LMFDB - Embedded newform 6017.2.a.d.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6017,2,Mod(1,6017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6017, 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("6017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6017 = 11 \cdot 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6017.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:	$48.0459868962$
Analytic rank:	$1$
Dimension:	$107$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	6017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.10238 q^{2} +0.723159 q^{3} +2.42000 q^{4} -4.03444 q^{5} -1.52035 q^{6} +0.772372 q^{7} -0.882990 q^{8} -2.47704 q^{9} +O(q^{10})$	\(q-2.10238 q^{2} +0.723159 q^{3} +2.42000 q^{4} -4.03444 q^{5} -1.52035 q^{6} +0.772372 q^{7} -0.882990 q^{8} -2.47704 q^{9} +8.48191 q^{10} -1.00000 q^{11} +1.75004 q^{12} -1.58645 q^{13} -1.62382 q^{14} -2.91754 q^{15} -2.98361 q^{16} -0.833073 q^{17} +5.20768 q^{18} -1.34661 q^{19} -9.76332 q^{20} +0.558547 q^{21} +2.10238 q^{22} +6.32897 q^{23} -0.638542 q^{24} +11.2767 q^{25} +3.33533 q^{26} -3.96077 q^{27} +1.86914 q^{28} -0.842661 q^{29} +6.13377 q^{30} -7.51768 q^{31} +8.03866 q^{32} -0.723159 q^{33} +1.75143 q^{34} -3.11608 q^{35} -5.99443 q^{36} +0.207654 q^{37} +2.83108 q^{38} -1.14726 q^{39} +3.56236 q^{40} +5.22005 q^{41} -1.17428 q^{42} +8.52016 q^{43} -2.42000 q^{44} +9.99346 q^{45} -13.3059 q^{46} +6.53823 q^{47} -2.15763 q^{48} -6.40344 q^{49} -23.7078 q^{50} -0.602444 q^{51} -3.83921 q^{52} +12.4424 q^{53} +8.32704 q^{54} +4.03444 q^{55} -0.681996 q^{56} -0.973811 q^{57} +1.77159 q^{58} -2.81862 q^{59} -7.06043 q^{60} -9.89190 q^{61} +15.8050 q^{62} -1.91320 q^{63} -10.9331 q^{64} +6.40045 q^{65} +1.52035 q^{66} +2.22376 q^{67} -2.01603 q^{68} +4.57685 q^{69} +6.55119 q^{70} +11.7983 q^{71} +2.18720 q^{72} +6.14604 q^{73} -0.436566 q^{74} +8.15482 q^{75} -3.25878 q^{76} -0.772372 q^{77} +2.41197 q^{78} -12.0104 q^{79} +12.0372 q^{80} +4.56686 q^{81} -10.9745 q^{82} +10.0547 q^{83} +1.35168 q^{84} +3.36098 q^{85} -17.9126 q^{86} -0.609378 q^{87} +0.882990 q^{88} -6.20955 q^{89} -21.0100 q^{90} -1.22533 q^{91} +15.3161 q^{92} -5.43648 q^{93} -13.7458 q^{94} +5.43280 q^{95} +5.81323 q^{96} +3.70062 q^{97} +13.4625 q^{98} +2.47704 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 107 q - 3 q^{2} - 18 q^{3} + 91 q^{4} - 15 q^{5} - 54 q^{7} - 3 q^{8} + 95 q^{9}+O(q^{10}) $ 107 * q - 3 * q^2 - 18 * q^3 + 91 * q^4 - 15 * q^5 - 54 * q^7 - 3 * q^8 + 95 * q^9	\( 107 q - 3 q^{2} - 18 q^{3} + 91 q^{4} - 15 q^{5} - 54 q^{7} - 3 q^{8} + 95 q^{9} - 14 q^{10} - 107 q^{11} - 50 q^{12} - 24 q^{13} - 17 q^{14} - 47 q^{15} + 63 q^{16} + 25 q^{17} - 37 q^{18} - 55 q^{19} - 31 q^{20} + 15 q^{21} + 3 q^{22} - 38 q^{23} + 4 q^{24} + 62 q^{25} - 16 q^{26} - 57 q^{27} - 101 q^{28} + 27 q^{29} - 14 q^{30} - 112 q^{31} - 4 q^{32} + 18 q^{33} - 66 q^{34} + 8 q^{35} + 35 q^{36} - 60 q^{37} - 45 q^{38} - 58 q^{39} - 50 q^{40} - 14 q^{41} - 36 q^{42} - 78 q^{43} - 91 q^{44} - 68 q^{45} - 18 q^{46} - 109 q^{47} - 99 q^{48} + 61 q^{49} - 32 q^{50} - 10 q^{51} - 111 q^{52} - 30 q^{53} - 3 q^{54} + 15 q^{55} - 44 q^{56} + q^{57} - 98 q^{58} - 48 q^{59} - 119 q^{60} - 30 q^{61} + 32 q^{62} - 126 q^{63} + 3 q^{64} + 43 q^{65} - 77 q^{67} + 53 q^{68} - 51 q^{69} - 87 q^{70} - 40 q^{71} - 82 q^{72} - 83 q^{73} + 11 q^{74} - 69 q^{75} - 108 q^{76} + 54 q^{77} - 53 q^{78} - 66 q^{79} - 96 q^{80} + 51 q^{81} - 133 q^{82} - 32 q^{83} + 27 q^{84} - 66 