LMFDB - Embedded newform 6014.2.a.j.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, 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("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.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:	$48.0220317756$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.88640 q^{3} +1.00000 q^{4} +4.44357 q^{5} +1.88640 q^{6} -1.18572 q^{7} -1.00000 q^{8} +0.558507 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.88640 q^{3} +1.00000 q^{4} +4.44357 q^{5} +1.88640 q^{6} -1.18572 q^{7} -1.00000 q^{8} +0.558507 q^{9} -4.44357 q^{10} -3.77665 q^{11} -1.88640 q^{12} +0.131308 q^{13} +1.18572 q^{14} -8.38236 q^{15} +1.00000 q^{16} +4.90354 q^{17} -0.558507 q^{18} +4.40005 q^{19} +4.44357 q^{20} +2.23674 q^{21} +3.77665 q^{22} +0.903170 q^{23} +1.88640 q^{24} +14.7453 q^{25} -0.131308 q^{26} +4.60563 q^{27} -1.18572 q^{28} -6.51534 q^{29} +8.38236 q^{30} -1.00000 q^{31} -1.00000 q^{32} +7.12428 q^{33} -4.90354 q^{34} -5.26883 q^{35} +0.558507 q^{36} +8.11097 q^{37} -4.40005 q^{38} -0.247700 q^{39} -4.44357 q^{40} -9.17929 q^{41} -2.23674 q^{42} -7.13870 q^{43} -3.77665 q^{44} +2.48177 q^{45} -0.903170 q^{46} -4.64054 q^{47} -1.88640 q^{48} -5.59407 q^{49} -14.7453 q^{50} -9.25004 q^{51} +0.131308 q^{52} +12.0483 q^{53} -4.60563 q^{54} -16.7818 q^{55} +1.18572 q^{56} -8.30027 q^{57} +6.51534 q^{58} +11.5328 q^{59} -8.38236 q^{60} +15.0897 q^{61} +1.00000 q^{62} -0.662232 q^{63} +1.00000 q^{64} +0.583477 q^{65} -7.12428 q^{66} -6.42278 q^{67} +4.90354 q^{68} -1.70374 q^{69} +5.26883 q^{70} -4.02396 q^{71} -0.558507 q^{72} +1.74705 q^{73} -8.11097 q^{74} -27.8156 q^{75} +4.40005 q^{76} +4.47804 q^{77} +0.247700 q^{78} -0.522499 q^{79} +4.44357 q^{80} -10.3636 q^{81} +9.17929 q^{82} -9.56086 q^{83} +2.23674 q^{84} +21.7892 q^{85} +7.13870 q^{86} +12.2905 q^{87} +3.77665 q^{88} -3.46090 q^{89} -2.48177 q^{90} -0.155694 q^{91} +0.903170 q^{92} +1.88640 q^{93} +4.64054 q^{94} +19.5520 q^{95} +1.88640 q^{96} +1.00000 q^{97} +5.59407 q^{98} -2.10929 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9}+O(q^{10}) $ 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9	\( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9} - 4 q^{11} - 2 q^{12} + 10 q^{13} - 5 q^{14} - q^{15} + 32 q^{16} + 14 q^{17} - 30 q^{18} + 33 q^{19} + 4 q^{22} - 2 q^{23} + 2 q^{24} + 46 q^{25} - 10 q^{26} - 5 q^{27} + 5 q^{28} - q^{29} + q^{30} - 32 q^{31} - 32 q^{32} + 32 q^{33} - 14 q^{34} + 8 q^{35} + 30 q^{36} + 31 q^{37} - 33 q^{38} + 4 q^{39} + 31 q^{41} + 15 q^{43} - 4 q^{44} + q^{45} + 2 q^{46} - 14 q^{47} - 2 q^{48} + 75 q^{49} - 46 q^{50} + 27 q^{51} + 10 q^{52} - 31 q^{53} + 5 q^{54} + 14 q^{55} - 5 q^{56} + 51 q^{57} + q^{58} - 8 q^{59} - q^{60} + 24 q^{61} + 32 q^{62} + 23 q^{63} + 32 q^{64} + 20 q^{65} - 32 q^{66} + 17 q^{67} + 14 q^{68} - 31 q^{69} - 8 q^{70} - 31 q^{71} - 30 q^{72} + 19 q^{73} - 31 q^{74} - 40 q^{75} + 33 q^{76} + 8 q^{77} - 4 q^{78} + 39 q^{79} + 116 q^{81} - 31 q^{82} - 6 q^{83} + 56 q^{85} - 15 q^{86} - 17 q^{87} + 4 q^{88} + 8 q^{89} - q^{90} + 34 q^{91} - 2 q^{92} + 2 q^{93} + 14 q^{94} - 22 q^{95} + 2 q^{96} + 32 q^{97} - 75 q^{98} - 27 q^{99}+O(q^{100}) \) 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9 - 4 * q^11 - 2 * q^12 + 10 * q^13 - 5 * q^14 - q^15 + 32 * q^16 + 14 * q^17 - 30 * q^18 + 33 * q^19 + 4 * q^22 - 2 * q^23 + 2 * q^24 + 46 * q^25 - 10 * q^26 - 5 * q^27 + 5 * q^28 - q^29 + q^30 - 32 * q^31 - 32 * q^32 + 32 * q^33 - 14 * q^34 + 8 * q^35 + 30 * q^36 + 31 * q^37 - 33 * q^38 + 4 * q^39 + 31 * q^41 + 15 * q^43 - 4 * q^44 + q^45 + 2 * q^46 - 14 * q^47 - 2 * q^48 + 75 * q^49 - 46 * q^50 + 27 * q^51 + 10 * q^52 - 31 * q^53 + 5 * q^54 + 14 * q^55 - 5 * q^56 + 51 * q^57 + q^58 - 8 * q^59 - q^60 + 24 * q^61 + 32 * q^62 + 23 * q^63 + 32 * q^64 + 20 * q^65 - 32 * q^66 + 17 * q^67 + 14 * q^68 - 31 * q^69 - 8 * q^70 - 31 * q^71 - 30 * q^72 + 19 * q^73 - 31 * q^74 - 40 * q^75 + 33 * q^76 + 8 * q^77 - 4 * q^78 + 39 * q^79 + 116 * q^81 - 31 * q^82 - 6 * q^83 + 56 * q^85 - 15 * q^86 - 17 * q^87 + 4 * q^88 + 8 * q^89 - q^90 + 34 * q^91 - 2 * q^92 + 2 * q^93 + 14 * q^94 - 22 * q^95 + 2 * q^96 + 32 * q^97 - 75 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.88640	−1.08911	−0.544557	−	0.838724i	$-0.683302\pi$
$3$	−1.88640	−1.08911	−0.544557	+	0.838724i	$0.683302\pi$
$4$	1.00000	0.500000
$5$	4.44357	1.98723	0.993613	−	0.112841i	$-0.0359949\pi$
$5$	4.44357	1.98723	0.993613	+	0.112841i	$0.0359949\pi$
$6$	1.88640	0.770120
$7$	−1.18572	−0.448159	−0.224080	−	0.974571i	$-0.571938\pi$
$7$	−1.18572	−0.448159	−0.224080	+	0.974571i	$0.571938\pi$
$8$	−1.00000	−0.353553
$9$	0.558507	0.186169
$10$	−4.44357	−1.40518
$11$	−3.77665	−1.13870	−0.569351	−	0.822094i	$-0.692806\pi$
$11$	−3.77665	−1.13870	−0.569351	+	0.822094i	$0.692806\pi$
$12$	−1.88640	−0.544557
$13$	0.131308	0.0364183	0.0182092	−	0.999834i	$-0.494204\pi$
$13$	0.131308	0.0364183	0.0182092	+	0.999834i	$0.494204\pi$
$14$	1.18572	0.316897
$15$	−8.38236	−2.16432
$16$	1.00000	0.250000
$17$	4.90354	1.18928	0.594641	−	0.803991i	$-0.297294\pi$
$17$	4.90354	1.18928	0.594641	+	0.803991i	$0.297294\pi$
$18$	−0.558507	−0.131641
$19$	4.40005	1.00944	0.504721	−	0.863283i	$-0.331595\pi$
$19$	4.40005	1.00944	0.504721	+	0.863283i	$0.331595\pi$
$20$	4.44357	0.993613
$21$	2.23674	0.488097
$22$	3.77665	0.805184
$23$	0.903170	0.188324	0.0941620	−	0.995557i	$-0.469983\pi$
$23$	0.903170	0.188324	0.0941620	+	0.995557i	$0.469983\pi$
$24$	1.88640	0.385060
$25$	14.7453	2.94907
$26$	−0.131308	−0.0257516
$27$	4.60563	0.886355
$28$	−1.18572	−0.224080
$29$	−6.51534	−1.20987	−0.604934	−	0.796275i	$-0.706801\pi$
$29$	−6.51534	−1.20987	−0.604934	+	0.796275i	$0.706801\pi$
$30$	8.38236	1.53040
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−1.00000	−0.176777
$33$	7.12428	1.24018
$34$	−4.90354	−0.840950
$35$	−5.26883	−0.890594
$36$	0.558507	0.0930846
$37$	8.11097	1.33344	0.666718	−	0.745310i	$-0.267699\pi$
$37$	8.11097	1.33344	0.666718	+	0.745310i	$0.267699\pi$
$38$	−4.40005	−0.713783
$39$	−0.247700	−0.0396637
