LMFDB - Embedded newform 6017.2.a.c.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6017,2,Mod(1,6017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6017, 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("6017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6017 = 11 \cdot 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6017.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:	$48.0459868962$
Analytic rank:	$1$
Dimension:	$106$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	6017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.32740 q^{2} -3.07559 q^{3} +3.41677 q^{4} -1.26158 q^{5} +7.15812 q^{6} +0.599145 q^{7} -3.29739 q^{8} +6.45928 q^{9} +O(q^{10})$	\(q-2.32740 q^{2} -3.07559 q^{3} +3.41677 q^{4} -1.26158 q^{5} +7.15812 q^{6} +0.599145 q^{7} -3.29739 q^{8} +6.45928 q^{9} +2.93620 q^{10} +1.00000 q^{11} -10.5086 q^{12} +1.48585 q^{13} -1.39445 q^{14} +3.88011 q^{15} +0.840783 q^{16} +3.03080 q^{17} -15.0333 q^{18} +5.86101 q^{19} -4.31053 q^{20} -1.84273 q^{21} -2.32740 q^{22} -1.31387 q^{23} +10.1414 q^{24} -3.40842 q^{25} -3.45817 q^{26} -10.6393 q^{27} +2.04714 q^{28} +6.74213 q^{29} -9.03054 q^{30} +2.93038 q^{31} +4.63794 q^{32} -3.07559 q^{33} -7.05387 q^{34} -0.755869 q^{35} +22.0699 q^{36} +0.755218 q^{37} -13.6409 q^{38} -4.56988 q^{39} +4.15992 q^{40} +5.51301 q^{41} +4.28876 q^{42} -9.33971 q^{43} +3.41677 q^{44} -8.14889 q^{45} +3.05790 q^{46} +8.42855 q^{47} -2.58591 q^{48} -6.64103 q^{49} +7.93273 q^{50} -9.32151 q^{51} +5.07682 q^{52} -11.8926 q^{53} +24.7619 q^{54} -1.26158 q^{55} -1.97561 q^{56} -18.0261 q^{57} -15.6916 q^{58} -2.97044 q^{59} +13.2574 q^{60} -1.92843 q^{61} -6.82016 q^{62} +3.87005 q^{63} -12.4759 q^{64} -1.87452 q^{65} +7.15812 q^{66} -6.53515 q^{67} +10.3556 q^{68} +4.04094 q^{69} +1.75921 q^{70} -8.59133 q^{71} -21.2987 q^{72} -5.44367 q^{73} -1.75769 q^{74} +10.4829 q^{75} +20.0257 q^{76} +0.599145 q^{77} +10.6359 q^{78} -2.92252 q^{79} -1.06072 q^{80} +13.3444 q^{81} -12.8310 q^{82} +6.65119 q^{83} -6.29618 q^{84} -3.82360 q^{85} +21.7372 q^{86} -20.7361 q^{87} -3.29739 q^{88} -6.64813 q^{89} +18.9657 q^{90} +0.890242 q^{91} -4.48920 q^{92} -9.01267 q^{93} -19.6166 q^{94} -7.39413 q^{95} -14.2644 q^{96} -12.4665 q^{97} +15.4563 q^{98} +6.45928 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9}+O(q^{10}) $ 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9} - 30 q^{10} + 106 q^{11} - 26 q^{12} - 72 q^{13} + 3 q^{14} - 46 q^{15} + 75 q^{16} - 65 q^{17} - 37 q^{18} - 63 q^{19} - 25 q^{20} - 27 q^{21} - 13 q^{22} - 23 q^{23} - 56 q^{24} + 74 q^{25} + 2 q^{26} - 54 q^{27} - 115 q^{28} - 45 q^{29} - 14 q^{30} - 89 q^{31} - 96 q^{32} - 15 q^{33} - 26 q^{34} - 52 q^{35} + 91 q^{36} - 35 q^{37} + 7 q^{38} - 34 q^{39} - 74 q^{40} - 32 q^{41} - 94 q^{43} + 93 q^{44} - 46 q^{45} - 20 q^{46} - 105 q^{47} - 57 q^{48} + 80 q^{49} - 60 q^{50} - 36 q^{51} - 137 q^{52} - 61 q^{54} - 12 q^{55} + 32 q^{56} - 71 q^{57} - 28 q^{58} - 15 q^{59} - 21 q^{60} - 80 q^{61} - 84 q^{62} - 182 q^{63} + 55 q^{64} - 73 q^{65} - 22 q^{66} - 58 q^{67} - 145 q^{68} - 8 q^{69} - 39 q^{70} - 11 q^{71} - 100 q^{72} - 155 q^{73} - 15 q^{74} - 15 q^{75} - 132 q^{76} - 66 q^{77} - 45 q^{78} - 50 q^{79} - 28 q^{80} + 114 q^{81} - 57 q^{82} - 96 q^{83} - 27 q^{84} - 74 q^{85} + 54 q^{86} - 182 q^{87} - 39 q^{88} + 9 q^{89} - 53 q^{90} + 6 q^{91} - 18 q^{92} - 26 q^{93} - 33 q^{94} - 49 q^{95} - 56 q^{96} - 102 q^{97} - 76 q^{98} + 97 q^{99}+O(q^{100}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9 - 30 * q^10 + 106 * q^11 - 26 * q^12 - 72 * q^13 + 3 * q^14 - 46 * q^15 + 75 * q^16 - 65 * q^17 - 37 * q^18 - 63 * q^19 - 25 * q^20 - 27 * q^21 - 13 * q^22 - 23 * q^23 - 56 * q^24 + 74 * q^25 + 2 * q^26 - 54 * q^27 - 115 * q^28 - 45 * q^29 - 14 * q^30 - 89 * q^31 - 96 * q^32 - 15 * q^33 - 26 * q^34 - 52 * q^35 + 91 * q^36 - 35 * q^37 + 7 * q^38 - 34 * q^39 - 74 * q^40 - 32 * q^41 - 94 * q^43 + 93 * q^44 - 46 * q^45 - 20 * q^46 - 105 * q^47 - 57 * q^48 + 80 * q^49 - 60 * q^50 - 36 * q^51 - 137 * q^52 - 61 * q^54 - 12 * q^55 + 32 * q^56 - 71 * q^57 - 28 * q^58 - 15 * q^59 - 21 * q^60 - 80 * q^61 - 84 * q^62 - 182 * q^63 + 55 * q^64 - 73 * q^65 - 22 * q^66 - 58 * q^67 - 145 * q^68 - 8 * q^69 - 39 * q^70 - 11 * q^71 - 100 * q^72 - 155 * q^73 - 15 * q^74 - 15 * q^75 - 132 * q^76 - 66 * q^77 - 45 * q^78 - 50 * q^79 - 28 * q^80 + 114 * q^81 - 57 * q^82 - 96 * q^83 - 27 * q^84 - 74 * q^85 + 54 * q^86 - 182 * q^87 - 39 * q^88 + 9 * q^89 - 53 * q^90 + 6 * q^91 - 18 * q^92 - 26 * q^93 - 33 * q^94 - 49 * q^95 - 56 * q^96 - 102 * q^97 - 76 * q^98 + 97 * 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 $

$2$	−2.32740	−1.64572	−0.822859	−	0.568246i	$-0.807622\pi$
$2$	−2.32740	−1.64572	−0.822859	+	0.568246i	$0.807622\pi$
$3$	−3.07559	−1.77569	−0.887847	−	0.460138i	$-0.847800\pi$
$3$	−3.07559	−1.77569	−0.887847	+	0.460138i	$0.847800\pi$
$4$	3.41677	1.70839
$5$	−1.26158	−0.564196	−0.282098	−	0.959386i	$-0.591030\pi$
$5$	−1.26158	−0.564196	−0.282098	+	0.959386i	$0.591030\pi$
$6$	7.15812	2.92229
$7$	0.599145	0.226456	0.113228	−	0.993569i	$-0.463881\pi$
$7$	0.599145	0.226456	0.113228	+	0.993569i	$0.463881\pi$
$8$	−3.29739	−1.16580
$9$	6.45928	2.15309
$10$	2.93620	0.928506
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−10.5086	−3.03357
$13$	1.48585	0.412101	0.206051	−	0.978541i	$-0.433939\pi$
$13$	1.48585	0.412101	0.206051	+	0.978541i	$0.433939\pi$
$14$	−1.39445	−0.372682
$15$	3.88011	1.00184
$16$	0.840783	0.210196
$17$	3.03080	0.735077	0.367539	−	0.930008i	$-0.380201\pi$
$17$	3.03080	0.735077	0.367539	+	0.930008i	$0.380201\pi$
$18$	−15.0333	−3.54338
$19$	5.86101	1.34461	0.672303	−	0.740276i	$-0.265305\pi$
$19$	5.86101	1.34461	0.672303	+	0.740276i	$0.265305\pi$
$20$	−4.31053	−0.963864
$21$	−1.84273	−0.402116
$22$	−2.32740	−0.496202
$23$	−1.31387	−0.273961	−0.136981	−	0.990574i	$-0.543740\pi$
$23$	−1.31387	−0.273961	−0.136981	+	0.990574i	$0.543740\pi$
$24$	10.1414	2.07011
$25$	−3.40842	−0.681683
$26$	−3.45817	−0.678202
$27$	−10.6393	−2.04754
$28$	2.04714	0.386873
$29$	6.74213	1.25198	0.625991	−	0.779830i	$-0.284695\pi$
