LMFDB - Embedded newform 6015.2.a.g.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.942366 q^{2} -1.00000 q^{3} -1.11195 q^{4} +1.00000 q^{5} +0.942366 q^{6} +5.06770 q^{7} +2.93259 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.942366 q^{2} -1.00000 q^{3} -1.11195 q^{4} +1.00000 q^{5} +0.942366 q^{6} +5.06770 q^{7} +2.93259 q^{8} +1.00000 q^{9} -0.942366 q^{10} +0.595429 q^{11} +1.11195 q^{12} +2.07592 q^{13} -4.77563 q^{14} -1.00000 q^{15} -0.539679 q^{16} +1.13559 q^{17} -0.942366 q^{18} -3.01318 q^{19} -1.11195 q^{20} -5.06770 q^{21} -0.561112 q^{22} +5.50131 q^{23} -2.93259 q^{24} +1.00000 q^{25} -1.95627 q^{26} -1.00000 q^{27} -5.63502 q^{28} +3.69982 q^{29} +0.942366 q^{30} +5.05120 q^{31} -5.35661 q^{32} -0.595429 q^{33} -1.07014 q^{34} +5.06770 q^{35} -1.11195 q^{36} +3.37949 q^{37} +2.83952 q^{38} -2.07592 q^{39} +2.93259 q^{40} +0.973038 q^{41} +4.77563 q^{42} +0.997756 q^{43} -0.662086 q^{44} +1.00000 q^{45} -5.18425 q^{46} +5.67223 q^{47} +0.539679 q^{48} +18.6816 q^{49} -0.942366 q^{50} -1.13559 q^{51} -2.30831 q^{52} +13.6701 q^{53} +0.942366 q^{54} +0.595429 q^{55} +14.8615 q^{56} +3.01318 q^{57} -3.48659 q^{58} -13.7272 q^{59} +1.11195 q^{60} -13.3477 q^{61} -4.76008 q^{62} +5.06770 q^{63} +6.12724 q^{64} +2.07592 q^{65} +0.561112 q^{66} +10.6267 q^{67} -1.26271 q^{68} -5.50131 q^{69} -4.77563 q^{70} +0.309151 q^{71} +2.93259 q^{72} +11.5130 q^{73} -3.18471 q^{74} -1.00000 q^{75} +3.35050 q^{76} +3.01746 q^{77} +1.95627 q^{78} -7.89600 q^{79} -0.539679 q^{80} +1.00000 q^{81} -0.916958 q^{82} +9.12197 q^{83} +5.63502 q^{84} +1.13559 q^{85} -0.940251 q^{86} -3.69982 q^{87} +1.74615 q^{88} +4.28235 q^{89} -0.942366 q^{90} +10.5201 q^{91} -6.11717 q^{92} -5.05120 q^{93} -5.34531 q^{94} -3.01318 q^{95} +5.35661 q^{96} -6.88522 q^{97} -17.6049 q^{98} +0.595429 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{3} + 36 q^{4} + 36 q^{5} - 4 q^{7} - 3 q^{8} + 36 q^{9}+O(q^{10}) $ 36 * q - 36 * q^3 + 36 * q^4 + 36 * q^5 - 4 * q^7 - 3 * q^8 + 36 * q^9	\( 36 q - 36 q^{3} + 36 q^{4} + 36 q^{5} - 4 q^{7} - 3 q^{8} + 36 q^{9} + 15 q^{11} - 36 q^{12} + 8 q^{13} + 10 q^{14} - 36 q^{15} + 36 q^{16} + 32 q^{17} + 5 q^{19} + 36 q^{20} + 4 q^{21} + q^{22} - 10 q^{23} + 3 q^{24} + 36 q^{25} + 22 q^{26} - 36 q^{27} + 61 q^{29} + 15 q^{31} - q^{32} - 15 q^{33} + 26 q^{34} - 4 q^{35} + 36 q^{36} + 16 q^{37} + 20 q^{38} - 8 q^{39} - 3 q^{40} + 61 q^{41} - 10 q^{42} - 35 q^{43} + 39 q^{44} + 36 q^{45} + 11 q^{46} - 28 q^{47} - 36 q^{48} + 68 q^{49} - 32 q^{51} + 4 q^{52} + 33 q^{53} + 15 q^{55} + 23 q^{56} - 5 q^{57} + 6 q^{58} + 35 q^{59} - 36 q^{60} + 55 q^{61} + q^{62} - 4 q^{63} + 15 q^{64} + 8 q^{65} - q^{66} - 34 q^{67} + 60 q^{68} + 10 q^{69} + 10 q^{70} + 42 q^{71} - 3 q^{72} + 53 q^{73} + 54 q^{74} - 36 q^{75} + 20 q^{76} + 20 q^{77} - 22 q^{78} + 25 q^{79} + 36 q^{80} + 36 q^{81} - 15 q^{82} - 11 q^{83} + 32 q^{85} + 53 q^{86} - 61 q^{87} + 27 q^{88} + 81 q^{89} + 15 q^{91} - 7 q^{92} - 15 q^{93} + 56 q^{94} + 5 q^{95} + q^{96} + 47 q^{97} - 3 q^{98} + 15 q^{99}+O(q^{100}) \) 36 * q - 36 * q^3 + 36 * q^4 + 36 * q^5 - 4 * q^7 - 3 * q^8 + 36 * q^9 + 15 * q^11 - 36 * q^12 + 8 * q^13 + 10 * q^14 - 36 * q^15 + 36 * q^16 + 32 * q^17 + 5 * q^19 + 36 * q^20 + 4 * q^21 + q^22 - 10 * q^23 + 3 * q^24 + 36 * q^25 + 22 * q^26 - 36 * q^27 + 61 * q^29 + 15 * q^31 - q^32 - 15 * q^33 + 26 * q^34 - 4 * q^35 + 36 * q^36 + 16 * q^37 + 20 * q^38 - 8 * q^39 - 3 * q^40 + 61 * q^41 - 10 * q^42 - 35 * q^43 + 39 * q^44 + 36 * q^45 + 11 * q^46 - 28 * q^47 - 36 * q^48 + 68 * q^49 - 32 * q^51 + 4 * q^52 + 33 * q^53 + 15 * q^55 + 23 * q^56 - 5 * q^57 + 6 * q^58 + 35 * q^59 - 36 * q^60 + 55 * q^61 + q^62 - 4 * q^63 + 15 * q^64 + 8 * q^65 - q^66 - 34 * q^67 + 60 * q^68 + 10 * q^69 + 10 * q^70 + 42 * q^71 - 3 * q^72 + 53 * q^73 + 54 * q^74 - 36 * q^75 + 20 * q^76 + 20 * q^77 - 22 * q^78 + 25 * q^79 + 36 * q^80 + 36 * q^81 - 15 * q^82 - 11 * q^83 + 32 * q^85 + 53 * q^86 - 61 * q^87 + 27 * q^88 + 81 * q^89 + 15 * q^91 - 7 * q^92 - 15 * q^93 + 56 * q^94 + 5 * q^95 + q^96 + 47 * q^97 - 3 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.942366	−0.666353	−0.333177	−	0.942864i	$-0.608121\pi$
$2$	−0.942366	−0.666353	−0.333177	+	0.942864i	$0.608121\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.11195	−0.555974
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.942366	0.384719
$7$	5.06770	1.91541	0.957706	−	0.287750i	$-0.0929072\pi$
$7$	5.06770	1.91541	0.957706	+	0.287750i	$0.0929072\pi$
$8$	2.93259	1.03683
$9$	1.00000	0.333333
$10$	−0.942366	−0.298002
$11$	0.595429	0.179529	0.0897643	−	0.995963i	$-0.471389\pi$
$11$	0.595429	0.179529	0.0897643	+	0.995963i	$0.471389\pi$
$12$	1.11195	0.320992
$13$	2.07592	0.575755	0.287878	−	0.957667i	$-0.407050\pi$
$13$	2.07592	0.575755	0.287878	+	0.957667i	$0.407050\pi$
$14$	−4.77563	−1.27634
$15$	−1.00000	−0.258199
$16$	−0.539679	−0.134920
$17$	1.13559	0.275420	0.137710	−	0.990473i	$-0.456026\pi$
$17$	1.13559	0.275420	0.137710	+	0.990473i	$0.456026\pi$
$18$	−0.942366	−0.222118
$19$	−3.01318	−0.691271	−0.345635	−	0.938369i	$-0.612337\pi$
$19$	−3.01318	−0.691271	−0.345635	+	0.938369i	$0.612337\pi$
$20$	−1.11195	−0.248639
$21$	−5.06770	−1.10586
$22$	−0.561112	−0.119629
$23$	5.50131	1.14710	0.573552	−	0.819169i	$-0.305565\pi$
$23$	5.50131	1.14710	0.573552	+	0.819169i	$0.305565\pi$
$24$	−2.93259	−0.598613
$25$	1.00000	0.200000
$26$	−1.95627	−0.383656
$27$	−1.00000	−0.192450
$28$	−5.63502	−1.06492
$29$	3.69982	0.687040	0.343520	−	0.939145i	$-0.388381\pi$
$29$	3.69982	0.687040	0.343520	+	0.939145i	$0.388381\pi$
$30$	0.942366	0.172052
$31$	5.05120	0.907223	0.453611	−	0.891200i	$-0.350135\pi$
$31$	5.05120	0.907223	0.453611	+	0.891200i	$0.350135\pi$
$32$	−5.35661	−0.946924
$33$	−0.595429	−0.103651
$34$	−1.07014	−0.183527
$35$	5.06770	0.856598
$36$	−1.11195	−0.185325
$37$	3.37949	0.555584	0.277792	−	0.960641i	$-0.410397\pi$
$37$	3.37949	0.555584	0.277792	+	0.960641i	$0.410397\pi$
$38$	2.83952	0.460630
$39$	−2.07592	−0.332413
$40$	2.93259	0.463683
$41$	0.973038	0.151963	0.0759815	−	0.997109i	$-0.475791\pi$
