$476$	0.0326911	0.00149840
$477$	−10.4558	−0.478736
$478$	−1.68758	−0.0771880
$479$	16.5077	0.754254	0.377127	−	0.926161i	$-0.376912\pi$
$479$	16.5077	0.754254	0.377127	+	0.926161i	$0.376912\pi$
$480$	−4.72697	−0.215756
$481$	5.16996	0.235730
$482$	−12.9567	−0.590160
$483$	−0.0753759	−0.00342972
$484$	1.00000	0.0454545
$485$	7.90751	0.359061
$486$	−12.1904	−0.552967
$487$	39.4398	1.78719	0.893593	−	0.448877i	$-0.148176\pi$
$487$	39.4398	1.78719	0.893593	+	0.448877i	$0.148176\pi$
$488$	−1.47967	−0.0669813
$489$	40.9317	1.85099
$490$	16.0609	0.725555
$491$	15.1536	0.683875	0.341937	−	0.939723i	$-0.388917\pi$
$491$	15.1536	0.683875	0.341937	+	0.939723i	$0.388917\pi$
$492$	−11.9896	−0.540531
$493$	−0.882547	−0.0397479
$494$	−27.5789	−1.24083
$495$	2.85483	0.128315
$496$	−6.37837	−0.286397
$497$	−0.106675	−0.00478503
$498$	−35.9608	−1.61144
$499$	1.52123	0.0680998	0.0340499	−	0.999420i	$-0.489159\pi$
$499$	1.52123	0.0680998	0.0340499	+	0.999420i	$0.489159\pi$
$500$	10.8652	0.485906
$501$	−11.9101	−0.532102
$502$	9.04731	0.403801
$503$	10.7458	0.479133	0.239566	−	0.970880i	$-0.422995\pi$
$503$	10.7458	0.479133	0.239566	+	0.970880i	$0.422995\pi$
$504$	0.0184443	0.000821574 0
$505$	15.0891	0.671456
$506$	2.46813	0.109722
$507$	73.6202	3.26959
$508$	17.9539	0.796574
$509$	−7.59464	−0.336627	−0.168313	−	0.985734i	$-0.553832\pi$
$509$	−7.59464	−0.336627	−0.168313	+	0.985734i	$0.553832\pi$
$510$	−10.4243	−0.461597
$511$	0.232070	0.0102662
$512$	1.00000	0.0441942
$513$	−14.2897	−0.630907
$514$	22.9705	1.01318
$515$	19.8287	0.873755
$516$	−10.7929	−0.475133
$517$	−7.82007	−0.343926
$518$	−0.0109782	−0.000482354 0
$519$	−32.5327	−1.42803
$520$	16.0179	0.702433
$521$	39.2291	1.71866	0.859330	−	0.511422i	$-0.170881\pi$
$521$	39.2291	1.71866	0.859330	+	0.511422i	$0.170881\pi$
$522$	−0.497932	−0.0217939
$523$	−18.6857	−0.817069	−0.408535	−	0.912743i	$-0.633960\pi$
$523$	−18.6857	−0.817069	−0.408535	+	0.912743i	$0.633960\pi$
$524$	19.1598	0.836999
$525$	0.00808197	0.000352726 0
$526$	25.2751	1.10205
$527$	−14.0661	−0.612730
$528$	−2.06015	−0.0896565
$529$	−16.9083	−0.735145
$530$	19.2816	0.837539
$531$	3.49530	0.151683
$532$	0.0585626	0.00253901
$533$	40.6281	1.75980
$534$	11.9560	0.517385
$535$	11.6980	0.505750
$536$	6.49105	0.280371
$537$	−12.8226	−0.553337
$538$	2.36398	0.101918
$539$	6.99978	0.301502
$540$	8.29953	0.357155
$541$	−20.5914	−0.885293	−0.442647	−	0.896696i	$-0.645960\pi$
$541$	−20.5914	−0.885293	−0.442647	+	0.896696i	$0.645960\pi$
$542$	3.42840	0.147262
$543$	−17.4859	−0.750391
$544$	2.20528	0.0945508
$545$	25.8977	1.10934
$546$	−0.213200	−0.00912410
$547$	−16.3250	−0.698007	−0.349004	−	0.937121i	$-0.613480\pi$
$547$	−16.3250	−0.698007	−0.349004	+	0.937121i	$0.613480\pi$
$548$	−3.50614	−0.149775
$549$	−1.84103	−0.0785731
$550$	−0.264638	−0.0112842
$551$	−1.58099	−0.0673523
$552$	−5.08472	−0.216420
$553$	0.151326	0.00643504
$554$	−11.1458	−0.473540
$555$	3.50065	0.148594
$556$	−5.24228	−0.222322