$29$	6.74213	1.25198	0.625991	+	0.779830i	$0.284695\pi$
$30$	−9.03054	−1.64874
$31$	2.93038	0.526312	0.263156	−	0.964753i	$-0.415237\pi$
$31$	2.93038	0.526312	0.263156	+	0.964753i	$0.415237\pi$
$32$	4.63794	0.819880
$33$	−3.07559	−0.535392
$34$	−7.05387	−1.20973
$35$	−0.755869	−0.127765
$36$	22.0699	3.67831
$37$	0.755218	0.124157	0.0620786	−	0.998071i	$-0.480227\pi$
$37$	0.755218	0.124157	0.0620786	+	0.998071i	$0.480227\pi$
$38$	−13.6409	−2.21284
$39$	−4.56988	−0.731766
$40$	4.15992	0.657741
$41$	5.51301	0.860988	0.430494	−	0.902593i	$-0.358339\pi$
$41$	5.51301	0.860988	0.430494	+	0.902593i	$0.358339\pi$
$42$	4.28876	0.661769
$43$	−9.33971	−1.42429	−0.712146	−	0.702031i	$-0.752277\pi$
$43$	−9.33971	−1.42429	−0.712146	+	0.702031i	$0.752277\pi$
$44$	3.41677	0.515098
$45$	−8.14889	−1.21477
$46$	3.05790	0.450863
$47$	8.42855	1.22943	0.614715	−	0.788749i	$-0.289271\pi$
$47$	8.42855	1.22943	0.614715	+	0.788749i	$0.289271\pi$
$48$	−2.58591	−0.373244
$49$	−6.64103	−0.948718
$50$	7.93273	1.12186
$51$	−9.32151	−1.30527
$52$	5.07682	0.704028
$53$	−11.8926	−1.63358	−0.816788	−	0.576938i	$-0.804247\pi$
$53$	−11.8926	−1.63358	−0.816788	+	0.576938i	$0.804247\pi$
$54$	24.7619	3.36967
$55$	−1.26158	−0.170111
$56$	−1.97561	−0.264003
$57$	−18.0261	−2.38761
$58$	−15.6916	−2.06041
$59$	−2.97044	−0.386719	−0.193359	−	0.981128i	$-0.561938\pi$
$59$	−2.97044	−0.386719	−0.193359	+	0.981128i	$0.561938\pi$
$60$	13.2574	1.71153
$61$	−1.92843	−0.246910	−0.123455	−	0.992350i	$-0.539397\pi$
$61$	−1.92843	−0.246910	−0.123455	+	0.992350i	$0.539397\pi$
$62$	−6.82016	−0.866162
$63$	3.87005	0.487580
$64$	−12.4759	−1.55949
$65$	−1.87452	−0.232506
$66$	7.15812	0.881104
$67$	−6.53515	−0.798396	−0.399198	−	0.916865i	$-0.630711\pi$
$67$	−6.53515	−0.798396	−0.399198	+	0.916865i	$0.630711\pi$
$68$	10.3556	1.25580
$69$	4.04094	0.486472
$70$	1.75921	0.210265
$71$	−8.59133	−1.01960	−0.509802	−	0.860292i	$-0.670281\pi$
$71$	−8.59133	−1.01960	−0.509802	+	0.860292i	$0.670281\pi$
$72$	−21.2987	−2.51008
$73$	−5.44367	−0.637134	−0.318567	−	0.947900i	$-0.603202\pi$
$73$	−5.44367	−0.637134	−0.318567	+	0.947900i	$0.603202\pi$
$74$	−1.75769	−0.204328
$75$	10.4829	1.21046
$76$	20.0257	2.29711
$77$	0.599145	0.0682789
$78$	10.6359	1.20428
$79$	−2.92252	−0.328809	−0.164404	−	0.986393i	$-0.552570\pi$
$79$	−2.92252	−0.328809	−0.164404	+	0.986393i	$0.552570\pi$
$80$	−1.06072	−0.118592
$81$	13.3444	1.48272
$82$	−12.8310	−1.41694
$83$	6.65119	0.730063	0.365031	−	0.930995i	$-0.381058\pi$
$83$	6.65119	0.730063	0.365031	+	0.930995i	$0.381058\pi$
$84$	−6.29618	−0.686969
$85$	−3.82360	−0.414727
$86$	21.7372	2.34398
$87$	−20.7361	−2.22314
$88$	−3.29739	−0.351503
$89$	−6.64813	−0.704700	−0.352350	−	0.935868i	$-0.614617\pi$
$89$	−6.64813	−0.704700	−0.352350	+	0.935868i	$0.614617\pi$
$90$	18.9657	1.99916
$91$	0.890242	0.0933227
$92$	−4.48920	−0.468032
$93$	−9.01267	−0.934570
$94$	−19.6166	−2.02330
$95$	−7.39413	−0.758621
$96$	−14.2644	−1.45586
$97$	−12.4665	−1.26578	−0.632891	−	0.774241i	$-0.718132\pi$
$97$	−12.4665	−1.26578	−0.632891	+	0.774241i	$0.718132\pi$
$98$	15.4563	1.56132
$99$	6.45928	0.649182
$100$	−11.6458	−1.16458
$101$	4.01472	0.399479	0.199740	−	0.979849i	$-0.435990\pi$
$101$	4.01472	0.399479	0.199740	+	0.979849i	$0.435990\pi$
$102$	21.6948	2.14811
$103$	−9.06336	−0.893040	−0.446520	−	0.894774i	$-0.647337\pi$
$103$	−9.06336	−0.893040	−0.446520	+	0.894774i	$0.647337\pi$
$104$	−4.89943	−0.480429
$105$	2.32475	0.226872
$106$	27.6788	2.68840
$107$	4.43708	0.428949	0.214474	−	0.976730i	$-0.431196\pi$
$107$	4.43708	0.428949	0.214474	+	0.976730i	$0.431196\pi$
$108$	−36.3522	−3.49799
$109$	13.3755	1.28114	0.640570	−	0.767900i	$-0.278698\pi$
$109$	13.3755	1.28114	0.640570	+	0.767900i	$0.278698\pi$
$110$	2.93620	0.279955
$111$	−2.32274	−0.220465
$112$	0.503751	0.0476000
$113$	−7.11965	−0.669760	−0.334880	−	0.942261i	$-0.608696\pi$
$113$	−7.11965	−0.669760	−0.334880	+	0.942261i	$0.608696\pi$
$114$	41.9538	3.92933
$115$	1.65756	0.154568
$116$	23.0363	2.13887
$117$	9.59754	0.887293
$118$	6.91339	0.636430
$119$	1.81589	0.166462
$120$	−12.7942	−1.16795
$121$	1.00000	0.0909091
$122$	4.48821	0.406343
$123$	−16.9558	−1.52885
$124$	10.0125	0.899145
$125$	10.6079	0.948798
$126$	−9.00713	−0.802419
$127$	−1.34382	−0.119245	−0.0596223	−	0.998221i	$-0.518990\pi$
$127$	−1.34382	−0.119245	−0.0596223	+	0.998221i	$0.518990\pi$
$128$	19.7604	1.74659
$129$	28.7252	2.52911
$130$	4.36275	0.382639
$131$	−2.41096	−0.210646	−0.105323	−	0.994438i	$-0.533588\pi$
$131$	−2.41096	−0.210646	−0.105323	+	0.994438i	$0.533588\pi$
$132$	−10.5086	−0.914656
$133$	3.51159	0.304494
$134$	15.2099	1.31393
$135$	13.4224	1.15521
$136$	−9.99372	−0.856955
$137$	−4.70465	−0.401945	−0.200973	−	0.979597i	$-0.564410\pi$
$137$	−4.70465	−0.401945	−0.200973	+	0.979597i	$0.564410\pi$
$138$	−9.40486	−0.800595
$139$	−8.67075	−0.735443	−0.367722	−	0.929936i	$-0.619862\pi$
$139$	−8.67075	−0.735443	−0.367722	+	0.929936i	$0.619862\pi$
$140$	−2.58263	−0.218272
$141$	−25.9228	−2.18309
$142$	19.9954	1.67798
$143$	1.48585	0.124253
$144$	5.43085	0.452571
$145$	−8.50573	−0.706363
$146$	12.6696	1.04854
$147$	20.4251	1.68463
$148$	2.58041	0.212108
$149$	15.8353	1.29728	0.648641	−	0.761094i	$-0.275338\pi$
$149$	15.8353	1.29728	0.648641	+	0.761094i	$0.275338\pi$
$150$	−24.3979	−1.99208
$151$	−7.08609	−0.576658	−0.288329	−	0.957531i	$-0.593100\pi$
$151$	−7.08609	−0.576658	−0.288329	+	0.957531i	$0.593100\pi$
$152$	−19.3260	−1.56755
$153$	19.5768	1.58269
$154$	−1.39445	−0.112368
$155$	−3.69691	−0.296943
$156$	−15.6142	−1.25014
$157$	9.84115	0.785409	0.392704	−	0.919665i	$-0.371540\pi$
$157$	9.84115	0.785409	0.392704	+	0.919665i	$0.371540\pi$
$158$	6.80186	0.541127
$159$	36.5768	2.90073
$160$	−5.85113	−0.462572
$161$	−0.787201	−0.0620401
$162$	−31.0578	−2.44013
$163$	−19.5654	−1.53248	−0.766240	−	0.642554i	$-0.777875\pi$
$163$	−19.5654	−1.53248	−0.766240	+	0.642554i	$0.777875\pi$
$164$	18.8367	1.47090
$165$	3.88011	0.302066
$166$	−15.4800	−1.20148
$167$	6.46145	0.500002	0.250001	−	0.968246i	$-0.419569\pi$
$167$	6.46145	0.500002	0.250001	+	0.968246i	$0.419569\pi$
$168$	6.07619	0.468788
