LMFDB - Embedded newform 6031.2.a.c.1.6

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			1.6
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)

$f(q)$	$=$	$q-2.64313 q^{2} +2.88413 q^{3} +4.98613 q^{4} -1.94351 q^{5} -7.62312 q^{6} -0.878417 q^{7} -7.89274 q^{8} +5.31819 q^{9} +O(q^{10})$	\(q-2.64313 q^{2} +2.88413 q^{3} +4.98613 q^{4} -1.94351 q^{5} -7.62312 q^{6} -0.878417 q^{7} -7.89274 q^{8} +5.31819 q^{9} +5.13695 q^{10} +6.38425 q^{11} +14.3806 q^{12} -2.53851 q^{13} +2.32177 q^{14} -5.60533 q^{15} +10.8893 q^{16} -4.24270 q^{17} -14.0567 q^{18} -6.93399 q^{19} -9.69060 q^{20} -2.53347 q^{21} -16.8744 q^{22} +2.83533 q^{23} -22.7637 q^{24} -1.22277 q^{25} +6.70960 q^{26} +6.68594 q^{27} -4.37990 q^{28} -7.67426 q^{29} +14.8156 q^{30} +8.96754 q^{31} -12.9963 q^{32} +18.4130 q^{33} +11.2140 q^{34} +1.70721 q^{35} +26.5172 q^{36} -1.00000 q^{37} +18.3274 q^{38} -7.32137 q^{39} +15.3396 q^{40} -8.31661 q^{41} +6.69628 q^{42} +8.71796 q^{43} +31.8327 q^{44} -10.3359 q^{45} -7.49415 q^{46} +13.4215 q^{47} +31.4060 q^{48} -6.22838 q^{49} +3.23195 q^{50} -12.2365 q^{51} -12.6573 q^{52} -2.05619 q^{53} -17.6718 q^{54} -12.4078 q^{55} +6.93312 q^{56} -19.9985 q^{57} +20.2841 q^{58} +3.88739 q^{59} -27.9489 q^{60} -2.88332 q^{61} -23.7024 q^{62} -4.67159 q^{63} +12.5723 q^{64} +4.93361 q^{65} -48.6679 q^{66} -2.11646 q^{67} -21.1547 q^{68} +8.17746 q^{69} -4.51238 q^{70} -9.15324 q^{71} -41.9751 q^{72} +6.65910 q^{73} +2.64313 q^{74} -3.52663 q^{75} -34.5738 q^{76} -5.60803 q^{77} +19.3513 q^{78} +2.72864 q^{79} -21.1634 q^{80} +3.32855 q^{81} +21.9819 q^{82} -16.1402 q^{83} -12.6322 q^{84} +8.24572 q^{85} -23.0427 q^{86} -22.1335 q^{87} -50.3892 q^{88} -7.30708 q^{89} +27.3192 q^{90} +2.22987 q^{91} +14.1373 q^{92} +25.8635 q^{93} -35.4747 q^{94} +13.4763 q^{95} -37.4829 q^{96} -1.80231 q^{97} +16.4624 q^{98} +33.9526 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.64313	−1.86897	−0.934487	−	0.355996i	$-0.884142\pi$
$2$	−2.64313	−1.86897	−0.934487	+	0.355996i	$0.884142\pi$
$3$	2.88413	1.66515	0.832576	−	0.553911i	$-0.186865\pi$
$3$	2.88413	1.66515	0.832576	+	0.553911i	$0.186865\pi$
$4$	4.98613	2.49307
$5$	−1.94351	−0.869164	−0.434582	−	0.900632i	$-0.643104\pi$
$5$	−1.94351	−0.869164	−0.434582	+	0.900632i	$0.643104\pi$
$6$	−7.62312	−3.11213
$7$	−0.878417	−0.332010	−0.166005	−	0.986125i	$-0.553087\pi$
$7$	−0.878417	−0.332010	−0.166005	+	0.986125i	$0.553087\pi$
$8$	−7.89274	−2.79050
$9$	5.31819	1.77273
$10$	5.13695	1.62445
$11$	6.38425	1.92492	0.962461	−	0.271419i	$-0.0874929\pi$
$11$	6.38425	1.92492	0.962461	+	0.271419i	$0.0874929\pi$
$12$	14.3806	4.15133
$13$	−2.53851	−0.704055	−0.352027	−	0.935990i	$-0.614508\pi$
$13$	−2.53851	−0.704055	−0.352027	+	0.935990i	$0.614508\pi$
$14$	2.32177	0.620519
$15$	−5.60533	−1.44729
$16$	10.8893	2.72232
$17$	−4.24270	−1.02901	−0.514503	−	0.857489i	$-0.672023\pi$
$17$	−4.24270	−1.02901	−0.514503	+	0.857489i	$0.672023\pi$
$18$	−14.0567	−3.31319
$19$	−6.93399	−1.59077	−0.795384	−	0.606106i	$-0.792731\pi$
$19$	−6.93399	−1.59077	−0.795384	+	0.606106i	$0.792731\pi$
$20$	−9.69060	−2.16688
$21$	−2.53347	−0.552848
$22$	−16.8744	−3.59763
$23$	2.83533	0.591208	0.295604	−	0.955311i	$-0.404479\pi$
$23$	2.83533	0.591208	0.295604	+	0.955311i	$0.404479\pi$
$24$	−22.7637	−4.64661
$25$	−1.22277	−0.244554
$26$	6.70960	1.31586
$27$	6.68594	1.28671
$28$	−4.37990	−0.827724
$29$	−7.67426	−1.42507	−0.712537	−	0.701635i	$-0.752454\pi$
$29$	−7.67426	−1.42507	−0.712537	+	0.701635i	$0.752454\pi$
$30$	14.8156	2.70495
$31$	8.96754	1.61062	0.805309	−	0.592855i	$-0.201999\pi$
$31$	8.96754	1.61062	0.805309	+	0.592855i	$0.201999\pi$
$32$	−12.9963	−2.29744
$33$	18.4130	3.20529
$34$	11.2140	1.92319
$35$	1.70721	0.288571
$36$	26.5172	4.41953
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	18.3274	2.97310
$39$	−7.32137	−1.17236
$40$	15.3396	2.42541
$41$	−8.31661	−1.29884	−0.649418	−	0.760432i	$-0.724987\pi$
$41$	−8.31661	−1.29884	−0.649418	+	0.760432i	$0.724987\pi$
$42$	6.69628	1.03326
$43$	8.71796	1.32948	0.664738	−	0.747076i	$-0.268543\pi$
$43$	8.71796	1.32948	0.664738	+	0.747076i	$0.268543\pi$
$44$	31.8327	4.79896
$45$	−10.3359	−1.54079
$46$	−7.49415	−1.10495
$47$	13.4215	1.95772	0.978862	−	0.204523i	$-0.0655643\pi$
$47$	13.4215	1.95772	0.978862	+	0.204523i	$0.0655643\pi$
$48$	31.4060	4.53307
$49$	−6.22838	−0.889769
$50$	3.23195	0.457066
$51$	−12.2365	−1.71345
$52$	−12.6573	−1.75526
$53$	−2.05619	−0.282439	−0.141220	−	0.989978i	$-0.545102\pi$
$53$	−2.05619	−0.282439	−0.141220	+	0.989978i	$0.545102\pi$
$54$	−17.6718	−2.40483
$55$	−12.4078	−1.67307
$56$	6.93312	0.926477
$57$	−19.9985	−2.64887
$58$	20.2841	2.66343
$59$	3.88739	0.506095	0.253047	−	0.967454i	$-0.418567\pi$
$59$	3.88739	0.506095	0.253047	+	0.967454i	$0.418567\pi$
$60$	−27.9489	−3.60819
$61$	−2.88332	−0.369171	−0.184586	−	0.982816i	$-0.559094\pi$
$61$	−2.88332	−0.369171	−0.184586	+	0.982816i	$0.559094\pi$
$62$	−23.7024	−3.01021
$63$	−4.67159	−0.588564
$64$	12.5723	1.57153
$65$	4.93361	0.611939
$66$	−48.6679	−5.99060
$67$	−2.11646	−0.258567	−0.129284	−	0.991608i	$-0.541268\pi$
$67$	−2.11646	−0.258567	−0.129284	+	0.991608i	$0.541268\pi$
$68$	−21.1547	−2.56538
$69$	8.17746	0.984450
$70$	−4.51238	−0.539333
$71$	−9.15324	−1.08629	−0.543145	−	0.839639i	$-0.682767\pi$
$71$	−9.15324	−1.08629	−0.543145	+	0.839639i	$0.682767\pi$
$72$	−41.9751	−4.94681
$73$	6.65910	0.779389	0.389694	−	0.920944i	$-0.372581\pi$