$40$	−4.44357	−0.702591
$41$	−9.17929	−1.43356	−0.716782	−	0.697297i	$-0.754386\pi$
$41$	−9.17929	−1.43356	−0.716782	+	0.697297i	$0.754386\pi$
$42$	−2.23674	−0.345136
$43$	−7.13870	−1.08864	−0.544321	−	0.838877i	$-0.683213\pi$
$43$	−7.13870	−1.08864	−0.544321	+	0.838877i	$0.683213\pi$
$44$	−3.77665	−0.569351
$45$	2.48177	0.369960
$46$	−0.903170	−0.133165
$47$	−4.64054	−0.676892	−0.338446	−	0.940986i	$-0.609901\pi$
$47$	−4.64054	−0.676892	−0.338446	+	0.940986i	$0.609901\pi$
$48$	−1.88640	−0.272278
$49$	−5.59407	−0.799153
$50$	−14.7453	−2.08531
$51$	−9.25004	−1.29526
$52$	0.131308	0.0182092
$53$	12.0483	1.65496	0.827482	−	0.561492i	$-0.189772\pi$
$53$	12.0483	1.65496	0.827482	+	0.561492i	$0.189772\pi$
$54$	−4.60563	−0.626747
$55$	−16.7818	−2.26286
$56$	1.18572	0.158448
$57$	−8.30027	−1.09940
$58$	6.51534	0.855506
$59$	11.5328	1.50144	0.750719	−	0.660621i	$-0.229707\pi$
$59$	11.5328	1.50144	0.750719	+	0.660621i	$0.229707\pi$
$60$	−8.38236	−1.08216
$61$	15.0897	1.93203	0.966017	−	0.258477i	$-0.0832206\pi$
$61$	15.0897	1.93203	0.966017	+	0.258477i	$0.0832206\pi$
$62$	1.00000	0.127000
$63$	−0.662232	−0.0834334
$64$	1.00000	0.125000
$65$	0.583477	0.0723715
$66$	−7.12428	−0.876938
$67$	−6.42278	−0.784667	−0.392334	−	0.919823i	$-0.628332\pi$
$67$	−6.42278	−0.784667	−0.392334	+	0.919823i	$0.628332\pi$
$68$	4.90354	0.594641
$69$	−1.70374	−0.205106
$70$	5.26883	0.629745
$71$	−4.02396	−0.477556	−0.238778	−	0.971074i	$-0.576747\pi$
$71$	−4.02396	−0.477556	−0.238778	+	0.971074i	$0.576747\pi$
$72$	−0.558507	−0.0658207
$73$	1.74705	0.204476	0.102238	−	0.994760i	$-0.467400\pi$
$73$	1.74705	0.204476	0.102238	+	0.994760i	$0.467400\pi$
$74$	−8.11097	−0.942881
$75$	−27.8156	−3.21187
$76$	4.40005	0.504721
$77$	4.47804	0.510320
$78$	0.247700	0.0280465
$79$	−0.522499	−0.0587858	−0.0293929	−	0.999568i	$-0.509357\pi$
$79$	−0.522499	−0.0587858	−0.0293929	+	0.999568i	$0.509357\pi$
$80$	4.44357	0.496807
$81$	−10.3636	−1.15151
$82$	9.17929	1.01368
$83$	−9.56086	−1.04944	−0.524720	−	0.851275i	$-0.675830\pi$
$83$	−9.56086	−1.04944	−0.524720	+	0.851275i	$0.675830\pi$
$84$	2.23674	0.244048
$85$	21.7892	2.36337
$86$	7.13870	0.769786
$87$	12.2905	1.31768
$88$	3.77665	0.402592
$89$	−3.46090	−0.366854	−0.183427	−	0.983033i	$-0.558719\pi$
$89$	−3.46090	−0.366854	−0.183427	+	0.983033i	$0.558719\pi$
$90$	−2.48177	−0.261601
$91$	−0.155694	−0.0163212
$92$	0.903170	0.0941620
$93$	1.88640	0.195611
$94$	4.64054	0.478635
$95$	19.5520	2.00599
$96$	1.88640	0.192530
$97$	1.00000	0.101535
$97$	1.00000	0.101535
$98$	5.59407	0.565087
$99$	−2.10929	−0.211991
$100$	14.7453	1.47453
$101$	8.56587	0.852336	0.426168	−	0.904644i	$-0.359863\pi$
$101$	8.56587	0.852336	0.426168	+	0.904644i	$0.359863\pi$
$102$	9.25004	0.915890
$103$	15.4840	1.52568	0.762842	−	0.646585i	$-0.223804\pi$
$103$	15.4840	1.52568	0.762842	+	0.646585i	$0.223804\pi$
$104$	−0.131308	−0.0128758
$105$	9.93912	0.969959
$106$	−12.0483	−1.17024
$107$	−9.10411	−0.880127	−0.440064	−	0.897967i	$-0.645044\pi$
$107$	−9.10411	−0.880127	−0.440064	+	0.897967i	$0.645044\pi$
$108$	4.60563	0.443177
$109$	6.49446	0.622056	0.311028	−	0.950401i	$-0.399327\pi$
$109$	6.49446	0.622056	0.311028	+	0.950401i	$0.399327\pi$
$110$	16.7818	1.60008
$111$	−15.3005	−1.45226
$112$	−1.18572	−0.112040
$113$	−0.469130	−0.0441320	−0.0220660	−	0.999757i	$-0.507024\pi$
$113$	−0.469130	−0.0441320	−0.0220660	+	0.999757i	$0.507024\pi$
$114$	8.30027	0.777391
$115$	4.01330	0.374242
$116$	−6.51534	−0.604934
$117$	0.0733366	0.00677997
$118$	−11.5328	−1.06168
$119$	−5.81422	−0.532988
$120$	8.38236	0.765201
$121$	3.26309	0.296644
$122$	−15.0897	−1.36615
$123$	17.3158	1.56131
$124$	−1.00000	−0.0898027
$125$	43.3041	3.87324
$126$	0.662232	0.0589964
$127$	−7.04144	−0.624827	−0.312413	−	0.949946i	$-0.601137\pi$
$127$	−7.04144	−0.624827	−0.312413	+	0.949946i	$0.601137\pi$
$128$	−1.00000	−0.0883883
$129$	13.4664	1.18565
$130$	−0.583477	−0.0511743
$131$	−7.22399	−0.631163	−0.315581	−	0.948899i	$-0.602200\pi$
$131$	−7.22399	−0.631163	−0.315581	+	0.948899i	$0.602200\pi$
$132$	7.12428	0.620089
$133$	−5.21723	−0.452391
$134$	6.42278	0.554843
$135$	20.4655	1.76139
$136$	−4.90354	−0.420475
$137$	−2.15385	−0.184016	−0.0920081	−	0.995758i	$-0.529329\pi$
$137$	−2.15385	−0.184016	−0.0920081	+	0.995758i	$0.529329\pi$
$138$	1.70374	0.145032
$139$	13.1677	1.11687	0.558433	−	0.829550i	$-0.311403\pi$
$139$	13.1677	1.11687	0.558433	+	0.829550i	$0.311403\pi$
$140$	−5.26883	−0.445297
$141$	8.75392	0.737213
$142$	4.02396	0.337683
$143$	−0.495905	−0.0414697
$144$	0.558507	0.0465423
$145$	−28.9514	−2.40428
$146$	−1.74705	−0.144587
$147$	10.5527	0.870369
$148$	8.11097	0.666718
$149$	−10.9088	−0.893680	−0.446840	−	0.894614i	$-0.647451\pi$
$149$	−10.9088	−0.893680	−0.446840	+	0.894614i	$0.647451\pi$
$150$	27.8156	2.27114
$151$	5.37340	0.437281	0.218641	−	0.975805i	$-0.429838\pi$
$151$	5.37340	0.437281	0.218641	+	0.975805i	$0.429838\pi$
$152$	−4.40005	−0.356892
$153$	2.73866	0.221408
$154$	−4.47804	−0.360851
$155$	−4.44357	−0.356916
$156$	−0.247700	−0.0198319
$157$	−7.19144	−0.573939	−0.286970	−	0.957940i	$-0.592648\pi$
$157$	−7.19144	−0.573939	−0.286970	+	0.957940i	$0.592648\pi$
$158$	0.522499	0.0415678
$159$	−22.7280	−1.80245
$160$	−4.44357	−0.351295
$161$	−1.07091	−0.0843992
$162$	10.3636	0.814241
$163$	19.1794	1.50224	0.751121	−	0.660164i	$-0.229513\pi$
$163$	19.1794	1.50224	0.751121	+	0.660164i	$0.229513\pi$
$164$	−9.17929	−0.716782
$165$	31.6572	2.46451
$166$	9.56086	0.742067
$167$	13.5109	1.04551	0.522753	−	0.852484i	$-0.324905\pi$
$167$	13.5109	1.04551	0.522753	+	0.852484i	$0.324905\pi$
$168$	−2.23674	−0.172568
$169$	−12.9828	−0.998674
$170$	−21.7892	−1.67116
$171$	2.45746	0.187927
$172$	−7.13870	−0.544321
$173$	−6.55825	−0.498614	−0.249307	−	0.968424i	$-0.580203\pi$
$173$	−6.55825	−0.498614	−0.249307	+	0.968424i	$0.580203\pi$
$174$	−12.2905	−0.931744
$175$	−17.4838	−1.32165
$176$	−3.77665	−0.284676
$177$	−21.7554	−1.63524
$178$	3.46090	0.259405
$179$	16.5337	1.23579	0.617895	−	0.786261i	$-0.287986\pi$
$179$	16.5337	1.23579	0.617895	+	0.786261i	$0.287986\pi$
