LMFDB - Embedded newform 195.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [195,2,Mod(1,195)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(195, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("195.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	195.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:	$1.55708283941$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.316.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 2 $ x^3 - x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.34292$ of defining polynomial
Character	$\chi$	$=$	195.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.48929 q^{2} -1.00000 q^{3} +4.19656 q^{4} -1.00000 q^{5} +2.48929 q^{6} -1.19656 q^{7} -5.46787 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.48929 q^{2} -1.00000 q^{3} +4.19656 q^{4} -1.00000 q^{5} +2.48929 q^{6} -1.19656 q^{7} -5.46787 q^{8} +1.00000 q^{9} +2.48929 q^{10} -1.19656 q^{11} -4.19656 q^{12} +1.00000 q^{13} +2.97858 q^{14} +1.00000 q^{15} +5.21798 q^{16} +6.17513 q^{17} -2.48929 q^{18} +6.97858 q^{19} -4.19656 q^{20} +1.19656 q^{21} +2.97858 q^{22} +4.17513 q^{23} +5.46787 q^{24} +1.00000 q^{25} -2.48929 q^{26} -1.00000 q^{27} -5.02142 q^{28} +6.00000 q^{29} -2.48929 q^{30} -2.97858 q^{31} -2.05333 q^{32} +1.19656 q^{33} -15.3717 q^{34} +1.19656 q^{35} +4.19656 q^{36} +7.78202 q^{37} -17.3717 q^{38} -1.00000 q^{39} +5.46787 q^{40} -6.17513 q^{41} -2.97858 q^{42} -9.95715 q^{43} -5.02142 q^{44} -1.00000 q^{45} -10.3931 q^{46} -1.02142 q^{47} -5.21798 q^{48} -5.56825 q^{49} -2.48929 q^{50} -6.17513 q^{51} +4.19656 q^{52} +10.1751 q^{53} +2.48929 q^{54} +1.19656 q^{55} +6.54262 q^{56} -6.97858 q^{57} -14.9357 q^{58} +5.37169 q^{59} +4.19656 q^{60} +12.5682 q^{61} +7.41454 q^{62} -1.19656 q^{63} -5.32464 q^{64} -1.00000 q^{65} -2.97858 q^{66} +9.37169 q^{67} +25.9143 q^{68} -4.17513 q^{69} -2.97858 q^{70} -5.19656 q^{71} -5.46787 q^{72} -11.9572 q^{73} -19.3717 q^{74} -1.00000 q^{75} +29.2860 q^{76} +1.43175 q^{77} +2.48929 q^{78} -1.78202 q^{79} -5.21798 q^{80} +1.00000 q^{81} +15.3717 q^{82} -5.37169 q^{83} +5.02142 q^{84} -6.17513 q^{85} +24.7862 q^{86} -6.00000 q^{87} +6.54262 q^{88} +10.1751 q^{89} +2.48929 q^{90} -1.19656 q^{91} +17.5212 q^{92} +2.97858 q^{93} +2.54262 q^{94} -6.97858 q^{95} +2.05333 q^{96} -1.82487 q^{97} +13.8610 q^{98} -1.19656 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{3} + 8 q^{4} - 3 q^{5} + q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^3 + 8 * q^4 - 3 * q^5 + q^7 + 6 * q^8 + 3 * q^9	$ 3 q - 3 q^{3} + 8 q^{4} - 3 q^{5} + q^{7} + 6 q^{8} + 3 q^{9} + q^{11} - 8 q^{12} + 3 q^{13} - 6 q^{14} + 3 q^{15} + 26 q^{16} - q^{17} + 6 q^{19} - 8 q^{20} - q^{21} - 6 q^{22} - 7 q^{23} - 6 q^{24} + 3 q^{25} - 3 q^{27} - 30 q^{28} + 18 q^{29} + 6 q^{31} + 22 q^{32} - q^{33} - 22 q^{34} - q^{35} + 8 q^{36} + 13 q^{37} - 28 q^{38} - 3 q^{39} - 6 q^{40} + q^{41} + 6 q^{42} - 30 q^{44} - 3 q^{45} - 22 q^{46} - 18 q^{47} - 26 q^{48} + 12 q^{49} + q^{51} + 8 q^{52} + 11 q^{53} - q^{55} - 16 q^{56} - 6 q^{57} - 8 q^{59} + 8 q^{60} + 9 q^{61} + 28 q^{62} + q^{63} + 30 q^{64} - 3 q^{65} + 6 q^{66} + 4 q^{67} + 18 q^{68} + 7 q^{69} + 6 q^{70} - 11 q^{71} + 6 q^{72} - 6 q^{73} - 34 q^{74} - 3 q^{75} + 4 q^{76} + 33 q^{77} + 5 q^{79} - 26 q^{80} + 3 q^{81} + 22 q^{82} + 8 q^{83} + 30 q^{84} + q^{85} + 56 q^{86} - 18 q^{87} - 16 q^{88} + 11 q^{89} + q^{91} + 2 q^{92} - 6 q^{93} - 28 q^{94} - 6 q^{95} - 22 q^{96} - 25 q^{97} + 10 q^{98} + q^{99}+O(q^{100}) $ 3 * q - 3 * q^3 + 8 * q^4 - 3 * q^5 + q^7 + 6 * q^8 + 3 * q^9 + q^11 - 8 * q^12 + 3 * q^13 - 6 * q^14 + 3 * q^15 + 26 * q^16 - q^17 + 6 * q^19 - 8 * q^20 - q^21 - 6 * q^22 - 7 * q^23 - 6 * q^24 + 3 * q^25 - 3 * q^27 - 30 * q^28 + 18 * q^29 + 6 * q^31 + 22 * q^32 - q^33 - 22 * q^34 - q^35 + 8 * q^36 + 13 * q^37 - 28 * q^38 - 3 * q^39 - 6 * q^40 + q^41 + 6 * q^42 - 30 * q^44 - 3 * q^45 - 22 * q^46 - 18 * q^47 - 26 * q^48 + 12 * q^49 + q^51 + 8 * q^52 + 11 * q^53 - q^55 - 16 * q^56 - 6 * q^57 - 8 * q^59 + 8 * q^60 + 9 * q^61 + 28 * q^62 + q^63 + 30 * q^64 - 3 * q^65 + 6 * q^66 + 4 * q^67 + 18 * q^68 + 7 * q^69 + 6 * q^70 - 11 * q^71 + 6 * q^72 - 6 * q^73 - 34 * q^74 - 3 * q^75 + 4 * q^76 + 33 * q^77 + 5 * q^79 - 26 * q^80 + 3 * q^81 + 22 * q^82 + 8 * q^83 + 30 * q^84 + q^85 + 56 * q^86 - 18 * q^87 - 16 * q^88 + 11 * q^89 + q^91 + 2 * q^92 - 6 * q^93 - 28 * q^94 - 6 * q^95 - 22 * q^96 - 25 * q^97 + 10 * q^98 + 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 $

$2$	−2.48929	−1.76019	−0.880096	−	0.474795i	$-0.842522\pi$
$2$	−2.48929	−1.76019	−0.880096	+	0.474795i	$0.842522\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.19656	2.09828
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.48929	1.01625
$7$	−1.19656	−0.452256	−0.226128	−	0.974098i	$-0.572607\pi$
$7$	−1.19656	−0.452256	−0.226128	+	0.974098i	$0.572607\pi$
$8$	−5.46787	−1.93318
$9$	1.00000	0.333333
$10$	2.48929	0.787182
$11$	−1.19656	−0.360776	−0.180388	−	0.983596i	$-0.557735\pi$
$11$	−1.19656	−0.360776	−0.180388	+	0.983596i	$0.557735\pi$
$12$	−4.19656	−1.21144
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	2.97858	0.796058
$15$	1.00000	0.258199
$16$	5.21798	1.30450
$17$	6.17513	1.49769	0.748845	−	0.662745i	$-0.230609\pi$
$17$	6.17513	1.49769	0.748845	+	0.662745i	$0.230609\pi$
$18$	−2.48929	−0.586731
$19$	6.97858	1.60100	0.800498	−	0.599336i	$-0.204569\pi$
$19$	6.97858	1.60100	0.800498	+	0.599336i	$0.204569\pi$
$20$	−4.19656	−0.938379
$21$	1.19656	0.261110
$22$	2.97858	0.635035
$23$	4.17513	0.870576	0.435288	−	0.900291i	$-0.356647\pi$
$23$	4.17513	0.870576	0.435288	+	0.900291i	$0.356647\pi$
$24$	5.46787	1.11612
$25$	1.00000	0.200000
$26$	−2.48929	−0.488190
$27$	−1.00000	−0.192450
$28$	−5.02142	−0.948960
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	−2.48929	−0.454480
$31$	−2.97858	−0.534968	−0.267484	−	0.963562i	$-0.586192\pi$
$31$	−2.97858	−0.534968	−0.267484	+	0.963562i	$0.586192\pi$
$32$	−2.05333	−0.362980
$33$	1.19656	0.208294
$34$	−15.3717	−2.63622
$35$	1.19656	0.202255
$36$	4.19656	0.699426
$37$	7.78202	1.27936	0.639678	−	0.768643i	$-0.279068\pi$
$37$	7.78202	1.27936	0.639678	+	0.768643i	$0.279068\pi$