$73$	6.65910	0.779389	0.389694	+	0.920944i	$0.372581\pi$
$74$	2.64313	0.307258
$75$	−3.52663	−0.407220
$76$	−34.5738	−3.96589
$77$	−5.60803	−0.639094
$78$	19.3513	2.19111
$79$	2.72864	0.306996	0.153498	−	0.988149i	$-0.450946\pi$
$79$	2.72864	0.306996	0.153498	+	0.988149i	$0.450946\pi$
$80$	−21.1634	−2.36614
$81$	3.32855	0.369839
$82$	21.9819	2.42749
$83$	−16.1402	−1.77161	−0.885807	−	0.464054i	$-0.846394\pi$
$83$	−16.1402	−1.77161	−0.885807	+	0.464054i	$0.846394\pi$
$84$	−12.6322	−1.37829
$85$	8.24572	0.894374
$86$	−23.0427	−2.48476
$87$	−22.1335	−2.37296
$88$	−50.3892	−5.37151
$89$	−7.30708	−0.774549	−0.387275	−	0.921964i	$-0.626583\pi$
$89$	−7.30708	−0.774549	−0.387275	+	0.921964i	$0.626583\pi$
$90$	27.3192	2.87970
$91$	2.22987	0.233753
$92$	14.1373	1.47392
$93$	25.8635	2.68192
$94$	−35.4747	−3.65894
$95$	13.4763	1.38264
$96$	−37.4829	−3.82558
$97$	−1.80231	−0.182996	−0.0914982	−	0.995805i	$-0.529166\pi$
$97$	−1.80231	−0.182996	−0.0914982	+	0.995805i	$0.529166\pi$
$98$	16.4624	1.66296
$99$	33.9526	3.41237
$100$	−6.09691	−0.609691
$101$	−12.0078	−1.19483	−0.597413	−	0.801934i	$-0.703805\pi$
$101$	−12.0078	−1.19483	−0.597413	+	0.801934i	$0.703805\pi$
$102$	32.3426	3.20239
$103$	14.7029	1.44872	0.724358	−	0.689424i	$-0.242136\pi$
$103$	14.7029	1.44872	0.724358	+	0.689424i	$0.242136\pi$
$104$	20.0358	1.96467
$105$	4.92381	0.480515
$106$	5.43478	0.527872
$107$	−18.1797	−1.75750	−0.878750	−	0.477283i	$-0.841622\pi$
$107$	−18.1797	−1.75750	−0.878750	+	0.477283i	$0.841622\pi$
$108$	33.3370	3.20786
$109$	−0.465552	−0.0445918	−0.0222959	−	0.999751i	$-0.507098\pi$
$109$	−0.465552	−0.0445918	−0.0222959	+	0.999751i	$0.507098\pi$
$110$	32.7955	3.12693
$111$	−2.88413	−0.273749
$112$	−9.56531	−0.903837
$113$	−11.5110	−1.08287	−0.541434	−	0.840743i	$-0.682118\pi$
$113$	−11.5110	−1.08287	−0.541434	+	0.840743i	$0.682118\pi$
$114$	52.8587	4.95067
$115$	−5.51049	−0.513856
$116$	−38.2649	−3.55280
$117$	−13.5002	−1.24810
$118$	−10.2749	−0.945878
$119$	3.72686	0.341640
$120$	44.2414	4.03867
$121$	29.7586	2.70533
$122$	7.62098	0.689972
$123$	−23.9862	−2.16276
$124$	44.7134	4.01538
$125$	12.0940	1.08172
$126$	12.3476	1.10001
$127$	−17.6689	−1.56786	−0.783932	−	0.620846i	$-0.786789\pi$
$127$	−17.6689	−1.56786	−0.783932	+	0.620846i	$0.786789\pi$
$128$	−7.23761	−0.639720
$129$	25.1437	2.21378
$130$	−13.0402	−1.14370
$131$	−11.7415	−1.02586	−0.512929	−	0.858431i	$-0.671440\pi$
$131$	−11.7415	−1.02586	−0.512929	+	0.858431i	$0.671440\pi$
$132$	91.8096	7.99100
$133$	6.09094	0.528151
$134$	5.59409	0.483256
$135$	−12.9942	−1.11836
$136$	33.4865	2.87144
$137$	−6.72578	−0.574622	−0.287311	−	0.957837i	$-0.592761\pi$
$137$	−6.72578	−0.574622	−0.287311	+	0.957837i	$0.592761\pi$
$138$	−21.6141	−1.83991
$139$	12.3864	1.05060	0.525301	−	0.850917i	$-0.323953\pi$
$139$	12.3864	1.05060	0.525301	+	0.850917i	$0.323953\pi$
$140$	8.51238	0.719428
$141$	38.7092	3.25991
$142$	24.1932	2.03025
$143$	−16.2064	−1.35525
$144$	57.9111	4.82593
$145$	14.9150	1.23862
$146$	−17.6009	−1.45666
$147$	−17.9634	−1.48160
$148$	−4.98613	−0.409858
$149$	−16.0699	−1.31650	−0.658249	−	0.752800i	$-0.728703\pi$
$149$	−16.0699	−1.31650	−0.658249	+	0.752800i	$0.728703\pi$
$150$	9.32134	0.761084
$151$	−0.226081	−0.0183982	−0.00919912	−	0.999958i	$-0.502928\pi$
$151$	−0.226081	−0.0183982	−0.00919912	+	0.999958i	$0.502928\pi$
$152$	54.7282	4.43904
$153$	−22.5635	−1.82415
$154$	14.8227	1.19445
$155$	−17.4285	−1.39989
$156$	−36.5053	−2.92277
$157$	7.21537	0.575849	0.287925	−	0.957653i	$-0.407035\pi$
$157$	7.21537	0.575849	0.287925	+	0.957653i	$0.407035\pi$
$158$	−7.21215	−0.573768
$159$	−5.93031	−0.470304
$160$	25.2583	1.99685
$161$	−2.49060	−0.196287
$162$	−8.79779	−0.691220
$163$	−1.00000	−0.0783260
$163$	−1.00000	−0.0783260
$164$	−41.4677	−3.23808
$165$	−35.7858	−2.78592
$166$	42.6606	3.31110
$167$	1.53310	0.118635	0.0593176	−	0.998239i	$-0.481108\pi$
$167$	1.53310	0.118635	0.0593176	+	0.998239i	$0.481108\pi$
$168$	19.9960	1.54272
$169$	−6.55599	−0.504307
$170$	−21.7945	−1.67156
$171$	−36.8763	−2.82000
$172$	43.4689	3.31447
$173$	6.19822	0.471242	0.235621	−	0.971845i	$-0.424288\pi$
$173$	6.19822	0.471242	0.235621	+	0.971845i	$0.424288\pi$
$174$	58.5018	4.43501
$175$	1.07410	0.0811946
$176$	69.5197	5.24025
$177$	11.2117	0.842724
$178$	19.3136	1.44761
$179$	−13.6172	−1.01780	−0.508899	−	0.860826i	$-0.669947\pi$
$179$	−13.6172	−1.01780	−0.508899	+	0.860826i	$0.669947\pi$
$180$	−51.5364	−3.84130
$181$	13.0458	0.969685	0.484843	−	0.874601i	$-0.338877\pi$
$181$	13.0458	0.969685	0.484843	+	0.874601i	$0.338877\pi$
$182$	−5.89382	−0.436879
$183$	−8.31586	−0.614726
$184$	−22.3785	−1.64977
$185$	1.94351	0.142890
$186$	−68.3607	−5.01245
$187$	−27.0864	−1.98076
$188$	66.9213	4.88074
$189$	−5.87305	−0.427201
$190$	−35.6196	−2.58411
$191$	−19.5388	−1.41378	−0.706890	−	0.707323i	$-0.749903\pi$
$191$	−19.5388	−1.41378	−0.706890	+	0.707323i	$0.749903\pi$
$192$	36.2600	2.61684
$193$	11.7310	0.844414	0.422207	−	0.906499i	$-0.361256\pi$
$193$	11.7310	0.844414	0.422207	+	0.906499i	$0.361256\pi$
$194$	4.76373	0.342016
$195$	14.2291	1.01897
$196$	−31.0556	−2.21825
$197$	10.1442	0.722743	0.361372	−	0.932422i	$-0.382309\pi$
$197$	10.1442	0.722743	0.361372	+	0.932422i	$0.382309\pi$
$198$	−89.7412	−6.37763
$199$	−24.6913	−1.75032	−0.875160	−	0.483833i	$-0.839244\pi$
$199$	−24.6913	−1.75032	−0.875160	+	0.483833i	$0.839244\pi$
$200$	9.65102	0.682430
$201$	−6.10415	−0.430554
$202$	31.7383	2.23310
$203$	6.74120	0.473139
$204$	−61.0127	−4.27174
