LMFDB - Embedded newform 6031.2.a.c.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6031,2,Mod(1,6031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6031, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6031 = 37 \cdot 163 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6031.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1577774590$
Analytic rank:	$1$
Dimension:	$110$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	6031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.33551 q^{2} +0.518713 q^{3} +3.45460 q^{4} -1.17306 q^{5} -1.21146 q^{6} -2.50606 q^{7} -3.39724 q^{8} -2.73094 q^{9} +O(q^{10})$	\(q-2.33551 q^{2} +0.518713 q^{3} +3.45460 q^{4} -1.17306 q^{5} -1.21146 q^{6} -2.50606 q^{7} -3.39724 q^{8} -2.73094 q^{9} +2.73970 q^{10} +5.62807 q^{11} +1.79195 q^{12} +0.500177 q^{13} +5.85293 q^{14} -0.608484 q^{15} +1.02508 q^{16} -4.81786 q^{17} +6.37813 q^{18} +6.63611 q^{19} -4.05247 q^{20} -1.29993 q^{21} -13.1444 q^{22} +7.19678 q^{23} -1.76220 q^{24} -3.62392 q^{25} -1.16817 q^{26} -2.97271 q^{27} -8.65745 q^{28} +1.64242 q^{29} +1.42112 q^{30} -4.86969 q^{31} +4.40039 q^{32} +2.91936 q^{33} +11.2522 q^{34} +2.93977 q^{35} -9.43430 q^{36} -1.00000 q^{37} -15.4987 q^{38} +0.259448 q^{39} +3.98518 q^{40} -6.72318 q^{41} +3.03599 q^{42} -1.74449 q^{43} +19.4428 q^{44} +3.20356 q^{45} -16.8081 q^{46} -4.67858 q^{47} +0.531725 q^{48} -0.719660 q^{49} +8.46370 q^{50} -2.49909 q^{51} +1.72791 q^{52} +0.546874 q^{53} +6.94280 q^{54} -6.60209 q^{55} +8.51370 q^{56} +3.44224 q^{57} -3.83590 q^{58} -12.3711 q^{59} -2.10207 q^{60} +13.2708 q^{61} +11.3732 q^{62} +6.84389 q^{63} -12.3273 q^{64} -0.586739 q^{65} -6.81819 q^{66} +7.64936 q^{67} -16.6438 q^{68} +3.73307 q^{69} -6.86586 q^{70} -2.40565 q^{71} +9.27765 q^{72} +1.88290 q^{73} +2.33551 q^{74} -1.87978 q^{75} +22.9251 q^{76} -14.1043 q^{77} -0.605944 q^{78} -10.9669 q^{79} -1.20249 q^{80} +6.65082 q^{81} +15.7021 q^{82} +16.9417 q^{83} -4.49074 q^{84} +5.65165 q^{85} +4.07427 q^{86} +0.851947 q^{87} -19.1199 q^{88} -10.7636 q^{89} -7.48195 q^{90} -1.25347 q^{91} +24.8620 q^{92} -2.52598 q^{93} +10.9269 q^{94} -7.78458 q^{95} +2.28254 q^{96} +13.4771 q^{97} +1.68077 q^{98} -15.3699 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9}+O(q^{10}) $ 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9	\( 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9} - 17 q^{10} - 9 q^{11} - 21 q^{13} - 29 q^{14} - 23 q^{15} + 79 q^{16} - 76 q^{17} - 31 q^{18} - 27 q^{19} - 67 q^{20} - 30 q^{21} - 28 q^{22} - 32 q^{23} - 63 q^{24} + 66 q^{25} - 55 q^{26} - 4 q^{28} - 81 q^{29} - 48 q^{30} - 30 q^{31} - 73 q^{32} - 53 q^{33} - 23 q^{34} - 78 q^{35} + 7 q^{36} - 110 q^{37} - 50 q^{38} - 64 q^{39} - 37 q^{40} - 123 q^{41} - 63 q^{42} - 40 q^{43} - 31 q^{44} - 73 q^{45} + 16 q^{46} - 37 q^{47} - 29 q^{48} + 46 q^{49} - 58 q^{50} - 73 q^{51} - 39 q^{52} - 16 q^{53} - 53 q^{54} - 59 q^{55} - 113 q^{56} - 39 q^{57} + 11 q^{58} - 93 q^{59} - 18 q^{60} - 66 q^{61} - 40 q^{62} - 21 q^{63} + 23 q^{64} - 92 q^{65} - 31 q^{66} + q^{67} - 121 q^{68} - 80 q^{69} - 3 q^{70} - 75 q^{71} - 114 q^{72} - 39 q^{73} + 9 q^{74} - 25 q^{75} - 58 q^{76} - 31 q^{77} + 68 q^{78} - 36 q^{79} - 82 q^{80} - 50 q^{81} - 18 q^{82} - 57 q^{83} - 9 q^{84} - 14 q^{85} - 58 q^{86} - 58 q^{87} - 15 q^{88} - 181 q^{89} + 8 q^{90} - 55 q^{91} - 116 q^{92} - 86 q^{93} - 39 q^{94} - 70 q^{95} - 127 q^{96} - 91 q^{97} - 19 q^{98} - 21 q^{99}+O(q^{100}) \) 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9 - 17 * q^10 - 9 * q^11 - 21 * q^13 - 29 * q^14 - 23 * q^15 + 79 * q^16 - 76 * q^17 - 31 * q^18 - 27 * q^19 - 67 * q^20 - 30 * q^21 - 28 * q^22 - 32 * q^23 - 63 * q^24 + 66 * q^25 - 55 * q^26 - 4 * q^28 - 81 * q^29 - 48 * q^30 - 30 * q^31 - 73 * q^32 - 53 * q^33 - 23 * q^34 - 78 * q^35 + 7 * q^36 - 110 * q^37 - 50 * q^38 - 64 * q^39 - 37 * q^40 - 123 * q^41 - 63 * q^42 - 40 * q^43 - 31 * q^44 - 73 * q^45 + 16 * q^46 - 37 * q^47 - 29 * q^48 + 46 * q^49 - 58 * q^50 - 73 * q^51 - 39 * q^52 - 16 * q^53 - 53 * q^54 - 59 * q^55 - 113 * q^56 - 39 * q^57 + 11 * q^58 - 93 * q^59 - 18 * q^60 - 66 * q^61 - 40 * q^62 - 21 * q^63 + 23 * q^64 - 92 * q^65 - 31 * q^66 + q^67 - 121 * q^68 - 80 * q^69 - 3 * q^70 - 75 * q^71 - 114 * q^72 - 39 * q^73 + 9 * q^74 - 25 * q^75 - 58 * q^76 - 31 * q^77 + 68 * q^78 - 36 * q^79 - 82 * q^80 - 50 * q^81 - 18 * q^82 - 57 * q^83 - 9 * q^84 - 14 * q^85 - 58 * q^86 - 58 * q^87 - 15 * q^88 - 181 * q^89 + 8 * q^90 - 55 * q^91 - 116 * q^92 - 86 * q^93 - 39 * q^94 - 70 * q^95 - 127 * q^96 - 91 * q^97 - 19 * q^98 - 21 * 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 $

$2$	−2.33551	−1.65145	−0.825727	−	0.564070i	$-0.809235\pi$
$2$	−2.33551	−1.65145	−0.825727	+	0.564070i	$0.809235\pi$
$3$	0.518713	0.299479	0.149740	−	0.988725i	$-0.452156\pi$
$3$	0.518713	0.299479	0.149740	+	0.988725i	$0.452156\pi$
$4$	3.45460	1.72730
$5$	−1.17306	−0.524610	−0.262305	−	0.964985i	$-0.584483\pi$
$5$	−1.17306	−0.524610	−0.262305	+	0.964985i	$0.584483\pi$
$6$	−1.21146	−0.494577
$7$	−2.50606	−0.947202	−0.473601	−	0.880740i	$-0.657046\pi$
$7$	−2.50606	−0.947202	−0.473601	+	0.880740i	$0.657046\pi$
$8$	−3.39724	−1.20111
$9$	−2.73094	−0.910312
$10$	2.73970	0.866370
$11$	5.62807	1.69693	0.848464	−	0.529253i	$-0.177528\pi$
$11$	5.62807	1.69693	0.848464	+	0.529253i	$0.177528\pi$
$12$	1.79195	0.517291
$13$	0.500177	0.138724	0.0693621	−	0.997592i	$-0.477904\pi$
$13$	0.500177	0.138724	0.0693621	+	0.997592i	$0.477904\pi$
$14$	5.85293	1.56426
$15$	−0.608484	−0.157110
$16$	1.02508	0.256271
$17$	−4.81786	−1.16850	−0.584251	−	0.811573i	$-0.698612\pi$
$17$	−4.81786	−1.16850	−0.584251	+	0.811573i	$0.698612\pi$
$18$	6.37813	1.50334
$19$	6.63611	1.52243	0.761214	−	0.648501i	$-0.224604\pi$
$19$	6.63611	1.52243	0.761214	+	0.648501i	$0.224604\pi$
$20$	−4.05247	−0.906160
$21$	−1.29993	−0.283667
$22$	−13.1444	−2.80240
$23$	7.19678	1.50063	0.750316	−	0.661079i	$-0.229901\pi$
$23$	7.19678	1.50063	0.750316	+	0.661079i	$0.229901\pi$
$24$	−1.76220	−0.359707
$25$	−3.62392	−0.724784
$26$	−1.16817	−0.229097
$27$	−2.97271	−0.572099
$28$	−8.65745	−1.63610