q^{85} - 46 q^{86} - 136 q^{87} + 3 q^{88} - 56 q^{89} + 9 q^{90} - 86 q^{91} - 94 q^{92} - 33 q^{93} - 93 q^{94} - 25 q^{95} - 4 q^{96} - 109 q^{97} - 38 q^{98} - 95 q^{99}+O(q^{100}) \) 107 * q - 3 * q^2 - 18 * q^3 + 91 * q^4 - 15 * q^5 - 54 * q^7 - 3 * q^8 + 95 * q^9 - 14 * q^10 - 107 * q^11 - 50 * q^12 - 24 * q^13 - 17 * q^14 - 47 * q^15 + 63 * q^16 + 25 * q^17 - 37 * q^18 - 55 * q^19 - 31 * q^20 + 15 * q^21 + 3 * q^22 - 38 * q^23 + 4 * q^24 + 62 * q^25 - 16 * q^26 - 57 * q^27 - 101 * q^28 + 27 * q^29 - 14 * q^30 - 112 * q^31 - 4 * q^32 + 18 * q^33 - 66 * q^34 + 8 * q^35 + 35 * q^36 - 60 * q^37 - 45 * q^38 - 58 * q^39 - 50 * q^40 - 14 * q^41 - 36 * q^42 - 78 * q^43 - 91 * q^44 - 68 * q^45 - 18 * q^46 - 109 * q^47 - 99 * q^48 + 61 * q^49 - 32 * q^50 - 10 * q^51 - 111 * q^52 - 30 * q^53 - 3 * q^54 + 15 * q^55 - 44 * q^56 + q^57 - 98 * q^58 - 48 * q^59 - 119 * q^60 - 30 * q^61 + 32 * q^62 - 126 * q^63 + 3 * q^64 + 43 * q^65 - 77 * q^67 + 53 * q^68 - 51 * q^69 - 87 * q^70 - 40 * q^71 - 82 * q^72 - 83 * q^73 + 11 * q^74 - 69 * q^75 - 108 * q^76 + 54 * q^77 - 53 * q^78 - 66 * q^79 - 96 * q^80 + 51 * q^81 - 133 * q^82 - 32 * q^83 + 27 * q^84 - 66 * q^85 - 46 * q^86 - 136 * q^87 + 3 * q^88 - 56 * q^89 + 9 * q^90 - 86 * q^91 - 94 * q^92 - 33 * q^93 - 93 * q^94 - 25 * q^95 - 4 * q^96 - 109 * q^97 - 38 * q^98 - 95 * 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 $

$2$	−2.10238	−1.48661	−0.743303	−	0.668955i	$-0.766742\pi$
$2$	−2.10238	−1.48661	−0.743303	+	0.668955i	$0.766742\pi$
$3$	0.723159	0.417516	0.208758	−	0.977967i	$-0.433058\pi$
$3$	0.723159	0.417516	0.208758	+	0.977967i	$0.433058\pi$
$4$	2.42000	1.21000
$5$	−4.03444	−1.80425	−0.902127	−	0.431470i	$-0.857995\pi$
$5$	−4.03444	−1.80425	−0.902127	+	0.431470i	$0.857995\pi$
$6$	−1.52035	−0.620682
$7$	0.772372	0.291929	0.145965	−	0.989290i	$-0.453371\pi$
$7$	0.772372	0.291929	0.145965	+	0.989290i	$0.453371\pi$
$8$	−0.882990	−0.312184
$9$	−2.47704	−0.825680
$10$	8.48191	2.68222
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.75004	0.505193
$13$	−1.58645	−0.440003	−0.220002	−	0.975500i	$-0.570606\pi$
$13$	−1.58645	−0.440003	−0.220002	+	0.975500i	$0.570606\pi$
$14$	−1.62382	−0.433983
$15$	−2.91754	−0.753305
$16$	−2.98361	−0.745903
$17$	−0.833073	−0.202050	−0.101025	−	0.994884i	$-0.532212\pi$
$17$	−0.833073	−0.202050	−0.101025	+	0.994884i	$0.532212\pi$
$18$	5.20768	1.22746
$19$	−1.34661	−0.308933	−0.154466	−	0.987998i	$-0.549366\pi$
$19$	−1.34661	−0.308933	−0.154466	+	0.987998i	$0.549366\pi$
$20$	−9.76332	−2.18314
$21$	0.558547	0.121885
$22$	2.10238	0.448229
$23$	6.32897	1.31968	0.659841	−	0.751405i	$-0.270624\pi$
$23$	6.32897	1.31968	0.659841	+	0.751405i	$0.270624\pi$
$24$	−0.638542	−0.130342
$25$	11.2767	2.25533
$26$	3.33533	0.654112
$27$	−3.96077	−0.762251
$28$	1.86914	0.353233
$29$	−0.842661	−0.156478	−0.0782391	−	0.996935i	$-0.524930\pi$
$29$	−0.842661	−0.156478	−0.0782391	+	0.996935i	$0.524930\pi$
$30$	6.13377	1.11987
$31$	−7.51768	−1.35021	−0.675107	−	0.737719i	$-0.735903\pi$
$31$	−7.51768	−1.35021	−0.675107	+	0.737719i	$0.735903\pi$
$32$	8.03866	1.42105
$33$	−0.723159	−0.125886
$34$	1.75143	0.300368
$35$	−3.11608	−0.526714
$36$	−5.99443	−0.999071
$37$	0.207654	0.0341380	0.0170690	−	0.999854i	$-0.494566\pi$
$37$	0.207654	0.0341380	0.0170690	+	0.999854i	$0.494566\pi$
$38$	2.83108	0.459262
$39$	−1.14726	−0.183708
$40$	3.56236	0.563259
$41$	5.22005	0.815235	0.407618	−	0.913153i	$-0.366360\pi$
$41$	5.22005	0.815235	0.407618	+	0.913153i	$0.366360\pi$