$180$	2.48177	0.184980
$181$	17.0474	1.26712	0.633561	−	0.773693i	$-0.281593\pi$
$181$	17.0474	1.26712	0.633561	+	0.773693i	$0.281593\pi$
$182$	0.155694	0.0115408
$183$	−28.4652	−2.10421
$184$	−0.903170	−0.0665826
$185$	36.0417	2.64984
$186$	−1.88640	−0.138318
$187$	−18.5189	−1.35424
$188$	−4.64054	−0.338446
$189$	−5.46098	−0.397228
$190$	−19.5520	−1.41845
$191$	13.7146	0.992355	0.496177	−	0.868221i	$-0.334737\pi$
$191$	13.7146	0.992355	0.496177	+	0.868221i	$0.334737\pi$
$192$	−1.88640	−0.136139
$193$	5.20458	0.374634	0.187317	−	0.982300i	$-0.440021\pi$
$193$	5.20458	0.374634	0.187317	+	0.982300i	$0.440021\pi$
$194$	−1.00000	−0.0717958
$195$	−1.10067	−0.0788208
$196$	−5.59407	−0.399577
$197$	19.8184	1.41201	0.706003	−	0.708209i	$-0.250497\pi$
$197$	19.8184	1.41201	0.706003	+	0.708209i	$0.250497\pi$
$198$	2.10929	0.149900
$199$	14.1727	1.00468	0.502338	−	0.864671i	$-0.332473\pi$
$199$	14.1727	1.00468	0.502338	+	0.864671i	$0.332473\pi$
$200$	−14.7453	−1.04265
$201$	12.1159	0.854592
$202$	−8.56587	−0.602692
$203$	7.72536	0.542214
$204$	−9.25004	−0.647632
$205$	−40.7888	−2.84882
$206$	−15.4840	−1.07882
$207$	0.504427	0.0350601
$208$	0.131308	0.00910458
$209$	−16.6175	−1.14945
$210$	−9.93912	−0.685864
$211$	−13.3381	−0.918232	−0.459116	−	0.888376i	$-0.651834\pi$
$211$	−13.3381	−0.918232	−0.459116	+	0.888376i	$0.651834\pi$
$212$	12.0483	0.827482
$213$	7.59079	0.520113
$214$	9.10411	0.622344
$215$	−31.7213	−2.16338
$216$	−4.60563	−0.313374
$217$	1.18572	0.0804918
$218$	−6.49446	−0.439860
$219$	−3.29563	−0.222698
$220$	−16.7818	−1.13143
$221$	0.643875	0.0433117
$222$	15.3005	1.02690
$223$	−17.6825	−1.18411	−0.592053	−	0.805899i	$-0.701682\pi$
$223$	−17.6825	−1.18411	−0.592053	+	0.805899i	$0.701682\pi$
$224$	1.18572	0.0792241
$225$	8.23538	0.549025
$226$	0.469130	0.0312060
$227$	−15.6434	−1.03829	−0.519146	−	0.854686i	$-0.673750\pi$
$227$	−15.6434	−1.03829	−0.519146	+	0.854686i	$0.673750\pi$
$228$	−8.30027	−0.549699
$229$	3.77283	0.249316	0.124658	−	0.992200i	$-0.460217\pi$
$229$	3.77283	0.249316	0.124658	+	0.992200i	$0.460217\pi$
$230$	−4.01330	−0.264629
$231$	−8.44738	−0.555797
$232$	6.51534	0.427753
$233$	−18.1144	−1.18671	−0.593356	−	0.804940i	$-0.702197\pi$
$233$	−18.1144	−1.18671	−0.593356	+	0.804940i	$0.702197\pi$
$234$	−0.0733366	−0.00479416
$235$	−20.6206	−1.34514
$236$	11.5328	0.750719
$237$	0.985643	0.0640244
$238$	5.81422	0.376880
$239$	−15.7775	−1.02056	−0.510282	−	0.860007i	$-0.670459\pi$
$239$	−15.7775	−1.02056	−0.510282	+	0.860007i	$0.670459\pi$
$240$	−8.38236	−0.541079
$241$	−7.76628	−0.500270	−0.250135	−	0.968211i	$-0.580475\pi$
$241$	−7.76628	−0.500270	−0.250135	+	0.968211i	$0.580475\pi$
$242$	−3.26309	−0.209759
$243$	5.73299	0.367771
$244$	15.0897	0.966017
$245$	−24.8577	−1.58810
$246$	−17.3158	−1.10402
$247$	0.577763	0.0367622
$248$	1.00000	0.0635001
$249$	18.0356	1.14296
$250$	−43.3041	−2.73879
$251$	25.6604	1.61967	0.809835	−	0.586658i	$-0.199557\pi$
$251$	25.6604	1.61967	0.809835	+	0.586658i	$0.199557\pi$
$252$	−0.662232	−0.0417167
$253$	−3.41096	−0.214445
$254$	7.04144	0.441819
$255$	−41.1032	−2.57398
$256$	1.00000	0.0625000
$257$	−16.3355	−1.01898	−0.509491	−	0.860476i	$-0.670166\pi$
$257$	−16.3355	−1.01898	−0.509491	+	0.860476i	$0.670166\pi$
$258$	−13.4664	−0.838385
$259$	−9.61733	−0.597592
$260$	0.583477	0.0361857
$261$	−3.63887	−0.225240
$262$	7.22399	0.446300
$263$	19.2400	1.18639	0.593196	−	0.805058i	$-0.297866\pi$
$263$	19.2400	1.18639	0.593196	+	0.805058i	$0.297866\pi$
$264$	−7.12428	−0.438469
$265$	53.5376	3.28879
$266$	5.21723	0.319889
$267$	6.52864	0.399546
$268$	−6.42278	−0.392334
$269$	10.8315	0.660407	0.330204	−	0.943910i	$-0.392883\pi$
$269$	10.8315	0.660407	0.330204	+	0.943910i	$0.392883\pi$
$270$	−20.4655	−1.24549
$271$	15.3999	0.935475	0.467737	−	0.883867i	$-0.345069\pi$
$271$	15.3999	0.935475	0.467737	+	0.883867i	$0.345069\pi$
$272$	4.90354	0.297321
$273$	0.293702	0.0177757
$274$	2.15385	0.130119
$275$	−55.6880	−3.35811
$276$	−1.70374	−0.102553
$277$	−14.9583	−0.898759	−0.449380	−	0.893341i	$-0.648355\pi$
$277$	−14.9583	−0.898759	−0.449380	+	0.893341i	$0.648355\pi$
$278$	−13.1677	−0.789743
$279$	−0.558507	−0.0334370
$280$	5.26883	0.314873
$281$	30.5908	1.82489	0.912446	−	0.409198i	$-0.134191\pi$
$281$	30.5908	1.82489	0.912446	+	0.409198i	$0.134191\pi$
$282$	−8.75392	−0.521288
$283$	−15.8485	−0.942097	−0.471049	−	0.882107i	$-0.656124\pi$
$283$	−15.8485	−0.942097	−0.471049	+	0.882107i	$0.656124\pi$
$284$	−4.02396	−0.238778
$285$	−36.8828	−2.18475
$286$	0.495905	0.0293235
$287$	10.8841	0.642465
$288$	−0.558507	−0.0329104
$289$	7.04469	0.414393
$290$	28.9514	1.70008
$291$	−1.88640	−0.110583
$292$	1.74705	0.102238
$293$	−13.7830	−0.805214	−0.402607	−	0.915373i	$-0.631896\pi$
$293$	−13.7830	−0.805214	−0.402607	+	0.915373i	$0.631896\pi$
$294$	−10.5527	−0.615444
$295$	51.2467	2.98370
$296$	−8.11097	−0.471441
$297$	−17.3939	−1.00929
$298$	10.9088	0.631927
$299$	0.118594	0.00685844
$300$	−27.8156	−1.60594
$301$	8.46449	0.487885
$302$	−5.37340	−0.309204
$303$	−16.1587	−0.928291
$304$	4.40005	0.252360
$305$	67.0521	3.83939
$306$	−2.73866	−0.156559
$307$	1.47855	0.0843852	0.0421926	−	0.999109i	$-0.486566\pi$
$307$	1.47855	0.0843852	0.0421926	+	0.999109i	$0.486566\pi$
$308$	4.47804	0.255160
$309$	−29.2090	−1.66164
$310$	4.44357	0.252378
$311$	18.7666	1.06416	0.532079	−	0.846694i	$-0.321411\pi$
$311$	18.7666	1.06416	0.532079	+	0.846694i	$0.321411\pi$
$312$	0.247700	0.0140232
$313$	9.97407	0.563768	0.281884	−	0.959449i	$-0.409041\pi$
$313$	9.97407	0.563768	0.281884	+	0.959449i	$0.409041\pi$
$314$	7.19144	0.405836
$315$	−2.94268	−0.165801
$316$	−0.522499	−0.0293929
$317$	26.9689	1.51472	0.757362	−	0.652995i	$-0.226488\pi$
$317$	26.9689	1.51472	0.757362	+	0.652995i	$0.226488\pi$
$318$	22.7280	1.27452
$319$	24.6062	1.37768
$320$	4.44357	0.248403
$321$	17.1740	0.958559
$322$	1.07091	0.0596792
$323$	21.5758	1.20051
$324$	−10.3636	−0.575755
$325$	1.93618	0.107400
$326$	−19.1794	−1.06225
$327$	−12.2512	−0.677490
$328$	9.17929	0.506841
$329$	5.50237	0.303356