$169$	−10.7922	−0.830172
$170$	8.89902	0.682524
$171$	37.8579	2.89506
$172$	−31.9117	−2.43324
$173$	−7.20310	−0.547642	−0.273821	−	0.961781i	$-0.588288\pi$
$173$	−7.20310	−0.547642	−0.273821	+	0.961781i	$0.588288\pi$
$174$	48.2610	3.65866
$175$	−2.04214	−0.154371
$176$	0.840783	0.0633764
$177$	9.13587	0.686694
$178$	15.4728	1.15974
$179$	−8.81980	−0.659223	−0.329612	−	0.944117i	$-0.606918\pi$
$179$	−8.81980	−0.659223	−0.329612	+	0.944117i	$0.606918\pi$
$180$	−27.8429	−2.07529
$181$	−9.19110	−0.683169	−0.341585	−	0.939851i	$-0.610964\pi$
$181$	−9.19110	−0.683169	−0.341585	+	0.939851i	$0.610964\pi$
$182$	−2.07194	−0.153583
$183$	5.93105	0.438436
$184$	4.33235	0.319385
$185$	−0.952768	−0.0700489
$186$	20.9761	1.53804
$187$	3.03080	0.221634
$188$	28.7984	2.10034
$189$	−6.37451	−0.463677
$190$	17.2091	1.24848
$191$	5.68987	0.411704	0.205852	−	0.978583i	$-0.434003\pi$
$191$	5.68987	0.411704	0.205852	+	0.978583i	$0.434003\pi$
$192$	38.3708	2.76917
$193$	12.9483	0.932037	0.466019	−	0.884775i	$-0.345688\pi$
$193$	12.9483	0.932037	0.466019	+	0.884775i	$0.345688\pi$
$194$	29.0145	2.08312
$195$	5.76527	0.412859
$196$	−22.6909	−1.62078
$197$	22.2473	1.58505	0.792527	−	0.609837i	$-0.208765\pi$
$197$	22.2473	1.58505	0.792527	+	0.609837i	$0.208765\pi$
$198$	−15.0333	−1.06837
$199$	14.0715	0.997500	0.498750	−	0.866746i	$-0.333793\pi$
$199$	14.0715	0.997500	0.498750	+	0.866746i	$0.333793\pi$
$200$	11.2389	0.794708
$201$	20.0995	1.41771
$202$	−9.34383	−0.657430
$203$	4.03951	0.283518
$204$	−31.8495	−2.22991
$205$	−6.95511	−0.485766
$206$	21.0940	1.46969
$207$	−8.48667	−0.589864
$208$	1.24928	0.0866220
$209$	5.86101	0.405414
$210$	−5.41061	−0.373367
$211$	−11.8254	−0.814093	−0.407046	−	0.913408i	$-0.633441\pi$
$211$	−11.8254	−0.814093	−0.407046	+	0.913408i	$0.633441\pi$
$212$	−40.6343	−2.79078
$213$	26.4234	1.81050
$214$	−10.3268	−0.705928
$215$	11.7828	0.803580
$216$	35.0820	2.38703
$217$	1.75573	0.119186
$218$	−31.1301	−2.10839
$219$	16.7425	1.13135
$220$	−4.31053	−0.290616
$221$	4.50332	0.302926
$222$	5.40595	0.362823
$223$	−12.8055	−0.857519	−0.428759	−	0.903419i	$-0.641049\pi$
$223$	−12.8055	−0.857519	−0.428759	+	0.903419i	$0.641049\pi$
$224$	2.77880	0.185666
$225$	−22.0159	−1.46773
$226$	16.5702	1.10224
$227$	−14.5984	−0.968930	−0.484465	−	0.874811i	$-0.660986\pi$
$227$	−14.5984	−0.968930	−0.484465	+	0.874811i	$0.660986\pi$
$228$	−61.5910	−4.07896
$229$	21.5271	1.42255	0.711276	−	0.702913i	$-0.248118\pi$
$229$	21.5271	1.42255	0.711276	+	0.702913i	$0.248118\pi$
$230$	−3.85779	−0.254375
$231$	−1.84273	−0.121243
$232$	−22.2314	−1.45956
$233$	−15.4722	−1.01362	−0.506808	−	0.862059i	$-0.669175\pi$
$233$	−15.4722	−1.01362	−0.506808	+	0.862059i	$0.669175\pi$
$234$	−22.3373	−1.46023
$235$	−10.6333	−0.693639
$236$	−10.1493	−0.660665
$237$	8.98848	0.583864
$238$	−4.22629	−0.273950
$239$	−25.8610	−1.67281	−0.836406	−	0.548111i	$-0.815347\pi$
$239$	−25.8610	−1.67281	−0.836406	+	0.548111i	$0.815347\pi$
$240$	3.26233	0.210582
$241$	20.7697	1.33790	0.668948	−	0.743309i	$-0.266745\pi$
$241$	20.7697	1.33790	0.668948	+	0.743309i	$0.266745\pi$
$242$	−2.32740	−0.149611
$243$	−9.12407	−0.585309
$244$	−6.58899	−0.421817
$245$	8.37818	0.535262
$246$	39.4628	2.51606
$247$	8.70859	0.554114
$248$	−9.66261	−0.613576
$249$	−20.4564	−1.29637
$250$	−24.6888	−1.56145
$251$	−1.62608	−0.102637	−0.0513185	−	0.998682i	$-0.516342\pi$
$251$	−1.62608	−0.102637	−0.0513185	+	0.998682i	$0.516342\pi$
$252$	13.2231	0.832974
$253$	−1.31387	−0.0826025
$254$	3.12760	0.196243
$255$	11.7598	0.736429
$256$	−21.0386	−1.31491
$257$	26.8034	1.67195	0.835975	−	0.548768i	$-0.184903\pi$
$257$	26.8034	1.67195	0.835975	+	0.548768i	$0.184903\pi$
$258$	−66.8548	−4.16220
$259$	0.452485	0.0281161
$260$	−6.40481	−0.397210
$261$	43.5493	2.69563
$262$	5.61125	0.346664
$263$	4.93641	0.304392	0.152196	−	0.988350i	$-0.451366\pi$
$263$	4.93641	0.304392	0.152196	+	0.988350i	$0.451366\pi$
$264$	10.1414	0.624162
$265$	15.0035	0.921656
$266$	−8.17287	−0.501111
$267$	20.4469	1.25133
$268$	−22.3291	−1.36397
$269$	−4.98870	−0.304167	−0.152083	−	0.988368i	$-0.548598\pi$
$269$	−4.98870	−0.304167	−0.152083	+	0.988368i	$0.548598\pi$
$270$	−31.2392	−1.90115
$271$	25.3831	1.54191	0.770957	−	0.636888i	$-0.219778\pi$
$271$	25.3831	1.54191	0.770957	+	0.636888i	$0.219778\pi$
$272$	2.54825	0.154510
$273$	−2.73802	−0.165713
$274$	10.9496	0.661488
$275$	−3.40842	−0.205535
$276$	13.8070	0.831082
$277$	−21.5445	−1.29448	−0.647242	−	0.762284i	$-0.724078\pi$
$277$	−21.5445	−1.29448	−0.647242	+	0.762284i	$0.724078\pi$
$278$	20.1803	1.21033
$279$	18.9282	1.13320
$280$	2.49239	0.148949
$281$	25.9749	1.54953	0.774767	−	0.632247i	$-0.217867\pi$
$281$	25.9749	1.54953	0.774767	+	0.632247i	$0.217867\pi$
$282$	60.3326	3.59276
$283$	−18.8315	−1.11942	−0.559709	−	0.828689i	$-0.689087\pi$
$283$	−18.8315	−1.11942	−0.559709	+	0.828689i	$0.689087\pi$
$284$	−29.3546	−1.74188
$285$	22.7413	1.34708
$286$	−3.45817	−0.204486
$287$	3.30310	0.194976
$288$	29.9577	1.76528
$289$	−7.81425	−0.459662
$290$	19.7962	1.16247
$291$	38.3419	2.24764
$292$	−18.5998	−1.08847
$293$	−17.7174	−1.03506	−0.517532	−	0.855664i	$-0.673149\pi$
$293$	−17.7174	−1.03506	−0.517532	+	0.855664i	$0.673149\pi$
$294$	−47.5373	−2.77243
$295$	3.74745	0.218185
$296$	−2.49025	−0.144743
$297$	−10.6393	−0.617357
$298$	−36.8551	−2.13496
$299$	−1.95222	−0.112900
$300$	35.8177	2.06794
$301$	−5.59584	−0.322539
$302$	16.4921	0.949016
$303$	−12.3476	−0.709353
$304$	4.92784	0.282631
$305$	2.43286	0.139305
$306$	−45.5629	−2.60466
$307$	9.95065	0.567914	0.283957	−	0.958837i	$-0.408353\pi$
$307$	9.95065	0.567914	0.283957	+	0.958837i	$0.408353\pi$
$308$	2.04714	0.116647
$309$	27.8752	1.58577
$310$	8.60418	0.488685
$311$	−6.58665	−0.373495	−0.186747	−	0.982408i	$-0.559795\pi$
$311$	−6.58665	−0.373495	−0.186747	+	0.982408i	$0.559795\pi$
$312$	15.0687	0.853095
$313$	−34.8239	−1.96837	−0.984183	−	0.177156i	$-0.943310\pi$
$313$	−34.8239	−1.96837	−0.984183	+	0.177156i	$0.943310\pi$
$314$	−22.9042	−1.29256
$315$	−4.88237	−0.275090
$316$	−9.98557	−0.561732
$317$	13.2304	0.743093	0.371546	−	0.928414i	$-0.378828\pi$