$557$	24.3703	1.03260	0.516301	−	0.856407i	$-0.327308\pi$
$557$	24.3703	1.03260	0.516301	+	0.856407i	$0.327308\pi$
$558$	−7.93608	−0.335961
$559$	36.5732	1.54688
$560$	−0.0340134	−0.00143733
$561$	−4.54322	−0.191815
$562$	0.927280	0.0391149
$563$	0.191534	0.00807218	0.00403609	−	0.999992i	$-0.498715\pi$
$563$	0.191534	0.00807218	0.00403609	+	0.999992i	$0.498715\pi$
$564$	16.1105	0.678375
$565$	20.0150	0.842038
$566$	−27.6861	−1.16373
$567$	−0.165800	−0.00696295
$568$	−7.19610	−0.301942
$569$	9.03349	0.378703	0.189352	−	0.981909i	$-0.439361\pi$
$569$	9.03349	0.378703	0.189352	+	0.981909i	$0.439361\pi$
$570$	−18.6740	−0.782169
$571$	−30.0164	−1.25615	−0.628073	−	0.778154i	$-0.716156\pi$
$571$	−30.0164	−1.25615	−0.628073	+	0.778154i	$0.716156\pi$
$572$	6.98107	0.291893
$573$	37.9180	1.58405
$574$	−0.0862720	−0.00360092
$575$	−0.653162	−0.0272387
$576$	1.24422	0.0518424
$577$	−25.1474	−1.04690	−0.523449	−	0.852057i	$-0.675355\pi$
$577$	−25.1474	−1.04690	−0.523449	+	0.852057i	$0.675355\pi$
$578$	−12.1367	−0.504821
$579$	10.1976	0.423798
$580$	0.918243	0.0381280
$581$	−0.258759	−0.0107351
$582$	−7.09993	−0.294302
$583$	8.40347	0.348036
$584$	15.6550	0.647808
$585$	19.9298	0.823996
$586$	−14.8290	−0.612582
$587$	7.11085	0.293496	0.146748	−	0.989174i	$-0.453119\pi$
$587$	7.11085	0.293496	0.146748	+	0.989174i	$0.453119\pi$
$588$	−14.4206	−0.594695
$589$	−25.1979	−1.03826
$590$	−6.44572	−0.265366
$591$	2.06015	0.0847433
$592$	−0.740568	−0.0304372
$593$	7.51101	0.308440	0.154220	−	0.988037i	$-0.450713\pi$
$593$	7.51101	0.308440	0.154220	+	0.988037i	$0.450713\pi$
$594$	3.61717	0.148414
$595$	−0.0750092	−0.00307508
$596$	−2.71387	−0.111165
$597$	41.1584	1.68450
$598$	17.2302	0.704595
$599$	15.8649	0.648224	0.324112	−	0.946019i	$-0.394935\pi$
$599$	15.8649	0.648224	0.324112	+	0.946019i	$0.394935\pi$
$600$	0.545195	0.0222575
$601$	−15.4036	−0.628328	−0.314164	−	0.949369i	$-0.601724\pi$
$601$	−15.4036	−0.628328	−0.314164	+	0.949369i	$0.601724\pi$
$602$	−0.0776616	−0.00316525
$603$	8.07629	0.328892
$604$	−19.3982	−0.789301
$605$	−2.29448	−0.0932839
$606$	−13.5481	−0.550353
$607$	−29.0544	−1.17928	−0.589641	−	0.807666i	$-0.700731\pi$
$607$	−29.0544	−1.17928	−0.589641	+	0.807666i	$0.700731\pi$
$608$	3.95053	0.160215
$609$	−0.0122219	−0.000495255 0
$610$	3.39506	0.137462
$611$	−54.5925	−2.20857
$612$	2.74385	0.110914
$613$	−33.6154	−1.35771	−0.678857	−	0.734271i	$-0.737524\pi$
$613$	−33.6154	−1.35771	−0.678857	+	0.734271i	$0.737524\pi$
$614$	29.8585	1.20499
$615$	27.5098	1.10930
$616$	−0.0148240	−0.000597276 0
$617$	−5.09336	−0.205051	−0.102526	−	0.994730i	$-0.532692\pi$
$617$	−5.09336	−0.205051	−0.102526	+	0.994730i	$0.532692\pi$
$618$	−17.8036	−0.716166
$619$	−29.2780	−1.17678	−0.588391	−	0.808576i	$-0.700238\pi$
$619$	−29.2780	−1.17678	−0.588391	+	0.808576i	$0.700238\pi$
$620$	14.6350	0.587757
$621$	8.92766	0.358255
$622$	14.9065	0.597694
$623$	0.0860303	0.00344673
$624$	−14.3821	−0.575743
$625$	−26.2532	−1.05013