$330$	−31.6572	−1.74267
$331$	0.940109	0.0516731	0.0258365	−	0.999666i	$-0.491775\pi$
$331$	0.940109	0.0516731	0.0258365	+	0.999666i	$0.491775\pi$
$332$	−9.56086	−0.524720
$333$	4.53004	0.248244
$334$	−13.5109	−0.739284
$335$	−28.5401	−1.55931
$336$	2.23674	0.122024
$337$	0.223186	0.0121577	0.00607886	−	0.999982i	$-0.498065\pi$
$337$	0.223186	0.0121577	0.00607886	+	0.999982i	$0.498065\pi$
$338$	12.9828	0.706169
$339$	0.884966	0.0480648
$340$	21.7892	1.18169
$341$	3.77665	0.204517
$342$	−2.45746	−0.132884
$343$	14.9330	0.806307
$344$	7.13870	0.384893
$345$	−7.57069	−0.407592
$346$	6.55825	0.352573
$347$	0.411155	0.0220720	0.0110360	−	0.999939i	$-0.496487\pi$
$347$	0.411155	0.0220720	0.0110360	+	0.999939i	$0.496487\pi$
$348$	12.2905	0.658842
$349$	−33.1529	−1.77463	−0.887316	−	0.461162i	$-0.847433\pi$
$349$	−33.1529	−1.77463	−0.887316	+	0.461162i	$0.847433\pi$
$350$	17.4838	0.934550
$351$	0.604757	0.0322796
$352$	3.77665	0.201296
$353$	31.4257	1.67262	0.836311	−	0.548255i	$-0.184708\pi$
$353$	31.4257	1.67262	0.836311	+	0.548255i	$0.184708\pi$
$354$	21.7554	1.15629
$355$	−17.8807	−0.949011
$356$	−3.46090	−0.183427
$357$	10.9679	0.580485
$358$	−16.5337	−0.873835
$359$	4.50000	0.237501	0.118750	−	0.992924i	$-0.462111\pi$
$359$	4.50000	0.237501	0.118750	+	0.992924i	$0.462111\pi$
$360$	−2.48177	−0.130801
$361$	0.360479	0.0189726
$362$	−17.0474	−0.895991
$363$	−6.15549	−0.323079
$364$	−0.155694	−0.00816061
$365$	7.76313	0.406341
$366$	28.4652	1.48790
$367$	22.7145	1.18569	0.592845	−	0.805317i	$-0.298005\pi$
$367$	22.7145	1.18569	0.592845	+	0.805317i	$0.298005\pi$
$368$	0.903170	0.0470810
$369$	−5.12670	−0.266885
$370$	−36.0417	−1.87372
$371$	−14.2859	−0.741688
$372$	1.88640	0.0978053
$373$	3.81907	0.197744	0.0988719	−	0.995100i	$-0.468477\pi$
$373$	3.81907	0.197744	0.0988719	+	0.995100i	$0.468477\pi$
$374$	18.5189	0.957592
$375$	−81.6889	−4.21840
$376$	4.64054	0.239318
$377$	−0.855517	−0.0440614
$378$	5.46098	0.280883
$379$	−23.8326	−1.22420	−0.612099	−	0.790781i	$-0.709674\pi$
$379$	−23.8326	−1.22420	−0.612099	+	0.790781i	$0.709674\pi$
$380$	19.5520	1.00299
$381$	13.2830	0.680508
$382$	−13.7146	−0.701701
$383$	−22.4673	−1.14803	−0.574014	−	0.818846i	$-0.694614\pi$
$383$	−22.4673	−1.14803	−0.574014	+	0.818846i	$0.694614\pi$
$384$	1.88640	0.0962650
$385$	19.8985	1.01412
$386$	−5.20458	−0.264906
$387$	−3.98702	−0.202671
$388$	1.00000	0.0507673
$389$	21.4446	1.08729	0.543643	−	0.839316i	$-0.317044\pi$
$389$	21.4446	1.08729	0.543643	+	0.839316i	$0.317044\pi$
$390$	1.10067	0.0557347
$391$	4.42873	0.223970
$392$	5.59407	0.282543
$393$	13.6273	0.687408
$394$	−19.8184	−0.998439
$395$	−2.32176	−0.116821
$396$	−2.10929	−0.105996
$397$	17.1525	0.860860	0.430430	−	0.902624i	$-0.358362\pi$
$397$	17.1525	0.860860	0.430430	+	0.902624i	$0.358362\pi$
$398$	−14.1727	−0.710413
$399$	9.84178	0.492705
$400$	14.7453	0.737267
$401$	15.5381	0.775934	0.387967	−	0.921673i	$-0.373177\pi$
$401$	15.5381	0.775934	0.387967	+	0.921673i	$0.373177\pi$
$402$	−12.1159	−0.604288
$403$	−0.131308	−0.00654092
$404$	8.56587	0.426168
$405$	−46.0514	−2.28831
$406$	−7.72536	−0.383403
$407$	−30.6323	−1.51839
$408$	9.25004	0.457945
$409$	33.4728	1.65512	0.827561	−	0.561376i	$-0.189728\pi$
$409$	33.4728	1.65512	0.827561	+	0.561376i	$0.189728\pi$
$410$	40.7888	2.01442
$411$	4.06303	0.200415
$412$	15.4840	0.762842
$413$	−13.6746	−0.672884
$414$	−0.504427	−0.0247912
$415$	−42.4844	−2.08548
$416$	−0.131308	−0.00643791
$417$	−24.8395	−1.21639
$418$	16.6175	0.812787
$419$	−27.9281	−1.36438	−0.682188	−	0.731177i	$-0.738971\pi$
$419$	−27.9281	−1.36438	−0.682188	+	0.731177i	$0.738971\pi$
$420$	9.93912	0.484979
$421$	23.8382	1.16180	0.580901	−	0.813975i	$-0.302701\pi$
$421$	23.8382	1.16180	0.580901	+	0.813975i	$0.302701\pi$
$422$	13.3381	0.649288
$423$	−2.59178	−0.126016
$424$	−12.0483	−0.585118
$425$	72.3043	3.50728
$426$	−7.59079	−0.367775
$427$	−17.8921	−0.865860
$428$	−9.10411	−0.440064
$429$	0.935475	0.0451652
$430$	31.7213	1.52974
$431$	13.9136	0.670192	0.335096	−	0.942184i	$-0.391231\pi$
$431$	13.9136	0.670192	0.335096	+	0.942184i	$0.391231\pi$
$432$	4.60563	0.221589
$433$	−12.2802	−0.590149	−0.295075	−	0.955474i	$-0.595345\pi$
$433$	−12.2802	−0.590149	−0.295075	+	0.955474i	$0.595345\pi$
$434$	−1.18572	−0.0569163
$435$	54.6139	2.61854
$436$	6.49446	0.311028
$437$	3.97400	0.190102
$438$	3.29563	0.157471
$439$	22.2354	1.06124	0.530619	−	0.847610i	$-0.321959\pi$
$439$	22.2354	1.06124	0.530619	+	0.847610i	$0.321959\pi$
$440$	16.7818	0.800042
$441$	−3.12433	−0.148778
$442$	−0.643875	−0.0306260
$443$	21.5582	1.02426	0.512131	−	0.858907i	$-0.328856\pi$
$443$	21.5582	1.02426	0.512131	+	0.858907i	$0.328856\pi$
$444$	−15.3005	−0.726131
$445$	−15.3787	−0.729022
$446$	17.6825	0.837290
$447$	20.5783	0.973319
$448$	−1.18572	−0.0560199
$449$	2.44827	0.115541	0.0577705	−	0.998330i	$-0.481601\pi$
$449$	2.44827	0.115541	0.0577705	+	0.998330i	$0.481601\pi$
$450$	−8.23538	−0.388220
$451$	34.6670	1.63240
$452$	−0.469130	−0.0220660
$453$	−10.1364	−0.476249
$454$	15.6434	0.734183
$455$	−0.691840	−0.0324340
$456$	8.30027	0.388696
$457$	−26.6441	−1.24636	−0.623178	−	0.782080i	$-0.714159\pi$
$457$	−26.6441	−1.24636	−0.623178	+	0.782080i	$0.714159\pi$
$458$	−3.77283	−0.176293
$459$	22.5839	1.05413
$460$	4.01330	0.187121
$461$	13.4005	0.624122	0.312061	−	0.950062i	$-0.398981\pi$
$461$	13.4005	0.624122	0.312061	+	0.950062i	$0.398981\pi$
$462$	8.44738	0.393008
$463$	−23.9567	−1.11336	−0.556681	−	0.830727i	$-0.687925\pi$
$463$	−23.9567	−1.11336	−0.556681	+	0.830727i	$0.687925\pi$
$464$	−6.51534	−0.302467
$465$	8.38236	0.388723
$466$	18.1144	0.839132
$467$	1.90857	0.0883180	0.0441590	−	0.999025i	$-0.485939\pi$
$467$	1.90857	0.0883180	0.0441590	+	0.999025i	$0.485939\pi$
$468$	0.0733366	0.00338998
$469$	7.61560	0.351656
$470$	20.6206	0.951156
$471$	13.5659	0.625085
$472$	−11.5328	−0.530839
$473$	26.9604	1.23964
$474$	−0.985643	−0.0452721
$475$	64.8803	2.97691
$476$	−5.81422	−0.266494
$477$	6.72908	0.308103
$478$	15.7775	0.721648
$479$	29.3971	1.34319	0.671594	−	0.740919i	$-0.265610\pi$
