LMFDB - Embedded newform 195.2.a.e.1.2

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			1.2
Root			$-1.81361$ 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)

$f(q)$	$=$	$q-0.289169 q^{2} -1.00000 q^{3} -1.91638 q^{4} -1.00000 q^{5} +0.289169 q^{6} +4.91638 q^{7} +1.13249 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.289169 q^{2} -1.00000 q^{3} -1.91638 q^{4} -1.00000 q^{5} +0.289169 q^{6} +4.91638 q^{7} +1.13249 q^{8} +1.00000 q^{9} +0.289169 q^{10} +4.91638 q^{11} +1.91638 q^{12} +1.00000 q^{13} -1.42166 q^{14} +1.00000 q^{15} +3.50528 q^{16} -4.33804 q^{17} -0.289169 q^{18} +2.57834 q^{19} +1.91638 q^{20} -4.91638 q^{21} -1.42166 q^{22} -6.33804 q^{23} -1.13249 q^{24} +1.00000 q^{25} -0.289169 q^{26} -1.00000 q^{27} -9.42166 q^{28} +6.00000 q^{29} -0.289169 q^{30} +1.42166 q^{31} -3.27861 q^{32} -4.91638 q^{33} +1.25443 q^{34} -4.91638 q^{35} -1.91638 q^{36} +9.49472 q^{37} -0.745574 q^{38} -1.00000 q^{39} -1.13249 q^{40} +4.33804 q^{41} +1.42166 q^{42} -1.15667 q^{43} -9.42166 q^{44} -1.00000 q^{45} +1.83276 q^{46} -5.42166 q^{47} -3.50528 q^{48} +17.1708 q^{49} -0.289169 q^{50} +4.33804 q^{51} -1.91638 q^{52} -0.338044 q^{53} +0.289169 q^{54} -4.91638 q^{55} +5.56777 q^{56} -2.57834 q^{57} -1.73501 q^{58} -11.2544 q^{59} -1.91638 q^{60} -10.1708 q^{61} -0.411100 q^{62} +4.91638 q^{63} -6.06249 q^{64} -1.00000 q^{65} +1.42166 q^{66} -7.25443 q^{67} +8.31335 q^{68} +6.33804 q^{69} +1.42166 q^{70} +0.916382 q^{71} +1.13249 q^{72} -3.15667 q^{73} -2.74557 q^{74} -1.00000 q^{75} -4.94108 q^{76} +24.1708 q^{77} +0.289169 q^{78} -3.49472 q^{79} -3.50528 q^{80} +1.00000 q^{81} -1.25443 q^{82} +11.2544 q^{83} +9.42166 q^{84} +4.33804 q^{85} +0.334474 q^{86} -6.00000 q^{87} +5.56777 q^{88} -0.338044 q^{89} +0.289169 q^{90} +4.91638 q^{91} +12.1461 q^{92} -1.42166 q^{93} +1.56777 q^{94} -2.57834 q^{95} +3.27861 q^{96} -12.3380 q^{97} -4.96526 q^{98} +4.91638 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.289169	−0.204473	−0.102237	−	0.994760i	$-0.532600\pi$
$2$	−0.289169	−0.204473	−0.102237	+	0.994760i	$0.532600\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.91638	−0.958191
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.289169	0.118053
$7$	4.91638	1.85822	0.929109	−	0.369807i	$-0.120576\pi$
$7$	4.91638	1.85822	0.929109	+	0.369807i	$0.120576\pi$
$8$	1.13249	0.400397
$9$	1.00000	0.333333
$10$	0.289169	0.0914431
$11$	4.91638	1.48234	0.741172	−	0.671315i	$-0.234270\pi$
$11$	4.91638	1.48234	0.741172	+	0.671315i	$0.234270\pi$
$12$	1.91638	0.553212
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−1.42166	−0.379955
$15$	1.00000	0.258199
$16$	3.50528	0.876320
$17$	−4.33804	−1.05213	−0.526065	−	0.850444i	$-0.676333\pi$
$17$	−4.33804	−1.05213	−0.526065	+	0.850444i	$0.676333\pi$
$18$	−0.289169	−0.0681577
$19$	2.57834	0.591511	0.295756	−	0.955264i	$-0.404429\pi$
$19$	2.57834	0.591511	0.295756	+	0.955264i	$0.404429\pi$
$20$	1.91638	0.428516
$21$	−4.91638	−1.07284
$22$	−1.42166	−0.303100
$23$	−6.33804	−1.32157	−0.660787	−	0.750574i	$-0.729777\pi$
$23$	−6.33804	−1.32157	−0.660787	+	0.750574i	$0.729777\pi$
$24$	−1.13249	−0.231169
$25$	1.00000	0.200000
$26$	−0.289169	−0.0567106
$27$	−1.00000	−0.192450
$28$	−9.42166	−1.78053
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	−0.289169	−0.0527947
$31$	1.42166	0.255338	0.127669	−	0.991817i	$-0.459250\pi$
$31$	1.42166	0.255338	0.127669	+	0.991817i	$0.459250\pi$
$32$	−3.27861	−0.579581
$33$	−4.91638	−0.855832
$34$	1.25443	0.215132
$35$	−4.91638	−0.831020
$36$	−1.91638	−0.319397
$37$	9.49472	1.56092	0.780461	−	0.625204i	$-0.214984\pi$
$37$	9.49472	1.56092	0.780461	+	0.625204i	$0.214984\pi$
$38$	−0.745574	−0.120948
$39$	−1.00000	−0.160128
$40$	−1.13249	−0.179063
$41$	4.33804	0.677489	0.338744	−	0.940878i	$-0.389998\pi$
$41$	4.33804	0.677489	0.338744	+	0.940878i	$0.389998\pi$
$42$	1.42166	0.219367
$43$	−1.15667	−0.176391	−0.0881956	−	0.996103i	$-0.528110\pi$
$43$	−1.15667	−0.176391	−0.0881956	+	0.996103i	$0.528110\pi$
$44$	−9.42166	−1.42037
$45$	−1.00000	−0.149071
$46$	1.83276	0.270226
$47$	−5.42166	−0.790831	−0.395415	−	0.918502i	$-0.629399\pi$
$47$	−5.42166	−0.790831	−0.395415	+	0.918502i	$0.629399\pi$
$48$	−3.50528	−0.505944
$49$	17.1708	2.45297
$50$	−0.289169	−0.0408946
$51$	4.33804	0.607448
$52$	−1.91638	−0.265754
$53$	−0.338044	−0.0464340	−0.0232170	−	0.999730i	$-0.507391\pi$
$53$	−0.338044	−0.0464340	−0.0232170	+	0.999730i	$0.507391\pi$
$54$	0.289169	0.0393509
$55$	−4.91638	−0.662925
$56$	5.56777	0.744025
$57$	−2.57834	−0.341509
$58$	−1.73501	−0.227818
$59$	−11.2544	−1.46520	−0.732601	−	0.680659i	$-0.761694\pi$
$59$	−11.2544	−1.46520	−0.732601	+	0.680659i	$0.761694\pi$
$60$	−1.91638	−0.247404
$61$	−10.1708	−1.30224	−0.651119	−	0.758975i	$-0.725700\pi$
$61$	−10.1708	−1.30224	−0.651119	+	0.758975i	$0.725700\pi$
$62$	−0.411100	−0.0522098
$63$	4.91638	0.619406
$64$	−6.06249	−0.757812
$65$	−1.00000	−0.124035
$66$	1.42166	0.174995
$67$	−7.25443	−0.886269	−0.443135	−	0.896455i	$-0.646134\pi$
$67$	−7.25443	−0.886269	−0.443135	+	0.896455i	$0.646134\pi$
$68$	8.31335	1.00814
$69$	6.33804	0.763011
$70$	1.42166	0.169921
$71$	0.916382	0.108754	0.0543772	−	0.998520i	$-0.482683\pi$
$71$	0.916382	0.108754	0.0543772	+	0.998520i	$0.482683\pi$
$72$	1.13249	0.133466
$73$	−3.15667	−0.369461	−0.184730	−	0.982789i	$-0.559141\pi$
$73$	−3.15667	−0.369461	−0.184730	+	0.982789i	$0.559141\pi$
$74$	−2.74557	−0.319166
$75$	−1.00000	−0.115470
$76$	−4.94108	−0.566780
$77$	24.1708	2.75452
$78$	0.289169	0.0327419
$79$	−3.49472	−0.393187	−0.196593	−	0.980485i	$-0.562988\pi$
$79$	−3.49472	−0.393187	−0.196593	+	0.980485i	$0.562988\pi$
$80$	−3.50528	−0.391902