$41$	0.973038	0.151963	0.0759815	+	0.997109i	$0.475791\pi$
$42$	4.77563	0.736895
$43$	0.997756	0.152156	0.0760782	−	0.997102i	$-0.475760\pi$
$43$	0.997756	0.152156	0.0760782	+	0.997102i	$0.475760\pi$
$44$	−0.662086	−0.0998132
$45$	1.00000	0.149071
$46$	−5.18425	−0.764376
$47$	5.67223	0.827380	0.413690	−	0.910418i	$-0.364240\pi$
$47$	5.67223	0.827380	0.413690	+	0.910418i	$0.364240\pi$
$48$	0.539679	0.0778959
$49$	18.6816	2.66880
$50$	−0.942366	−0.133271
$51$	−1.13559	−0.159014
$52$	−2.30831	−0.320105
$53$	13.6701	1.87773	0.938864	−	0.344288i	$-0.111880\pi$
$53$	13.6701	1.87773	0.938864	+	0.344288i	$0.111880\pi$
$54$	0.942366	0.128240
$55$	0.595429	0.0802876
$56$	14.8615	1.98595
$57$	3.01318	0.399105
$58$	−3.48659	−0.457811
$59$	−13.7272	−1.78713	−0.893563	−	0.448938i	$-0.851802\pi$
$59$	−13.7272	−1.78713	−0.893563	+	0.448938i	$0.851802\pi$
$60$	1.11195	0.143552
$61$	−13.3477	−1.70899	−0.854496	−	0.519458i	$-0.826134\pi$
$61$	−13.3477	−1.70899	−0.854496	+	0.519458i	$0.826134\pi$
$62$	−4.76008	−0.604531
$63$	5.06770	0.638470
$64$	6.12724	0.765905
$65$	2.07592	0.257486
$66$	0.561112	0.0690681
$67$	10.6267	1.29825	0.649127	−	0.760680i	$-0.275134\pi$
$67$	10.6267	1.29825	0.649127	+	0.760680i	$0.275134\pi$
$68$	−1.26271	−0.153126
$69$	−5.50131	−0.662280
$70$	−4.77563	−0.570797
$71$	0.309151	0.0366895	0.0183448	−	0.999832i	$-0.494160\pi$
$71$	0.309151	0.0366895	0.0183448	+	0.999832i	$0.494160\pi$
$72$	2.93259	0.345609
$73$	11.5130	1.34750	0.673748	−	0.738961i	$-0.264683\pi$
$73$	11.5130	1.34750	0.673748	+	0.738961i	$0.264683\pi$
$74$	−3.18471	−0.370215
$75$	−1.00000	−0.115470
$76$	3.35050	0.384328
$77$	3.01746	0.343871
$78$	1.95627	0.221504
$79$	−7.89600	−0.888369	−0.444185	−	0.895935i	$-0.646507\pi$
$79$	−7.89600	−0.888369	−0.444185	+	0.895935i	$0.646507\pi$
$80$	−0.539679	−0.0603379
$81$	1.00000	0.111111
$82$	−0.916958	−0.101261
$83$	9.12197	1.00127	0.500633	−	0.865660i	$-0.333101\pi$
$83$	9.12197	1.00127	0.500633	+	0.865660i	$0.333101\pi$
$84$	5.63502	0.614831
$85$	1.13559	0.123172
$86$	−0.940251	−0.101390
$87$	−3.69982	−0.396663
$88$	1.74615	0.186140
$89$	4.28235	0.453928	0.226964	−	0.973903i	$-0.427120\pi$
$89$	4.28235	0.453928	0.226964	+	0.973903i	$0.427120\pi$
$90$	−0.942366	−0.0993340
$91$	10.5201	1.10281
$92$	−6.11717	−0.637759
$93$	−5.05120	−0.523785
$94$	−5.34531	−0.551327
$95$	−3.01318	−0.309146
$96$	5.35661	0.546707
$97$	−6.88522	−0.699088	−0.349544	−	0.936920i	$-0.613663\pi$
$97$	−6.88522	−0.699088	−0.349544	+	0.936920i	$0.613663\pi$
$98$	−17.6049	−1.77836
$99$	0.595429	0.0598429
$100$	−1.11195	−0.111195
$101$	6.71604	0.668271	0.334136	−	0.942525i	$-0.391556\pi$
$101$	6.71604	0.668271	0.334136	+	0.942525i	$0.391556\pi$
$102$	1.07014	0.105959
$103$	−6.59130	−0.649460	−0.324730	−	0.945807i	$-0.605273\pi$
$103$	−6.59130	−0.649460	−0.324730	+	0.945807i	$0.605273\pi$
$104$	6.08781	0.596959
$105$	−5.06770	−0.494557
$106$	−12.8822	−1.25123
$107$	−9.15925	−0.885458	−0.442729	−	0.896655i	$-0.645990\pi$
$107$	−9.15925	−0.885458	−0.442729	+	0.896655i	$0.645990\pi$
$108$	1.11195	0.106997
$109$	−20.4691	−1.96058	−0.980291	−	0.197559i	$-0.936699\pi$
$109$	−20.4691	−1.96058	−0.980291	+	0.197559i	$0.936699\pi$
$110$	−0.561112	−0.0534999
$111$	−3.37949	−0.320767
$112$	−2.73493	−0.258427
$113$	7.06740	0.664845	0.332423	−	0.943131i	$-0.392134\pi$
$113$	7.06740	0.664845	0.332423	+	0.943131i	$0.392134\pi$
$114$	−2.83952	−0.265945
$115$	5.50131	0.513000
$116$	−4.11401	−0.381976
$117$	2.07592	0.191918
$118$	12.9360	1.19086
$119$	5.75482	0.527543
$120$	−2.93259	−0.267708
$121$	−10.6455	−0.967769
$122$	12.5784	1.13879
$123$	−0.973038	−0.0877359
$124$	−5.61667	−0.504392
$125$	1.00000	0.0894427
$126$	−4.77563	−0.425447
$127$	1.85884	0.164946	0.0824728	−	0.996593i	$-0.473718\pi$
$127$	1.85884	0.164946	0.0824728	+	0.996593i	$0.473718\pi$
$128$	4.93912	0.436560
$129$	−0.997756	−0.0878475
$130$	−1.95627	−0.171576
$131$	2.30477	0.201368	0.100684	−	0.994918i	$-0.467897\pi$
$131$	2.30477	0.201368	0.100684	+	0.994918i	$0.467897\pi$
$132$	0.662086	0.0576272
$133$	−15.2699	−1.32407
$134$	−10.0142	−0.865096
$135$	−1.00000	−0.0860663
$136$	3.33021	0.285563
$137$	−1.84175	−0.157352	−0.0786759	−	0.996900i	$-0.525069\pi$
$137$	−1.84175	−0.157352	−0.0786759	+	0.996900i	$0.525069\pi$
$138$	5.18425	0.441313
$139$	−13.1492	−1.11530	−0.557649	−	0.830077i	$-0.688297\pi$
$139$	−13.1492	−1.11530	−0.557649	+	0.830077i	$0.688297\pi$
$140$	−5.63502	−0.476246
$141$	−5.67223	−0.477688
$142$	−0.291333	−0.0244482
$143$	1.23606	0.103365
$144$	−0.539679	−0.0449732
$145$	3.69982	0.307254
$146$	−10.8495	−0.897908
$147$	−18.6816	−1.54083
$148$	−3.75781	−0.308890
$149$	−3.09131	−0.253250	−0.126625	−	0.991951i	$-0.540414\pi$
$149$	−3.09131	−0.253250	−0.126625	+	0.991951i	$0.540414\pi$
$150$	0.942366	0.0769438
$151$	15.3227	1.24694	0.623472	−	0.781846i	$-0.285721\pi$
$151$	15.3227	1.24694	0.623472	+	0.781846i	$0.285721\pi$
$152$	−8.83642	−0.716728
$153$	1.13559	0.0918068
$154$	−2.84355	−0.229140
$155$	5.05120	0.405722
$156$	2.30831	0.184813
$157$	−9.04588	−0.721940	−0.360970	−	0.932577i	$-0.617554\pi$
$157$	−9.04588	−0.721940	−0.360970	+	0.932577i	$0.617554\pi$
$158$	7.44092	0.591968
$159$	−13.6701	−1.08411
$160$	−5.35661	−0.423477
$161$	27.8790	2.19717
$162$	−0.942366	−0.0740392
$163$	−1.28579	−0.100711	−0.0503553	−	0.998731i	$-0.516035\pi$
$163$	−1.28579	−0.100711	−0.0503553	+	0.998731i	$0.516035\pi$
$164$	−1.08197	−0.0844875
$165$	−0.595429	−0.0463541
$166$	−8.59623	−0.667196
$167$	−18.4406	−1.42697	−0.713487	−	0.700669i	$-0.752885\pi$
$167$	−18.4406	−1.42697	−0.713487	+	0.700669i	$0.752885\pi$
$168$	−14.8615	−1.14659
$169$	−8.69057	−0.668506
$170$	−1.07014	−0.0820759
$171$	−3.01318	−0.230424
$172$	−1.10945	−0.0845949
$173$	−2.53716	−0.192896	−0.0964482	−	0.995338i	$-0.530748\pi$
$173$	−2.53716	−0.192896	−0.0964482	+	0.995338i	$0.530748\pi$
$174$	3.48659	0.264317
$175$	5.06770	0.383082
$176$	−0.321341	−0.0242220
$177$	13.7272	1.03180
$178$	−4.03554	−0.302476
$179$	−5.53040	−0.413361	−0.206681	−	0.978408i	$-0.566266\pi$
$179$	−5.53040	−0.413361	−0.206681	+	0.978408i	$0.566266\pi$