$317$	13.2304	0.743093	0.371546	+	0.928414i	$0.378828\pi$
$318$	−85.1288	−4.77379
$319$	6.74213	0.377487
$320$	15.7393	0.879855
$321$	−13.6467	−0.761682
$322$	1.83213	0.102100
$323$	17.7635	0.988390
$324$	45.5949	2.53305
$325$	−5.06441	−0.280923
$326$	45.5364	2.52203
$327$	−41.1376	−2.27491
$328$	−18.1785	−1.00374
$329$	5.04993	0.278411
$330$	−9.03054	−0.497115
$331$	10.5750	0.581254	0.290627	−	0.956836i	$-0.406136\pi$
$331$	10.5750	0.581254	0.290627	+	0.956836i	$0.406136\pi$
$332$	22.7256	1.24723
$333$	4.87817	0.267322
$334$	−15.0383	−0.822862
$335$	8.24462	0.450452
$336$	−1.54933	−0.0845231
$337$	14.6928	0.800365	0.400183	−	0.916435i	$-0.368947\pi$
$337$	14.6928	0.800365	0.400183	+	0.916435i	$0.368947\pi$
$338$	25.1178	1.36623
$339$	21.8972	1.18929
$340$	−13.0644	−0.708514
$341$	2.93038	0.158689
$342$	−88.1102	−4.76446
$343$	−8.17295	−0.441298
$344$	30.7966	1.66044
$345$	−5.09797	−0.274465
$346$	16.7645	0.901263
$347$	11.0607	0.593768	0.296884	−	0.954914i	$-0.404052\pi$
$347$	11.0607	0.593768	0.296884	+	0.954914i	$0.404052\pi$
$348$	−70.8503	−3.79798
$349$	−19.6971	−1.05436	−0.527180	−	0.849754i	$-0.676751\pi$
$349$	−19.6971	−1.05436	−0.527180	+	0.849754i	$0.676751\pi$
$350$	4.75286	0.254051
$351$	−15.8085	−0.843794
$352$	4.63794	0.247203
$353$	6.06512	0.322814	0.161407	−	0.986888i	$-0.448397\pi$
$353$	6.06512	0.322814	0.161407	+	0.986888i	$0.448397\pi$
$354$	−21.2628	−1.13010
$355$	10.8387	0.575256
$356$	−22.7151	−1.20390
$357$	−5.58494	−0.295586
$358$	20.5272	1.08489
$359$	18.9962	1.00258	0.501290	−	0.865279i	$-0.332859\pi$
$359$	18.9962	1.00258	0.501290	+	0.865279i	$0.332859\pi$
$360$	26.8701	1.41618
$361$	15.3514	0.807968
$362$	21.3913	1.12430
$363$	−3.07559	−0.161427
$364$	3.04175	0.159431
$365$	6.86763	0.359468
$366$	−13.8039	−0.721542
$367$	−18.4004	−0.960494	−0.480247	−	0.877133i	$-0.659453\pi$
$367$	−18.4004	−0.960494	−0.480247	+	0.877133i	$0.659453\pi$
$368$	−1.10468	−0.0575855
$369$	35.6101	1.85379
$370$	2.21747	0.115281
$371$	−7.12540	−0.369932
$372$	−30.7942	−1.59661
$373$	30.0371	1.55526	0.777632	−	0.628720i	$-0.216421\pi$
$373$	30.0371	1.55526	0.777632	+	0.628720i	$0.216421\pi$
$374$	−7.05387	−0.364747
$375$	−32.6256	−1.68478
$376$	−27.7922	−1.43327
$377$	10.0178	0.515944
$378$	14.8360	0.763081
$379$	8.65654	0.444656	0.222328	−	0.974972i	$-0.428634\pi$
$379$	8.65654	0.444656	0.222328	+	0.974972i	$0.428634\pi$
$380$	−25.2640	−1.29602
$381$	4.13304	0.211742
$382$	−13.2426	−0.677549
$383$	−18.6866	−0.954843	−0.477421	−	0.878674i	$-0.658428\pi$
$383$	−18.6866	−0.954843	−0.477421	+	0.878674i	$0.658428\pi$
$384$	−60.7751	−3.10142
$385$	−0.755869	−0.0385227
$386$	−30.1358	−1.53387
$387$	−60.3278	−3.06663
$388$	−42.5952	−2.16245
$389$	31.3284	1.58841	0.794206	−	0.607648i	$-0.207887\pi$
$389$	31.3284	1.58841	0.794206	+	0.607648i	$0.207887\pi$
$390$	−13.4181	−0.679450
$391$	−3.98209	−0.201383
$392$	21.8980	1.10602
$393$	7.41512	0.374044
$394$	−51.7782	−2.60855
$395$	3.68699	0.185513
$396$	22.0699	1.10905
$397$	−4.38014	−0.219833	−0.109916	−	0.993941i	$-0.535058\pi$
$397$	−4.38014	−0.219833	−0.109916	+	0.993941i	$0.535058\pi$
$398$	−32.7499	−1.64160
$399$	−10.8002	−0.540688
$400$	−2.86574	−0.143287
$401$	−0.895888	−0.0447385	−0.0223693	−	0.999750i	$-0.507121\pi$
$401$	−0.895888	−0.0447385	−0.0223693	+	0.999750i	$0.507121\pi$
$402$	−46.7794	−2.33315
$403$	4.35412	0.216894
$404$	13.7174	0.682464
$405$	−16.8351	−0.836541
$406$	−9.40155	−0.466591
$407$	0.755218	0.0374348
$408$	30.7366	1.52169
$409$	8.26149	0.408504	0.204252	−	0.978918i	$-0.434524\pi$
$409$	8.26149	0.408504	0.204252	+	0.978918i	$0.434524\pi$
$410$	16.1873	0.799433
$411$	14.4696	0.713732
$412$	−30.9674	−1.52566
$413$	−1.77973	−0.0875746
$414$	19.7518	0.970750
$415$	−8.39101	−0.411898
$416$	6.89130	0.337874
$417$	26.6677	1.30592
$418$	−13.6409	−0.667197
$419$	−32.8640	−1.60551	−0.802756	−	0.596307i	$-0.796634\pi$
$419$	−32.8640	−1.60551	−0.802756	+	0.596307i	$0.796634\pi$
$420$	7.94313	0.387585
$421$	1.08937	0.0530928	0.0265464	−	0.999648i	$-0.491549\pi$
$421$	1.08937	0.0530928	0.0265464	+	0.999648i	$0.491549\pi$
$422$	27.5223	1.33977
$423$	54.4424	2.64708
$424$	39.2145	1.90443
$425$	−10.3302	−0.501090
$426$	−61.4978	−2.97958
$427$	−1.15541	−0.0559141
$428$	15.1605	0.732810
$429$	−4.56988	−0.220636
$430$	−27.4232	−1.32247
$431$	−24.5816	−1.18406	−0.592028	−	0.805917i	$-0.701672\pi$
$431$	−24.5816	−1.18406	−0.592028	+	0.805917i	$0.701672\pi$
$432$	−8.94537	−0.430385
$433$	−25.5381	−1.22728	−0.613641	−	0.789585i	$-0.710296\pi$
$433$	−25.5381	−1.22728	−0.613641	+	0.789585i	$0.710296\pi$
$434$	−4.08627	−0.196147
$435$	26.1602	1.25428
$436$	45.7010	2.18868
$437$	−7.70062	−0.368370
$438$	−38.9665	−1.86189
$439$	−5.15845	−0.246199	−0.123100	−	0.992394i	$-0.539283\pi$
$439$	−5.15845	−0.246199	−0.123100	+	0.992394i	$0.539283\pi$
$440$	4.15992	0.198316
$441$	−42.8962	−2.04268
$442$	−10.4810	−0.498531
$443$	−27.1359	−1.28926	−0.644632	−	0.764493i	$-0.722990\pi$
$443$	−27.1359	−1.28926	−0.644632	+	0.764493i	$0.722990\pi$
$444$	−7.93629	−0.376640
$445$	8.38714	0.397589
$446$	29.8034	1.41123
$447$	−48.7031	−2.30358
$448$	−7.47487	−0.353154
$449$	−24.9526	−1.17758	−0.588792	−	0.808284i	$-0.700396\pi$
$449$	−24.9526	−1.17758	−0.588792	+	0.808284i	$0.700396\pi$
$450$	51.2397	2.41546
$451$	5.51301	0.259598
$452$	−24.3262	−1.14421
$453$	21.7939	1.02397
$454$	33.9763	1.59459
$455$	−1.12311	−0.0526522
$456$	59.4389	2.78348
$457$	−16.2422	−0.759779	−0.379889	−	0.925032i	$-0.624038\pi$
$457$	−16.2422	−0.759779	−0.379889	+	0.925032i	$0.624038\pi$
$458$	−50.1021	−2.34112
$459$	−32.2457	−1.50510
$460$	5.66349	0.264061
$461$	−3.86531	−0.180025	−0.0900127	−	0.995941i	$-0.528691\pi$
$461$	−3.86531	−0.180025	−0.0900127	+	0.995941i	$0.528691\pi$
$462$	4.28876	0.199531
$463$	9.76584	0.453857	0.226928	−	0.973911i	$-0.427132\pi$
$463$	9.76584	0.453857	0.226928	+	0.973911i	$0.427132\pi$
$464$	5.66867	0.263161
$465$	11.3702	0.527281
$466$	36.0099	1.66813
$467$	−5.12102	−0.236973	−0.118486	−	0.992956i	$-0.537804\pi$
$467$	−5.12102	−0.236973	−0.118486	+	0.992956i	$0.537804\pi$
$468$	32.7926	1.51584
$469$	−3.91551	−0.180801
$470$	24.7479	1.14153