$205$	16.1634	1.12890
$206$	−38.8616	−2.70761
$207$	15.0788	1.04805
$208$	−27.6425	−1.91666
$209$	−44.2683	−3.06210
$210$	−13.0143	−0.898070
$211$	−0.407134	−0.0280283	−0.0140141	−	0.999902i	$-0.504461\pi$
$211$	−0.407134	−0.0280283	−0.0140141	+	0.999902i	$0.504461\pi$
$212$	−10.2524	−0.704140
$213$	−26.3991	−1.80884
$214$	48.0513	3.28472
$215$	−16.9434	−1.15553
$216$	−52.7704	−3.59057
$217$	−7.87724	−0.534742
$218$	1.23051	0.0833409
$219$	19.2057	1.29780
$220$	−61.8672	−4.17108
$221$	10.7701	0.724476
$222$	7.62312	0.511630
$223$	1.40037	0.0937755	0.0468877	−	0.998900i	$-0.485070\pi$
$223$	1.40037	0.0937755	0.0468877	+	0.998900i	$0.485070\pi$
$224$	11.4161	0.762772
$225$	−6.50293	−0.433529
$226$	30.4252	2.02385
$227$	24.8039	1.64629	0.823146	−	0.567830i	$-0.192217\pi$
$227$	24.8039	1.64629	0.823146	+	0.567830i	$0.192217\pi$
$228$	−99.7153	−6.60381
$229$	10.1675	0.671887	0.335943	−	0.941882i	$-0.390945\pi$
$229$	10.1675	0.671887	0.335943	+	0.941882i	$0.390945\pi$
$230$	14.5649	0.960384
$231$	−16.1743	−1.06419
$232$	60.5709	3.97667
$233$	−17.5953	−1.15271	−0.576354	−	0.817200i	$-0.695525\pi$
$233$	−17.5953	−1.15271	−0.576354	+	0.817200i	$0.695525\pi$
$234$	35.6829	2.33266
$235$	−26.0848	−1.70158
$236$	19.3830	1.26173
$237$	7.86975	0.511195
$238$	−9.85057	−0.638517
$239$	−8.14763	−0.527027	−0.263513	−	0.964656i	$-0.584881\pi$
$239$	−8.14763	−0.527027	−0.263513	+	0.964656i	$0.584881\pi$
$240$	−61.0379	−3.93998
$241$	−2.44120	−0.157252	−0.0786259	−	0.996904i	$-0.525053\pi$
$241$	−2.44120	−0.157252	−0.0786259	+	0.996904i	$0.525053\pi$
$242$	−78.6558	−5.05619
$243$	−10.4579	−0.670873
$244$	−14.3766	−0.920368
$245$	12.1049	0.773355
$246$	63.3985	4.04214
$247$	17.6020	1.11999
$248$	−70.7785	−4.49444
$249$	−46.5503	−2.95001
$250$	−31.9660	−2.02171
$251$	−25.3986	−1.60315	−0.801574	−	0.597896i	$-0.796004\pi$
$251$	−25.3986	−1.60315	−0.801574	+	0.597896i	$0.796004\pi$
$252$	−23.2932	−1.46733
$253$	18.1015	1.13803
$254$	46.7013	2.93030
$255$	23.7817	1.48927
$256$	−6.01459	−0.375912
$257$	−1.34126	−0.0836657	−0.0418328	−	0.999125i	$-0.513320\pi$
$257$	−1.34126	−0.0836657	−0.0418328	+	0.999125i	$0.513320\pi$
$258$	−66.4581	−4.13750
$259$	0.878417	0.0545822
$260$	24.5996	1.52560
$261$	−40.8131	−2.52627
$262$	31.0343	1.91730
$263$	28.8410	1.77841	0.889206	−	0.457506i	$-0.151257\pi$
$263$	28.8410	1.77841	0.889206	+	0.457506i	$0.151257\pi$
$264$	−145.329	−8.94437
$265$	3.99622	0.245486
$266$	−16.0991	−0.987101
$267$	−21.0746	−1.28974
$268$	−10.5530	−0.644626
$269$	−29.0516	−1.77131	−0.885654	−	0.464346i	$-0.846290\pi$
$269$	−29.0516	−1.77131	−0.885654	+	0.464346i	$0.846290\pi$
$270$	34.3453	2.09019
$271$	14.8071	0.899465	0.449732	−	0.893163i	$-0.351519\pi$
$271$	14.8071	0.899465	0.449732	+	0.893163i	$0.351519\pi$
$272$	−46.1999	−2.80128
$273$	6.43122	0.389235
$274$	17.7771	1.07395
$275$	−7.80648	−0.470748
$276$	40.7739	2.45430
$277$	−14.7630	−0.887021	−0.443510	−	0.896269i	$-0.646267\pi$
$277$	−14.7630	−0.887021	−0.443510	+	0.896269i	$0.646267\pi$
$278$	−32.7389	−1.96355
$279$	47.6911	2.85519
$280$	−13.4746	−0.805260
$281$	20.7699	1.23903	0.619513	−	0.784986i	$-0.287330\pi$
$281$	20.7699	1.23903	0.619513	+	0.784986i	$0.287330\pi$
$282$	−102.314	−6.09268
$283$	25.0117	1.48679	0.743395	−	0.668853i	$-0.233214\pi$
$283$	25.0117	1.48679	0.743395	+	0.668853i	$0.233214\pi$
$284$	−45.6393	−2.70819
$285$	38.8673	2.30230
$286$	42.8357	2.53293
$287$	7.30545	0.431227
$288$	−69.1165	−4.07273
$289$	1.00048	0.0588520
$290$	−39.4222	−2.31495
$291$	−5.19808	−0.304717
$292$	33.2032	1.94307
$293$	2.61477	0.152756	0.0763782	−	0.997079i	$-0.475664\pi$
$293$	2.61477	0.152756	0.0763782	+	0.997079i	$0.475664\pi$
$294$	47.4797	2.76907
$295$	−7.55517	−0.439879
$296$	7.89274	0.458756
$297$	42.6847	2.47682
$298$	42.4749	2.46050
$299$	−7.19750	−0.416242
$300$	−17.5843	−1.01523
$301$	−7.65801	−0.441400
$302$	0.597562	0.0343858
$303$	−34.6322	−1.98957
$304$	−75.5061	−4.33057
$305$	5.60376	0.320870
$306$	59.6381	3.40929
$307$	−12.1624	−0.694146	−0.347073	−	0.937838i	$-0.612824\pi$
$307$	−12.1624	−0.694146	−0.347073	+	0.937838i	$0.612824\pi$
$308$	−27.9624	−1.59330
$309$	42.4049	2.41233
$310$	46.0658	2.61636
$311$	8.74910	0.496116	0.248058	−	0.968745i	$-0.420208\pi$
$311$	8.74910	0.496116	0.248058	+	0.968745i	$0.420208\pi$
$312$	57.7857	3.27147
$313$	−16.2085	−0.916156	−0.458078	−	0.888912i	$-0.651462\pi$
$313$	−16.2085	−0.916156	−0.458078	+	0.888912i	$0.651462\pi$
$314$	−19.0712	−1.07625
$315$	9.07927	0.511559
$316$	13.6054	0.765362
$317$	17.5914	0.988034	0.494017	−	0.869452i	$-0.335528\pi$
$317$	17.5914	0.988034	0.494017	+	0.869452i	$0.335528\pi$
$318$	15.6746	0.878987
$319$	−48.9943	−2.74316
$320$	−24.4343	−1.36592
$321$	−52.4326	−2.92650
$322$	6.58299	0.366856
$323$	29.4188	1.63691
$324$	16.5966	0.922033
$325$	3.10401	0.172180
$326$	2.64313	0.146389
$327$	−1.34271	−0.0742520
$328$	65.6408	3.62441
$329$	−11.7897	−0.649985
$330$	94.5865	5.20681
$331$	6.66919	0.366572	0.183286	−	0.983060i	$-0.441327\pi$
$331$	6.66919	0.366572	0.183286	+	0.983060i	$0.441327\pi$
$332$	−80.4771	−4.41675
$333$	−5.31819	−0.291435
$334$	−4.05219	−0.221726
$335$	4.11337	0.224737
$336$	−27.5876	−1.50503
$337$	15.2590	0.831212	0.415606	−	0.909545i	$-0.363569\pi$
$337$	15.2590	0.831212	0.415606	+	0.909545i	$0.363569\pi$
$338$	17.3283	0.942537
$339$	−33.1993	−1.80314
$340$	41.1143	2.22973
$341$	57.2510	3.10032
$342$	97.4688	5.27051
$343$	11.6200	0.627423
$344$	−68.8086	−3.70991