$38$	−17.3717	−2.81806
$39$	−1.00000	−0.160128
$40$	5.46787	0.864545
$41$	−6.17513	−0.964394	−0.482197	−	0.876063i	$-0.660161\pi$
$41$	−6.17513	−0.964394	−0.482197	+	0.876063i	$0.660161\pi$
$42$	−2.97858	−0.459604
$43$	−9.95715	−1.51845	−0.759226	−	0.650827i	$-0.774422\pi$
$43$	−9.95715	−1.51845	−0.759226	+	0.650827i	$0.774422\pi$
$44$	−5.02142	−0.757008
$45$	−1.00000	−0.149071
$46$	−10.3931	−1.53238
$47$	−1.02142	−0.148990	−0.0744949	−	0.997221i	$-0.523734\pi$
$47$	−1.02142	−0.148990	−0.0744949	+	0.997221i	$0.523734\pi$
$48$	−5.21798	−0.753151
$49$	−5.56825	−0.795464
$50$	−2.48929	−0.352039
$51$	−6.17513	−0.864692
$52$	4.19656	0.581958
$53$	10.1751	1.39766	0.698831	−	0.715287i	$-0.253704\pi$
$53$	10.1751	1.39766	0.698831	+	0.715287i	$0.253704\pi$
$54$	2.48929	0.338749
$55$	1.19656	0.161344
$56$	6.54262	0.874294
$57$	−6.97858	−0.924335
$58$	−14.9357	−1.96116
$59$	5.37169	0.699335	0.349667	−	0.936874i	$-0.386295\pi$
$59$	5.37169	0.699335	0.349667	+	0.936874i	$0.386295\pi$
$60$	4.19656	0.541773
$61$	12.5682	1.60920	0.804600	−	0.593818i	$-0.202380\pi$
$61$	12.5682	1.60920	0.804600	+	0.593818i	$0.202380\pi$
$62$	7.41454	0.941647
$63$	−1.19656	−0.150752
$64$	−5.32464	−0.665579
$65$	−1.00000	−0.124035
$66$	−2.97858	−0.366638
$67$	9.37169	1.14493	0.572467	−	0.819928i	$-0.305986\pi$
$67$	9.37169	1.14493	0.572467	+	0.819928i	$0.305986\pi$
$68$	25.9143	3.14257
$69$	−4.17513	−0.502627
$70$	−2.97858	−0.356008
$71$	−5.19656	−0.616718	−0.308359	−	0.951270i	$-0.599780\pi$
$71$	−5.19656	−0.616718	−0.308359	+	0.951270i	$0.599780\pi$
$72$	−5.46787	−0.644394
$73$	−11.9572	−1.39948	−0.699740	−	0.714398i	$-0.746701\pi$
$73$	−11.9572	−1.39948	−0.699740	+	0.714398i	$0.746701\pi$
$74$	−19.3717	−2.25191
$75$	−1.00000	−0.115470
$76$	29.2860	3.35933
$77$	1.43175	0.163163
$78$	2.48929	0.281856
$79$	−1.78202	−0.200493	−0.100246	−	0.994963i	$-0.531963\pi$
$79$	−1.78202	−0.200493	−0.100246	+	0.994963i	$0.531963\pi$
$80$	−5.21798	−0.583388
$81$	1.00000	0.111111
$82$	15.3717	1.69752
$83$	−5.37169	−0.589620	−0.294810	−	0.955556i	$-0.595256\pi$
$83$	−5.37169	−0.589620	−0.294810	+	0.955556i	$0.595256\pi$
$84$	5.02142	0.547882
$85$	−6.17513	−0.669787
$86$	24.7862	2.67277
$87$	−6.00000	−0.643268
$88$	6.54262	0.697445
$89$	10.1751	1.07856	0.539281	−	0.842126i	$-0.318696\pi$
$89$	10.1751	1.07856	0.539281	+	0.842126i	$0.318696\pi$
$90$	2.48929	0.262394
$91$	−1.19656	−0.125433
$92$	17.5212	1.82671
$93$	2.97858	0.308864
$94$	2.54262	0.262251
$95$	−6.97858	−0.715987
$96$	2.05333	0.209567
$97$	−1.82487	−0.185287	−0.0926435	−	0.995699i	$-0.529532\pi$
$97$	−1.82487	−0.185287	−0.0926435	+	0.995699i	$0.529532\pi$
$98$	13.8610	1.40017
$99$	−1.19656	−0.120259
$100$	4.19656	0.419656
$101$	−10.3503	−1.02989	−0.514945	−	0.857223i	$-0.672188\pi$
$101$	−10.3503	−1.02989	−0.514945	+	0.857223i	$0.672188\pi$
$102$	15.3717	1.52202
$103$	18.7434	1.84684	0.923420	−	0.383790i	$-0.125381\pi$
$103$	18.7434	1.84684	0.923420	+	0.383790i	$0.125381\pi$
$104$	−5.46787	−0.536168
$105$	−1.19656	−0.116772
$106$	−25.3288	−2.46016
$107$	−18.5682	−1.79506	−0.897530	−	0.440953i	$-0.854641\pi$
$107$	−18.5682	−1.79506	−0.897530	+	0.440953i	$0.854641\pi$
$108$	−4.19656	−0.403814
$109$	8.39312	0.803915	0.401957	−	0.915658i	$-0.368330\pi$
$109$	8.39312	0.803915	0.401957	+	0.915658i	$0.368330\pi$
$110$	−2.97858	−0.283996
$111$	−7.78202	−0.738637
$112$	−6.24361	−0.589966
$113$	7.95715	0.748546	0.374273	−	0.927319i	$-0.377892\pi$
$113$	7.95715	0.748546	0.374273	+	0.927319i	$0.377892\pi$
$114$	17.3717	1.62701
$115$	−4.17513	−0.389333
$116$	25.1793	2.33784
$117$	1.00000	0.0924500
$118$	−13.3717	−1.23096
$119$	−7.38890	−0.677340
$120$	−5.46787	−0.499146
$121$	−9.56825	−0.869841
$122$	−31.2860	−2.83250
$123$	6.17513	0.556793
$124$	−12.4998	−1.12251
$125$	−1.00000	−0.0894427
$126$	2.97858	0.265353
$127$	−10.3931	−0.922240	−0.461120	−	0.887338i	$-0.652552\pi$
$127$	−10.3931	−0.922240	−0.461120	+	0.887338i	$0.652552\pi$
$128$	17.3612	1.53453
$129$	9.95715	0.876679
$130$	2.48929	0.218325
$131$	−6.39312	−0.558569	−0.279285	−	0.960208i	$-0.590097\pi$
$131$	−6.39312	−0.558569	−0.279285	+	0.960208i	$0.590097\pi$
$132$	5.02142	0.437059
$133$	−8.35027	−0.724060
$134$	−23.3288	−2.01531
$135$	1.00000	0.0860663
$136$	−33.7648	−2.89531
$137$	16.7434	1.43048	0.715242	−	0.698877i	$-0.246316\pi$
$137$	16.7434	1.43048	0.715242	+	0.698877i	$0.246316\pi$
$138$	10.3931	0.884721
$139$	5.78202	0.490424	0.245212	−	0.969469i	$-0.421142\pi$
$139$	5.78202	0.490424	0.245212	+	0.969469i	$0.421142\pi$
$140$	5.02142	0.424388
$141$	1.02142	0.0860193
$142$	12.9357	1.08554
$143$	−1.19656	−0.100061
$144$	5.21798	0.434832
$145$	−6.00000	−0.498273
$146$	29.7648	2.46335
$147$	5.56825	0.459262
$148$	32.6577	2.68445
$149$	15.3461	1.25720	0.628599	−	0.777730i	$-0.283629\pi$
$149$	15.3461	1.25720	0.628599	+	0.777730i	$0.283629\pi$
$150$	2.48929	0.203250
$151$	−8.58546	−0.698675	−0.349337	−	0.936997i	$-0.613593\pi$
$151$	−8.58546	−0.698675	−0.349337	+	0.936997i	$0.613593\pi$
$152$	−38.1579	−3.09502
$153$	6.17513	0.499230
$154$	−3.56404	−0.287198
$155$	2.97858	0.239245
$156$	−4.19656	−0.335994
$157$	2.78623	0.222365	0.111183	−	0.993800i	$-0.464536\pi$
$157$	2.78623	0.222365	0.111183	+	0.993800i	$0.464536\pi$
$158$	4.43596	0.352906
$159$	−10.1751	−0.806941
$160$	2.05333	0.162330
$161$	−4.99579	−0.393723
$162$	−2.48929	−0.195577
$163$	8.76060	0.686183	0.343091	−	0.939302i	$-0.388526\pi$
$163$	8.76060	0.686183	0.343091	+	0.939302i	$0.388526\pi$
$164$	−25.9143	−2.02357
$165$	−1.19656	−0.0931519
$166$	13.3717	1.03784
$167$	−17.3717	−1.34426	−0.672131	−	0.740432i	$-0.734621\pi$
$167$	−17.3717	−1.34426	−0.672131	+	0.740432i	$0.734621\pi$
$168$	−6.54262	−0.504774
$169$	1.00000	0.0769231
$170$	15.3717	1.17895
$171$	6.97858	0.533665
$172$	−41.7858	−3.18614
$173$	−7.95715	−0.604971	−0.302486	−	0.953154i	$-0.597816\pi$
$173$	−7.95715	−0.604971	−0.302486	+	0.953154i	$0.597816\pi$
$174$	14.9357	1.13227
$175$	−1.19656	−0.0904513
$176$	−6.24361	−0.470630
$177$	−5.37169	−0.403761
$178$	−25.3288	−1.89848
$179$	−15.5640	−1.16331	−0.581655	−	0.813435i	$-0.697595\pi$
$179$	−15.5640	−1.16331	−0.581655	+	0.813435i	$0.697595\pi$