$479$	29.3971	1.34319	0.671594	+	0.740919i	$0.265610\pi$
$480$	8.38236	0.382601
$481$	1.06504	0.0485615
$482$	7.76628	0.353745
$483$	2.02016	0.0919203
$484$	3.26309	0.148322
$485$	4.44357	0.201772
$486$	−5.73299	−0.260054
$487$	−16.0758	−0.728463	−0.364232	−	0.931308i	$-0.618668\pi$
$487$	−16.0758	−0.728463	−0.364232	+	0.931308i	$0.618668\pi$
$488$	−15.0897	−0.683077
$489$	−36.1799	−1.63611
$490$	24.8577	1.12295
$491$	0.253114	0.0114229	0.00571143	−	0.999984i	$-0.498182\pi$
$491$	0.253114	0.0114229	0.00571143	+	0.999984i	$0.498182\pi$
$492$	17.3158	0.780657
$493$	−31.9482	−1.43888
$494$	−0.577763	−0.0259948
$495$	−9.37277	−0.421275
$496$	−1.00000	−0.0449013
$497$	4.77128	0.214021
$498$	−18.0356	−0.808195
$499$	18.6289	0.833944	0.416972	−	0.908919i	$-0.363091\pi$
$499$	18.6289	0.833944	0.416972	+	0.908919i	$0.363091\pi$
$500$	43.3041	1.93662
$501$	−25.4870	−1.13868
$502$	−25.6604	−1.14528
$503$	28.8883	1.28807	0.644033	−	0.764998i	$-0.277260\pi$
$503$	28.8883	1.28807	0.644033	+	0.764998i	$0.277260\pi$
$504$	0.662232	0.0294982
$505$	38.0631	1.69378
$506$	3.41096	0.151636
$507$	24.4907	1.08767
$508$	−7.04144	−0.312413
$509$	−21.5723	−0.956177	−0.478089	−	0.878312i	$-0.658670\pi$
$509$	−21.5723	−0.956177	−0.478089	+	0.878312i	$0.658670\pi$
$510$	41.1032	1.82008
$511$	−2.07151	−0.0916380
$512$	−1.00000	−0.0441942
$513$	20.2650	0.894723
$514$	16.3355	0.720529
$515$	68.8043	3.03188
$516$	13.4664	0.592827
$517$	17.5257	0.770779
$518$	9.61733	0.422561
$519$	12.3715	0.543048
$520$	−0.583477	−0.0255872
$521$	−16.6080	−0.727608	−0.363804	−	0.931476i	$-0.618522\pi$
$521$	−16.6080	−0.727608	−0.363804	+	0.931476i	$0.618522\pi$
$522$	3.63887	0.159269
$523$	−11.0535	−0.483336	−0.241668	−	0.970359i	$-0.577695\pi$
$523$	−11.0535	−0.483336	−0.241668	+	0.970359i	$0.577695\pi$
$524$	−7.22399	−0.315581
$525$	32.9815	1.43943
$526$	−19.2400	−0.838906
$527$	−4.90354	−0.213601
$528$	7.12428	0.310044
$529$	−22.1843	−0.964534
$530$	−53.5376	−2.32553
$531$	6.44114	0.279522
$532$	−5.21723	−0.226195
$533$	−1.20532	−0.0522080
$534$	−6.52864	−0.282522
$535$	−40.4548	−1.74901
$536$	6.42278	0.277422
$537$	−31.1892	−1.34592
$538$	−10.8315	−0.466978
$539$	21.1269	0.909998
$540$	20.4655	0.880693
$541$	37.9108	1.62991	0.814956	−	0.579523i	$-0.196761\pi$
$541$	37.9108	1.62991	0.814956	+	0.579523i	$0.196761\pi$
$542$	−15.3999	−0.661481
$543$	−32.1582	−1.38004
$544$	−4.90354	−0.210237
$545$	28.8586	1.23617
$546$	−0.293702	−0.0125693
$547$	37.1478	1.58833	0.794163	−	0.607705i	$-0.207910\pi$
$547$	37.1478	1.58833	0.794163	+	0.607705i	$0.207910\pi$
$548$	−2.15385	−0.0920081
$549$	8.42769	0.359685
$550$	55.6880	2.37454
$551$	−28.6679	−1.22129
$552$	1.70374	0.0725160
$553$	0.619537	0.0263454
$554$	14.9583	0.635519
$555$	−67.9891	−2.88597
$556$	13.1677	0.558433
$557$	3.88929	0.164794	0.0823972	−	0.996600i	$-0.473742\pi$
$557$	3.88929	0.164794	0.0823972	+	0.996600i	$0.473742\pi$
$558$	0.558507	0.0236435
$559$	−0.937370	−0.0396465
$560$	−5.26883	−0.222649
$561$	34.9342	1.47492
$562$	−30.5908	−1.29039
$563$	−42.0303	−1.77137	−0.885683	−	0.464291i	$-0.846309\pi$
$563$	−42.0303	−1.77137	−0.885683	+	0.464291i	$0.846309\pi$
$564$	8.75392	0.368606
$565$	−2.08461	−0.0877003
$566$	15.8485	0.666164
$567$	12.2883	0.516060
$568$	4.02396	0.168841
$569$	25.9965	1.08983	0.544915	−	0.838491i	$-0.316562\pi$
$569$	25.9965	1.08983	0.544915	+	0.838491i	$0.316562\pi$
$570$	36.8828	1.54485
$571$	15.7847	0.660569	0.330285	−	0.943881i	$-0.392855\pi$
$571$	15.7847	0.660569	0.330285	+	0.943881i	$0.392855\pi$
$572$	−0.495905	−0.0207348
$573$	−25.8713	−1.08079
$574$	−10.8841	−0.454291
$575$	13.3175	0.555380
$576$	0.558507	0.0232711
$577$	9.54921	0.397539	0.198769	−	0.980046i	$-0.436306\pi$
$577$	9.54921	0.397539	0.198769	+	0.980046i	$0.436306\pi$
$578$	−7.04469	−0.293020
$579$	−9.81792	−0.408019
$580$	−28.9514	−1.20214
$581$	11.3365	0.470317
$582$	1.88640	0.0781938
$583$	−45.5023	−1.88451
$584$	−1.74705	−0.0722933
$585$	0.325876	0.0134733
$586$	13.7830	0.569372
$587$	4.44939	0.183646	0.0918230	−	0.995775i	$-0.470731\pi$
$587$	4.44939	0.183646	0.0918230	+	0.995775i	$0.470731\pi$
$588$	10.5527	0.435184
$589$	−4.40005	−0.181301
$590$	−51.2467	−2.10979
$591$	−37.3855	−1.53783
$592$	8.11097	0.333359
$593$	7.46602	0.306593	0.153296	−	0.988180i	$-0.451011\pi$
$593$	7.46602	0.306593	0.153296	+	0.988180i	$0.451011\pi$
$594$	17.3939	0.713679
$595$	−25.8359	−1.05917
$596$	−10.9088	−0.446840
$597$	−26.7354	−1.09421
$598$	−0.118594	−0.00484965
$599$	−37.3098	−1.52444	−0.762219	−	0.647319i	$-0.775890\pi$
$599$	−37.3098	−1.52444	−0.762219	+	0.647319i	$0.775890\pi$
$600$	27.8156	1.13557
$601$	−9.80150	−0.399811	−0.199906	−	0.979815i	$-0.564064\pi$
$601$	−9.80150	−0.399811	−0.199906	+	0.979815i	$0.564064\pi$
$602$	−8.46449	−0.344987
$603$	−3.58717	−0.146081
$604$	5.37340	0.218641
$605$	14.4998	0.589499
$606$	16.1587	0.656401
$607$	2.79642	0.113503	0.0567516	−	0.998388i	$-0.481926\pi$
$607$	2.79642	0.113503	0.0567516	+	0.998388i	$0.481926\pi$
$608$	−4.40005	−0.178446
$609$	−14.5731	−0.590533
$610$	−67.0521	−2.71486
$611$	−0.609341	−0.0246513
$612$	2.73866	0.110704
$613$	25.0320	1.01103	0.505516	−	0.862817i	$-0.331302\pi$
$613$	25.0320	1.01103	0.505516	+	0.862817i	$0.331302\pi$
$614$	−1.47855	−0.0596694
$615$	76.9441	3.10268
$616$	−4.47804	−0.180426
$617$	−15.1004	−0.607919	−0.303960	−	0.952685i	$-0.598309\pi$
$617$	−15.1004	−0.607919	−0.303960	+	0.952685i	$0.598309\pi$
$618$	29.2090	1.17496
$619$	9.39200	0.377497	0.188748	−	0.982026i	$-0.439557\pi$
$619$	9.39200	0.377497	0.188748	+	0.982026i	$0.439557\pi$
$620$	−4.44357	−0.178458
$621$	4.15967	0.166922
$622$	−18.7666	−0.752474
$623$	4.10365	0.164409
$624$	−0.247700	−0.00991593
$625$	118.698	4.74793
$626$	−9.97407	−0.398644
$627$	31.3472	1.25189
$628$	−7.19144	−0.286970
$629$	39.7724	1.58583
$630$	2.94268	0.117239
$631$	−10.6354	−0.423390	−0.211695	−	0.977336i	$-0.567898\pi$
$631$	−10.6354	−0.423390	−0.211695	+	0.977336i	$0.567898\pi$
$632$	0.522499	0.0207839
$633$	25.1610	1.00006
$634$	−26.9689	−1.07107
$635$	−31.2892	−1.24167