$180$	−1.11195	−0.0828797
$181$	−5.96444	−0.443333	−0.221667	−	0.975123i	$-0.571150\pi$
$181$	−5.96444	−0.443333	−0.221667	+	0.975123i	$0.571150\pi$
$182$	−9.91380	−0.734860
$183$	13.3477	0.986687
$184$	16.1331	1.18935
$185$	3.37949	0.248465
$186$	4.76008	0.349026
$187$	0.676162	0.0494458
$188$	−6.30722	−0.460001
$189$	−5.06770	−0.368621
$190$	2.83952	0.206000
$191$	6.84134	0.495022	0.247511	−	0.968885i	$-0.420387\pi$
$191$	6.84134	0.495022	0.247511	+	0.968885i	$0.420387\pi$
$192$	−6.12724	−0.442196
$193$	8.66646	0.623825	0.311913	−	0.950111i	$-0.399030\pi$
$193$	8.66646	0.623825	0.311913	+	0.950111i	$0.399030\pi$
$194$	6.48839	0.465839
$195$	−2.07592	−0.148659
$196$	−20.7730	−1.48378
$197$	−10.8299	−0.771601	−0.385801	−	0.922582i	$-0.626075\pi$
$197$	−10.8299	−0.771601	−0.385801	+	0.922582i	$0.626075\pi$
$198$	−0.561112	−0.0398765
$199$	2.00671	0.142252	0.0711258	−	0.997467i	$-0.477341\pi$
$199$	2.00671	0.142252	0.0711258	+	0.997467i	$0.477341\pi$
$200$	2.93259	0.207366
$201$	−10.6267	−0.749547
$202$	−6.32897	−0.445305
$203$	18.7496	1.31596
$204$	1.26271	0.0884076
$205$	0.973038	0.0679599
$206$	6.21141	0.432770
$207$	5.50131	0.382368
$208$	−1.12033	−0.0776808
$209$	−1.79413	−0.124103
$210$	4.77563	0.329550
$211$	−17.2299	−1.18615	−0.593076	−	0.805147i	$-0.702087\pi$
$211$	−17.2299	−1.18615	−0.593076	+	0.805147i	$0.702087\pi$
$212$	−15.2004	−1.04397
$213$	−0.309151	−0.0211827
$214$	8.63136	0.590028
$215$	0.997756	0.0680464
$216$	−2.93259	−0.199538
$217$	25.5980	1.73770
$218$	19.2894	1.30644
$219$	−11.5130	−0.777977
$220$	−0.662086	−0.0446378
$221$	2.35738	0.158575
$222$	3.18471	0.213744
$223$	−0.0458098	−0.00306765	−0.00153383	−	0.999999i	$-0.500488\pi$
$223$	−0.0458098	−0.00306765	−0.00153383	+	0.999999i	$0.500488\pi$
$224$	−27.1457	−1.81375
$225$	1.00000	0.0666667
$226$	−6.66007	−0.443022
$227$	17.7842	1.18038	0.590188	−	0.807266i	$-0.299054\pi$
$227$	17.7842	1.18038	0.590188	+	0.807266i	$0.299054\pi$
$228$	−3.35050	−0.221892
$229$	3.64821	0.241080	0.120540	−	0.992708i	$-0.461537\pi$
$229$	3.64821	0.241080	0.120540	+	0.992708i	$0.461537\pi$
$230$	−5.18425	−0.341839
$231$	−3.01746	−0.198534
$232$	10.8501	0.712342
$233$	−1.85111	−0.121271	−0.0606353	−	0.998160i	$-0.519313\pi$
$233$	−1.85111	−0.121271	−0.0606353	+	0.998160i	$0.519313\pi$
$234$	−1.95627	−0.127885
$235$	5.67223	0.370015
$236$	15.2639	0.993595
$237$	7.89600	0.512900
$238$	−5.42314	−0.351530
$239$	−17.4125	−1.12632	−0.563159	−	0.826348i	$-0.690414\pi$
$239$	−17.4125	−1.12632	−0.563159	+	0.826348i	$0.690414\pi$
$240$	0.539679	0.0348361
$241$	13.7618	0.886475	0.443238	−	0.896404i	$-0.353830\pi$
$241$	13.7618	0.886475	0.443238	+	0.896404i	$0.353830\pi$
$242$	10.0319	0.644876
$243$	−1.00000	−0.0641500
$244$	14.8419	0.950155
$245$	18.6816	1.19352
$246$	0.916958	0.0584631
$247$	−6.25510	−0.398003
$248$	14.8131	0.940634
$249$	−9.12197	−0.578081
$250$	−0.942366	−0.0596004
$251$	6.64144	0.419204	0.209602	−	0.977787i	$-0.432783\pi$
$251$	6.64144	0.419204	0.209602	+	0.977787i	$0.432783\pi$
$252$	−5.63502	−0.354973
$253$	3.27564	0.205938
$254$	−1.75171	−0.109912
$255$	−1.13559	−0.0711132
$256$	−16.9089	−1.05681
$257$	−1.55527	−0.0970150	−0.0485075	−	0.998823i	$-0.515446\pi$
$257$	−1.55527	−0.0970150	−0.0485075	+	0.998823i	$0.515446\pi$
$258$	0.940251	0.0585375
$259$	17.1262	1.06417
$260$	−2.30831	−0.143155
$261$	3.69982	0.229013
$262$	−2.17193	−0.134182
$263$	−27.5512	−1.69888	−0.849439	−	0.527686i	$-0.823060\pi$
$263$	−27.5512	−1.69888	−0.849439	+	0.527686i	$0.823060\pi$
$264$	−1.74615	−0.107468
$265$	13.6701	0.839746
$266$	14.3898	0.882296
$267$	−4.28235	−0.262075
$268$	−11.8163	−0.721795
$269$	−7.52047	−0.458531	−0.229266	−	0.973364i	$-0.573632\pi$
$269$	−7.52047	−0.458531	−0.229266	+	0.973364i	$0.573632\pi$
$270$	0.942366	0.0573505
$271$	17.8644	1.08519	0.542593	−	0.839996i	$-0.317443\pi$
$271$	17.8644	1.08519	0.542593	+	0.839996i	$0.317443\pi$
$272$	−0.612852	−0.0371596
$273$	−10.5201	−0.636707
$274$	1.73561	0.104852
$275$	0.595429	0.0359057
$276$	6.11717	0.368210
$277$	−21.4155	−1.28673	−0.643365	−	0.765560i	$-0.722462\pi$
$277$	−21.4155	−1.28673	−0.643365	+	0.765560i	$0.722462\pi$
$278$	12.3913	0.743182
$279$	5.05120	0.302408
$280$	14.8615	0.888144
$281$	−9.90097	−0.590642	−0.295321	−	0.955398i	$-0.595427\pi$
$281$	−9.90097	−0.590642	−0.295321	+	0.955398i	$0.595427\pi$
$282$	5.34531	0.318309
$283$	−4.31714	−0.256627	−0.128314	−	0.991734i	$-0.540956\pi$
$283$	−4.31714	−0.256627	−0.128314	+	0.991734i	$0.540956\pi$
$284$	−0.343760	−0.0203984
$285$	3.01318	0.178485
$286$	−1.16482	−0.0688773
$287$	4.93107	0.291072
$288$	−5.35661	−0.315641
$289$	−15.7104	−0.924144
$290$	−3.48659	−0.204739
$291$	6.88522	0.403619
$292$	−12.8019	−0.749172
$293$	−2.88702	−0.168661	−0.0843307	−	0.996438i	$-0.526875\pi$
$293$	−2.88702	−0.168661	−0.0843307	+	0.996438i	$0.526875\pi$
$294$	17.6049	1.02674
$295$	−13.7272	−0.799227
$296$	9.91066	0.576045
$297$	−0.595429	−0.0345503
$298$	2.91314	0.168754
$299$	11.4203	0.660451
$300$	1.11195	0.0641983
$301$	5.05633	0.291442
$302$	−14.4396	−0.830905
$303$	−6.71604	−0.385827
$304$	1.62615	0.0932660
$305$	−13.3477	−0.764285
$306$	−1.07014	−0.0611757
$307$	−13.8861	−0.792522	−0.396261	−	0.918138i	$-0.629692\pi$
$307$	−13.8861	−0.792522	−0.396261	+	0.918138i	$0.629692\pi$
$308$	−3.35525	−0.191183
$309$	6.59130	0.374966
$310$	−4.76008	−0.270354
$311$	0.348848	0.0197814	0.00989068	−	0.999951i	$-0.496852\pi$
$311$	0.348848	0.0197814	0.00989068	+	0.999951i	$0.496852\pi$
$312$	−6.08781	−0.344655
$313$	−4.65535	−0.263136	−0.131568	−	0.991307i	$-0.542001\pi$
$313$	−4.65535	−0.263136	−0.131568	+	0.991307i	$0.542001\pi$
$314$	8.52453	0.481067
$315$	5.06770	0.285533
$316$	8.77993	0.493910
$317$	35.3031	1.98282	0.991410	−	0.130791i	$-0.0417518\pi$
$317$	35.3031	1.98282	0.991410	+	0.130791i	$0.0417518\pi$
$318$	12.8822	0.722398
$319$	2.20298	0.123343
$320$	6.12724	0.342523
$321$	9.15925	0.511219
$322$	−26.2722	−1.46409
$323$	−3.42173	−0.190390
$324$	−1.11195	−0.0617748
$325$	2.07592	0.115151
$326$	1.21168	0.0671088
$327$	20.4691	1.13194
