LMFDB - Embedded newform 667.2.a.c.1.8

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			1.8
Root			$1.18857$ 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)

$f(q)$	$=$	$q+1.18857 q^{2} -2.80137 q^{3} -0.587311 q^{4} -2.45282 q^{5} -3.32961 q^{6} -2.24002 q^{7} -3.07519 q^{8} +4.84766 q^{9} +O(q^{10})$	\(q+1.18857 q^{2} -2.80137 q^{3} -0.587311 q^{4} -2.45282 q^{5} -3.32961 q^{6} -2.24002 q^{7} -3.07519 q^{8} +4.84766 q^{9} -2.91534 q^{10} -0.270482 q^{11} +1.64527 q^{12} +5.10390 q^{13} -2.66241 q^{14} +6.87124 q^{15} -2.48044 q^{16} +3.58126 q^{17} +5.76177 q^{18} +0.250632 q^{19} +1.44057 q^{20} +6.27512 q^{21} -0.321486 q^{22} -1.00000 q^{23} +8.61474 q^{24} +1.01632 q^{25} +6.06632 q^{26} -5.17598 q^{27} +1.31559 q^{28} +1.00000 q^{29} +8.16693 q^{30} -4.65149 q^{31} +3.20221 q^{32} +0.757721 q^{33} +4.25656 q^{34} +5.49436 q^{35} -2.84708 q^{36} +3.58910 q^{37} +0.297893 q^{38} -14.2979 q^{39} +7.54288 q^{40} +3.14829 q^{41} +7.45839 q^{42} -4.04337 q^{43} +0.158857 q^{44} -11.8904 q^{45} -1.18857 q^{46} +0.357493 q^{47} +6.94864 q^{48} -1.98231 q^{49} +1.20796 q^{50} -10.0324 q^{51} -2.99758 q^{52} +6.68748 q^{53} -6.15199 q^{54} +0.663444 q^{55} +6.88849 q^{56} -0.702112 q^{57} +1.18857 q^{58} +8.05588 q^{59} -4.03556 q^{60} +0.731406 q^{61} -5.52861 q^{62} -10.8589 q^{63} +8.76692 q^{64} -12.5189 q^{65} +0.900601 q^{66} +1.58166 q^{67} -2.10331 q^{68} +2.80137 q^{69} +6.53041 q^{70} -3.90259 q^{71} -14.9075 q^{72} -8.90294 q^{73} +4.26589 q^{74} -2.84707 q^{75} -0.147199 q^{76} +0.605886 q^{77} -16.9940 q^{78} +13.5151 q^{79} +6.08408 q^{80} -0.0431602 q^{81} +3.74195 q^{82} +11.3724 q^{83} -3.68545 q^{84} -8.78417 q^{85} -4.80581 q^{86} -2.80137 q^{87} +0.831784 q^{88} +11.2229 q^{89} -14.1326 q^{90} -11.4328 q^{91} +0.587311 q^{92} +13.0305 q^{93} +0.424904 q^{94} -0.614754 q^{95} -8.97056 q^{96} +11.5510 q^{97} -2.35611 q^{98} -1.31121 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.18857	0.840443	0.420222	−	0.907422i	$-0.361952\pi$
$2$	1.18857	0.840443	0.420222	+	0.907422i	$0.361952\pi$
$3$	−2.80137	−1.61737	−0.808685	−	0.588242i	$-0.799820\pi$
$3$	−2.80137	−1.61737	−0.808685	+	0.588242i	$0.799820\pi$
$4$	−0.587311	−0.293655
$5$	−2.45282	−1.09693	−0.548467	−	0.836172i	$-0.684788\pi$
$5$	−2.45282	−1.09693	−0.548467	+	0.836172i	$0.684788\pi$
$6$	−3.32961	−1.35931
$7$	−2.24002	−0.846648	−0.423324	−	0.905978i	$-0.639137\pi$
$7$	−2.24002	−0.846648	−0.423324	+	0.905978i	$0.639137\pi$
$8$	−3.07519	−1.08724
$9$	4.84766	1.61589
$10$	−2.91534	−0.921910
$11$	−0.270482	−0.0815535	−0.0407767	−	0.999168i	$-0.512983\pi$
$11$	−0.270482	−0.0815535	−0.0407767	+	0.999168i	$0.512983\pi$
$12$	1.64527	0.474950
$13$	5.10390	1.41557	0.707784	−	0.706429i	$-0.249695\pi$
$13$	5.10390	1.41557	0.707784	+	0.706429i	$0.249695\pi$
$14$	−2.66241	−0.711559
$15$	6.87124	1.77415
$16$	−2.48044	−0.620111
$17$	3.58126	0.868583	0.434291	−	0.900772i	$-0.356999\pi$
$17$	3.58126	0.868583	0.434291	+	0.900772i	$0.356999\pi$
$18$	5.76177	1.35806
$19$	0.250632	0.0574989	0.0287494	−	0.999587i	$-0.490848\pi$
$19$	0.250632	0.0574989	0.0287494	+	0.999587i	$0.490848\pi$
$20$	1.44057	0.322121
$21$	6.27512	1.36934
$22$	−0.321486	−0.0685411
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	8.61474	1.75848
$25$	1.01632	0.203263
$26$	6.06632	1.18970
$27$	−5.17598	−0.996118
$28$	1.31559	0.248623
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	8.16693	1.49107
$31$	−4.65149	−0.835433	−0.417717	−	0.908577i	$-0.637169\pi$
$31$	−4.65149	−0.835433	−0.417717	+	0.908577i	$0.637169\pi$
$32$	3.20221	0.566076
$33$	0.757721	0.131902
$34$	4.25656	0.729994
$35$	5.49436	0.928716
$36$	−2.84708	−0.474514
$37$	3.58910	0.590045	0.295022	−	0.955490i	$-0.404673\pi$
$37$	3.58910	0.590045	0.295022	+	0.955490i	$0.404673\pi$
$38$	0.297893	0.0483245
$39$	−14.2979	−2.28950
$40$	7.54288	1.19263
$41$	3.14829	0.491681	0.245840	−	0.969310i	$-0.420936\pi$
$41$	3.14829	0.491681	0.245840	+	0.969310i	$0.420936\pi$
$42$	7.45839	1.15085
$43$	−4.04337	−0.616608	−0.308304	−	0.951288i	$-0.599761\pi$
$43$	−4.04337	−0.616608	−0.308304	+	0.951288i	$0.599761\pi$
$44$	0.158857	0.0239486
$45$	−11.8904	−1.77252
$46$	−1.18857	−0.175244
$47$	0.357493	0.0521457	0.0260729	−	0.999660i	$-0.491700\pi$
$47$	0.357493	0.0521457	0.0260729	+	0.999660i	$0.491700\pi$
$48$	6.94864	1.00295
$49$	−1.98231	−0.283187
$50$	1.20796	0.170831
$51$	−10.0324	−1.40482
$52$	−2.99758	−0.415689
$53$	6.68748	0.918596	0.459298	−	0.888282i	$-0.348101\pi$
$53$	6.68748	0.918596	0.459298	+	0.888282i	$0.348101\pi$
$54$	−6.15199	−0.837180
$55$	0.663444	0.0894588
$56$	6.88849	0.920513
$57$	−0.702112	−0.0929970
$58$	1.18857	0.156066
$59$	8.05588	1.04879	0.524393	−	0.851476i	$-0.324292\pi$
$59$	8.05588	1.04879	0.524393	+	0.851476i	$0.324292\pi$
$60$	−4.03556	−0.520988
$61$	0.731406	0.0936470	0.0468235	−	0.998903i	$-0.485090\pi$
$61$	0.731406	0.0936470	0.0468235	+	0.998903i	$0.485090\pi$
$62$	−5.52861	−0.702134
$63$	−10.8589	−1.36809
$64$	8.76692	1.09587
$65$	−12.5189	−1.55278
$66$	0.900601	0.110856
$67$	1.58166	0.193230	0.0966150	−	0.995322i	$-0.469198\pi$
$67$	1.58166	0.193230	0.0966150	+	0.995322i	$0.469198\pi$
$68$	−2.10331	−0.255064
$69$	2.80137	0.337245
$70$	6.53041	0.780533
$71$	−3.90259	−0.463152	−0.231576	−	0.972817i	$-0.574388\pi$
$71$	−3.90259	−0.463152	−0.231576	+	0.972817i	$0.574388\pi$
$72$	−14.9075	−1.75686
$73$	−8.90294	−1.04201	−0.521005	−	0.853554i	$-0.674443\pi$
$73$	−8.90294	−1.04201	−0.521005	+	0.853554i	$0.674443\pi$
$74$	4.26589	0.495899
$75$	−2.84707	−0.328752