$636$	−22.7280	−0.901223
$637$	−0.734547	−0.0291038
$638$	−24.6062	−0.974167
$639$	−2.24741	−0.0889061
$640$	−4.44357	−0.175648
$641$	−16.7276	−0.660702	−0.330351	−	0.943858i	$-0.607167\pi$
$641$	−16.7276	−0.660702	−0.330351	+	0.943858i	$0.607167\pi$
$642$	−17.1740	−0.677803
$643$	34.0538	1.34295	0.671476	−	0.741026i	$-0.265660\pi$
$643$	34.0538	1.34295	0.671476	+	0.741026i	$0.265660\pi$
$644$	−1.07091	−0.0421996
$645$	59.8391	2.35616
$646$	−21.5758	−0.848890
$647$	−36.2499	−1.42513	−0.712566	−	0.701605i	$-0.752467\pi$
$647$	−36.2499	−1.42513	−0.712566	+	0.701605i	$0.752467\pi$
$648$	10.3636	0.407120
$649$	−43.5552	−1.70969
$650$	−1.93618	−0.0759434
$651$	−2.23674	−0.0876648
$652$	19.1794	0.751121
$653$	21.6400	0.846838	0.423419	−	0.905934i	$-0.360830\pi$
$653$	21.6400	0.846838	0.423419	+	0.905934i	$0.360830\pi$
$654$	12.2512	0.479058
$655$	−32.1003	−1.25426
$656$	−9.17929	−0.358391
$657$	0.975738	0.0380672
$658$	−5.50237	−0.214505
$659$	43.9664	1.71269	0.856344	−	0.516406i	$-0.172730\pi$
$659$	43.9664	1.71269	0.856344	+	0.516406i	$0.172730\pi$
$660$	31.6572	1.23226
$661$	−2.58035	−0.100364	−0.0501819	−	0.998740i	$-0.515980\pi$
$661$	−2.58035	−0.100364	−0.0501819	+	0.998740i	$0.515980\pi$
$662$	−0.940109	−0.0365384
$663$	−1.21461	−0.0471714
$664$	9.56086	0.371033
$665$	−23.1831	−0.899003
$666$	−4.53004	−0.175535
$667$	−5.88446	−0.227847
$668$	13.5109	0.522753
$669$	33.3562	1.28963
$670$	28.5401	1.10260
$671$	−56.9884	−2.20001
$672$	−2.23674	−0.0862841
$673$	19.5465	0.753463	0.376731	−	0.926323i	$-0.377048\pi$
$673$	19.5465	0.753463	0.376731	+	0.926323i	$0.377048\pi$
$674$	−0.223186	−0.00859681
$675$	67.9116	2.61392
$676$	−12.9828	−0.499337
$677$	−30.8814	−1.18687	−0.593434	−	0.804883i	$-0.702228\pi$
$677$	−30.8814	−1.18687	−0.593434	+	0.804883i	$0.702228\pi$
$678$	−0.884966	−0.0339869
$679$	−1.18572	−0.0455037
$680$	−21.7892	−0.835579
$681$	29.5098	1.13082
$682$	−3.77665	−0.144615
$683$	16.1464	0.617825	0.308912	−	0.951090i	$-0.400035\pi$
$683$	16.1464	0.617825	0.308912	+	0.951090i	$0.400035\pi$
$684$	2.45746	0.0939634
$685$	−9.57081	−0.365682
$686$	−14.9330	−0.570145
$687$	−7.11707	−0.271533
$688$	−7.13870	−0.272160
$689$	1.58204	0.0602711
$690$	7.57069	0.288211
$691$	−12.2405	−0.465651	−0.232826	−	0.972518i	$-0.574797\pi$
$691$	−12.2405	−0.465651	−0.232826	+	0.972518i	$0.574797\pi$
$692$	−6.55825	−0.249307
$693$	2.50102	0.0950059
$694$	−0.411155	−0.0156072
$695$	58.5114	2.21946
$696$	−12.2905	−0.465872
$697$	−45.0110	−1.70491
$698$	33.1529	1.25485
$699$	34.1710	1.29246
$700$	−17.4838	−0.660826
$701$	−14.2912	−0.539773	−0.269886	−	0.962892i	$-0.586986\pi$
$701$	−14.2912	−0.539773	−0.269886	+	0.962892i	$0.586986\pi$
$702$	−0.604757	−0.0228251
$703$	35.6887	1.34603
$704$	−3.77665	−0.142338
$705$	38.8987	1.46501
$706$	−31.4257	−1.18272
$707$	−10.1567	−0.381982
$708$	−21.7554	−0.817619
$709$	48.4061	1.81793	0.908964	−	0.416875i	$-0.136875\pi$
$709$	48.4061	1.81793	0.908964	+	0.416875i	$0.136875\pi$
$710$	17.8807	0.671052
$711$	−0.291820	−0.0109441
$712$	3.46090	0.129703
$713$	−0.903170	−0.0338240
$714$	−10.9679	−0.410465
$715$	−2.20359	−0.0824096
$716$	16.5337	0.617895
$717$	29.7628	1.11151
$718$	−4.50000	−0.167939
$719$	−12.4461	−0.464160	−0.232080	−	0.972697i	$-0.574553\pi$
$719$	−12.4461	−0.464160	−0.232080	+	0.972697i	$0.574553\pi$
$720$	2.48177	0.0924900
$721$	−18.3597	−0.683750
$722$	−0.360479	−0.0134156
$723$	14.6503	0.544851
$724$	17.0474	0.633561
$725$	−96.0709	−3.56798
$726$	6.15549	0.228452
$727$	32.3828	1.20101	0.600506	−	0.799620i	$-0.294966\pi$
$727$	32.3828	1.20101	0.600506	+	0.799620i	$0.294966\pi$
$728$	0.155694	0.00577042
$729$	20.2761	0.750965
$730$	−7.76313	−0.287326
$731$	−35.0049	−1.29470
$732$	−28.4652	−1.05210
$733$	−39.4541	−1.45727	−0.728635	−	0.684902i	$-0.759845\pi$
$733$	−39.4541	−1.45727	−0.728635	+	0.684902i	$0.759845\pi$
$734$	−22.7145	−0.838409
$735$	46.8915	1.72962
$736$	−0.903170	−0.0332913
$737$	24.2566	0.893503
$738$	5.12670	0.188716
$739$	2.14151	0.0787765	0.0393883	−	0.999224i	$-0.487459\pi$
$739$	2.14151	0.0787765	0.0393883	+	0.999224i	$0.487459\pi$
$740$	36.0417	1.32492
$741$	−1.08989	−0.0400382
$742$	14.2859	0.524453
$743$	−34.5700	−1.26825	−0.634125	−	0.773230i	$-0.718640\pi$
$743$	−34.5700	−1.26825	−0.634125	+	0.773230i	$0.718640\pi$
$744$	−1.88640	−0.0691588
$745$	−48.4739	−1.77594
$746$	−3.81907	−0.139826
$747$	−5.33981	−0.195373
$748$	−18.5189	−0.677120
$749$	10.7949	0.394437
$750$	81.6889	2.98286
$751$	46.6467	1.70216	0.851080	−	0.525035i	$-0.175948\pi$
$751$	46.6467	1.70216	0.851080	+	0.525035i	$0.175948\pi$
$752$	−4.64054	−0.169223
$753$	−48.4058	−1.76400
$754$	0.855517	0.0311561
$755$	23.8771	0.868976
$756$	−5.46098	−0.198614
$757$	15.8126	0.574719	0.287359	−	0.957823i	$-0.407223\pi$
$757$	15.8126	0.574719	0.287359	+	0.957823i	$0.407223\pi$
$758$	23.8326	0.865638
$759$	6.43443	0.233555
$760$	−19.5520	−0.709224
$761$	17.5127	0.634836	0.317418	−	0.948286i	$-0.397184\pi$
$761$	17.5127	0.634836	0.317418	+	0.948286i	$0.397184\pi$
$762$	−13.2830	−0.481192
$763$	−7.70060	−0.278780
$764$	13.7146	0.496177
$765$	12.1694	0.439987
$766$	22.4673	0.811778
$767$	1.51435	0.0546799
$768$	−1.88640	−0.0680696
$769$	7.96180	0.287110	0.143555	−	0.989642i	$-0.454147\pi$
$769$	7.96180	0.287110	0.143555	+	0.989642i	$0.454147\pi$
$770$	−19.8985	−0.717093
$771$	30.8153	1.10979
$772$	5.20458	0.187317
$773$	46.6578	1.67816	0.839082	−	0.544004i	$-0.183092\pi$
$773$	46.6578	1.67816	0.839082	+	0.544004i	$0.183092\pi$
$774$	3.98702	0.143310
$775$	−14.7453	−0.529668
$776$	−1.00000	−0.0358979
$777$	18.1421	0.650845
$778$	−21.4446	−0.768828
$779$	−40.3894	−1.44710
$780$	−1.10067	−0.0394104
$781$	15.1971	0.543794
$782$	−4.42873	−0.158371
$783$	−30.0073	−1.07237
$784$	−5.59407	−0.199788
$785$	−31.9557	−1.14055
$786$	−13.6273	−0.486071
$787$	1.05922	0.0377572	0.0188786	−	0.999822i	$-0.493990\pi$
$787$	1.05922	0.0377572	0.0188786	+	0.999822i	$0.493990\pi$
$788$	19.8184	0.706003
$789$	−36.2944	−1.29212
$790$	2.32176	0.0826046
$791$	0.556256	0.0197782
$792$	2.10929	0.0749502