$328$	2.85352	0.157560
$329$	28.7452	1.58477
$330$	0.561112	0.0308882
$331$	7.39080	0.406235	0.203118	−	0.979154i	$-0.434893\pi$
$331$	7.39080	0.406235	0.203118	+	0.979154i	$0.434893\pi$
$332$	−10.1431	−0.556677
$333$	3.37949	0.185195
$334$	17.3777	0.950868
$335$	10.6267	0.580597
$336$	2.73493	0.149203
$337$	10.0431	0.547082	0.273541	−	0.961860i	$-0.411805\pi$
$337$	10.0431	0.547082	0.273541	+	0.961860i	$0.411805\pi$
$338$	8.18970	0.445461
$339$	−7.06740	−0.383848
$340$	−1.26271	−0.0684802
$341$	3.00763	0.162872
$342$	2.83952	0.153543
$343$	59.1989	3.19644
$344$	2.92601	0.157760
$345$	−5.50131	−0.296181
$346$	2.39093	0.128537
$347$	−6.89254	−0.370011	−0.185005	−	0.982737i	$-0.559230\pi$
$347$	−6.89254	−0.370011	−0.185005	+	0.982737i	$0.559230\pi$
$348$	4.11401	0.220534
$349$	31.2074	1.67050	0.835248	−	0.549873i	$-0.185324\pi$
$349$	31.2074	1.67050	0.835248	+	0.549873i	$0.185324\pi$
$350$	−4.77563	−0.255268
$351$	−2.07592	−0.110804
$352$	−3.18948	−0.170000
$353$	−5.91600	−0.314877	−0.157438	−	0.987529i	$-0.550324\pi$
$353$	−5.91600	−0.314877	−0.157438	+	0.987529i	$0.550324\pi$
$354$	−12.9360	−0.687541
$355$	0.309151	0.0164080
$356$	−4.76174	−0.252372
$357$	−5.75482	−0.304577
$358$	5.21165	0.275445
$359$	23.1193	1.22019	0.610094	−	0.792329i	$-0.291132\pi$
$359$	23.1193	1.22019	0.610094	+	0.792329i	$0.291132\pi$
$360$	2.93259	0.154561
$361$	−9.92076	−0.522145
$362$	5.62068	0.295416
$363$	10.6455	0.558742
$364$	−11.6978	−0.613132
$365$	11.5130	0.602619
$366$	−12.5784	−0.657482
$367$	2.24057	0.116957	0.0584783	−	0.998289i	$-0.481375\pi$
$367$	2.24057	0.116957	0.0584783	+	0.998289i	$0.481375\pi$
$368$	−2.96894	−0.154767
$369$	0.973038	0.0506544
$370$	−3.18471	−0.165565
$371$	69.2758	3.59662
$372$	5.61667	0.291211
$373$	7.76083	0.401841	0.200920	−	0.979608i	$-0.435607\pi$
$373$	7.76083	0.401841	0.200920	+	0.979608i	$0.435607\pi$
$374$	−0.637191	−0.0329484
$375$	−1.00000	−0.0516398
$376$	16.6343	0.857850
$377$	7.68052	0.395567
$378$	4.77563	0.245632
$379$	−15.9027	−0.816866	−0.408433	−	0.912788i	$-0.633925\pi$
$379$	−15.9027	−0.816866	−0.408433	+	0.912788i	$0.633925\pi$
$380$	3.35050	0.171877
$381$	−1.85884	−0.0952314
$382$	−6.44705	−0.329860
$383$	38.1366	1.94869	0.974345	−	0.225060i	$-0.0722577\pi$
$383$	38.1366	1.94869	0.974345	+	0.225060i	$0.0722577\pi$
$384$	−4.93912	−0.252048
$385$	3.01746	0.153784
$386$	−8.16697	−0.415688
$387$	0.997756	0.0507188
$388$	7.65600	0.388674
$389$	−1.34946	−0.0684203	−0.0342102	−	0.999415i	$-0.510892\pi$
$389$	−1.34946	−0.0684203	−0.0342102	+	0.999415i	$0.510892\pi$
$390$	1.95627	0.0990597
$391$	6.24722	0.315936
$392$	54.7855	2.76709
$393$	−2.30477	−0.116260
$394$	10.2058	0.514159
$395$	−7.89600	−0.397291
$396$	−0.662086	−0.0332711
$397$	−16.7898	−0.842654	−0.421327	−	0.906909i	$-0.638436\pi$
$397$	−16.7898	−0.842654	−0.421327	+	0.906909i	$0.638436\pi$
$398$	−1.89105	−0.0947898
$399$	15.2699	0.764451
$400$	−0.539679	−0.0269839
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	10.0142	0.499463
$403$	10.4859	0.522338
$404$	−7.46789	−0.371541
$405$	1.00000	0.0496904
$406$	−17.6690	−0.876897
$407$	2.01225	0.0997433
$408$	−3.33021	−0.164870
$409$	35.1359	1.73736	0.868680	−	0.495373i	$-0.164969\pi$
$409$	35.1359	1.73736	0.868680	+	0.495373i	$0.164969\pi$
$410$	−0.916958	−0.0452853
$411$	1.84175	0.0908470
$412$	7.32918	0.361083
$413$	−69.5652	−3.42308
$414$	−5.18425	−0.254792
$415$	9.12197	0.447780
$416$	−11.1199	−0.545196
$417$	13.1492	0.643918
$418$	1.69073	0.0826963
$419$	−6.75881	−0.330190	−0.165095	−	0.986278i	$-0.552793\pi$
$419$	−6.75881	−0.330190	−0.165095	+	0.986278i	$0.552793\pi$
$420$	5.63502	0.274961
$421$	−5.62047	−0.273925	−0.136962	−	0.990576i	$-0.543734\pi$
$421$	−5.62047	−0.273925	−0.136962	+	0.990576i	$0.543734\pi$
$422$	16.2368	0.790396
$423$	5.67223	0.275793
$424$	40.0887	1.94688
$425$	1.13559	0.0550841
$426$	0.291333	0.0141152
$427$	−67.6419	−3.27342
$428$	10.1846	0.492291
$429$	−1.23606	−0.0596776
$430$	−0.940251	−0.0453429
$431$	8.16293	0.393194	0.196597	−	0.980484i	$-0.437011\pi$
$431$	8.16293	0.393194	0.196597	+	0.980484i	$0.437011\pi$
$432$	0.539679	0.0259653
$433$	−35.8847	−1.72451	−0.862255	−	0.506475i	$-0.830948\pi$
$433$	−35.8847	−1.72451	−0.862255	+	0.506475i	$0.830948\pi$
$434$	−24.1227	−1.15792
$435$	−3.69982	−0.177393
$436$	22.7605	1.09003
$437$	−16.5764	−0.792959
$438$	10.8495	0.518408
$439$	37.8372	1.80587	0.902936	−	0.429775i	$-0.141407\pi$
$439$	37.8372	1.80587	0.902936	+	0.429775i	$0.141407\pi$
$440$	1.74615	0.0832445
$441$	18.6816	0.889600
$442$	−2.22152	−0.105667
$443$	18.0471	0.857445	0.428723	−	0.903436i	$-0.358964\pi$
$443$	18.0471	0.857445	0.428723	+	0.903436i	$0.358964\pi$
$444$	3.75781	0.178338
$445$	4.28235	0.203003
$446$	0.0431696	0.00204414
$447$	3.09131	0.146214
$448$	31.0510	1.46702
$449$	11.0751	0.522664	0.261332	−	0.965249i	$-0.415838\pi$
$449$	11.0751	0.522664	0.261332	+	0.965249i	$0.415838\pi$
$450$	−0.942366	−0.0444235
$451$	0.579375	0.0272817
$452$	−7.85858	−0.369636
$453$	−15.3227	−0.719924
$454$	−16.7592	−0.786547
$455$	10.5201	0.493191
$456$	8.83642	0.413803
$457$	5.44774	0.254834	0.127417	−	0.991849i	$-0.459331\pi$
$457$	5.44774	0.254834	0.127417	+	0.991849i	$0.459331\pi$
$458$	−3.43794	−0.160645
$459$	−1.13559	−0.0530047
$460$	−6.11717	−0.285215
$461$	−9.32639	−0.434373	−0.217187	−	0.976130i	$-0.569688\pi$
$461$	−9.32639	−0.434373	−0.217187	+	0.976130i	$0.569688\pi$
$462$	2.84355	0.132294
$463$	−38.1357	−1.77232	−0.886158	−	0.463383i	$-0.846636\pi$
$463$	−38.1357	−1.77232	−0.886158	+	0.463383i	$0.846636\pi$
$464$	−1.99672	−0.0926952
$465$	−5.05120	−0.234244
$466$	1.74443	0.0808090
$467$	25.2940	1.17047	0.585234	−	0.810864i	$-0.301002\pi$
$467$	25.2940	1.17047	0.585234	+	0.810864i	$0.301002\pi$
$468$	−2.30831	−0.106702
$469$	53.8528	2.48669
$470$	−5.34531	−0.246561
$471$	9.04588	0.416812
$472$	−40.2562	−1.85294
$473$	0.594093	0.0273164
$474$	−7.44092	−0.341773
$475$	−3.01318	−0.138254
$476$	−6.39905	−0.293300
$477$	13.6701	0.625909
$478$	16.4089	0.750526
$479$	−10.5224	−0.480782	−0.240391	−	0.970676i	$-0.577276\pi$