$29$	1.64242	0.304990	0.152495	−	0.988304i	$-0.451269\pi$
$29$	1.64242	0.304990	0.152495	+	0.988304i	$0.451269\pi$
$30$	1.42112	0.259460
$31$	−4.86969	−0.874623	−0.437311	−	0.899310i	$-0.644069\pi$
$31$	−4.86969	−0.874623	−0.437311	+	0.899310i	$0.644069\pi$
$32$	4.40039	0.777887
$33$	2.91936	0.508195
$34$	11.2522	1.92973
$35$	2.93977	0.496912
$36$	−9.43430	−1.57238
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−15.4987	−2.51422
$39$	0.259448	0.0415450
$40$	3.98518	0.630113
$41$	−6.72318	−1.04998	−0.524992	−	0.851107i	$-0.675932\pi$
$41$	−6.72318	−1.04998	−0.524992	+	0.851107i	$0.675932\pi$
$42$	3.03599	0.468464
$43$	−1.74449	−0.266032	−0.133016	−	0.991114i	$-0.542466\pi$
$43$	−1.74449	−0.266032	−0.133016	+	0.991114i	$0.542466\pi$
$44$	19.4428	2.93111
$45$	3.20356	0.477559
$46$	−16.8081	−2.47823
$47$	−4.67858	−0.682441	−0.341220	−	0.939983i	$-0.610840\pi$
$47$	−4.67858	−0.682441	−0.341220	+	0.939983i	$0.610840\pi$
$48$	0.531725	0.0767478
$49$	−0.719660	−0.102809
$50$	8.46370	1.19695
$51$	−2.49909	−0.349942
$52$	1.72791	0.239618
$53$	0.546874	0.0751190	0.0375595	−	0.999294i	$-0.488042\pi$
$53$	0.546874	0.0751190	0.0375595	+	0.999294i	$0.488042\pi$
$54$	6.94280	0.944796
$55$	−6.60209	−0.890226
$56$	8.51370	1.13769
$57$	3.44224	0.455936
$58$	−3.83590	−0.503678
$59$	−12.3711	−1.61057	−0.805287	−	0.592885i	$-0.797989\pi$
$59$	−12.3711	−1.61057	−0.805287	+	0.592885i	$0.797989\pi$
$60$	−2.10207	−0.271376
$61$	13.2708	1.69915	0.849575	−	0.527467i	$-0.176858\pi$
$61$	13.2708	1.69915	0.849575	+	0.527467i	$0.176858\pi$
$62$	11.3732	1.44440
$63$	6.84389	0.862249
$64$	−12.3273	−1.54092
$65$	−0.586739	−0.0727761
$66$	−6.81819	−0.839261
$67$	7.64936	0.934518	0.467259	−	0.884120i	$-0.345242\pi$
$67$	7.64936	0.934518	0.467259	+	0.884120i	$0.345242\pi$
$68$	−16.6438	−2.01836
$69$	3.73307	0.449408
$70$	−6.86586	−0.820627
$71$	−2.40565	−0.285498	−0.142749	−	0.989759i	$-0.545594\pi$
$71$	−2.40565	−0.285498	−0.142749	+	0.989759i	$0.545594\pi$
$72$	9.27765	1.09338
$73$	1.88290	0.220377	0.110189	−	0.993911i	$-0.464855\pi$
$73$	1.88290	0.220377	0.110189	+	0.993911i	$0.464855\pi$
$74$	2.33551	0.271497
$75$	−1.87978	−0.217058
$76$	22.9251	2.62969
$77$	−14.1043	−1.60733
$78$	−0.605944	−0.0686097
$79$	−10.9669	−1.23387	−0.616937	−	0.787013i	$-0.711627\pi$
$79$	−10.9669	−1.23387	−0.616937	+	0.787013i	$0.711627\pi$
$80$	−1.20249	−0.134442
$81$	6.65082	0.738980
$82$	15.7021	1.73400
$83$	16.9417	1.85960	0.929799	−	0.368067i	$-0.119980\pi$
$83$	16.9417	1.85960	0.929799	+	0.368067i	$0.119980\pi$
$84$	−4.49074	−0.489979
$85$	5.65165	0.613008
$86$	4.07427	0.439339
$87$	0.851947	0.0913383
$88$	−19.1199	−2.03819
$89$	−10.7636	−1.14094	−0.570468	−	0.821320i	$-0.693238\pi$
$89$	−10.7636	−1.14094	−0.570468	+	0.821320i	$0.693238\pi$
$90$	−7.48195	−0.788667
$91$	−1.25347	−0.131400
$92$	24.8620	2.59205
$93$	−2.52598	−0.261932
$94$	10.9269	1.12702
$95$	−7.78458	−0.798681
$96$	2.28254	0.232961
$97$	13.4771	1.36840	0.684198	−	0.729296i	$-0.260152\pi$
$97$	13.4771	1.36840	0.684198	+	0.729296i	$0.260152\pi$
$98$	1.68077	0.169784
$99$	−15.3699	−1.54473
$100$	−12.5192	−1.25192
$101$	7.55591	0.751841	0.375921	−	0.926652i	$-0.377326\pi$
$101$	7.55591	0.751841	0.375921	+	0.926652i	$0.377326\pi$
$102$	5.83664	0.577914
$103$	19.4000	1.91154	0.955769	−	0.294119i	$-0.0950262\pi$
$103$	19.4000	1.91154	0.955769	+	0.294119i	$0.0950262\pi$
$104$	−1.69922	−0.166622
$105$	1.52490	0.148815
$106$	−1.27723	−0.124056
$107$	2.44892	0.236746	0.118373	−	0.992969i	$-0.462232\pi$
$107$	2.44892	0.236746	0.118373	+	0.992969i	$0.462232\pi$
$108$	−10.2696	−0.988188
$109$	−6.46061	−0.618814	−0.309407	−	0.950930i	$-0.600130\pi$
$109$	−6.46061	−0.618814	−0.309407	+	0.950930i	$0.600130\pi$
$110$	15.4192	1.47017
$111$	−0.518713	−0.0492341
$112$	−2.56892	−0.242740
$113$	3.23308	0.304143	0.152071	−	0.988370i	$-0.451406\pi$
$113$	3.23308	0.304143	0.152071	+	0.988370i	$0.451406\pi$
$114$	−8.03938	−0.752957
$115$	−8.44228	−0.787247
$116$	5.67392	0.526811
$117$	−1.36595	−0.126282
$118$	28.8927	2.65979
$119$	12.0738	1.10681
$120$	2.06717	0.188706
$121$	20.6752	1.87956
$122$	−30.9941	−2.80607
$123$	−3.48740	−0.314449
$124$	−16.8229	−1.51074
$125$	10.1164	0.904839
$126$	−15.9840	−1.42397
$127$	−4.68167	−0.415431	−0.207715	−	0.978189i	$-0.566603\pi$
$127$	−4.68167	−0.415431	−0.207715	+	0.978189i	$0.566603\pi$
$128$	19.9898	1.76687
$129$	−0.904889	−0.0796710
$130$	1.37034	0.120186
$131$	−3.58672	−0.313374	−0.156687	−	0.987648i	$-0.550081\pi$
$131$	−3.58672	−0.313374	−0.156687	+	0.987648i	$0.550081\pi$
$132$	10.0852	0.877806
$133$	−16.6305	−1.44205
$134$	−17.8652	−1.54331
$135$	3.48718	0.300129
$136$	16.3674	1.40350
$137$	−3.66198	−0.312864	−0.156432	−	0.987689i	$-0.549999\pi$
$137$	−3.66198	−0.312864	−0.156432	+	0.987689i	$0.549999\pi$
$138$	−8.71861	−0.742177
$139$	−9.24534	−0.784179	−0.392090	−	0.919927i	$-0.628248\pi$
$139$	−9.24534	−0.784179	−0.392090	+	0.919927i	$0.628248\pi$
$140$	10.1557	0.858317
$141$	−2.42684	−0.204377
$142$	5.61842	0.471487
$143$	2.81503	0.235405
$144$	−2.79944	−0.233286
$145$	−1.92667	−0.160001
$146$	−4.39754	−0.363943
$147$	−0.373297	−0.0307890
$148$	−3.45460	−0.283967
$149$	10.9281	0.895266	0.447633	−	0.894217i	$-0.352267\pi$
$149$	10.9281	0.895266	0.447633	+	0.894217i	$0.352267\pi$
$150$	4.39024	0.358461
$151$	1.89050	0.153847	0.0769233	−	0.997037i	$-0.475490\pi$
$151$	1.89050	0.153847	0.0769233	+	0.997037i	$0.475490\pi$
$152$	−22.5445	−1.82860
$153$	13.1573	1.06370
$154$	32.9407	2.65444
$155$	5.71246	0.458836
$156$	0.896292	0.0717608
$157$	15.8803	1.26739	0.633694	−	0.773584i	$-0.281538\pi$
$157$	15.8803	1.26739	0.633694	+	0.773584i	$0.281538\pi$
$158$	25.6133	2.03769
$159$	0.283671	0.0224966
$160$	−5.16194	−0.408087
$161$	−18.0356	−1.42140
$162$	−15.5331	−1.22039
$163$	−1.00000	−0.0783260
$163$	−1.00000	−0.0783260
$164$	−23.2259	−1.81364
$165$	−3.42459	−0.266604
$166$	−39.5676	−3.07104
$167$	−5.33612	−0.412921	−0.206461	−	0.978455i	$-0.566195\pi$
$167$	−5.33612	−0.412921	−0.206461	+	0.978455i	$0.566195\pi$
$168$	4.41617	0.340715
$169$	−12.7498	−0.980756
$170$	−13.1995	−1.01235
$171$	−18.1228	−1.38588
$172$	−6.02651	−0.459517
