LMFDB - Embedded newform 6031.2.a.e.1.9

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:	$0$
Dimension:	$134$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q-2.49038 q^{2} +1.16097 q^{3} +4.20199 q^{4} +0.527322 q^{5} -2.89126 q^{6} +0.382261 q^{7} -5.48378 q^{8} -1.65215 q^{9} +O(q^{10})$	\(q-2.49038 q^{2} +1.16097 q^{3} +4.20199 q^{4} +0.527322 q^{5} -2.89126 q^{6} +0.382261 q^{7} -5.48378 q^{8} -1.65215 q^{9} -1.31323 q^{10} -1.85448 q^{11} +4.87838 q^{12} -1.72610 q^{13} -0.951975 q^{14} +0.612205 q^{15} +5.25272 q^{16} +2.38443 q^{17} +4.11448 q^{18} -4.10337 q^{19} +2.21580 q^{20} +0.443794 q^{21} +4.61835 q^{22} -7.98819 q^{23} -6.36651 q^{24} -4.72193 q^{25} +4.29863 q^{26} -5.40101 q^{27} +1.60626 q^{28} -8.27501 q^{29} -1.52462 q^{30} +6.07260 q^{31} -2.11370 q^{32} -2.15299 q^{33} -5.93813 q^{34} +0.201575 q^{35} -6.94231 q^{36} +1.00000 q^{37} +10.2189 q^{38} -2.00395 q^{39} -2.89172 q^{40} +8.20067 q^{41} -1.10521 q^{42} -12.0209 q^{43} -7.79249 q^{44} -0.871215 q^{45} +19.8936 q^{46} +11.9386 q^{47} +6.09825 q^{48} -6.85388 q^{49} +11.7594 q^{50} +2.76825 q^{51} -7.25303 q^{52} +4.64486 q^{53} +13.4505 q^{54} -0.977908 q^{55} -2.09624 q^{56} -4.76388 q^{57} +20.6079 q^{58} +6.03092 q^{59} +2.57248 q^{60} +8.19908 q^{61} -15.1231 q^{62} -0.631552 q^{63} -5.24153 q^{64} -0.910209 q^{65} +5.36177 q^{66} +2.69498 q^{67} +10.0193 q^{68} -9.27405 q^{69} -0.501997 q^{70} -2.29815 q^{71} +9.06002 q^{72} +14.1681 q^{73} -2.49038 q^{74} -5.48202 q^{75} -17.2423 q^{76} -0.708895 q^{77} +4.99059 q^{78} -14.8901 q^{79} +2.76988 q^{80} -1.31396 q^{81} -20.4228 q^{82} -7.83122 q^{83} +1.86481 q^{84} +1.25736 q^{85} +29.9366 q^{86} -9.60704 q^{87} +10.1696 q^{88} +0.271338 q^{89} +2.16965 q^{90} -0.659819 q^{91} -33.5663 q^{92} +7.05011 q^{93} -29.7318 q^{94} -2.16380 q^{95} -2.45394 q^{96} -2.14607 q^{97} +17.0687 q^{98} +3.06387 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9}+O(q^{10}) $ 134 * q + 9 * q^2 + 7 * q^3 + 149 * q^4 + 22 * q^5 + 20 * q^6 + 11 * q^7 + 27 * q^8 + 181 * q^9	\( 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9} + 15 q^{10} + 20 q^{11} + 28 q^{12} + 11 q^{13} + 17 q^{14} - 13 q^{15} + 143 q^{16} + 76 q^{17} + 23 q^{18} + 15 q^{19} + 67 q^{20} + 63 q^{21} + 2 q^{22} + 22 q^{23} + 33 q^{24} + 160 q^{25} + 65 q^{26} + 31 q^{27} + 10 q^{28} + 73 q^{29} + 20 q^{30} + 10 q^{31} + 53 q^{32} + 72 q^{33} - 7 q^{34} + 52 q^{35} + 201 q^{36} + 134 q^{37} + 70 q^{38} + 6 q^{39} + 11 q^{40} + 182 q^{41} - 15 q^{42} + 12 q^{43} + 33 q^{44} + 29 q^{45} + 24 q^{46} + 80 q^{47} + 21 q^{48} + 229 q^{49} + 37 q^{50} + 57 q^{51} - 15 q^{52} + 75 q^{53} + 95 q^{54} - 9 q^{55} + 39 q^{56} + 19 q^{57} - 21 q^{58} + 91 q^{59} + 62 q^{60} + 58 q^{61} + 108 q^{62} + 9 q^{63} + 167 q^{64} + 76 q^{65} + 105 q^{66} - 17 q^{67} + 109 q^{68} + 48 q^{69} - 55 q^{70} + 56 q^{71} + 48 q^{72} + 54 q^{73} + 9 q^{74} + 28 q^{75} + 82 q^{76} + 156 q^{77} + 16 q^{78} - 2 q^{79} + 98 q^{80} + 270 q^{81} - 42 q^{82} + 130 q^{83} + 229 q^{84} + 22 q^{85} + 72 q^{86} + 22 q^{87} + 61 q^{88} + 157 q^{89} + 176 q^{90} + 31 q^{91} - 18 q^{92} + 36 q^{93} + 83 q^{94} + 98 q^{95} + 111 q^{96} + 35 q^{97} + 53 q^{98} + 55 q^{99}+O(q^{100}) \) 134 * q + 9 * q^2 + 7 * q^3 + 149 * q^4 + 22 * q^5 + 20 * q^6 + 11 * q^7 + 27 * q^8 + 181 * q^9 + 15 * q^10 + 20 * q^11 + 28 * q^12 + 11 * q^13 + 17 * q^14 - 13 * q^15 + 143 * q^16 + 76 * q^17 + 23 * q^18 + 15 * q^19 + 67 * q^20 + 63 * q^21 + 2 * q^22 + 22 * q^23 + 33 * q^24 + 160 * q^25 + 65 * q^26 + 31 * q^27 + 10 * q^28 + 73 * q^29 + 20 * q^30 + 10 * q^31 + 53 * q^32 + 72 * q^33 - 7 * q^34 + 52 * q^35 + 201 * q^36 + 134 * q^37 + 70 * q^38 + 6 * q^39 + 11 * q^40 + 182 * q^41 - 15 * q^42 + 12 * q^43 + 33 * q^44 + 29 * q^45 + 24 * q^46 + 80 * q^47 + 21 * q^48 + 229 * q^49 + 37 * q^50 + 57 * q^51 - 15 * q^52 + 75 * q^53 + 95 * q^54 - 9 * q^55 + 39 * q^56 + 19 * q^57 - 21 * q^58 + 91 * q^59 + 62 * q^60 + 58 * q^61 + 108 * q^62 + 9 * q^63 + 167 * q^64 + 76 * q^65 + 105 * q^66 - 17 * q^67 + 109 * q^68 + 48 * q^69 - 55 * q^70 + 56 * q^71 + 48 * q^72 + 54 * q^73 + 9 * q^74 + 28 * q^75 + 82 * q^76 + 156 * q^77 + 16 * q^78 - 2 * q^79 + 98 * q^80 + 270 * q^81 - 42 * q^82 + 130 * q^83 + 229 * q^84 + 22 * q^85 + 72 * q^86 + 22 * q^87 + 61 * q^88 + 157 * q^89 + 176 * q^90 + 31 * q^91 - 18 * q^92 + 36 * q^93 + 83 * q^94 + 98 * q^95 + 111 * q^96 + 35 * q^97 + 53 * q^98 + 55 * 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 $

$2$	−2.49038	−1.76096	−0.880482	−	0.474080i	$-0.842781\pi$
$2$	−2.49038	−1.76096	−0.880482	+	0.474080i	$0.842781\pi$
$3$	1.16097	0.670286	0.335143	−	0.942167i	$-0.391215\pi$
$3$	1.16097	0.670286	0.335143	+	0.942167i	$0.391215\pi$
$4$	4.20199	2.10099
$5$	0.527322	0.235826	0.117913	−	0.993024i	$-0.462380\pi$
$5$	0.527322	0.235826	0.117913	+	0.993024i	$0.462380\pi$
$6$	−2.89126	−1.18035
$7$	0.382261	0.144481	0.0722405	−	0.997387i	$-0.476985\pi$
$7$	0.382261	0.144481	0.0722405	+	0.997387i	$0.476985\pi$
$8$	−5.48378	−1.93881
$9$	−1.65215	−0.550716
$10$	−1.31323	−0.415280
$11$	−1.85448	−0.559146	−0.279573	−	0.960124i	$-0.590193\pi$
$11$	−1.85448	−0.559146	−0.279573	+	0.960124i	$0.590193\pi$
$12$	4.87838	1.40827
$13$	−1.72610	−0.478733	−0.239367	−	0.970929i	$-0.576940\pi$
$13$	−1.72610	−0.478733	−0.239367	+	0.970929i	$0.576940\pi$
$14$	−0.951975	−0.254426
$15$	0.612205	0.158071
$16$	5.25272	1.31318
$17$	2.38443	0.578309	0.289154	−	0.957282i	$-0.406626\pi$
$17$	2.38443	0.578309	0.289154	+	0.957282i	$0.406626\pi$
$18$	4.11448	0.969791
$19$	−4.10337	−0.941377	−0.470688	−	0.882300i	$-0.655994\pi$
$19$	−4.10337	−0.941377	−0.470688	+	0.882300i	$0.655994\pi$
$20$	2.21580	0.495468
$21$	0.443794	0.0968437
$22$	4.61835	0.984636
$23$	−7.98819	−1.66565	−0.832826	−	0.553535i	$-0.813279\pi$
$23$	−7.98819	−1.66565	−0.832826	+	0.553535i	$0.813279\pi$
$24$	−6.36651	−1.29956
$25$	−4.72193	−0.944386
$26$	4.29863	0.843032
$27$	−5.40101	−1.03942
$28$	1.60626	0.303554
$29$	−8.27501	−1.53663	−0.768315	−	0.640071i	$-0.778905\pi$
$29$	−8.27501	−1.53663	−0.768315	+	0.640071i	$0.778905\pi$
$30$	−1.52462	−0.278357