$180$	−4.19656	−0.312793
$181$	15.7820	1.17307	0.586534	−	0.809925i	$-0.300492\pi$
$181$	15.7820	1.17307	0.586534	+	0.809925i	$0.300492\pi$
$182$	2.97858	0.220787
$183$	−12.5682	−0.929072
$184$	−22.8291	−1.68298
$185$	−7.78202	−0.572145
$186$	−7.41454	−0.543660
$187$	−7.38890	−0.540330
$188$	−4.28646	−0.312622
$189$	1.19656	0.0870368
$190$	17.3717	1.26028
$191$	10.7434	0.777364	0.388682	−	0.921372i	$-0.372930\pi$
$191$	10.7434	0.777364	0.388682	+	0.921372i	$0.372930\pi$
$192$	5.32464	0.384272
$193$	9.73917	0.701041	0.350521	−	0.936555i	$-0.386005\pi$
$193$	9.73917	0.701041	0.350521	+	0.936555i	$0.386005\pi$
$194$	4.54262	0.326141
$195$	1.00000	0.0716115
$196$	−23.3675	−1.66911
$197$	−9.56404	−0.681410	−0.340705	−	0.940170i	$-0.610666\pi$
$197$	−9.56404	−0.681410	−0.340705	+	0.940170i	$0.610666\pi$
$198$	2.97858	0.211678
$199$	5.95715	0.422291	0.211146	−	0.977455i	$-0.432281\pi$
$199$	5.95715	0.422291	0.211146	+	0.977455i	$0.432281\pi$
$200$	−5.46787	−0.386636
$201$	−9.37169	−0.661028
$202$	25.7648	1.81281
$203$	−7.17935	−0.503891
$204$	−25.9143	−1.81436
$205$	6.17513	0.431290
$206$	−46.6577	−3.25080
$207$	4.17513	0.290192
$208$	5.21798	0.361802
$209$	−8.35027	−0.577600
$210$	2.97858	0.205541
$211$	23.9143	1.64633	0.823164	−	0.567803i	$-0.192206\pi$
$211$	23.9143	1.64633	0.823164	+	0.567803i	$0.192206\pi$
$212$	42.7005	2.93269
$213$	5.19656	0.356062
$214$	46.2217	3.15965
$215$	9.95715	0.679072
$216$	5.46787	0.372041
$217$	3.56404	0.241943
$218$	−20.8929	−1.41504
$219$	11.9572	0.807990
$220$	5.02142	0.338544
$221$	6.17513	0.415385
$222$	19.3717	1.30014
$223$	2.62831	0.176004	0.0880022	−	0.996120i	$-0.471952\pi$
$223$	2.62831	0.176004	0.0880022	+	0.996120i	$0.471952\pi$
$224$	2.45692	0.164160
$225$	1.00000	0.0666667
$226$	−19.8077	−1.31759
$227$	15.7648	1.04635	0.523174	−	0.852226i	$-0.324748\pi$
$227$	15.7648	1.04635	0.523174	+	0.852226i	$0.324748\pi$
$228$	−29.2860	−1.93951
$229$	8.74338	0.577779	0.288890	−	0.957362i	$-0.406714\pi$
$229$	8.74338	0.577779	0.288890	+	0.957362i	$0.406714\pi$
$230$	10.3931	0.685302
$231$	−1.43175	−0.0942022
$232$	−32.8072	−2.15390
$233$	−2.17513	−0.142498	−0.0712489	−	0.997459i	$-0.522698\pi$
$233$	−2.17513	−0.142498	−0.0712489	+	0.997459i	$0.522698\pi$
$234$	−2.48929	−0.162730
$235$	1.02142	0.0666303
$236$	22.5426	1.46740
$237$	1.78202	0.115755
$238$	18.3931	1.19225
$239$	2.80344	0.181340	0.0906698	−	0.995881i	$-0.471099\pi$
$239$	2.80344	0.181340	0.0906698	+	0.995881i	$0.471099\pi$
$240$	5.21798	0.336819
$241$	−6.00000	−0.386494	−0.193247	−	0.981150i	$-0.561902\pi$
$241$	−6.00000	−0.386494	−0.193247	+	0.981150i	$0.561902\pi$
$242$	23.8181	1.53109
$243$	−1.00000	−0.0641500
$244$	52.7434	3.37655
$245$	5.56825	0.355742
$246$	−15.3717	−0.980063
$247$	6.97858	0.444036
$248$	16.2865	1.03419
$249$	5.37169	0.340417
$250$	2.48929	0.157436
$251$	−23.9143	−1.50946	−0.754729	−	0.656037i	$-0.772232\pi$
$251$	−23.9143	−1.50946	−0.754729	+	0.656037i	$0.772232\pi$
$252$	−5.02142	−0.316320
$253$	−4.99579	−0.314083
$254$	25.8715	1.62332
$255$	6.17513	0.386702
$256$	−32.5678	−2.03549
$257$	−19.9572	−1.24489	−0.622447	−	0.782662i	$-0.713861\pi$
$257$	−19.9572	−1.24489	−0.622447	+	0.782662i	$0.713861\pi$
$258$	−24.7862	−1.54312
$259$	−9.31163	−0.578597
$260$	−4.19656	−0.260259
$261$	6.00000	0.371391
$262$	15.9143	0.983189
$263$	8.00000	0.493301	0.246651	−	0.969104i	$-0.420670\pi$
$263$	8.00000	0.493301	0.246651	+	0.969104i	$0.420670\pi$
$264$	−6.54262	−0.402670
$265$	−10.1751	−0.625054
$266$	20.7862	1.27449
$267$	−10.1751	−0.622708
$268$	39.3288	2.40239
$269$	−2.35027	−0.143298	−0.0716492	−	0.997430i	$-0.522826\pi$
$269$	−2.35027	−0.143298	−0.0716492	+	0.997430i	$0.522826\pi$
$270$	−2.48929	−0.151493
$271$	10.9786	0.666901	0.333451	−	0.942768i	$-0.391787\pi$
$271$	10.9786	0.666901	0.333451	+	0.942768i	$0.391787\pi$
$272$	32.2217	1.95373
$273$	1.19656	0.0724190
$274$	−41.6791	−2.51793
$275$	−1.19656	−0.0721551
$276$	−17.5212	−1.05465
$277$	1.21377	0.0729283	0.0364642	−	0.999335i	$-0.488391\pi$
$277$	1.21377	0.0729283	0.0364642	+	0.999335i	$0.488391\pi$
$278$	−14.3931	−0.863242
$279$	−2.97858	−0.178323
$280$	−6.54262	−0.390996
$281$	11.9572	0.713304	0.356652	−	0.934237i	$-0.383918\pi$
$281$	11.9572	0.713304	0.356652	+	0.934237i	$0.383918\pi$
$282$	−2.54262	−0.151411
$283$	−29.8715	−1.77567	−0.887837	−	0.460158i	$-0.847793\pi$
$283$	−29.8715	−1.77567	−0.887837	+	0.460158i	$0.847793\pi$
$284$	−21.8077	−1.29405
$285$	6.97858	0.413375
$286$	2.97858	0.176127
$287$	7.38890	0.436153
$288$	−2.05333	−0.120993
$289$	21.1323	1.24308
$290$	14.9357	0.877056
$291$	1.82487	0.106975
$292$	−50.1789	−2.93650
$293$	0.777809	0.0454401	0.0227200	−	0.999742i	$-0.492767\pi$
$293$	0.777809	0.0454401	0.0227200	+	0.999742i	$0.492767\pi$
$294$	−13.8610	−0.808389
$295$	−5.37169	−0.312752
$296$	−42.5510	−2.47323
$297$	1.19656	0.0694313
$298$	−38.2008	−2.21291
$299$	4.17513	0.241454
$300$	−4.19656	−0.242288
$301$	11.9143	0.686729
$302$	21.3717	1.22980
$303$	10.3503	0.594607
$304$	36.4141	2.08849
$305$	−12.5682	−0.719656
$306$	−15.3717	−0.878741
$307$	0.760597	0.0434095	0.0217048	−	0.999764i	$-0.493091\pi$
$307$	0.760597	0.0434095	0.0217048	+	0.999764i	$0.493091\pi$
$308$	6.00842	0.342362
$309$	−18.7434	−1.06627
$310$	−7.41454	−0.421117
$311$	−23.1281	−1.31147	−0.655736	−	0.754990i	$-0.727642\pi$
$311$	−23.1281	−1.31147	−0.655736	+	0.754990i	$0.727642\pi$
$312$	5.46787	0.309557
$313$	−33.9143	−1.91695	−0.958475	−	0.285176i	$-0.907948\pi$
$313$	−33.9143	−1.91695	−0.958475	+	0.285176i	$0.907948\pi$
$314$	−6.93573	−0.391406
$315$	1.19656	0.0674184
$316$	−7.47835	−0.420690
$317$	9.64973	0.541983	0.270991	−	0.962582i	$-0.412648\pi$
$317$	9.64973	0.541983	0.270991	+	0.962582i	$0.412648\pi$
$318$	25.3288	1.42037
$319$	−7.17935	−0.401966
$320$	5.32464	0.297656
$321$	18.5682	1.03638
$322$	12.4360	0.693029
$323$	43.0937	2.39780
$324$	4.19656	0.233142
$325$	1.00000	0.0554700
$326$	−21.8077	−1.20781
$327$	−8.39312	−0.464140
$328$	33.7648	1.86435
$329$	1.22219	0.0673816
$330$	2.97858	0.163965
$331$	15.3288	0.842550	0.421275	−	0.906933i	$-0.361583\pi$
$331$	15.3288	0.842550	0.421275	+	0.906933i	$0.361583\pi$