$173$	12.3193	0.936623	0.468311	−	0.883564i	$-0.344863\pi$
$173$	12.3193	0.936623	0.468311	+	0.883564i	$0.344863\pi$
$174$	−1.98973	−0.150841
$175$	9.08177	0.686517
$176$	5.76924	0.434873
$177$	−6.41703	−0.482334
$178$	25.1384	1.88420
$179$	4.81484	0.359878	0.179939	−	0.983678i	$-0.442410\pi$
$179$	4.81484	0.359878	0.179939	+	0.983678i	$0.442410\pi$
$180$	11.0670	0.824889
$181$	−20.2035	−1.50172	−0.750858	−	0.660464i	$-0.770360\pi$
$181$	−20.2035	−1.50172	−0.750858	+	0.660464i	$0.770360\pi$
$182$	2.92750	0.217001
$183$	6.88374	0.508861
$184$	−24.4492	−1.80242
$185$	1.17306	0.0862454
$186$	5.89944	0.432568
$187$	−27.1153	−1.98286
$188$	−16.1626	−1.17878
$189$	7.44980	0.541893
$190$	18.1810	1.31899
$191$	−14.4270	−1.04390	−0.521952	−	0.852975i	$-0.674796\pi$
$191$	−14.4270	−1.04390	−0.521952	+	0.852975i	$0.674796\pi$
$192$	−6.39435	−0.461473
$193$	16.5945	1.19450	0.597249	−	0.802056i	$-0.296260\pi$
$193$	16.5945	1.19450	0.597249	+	0.802056i	$0.296260\pi$
$194$	−31.4760	−2.25984
$195$	−0.304350	−0.0217949
$196$	−2.48614	−0.177581
$197$	−1.09249	−0.0778368	−0.0389184	−	0.999242i	$-0.512391\pi$
$197$	−1.09249	−0.0778368	−0.0389184	+	0.999242i	$0.512391\pi$
$198$	35.8966	2.55106
$199$	−15.1661	−1.07509	−0.537547	−	0.843234i	$-0.680649\pi$
$199$	−15.1661	−1.07509	−0.537547	+	0.843234i	$0.680649\pi$
$200$	12.3113	0.870543
$201$	3.96783	0.279869
$202$	−17.6469	−1.24163
$203$	−4.11601	−0.288887
$204$	−8.63336	−0.604456
$205$	7.88672	0.550832
$206$	−45.3089	−3.15682
$207$	−19.6539	−1.36604
$208$	0.512723	0.0355509
$209$	37.3485	2.58345
$210$	−3.56141	−0.245761
$211$	3.04722	0.209779	0.104890	−	0.994484i	$-0.466551\pi$
$211$	3.04722	0.209779	0.104890	+	0.994484i	$0.466551\pi$
$212$	1.88923	0.129753
$213$	−1.24784	−0.0855008
$214$	−5.71948	−0.390975
$215$	2.04639	0.139563
$216$	10.0990	0.687152
$217$	12.2037	0.828444
$218$	15.0888	1.02194
$219$	0.976687	0.0659984
$220$	−22.8076	−1.53769
$221$	−2.40978	−0.162099
$222$	1.21146	0.0813079
$223$	3.48112	0.233113	0.116557	−	0.993184i	$-0.462814\pi$
$223$	3.48112	0.233113	0.116557	+	0.993184i	$0.462814\pi$
$224$	−11.0277	−0.736816
$225$	9.89670	0.659780
$226$	−7.55089	−0.502278
$227$	−25.5482	−1.69569	−0.847847	−	0.530241i	$-0.822101\pi$
$227$	−25.5482	−1.69569	−0.847847	+	0.530241i	$0.822101\pi$
$228$	11.8916	0.787539
$229$	−26.1314	−1.72681	−0.863405	−	0.504512i	$-0.831672\pi$
$229$	−26.1314	−1.72681	−0.863405	+	0.504512i	$0.831672\pi$
$230$	19.7170	1.30010
$231$	−7.31609	−0.481363
$232$	−5.57971	−0.366326
$233$	−19.8522	−1.30056	−0.650281	−	0.759694i	$-0.725349\pi$
$233$	−19.8522	−1.30056	−0.650281	+	0.759694i	$0.725349\pi$
$234$	3.19019	0.208549
$235$	5.48827	0.358015
$236$	−42.7371	−2.78195
$237$	−5.68868	−0.369520
$238$	−28.1986	−1.82784
$239$	−29.6065	−1.91509	−0.957543	−	0.288291i	$-0.906913\pi$
$239$	−29.6065	−1.91509	−0.957543	+	0.288291i	$0.906913\pi$
$240$	−0.623747	−0.0402627
$241$	13.1872	0.849461	0.424730	−	0.905320i	$-0.360369\pi$
$241$	13.1872	0.849461	0.424730	+	0.905320i	$0.360369\pi$
$242$	−48.2872	−3.10402
$243$	12.3680	0.793408
$244$	45.8453	2.93495
$245$	0.844207	0.0539344
$246$	8.14487	0.519298
$247$	3.31923	0.211197
$248$	16.5435	1.05052
$249$	8.78791	0.556911
$250$	−23.6270	−1.49430
$251$	1.67437	0.105685	0.0528426	−	0.998603i	$-0.483172\pi$
$251$	1.67437	0.105685	0.0528426	+	0.998603i	$0.483172\pi$
$252$	23.6429	1.48937
$253$	40.5040	2.54646
$254$	10.9341	0.686065
$255$	2.93159	0.183583
$256$	−22.0317	−1.37698
$257$	−20.6569	−1.28854	−0.644272	−	0.764797i	$-0.722839\pi$
$257$	−20.6569	−1.28854	−0.644272	+	0.764797i	$0.722839\pi$
$258$	2.11338	0.131573
$259$	2.50606	0.155719
$260$	−2.02695	−0.125706
$261$	−4.48535	−0.277636
$262$	8.37683	0.517522
$263$	−20.0477	−1.23620	−0.618099	−	0.786101i	$-0.712097\pi$
$263$	−20.0477	−1.23620	−0.618099	+	0.786101i	$0.712097\pi$
$264$	−9.91777	−0.610396
$265$	−0.641518	−0.0394082
$266$	38.8407	2.38147
$267$	−5.58320	−0.341687
$268$	26.4255	1.61420
$269$	5.42142	0.330550	0.165275	−	0.986248i	$-0.447149\pi$
$269$	5.42142	0.330550	0.165275	+	0.986248i	$0.447149\pi$
$270$	−8.14435	−0.495649
$271$	−11.2100	−0.680959	−0.340479	−	0.940252i	$-0.610589\pi$
$271$	−11.2100	−0.680959	−0.340479	+	0.940252i	$0.610589\pi$
$272$	−4.93871	−0.299453
$273$	−0.650194	−0.0393515
$274$	8.55258	0.516680
$275$	−20.3957	−1.22991
$276$	12.8963	0.776264
$277$	−25.2447	−1.51681	−0.758405	−	0.651784i	$-0.774021\pi$
$277$	−25.2447	−1.51681	−0.758405	+	0.651784i	$0.774021\pi$
$278$	21.5926	1.29504
$279$	13.2988	0.796180
$280$	−9.98711	−0.596844
$281$	−7.61180	−0.454082	−0.227041	−	0.973885i	$-0.572905\pi$
$281$	−7.61180	−0.454082	−0.227041	+	0.973885i	$0.572905\pi$
$282$	5.66791	0.337519
$283$	17.5799	1.04501	0.522507	−	0.852635i	$-0.324997\pi$
$283$	17.5799	1.04501	0.522507	+	0.852635i	$0.324997\pi$
$284$	−8.31057	−0.493141
$285$	−4.03797	−0.239188
$286$	−6.57453	−0.388760
$287$	16.8487	0.994547
$288$	−12.0172	−0.708120
$289$	6.21175	0.365397
$290$	4.49975	0.264234
$291$	6.99077	0.409806
$292$	6.50468	0.380658
$293$	−8.99199	−0.525318	−0.262659	−	0.964889i	$-0.584599\pi$
$293$	−8.99199	−0.525318	−0.262659	+	0.964889i	$0.584599\pi$
$294$	0.871839	0.0508467
$295$	14.5120	0.844923
$296$	3.39724	0.197461
$297$	−16.7307	−0.970811
$298$	−25.5227	−1.47849
$299$	3.59966	0.208174
$300$	−6.49389	−0.374925
$301$	4.37179	0.251986
$302$	−4.41528	−0.254071
$303$	3.91935	0.225161
$304$	6.80256	0.390154
$305$	−15.5675	−0.891392
$306$	−30.7289	−1.75665
$307$	26.3722	1.50514	0.752569	−	0.658513i	$-0.228814\pi$
$307$	26.3722	1.50514	0.752569	+	0.658513i	$0.228814\pi$
$308$	−48.7248	−2.77635
$309$	10.0630	0.572466
$310$	−13.3415	−0.757747
$311$	8.01461	0.454467	0.227233	−	0.973840i	$-0.427032\pi$
$311$	8.01461	0.454467	0.227233	+	0.973840i	$0.427032\pi$
$312$	−0.881409	−0.0499000
$313$	30.2701	1.71097	0.855485	−	0.517828i	$-0.173259\pi$
$313$	30.2701	1.71097	0.855485	+	0.517828i	$0.173259\pi$
$314$	−37.0886	−2.09303
$315$	−8.02832	−0.452345
$316$	−37.8863	−2.13127
$317$	−27.3660	−1.53703	−0.768515	−	0.639832i	$-0.779004\pi$
$317$	−27.3660	−1.53703	−0.768515	+	0.639832i	$0.779004\pi$
$318$	−0.662516	−0.0371521