$626$	3.00386	0.120058
$627$	−8.13868	−0.325027
$628$	−17.2270	−0.687431
$629$	−1.63316	−0.0651185
$630$	−0.0423201	−0.00168607
$631$	−46.4303	−1.84836	−0.924181	−	0.381954i	$-0.875251\pi$
$631$	−46.4303	−1.84836	−0.924181	+	0.381954i	$0.875251\pi$
$632$	10.2082	0.406059
$633$	−2.56168	−0.101818
$634$	−4.38038	−0.173967
$635$	−41.1948	−1.63476
$636$	−17.3124	−0.686482
$637$	48.8660	1.93614
$638$	0.400196	0.0158439
$639$	−8.95352	−0.354196
$640$	−2.29448	−0.0906973
$641$	18.7444	0.740359	0.370179	−	0.928960i	$-0.379296\pi$
$641$	18.7444	0.740359	0.370179	+	0.928960i	$0.379296\pi$
$642$	−10.5033	−0.414534
$643$	−37.8832	−1.49397	−0.746984	−	0.664842i	$-0.768499\pi$
$643$	−37.8832	−1.49397	−0.746984	+	0.664842i	$0.768499\pi$
$644$	−0.0365876	−0.00144175
$645$	24.7642	0.975088
$646$	8.71203	0.342770
$647$	1.68558	0.0662672	0.0331336	−	0.999451i	$-0.489451\pi$
$647$	1.68558	0.0662672	0.0331336	+	0.999451i	$0.489451\pi$
$648$	−11.1846	−0.439372
$649$	−2.80923	−0.110272
$650$	−1.84746	−0.0724633
$651$	−0.194793	−0.00763455
$652$	19.8683	0.778103
$653$	7.36704	0.288295	0.144147	−	0.989556i	$-0.453956\pi$
$653$	7.36704	0.288295	0.144147	+	0.989556i	$0.453956\pi$
$654$	−23.2529	−0.909259
$655$	−43.9617	−1.71773
$656$	−5.81975	−0.227223
$657$	19.4782	0.759918
$658$	0.115925	0.00451922
$659$	16.7272	0.651599	0.325799	−	0.945439i	$-0.394367\pi$
$659$	16.7272	0.651599	0.325799	+	0.945439i	$0.394367\pi$
$660$	4.72697	0.183997
$661$	−45.0788	−1.75336	−0.876681	−	0.481072i	$-0.840248\pi$
$661$	−45.0788	−1.75336	−0.876681	+	0.481072i	$0.840248\pi$
$662$	−6.09976	−0.237074
$663$	−31.7165	−1.23177
$664$	−17.4554	−0.677402
$665$	−0.134371	−0.00521067
$666$	−0.921429	−0.0357046
$667$	0.987737	0.0382453
$668$	−5.78116	−0.223680
$669$	−24.2705	−0.938353
$670$	−14.8936	−0.575390
$671$	1.47967	0.0571218
$672$	0.0305397	0.00117809
$673$	−2.49908	−0.0963323	−0.0481662	−	0.998839i	$-0.515338\pi$
$673$	−2.49908	−0.0963323	−0.0481662	+	0.998839i	$0.515338\pi$
$674$	−14.2478	−0.548805
$675$	−0.957243	−0.0368443
$676$	35.7354	1.37444
$677$	17.8460	0.685878	0.342939	−	0.939358i	$-0.388578\pi$
$677$	17.8460	0.685878	0.342939	+	0.939358i	$0.388578\pi$
$678$	−17.9709	−0.690170
$679$	−0.0510882	−0.00196059
$680$	−5.05998	−0.194041
$681$	58.5394	2.24324
$682$	6.37837	0.244240
$683$	16.1325	0.617292	0.308646	−	0.951177i	$-0.400124\pi$
$683$	16.1325	0.617292	0.308646	+	0.951177i	$0.400124\pi$
$684$	4.91532	0.187942
$685$	8.04477	0.307375
$686$	−0.207533	−0.00792364
$687$	40.5076	1.54546
$688$	−5.23891	−0.199731
$689$	58.6652	2.23497
$690$	11.6668	0.444147
$691$	−21.2022	−0.806569	−0.403284	−	0.915075i	$-0.632131\pi$
$691$	−21.2022	−0.806569	−0.403284	+	0.915075i	$0.632131\pi$
$692$	−15.7914	−0.600301
$693$	−0.0184443	−0.000700641 0
$694$	32.8817	1.24817
$695$	12.0283	0.456259
$696$	−0.824465	−0.0312513
$697$	−12.8342	−0.486130
$698$	1.05250	0.0398375
$699$	−26.6487	−1.00795
$700$	0.00392300	0.000148275 0