$345$	−15.8930	−0.855648
$346$	−16.3827	−0.880739
$347$	4.21977	0.226529	0.113265	−	0.993565i	$-0.463869\pi$
$347$	4.21977	0.226529	0.113265	+	0.993565i	$0.463869\pi$
$348$	−110.361	−5.91596
$349$	−29.6402	−1.58661	−0.793303	−	0.608827i	$-0.791640\pi$
$349$	−29.6402	−1.58661	−0.793303	+	0.608827i	$0.791640\pi$
$350$	−2.83900	−0.151751
$351$	−16.9723	−0.905915
$352$	−82.9713	−4.42239
$353$	3.90581	0.207885	0.103943	−	0.994583i	$-0.466854\pi$
$353$	3.90581	0.207885	0.103943	+	0.994583i	$0.466854\pi$
$354$	−29.6340	−1.57503
$355$	17.7894	0.944163
$356$	−36.4341	−1.93100
$357$	10.7487	0.568883
$358$	35.9920	1.90224
$359$	29.5976	1.56210	0.781052	−	0.624466i	$-0.214683\pi$
$359$	29.5976	1.56210	0.781052	+	0.624466i	$0.214683\pi$
$360$	81.5789	4.29959
$361$	29.0803	1.53054
$362$	−34.4817	−1.81232
$363$	85.8276	4.50478
$364$	11.1184	0.582763
$365$	−12.9420	−0.677417
$366$	21.9799	1.14891
$367$	−26.1796	−1.36656	−0.683282	−	0.730155i	$-0.739448\pi$
$367$	−26.1796	−1.36656	−0.683282	+	0.730155i	$0.739448\pi$
$368$	30.8747	1.60945
$369$	−44.2293	−2.30248
$370$	−5.13695	−0.267057
$371$	1.80619	0.0937728
$372$	128.959	6.68621
$373$	9.74456	0.504554	0.252277	−	0.967655i	$-0.418821\pi$
$373$	9.74456	0.504554	0.252277	+	0.967655i	$0.418821\pi$
$374$	71.5929	3.70198
$375$	34.8807	1.80123
$376$	−105.932	−5.46304
$377$	19.4811	1.00333
$378$	15.5232	0.798429
$379$	−11.7305	−0.602556	−0.301278	−	0.953536i	$-0.597413\pi$
$379$	−11.7305	−0.602556	−0.301278	+	0.953536i	$0.597413\pi$
$380$	67.1945	3.44701
$381$	−50.9594	−2.61073
$382$	51.6437	2.64232
$383$	10.0961	0.515886	0.257943	−	0.966160i	$-0.416955\pi$
$383$	10.0961	0.515886	0.257943	+	0.966160i	$0.416955\pi$
$384$	−20.8742	−1.06523
$385$	10.8993	0.555478
$386$	−31.0065	−1.57819
$387$	46.3638	2.35680
$388$	−8.98653	−0.456222
$389$	11.6593	0.591152	0.295576	−	0.955319i	$-0.404488\pi$
$389$	11.6593	0.591152	0.295576	+	0.955319i	$0.404488\pi$
$390$	−37.6095	−1.90443
$391$	−12.0295	−0.608356
$392$	49.1590	2.48290
$393$	−33.8639	−1.70821
$394$	−26.8124	−1.35079
$395$	−5.30314	−0.266830
$396$	169.292	8.50726
$397$	−21.9428	−1.10128	−0.550639	−	0.834743i	$-0.685616\pi$
$397$	−21.9428	−1.10128	−0.550639	+	0.834743i	$0.685616\pi$
$398$	65.2623	3.27131
$399$	17.5670	0.879452
$400$	−13.3151	−0.665755
$401$	−20.2421	−1.01084	−0.505421	−	0.862873i	$-0.668663\pi$
$401$	−20.2421	−1.01084	−0.505421	+	0.862873i	$0.668663\pi$
$402$	16.1341	0.804694
$403$	−22.7642	−1.13396
$404$	−59.8727	−2.97878
$405$	−6.46907	−0.321451
$406$	−17.8179	−0.884285
$407$	−6.38425	−0.316455
$408$	96.5793	4.78139
$409$	−32.3814	−1.60116	−0.800578	−	0.599229i	$-0.795474\pi$
$409$	−32.3814	−1.60116	−0.800578	+	0.599229i	$0.795474\pi$
$410$	−42.7220	−2.10989
$411$	−19.3980	−0.956833
$412$	73.3104	3.61174
$413$	−3.41475	−0.168029
$414$	−39.8553	−1.95878
$415$	31.3686	1.53982
$416$	32.9911	1.61752
$417$	35.7240	1.74941
$418$	117.007	5.72300
$419$	−18.3185	−0.894917	−0.447458	−	0.894305i	$-0.647671\pi$
$419$	−18.3185	−0.894917	−0.447458	+	0.894305i	$0.647671\pi$
$420$	24.5508	1.19796
$421$	15.2533	0.743400	0.371700	−	0.928353i	$-0.378775\pi$
$421$	15.2533	0.743400	0.371700	+	0.928353i	$0.378775\pi$
$422$	1.07611	0.0523841
$423$	71.3779	3.47051
$424$	16.2290	0.788148
$425$	5.18785	0.251648
$426$	69.7762	3.38067
$427$	2.53276	0.122569
$428$	−90.6465	−4.38156
$429$	−46.7414	−2.25670
$430$	44.7837	2.15966
$431$	−10.1055	−0.486766	−0.243383	−	0.969930i	$-0.578257\pi$
$431$	−10.1055	−0.486766	−0.243383	+	0.969930i	$0.578257\pi$
$432$	72.8050	3.50283
$433$	−3.97948	−0.191242	−0.0956208	−	0.995418i	$-0.530484\pi$
$433$	−3.97948	−0.191242	−0.0956208	+	0.995418i	$0.530484\pi$
$434$	20.8206	0.999419
$435$	43.0167	2.06249
$436$	−2.32130	−0.111170
$437$	−19.6602	−0.940474
$438$	−50.7631	−2.42556
$439$	−12.0025	−0.572850	−0.286425	−	0.958103i	$-0.592467\pi$
$439$	−12.0025	−0.572850	−0.286425	+	0.958103i	$0.592467\pi$
$440$	97.9318	4.66872
$441$	−33.1237	−1.57732
$442$	−28.4668	−1.35403
$443$	11.3542	0.539456	0.269728	−	0.962937i	$-0.413066\pi$
$443$	11.3542	0.539456	0.269728	+	0.962937i	$0.413066\pi$
$444$	−14.3806	−0.682475
$445$	14.2014	0.673210
$446$	−3.70135	−0.175264
$447$	−46.3477	−2.19217
$448$	−11.0437	−0.521765
$449$	4.01690	0.189569	0.0947846	−	0.995498i	$-0.469784\pi$
$449$	4.01690	0.189569	0.0947846	+	0.995498i	$0.469784\pi$
$450$	17.1881	0.810254
$451$	−53.0953	−2.50016
$452$	−57.3956	−2.69966
$453$	−0.652047	−0.0306358
$454$	−65.5599	−3.07688
$455$	−4.33376	−0.203170
$456$	157.843	7.39168
$457$	12.7013	0.594140	0.297070	−	0.954856i	$-0.403990\pi$
$457$	12.7013	0.594140	0.297070	+	0.954856i	$0.403990\pi$
$458$	−26.8740	−1.25574
$459$	−28.3664	−1.32403
$460$	−27.4761	−1.28108
$461$	2.87827	0.134054	0.0670271	−	0.997751i	$-0.478649\pi$
$461$	2.87827	0.134054	0.0670271	+	0.997751i	$0.478649\pi$
$462$	42.7507	1.98894
$463$	−6.63035	−0.308139	−0.154069	−	0.988060i	$-0.549238\pi$
$463$	−6.63035	−0.308139	−0.154069	+	0.988060i	$0.549238\pi$
$464$	−83.5670	−3.87950
$465$	−50.2660	−2.33103
$466$	46.5067	2.15438
$467$	−3.29391	−0.152424	−0.0762120	−	0.997092i	$-0.524283\pi$
$467$	−3.29391	−0.152424	−0.0762120	+	0.997092i	$0.524283\pi$
$468$	−67.3140	−3.11159
$469$	1.85914	0.0858470
$470$	68.9454	3.18021
$471$	20.8100	0.958876
$472$	−30.6821	−1.41226
$473$	55.6576	2.55914
$474$	−20.8008	−0.955410
$475$	8.47870	0.389029
$476$	18.5826	0.851733
$477$	−10.9352	−0.500689
$478$	21.5353	0.984999
$479$	−15.7935	−0.721624	−0.360812	−	0.932639i	$-0.617500\pi$