$332$	−22.5426	−1.23719
$333$	7.78202	0.426452
$334$	43.2432	2.36616
$335$	−9.37169	−0.512030
$336$	6.24361	0.340617
$337$	−22.3503	−1.21750	−0.608748	−	0.793363i	$-0.708328\pi$
$337$	−22.3503	−1.21750	−0.608748	+	0.793363i	$0.708328\pi$
$338$	−2.48929	−0.135399
$339$	−7.95715	−0.432173
$340$	−25.9143	−1.40540
$341$	3.56404	0.193004
$342$	−17.3717	−0.939354
$343$	15.0386	0.812010
$344$	54.4444	2.93544
$345$	4.17513	0.224782
$346$	19.8077	1.06487
$347$	−5.78202	−0.310395	−0.155198	−	0.987883i	$-0.549601\pi$
$347$	−5.78202	−0.310395	−0.155198	+	0.987883i	$0.549601\pi$
$348$	−25.1793	−1.34975
$349$	−27.5212	−1.47318	−0.736588	−	0.676342i	$-0.763564\pi$
$349$	−27.5212	−1.47318	−0.736588	+	0.676342i	$0.763564\pi$
$350$	2.97858	0.159212
$351$	−1.00000	−0.0533761
$352$	2.45692	0.130955
$353$	−28.7434	−1.52986	−0.764928	−	0.644116i	$-0.777225\pi$
$353$	−28.7434	−1.52986	−0.764928	+	0.644116i	$0.777225\pi$
$354$	13.3717	0.710697
$355$	5.19656	0.275805
$356$	42.7005	2.26312
$357$	7.38890	0.391062
$358$	38.7434	2.04765
$359$	−12.5855	−0.664235	−0.332118	−	0.943238i	$-0.607763\pi$
$359$	−12.5855	−0.664235	−0.332118	+	0.943238i	$0.607763\pi$
$360$	5.46787	0.288182
$361$	29.7005	1.56319
$362$	−39.2860	−2.06483
$363$	9.56825	0.502203
$364$	−5.02142	−0.263194
$365$	11.9572	0.625866
$366$	31.2860	1.63535
$367$	−27.9143	−1.45712	−0.728558	−	0.684985i	$-0.759809\pi$
$367$	−27.9143	−1.45712	−0.728558	+	0.684985i	$0.759809\pi$
$368$	21.7858	1.13566
$369$	−6.17513	−0.321465
$370$	19.3717	1.00709
$371$	−12.1751	−0.632102
$372$	12.4998	0.648083
$373$	−2.35027	−0.121692	−0.0608462	−	0.998147i	$-0.519380\pi$
$373$	−2.35027	−0.121692	−0.0608462	+	0.998147i	$0.519380\pi$
$374$	18.3931	0.951085
$375$	1.00000	0.0516398
$376$	5.58500	0.288025
$377$	6.00000	0.309016
$378$	−2.97858	−0.153201
$379$	24.5510	1.26110	0.630551	−	0.776148i	$-0.282829\pi$
$379$	24.5510	1.26110	0.630551	+	0.776148i	$0.282829\pi$
$380$	−29.2860	−1.50234
$381$	10.3931	0.532455
$382$	−26.7434	−1.36831
$383$	5.80765	0.296757	0.148379	−	0.988931i	$-0.452595\pi$
$383$	5.80765	0.296757	0.148379	+	0.988931i	$0.452595\pi$
$384$	−17.3612	−0.885961
$385$	−1.43175	−0.0729687
$386$	−24.2436	−1.23397
$387$	−9.95715	−0.506151
$388$	−7.65815	−0.388784
$389$	13.6497	0.692069	0.346034	−	0.938222i	$-0.387528\pi$
$389$	13.6497	0.692069	0.346034	+	0.938222i	$0.387528\pi$
$390$	−2.48929	−0.126050
$391$	25.7820	1.30385
$392$	30.4464	1.53778
$393$	6.39312	0.322490
$394$	23.8077	1.19941
$395$	1.78202	0.0896631
$396$	−5.02142	−0.252336
$397$	−12.1323	−0.608902	−0.304451	−	0.952528i	$-0.598473\pi$
$397$	−12.1323	−0.608902	−0.304451	+	0.952528i	$0.598473\pi$
$398$	−14.8291	−0.743314
$399$	8.35027	0.418036
$400$	5.21798	0.260899
$401$	−37.4439	−1.86986	−0.934930	−	0.354832i	$-0.884538\pi$
$401$	−37.4439	−1.86986	−0.934930	+	0.354832i	$0.884538\pi$
$402$	23.3288	1.16354
$403$	−2.97858	−0.148373
$404$	−43.4355	−2.16100
$405$	−1.00000	−0.0496904
$406$	17.8715	0.886946
$407$	−9.31163	−0.461561
$408$	33.7648	1.67161
$409$	−14.0000	−0.692255	−0.346128	−	0.938187i	$-0.612504\pi$
$409$	−14.0000	−0.692255	−0.346128	+	0.938187i	$0.612504\pi$
$410$	−15.3717	−0.759154
$411$	−16.7434	−0.825890
$412$	78.6577	3.87519
$413$	−6.42754	−0.316279
$414$	−10.3931	−0.510794
$415$	5.37169	0.263686
$416$	−2.05333	−0.100673
$417$	−5.78202	−0.283147
$418$	20.7862	1.01669
$419$	3.17935	0.155321	0.0776606	−	0.996980i	$-0.475255\pi$
$419$	3.17935	0.155321	0.0776606	+	0.996980i	$0.475255\pi$
$420$	−5.02142	−0.245020
$421$	−16.3074	−0.794775	−0.397388	−	0.917651i	$-0.630083\pi$
$421$	−16.3074	−0.794775	−0.397388	+	0.917651i	$0.630083\pi$
$422$	−59.5296	−2.89786
$423$	−1.02142	−0.0496633
$424$	−55.6363	−2.70194
$425$	6.17513	0.299538
$426$	−12.9357	−0.626738
$427$	−15.0386	−0.727771
$428$	−77.9227	−3.76654
$429$	1.19656	0.0577703
$430$	−24.7862	−1.19530
$431$	4.58546	0.220874	0.110437	−	0.993883i	$-0.464775\pi$
$431$	4.58546	0.220874	0.110437	+	0.993883i	$0.464775\pi$
$432$	−5.21798	−0.251050
$433$	−38.3503	−1.84300	−0.921498	−	0.388383i	$-0.873034\pi$
$433$	−38.3503	−1.84300	−0.921498	+	0.388383i	$0.873034\pi$
$434$	−8.87192	−0.425866
$435$	6.00000	0.287678
$436$	35.2222	1.68684
$437$	29.1365	1.39379
$438$	−29.7648	−1.42222
$439$	7.73917	0.369371	0.184685	−	0.982798i	$-0.440873\pi$
$439$	7.73917	0.369371	0.184685	+	0.982798i	$0.440873\pi$
$440$	−6.54262	−0.311907
$441$	−5.56825	−0.265155
$442$	−15.3717	−0.731157
$443$	34.9185	1.65903	0.829514	−	0.558485i	$-0.188617\pi$
$443$	34.9185	1.65903	0.829514	+	0.558485i	$0.188617\pi$
$444$	−32.6577	−1.54987
$445$	−10.1751	−0.482348
$446$	−6.54262	−0.309802
$447$	−15.3461	−0.725844
$448$	6.37123	0.301012
$449$	−6.17513	−0.291423	−0.145711	−	0.989327i	$-0.546547\pi$
$449$	−6.17513	−0.291423	−0.145711	+	0.989327i	$0.546547\pi$
$450$	−2.48929	−0.117346
$451$	7.38890	0.347930
$452$	33.3927	1.57066
$453$	8.58546	0.403380
$454$	−39.2432	−1.84177
$455$	1.19656	0.0560955
$456$	38.1579	1.78691
$457$	1.38890	0.0649702	0.0324851	−	0.999472i	$-0.489658\pi$
$457$	1.38890	0.0649702	0.0324851	+	0.999472i	$0.489658\pi$
$458$	−21.7648	−1.01700
$459$	−6.17513	−0.288231
$460$	−17.5212	−0.816930
$461$	28.4826	1.32657	0.663283	−	0.748369i	$-0.269163\pi$
$461$	28.4826	1.32657	0.663283	+	0.748369i	$0.269163\pi$
$462$	3.56404	0.165814
$463$	16.3759	0.761053	0.380526	−	0.924770i	$-0.375743\pi$
$463$	16.3759	0.761053	0.380526	+	0.924770i	$0.375743\pi$
$464$	31.3079	1.45343
$465$	−2.97858	−0.138128
$466$	5.41454	0.250824
$467$	25.7476	1.19146	0.595728	−	0.803186i	$-0.296864\pi$
$467$	25.7476	1.19146	0.595728	+	0.803186i	$0.296864\pi$
$468$	4.19656	0.193986
$469$	−11.2138	−0.517804
$470$	−2.54262	−0.117282
$471$	−2.78623	−0.128383
$472$	−29.3717	−1.35194
$473$	11.9143	0.547820
$474$	−4.43596	−0.203750
$475$	6.97858	0.320199
$476$	−31.0080	−1.42125
$477$	10.1751	0.465887
$478$	−6.97858	−0.319193
$479$	−7.58967	−0.346781	−0.173391	−	0.984853i	$-0.555472\pi$
$479$	−7.58967	−0.346781	−0.173391	+	0.984853i	$0.555472\pi$
$480$	−2.05333	−0.0937212
$481$	7.78202	0.354830
$482$	14.9357	0.680304
$483$	4.99579	0.227316
$484$	−40.1537	−1.82517
$485$	1.82487	0.0828629
$486$	2.48929	0.112916