$701$	−0.257121	−0.00971134	−0.00485567	−	0.999988i	$-0.501546\pi$
$701$	−0.257121	−0.00971134	−0.00485567	+	0.999988i	$0.501546\pi$
$702$	25.2517	0.953066
$703$	−2.92563	−0.110342
$704$	−1.00000	−0.0376889
$705$	−36.9653	−1.39219
$706$	−29.2241	−1.09986
$707$	−0.0974864	−0.00366635
$708$	5.78744	0.217505
$709$	−33.2584	−1.24905	−0.624523	−	0.781006i	$-0.714707\pi$
$709$	−33.2584	−1.24905	−0.624523	+	0.781006i	$0.714707\pi$
$710$	16.5113	0.619658
$711$	12.7012	0.476332
$712$	5.80344	0.217493
$713$	15.7426	0.589567
$714$	0.0673486	0.00252046
$715$	−16.0179	−0.599037
$716$	−6.22412	−0.232606
$717$	−3.47666	−0.129838
$718$	−21.8626	−0.815904
$719$	−20.4653	−0.763226	−0.381613	−	0.924322i	$-0.624631\pi$
$719$	−20.4653	−0.763226	−0.381613	+	0.924322i	$0.624631\pi$
$720$	−2.85483	−0.106393
$721$	−0.128107	−0.00477097
$722$	−3.39334	−0.126287
$723$	−26.6927	−0.992712
$724$	−8.48768	−0.315442
$725$	−0.105907	−0.00393330
$726$	2.06015	0.0764593
$727$	−9.72180	−0.360562	−0.180281	−	0.983615i	$-0.557701\pi$
$727$	−9.72180	−0.360562	−0.180281	+	0.983615i	$0.557701\pi$
$728$	−0.103487	−0.00383550
$729$	8.43971	0.312582
$730$	−35.9201	−1.32946
$731$	−11.5533	−0.427313
$732$	−3.04833	−0.112670
$733$	10.0197	0.370088	0.185044	−	0.982730i	$-0.440757\pi$
$733$	10.0197	0.370088	0.185044	+	0.982730i	$0.440757\pi$
$734$	−32.3002	−1.19222
$735$	33.0878	1.22046
$736$	−2.46813	−0.0909765
$737$	−6.49105	−0.239101
$738$	−7.24104	−0.266546
$739$	21.9216	0.806397	0.403199	−	0.915112i	$-0.367898\pi$
$739$	21.9216	0.806397	0.403199	+	0.915112i	$0.367898\pi$
$740$	1.69922	0.0624645
$741$	−56.8167	−2.08721
$742$	−0.124573	−0.00457322
$743$	−31.2974	−1.14819	−0.574095	−	0.818789i	$-0.694646\pi$
$743$	−31.2974	−1.14819	−0.574095	+	0.818789i	$0.694646\pi$
$744$	−13.1404	−0.481750
$745$	6.22693	0.228137
$746$	8.61803	0.315529
$747$	−21.7184	−0.794633
$748$	−2.20528	−0.0806332
$749$	−0.0755777	−0.00276155
$750$	22.3839	0.817345
$751$	15.5280	0.566624	0.283312	−	0.959028i	$-0.408567\pi$
$751$	15.5280	0.566624	0.283312	+	0.959028i	$0.408567\pi$
$752$	7.82007	0.285169
$753$	18.6388	0.679236
$754$	2.79380	0.101744
$755$	44.5087	1.61984
$756$	−0.0536210	−0.00195018
$757$	−1.98517	−0.0721523	−0.0360762	−	0.999349i	$-0.511486\pi$
$757$	−1.98517	−0.0721523	−0.0360762	+	0.999349i	$0.511486\pi$
$758$	7.63252	0.277226
$759$	5.08472	0.184564
$760$	−9.06440	−0.328800
$761$	−32.8892	−1.19223	−0.596117	−	0.802898i	$-0.703290\pi$
$761$	−32.8892	−1.19223	−0.596117	+	0.802898i	$0.703290\pi$
$762$	36.9876	1.33992
$763$	−0.167318	−0.00605733
$764$	18.4055	0.665886
$765$	−6.29572	−0.227622
$766$	9.28159	0.335357
$767$	−19.6114	−0.708128
$768$	2.06015	0.0743393
$769$	−23.0435	−0.830969	−0.415485	−	0.909600i	$-0.636388\pi$
$769$	−23.0435	−0.830969	−0.415485	+	0.909600i	$0.636388\pi$
$770$	0.0340134	0.00122576
$771$	47.3226	1.70428
$772$	4.94993	0.178152
$773$	11.3003	0.406442	0.203221	−	0.979133i	$-0.434859\pi$
$773$	11.3003	0.406442	0.203221	+	0.979133i	$0.434859\pi$
$774$	−6.51834	−0.234297