$479$	−10.5224	−0.480782	−0.240391	+	0.970676i	$0.577276\pi$
$480$	5.35661	0.244495
$481$	7.01553	0.319881
$482$	−12.9686	−0.590706
$483$	−27.8790	−1.26854
$484$	11.8372	0.538054
$485$	−6.88522	−0.312642
$486$	0.942366	0.0427466
$487$	−19.1862	−0.869411	−0.434705	−	0.900573i	$-0.643148\pi$
$487$	−19.1862	−0.869411	−0.434705	+	0.900573i	$0.643148\pi$
$488$	−39.1432	−1.77193
$489$	1.28579	0.0581453
$490$	−17.6049	−0.795308
$491$	27.7761	1.25352	0.626759	−	0.779213i	$-0.284381\pi$
$491$	27.7761	1.25352	0.626759	+	0.779213i	$0.284381\pi$
$492$	1.08197	0.0487789
$493$	4.20147	0.189225
$494$	5.89459	0.265210
$495$	0.595429	0.0267625
$496$	−2.72603	−0.122402
$497$	1.56669	0.0702755
$498$	8.59623	0.385206
$499$	−24.7107	−1.10620	−0.553100	−	0.833115i	$-0.686555\pi$
$499$	−24.7107	−1.10620	−0.553100	+	0.833115i	$0.686555\pi$
$500$	−1.11195	−0.0497278
$501$	18.4406	0.823864
$502$	−6.25866	−0.279338
$503$	18.5567	0.827400	0.413700	−	0.910413i	$-0.364236\pi$
$503$	18.5567	0.827400	0.413700	+	0.910413i	$0.364236\pi$
$504$	14.8615	0.661984
$505$	6.71604	0.298860
$506$	−3.08685	−0.137227
$507$	8.69057	0.385962
$508$	−2.06694	−0.0917054
$509$	39.7383	1.76137	0.880684	−	0.473703i	$-0.157083\pi$
$509$	39.7383	1.76137	0.880684	+	0.473703i	$0.157083\pi$
$510$	1.07014	0.0473865
$511$	58.3445	2.58101
$512$	6.05616	0.267647
$513$	3.01318	0.133035
$514$	1.46563	0.0646462
$515$	−6.59130	−0.290447
$516$	1.10945	0.0488409
$517$	3.37741	0.148538
$518$	−16.1392	−0.709115
$519$	2.53716	0.111369
$520$	6.08781	0.266968
$521$	43.4155	1.90207	0.951034	−	0.309087i	$-0.100023\pi$
$521$	43.4155	1.90207	0.951034	+	0.309087i	$0.100023\pi$
$522$	−3.48659	−0.152604
$523$	−19.0285	−0.832057	−0.416028	−	0.909352i	$-0.636578\pi$
$523$	−19.0285	−0.832057	−0.416028	+	0.909352i	$0.636578\pi$
$524$	−2.56278	−0.111956
$525$	−5.06770	−0.221173
$526$	25.9633	1.13205
$527$	5.73608	0.249868
$528$	0.321341	0.0139846
$529$	7.26446	0.315846
$530$	−12.8822	−0.559567
$531$	−13.7272	−0.595709
$532$	16.9793	0.736146
$533$	2.01995	0.0874936
$534$	4.03554	0.174635
$535$	−9.15925	−0.395989
$536$	31.1637	1.34607
$537$	5.53040	0.238654
$538$	7.08703	0.305544
$539$	11.1236	0.479126
$540$	1.11195	0.0478506
$541$	12.7561	0.548429	0.274214	−	0.961669i	$-0.411582\pi$
$541$	12.7561	0.548429	0.274214	+	0.961669i	$0.411582\pi$
$542$	−16.8348	−0.723117
$543$	5.96444	0.255958
$544$	−6.08290	−0.260802
$545$	−20.4691	−0.876799
$546$	9.91380	0.424271
$547$	−6.24857	−0.267170	−0.133585	−	0.991037i	$-0.542649\pi$
$547$	−6.24857	−0.267170	−0.133585	+	0.991037i	$0.542649\pi$
$548$	2.04793	0.0874834
$549$	−13.3477	−0.569664
$550$	−0.561112	−0.0239259
$551$	−11.1482	−0.474930
$552$	−16.1331	−0.686671
$553$	−40.0146	−1.70159
$554$	20.1812	0.857417
$555$	−3.37949	−0.143451
$556$	14.6212	0.620076
$557$	−35.1068	−1.48752	−0.743762	−	0.668445i	$-0.766960\pi$
$557$	−35.1068	−1.48752	−0.743762	+	0.668445i	$0.766960\pi$
$558$	−4.76008	−0.201510
$559$	2.07126	0.0876049
$560$	−2.73493	−0.115572
$561$	−0.676162	−0.0285476
$562$	9.33033	0.393576
$563$	2.41600	0.101822	0.0509111	−	0.998703i	$-0.483787\pi$
$563$	2.41600	0.101822	0.0509111	+	0.998703i	$0.483787\pi$
$564$	6.30722	0.265582
$565$	7.06740	0.297328
$566$	4.06833	0.171004
$567$	5.06770	0.212823
$568$	0.906614	0.0380407
$569$	3.59801	0.150837	0.0754183	−	0.997152i	$-0.475971\pi$
$569$	3.59801	0.150837	0.0754183	+	0.997152i	$0.475971\pi$
$570$	−2.83952	−0.118934
$571$	3.47695	0.145506	0.0727530	−	0.997350i	$-0.476822\pi$
$571$	3.47695	0.145506	0.0727530	+	0.997350i	$0.476822\pi$
$572$	−1.37443	−0.0574680
$573$	−6.84134	−0.285801
$574$	−4.64687	−0.193957
$575$	5.50131	0.229421
$576$	6.12724	0.255302
$577$	−36.3649	−1.51389	−0.756946	−	0.653478i	$-0.773309\pi$
$577$	−36.3649	−1.51389	−0.756946	+	0.653478i	$0.773309\pi$
$578$	14.8050	0.615806
$579$	−8.66646	−0.360166
$580$	−4.11401	−0.170825
$581$	46.2274	1.91784
$582$	−6.48839	−0.268952
$583$	8.13956	0.337106
$584$	33.7630	1.39712
$585$	2.07592	0.0858286
$586$	2.72063	0.112388
$587$	−11.1503	−0.460221	−0.230110	−	0.973165i	$-0.573909\pi$
$587$	−11.1503	−0.460221	−0.230110	+	0.973165i	$0.573909\pi$
$588$	20.7730	0.856662
$589$	−15.2202	−0.627136
$590$	12.9360	0.532567
$591$	10.8299	0.445484
$592$	−1.82384	−0.0749593
$593$	29.7632	1.22223	0.611113	−	0.791543i	$-0.290722\pi$
$593$	29.7632	1.22223	0.611113	+	0.791543i	$0.290722\pi$
$594$	0.561112	0.0230227
$595$	5.75482	0.235925
$596$	3.43737	0.140800
$597$	−2.00671	−0.0821290
$598$	−10.7621	−0.440094
$599$	−28.4181	−1.16113	−0.580566	−	0.814213i	$-0.697169\pi$
$599$	−28.4181	−1.16113	−0.580566	+	0.814213i	$0.697169\pi$
$600$	−2.93259	−0.119723
$601$	−36.0533	−1.47065	−0.735323	−	0.677717i	$-0.762969\pi$
$601$	−36.0533	−1.47065	−0.735323	+	0.677717i	$0.762969\pi$
$602$	−4.76491	−0.194203
$603$	10.6267	0.432751
$604$	−17.0380	−0.693268
$605$	−10.6455	−0.432800
$606$	6.32897	0.257097
$607$	32.4733	1.31805	0.659026	−	0.752120i	$-0.270969\pi$
$607$	32.4733	1.31805	0.659026	+	0.752120i	$0.270969\pi$
$608$	16.1404	0.654580
$609$	−18.7496	−0.759772
$610$	12.5784	0.509283
$611$	11.7751	0.476368
$612$	−1.26271	−0.0510422
$613$	−28.6501	−1.15717	−0.578583	−	0.815624i	$-0.696394\pi$
$613$	−28.6501	−1.15717	−0.578583	+	0.815624i	$0.696394\pi$
$614$	13.0858	0.528099
$615$	−0.973038	−0.0392367
$616$	8.84897	0.356535
$617$	−5.35913	−0.215750	−0.107875	−	0.994164i	$-0.534405\pi$
$617$	−5.35913	−0.215750	−0.107875	+	0.994164i	$0.534405\pi$
$618$	−6.21141	−0.249860
$619$	−36.3439	−1.46078	−0.730392	−	0.683028i	$-0.760663\pi$
$619$	−36.3439	−1.46078	−0.730392	+	0.683028i	$0.760663\pi$
$620$	−5.61667	−0.225571
$621$	−5.50131	−0.220760
$622$	−0.328742	−0.0131814
$623$	21.7017	0.869459
$624$	1.12033	0.0448490
$625$	1.00000	0.0400000
$626$	4.38704	0.175341
$627$	1.79413	0.0716508
$628$	10.0585	0.401380
$629$	3.83770	0.153019
$630$	−4.77563	−0.190266
$631$	−33.4971	−1.33350	−0.666750	−	0.745281i	$-0.732315\pi$
$631$	−33.4971	−1.33350	−0.666750	+	0.745281i	$0.732315\pi$
$632$	−23.1557	−0.921086
$633$	17.2299	0.684825
$634$	−33.2684	−1.32126
$635$	1.85884	0.0737659
$636$	15.2004	0.602735