$487$	4.41033	0.199851	0.0999255	−	0.994995i	$-0.468140\pi$
$487$	4.41033	0.199851	0.0999255	+	0.994995i	$0.468140\pi$
$488$	−68.7215	−3.11088
$489$	−8.76060	−0.396168
$490$	−13.8610	−0.626175
$491$	−0.0856914	−0.00386720	−0.00193360	−	0.999998i	$-0.500615\pi$
$491$	−0.0856914	−0.00386720	−0.00193360	+	0.999998i	$0.500615\pi$
$492$	25.9143	1.16831
$493$	37.0508	1.66868
$494$	−17.3717	−0.781589
$495$	1.19656	0.0537813
$496$	−15.5422	−0.697863
$497$	6.21798	0.278915
$498$	−13.3717	−0.599200
$499$	−17.7220	−0.793344	−0.396672	−	0.917960i	$-0.629835\pi$
$499$	−17.7220	−0.793344	−0.396672	+	0.917960i	$0.629835\pi$
$500$	−4.19656	−0.187676
$501$	17.3717	0.776110
$502$	59.5296	2.65694
$503$	−8.70054	−0.387938	−0.193969	−	0.981008i	$-0.562136\pi$
$503$	−8.70054	−0.387938	−0.193969	+	0.981008i	$0.562136\pi$
$504$	6.54262	0.291431
$505$	10.3503	0.460581
$506$	12.4360	0.552846
$507$	−1.00000	−0.0444116
$508$	−43.6153	−1.93512
$509$	−33.3545	−1.47841	−0.739206	−	0.673480i	$-0.764799\pi$
$509$	−33.3545	−1.47841	−0.739206	+	0.673480i	$0.764799\pi$
$510$	−15.3717	−0.680670
$511$	14.3074	0.632923
$512$	46.3482	2.04832
$513$	−6.97858	−0.308112
$514$	49.6791	2.19125
$515$	−18.7434	−0.825932
$516$	41.7858	1.83952
$517$	1.22219	0.0537519
$518$	23.1793	1.01844
$519$	7.95715	0.349280
$520$	5.46787	0.239782
$521$	18.7005	0.819285	0.409643	−	0.912246i	$-0.365653\pi$
$521$	18.7005	0.819285	0.409643	+	0.912246i	$0.365653\pi$
$522$	−14.9357	−0.653719
$523$	−4.00000	−0.174908	−0.0874539	−	0.996169i	$-0.527873\pi$
$523$	−4.00000	−0.174908	−0.0874539	+	0.996169i	$0.527873\pi$
$524$	−26.8291	−1.17203
$525$	1.19656	0.0522221
$526$	−19.9143	−0.868305
$527$	−18.3931	−0.801217
$528$	6.24361	0.271718
$529$	−5.56825	−0.242098
$530$	25.3288	1.10021
$531$	5.37169	0.233112
$532$	−35.0424	−1.51928
$533$	−6.17513	−0.267475
$534$	25.3288	1.09609
$535$	18.5682	0.802775
$536$	−51.2432	−2.21337
$537$	15.5640	0.671638
$538$	5.85050	0.252233
$539$	6.66273	0.286984
$540$	4.19656	0.180591
$541$	−41.5296	−1.78550	−0.892749	−	0.450555i	$-0.851226\pi$
$541$	−41.5296	−1.78550	−0.892749	+	0.450555i	$0.851226\pi$
$542$	−27.3288	−1.17387
$543$	−15.7820	−0.677271
$544$	−12.6796	−0.543632
$545$	−8.39312	−0.359522
$546$	−2.97858	−0.127471
$547$	−7.91431	−0.338391	−0.169196	−	0.985582i	$-0.554117\pi$
$547$	−7.91431	−0.338391	−0.169196	+	0.985582i	$0.554117\pi$
$548$	70.2646	3.00155
$549$	12.5682	0.536400
$550$	2.97858	0.127007
$551$	41.8715	1.78378
$552$	22.8291	0.971670
$553$	2.13229	0.0906742
$554$	−3.02142	−0.128368
$555$	7.78202	0.330328
$556$	24.2646	1.02905
$557$	42.7005	1.80928	0.904640	−	0.426177i	$-0.140140\pi$
$557$	42.7005	1.80928	0.904640	+	0.426177i	$0.140140\pi$
$558$	7.41454	0.313882
$559$	−9.95715	−0.421143
$560$	6.24361	0.263841
$561$	7.38890	0.311960
$562$	−29.7648	−1.25555
$563$	1.04706	0.0441282	0.0220641	−	0.999757i	$-0.492976\pi$
$563$	1.04706	0.0441282	0.0220641	+	0.999757i	$0.492976\pi$
$564$	4.28646	0.180493
$565$	−7.95715	−0.334760
$566$	74.3587	3.12553
$567$	−1.19656	−0.0502507
$568$	28.4141	1.19223
$569$	16.7778	0.703362	0.351681	−	0.936120i	$-0.385610\pi$
$569$	16.7778	0.703362	0.351681	+	0.936120i	$0.385610\pi$
$570$	−17.3717	−0.727620
$571$	−20.6111	−0.862548	−0.431274	−	0.902221i	$-0.641936\pi$
$571$	−20.6111	−0.862548	−0.431274	+	0.902221i	$0.641936\pi$
$572$	−5.02142	−0.209956
$573$	−10.7434	−0.448811
$574$	−18.3931	−0.767714
$575$	4.17513	0.174115
$576$	−5.32464	−0.221860
$577$	1.38890	0.0578208	0.0289104	−	0.999582i	$-0.490796\pi$
$577$	1.38890	0.0578208	0.0289104	+	0.999582i	$0.490796\pi$
$578$	−52.6044	−2.18805
$579$	−9.73917	−0.404746
$580$	−25.1793	−1.04552
$581$	6.42754	0.266659
$582$	−4.54262	−0.188298
$583$	−12.1751	−0.504243
$584$	65.3801	2.70545
$585$	−1.00000	−0.0413449
$586$	−1.93619	−0.0799833
$587$	−0.935731	−0.0386218	−0.0193109	−	0.999814i	$-0.506147\pi$
$587$	−0.935731	−0.0386218	−0.0193109	+	0.999814i	$0.506147\pi$
$588$	23.3675	0.963659
$589$	−20.7862	−0.856482
$590$	13.3717	0.550504
$591$	9.56404	0.393412
$592$	40.6064	1.66891
$593$	−0.478807	−0.0196622	−0.00983112	−	0.999952i	$-0.503129\pi$
$593$	−0.478807	−0.0196622	−0.00983112	+	0.999952i	$0.503129\pi$
$594$	−2.97858	−0.122213
$595$	7.38890	0.302916
$596$	64.4006	2.63795
$597$	−5.95715	−0.243810
$598$	−10.3931	−0.425006
$599$	29.0852	1.18839	0.594195	−	0.804321i	$-0.297471\pi$
$599$	29.0852	1.18839	0.594195	+	0.804321i	$0.297471\pi$
$600$	5.46787	0.223225
$601$	11.4318	0.466311	0.233155	−	0.972439i	$-0.425095\pi$
$601$	11.4318	0.466311	0.233155	+	0.972439i	$0.425095\pi$
$602$	−29.6582	−1.20878
$603$	9.37169	0.381645
$604$	−36.0294	−1.46601
$605$	9.56825	0.389005
$606$	−25.7648	−1.04662
$607$	27.9143	1.13301	0.566503	−	0.824059i	$-0.308296\pi$
$607$	27.9143	1.13301	0.566503	+	0.824059i	$0.308296\pi$
$608$	−14.3293	−0.581130
$609$	7.17935	0.290922
$610$	31.2860	1.26673
$611$	−1.02142	−0.0413223
$612$	25.9143	1.04752
$613$	−4.65394	−0.187971	−0.0939855	−	0.995574i	$-0.529961\pi$
$613$	−4.65394	−0.187971	−0.0939855	+	0.995574i	$0.529961\pi$
$614$	−1.89334	−0.0764092
$615$	−6.17513	−0.249005
$616$	−7.82862	−0.315424
$617$	−15.9572	−0.642411	−0.321205	−	0.947010i	$-0.604088\pi$
$617$	−15.9572	−0.642411	−0.321205	+	0.947010i	$0.604088\pi$
$618$	46.6577	1.87685
$619$	1.02142	0.0410545	0.0205272	−	0.999789i	$-0.493466\pi$
$619$	1.02142	0.0410545	0.0205272	+	0.999789i	$0.493466\pi$
$620$	12.4998	0.502003
$621$	−4.17513	−0.167542
$622$	57.5725	2.30845
$623$	−12.1751	−0.487786
$624$	−5.21798	−0.208886
$625$	1.00000	0.0400000
$626$	84.4225	3.37420
$627$	8.35027	0.333478
$628$	11.6926	0.466585
$629$	48.0550	1.91608
$630$	−2.97858	−0.118669
$631$	−20.4998	−0.816083	−0.408041	−	0.912963i	$-0.633788\pi$
$631$	−20.4998	−0.816083	−0.408041	+	0.912963i	$0.633788\pi$
$632$	9.74384	0.387589
$633$	−23.9143	−0.950508
$634$	−24.0210	−0.953994
$635$	10.3931	0.412438
$636$	−42.7005	−1.69319
$637$	−5.56825	−0.220622
$638$	17.8715	0.707538
$639$	−5.19656	−0.205573
$640$	−17.3612	−0.686262
$641$	38.2646	1.51136	0.755680	−	0.654941i	$-0.227307\pi$
$641$	38.2646	1.51136	0.755680	+	0.654941i	$0.227307\pi$
$642$	−46.2217	−1.82423
$643$	−33.1109	−1.30577	−0.652883	−	0.757459i	$-0.726440\pi$