$775$	−1.68796	−0.0606333
$776$	−3.44632	−0.123716
$777$	−0.0226167	−0.000811370 0
$778$	−18.9220	−0.678386
$779$	−22.9911	−0.823741
$780$	32.9993	1.18157
$781$	7.19610	0.257497
$782$	−5.44293	−0.194639
$783$	1.44758	0.0517323
$784$	−6.99978	−0.249992
$785$	39.5269	1.41078
$786$	39.4720	1.40792
$787$	−42.3263	−1.50877	−0.754384	−	0.656433i	$-0.772065\pi$
$787$	−42.3263	−1.50877	−0.754384	+	0.656433i	$0.772065\pi$
$788$	1.00000	0.0356235
$789$	52.0705	1.85376
$790$	−23.4224	−0.833333
$791$	−0.129312	−0.00459779
$792$	−1.24422	−0.0442114
$793$	10.3296	0.366817
$794$	2.41179	0.0855912
$795$	39.7230	1.40883
$796$	19.9783	0.708113
$797$	−14.8879	−0.527358	−0.263679	−	0.964610i	$-0.584936\pi$
$797$	−14.8879	−0.527358	−0.263679	+	0.964610i	$0.584936\pi$
$798$	0.120648	0.00427089
$799$	17.2455	0.610101
$800$	0.264638	0.00935638
$801$	7.22075	0.255133
$802$	1.77189	0.0625675
$803$	−15.6550	−0.552452
$804$	13.3725	0.471613
$805$	0.0839495	0.00295883
$806$	44.5279	1.56843
$807$	4.87016	0.171438
$808$	−6.57626	−0.231352
$809$	32.6487	1.14787	0.573933	−	0.818902i	$-0.305417\pi$
$809$	32.6487	1.14787	0.573933	+	0.818902i	$0.305417\pi$
$810$	25.6628	0.901698
$811$	36.9053	1.29592	0.647959	−	0.761675i	$-0.275623\pi$
$811$	36.9053	1.29592	0.647959	+	0.761675i	$0.275623\pi$
$812$	−0.00593251	−0.000208190 0
$813$	7.06302	0.247711
$814$	0.740568	0.0259569
$815$	−45.5874	−1.59686
$816$	4.54322	0.159044
$817$	−20.6964	−0.724077
$818$	−11.6274	−0.406544
$819$	−0.128761	−0.00449927
$820$	13.3533	0.466318
$821$	−45.8568	−1.60041	−0.800206	−	0.599725i	$-0.795277\pi$
$821$	−45.8568	−1.60041	−0.800206	+	0.599725i	$0.795277\pi$
$822$	−7.22318	−0.251937
$823$	15.4538	0.538687	0.269344	−	0.963044i	$-0.413193\pi$
$823$	15.4538	0.538687	0.269344	+	0.963044i	$0.413193\pi$
$824$	−8.64190	−0.301055
$825$	−0.545195	−0.0189812
$826$	0.0416440	0.00144898
$827$	−19.7818	−0.687881	−0.343941	−	0.938991i	$-0.611762\pi$
$827$	−19.7818	−0.687881	−0.343941	+	0.938991i	$0.611762\pi$
$828$	−3.07089	−0.106721
$829$	−45.3532	−1.57518	−0.787590	−	0.616200i	$-0.788671\pi$
$829$	−45.3532	−1.57518	−0.787590	+	0.616200i	$0.788671\pi$
$830$	40.0511	1.39019
$831$	−22.9620	−0.796544
$832$	−6.98107	−0.242025
$833$	−15.4365	−0.534843
$834$	−10.7999	−0.373969
$835$	13.2648	0.459046
$836$	−3.95053	−0.136632
$837$	23.0717	0.797474
$838$	−34.4452	−1.18989
$839$	32.7785	1.13164	0.565820	−	0.824529i	$-0.308560\pi$
$839$	32.7785	1.13164	0.565820	+	0.824529i	$0.308560\pi$
$840$	−0.0700727	−0.00241774
$841$	−28.8398	−0.994477
$842$	14.1560	0.487847
$843$	1.91034	0.0657955
$844$	−1.24344	−0.0428011
$845$	−81.9941	−2.82068
$846$	9.72987	0.334520
$847$	0.0148240	0.000509359 0
$848$	−8.40347	−0.288576
$849$	−57.0374	−1.95752
$850$	0.583602	0.0200174
$851$	1.82782	0.0626568
$852$	−14.8250	−0.507898
$853$	−50.3174	−1.72284	−0.861418	−	0.507897i	$-0.830423\pi$
$853$	−50.3174	−1.72284	−0.861418	+	0.507897i	$0.830423\pi$
$854$	−0.0219346	−0.000750585 0
$855$	−11.2781	−0.385703