$793$	1.98140	0.0703615
$794$	−17.1525	−0.608720
$795$	−100.993	−3.58187
$796$	14.1727	0.502338
$797$	−43.4207	−1.53804	−0.769019	−	0.639226i	$-0.779255\pi$
$797$	−43.4207	−1.53804	−0.769019	+	0.639226i	$0.779255\pi$
$798$	−9.84178	−0.348395
$799$	−22.7551	−0.805016
$800$	−14.7453	−0.521327
$801$	−1.93294	−0.0682969
$802$	−15.5381	−0.548668
$803$	−6.59798	−0.232838
$804$	12.1159	0.427296
$805$	−4.75865	−0.167720
$806$	0.131308	0.00462513
$807$	−20.4325	−0.719258
$808$	−8.56587	−0.301346
$809$	−23.0505	−0.810411	−0.405206	−	0.914226i	$-0.632800\pi$
$809$	−23.0505	−0.810411	−0.405206	+	0.914226i	$0.632800\pi$
$810$	46.0514	1.61808
$811$	7.61290	0.267325	0.133663	−	0.991027i	$-0.457326\pi$
$811$	7.61290	0.267325	0.133663	+	0.991027i	$0.457326\pi$
$812$	7.72536	0.271107
$813$	−29.0503	−1.01884
$814$	30.6323	1.07366
$815$	85.2249	2.98530
$816$	−9.25004	−0.323816
$817$	−31.4107	−1.09892
$818$	−33.4728	−1.17035
$819$	−0.0869565	−0.00303851
$820$	−40.7888	−1.42441
$821$	45.8707	1.60090	0.800450	−	0.599400i	$-0.204594\pi$
$821$	45.8707	1.60090	0.800450	+	0.599400i	$0.204594\pi$
$822$	−4.06303	−0.141715
$823$	54.9205	1.91441	0.957204	−	0.289414i	$-0.0934605\pi$
$823$	54.9205	1.91441	0.957204	+	0.289414i	$0.0934605\pi$
$824$	−15.4840	−0.539411
$825$	105.050	3.65737
$826$	13.6746	0.475801
$827$	1.60120	0.0556791	0.0278395	−	0.999612i	$-0.491137\pi$
$827$	1.60120	0.0556791	0.0278395	+	0.999612i	$0.491137\pi$
$828$	0.504427	0.0175301
$829$	3.45407	0.119965	0.0599825	−	0.998199i	$-0.480896\pi$
$829$	3.45407	0.119965	0.0599825	+	0.998199i	$0.480896\pi$
$830$	42.4844	1.47465
$831$	28.2174	0.978851
$832$	0.131308	0.00455229
$833$	−27.4307	−0.950419
$834$	24.8395	0.860120
$835$	60.0367	2.07766
$836$	−16.6175	−0.574727
$837$	−4.60563	−0.159194
$838$	27.9281	0.964759
$839$	−46.2471	−1.59663	−0.798314	−	0.602241i	$-0.794275\pi$
$839$	−46.2471	−1.59663	−0.798314	+	0.602241i	$0.794275\pi$
$840$	−9.93912	−0.342932
$841$	13.4497	0.463782
$842$	−23.8382	−0.821517
$843$	−57.7064	−1.98751
$844$	−13.3381	−0.459116
$845$	−57.6898	−1.98459
$846$	2.59178	0.0891071
$847$	−3.86910	−0.132944
$848$	12.0483	0.413741
$849$	29.8967	1.02605
$850$	−72.3043	−2.48002
$851$	7.32558	0.251118
$852$	7.59079	0.260056
$853$	11.7308	0.401656	0.200828	−	0.979627i	$-0.435637\pi$
$853$	11.7308	0.401656	0.200828	+	0.979627i	$0.435637\pi$
$854$	17.8921	0.612255
$855$	10.9199	0.373453
$856$	9.10411	0.311172
$857$	−24.6848	−0.843218	−0.421609	−	0.906778i	$-0.638535\pi$
$857$	−24.6848	−0.843218	−0.421609	+	0.906778i	$0.638535\pi$
$858$	−0.935475	−0.0319366
$859$	16.8655	0.575445	0.287722	−	0.957714i	$-0.407102\pi$
$859$	16.8655	0.575445	0.287722	+	0.957714i	$0.407102\pi$
$860$	−31.7213	−1.08169
$861$	−20.5317	−0.699718
$862$	−13.9136	−0.473897
$863$	−3.44619	−0.117310	−0.0586548	−	0.998278i	$-0.518681\pi$
$863$	−3.44619	−0.117310	−0.0586548	+	0.998278i	$0.518681\pi$
$864$	−4.60563	−0.156687
$865$	−29.1420	−0.990859
$866$	12.2802	0.417299
$867$	−13.2891	−0.451321
$868$	1.18572	0.0402459
$869$	1.97330	0.0669395
$870$	−54.6139	−1.85159
$871$	−0.843363	−0.0285763
$872$	−6.49446	−0.219930
$873$	0.558507	0.0189026
$874$	−3.97400	−0.134422
$875$	−51.3465	−1.73583
$876$	−3.29563	−0.111349
$877$	18.4890	0.624331	0.312165	−	0.950028i	$-0.398946\pi$
$877$	18.4890	0.624331	0.312165	+	0.950028i	$0.398946\pi$
$878$	−22.2354	−0.750409
$879$	26.0003	0.876970
$880$	−16.7818	−0.565715
$881$	50.4180	1.69863	0.849314	−	0.527889i	$-0.177016\pi$
$881$	50.4180	1.69863	0.849314	+	0.527889i	$0.177016\pi$
$882$	3.12433	0.105202
$883$	1.64878	0.0554859	0.0277430	−	0.999615i	$-0.491168\pi$
$883$	1.64878	0.0554859	0.0277430	+	0.999615i	$0.491168\pi$
$884$	0.643875	0.0216558
$885$	−96.6718	−3.24959
$886$	−21.5582	−0.724263
$887$	4.66435	0.156614	0.0783068	−	0.996929i	$-0.475049\pi$
$887$	4.66435	0.156614	0.0783068	+	0.996929i	$0.475049\pi$
$888$	15.3005	0.513452
$889$	8.34917	0.280022
$890$	15.3787	0.515497
$891$	39.1397	1.31123
$892$	−17.6825	−0.592053
$893$	−20.4186	−0.683283
$894$	−20.5783	−0.688241
$895$	73.4688	2.45579
$896$	1.18572	0.0396121
$897$	−0.223715	−0.00746963
$898$	−2.44827	−0.0816999
$899$	6.51534	0.217299
$900$	8.23538	0.274513
$901$	59.0794	1.96822
$902$	−34.6670	−1.15428
$903$	−15.9674	−0.531362
$904$	0.469130	0.0156030
$905$	75.7513	2.51806
$906$	10.1364	0.336759
$907$	−32.0107	−1.06290	−0.531449	−	0.847090i	$-0.678352\pi$
$907$	−32.0107	−1.06290	−0.531449	+	0.847090i	$0.678352\pi$
$908$	−15.6434	−0.519146
$909$	4.78410	0.158679
$910$	0.691840	0.0229343
$911$	−23.2323	−0.769720	−0.384860	−	0.922975i	$-0.625750\pi$
$911$	−23.2323	−0.769720	−0.384860	+	0.922975i	$0.625750\pi$
$912$	−8.30027	−0.274849
$913$	36.1080	1.19500
$914$	26.6441	0.881307
$915$	−126.487	−4.18153
$916$	3.77283	0.124658
$917$	8.56562	0.282862
$918$	−22.5839	−0.745380
$919$	47.5274	1.56778	0.783892	−	0.620897i	$-0.213232\pi$
$919$	47.5274	1.56778	0.783892	+	0.620897i	$0.213232\pi$
$920$	−4.01330	−0.132315
$921$	−2.78913	−0.0919051
$922$	−13.4005	−0.441321
$923$	−0.528378	−0.0173918
$924$	−8.44738	−0.277899
$925$	119.599	3.93239
$926$	23.9567	0.787265
$927$	8.64793	0.284035
$928$	6.51534	0.213877
$929$	−43.2103	−1.41768	−0.708842	−	0.705367i	$-0.750782\pi$
$929$	−43.2103	−1.41768	−0.708842	+	0.705367i	$0.750782\pi$
$930$	−8.38236	−0.274868
$931$	−24.6142	−0.806698
$932$	−18.1144	−0.593356
$933$	−35.4014	−1.15899
$934$	−1.90857	−0.0624503
$935$	−82.2903	−2.69118
$936$	−0.0733366	−0.00239708
$937$	−48.5422	−1.58580	−0.792902	−	0.609349i	$-0.791431\pi$
$937$	−48.5422	−1.58580	−0.792902	+	0.609349i	$0.791431\pi$
$938$	−7.61560	−0.248658
$939$	−18.8151	−0.614007
$940$	−20.6206	−0.672569
$941$	−8.37183	−0.272914	−0.136457	−	0.990646i	$-0.543572\pi$
$941$	−8.37183	−0.272914	−0.136457	+	0.990646i	$0.543572\pi$
$942$	−13.5659	−0.442002
$943$	−8.29046	−0.269974
$944$	11.5328	0.375360
$945$	−24.2663	−0.789382
$946$	−26.9604	−0.876557
$947$	−50.3700	−1.63681	−0.818403	−	0.574645i	$-0.805140\pi$
$947$	−50.3700	−1.63681	−0.818403	+	0.574645i	$0.805140\pi$
$948$	0.985643	0.0320122
$949$	0.229401	0.00744669