$643$	−33.1109	−1.30577	−0.652883	+	0.757459i	$0.726440\pi$
$644$	−20.9651	−0.826141
$645$	−9.95715	−0.392063
$646$	−107.273	−4.22058
$647$	−16.9614	−0.666820	−0.333410	−	0.942782i	$-0.608199\pi$
$647$	−16.9614	−0.666820	−0.333410	+	0.942782i	$0.608199\pi$
$648$	−5.46787	−0.214798
$649$	−6.42754	−0.252303
$650$	−2.48929	−0.0976379
$651$	−3.56404	−0.139686
$652$	36.7643	1.43980
$653$	−19.1709	−0.750216	−0.375108	−	0.926981i	$-0.622394\pi$
$653$	−19.1709	−0.750216	−0.375108	+	0.926981i	$0.622394\pi$
$654$	20.8929	0.816976
$655$	6.39312	0.249800
$656$	−32.2217	−1.25805
$657$	−11.9572	−0.466493
$658$	−3.04239	−0.118605
$659$	37.8715	1.47526	0.737631	−	0.675204i	$-0.235944\pi$
$659$	37.8715	1.47526	0.737631	+	0.675204i	$0.235944\pi$
$660$	−5.02142	−0.195459
$661$	24.3931	0.948782	0.474391	−	0.880314i	$-0.342668\pi$
$661$	24.3931	0.948782	0.474391	+	0.880314i	$0.342668\pi$
$662$	−38.1579	−1.48305
$663$	−6.17513	−0.239822
$664$	29.3717	1.13984
$665$	8.35027	0.323810
$666$	−19.3717	−0.750638
$667$	25.0508	0.969971
$668$	−72.9013	−2.82064
$669$	−2.62831	−0.101616
$670$	23.3288	0.901272
$671$	−15.0386	−0.580560
$672$	−2.45692	−0.0947779
$673$	−21.1281	−0.814428	−0.407214	−	0.913333i	$-0.633500\pi$
$673$	−21.1281	−0.814428	−0.407214	+	0.913333i	$0.633500\pi$
$674$	55.6363	2.14303
$675$	−1.00000	−0.0384900
$676$	4.19656	0.161406
$677$	−15.3973	−0.591767	−0.295884	−	0.955224i	$-0.595614\pi$
$677$	−15.3973	−0.591767	−0.295884	+	0.955224i	$0.595614\pi$
$678$	19.8077	0.760708
$679$	2.18356	0.0837972
$680$	33.7648	1.29482
$681$	−15.7648	−0.604109
$682$	−8.87192	−0.339723
$683$	30.0722	1.15068	0.575341	−	0.817914i	$-0.304869\pi$
$683$	30.0722	1.15068	0.575341	+	0.817914i	$0.304869\pi$
$684$	29.2860	1.11978
$685$	−16.7434	−0.639732
$686$	−37.4355	−1.42929
$687$	−8.74338	−0.333581
$688$	−51.9562	−1.98081
$689$	10.1751	0.387642
$690$	−10.3931	−0.395659
$691$	−8.14950	−0.310022	−0.155011	−	0.987913i	$-0.549541\pi$
$691$	−8.14950	−0.310022	−0.155011	+	0.987913i	$0.549541\pi$
$692$	−33.3927	−1.26940
$693$	1.43175	0.0543877
$694$	14.3931	0.546355
$695$	−5.78202	−0.219325
$696$	32.8072	1.24355
$697$	−38.1323	−1.44436
$698$	68.5082	2.59307
$699$	2.17513	0.0822712
$700$	−5.02142	−0.189792
$701$	−28.6921	−1.08369	−0.541843	−	0.840480i	$-0.682273\pi$
$701$	−28.6921	−1.08369	−0.541843	+	0.840480i	$0.682273\pi$
$702$	2.48929	0.0939521
$703$	54.3074	2.04824
$704$	6.37123	0.240125
$705$	−1.02142	−0.0384690
$706$	71.5506	2.69284
$707$	12.3847	0.465774
$708$	−22.5426	−0.847203
$709$	12.3074	0.462215	0.231108	−	0.972928i	$-0.425765\pi$
$709$	12.3074	0.462215	0.231108	+	0.972928i	$0.425765\pi$
$710$	−12.9357	−0.485469
$711$	−1.78202	−0.0668310
$712$	−55.6363	−2.08506
$713$	−12.4360	−0.465730
$714$	−18.3931	−0.688345
$715$	1.19656	0.0447487
$716$	−65.3154	−2.44095
$717$	−2.80344	−0.104696
$718$	31.3288	1.16918
$719$	−28.7862	−1.07355	−0.536773	−	0.843727i	$-0.680357\pi$
$719$	−28.7862	−1.07355	−0.536773	+	0.843727i	$0.680357\pi$
$720$	−5.21798	−0.194463
$721$	−22.4275	−0.835245
$722$	−73.9332	−2.75151
$723$	6.00000	0.223142
$724$	66.2302	2.46142
$725$	6.00000	0.222834
$726$	−23.8181	−0.883974
$727$	34.3931	1.27557	0.637785	−	0.770214i	$-0.279851\pi$
$727$	34.3931	1.27557	0.637785	+	0.770214i	$0.279851\pi$
$728$	6.54262	0.242485
$729$	1.00000	0.0370370
$730$	−29.7648	−1.10164
$731$	−61.4868	−2.27417
$732$	−52.7434	−1.94945
$733$	−29.0042	−1.07129	−0.535647	−	0.844442i	$-0.679932\pi$
$733$	−29.0042	−1.07129	−0.535647	+	0.844442i	$0.679932\pi$
$734$	69.4868	2.56480
$735$	−5.56825	−0.205388
$736$	−8.57292	−0.316002
$737$	−11.2138	−0.413065
$738$	15.3717	0.565840
$739$	−6.27804	−0.230941	−0.115471	−	0.993311i	$-0.536838\pi$
$739$	−6.27804	−0.230941	−0.115471	+	0.993311i	$0.536838\pi$
$740$	−32.6577	−1.20052
$741$	−6.97858	−0.256364
$742$	30.3074	1.11262
$743$	12.2352	0.448866	0.224433	−	0.974490i	$-0.427947\pi$
$743$	12.2352	0.448866	0.224433	+	0.974490i	$0.427947\pi$
$744$	−16.2865	−0.597091
$745$	−15.3461	−0.562236
$746$	5.85050	0.214202
$747$	−5.37169	−0.196540
$748$	−31.0080	−1.13376
$749$	22.2180	0.811827
$750$	−2.48929	−0.0908960
$751$	−28.8757	−1.05369	−0.526844	−	0.849962i	$-0.676625\pi$
$751$	−28.8757	−1.05369	−0.526844	+	0.849962i	$0.676625\pi$
$752$	−5.32976	−0.194357
$753$	23.9143	0.871486
$754$	−14.9357	−0.543927
$755$	8.58546	0.312457
$756$	5.02142	0.182627
$757$	30.3503	1.10310	0.551550	−	0.834142i	$-0.314037\pi$
$757$	30.3503	1.10310	0.551550	+	0.834142i	$0.314037\pi$
$758$	−61.1146	−2.21978
$759$	4.99579	0.181336
$760$	38.1579	1.38413
$761$	−27.1709	−0.984945	−0.492473	−	0.870328i	$-0.663907\pi$
$761$	−27.1709	−0.984945	−0.492473	+	0.870328i	$0.663907\pi$
$762$	−25.8715	−0.937224
$763$	−10.0428	−0.363575
$764$	45.0852	1.63113
$765$	−6.17513	−0.223262
$766$	−14.4569	−0.522350
$767$	5.37169	0.193961
$768$	32.5678	1.17519
$769$	−38.3503	−1.38295	−0.691473	−	0.722402i	$-0.743038\pi$
$769$	−38.3503	−1.38295	−0.691473	+	0.722402i	$0.743038\pi$
$770$	3.56404	0.128439
$771$	19.9572	0.718739
$772$	40.8710	1.47098
$773$	−50.2646	−1.80789	−0.903946	−	0.427647i	$-0.859342\pi$
$773$	−50.2646	−1.80789	−0.903946	+	0.427647i	$0.859342\pi$
$774$	24.7862	0.890923
$775$	−2.97858	−0.106994
$776$	9.97812	0.358194
$777$	9.31163	0.334053
$778$	−33.9781	−1.21817
$779$	−43.0937	−1.54399
$780$	4.19656	0.150261
$781$	6.21798	0.222497
$782$	−64.1789	−2.29503
$783$	−6.00000	−0.214423
$784$	−29.0550	−1.03768
$785$	−2.78623	−0.0994448
$786$	−15.9143	−0.567645
$787$	−13.2860	−0.473595	−0.236797	−	0.971559i	$-0.576098\pi$
$787$	−13.2860	−0.473595	−0.236797	+	0.971559i	$0.576098\pi$
$788$	−40.1360	−1.42979
$789$	−8.00000	−0.284808
$790$	−4.43596	−0.157824
$791$	−9.52119	−0.338535
$792$	6.54262	0.232482
$793$	12.5682	0.446312
$794$	30.2008	1.07179
$795$	10.1751	0.360875
$796$	24.9995	0.886085
$797$	9.82487	0.348015	0.174007	−	0.984744i	$-0.444328\pi$
$797$	9.82487	0.348015	0.174007	+	0.984744i	$0.444328\pi$
$798$	−20.7862	−0.735825
$799$	−6.30742	−0.223141
$800$	−2.05333	−0.0725961
$801$	10.1751	0.359521
$802$	93.2087	3.29131
$803$	14.3074	0.504898
$804$	−39.3288	−1.38702
$805$	4.99579	0.176078
$806$	7.41454	0.261166