$856$	−5.09834	−0.174258
$857$	−34.7486	−1.18699	−0.593494	−	0.804838i	$-0.702252\pi$
$857$	−34.7486	−1.18699	−0.593494	+	0.804838i	$0.702252\pi$
$858$	14.3821	0.490995
$859$	−9.48354	−0.323574	−0.161787	−	0.986826i	$-0.551726\pi$
$859$	−9.48354	−0.323574	−0.161787	+	0.986826i	$0.551726\pi$
$860$	12.0206	0.409898
$861$	−0.177733	−0.00605714
$862$	−14.8061	−0.504298
$863$	42.0136	1.43016	0.715080	−	0.699042i	$-0.246390\pi$
$863$	42.0136	1.43016	0.715080	+	0.699042i	$0.246390\pi$
$864$	−3.61717	−0.123059
$865$	36.2332	1.23196
$866$	6.79624	0.230946
$867$	−25.0035	−0.849162
$868$	−0.0945530	−0.00320934
$869$	−10.2082	−0.346289
$870$	1.89172	0.0641352
$871$	−45.3145	−1.53542
$872$	−11.2870	−0.382225
$873$	−4.28797	−0.145126
$874$	−9.75041	−0.329813
$875$	0.161066	0.00544501
$876$	32.2516	1.08968
$877$	10.0039	0.337807	0.168903	−	0.985633i	$-0.445977\pi$
$877$	10.0039	0.337807	0.168903	+	0.985633i	$0.445977\pi$
$878$	−14.5879	−0.492317
$879$	−30.5500	−1.03043
$880$	2.29448	0.0773469
$881$	52.2900	1.76170	0.880848	−	0.473399i	$-0.156973\pi$
$881$	52.2900	1.76170	0.880848	+	0.473399i	$0.156973\pi$
$882$	−8.70925	−0.293256
$883$	28.7765	0.968406	0.484203	−	0.874956i	$-0.339110\pi$
$883$	28.7765	0.968406	0.484203	+	0.874956i	$0.339110\pi$
$884$	−15.3952	−0.517798
$885$	−13.2792	−0.446374
$886$	37.8462	1.27147
$887$	−13.3276	−0.447496	−0.223748	−	0.974647i	$-0.571829\pi$
$887$	−13.3276	−0.447496	−0.223748	+	0.974647i	$0.571829\pi$
$888$	−1.52568	−0.0511985
$889$	0.266148	0.00892632
$890$	−13.3159	−0.446349
$891$	11.1846	0.374697
$892$	−11.7810	−0.394456
$893$	30.8934	1.03381
$894$	−5.59099	−0.186991
$895$	14.2811	0.477365
$896$	0.0148240	0.000495235 0
$897$	35.4968	1.18520
$898$	34.8467	1.16285
$899$	2.55260	0.0851340
$900$	0.329268	0.0109756
$901$	−18.5320	−0.617392
$902$	5.81975	0.193777
$903$	−0.159995	−0.00532428
$904$	−8.72312	−0.290127
$905$	19.4748	0.647364
$906$	−39.9632	−1.32769
$907$	22.0462	0.732033	0.366016	−	0.930608i	$-0.380721\pi$
$907$	22.0462	0.732033	0.366016	+	0.930608i	$0.380721\pi$
$908$	28.4151	0.942989
$909$	−8.18230	−0.271390
$910$	0.237450	0.00787139
$911$	−1.56673	−0.0519082	−0.0259541	−	0.999663i	$-0.508262\pi$
$911$	−1.56673	−0.0519082	−0.0259541	+	0.999663i	$0.508262\pi$
$912$	8.13868	0.269499
$913$	17.4554	0.577690
$914$	12.0551	0.398748
$915$	6.99434	0.231226
$916$	19.6624	0.649665
$917$	0.284025	0.00937932
$918$	−7.97689	−0.263277
$919$	17.9313	0.591499	0.295750	−	0.955265i	$-0.404431\pi$
$919$	17.9313	0.591499	0.295750	+	0.955265i	$0.404431\pi$
$920$	5.66308	0.186706
$921$	61.5130	2.02692
$922$	−33.4393	−1.10127
$923$	50.2365	1.65355
$924$	−0.0305397	−0.00100468
$925$	−0.195983	−0.00644387
$926$	27.7496	0.911908
$927$	−10.7524	−0.353155
$928$	−0.400196	−0.0131371
$929$	32.7321	1.07390	0.536952	−	0.843613i	$-0.319576\pi$
$929$	32.7321	1.07390	0.536952	+	0.843613i	$0.319576\pi$
$930$	30.1504	0.988670
$931$	−27.6528	−0.906284
$932$	−12.9353	−0.423711
$933$	30.7095	1.00538