$81$	1.00000	0.111111
$82$	−1.25443	−0.138528
$83$	11.2544	1.23533	0.617667	−	0.786440i	$-0.288078\pi$
$83$	11.2544	1.23533	0.617667	+	0.786440i	$0.288078\pi$
$84$	9.42166	1.02799
$85$	4.33804	0.470527
$86$	0.334474	0.0360672
$87$	−6.00000	−0.643268
$88$	5.56777	0.593527
$89$	−0.338044	−0.0358326	−0.0179163	−	0.999839i	$-0.505703\pi$
$89$	−0.338044	−0.0358326	−0.0179163	+	0.999839i	$0.505703\pi$
$90$	0.289169	0.0304810
$91$	4.91638	0.515377
$92$	12.1461	1.26632
$93$	−1.42166	−0.147420
$94$	1.56777	0.161704
$95$	−2.57834	−0.264532
$96$	3.27861	0.334621
$97$	−12.3380	−1.25274	−0.626369	−	0.779526i	$-0.715460\pi$
$97$	−12.3380	−1.25274	−0.626369	+	0.779526i	$0.715460\pi$
$98$	−4.96526	−0.501567
$99$	4.91638	0.494115
$100$	−1.91638	−0.191638
$101$	10.6761	1.06231	0.531155	−	0.847274i	$-0.321758\pi$
$101$	10.6761	1.06231	0.531155	+	0.847274i	$0.321758\pi$
$102$	−1.25443	−0.124207
$103$	−14.5089	−1.42960	−0.714800	−	0.699329i	$-0.753482\pi$
$103$	−14.5089	−1.42960	−0.714800	+	0.699329i	$0.753482\pi$
$104$	1.13249	0.111050
$105$	4.91638	0.479790
$106$	0.0977518	0.00949450
$107$	4.17081	0.403207	0.201604	−	0.979467i	$-0.435385\pi$
$107$	4.17081	0.403207	0.201604	+	0.979467i	$0.435385\pi$
$108$	1.91638	0.184404
$109$	−3.83276	−0.367112	−0.183556	−	0.983009i	$-0.558761\pi$
$109$	−3.83276	−0.367112	−0.183556	+	0.983009i	$0.558761\pi$
$110$	1.42166	0.135550
$111$	−9.49472	−0.901199
$112$	17.2333	1.62839
$113$	−0.843326	−0.0793334	−0.0396667	−	0.999213i	$-0.512630\pi$
$113$	−0.843326	−0.0793334	−0.0396667	+	0.999213i	$0.512630\pi$
$114$	0.745574	0.0698294
$115$	6.33804	0.591026
$116$	−11.4983	−1.06759
$117$	1.00000	0.0924500
$118$	3.25443	0.299594
$119$	−21.3275	−1.95509
$120$	1.13249	0.103382
$121$	13.1708	1.19735
$122$	2.94108	0.266273
$123$	−4.33804	−0.391148
$124$	−2.72445	−0.244663
$125$	−1.00000	−0.0894427
$126$	−1.42166	−0.126652
$127$	1.83276	0.162631	0.0813157	−	0.996688i	$-0.474088\pi$
$127$	1.83276	0.162631	0.0813157	+	0.996688i	$0.474088\pi$
$128$	8.31029	0.734533
$129$	1.15667	0.101839
$130$	0.289169	0.0253618
$131$	5.83276	0.509611	0.254805	−	0.966992i	$-0.417989\pi$
$131$	5.83276	0.509611	0.254805	+	0.966992i	$0.417989\pi$
$132$	9.42166	0.820050
$133$	12.6761	1.09916
$134$	2.09775	0.181218
$135$	1.00000	0.0860663
$136$	−4.91281	−0.421270
$137$	−16.5089	−1.41045	−0.705223	−	0.708985i	$-0.749153\pi$
$137$	−16.5089	−1.41045	−0.705223	+	0.708985i	$0.749153\pi$
$138$	−1.83276	−0.156015
$139$	7.49472	0.635694	0.317847	−	0.948142i	$-0.397040\pi$
$139$	7.49472	0.635694	0.317847	+	0.948142i	$0.397040\pi$
$140$	9.42166	0.796276
$141$	5.42166	0.456586
$142$	−0.264989	−0.0222374
$143$	4.91638	0.411128
$144$	3.50528	0.292107
$145$	−6.00000	−0.498273
$146$	0.912811	0.0755448
$147$	−17.1708	−1.41622
$148$	−18.1955	−1.49566
$149$	20.4842	1.67813	0.839064	−	0.544033i	$-0.183103\pi$
$149$	20.4842	1.67813	0.839064	+	0.544033i	$0.183103\pi$
$150$	0.289169	0.0236105
$151$	−16.4111	−1.33552	−0.667758	−	0.744378i	$-0.732746\pi$
$151$	−16.4111	−1.33552	−0.667758	+	0.744378i	$0.732746\pi$
$152$	2.91995	0.236839
$153$	−4.33804	−0.350710
$154$	−6.98944	−0.563225
$155$	−1.42166	−0.114191
$156$	1.91638	0.153433
$157$	−21.6655	−1.72910	−0.864549	−	0.502549i	$-0.832396\pi$
$157$	−21.6655	−1.72910	−0.864549	+	0.502549i	$0.832396\pi$
$158$	1.01056	0.0803961
$159$	0.338044	0.0268087
$160$	3.27861	0.259197
$161$	−31.1602	−2.45577
$162$	−0.289169	−0.0227192
$163$	6.07306	0.475678	0.237839	−	0.971305i	$-0.423561\pi$
$163$	6.07306	0.475678	0.237839	+	0.971305i	$0.423561\pi$
$164$	−8.31335	−0.649163
$165$	4.91638	0.382740
$166$	−3.25443	−0.252592
$167$	−0.745574	−0.0576942	−0.0288471	−	0.999584i	$-0.509184\pi$
$167$	−0.745574	−0.0576942	−0.0288471	+	0.999584i	$0.509184\pi$
$168$	−5.56777	−0.429563
$169$	1.00000	0.0769231
$170$	−1.25443	−0.0962101
$171$	2.57834	0.197170
$172$	2.21663	0.169016
$173$	0.843326	0.0641169	0.0320584	−	0.999486i	$-0.489794\pi$
$173$	0.843326	0.0641169	0.0320584	+	0.999486i	$0.489794\pi$
$174$	1.73501	0.131531
$175$	4.91638	0.371644
$176$	17.2333	1.29901
$177$	11.2544	0.845934
$178$	0.0977518	0.00732681
$179$	−18.9894	−1.41934	−0.709669	−	0.704536i	$-0.751155\pi$
$179$	−18.9894	−1.41934	−0.709669	+	0.704536i	$0.751155\pi$
$180$	1.91638	0.142839
$181$	17.4947	1.30037	0.650186	−	0.759775i	$-0.274691\pi$
$181$	17.4947	1.30037	0.650186	+	0.759775i	$0.274691\pi$
$182$	−1.42166	−0.105381
$183$	10.1708	0.751848
$184$	−7.17780	−0.529154
$185$	−9.49472	−0.698066
$186$	0.411100	0.0301433
$187$	−21.3275	−1.55962
$188$	10.3900	0.757767
$189$	−4.91638	−0.357614
$190$	0.745574	0.0540896
$191$	−22.5089	−1.62868	−0.814342	−	0.580386i	$-0.802902\pi$
$191$	−22.5089	−1.62868	−0.814342	+	0.580386i	$0.802902\pi$
$192$	6.06249	0.437523
$193$	2.65139	0.190851	0.0954257	−	0.995437i	$-0.469579\pi$
$193$	2.65139	0.190851	0.0954257	+	0.995437i	$0.469579\pi$
$194$	3.56777	0.256151
$195$	1.00000	0.0716115
$196$	−32.9058	−2.35042
$197$	−12.9894	−0.925459	−0.462730	−	0.886500i	$-0.653130\pi$
$197$	−12.9894	−0.925459	−0.462730	+	0.886500i	$0.653130\pi$
$198$	−1.42166	−0.101033
$199$	−2.84333	−0.201558	−0.100779	−	0.994909i	$-0.532134\pi$
$199$	−2.84333	−0.201558	−0.100779	+	0.994909i	$0.532134\pi$
$200$	1.13249	0.0800794
$201$	7.25443	0.511688
$202$	−3.08719	−0.217214
$203$	29.4983	2.07037
$204$	−8.31335	−0.582051
$205$	−4.33804	−0.302982
$206$	4.19550	0.292315
$207$	−6.33804	−0.440525
$208$	3.50528	0.243048
$209$	12.6761	0.876823
$210$	−1.42166	−0.0981041
$211$	6.31335	0.434629	0.217314	−	0.976102i	$-0.430270\pi$
$211$	6.31335	0.434629	0.217314	+	0.976102i	$0.430270\pi$
$212$	0.647822	0.0444926
$213$	−0.916382	−0.0627894