$807$	2.35027	0.0827334
$808$	56.5939	1.99097
$809$	−9.91431	−0.348569	−0.174284	−	0.984695i	$-0.555761\pi$
$809$	−9.91431	−0.348569	−0.174284	+	0.984695i	$0.555761\pi$
$810$	2.48929	0.0874647
$811$	−36.5855	−1.28469	−0.642345	−	0.766416i	$-0.722038\pi$
$811$	−36.5855	−1.28469	−0.642345	+	0.766416i	$0.722038\pi$
$812$	−30.1285	−1.05730
$813$	−10.9786	−0.385036
$814$	23.1793	0.812436
$815$	−8.76060	−0.306870
$816$	−32.2217	−1.12799
$817$	−69.4868	−2.43103
$818$	34.8500	1.21850
$819$	−1.19656	−0.0418111
$820$	25.9143	0.904967
$821$	−34.4741	−1.20316	−0.601578	−	0.798814i	$-0.705461\pi$
$821$	−34.4741	−1.20316	−0.601578	+	0.798814i	$0.705461\pi$
$822$	41.6791	1.45373
$823$	13.2566	0.462097	0.231048	−	0.972942i	$-0.425784\pi$
$823$	13.2566	0.462097	0.231048	+	0.972942i	$0.425784\pi$
$824$	−102.486	−3.57028
$825$	1.19656	0.0416588
$826$	16.0000	0.556711
$827$	28.1495	0.978854	0.489427	−	0.872044i	$-0.337206\pi$
$827$	28.1495	0.978854	0.489427	+	0.872044i	$0.337206\pi$
$828$	17.5212	0.608904
$829$	16.3418	0.567576	0.283788	−	0.958887i	$-0.408409\pi$
$829$	16.3418	0.567576	0.283788	+	0.958887i	$0.408409\pi$
$830$	−13.3717	−0.464138
$831$	−1.21377	−0.0421052
$832$	−5.32464	−0.184599
$833$	−34.3847	−1.19136
$834$	14.3931	0.498393
$835$	17.3717	0.601172
$836$	−35.0424	−1.21197
$837$	2.97858	0.102955
$838$	−7.91431	−0.273395
$839$	−30.3675	−1.04840	−0.524201	−	0.851595i	$-0.675636\pi$
$839$	−30.3675	−1.04840	−0.524201	+	0.851595i	$0.675636\pi$
$840$	6.54262	0.225742
$841$	7.00000	0.241379
$842$	40.5939	1.39896
$843$	−11.9572	−0.411826
$844$	100.358	3.45446
$845$	−1.00000	−0.0344010
$846$	2.54262	0.0874169
$847$	11.4490	0.393391
$848$	53.0937	1.82324
$849$	29.8715	1.02519
$850$	−15.3717	−0.527245
$851$	32.4910	1.11378
$852$	21.8077	0.747118
$853$	−42.1407	−1.44287	−0.721435	−	0.692482i	$-0.756517\pi$
$853$	−42.1407	−1.44287	−0.721435	+	0.692482i	$0.756517\pi$
$854$	37.4355	1.28102
$855$	−6.97858	−0.238662
$856$	101.529	3.47018
$857$	−2.17513	−0.0743012	−0.0371506	−	0.999310i	$-0.511828\pi$
$857$	−2.17513	−0.0743012	−0.0371506	+	0.999310i	$0.511828\pi$
$858$	−2.97858	−0.101687
$859$	18.5682	0.633541	0.316770	−	0.948502i	$-0.397402\pi$
$859$	18.5682	0.633541	0.316770	+	0.948502i	$0.397402\pi$
$860$	41.7858	1.42488
$861$	−7.38890	−0.251813
$862$	−11.4145	−0.388781
$863$	33.7220	1.14791	0.573954	−	0.818887i	$-0.305409\pi$
$863$	33.7220	1.14791	0.573954	+	0.818887i	$0.305409\pi$
$864$	2.05333	0.0698556
$865$	7.95715	0.270551
$866$	95.4649	3.24403
$867$	−21.1323	−0.717690
$868$	14.9567	0.507663
$869$	2.13229	0.0723330
$870$	−14.9357	−0.506369
$871$	9.37169	0.317548
$872$	−45.8924	−1.55411
$873$	−1.82487	−0.0617623
$874$	−72.5292	−2.45334
$875$	1.19656	0.0404510
$876$	50.1789	1.69539
$877$	43.4868	1.46844	0.734222	−	0.678910i	$-0.237547\pi$
$877$	43.4868	1.46844	0.734222	+	0.678910i	$0.237547\pi$
$878$	−19.2650	−0.650164
$879$	−0.777809	−0.0262348
$880$	6.24361	0.210472
$881$	26.7005	0.899564	0.449782	−	0.893138i	$-0.351502\pi$
$881$	26.7005	0.899564	0.449782	+	0.893138i	$0.351502\pi$
$882$	13.8610	0.466724
$883$	20.2990	0.683116	0.341558	−	0.939861i	$-0.389045\pi$
$883$	20.2990	0.683116	0.341558	+	0.939861i	$0.389045\pi$
$884$	25.9143	0.871593
$885$	5.37169	0.180567
$886$	−86.9223	−2.92021
$887$	36.0550	1.21061	0.605305	−	0.795994i	$-0.293051\pi$
$887$	36.0550	1.21061	0.605305	+	0.795994i	$0.293051\pi$
$888$	42.5510	1.42792
$889$	12.4360	0.417089
$890$	25.3288	0.849025
$891$	−1.19656	−0.0400862
$892$	11.0298	0.369307
$893$	−7.12808	−0.238532
$894$	38.2008	1.27762
$895$	15.5640	0.520248
$896$	−20.7737	−0.694000
$897$	−4.17513	−0.139404
$898$	15.3717	0.512960
$899$	−17.8715	−0.596047
$900$	4.19656	0.139885
$901$	62.8328	2.09326
$902$	−18.3931	−0.612424
$903$	−11.9143	−0.396483
$904$	−43.5087	−1.44708
$905$	−15.7820	−0.524612
$906$	−21.3717	−0.710027
$907$	−7.26504	−0.241232	−0.120616	−	0.992699i	$-0.538487\pi$
$907$	−7.26504	−0.241232	−0.120616	+	0.992699i	$0.538487\pi$
$908$	66.1579	2.19553
$909$	−10.3503	−0.343297
$910$	−2.97858	−0.0987389
$911$	−6.65769	−0.220579	−0.110290	−	0.993899i	$-0.535178\pi$
$911$	−6.65769	−0.220579	−0.110290	+	0.993899i	$0.535178\pi$
$912$	−36.4141	−1.20579
$913$	6.42754	0.212721
$914$	−3.45738	−0.114360
$915$	12.5682	0.415494
$916$	36.6921	1.21234
$917$	7.64973	0.252616
$918$	15.3717	0.507341
$919$	−27.1831	−0.896688	−0.448344	−	0.893861i	$-0.647986\pi$
$919$	−27.1831	−0.896688	−0.448344	+	0.893861i	$0.647986\pi$
$920$	22.8291	0.752652
$921$	−0.760597	−0.0250625
$922$	−70.9013	−2.33501
$923$	−5.19656	−0.171047
$924$	−6.00842	−0.197663
$925$	7.78202	0.255871
$926$	−40.7643	−1.33960
$927$	18.7434	0.615614
$928$	−12.3200	−0.404423
$929$	−15.3973	−0.505170	−0.252585	−	0.967575i	$-0.581281\pi$
$929$	−15.3973	−0.505170	−0.252585	+	0.967575i	$0.581281\pi$
$930$	7.41454	0.243132
$931$	−38.8585	−1.27353
$932$	−9.12808	−0.299000
$933$	23.1281	0.757179
$934$	−64.0932	−2.09719
$935$	7.38890	0.241643
$936$	−5.46787	−0.178723
$937$	1.12808	0.0368527	0.0184264	−	0.999830i	$-0.494134\pi$
$937$	1.12808	0.0368527	0.0184264	+	0.999830i	$0.494134\pi$
$938$	27.9143	0.911434
$939$	33.9143	1.10675
$940$	4.28646	0.139809
$941$	−30.1407	−0.982559	−0.491280	−	0.871002i	$-0.663471\pi$
$941$	−30.1407	−0.982559	−0.491280	+	0.871002i	$0.663471\pi$
$942$	6.93573	0.225978
$943$	−25.7820	−0.839578
$944$	28.0294	0.912279
$945$	−1.19656	−0.0389240
$946$	−29.6582	−0.964270
$947$	−20.0294	−0.650868	−0.325434	−	0.945565i	$-0.605510\pi$
$947$	−20.0294	−0.650868	−0.325434	+	0.945565i	$0.605510\pi$
$948$	7.47835	0.242885
$949$	−11.9572	−0.388146
$950$	−17.3717	−0.563612
$951$	−9.64973	−0.312914
$952$	40.4015	1.30942
$953$	−43.2259	−1.40023	−0.700113	−	0.714032i	$-0.746867\pi$
$953$	−43.2259	−1.40023	−0.700113	+	0.714032i	$0.746867\pi$
$954$	−25.3288	−0.820052
$955$	−10.7434	−0.347648
$956$	11.7648	0.380501
$957$	7.17935	0.232075
$958$	18.8929	0.610401
$959$	−20.0344	−0.646945
$960$	−5.32464	−0.171852
$961$	−22.1281	−0.713809
$962$	−19.3717	−0.624568
$963$	−18.5682	−0.598353
$964$	−25.1793	−0.810972
$965$	−9.73917	−0.313515
$966$	−12.4360	−0.400120
$967$	57.6875	1.85511	0.927553	−	0.373691i	$-0.121908\pi$