$42$	−1.17428	−0.181195
$43$	8.52016	1.29931	0.649656	−	0.760228i	$-0.274913\pi$
$43$	8.52016	1.29931	0.649656	+	0.760228i	$0.274913\pi$
$44$	−2.42000	−0.364828
$45$	9.99346	1.48974
$46$	−13.3059	−1.96185
$47$	6.53823	0.953699	0.476850	−	0.878985i	$-0.341779\pi$
$47$	6.53823	0.953699	0.476850	+	0.878985i	$0.341779\pi$
$48$	−2.15763	−0.311427
$49$	−6.40344	−0.914777
$50$	−23.7078	−3.35279
$51$	−0.602444	−0.0843590
$52$	−3.83921	−0.532403
$53$	12.4424	1.70910	0.854549	−	0.519370i	$-0.173833\pi$
$53$	12.4424	1.70910	0.854549	+	0.519370i	$0.173833\pi$
$54$	8.32704	1.13317
$55$	4.03444	0.544003
$56$	−0.681996	−0.0911356
$57$	−0.973811	−0.128984
$58$	1.77159	0.232621
$59$	−2.81862	−0.366953	−0.183477	−	0.983024i	$-0.558735\pi$
$59$	−2.81862	−0.366953	−0.183477	+	0.983024i	$0.558735\pi$
$60$	−7.06043	−0.911497
$61$	−9.89190	−1.26653	−0.633264	−	0.773936i	$-0.718285\pi$
$61$	−9.89190	−1.26653	−0.633264	+	0.773936i	$0.718285\pi$
$62$	15.8050	2.00724
$63$	−1.91320	−0.241040
$64$	−10.9331	−1.36664
$65$	6.40045	0.793878
$66$	1.52035	0.187143
$67$	2.22376	0.271675	0.135837	−	0.990731i	$-0.456627\pi$
$67$	2.22376	0.271675	0.135837	+	0.990731i	$0.456627\pi$
$68$	−2.01603	−0.244480
$69$	4.57685	0.550989
$70$	6.55119	0.783017
$71$	11.7983	1.40020	0.700102	−	0.714043i	$-0.253138\pi$
$71$	11.7983	1.40020	0.700102	+	0.714043i	$0.253138\pi$
$72$	2.18720	0.257764
$73$	6.14604	0.719339	0.359670	−	0.933080i	$-0.382889\pi$
$73$	6.14604	0.719339	0.359670	+	0.933080i	$0.382889\pi$
$74$	−0.436566	−0.0507498
$75$	8.15482	0.941638
$76$	−3.25878	−0.373808
$77$	−0.772372	−0.0880199
$78$	2.41197	0.273102
$79$	−12.0104	−1.35128	−0.675640	−	0.737232i	$-0.736133\pi$
$79$	−12.0104	−1.35128	−0.675640	+	0.737232i	$0.736133\pi$
$80$	12.0372	1.34580
$81$	4.56686	0.507428
$82$	−10.9745	−1.21193
$83$	10.0547	1.10365	0.551826	−	0.833959i	$-0.313931\pi$
$83$	10.0547	1.10365	0.551826	+	0.833959i	$0.313931\pi$
$84$	1.35168	0.147481
$85$	3.36098	0.364549
$86$	−17.9126	−1.93157
$87$	−0.609378	−0.0653322
$88$	0.882990	0.0941270
$89$	−6.20955	−0.658211	−0.329106	−	0.944293i	$-0.606747\pi$
$89$	−6.20955	−0.658211	−0.329106	+	0.944293i	$0.606747\pi$
$90$	−21.0100	−2.21465
$91$	−1.22533	−0.128450
$92$	15.3161	1.59681
$93$	−5.43648	−0.563736
$94$	−13.7458	−1.41778
$95$	5.43280	0.557394
$96$	5.81323	0.593310
$97$	3.70062	0.375741	0.187870	−	0.982194i	$-0.439841\pi$
$97$	3.70062	0.375741	0.187870	+	0.982194i	$0.439841\pi$
$98$	13.4625	1.35991
$99$	2.47704	0.248952
$100$	27.2895	2.72895
$101$	1.66133	0.165309	0.0826543	−	0.996578i	$-0.473660\pi$
$101$	1.66133	0.165309	0.0826543	+	0.996578i	$0.473660\pi$
$102$	1.26657	0.125409
$103$	−11.7731	−1.16004	−0.580020	−	0.814602i	$-0.696955\pi$
$103$	−11.7731	−1.16004	−0.580020	+	0.814602i	$0.696955\pi$
$104$	1.40082	0.137362
$105$	−2.25342	−0.219912
$106$	−26.1587	−2.54076
$107$	−15.0847	−1.45830	−0.729149	−	0.684355i	$-0.760084\pi$
$107$	−15.0847	−1.45830	−0.729149	+	0.684355i	$0.760084\pi$
$108$	−9.58505	−0.922322
$109$	−14.3562	−1.37508	−0.687539	−	0.726148i	$-0.741309\pi$
$109$	−14.3562	−1.37508	−0.687539	+	0.726148i	$0.741309\pi$
$110$	−8.48191	−0.808718
$111$	0.150167	0.0142532
$112$	−2.30446	−0.217751
$113$	16.4192	1.54458	0.772292	−	0.635267i	$-0.219110\pi$
$113$	16.4192	1.54458	0.772292	+	0.635267i	$0.219110\pi$
$114$	2.04732	0.191749
$115$	−25.5338	−2.38104
$116$	−2.03924	−0.189338
$117$	3.92971	0.363302
$118$	5.92581	0.545515
$119$	−0.643442	−0.0589842
$120$	2.57616	0.235170
$121$	1.00000	0.0909091
$122$	20.7965	1.88283