$214$	−1.20607	−0.0824450
$215$	1.15667	0.0788845
$216$	−1.13249	−0.0770565
$217$	6.98944	0.474474
$218$	1.10831	0.0750645
$219$	3.15667	0.213308
$220$	9.42166	0.635208
$221$	−4.33804	−0.291808
$222$	2.74557	0.184271
$223$	19.2544	1.28937	0.644686	−	0.764448i	$-0.276988\pi$
$223$	19.2544	1.28937	0.644686	+	0.764448i	$0.276988\pi$
$224$	−16.1189	−1.07699
$225$	1.00000	0.0666667
$226$	0.243863	0.0162215
$227$	−13.0872	−0.868627	−0.434314	−	0.900762i	$-0.643009\pi$
$227$	−13.0872	−0.868627	−0.434314	+	0.900762i	$0.643009\pi$
$228$	4.94108	0.327231
$229$	−24.5089	−1.61959	−0.809795	−	0.586713i	$-0.800422\pi$
$229$	−24.5089	−1.61959	−0.809795	+	0.586713i	$0.800422\pi$
$230$	−1.83276	−0.120849
$231$	−24.1708	−1.59032
$232$	6.79497	0.446111
$233$	8.33804	0.546243	0.273122	−	0.961979i	$-0.411944\pi$
$233$	8.33804	0.546243	0.273122	+	0.961979i	$0.411944\pi$
$234$	−0.289169	−0.0189035
$235$	5.42166	0.353670
$236$	21.5678	1.40394
$237$	3.49472	0.227006
$238$	6.16724	0.399763
$239$	8.91638	0.576753	0.288376	−	0.957517i	$-0.406885\pi$
$239$	8.91638	0.576753	0.288376	+	0.957517i	$0.406885\pi$
$240$	3.50528	0.226265
$241$	−6.00000	−0.386494	−0.193247	−	0.981150i	$-0.561902\pi$
$241$	−6.00000	−0.386494	−0.193247	+	0.981150i	$0.561902\pi$
$242$	−3.80858	−0.244825
$243$	−1.00000	−0.0641500
$244$	19.4911	1.24779
$245$	−17.1708	−1.09700
$246$	1.25443	0.0799793
$247$	2.57834	0.164056
$248$	1.61003	0.102237
$249$	−11.2544	−0.713220
$250$	0.289169	0.0182886
$251$	−6.31335	−0.398495	−0.199248	−	0.979949i	$-0.563850\pi$
$251$	−6.31335	−0.398495	−0.199248	+	0.979949i	$0.563850\pi$
$252$	−9.42166	−0.593509
$253$	−31.1602	−1.95903
$254$	−0.529977	−0.0332537
$255$	−4.33804	−0.271659
$256$	9.72191	0.607619
$257$	−11.1567	−0.695934	−0.347967	−	0.937507i	$-0.613128\pi$
$257$	−11.1567	−0.695934	−0.347967	+	0.937507i	$0.613128\pi$
$258$	−0.334474	−0.0208234
$259$	46.6797	2.90053
$260$	1.91638	0.118849
$261$	6.00000	0.371391
$262$	−1.68665	−0.104202
$263$	8.00000	0.493301	0.246651	−	0.969104i	$-0.420670\pi$
$263$	8.00000	0.493301	0.246651	+	0.969104i	$0.420670\pi$
$264$	−5.56777	−0.342673
$265$	0.338044	0.0207659
$266$	−3.66553	−0.224748
$267$	0.338044	0.0206880
$268$	13.9022	0.849215
$269$	18.6761	1.13870	0.569351	−	0.822095i	$-0.307195\pi$
$269$	18.6761	1.13870	0.569351	+	0.822095i	$0.307195\pi$
$270$	−0.289169	−0.0175982
$271$	6.57834	0.399606	0.199803	−	0.979836i	$-0.435970\pi$
$271$	6.57834	0.399606	0.199803	+	0.979836i	$0.435970\pi$
$272$	−15.2061	−0.922003
$273$	−4.91638	−0.297553
$274$	4.77384	0.288398
$275$	4.91638	0.296469
$276$	−12.1461	−0.731110
$277$	25.6655	1.54209	0.771046	−	0.636779i	$-0.219734\pi$
$277$	25.6655	1.54209	0.771046	+	0.636779i	$0.219734\pi$
$278$	−2.16724	−0.129982
$279$	1.42166	0.0851127
$280$	−5.56777	−0.332738
$281$	3.15667	0.188311	0.0941557	−	0.995557i	$-0.469985\pi$
$281$	3.15667	0.188311	0.0941557	+	0.995557i	$0.469985\pi$
$282$	−1.56777	−0.0933596
$283$	−3.47002	−0.206271	−0.103136	−	0.994667i	$-0.532888\pi$
$283$	−3.47002	−0.206271	−0.103136	+	0.994667i	$0.532888\pi$
$284$	−1.75614	−0.104208
$285$	2.57834	0.152728
$286$	−1.42166	−0.0840647
$287$	21.3275	1.25892
$288$	−3.27861	−0.193194
$289$	1.81863	0.106978
$290$	1.73501	0.101883
$291$	12.3380	0.723269
$292$	6.04939	0.354014
$293$	28.6550	1.67404	0.837020	−	0.547172i	$-0.184296\pi$
$293$	28.6550	1.67404	0.837020	+	0.547172i	$0.184296\pi$
$294$	4.96526	0.289580
$295$	11.2544	0.655258
$296$	10.7527	0.624989
$297$	−4.91638	−0.285277
$298$	−5.92337	−0.343132
$299$	−6.33804	−0.366539
$300$	1.91638	0.110642
$301$	−5.68665	−0.327773
$302$	4.74557	0.273077
$303$	−10.6761	−0.613325
$304$	9.03780	0.518353
$305$	10.1708	0.582379
$306$	1.25443	0.0717108
$307$	−1.92694	−0.109977	−0.0549883	−	0.998487i	$-0.517512\pi$
$307$	−1.92694	−0.109977	−0.0549883	+	0.998487i	$0.517512\pi$
$308$	−46.3205	−2.63935
$309$	14.5089	0.825380
$310$	0.411100	0.0233489
$311$	−29.9789	−1.69995	−0.849973	−	0.526826i	$-0.823382\pi$
$311$	−29.9789	−1.69995	−0.849973	+	0.526826i	$0.823382\pi$
$312$	−1.13249	−0.0641149
$313$	−16.3133	−0.922085	−0.461042	−	0.887378i	$-0.652524\pi$
$313$	−16.3133	−0.922085	−0.461042	+	0.887378i	$0.652524\pi$
$314$	6.26499	0.353554
$315$	−4.91638	−0.277007
$316$	6.69721	0.376748
$317$	30.6761	1.72294	0.861470	−	0.507808i	$-0.169544\pi$
$317$	30.6761	1.72294	0.861470	+	0.507808i	$0.169544\pi$
$318$	−0.0977518	−0.00548165
$319$	29.4983	1.65159
$320$	6.06249	0.338904
$321$	−4.17081	−0.232792
$322$	9.01056	0.502139
$323$	−11.1849	−0.622347
$324$	−1.91638	−0.106466
$325$	1.00000	0.0554700
$326$	−1.75614	−0.0972634
$327$	3.83276	0.211952
$328$	4.91281	0.271265
$329$	−26.6550	−1.46954
$330$	−1.42166	−0.0782600
$331$	−10.0978	−0.555023	−0.277511	−	0.960722i	$-0.589510\pi$
$331$	−10.0978	−0.555023	−0.277511	+	0.960722i	$0.589510\pi$
$332$	−21.5678	−1.18369
$333$	9.49472	0.520307
$334$	0.215597	0.0117969
$335$	7.25443	0.396352
$336$	−17.2333	−0.940154
$337$	−1.32391	−0.0721180	−0.0360590	−	0.999350i	$-0.511480\pi$
$337$	−1.32391	−0.0721180	−0.0360590	+	0.999350i	$0.511480\pi$
$338$	−0.289169	−0.0157287
$339$	0.843326	0.0458032
$340$	−8.31335	−0.450855
$341$	6.98944	0.378499
$342$	−0.745574	−0.0403160
$343$	50.0036	2.69994
$344$	−1.30993	−0.0706265
$345$	−6.33804	−0.341229
$346$	−0.243863	−0.0131102
$347$	−7.49472	−0.402338	−0.201169	−	0.979557i	$-0.564474\pi$
$347$	−7.49472	−0.402338	−0.201169	+	0.979557i	$0.564474\pi$
$348$	11.4983	0.616373
$349$	−22.1461	−1.18545	−0.592727	−	0.805403i	$-0.701949\pi$
$349$	−22.1461	−1.18545	−0.592727	+	0.805403i	$0.701949\pi$
$350$	−1.42166	−0.0759911
$351$	−1.00000	−0.0533761
$352$	−16.1189	−0.859139