$637$	38.7814	1.53658
$638$	−2.07601	−0.0821902
$639$	0.309151	0.0122298
$640$	4.93912	0.195236
$641$	19.1194	0.755173	0.377586	−	0.925974i	$-0.376754\pi$
$641$	19.1194	0.755173	0.377586	+	0.925974i	$0.376754\pi$
$642$	−8.63136	−0.340653
$643$	−36.5341	−1.44076	−0.720381	−	0.693578i	$-0.756033\pi$
$643$	−36.5341	−1.44076	−0.720381	+	0.693578i	$0.756033\pi$
$644$	−31.0000	−1.22157
$645$	−0.997756	−0.0392866
$646$	3.22452	0.126867
$647$	−25.9514	−1.02025	−0.510127	−	0.860099i	$-0.670401\pi$
$647$	−25.9514	−1.02025	−0.510127	+	0.860099i	$0.670401\pi$
$648$	2.93259	0.115203
$649$	−8.17356	−0.320840
$650$	−1.95627	−0.0767313
$651$	−25.5980	−1.00326
$652$	1.42973	0.0559924
$653$	1.89006	0.0739638	0.0369819	−	0.999316i	$-0.488226\pi$
$653$	1.89006	0.0739638	0.0369819	+	0.999316i	$0.488226\pi$
$654$	−19.2894	−0.754273
$655$	2.30477	0.0900547
$656$	−0.525128	−0.0205028
$657$	11.5130	0.449165
$658$	−27.0885	−1.05602
$659$	−35.0686	−1.36608	−0.683039	−	0.730382i	$-0.739342\pi$
$659$	−35.0686	−1.36608	−0.683039	+	0.730382i	$0.739342\pi$
$660$	0.662086	0.0257717
$661$	1.83675	0.0714411	0.0357206	−	0.999362i	$-0.488627\pi$
$661$	1.83675	0.0714411	0.0357206	+	0.999362i	$0.488627\pi$
$662$	−6.96484	−0.270696
$663$	−2.35738	−0.0915532
$664$	26.7510	1.03814
$665$	−15.2699	−0.592141
$666$	−3.18471	−0.123405
$667$	20.3539	0.788106
$668$	20.5049	0.793360
$669$	0.0458098	0.00177111
$670$	−10.0142	−0.386883
$671$	−7.94758	−0.306813
$672$	27.1457	1.04717
$673$	−0.112592	−0.00434009	−0.00217005	−	0.999998i	$-0.500691\pi$
$673$	−0.112592	−0.00434009	−0.00217005	+	0.999998i	$0.500691\pi$
$674$	−9.46426	−0.364550
$675$	−1.00000	−0.0384900
$676$	9.66346	0.371672
$677$	43.8040	1.68352	0.841762	−	0.539849i	$-0.181519\pi$
$677$	43.8040	1.68352	0.841762	+	0.539849i	$0.181519\pi$
$678$	6.66007	0.255779
$679$	−34.8922	−1.33904
$680$	3.33021	0.127708
$681$	−17.7842	−0.681490
$682$	−2.83429	−0.108531
$683$	23.3711	0.894272	0.447136	−	0.894466i	$-0.352444\pi$
$683$	23.3711	0.894272	0.447136	+	0.894466i	$0.352444\pi$
$684$	3.35050	0.128109
$685$	−1.84175	−0.0703698
$686$	−55.7870	−2.12996
$687$	−3.64821	−0.139188
$688$	−0.538468	−0.0205289
$689$	28.3779	1.08111
$690$	5.18425	0.197361
$691$	32.8646	1.25023	0.625115	−	0.780533i	$-0.285052\pi$
$691$	32.8646	1.25023	0.625115	+	0.780533i	$0.285052\pi$
$692$	2.82118	0.107245
$693$	3.01746	0.114624
$694$	6.49529	0.246558
$695$	−13.1492	−0.498777
$696$	−10.8501	−0.411271
$697$	1.10497	0.0418537
$698$	−29.4088	−1.11314
$699$	1.85111	0.0700156
$700$	−5.63502	−0.212984
$701$	36.4366	1.37619	0.688096	−	0.725620i	$-0.258447\pi$
$701$	36.4366	1.37619	0.688096	+	0.725620i	$0.258447\pi$
$702$	1.95627	0.0738347
$703$	−10.1830	−0.384059
$704$	3.64834	0.137502
$705$	−5.67223	−0.213629
$706$	5.57504	0.209819
$707$	34.0349	1.28001
$708$	−15.2639	−0.573652
$709$	27.6903	1.03993	0.519966	−	0.854187i	$-0.325945\pi$
$709$	27.6903	1.03993	0.519966	+	0.854187i	$0.325945\pi$
$710$	−0.291333	−0.0109335
$711$	−7.89600	−0.296123
$712$	12.5584	0.470645
$713$	27.7882	1.04068
$714$	5.42314	0.202956
$715$	1.23606	0.0462260
$716$	6.14951	0.229818
$717$	17.4125	0.650280
$718$	−21.7868	−0.813076
$719$	34.6662	1.29283	0.646416	−	0.762985i	$-0.276267\pi$
$719$	34.6662	1.29283	0.646416	+	0.762985i	$0.276267\pi$
$720$	−0.539679	−0.0201126
$721$	−33.4027	−1.24398
$722$	9.34898	0.347933
$723$	−13.7618	−0.511807
$724$	6.63214	0.246481
$725$	3.69982	0.137408
$726$	−10.0319	−0.372319
$727$	−20.2716	−0.751831	−0.375916	−	0.926654i	$-0.622672\pi$
$727$	−20.2716	−0.751831	−0.375916	+	0.926654i	$0.622672\pi$
$728$	30.8512	1.14342
$729$	1.00000	0.0370370
$730$	−10.8495	−0.401557
$731$	1.13304	0.0419070
$732$	−14.8419	−0.548572
$733$	−43.3269	−1.60032	−0.800158	−	0.599789i	$-0.795251\pi$
$733$	−43.3269	−1.60032	−0.800158	+	0.599789i	$0.795251\pi$
$734$	−2.11143	−0.0779344
$735$	−18.6816	−0.689081
$736$	−29.4684	−1.08622
$737$	6.32743	0.233074
$738$	−0.916958	−0.0337537
$739$	−8.38139	−0.308314	−0.154157	−	0.988046i	$-0.549266\pi$
$739$	−8.38139	−0.308314	−0.154157	+	0.988046i	$0.549266\pi$
$740$	−3.75781	−0.138140
$741$	6.25510	0.229787
$742$	−65.2831	−2.39662
$743$	22.5028	0.825546	0.412773	−	0.910834i	$-0.364560\pi$
$743$	22.5028	0.825546	0.412773	+	0.910834i	$0.364560\pi$
$744$	−14.8131	−0.543075
$745$	−3.09131	−0.113257
$746$	−7.31354	−0.267768
$747$	9.12197	0.333755
$748$	−0.751856	−0.0274906
$749$	−46.4163	−1.69602
$750$	0.942366	0.0344103
$751$	18.3363	0.669101	0.334551	−	0.942378i	$-0.391416\pi$
$751$	18.3363	0.669101	0.334551	+	0.942378i	$0.391416\pi$
$752$	−3.06118	−0.111630
$753$	−6.64144	−0.242027
$754$	−7.23786	−0.263587
$755$	15.3227	0.557650
$756$	5.63502	0.204944
$757$	−8.23019	−0.299131	−0.149566	−	0.988752i	$-0.547788\pi$
$757$	−8.23019	−0.299131	−0.149566	+	0.988752i	$0.547788\pi$
$758$	14.9861	0.544321
$759$	−3.27564	−0.118898
$760$	−8.83642	−0.320531
$761$	−33.1110	−1.20027	−0.600137	−	0.799897i	$-0.704887\pi$
$761$	−33.1110	−1.20027	−0.600137	+	0.799897i	$0.704887\pi$
$762$	1.75171	0.0634578
$763$	−103.731	−3.75532
$764$	−7.60721	−0.275219
$765$	1.13559	0.0410572
$766$	−35.9386	−1.29852
$767$	−28.4965	−1.02895
$768$	16.9089	0.610149
$769$	24.9021	0.897992	0.448996	−	0.893534i	$-0.351782\pi$
$769$	24.9021	0.897992	0.448996	+	0.893534i	$0.351782\pi$
$770$	−2.84355	−0.102474
$771$	1.55527	0.0560116
$772$	−9.63664	−0.346830
$773$	−8.22005	−0.295655	−0.147827	−	0.989013i	$-0.547228\pi$
$773$	−8.22005	−0.295655	−0.147827	+	0.989013i	$0.547228\pi$
$774$	−0.940251	−0.0337966
$775$	5.05120	0.181445
$776$	−20.1915	−0.724834
$777$	−17.1262	−0.614400
$778$	1.27168	0.0455921
$779$	−2.93194	−0.105048
$780$	2.30831	0.0826507
$781$	0.184078	0.00658682
$782$	−5.88717	−0.210525
$783$	−3.69982	−0.132221
$784$	−10.0821	−0.360074
$785$	−9.04588	−0.322861
$786$	2.17193	0.0774703
$787$	54.3126	1.93604	0.968018	−	0.250880i	$-0.0807199\pi$
$787$	54.3126	1.93604	0.968018	+	0.250880i	$0.0807199\pi$
$788$	12.0423	0.428990
$789$	27.5512	0.980848
$790$	7.44092	0.264736
$791$	35.8155	1.27345
$792$	1.74615	0.0620468
$793$	−27.7086	−0.983962
$794$	15.8221	0.561505