$319$	9.24368	0.517547
$320$	14.4607	0.808380
$321$	1.27029	0.0709006
$322$	42.1222	2.34738
$323$	−31.9718	−1.77896
$324$	22.9760	1.27644
$325$	−1.81260	−0.100545
$326$	2.33551	0.129352
$327$	−3.35120	−0.185322
$328$	22.8403	1.26114
$329$	11.7248	0.646409
$330$	7.99817	0.440285
$331$	−21.9562	−1.20682	−0.603411	−	0.797430i	$-0.706192\pi$
$331$	−21.9562	−1.20682	−0.603411	+	0.797430i	$0.706192\pi$
$332$	58.5270	3.21209
$333$	2.73094	0.149654
$334$	12.4626	0.681921
$335$	−8.97319	−0.490258
$336$	−1.33253	−0.0726957
$337$	−0.238574	−0.0129959	−0.00649797	−	0.999979i	$-0.502068\pi$
$337$	−0.238574	−0.0129959	−0.00649797	+	0.999979i	$0.502068\pi$
$338$	29.7773	1.61967
$339$	1.67704	0.0910845
$340$	19.5242	1.05885
$341$	−27.4070	−1.48417
$342$	42.3259	2.28872
$343$	19.3459	1.04458
$344$	5.92645	0.319533
$345$	−4.37912	−0.235764
$346$	−28.7720	−1.54679
$347$	12.1603	0.652802	0.326401	−	0.945231i	$-0.394164\pi$
$347$	12.1603	0.652802	0.326401	+	0.945231i	$0.394164\pi$
$348$	2.94314	0.157769
$349$	3.64789	0.195267	0.0976336	−	0.995222i	$-0.468873\pi$
$349$	3.64789	0.195267	0.0976336	+	0.995222i	$0.468873\pi$
$350$	−21.2106	−1.13375
$351$	−1.48688	−0.0793639
$352$	24.7657	1.32002
$353$	−5.13199	−0.273148	−0.136574	−	0.990630i	$-0.543609\pi$
$353$	−5.13199	−0.273148	−0.136574	+	0.990630i	$0.543609\pi$
$354$	14.9870	0.796552
$355$	2.82198	0.149775
$356$	−37.1838	−1.97074
$357$	6.26286	0.331466
$358$	−11.2451	−0.594322
$359$	−12.6781	−0.669126	−0.334563	−	0.942373i	$-0.608589\pi$
$359$	−12.6781	−0.669126	−0.334563	+	0.942373i	$0.608589\pi$
$360$	−10.8833	−0.573599
$361$	25.0379	1.31779
$362$	47.1855	2.48002
$363$	10.7245	0.562891
$364$	−4.33026	−0.226967
$365$	−2.20876	−0.115612
$366$	−16.0770	−0.840360
$367$	−25.3427	−1.32288	−0.661440	−	0.749998i	$-0.730054\pi$
$367$	−25.3427	−1.32288	−0.661440	+	0.749998i	$0.730054\pi$
$368$	7.37730	0.384568
$369$	18.3606	0.955814
$370$	−2.73970	−0.142430
$371$	−1.37050	−0.0711528
$372$	−8.72625	−0.452435
$373$	33.3907	1.72891	0.864453	−	0.502714i	$-0.167665\pi$
$373$	33.3907	1.72891	0.864453	+	0.502714i	$0.167665\pi$
$374$	63.3279	3.27461
$375$	5.24752	0.270981
$376$	15.8943	0.819684
$377$	0.821502	0.0423095
$378$	−17.3991	−0.894912
$379$	19.8298	1.01859	0.509295	−	0.860592i	$-0.329906\pi$
$379$	19.8298	1.01859	0.509295	+	0.860592i	$0.329906\pi$
$380$	−26.8926	−1.37956
$381$	−2.42844	−0.124413
$382$	33.6945	1.72396
$383$	−23.7546	−1.21381	−0.606903	−	0.794776i	$-0.707588\pi$
$383$	−23.7546	−1.21381	−0.606903	+	0.794776i	$0.707588\pi$
$384$	10.3690	0.529140
$385$	16.5452	0.843223
$386$	−38.7566	−1.97266
$387$	4.76408	0.242172
$388$	46.5582	2.36363
$389$	−17.7569	−0.900309	−0.450155	−	0.892951i	$-0.648631\pi$
$389$	−17.7569	−0.900309	−0.450155	+	0.892951i	$0.648631\pi$
$390$	0.710812	0.0359933
$391$	−34.6731	−1.75349
$392$	2.44486	0.123484
$393$	−1.86048	−0.0938489
$394$	2.55152	0.128544
$395$	12.8649	0.647302
$396$	−53.0970	−2.66822
$397$	20.7807	1.04295	0.521476	−	0.853266i	$-0.325381\pi$
$397$	20.7807	1.04295	0.521476	+	0.853266i	$0.325381\pi$
$398$	35.4205	1.77547
$399$	−8.62646	−0.431863
$400$	−3.71482	−0.185741
$401$	−34.1722	−1.70648	−0.853240	−	0.521518i	$-0.825366\pi$
$401$	−34.1722	−1.70648	−0.853240	+	0.521518i	$0.825366\pi$
$402$	−9.26690	−0.462191
$403$	−2.43571	−0.121331
$404$	26.1027	1.29866
$405$	−7.80184	−0.387677
$406$	9.61299	0.477085
$407$	−5.62807	−0.278973
$408$	8.49001	0.420318
$409$	−2.97649	−0.147178	−0.0735890	−	0.997289i	$-0.523445\pi$
$409$	−2.97649	−0.147178	−0.0735890	+	0.997289i	$0.523445\pi$
$410$	−18.4195	−0.909675
$411$	−1.89952	−0.0936962
$412$	67.0193	3.30180
$413$	31.0026	1.52554
$414$	45.9020	2.25596
$415$	−19.8738	−0.975564
$416$	2.20098	0.107912
$417$	−4.79568	−0.234846
$418$	−87.2278	−4.26645
$419$	8.39651	0.410196	0.205098	−	0.978741i	$-0.434249\pi$
$419$	8.39651	0.410196	0.205098	+	0.978741i	$0.434249\pi$
$420$	5.26792	0.257048
$421$	5.92830	0.288928	0.144464	−	0.989510i	$-0.453854\pi$
$421$	5.92830	0.288928	0.144464	+	0.989510i	$0.453854\pi$
$422$	−7.11680	−0.346441
$423$	12.7769	0.621234
$424$	−1.85786	−0.0902259
$425$	17.4595	0.846912
$426$	2.91435	0.141201
$427$	−33.2574	−1.60944
$428$	8.46005	0.408932
$429$	1.46020	0.0704989
$430$	−4.77937	−0.230482
$431$	−10.1609	−0.489432	−0.244716	−	0.969595i	$-0.578695\pi$
$431$	−10.1609	−0.489432	−0.244716	+	0.969595i	$0.578695\pi$
$432$	−3.04728	−0.146612
$433$	36.8706	1.77189	0.885943	−	0.463794i	$-0.153512\pi$
$433$	36.8706	1.77189	0.885943	+	0.463794i	$0.153512\pi$
$434$	−28.5020	−1.36814
$435$	−0.999389	−0.0479170
$436$	−22.3188	−1.06888
$437$	47.7586	2.28460
$438$	−2.28106	−0.108993
$439$	−5.64069	−0.269215	−0.134608	−	0.990899i	$-0.542977\pi$
$439$	−5.64069	−0.269215	−0.134608	+	0.990899i	$0.542977\pi$
$440$	22.4289	1.06926
$441$	1.96535	0.0935879
$442$	5.62807	0.267700
$443$	−21.7721	−1.03442	−0.517212	−	0.855858i	$-0.673030\pi$
$443$	−21.7721	−1.03442	−0.517212	+	0.855858i	$0.673030\pi$
$444$	−1.79195	−0.0850422
$445$	12.6263	0.598546
$446$	−8.13019	−0.384976
$447$	5.66856	0.268114
$448$	30.8930	1.45956
$449$	−2.99668	−0.141422	−0.0707110	−	0.997497i	$-0.522527\pi$
$449$	−2.99668	−0.141422	−0.0707110	+	0.997497i	$0.522527\pi$
$450$	−23.1138	−1.08960
$451$	−37.8386	−1.78175
$452$	11.1690	0.525347
$453$	0.980627	0.0460739
$454$	59.6681	2.80036
$455$	1.47040	0.0689336
$456$	−11.6941	−0.547627
$457$	7.76752	0.363349	0.181675	−	0.983359i	$-0.441848\pi$
$457$	7.76752	0.363349	0.181675	+	0.983359i	$0.441848\pi$
$458$	61.0300	2.85175
$459$	14.3221	0.668499
$460$	−29.1647	−1.35981
$461$	3.09547	0.144170	0.0720852	−	0.997398i	$-0.477035\pi$
$461$	3.09547	0.144170	0.0720852	+	0.997398i	$0.477035\pi$
$462$	17.0868	0.794949
$463$	22.2395	1.03356	0.516779	−	0.856119i	$-0.327131\pi$
$463$	22.2395	1.03356	0.516779	+	0.856119i	$0.327131\pi$
$464$	1.68362	0.0781601
$465$	2.96313	0.137412
$466$	46.3650	2.14782
$467$	−23.6224	−1.09311	−0.546556	−	0.837422i	$-0.684062\pi$
$467$	−23.6224	−1.09311	−0.546556	+	0.837422i	$0.684062\pi$
$468$	−4.71882	−0.218128
$469$	−19.1698	−0.885177
$470$	−12.8179	−0.591246
$471$	8.23734	0.379556
$472$	42.0275	1.93447
$473$	−9.81810	−0.451437