$479$	−15.7935	−0.721624	−0.360812	+	0.932639i	$0.617500\pi$
$480$	72.8483	3.32505
$481$	2.53851	0.115746
$482$	6.45242	0.293900
$483$	−7.18322	−0.326848
$484$	148.380	6.74456
$485$	3.50280	0.159054
$486$	27.6415	1.25384
$487$	9.94201	0.450516	0.225258	−	0.974299i	$-0.427678\pi$
$487$	9.94201	0.450516	0.225258	+	0.974299i	$0.427678\pi$
$488$	22.7573	1.03017
$489$	−2.88413	−0.130425
$490$	−31.9949	−1.44538
$491$	−5.97942	−0.269848	−0.134924	−	0.990856i	$-0.543079\pi$
$491$	−5.97942	−0.269848	−0.134924	+	0.990856i	$0.543079\pi$
$492$	−119.598	−5.39190
$493$	32.5596	1.46641
$494$	−46.5243	−2.09323
$495$	−65.9872	−2.96590
$496$	97.6499	4.38461
$497$	8.04036	0.360659
$498$	123.038	5.51349
$499$	−27.8565	−1.24703	−0.623514	−	0.781813i	$-0.714295\pi$
$499$	−27.8565	−1.24703	−0.623514	+	0.781813i	$0.714295\pi$
$500$	60.3024	2.69680
$501$	4.42167	0.197546
$502$	67.1319	2.99624
$503$	−15.7599	−0.702698	−0.351349	−	0.936245i	$-0.614277\pi$
$503$	−15.7599	−0.702698	−0.351349	+	0.936245i	$0.614277\pi$
$504$	36.8716	1.64239
$505$	23.3374	1.03850
$506$	−47.8445	−2.12695
$507$	−18.9083	−0.839748
$508$	−88.0997	−3.90879
$509$	4.27480	0.189477	0.0947385	−	0.995502i	$-0.469798\pi$
$509$	4.27480	0.189477	0.0947385	+	0.995502i	$0.469798\pi$
$510$	−62.8581	−2.78340
$511$	−5.84947	−0.258765
$512$	30.3726	1.34229
$513$	−46.3603	−2.04686
$514$	3.54513	0.156369
$515$	−28.5751	−1.25917
$516$	125.370	5.51910
$517$	85.6860	3.76847
$518$	−2.32177	−0.102013
$519$	17.8764	0.784689
$520$	−38.9397	−1.70762
$521$	−28.6922	−1.25703	−0.628514	−	0.777798i	$-0.716336\pi$
$521$	−28.6922	−1.25703	−0.628514	+	0.777798i	$0.716336\pi$
$522$	107.874	4.72153
$523$	−9.47028	−0.414107	−0.207053	−	0.978330i	$-0.566387\pi$
$523$	−9.47028	−0.414107	−0.207053	+	0.978330i	$0.566387\pi$
$524$	−58.5446	−2.55753
$525$	3.09785	0.135201
$526$	−76.2305	−3.32381
$527$	−38.0466	−1.65733
$528$	200.504	8.72580
$529$	−14.9609	−0.650474
$530$	−10.5625	−0.458807
$531$	20.6739	0.897169
$532$	30.3702	1.31672
$533$	21.1118	0.914451
$534$	55.7028	2.41049
$535$	35.3324	1.52755
$536$	16.7047	0.721533
$537$	−39.2737	−1.69479
$538$	76.7872	3.31053
$539$	−39.7635	−1.71274
$540$	−64.7908	−2.78815
$541$	41.4129	1.78048	0.890241	−	0.455490i	$-0.150536\pi$
$541$	41.4129	1.78048	0.890241	+	0.455490i	$0.150536\pi$
$542$	−39.1370	−1.68108
$543$	37.6257	1.61467
$544$	55.1392	2.36407
$545$	0.904804	0.0387575
$546$	−16.9985	−0.727470
$547$	1.66531	0.0712033	0.0356017	−	0.999366i	$-0.488665\pi$
$547$	1.66531	0.0712033	0.0356017	+	0.999366i	$0.488665\pi$
$548$	−33.5356	−1.43257
$549$	−15.3340	−0.654440
$550$	20.6335	0.879817
$551$	53.2132	2.26696
$552$	−64.5425	−2.74711
$553$	−2.39688	−0.101926
$554$	39.0204	1.65782
$555$	5.60533	0.237933
$556$	61.7603	2.61922
$557$	−12.2538	−0.519211	−0.259605	−	0.965715i	$-0.583593\pi$
$557$	−12.2538	−0.519211	−0.259605	+	0.965715i	$0.583593\pi$
$558$	−126.054	−5.33628
$559$	−22.1306	−0.936024
$560$	18.5903	0.785582
$561$	−78.1207	−3.29826
$562$	−54.8975	−2.31571
$563$	−27.7700	−1.17037	−0.585183	−	0.810901i	$-0.698977\pi$
$563$	−27.7700	−1.17037	−0.585183	+	0.810901i	$0.698977\pi$
$564$	193.009	8.12716
$565$	22.3718	0.941190
$566$	−66.1091	−2.77877
$567$	−2.92386	−0.122790
$568$	72.2441	3.03130
$569$	−17.6114	−0.738307	−0.369154	−	0.929368i	$-0.620352\pi$
$569$	−17.6114	−0.738307	−0.369154	+	0.929368i	$0.620352\pi$
$570$	−102.731	−4.30294
$571$	1.08528	0.0454175	0.0227088	−	0.999742i	$-0.492771\pi$
$571$	1.08528	0.0454175	0.0227088	+	0.999742i	$0.492771\pi$
$572$	−80.8075	−3.37873
$573$	−56.3525	−2.35416
$574$	−19.3092	−0.805952
$575$	−3.46697	−0.144582
$576$	66.8616	2.78590
$577$	−41.2545	−1.71745	−0.858723	−	0.512440i	$-0.828742\pi$
$577$	−41.2545	−1.71745	−0.858723	+	0.512440i	$0.828742\pi$
$578$	−2.64441	−0.109993
$579$	33.8336	1.40608
$580$	74.3681	3.08797
$581$	14.1778	0.588194
$582$	13.7392	0.569508
$583$	−13.1272	−0.543674
$584$	−52.5586	−2.17489
$585$	26.2378	1.08480
$586$	−6.91117	−0.285498
$587$	38.5771	1.59225	0.796124	−	0.605134i	$-0.206880\pi$
$587$	38.5771	1.59225	0.796124	+	0.605134i	$0.206880\pi$
$588$	−89.5682	−3.69373
$589$	−62.1809	−2.56212
$590$	19.9693	0.822123
$591$	29.2571	1.20348
$592$	−10.8893	−0.447546
$593$	−29.2990	−1.20317	−0.601583	−	0.798810i	$-0.705463\pi$
$593$	−29.2990	−1.20317	−0.601583	+	0.798810i	$0.705463\pi$
$594$	−112.821	−4.62911
$595$	−7.24318	−0.296941
$596$	−80.1267	−3.28212
$597$	−71.2129	−2.91455
$598$	19.0239	0.777947
$599$	14.1538	0.578308	0.289154	−	0.957283i	$-0.406626\pi$
$599$	14.1538	0.578308	0.289154	+	0.957283i	$0.406626\pi$
$600$	27.8348	1.13635
$601$	33.7007	1.37468	0.687340	−	0.726335i	$-0.258778\pi$
$601$	33.7007	1.37468	0.687340	+	0.726335i	$0.258778\pi$
$602$	20.2411	0.824966
$603$	−11.2558	−0.458370
$604$	−1.12727	−0.0458680
$605$	−57.8361	−2.35137
$606$	91.5373	3.71845
$607$	−11.2679	−0.457349	−0.228674	−	0.973503i	$-0.573439\pi$
$607$	−11.2679	−0.457349	−0.228674	+	0.973503i	$0.573439\pi$
$608$	90.1160	3.65468
$609$	19.4425	0.787849
$610$	−14.8115	−0.599698
$611$	−34.0705	−1.37834
$612$	−112.504	−4.54772
$613$	−32.8396	−1.32638	−0.663189	−	0.748452i	$-0.730798\pi$
$613$	−32.8396	−1.32638	−0.663189	+	0.748452i	$0.730798\pi$
$614$	32.1469	1.29734
$615$	46.6173	1.87979
$616$	44.2627	1.78340
$617$	−17.7111	−0.713022	−0.356511	−	0.934291i	$-0.616034\pi$
$617$	−17.7111	−0.713022	−0.356511	+	0.934291i	$0.616034\pi$
$618$	−112.082	−4.50859
$619$	−30.8656	−1.24059	−0.620297	−	0.784367i	$-0.712988\pi$