$31$	6.07260	1.09067	0.545336	−	0.838218i	$-0.316402\pi$
$31$	6.07260	1.09067	0.545336	+	0.838218i	$0.316402\pi$
$32$	−2.11370	−0.373653
$33$	−2.15299	−0.374788
$34$	−5.93813	−1.01838
$35$	0.201575	0.0340723
$36$	−6.94231	−1.15705
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	10.2189	1.65773
$39$	−2.00395	−0.320888
$40$	−2.89172	−0.457221
$41$	8.20067	1.28073	0.640365	−	0.768071i	$-0.278783\pi$
$41$	8.20067	1.28073	0.640365	+	0.768071i	$0.278783\pi$
$42$	−1.10521	−0.170538
$43$	−12.0209	−1.83317	−0.916586	−	0.399837i	$-0.869067\pi$
$43$	−12.0209	−1.83317	−0.916586	+	0.399837i	$0.869067\pi$
$44$	−7.79249	−1.17476
$45$	−0.871215	−0.129873
$46$	19.8936	2.93315
$47$	11.9386	1.74143	0.870715	−	0.491787i	$-0.163656\pi$
$47$	11.9386	1.74143	0.870715	+	0.491787i	$0.163656\pi$
$48$	6.09825	0.880207
$49$	−6.85388	−0.979125
$50$	11.7594	1.66303
$51$	2.76825	0.387632
$52$	−7.25303	−1.00581
$53$	4.64486	0.638020	0.319010	−	0.947751i	$-0.396650\pi$
$53$	4.64486	0.638020	0.319010	+	0.947751i	$0.396650\pi$
$54$	13.4505	1.83039
$55$	−0.977908	−0.131861
$56$	−2.09624	−0.280121
$57$	−4.76388	−0.630992
$58$	20.6079	2.70595
$59$	6.03092	0.785159	0.392580	−	0.919718i	$-0.371583\pi$
$59$	6.03092	0.785159	0.392580	+	0.919718i	$0.371583\pi$
$60$	2.57248	0.332106
$61$	8.19908	1.04978	0.524892	−	0.851169i	$-0.324106\pi$
$61$	8.19908	1.04978	0.524892	+	0.851169i	$0.324106\pi$
$62$	−15.1231	−1.92063
$63$	−0.631552	−0.0795681
$64$	−5.24153	−0.655191
$65$	−0.910209	−0.112898
$66$	5.36177	0.659988
$67$	2.69498	0.329244	0.164622	−	0.986357i	$-0.447360\pi$
$67$	2.69498	0.329244	0.164622	+	0.986357i	$0.447360\pi$
$68$	10.0193	1.21502
$69$	−9.27405	−1.11646
$70$	−0.501997	−0.0600002
$71$	−2.29815	−0.272740	−0.136370	−	0.990658i	$-0.543544\pi$
$71$	−2.29815	−0.272740	−0.136370	+	0.990658i	$0.543544\pi$
$72$	9.06002	1.06773
$73$	14.1681	1.65826	0.829128	−	0.559059i	$-0.188837\pi$
$73$	14.1681	1.65826	0.829128	+	0.559059i	$0.188837\pi$
$74$	−2.49038	−0.289501
$75$	−5.48202	−0.633009
$76$	−17.2423	−1.97783
$77$	−0.708895	−0.0807861
$78$	4.99059	0.565073
$79$	−14.8901	−1.67527	−0.837633	−	0.546234i	$-0.816061\pi$
$79$	−14.8901	−1.67527	−0.837633	+	0.546234i	$0.816061\pi$
$80$	2.76988	0.309682
$81$	−1.31396	−0.145996
$82$	−20.4228	−2.25532
$83$	−7.83122	−0.859588	−0.429794	−	0.902927i	$-0.641414\pi$
$83$	−7.83122	−0.859588	−0.429794	+	0.902927i	$0.641414\pi$
$84$	1.86481	0.203468
$85$	1.25736	0.136380
$86$	29.9366	3.22815
$87$	−9.60704	−1.02998
$88$	10.1696	1.08408
$89$	0.271338	0.0287618	0.0143809	−	0.999897i	$-0.495422\pi$
$89$	0.271338	0.0287618	0.0143809	+	0.999897i	$0.495422\pi$
$90$	2.16965	0.228702
$91$	−0.659819	−0.0691679
$92$	−33.5663	−3.49952
$93$	7.05011	0.731062
$94$	−29.7318	−3.06660
$95$	−2.16380	−0.222001
$96$	−2.45394	−0.250454
$97$	−2.14607	−0.217900	−0.108950	−	0.994047i	$-0.534749\pi$
$97$	−2.14607	−0.217900	−0.108950	+	0.994047i	$0.534749\pi$
$98$	17.0687	1.72420
$99$	3.06387	0.307931
$100$	−19.8415	−1.98415
$101$	14.5273	1.44552	0.722762	−	0.691097i	$-0.242872\pi$
$101$	14.5273	1.44552	0.722762	+	0.691097i	$0.242872\pi$
$102$	−6.89399	−0.682607
$103$	10.5191	1.03648	0.518239	−	0.855236i	$-0.326588\pi$
$103$	10.5191	1.03648	0.518239	+	0.855236i	$0.326588\pi$
$104$	9.46554	0.928172
$105$	0.234022	0.0228382
$106$	−11.5675	−1.12353
$107$	9.46565	0.915079	0.457540	−	0.889189i	$-0.348731\pi$
$107$	9.46565	0.915079	0.457540	+	0.889189i	$0.348731\pi$
$108$	−22.6950	−2.18382
$109$	16.9647	1.62492	0.812460	−	0.583017i	$-0.198128\pi$
$109$	16.9647	1.62492	0.812460	+	0.583017i	$0.198128\pi$
$110$	2.43536	0.232203
$111$	1.16097	0.110194
$112$	2.00791	0.189730
$113$	15.6048	1.46798	0.733989	−	0.679162i	$-0.237656\pi$
$113$	15.6048	1.46798	0.733989	+	0.679162i	$0.237656\pi$
$114$	11.8639	1.11115
$115$	−4.21235	−0.392804
$116$	−34.7715	−3.22845
$117$	2.85177	0.263646
$118$	−15.0193	−1.38264
$119$	0.911474	0.0835546
$120$	−3.35720	−0.306469
$121$	−7.56091	−0.687355
$122$	−20.4188	−1.84863
$123$	9.52074	0.858456
$124$	25.5170	2.29149
$125$	−5.12659	−0.458536
$126$	1.57280	0.140116
$127$	3.60092	0.319530	0.159765	−	0.987155i	$-0.448926\pi$
$127$	3.60092	0.319530	0.159765	+	0.987155i	$0.448926\pi$
$128$	17.2808	1.52742
$129$	−13.9559	−1.22875
$130$	2.26677	0.198808
$131$	18.6481	1.62929	0.814644	−	0.579961i	$-0.196932\pi$
$131$	18.6481	1.62929	0.814644	+	0.579961i	$0.196932\pi$
$132$	−9.04685	−0.787428
$133$	−1.56856	−0.136011
$134$	−6.71152	−0.579787
$135$	−2.84807	−0.245123
$136$	−13.0757	−1.12123
$137$	1.33300	0.113886	0.0569429	−	0.998377i	$-0.481865\pi$
$137$	1.33300	0.113886	0.0569429	+	0.998377i	$0.481865\pi$
$138$	23.0959	1.96605
$139$	0.296756	0.0251705	0.0125853	−	0.999921i	$-0.495994\pi$
$139$	0.296756	0.0251705	0.0125853	+	0.999921i	$0.495994\pi$
$140$	0.847014	0.0715858
$141$	13.8604	1.16726
$142$	5.72326	0.480285
$143$	3.20101	0.267682
$144$	−8.67827	−0.723190
$145$	−4.36360	−0.362377
$146$	−35.2841	−2.92013
$147$	−7.95715	−0.656294
$148$	4.20199	0.345401
$149$	19.4470	1.59316	0.796582	−	0.604531i	$-0.206639\pi$
$149$	19.4470	1.59316	0.796582	+	0.604531i	$0.206639\pi$
$150$	13.6523	1.11471
$151$	11.5065	0.936383	0.468192	−	0.883627i	$-0.344906\pi$
$151$	11.5065	0.936383	0.468192	+	0.883627i	$0.344906\pi$
$152$	22.5020	1.82515
$153$	−3.93943	−0.318484
$154$	1.76542	0.142261
$155$	3.20222	0.257208
$156$	−8.42056	−0.674184
$157$	7.46728	0.595954	0.297977	−	0.954573i	$-0.403688\pi$
$157$	7.46728	0.595954	0.297977	+	0.954573i	$0.403688\pi$
$158$	37.0819	2.95008
$159$	5.39254	0.427656
$160$	−1.11460	−0.0881170
$161$	−3.05357	−0.240655
$162$	3.27226	0.257093
$163$	−1.00000	−0.0783260
$163$	−1.00000	−0.0783260
$164$	34.4591	2.69081
$165$	−1.13532	−0.0883847
$166$	19.5027	1.51370
$167$	3.29605	0.255056	0.127528	−	0.991835i	$-0.459296\pi$
$167$	3.29605	0.255056	0.127528	+	0.991835i	$0.459296\pi$
$168$	−2.43367	−0.187761
$169$	−10.0206	−0.770815
$170$	−3.13131	−0.240160
$171$	6.77937	0.518431
$172$	−50.5117	−3.85148
$173$	17.2122	1.30862	0.654309	−	0.756227i	$-0.272960\pi$
$173$	17.2122	1.30862	0.654309	+	0.756227i	$0.272960\pi$
$174$	23.9252	1.81376
$175$	−1.80501	−0.136446
$176$	−9.74106	−0.734260