$795$	−13.6701	−0.484827
$796$	−2.23135	−0.0790882
$797$	24.8205	0.879186	0.439593	−	0.898197i	$-0.355123\pi$
$797$	24.8205	0.879186	0.439593	+	0.898197i	$0.355123\pi$
$798$	−14.3898	−0.509394
$799$	6.44131	0.227877
$800$	−5.35661	−0.189385
$801$	4.28235	0.151309
$802$	0.942366	0.0332761
$803$	6.85518	0.241914
$804$	11.8163	0.416729
$805$	27.8790	0.982606
$806$	−9.88152	−0.348062
$807$	7.52047	0.264733
$808$	19.6954	0.692882
$809$	−30.9268	−1.08733	−0.543663	−	0.839303i	$-0.682963\pi$
$809$	−30.9268	−1.08733	−0.543663	+	0.839303i	$0.682963\pi$
$810$	−0.942366	−0.0331113
$811$	−12.9149	−0.453504	−0.226752	−	0.973953i	$-0.572811\pi$
$811$	−12.9149	−0.453504	−0.226752	+	0.973953i	$0.572811\pi$
$812$	−20.8486	−0.731641
$813$	−17.8644	−0.626532
$814$	−1.89627	−0.0664643
$815$	−1.28579	−0.0450391
$816$	0.612852	0.0214541
$817$	−3.00642	−0.105181
$818$	−33.1109	−1.15770
$819$	10.5201	0.367603
$820$	−1.08197	−0.0377839
$821$	−7.09545	−0.247633	−0.123817	−	0.992305i	$-0.539513\pi$
$821$	−7.09545	−0.247633	−0.123817	+	0.992305i	$0.539513\pi$
$822$	−1.73561	−0.0605362
$823$	−8.98791	−0.313299	−0.156649	−	0.987654i	$-0.550069\pi$
$823$	−8.98791	−0.313299	−0.156649	+	0.987654i	$0.550069\pi$
$824$	−19.3296	−0.673378
$825$	−0.595429	−0.0207302
$826$	65.5559	2.28098
$827$	−46.7352	−1.62514	−0.812570	−	0.582863i	$-0.801932\pi$
$827$	−46.7352	−1.62514	−0.812570	+	0.582863i	$0.801932\pi$
$828$	−6.11717	−0.212586
$829$	−13.4486	−0.467090	−0.233545	−	0.972346i	$-0.575033\pi$
$829$	−13.4486	−0.467090	−0.233545	+	0.972346i	$0.575033\pi$
$830$	−8.59623	−0.298379
$831$	21.4155	0.742894
$832$	12.7196	0.440974
$833$	21.2146	0.735042
$834$	−12.3913	−0.429077
$835$	−18.4406	−0.638162
$836$	1.99498	0.0689979
$837$	−5.05120	−0.174595
$838$	6.36927	0.220023
$839$	−39.7747	−1.37317	−0.686587	−	0.727047i	$-0.740892\pi$
$839$	−39.7747	−1.37317	−0.686587	+	0.727047i	$0.740892\pi$
$840$	−14.8615	−0.512770
$841$	−15.3113	−0.527976
$842$	5.29654	0.182531
$843$	9.90097	0.341007
$844$	19.1587	0.659469
$845$	−8.69057	−0.298965
$846$	−5.34531	−0.183776
$847$	−53.9480	−1.85368
$848$	−7.37745	−0.253343
$849$	4.31714	0.148164
$850$	−1.07014	−0.0367054
$851$	18.5916	0.637313
$852$	0.343760	0.0117770
$853$	47.8106	1.63701	0.818503	−	0.574503i	$-0.194805\pi$
$853$	47.8106	1.63701	0.818503	+	0.574503i	$0.194805\pi$
$854$	63.7434	2.18126
$855$	−3.01318	−0.103049
$856$	−26.8603	−0.918067
$857$	51.4646	1.75800	0.878999	−	0.476825i	$-0.158212\pi$
$857$	51.4646	1.75800	0.878999	+	0.476825i	$0.158212\pi$
$858$	1.16482	0.0397663
$859$	−49.5019	−1.68898	−0.844492	−	0.535569i	$-0.820097\pi$
$859$	−49.5019	−1.68898	−0.844492	+	0.535569i	$0.820097\pi$
$860$	−1.10945	−0.0378320
$861$	−4.93107	−0.168050
$862$	−7.69246	−0.262006
$863$	11.8858	0.404596	0.202298	−	0.979324i	$-0.435159\pi$
$863$	11.8858	0.404596	0.202298	+	0.979324i	$0.435159\pi$
$864$	5.35661	0.182236
$865$	−2.53716	−0.0862659
$866$	33.8165	1.14913
$867$	15.7104	0.533555
$868$	−28.4636	−0.966118
$869$	−4.70151	−0.159488
$870$	3.48659	0.118206
$871$	22.0601	0.747477
$872$	−60.0274	−2.03279
$873$	−6.88522	−0.233029
$874$	15.6211	0.528391
$875$	5.06770	0.171320
$876$	12.8019	0.432535
$877$	0.405832	0.0137040	0.00685199	−	0.999977i	$-0.497819\pi$
$877$	0.405832	0.0137040	0.00685199	+	0.999977i	$0.497819\pi$
$878$	−35.6565	−1.20335
$879$	2.88702	0.0973768
$880$	−0.321341	−0.0108324
$881$	15.3765	0.518046	0.259023	−	0.965871i	$-0.416599\pi$
$881$	15.3765	0.518046	0.259023	+	0.965871i	$0.416599\pi$
$882$	−17.6049	−0.592788
$883$	31.9118	1.07392	0.536959	−	0.843609i	$-0.319573\pi$
$883$	31.9118	1.07392	0.536959	+	0.843609i	$0.319573\pi$
$884$	−2.62129	−0.0881634
$885$	13.7272	0.461434
$886$	−17.0070	−0.571361
$887$	26.6608	0.895182	0.447591	−	0.894238i	$-0.352282\pi$
$887$	26.6608	0.895182	0.447591	+	0.894238i	$0.352282\pi$
$888$	−9.91066	−0.332580
$889$	9.42006	0.315939
$890$	−4.03554	−0.135271
$891$	0.595429	0.0199476
$892$	0.0509381	0.00170553
$893$	−17.0914	−0.571943
$894$	−2.91314	−0.0974301
$895$	−5.53040	−0.184861
$896$	25.0300	0.836193
$897$	−11.4203	−0.381312
$898$	−10.4367	−0.348279
$899$	18.6886	0.623298
$900$	−1.11195	−0.0370649
$901$	15.5236	0.517165
$902$	−0.545983	−0.0181793
$903$	−5.05633	−0.168264
$904$	20.7258	0.689330
$905$	−5.96444	−0.198265
$906$	14.4396	0.479723
$907$	−19.4362	−0.645368	−0.322684	−	0.946507i	$-0.604585\pi$
$907$	−19.4362	−0.645368	−0.322684	+	0.946507i	$0.604585\pi$
$908$	−19.7750	−0.656258
$909$	6.71604	0.222757
$910$	−9.91380	−0.328639
$911$	15.7644	0.522297	0.261148	−	0.965299i	$-0.415899\pi$
$911$	15.7644	0.522297	0.261148	+	0.965299i	$0.415899\pi$
$912$	−1.62615	−0.0538472
$913$	5.43148	0.179756
$914$	−5.13376	−0.169810
$915$	13.3477	0.441260
$916$	−4.05661	−0.134034
$917$	11.6799	0.385703
$918$	1.07014	0.0353198
$919$	−45.7533	−1.50926	−0.754630	−	0.656150i	$-0.772184\pi$
$919$	−45.7533	−1.50926	−0.754630	+	0.656150i	$0.772184\pi$
$920$	16.1331	0.531893
$921$	13.8861	0.457563
$922$	8.78886	0.289446
$923$	0.641772	0.0211242
$924$	3.35525	0.110380
$925$	3.37949	0.111117
$926$	35.9378	1.18099
$927$	−6.59130	−0.216487
$928$	−19.8185	−0.650574
$929$	−10.6499	−0.349412	−0.174706	−	0.984621i	$-0.555897\pi$
$929$	−10.6499	−0.349412	−0.174706	+	0.984621i	$0.555897\pi$
$930$	4.76008	0.156089
$931$	−56.2910	−1.84486
$932$	2.05834	0.0674232
$933$	−0.348848	−0.0114208
$934$	−23.8362	−0.779946
$935$	0.676162	0.0221129
$936$	6.08781	0.198986
$937$	5.34415	0.174586	0.0872929	−	0.996183i	$-0.472178\pi$
$937$	5.34415	0.174586	0.0872929	+	0.996183i	$0.472178\pi$
$938$	−50.7490	−1.65701
$939$	4.65535	0.151922
$940$	−6.30722	−0.205719
$941$	49.2884	1.60676	0.803379	−	0.595469i	$-0.203034\pi$
$941$	49.2884	1.60676	0.803379	+	0.595469i	$0.203034\pi$
$942$	−8.52453	−0.277744
$943$	5.35299	0.174317
$944$	7.40826	0.241118
$945$	−5.06770	−0.164852
$946$	−0.559853	−0.0182024
$947$	−38.3815	−1.24723	−0.623616	−	0.781731i	$-0.714337\pi$
$947$	−38.3815	−1.24723	−0.623616	+	0.781731i	$0.714337\pi$
$948$	−8.77993	−0.285159
$949$	23.9000	0.775828
$950$	2.83952	0.0921260
$951$	−35.3031	−1.14478
$952$	16.8765	0.546971