$123$	3.77493	0.340374
$124$	−18.1927	−1.63376
$125$	−25.3228	−2.26494
$126$	4.02226	0.358332
$127$	2.29153	0.203341	0.101670	−	0.994818i	$-0.467581\pi$
$127$	2.29153	0.203341	0.101670	+	0.994818i	$0.467581\pi$
$128$	6.90816	0.610601
$129$	6.16143	0.542484
$130$	−13.4562	−1.18018
$131$	−0.340123	−0.0297167	−0.0148583	−	0.999890i	$-0.504730\pi$
$131$	−0.340123	−0.0297167	−0.0148583	+	0.999890i	$0.504730\pi$
$132$	−1.75004	−0.152322
$133$	−1.04008	−0.0901865
$134$	−4.67518	−0.403874
$135$	15.9795	1.37529
$136$	0.735595	0.0630767
$137$	12.7708	1.09109	0.545543	−	0.838083i	$-0.316323\pi$
$137$	12.7708	1.09109	0.545543	+	0.838083i	$0.316323\pi$
$138$	−9.62228	−0.819103
$139$	17.6481	1.49689	0.748446	−	0.663196i	$-0.230801\pi$
$139$	17.6481	1.49689	0.748446	+	0.663196i	$0.230801\pi$
$140$	−7.54091	−0.637323
$141$	4.72818	0.398185
$142$	−24.8045	−2.08155
$143$	1.58645	0.132666
$144$	7.39053	0.615878
$145$	3.39966	0.282326
$146$	−12.9213	−1.06937
$147$	−4.63071	−0.381934
$148$	0.502521	0.0413070
$149$	13.7404	1.12566	0.562830	−	0.826573i	$-0.309713\pi$
$149$	13.7404	1.12566	0.562830	+	0.826573i	$0.309713\pi$
$150$	−17.1445	−1.39984
$151$	−7.96574	−0.648243	−0.324122	−	0.946015i	$-0.605069\pi$
$151$	−7.96574	−0.648243	−0.324122	+	0.946015i	$0.605069\pi$
$152$	1.18904	0.0964439
$153$	2.06356	0.166829
$154$	1.62382	0.130851
$155$	30.3296	2.43613
$156$	−2.77636	−0.222287
$157$	15.1860	1.21197	0.605987	−	0.795474i	$-0.292778\pi$
$157$	15.1860	1.21197	0.605987	+	0.795474i	$0.292778\pi$
$158$	25.2505	2.00882
$159$	8.99785	0.713576
$160$	−32.4315	−2.56393
$161$	4.88832	0.385254
$162$	−9.60126	−0.754346
$163$	7.08737	0.555125	0.277563	−	0.960708i	$-0.410473\pi$
$163$	7.08737	0.555125	0.277563	+	0.960708i	$0.410473\pi$
$164$	12.6325	0.986433
$165$	2.91754	0.227130
$166$	−21.1389	−1.64070
$167$	2.74186	0.212172	0.106086	−	0.994357i	$-0.466168\pi$
$167$	2.74186	0.212172	0.106086	+	0.994357i	$0.466168\pi$
$168$	−0.493192	−0.0380506
$169$	−10.4832	−0.806397
$170$	−7.06605	−0.541941
$171$	3.33560	0.255080
$172$	20.6188	1.57217
$173$	3.99705	0.303890	0.151945	−	0.988389i	$-0.451446\pi$
$173$	3.99705	0.303890	0.151945	+	0.988389i	$0.451446\pi$
$174$	1.28114	0.0971232
$175$	8.70978	0.658397
$176$	2.98361	0.224898
$177$	−2.03831	−0.153209
$178$	13.0548	0.978501
$179$	−18.4767	−1.38101	−0.690505	−	0.723328i	$-0.742612\pi$
$179$	−18.4767	−1.38101	−0.690505	+	0.723328i	$0.742612\pi$
$180$	24.1841	1.80258
$181$	18.1002	1.34538	0.672688	−	0.739926i	$-0.265140\pi$
$181$	18.1002	1.34538	0.672688	+	0.739926i	$0.265140\pi$
$182$	2.57611	0.190954
$183$	−7.15342	−0.528796
$184$	−5.58842	−0.411984
$185$	−0.837765	−0.0615937
$186$	11.4295	0.838054
$187$	0.833073	0.0609203
$188$	15.8225	1.15397
$189$	−3.05919	−0.222523
$190$	−11.4218	−0.828625
$191$	19.6776	1.42382	0.711911	−	0.702270i	$-0.247830\pi$
$191$	19.6776	1.42382	0.711911	+	0.702270i	$0.247830\pi$
$192$	−7.90636	−0.570592
$193$	−3.49557	−0.251617	−0.125808	−	0.992055i	$-0.540152\pi$
$193$	−3.49557	−0.251617	−0.125808	+	0.992055i	$0.540152\pi$
$194$	−7.78010	−0.558579
$195$	4.62854	0.331457
$196$	−15.4963	−1.10688
$197$	−19.6238	−1.39814	−0.699069	−	0.715054i	$-0.746402\pi$
$197$	−19.6238	−1.39814	−0.699069	+	0.715054i	$0.746402\pi$
$198$	−5.20768	−0.370094
$199$	−24.5074	−1.73728	−0.868640	−	0.495444i	$-0.835006\pi$
$199$	−24.5074	−1.73728	−0.868640	+	0.495444i	$0.835006\pi$
$200$	−9.95718	−0.704079
$201$	1.60813	0.113429
$202$	−3.49275	−0.245749
$203$	−0.650847	−0.0456805
$204$	−1.45791	−0.102074