$76$	−0.147199	−0.0168849
$77$	0.605886	0.0690471
$78$	−16.9940	−1.92419
$79$	13.5151	1.52056	0.760281	−	0.649594i	$-0.225061\pi$
$79$	13.5151	1.52056	0.760281	+	0.649594i	$0.225061\pi$
$80$	6.08408	0.680221
$81$	−0.0431602	−0.00479558
$82$	3.74195	0.413230
$83$	11.3724	1.24828	0.624142	−	0.781311i	$-0.285449\pi$
$83$	11.3724	1.24828	0.624142	+	0.781311i	$0.285449\pi$
$84$	−3.68545	−0.402115
$85$	−8.78417	−0.952777
$86$	−4.80581	−0.518224
$87$	−2.80137	−0.300338
$88$	0.831784	0.0886685
$89$	11.2229	1.18962	0.594812	−	0.803865i	$-0.297226\pi$
$89$	11.2229	1.18962	0.594812	+	0.803865i	$0.297226\pi$
$90$	−14.1326	−1.48970
$91$	−11.4328	−1.19849
$92$	0.587311	0.0612314
$93$	13.0305	1.35120
$94$	0.424904	0.0438255
$95$	−0.614754	−0.0630725
$96$	−8.97056	−0.915554
$97$	11.5510	1.17283	0.586416	−	0.810010i	$-0.300539\pi$
$97$	11.5510	1.17283	0.586416	+	0.810010i	$0.300539\pi$
$98$	−2.35611	−0.238003
$99$	−1.31121	−0.131781
$100$	−0.596893	−0.0596893
$101$	8.44579	0.840388	0.420194	−	0.907434i	$-0.361962\pi$
$101$	8.44579	0.840388	0.420194	+	0.907434i	$0.361962\pi$
$102$	−11.9242	−1.18067
$103$	15.3708	1.51453	0.757265	−	0.653107i	$-0.226535\pi$
$103$	15.3708	1.51453	0.757265	+	0.653107i	$0.226535\pi$
$104$	−15.6955	−1.53907
$105$	−15.3917	−1.50208
$106$	7.94851	0.772028
$107$	−6.78017	−0.655464	−0.327732	−	0.944771i	$-0.606284\pi$
$107$	−6.78017	−0.655464	−0.327732	+	0.944771i	$0.606284\pi$
$108$	3.03991	0.292515
$109$	−15.4197	−1.47694	−0.738470	−	0.674287i	$-0.764451\pi$
$109$	−15.4197	−1.47694	−0.738470	+	0.674287i	$0.764451\pi$
$110$	0.788547	0.0751850
$111$	−10.0544	−0.954321
$112$	5.55624	0.525016
$113$	7.79673	0.733454	0.366727	−	0.930329i	$-0.380478\pi$
$113$	7.79673	0.733454	0.366727	+	0.930329i	$0.380478\pi$
$114$	−0.834507	−0.0781587
$115$	2.45282	0.228726
$116$	−0.587311	−0.0545304
$117$	24.7420	2.28740
$118$	9.57494	0.881445
$119$	−8.02209	−0.735384
$120$	−21.1304	−1.92893
$121$	−10.9268	−0.993349
$122$	0.869325	0.0787050
$123$	−8.81953	−0.795230
$124$	2.73187	0.245329
$125$	9.77125	0.873967
$126$	−12.9065	−1.14980
$127$	5.60983	0.497792	0.248896	−	0.968530i	$-0.419932\pi$
$127$	5.60983	0.497792	0.248896	+	0.968530i	$0.419932\pi$
$128$	4.01565	0.354937
$129$	11.3270	0.997284
$130$	−14.8796	−1.30503
$131$	−12.3992	−1.08332	−0.541661	−	0.840597i	$-0.682204\pi$
$131$	−12.3992	−1.08332	−0.541661	+	0.840597i	$0.682204\pi$
$132$	−0.445018	−0.0387338
$133$	−0.561420	−0.0486813
$134$	1.87990	0.162399
$135$	12.6957	1.09268
$136$	−11.0130	−0.944361
$137$	−6.81840	−0.582535	−0.291267	−	0.956642i	$-0.594077\pi$
$137$	−6.81840	−0.582535	−0.291267	+	0.956642i	$0.594077\pi$
$138$	3.32961	0.283435
$139$	11.5227	0.977340	0.488670	−	0.872469i	$-0.337482\pi$
$139$	11.5227	0.977340	0.488670	+	0.872469i	$0.337482\pi$
$140$	−3.22690	−0.272723
$141$	−1.00147	−0.0843390
$142$	−4.63849	−0.389253
$143$	−1.38052	−0.115444
$144$	−12.0244	−1.00203
$145$	−2.45282	−0.203695
$146$	−10.5817	−0.875750
$147$	5.55319	0.458019
$148$	−2.10792	−0.173270
$149$	5.48395	0.449262	0.224631	−	0.974444i	$-0.427882\pi$
$149$	5.48395	0.449262	0.224631	+	0.974444i	$0.427882\pi$
$150$	−3.38393	−0.276297
$151$	−7.48853	−0.609408	−0.304704	−	0.952447i	$-0.598557\pi$
$151$	−7.48853	−0.609408	−0.304704	+	0.952447i	$0.598557\pi$
$152$	−0.770741	−0.0625153
$153$	17.3607	1.40353
$154$	0.720135	0.0580301
$155$	11.4093	0.916414
$156$	8.39732	0.672323
$157$	−4.50112	−0.359229	−0.179614	−	0.983737i	$-0.557485\pi$
$157$	−4.50112	−0.359229	−0.179614	+	0.983737i	$0.557485\pi$
$158$	16.0635	1.27795
$159$	−18.7341	−1.48571
$160$	−7.85443	−0.620947
$161$	2.24002	0.176538
$162$	−0.0512988	−0.00403041
$163$	−8.47294	−0.663652	−0.331826	−	0.943341i	$-0.607665\pi$
$163$	−8.47294	−0.663652	−0.331826	+	0.943341i	$0.607665\pi$
$164$	−1.84903	−0.144385
$165$	−1.85855	−0.144688
$166$	13.5169	1.04911
$167$	−18.8068	−1.45531	−0.727655	−	0.685943i	$-0.759390\pi$
$167$	−18.8068	−1.45531	−0.727655	+	0.685943i	$0.759390\pi$
$168$	−19.2972	−1.48881
$169$	13.0498	1.00383
$170$	−10.4406	−0.800755
$171$	1.21498	0.0929117
$172$	2.37472	0.181070
$173$	22.0804	1.67874	0.839370	−	0.543560i	$-0.182924\pi$
$173$	22.0804	1.67874	0.839370	+	0.543560i	$0.182924\pi$
$174$	−3.32961	−0.252417
$175$	−2.27657	−0.172092
$176$	0.670916	0.0505722
$177$	−22.5675	−1.69628
$178$	13.3391	0.999811
$179$	9.54901	0.713726	0.356863	−	0.934157i	$-0.383846\pi$
$179$	9.54901	0.713726	0.356863	+	0.934157i	$0.383846\pi$
$180$	6.98338	0.520510
$181$	−0.785526	−0.0583877	−0.0291938	−	0.999574i	$-0.509294\pi$
$181$	−0.785526	−0.0583877	−0.0291938	+	0.999574i	$0.509294\pi$
$182$	−13.5887	−1.00726
$183$	−2.04894	−0.151462
$184$	3.07519	0.226706
$185$	−8.80341	−0.647240
$186$	15.4877	1.13561
$187$	−0.968667	−0.0708359
$188$	−0.209960	−0.0153129
$189$	11.5943	0.843361
$190$	−0.730676	−0.0530088
$191$	−18.4700	−1.33644	−0.668221	−	0.743963i	$-0.732944\pi$
$191$	−18.4700	−1.33644	−0.668221	+	0.743963i	$0.732944\pi$
$192$	−24.5594	−1.77242
$193$	9.01839	0.649158	0.324579	−	0.945859i	$-0.394777\pi$
$193$	9.01839	0.649158	0.324579	+	0.945859i	$0.394777\pi$
$194$	13.7292	0.985698
$195$	35.0702	2.51143
$196$	1.16423	0.0831595
$197$	18.5072	1.31859	0.659293	−	0.751886i	$-0.270856\pi$
$197$	18.5072	1.31859	0.659293	+	0.751886i	$0.270856\pi$
$198$	−1.55846	−0.110755
$199$	−12.9100	−0.915168	−0.457584	−	0.889166i	$-0.651285\pi$
$199$	−12.9100	−0.915168	−0.457584	+	0.889166i	$0.651285\pi$
$200$	−3.12536	−0.220996
$201$	−4.43080	−0.312525
$202$	10.0384	0.706298
$203$	−2.24002	−0.157219
$204$	5.89215	0.412533