$474$	13.2860	0.610245
$475$	−24.0487	−1.10343
$476$	41.7104	1.91179
$477$	−1.49348	−0.0683817
$478$	69.1463	3.16268
$479$	7.94193	0.362876	0.181438	−	0.983402i	$-0.441925\pi$
$479$	7.94193	0.362876	0.181438	+	0.983402i	$0.441925\pi$
$480$	−2.67757	−0.122214
$481$	−0.500177	−0.0228061
$482$	−30.7988	−1.40285
$483$	−9.35529	−0.425680
$484$	71.4247	3.24658
$485$	−15.8095	−0.717875
$486$	−28.8856	−1.31028
$487$	9.22361	0.417962	0.208981	−	0.977920i	$-0.432985\pi$
$487$	9.22361	0.417962	0.208981	+	0.977920i	$0.432985\pi$
$488$	−45.0841	−2.04086
$489$	−0.518713	−0.0234570
$490$	−1.97165	−0.0890702
$491$	−34.5821	−1.56067	−0.780334	−	0.625363i	$-0.784951\pi$
$491$	−34.5821	−1.56067	−0.780334	+	0.625363i	$0.784951\pi$
$492$	−12.0476	−0.543148
$493$	−7.91296	−0.356382
$494$	−7.75209	−0.348783
$495$	18.0299	0.810383
$496$	−4.99184	−0.224140
$497$	6.02870	0.270424
$498$	−20.5243	−0.919714
$499$	−14.9710	−0.670193	−0.335096	−	0.942184i	$-0.608769\pi$
$499$	−14.9710	−0.670193	−0.335096	+	0.942184i	$0.608769\pi$
$500$	34.9482	1.56293
$501$	−2.76792	−0.123661
$502$	−3.91050	−0.174534
$503$	−8.99657	−0.401137	−0.200569	−	0.979680i	$-0.564279\pi$
$503$	−8.99657	−0.401137	−0.200569	+	0.979680i	$0.564279\pi$
$504$	−23.2504	−1.03565
$505$	−8.86357	−0.394424
$506$	−94.5975	−4.20537
$507$	−6.61351	−0.293716
$508$	−16.1733	−0.717575
$509$	9.79440	0.434129	0.217065	−	0.976157i	$-0.430352\pi$
$509$	9.79440	0.434129	0.217065	+	0.976157i	$0.430352\pi$
$510$	−6.84675	−0.303179
$511$	−4.71867	−0.208742
$512$	11.4757	0.507158
$513$	−19.7272	−0.870979
$514$	48.2444	2.12797
$515$	−22.7574	−1.00281
$516$	−3.12603	−0.137616
$517$	−26.3314	−1.15805
$518$	−5.85293	−0.257163
$519$	6.39021	0.280499
$520$	1.99330	0.0874118
$521$	−5.82642	−0.255260	−0.127630	−	0.991822i	$-0.540737\pi$
$521$	−5.82642	−0.255260	−0.127630	+	0.991822i	$0.540737\pi$
$522$	10.4756	0.458504
$523$	−33.1972	−1.45161	−0.725805	−	0.687900i	$-0.758533\pi$
$523$	−33.1972	−1.45161	−0.725805	+	0.687900i	$0.758533\pi$
$524$	−12.3907	−0.541291
$525$	4.71083	0.205598
$526$	46.8217	2.04152
$527$	23.4615	1.02200
$528$	2.99258	0.130236
$529$	28.7936	1.25190
$530$	1.49827	0.0650808
$531$	33.7846	1.46612
$532$	−57.4518	−2.49085
$533$	−3.36278	−0.145658
$534$	13.0396	0.564280
$535$	−2.87274	−0.124199
$536$	−25.9867	−1.12246
$537$	2.49752	0.107776
$538$	−12.6618	−0.545888
$539$	−4.05030	−0.174459
$540$	12.0468	0.518413
$541$	−12.4893	−0.536955	−0.268478	−	0.963286i	$-0.586521\pi$
$541$	−12.4893	−0.536955	−0.268478	+	0.963286i	$0.586521\pi$
$542$	26.1810	1.12457
$543$	−10.4798	−0.449733
$544$	−21.2005	−0.908963
$545$	7.57870	0.324636
$546$	1.51853	0.0649872
$547$	−27.0556	−1.15681	−0.578407	−	0.815749i	$-0.696325\pi$
$547$	−27.0556	−1.15681	−0.578407	+	0.815749i	$0.696325\pi$
$548$	−12.6507	−0.540410
$549$	−36.2417	−1.54676
$550$	47.6343	2.03113
$551$	10.8993	0.464326
$552$	−12.6821	−0.539787
$553$	27.4837	1.16873
$554$	58.9593	2.50494
$555$	0.608484	0.0258287
$556$	−31.9390	−1.35451
$557$	−34.4796	−1.46095	−0.730474	−	0.682940i	$-0.760701\pi$
$557$	−34.4796	−1.46095	−0.730474	+	0.682940i	$0.760701\pi$
$558$	−31.0595	−1.31485
$559$	−0.872552	−0.0369050
$560$	3.01351	0.127344
$561$	−14.0650	−0.593827
$562$	17.7774	0.749895
$563$	−33.6451	−1.41797	−0.708986	−	0.705222i	$-0.750847\pi$
$563$	−33.6451	−1.41797	−0.708986	+	0.705222i	$0.750847\pi$
$564$	−8.38378	−0.353021
$565$	−3.79261	−0.159556
$566$	−41.0579	−1.72579
$567$	−16.6674	−0.699963
$568$	8.17257	0.342914
$569$	17.3359	0.726761	0.363380	−	0.931641i	$-0.381623\pi$
$569$	17.3359	0.726761	0.363380	+	0.931641i	$0.381623\pi$
$570$	9.43071	0.395009
$571$	−11.0851	−0.463895	−0.231948	−	0.972728i	$-0.574510\pi$
$571$	−11.0851	−0.463895	−0.231948	+	0.972728i	$0.574510\pi$
$572$	9.72482	0.406615
$573$	−7.48350	−0.312628
$574$	−39.3503	−1.64245
$575$	−26.0806	−1.08763
$576$	33.6651	1.40271
$577$	−14.6196	−0.608621	−0.304310	−	0.952573i	$-0.598426\pi$
$577$	−14.6196	−0.608621	−0.304310	+	0.952573i	$0.598426\pi$
$578$	−14.5076	−0.603437
$579$	8.60779	0.357727
$580$	−6.65588	−0.276370
$581$	−42.4571	−1.76142
$582$	−16.3270	−0.676777
$583$	3.07785	0.127471
$584$	−6.39668	−0.264696
$585$	1.60235	0.0662489
$586$	21.0009	0.867538
$587$	−41.4903	−1.71249	−0.856244	−	0.516572i	$-0.827208\pi$
$587$	−41.4903	−1.71249	−0.856244	+	0.516572i	$0.827208\pi$
$588$	−1.28959	−0.0531820
$589$	−32.3158	−1.33155
$590$	−33.8930	−1.39535
$591$	−0.566690	−0.0233105
$592$	−1.02508	−0.0421307
$593$	−32.7698	−1.34570	−0.672848	−	0.739781i	$-0.734929\pi$
$593$	−32.7698	−1.34570	−0.672848	+	0.739781i	$0.734929\pi$
$594$	39.0746	1.60325
$595$	−14.1634	−0.580642
$596$	37.7523	1.54639
$597$	−7.86684	−0.321968
$598$	−8.40704	−0.343790
$599$	29.0301	1.18614	0.593069	−	0.805152i	$-0.297916\pi$
$599$	29.0301	1.18614	0.593069	+	0.805152i	$0.297916\pi$
$600$	6.38606	0.260710
$601$	7.08671	0.289073	0.144536	−	0.989499i	$-0.453831\pi$
$601$	7.08671	0.289073	0.144536	+	0.989499i	$0.453831\pi$
$602$	−10.2104	−0.416143
$603$	−20.8899	−0.850703
$604$	6.53092	0.265739
$605$	−24.2533	−0.986039
$606$	−9.15369	−0.371843
$607$	−35.4457	−1.43870	−0.719348	−	0.694650i	$-0.755559\pi$
$607$	−35.4457	−1.43870	−0.719348	+	0.694650i	$0.755559\pi$
$608$	29.2015	1.18428
$609$	−2.13503	−0.0865158
$610$	36.3580	1.47209
$611$	−2.34012	−0.0946710
$612$	45.4531	1.83733
$613$	−8.92299	−0.360396	−0.180198	−	0.983630i	$-0.557674\pi$
$613$	−8.92299	−0.360396	−0.180198	+	0.983630i	$0.557674\pi$
$614$	−61.5924	−2.48567
$615$	4.09095	0.164963
$616$	47.9157	1.93058
$617$	−8.96402	−0.360878	−0.180439	−	0.983586i	$-0.557752\pi$
$617$	−8.96402	−0.360878	−0.180439	+	0.983586i	$0.557752\pi$
$618$	−23.5023	−0.945402
$619$	−32.6150	−1.31091	−0.655453	−	0.755236i	$-0.727522\pi$
$619$	−32.6150	−1.31091	−0.655453	+	0.755236i	$0.727522\pi$
$620$	19.7343	0.792548
$621$	−21.3940	−0.858510
$622$	−18.7182	−0.750531
$623$	26.9741	1.08070
$624$	0.265956	0.0106468
$625$	6.25241	0.250096
$626$	−70.6962	−2.82559
$627$	19.3732	0.773690
$628$	54.8602	2.18916
$629$	4.81786	0.192101
$630$	18.7502	0.747027
$631$	9.99505	0.397897	0.198948	−	0.980010i	$-0.436247\pi$
$631$	9.99505	0.397897	0.198948	+	0.980010i	$0.436247\pi$