$205$	−21.0600	−1.47089
$206$	24.7516	1.72452
$207$	−15.6771	−1.08964
$208$	4.73336	0.328200
$209$	1.34661	0.0931468
$210$	4.73755	0.326922
$211$	21.2189	1.46077	0.730384	−	0.683037i	$-0.239341\pi$
$211$	21.2189	1.46077	0.730384	+	0.683037i	$0.239341\pi$
$212$	30.1106	2.06801
$213$	8.53206	0.584607
$214$	31.7138	2.16791
$215$	−34.3740	−2.34429
$216$	3.49732	0.237963
$217$	−5.80644	−0.394167
$218$	30.1822	2.04420
$219$	4.44456	0.300336
$220$	9.76332	0.658243
$221$	1.32163	0.0889026
$222$	−0.315707	−0.0211889
$223$	−10.8894	−0.729210	−0.364605	−	0.931162i	$-0.618796\pi$
$223$	−10.8894	−0.729210	−0.364605	+	0.931162i	$0.618796\pi$
$224$	6.20883	0.414845
$225$	−27.9328	−1.86218
$226$	−34.5193	−2.29619
$227$	−7.74915	−0.514329	−0.257165	−	0.966368i	$-0.582788\pi$
$227$	−7.74915	−0.514329	−0.257165	+	0.966368i	$0.582788\pi$
$228$	−2.35662	−0.156071
$229$	−16.1111	−1.06465	−0.532325	−	0.846540i	$-0.678682\pi$
$229$	−16.1111	−1.06465	−0.532325	+	0.846540i	$0.678682\pi$
$230$	53.6818	3.53967
$231$	−0.558547	−0.0367497
$232$	0.744061	0.0488500
$233$	−4.27350	−0.279966	−0.139983	−	0.990154i	$-0.544705\pi$
$233$	−4.27350	−0.279966	−0.139983	+	0.990154i	$0.544705\pi$
$234$	−8.26174	−0.540087
$235$	−26.3781	−1.72072
$236$	−6.82105	−0.444013
$237$	−8.68546	−0.564181
$238$	1.35276	0.0876863
$239$	−23.0030	−1.48794	−0.743971	−	0.668211i	$-0.767060\pi$
$239$	−23.0030	−1.48794	−0.743971	+	0.668211i	$0.767060\pi$
$240$	8.70480	0.561893
$241$	−6.78435	−0.437018	−0.218509	−	0.975835i	$-0.570119\pi$
$241$	−6.78435	−0.437018	−0.218509	+	0.975835i	$0.570119\pi$
$242$	−2.10238	−0.135146
$243$	15.1849	0.974110
$244$	−23.9384	−1.53250
$245$	25.8343	1.65049
$246$	−7.93633	−0.506002
$247$	2.13633	0.135931
$248$	6.63803	0.421516
$249$	7.27118	0.460792
$250$	53.2381	3.36707
$251$	−6.87116	−0.433704	−0.216852	−	0.976204i	$-0.569579\pi$
$251$	−6.87116	−0.433704	−0.216852	+	0.976204i	$0.569579\pi$
$252$	−4.62993	−0.291658
$253$	−6.32897	−0.397899
$254$	−4.81767	−0.302287
$255$	2.43052	0.152205
$256$	7.34260	0.458913
$257$	−28.1882	−1.75833	−0.879167	−	0.476514i	$-0.841900\pi$
$257$	−28.1882	−1.75833	−0.879167	+	0.476514i	$0.841900\pi$
$258$	−12.9537	−0.806460
$259$	0.160386	0.00996589
$260$	15.4891	0.960590
$261$	2.08731	0.129201
$262$	0.715067	0.0441770
$263$	−15.5313	−0.957699	−0.478850	−	0.877897i	$-0.658946\pi$
$263$	−15.5313	−0.957699	−0.478850	+	0.877897i	$0.658946\pi$
$264$	0.638542	0.0392995
$265$	−50.1982	−3.08365
$266$	2.18664	0.134072
$267$	−4.49049	−0.274814
$268$	5.38148	0.328726
$269$	1.16379	0.0709577	0.0354788	−	0.999370i	$-0.488704\pi$
$269$	1.16379	0.0709577	0.0354788	+	0.999370i	$0.488704\pi$
$270$	−33.5949	−2.04452
$271$	11.4670	0.696573	0.348287	−	0.937388i	$-0.386764\pi$
$271$	11.4670	0.696573	0.348287	+	0.937388i	$0.386764\pi$
$272$	2.48557	0.150710
$273$	−0.886110	−0.0536298
$274$	−26.8491	−1.62202
$275$	−11.2767	−0.680009
$276$	11.0760	0.666695
$277$	13.8386	0.831480	0.415740	−	0.909483i	$-0.363523\pi$
$277$	13.8386	0.831480	0.415740	+	0.909483i	$0.363523\pi$
$278$	−37.1030	−2.22529
$279$	18.6216	1.11485
$280$	2.75147	0.164432
$281$	−4.16323	−0.248358	−0.124179	−	0.992260i	$-0.539630\pi$
$281$	−4.16323	−0.248358	−0.124179	+	0.992260i	$0.539630\pi$
$282$	−9.94043	−0.591944
$283$	−6.56387	−0.390182	−0.195091	−	0.980785i	$-0.562500\pi$
$283$	−6.56387	−0.390182	−0.195091	+	0.980785i	$0.562500\pi$
$284$	28.5519	1.69424
$285$	3.92878	0.232721
$286$	−3.33533	−0.197222
$287$	4.03182	0.237991
$288$	−19.9121	−1.17333
$289$	−16.3060	−0.959176