$934$	36.9712	1.20974
$935$	5.05998	0.165479
$936$	−8.68598	−0.283910
$937$	5.35614	0.174977	0.0874887	−	0.996166i	$-0.472116\pi$
$937$	5.35614	0.174977	0.0874887	+	0.996166i	$0.472116\pi$
$938$	0.0962234	0.00314181
$939$	6.18839	0.201951
$940$	−17.9430	−0.585236
$941$	−23.2943	−0.759373	−0.379686	−	0.925115i	$-0.623968\pi$
$941$	−23.2943	−0.759373	−0.379686	+	0.925115i	$0.623968\pi$
$942$	−35.4901	−1.15633
$943$	14.3639	0.467753
$944$	2.80923	0.0914327
$945$	0.123032	0.00400224
$946$	5.23891	0.170332
$947$	−51.5452	−1.67500	−0.837498	−	0.546441i	$-0.815982\pi$
$947$	−51.5452	−1.67500	−0.837498	+	0.546441i	$0.815982\pi$
$948$	21.0304	0.683035
$949$	−109.289	−3.54766
$950$	1.04546	0.0339192
$951$	−9.02424	−0.292631
$952$	0.0326911	0.00105953
$953$	−29.8212	−0.966005	−0.483002	−	0.875619i	$-0.660454\pi$
$953$	−29.8212	−0.966005	−0.483002	+	0.875619i	$0.660454\pi$
$954$	−10.4558	−0.338518
$955$	−42.2310	−1.36656
$956$	−1.68758	−0.0545801
$957$	0.824465	0.0266512
$958$	16.5077	0.533338
$959$	−0.0519750	−0.00167836
$960$	−4.72697	−0.152562
$961$	9.68360	0.312374
$962$	5.16996	0.166686
$963$	−6.34344	−0.204415
$964$	−12.9567	−0.417306
$965$	−11.3575	−0.365611
$966$	−0.0753759	−0.00242518
$967$	21.3823	0.687608	0.343804	−	0.939041i	$-0.388284\pi$
$967$	21.3823	0.687608	0.343804	+	0.939041i	$0.388284\pi$
$968$	1.00000	0.0321412
$969$	17.9481	0.576576
$970$	7.90751	0.253895
$971$	51.5263	1.65356	0.826778	−	0.562528i	$-0.190171\pi$
$971$	51.5263	1.65356	0.826778	+	0.562528i	$0.190171\pi$
$972$	−12.1904	−0.391007
$973$	−0.0777115	−0.00249132
$974$	39.4398	1.26373
$975$	−3.80604	−0.121891
$976$	−1.47967	−0.0473629
$977$	−29.6082	−0.947249	−0.473624	−	0.880727i	$-0.657055\pi$
$977$	−29.6082	−0.947249	−0.473624	+	0.880727i	$0.657055\pi$
$978$	40.9317	1.30885
$979$	−5.80344	−0.185479
$980$	16.0609	0.513045
$981$	−14.0435	−0.448373
$982$	15.1536	0.483572
$983$	15.5558	0.496154	0.248077	−	0.968740i	$-0.420201\pi$
$983$	15.5558	0.496154	0.248077	+	0.968740i	$0.420201\pi$
$984$	−11.9896	−0.382213
$985$	−2.29448	−0.0731082
$986$	−0.882547	−0.0281060
$987$	0.238822	0.00760180
$988$	−27.5789	−0.877402
$989$	12.9303	0.411160
$990$	2.85483	0.0907326
$991$	−13.4251	−0.426464	−0.213232	−	0.977002i	$-0.568399\pi$
$991$	−13.4251	−0.426464	−0.213232	+	0.977002i	$0.568399\pi$
$992$	−6.37837	−0.202513
$993$	−12.5664	−0.398783
$994$	−0.106675	−0.00338353
$995$	−45.8399	−1.45322
$996$	−35.9608	−1.13946
$997$	12.0128	0.380449	0.190225	−	0.981741i	$-0.439078\pi$
$997$	12.0128	0.380449	0.190225	+	0.981741i	$0.439078\pi$
$998$	1.52123	0.0481538
$999$	2.67876	0.0847524