$177$	7.00172	0.526282
$178$	−0.675735	−0.0506485
$179$	6.16125	0.460514	0.230257	−	0.973130i	$-0.426043\pi$
$179$	6.16125	0.460514	0.230257	+	0.973130i	$0.426043\pi$
$180$	−3.66083	−0.272862
$181$	1.47460	0.109607	0.0548033	−	0.998497i	$-0.482547\pi$
$181$	1.47460	0.109607	0.0548033	+	0.998497i	$0.482547\pi$
$182$	1.64320	0.121802
$183$	9.51888	0.703656
$184$	43.8055	3.22938
$185$	0.527322	0.0387695
$186$	−17.5574	−1.28737
$187$	−4.42187	−0.323359
$188$	50.1660	3.65873
$189$	−2.06459	−0.150177
$190$	5.38867	0.390935
$191$	0.664648	0.0480923	0.0240461	−	0.999711i	$-0.492345\pi$
$191$	0.664648	0.0480923	0.0240461	+	0.999711i	$0.492345\pi$
$192$	−6.08525	−0.439165
$193$	12.9560	0.932595	0.466297	−	0.884628i	$-0.345588\pi$
$193$	12.9560	0.932595	0.466297	+	0.884628i	$0.345588\pi$
$194$	5.34452	0.383714
$195$	−1.05673	−0.0756737
$196$	−28.7999	−2.05714
$197$	−6.73300	−0.479706	−0.239853	−	0.970809i	$-0.577099\pi$
$197$	−6.73300	−0.479706	−0.239853	+	0.970809i	$0.577099\pi$
$198$	−7.63021	−0.542255
$199$	21.1159	1.49687	0.748434	−	0.663210i	$-0.230806\pi$
$199$	21.1159	1.49687	0.748434	+	0.663210i	$0.230806\pi$
$200$	25.8940	1.83099
$201$	3.12879	0.220688
$202$	−36.1786	−2.54551
$203$	−3.16321	−0.222014
$204$	11.6321	0.814413
$205$	4.32440	0.302029
$206$	−26.1965	−1.82520
$207$	13.1977	0.917302
$208$	−9.06670	−0.628663
$209$	7.60960	0.526367
$210$	−0.582804	−0.0402173
$211$	7.54425	0.519368	0.259684	−	0.965694i	$-0.416382\pi$
$211$	7.54425	0.519368	0.259684	+	0.965694i	$0.416382\pi$
$212$	19.5176	1.34048
$213$	−2.66808	−0.182814
$214$	−23.5731	−1.61142
$215$	−6.33890	−0.432309
$216$	29.6179	2.01525
$217$	2.32132	0.157581
$218$	−42.2484	−2.86143
$219$	16.4488	1.11151
$220$	−4.10916	−0.277039
$221$	−4.11575	−0.276855
$222$	−2.89126	−0.194048
$223$	−6.34855	−0.425131	−0.212565	−	0.977147i	$-0.568182\pi$
$223$	−6.34855	−0.425131	−0.212565	+	0.977147i	$0.568182\pi$
$224$	−0.807985	−0.0539858
$225$	7.80133	0.520089
$226$	−38.8619	−2.58506
$227$	15.2973	1.01532	0.507660	−	0.861557i	$-0.330511\pi$
$227$	15.2973	1.01532	0.507660	+	0.861557i	$0.330511\pi$
$228$	−20.0178	−1.32571
$229$	−6.61267	−0.436977	−0.218489	−	0.975839i	$-0.570113\pi$
$229$	−6.61267	−0.436977	−0.218489	+	0.975839i	$0.570113\pi$
$230$	10.4903	0.691713
$231$	−0.823006	−0.0541498
$232$	45.3783	2.97923
$233$	−21.1378	−1.38478	−0.692391	−	0.721522i	$-0.743443\pi$
$233$	−21.1378	−1.38478	−0.692391	+	0.721522i	$0.743443\pi$
$234$	−7.10198	−0.464271
$235$	6.29551	0.410674
$236$	25.3419	1.64961
$237$	−17.2869	−1.12291
$238$	−2.26991	−0.147137
$239$	−26.3377	−1.70365	−0.851823	−	0.523830i	$-0.824503\pi$
$239$	−26.3377	−1.70365	−0.851823	+	0.523830i	$0.824503\pi$
$240$	3.21574	0.207575
$241$	−6.74200	−0.434290	−0.217145	−	0.976139i	$-0.569674\pi$
$241$	−6.74200	−0.434290	−0.217145	+	0.976139i	$0.569674\pi$
$242$	18.8295	1.21041
$243$	14.6775	0.941565
$244$	34.4524	2.20559
$245$	−3.61420	−0.230903
$246$	−23.7102	−1.51171
$247$	7.08280	0.450668
$248$	−33.3008	−2.11460
$249$	−9.09181	−0.576170
$250$	12.7672	0.807466
$251$	−13.7465	−0.867673	−0.433837	−	0.900992i	$-0.642840\pi$
$251$	−13.7465	−0.867673	−0.433837	+	0.900992i	$0.642840\pi$
$252$	−2.65377	−0.167172
$253$	14.8139	0.931343
$254$	−8.96765	−0.562680
$255$	1.45976	0.0914137
$256$	−32.5527	−2.03454
$257$	−20.4249	−1.27407	−0.637036	−	0.770834i	$-0.719840\pi$
$257$	−20.4249	−1.27407	−0.637036	+	0.770834i	$0.719840\pi$
$258$	34.7555	2.16379
$259$	0.382261	0.0237525
$260$	−3.82469	−0.237197
$261$	13.6715	0.846247
$262$	−46.4407	−2.86912
$263$	0.159583	0.00984031	0.00492016	−	0.999988i	$-0.498434\pi$
$263$	0.159583	0.00984031	0.00492016	+	0.999988i	$0.498434\pi$
$264$	11.8066	0.726643
$265$	2.44934	0.150462
$266$	3.90630	0.239511
$267$	0.315015	0.0192786
$268$	11.3243	0.691740
$269$	4.80166	0.292763	0.146381	−	0.989228i	$-0.453237\pi$
$269$	4.80166	0.292763	0.146381	+	0.989228i	$0.453237\pi$
$270$	7.09277	0.431652
$271$	−13.3584	−0.811465	−0.405732	−	0.913992i	$-0.632983\pi$
$271$	−13.3584	−0.811465	−0.405732	+	0.913992i	$0.632983\pi$
$272$	12.5247	0.759423
$273$	−0.766030	−0.0463623
$274$	−3.31967	−0.200549
$275$	8.75672	0.528050
$276$	−38.9694	−2.34568
$277$	−13.1256	−0.788639	−0.394320	−	0.918973i	$-0.629020\pi$
$277$	−13.1256	−0.788639	−0.394320	+	0.918973i	$0.629020\pi$
$278$	−0.739035	−0.0443244
$279$	−10.0328	−0.600651
$280$	−1.10539	−0.0660598
$281$	28.9837	1.72902	0.864512	−	0.502613i	$-0.167628\pi$
$281$	28.9837	1.72902	0.864512	+	0.502613i	$0.167628\pi$
$282$	−34.5177	−2.05550
$283$	−21.1320	−1.25617	−0.628085	−	0.778145i	$-0.716161\pi$
$283$	−21.1320	−1.25617	−0.628085	+	0.778145i	$0.716161\pi$
$284$	−9.65679	−0.573025
$285$	−2.51210	−0.148804
$286$	−7.97172	−0.471378
$287$	3.13480	0.185041
$288$	3.49215	0.205777
$289$	−11.3145	−0.665559
$290$	10.8670	0.638133
$291$	−2.49152	−0.146055
$292$	59.5344	3.48399
$293$	22.7274	1.32775	0.663875	−	0.747844i	$-0.268911\pi$
$293$	22.7274	1.32775	0.663875	+	0.747844i	$0.268911\pi$
$294$	19.8163	1.15571
$295$	3.18024	0.185161
$296$	−5.48378	−0.318738
$297$	10.0160	0.581190
$298$	−48.4305	−2.80550
$299$	13.7884	0.797403
$300$	−23.0354	−1.32995
$301$	−4.59513	−0.264859
$302$	−28.6555	−1.64894
$303$	16.8658	0.968915
$304$	−21.5538	−1.23620
$305$	4.32356	0.247566
$306$	9.81067	0.560839
$307$	−18.8323	−1.07482	−0.537408	−	0.843322i	$-0.680596\pi$
$307$	−18.8323	−1.07482	−0.537408	+	0.843322i	$0.680596\pi$
$308$	−2.97877	−0.169731
$309$	12.2124	0.694737
$310$	−7.97474	−0.452935
$311$	22.4201	1.27133	0.635663	−	0.771967i	$-0.280727\pi$
$311$	22.4201	1.27133	0.635663	+	0.771967i	$0.280727\pi$
$312$	10.9892	0.622141
$313$	8.43955	0.477032	0.238516	−	0.971139i	$-0.423339\pi$
$313$	8.43955	0.477032	0.238516	+	0.971139i	$0.423339\pi$
$314$	−18.5963	−1.04945
$315$	−0.333031	−0.0187642
$316$	−62.5679	−3.51972
$317$	−25.8927	−1.45428	−0.727139	−	0.686490i	$-0.759150\pi$
$317$	−25.8927	−1.45428	−0.727139	+	0.686490i	$0.759150\pi$
$318$	−13.4295	−0.753087
$319$	15.3458	0.859201
$320$	−2.76397	−0.154511
$321$	10.9893	0.613365
$322$	7.60455	0.423785
$323$	−9.78418	−0.544406
$324$	−5.52124	−0.306736
$325$	8.15051	0.452109
$326$	2.49038	0.137929