$967$	57.6875	1.85511	0.927553	+	0.373691i	$0.121908\pi$
$968$	52.3179	1.68156
$969$	−43.0937	−1.38437
$970$	−4.54262	−0.145855
$971$	−19.5296	−0.626735	−0.313368	−	0.949632i	$-0.601457\pi$
$971$	−19.5296	−0.626735	−0.313368	+	0.949632i	$0.601457\pi$
$972$	−4.19656	−0.134605
$973$	−6.91852	−0.221798
$974$	−10.9786	−0.351776
$975$	−1.00000	−0.0320256
$976$	65.5809	2.09919
$977$	−40.3074	−1.28955	−0.644774	−	0.764373i	$-0.723049\pi$
$977$	−40.3074	−1.28955	−0.644774	+	0.764373i	$0.723049\pi$
$978$	21.8077	0.697332
$979$	−12.1751	−0.389119
$980$	23.3675	0.746447
$981$	8.39312	0.267972
$982$	0.213311	0.00680702
$983$	32.2008	1.02705	0.513523	−	0.858076i	$-0.328340\pi$
$983$	32.2008	1.02705	0.513523	+	0.858076i	$0.328340\pi$
$984$	−33.7648	−1.07638
$985$	9.56404	0.304736
$986$	−92.2302	−2.93721
$987$	−1.22219	−0.0389028
$988$	29.2860	0.931712
$989$	−41.5725	−1.32193
$990$	−2.97858	−0.0946654
$991$	26.4826	0.841246	0.420623	−	0.907235i	$-0.361811\pi$
$991$	26.4826	0.841246	0.420623	+	0.907235i	$0.361811\pi$
$992$	6.11599	0.194183
$993$	−15.3288	−0.486446
$994$	−15.4783	−0.490943
$995$	−5.95715	−0.188854
$996$	22.5426	0.714290
$997$	35.1365	1.11278	0.556392	−	0.830920i	$-0.312185\pi$
$997$	35.1365	1.11278	0.556392	+	0.830920i	$0.312185\pi$
$998$	44.1151	1.39644
$999$	−7.78202	−0.246212

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.2.a.e.1.1	✓	3
3.2	odd	2		585.2.a.n.1.3		3
4.3	odd	2		3120.2.a.bj.1.2		3
5.2	odd	4		975.2.c.i.274.2		6
5.3	odd	4		975.2.c.i.274.5		6
5.4	even	2		975.2.a.o.1.3		3
7.6	odd	2		9555.2.a.bq.1.1		3
12.11	even	2		9360.2.a.dd.1.2		3
13.12	even	2		2535.2.a.bc.1.3		3
15.2	even	4		2925.2.c.w.2224.5		6
15.8	even	4		2925.2.c.w.2224.2		6
15.14	odd	2		2925.2.a.bh.1.1		3
39.38	odd	2		7605.2.a.bx.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.a.e.1.1	✓	3	1.1	even	1	trivial
585.2.a.n.1.3		3	3.2	odd	2
975.2.a.o.1.3		3	5.4	even	2
975.2.c.i.274.2		6	5.2	odd	4
975.2.c.i.274.5		6	5.3	odd	4
2535.2.a.bc.1.3		3	13.12	even	2
2925.2.a.bh.1.1		3	15.14	odd	2
2925.2.c.w.2224.2		6	15.8	even	4
2925.2.c.w.2224.5		6	15.2	even	4
3120.2.a.bj.1.2		3	4.3	odd	2
7605.2.a.bx.1.1		3	39.38	odd	2
9360.2.a.dd.1.2		3	12.11	even	2
9555.2.a.bq.1.1		3	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	195.a (trivial)

\(f(q)\)	\(=\)	\(q-2.48929 q^{2} -1.00000 q^{3} +4.19656 q^{4} -1.00000 q^{5} +2.48929 q^{6} -1.19656 q^{7} -5.46787 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.48929 q^{2} -1.00000 q^{3} +4.19656 q^{4} -1.00000 q^{5} +2.48929 q^{6} -1.19656 q^{7} -5.46787 q^{8} +1.00000 q^{9} +2.48929 q^{10} -1.19656 q^{11} -4.19656 q^{12} +1.00000 q^{13} +2.97858 q^{14} +1.00000 q^{15} +5.21798 q^{16} +6.17513 q^{17} -2.48929 q^{18} +6.97858 q^{19} -4.19656 q^{20} +1.19656 q^{21} +2.97858 q^{22} +4.17513 q^{23} +5.46787 q^{24} +1.00000 q^{25} -2.48929 q^{26} -1.00000 q^{27} -5.02142 q^{28} +6.00000 q^{29} -2.48929 q^{30} -2.97858 q^{31} -2.05333 q^{32} +1.19656 q^{33} -15.3717 q^{34} +1.19656 q^{35} +4.19656 q^{36} +7.78202 q^{37} -17.3717 q^{38} -1.00000 q^{39} +5.46787 q^{40} -6.17513 q^{41} -2.97858 q^{42} -9.95715 q^{43} -5.02142 q^{44} -1.00000 q^{45} -10.3931 q^{46} -1.02142 q^{47} -5.21798 q^{48} -5.56825 q^{49} -2.48929 q^{50} -6.17513 q^{51} +4.19656 q^{52} +10.1751 q^{53} +2.48929 q^{54} +1.19656 q^{55} +6.54262 q^{56} -6.97858 q^{57} -14.9357 q^{58} +5.37169 q^{59} +4.19656 q^{60} +12.5682 q^{61} +7.41454 q^{62} -1.19656 q^{63} -5.32464 q^{64} -1.00000 q^{65} -2.97858 q^{66} +9.37169 q^{67} +25.9143 q^{68} -4.17513 q^{69} -2.97858 q^{70} -5.19656 q^{71} -5.46787 q^{72} -11.9572 q^{73} -19.3717 q^{74} -1.00000 q^{75} +29.2860 q^{76} +1.43175 q^{77} +2.48929 q^{78} -1.78202 q^{79} -5.21798 q^{80} +1.00000 q^{81} +15.3717 q^{82} -5.37169 q^{83} +5.02142 q^{84} -6.17513 q^{85} +24.7862 q^{86} -6.00000 q^{87} +6.54262 q^{88} +10.1751 q^{89} +2.48929 q^{90} -1.19656 q^{91} +17.5212 q^{92} +2.97858 q^{93} +2.54262 q^{94} -6.97858 q^{95} +2.05333 q^{96} -1.82487 q^{97} +13.8610 q^{98} -1.19656 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{3} + 8 q^{4} - 3 q^{5} + q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^3 + 8 * q^4 - 3 * q^5 + q^7 + 6 * q^8 + 3 * q^9	\( 3 q - 3 q^{3} + 8 q^{4} - 3 q^{5} + q^{7} + 6 q^{8} + 3 q^{9} + q^{11} - 8 q^{12} + 3 q^{13} - 6 q^{14} + 3 q^{15} + 26 q^{16} - q^{17} + 6 q^{19} - 8 q^{20} - q^{21} - 6 q^{22} - 7 q^{23} - 6 q^{24} + 3 q^{25} - 3 q^{27} - 30 q^{28} + 18 q^{29} + 6 q^{31} + 22 q^{32} - q^{33} - 22 q^{34} - q^{35} + 8 q^{36} + 13 q^{37} - 28 q^{38} - 3 q^{39} - 6 q^{40} + q^{41} + 6 q^{42} - 30 q^{44} - 3 q^{45} - 22 q^{46} - 18 q^{47} - 26 q^{48} + 12 q^{49} + q^{51} + 8 q^{52} + 11 q^{53} - q^{55} - 16 q^{56} - 6 q^{57} - 8 q^{59} + 8 q^{60} + 9 q^{61} + 28 q^{62} + q^{63} + 30 q^{64} - 3 q^{65} + 6 q^{66} + 4 q^{67} + 18 q^{68} + 7 q^{69} + 6 q^{70} - 11 q^{71} + 6 q^{72} - 6 q^{73} - 34 q^{74} - 3 q^{75} + 4 q^{76} + 33 q^{77} + 5 q^{79} - 26 q^{80} + 3 q^{81} + 22 q^{82} + 8 q^{83} + 30 q^{84} + q^{85} + 56 q^{86} - 18 q^{87} - 16 q^{88} + 11 q^{89} + q^{91} + 2 q^{92} - 6 q^{93} - 28 q^{94} - 6 q^{95} - 22 q^{96} - 25 q^{97} + 10 q^{98} + q^{99}+O(q^{100}) \) 3 * q - 3 * q^3 + 8 * q^4 - 3 * q^5 + q^7 + 6 * q^8 + 3 * q^9 + q^11 - 8 * q^12 + 3 * q^13 - 6 * q^14 + 3 * q^15 + 26 * q^16 - q^17 + 6 * q^19 - 8 * q^20 - q^21 - 6 * q^22 - 7 * q^23 - 6 * q^24 + 3 * q^25 - 3 * q^27 - 30 * q^28 + 18 * q^29 + 6 * q^31 + 22 * q^32 - q^33 - 22 * q^34 - q^35 + 8 * q^36 + 13 * q^37 - 28 * q^38 - 3 * q^39 - 6 * q^40 + q^41 + 6 * q^42 - 30 * q^44 - 3 * q^45 - 22 * q^46 - 18 * q^47 - 26 * q^48 + 12 * q^49 + q^51 + 8 * q^52 + 11 * q^53 - q^55 - 16 * q^56 - 6 * q^57 - 8 * q^59 + 8 * q^60 + 9 * q^61 + 28 * q^62 + q^63 + 30 * q^64 - 3 * q^65 + 6 * q^66 + 4 * q^67 + 18 * q^68 + 7 * q^69 + 6 * q^70 - 11 * q^71 + 6 * q^72 - 6 * q^73 - 34 * q^74 - 3 * q^75 + 4 * q^76 + 33 * q^77 + 5 * q^79 - 26 * q^80 + 3 * q^81 + 22 * q^82 + 8 * q^83 + 30 * q^84 + q^85 + 56 * q^86 - 18 * q^87 - 16 * q^88 + 11 * q^89 + q^91 + 2 * q^92 - 6 * q^93 - 28 * q^94 - 6 * q^95 - 22 * q^96 - 25 * q^97 + 10 * q^98 + q^99

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