$205$	−7.72219	−0.539341
$206$	18.2692	1.27288
$207$	−4.84766	−0.336936
$208$	−12.6599	−0.877809
$209$	−0.0677915	−0.00468924
$210$	−18.2941	−1.26241
$211$	7.21884	0.496966	0.248483	−	0.968636i	$-0.420068\pi$
$211$	7.21884	0.496966	0.248483	+	0.968636i	$0.420068\pi$
$212$	−3.92763	−0.269751
$213$	10.9326	0.749089
$214$	−8.05868	−0.550880
$215$	9.91765	0.676378
$216$	15.9171	1.08302
$217$	10.4194	0.707318
$218$	−18.3273	−1.24128
$219$	24.9404	1.68532
$220$	−0.389648	−0.0262701
$221$	18.2784	1.22954
$222$	−11.9503	−0.802053
$223$	22.1908	1.48601	0.743004	−	0.669287i	$-0.233400\pi$
$223$	22.1908	1.48601	0.743004	+	0.669287i	$0.233400\pi$
$224$	−7.17301	−0.479267
$225$	4.92675	0.328450
$226$	9.26692	0.616427
$227$	12.9479	0.859384	0.429692	−	0.902976i	$-0.358622\pi$
$227$	12.9479	0.859384	0.429692	+	0.902976i	$0.358622\pi$
$228$	0.412358	0.0273091
$229$	13.3468	0.881984	0.440992	−	0.897511i	$-0.354627\pi$
$229$	13.3468	0.881984	0.440992	+	0.897511i	$0.354627\pi$
$230$	2.91534	0.192232
$231$	−1.69731	−0.111675
$232$	−3.07519	−0.201896
$233$	14.9611	0.980136	0.490068	−	0.871684i	$-0.336972\pi$
$233$	14.9611	0.980136	0.490068	+	0.871684i	$0.336972\pi$
$234$	29.4075	1.92243
$235$	−0.876865	−0.0572004
$236$	−4.73131	−0.307982
$237$	−37.8606	−2.45931
$238$	−9.53478	−0.618048
$239$	−30.3026	−1.96011	−0.980057	−	0.198716i	$-0.936323\pi$
$239$	−30.3026	−1.96011	−0.980057	+	0.198716i	$0.936323\pi$
$240$	−17.0437	−1.10017
$241$	−14.4573	−0.931276	−0.465638	−	0.884975i	$-0.654175\pi$
$241$	−14.4573	−0.931276	−0.465638	+	0.884975i	$0.654175\pi$
$242$	−12.9873	−0.834853
$243$	15.6488	1.00387
$244$	−0.429563	−0.0275000
$245$	4.86225	0.310638
$246$	−10.4826	−0.668346
$247$	1.27920	0.0813936
$248$	14.3042	0.908319
$249$	−31.8583	−2.01894
$250$	11.6138	0.734520
$251$	25.7720	1.62671	0.813356	−	0.581766i	$-0.197638\pi$
$251$	25.7720	1.62671	0.813356	+	0.581766i	$0.197638\pi$
$252$	6.37753	0.401746
$253$	0.270482	0.0170051
$254$	6.66766	0.418366
$255$	24.6077	1.54099
$256$	−12.7610	−0.797561
$257$	24.8104	1.54763	0.773815	−	0.633411i	$-0.218346\pi$
$257$	24.8104	1.54763	0.773815	+	0.633411i	$0.218346\pi$
$258$	13.4629	0.838161
$259$	−8.03966	−0.499560
$260$	7.35251	0.455983
$261$	4.84766	0.300063
$262$	−14.7373	−0.910471
$263$	13.5794	0.837341	0.418671	−	0.908138i	$-0.362496\pi$
$263$	13.5794	0.837341	0.418671	+	0.908138i	$0.362496\pi$
$264$	−2.33013	−0.143410
$265$	−16.4032	−1.00764
$266$	−0.667285	−0.0409139
$267$	−31.4394	−1.92406
$268$	−0.928924	−0.0567431
$269$	24.0089	1.46385	0.731924	−	0.681386i	$-0.238622\pi$
$269$	24.0089	1.46385	0.731924	+	0.681386i	$0.238622\pi$
$270$	15.0897	0.918331
$271$	6.94160	0.421672	0.210836	−	0.977521i	$-0.432381\pi$
$271$	6.94160	0.421672	0.210836	+	0.977521i	$0.432381\pi$
$272$	−8.88311	−0.538618
$273$	32.0276	1.93840
$274$	−8.10411	−0.489587
$275$	−0.274895	−0.0165768
$276$	−1.64527	−0.0990339
$277$	16.0603	0.964969	0.482485	−	0.875904i	$-0.339734\pi$
$277$	16.0603	0.964969	0.482485	+	0.875904i	$0.339734\pi$
$278$	13.6955	0.821399
$279$	−22.5489	−1.34997
$280$	−16.8962	−1.00974
$281$	−19.5284	−1.16497	−0.582484	−	0.812842i	$-0.697919\pi$
$281$	−19.5284	−1.16497	−0.582484	+	0.812842i	$0.697919\pi$
$282$	−1.19031	−0.0708821
$283$	−20.8211	−1.23769	−0.618843	−	0.785514i	$-0.712398\pi$
$283$	−20.8211	−1.23769	−0.618843	+	0.785514i	$0.712398\pi$
$284$	2.29203	0.136007
$285$	1.72215	0.102012
$286$	−1.64083	−0.0970245
$287$	−7.05224	−0.416280
$288$	15.5232	0.914715
$289$	−4.17459	−0.245564
$290$	−2.91534	−0.171194
$291$	−32.3587	−1.89690
$292$	5.22879	0.305992
$293$	15.0317	0.878160	0.439080	−	0.898448i	$-0.355304\pi$
$293$	15.0317	0.878160	0.439080	+	0.898448i	$0.355304\pi$
$294$	6.60033	0.384939
$295$	−19.7596	−1.15045
$296$	−11.0372	−0.641523
$297$	1.40001	0.0812369
$298$	6.51803	0.377579
$299$	−5.10390	−0.295166
$300$	1.67212	0.0965397
$301$	9.05723	0.522050
$302$	−8.90061	−0.512172
$303$	−23.6598	−1.35922
$304$	−0.621678	−0.0356557
$305$	−1.79401	−0.102725
$306$	20.6344	1.17959
$307$	23.5758	1.34554	0.672771	−	0.739851i	$-0.265104\pi$
$307$	23.5758	1.34554	0.672771	+	0.739851i	$0.265104\pi$
$308$	−0.355843	−0.0202761
$309$	−43.0593	−2.44956
$310$	13.5607	0.770194
$311$	−26.6440	−1.51084	−0.755420	−	0.655241i	$-0.772567\pi$
$311$	−26.6440	−1.51084	−0.755420	+	0.655241i	$0.772567\pi$
$312$	43.9688	2.48924
$313$	−23.0068	−1.30042	−0.650211	−	0.759753i	$-0.725320\pi$
$313$	−23.0068	−1.30042	−0.650211	+	0.759753i	$0.725320\pi$
$314$	−5.34988	−0.301911
$315$	26.6348	1.50070
$316$	−7.93754	−0.446521
$317$	−28.2169	−1.58482	−0.792410	−	0.609989i	$-0.791174\pi$
$317$	−28.2169	−1.58482	−0.792410	+	0.609989i	$0.791174\pi$
$318$	−22.2667	−1.24866
$319$	−0.270482	−0.0151441
$320$	−21.5037	−1.20209
$321$	18.9938	1.06013
$322$	2.66241	0.148370
$323$	0.897577	0.0499425
$324$	0.0253485	0.00140825
$325$	5.18717	0.287733
$326$	−10.0706	−0.557762
$327$	43.1963	2.38876
$328$	−9.68160	−0.534577
$329$	−0.800791	−0.0441491
$330$	−2.20901	−0.121602
$331$	−22.7095	−1.24823	−0.624114	−	0.781333i	$-0.714540\pi$
$331$	−22.7095	−1.24823	−0.624114	+	0.781333i	$0.714540\pi$
$332$	−6.67914	−0.366565
$333$	17.3988	0.953446
$334$	−22.3531	−1.22311
$335$	−3.87951	−0.211960
$336$	−15.5651	−0.849145
$337$	−14.1878	−0.772856	−0.386428	−	0.922320i	$-0.626291\pi$
$337$	−14.1878	−0.772856	−0.386428	+	0.922320i	$0.626291\pi$
$338$	15.5106	0.843663
$339$	−21.8415	−1.18627
$340$	5.15904	0.279788
$341$	1.25815	0.0681325
$342$	1.44408	0.0780870
$343$	20.1206	1.08641
$344$	12.4341	0.670404
$345$	−6.87124	−0.369935
$346$	26.2440	1.41089