$353$	4.50885	0.239982	0.119991	−	0.992775i	$-0.461713\pi$
$353$	4.50885	0.239982	0.119991	+	0.992775i	$0.461713\pi$
$354$	−3.25443	−0.172971
$355$	−0.916382	−0.0486365
$356$	0.647822	0.0343345
$357$	21.3275	1.12877
$358$	5.49115	0.290216
$359$	−20.4111	−1.07726	−0.538628	−	0.842543i	$-0.681057\pi$
$359$	−20.4111	−1.07726	−0.538628	+	0.842543i	$0.681057\pi$
$360$	−1.13249	−0.0596877
$361$	−12.3522	−0.650115
$362$	−5.05892	−0.265891
$363$	−13.1708	−0.691288
$364$	−9.42166	−0.493829
$365$	3.15667	0.165228
$366$	−2.94108	−0.153733
$367$	−10.3133	−0.538352	−0.269176	−	0.963091i	$-0.586751\pi$
$367$	−10.3133	−0.538352	−0.269176	+	0.963091i	$0.586751\pi$
$368$	−22.2166	−1.15812
$369$	4.33804	0.225830
$370$	2.74557	0.142736
$371$	−1.66196	−0.0862844
$372$	2.72445	0.141256
$373$	18.6761	0.967011	0.483506	−	0.875341i	$-0.339363\pi$
$373$	18.6761	0.967011	0.483506	+	0.875341i	$0.339363\pi$
$374$	6.16724	0.318900
$375$	1.00000	0.0516398
$376$	−6.14000	−0.316646
$377$	6.00000	0.309016
$378$	1.42166	0.0731224
$379$	−28.7527	−1.47693	−0.738464	−	0.674293i	$-0.764448\pi$
$379$	−28.7527	−1.47693	−0.738464	+	0.674293i	$0.764448\pi$
$380$	4.94108	0.253472
$381$	−1.83276	−0.0938953
$382$	6.50885	0.333022
$383$	−14.2439	−0.727827	−0.363914	−	0.931433i	$-0.618560\pi$
$383$	−14.2439	−0.727827	−0.363914	+	0.931433i	$0.618560\pi$
$384$	−8.31029	−0.424083
$385$	−24.1708	−1.23186
$386$	−0.766699	−0.0390240
$387$	−1.15667	−0.0587971
$388$	23.6444	1.20036
$389$	34.6761	1.75815	0.879074	−	0.476686i	$-0.158162\pi$
$389$	34.6761	1.75815	0.879074	+	0.476686i	$0.158162\pi$
$390$	−0.289169	−0.0146426
$391$	27.4947	1.39047
$392$	19.4458	0.982163
$393$	−5.83276	−0.294224
$394$	3.75614	0.189231
$395$	3.49472	0.175838
$396$	−9.42166	−0.473456
$397$	7.18137	0.360423	0.180211	−	0.983628i	$-0.442322\pi$
$397$	7.18137	0.360423	0.180211	+	0.983628i	$0.442322\pi$
$398$	0.822200	0.0412132
$399$	−12.6761	−0.634598
$400$	3.50528	0.175264
$401$	37.8610	1.89069	0.945345	−	0.326072i	$-0.105725\pi$
$401$	37.8610	1.89069	0.945345	+	0.326072i	$0.105725\pi$
$402$	−2.09775	−0.104626
$403$	1.42166	0.0708181
$404$	−20.4595	−1.01790
$405$	−1.00000	−0.0496904
$406$	−8.52998	−0.423336
$407$	46.6797	2.31382
$408$	4.91281	0.243220
$409$	−14.0000	−0.692255	−0.346128	−	0.938187i	$-0.612504\pi$
$409$	−14.0000	−0.692255	−0.346128	+	0.938187i	$0.612504\pi$
$410$	1.25443	0.0619517
$411$	16.5089	0.814322
$412$	27.8045	1.36983
$413$	−55.3311	−2.72266
$414$	1.83276	0.0900754
$415$	−11.2544	−0.552458
$416$	−3.27861	−0.160747
$417$	−7.49472	−0.367018
$418$	−3.66553	−0.179287
$419$	−33.4983	−1.63650	−0.818249	−	0.574864i	$-0.805055\pi$
$419$	−33.4983	−1.63650	−0.818249	+	0.574864i	$0.805055\pi$
$420$	−9.42166	−0.459730
$421$	13.5194	0.658896	0.329448	−	0.944174i	$-0.393137\pi$
$421$	13.5194	0.658896	0.329448	+	0.944174i	$0.393137\pi$
$422$	−1.82562	−0.0888699
$423$	−5.42166	−0.263610
$424$	−0.382833	−0.0185920
$425$	−4.33804	−0.210426
$426$	0.264989	0.0128387
$427$	−50.0036	−2.41984
$428$	−7.99286	−0.386349
$429$	−4.91638	−0.237365
$430$	−0.334474	−0.0161298
$431$	12.4111	0.597822	0.298911	−	0.954281i	$-0.403377\pi$
$431$	12.4111	0.597822	0.298911	+	0.954281i	$0.403377\pi$
$432$	−3.50528	−0.168648
$433$	−17.3239	−0.832534	−0.416267	−	0.909242i	$-0.636662\pi$
$433$	−17.3239	−0.832534	−0.416267	+	0.909242i	$0.636662\pi$
$434$	−2.02113	−0.0970171
$435$	6.00000	0.287678
$436$	7.34504	0.351763
$437$	−16.3416	−0.781725
$438$	−0.912811	−0.0436158
$439$	0.651393	0.0310893	0.0155446	−	0.999879i	$-0.495052\pi$
$439$	0.651393	0.0310893	0.0155446	+	0.999879i	$0.495052\pi$
$440$	−5.56777	−0.265433
$441$	17.1708	0.817658
$442$	1.25443	0.0596670
$443$	−8.84690	−0.420329	−0.210164	−	0.977666i	$-0.567400\pi$
$443$	−8.84690	−0.420329	−0.210164	+	0.977666i	$0.567400\pi$
$444$	18.1955	0.863520
$445$	0.338044	0.0160248
$446$	−5.56777	−0.263642
$447$	−20.4842	−0.968867
$448$	−29.8055	−1.40818
$449$	4.33804	0.204725	0.102362	−	0.994747i	$-0.467360\pi$
$449$	4.33804	0.204725	0.102362	+	0.994747i	$0.467360\pi$
$450$	−0.289169	−0.0136315
$451$	21.3275	1.00427
$452$	1.61613	0.0760166
$453$	16.4111	0.771061
$454$	3.78440	0.177611
$455$	−4.91638	−0.230484
$456$	−2.91995	−0.136739
$457$	15.3275	0.716989	0.358495	−	0.933532i	$-0.383290\pi$
$457$	15.3275	0.716989	0.358495	+	0.933532i	$0.383290\pi$
$458$	7.08719	0.331163
$459$	4.33804	0.202483
$460$	−12.1461	−0.566315
$461$	−11.8575	−0.552257	−0.276128	−	0.961121i	$-0.589052\pi$
$461$	−11.8575	−0.552257	−0.276128	+	0.961121i	$0.589052\pi$
$462$	6.98944	0.325178
$463$	−26.4147	−1.22759	−0.613797	−	0.789464i	$-0.710359\pi$
$463$	−26.4147	−1.22759	−0.613797	+	0.789464i	$0.710359\pi$
$464$	21.0317	0.976372
$465$	1.42166	0.0659280
$466$	−2.41110	−0.111692
$467$	−33.6691	−1.55802	−0.779010	−	0.627012i	$-0.784278\pi$
$467$	−33.6691	−1.55802	−0.779010	+	0.627012i	$0.784278\pi$
$468$	−1.91638	−0.0885848
$469$	−35.6655	−1.64688
$470$	−1.56777	−0.0723160
$471$	21.6655	0.998295
$472$	−12.7456	−0.586663
$473$	−5.68665	−0.261473
$474$	−1.01056	−0.0464167
$475$	2.57834	0.118302
$476$	40.8716	1.87335
$477$	−0.338044	−0.0154780
$478$	−2.57834	−0.117930
$479$	10.7491	0.491141	0.245570	−	0.969379i	$-0.421025\pi$
$479$	10.7491	0.491141	0.245570	+	0.969379i	$0.421025\pi$
$480$	−3.27861	−0.149647
$481$	9.49472	0.432922
$482$	1.73501	0.0790276
$483$	31.1602	1.41784
$484$	−25.2403	−1.14729
$485$	12.3380	0.560242
$486$	0.289169	0.0131170
$487$	22.7491	1.03086	0.515431	−	0.856931i	$-0.327632\pi$
$487$	22.7491	1.03086	0.515431	+	0.856931i	$0.327632\pi$
$488$	−11.5184	−0.521413
$489$	−6.07306	−0.274633
$490$	4.96526	0.224307
$491$	−17.6867	−0.798187	−0.399094	−	0.916910i	$-0.630675\pi$