$632$	37.2572	1.48201
$633$	1.58063	0.0628245
$634$	63.9136	2.53833
$635$	5.49189	0.217939
$636$	0.979971	0.0388584
$637$	−0.359957	−0.0142620
$638$	−21.5887	−0.854705
$639$	6.56968	0.259892
$640$	−23.4493	−0.926916
$641$	22.7576	0.898872	0.449436	−	0.893313i	$-0.351625\pi$
$641$	22.7576	0.898872	0.449436	+	0.893313i	$0.351625\pi$
$642$	−2.96677	−0.117089
$643$	−30.9356	−1.21998	−0.609991	−	0.792408i	$-0.708827\pi$
$643$	−30.9356	−1.21998	−0.609991	+	0.792408i	$0.708827\pi$
$644$	−62.3057	−2.45519
$645$	1.06149	0.0417962
$646$	74.6705	2.93787
$647$	−3.80830	−0.149720	−0.0748599	−	0.997194i	$-0.523851\pi$
$647$	−3.80830	−0.149720	−0.0748599	+	0.997194i	$0.523851\pi$
$648$	−22.5945	−0.887594
$649$	−69.6252	−2.73303
$650$	4.23335	0.166046
$651$	6.33025	0.248102
$652$	−3.45460	−0.135293
$653$	5.41859	0.212046	0.106023	−	0.994364i	$-0.466188\pi$
$653$	5.41859	0.212046	0.106023	+	0.994364i	$0.466188\pi$
$654$	7.82677	0.306051
$655$	4.20746	0.164399
$656$	−6.89182	−0.269080
$657$	−5.14209	−0.200612
$658$	−27.3834	−1.06752
$659$	41.9786	1.63525	0.817627	−	0.575749i	$-0.195289\pi$
$659$	41.9786	1.63525	0.817627	+	0.575749i	$0.195289\pi$
$660$	−11.8306	−0.460506
$661$	−24.6020	−0.956907	−0.478454	−	0.878113i	$-0.658802\pi$
$661$	−24.6020	−0.956907	−0.478454	+	0.878113i	$0.658802\pi$
$662$	51.2789	1.99301
$663$	−1.24999	−0.0485454
$664$	−57.5552	−2.23358
$665$	19.5086	0.756512
$666$	−6.37813	−0.247147
$667$	11.8202	0.457678
$668$	−18.4342	−0.713240
$669$	1.80570	0.0698126
$670$	20.9570	0.809638
$671$	74.6890	2.88334
$672$	−5.72019	−0.220661
$673$	−36.1074	−1.39184	−0.695918	−	0.718121i	$-0.745002\pi$
$673$	−36.1074	−1.39184	−0.695918	+	0.718121i	$0.745002\pi$
$674$	0.557191	0.0214622
$675$	10.7729	0.414648
$676$	−44.0456	−1.69406
$677$	−50.9817	−1.95939	−0.979693	−	0.200505i	$-0.935742\pi$
$677$	−50.9817	−1.95939	−0.979693	+	0.200505i	$0.935742\pi$
$678$	−3.91675	−0.150422
$679$	−33.7745	−1.29615
$680$	−19.2000	−0.736288
$681$	−13.2522	−0.507825
$682$	64.0093	2.45104
$683$	11.1537	0.426783	0.213391	−	0.976967i	$-0.431549\pi$
$683$	11.1537	0.426783	0.213391	+	0.976967i	$0.431549\pi$
$684$	−62.6071	−2.39384
$685$	4.29573	0.164132
$686$	−45.1826	−1.72508
$687$	−13.5547	−0.517144
$688$	−1.78824	−0.0681762
$689$	0.273534	0.0104208
$690$	10.2275	0.389354
$691$	−4.52991	−0.172326	−0.0861630	−	0.996281i	$-0.527461\pi$
$691$	−4.52991	−0.172326	−0.0861630	+	0.996281i	$0.527461\pi$
$692$	42.5585	1.61783
$693$	38.5179	1.46318
$694$	−28.4006	−1.07807
$695$	10.8454	0.411388
$696$	−2.89427	−0.109707
$697$	32.3913	1.22691
$698$	−8.51969	−0.322475
$699$	−10.2976	−0.389492
$700$	31.3739	1.18582
$701$	48.2693	1.82311	0.911553	−	0.411183i	$-0.134884\pi$
$701$	48.2693	1.82311	0.911553	+	0.411183i	$0.134884\pi$
$702$	3.47263	0.131066
$703$	−6.63611	−0.250286
$704$	−69.3791	−2.61482
$705$	2.84684	0.107218
$706$	11.9858	0.451092
$707$	−18.9356	−0.712146
$708$	−22.1683	−0.833136
$709$	−35.8994	−1.34823	−0.674116	−	0.738626i	$-0.735475\pi$
$709$	−35.8994	−1.34823	−0.674116	+	0.738626i	$0.735475\pi$
$710$	−6.59076	−0.247347
$711$	29.9499	1.12321
$712$	36.5664	1.37038
$713$	−35.0461	−1.31249
$714$	−14.6270	−0.547401
$715$	−3.30221	−0.123496
$716$	16.6334	0.621618
$717$	−15.3573	−0.573529
$718$	29.6099	1.10503
$719$	13.3899	0.499359	0.249680	−	0.968329i	$-0.419675\pi$
$719$	13.3899	0.499359	0.249680	+	0.968329i	$0.419675\pi$
$720$	3.28392	0.122384
$721$	−48.6175	−1.81061
$722$	−58.4763	−2.17626
$723$	6.84037	0.254396
$724$	−69.7952	−2.59392
$725$	−5.95201	−0.221052
$726$	−25.0472	−0.929589
$727$	47.5708	1.76430	0.882152	−	0.470964i	$-0.156094\pi$
$727$	47.5708	1.76430	0.882152	+	0.470964i	$0.156094\pi$
$728$	4.25835	0.157825
$729$	−13.5370	−0.501371
$730$	5.15859	0.190928
$731$	8.40469	0.310859
$732$	23.7806	0.878956
$733$	2.94688	0.108845	0.0544227	−	0.998518i	$-0.482668\pi$
$733$	2.94688	0.108845	0.0544227	+	0.998518i	$0.482668\pi$
$734$	59.1882	2.18468
$735$	0.437902	0.0161522
$736$	31.6687	1.16732
$737$	43.0512	1.58581
$738$	−42.8813	−1.57848
$739$	21.7336	0.799484	0.399742	−	0.916628i	$-0.369100\pi$
$739$	21.7336	0.799484	0.399742	+	0.916628i	$0.369100\pi$
$740$	4.05247	0.148972
$741$	1.72173	0.0632493
$742$	3.20082	0.117506
$743$	−17.5497	−0.643837	−0.321918	−	0.946767i	$-0.604328\pi$
$743$	−17.5497	−0.643837	−0.321918	+	0.946767i	$0.604328\pi$
$744$	8.58135	0.314608
$745$	−12.8194	−0.469666
$746$	−77.9843	−2.85521
$747$	−46.2668	−1.69282
$748$	−93.6725	−3.42501
$749$	−6.13714	−0.224246
$750$	−12.2556	−0.447512
$751$	7.36068	0.268595	0.134298	−	0.990941i	$-0.457122\pi$
$751$	7.36068	0.268595	0.134298	+	0.990941i	$0.457122\pi$
$752$	−4.79593	−0.174890
$753$	0.868517	0.0316505
$754$	−1.91863	−0.0698723
$755$	−2.21767	−0.0807094
$756$	25.7361	0.936014
$757$	−4.68018	−0.170104	−0.0850521	−	0.996377i	$-0.527106\pi$
$757$	−4.68018	−0.170104	−0.0850521	+	0.996377i	$0.527106\pi$
$758$	−46.3127	−1.68215
$759$	21.0100	0.762614
$760$	26.4461	0.959301
$761$	−31.5394	−1.14330	−0.571651	−	0.820497i	$-0.693697\pi$
$761$	−31.5394	−1.14330	−0.571651	+	0.820497i	$0.693697\pi$
$762$	5.67165	0.205462
$763$	16.1907	0.586142
$764$	−49.8397	−1.80314
$765$	−15.4343	−0.558029
$766$	55.4792	2.00455
$767$	−6.18771	−0.223425
$768$	−11.4281	−0.412378
$769$	−4.77772	−0.172289	−0.0861445	−	0.996283i	$-0.527455\pi$
$769$	−4.77772	−0.172289	−0.0861445	+	0.996283i	$0.527455\pi$
$770$	−38.6416	−1.39255
$771$	−10.7150	−0.385892
$772$	57.3274	2.06326
$773$	33.0650	1.18927	0.594633	−	0.803997i	$-0.297297\pi$
$773$	33.0650	1.18927	0.594633	+	0.803997i	$0.297297\pi$
$774$	−11.1266	−0.399936
$775$	17.6474	0.633913
$776$	−45.7851	−1.64359
$777$	1.29993	0.0466346
$778$	41.4713	1.48682
$779$	−44.6158	−1.59853
$780$	−1.05141	−0.0376464
$781$	−13.5392	−0.484470
$782$	80.9792	2.89581
$783$	−4.88246	−0.174485
$784$	−0.737711	−0.0263468
$785$	−18.6286	−0.664884
$786$	4.34517	0.154987
$787$	−51.8067	−1.84671	−0.923355	−	0.383947i	$-0.874564\pi$
$787$	−51.8067	−1.84671	−0.923355	+	0.383947i	$0.874564\pi$
$788$	−3.77412	−0.134448
$789$	−10.3990	−0.370216
$790$	−30.0461	−1.06899
$791$	−8.10230	−0.288085
$792$	52.2153	1.85539