$471$	−30.2674	−1.39465
$472$	9.79470	0.450838
$473$	−9.33971	−0.429440
$474$	−20.9197	−0.960876
$475$	−19.9767	−0.916596
$476$	6.20448	0.284382
$477$	−76.8177	−3.51724
$478$	60.1889	2.75297
$479$	−33.9782	−1.55250	−0.776252	−	0.630423i	$-0.782882\pi$
$479$	−33.9782	−1.55250	−0.776252	+	0.630423i	$0.782882\pi$
$480$	17.9957	0.821388
$481$	1.12214	0.0511653
$482$	−48.3394	−2.20180
$483$	2.42111	0.110164
$484$	3.41677	0.155308
$485$	15.7275	0.714149
$486$	21.2353	0.963254
$487$	−34.9174	−1.58226	−0.791130	−	0.611648i	$-0.790507\pi$
$487$	−34.9174	−1.58226	−0.791130	+	0.611648i	$0.790507\pi$
$488$	6.35877	0.287848
$489$	60.1752	2.72122
$490$	−19.4993	−0.880891
$491$	−0.442418	−0.0199660	−0.00998302	−	0.999950i	$-0.503178\pi$
$491$	−0.442418	−0.0199660	−0.00998302	+	0.999950i	$0.503178\pi$
$492$	−57.9341	−2.61187
$493$	20.4340	0.920303
$494$	−20.2683	−0.911916
$495$	−8.14889	−0.366266
$496$	2.46382	0.110629
$497$	−5.14746	−0.230895
$498$	47.6100	2.13346
$499$	−23.7518	−1.06328	−0.531638	−	0.846972i	$-0.678423\pi$
$499$	−23.7518	−1.06328	−0.531638	+	0.846972i	$0.678423\pi$
$500$	36.2447	1.62091
$501$	−19.8728	−0.887851
$502$	3.78452	0.168911
$503$	29.1178	1.29830	0.649149	−	0.760662i	$-0.275125\pi$
$503$	29.1178	1.29830	0.649149	+	0.760662i	$0.275125\pi$
$504$	−12.7610	−0.568422
$505$	−5.06488	−0.225384
$506$	3.05790	0.135940
$507$	33.1926	1.47413
$508$	−4.59152	−0.203716
$509$	0.324499	0.0143832	0.00719158	−	0.999974i	$-0.497711\pi$
$509$	0.324499	0.0143832	0.00719158	+	0.999974i	$0.497711\pi$
$510$	−27.3698	−1.21195
$511$	−3.26155	−0.144282
$512$	9.44428	0.417382
$513$	−62.3572	−2.75314
$514$	−62.3821	−2.75156
$515$	11.4342	0.503849
$516$	98.1473	4.32069
$517$	8.42855	0.370687
$518$	−1.05311	−0.0462711
$519$	22.1538	0.972445
$520$	6.18102	0.271056
$521$	−23.3740	−1.02403	−0.512017	−	0.858975i	$-0.671102\pi$
$521$	−23.3740	−1.02403	−0.512017	+	0.858975i	$0.671102\pi$
$522$	−101.356	−4.43625
$523$	−37.8723	−1.65604	−0.828020	−	0.560698i	$-0.810533\pi$
$523$	−37.8723	−1.65604	−0.828020	+	0.560698i	$0.810533\pi$
$524$	−8.23769	−0.359865
$525$	6.28078	0.274116
$526$	−11.4890	−0.500943
$527$	8.88141	0.386880
$528$	−2.58591	−0.112537
$529$	−21.2737	−0.924945
$530$	−34.9190	−1.51679
$531$	−19.1869	−0.832641
$532$	11.9983	0.520193
$533$	8.19153	0.354814
$534$	−47.5881	−2.05934
$535$	−5.59773	−0.242011
$536$	21.5489	0.930772
$537$	27.1261	1.17058
$538$	11.6107	0.500572
$539$	−6.64103	−0.286049
$540$	45.8612	1.97355
$541$	−4.25778	−0.183056	−0.0915281	−	0.995802i	$-0.529175\pi$
$541$	−4.25778	−0.183056	−0.0915281	+	0.995802i	$0.529175\pi$
$542$	−59.0765	−2.53755
$543$	28.2681	1.21310
$544$	14.0567	0.602675
$545$	−16.8742	−0.722813
$546$	6.37246	0.272716
$547$	1.00000	0.0427569
$547$	1.00000	0.0427569
$548$	−16.0747	−0.686677
$549$	−12.4562	−0.531619
$550$	7.93273	0.338253
$551$	39.5157	1.68342
$552$	−13.3245	−0.567130
$553$	−1.75101	−0.0744606
$554$	50.1426	2.13036
$555$	2.93033	0.124385
$556$	−29.6260	−1.25642
$557$	11.6817	0.494969	0.247485	−	0.968892i	$-0.420396\pi$
$557$	11.6817	0.494969	0.247485	+	0.968892i	$0.420396\pi$
$558$	−44.0533	−1.86493
$559$	−13.8774	−0.586953
$560$	−0.635522	−0.0268557
$561$	−9.32151	−0.393555
$562$	−60.4539	−2.55010
$563$	−19.6636	−0.828721	−0.414360	−	0.910113i	$-0.635995\pi$
$563$	−19.6636	−0.828721	−0.414360	+	0.910113i	$0.635995\pi$
$564$	−88.5723	−3.72957
$565$	8.98201	0.377876
$566$	43.8284	1.84225
$567$	7.99526	0.335769
$568$	28.3290	1.18866
$569$	6.22920	0.261142	0.130571	−	0.991439i	$-0.458319\pi$
$569$	6.22920	0.261142	0.130571	+	0.991439i	$0.458319\pi$
$570$	−52.9281	−2.21691
$571$	29.0965	1.21765	0.608826	−	0.793304i	$-0.291641\pi$
$571$	29.0965	1.21765	0.608826	+	0.793304i	$0.291641\pi$
$572$	5.07682	0.212272
$573$	−17.4997	−0.731061
$574$	−7.68761	−0.320875
$575$	4.47823	0.186755
$576$	−80.5852	−3.35772
$577$	−2.46159	−0.102477	−0.0512387	−	0.998686i	$-0.516317\pi$
$577$	−2.46159	−0.102477	−0.0512387	+	0.998686i	$0.516317\pi$
$578$	18.1868	0.756473
$579$	−39.8236	−1.65501
$580$	−29.0621	−1.20674
$581$	3.98503	0.165327
$582$	−89.2369	−3.69899
$583$	−11.8926	−0.492542
$584$	17.9499	0.742772
$585$	−12.1081	−0.500607
$586$	41.2355	1.70342
$587$	15.9484	0.658261	0.329130	−	0.944285i	$-0.393244\pi$
$587$	15.9484	0.658261	0.329130	+	0.944285i	$0.393244\pi$
$588$	69.7879	2.87800
$589$	17.1750	0.707683
$590$	−8.72180	−0.359071
$591$	−68.4236	−2.81457
$592$	0.634975	0.0260973
$593$	−12.7634	−0.524130	−0.262065	−	0.965050i	$-0.584403\pi$
$593$	−12.7634	−0.524130	−0.262065	+	0.965050i	$0.584403\pi$
$594$	24.7619	1.01599
$595$	−2.29089	−0.0939173
$596$	54.1058	2.21626
$597$	−43.2781	−1.77126
$598$	4.54359	0.185801
$599$	9.87514	0.403487	0.201744	−	0.979438i	$-0.435339\pi$
$599$	9.87514	0.403487	0.201744	+	0.979438i	$0.435339\pi$
$600$	−34.5662	−1.41116
$601$	−6.94106	−0.283132	−0.141566	−	0.989929i	$-0.545214\pi$
$601$	−6.94106	−0.283132	−0.141566	+	0.989929i	$0.545214\pi$
$602$	13.0237	0.530808
$603$	−42.2124	−1.71902
$604$	−24.2115	−0.985154
$605$	−1.26158	−0.0512905
$606$	28.7378	1.16739
$607$	29.2989	1.18921	0.594603	−	0.804019i	$-0.297309\pi$
$607$	29.2989	1.18921	0.594603	+	0.804019i	$0.297309\pi$
$608$	27.1830	1.10242
$609$	−12.4239	−0.503442
$610$	−5.66223	−0.229257
$611$	12.5236	0.506650
$612$	66.8894	2.70384
$613$	31.3333	1.26554	0.632770	−	0.774340i	$-0.281918\pi$
$613$	31.3333	1.26554	0.632770	+	0.774340i	$0.281918\pi$
$614$	−23.1591	−0.934625
$615$	21.3911	0.862572
$616$	−1.97561	−0.0795998
$617$	20.2638	0.815792	0.407896	−	0.913028i	$-0.366263\pi$
$617$	20.2638	0.815792	0.407896	+	0.913028i	$0.366263\pi$
$618$	−64.8767	−2.60972
$619$	−14.3073	−0.575058	−0.287529	−	0.957772i	$-0.592834\pi$
$619$	−14.3073	−0.575058	−0.287529	+	0.957772i	$0.592834\pi$
$620$	−12.6315	−0.507293
$621$	13.9787	0.560947
$622$	15.3297	0.614666
$623$	−3.98319	−0.159583
$624$	−3.84228	−0.153814
$625$	3.65939	0.146376
$626$	81.0491	3.23937
$627$	−18.0261	−0.719892
$628$	33.6249	1.34178
$629$	2.28892	0.0912651
$630$	11.3632	0.452721
$631$	−3.15968	−0.125785	−0.0628924	−	0.998020i	$-0.520033\pi$
$631$	−3.15968	−0.125785	−0.0628924	+	0.998020i	$0.520033\pi$