$290$	−7.14737	−0.419708
$291$	2.67614	0.156878
$292$	14.8734	0.870399
$293$	−4.17291	−0.243784	−0.121892	−	0.992543i	$-0.538896\pi$
$293$	−4.17291	−0.243784	−0.121892	+	0.992543i	$0.538896\pi$
$294$	9.73550	0.567786
$295$	11.3715	0.662077
$296$	−0.183356	−0.0106574
$297$	3.96077	0.229827
$298$	−28.8876	−1.67341
$299$	−10.0406	−0.580665
$300$	19.7346	1.13938
$301$	6.58073	0.379307
$302$	16.7470	0.963682
$303$	1.20141	0.0690190
$304$	4.01775	0.230434
$305$	39.9082	2.28514
$306$	−4.33837	−0.248008
$307$	21.6208	1.23397	0.616983	−	0.786976i	$-0.288355\pi$
$307$	21.6208	1.23397	0.616983	+	0.786976i	$0.288355\pi$
$308$	−1.86914	−0.106504
$309$	−8.51384	−0.484335
$310$	−63.7643	−3.62157
$311$	−7.43622	−0.421669	−0.210835	−	0.977522i	$-0.567618\pi$
$311$	−7.43622	−0.421669	−0.210835	+	0.977522i	$0.567618\pi$
$312$	1.01302	0.0573508
$313$	−16.0894	−0.909425	−0.454712	−	0.890638i	$-0.650258\pi$
$313$	−16.0894	−0.909425	−0.454712	+	0.890638i	$0.650258\pi$
$314$	−31.9267	−1.80173
$315$	7.71867	0.434898
$316$	−29.0652	−1.63505
$317$	23.1267	1.29893	0.649463	−	0.760394i	$-0.274994\pi$
$317$	23.1267	1.29893	0.649463	+	0.760394i	$0.274994\pi$
$318$	−18.9169	−1.06081
$319$	0.842661	0.0471800
$320$	44.1088	2.46576
$321$	−10.9087	−0.608862
$322$	−10.2771	−0.572720
$323$	1.12182	0.0624198
$324$	11.0518	0.613987
$325$	−17.8899	−0.992354
$326$	−14.9003	−0.825253
$327$	−10.3818	−0.574117
$328$	−4.60925	−0.254503
$329$	5.04995	0.278413
$330$	−6.13377	−0.337653
$331$	28.2789	1.55435	0.777175	−	0.629284i	$-0.216652\pi$
$331$	28.2789	1.55435	0.777175	+	0.629284i	$0.216652\pi$
$332$	24.3324	1.33542
$333$	−0.514367	−0.0281871
$334$	−5.76443	−0.315416
$335$	−8.97160	−0.490171
$336$	−1.66649	−0.0909144
$337$	7.35896	0.400868	0.200434	−	0.979707i	$-0.435765\pi$
$337$	7.35896	0.400868	0.200434	+	0.979707i	$0.435765\pi$
$338$	22.0396	1.19879
$339$	11.8737	0.644889
$340$	8.13355	0.441104
$341$	7.51768	0.407105
$342$	−7.01270	−0.379203
$343$	−10.3524	−0.558979
$344$	−7.52322	−0.405625
$345$	−18.4650	−0.994123
$346$	−8.40330	−0.451764
$347$	28.1581	1.51161	0.755803	−	0.654799i	$-0.227247\pi$
$347$	28.1581	1.51161	0.755803	+	0.654799i	$0.227247\pi$
$348$	−1.47469	−0.0790518
$349$	25.4531	1.36247	0.681237	−	0.732063i	$-0.261443\pi$
$349$	25.4531	1.36247	0.681237	+	0.732063i	$0.261443\pi$
$350$	−18.3113	−0.978777
$351$	6.28358	0.335393
$352$	−8.03866	−0.428462
$353$	−3.29645	−0.175452	−0.0877261	−	0.996145i	$-0.527960\pi$
$353$	−3.29645	−0.175452	−0.0877261	+	0.996145i	$0.527960\pi$
$354$	4.28530	0.227761
$355$	−47.5996	−2.52632
$356$	−15.0271	−0.796434
$357$	−0.465311	−0.0246268
$358$	38.8449	2.05302
$359$	−29.2113	−1.54171	−0.770857	−	0.637009i	$-0.780172\pi$
$359$	−29.2113	−1.54171	−0.770857	+	0.637009i	$0.780172\pi$
$360$	−8.82412	−0.465072
$361$	−17.1866	−0.904560
$362$	−38.0534	−2.00004
$363$	0.723159	0.0379560
$364$	−2.96530	−0.155424
$365$	−24.7958	−1.29787
$366$	15.0392	0.786111
$367$	0.828884	0.0432674	0.0216337	−	0.999766i	$-0.493113\pi$
$367$	0.828884	0.0432674	0.0216337	+	0.999766i	$0.493113\pi$
$368$	−18.8832	−0.984355
$369$	−12.9303	−0.673124
$370$	1.76130	0.0915656
$371$	9.61018	0.498935
$372$	−13.1562	−0.682120
$373$	13.0319	0.674766	0.337383	−	0.941367i	$-0.390458\pi$
$373$	13.0319	0.674766	0.337383	+	0.941367i	$0.390458\pi$
$374$	−1.75143	−0.0905645
$375$	−18.3124	−0.945649
$376$	−5.77319	−0.297730
$377$	1.33684	0.0688509
$378$	6.43157	0.330804
$379$	25.2054	1.29471	0.647357	−	0.762187i	$-0.275874\pi$
$379$	25.2054	1.29471	0.647357	+	0.762187i	$0.275874\pi$