$793$	6.63774	0.235713
$794$	−48.5335	−1.72239
$795$	−0.332764	−0.0118019
$796$	−52.3927	−1.85701
$797$	−41.3733	−1.46552	−0.732759	−	0.680489i	$-0.761768\pi$
$797$	−41.3733	−1.46552	−0.732759	+	0.680489i	$0.761768\pi$
$798$	20.1472	0.713202
$799$	22.5407	0.797434
$800$	−15.9467	−0.563800
$801$	29.3946	1.03861
$802$	79.8096	2.81817
$803$	10.5971	0.373964
$804$	13.7073	0.483418
$805$	21.1569	0.745682
$806$	5.68862	0.200373
$807$	2.81216	0.0989928
$808$	−25.6693	−0.903042
$809$	−36.0727	−1.26825	−0.634124	−	0.773232i	$-0.718639\pi$
$809$	−36.0727	−1.26825	−0.634124	+	0.773232i	$0.718639\pi$
$810$	18.2213	0.640230
$811$	−9.09742	−0.319454	−0.159727	−	0.987161i	$-0.551061\pi$
$811$	−9.09742	−0.319454	−0.159727	+	0.987161i	$0.551061\pi$
$812$	−14.2192	−0.498996
$813$	−5.81478	−0.203933
$814$	13.1444	0.460712
$815$	1.17306	0.0410906
$816$	−2.56177	−0.0896800
$817$	−11.5766	−0.405014
$818$	6.95162	0.243058
$819$	3.42316	0.119615
$820$	27.2455	0.951454
$821$	−20.1285	−0.702490	−0.351245	−	0.936284i	$-0.614242\pi$
$821$	−20.1285	−0.702490	−0.351245	+	0.936284i	$0.614242\pi$
$822$	4.43634	0.154735
$823$	20.1839	0.703566	0.351783	−	0.936082i	$-0.385576\pi$
$823$	20.1839	0.703566	0.351783	+	0.936082i	$0.385576\pi$
$824$	−65.9065	−2.29596
$825$	−10.5795	−0.368332
$826$	−72.4069	−2.51936
$827$	44.0255	1.53092	0.765458	−	0.643486i	$-0.222513\pi$
$827$	44.0255	1.53092	0.765458	+	0.643486i	$0.222513\pi$
$828$	−67.8966	−2.35957
$829$	−13.9575	−0.484762	−0.242381	−	0.970181i	$-0.577928\pi$
$829$	−13.9575	−0.484762	−0.242381	+	0.970181i	$0.577928\pi$
$830$	46.4153	1.61110
$831$	−13.0948	−0.454253
$832$	−6.16584	−0.213762
$833$	3.46722	0.120132
$834$	11.2004	0.387837
$835$	6.25961	0.216623
$836$	129.024	4.46240
$837$	14.4762	0.500371
$838$	−19.6101	−0.677420
$839$	−6.39941	−0.220932	−0.110466	−	0.993880i	$-0.535234\pi$
$839$	−6.39941	−0.220932	−0.110466	+	0.993880i	$0.535234\pi$
$840$	−5.18045	−0.178742
$841$	−26.3024	−0.906981
$842$	−13.8456	−0.477151
$843$	−3.94834	−0.135988
$844$	10.5269	0.362352
$845$	14.9564	0.514514
$846$	−29.8406	−1.02594
$847$	−51.8133	−1.78033
$848$	0.560592	0.0192508
$849$	9.11891	0.312960
$850$	−40.7769	−1.39864
$851$	−7.19678	−0.246702
$852$	−4.31080	−0.147686
$853$	−18.2254	−0.624024	−0.312012	−	0.950078i	$-0.601003\pi$
$853$	−18.2254	−0.624024	−0.312012	+	0.950078i	$0.601003\pi$
$854$	77.6730	2.65792
$855$	21.2592	0.727049
$856$	−8.31958	−0.284357
$857$	7.92846	0.270831	0.135416	−	0.990789i	$-0.456763\pi$
$857$	7.92846	0.270831	0.135416	+	0.990789i	$0.456763\pi$
$858$	−3.41030	−0.116426
$859$	36.2315	1.23620	0.618102	−	0.786098i	$-0.287902\pi$
$859$	36.2315	1.23620	0.618102	+	0.786098i	$0.287902\pi$
$860$	7.06949	0.241067
$861$	8.73965	0.297846
$862$	23.7308	0.808275
$863$	27.8764	0.948925	0.474462	−	0.880276i	$-0.342642\pi$
$863$	27.8764	0.948925	0.474462	+	0.880276i	$0.342642\pi$
$864$	−13.0811	−0.445028
$865$	−14.4514	−0.491362
$866$	−86.1116	−2.92619
$867$	3.22212	0.109429
$868$	42.1591	1.43097
$869$	−61.7226	−2.09379
$870$	2.33408	0.0791328
$871$	3.82603	0.129640
$872$	21.9482	0.743261
$873$	−36.8052	−1.24567
$874$	−111.541	−3.77292
$875$	−25.3523	−0.857065
$876$	3.37407	0.113999
$877$	22.4139	0.756864	0.378432	−	0.925629i	$-0.376463\pi$
$877$	22.4139	0.756864	0.378432	+	0.925629i	$0.376463\pi$
$878$	13.1739	0.444597
$879$	−4.66427	−0.157322
$880$	−6.76769	−0.228139
$881$	5.12484	0.172660	0.0863301	−	0.996267i	$-0.472486\pi$
$881$	5.12484	0.172660	0.0863301	+	0.996267i	$0.472486\pi$
$882$	−4.59008	−0.154556
$883$	−50.5508	−1.70117	−0.850586	−	0.525836i	$-0.823752\pi$
$883$	−50.5508	−1.70117	−0.850586	+	0.525836i	$0.823752\pi$
$884$	−8.32484	−0.279995
$885$	7.52759	0.253037
$886$	50.8489	1.70830
$887$	8.57599	0.287954	0.143977	−	0.989581i	$-0.454011\pi$
$887$	8.57599	0.287954	0.143977	+	0.989581i	$0.454011\pi$
$888$	1.76220	0.0591354
$889$	11.7325	0.393497
$890$	−29.4889	−0.988472
$891$	37.4313	1.25400
$892$	12.0259	0.402657
$893$	−31.0476	−1.03897
$894$	−13.2390	−0.442778
$895$	−5.64811	−0.188795
$896$	−50.0957	−1.67358
$897$	1.86719	0.0623438
$898$	6.99877	0.233552
$899$	−7.99810	−0.266752
$900$	34.1892	1.13964
$901$	−2.63476	−0.0877767
$902$	88.3723	2.94248
$903$	2.26771	0.0754646
$904$	−10.9836	−0.365308
$905$	23.7000	0.787815
$906$	−2.29026	−0.0760889
$907$	−27.7746	−0.922240	−0.461120	−	0.887338i	$-0.652552\pi$
$907$	−27.7746	−0.922240	−0.461120	+	0.887338i	$0.652552\pi$
$908$	−88.2589	−2.92898
$909$	−20.6347	−0.684410
$910$	−3.43414	−0.113841
$911$	21.2942	0.705509	0.352754	−	0.935716i	$-0.385245\pi$
$911$	21.2942	0.705509	0.352754	+	0.935716i	$0.385245\pi$
$912$	3.52858	0.116843
$913$	95.3494	3.15561
$914$	−18.1411	−0.600054
$915$	−8.07507	−0.266953
$916$	−90.2735	−2.98272
$917$	8.98855	0.296828
$918$	−33.4494	−1.10400
$919$	−14.1468	−0.466660	−0.233330	−	0.972398i	$-0.574962\pi$
$919$	−14.1468	−0.466660	−0.233330	+	0.972398i	$0.574962\pi$
$920$	28.6805	0.945567
$921$	13.6796	0.450758
$922$	−7.22950	−0.238091
$923$	−1.20325	−0.0396055
$924$	−25.2742	−0.831460
$925$	3.62392	0.119154
$926$	−51.9406	−1.70687
$927$	−52.9801	−1.74010
$928$	7.22731	0.237248
$929$	−33.6828	−1.10510	−0.552549	−	0.833480i	$-0.686345\pi$
$929$	−33.6828	−1.10510	−0.552549	+	0.833480i	$0.686345\pi$
$930$	−6.92042	−0.226930
$931$	−4.77574	−0.156519
$932$	−68.5816	−2.24646
$933$	4.15729	0.136103
$934$	55.1703	1.80523
$935$	31.8079	1.04023
$936$	4.64047	0.151678
$937$	35.0006	1.14342	0.571710	−	0.820456i	$-0.306280\pi$
$937$	35.0006	1.14342	0.571710	+	0.820456i	$0.306280\pi$
$938$	44.7712	1.46183
$939$	15.7015	0.512400
$940$	18.9598	0.618401
$941$	58.9537	1.92184	0.960918	−	0.276834i	$-0.0892851\pi$
$941$	58.9537	1.92184	0.960918	+	0.276834i	$0.0892851\pi$
$942$	−19.2384	−0.626820
$943$	−48.3852	−1.57564
$944$	−12.6814	−0.412743
$945$	−8.73909	−0.284283
$946$	22.9303	0.745527
$947$	26.6971	0.867539	0.433769	−	0.901024i	$-0.357183\pi$
$947$	26.6971	0.867539	0.433769	+	0.901024i	$0.357183\pi$
$948$	−19.6521	−0.638272
$949$	0.941784	0.0305716
$950$	56.1660	1.82227
$951$	−14.1951	−0.460309
$952$	−41.0178	−1.32939
$953$	−24.2441	−0.785342	−0.392671	−	0.919679i	$-0.628449\pi$