$347$	−28.5481	−1.53254	−0.766270	−	0.642519i	$-0.777889\pi$
$347$	−28.5481	−1.53254	−0.766270	+	0.642519i	$0.777889\pi$
$348$	1.64527	0.0881959
$349$	−17.1768	−0.919453	−0.459726	−	0.888061i	$-0.652052\pi$
$349$	−17.1768	−0.919453	−0.459726	+	0.888061i	$0.652052\pi$
$350$	−2.70585	−0.144634
$351$	−26.4177	−1.41007
$352$	−0.866141	−0.0461655
$353$	−7.41216	−0.394509	−0.197255	−	0.980352i	$-0.563203\pi$
$353$	−7.41216	−0.394509	−0.197255	+	0.980352i	$0.563203\pi$
$354$	−26.8229	−1.42562
$355$	9.57234	0.508047
$356$	−6.59133	−0.349340
$357$	22.4728	1.18939
$358$	11.3496	0.599846
$359$	31.1387	1.64344	0.821720	−	0.569892i	$-0.193015\pi$
$359$	31.1387	1.64344	0.821720	+	0.569892i	$0.193015\pi$
$360$	36.5653	1.92716
$361$	−18.9372	−0.996694
$362$	−0.933649	−0.0490715
$363$	30.6101	1.60661
$364$	6.71463	0.351942
$365$	21.8373	1.14302
$366$	−2.43530	−0.127295
$367$	7.17549	0.374558	0.187279	−	0.982307i	$-0.440033\pi$
$367$	7.17549	0.374558	0.187279	+	0.982307i	$0.440033\pi$
$368$	2.48044	0.129302
$369$	15.2619	0.794501
$370$	−10.4634	−0.543968
$371$	−14.9801	−0.777728
$372$	−7.65298	−0.396789
$373$	33.9245	1.75654	0.878272	−	0.478162i	$-0.158697\pi$
$373$	33.9245	1.75654	0.878272	+	0.478162i	$0.158697\pi$
$374$	−1.15132	−0.0595336
$375$	−27.3729	−1.41353
$376$	−1.09936	−0.0566951
$377$	5.10390	0.262864
$378$	13.7806	0.708797
$379$	28.2639	1.45182	0.725909	−	0.687791i	$-0.241419\pi$
$379$	28.2639	1.45182	0.725909	+	0.687791i	$0.241419\pi$
$380$	0.361052	0.0185216
$381$	−15.7152	−0.805114
$382$	−21.9528	−1.12320
$383$	37.4192	1.91203	0.956015	−	0.293318i	$-0.0947596\pi$
$383$	37.4192	1.91203	0.956015	+	0.293318i	$0.0947596\pi$
$384$	−11.2493	−0.574064
$385$	−1.48613	−0.0757401
$386$	10.7189	0.545580
$387$	−19.6009	−0.996370
$388$	−6.78406	−0.344408
$389$	−10.5424	−0.534523	−0.267261	−	0.963624i	$-0.586119\pi$
$389$	−10.5424	−0.534523	−0.267261	+	0.963624i	$0.586119\pi$
$390$	41.6832	2.11071
$391$	−3.58126	−0.181112
$392$	6.09599	0.307894
$393$	34.7347	1.75213
$394$	21.9971	1.10820
$395$	−33.1500	−1.66796
$396$	0.770086	0.0386983
$397$	28.4890	1.42982	0.714911	−	0.699215i	$-0.246467\pi$
$397$	28.4890	1.42982	0.714911	+	0.699215i	$0.246467\pi$
$398$	−15.3444	−0.769147
$399$	1.57274	0.0787357
$400$	−2.52091	−0.126046
$401$	8.12691	0.405838	0.202919	−	0.979195i	$-0.434957\pi$
$401$	8.12691	0.405838	0.202919	+	0.979195i	$0.434957\pi$
$402$	−5.26630	−0.262659
$403$	−23.7408	−1.18261
$404$	−4.96031	−0.246784
$405$	0.105864	0.00526043
$406$	−2.66241	−0.132133
$407$	−0.970789	−0.0481202
$408$	30.8516	1.52738
$409$	−32.4682	−1.60545	−0.802725	−	0.596349i	$-0.796618\pi$
$409$	−32.4682	−1.60545	−0.802725	+	0.596349i	$0.796618\pi$
$410$	−9.17833	−0.453286
$411$	19.1008	0.942175
$412$	−9.02744	−0.444750
$413$	−18.0453	−0.887952
$414$	−5.76177	−0.283175
$415$	−27.8944	−1.36928
$416$	16.3438	0.801319
$417$	−32.2792	−1.58072
$418$	−0.0805747	−0.00394104
$419$	−1.56846	−0.0766242	−0.0383121	−	0.999266i	$-0.512198\pi$
$419$	−1.56846	−0.0766242	−0.0383121	+	0.999266i	$0.512198\pi$
$420$	9.03973	0.441094
$421$	30.1884	1.47129	0.735645	−	0.677367i	$-0.236879\pi$
$421$	30.1884	1.47129	0.735645	+	0.677367i	$0.236879\pi$
$422$	8.58007	0.417671
$423$	1.73301	0.0842616
$424$	−20.5653	−0.998738
$425$	3.63969	0.176551
$426$	12.9941	0.629566
$427$	−1.63836	−0.0792860
$428$	3.98207	0.192481
$429$	3.86733	0.186717
$430$	11.7878	0.568458
$431$	23.0917	1.11229	0.556144	−	0.831086i	$-0.312280\pi$
$431$	23.0917	1.11229	0.556144	+	0.831086i	$0.312280\pi$
$432$	12.8387	0.617704
$433$	−29.0918	−1.39806	−0.699030	−	0.715092i	$-0.746385\pi$
$433$	−29.0918	−1.39806	−0.699030	+	0.715092i	$0.746385\pi$
$434$	12.3842	0.594460
$435$	6.87124	0.329451
$436$	9.05616	0.433711
$437$	−0.250632	−0.0119893
$438$	29.6433	1.41641
$439$	−20.5340	−0.980035	−0.490017	−	0.871713i	$-0.663010\pi$
$439$	−20.5340	−0.980035	−0.490017	+	0.871713i	$0.663010\pi$
$440$	−2.04022	−0.0972635
$441$	−9.60958	−0.457599
$442$	21.7251	1.03336
$443$	13.6309	0.647625	0.323813	−	0.946121i	$-0.395035\pi$
$443$	13.6309	0.647625	0.323813	+	0.946121i	$0.395035\pi$
$444$	5.90506	0.280242
$445$	−27.5277	−1.30494
$446$	26.3753	1.24891
$447$	−15.3626	−0.726624
$448$	−19.6381	−0.927812
$449$	3.61395	0.170553	0.0852763	−	0.996357i	$-0.472823\pi$
$449$	3.61395	0.170553	0.0852763	+	0.996357i	$0.472823\pi$
$450$	5.85577	0.276044
$451$	−0.851558	−0.0400983
$452$	−4.57910	−0.215383
$453$	20.9781	0.985638
$454$	15.3895	0.722263
$455$	28.0427	1.31466
$456$	2.15913	0.101110
$457$	7.64767	0.357743	0.178871	−	0.983872i	$-0.442755\pi$
$457$	7.64767	0.357743	0.178871	+	0.983872i	$0.442755\pi$
$458$	15.8636	0.741258
$459$	−18.5365	−0.865211
$460$	−1.44057	−0.0671668
$461$	1.84092	0.0857400	0.0428700	−	0.999081i	$-0.486350\pi$
$461$	1.84092	0.0857400	0.0428700	+	0.999081i	$0.486350\pi$
$462$	−2.01736	−0.0938562
$463$	−31.8243	−1.47900	−0.739501	−	0.673156i	$-0.764938\pi$
$463$	−31.8243	−1.47900	−0.739501	+	0.673156i	$0.764938\pi$
$464$	−2.48044	−0.115152
$465$	−31.9616	−1.48218
$466$	17.7823	0.823748
$467$	19.5865	0.906355	0.453178	−	0.891420i	$-0.350290\pi$
$467$	19.5865	0.906355	0.453178	+	0.891420i	$0.350290\pi$
$468$	−14.5312	−0.671707
$469$	−3.54294	−0.163598
$470$	−1.04221	−0.0480737
$471$	12.6093	0.581006
$472$	−24.7734	−1.14029
$473$	1.09366	0.0502866
$474$	−44.9999	−2.06691
$475$	0.254721	0.0116874
$476$	4.71146	0.215949
$477$	32.4187	1.48435
$478$	−36.0167	−1.64736
$479$	−24.2519	−1.10810	−0.554049	−	0.832484i	$-0.686918\pi$
$479$	−24.2519	−1.10810	−0.554049	+	0.832484i	$0.686918\pi$