$380$	13.1474	0.674445
$381$	1.65714	0.0848980
$382$	−41.3698	−2.11666
$383$	−1.55511	−0.0794624	−0.0397312	−	0.999210i	$-0.512650\pi$
$383$	−1.55511	−0.0794624	−0.0397312	+	0.999210i	$0.512650\pi$
$384$	4.99570	0.254936
$385$	3.11608	0.158810
$386$	7.34901	0.374055
$387$	−21.1048	−1.07282
$388$	8.95548	0.454646
$389$	36.2268	1.83677	0.918387	−	0.395683i	$-0.129492\pi$
$389$	36.2268	1.83677	0.918387	+	0.395683i	$0.129492\pi$
$390$	−9.73094	−0.492746
$391$	−5.27250	−0.266642
$392$	5.65417	0.285579
$393$	−0.245963	−0.0124072
$394$	41.2567	2.07848
$395$	48.4553	2.43805
$396$	5.99443	0.301231
$397$	−17.3581	−0.871178	−0.435589	−	0.900146i	$-0.643460\pi$
$397$	−17.3581	−0.871178	−0.435589	+	0.900146i	$0.643460\pi$
$398$	51.5237	2.58265
$399$	−0.752144	−0.0376543
$400$	−33.6452	−1.68226
$401$	−21.5873	−1.07802	−0.539009	−	0.842300i	$-0.681201\pi$
$401$	−21.5873	−1.07802	−0.539009	+	0.842300i	$0.681201\pi$
$402$	−3.38090	−0.168624
$403$	11.9265	0.594099
$404$	4.02041	0.200023
$405$	−18.4247	−0.915530
$406$	1.36833	0.0679090
$407$	−0.207654	−0.0102930
$408$	0.531952	0.0263355
$409$	−8.44589	−0.417622	−0.208811	−	0.977956i	$-0.566959\pi$
$409$	−8.44589	−0.417622	−0.208811	+	0.977956i	$0.566959\pi$
$410$	44.2760	2.18664
$411$	9.23535	0.455546
$412$	−28.4909	−1.40365
$413$	−2.17702	−0.107124
$414$	32.9593	1.61986
$415$	−40.5652	−1.99127
$416$	−12.7530	−0.625266
$417$	12.7624	0.624976
$418$	−2.83108	−0.138473
$419$	−14.7376	−0.719980	−0.359990	−	0.932956i	$-0.617220\pi$
$419$	−14.7376	−0.719980	−0.359990	+	0.932956i	$0.617220\pi$
$420$	−5.45328	−0.266093
$421$	−20.6170	−1.00481	−0.502406	−	0.864632i	$-0.667552\pi$
$421$	−20.6170	−1.00481	−0.502406	+	0.864632i	$0.667552\pi$
$422$	−44.6101	−2.17159
$423$	−16.1955	−0.787451
$424$	−10.9865	−0.533553
$425$	−9.39428	−0.455690
$426$	−17.9376	−0.869081
$427$	−7.64022	−0.369736
$428$	−36.5050	−1.76454
$429$	1.14726	0.0553902
$430$	72.2672	3.48504
$431$	−21.8302	−1.05152	−0.525762	−	0.850632i	$-0.676220\pi$
$431$	−21.8302	−1.05152	−0.525762	+	0.850632i	$0.676220\pi$
$432$	11.8174	0.568565
$433$	−9.09869	−0.437255	−0.218628	−	0.975808i	$-0.570158\pi$
$433$	−9.09869	−0.437255	−0.218628	+	0.975808i	$0.570158\pi$
$434$	12.2073	0.585971
$435$	2.45850	0.117876
$436$	−34.7420	−1.66384
$437$	−8.52264	−0.407693
$438$	−9.34415	−0.446481
$439$	−7.29723	−0.348278	−0.174139	−	0.984721i	$-0.555714\pi$
$439$	−7.29723	−0.348278	−0.174139	+	0.984721i	$0.555714\pi$
$440$	−3.56236	−0.169829
$441$	15.8616	0.755314
$442$	−2.77857	−0.132163
$443$	−9.71740	−0.461687	−0.230844	−	0.972991i	$-0.574149\pi$
$443$	−9.71740	−0.461687	−0.230844	+	0.972991i	$0.574149\pi$
$444$	0.363402	0.0172463
$445$	25.0520	1.18758
$446$	22.8937	1.08405
$447$	9.93651	0.469981
$448$	−8.44441	−0.398961
$449$	−20.1836	−0.952524	−0.476262	−	0.879303i	$-0.658009\pi$
$449$	−20.1836	−0.952524	−0.476262	+	0.879303i	$0.658009\pi$
$450$	58.7253	2.76833
$451$	−5.22005	−0.245803
$452$	39.7343	1.86894
$453$	−5.76050	−0.270652
$454$	16.2917	0.764605
$455$	4.94352	0.231756
$456$	0.859865	0.0402669
$457$	−9.54160	−0.446337	−0.223169	−	0.974780i	$-0.571640\pi$
$457$	−9.54160	−0.446337	−0.223169	+	0.974780i	$0.571640\pi$
$458$	33.8716	1.58272
$459$	3.29961	0.154013
$460$	−61.7918	−2.88106
$461$	−30.9032	−1.43930	−0.719652	−	0.694334i	$-0.755699\pi$
$461$	−30.9032	−1.43930	−0.719652	+	0.694334i	$0.755699\pi$
$462$	1.17428	0.0546324
$463$	20.5800	0.956434	0.478217	−	0.878242i	$-0.341283\pi$
$463$	20.5800	0.956434	0.478217	+	0.878242i	$0.341283\pi$