$953$	−16.2121	−0.525160	−0.262580	−	0.964910i	$-0.584573\pi$
$953$	−16.2121	−0.525160	−0.262580	+	0.964910i	$0.584573\pi$
$954$	−12.8822	−0.417077
$955$	6.84134	0.221381
$956$	19.3617	0.626203
$957$	−2.20298	−0.0712123
$958$	9.91597	0.320370
$959$	−9.33346	−0.301393
$960$	−6.12724	−0.197756
$961$	−5.48537	−0.176947
$962$	−6.61120	−0.213154
$963$	−9.15925	−0.295153
$964$	−15.3024	−0.492857
$965$	8.66646	0.278983
$966$	26.2722	0.845295
$967$	39.4485	1.26858	0.634289	−	0.773096i	$-0.281293\pi$
$967$	39.4485	1.26858	0.634289	+	0.773096i	$0.281293\pi$
$968$	−31.2188	−1.00341
$969$	3.42173	0.109922
$970$	6.48839	0.208330
$971$	−40.0943	−1.28669	−0.643344	−	0.765578i	$-0.722453\pi$
$971$	−40.0943	−1.28669	−0.643344	+	0.765578i	$0.722453\pi$
$972$	1.11195	0.0356657
$973$	−66.6361	−2.13625
$974$	18.0804	0.579335
$975$	−2.07592	−0.0664825
$976$	7.20345	0.230577
$977$	20.5221	0.656560	0.328280	−	0.944580i	$-0.393531\pi$
$977$	20.5221	0.656560	0.328280	+	0.944580i	$0.393531\pi$
$978$	−1.21168	−0.0387453
$979$	2.54983	0.0814931
$980$	−20.7730	−0.663568
$981$	−20.4691	−0.653527
$982$	−26.1753	−0.835286
$983$	17.6293	0.562288	0.281144	−	0.959666i	$-0.409286\pi$
$983$	17.6293	0.562288	0.281144	+	0.959666i	$0.409286\pi$
$984$	−2.85352	−0.0909670
$985$	−10.8299	−0.345071
$986$	−3.95932	−0.126091
$987$	−28.7452	−0.914969
$988$	6.95535	0.221279
$989$	5.48897	0.174539
$990$	−0.561112	−0.0178333
$991$	16.4293	0.521894	0.260947	−	0.965353i	$-0.415965\pi$
$991$	16.4293	0.521894	0.260947	+	0.965353i	$0.415965\pi$
$992$	−27.0573	−0.859070
$993$	−7.39080	−0.234540
$994$	−1.47639	−0.0468283
$995$	2.00671	0.0636169
$996$	10.1431	0.321398
$997$	−19.8921	−0.629990	−0.314995	−	0.949093i	$-0.602003\pi$
$997$	−19.8921	−0.629990	−0.314995	+	0.949093i	$0.602003\pi$
$998$	23.2865	0.737120
$999$	−3.37949	−0.106922

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.g.1.13	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.g.1.13	✓	36	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-0.942366 q^{2} -1.00000 q^{3} -1.11195 q^{4} +1.00000 q^{5} +0.942366 q^{6} +5.06770 q^{7} +2.93259 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.942366 q^{2} -1.00000 q^{3} -1.11195 q^{4} +1.00000 q^{5} +0.942366 q^{6} +5.06770 q^{7} +2.93259 q^{8} +1.00000 q^{9} -0.942366 q^{10} +0.595429 q^{11} +1.11195 q^{12} +2.07592 q^{13} -4.77563 q^{14} -1.00000 q^{15} -0.539679 q^{16} +1.13559 q^{17} -0.942366 q^{18} -3.01318 q^{19} -1.11195 q^{20} -5.06770 q^{21} -0.561112 q^{22} +5.50131 q^{23} -2.93259 q^{24} +1.00000 q^{25} -1.95627 q^{26} -1.00000 q^{27} -5.63502 q^{28} +3.69982 q^{29} +0.942366 q^{30} +5.05120 q^{31} -5.35661 q^{32} -0.595429 q^{33} -1.07014 q^{34} +5.06770 q^{35} -1.11195 q^{36} +3.37949 q^{37} +2.83952 q^{38} -2.07592 q^{39} +2.93259 q^{40} +0.973038 q^{41} +4.77563 q^{42} +0.997756 q^{43} -0.662086 q^{44} +1.00000 q^{45} -5.18425 q^{46} +5.67223 q^{47} +0.539679 q^{48} +18.6816 q^{49} -0.942366 q^{50} -1.13559 q^{51} -2.30831 q^{52} +13.6701 q^{53} +0.942366 q^{54} +0.595429 q^{55} +14.8615 q^{56} +3.01318 q^{57} -3.48659 q^{58} -13.7272 q^{59} +1.11195 q^{60} -13.3477 q^{61} -4.76008 q^{62} +5.06770 q^{63} +6.12724 q^{64} +2.07592 q^{65} +0.561112 q^{66} +10.6267 q^{67} -1.26271 q^{68} -5.50131 q^{69} -4.77563 q^{70} +0.309151 q^{71} +2.93259 q^{72} +11.5130 q^{73} -3.18471 q^{74} -1.00000 q^{75} +3.35050 q^{76} +3.01746 q^{77} +1.95627 q^{78} -7.89600 q^{79} -0.539679 q^{80} +1.00000 q^{81} -0.916958 q^{82} +9.12197 q^{83} +5.63502 q^{84} +1.13559 q^{85} -0.940251 q^{86} -3.69982 q^{87} +1.74615 q^{88} +4.28235 q^{89} -0.942366 q^{90} +10.5201 q^{91} -6.11717 q^{92} -5.05120 q^{93} -5.34531 q^{94} -3.01318 q^{95} +5.35661 q^{96} -6.88522 q^{97} -17.6049 q^{98} +0.595429 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{3} + 36 q^{4} + 36 q^{5} - 4 q^{7} - 3 q^{8} + 36 q^{9}+O(q^{10}) \) 36 * q - 36 * q^3 + 36 * q^4 + 36 * q^5 - 4 * q^7 - 3 * q^8 + 36 * q^9	\( 36 q - 36 q^{3} + 36 q^{4} + 36 q^{5} - 4 q^{7} - 3 q^{8} + 36 q^{9} + 15 q^{11} - 36 q^{12} + 8 q^{13} + 10 q^{14} - 36 q^{15} + 36 q^{16} + 32 q^{17} + 5 q^{19} + 36 q^{20} + 4 q^{21} + q^{22} - 10 q^{23} + 3 q^{24} + 36 q^{25} + 22 q^{26} - 36 q^{27} + 61 q^{29} + 15 q^{31} - q^{32} - 15 q^{33} + 26 q^{34} - 4 q^{35} + 36 q^{36} + 16 q^{37} + 20 q^{38} - 8 q^{39} - 3 q^{40} + 61 q^{41} - 10 q^{42} - 35 q^{43} + 39 q^{44} + 36 q^{45} + 11 q^{46} - 28 q^{47} - 36 q^{48} + 68 q^{49} - 32 q^{51} + 4 q^{52} + 33 q^{53} + 15 q^{55} + 23 q^{56} - 5 q^{57} + 6 q^{58} + 35 q^{59} - 36 q^{60} + 55 q^{61} + q^{62} - 4 q^{63} + 15 q^{64} + 8 q^{65} - q^{66} - 34 q^{67} + 60 q^{68} + 10 q^{69} + 10 q^{70} + 42 q^{71} - 3 q^{72} + 53 q^{73} + 54 q^{74} - 36 q^{75} + 20 q^{76} + 20 q^{77} - 22 q^{78} + 25 q^{79} + 36 q^{80} + 36 q^{81} - 15 q^{82} - 11 q^{83} + 32 q^{85} + 53 q^{86} - 61 q^{87} + 27 q^{88} + 81 q^{89} + 15 q^{91} - 7 q^{92} - 15 q^{93} + 56 q^{94} + 5 q^{95} + q^{96} + 47 q^{97} - 3 q^{98} + 15 q^{99}+O(q^{100}) \) 36 * q - 36 * q^3 + 36 * q^4 + 36 * q^5 - 4 * q^7 - 3 * q^8 + 36 * q^9 + 15 * q^11 - 36 * q^12 + 8 * q^13 + 10 * q^14 - 36 * q^15 + 36 * q^16 + 32 * q^17 + 5 * q^19 + 36 * q^20 + 4 * q^21 + q^22 - 10 * q^23 + 3 * q^24 + 36 * q^25 + 22 * q^26 - 36 * q^27 + 61 * q^29 + 15 * q^31 - q^32 - 15 * q^33 + 26 * q^34 - 4 * q^35 + 36 * q^36 + 16 * q^37 + 20 * q^38 - 8 * q^39 - 3 * q^40 + 61 * q^41 - 10 * q^42 - 35 * q^43 + 39 * q^44 + 36 * q^45 + 11 * q^46 - 28 * q^47 - 36 * q^48 + 68 * q^49 - 32 * q^51 + 4 * q^52 + 33 * q^53 + 15 * q^55 + 23 * q^56 - 5 * q^57 + 6 * q^58 + 35 * q^59 - 36 * q^60 + 55 * q^61 + q^62 - 4 * q^63 + 15 * q^64 + 8 * q^65 - q^66 - 34 * q^67 + 60 * q^68 + 10 * q^69 + 10 * q^70 + 42 * q^71 - 3 * q^72 + 53 * q^73 + 54 * q^74 - 36 * q^75 + 20 * q^76 + 20 * q^77 - 22 * q^78 + 25 * q^79 + 36 * q^80 + 36 * q^81 - 15 * q^82 - 11 * q^83 + 32 * q^85 + 53 * q^86 - 61 * q^87 + 27 * q^88 + 81 * q^89 + 15 * q^91 - 7 * q^92 - 15 * q^93 + 56 * q^94 + 5 * q^95 + q^96 + 47 * q^97 - 3 * q^98 + 15 * q^99

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