$619$	−30.8656	−1.24059	−0.620297	+	0.784367i	$0.712988\pi$
$620$	−86.9008	−3.49002
$621$	18.9569	0.760713
$622$	−23.1250	−0.927228
$623$	6.41867	0.257158
$624$	−79.7243	−3.19153
$625$	−17.3910	−0.695639
$626$	42.8410	1.71227
$627$	−127.675	−5.09887
$628$	35.9768	1.43563
$629$	4.24270	0.169167
$630$	−23.9977	−0.956091
$631$	−21.9063	−0.872077	−0.436039	−	0.899928i	$-0.643619\pi$
$631$	−21.9063	−0.872077	−0.436039	+	0.899928i	$0.643619\pi$
$632$	−21.5364	−0.856674
$633$	−1.17423	−0.0466713
$634$	−46.4965	−1.84661
$635$	34.3397	1.36273
$636$	−29.5693	−1.17250
$637$	15.8108	0.626446
$638$	129.498	5.12689
$639$	−48.6786	−1.92570
$640$	14.0664	0.556022
$641$	−15.9332	−0.629324	−0.314662	−	0.949204i	$-0.601891\pi$
$641$	−15.9332	−0.629324	−0.314662	+	0.949204i	$0.601891\pi$
$642$	138.586	5.46956
$643$	−20.9378	−0.825705	−0.412853	−	0.910798i	$-0.635468\pi$
$643$	−20.9378	−0.825705	−0.412853	+	0.910798i	$0.635468\pi$
$644$	−12.4185	−0.489357
$645$	−48.8670	−1.92414
$646$	−77.7578	−3.05934
$647$	−15.9930	−0.628748	−0.314374	−	0.949299i	$-0.601795\pi$
$647$	−15.9930	−0.628748	−0.314374	+	0.949299i	$0.601795\pi$
$648$	−26.2714	−1.03204
$649$	24.8180	0.974193
$650$	−8.20431	−0.321800
$651$	−22.7190	−0.890426
$652$	−4.98613	−0.195272
$653$	27.6542	1.08219	0.541097	−	0.840960i	$-0.318009\pi$
$653$	27.6542	1.08219	0.541097	+	0.840960i	$0.318009\pi$
$654$	3.54896	0.138775
$655$	22.8197	0.891639
$656$	−90.5617	−3.53584
$657$	35.4143	1.38165
$658$	31.1616	1.21480
$659$	36.0574	1.40460	0.702298	−	0.711883i	$-0.252157\pi$
$659$	36.0574	1.40460	0.702298	+	0.711883i	$0.252157\pi$
$660$	−178.433	−6.94548
$661$	40.7805	1.58618	0.793090	−	0.609105i	$-0.208471\pi$
$661$	40.7805	1.58618	0.793090	+	0.609105i	$0.208471\pi$
$662$	−17.6275	−0.685114
$663$	31.0624	1.20636
$664$	127.390	4.94370
$665$	−11.8378	−0.459050
$666$	14.0567	0.544684
$667$	−21.7591	−0.842514
$668$	7.64426	0.295765
$669$	4.03883	0.156150
$670$	−10.8722	−0.420028
$671$	−18.4078	−0.710626
$672$	32.9256	1.27013
$673$	14.6133	0.563301	0.281651	−	0.959517i	$-0.409118\pi$
$673$	14.6133	0.563301	0.281651	+	0.959517i	$0.409118\pi$
$674$	−40.3316	−1.55352
$675$	−8.17539	−0.314671
$676$	−32.6891	−1.25727
$677$	39.0554	1.50102	0.750510	−	0.660859i	$-0.229808\pi$
$677$	39.0554	1.50102	0.750510	+	0.660859i	$0.229808\pi$
$678$	87.7501	3.37002
$679$	1.58318	0.0607567
$680$	−65.0813	−2.49575
$681$	71.5376	2.74133
$682$	−151.322	−5.79441
$683$	−0.199633	−0.00763876	−0.00381938	−	0.999993i	$-0.501216\pi$
$683$	−0.199633	−0.00763876	−0.00381938	+	0.999993i	$0.501216\pi$
$684$	−183.870	−7.03045
$685$	13.0716	0.499441
$686$	−30.7133	−1.17264
$687$	29.3243	1.11879
$688$	94.9322	3.61926
$689$	5.21965	0.198853
$690$	42.0072	1.59919
$691$	−21.1516	−0.804646	−0.402323	−	0.915498i	$-0.631797\pi$
$691$	−21.1516	−0.804646	−0.402323	+	0.915498i	$0.631797\pi$
$692$	30.9051	1.17484
$693$	−29.8246	−1.13294
$694$	−11.1534	−0.423377
$695$	−24.0731	−0.913145
$696$	174.694	6.62177
$697$	35.2849	1.33651
$698$	78.3430	2.96533
$699$	−50.7472	−1.91943
$700$	5.35563	0.202424
$701$	31.3313	1.18337	0.591684	−	0.806170i	$-0.298463\pi$
$701$	31.3313	1.18337	0.591684	+	0.806170i	$0.298463\pi$
$702$	44.8600	1.69313
$703$	6.93399	0.261521
$704$	80.2644	3.02508
$705$	−75.2318	−2.83339
$706$	−10.3236	−0.388532
$707$	10.5479	0.396695
$708$	55.9031	2.10097
$709$	14.9038	0.559725	0.279862	−	0.960040i	$-0.409711\pi$
$709$	14.9038	0.559725	0.279862	+	0.960040i	$0.409711\pi$
$710$	−47.0197	−1.76462
$711$	14.5114	0.544221
$712$	57.6729	2.16138
$713$	25.4260	0.952210
$714$	−28.4103	−1.06323
$715$	31.4974	1.17793
$716$	−67.8972	−2.53744
$717$	−23.4988	−0.877579
$718$	−78.2304	−2.91953
$719$	−40.4532	−1.50865	−0.754324	−	0.656502i	$-0.772035\pi$
$719$	−40.4532	−1.50865	−0.754324	+	0.656502i	$0.772035\pi$
$720$	−112.551	−4.19452
$721$	−12.9152	−0.480989
$722$	−76.8629	−2.86054
$723$	−7.04074	−0.261848
$724$	65.0480	2.41749
$725$	9.38387	0.348508
$726$	−226.853	−8.41932
$727$	10.1678	0.377104	0.188552	−	0.982063i	$-0.439621\pi$
$727$	10.1678	0.377104	0.188552	+	0.982063i	$0.439621\pi$
$728$	−17.5997	−0.652290
$729$	−40.1475	−1.48694
$730$	34.2074	1.26607
$731$	−36.9877	−1.36804
$732$	−41.4640	−1.53255
$733$	−33.3033	−1.23008	−0.615042	−	0.788494i	$-0.710861\pi$
$733$	−33.3033	−1.23008	−0.615042	+	0.788494i	$0.710861\pi$
$734$	69.1961	2.55407
$735$	34.9121	1.28775
$736$	−36.8487	−1.35826
$737$	−13.5120	−0.497722
$738$	116.904	4.30328
$739$	33.3819	1.22797	0.613986	−	0.789317i	$-0.289565\pi$
$739$	33.3819	1.22797	0.613986	+	0.789317i	$0.289565\pi$
$740$	9.69060	0.356233
$741$	50.7663	1.86495
$742$	−4.77400	−0.175259
$743$	44.0580	1.61633	0.808166	−	0.588955i	$-0.200460\pi$
$743$	44.0580	1.61633	0.808166	+	0.588955i	$0.200460\pi$
$744$	−204.134	−7.48392
$745$	31.2320	1.14425
$746$	−25.7561	−0.943000
$747$	−85.8364	−3.14059
$748$	−135.057	−4.93816
$749$	15.9694	0.583508
$750$	−92.1941	−3.36645
$751$	−26.3217	−0.960492	−0.480246	−	0.877134i	$-0.659453\pi$
$751$	−26.3217	−0.960492	−0.480246	+	0.877134i	$0.659453\pi$
$752$	146.150	5.32954
$753$	−73.2529	−2.66948
$754$	−51.4912	−1.87520
$755$	0.439391	0.0159911
$756$	−29.2838	−1.06504
$757$	−14.9547	−0.543537	−0.271768	−	0.962363i	$-0.587608\pi$
$757$	−14.9547	−0.543537	−0.271768	+	0.962363i	$0.587608\pi$
$758$	31.0052	1.12616
$759$	52.2069	1.89499
$760$	−106.365	−3.85826
$761$	19.9167	0.721981	0.360990	−	0.932570i	$-0.382439\pi$
$761$	19.9167	0.721981	0.360990	+	0.932570i	$0.382439\pi$