$491$	−17.6867	−0.798187	−0.399094	+	0.916910i	$0.630675\pi$
$492$	8.31335	0.374795
$493$	−26.0283	−1.17225
$494$	−0.745574	−0.0335450
$495$	−4.91638	−0.220975
$496$	4.98333	0.223758
$497$	4.50528	0.202089
$498$	3.25443	0.145834
$499$	19.9305	0.892212	0.446106	−	0.894980i	$-0.352810\pi$
$499$	19.9305	0.892212	0.446106	+	0.894980i	$0.352810\pi$
$500$	1.91638	0.0857032
$501$	0.745574	0.0333098
$502$	1.82562	0.0814815
$503$	33.3522	1.48710	0.743550	−	0.668680i	$-0.233140\pi$
$503$	33.3522	1.48710	0.743550	+	0.668680i	$0.233140\pi$
$504$	5.56777	0.248008
$505$	−10.6761	−0.475080
$506$	9.01056	0.400568
$507$	−1.00000	−0.0444116
$508$	−3.51227	−0.155832
$509$	13.8363	0.613285	0.306642	−	0.951825i	$-0.400794\pi$
$509$	13.8363	0.613285	0.306642	+	0.951825i	$0.400794\pi$
$510$	1.25443	0.0555469
$511$	−15.5194	−0.686538
$512$	−19.4319	−0.858775
$513$	−2.57834	−0.113836
$514$	3.22616	0.142300
$515$	14.5089	0.639336
$516$	−2.21663	−0.0975817
$517$	−26.6550	−1.17228
$518$	−13.4983	−0.593081
$519$	−0.843326	−0.0370179
$520$	−1.13249	−0.0496632
$521$	−23.3522	−1.02308	−0.511539	−	0.859260i	$-0.670924\pi$
$521$	−23.3522	−1.02308	−0.511539	+	0.859260i	$0.670924\pi$
$522$	−1.73501	−0.0759394
$523$	−4.00000	−0.174908	−0.0874539	−	0.996169i	$-0.527873\pi$
$523$	−4.00000	−0.174908	−0.0874539	+	0.996169i	$0.527873\pi$
$524$	−11.1778	−0.488304
$525$	−4.91638	−0.214568
$526$	−2.31335	−0.100867
$527$	−6.16724	−0.268649
$528$	−17.2333	−0.749983
$529$	17.1708	0.746557
$530$	−0.0977518	−0.00424607
$531$	−11.2544	−0.488400
$532$	−24.2922	−1.05320
$533$	4.33804	0.187902
$534$	−0.0977518	−0.00423014
$535$	−4.17081	−0.180320
$536$	−8.21560	−0.354860
$537$	18.9894	0.819455
$538$	−5.40054	−0.232834
$539$	84.4182	3.63615
$540$	−1.91638	−0.0824679
$541$	16.1744	0.695391	0.347695	−	0.937608i	$-0.386964\pi$
$541$	16.1744	0.695391	0.347695	+	0.937608i	$0.386964\pi$
$542$	−1.90225	−0.0817086
$543$	−17.4947	−0.750770
$544$	14.2227	0.609795
$545$	3.83276	0.164178
$546$	1.42166	0.0608416
$547$	9.68665	0.414171	0.207086	−	0.978323i	$-0.433602\pi$
$547$	9.68665	0.414171	0.207086	+	0.978323i	$0.433602\pi$
$548$	31.6373	1.35148
$549$	−10.1708	−0.434079
$550$	−1.42166	−0.0606199
$551$	15.4700	0.659045
$552$	7.17780	0.305507
$553$	−17.1814	−0.730626
$554$	−7.42166	−0.315316
$555$	9.49472	0.403028
$556$	−14.3627	−0.609116
$557$	0.647822	0.0274491	0.0137246	−	0.999906i	$-0.495631\pi$
$557$	0.647822	0.0274491	0.0137246	+	0.999906i	$0.495631\pi$
$558$	−0.411100	−0.0174033
$559$	−1.15667	−0.0489221
$560$	−17.2333	−0.728240
$561$	21.3275	0.900447
$562$	−0.912811	−0.0385046
$563$	−16.3169	−0.687676	−0.343838	−	0.939029i	$-0.611727\pi$
$563$	−16.3169	−0.687676	−0.343838	+	0.939029i	$0.611727\pi$
$564$	−10.3900	−0.437497
$565$	0.843326	0.0354790
$566$	1.00342	0.0421769
$567$	4.91638	0.206469
$568$	1.03780	0.0435450
$569$	44.6550	1.87203	0.936017	−	0.351956i	$-0.114483\pi$
$569$	44.6550	1.87203	0.936017	+	0.351956i	$0.114483\pi$
$570$	−0.745574	−0.0312287
$571$	−6.67252	−0.279236	−0.139618	−	0.990205i	$-0.544587\pi$
$571$	−6.67252	−0.279236	−0.139618	+	0.990205i	$0.544587\pi$
$572$	−9.42166	−0.393940
$573$	22.5089	0.940321
$574$	−6.16724	−0.257415
$575$	−6.33804	−0.264315
$576$	−6.06249	−0.252604
$577$	15.3275	0.638091	0.319046	−	0.947739i	$-0.396638\pi$
$577$	15.3275	0.638091	0.319046	+	0.947739i	$0.396638\pi$
$578$	−0.525891	−0.0218742
$579$	−2.65139	−0.110188
$580$	11.4983	0.477440
$581$	55.3311	2.29552
$582$	−3.56777	−0.147889
$583$	−1.66196	−0.0688312
$584$	−3.57492	−0.147931
$585$	−1.00000	−0.0413449
$586$	−8.28611	−0.342296
$587$	12.2650	0.506230	0.253115	−	0.967436i	$-0.418545\pi$
$587$	12.2650	0.506230	0.253115	+	0.967436i	$0.418545\pi$
$588$	32.9058	1.35701
$589$	3.66553	0.151035
$590$	−3.25443	−0.133983
$591$	12.9894	0.534314
$592$	33.2817	1.36787
$593$	−5.85389	−0.240390	−0.120195	−	0.992750i	$-0.538352\pi$
$593$	−5.85389	−0.240390	−0.120195	+	0.992750i	$0.538352\pi$
$594$	1.42166	0.0583315
$595$	21.3275	0.874342
$596$	−39.2555	−1.60797
$597$	2.84333	0.116370
$598$	1.83276	0.0749473
$599$	27.1355	1.10873	0.554364	−	0.832274i	$-0.312961\pi$
$599$	27.1355	1.10873	0.554364	+	0.832274i	$0.312961\pi$
$600$	−1.13249	−0.0462339
$601$	34.1708	1.39386	0.696928	−	0.717141i	$-0.254550\pi$
$601$	34.1708	1.39386	0.696928	+	0.717141i	$0.254550\pi$
$602$	1.64440	0.0670208
$603$	−7.25443	−0.295423
$604$	31.4499	1.27968
$605$	−13.1708	−0.535469
$606$	3.08719	0.125408
$607$	10.3133	0.418606	0.209303	−	0.977851i	$-0.432881\pi$
$607$	10.3133	0.418606	0.209303	+	0.977851i	$0.432881\pi$
$608$	−8.45335	−0.342829
$609$	−29.4983	−1.19533
$610$	−2.94108	−0.119081
$611$	−5.42166	−0.219337
$612$	8.31335	0.336047
$613$	0.484156	0.0195549	0.00977744	−	0.999952i	$-0.496888\pi$
$613$	0.484156	0.0195549	0.00977744	+	0.999952i	$0.496888\pi$
$614$	0.557212	0.0224872
$615$	4.33804	0.174927
$616$	27.3733	1.10290
$617$	−7.15667	−0.288117	−0.144058	−	0.989569i	$-0.546015\pi$
$617$	−7.15667	−0.288117	−0.144058	+	0.989569i	$0.546015\pi$
$618$	−4.19550	−0.168768
$619$	5.42166	0.217915	0.108958	−	0.994046i	$-0.465249\pi$
$619$	5.42166	0.217915	0.108958	+	0.994046i	$0.465249\pi$
$620$	2.72445	0.109416
$621$	6.33804	0.254337
$622$	8.66895	0.347593
$623$	−1.66196	−0.0665848
$624$	−3.50528	−0.140324
$625$	1.00000	0.0400000
$626$	4.71731	0.188542
$627$	−12.6761	−0.506234
$628$	41.5194	1.65681
$629$	−41.1885	−1.64229
$630$	1.42166	0.0566404
$631$	−10.7244	−0.426934	−0.213467	−	0.976950i	$-0.568476\pi$
$631$	−10.7244	−0.426934	−0.213467	+	0.976950i	$0.568476\pi$
$632$	−3.95775	−0.157431
$633$	−6.31335	−0.250933
$634$	−8.87056	−0.352295
$635$	−1.83276	−0.0727310
$636$	−0.647822	−0.0256878