$950$	−64.8803	−2.10499
$951$	−50.8742	−1.64971
$952$	5.81422	0.188440
$953$	−47.9827	−1.55431	−0.777157	−	0.629307i	$-0.783339\pi$
$953$	−47.9827	−1.55431	−0.777157	+	0.629307i	$0.783339\pi$
$954$	−6.72908	−0.217862
$955$	60.9419	1.97203
$956$	−15.7775	−0.510282
$957$	−46.4171	−1.50045
$958$	−29.3971	−0.949777
$959$	2.55387	0.0824686
$960$	−8.38236	−0.270539
$961$	1.00000	0.0322581
$962$	−1.06504	−0.0343382
$963$	−5.08471	−0.163852
$964$	−7.76628	−0.250135
$965$	23.1269	0.744482
$966$	−2.02016	−0.0649975
$967$	−44.0893	−1.41782	−0.708908	−	0.705301i	$-0.750812\pi$
$967$	−44.0893	−1.41782	−0.708908	+	0.705301i	$0.750812\pi$
$968$	−3.26309	−0.104880
$969$	−40.7007	−1.30749
$970$	−4.44357	−0.142675
$971$	−11.1343	−0.357316	−0.178658	−	0.983911i	$-0.557175\pi$
$971$	−11.1343	−0.357316	−0.178658	+	0.983911i	$0.557175\pi$
$972$	5.73299	0.183886
$973$	−15.6131	−0.500534
$974$	16.0758	0.515101
$975$	−3.65242	−0.116971
$976$	15.0897	0.483009
$977$	1.36740	0.0437469	0.0218735	−	0.999761i	$-0.493037\pi$
$977$	1.36740	0.0437469	0.0218735	+	0.999761i	$0.493037\pi$
$978$	36.1799	1.15691
$979$	13.0706	0.417738
$980$	−24.8577	−0.794049
$981$	3.62720	0.115808
$982$	−0.253114	−0.00807718
$983$	−13.7737	−0.439312	−0.219656	−	0.975577i	$-0.570494\pi$
$983$	−13.7737	−0.439312	−0.219656	+	0.975577i	$0.570494\pi$
$984$	−17.3158	−0.552008
$985$	88.0647	2.80597
$986$	31.9482	1.01744
$987$	−10.3797	−0.330389
$988$	0.577763	0.0183811
$989$	−6.44746	−0.205017
$990$	9.37277	0.297886
$991$	29.5153	0.937585	0.468793	−	0.883308i	$-0.344689\pi$
$991$	29.5153	0.937585	0.468793	+	0.883308i	$0.344689\pi$
$992$	1.00000	0.0317500
$993$	−1.77342	−0.0562779
$994$	−4.77128	−0.151336
$995$	62.9774	1.99652
$996$	18.0356	0.571480
$997$	38.5275	1.22018	0.610090	−	0.792332i	$-0.291133\pi$
$997$	38.5275	1.22018	0.610090	+	0.792332i	$0.291133\pi$
$998$	−18.6289	−0.589687
$999$	37.3562	1.18190

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.j.1.8	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.j.1.8	✓	32	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:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.88640 q^{3} +1.00000 q^{4} +4.44357 q^{5} +1.88640 q^{6} -1.18572 q^{7} -1.00000 q^{8} +0.558507 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.88640 q^{3} +1.00000 q^{4} +4.44357 q^{5} +1.88640 q^{6} -1.18572 q^{7} -1.00000 q^{8} +0.558507 q^{9} -4.44357 q^{10} -3.77665 q^{11} -1.88640 q^{12} +0.131308 q^{13} +1.18572 q^{14} -8.38236 q^{15} +1.00000 q^{16} +4.90354 q^{17} -0.558507 q^{18} +4.40005 q^{19} +4.44357 q^{20} +2.23674 q^{21} +3.77665 q^{22} +0.903170 q^{23} +1.88640 q^{24} +14.7453 q^{25} -0.131308 q^{26} +4.60563 q^{27} -1.18572 q^{28} -6.51534 q^{29} +8.38236 q^{30} -1.00000 q^{31} -1.00000 q^{32} +7.12428 q^{33} -4.90354 q^{34} -5.26883 q^{35} +0.558507 q^{36} +8.11097 q^{37} -4.40005 q^{38} -0.247700 q^{39} -4.44357 q^{40} -9.17929 q^{41} -2.23674 q^{42} -7.13870 q^{43} -3.77665 q^{44} +2.48177 q^{45} -0.903170 q^{46} -4.64054 q^{47} -1.88640 q^{48} -5.59407 q^{49} -14.7453 q^{50} -9.25004 q^{51} +0.131308 q^{52} +12.0483 q^{53} -4.60563 q^{54} -16.7818 q^{55} +1.18572 q^{56} -8.30027 q^{57} +6.51534 q^{58} +11.5328 q^{59} -8.38236 q^{60} +15.0897 q^{61} +1.00000 q^{62} -0.662232 q^{63} +1.00000 q^{64} +0.583477 q^{65} -7.12428 q^{66} -6.42278 q^{67} +4.90354 q^{68} -1.70374 q^{69} +5.26883 q^{70} -4.02396 q^{71} -0.558507 q^{72} +1.74705 q^{73} -8.11097 q^{74} -27.8156 q^{75} +4.40005 q^{76} +4.47804 q^{77} +0.247700 q^{78} -0.522499 q^{79} +4.44357 q^{80} -10.3636 q^{81} +9.17929 q^{82} -9.56086 q^{83} +2.23674 q^{84} +21.7892 q^{85} +7.13870 q^{86} +12.2905 q^{87} +3.77665 q^{88} -3.46090 q^{89} -2.48177 q^{90} -0.155694 q^{91} +0.903170 q^{92} +1.88640 q^{93} +4.64054 q^{94} +19.5520 q^{95} +1.88640 q^{96} +1.00000 q^{97} +5.59407 q^{98} -2.10929 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9}+O(q^{10}) \) 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9	\( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9} - 4 q^{11} - 2 q^{12} + 10 q^{13} - 5 q^{14} - q^{15} + 32 q^{16} + 14 q^{17} - 30 q^{18} + 33 q^{19} + 4 q^{22} - 2 q^{23} + 2 q^{24} + 46 q^{25} - 10 q^{26} - 5 q^{27} + 5 q^{28} - q^{29} + q^{30} - 32 q^{31} - 32 q^{32} + 32 q^{33} - 14 q^{34} + 8 q^{35} + 30 q^{36} + 31 q^{37} - 33 q^{38} + 4 q^{39} + 31 q^{41} + 15 q^{43} - 4 q^{44} + q^{45} + 2 q^{46} - 14 q^{47} - 2 q^{48} + 75 q^{49} - 46 q^{50} + 27 q^{51} + 10 q^{52} - 31 q^{53} + 5 q^{54} + 14 q^{55} - 5 q^{56} + 51 q^{57} + q^{58} - 8 q^{59} - q^{60} + 24 q^{61} + 32 q^{62} + 23 q^{63} + 32 q^{64} + 20 q^{65} - 32 q^{66} + 17 q^{67} + 14 q^{68} - 31 q^{69} - 8 q^{70} - 31 q^{71} - 30 q^{72} + 19 q^{73} - 31 q^{74} - 40 q^{75} + 33 q^{76} + 8 q^{77} - 4 q^{78} + 39 q^{79} + 116 q^{81} - 31 q^{82} - 6 q^{83} + 56 q^{85} - 15 q^{86} - 17 q^{87} + 4 q^{88} + 8 q^{89} - q^{90} + 34 q^{91} - 2 q^{92} + 2 q^{93} + 14 q^{94} - 22 q^{95} + 2 q^{96} + 32 q^{97} - 75 q^{98} - 27 q^{99}+O(q^{100}) \) 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9 - 4 * q^11 - 2 * q^12 + 10 * q^13 - 5 * q^14 - q^15 + 32 * q^16 + 14 * q^17 - 30 * q^18 + 33 * q^19 + 4 * q^22 - 2 * q^23 + 2 * q^24 + 46 * q^25 - 10 * q^26 - 5 * q^27 + 5 * q^28 - q^29 + q^30 - 32 * q^31 - 32 * q^32 + 32 * q^33 - 14 * q^34 + 8 * q^35 + 30 * q^36 + 31 * q^37 - 33 * q^38 + 4 * q^39 + 31 * q^41 + 15 * q^43 - 4 * q^44 + q^45 + 2 * q^46 - 14 * q^47 - 2 * q^48 + 75 * q^49 - 46 * q^50 + 27 * q^51 + 10 * q^52 - 31 * q^53 + 5 * q^54 + 14 * q^55 - 5 * q^56 + 51 * q^57 + q^58 - 8 * q^59 - q^60 + 24 * q^61 + 32 * q^62 + 23 * q^63 + 32 * q^64 + 20 * q^65 - 32 * q^66 + 17 * q^67 + 14 * q^68 - 31 * q^69 - 8 * q^70 - 31 * q^71 - 30 * q^72 + 19 * q^73 - 31 * q^74 - 40 * q^75 + 33 * q^76 + 8 * q^77 - 4 * q^78 + 39 * q^79 + 116 * q^81 - 31 * q^82 - 6 * q^83 + 56 * q^85 - 15 * q^86 - 17 * q^87 + 4 * q^88 + 8 * q^89 - q^90 + 34 * q^91 - 2 * q^92 + 2 * q^93 + 14 * q^94 - 22 * q^95 + 2 * q^96 + 32 * q^97 - 75 * q^98 - 27 * q^99

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