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.d.1.16	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.d.1.16	✓	17	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:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.06015 q^{3} +1.00000 q^{4} -2.29448 q^{5} +2.06015 q^{6} +0.0148240 q^{7} +1.00000 q^{8} +1.24422 q^{9} -2.29448 q^{10} -1.00000 q^{11} +2.06015 q^{12} -6.98107 q^{13} +0.0148240 q^{14} -4.72697 q^{15} +1.00000 q^{16} +2.20528 q^{17} +1.24422 q^{18} +3.95053 q^{19} -2.29448 q^{20} +0.0305397 q^{21} -1.00000 q^{22} -2.46813 q^{23} +2.06015 q^{24} +0.264638 q^{25} -6.98107 q^{26} -3.61717 q^{27} +0.0148240 q^{28} -0.400196 q^{29} -4.72697 q^{30} -6.37837 q^{31} +1.00000 q^{32} -2.06015 q^{33} +2.20528 q^{34} -0.0340134 q^{35} +1.24422 q^{36} -0.740568 q^{37} +3.95053 q^{38} -14.3821 q^{39} -2.29448 q^{40} -5.81975 q^{41} +0.0305397 q^{42} -5.23891 q^{43} -1.00000 q^{44} -2.85483 q^{45} -2.46813 q^{46} +7.82007 q^{47} +2.06015 q^{48} -6.99978 q^{49} +0.264638 q^{50} +4.54322 q^{51} -6.98107 q^{52} -8.40347 q^{53} -3.61717 q^{54} +2.29448 q^{55} +0.0148240 q^{56} +8.13868 q^{57} -0.400196 q^{58} +2.80923 q^{59} -4.72697 q^{60} -1.47967 q^{61} -6.37837 q^{62} +0.0184443 q^{63} +1.00000 q^{64} +16.0179 q^{65} -2.06015 q^{66} +6.49105 q^{67} +2.20528 q^{68} -5.08472 q^{69} -0.0340134 q^{70} -7.19610 q^{71} +1.24422 q^{72} +15.6550 q^{73} -0.740568 q^{74} +0.545195 q^{75} +3.95053 q^{76} -0.0148240 q^{77} -14.3821 q^{78} +10.2082 q^{79} -2.29448 q^{80} -11.1846 q^{81} -5.81975 q^{82} -17.4554 q^{83} +0.0305397 q^{84} -5.05998 q^{85} -5.23891 q^{86} -0.824465 q^{87} -1.00000 q^{88} +5.80344 q^{89} -2.85483 q^{90} -0.103487 q^{91} -2.46813 q^{92} -13.1404 q^{93} +7.82007 q^{94} -9.06440 q^{95} +2.06015 q^{96} -3.44632 q^{97} -6.99978 q^{98} -1.24422 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 17 q^{2} - 7 q^{3} + 17 q^{4} - 4 q^{5} - 7 q^{6} - 5 q^{7} + 17 q^{8} + 12 q^{9} - 4 q^{10} - 17 q^{11} - 7 q^{12} - 18 q^{13} - 5 q^{14} - 16 q^{15} + 17 q^{16} - 10 q^{17} + 12 q^{18} - 31 q^{19}+ \cdots - 12 q^{99}+O(q^{100}) \) 17 * q + 17 * q^2 - 7 * q^3 + 17 * q^4 - 4 * q^5 - 7 * q^6 - 5 * q^7 + 17 * q^8 + 12 * q^9 - 4 * q^10 - 17 * q^11 - 7 * q^12 - 18 * q^13 - 5 * q^14 - 16 * q^15 + 17 * q^16 - 10 * q^17 + 12 * q^18 - 31 * q^19 - 4 * q^20 - 13 * q^21 - 17 * q^22 - 6 * q^23 - 7 * q^24 + 3 * q^25 - 18 * q^26 - 37 * q^27 - 5 * q^28 - 16 * q^29 - 16 * q^30 - 30 * q^31 + 17 * q^32 + 7 * q^33 - 10 * q^34 - 36 * q^35 + 12 * q^36 - 23 * q^37 - 31 * q^38 - 15 * q^39 - 4 * q^40 - 7 * q^41 - 13 * q^42 - 23 * q^43 - 17 * q^44 - 19 * q^45 - 6 * q^46 - 19 * q^47 - 7 * q^48 - 8 * q^49 + 3 * q^50 - 18 * q^51 - 18 * q^52 - 30 * q^53 - 37 * q^54 + 4 * q^55 - 5 * q^56 + 10 * q^57 - 16 * q^58 - 28 * q^59 - 16 * q^60 - 19 * q^61 - 30 * q^62 + 2 * q^63 + 17 * q^64 + 23 * q^65 + 7 * q^66 - 35 * q^67 - 10 * q^68 + q^69 - 36 * q^70 + q^71 + 12 * q^72 - 10 * q^73 - 23 * q^74 - 33 * q^75 - 31 * q^76 + 5 * q^77 - 15 * q^78 - 27 * q^79 - 4 * q^80 + 13 * q^81 - 7 * q^82 - 40 * q^83 - 13 * q^84 - 11 * q^85 - 23 * q^86 - 6 * q^87 - 17 * q^88 - 17 * q^89 - 19 * q^90 - 19 * q^91 - 6 * q^92 + 10 * q^93 - 19 * q^94 - 27 * q^95 - 7 * q^96 - 34 * q^97 - 8 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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