$762$	134.692	4.87939
$763$	0.408948	0.0148049
$764$	−97.4233	−3.52465
$765$	43.8523	1.58548
$766$	−26.6853	−0.964178
$767$	−9.86815	−0.356318
$768$	−17.3468	−0.625950
$769$	45.8727	1.65421	0.827107	−	0.562045i	$-0.189985\pi$
$769$	45.8727	1.65421	0.827107	+	0.562045i	$0.189985\pi$
$770$	−28.8081	−1.03817
$771$	−3.86837	−0.139316
$772$	58.4922	2.10518
$773$	24.6909	0.888068	0.444034	−	0.896010i	$-0.353547\pi$
$773$	24.6909	0.888068	0.444034	+	0.896010i	$0.353547\pi$
$774$	−122.545	−4.40480
$775$	−10.9653	−0.393884
$776$	14.2251	0.510652
$777$	2.53347	0.0908876
$778$	−30.8171	−1.10485
$779$	57.6673	2.06615
$780$	70.9484	2.54036
$781$	−58.4365	−2.09102
$782$	31.7954	1.13700
$783$	−51.3097	−1.83366
$784$	−67.8225	−2.42223
$785$	−14.0231	−0.500507
$786$	89.5068	3.19260
$787$	36.4998	1.30108	0.650538	−	0.759474i	$-0.274543\pi$
$787$	36.4998	1.30108	0.650538	+	0.759474i	$0.274543\pi$
$788$	50.5803	1.80185
$789$	83.1811	2.96133
$790$	14.0169	0.498698
$791$	10.1115	0.359523
$792$	−267.979	−9.52222
$793$	7.31932	0.259917
$794$	57.9977	2.05826
$795$	11.5256	0.408771
$796$	−123.114	−4.36367
$797$	15.2811	0.541283	0.270641	−	0.962680i	$-0.412764\pi$
$797$	15.2811	0.541283	0.270641	+	0.962680i	$0.412764\pi$
$798$	−46.4320	−1.64367
$799$	−56.9433	−2.01451
$800$	15.8915	0.561848
$801$	−38.8604	−1.37307
$802$	53.5025	1.88924
$803$	42.5133	1.50026
$804$	−30.4361	−1.07340
$805$	4.84051	0.170606
$806$	60.1686	2.11935
$807$	−83.7885	−2.94950
$808$	94.7748	3.33417
$809$	−16.3163	−0.573650	−0.286825	−	0.957983i	$-0.592600\pi$
$809$	−16.3163	−0.573650	−0.286825	+	0.957983i	$0.592600\pi$
$810$	17.0986	0.600783
$811$	20.3221	0.713605	0.356802	−	0.934180i	$-0.383867\pi$
$811$	20.3221	0.713605	0.356802	+	0.934180i	$0.383867\pi$
$812$	33.6125	1.17957
$813$	42.7054	1.49775
$814$	16.8744	0.591447
$815$	1.94351	0.0680782
$816$	−133.246	−4.66455
$817$	−60.4503	−2.11489
$818$	85.5881	2.99252
$819$	11.8588	0.414382
$820$	80.5929	2.81443
$821$	−27.9179	−0.974340	−0.487170	−	0.873307i	$-0.661971\pi$
$821$	−27.9179	−0.974340	−0.487170	+	0.873307i	$0.661971\pi$
$822$	51.2714	1.78830
$823$	−1.36460	−0.0475669	−0.0237834	−	0.999717i	$-0.507571\pi$
$823$	−1.36460	−0.0475669	−0.0237834	+	0.999717i	$0.507571\pi$
$824$	−116.046	−4.04265
$825$	−22.5149	−0.783867
$826$	9.02562	0.314041
$827$	−20.7797	−0.722581	−0.361291	−	0.932453i	$-0.617664\pi$
$827$	−20.7797	−0.722581	−0.361291	+	0.932453i	$0.617664\pi$
$828$	75.1850	2.61286
$829$	−10.1981	−0.354196	−0.177098	−	0.984193i	$-0.556671\pi$
$829$	−10.1981	−0.354196	−0.177098	+	0.984193i	$0.556671\pi$
$830$	−82.9112	−2.87789
$831$	−42.5783	−1.47702
$832$	−31.9148	−1.10645
$833$	26.4251	0.915577
$834$	−94.4231	−3.26961
$835$	−2.97960	−0.103113
$836$	−220.728	−7.63403
$837$	59.9565	2.07240
$838$	48.4181	1.67258
$839$	4.70229	0.162341	0.0811705	−	0.996700i	$-0.474134\pi$
$839$	4.70229	0.162341	0.0811705	+	0.996700i	$0.474134\pi$
$840$	−38.8624	−1.34088
$841$	29.8942	1.03084
$842$	−40.3164	−1.38940
$843$	59.9029	2.06317
$844$	−2.03003	−0.0698764
$845$	12.7416	0.438325
$846$	−188.661	−6.48630
$847$	−26.1405	−0.898197
$848$	−22.3904	−0.768889
$849$	72.1368	2.47573
$850$	−13.7122	−0.470324
$851$	−2.83533	−0.0971939
$852$	−131.629	−4.50955
$853$	−3.58795	−0.122849	−0.0614245	−	0.998112i	$-0.519564\pi$
$853$	−3.58795	−0.122849	−0.0614245	+	0.998112i	$0.519564\pi$
$854$	−6.69440	−0.229078
$855$	71.6694	2.45104
$856$	143.488	4.90431
$857$	27.1131	0.926167	0.463083	−	0.886315i	$-0.346743\pi$
$857$	27.1131	0.926167	0.463083	+	0.886315i	$0.346743\pi$
$858$	123.544	4.21771
$859$	−13.7533	−0.469257	−0.234629	−	0.972085i	$-0.575387\pi$
$859$	−13.7533	−0.469257	−0.234629	+	0.972085i	$0.575387\pi$
$860$	−84.4823	−2.88082
$861$	21.0698	0.718058
$862$	26.7102	0.909753
$863$	−26.5277	−0.903014	−0.451507	−	0.892268i	$-0.649113\pi$
$863$	−26.5277	−0.903014	−0.451507	+	0.892268i	$0.649113\pi$
$864$	−86.8923	−2.95613
$865$	−12.0463	−0.409586
$866$	10.5183	0.357426
$867$	2.88552	0.0979975
$868$	−39.2770	−1.33315
$869$	17.4203	0.590944
$870$	−113.699	−3.85475
$871$	5.37266	0.182045
$872$	3.67448	0.124434
$873$	−9.58500	−0.324403
$874$	51.9644	1.75772
$875$	−10.6236	−0.359143
$876$	95.7622	3.23550
$877$	19.2935	0.651497	0.325748	−	0.945457i	$-0.394384\pi$
$877$	19.2935	0.651497	0.325748	+	0.945457i	$0.394384\pi$
$878$	31.7243	1.07064
$879$	7.54133	0.254363
$880$	−135.112	−4.55463
$881$	−47.5786	−1.60296	−0.801481	−	0.598020i	$-0.795954\pi$
$881$	−47.5786	−1.60296	−0.801481	+	0.598020i	$0.795954\pi$
$882$	87.5503	2.94797
$883$	18.2611	0.614535	0.307267	−	0.951623i	$-0.400585\pi$
$883$	18.2611	0.614535	0.307267	+	0.951623i	$0.400585\pi$
$884$	53.7012	1.80617
$885$	−21.7901	−0.732466
$886$	−30.0107	−1.00823
$887$	40.0420	1.34448	0.672239	−	0.740334i	$-0.265333\pi$
$887$	40.0420	1.34448	0.672239	+	0.740334i	$0.265333\pi$
$888$	22.7637	0.763898
$889$	15.5207	0.520547
$890$	−37.5361	−1.25821
$891$	21.2503	0.711912
$892$	6.98241	0.233789
$893$	−93.0644	−3.11428
$894$	122.503	4.09711
$895$	26.4651	0.884632
$896$	6.35764	0.212394
$897$	−20.7585	−0.693107
$898$	−10.6172	−0.354300
$899$	−68.8192	−2.29525
$900$	−32.4245	−1.08082
$901$	8.72379	0.290632
$902$	140.338	4.67273
$903$	−22.0867	−0.734998
$904$	90.8537	3.02175
$905$	−25.3546	−0.842815
$906$	1.72345	0.0572576
$907$	56.2759	1.86861	0.934305	−	0.356475i	$-0.116021\pi$
$907$	56.2759	1.86861	0.934305	+	0.356475i	$0.116021\pi$
$908$	123.676	4.10432
$909$	−63.8600	−2.11810