$637$	17.1708	0.680332
$638$	−8.52998	−0.337705
$639$	0.916382	0.0362515
$640$	−8.31029	−0.328493
$641$	−0.362741	−0.0143274	−0.00716370	−	0.999974i	$-0.502280\pi$
$641$	−0.362741	−0.0143274	−0.00716370	+	0.999974i	$0.502280\pi$
$642$	1.20607	0.0475996
$643$	−9.39697	−0.370580	−0.185290	−	0.982684i	$-0.559322\pi$
$643$	−9.39697	−0.370580	−0.185290	+	0.982684i	$0.559322\pi$
$644$	59.7149	2.35310
$645$	−1.15667	−0.0455440
$646$	3.23433	0.127253
$647$	18.0036	0.707793	0.353897	−	0.935285i	$-0.384856\pi$
$647$	18.0036	0.707793	0.353897	+	0.935285i	$0.384856\pi$
$648$	1.13249	0.0444886
$649$	−55.3311	−2.17193
$650$	−0.289169	−0.0113421
$651$	−6.98944	−0.273938
$652$	−11.6383	−0.455791
$653$	−34.8222	−1.36270	−0.681349	−	0.731959i	$-0.738606\pi$
$653$	−34.8222	−1.36270	−0.681349	+	0.731959i	$0.738606\pi$
$654$	−1.10831	−0.0433385
$655$	−5.83276	−0.227905
$656$	15.2061	0.593697
$657$	−3.15667	−0.123154
$658$	7.70778	0.300480
$659$	11.4700	0.446809	0.223404	−	0.974726i	$-0.428283\pi$
$659$	11.4700	0.446809	0.223404	+	0.974726i	$0.428283\pi$
$660$	−9.42166	−0.366738
$661$	12.1672	0.473251	0.236625	−	0.971601i	$-0.423959\pi$
$661$	12.1672	0.473251	0.236625	+	0.971601i	$0.423959\pi$
$662$	2.91995	0.113487
$663$	4.33804	0.168476
$664$	12.7456	0.494624
$665$	−12.6761	−0.491558
$666$	−2.74557	−0.106389
$667$	−38.0283	−1.47246
$668$	1.42880	0.0552821
$669$	−19.2544	−0.744419
$670$	−2.09775	−0.0810432
$671$	−50.0036	−1.93037
$672$	16.1189	0.621799
$673$	−27.9789	−1.07851	−0.539253	−	0.842144i	$-0.681293\pi$
$673$	−27.9789	−1.07851	−0.539253	+	0.842144i	$0.681293\pi$
$674$	0.382833	0.0147462
$675$	−1.00000	−0.0384900
$676$	−1.91638	−0.0737070
$677$	22.9930	0.883693	0.441847	−	0.897091i	$-0.354324\pi$
$677$	22.9930	0.883693	0.441847	+	0.897091i	$0.354324\pi$
$678$	−0.243863	−0.00936551
$679$	−60.6585	−2.32786
$680$	4.91281	0.188398
$681$	13.0872	0.501502
$682$	−2.02113	−0.0773929
$683$	−28.6066	−1.09460	−0.547301	−	0.836936i	$-0.684345\pi$
$683$	−28.6066	−1.09460	−0.547301	+	0.836936i	$0.684345\pi$
$684$	−4.94108	−0.188927
$685$	16.5089	0.630771
$686$	−14.4595	−0.552065
$687$	24.5089	0.935071
$688$	−4.05447	−0.154575
$689$	−0.338044	−0.0128785
$690$	1.83276	0.0697721
$691$	−19.4005	−0.738031	−0.369016	−	0.929423i	$-0.620305\pi$
$691$	−19.4005	−0.738031	−0.369016	+	0.929423i	$0.620305\pi$
$692$	−1.61613	−0.0614362
$693$	24.1708	0.918173
$694$	2.16724	0.0822672
$695$	−7.49472	−0.284291
$696$	−6.79497	−0.257563
$697$	−18.8186	−0.712806
$698$	6.40396	0.242393
$699$	−8.33804	−0.315374
$700$	−9.42166	−0.356105
$701$	−38.9683	−1.47181	−0.735906	−	0.677083i	$-0.763244\pi$
$701$	−38.9683	−1.47181	−0.735906	+	0.677083i	$0.763244\pi$
$702$	0.289169	0.0109140
$703$	24.4806	0.923303
$704$	−29.8055	−1.12334
$705$	−5.42166	−0.204192
$706$	−1.30382	−0.0490698
$707$	52.4877	1.97400
$708$	−21.5678	−0.810567
$709$	−17.5194	−0.657955	−0.328978	−	0.944338i	$-0.606704\pi$
$709$	−17.5194	−0.657955	−0.328978	+	0.944338i	$0.606704\pi$
$710$	0.264989	0.00994485
$711$	−3.49472	−0.131062
$712$	−0.382833	−0.0143473
$713$	−9.01056	−0.337448
$714$	−6.16724	−0.230803
$715$	−4.91638	−0.183862
$716$	36.3910	1.36000
$717$	−8.91638	−0.332988
$718$	5.90225	0.220270
$719$	−4.33447	−0.161649	−0.0808243	−	0.996728i	$-0.525755\pi$
$719$	−4.33447	−0.161649	−0.0808243	+	0.996728i	$0.525755\pi$
$720$	−3.50528	−0.130634
$721$	−71.3311	−2.65651
$722$	3.57186	0.132931
$723$	6.00000	0.223142
$724$	−33.5266	−1.24600
$725$	6.00000	0.222834
$726$	3.80858	0.141350
$727$	22.1672	0.822137	0.411069	−	0.911604i	$-0.365156\pi$
$727$	22.1672	0.822137	0.411069	+	0.911604i	$0.365156\pi$
$728$	5.56777	0.206355
$729$	1.00000	0.0370370
$730$	−0.912811	−0.0337846
$731$	5.01770	0.185586
$732$	−19.4911	−0.720414
$733$	−2.83976	−0.104889	−0.0524444	−	0.998624i	$-0.516701\pi$
$733$	−2.83976	−0.104889	−0.0524444	+	0.998624i	$0.516701\pi$
$734$	2.98230	0.110079
$735$	17.1708	0.633355
$736$	20.7799	0.765959
$737$	−35.6655	−1.31376
$738$	−1.25443	−0.0461761
$739$	−43.9305	−1.61601	−0.808005	−	0.589176i	$-0.799453\pi$
$739$	−43.9305	−1.61601	−0.808005	+	0.589176i	$0.799453\pi$
$740$	18.1955	0.668880
$741$	−2.57834	−0.0947176
$742$	0.480585	0.0176428
$743$	41.0872	1.50734	0.753671	−	0.657251i	$-0.228281\pi$
$743$	41.0872	1.50734	0.753671	+	0.657251i	$0.228281\pi$
$744$	−1.61003	−0.0590264
$745$	−20.4842	−0.750481
$746$	−5.40054	−0.197728
$747$	11.2544	0.411778
$748$	40.8716	1.49441
$749$	20.5053	0.749247
$750$	−0.289169	−0.0105589
$751$	23.6902	0.864468	0.432234	−	0.901761i	$-0.357725\pi$
$751$	23.6902	0.864468	0.432234	+	0.901761i	$0.357725\pi$
$752$	−19.0045	−0.693021
$753$	6.31335	0.230071
$754$	−1.73501	−0.0631854
$755$	16.4111	0.597261
$756$	9.42166	0.342663
$757$	9.32391	0.338883	0.169442	−	0.985540i	$-0.445804\pi$
$757$	9.32391	0.338883	0.169442	+	0.985540i	$0.445804\pi$
$758$	8.31438	0.301992
$759$	31.1602	1.13105
$760$	−2.91995	−0.105918
$761$	−42.8222	−1.55230	−0.776152	−	0.630546i	$-0.782831\pi$
$761$	−42.8222	−1.55230	−0.776152	+	0.630546i	$0.782831\pi$
$762$	0.529977	0.0191991
$763$	−18.8433	−0.682174
$764$	43.1355	1.56059
$765$	4.33804	0.156842
$766$	4.11888	0.148821
$767$	−11.2544	−0.406374
$768$	−9.72191	−0.350809
$769$	−17.3239	−0.624716	−0.312358	−	0.949964i	$-0.601119\pi$
$769$	−17.3239	−0.624716	−0.312358	+	0.949964i	$0.601119\pi$
$770$	6.98944	0.251882
$771$	11.1567	0.401798
$772$	−5.08108	−0.182872
$773$	−11.6373	−0.418563	−0.209282	−	0.977855i	$-0.567113\pi$
$773$	−11.6373	−0.418563	−0.209282	+	0.977855i	$0.567113\pi$
$774$	0.334474	0.0120224
$775$	1.42166	0.0510676
$776$	−13.9728	−0.501593
$777$	−46.6797	−1.67462
$778$	−10.0272	−0.359494
$779$	11.1849	0.400742