$327$	19.6955	1.08916
$328$	−44.9707	−2.48309
$329$	4.56368	0.251604
$330$	2.82738	0.155642
$331$	−3.20182	−0.175988	−0.0879939	−	0.996121i	$-0.528046\pi$
$331$	−3.20182	−0.175988	−0.0879939	+	0.996121i	$0.528046\pi$
$332$	−32.9067	−1.80599
$333$	−1.65215	−0.0905372
$334$	−8.20840	−0.449144
$335$	1.42112	0.0776442
$336$	2.33112	0.127173
$337$	−4.16300	−0.226773	−0.113387	−	0.993551i	$-0.536170\pi$
$337$	−4.16300	−0.226773	−0.113387	+	0.993551i	$0.536170\pi$
$338$	24.9551	1.35738
$339$	18.1167	0.983965
$340$	5.28342	0.286534
$341$	−11.2615	−0.609845
$342$	−16.8832	−0.912939
$343$	−5.29580	−0.285946
$344$	65.9201	3.55417
$345$	−4.89041	−0.263291
$346$	−42.8649	−2.30443
$347$	−21.1262	−1.13412	−0.567058	−	0.823678i	$-0.691918\pi$
$347$	−21.1262	−1.13412	−0.567058	+	0.823678i	$0.691918\pi$
$348$	−40.3687	−2.16399
$349$	−2.42028	−0.129555	−0.0647773	−	0.997900i	$-0.520634\pi$
$349$	−2.42028	−0.129555	−0.0647773	+	0.997900i	$0.520634\pi$
$350$	4.49516	0.240276
$351$	9.32266	0.497607
$352$	3.91981	0.208927
$353$	15.0442	0.800720	0.400360	−	0.916358i	$-0.368885\pi$
$353$	15.0442	0.800720	0.400360	+	0.916358i	$0.368885\pi$
$354$	−17.4369	−0.926763
$355$	−1.21186	−0.0643191
$356$	1.14016	0.0604283
$357$	1.05819	0.0560055
$358$	−15.3439	−0.810948
$359$	17.3747	0.917000	0.458500	−	0.888694i	$-0.348387\pi$
$359$	17.3747	0.917000	0.458500	+	0.888694i	$0.348387\pi$
$360$	4.77755	0.251799
$361$	−2.16239	−0.113810
$362$	−3.67232	−0.193013
$363$	−8.77799	−0.460725
$364$	−2.77255	−0.145321
$365$	7.47118	0.391059
$366$	−23.7056	−1.23911
$367$	24.4122	1.27431	0.637153	−	0.770737i	$-0.280112\pi$
$367$	24.4122	1.27431	0.637153	+	0.770737i	$0.280112\pi$
$368$	−41.9597	−2.18730
$369$	−13.5487	−0.705319
$370$	−1.31323	−0.0682717
$371$	1.77555	0.0921819
$372$	29.6245	1.53596
$373$	−5.36064	−0.277564	−0.138782	−	0.990323i	$-0.544319\pi$
$373$	−5.36064	−0.277564	−0.138782	+	0.990323i	$0.544319\pi$
$374$	11.0121	0.569424
$375$	−5.95182	−0.307351
$376$	−65.4689	−3.37630
$377$	14.2835	0.735636
$378$	5.14162	0.264456
$379$	21.8103	1.12032	0.560161	−	0.828384i	$-0.310739\pi$
$379$	21.8103	1.12032	0.560161	+	0.828384i	$0.310739\pi$
$380$	−9.09224	−0.466422
$381$	4.18056	0.214176
$382$	−1.65523	−0.0846887
$383$	−3.07916	−0.157337	−0.0786687	−	0.996901i	$-0.525067\pi$
$383$	−3.07916	−0.157337	−0.0786687	+	0.996901i	$0.525067\pi$
$384$	20.0625	1.02381
$385$	−0.373816	−0.0190514
$386$	−32.2654	−1.64227
$387$	19.8603	1.00956
$388$	−9.01774	−0.457807
$389$	−29.8535	−1.51363	−0.756815	−	0.653629i	$-0.773246\pi$
$389$	−29.8535	−1.51363	−0.756815	+	0.653629i	$0.773246\pi$
$390$	2.63165	0.133259
$391$	−19.0473	−0.963261
$392$	37.5852	1.89834
$393$	21.6498	1.09209
$394$	16.7677	0.844745
$395$	−7.85187	−0.395071
$396$	12.8744	0.646961
$397$	−13.2825	−0.666627	−0.333314	−	0.942816i	$-0.608167\pi$
$397$	−13.2825	−0.666627	−0.333314	+	0.942816i	$0.608167\pi$
$398$	−52.5866	−2.63593
$399$	−1.82105	−0.0911664
$400$	−24.8030	−1.24015
$401$	18.6793	0.932798	0.466399	−	0.884575i	$-0.345551\pi$
$401$	18.6793	0.932798	0.466399	+	0.884575i	$0.345551\pi$
$402$	−7.79188	−0.388623
$403$	−10.4819	−0.522141
$404$	61.0437	3.03704
$405$	−0.692880	−0.0344295
$406$	7.87760	0.390959
$407$	−1.85448	−0.0919231
$408$	−15.1805	−0.751545
$409$	−18.2499	−0.902399	−0.451199	−	0.892423i	$-0.649004\pi$
$409$	−18.2499	−0.902399	−0.451199	+	0.892423i	$0.649004\pi$
$410$	−10.7694	−0.531862
$411$	1.54757	0.0763361
$412$	44.2011	2.17763
$413$	2.30539	0.113441
$414$	−32.8672	−1.61534
$415$	−4.12957	−0.202713
$416$	3.64845	0.178880
$417$	0.344525	0.0168715
$418$	−18.9508	−0.926914
$419$	−15.2162	−0.743360	−0.371680	−	0.928361i	$-0.621218\pi$
$419$	−15.2162	−0.743360	−0.371680	+	0.928361i	$0.621218\pi$
$420$	0.983358	0.0479830
$421$	14.5016	0.706766	0.353383	−	0.935479i	$-0.385031\pi$
$421$	14.5016	0.706766	0.353383	+	0.935479i	$0.385031\pi$
$422$	−18.7880	−0.914588
$423$	−19.7244	−0.959034
$424$	−25.4714	−1.23700
$425$	−11.2591	−0.546147
$426$	6.64453	0.321929
$427$	3.13419	0.151674
$428$	39.7746	1.92258
$429$	3.71628	0.179423
$430$	15.7863	0.761281
$431$	−6.98628	−0.336517	−0.168259	−	0.985743i	$-0.553814\pi$
$431$	−6.98628	−0.336517	−0.168259	+	0.985743i	$0.553814\pi$
$432$	−28.3700	−1.36495
$433$	27.5557	1.32424	0.662120	−	0.749398i	$-0.269657\pi$
$433$	27.5557	1.32424	0.662120	+	0.749398i	$0.269657\pi$
$434$	−5.78096	−0.277495
$435$	−5.06600	−0.242896
$436$	71.2853	3.41395
$437$	32.7785	1.56801
$438$	−40.9637	−1.95732
$439$	−17.5332	−0.836813	−0.418406	−	0.908260i	$-0.637411\pi$
$439$	−17.5332	−0.836813	−0.418406	+	0.908260i	$0.637411\pi$
$440$	5.36263	0.255653
$441$	11.3236	0.539220
$442$	10.2498	0.487532
$443$	−21.4002	−1.01675	−0.508377	−	0.861135i	$-0.669754\pi$
$443$	−21.4002	−1.01675	−0.508377	+	0.861135i	$0.669754\pi$
$444$	4.87838	0.231518
$445$	0.143083	0.00678277
$446$	15.8103	0.748640
$447$	22.5774	1.06788
$448$	−2.00363	−0.0946627
$449$	5.77678	0.272623	0.136312	−	0.990666i	$-0.456475\pi$
$449$	5.77678	0.272623	0.136312	+	0.990666i	$0.456475\pi$
$450$	−19.4283	−0.915858
$451$	−15.2080	−0.716116
$452$	65.5712	3.08421
$453$	13.3587	0.627645
$454$	−38.0962	−1.78794
$455$	−0.347937	−0.0163116
$456$	26.1241	1.22337
$457$	−33.8700	−1.58437	−0.792186	−	0.610279i	$-0.791057\pi$
$457$	−33.8700	−1.58437	−0.792186	+	0.610279i	$0.791057\pi$
$458$	16.4680	0.769501
$459$	−12.8783	−0.601108
$460$	−17.7002	−0.825278
$461$	−30.1649	−1.40492	−0.702460	−	0.711723i	$-0.747915\pi$
$461$	−30.1649	−1.40492	−0.702460	+	0.711723i	$0.747915\pi$
$462$	2.04960	0.0953558
$463$	−26.3831	−1.22612	−0.613062	−	0.790035i	$-0.710063\pi$
$463$	−26.3831	−1.22612	−0.613062	+	0.790035i	$0.710063\pi$
$464$	−43.4663	−2.01787
$465$	3.71768	0.172403
$466$	52.6411	2.43855
$467$	−34.8749	−1.61382	−0.806910	−	0.590674i	$-0.798862\pi$
$467$	−34.8749	−1.61382	−0.806910	+	0.590674i	$0.798862\pi$
$468$	11.9831	0.553919
$469$	1.03019	0.0475696
$470$	−15.6782	−0.723182
$471$	8.66928	0.399460
$472$	−33.0723	−1.52227
$473$	22.2925	1.02501
$474$	43.0510	1.97740
$475$	19.3758	0.889023
$476$	3.83000	0.175548
$477$	−7.67400	−0.351368
$478$	65.5909	3.00006