$910$	11.4547	0.379720
$911$	−32.8786	−1.08932	−0.544659	−	0.838658i	$-0.683341\pi$
$911$	−32.8786	−1.08932	−0.544659	+	0.838658i	$0.683341\pi$
$912$	−217.769	−7.21106
$913$	−103.043	−3.41022
$914$	−33.5711	−1.11043
$915$	16.1619	0.534297
$916$	50.6965	1.67506
$917$	10.3139	0.340596
$918$	74.9762	2.47458
$919$	−15.4881	−0.510904	−0.255452	−	0.966822i	$-0.582224\pi$
$919$	−15.4881	−0.510904	−0.255452	+	0.966822i	$0.582224\pi$
$920$	43.4929	1.43392
$921$	−35.0780	−1.15586
$922$	−7.60763	−0.250544
$923$	23.2355	0.764807
$924$	−80.6471	−2.65309
$925$	1.22277	0.0402045
$926$	17.5249	0.575903
$927$	78.1925	2.56818
$928$	99.7366	3.27401
$929$	31.0114	1.01745	0.508726	−	0.860929i	$-0.330117\pi$
$929$	31.0114	1.01745	0.508726	+	0.860929i	$0.330117\pi$
$930$	132.860	4.35664
$931$	43.1876	1.41542
$932$	−87.7327	−2.87378
$933$	25.2335	0.826108
$934$	8.70623	0.284877
$935$	52.6427	1.72160
$936$	106.554	3.48282
$937$	−23.9500	−0.782412	−0.391206	−	0.920303i	$-0.627942\pi$
$937$	−23.9500	−0.782412	−0.391206	+	0.920303i	$0.627942\pi$
$938$	−4.91394	−0.160446
$939$	−46.7472	−1.52554
$940$	−130.062	−4.24216
$941$	−9.63604	−0.314126	−0.157063	−	0.987589i	$-0.550203\pi$
$941$	−9.63604	−0.314126	−0.157063	+	0.987589i	$0.550203\pi$
$942$	−55.0037	−1.79212
$943$	−23.5803	−0.767882
$944$	42.3308	1.37775
$945$	11.4143	0.371308
$946$	−147.110	−4.78297
$947$	−30.2833	−0.984074	−0.492037	−	0.870574i	$-0.663748\pi$
$947$	−30.2833	−0.984074	−0.492037	+	0.870574i	$0.663748\pi$
$948$	39.2396	1.27444
$949$	−16.9042	−0.548732
$950$	−22.4103	−0.727086
$951$	50.7360	1.64523
$952$	−29.4151	−0.953349
$953$	−17.9895	−0.582738	−0.291369	−	0.956611i	$-0.594111\pi$
$953$	−17.9895	−0.582738	−0.291369	+	0.956611i	$0.594111\pi$
$954$	28.9032	0.935774
$955$	37.9739	1.22881
$956$	−40.6252	−1.31391
$957$	−141.306	−4.56777
$958$	41.7443	1.34870
$959$	5.90804	0.190780
$960$	−70.4716	−2.27446
$961$	49.4168	1.59409
$962$	−6.70960	−0.216326
$963$	−96.6831	−3.11557
$964$	−12.1722	−0.392039
$965$	−22.7993	−0.733934
$966$	18.9862	0.610870
$967$	−41.2037	−1.32502	−0.662512	−	0.749052i	$-0.730509\pi$
$967$	−41.2037	−1.32502	−0.662512	+	0.749052i	$0.730509\pi$
$968$	−234.877	−7.54923
$969$	84.8477	2.72570
$970$	−9.25834	−0.297268
$971$	40.1207	1.28753	0.643767	−	0.765222i	$-0.277371\pi$
$971$	40.1207	1.28753	0.643767	+	0.765222i	$0.277371\pi$
$972$	−52.1443	−1.67253
$973$	−10.8804	−0.348811
$974$	−26.2780	−0.842002
$975$	8.95237	0.286705
$976$	−31.3972	−1.00500
$977$	−33.6840	−1.07765	−0.538823	−	0.842419i	$-0.681131\pi$
$977$	−33.6840	−1.07765	−0.538823	+	0.842419i	$0.681131\pi$
$978$	7.62312	0.243761
$979$	−46.6502	−1.49095
$980$	60.3568	1.92803
$981$	−2.47589	−0.0790491
$982$	15.8044	0.504338
$983$	−6.94364	−0.221468	−0.110734	−	0.993850i	$-0.535320\pi$
$983$	−6.94364	−0.221468	−0.110734	+	0.993850i	$0.535320\pi$
$984$	189.316	6.03519
$985$	−19.7153	−0.628182
$986$	−86.0591	−2.74068
$987$	−34.0028	−1.08232
$988$	87.7658	2.79220
$989$	24.7183	0.785997
$990$	174.413	5.54320
$991$	40.7077	1.29312	0.646561	−	0.762862i	$-0.276206\pi$
$991$	40.7077	1.29312	0.646561	+	0.762862i	$0.276206\pi$
$992$	−116.544	−3.70029
$993$	19.2348	0.610398
$994$	−21.2517	−0.674063
$995$	47.9878	1.52132
$996$	−232.106	−7.35456
$997$	25.5862	0.810323	0.405162	−	0.914245i	$-0.367215\pi$
$997$	25.5862	0.810323	0.405162	+	0.914245i	$0.367215\pi$
$998$	73.6283	2.33066
$999$	−6.68594	−0.211534

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.c.1.6	✓	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.c.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-2.64313 q^{2} +2.88413 q^{3} +4.98613 q^{4} -1.94351 q^{5} -7.62312 q^{6} -0.878417 q^{7} -7.89274 q^{8} +5.31819 q^{9} +O(q^{10})\)	\(q-2.64313 q^{2} +2.88413 q^{3} +4.98613 q^{4} -1.94351 q^{5} -7.62312 q^{6} -0.878417 q^{7} -7.89274 q^{8} +5.31819 q^{9} +5.13695 q^{10} +6.38425 q^{11} +14.3806 q^{12} -2.53851 q^{13} +2.32177 q^{14} -5.60533 q^{15} +10.8893 q^{16} -4.24270 q^{17} -14.0567 q^{18} -6.93399 q^{19} -9.69060 q^{20} -2.53347 q^{21} -16.8744 q^{22} +2.83533 q^{23} -22.7637 q^{24} -1.22277 q^{25} +6.70960 q^{26} +6.68594 q^{27} -4.37990 q^{28} -7.67426 q^{29} +14.8156 q^{30} +8.96754 q^{31} -12.9963 q^{32} +18.4130 q^{33} +11.2140 q^{34} +1.70721 q^{35} +26.5172 q^{36} -1.00000 q^{37} +18.3274 q^{38} -7.32137 q^{39} +15.3396 q^{40} -8.31661 q^{41} +6.69628 q^{42} +8.71796 q^{43} +31.8327 q^{44} -10.3359 q^{45} -7.49415 q^{46} +13.4215 q^{47} +31.4060 q^{48} -6.22838 q^{49} +3.23195 q^{50} -12.2365 q^{51} -12.6573 q^{52} -2.05619 q^{53} -17.6718 q^{54} -12.4078 q^{55} +6.93312 q^{56} -19.9985 q^{57} +20.2841 q^{58} +3.88739 q^{59} -27.9489 q^{60} -2.88332 q^{61} -23.7024 q^{62} -4.67159 q^{63} +12.5723 q^{64} +4.93361 q^{65} -48.6679 q^{66} -2.11646 q^{67} -21.1547 q^{68} +8.17746 q^{69} -4.51238 q^{70} -9.15324 q^{71} -41.9751 q^{72} +6.65910 q^{73} +2.64313 q^{74} -3.52663 q^{75} -34.5738 q^{76} -5.60803 q^{77} +19.3513 q^{78} +2.72864 q^{79} -21.1634 q^{80} +3.32855 q^{81} +21.9819 q^{82} -16.1402 q^{83} -12.6322 q^{84} +8.24572 q^{85} -23.0427 q^{86} -22.1335 q^{87} -50.3892 q^{88} -7.30708 q^{89} +27.3192 q^{90} +2.22987 q^{91} +14.1373 q^{92} +25.8635 q^{93} -35.4747 q^{94} +13.4763 q^{95} -37.4829 q^{96} -1.80231 q^{97} +16.4624 q^{98} +33.9526 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9}+O(q^{10}) \) 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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