$480$	22.0032	1.00430
$481$	18.3184	0.835248
$482$	−17.1835	−0.782685
$483$	−6.27512	−0.285528
$484$	6.41745	0.291702
$485$	−28.3326	−1.28652
$486$	18.5997	0.843699
$487$	−16.8555	−0.763796	−0.381898	−	0.924204i	$-0.624729\pi$
$487$	−16.8555	−0.763796	−0.381898	+	0.924204i	$0.624729\pi$
$488$	−2.24921	−0.101817
$489$	23.7358	1.07337
$490$	5.77911	0.261073
$491$	20.8116	0.939212	0.469606	−	0.882876i	$-0.344396\pi$
$491$	20.8116	0.939212	0.469606	+	0.882876i	$0.344396\pi$
$492$	5.17980	0.233524
$493$	3.58126	0.161292
$494$	1.52041	0.0684067
$495$	3.21615	0.144555
$496$	11.5378	0.518061
$497$	8.74188	0.392127
$498$	−37.8657	−1.69680
$499$	6.70326	0.300079	0.150040	−	0.988680i	$-0.452060\pi$
$499$	6.70326	0.300079	0.150040	+	0.988680i	$0.452060\pi$
$500$	−5.73876	−0.256645
$501$	52.6846	2.35378
$502$	30.6317	1.36716
$503$	31.5150	1.40518	0.702592	−	0.711593i	$-0.252026\pi$
$503$	31.5150	1.40518	0.702592	+	0.711593i	$0.252026\pi$
$504$	33.3930	1.48744
$505$	−20.7160	−0.921850
$506$	0.321486	0.0142918
$507$	−36.5573	−1.62357
$508$	−3.29472	−0.146179
$509$	15.8028	0.700447	0.350223	−	0.936666i	$-0.386106\pi$
$509$	15.8028	0.700447	0.350223	+	0.936666i	$0.386106\pi$
$510$	29.2479	1.29512
$511$	19.9428	0.882216
$512$	−23.1986	−1.02524
$513$	−1.29727	−0.0572757
$514$	29.4888	1.30070
$515$	−37.7018	−1.66134
$516$	−6.65245	−0.292858
$517$	−0.0966956	−0.00425267
$518$	−9.55567	−0.419852
$519$	−61.8553	−2.71514
$520$	38.4981	1.68825
$521$	28.3329	1.24129	0.620643	−	0.784094i	$-0.286872\pi$
$521$	28.3329	1.24129	0.620643	+	0.784094i	$0.286872\pi$
$522$	5.76177	0.252186
$523$	3.98741	0.174357	0.0871787	−	0.996193i	$-0.472215\pi$
$523$	3.98741	0.174357	0.0871787	+	0.996193i	$0.472215\pi$
$524$	7.28218	0.318124
$525$	6.37750	0.278337
$526$	16.1400	0.703738
$527$	−16.6582	−0.725643
$528$	−1.87948	−0.0817940
$529$	1.00000	0.0434783
$530$	−19.4963	−0.846863
$531$	39.0522	1.69472
$532$	0.329728	0.0142955
$533$	16.0686	0.696007
$534$	−37.3679	−1.61707
$535$	16.6305	0.719000
$536$	−4.86389	−0.210088
$537$	−26.7503	−1.15436
$538$	28.5362	1.23028
$539$	0.536180	0.0230949
$540$	−7.45634	−0.320870
$541$	17.8138	0.765873	0.382937	−	0.923775i	$-0.374913\pi$
$541$	17.8138	0.765873	0.382937	+	0.923775i	$0.374913\pi$
$542$	8.25055	0.354392
$543$	2.20055	0.0944345
$544$	11.4679	0.491684
$545$	37.8217	1.62010
$546$	38.0669	1.62911
$547$	−13.1541	−0.562429	−0.281214	−	0.959645i	$-0.590737\pi$
$547$	−13.1541	−0.562429	−0.281214	+	0.959645i	$0.590737\pi$
$548$	4.00452	0.171065
$549$	3.54561	0.151323
$550$	−0.326731	−0.0139319
$551$	0.250632	0.0106773
$552$	−8.61474	−0.366668
$553$	−30.2740	−1.28738
$554$	19.0887	0.811002
$555$	24.6616	1.04683
$556$	−6.76739	−0.287001
$557$	−40.6143	−1.72088	−0.860442	−	0.509549i	$-0.829812\pi$
$557$	−40.6143	−1.72088	−0.860442	+	0.509549i	$0.829812\pi$
$558$	−26.8008	−1.13457
$559$	−20.6370	−0.872851
$560$	−13.6285	−0.575907
$561$	2.71359	0.114568
$562$	−23.2108	−0.979089
$563$	13.0949	0.551882	0.275941	−	0.961175i	$-0.411010\pi$
$563$	13.0949	0.551882	0.275941	+	0.961175i	$0.411010\pi$
$564$	0.588174	0.0247666
$565$	−19.1240	−0.804551
$566$	−24.7473	−1.04021
$567$	0.0966798	0.00406017
$568$	12.0012	0.503559
$569$	−14.8300	−0.621706	−0.310853	−	0.950458i	$-0.600615\pi$
$569$	−14.8300	−0.621706	−0.310853	+	0.950458i	$0.600615\pi$
$570$	2.04689	0.0857349
$571$	−33.0155	−1.38166	−0.690828	−	0.723019i	$-0.742754\pi$
$571$	−33.0155	−1.38166	−0.690828	+	0.723019i	$0.742754\pi$
$572$	0.810792	0.0339009
$573$	51.7412	2.16152
$574$	−8.38205	−0.349860
$575$	−1.01632	−0.0423833
$576$	42.4991	1.77080
$577$	5.82980	0.242698	0.121349	−	0.992610i	$-0.461278\pi$
$577$	5.82980	0.242698	0.121349	+	0.992610i	$0.461278\pi$
$578$	−4.96178	−0.206383
$579$	−25.2638	−1.04993
$580$	1.44057	0.0598163
$581$	−25.4744	−1.05686
$582$	−38.4605	−1.59424
$583$	−1.80885	−0.0749147
$584$	27.3782	1.13292
$585$	−60.6876	−2.50912
$586$	17.8661	0.738044
$587$	−13.1706	−0.543608	−0.271804	−	0.962353i	$-0.587620\pi$
$587$	−13.1706	−0.543608	−0.271804	+	0.962353i	$0.587620\pi$
$588$	−3.26145	−0.134500
$589$	−1.16581	−0.0480365
$590$	−23.4856	−0.966886
$591$	−51.8456	−2.13264
$592$	−8.90257	−0.365893
$593$	19.1559	0.786637	0.393319	−	0.919402i	$-0.371327\pi$
$593$	19.1559	0.786637	0.393319	+	0.919402i	$0.371327\pi$
$594$	1.66401	0.0682750
$595$	19.6767	0.806667
$596$	−3.22078	−0.131928
$597$	36.1658	1.48017
$598$	−6.06632	−0.248070
$599$	46.4926	1.89964	0.949819	−	0.312800i	$-0.101267\pi$
$599$	46.4926	1.89964	0.949819	+	0.312800i	$0.101267\pi$
$600$	8.75529	0.357433
$601$	−22.1735	−0.904474	−0.452237	−	0.891898i	$-0.649374\pi$
$601$	−22.1735	−0.904474	−0.452237	+	0.891898i	$0.649374\pi$
$602$	10.7651	0.438753
$603$	7.66733	0.312238
$604$	4.39809	0.178956
$605$	26.8015	1.08964
$606$	−28.1212	−1.14235
$607$	−26.1701	−1.06221	−0.531106	−	0.847305i	$-0.678223\pi$
$607$	−26.1701	−1.06221	−0.531106	+	0.847305i	$0.678223\pi$
$608$	0.802575	0.0325487
$609$	6.27512	0.254281
$610$	−2.13230	−0.0863341
$611$	1.82461	0.0738158
$612$	−10.1961	−0.412155
$613$	−12.8789	−0.520173	−0.260086	−	0.965585i	$-0.583751\pi$
$613$	−12.8789	−0.520173	−0.260086	+	0.965585i	$0.583751\pi$
$614$	28.0214	1.13085
$615$	21.6327	0.872314
$616$	−1.86321	−0.0750710
$617$	22.6128	0.910358	0.455179	−	0.890400i	$-0.349575\pi$
$617$	22.6128	0.910358	0.455179	+	0.890400i	$0.349575\pi$
$618$	−51.1788	−2.05871
$619$	2.79837	0.112476	0.0562380	−	0.998417i	$-0.482089\pi$
$619$	2.79837	0.112476	0.0562380	+	0.998417i	$0.482089\pi$
$620$	−6.70079	−0.269110
$621$	5.17598	0.207705