$479$	1.42175	0.0649616	0.0324808	−	0.999472i	$-0.489659\pi$
$479$	1.42175	0.0649616	0.0324808	+	0.999472i	$0.489659\pi$
$480$	−1.29402	−0.0590636
$481$	−1.72610	−0.0787032
$482$	16.7901	0.764769
$483$	−3.54511	−0.161308
$484$	−31.7708	−1.44413
$485$	−1.13167	−0.0513864
$486$	−36.5527	−1.65806
$487$	1.20818	0.0547477	0.0273739	−	0.999625i	$-0.491286\pi$
$487$	1.20818	0.0547477	0.0273739	+	0.999625i	$0.491286\pi$
$488$	−44.9620	−2.03533
$489$	−1.16097	−0.0525009
$490$	9.00073	0.406612
$491$	24.3644	1.09955	0.549775	−	0.835313i	$-0.314713\pi$
$491$	24.3644	1.09955	0.549775	+	0.835313i	$0.314713\pi$
$492$	40.0060	1.80361
$493$	−19.7312	−0.888647
$494$	−17.6389	−0.793610
$495$	1.61565	0.0726180
$496$	31.8977	1.43225
$497$	−0.878492	−0.0394058
$498$	22.6421	1.01461
$499$	−26.3293	−1.17866	−0.589331	−	0.807892i	$-0.700609\pi$
$499$	−26.3293	−1.17866	−0.589331	+	0.807892i	$0.700609\pi$
$500$	−21.5419	−0.963381
$501$	3.82661	0.170960
$502$	34.2341	1.52794
$503$	6.55554	0.292297	0.146149	−	0.989263i	$-0.453312\pi$
$503$	6.55554	0.292297	0.146149	+	0.989263i	$0.453312\pi$
$504$	3.46329	0.154267
$505$	7.66058	0.340892
$506$	−36.8923	−1.64006
$507$	−11.6336	−0.516667
$508$	15.1310	0.671330
$509$	−10.2966	−0.456387	−0.228193	−	0.973616i	$-0.573282\pi$
$509$	−10.2966	−0.456387	−0.228193	+	0.973616i	$0.573282\pi$
$510$	−3.63535	−0.160976
$511$	5.41593	0.239587
$512$	46.5069	2.05533
$513$	22.1623	0.978489
$514$	50.8658	2.24360
$515$	5.54696	0.244428
$516$	−58.6426	−2.58160
$517$	−22.1400	−0.973715
$518$	−0.951975	−0.0418274
$519$	19.9828	0.877149
$520$	4.99139	0.218887
$521$	−25.8540	−1.13268	−0.566342	−	0.824171i	$-0.691642\pi$
$521$	−25.8540	−1.13268	−0.566342	+	0.824171i	$0.691642\pi$
$522$	−34.0473	−1.49021
$523$	−34.9202	−1.52695	−0.763477	−	0.645834i	$-0.776510\pi$
$523$	−34.9202	−1.52695	−0.763477	+	0.645834i	$0.776510\pi$
$524$	78.3589	3.42312
$525$	−2.09556	−0.0914579
$526$	−0.397422	−0.0173284
$527$	14.4797	0.630745
$528$	−11.3091	−0.492164
$529$	40.8112	1.77440
$530$	−6.09978	−0.264957
$531$	−9.96398	−0.432400
$532$	−6.59105	−0.285758
$533$	−14.1552	−0.613128
$534$	−0.784508	−0.0339490
$535$	4.99145	0.215799
$536$	−14.7787	−0.638342
$537$	7.15303	0.308676
$538$	−11.9580	−0.515544
$539$	12.7104	0.547474
$540$	−11.9676	−0.515001
$541$	14.6798	0.631136	0.315568	−	0.948903i	$-0.397805\pi$
$541$	14.6798	0.631136	0.315568	+	0.948903i	$0.397805\pi$
$542$	33.2675	1.42896
$543$	1.71197	0.0734678
$544$	−5.03997	−0.216087
$545$	8.94584	0.383198
$546$	1.90771	0.0816423
$547$	−10.2835	−0.439689	−0.219844	−	0.975535i	$-0.570555\pi$
$547$	−10.2835	−0.439689	−0.219844	+	0.975535i	$0.570555\pi$
$548$	5.60124	0.239273
$549$	−13.5461	−0.578133
$550$	−21.8076	−0.929877
$551$	33.9554	1.44655
$552$	50.8569	2.16461
$553$	−5.69190	−0.242044
$554$	32.6876	1.38876
$555$	0.612205	0.0259867
$556$	1.24696	0.0528831
$557$	28.7547	1.21837	0.609187	−	0.793026i	$-0.291496\pi$
$557$	28.7547	1.21837	0.609187	+	0.793026i	$0.291496\pi$
$558$	24.9856	1.05772
$559$	20.7493	0.877600
$560$	1.05882	0.0447431
$561$	−5.13366	−0.216743
$562$	−72.1804	−3.04475
$563$	20.4251	0.860815	0.430407	−	0.902635i	$-0.358370\pi$
$563$	20.4251	0.860815	0.430407	+	0.902635i	$0.358370\pi$
$564$	58.2413	2.45240
$565$	8.22877	0.346187
$566$	52.6268	2.21207
$567$	−0.502276	−0.0210936
$568$	12.6025	0.528791
$569$	−11.8251	−0.495734	−0.247867	−	0.968794i	$-0.579730\pi$
$569$	−11.8251	−0.495734	−0.247867	+	0.968794i	$0.579730\pi$
$570$	6.25609	0.262039
$571$	46.0808	1.92842	0.964211	−	0.265135i	$-0.0854165\pi$
$571$	46.0808	1.92842	0.964211	+	0.265135i	$0.0854165\pi$
$572$	13.4506	0.562398
$573$	0.771637	0.0322356
$574$	−7.80683	−0.325851
$575$	37.7197	1.57302
$576$	8.65978	0.360824
$577$	41.4296	1.72474	0.862369	−	0.506280i	$-0.168980\pi$
$577$	41.4296	1.72474	0.862369	+	0.506280i	$0.168980\pi$
$578$	28.1774	1.17203
$579$	15.0416	0.625106
$580$	−18.3358	−0.761352
$581$	−2.99357	−0.124194
$582$	6.20483	0.257198
$583$	−8.61379	−0.356747
$584$	−77.6950	−3.21504
$585$	1.50380	0.0621745
$586$	−56.5999	−2.33812
$587$	7.18959	0.296746	0.148373	−	0.988931i	$-0.452596\pi$
$587$	7.18959	0.296746	0.148373	+	0.988931i	$0.452596\pi$
$588$	−33.4358	−1.37887
$589$	−24.9181	−1.02673
$590$	−7.92000	−0.326061
$591$	−7.81681	−0.321541
$592$	5.25272	0.215885
$593$	28.0165	1.15050	0.575251	−	0.817977i	$-0.304904\pi$
$593$	28.0165	1.15050	0.575251	+	0.817977i	$0.304904\pi$
$594$	−24.9438	−1.02345
$595$	0.480640	0.0197043
$596$	81.7162	3.34723
$597$	24.5149	1.00333
$598$	−34.3383	−1.40420
$599$	8.58619	0.350822	0.175411	−	0.984495i	$-0.443875\pi$
$599$	8.58619	0.350822	0.175411	+	0.984495i	$0.443875\pi$
$600$	30.0622	1.22728
$601$	2.88509	0.117685	0.0588427	−	0.998267i	$-0.481259\pi$
$601$	2.88509	0.117685	0.0588427	+	0.998267i	$0.481259\pi$
$602$	11.4436	0.466407
$603$	−4.45251	−0.181320
$604$	48.3500	1.96733
$605$	−3.98704	−0.162096
$606$	−42.0022	−1.70622
$607$	−16.1984	−0.657475	−0.328737	−	0.944421i	$-0.606623\pi$
$607$	−16.1984	−0.657475	−0.328737	+	0.944421i	$0.606623\pi$
$608$	8.67329	0.351748
$609$	−3.67240	−0.148813
$610$	−10.7673	−0.435955
$611$	−20.6073	−0.833680
$612$	−16.5534	−0.669133
$613$	−7.34954	−0.296845	−0.148423	−	0.988924i	$-0.547420\pi$
$613$	−7.34954	−0.296845	−0.148423	+	0.988924i	$0.547420\pi$
$614$	46.8996	1.89271
$615$	5.02050	0.202446
$616$	3.88742	0.156629
$617$	30.3270	1.22092	0.610460	−	0.792047i	$-0.290984\pi$
$617$	30.3270	1.22092	0.610460	+	0.792047i	$0.290984\pi$
$618$	−30.4134	−1.22341
$619$	−6.10297	−0.245299	−0.122649	−	0.992450i	$-0.539139\pi$
$619$	−6.10297	−0.245299	−0.122649	+	0.992450i	$0.539139\pi$
$620$	13.4557	0.540393
$621$	43.1442	1.73132
$622$	−55.8345	−2.23876
$623$	0.103722	0.00415553
$624$	−10.5262	−0.421384
$625$	20.9063	0.836252
$626$	−21.0177	−0.840035
$627$	8.83452	0.352817
$628$	31.3774	1.25209
$629$	2.38443	0.0950734
$630$	0.829374	0.0330431
$631$	−16.4731	−0.655783	−0.327892	−	0.944715i	$-0.606338\pi$
$631$	−16.4731	−0.655783	−0.327892	+	0.944715i	$0.606338\pi$
$632$	81.6540	3.24802
$633$	8.75865	0.348125
$634$	64.4826	2.56093
$635$	1.89884	0.0753533
$636$	22.6594	0.898503
$637$	11.8305	0.468740