$632$	9.63667	0.383326
$633$	36.3701	1.44558
$634$	−30.7924	−1.22292
$635$	1.69533	0.0672773
$636$	124.975	4.95557
$637$	−9.86759	−0.390968
$638$	−15.6916	−0.621237
$639$	−55.4938	−2.19530
$640$	−24.9294	−0.985420
$641$	32.0601	1.26630	0.633150	−	0.774029i	$-0.281762\pi$
$641$	32.0601	1.26630	0.633150	+	0.774029i	$0.281762\pi$
$642$	31.7612	1.25351
$643$	−16.4784	−0.649844	−0.324922	−	0.945741i	$-0.605338\pi$
$643$	−16.4784	−0.649844	−0.324922	+	0.945741i	$0.605338\pi$
$644$	−2.68968	−0.105988
$645$	−36.2391	−1.42691
$646$	−41.3428	−1.62661
$647$	−10.4922	−0.412491	−0.206245	−	0.978500i	$-0.566125\pi$
$647$	−10.4922	−0.412491	−0.206245	+	0.978500i	$0.566125\pi$
$648$	−44.0018	−1.72855
$649$	−2.97044	−0.116600
$650$	11.7869	0.462319
$651$	−5.39990	−0.211639
$652$	−66.8505	−2.61807
$653$	−34.9327	−1.36702	−0.683511	−	0.729940i	$-0.739548\pi$
$653$	−34.9327	−1.36702	−0.683511	+	0.729940i	$0.739548\pi$
$654$	95.7434	3.74386
$655$	3.04161	0.118846
$656$	4.63525	0.180976
$657$	−35.1622	−1.37181
$658$	−11.7532	−0.458187
$659$	−15.5209	−0.604608	−0.302304	−	0.953212i	$-0.597756\pi$
$659$	−15.5209	−0.604608	−0.302304	+	0.953212i	$0.597756\pi$
$660$	13.2574	0.516045
$661$	27.8124	1.08178	0.540888	−	0.841095i	$-0.318088\pi$
$661$	27.8124	1.08178	0.540888	+	0.841095i	$0.318088\pi$
$662$	−24.6122	−0.956579
$663$	−13.8504	−0.537905
$664$	−21.9316	−0.851109
$665$	−4.43015	−0.171794
$666$	−11.3534	−0.439936
$667$	−8.85830	−0.342995
$668$	22.0773	0.854196
$669$	39.3845	1.52269
$670$	−19.1885	−0.741316
$671$	−1.92843	−0.0744460
$672$	−8.54646	−0.329687
$673$	−16.6229	−0.640764	−0.320382	−	0.947288i	$-0.603811\pi$
$673$	−16.6229	−0.640764	−0.320382	+	0.947288i	$0.603811\pi$
$674$	−34.1959	−1.31718
$675$	36.2633	1.39577
$676$	−36.8746	−1.41825
$677$	13.3423	0.512785	0.256393	−	0.966573i	$-0.417466\pi$
$677$	13.3423	0.512785	0.256393	+	0.966573i	$0.417466\pi$
$678$	−50.9633	−1.95724
$679$	−7.46925	−0.286644
$680$	12.6079	0.483490
$681$	44.8988	1.72052
$682$	−6.82016	−0.261158
$683$	26.4190	1.01090	0.505448	−	0.862857i	$-0.331327\pi$
$683$	26.4190	1.01090	0.505448	+	0.862857i	$0.331327\pi$
$684$	129.352	4.94588
$685$	5.93529	0.226776
$686$	19.0217	0.726252
$687$	−66.2086	−2.52602
$688$	−7.85267	−0.299380
$689$	−17.6707	−0.673199
$690$	11.8650	0.451692
$691$	10.5924	0.402952	0.201476	−	0.979493i	$-0.435426\pi$
$691$	10.5924	0.402952	0.201476	+	0.979493i	$0.435426\pi$
$692$	−24.6114	−0.935583
$693$	3.87005	0.147011
$694$	−25.7426	−0.977175
$695$	10.9388	0.414934
$696$	68.3748	2.59174
$697$	16.7088	0.632893
$698$	45.8428	1.73518
$699$	47.5861	1.79987
$700$	−6.97751	−0.263725
$701$	−45.5990	−1.72225	−0.861125	−	0.508394i	$-0.830239\pi$
$701$	−45.5990	−1.72225	−0.861125	+	0.508394i	$0.830239\pi$
$702$	36.7926	1.38865
$703$	4.42634	0.166943
$704$	−12.4759	−0.470203
$705$	32.7037	1.23169
$706$	−14.1159	−0.531260
$707$	2.40540	0.0904643
$708$	31.2152	1.17314
$709$	35.5322	1.33444	0.667220	−	0.744861i	$-0.267484\pi$
$709$	35.5322	1.33444	0.667220	+	0.744861i	$0.267484\pi$
$710$	−25.2258	−0.946708
$711$	−18.8774	−0.707956
$712$	21.9215	0.821541
$713$	−3.85015	−0.144189
$714$	12.9984	0.486452
$715$	−1.87452	−0.0701031
$716$	−30.1353	−1.12621
$717$	79.5380	2.97040
$718$	−44.2116	−1.64996
$719$	−18.5736	−0.692680	−0.346340	−	0.938109i	$-0.612576\pi$
$719$	−18.5736	−0.692680	−0.346340	+	0.938109i	$0.612576\pi$
$720$	−6.85145	−0.255339
$721$	−5.43027	−0.202234
$722$	−35.7288	−1.32969
$723$	−63.8793	−2.37570
$724$	−31.4039	−1.16712
$725$	−22.9800	−0.853455
$726$	7.15812	0.265663
$727$	−17.0223	−0.631321	−0.315660	−	0.948872i	$-0.602226\pi$
$727$	−17.0223	−0.631321	−0.315660	+	0.948872i	$0.602226\pi$
$728$	−2.93547	−0.108796
$729$	−11.9714	−0.443384
$730$	−15.9837	−0.591583
$731$	−28.3068	−1.04697
$732$	20.2651	0.749018
$733$	31.7063	1.17110	0.585550	−	0.810636i	$-0.300879\pi$
$733$	31.7063	1.17110	0.585550	+	0.810636i	$0.300879\pi$
$734$	42.8250	1.58070
$735$	−25.7679	−0.950463
$736$	−6.09366	−0.224615
$737$	−6.53515	−0.240725
$738$	−82.8788	−3.05081
$739$	10.5885	0.389503	0.194751	−	0.980853i	$-0.437610\pi$
$739$	10.5885	0.389503	0.194751	+	0.980853i	$0.437610\pi$
$740$	−3.25539	−0.119671
$741$	−26.7841	−0.983938
$742$	16.5836	0.608804
$743$	−0.934902	−0.0342982	−0.0171491	−	0.999853i	$-0.505459\pi$
$743$	−0.934902	−0.0342982	−0.0171491	+	0.999853i	$0.505459\pi$
$744$	29.7183	1.08952
$745$	−19.9776	−0.731921
$746$	−69.9083	−2.55952
$747$	42.9619	1.57189
$748$	10.3556	0.378636
$749$	2.65845	0.0971378
$750$	75.9326	2.77267
$751$	20.9014	0.762702	0.381351	−	0.924430i	$-0.375459\pi$
$751$	20.9014	0.762702	0.381351	+	0.924430i	$0.375459\pi$
$752$	7.08659	0.258421
$753$	5.00115	0.182252
$754$	−23.3154	−0.849097
$755$	8.93967	0.325348
$756$	−21.7802	−0.792139
$757$	−47.3148	−1.71969	−0.859844	−	0.510558i	$-0.829439\pi$
$757$	−47.3148	−1.71969	−0.859844	+	0.510558i	$0.829439\pi$
$758$	−20.1472	−0.731779
$759$	4.04094	0.146677
$760$	24.3813	0.884403
$761$	−6.35314	−0.230301	−0.115151	−	0.993348i	$-0.536735\pi$
$761$	−6.35314	−0.230301	−0.115151	+	0.993348i	$0.536735\pi$
$762$	−9.61922	−0.348468
$763$	8.01386	0.290121
$764$	19.4410	0.703350
$765$	−24.6977	−0.892946
$766$	43.4912	1.57140
$767$	−4.41364	−0.159367
$768$	64.7062	2.33488
$769$	−36.6873	−1.32298	−0.661490	−	0.749954i	$-0.730075\pi$
$769$	−36.6873	−1.32298	−0.661490	+	0.749954i	$0.730075\pi$
$770$	1.75921	0.0633974
$771$	−82.4364	−2.96887
$772$	44.2413	1.59228
$773$	1.47629	0.0530984	0.0265492	−	0.999648i	$-0.491548\pi$
$773$	1.47629	0.0530984	0.0265492	+	0.999648i	$0.491548\pi$
$774$	140.407	5.04681
$775$	−9.98797	−0.358778
$776$	41.1069	1.47565
$777$	−1.39166	−0.0499256
$778$	−72.9136	−2.61408
$779$	32.3118	1.15769
$780$	19.6986	0.705323
$781$	−8.59133	−0.307422
$782$	9.26789	0.331419
$783$	−71.7318	−2.56348
$784$	−5.58366	−0.199417
$785$	−12.4154	−0.443124
$786$	−17.2579	−0.615570
$787$	20.5342	0.731965	0.365982	−	0.930622i	$-0.380733\pi$
$787$	20.5342	0.731965	0.365982	+	0.930622i	$0.380733\pi$
$788$	76.0139	2.70788
$789$	−15.1824	−0.540507
$790$	−8.58108	−0.305301
$791$	−4.26570	−0.151671
$792$	−21.2987	−0.756818