$622$	−31.6681	−1.26978
$623$	−25.1395	−1.00719
$624$	35.4652	1.41974
$625$	−29.0487	−1.16195
$626$	−27.3451	−1.09293
$627$	0.189909	0.00758423
$628$	2.64356	0.105489
$629$	12.8535	0.512503
$630$	31.6572	1.26125
$631$	11.8215	0.470606	0.235303	−	0.971922i	$-0.424392\pi$
$631$	11.8215	0.470606	0.235303	+	0.971922i	$0.424392\pi$
$632$	−41.5613	−1.65322
$633$	−20.2226	−0.803778
$634$	−33.5377	−1.33195
$635$	−13.7599	−0.546045
$636$	11.0027	0.436287
$637$	−10.1175	−0.400871
$638$	−0.321486	−0.0127278
$639$	−18.9184	−0.748402
$640$	−9.84966	−0.389342
$641$	8.74272	0.345317	0.172658	−	0.984982i	$-0.444764\pi$
$641$	8.74272	0.345317	0.172658	+	0.984982i	$0.444764\pi$
$642$	22.5753	0.890977
$643$	−33.9965	−1.34069	−0.670346	−	0.742049i	$-0.733854\pi$
$643$	−33.9965	−1.34069	−0.670346	+	0.742049i	$0.733854\pi$
$644$	−1.31559	−0.0518414
$645$	−27.7830	−1.09395
$646$	1.06683	0.0419739
$647$	−33.8286	−1.32994	−0.664970	−	0.746870i	$-0.731556\pi$
$647$	−33.8286	−1.32994	−0.664970	+	0.746870i	$0.731556\pi$
$648$	0.132726	0.00521397
$649$	−2.17897	−0.0855322
$650$	6.16530	0.241823
$651$	−29.1887	−1.14399
$652$	4.97625	0.194885
$653$	−6.65479	−0.260422	−0.130211	−	0.991486i	$-0.541565\pi$
$653$	−6.65479	−0.260422	−0.130211	+	0.991486i	$0.541565\pi$
$654$	51.3416	2.00762
$655$	30.4130	1.18833
$656$	−7.80917	−0.304897
$657$	−43.1584	−1.68377
$658$	−0.951793	−0.0371048
$659$	−30.7096	−1.19628	−0.598138	−	0.801393i	$-0.704093\pi$
$659$	−30.7096	−1.19628	−0.598138	+	0.801393i	$0.704093\pi$
$660$	1.09155	0.0424884
$661$	−37.0799	−1.44224	−0.721120	−	0.692810i	$-0.756372\pi$
$661$	−37.0799	−1.44224	−0.721120	+	0.692810i	$0.756372\pi$
$662$	−26.9918	−1.04906
$663$	−51.2045	−1.98862
$664$	−34.9723	−1.35719
$665$	1.37706	0.0534002
$666$	20.6796	0.801317
$667$	−1.00000	−0.0387202
$668$	11.0454	0.427360
$669$	−62.1647	−2.40343
$670$	−4.61106	−0.178141
$671$	−0.197833	−0.00763724
$672$	20.0942	0.775152
$673$	13.1912	0.508483	0.254241	−	0.967141i	$-0.418174\pi$
$673$	13.1912	0.508483	0.254241	+	0.967141i	$0.418174\pi$
$674$	−16.8631	−0.649542
$675$	−5.26043	−0.202474
$676$	−7.66430	−0.294781
$677$	9.75914	0.375074	0.187537	−	0.982258i	$-0.439949\pi$
$677$	9.75914	0.375074	0.187537	+	0.982258i	$0.439949\pi$
$678$	−25.9601	−0.996990
$679$	−25.8746	−0.992975
$680$	27.0130	1.03590
$681$	−36.2719	−1.38994
$682$	1.49539	0.0572615
$683$	4.12121	0.157694	0.0788469	−	0.996887i	$-0.474876\pi$
$683$	4.12121	0.157694	0.0788469	+	0.996887i	$0.474876\pi$
$684$	−0.713570	−0.0272840
$685$	16.7243	0.639002
$686$	23.9146	0.913064
$687$	−37.3894	−1.42650
$688$	10.0294	0.382366
$689$	34.1323	1.30034
$690$	−8.16693	−0.310910
$691$	−47.3810	−1.80246	−0.901228	−	0.433344i	$-0.857333\pi$
$691$	−47.3810	−1.80246	−0.901228	+	0.433344i	$0.857333\pi$
$692$	−12.9680	−0.492971
$693$	2.93713	0.111572
$694$	−33.9312	−1.28801
$695$	−28.2630	−1.07208
$696$	8.61474	0.326541
$697$	11.2749	0.427065
$698$	−20.4158	−0.772748
$699$	−41.9116	−1.58524
$700$	1.33705	0.0505358
$701$	0.536333	0.0202570	0.0101285	−	0.999949i	$-0.496776\pi$
$701$	0.536333	0.0202570	0.0101285	+	0.999949i	$0.496776\pi$
$702$	−31.3992	−1.18509
$703$	0.899544	0.0339269
$704$	−2.37130	−0.0893717
$705$	2.45642	0.0925142
$706$	−8.80984	−0.331563
$707$	−18.9187	−0.711513
$708$	13.2541	0.498121
$709$	12.7191	0.477677	0.238839	−	0.971059i	$-0.423233\pi$
$709$	12.7191	0.477677	0.238839	+	0.971059i	$0.423233\pi$
$710$	11.3774	0.426985
$711$	65.5164	2.45706
$712$	−34.5125	−1.29341
$713$	4.65149	0.174200
$714$	26.7104	0.999613
$715$	3.38615	0.126635
$716$	−5.60824	−0.209590
$717$	84.8888	3.17023
$718$	37.0104	1.38122
$719$	0.927663	0.0345960	0.0172980	−	0.999850i	$-0.494494\pi$
$719$	0.927663	0.0345960	0.0172980	+	0.999850i	$0.494494\pi$
$720$	29.4935	1.09916
$721$	−34.4309	−1.28227
$722$	−22.5081	−0.837664
$723$	40.5002	1.50622
$724$	0.461348	0.0171459
$725$	1.01632	0.0377450
$726$	36.3821	1.35027
$727$	12.8206	0.475488	0.237744	−	0.971328i	$-0.423592\pi$
$727$	12.8206	0.475488	0.237744	+	0.971328i	$0.423592\pi$
$728$	35.1582	1.30305
$729$	−43.7087	−1.61884
$730$	25.9551	0.960640
$731$	−14.4804	−0.535575
$732$	1.20336	0.0444776
$733$	−18.7464	−0.692413	−0.346207	−	0.938158i	$-0.612530\pi$
$733$	−18.7464	−0.692413	−0.346207	+	0.938158i	$0.612530\pi$
$734$	8.52855	0.314794
$735$	−13.6210	−0.502416
$736$	−3.20221	−0.118035
$737$	−0.427810	−0.0157586
$738$	18.1397	0.667733
$739$	−1.73116	−0.0636819	−0.0318409	−	0.999493i	$-0.510137\pi$
$739$	−1.73116	−0.0636819	−0.0318409	+	0.999493i	$0.510137\pi$
$740$	5.17034	0.190066
$741$	−3.58351	−0.131644
$742$	−17.8048	−0.653636
$743$	37.2951	1.36822	0.684112	−	0.729377i	$-0.260190\pi$
$743$	37.2951	1.36822	0.684112	+	0.729377i	$0.260190\pi$
$744$	−40.0714	−1.46909
$745$	−13.4511	−0.492811
$746$	40.3215	1.47627
$747$	55.1296	2.01709
$748$	0.568909	0.0208014
$749$	15.1877	0.554947
$750$	−32.5345	−1.18799
$751$	28.6370	1.04498	0.522489	−	0.852646i	$-0.325004\pi$
$751$	28.6370	1.04498	0.522489	+	0.852646i	$0.325004\pi$
$752$	−0.886742	−0.0323361
$753$	−72.1968	−2.63100
$754$	6.06632	0.220922
$755$	18.3680	0.668480
$756$	−6.80946	−0.247658
$757$	3.71936	0.135182	0.0675912	−	0.997713i	$-0.478469\pi$
$757$	3.71936	0.135182	0.0675912	+	0.997713i	$0.478469\pi$
$758$	33.5935	1.22017
$759$	−0.757721	−0.0275035
$760$	1.89049	0.0685751
$761$	−11.7584	−0.426243	−0.213122	−	0.977026i	$-0.568363\pi$
$761$	−11.7584	−0.426243	−0.213122	+	0.977026i	$0.568363\pi$
$762$	−18.6786	−0.676653
$763$	34.5404	1.25045
$764$	10.8476	0.392453
$765$	−42.5827	−1.53958
$766$	44.4751	1.60695