$638$	−38.2169	−1.51302
$639$	3.79688	0.150202
$640$	9.11254	0.360205
$641$	18.3684	0.725507	0.362753	−	0.931885i	$-0.381837\pi$
$641$	18.3684	0.725507	0.362753	+	0.931885i	$0.381837\pi$
$642$	−27.3676	−1.08011
$643$	−19.0027	−0.749395	−0.374698	−	0.927147i	$-0.622253\pi$
$643$	−19.0027	−0.749395	−0.374698	+	0.927147i	$0.622253\pi$
$644$	−12.8311	−0.505615
$645$	−7.35927	−0.289771
$646$	24.3663	0.958680
$647$	−25.2411	−0.992332	−0.496166	−	0.868228i	$-0.665259\pi$
$647$	−25.2411	−0.992332	−0.496166	+	0.868228i	$0.665259\pi$
$648$	7.20547	0.283058
$649$	−11.1842	−0.439019
$650$	−20.2979	−0.796147
$651$	2.69498	0.105625
$652$	−4.20199	−0.164563
$653$	24.6929	0.966309	0.483155	−	0.875535i	$-0.339491\pi$
$653$	24.6929	0.966309	0.483155	+	0.875535i	$0.339491\pi$
$654$	−49.0492	−1.91797
$655$	9.83354	0.384228
$656$	43.0759	1.68183
$657$	−23.4079	−0.913228
$658$	−11.3653	−0.443065
$659$	−23.4544	−0.913654	−0.456827	−	0.889556i	$-0.651014\pi$
$659$	−23.4544	−0.913654	−0.456827	+	0.889556i	$0.651014\pi$
$660$	−4.77061	−0.185696
$661$	−2.38787	−0.0928773	−0.0464387	−	0.998921i	$-0.514787\pi$
$661$	−2.38787	−0.0928773	−0.0464387	+	0.998921i	$0.514787\pi$
$662$	7.97374	0.309908
$663$	−4.77826	−0.185572
$664$	42.9447	1.66658
$665$	−0.827135	−0.0320749
$666$	4.11448	0.159433
$667$	66.1023	2.55949
$668$	13.8499	0.535870
$669$	−7.37048	−0.284959
$670$	−3.53913	−0.136729
$671$	−15.2050	−0.586983
$672$	−0.938047	−0.0361859
$673$	4.79088	0.184675	0.0923374	−	0.995728i	$-0.470566\pi$
$673$	4.79088	0.184675	0.0923374	+	0.995728i	$0.470566\pi$
$674$	10.3674	0.399339
$675$	25.5032	0.981618
$676$	−42.1064	−1.61948
$677$	13.3736	0.513991	0.256995	−	0.966413i	$-0.417268\pi$
$677$	13.3736	0.513991	0.256995	+	0.966413i	$0.417268\pi$
$678$	−45.1175	−1.73273
$679$	−0.820357	−0.0314824
$680$	−6.89510	−0.264415
$681$	17.7598	0.680555
$682$	28.0454	1.07392
$683$	−12.3922	−0.474173	−0.237087	−	0.971489i	$-0.576193\pi$
$683$	−12.3922	−0.474173	−0.237087	+	0.971489i	$0.576193\pi$
$684$	28.4868	1.08922
$685$	0.702920	0.0268572
$686$	13.1885	0.503541
$687$	−7.67711	−0.292900
$688$	−63.1425	−2.40729
$689$	−8.01747	−0.305441
$690$	12.1790	0.463646
$691$	−28.6195	−1.08874	−0.544369	−	0.838846i	$-0.683231\pi$
$691$	−28.6195	−1.08874	−0.544369	+	0.838846i	$0.683231\pi$
$692$	72.3254	2.74940
$693$	1.17120	0.0444902
$694$	52.6123	1.99714
$695$	0.156486	0.00593585
$696$	52.6829	1.99694
$697$	19.5539	0.740657
$698$	6.02741	0.228141
$699$	−24.5403	−0.928201
$700$	−7.58463	−0.286672
$701$	16.1120	0.608543	0.304271	−	0.952585i	$-0.401587\pi$
$701$	16.1120	0.608543	0.304271	+	0.952585i	$0.401587\pi$
$702$	−23.2169	−0.876267
$703$	−4.10337	−0.154761
$704$	9.72030	0.366348
$705$	7.30890	0.275269
$706$	−37.4657	−1.41004
$707$	5.55323	0.208851
$708$	29.4211	1.10571
$709$	4.55813	0.171184	0.0855921	−	0.996330i	$-0.472722\pi$
$709$	4.55813	0.171184	0.0855921	+	0.996330i	$0.472722\pi$
$710$	3.01800	0.113264
$711$	24.6006	0.922596
$712$	−1.48796	−0.0557636
$713$	−48.5091	−1.81668
$714$	−2.63530	−0.0986237
$715$	1.68796	0.0631262
$716$	25.8895	0.967536
$717$	−30.5773	−1.14193
$718$	−43.2695	−1.61480
$719$	15.0367	0.560776	0.280388	−	0.959887i	$-0.409537\pi$
$719$	15.0367	0.560776	0.280388	+	0.959887i	$0.409537\pi$
$720$	−4.57625	−0.170547
$721$	4.02104	0.149751
$722$	5.38517	0.200415
$723$	−7.82725	−0.291099
$724$	6.19627	0.230283
$725$	39.0740	1.45117
$726$	21.8605	0.811320
$727$	−33.7709	−1.25250	−0.626248	−	0.779624i	$-0.715410\pi$
$727$	−33.7709	−1.25250	−0.626248	+	0.779624i	$0.715410\pi$
$728$	3.61830	0.134103
$729$	20.9821	0.777114
$730$	−18.6061	−0.688641
$731$	−28.6630	−1.06014
$732$	39.9982	1.47838
$733$	−6.11213	−0.225757	−0.112878	−	0.993609i	$-0.536007\pi$
$733$	−6.11213	−0.225757	−0.112878	+	0.993609i	$0.536007\pi$
$734$	−60.7956	−2.24401
$735$	−4.19598	−0.154771
$736$	16.8846	0.622376
$737$	−4.99778	−0.184096
$738$	33.7415	1.24204
$739$	43.9543	1.61688	0.808442	−	0.588576i	$-0.200311\pi$
$739$	43.9543	1.61688	0.808442	+	0.588576i	$0.200311\pi$
$740$	2.21580	0.0814545
$741$	8.22292	0.302077
$742$	−4.42179	−0.162329
$743$	30.9766	1.13642	0.568211	−	0.822883i	$-0.307636\pi$
$743$	30.9766	1.13642	0.568211	+	0.822883i	$0.307636\pi$
$744$	−38.6613	−1.41739
$745$	10.2549	0.375709
$746$	13.3500	0.488779
$747$	12.9383	0.473389
$748$	−18.5806	−0.679375
$749$	3.61835	0.132212
$750$	14.8223	0.541233
$751$	−8.36341	−0.305185	−0.152592	−	0.988289i	$-0.548762\pi$
$751$	−8.36341	−0.305185	−0.152592	+	0.988289i	$0.548762\pi$
$752$	62.7104	2.28681
$753$	−15.9593	−0.581590
$754$	−35.5712	−1.29543
$755$	6.06762	0.220823
$756$	−8.67539	−0.315521
$757$	−46.8245	−1.70186	−0.850932	−	0.525275i	$-0.823962\pi$
$757$	−46.8245	−1.70186	−0.850932	+	0.525275i	$0.823962\pi$
$758$	−54.3160	−1.97285
$759$	17.1985	0.624267
$760$	11.8658	0.430417
$761$	−0.567049	−0.0205555	−0.0102778	−	0.999947i	$-0.503272\pi$
$761$	−0.567049	−0.0205555	−0.0102778	+	0.999947i	$0.503272\pi$
$762$	−10.4112	−0.377157
$763$	6.48493	0.234770
$764$	2.79284	0.101042
$765$	−2.07735	−0.0751067
$766$	7.66826	0.277066
$767$	−10.4100	−0.375882
$768$	−37.7927	−1.36373
$769$	14.0738	0.507514	0.253757	−	0.967268i	$-0.418334\pi$
$769$	14.0738	0.507514	0.253757	+	0.967268i	$0.418334\pi$
$770$	0.930943	0.0335489
$771$	−23.7127	−0.853993
$772$	54.4410	1.95938
$773$	−39.0565	−1.40477	−0.702383	−	0.711799i	$-0.747881\pi$
$773$	−39.0565	−1.40477	−0.702383	+	0.711799i	$0.747881\pi$
$774$	−49.4598	−1.77779
$775$	−28.6744	−1.03002
$776$	11.7686	0.422467
$777$	0.443794	0.0159210
$778$	74.3464	2.66545
$779$	−33.6504	−1.20565
$780$	−4.44035	−0.158990
$781$	4.26187	0.152502
$782$	47.4349	1.69627
$783$	44.6934	1.59721
$784$	−36.0015	−1.28577
$785$	3.93766	0.140541
$786$	−53.9163	−1.92313
$787$	17.2668	0.615496	0.307748	−	0.951468i	$-0.400425\pi$
$787$	17.2668	0.615496	0.307748	+	0.951468i	$0.400425\pi$
$788$	−28.2920	−1.00786
$789$	0.185271	0.00659583
$790$	19.5541	0.695705
$791$	5.96511	0.212095
$792$	−16.8016	−0.597019
$793$	−14.1524	−0.502566
$794$	33.0783	1.17391
$795$	2.84361	0.100852
$796$	88.7288	3.14491
$797$	24.7435	0.876460	0.438230	−	0.898863i	$-0.355606\pi$