$780$	−1.91638	−0.0686175
$781$	4.50528	0.161212
$782$	−7.95061	−0.284313
$783$	−6.00000	−0.214423
$784$	60.1885	2.14959
$785$	21.6655	0.773276
$786$	1.68665	0.0601609
$787$	20.9411	0.746469	0.373234	−	0.927737i	$-0.378249\pi$
$787$	20.9411	0.746469	0.373234	+	0.927737i	$0.378249\pi$
$788$	24.8927	0.886766
$789$	−8.00000	−0.284808
$790$	−1.01056	−0.0359542
$791$	−4.14611	−0.147419
$792$	5.56777	0.197842
$793$	−10.1708	−0.361176
$794$	−2.07663	−0.0736967
$795$	−0.338044	−0.0119892
$796$	5.44890	0.193131
$797$	20.3380	0.720410	0.360205	−	0.932873i	$-0.382707\pi$
$797$	20.3380	0.720410	0.360205	+	0.932873i	$0.382707\pi$
$798$	3.66553	0.129758
$799$	23.5194	0.832057
$800$	−3.27861	−0.115916
$801$	−0.338044	−0.0119442
$802$	−10.9482	−0.386595
$803$	−15.5194	−0.547668
$804$	−13.9022	−0.490294
$805$	31.1602	1.09825
$806$	−0.411100	−0.0144804
$807$	−18.6761	−0.657429
$808$	12.0906	0.425346
$809$	7.68665	0.270248	0.135124	−	0.990829i	$-0.456857\pi$
$809$	7.68665	0.270248	0.135124	+	0.990829i	$0.456857\pi$
$810$	0.289169	0.0101603
$811$	−44.4111	−1.55948	−0.779742	−	0.626101i	$-0.784650\pi$
$811$	−44.4111	−1.55948	−0.779742	+	0.626101i	$0.784650\pi$
$812$	−56.5300	−1.98381
$813$	−6.57834	−0.230712
$814$	−13.4983	−0.473115
$815$	−6.07306	−0.212730
$816$	15.2061	0.532319
$817$	−2.98230	−0.104337
$818$	4.04836	0.141548
$819$	4.91638	0.171792
$820$	8.31335	0.290315
$821$	−46.4630	−1.62157	−0.810785	−	0.585343i	$-0.800960\pi$
$821$	−46.4630	−1.62157	−0.810785	+	0.585343i	$0.800960\pi$
$822$	−4.77384	−0.166507
$823$	46.5089	1.62120	0.810598	−	0.585603i	$-0.199142\pi$
$823$	46.5089	1.62120	0.810598	+	0.585603i	$0.199142\pi$
$824$	−16.4312	−0.572408
$825$	−4.91638	−0.171166
$826$	16.0000	0.556711
$827$	39.4005	1.37009	0.685045	−	0.728500i	$-0.259782\pi$
$827$	39.4005	1.37009	0.685045	+	0.728500i	$0.259782\pi$
$828$	12.1461	0.422107
$829$	47.6444	1.65476	0.827379	−	0.561644i	$-0.189831\pi$
$829$	47.6444	1.65476	0.827379	+	0.561644i	$0.189831\pi$
$830$	3.25443	0.112963
$831$	−25.6655	−0.890327
$832$	−6.06249	−0.210179
$833$	−74.4877	−2.58085
$834$	2.16724	0.0750453
$835$	0.745574	0.0258017
$836$	−24.2922	−0.840164
$837$	−1.42166	−0.0491399
$838$	9.68665	0.334620
$839$	−39.9058	−1.37770	−0.688851	−	0.724903i	$-0.741885\pi$
$839$	−39.9058	−1.37770	−0.688851	+	0.724903i	$0.741885\pi$
$840$	5.56777	0.192106
$841$	7.00000	0.241379
$842$	−3.90939	−0.134726
$843$	−3.15667	−0.108722
$844$	−12.0988	−0.416457
$845$	−1.00000	−0.0344010
$846$	1.56777	0.0539012
$847$	64.7527	2.22493
$848$	−1.18494	−0.0406910
$849$	3.47002	0.119091
$850$	1.25443	0.0430265
$851$	−60.1779	−2.06287
$852$	1.75614	0.0601643
$853$	29.5019	1.01012	0.505062	−	0.863083i	$-0.331470\pi$
$853$	29.5019	1.01012	0.505062	+	0.863083i	$0.331470\pi$
$854$	14.4595	0.494793
$855$	−2.57834	−0.0881773
$856$	4.72342	0.161443
$857$	8.33804	0.284822	0.142411	−	0.989808i	$-0.454515\pi$
$857$	8.33804	0.284822	0.142411	+	0.989808i	$0.454515\pi$
$858$	1.42166	0.0485348
$859$	−4.17081	−0.142306	−0.0711531	−	0.997465i	$-0.522668\pi$
$859$	−4.17081	−0.142306	−0.0711531	+	0.997465i	$0.522668\pi$
$860$	−2.21663	−0.0755864
$861$	−21.3275	−0.726839
$862$	−3.58890	−0.122238
$863$	−3.93051	−0.133796	−0.0668981	−	0.997760i	$-0.521310\pi$
$863$	−3.93051	−0.133796	−0.0668981	+	0.997760i	$0.521310\pi$
$864$	3.27861	0.111540
$865$	−0.843326	−0.0286739
$866$	5.00953	0.170231
$867$	−1.81863	−0.0617639
$868$	−13.3944	−0.454637
$869$	−17.1814	−0.582838
$870$	−1.73501	−0.0588224
$871$	−7.25443	−0.245807
$872$	−4.34058	−0.146991
$873$	−12.3380	−0.417580
$874$	4.72548	0.159842
$875$	−4.91638	−0.166204
$876$	−6.04939	−0.204390
$877$	−23.0177	−0.777253	−0.388626	−	0.921395i	$-0.627050\pi$
$877$	−23.0177	−0.777253	−0.388626	+	0.921395i	$0.627050\pi$
$878$	−0.188362	−0.00635692
$879$	−28.6550	−0.966508
$880$	−17.2333	−0.580934
$881$	−15.3522	−0.517228	−0.258614	−	0.965981i	$-0.583266\pi$
$881$	−15.3522	−0.517228	−0.258614	+	0.965981i	$0.583266\pi$
$882$	−4.96526	−0.167189
$883$	42.8011	1.44037	0.720185	−	0.693782i	$-0.244057\pi$
$883$	42.8011	1.44037	0.720185	+	0.693782i	$0.244057\pi$
$884$	8.31335	0.279608
$885$	−11.2544	−0.378313
$886$	2.55824	0.0859459
$887$	−53.1885	−1.78590	−0.892948	−	0.450160i	$-0.851367\pi$
$887$	−53.1885	−1.78590	−0.892948	+	0.450160i	$0.851367\pi$
$888$	−10.7527	−0.360837
$889$	9.01056	0.302205
$890$	−0.0977518	−0.00327665
$891$	4.91638	0.164705
$892$	−36.8988	−1.23546
$893$	−13.9789	−0.467785
$894$	5.92337	0.198107
$895$	18.9894	0.634747
$896$	40.8566	1.36492
$897$	6.33804	0.211621
$898$	−1.25443	−0.0418607
$899$	8.52998	0.284491
$900$	−1.91638	−0.0638794
$901$	1.46645	0.0488546
$902$	−6.16724	−0.205347
$903$	5.68665	0.189240
$904$	−0.955062	−0.0317649
$905$	−17.4947	−0.581544
$906$	−4.74557	−0.157661
$907$	11.8116	0.392199	0.196099	−	0.980584i	$-0.437172\pi$
$907$	11.8116	0.392199	0.196099	+	0.980584i	$0.437172\pi$
$908$	25.0800	0.832311
$909$	10.6761	0.354104
$910$	1.42166	0.0471277
$911$	44.1955	1.46426	0.732131	−	0.681164i	$-0.238526\pi$
$911$	44.1955	1.46426	0.732131	+	0.681164i	$0.238526\pi$
$912$	−9.03780	−0.299271
$913$	55.3311	1.83119
$914$	−4.43223	−0.146605
$915$	−10.1708	−0.336237
$916$	46.9683	1.55188
$917$	28.6761	0.946968
$918$	−1.25443	−0.0414022
$919$	55.2096	1.82120	0.910599	−	0.413291i	$-0.135621\pi$
$919$	55.2096	1.82120	0.910599	+	0.413291i	$0.135621\pi$
$920$	7.17780	0.236645
$921$	1.92694	0.0634950
$922$	3.42880	0.112922
$923$	0.916382	0.0301631
$924$	46.3205	1.52383
$925$	9.49472	0.312184
$926$	7.63829	0.251010
$927$	−14.5089	−0.476533
$928$	−19.6716	−0.645753
$929$	22.9930	0.754376	0.377188	−	0.926137i	$-0.376891\pi$
$929$	22.9930	0.754376	0.377188	+	0.926137i	$0.376891\pi$