$767$	41.1164	1.48463
$768$	35.7482	1.28995
$769$	8.27470	0.298393	0.149197	−	0.988808i	$-0.452331\pi$
$769$	8.27470	0.298393	0.149197	+	0.988808i	$0.452331\pi$
$770$	−1.76636	−0.0636552
$771$	−69.5031	−2.50309
$772$	−5.29660	−0.190629
$773$	−10.8503	−0.390257	−0.195129	−	0.980778i	$-0.562512\pi$
$773$	−10.8503	−0.390257	−0.195129	+	0.980778i	$0.562512\pi$
$774$	−23.2970	−0.837392
$775$	−4.72738	−0.169813
$776$	−35.5217	−1.27515
$777$	22.5220	0.807974
$778$	−12.5304	−0.449236
$779$	0.789063	0.0282711
$780$	−20.5971	−0.737494
$781$	1.05558	0.0377717
$782$	−4.25656	−0.152214
$783$	−5.17598	−0.184974
$784$	4.91701	0.175608
$785$	11.0404	0.394050
$786$	41.2845	1.47257
$787$	−2.85603	−0.101806	−0.0509032	−	0.998704i	$-0.516210\pi$
$787$	−2.85603	−0.101806	−0.0509032	+	0.998704i	$0.516210\pi$
$788$	−10.8695	−0.387210
$789$	−38.0409	−1.35429
$790$	−39.4009	−1.40182
$791$	−17.4648	−0.620978
$792$	4.03221	0.143278
$793$	3.73303	0.132564
$794$	33.8611	1.20168
$795$	45.9513	1.62973
$796$	7.58220	0.268744
$797$	10.7229	0.379826	0.189913	−	0.981801i	$-0.439179\pi$
$797$	10.7229	0.379826	0.189913	+	0.981801i	$0.439179\pi$
$798$	1.86931	0.0661729
$799$	1.28027	0.0452929
$800$	3.25445	0.115062
$801$	54.4048	1.92230
$802$	9.65937	0.341084
$803$	2.40809	0.0849796
$804$	2.60226	0.0917745
$805$	−5.49436	−0.193651
$806$	−28.2175	−0.993918
$807$	−67.2578	−2.36759
$808$	−25.9724	−0.913706
$809$	45.7098	1.60707	0.803535	−	0.595258i	$-0.202950\pi$
$809$	45.7098	1.60707	0.803535	+	0.595258i	$0.202950\pi$
$810$	0.125827	0.00442110
$811$	24.2070	0.850023	0.425011	−	0.905188i	$-0.360270\pi$
$811$	24.2070	0.850023	0.425011	+	0.905188i	$0.360270\pi$
$812$	1.31559	0.0461681
$813$	−19.4460	−0.682000
$814$	−1.15385	−0.0404423
$815$	20.7826	0.727982
$816$	24.8849	0.871144
$817$	−1.01340	−0.0354543
$818$	−38.5906	−1.34929
$819$	−55.4225	−1.93662
$820$	4.53533	0.158380
$821$	27.6627	0.965436	0.482718	−	0.875776i	$-0.339650\pi$
$821$	27.6627	0.965436	0.482718	+	0.875776i	$0.339650\pi$
$822$	22.7026	0.791844
$823$	25.9299	0.903861	0.451930	−	0.892053i	$-0.350736\pi$
$823$	25.9299	0.903861	0.451930	+	0.892053i	$0.350736\pi$
$824$	−47.2681	−1.64666
$825$	0.770083	0.0268108
$826$	−21.4481	−0.746273
$827$	49.6826	1.72763	0.863817	−	0.503805i	$-0.168067\pi$
$827$	49.6826	1.72763	0.863817	+	0.503805i	$0.168067\pi$
$828$	2.84708	0.0989430
$829$	56.8151	1.97327	0.986634	−	0.162950i	$-0.0521009\pi$
$829$	56.8151	1.97327	0.986634	+	0.162950i	$0.0521009\pi$
$830$	−33.1544	−1.15081
$831$	−44.9908	−1.56071
$832$	44.7455	1.55127
$833$	−7.09917	−0.245972
$834$	−38.3660	−1.32851
$835$	46.1295	1.59638
$836$	0.0398147	0.00137702
$837$	24.0760	0.832190
$838$	−1.86422	−0.0643983
$839$	−5.02733	−0.173563	−0.0867813	−	0.996227i	$-0.527658\pi$
$839$	−5.02733	−0.173563	−0.0867813	+	0.996227i	$0.527658\pi$
$840$	47.3325	1.63313
$841$	1.00000	0.0344828
$842$	35.8809	1.23654
$843$	54.7063	1.88418
$844$	−4.23971	−0.145937
$845$	−32.0088	−1.10114
$846$	2.05979	0.0708171
$847$	24.4763	0.841017
$848$	−16.5879	−0.569632
$849$	58.3276	2.00180
$850$	4.32601	0.148381
$851$	−3.58910	−0.123033
$852$	−6.42083	−0.219974
$853$	−41.9131	−1.43508	−0.717539	−	0.696518i	$-0.754732\pi$
$853$	−41.9131	−1.43508	−0.717539	+	0.696518i	$0.754732\pi$
$854$	−1.94730	−0.0666354
$855$	−2.98012	−0.101918
$856$	20.8503	0.712649
$857$	12.9893	0.443707	0.221853	−	0.975080i	$-0.428789\pi$
$857$	12.9893	0.443707	0.221853	+	0.975080i	$0.428789\pi$
$858$	4.59658	0.156925
$859$	27.9391	0.953269	0.476634	−	0.879102i	$-0.341857\pi$
$859$	27.9391	0.953269	0.476634	+	0.879102i	$0.341857\pi$
$860$	−5.82475	−0.198622
$861$	19.7559	0.673280
$862$	27.4460	0.934815
$863$	50.0500	1.70372	0.851861	−	0.523768i	$-0.175474\pi$
$863$	50.0500	1.70372	0.851861	+	0.523768i	$0.175474\pi$
$864$	−16.5746	−0.563878
$865$	−54.1591	−1.84147
$866$	−34.5775	−1.17499
$867$	11.6946	0.397168
$868$	−6.11945	−0.207708
$869$	−3.65558	−0.124007
$870$	8.16693	0.276885
$871$	8.07262	0.273530
$872$	47.4185	1.60579
$873$	55.9956	1.89516
$874$	−0.297893	−0.0100764
$875$	−21.8878	−0.739943
$876$	−14.6478	−0.494902
$877$	−22.5778	−0.762398	−0.381199	−	0.924493i	$-0.624489\pi$
$877$	−22.5778	−0.762398	−0.381199	+	0.924493i	$0.624489\pi$
$878$	−24.4060	−0.823663
$879$	−42.1093	−1.42031
$880$	−1.64564	−0.0554744
$881$	1.26810	0.0427232	0.0213616	−	0.999772i	$-0.493200\pi$
$881$	1.26810	0.0427232	0.0213616	+	0.999772i	$0.493200\pi$
$882$	−11.4216	−0.384586
$883$	−49.6727	−1.67162	−0.835809	−	0.549020i	$-0.815001\pi$
$883$	−49.6727	−1.67162	−0.835809	+	0.549020i	$0.815001\pi$
$884$	−10.7351	−0.361060
$885$	55.3539	1.86070
$886$	16.2013	0.544292
$887$	−35.3059	−1.18545	−0.592727	−	0.805403i	$-0.701949\pi$
$887$	−35.3059	−1.18545	−0.592727	+	0.805403i	$0.701949\pi$
$888$	30.9192	1.03758
$889$	−12.5661	−0.421455
$890$	−32.7185	−1.09673
$891$	0.0116741	0.000391096 0
$892$	−13.0329	−0.436375
$893$	0.0895992	0.00299832
$894$	−18.2594	−0.610686
$895$	−23.4220	−0.782910
$896$	−8.99514	−0.300506
$897$	14.2979	0.477393
$898$	4.29541	0.143340
$899$	−4.65149	−0.155136
$900$	−2.89354	−0.0964512
$901$	23.9496	0.797877
$902$	−1.01213	−0.0337003
$903$	−25.3726	−0.844349
$904$	−23.9764	−0.797444
$905$	1.92675	0.0640474
$906$	24.9339	0.828373
$907$	34.9622	1.16090	0.580450	−	0.814296i	$-0.302877\pi$
$907$	34.9622	1.16090	0.580450	+	0.814296i	$0.302877\pi$
$908$	−7.60446	−0.252363
$909$	40.9423	1.35797
$910$	33.3306	1.10490
$911$	−8.92983	−0.295858	−0.147929	−	0.988998i	$-0.547261\pi$
$911$	−8.92983	−0.295858	−0.147929	+	0.988998i	$0.547261\pi$