$797$	24.7435	0.876460	0.438230	+	0.898863i	$0.355606\pi$
$798$	4.53510	0.160541
$799$	28.4668	1.00708
$800$	9.98075	0.352873
$801$	−0.448291	−0.0158396
$802$	−46.5184	−1.64262
$803$	−26.2745	−0.927208
$804$	13.1471	0.463664
$805$	−1.61022	−0.0567527
$806$	26.1039	0.919471
$807$	5.57459	0.196235
$808$	−79.6647	−2.80260
$809$	−0.193945	−0.00681874	−0.00340937	−	0.999994i	$-0.501085\pi$
$809$	−0.193945	−0.00681874	−0.00340937	+	0.999994i	$0.501085\pi$
$810$	1.72553	0.0606291
$811$	8.16616	0.286753	0.143376	−	0.989668i	$-0.454204\pi$
$811$	8.16616	0.286753	0.143376	+	0.989668i	$0.454204\pi$
$812$	−13.2918	−0.466450
$813$	−15.5087	−0.543914
$814$	4.61835	0.161873
$815$	−0.527322	−0.0184713
$816$	14.5408	0.509031
$817$	49.3262	1.72571
$818$	45.4491	1.58909
$819$	1.09012	0.0380919
$820$	18.1711	0.634561
$821$	37.7657	1.31803	0.659015	−	0.752129i	$-0.270973\pi$
$821$	37.7657	1.31803	0.659015	+	0.752129i	$0.270973\pi$
$822$	−3.85404	−0.134425
$823$	53.2010	1.85447	0.927235	−	0.374481i	$-0.122179\pi$
$823$	53.2010	1.85447	0.927235	+	0.374481i	$0.122179\pi$
$824$	−57.6845	−2.00953
$825$	10.1663	0.353945
$826$	−5.74129	−0.199765
$827$	9.22360	0.320736	0.160368	−	0.987057i	$-0.448732\pi$
$827$	9.22360	0.320736	0.160368	+	0.987057i	$0.448732\pi$
$828$	55.4565	1.92724
$829$	−49.1078	−1.70558	−0.852791	−	0.522252i	$-0.825092\pi$
$829$	−49.1078	−1.70558	−0.852791	+	0.522252i	$0.825092\pi$
$830$	10.2842	0.356970
$831$	−15.2384	−0.528614
$832$	9.04738	0.313661
$833$	−16.3426	−0.566237
$834$	−0.857997	−0.0297100
$835$	1.73808	0.0601487
$836$	31.9755	1.10589
$837$	−32.7982	−1.13367
$838$	37.8941	1.30903
$839$	53.6156	1.85101	0.925507	−	0.378730i	$-0.123639\pi$
$839$	53.6156	1.85101	0.925507	+	0.378730i	$0.123639\pi$
$840$	−1.28333	−0.0442790
$841$	39.4758	1.36123
$842$	−36.1145	−1.24459
$843$	33.6492	1.15894
$844$	31.7008	1.09119
$845$	−5.28408	−0.181778
$846$	49.1213	1.68882
$847$	−2.89024	−0.0993098
$848$	24.3981	0.837836
$849$	−24.5337	−0.841993
$850$	28.0394	0.961745
$851$	−7.98819	−0.273832
$852$	−11.2112	−0.384091
$853$	−3.07633	−0.105332	−0.0526658	−	0.998612i	$-0.516772\pi$
$853$	−3.07633	−0.105332	−0.0526658	+	0.998612i	$0.516772\pi$
$854$	−7.80531	−0.267092
$855$	3.57491	0.122259
$856$	−51.9076	−1.77416
$857$	−39.1544	−1.33749	−0.668744	−	0.743493i	$-0.733168\pi$
$857$	−39.1544	−1.33749	−0.668744	+	0.743493i	$0.733168\pi$
$858$	−9.25493	−0.315958
$859$	−5.58857	−0.190679	−0.0953397	−	0.995445i	$-0.530394\pi$
$859$	−5.58857	−0.190679	−0.0953397	+	0.995445i	$0.530394\pi$
$860$	−26.6360	−0.908279
$861$	3.63941	0.124031
$862$	17.3985	0.592595
$863$	−20.9392	−0.712778	−0.356389	−	0.934338i	$-0.615992\pi$
$863$	−20.9392	−0.712778	−0.356389	+	0.934338i	$0.615992\pi$
$864$	11.4161	0.388384
$865$	9.07637	0.308606
$866$	−68.6240	−2.33194
$867$	−13.1358	−0.446115
$868$	9.75415	0.331078
$869$	27.6133	0.936718
$870$	12.6163	0.427732
$871$	−4.65180	−0.157620
$872$	−93.0305	−3.15041
$873$	3.54562	0.120001
$874$	−81.6308	−2.76120
$875$	−1.95970	−0.0662498
$876$	69.1176	2.33527
$877$	−2.86019	−0.0965818	−0.0482909	−	0.998833i	$-0.515377\pi$
$877$	−2.86019	−0.0965818	−0.0482909	+	0.998833i	$0.515377\pi$
$878$	43.6642	1.47360
$879$	26.3858	0.889973
$880$	−5.13668	−0.173157
$881$	30.9053	1.04123	0.520613	−	0.853793i	$-0.325704\pi$
$881$	30.9053	1.04123	0.520613	+	0.853793i	$0.325704\pi$
$882$	−28.2001	−0.949547
$883$	43.0026	1.44715	0.723576	−	0.690245i	$-0.242497\pi$
$883$	43.0026	1.44715	0.723576	+	0.690245i	$0.242497\pi$
$884$	−17.2943	−0.581671
$885$	3.69216	0.124111
$886$	53.2946	1.79047
$887$	56.3165	1.89092	0.945461	−	0.325735i	$-0.105612\pi$
$887$	56.3165	1.89092	0.945461	+	0.325735i	$0.105612\pi$
$888$	−6.36651	−0.213646
$889$	1.37649	0.0461660
$890$	−0.356330	−0.0119442
$891$	2.43671	0.0816329
$892$	−26.6765	−0.893197
$893$	−48.9886	−1.63934
$894$	−56.2264	−1.88049
$895$	3.24896	0.108601
$896$	6.60577	0.220683
$897$	16.0079	0.534488
$898$	−14.3864	−0.480080
$899$	−50.2509	−1.67596
$900$	32.7811	1.09270
$901$	11.0753	0.368973
$902$	37.8736	1.26105
$903$	−5.33481	−0.177531
$904$	−85.5734	−2.84613
$905$	0.777592	0.0258480
$906$	−33.2681	−1.10526
$907$	10.1758	0.337882	0.168941	−	0.985626i	$-0.445965\pi$
$907$	10.1758	0.337882	0.168941	+	0.985626i	$0.445965\pi$
$908$	64.2792	2.13318
$909$	−24.0013	−0.796073
$910$	0.866496	0.0287241
$911$	39.4004	1.30539	0.652696	−	0.757620i	$-0.273638\pi$
$911$	39.4004	1.30539	0.652696	+	0.757620i	$0.273638\pi$
$912$	−25.0234	−0.828606
$913$	14.5228	0.480635
$914$	84.3492	2.79002
$915$	5.01952	0.165940
$916$	−27.7863	−0.918086
$917$	7.12843	0.235401
$918$	32.0719	1.05853
$919$	57.7869	1.90621	0.953107	−	0.302632i	$-0.0978653\pi$
$919$	57.7869	1.90621	0.953107	+	0.302632i	$0.0978653\pi$
$920$	23.0996	0.761571
$921$	−21.8637	−0.720435
$922$	75.1221	2.47401
$923$	3.96683	0.130570
$924$	−3.45826	−0.113768
$925$	−4.72193	−0.155256
$926$	65.7038	2.15916
$927$	−17.3791	−0.570805
$928$	17.4909	0.574167
$929$	−26.1487	−0.857912	−0.428956	−	0.903325i	$-0.641118\pi$
$929$	−26.1487	−0.857912	−0.428956	+	0.903325i	$0.641118\pi$
$930$	−9.25843	−0.303596
$931$	28.1240	0.921726
$932$	−88.8207	−2.90942
$933$	26.0290	0.852152
$934$	86.8518	2.84188
$935$	−2.33175	−0.0762564
$936$	−15.6385	−0.511159
$937$	−2.46277	−0.0804552	−0.0402276	−	0.999191i	$-0.512808\pi$
$937$	−2.46277	−0.0804552	−0.0402276	+	0.999191i	$0.512808\pi$
$938$	−2.56555	−0.0837683
$939$	9.79806	0.319748
$940$	26.4537	0.862823
$941$	−0.551830	−0.0179891	−0.00899456	−	0.999960i	$-0.502863\pi$
$941$	−0.551830	−0.0179891	−0.00899456	+	0.999960i	$0.502863\pi$
$942$	−21.5898	−0.703434
$943$	−65.5085	−2.13325
$944$	31.6788	1.03106
$945$	−1.08871	−0.0354156
$946$	−55.5169	−1.80501
$947$	−26.4629	−0.859928	−0.429964	−	0.902846i	$-0.641474\pi$
$947$	−26.4629	−0.859928	−0.429964	+	0.902846i	$0.641474\pi$
$948$	−72.6395	−2.35922
$949$	−24.4556	−0.793862
$950$	−48.2531	−1.56554
$951$	−30.0606	−0.974782
$952$	−4.99832	−0.161997
$953$	24.6498	0.798486	0.399243	−	0.916845i	$-0.369273\pi$
$953$	24.6498	0.798486	0.399243	+	0.916845i	$0.369273\pi$
$954$	19.1112	0.618747
$955$	0.350484	0.0113414
$956$	−110.671	−3.57935
$957$	17.8160	0.575911