$793$	−2.86536	−0.101752
$794$	10.1943	0.361782
$795$	−46.1446	−1.63658
$796$	48.0790	1.70411
$797$	−12.5303	−0.443845	−0.221922	−	0.975064i	$-0.571233\pi$
$797$	−12.5303	−0.443845	−0.221922	+	0.975064i	$0.571233\pi$
$798$	25.1364	0.889820
$799$	25.5453	0.903726
$800$	−15.8080	−0.558898
$801$	−42.9421	−1.51728
$802$	2.08509	0.0736270
$803$	−5.44367	−0.192103
$804$	68.6753	2.42199
$805$	0.993116	0.0350027
$806$	−10.1338	−0.356946
$807$	15.3432	0.540107
$808$	−13.2381	−0.465714
$809$	−25.2177	−0.886608	−0.443304	−	0.896371i	$-0.646194\pi$
$809$	−25.2177	−0.886608	−0.443304	+	0.896371i	$0.646194\pi$
$810$	39.1819	1.37671
$811$	35.4366	1.24435	0.622175	−	0.782879i	$-0.286249\pi$
$811$	35.4366	1.24435	0.622175	+	0.782879i	$0.286249\pi$
$812$	13.8021	0.484359
$813$	−78.0681	−2.73797
$814$	−1.75769	−0.0616071
$815$	24.6833	0.864619
$816$	−7.83737	−0.274363
$817$	−54.7401	−1.91511
$818$	−19.2277	−0.672282
$819$	5.75032	0.200932
$820$	−23.7640	−0.829875
$821$	41.1793	1.43717	0.718584	−	0.695441i	$-0.244791\pi$
$821$	41.1793	1.43717	0.718584	+	0.695441i	$0.244791\pi$
$822$	−33.6764	−1.17460
$823$	−29.0771	−1.01356	−0.506782	−	0.862074i	$-0.669165\pi$
$823$	−29.0771	−1.01356	−0.506782	+	0.862074i	$0.669165\pi$
$824$	29.8854	1.04111
$825$	10.4829	0.364968
$826$	4.14213	0.144123
$827$	43.2599	1.50429	0.752147	−	0.658996i	$-0.229019\pi$
$827$	43.2599	1.50429	0.752147	+	0.658996i	$0.229019\pi$
$828$	−28.9970	−1.00772
$829$	33.4857	1.16301	0.581503	−	0.813544i	$-0.302465\pi$
$829$	33.4857	1.16301	0.581503	+	0.813544i	$0.302465\pi$
$830$	19.5292	0.677868
$831$	66.2622	2.29861
$832$	−18.5373	−0.642666
$833$	−20.1276	−0.697381
$834$	−62.0663	−2.14918
$835$	−8.15163	−0.282099
$836$	20.0257	0.692604
$837$	−31.1773	−1.07765
$838$	76.4876	2.64222
$839$	8.70338	0.300474	0.150237	−	0.988650i	$-0.451996\pi$
$839$	8.70338	0.300474	0.150237	+	0.988650i	$0.451996\pi$
$840$	−7.66559	−0.264488
$841$	16.4563	0.567459
$842$	−2.53540	−0.0873758
$843$	−79.8883	−2.75150
$844$	−40.4046	−1.39078
$845$	13.6153	0.468380
$846$	−126.709	−4.35634
$847$	0.599145	0.0205869
$848$	−9.99911	−0.343371
$849$	57.9182	1.98775
$850$	24.0425	0.824652
$851$	−0.992261	−0.0340143
$852$	90.2829	3.09304
$853$	15.0584	0.515590	0.257795	−	0.966200i	$-0.417004\pi$
$853$	15.0584	0.515590	0.257795	+	0.966200i	$0.417004\pi$
$854$	2.68909	0.0920187
$855$	−47.7607	−1.63338
$856$	−14.6308	−0.500069
$857$	−16.9262	−0.578189	−0.289094	−	0.957301i	$-0.593354\pi$
$857$	−16.9262	−0.578189	−0.289094	+	0.957301i	$0.593354\pi$
$858$	10.6359	0.363104
$859$	−35.4021	−1.20791	−0.603953	−	0.797020i	$-0.706408\pi$
$859$	−35.4021	−1.20791	−0.603953	+	0.797020i	$0.706408\pi$
$860$	40.2591	1.37282
$861$	−10.1590	−0.346217
$862$	57.2112	1.94862
$863$	−42.8410	−1.45833	−0.729163	−	0.684340i	$-0.760090\pi$
$863$	−42.8410	−1.45833	−0.729163	+	0.684340i	$0.760090\pi$
$864$	−49.3446	−1.67874
$865$	9.08729	0.308977
$866$	59.4372	2.01976
$867$	24.0335	0.816219
$868$	5.99891	0.203616
$869$	−2.92252	−0.0991396
$870$	−60.8851	−2.06420
$871$	−9.71028	−0.329020
$872$	−44.1042	−1.49356
$873$	−80.5247	−2.72535
$874$	17.9224	0.606234
$875$	6.35567	0.214861
$876$	57.2054	1.93279
$877$	−26.2919	−0.887816	−0.443908	−	0.896072i	$-0.646408\pi$
$877$	−26.2919	−0.887816	−0.443908	+	0.896072i	$0.646408\pi$
$878$	12.0057	0.405174
$879$	54.4916	1.83796
$880$	−1.06072	−0.0357567
$881$	−34.4620	−1.16106	−0.580528	−	0.814240i	$-0.697154\pi$
$881$	−34.4620	−1.16106	−0.580528	+	0.814240i	$0.697154\pi$
$882$	99.8365	3.36167
$883$	−4.28090	−0.144064	−0.0720318	−	0.997402i	$-0.522948\pi$
$883$	−4.28090	−0.144064	−0.0720318	+	0.997402i	$0.522948\pi$
$884$	15.3868	0.517515
$885$	−11.5256	−0.387430
$886$	63.1559	2.12177
$887$	16.7400	0.562073	0.281037	−	0.959697i	$-0.409322\pi$
$887$	16.7400	0.562073	0.281037	+	0.959697i	$0.409322\pi$
$888$	7.65899	0.257019
$889$	−0.805143	−0.0270036
$890$	−19.5202	−0.654319
$891$	13.3444	0.447056
$892$	−43.7534	−1.46497
$893$	49.3998	1.65310
$894$	113.351	3.79104
$895$	11.1269	0.371931
$896$	11.8394	0.395526
$897$	6.00424	0.200476
$898$	58.0745	1.93797
$899$	19.7570	0.658934
$900$	−75.2233	−2.50744
$901$	−36.0441	−1.20080
$902$	−12.8310	−0.427224
$903$	17.2105	0.572731
$904$	23.4762	0.780808
$905$	11.5953	0.385441
$906$	−50.7231	−1.68516
$907$	22.4839	0.746566	0.373283	−	0.927717i	$-0.378232\pi$
$907$	22.4839	0.746566	0.373283	+	0.927717i	$0.378232\pi$
$908$	−49.8794	−1.65531
$909$	25.9322	0.860116
$910$	2.61392	0.0866507
$911$	−24.5921	−0.814772	−0.407386	−	0.913256i	$-0.633560\pi$
$911$	−24.5921	−0.814772	−0.407386	+	0.913256i	$0.633560\pi$
$912$	−15.1560	−0.501866
$913$	6.65119	0.220122
$914$	37.8021	1.25038
$915$	−7.48250	−0.247364
$916$	73.5532	2.43027
$917$	−1.44451	−0.0477020
$918$	75.0485	2.47697
$919$	−4.09733	−0.135158	−0.0675792	−	0.997714i	$-0.521528\pi$
$919$	−4.09733	−0.135158	−0.0675792	+	0.997714i	$0.521528\pi$
$920$	−5.46560	−0.180196
$921$	−30.6042	−1.00844
$922$	8.99611	0.296271
$923$	−12.7655	−0.420180
$924$	−6.29618	−0.207129
$925$	−2.57410	−0.0846358
$926$	−22.7290	−0.746920
$927$	−58.5428	−1.92280
$928$	31.2696	1.02647
$929$	−30.4192	−0.998020	−0.499010	−	0.866596i	$-0.666303\pi$
$929$	−30.4192	−0.998020	−0.499010	+	0.866596i	$0.666303\pi$
$930$	−26.4630	−0.867755
$931$	−38.9231	−1.27565
$932$	−52.8649	−1.73165
$933$	20.2579	0.663212
$934$	11.9187	0.389990
$935$	−3.82360	−0.125045
$936$	−31.6468	−1.03441
$937$	−25.3829	−0.829224	−0.414612	−	0.909998i	$-0.636083\pi$
$937$	−25.3829	−0.829224	−0.414612	+	0.909998i	$0.636083\pi$
$938$	9.11293	0.297548
$939$	107.104	3.49522
$940$	−36.3315	−1.18500
$941$	29.7991	0.971422	0.485711	−	0.874119i	$-0.338561\pi$
$941$	29.7991	0.971422	0.485711	+	0.874119i	$0.338561\pi$
$942$	70.4441	2.29519
$943$	−7.24340	−0.235877
$944$	−2.49750	−0.0812866
$945$	8.04195	0.261605
$946$	21.7372	0.706738
$947$	32.2793	1.04893	0.524467	−	0.851430i	$-0.324264\pi$
$947$	32.2793	1.04893	0.524467	+	0.851430i	$0.324264\pi$
$948$	30.7116	0.997466
$949$	−8.08849	−0.262564
$950$	46.4938	1.50846
$951$	−40.6913	−1.31951
$952$	−5.98769	−0.194062
$953$	−41.6583	−1.34945	−0.674723	−	0.738071i	$-0.735737\pi$