$930$	−0.411100	−0.0134805
$931$	44.2721	1.45096
$932$	−15.9789	−0.523405
$933$	29.9789	0.981464
$934$	9.73604	0.318573
$935$	21.3275	0.697483
$936$	1.13249	0.0370167
$937$	7.97887	0.260658	0.130329	−	0.991471i	$-0.458397\pi$
$937$	7.97887	0.260658	0.130329	+	0.991471i	$0.458397\pi$
$938$	10.3133	0.336743
$939$	16.3133	0.532366
$940$	−10.3900	−0.338884
$941$	41.5019	1.35292	0.676461	−	0.736478i	$-0.263513\pi$
$941$	41.5019	1.35292	0.676461	+	0.736478i	$0.263513\pi$
$942$	−6.26499	−0.204124
$943$	−27.4947	−0.895351
$944$	−39.4499	−1.28399
$945$	4.91638	0.159930
$946$	1.64440	0.0534641
$947$	47.4499	1.54192	0.770958	−	0.636886i	$-0.219778\pi$
$947$	47.4499	1.54192	0.770958	+	0.636886i	$0.219778\pi$
$948$	−6.69721	−0.217515
$949$	−3.15667	−0.102470
$950$	−0.745574	−0.0241896
$951$	−30.6761	−0.994740
$952$	−24.1533	−0.782811
$953$	30.3663	0.983661	0.491831	−	0.870691i	$-0.336328\pi$
$953$	30.3663	0.983661	0.491831	+	0.870691i	$0.336328\pi$
$954$	0.0977518	0.00316483
$955$	22.5089	0.728369
$956$	−17.0872	−0.552639
$957$	−29.4983	−0.953544
$958$	−3.10831	−0.100425
$959$	−81.1638	−2.62092
$960$	−6.06249	−0.195666
$961$	−28.9789	−0.934802
$962$	−2.74557	−0.0885209
$963$	4.17081	0.134402
$964$	11.4983	0.370335
$965$	−2.65139	−0.0853514
$966$	−9.01056	−0.289910
$967$	−41.0943	−1.32150	−0.660752	−	0.750604i	$-0.729763\pi$
$967$	−41.0943	−1.32150	−0.660752	+	0.750604i	$0.729763\pi$
$968$	14.9159	0.479414
$969$	11.1849	0.359312
$970$	−3.56777	−0.114554
$971$	38.1744	1.22507	0.612537	−	0.790442i	$-0.290149\pi$
$971$	38.1744	1.22507	0.612537	+	0.790442i	$0.290149\pi$
$972$	1.91638	0.0614680
$973$	36.8469	1.18126
$974$	−6.57834	−0.210784
$975$	−1.00000	−0.0320256
$976$	−35.6515	−1.14118
$977$	−10.4806	−0.335304	−0.167652	−	0.985846i	$-0.553618\pi$
$977$	−10.4806	−0.335304	−0.167652	+	0.985846i	$0.553618\pi$
$978$	1.75614	0.0561551
$979$	−1.66196	−0.0531163
$980$	32.9058	1.05114
$981$	−3.83276	−0.122371
$982$	5.11442	0.163208
$983$	−0.0766264	−0.00244400	−0.00122200	−	0.999999i	$-0.500389\pi$
$983$	−0.0766264	−0.00244400	−0.00122200	+	0.999999i	$0.500389\pi$
$984$	−4.91281	−0.156615
$985$	12.9894	0.413878
$986$	7.52656	0.239694
$987$	26.6550	0.848437
$988$	−4.94108	−0.157197
$989$	7.33105	0.233114
$990$	1.42166	0.0451834
$991$	−13.8575	−0.440197	−0.220098	−	0.975478i	$-0.570638\pi$
$991$	−13.8575	−0.440197	−0.220098	+	0.975478i	$0.570638\pi$
$992$	−4.66107	−0.147989
$993$	10.0978	0.320442
$994$	−1.30279	−0.0413219
$995$	2.84333	0.0901395
$996$	21.5678	0.683401
$997$	−10.3416	−0.327522	−0.163761	−	0.986500i	$-0.552363\pi$
$997$	−10.3416	−0.327522	−0.163761	+	0.986500i	$0.552363\pi$
$998$	−5.76328	−0.182433
$999$	−9.49472	−0.300400

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.2.a.e.1.2	✓	3
3.2	odd	2		585.2.a.n.1.2		3
4.3	odd	2		3120.2.a.bj.1.1		3
5.2	odd	4		975.2.c.i.274.3		6
5.3	odd	4		975.2.c.i.274.4		6
5.4	even	2		975.2.a.o.1.2		3
7.6	odd	2		9555.2.a.bq.1.2		3
12.11	even	2		9360.2.a.dd.1.1		3
13.12	even	2		2535.2.a.bc.1.2		3
15.2	even	4		2925.2.c.w.2224.4		6
15.8	even	4		2925.2.c.w.2224.3		6
15.14	odd	2		2925.2.a.bh.1.2		3
39.38	odd	2		7605.2.a.bx.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.a.e.1.2	✓	3	1.1	even	1	trivial
585.2.a.n.1.2		3	3.2	odd	2
975.2.a.o.1.2		3	5.4	even	2
975.2.c.i.274.3		6	5.2	odd	4
975.2.c.i.274.4		6	5.3	odd	4
2535.2.a.bc.1.2		3	13.12	even	2
2925.2.a.bh.1.2		3	15.14	odd	2
2925.2.c.w.2224.3		6	15.8	even	4
2925.2.c.w.2224.4		6	15.2	even	4
3120.2.a.bj.1.1		3	4.3	odd	2
7605.2.a.bx.1.2		3	39.38	odd	2
9360.2.a.dd.1.1		3	12.11	even	2
9555.2.a.bq.1.2		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)

\(f(q)\)	\(=\)	\(q-0.289169 q^{2} -1.00000 q^{3} -1.91638 q^{4} -1.00000 q^{5} +0.289169 q^{6} +4.91638 q^{7} +1.13249 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.289169 q^{2} -1.00000 q^{3} -1.91638 q^{4} -1.00000 q^{5} +0.289169 q^{6} +4.91638 q^{7} +1.13249 q^{8} +1.00000 q^{9} +0.289169 q^{10} +4.91638 q^{11} +1.91638 q^{12} +1.00000 q^{13} -1.42166 q^{14} +1.00000 q^{15} +3.50528 q^{16} -4.33804 q^{17} -0.289169 q^{18} +2.57834 q^{19} +1.91638 q^{20} -4.91638 q^{21} -1.42166 q^{22} -6.33804 q^{23} -1.13249 q^{24} +1.00000 q^{25} -0.289169 q^{26} -1.00000 q^{27} -9.42166 q^{28} +6.00000 q^{29} -0.289169 q^{30} +1.42166 q^{31} -3.27861 q^{32} -4.91638 q^{33} +1.25443 q^{34} -4.91638 q^{35} -1.91638 q^{36} +9.49472 q^{37} -0.745574 q^{38} -1.00000 q^{39} -1.13249 q^{40} +4.33804 q^{41} +1.42166 q^{42} -1.15667 q^{43} -9.42166 q^{44} -1.00000 q^{45} +1.83276 q^{46} -5.42166 q^{47} -3.50528 q^{48} +17.1708 q^{49} -0.289169 q^{50} +4.33804 q^{51} -1.91638 q^{52} -0.338044 q^{53} +0.289169 q^{54} -4.91638 q^{55} +5.56777 q^{56} -2.57834 q^{57} -1.73501 q^{58} -11.2544 q^{59} -1.91638 q^{60} -10.1708 q^{61} -0.411100 q^{62} +4.91638 q^{63} -6.06249 q^{64} -1.00000 q^{65} +1.42166 q^{66} -7.25443 q^{67} +8.31335 q^{68} +6.33804 q^{69} +1.42166 q^{70} +0.916382 q^{71} +1.13249 q^{72} -3.15667 q^{73} -2.74557 q^{74} -1.00000 q^{75} -4.94108 q^{76} +24.1708 q^{77} +0.289169 q^{78} -3.49472 q^{79} -3.50528 q^{80} +1.00000 q^{81} -1.25443 q^{82} +11.2544 q^{83} +9.42166 q^{84} +4.33804 q^{85} +0.334474 q^{86} -6.00000 q^{87} +5.56777 q^{88} -0.338044 q^{89} +0.289169 q^{90} +4.91638 q^{91} +12.1461 q^{92} -1.42166 q^{93} +1.56777 q^{94} -2.57834 q^{95} +3.27861 q^{96} -12.3380 q^{97} -4.96526 q^{98} +4.91638 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{3} + 8 q^{4} - 3 q^{5} + q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 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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