$958$	−3.54071	−0.114395
$959$	0.509553	0.0164543
$960$	−3.20889	−0.103566
$961$	5.87651	0.189565
$962$	4.29863	0.138594
$963$	−15.6387	−0.503949
$964$	−28.3298	−0.912441
$965$	6.83200	0.219930
$966$	8.82866	0.284057
$967$	−12.5487	−0.403538	−0.201769	−	0.979433i	$-0.564669\pi$
$967$	−12.5487	−0.403538	−0.201769	+	0.979433i	$0.564669\pi$
$968$	41.4624	1.33265
$969$	−11.3591	−0.364908
$970$	2.81828	0.0904896
$971$	12.4662	0.400058	0.200029	−	0.979790i	$-0.435896\pi$
$971$	12.4662	0.400058	0.200029	+	0.979790i	$0.435896\pi$
$972$	61.6749	1.97822
$973$	0.113438	0.00363666
$974$	−3.00882	−0.0964088
$975$	9.46250	0.303042
$976$	43.0675	1.37856
$977$	−29.9320	−0.957609	−0.478805	−	0.877921i	$-0.658930\pi$
$977$	−29.9320	−0.957609	−0.478805	+	0.877921i	$0.658930\pi$
$978$	2.89126	0.0924522
$979$	−0.503191	−0.0160820
$980$	−15.1868	−0.485125
$981$	−28.0281	−0.894870
$982$	−60.6766	−1.93627
$983$	18.9008	0.602841	0.301420	−	0.953491i	$-0.402539\pi$
$983$	18.9008	0.602841	0.301420	+	0.953491i	$0.402539\pi$
$984$	−52.2097	−1.66438
$985$	−3.55046	−0.113127
$986$	49.1381	1.56487
$987$	5.29829	0.168647
$988$	29.7619	0.946851
$989$	96.0254	3.05343
$990$	−4.02358	−0.127878
$991$	20.4711	0.650287	0.325143	−	0.945665i	$-0.394587\pi$
$991$	20.4711	0.650287	0.325143	+	0.945665i	$0.394587\pi$
$992$	−12.8357	−0.407533
$993$	−3.71721	−0.117962
$994$	2.18778	0.0693921
$995$	11.1349	0.353000
$996$	−38.2037	−1.21053
$997$	−34.1043	−1.08009	−0.540047	−	0.841635i	$-0.681594\pi$
$997$	−34.1043	−1.08009	−0.540047	+	0.841635i	$0.681594\pi$
$998$	65.5700	2.07558
$999$	−5.40101	−0.170880

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.e.1.9	✓	134

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.e.1.9	✓	134	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)

\(f(q)\)	\(=\)	\(q-2.49038 q^{2} +1.16097 q^{3} +4.20199 q^{4} +0.527322 q^{5} -2.89126 q^{6} +0.382261 q^{7} -5.48378 q^{8} -1.65215 q^{9} +O(q^{10})\)	\(q-2.49038 q^{2} +1.16097 q^{3} +4.20199 q^{4} +0.527322 q^{5} -2.89126 q^{6} +0.382261 q^{7} -5.48378 q^{8} -1.65215 q^{9} -1.31323 q^{10} -1.85448 q^{11} +4.87838 q^{12} -1.72610 q^{13} -0.951975 q^{14} +0.612205 q^{15} +5.25272 q^{16} +2.38443 q^{17} +4.11448 q^{18} -4.10337 q^{19} +2.21580 q^{20} +0.443794 q^{21} +4.61835 q^{22} -7.98819 q^{23} -6.36651 q^{24} -4.72193 q^{25} +4.29863 q^{26} -5.40101 q^{27} +1.60626 q^{28} -8.27501 q^{29} -1.52462 q^{30} +6.07260 q^{31} -2.11370 q^{32} -2.15299 q^{33} -5.93813 q^{34} +0.201575 q^{35} -6.94231 q^{36} +1.00000 q^{37} +10.2189 q^{38} -2.00395 q^{39} -2.89172 q^{40} +8.20067 q^{41} -1.10521 q^{42} -12.0209 q^{43} -7.79249 q^{44} -0.871215 q^{45} +19.8936 q^{46} +11.9386 q^{47} +6.09825 q^{48} -6.85388 q^{49} +11.7594 q^{50} +2.76825 q^{51} -7.25303 q^{52} +4.64486 q^{53} +13.4505 q^{54} -0.977908 q^{55} -2.09624 q^{56} -4.76388 q^{57} +20.6079 q^{58} +6.03092 q^{59} +2.57248 q^{60} +8.19908 q^{61} -15.1231 q^{62} -0.631552 q^{63} -5.24153 q^{64} -0.910209 q^{65} +5.36177 q^{66} +2.69498 q^{67} +10.0193 q^{68} -9.27405 q^{69} -0.501997 q^{70} -2.29815 q^{71} +9.06002 q^{72} +14.1681 q^{73} -2.49038 q^{74} -5.48202 q^{75} -17.2423 q^{76} -0.708895 q^{77} +4.99059 q^{78} -14.8901 q^{79} +2.76988 q^{80} -1.31396 q^{81} -20.4228 q^{82} -7.83122 q^{83} +1.86481 q^{84} +1.25736 q^{85} +29.9366 q^{86} -9.60704 q^{87} +10.1696 q^{88} +0.271338 q^{89} +2.16965 q^{90} -0.659819 q^{91} -33.5663 q^{92} +7.05011 q^{93} -29.7318 q^{94} -2.16380 q^{95} -2.45394 q^{96} -2.14607 q^{97} +17.0687 q^{98} +3.06387 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9}+O(q^{10}) \) 134 * q + 9 * q^2 + 7 * q^3 + 149 * q^4 + 22 * q^5 + 20 * q^6 + 11 * q^7 + 27 * q^8 + 181 * q^9	\( 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9} + 15 q^{10} + 20 q^{11} + 28 q^{12} + 11 q^{13} + 17 q^{14} - 13 q^{15} + 143 q^{16} + 76 q^{17} + 23 q^{18} + 15 q^{19} + 67 q^{20} + 63 q^{21} + 2 q^{22} + 22 q^{23} + 33 q^{24} + 160 q^{25} + 65 q^{26} + 31 q^{27} + 10 q^{28} + 73 q^{29} + 20 q^{30} + 10 q^{31} + 53 q^{32} + 72 q^{33} - 7 q^{34} + 52 q^{35} + 201 q^{36} + 134 q^{37} + 70 q^{38} + 6 q^{39} + 11 q^{40} + 182 q^{41} - 15 q^{42} + 12 q^{43} + 33 q^{44} + 29 q^{45} + 24 q^{46} + 80 q^{47} + 21 q^{48} + 229 q^{49} + 37 q^{50} + 57 q^{51} - 15 q^{52} + 75 q^{53} + 95 q^{54} - 9 q^{55} + 39 q^{56} + 19 q^{57} - 21 q^{58} + 91 q^{59} + 62 q^{60} + 58 q^{61} + 108 q^{62} + 9 q^{63} + 167 q^{64} + 76 q^{65} + 105 q^{66} - 17 q^{67} + 109 q^{68} + 48 q^{69} - 55 q^{70} + 56 q^{71} + 48 q^{72} + 54 q^{73} + 9 q^{74} + 28 q^{75} + 82 q^{76} + 156 q^{77} + 16 q^{78} - 2 q^{79} + 98 q^{80} + 270 q^{81} - 42 q^{82} + 130 q^{83} + 229 q^{84} + 22 q^{85} + 72 q^{86} + 22 q^{87} + 61 q^{88} + 157 q^{89} + 176 q^{90} + 31 q^{91} - 18 q^{92} + 36 q^{93} + 83 q^{94} + 98 q^{95} + 111 q^{96} + 35 q^{97} + 53 q^{98} + 55 q^{99}+O(q^{100}) \) 134 * q + 9 * q^2 + 7 * q^3 + 149 * q^4 + 22 * q^5 + 20 * q^6 + 11 * q^7 + 27 * q^8 + 181 * q^9 + 15 * q^10 + 20 * q^11 + 28 * q^12 + 11 * q^13 + 17 * q^14 - 13 * q^15 + 143 * q^16 + 76 * q^17 + 23 * q^18 + 15 * q^19 + 67 * q^20 + 63 * q^21 + 2 * q^22 + 22 * q^23 + 33 * q^24 + 160 * q^25 + 65 * q^26 + 31 * q^27 + 10 * q^28 + 73 * q^29 + 20 * q^30 + 10 * q^31 + 53 * q^32 + 72 * q^33 - 7 * q^34 + 52 * q^35 + 201 * q^36 + 134 * q^37 + 70 * q^38 + 6 * q^39 + 11 * q^40 + 182 * q^41 - 15 * q^42 + 12 * q^43 + 33 * q^44 + 29 * q^45 + 24 * q^46 + 80 * q^47 + 21 * q^48 + 229 * q^49 + 37 * q^50 + 57 * q^51 - 15 * q^52 + 75 * q^53 + 95 * q^54 - 9 * q^55 + 39 * q^56 + 19 * q^57 - 21 * q^58 + 91 * q^59 + 62 * q^60 + 58 * q^61 + 108 * q^62 + 9 * q^63 + 167 * q^64 + 76 * q^65 + 105 * q^66 - 17 * q^67 + 109 * q^68 + 48 * q^69 - 55 * q^70 + 56 * q^71 + 48 * q^72 + 54 * q^73 + 9 * q^74 + 28 * q^75 + 82 * q^76 + 156 * q^77 + 16 * q^78 - 2 * q^79 + 98 * q^80 + 270 * q^81 - 42 * q^82 + 130 * q^83 + 229 * q^84 + 22 * q^85 + 72 * q^86 + 22 * q^87 + 61 * q^88 + 157 * q^89 + 176 * q^90 + 31 * q^91 - 18 * q^92 + 36 * q^93 + 83 * q^94 + 98 * q^95 + 111 * q^96 + 35 * q^97 + 53 * q^98 + 55 * q^99

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