$953$	−41.6583	−1.34945	−0.674723	+	0.738071i	$0.735737\pi$
$954$	178.785	5.78838
$955$	−7.17822	−0.232282
$956$	−88.3612	−2.85781
$957$	−20.7361	−0.670301
$958$	79.0807	2.55498
$959$	−2.81877	−0.0910227
$960$	−48.4078	−1.56235
$961$	−22.4129	−0.722995
$962$	−2.61167	−0.0842037
$963$	28.6603	0.923566
$964$	70.9655	2.28564
$965$	−16.3353	−0.525851
$966$	−5.63488	−0.181299
$967$	10.2163	0.328534	0.164267	−	0.986416i	$-0.447474\pi$
$967$	10.2163	0.328534	0.164267	+	0.986416i	$0.447474\pi$
$968$	−3.29739	−0.105982
$969$	−54.6334	−1.75508
$970$	−36.6041	−1.17529
$971$	22.4164	0.719375	0.359687	−	0.933073i	$-0.382883\pi$
$971$	22.4164	0.719375	0.359687	+	0.933073i	$0.382883\pi$
$972$	−31.1749	−0.999934
$973$	−5.19504	−0.166545
$974$	81.2667	2.60395
$975$	15.5761	0.498833
$976$	−1.62139	−0.0518994
$977$	34.1828	1.09360	0.546802	−	0.837262i	$-0.315845\pi$
$977$	34.1828	1.09360	0.546802	+	0.837262i	$0.315845\pi$
$978$	−140.052	−4.47836
$979$	−6.64813	−0.212475
$980$	28.6263	0.914435
$981$	86.3960	2.75841
$982$	1.02968	0.0328585
$983$	−37.1639	−1.18535	−0.592673	−	0.805443i	$-0.701927\pi$
$983$	−37.1639	−1.18535	−0.592673	+	0.805443i	$0.701927\pi$
$984$	55.9098	1.78234
$985$	−28.0667	−0.894280
$986$	−47.5581	−1.51456
$987$	−15.5315	−0.494374
$988$	29.7553	0.946641
$989$	12.2712	0.390201
$990$	18.9657	0.602770
$991$	15.1619	0.481634	0.240817	−	0.970571i	$-0.422585\pi$
$991$	15.1619	0.481634	0.240817	+	0.970571i	$0.422585\pi$
$992$	13.5909	0.431513
$993$	−32.5244	−1.03213
$994$	11.9802	0.379988
$995$	−17.7523	−0.562785
$996$	−69.8947	−2.21470
$997$	5.77715	0.182964	0.0914821	−	0.995807i	$-0.470840\pi$
$997$	5.77715	0.182964	0.0914821	+	0.995807i	$0.470840\pi$
$998$	55.2798	1.74985
$999$	−8.03502	−0.254217

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.c.1.14	✓	106

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.c.1.14	✓	106	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:	\( N \)	\(=\)	\( 6017 = 11 \cdot 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.32740 q^{2} -3.07559 q^{3} +3.41677 q^{4} -1.26158 q^{5} +7.15812 q^{6} +0.599145 q^{7} -3.29739 q^{8} +6.45928 q^{9} +O(q^{10})\)	\(q-2.32740 q^{2} -3.07559 q^{3} +3.41677 q^{4} -1.26158 q^{5} +7.15812 q^{6} +0.599145 q^{7} -3.29739 q^{8} +6.45928 q^{9} +2.93620 q^{10} +1.00000 q^{11} -10.5086 q^{12} +1.48585 q^{13} -1.39445 q^{14} +3.88011 q^{15} +0.840783 q^{16} +3.03080 q^{17} -15.0333 q^{18} +5.86101 q^{19} -4.31053 q^{20} -1.84273 q^{21} -2.32740 q^{22} -1.31387 q^{23} +10.1414 q^{24} -3.40842 q^{25} -3.45817 q^{26} -10.6393 q^{27} +2.04714 q^{28} +6.74213 q^{29} -9.03054 q^{30} +2.93038 q^{31} +4.63794 q^{32} -3.07559 q^{33} -7.05387 q^{34} -0.755869 q^{35} +22.0699 q^{36} +0.755218 q^{37} -13.6409 q^{38} -4.56988 q^{39} +4.15992 q^{40} +5.51301 q^{41} +4.28876 q^{42} -9.33971 q^{43} +3.41677 q^{44} -8.14889 q^{45} +3.05790 q^{46} +8.42855 q^{47} -2.58591 q^{48} -6.64103 q^{49} +7.93273 q^{50} -9.32151 q^{51} +5.07682 q^{52} -11.8926 q^{53} +24.7619 q^{54} -1.26158 q^{55} -1.97561 q^{56} -18.0261 q^{57} -15.6916 q^{58} -2.97044 q^{59} +13.2574 q^{60} -1.92843 q^{61} -6.82016 q^{62} +3.87005 q^{63} -12.4759 q^{64} -1.87452 q^{65} +7.15812 q^{66} -6.53515 q^{67} +10.3556 q^{68} +4.04094 q^{69} +1.75921 q^{70} -8.59133 q^{71} -21.2987 q^{72} -5.44367 q^{73} -1.75769 q^{74} +10.4829 q^{75} +20.0257 q^{76} +0.599145 q^{77} +10.6359 q^{78} -2.92252 q^{79} -1.06072 q^{80} +13.3444 q^{81} -12.8310 q^{82} +6.65119 q^{83} -6.29618 q^{84} -3.82360 q^{85} +21.7372 q^{86} -20.7361 q^{87} -3.29739 q^{88} -6.64813 q^{89} +18.9657 q^{90} +0.890242 q^{91} -4.48920 q^{92} -9.01267 q^{93} -19.6166 q^{94} -7.39413 q^{95} -14.2644 q^{96} -12.4665 q^{97} +15.4563 q^{98} +6.45928 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9}+O(q^{10}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9} - 30 q^{10} + 106 q^{11} - 26 q^{12} - 72 q^{13} + 3 q^{14} - 46 q^{15} + 75 q^{16} - 65 q^{17} - 37 q^{18} - 63 q^{19} - 25 q^{20} - 27 q^{21} - 13 q^{22} - 23 q^{23} - 56 q^{24} + 74 q^{25} + 2 q^{26} - 54 q^{27} - 115 q^{28} - 45 q^{29} - 14 q^{30} - 89 q^{31} - 96 q^{32} - 15 q^{33} - 26 q^{34} - 52 q^{35} + 91 q^{36} - 35 q^{37} + 7 q^{38} - 34 q^{39} - 74 q^{40} - 32 q^{41} - 94 q^{43} + 93 q^{44} - 46 q^{45} - 20 q^{46} - 105 q^{47} - 57 q^{48} + 80 q^{49} - 60 q^{50} - 36 q^{51} - 137 q^{52} - 61 q^{54} - 12 q^{55} + 32 q^{56} - 71 q^{57} - 28 q^{58} - 15 q^{59} - 21 q^{60} - 80 q^{61} - 84 q^{62} - 182 q^{63} + 55 q^{64} - 73 q^{65} - 22 q^{66} - 58 q^{67} - 145 q^{68} - 8 q^{69} - 39 q^{70} - 11 q^{71} - 100 q^{72} - 155 q^{73} - 15 q^{74} - 15 q^{75} - 132 q^{76} - 66 q^{77} - 45 q^{78} - 50 q^{79} - 28 q^{80} + 114 q^{81} - 57 q^{82} - 96 q^{83} - 27 q^{84} - 74 q^{85} + 54 q^{86} - 182 q^{87} - 39 q^{88} + 9 q^{89} - 53 q^{90} + 6 q^{91} - 18 q^{92} - 26 q^{93} - 33 q^{94} - 49 q^{95} - 56 q^{96} - 102 q^{97} - 76 q^{98} + 97 q^{99}+O(q^{100}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9 - 30 * q^10 + 106 * q^11 - 26 * q^12 - 72 * q^13 + 3 * q^14 - 46 * q^15 + 75 * q^16 - 65 * q^17 - 37 * q^18 - 63 * q^19 - 25 * q^20 - 27 * q^21 - 13 * q^22 - 23 * q^23 - 56 * q^24 + 74 * q^25 + 2 * q^26 - 54 * q^27 - 115 * q^28 - 45 * q^29 - 14 * q^30 - 89 * q^31 - 96 * q^32 - 15 * q^33 - 26 * q^34 - 52 * q^35 + 91 * q^36 - 35 * q^37 + 7 * q^38 - 34 * q^39 - 74 * q^40 - 32 * q^41 - 94 * q^43 + 93 * q^44 - 46 * q^45 - 20 * q^46 - 105 * q^47 - 57 * q^48 + 80 * q^49 - 60 * q^50 - 36 * q^51 - 137 * q^52 - 61 * q^54 - 12 * q^55 + 32 * q^56 - 71 * q^57 - 28 * q^58 - 15 * q^59 - 21 * q^60 - 80 * q^61 - 84 * q^62 - 182 * q^63 + 55 * q^64 - 73 * q^65 - 22 * q^66 - 58 * q^67 - 145 * q^68 - 8 * q^69 - 39 * q^70 - 11 * q^71 - 100 * q^72 - 155 * q^73 - 15 * q^74 - 15 * q^75 - 132 * q^76 - 66 * q^77 - 45 * q^78 - 50 * q^79 - 28 * q^80 + 114 * q^81 - 57 * q^82 - 96 * q^83 - 27 * q^84 - 74 * q^85 + 54 * q^86 - 182 * q^87 - 39 * q^88 + 9 * q^89 - 53 * q^90 + 6 * q^91 - 18 * q^92 - 26 * q^93 - 33 * q^94 - 49 * q^95 - 56 * q^96 - 102 * q^97 - 76 * q^98 + 97 * q^99

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