$912$	1.74155	0.0576685
$913$	−3.07603	−0.101802
$914$	9.08976	0.300663
$915$	5.02567	0.166144
$916$	−7.83875	−0.259000
$917$	27.7744	0.917193
$918$	−22.0319	−0.727160
$919$	48.3753	1.59576	0.797878	−	0.602819i	$-0.205956\pi$
$919$	48.3753	1.59576	0.797878	+	0.602819i	$0.205956\pi$
$920$	−7.54288	−0.248681
$921$	−66.0445	−2.17624
$922$	2.18805	0.0720596
$923$	−19.9184	−0.655623
$924$	0.996848	0.0327939
$925$	3.64766	0.119934
$926$	−37.8253	−1.24302
$927$	74.5125	2.44731
$928$	3.20221	0.105118
$929$	−9.45683	−0.310268	−0.155134	−	0.987893i	$-0.549581\pi$
$929$	−9.45683	−0.310268	−0.155134	+	0.987893i	$0.549581\pi$
$930$	−37.9884	−1.24569
$931$	−0.496831	−0.0162830
$932$	−8.78683	−0.287822
$933$	74.6395	2.44359
$934$	23.2798	0.761740
$935$	2.37596	0.0777023
$936$	−76.0863	−2.48696
$937$	47.8421	1.56293	0.781466	−	0.623948i	$-0.214472\pi$
$937$	47.8421	1.56293	0.781466	+	0.623948i	$0.214472\pi$
$938$	−4.21102	−0.137495
$939$	64.4506	2.10326
$940$	0.514993	0.0167972
$941$	−40.1070	−1.30745	−0.653726	−	0.756732i	$-0.726795\pi$
$941$	−40.1070	−1.30745	−0.653726	+	0.756732i	$0.726795\pi$
$942$	14.9870	0.488302
$943$	−3.14829	−0.102523
$944$	−19.9822	−0.650364
$945$	−28.4387	−0.925111
$946$	1.29989	0.0422630
$947$	1.28470	0.0417471	0.0208735	−	0.999782i	$-0.493355\pi$
$947$	1.28470	0.0417471	0.0208735	+	0.999782i	$0.493355\pi$
$948$	22.2360	0.722190
$949$	−45.4397	−1.47504
$950$	0.302753	0.00982260
$951$	79.0460	2.56324
$952$	24.6694	0.799541
$953$	−15.8789	−0.514367	−0.257184	−	0.966363i	$-0.582795\pi$
$953$	−15.8789	−0.514367	−0.257184	+	0.966363i	$0.582795\pi$
$954$	38.5317	1.24751
$955$	45.3035	1.46599
$956$	17.7971	0.575598
$957$	0.757721	0.0244936
$958$	−28.8250	−0.931294
$959$	15.2733	0.493202
$960$	60.2397	1.94423
$961$	−9.36360	−0.302052
$962$	21.7727	0.701979
$963$	−32.8680	−1.05916
$964$	8.49093	0.273474
$965$	−22.1205	−0.712083
$966$	−7.45839	−0.239970
$967$	2.03647	0.0654886	0.0327443	−	0.999464i	$-0.489575\pi$
$967$	2.03647	0.0654886	0.0327443	+	0.999464i	$0.489575\pi$
$968$	33.6021	1.08001
$969$	−2.51444	−0.0807756
$970$	−33.6752	−1.08124
$971$	22.1428	0.710598	0.355299	−	0.934753i	$-0.384379\pi$
$971$	22.1428	0.710598	0.355299	+	0.934753i	$0.384379\pi$
$972$	−9.19074	−0.294793
$973$	−25.8110	−0.827463
$974$	−20.0339	−0.641927
$975$	−14.5312	−0.465370
$976$	−1.81421	−0.0580715
$977$	−6.21388	−0.198800	−0.0993999	−	0.995048i	$-0.531692\pi$
$977$	−6.21388	−0.198800	−0.0993999	+	0.995048i	$0.531692\pi$
$978$	28.2116	0.902107
$979$	−3.03559	−0.0970180
$980$	−2.85565	−0.0912205
$981$	−74.7495	−2.38657
$982$	24.7359	0.789355
$983$	−14.9800	−0.477789	−0.238894	−	0.971046i	$-0.576785\pi$
$983$	−14.9800	−0.477789	−0.238894	+	0.971046i	$0.576785\pi$
$984$	27.1217	0.864609
$985$	−45.3949	−1.44640
$986$	4.25656	0.135557
$987$	2.24331	0.0714054
$988$	−0.751288	−0.0239017
$989$	4.04337	0.128572
$990$	3.82261	0.121490
$991$	32.2880	1.02566	0.512831	−	0.858489i	$-0.328597\pi$
$991$	32.2880	1.02566	0.512831	+	0.858489i	$0.328597\pi$
$992$	−14.8951	−0.472918
$993$	63.6177	2.01885
$994$	10.3903	0.329560
$995$	31.6660	1.00388
$996$	18.7107	0.592872
$997$	8.79624	0.278580	0.139290	−	0.990252i	$-0.455518\pi$
$997$	8.79624	0.278580	0.139290	+	0.990252i	$0.455518\pi$
$998$	7.96727	0.252199
$999$	−18.5771	−0.587754

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.2.a.c.1.8	✓	13
3.2	odd	2		6003.2.a.o.1.6		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.2.a.c.1.8	✓	13	1.1	even	1	trivial
6003.2.a.o.1.6		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)

\(f(q)\)	\(=\)	\(q+1.18857 q^{2} -2.80137 q^{3} -0.587311 q^{4} -2.45282 q^{5} -3.32961 q^{6} -2.24002 q^{7} -3.07519 q^{8} +4.84766 q^{9} +O(q^{10})\)	\(q+1.18857 q^{2} -2.80137 q^{3} -0.587311 q^{4} -2.45282 q^{5} -3.32961 q^{6} -2.24002 q^{7} -3.07519 q^{8} +4.84766 q^{9} -2.91534 q^{10} -0.270482 q^{11} +1.64527 q^{12} +5.10390 q^{13} -2.66241 q^{14} +6.87124 q^{15} -2.48044 q^{16} +3.58126 q^{17} +5.76177 q^{18} +0.250632 q^{19} +1.44057 q^{20} +6.27512 q^{21} -0.321486 q^{22} -1.00000 q^{23} +8.61474 q^{24} +1.01632 q^{25} +6.06632 q^{26} -5.17598 q^{27} +1.31559 q^{28} +1.00000 q^{29} +8.16693 q^{30} -4.65149 q^{31} +3.20221 q^{32} +0.757721 q^{33} +4.25656 q^{34} +5.49436 q^{35} -2.84708 q^{36} +3.58910 q^{37} +0.297893 q^{38} -14.2979 q^{39} +7.54288 q^{40} +3.14829 q^{41} +7.45839 q^{42} -4.04337 q^{43} +0.158857 q^{44} -11.8904 q^{45} -1.18857 q^{46} +0.357493 q^{47} +6.94864 q^{48} -1.98231 q^{49} +1.20796 q^{50} -10.0324 q^{51} -2.99758 q^{52} +6.68748 q^{53} -6.15199 q^{54} +0.663444 q^{55} +6.88849 q^{56} -0.702112 q^{57} +1.18857 q^{58} +8.05588 q^{59} -4.03556 q^{60} +0.731406 q^{61} -5.52861 q^{62} -10.8589 q^{63} +8.76692 q^{64} -12.5189 q^{65} +0.900601 q^{66} +1.58166 q^{67} -2.10331 q^{68} +2.80137 q^{69} +6.53041 q^{70} -3.90259 q^{71} -14.9075 q^{72} -8.90294 q^{73} +4.26589 q^{74} -2.84707 q^{75} -0.147199 q^{76} +0.605886 q^{77} -16.9940 q^{78} +13.5151 q^{79} +6.08408 q^{80} -0.0431602 q^{81} +3.74195 q^{82} +11.3724 q^{83} -3.68545 q^{84} -8.78417 q^{85} -4.80581 q^{86} -2.80137 q^{87} +0.831784 q^{88} +11.2229 q^{89} -14.1326 q^{90} -11.4328 q^{91} +0.587311 q^{92} +13.0305 q^{93} +0.424904 q^{94} -0.614754 q^{95} -8.97056 q^{96} +11.5510 q^{97} -2.35611 q^{98} -1.31121 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 4 q^{2} + 3 q^{3} + 12 q^{4} + 16 q^{5} + q^{7} + 6 q^{8} + 14 q^{9}+O(q^{10}) \) 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

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