$953$	−24.2441	−0.785342	−0.392671	+	0.919679i	$0.628449\pi$
$954$	3.48803	0.112929
$955$	16.9238	0.547643
$956$	−102.279	−3.30793
$957$	4.79482	0.154995
$958$	−18.5485	−0.599274
$959$	9.17714	0.296345
$960$	7.50098	0.242093
$961$	−7.28608	−0.235035
$962$	1.16817	0.0376632
$963$	−6.68785	−0.215513
$964$	45.5565	1.46728
$965$	−19.4664	−0.626646
$966$	21.8494	0.702992
$967$	−45.3916	−1.45970	−0.729848	−	0.683610i	$-0.760409\pi$
$967$	−45.3916	−1.45970	−0.729848	+	0.683610i	$0.760409\pi$
$968$	−70.2387	−2.25756
$969$	−16.5842	−0.532762
$970$	36.9233	1.18554
$971$	13.3232	0.427561	0.213780	−	0.976882i	$-0.431422\pi$
$971$	13.3232	0.427561	0.213780	+	0.976882i	$0.431422\pi$
$972$	42.7266	1.37046
$973$	23.1694	0.742776
$974$	−21.5418	−0.690245
$975$	−0.940221	−0.0301112
$976$	13.6037	0.435443
$977$	4.75908	0.152257	0.0761283	−	0.997098i	$-0.475744\pi$
$977$	4.75908	0.152257	0.0761283	+	0.997098i	$0.475744\pi$
$978$	1.21146	0.0387382
$979$	−60.5781	−1.93608
$980$	2.91640	0.0931610
$981$	17.6435	0.563314
$982$	80.7668	2.57737
$983$	34.4671	1.09933	0.549665	−	0.835385i	$-0.314755\pi$
$983$	34.4671	1.09933	0.549665	+	0.835385i	$0.314755\pi$
$984$	11.8476	0.377686
$985$	1.28156	0.0408340
$986$	18.4808	0.588549
$987$	6.08181	0.193586
$988$	11.4666	0.364802
$989$	−12.5547	−0.399216
$990$	−42.1090	−1.33831
$991$	42.0715	1.33644	0.668222	−	0.743962i	$-0.267056\pi$
$991$	42.0715	1.33644	0.668222	+	0.743962i	$0.267056\pi$
$992$	−21.4286	−0.680358
$993$	−11.3890	−0.361418
$994$	−14.0801	−0.446593
$995$	17.7908	0.564005
$996$	30.3588	0.961954
$997$	24.2567	0.768218	0.384109	−	0.923288i	$-0.374509\pi$
$997$	24.2567	0.768218	0.384109	+	0.923288i	$0.374509\pi$
$998$	34.9648	1.10679
$999$	2.97271	0.0940525

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.c.1.13	✓	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.c.1.13	✓	110	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6031 = 37 \cdot 163 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.33551 q^{2} +0.518713 q^{3} +3.45460 q^{4} -1.17306 q^{5} -1.21146 q^{6} -2.50606 q^{7} -3.39724 q^{8} -2.73094 q^{9} +O(q^{10})\)	\(q-2.33551 q^{2} +0.518713 q^{3} +3.45460 q^{4} -1.17306 q^{5} -1.21146 q^{6} -2.50606 q^{7} -3.39724 q^{8} -2.73094 q^{9} +2.73970 q^{10} +5.62807 q^{11} +1.79195 q^{12} +0.500177 q^{13} +5.85293 q^{14} -0.608484 q^{15} +1.02508 q^{16} -4.81786 q^{17} +6.37813 q^{18} +6.63611 q^{19} -4.05247 q^{20} -1.29993 q^{21} -13.1444 q^{22} +7.19678 q^{23} -1.76220 q^{24} -3.62392 q^{25} -1.16817 q^{26} -2.97271 q^{27} -8.65745 q^{28} +1.64242 q^{29} +1.42112 q^{30} -4.86969 q^{31} +4.40039 q^{32} +2.91936 q^{33} +11.2522 q^{34} +2.93977 q^{35} -9.43430 q^{36} -1.00000 q^{37} -15.4987 q^{38} +0.259448 q^{39} +3.98518 q^{40} -6.72318 q^{41} +3.03599 q^{42} -1.74449 q^{43} +19.4428 q^{44} +3.20356 q^{45} -16.8081 q^{46} -4.67858 q^{47} +0.531725 q^{48} -0.719660 q^{49} +8.46370 q^{50} -2.49909 q^{51} +1.72791 q^{52} +0.546874 q^{53} +6.94280 q^{54} -6.60209 q^{55} +8.51370 q^{56} +3.44224 q^{57} -3.83590 q^{58} -12.3711 q^{59} -2.10207 q^{60} +13.2708 q^{61} +11.3732 q^{62} +6.84389 q^{63} -12.3273 q^{64} -0.586739 q^{65} -6.81819 q^{66} +7.64936 q^{67} -16.6438 q^{68} +3.73307 q^{69} -6.86586 q^{70} -2.40565 q^{71} +9.27765 q^{72} +1.88290 q^{73} +2.33551 q^{74} -1.87978 q^{75} +22.9251 q^{76} -14.1043 q^{77} -0.605944 q^{78} -10.9669 q^{79} -1.20249 q^{80} +6.65082 q^{81} +15.7021 q^{82} +16.9417 q^{83} -4.49074 q^{84} +5.65165 q^{85} +4.07427 q^{86} +0.851947 q^{87} -19.1199 q^{88} -10.7636 q^{89} -7.48195 q^{90} -1.25347 q^{91} +24.8620 q^{92} -2.52598 q^{93} +10.9269 q^{94} -7.78458 q^{95} +2.28254 q^{96} +13.4771 q^{97} +1.68077 q^{98} -15.3699 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9}+O(q^{10}) \) 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9	\( 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9} - 17 q^{10} - 9 q^{11} - 21 q^{13} - 29 q^{14} - 23 q^{15} + 79 q^{16} - 76 q^{17} - 31 q^{18} - 27 q^{19} - 67 q^{20} - 30 q^{21} - 28 q^{22} - 32 q^{23} - 63 q^{24} + 66 q^{25} - 55 q^{26} - 4 q^{28} - 81 q^{29} - 48 q^{30} - 30 q^{31} - 73 q^{32} - 53 q^{33} - 23 q^{34} - 78 q^{35} + 7 q^{36} - 110 q^{37} - 50 q^{38} - 64 q^{39} - 37 q^{40} - 123 q^{41} - 63 q^{42} - 40 q^{43} - 31 q^{44} - 73 q^{45} + 16 q^{46} - 37 q^{47} - 29 q^{48} + 46 q^{49} - 58 q^{50} - 73 q^{51} - 39 q^{52} - 16 q^{53} - 53 q^{54} - 59 q^{55} - 113 q^{56} - 39 q^{57} + 11 q^{58} - 93 q^{59} - 18 q^{60} - 66 q^{61} - 40 q^{62} - 21 q^{63} + 23 q^{64} - 92 q^{65} - 31 q^{66} + q^{67} - 121 q^{68} - 80 q^{69} - 3 q^{70} - 75 q^{71} - 114 q^{72} - 39 q^{73} + 9 q^{74} - 25 q^{75} - 58 q^{76} - 31 q^{77} + 68 q^{78} - 36 q^{79} - 82 q^{80} - 50 q^{81} - 18 q^{82} - 57 q^{83} - 9 q^{84} - 14 q^{85} - 58 q^{86} - 58 q^{87} - 15 q^{88} - 181 q^{89} + 8 q^{90} - 55 q^{91} - 116 q^{92} - 86 q^{93} - 39 q^{94} - 70 q^{95} - 127 q^{96} - 91 q^{97} - 19 q^{98} - 21 q^{99}+O(q^{100}) \) 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9 - 17 * q^10 - 9 * q^11 - 21 * q^13 - 29 * q^14 - 23 * q^15 + 79 * q^16 - 76 * q^17 - 31 * q^18 - 27 * q^19 - 67 * q^20 - 30 * q^21 - 28 * q^22 - 32 * q^23 - 63 * q^24 + 66 * q^25 - 55 * q^26 - 4 * q^28 - 81 * q^29 - 48 * q^30 - 30 * q^31 - 73 * q^32 - 53 * q^33 - 23 * q^34 - 78 * q^35 + 7 * q^36 - 110 * q^37 - 50 * q^38 - 64 * q^39 - 37 * q^40 - 123 * q^41 - 63 * q^42 - 40 * q^43 - 31 * q^44 - 73 * q^45 + 16 * q^46 - 37 * q^47 - 29 * q^48 + 46 * q^49 - 58 * q^50 - 73 * q^51 - 39 * q^52 - 16 * q^53 - 53 * q^54 - 59 * q^55 - 113 * q^56 - 39 * q^57 + 11 * q^58 - 93 * q^59 - 18 * q^60 - 66 * q^61 - 40 * q^62 - 21 * q^63 + 23 * q^64 - 92 * q^65 - 31 * q^66 + q^67 - 121 * q^68 - 80 * q^69 - 3 * q^70 - 75 * q^71 - 114 * q^72 - 39 * q^73 + 9 * q^74 - 25 * q^75 - 58 * q^76 - 31 * q^77 + 68 * q^78 - 36 * q^79 - 82 * q^80 - 50 * q^81 - 18 * q^82 - 57 * q^83 - 9 * q^84 - 14 * q^85 - 58 * q^86 - 58 * q^87 - 15 * q^88 - 181 * q^89 + 8 * q^90 - 55 * q^91 - 116 * q^92 - 86 * q^93 - 39 * q^94 - 70 * q^95 - 127 * q^96 - 91 * q^97 - 19 * q^98 - 21 * q^99

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