$464$	2.51417	0.116718
$465$	21.9331	1.01712
$466$	8.98451	0.416200
$467$	−4.20553	−0.194609	−0.0973045	−	0.995255i	$-0.531022\pi$
$467$	−4.20553	−0.194609	−0.0973045	+	0.995255i	$0.531022\pi$
$468$	9.50989	0.439595
$469$	1.71757	0.0793098
$470$	55.4567	2.55803
$471$	10.9819	0.506019
$472$	2.48881	0.114557
$473$	−8.52016	−0.391757
$474$	18.2601	0.838715
$475$	−15.1852	−0.696747
$476$	−1.55713	−0.0713707
$477$	−30.8204	−1.41117
$478$	48.3611	2.21198
$479$	−6.23137	−0.284719	−0.142359	−	0.989815i	$-0.545469\pi$
$479$	−6.23137	−0.284719	−0.142359	+	0.989815i	$0.545469\pi$
$480$	−23.4531	−1.07048
$481$	−0.329433	−0.0150208
$482$	14.2633	0.649674
$483$	3.53503	0.160850
$484$	2.42000	0.110000
$485$	−14.9299	−0.677932
$486$	−31.9244	−1.44812
$487$	−18.8373	−0.853601	−0.426801	−	0.904346i	$-0.640359\pi$
$487$	−18.8373	−0.853601	−0.426801	+	0.904346i	$0.640359\pi$
$488$	8.73445	0.395390
$489$	5.12529	0.231774
$490$	−54.3134	−2.45363
$491$	34.6296	1.56281	0.781405	−	0.624024i	$-0.214503\pi$
$491$	34.6296	1.56281	0.781405	+	0.624024i	$0.214503\pi$
$492$	9.13531	0.411851
$493$	0.701998	0.0316164
$494$	−4.49138	−0.202077
$495$	−9.99346	−0.449173
$496$	22.4298	1.00713
$497$	9.11269	0.408760
$498$	−15.2868	−0.685017
$499$	−38.9767	−1.74484	−0.872419	−	0.488759i	$-0.837450\pi$
$499$	−38.9767	−1.74484	−0.872419	+	0.488759i	$0.837450\pi$
$500$	−61.2811	−2.74057
$501$	1.98280	0.0885851
$502$	14.4458	0.644747
$503$	39.4538	1.75916	0.879579	−	0.475752i	$-0.157824\pi$
$503$	39.4538	1.75916	0.879579	+	0.475752i	$0.157824\pi$
$504$	1.68933	0.0752489
$505$	−6.70253	−0.298259
$506$	13.3059	0.591519
$507$	−7.58099	−0.336684
$508$	5.54550	0.246042
$509$	−27.5346	−1.22045	−0.610225	−	0.792228i	$-0.708921\pi$
$509$	−27.5346	−1.22045	−0.610225	+	0.792228i	$0.708921\pi$
$510$	−5.10987	−0.226269
$511$	4.74702	0.209996
$512$	−29.2533	−1.29282
$513$	5.33360	0.235484
$514$	59.2623	2.61395
$515$	47.4979	2.09301
$516$	14.9106	0.656404
$517$	−6.53823	−0.287551
$518$	−0.337192	−0.0148153
$519$	2.89050	0.126879
$520$	−5.65153	−0.247836
$521$	−9.99751	−0.437999	−0.218999	−	0.975725i	$-0.570279\pi$
$521$	−9.99751	−0.437999	−0.218999	+	0.975725i	$0.570279\pi$
$522$	−4.38831	−0.192071
$523$	−22.2807	−0.974269	−0.487135	−	0.873327i	$-0.661958\pi$
$523$	−22.2807	−0.974269	−0.487135	+	0.873327i	$0.661958\pi$
$524$	−0.823096	−0.0359571
$525$	6.29855	0.274891
$526$	32.6526	1.42372
$527$	6.26277	0.272811
$528$	2.15763	0.0938986
$529$	17.0559	0.741562
$530$	105.536	4.58417
$531$	6.98184	0.302986
$532$	−2.51699	−0.109125
$533$	−8.28137	−0.358706
$534$	9.44072	0.408540
$535$	60.8584	2.63114
$536$	−1.96355	−0.0848126
$537$	−13.3616	−0.576594
$538$	−2.44673	−0.105486
$539$	6.40344	0.275816
$540$	38.6703	1.66410
$541$	3.33142	0.143229	0.0716144	−	0.997432i	$-0.477185\pi$
$541$	3.33142	0.143229	0.0716144	+	0.997432i	$0.477185\pi$
$542$	−24.1081	−1.03553
$543$	13.0893	0.561716
$544$	−6.69679	−0.287122
$545$	57.9193	2.48099
$546$	1.86294	0.0797264
$547$	−1.00000	−0.0427569
$547$	−1.00000	−0.0427569
$548$	30.9054	1.32021
$549$	24.5026	1.04575
$550$	23.7078	1.01090
$551$	1.13473	0.0483413
$552$	−4.04132	−0.172010
$553$	−9.27652	−0.394478
$554$	−29.0940	−1.23608
$555$	−0.605837	−0.0257164
$556$	42.7083	1.81124
$557$	−22.3689	−0.947801	−0.473901	−	0.880578i	$-0.657154\pi$
$557$	−22.3689	−0.947801	−0.473901	+	0.880578i	$0.657154\pi$
$558$	−39.1497	−1.65734
$559$	−13.5168	−0.571702
$560$	9.29718	0.392878
$561$	0.602444	0.0254352
$562$	8.75269	0.369210
$563$	24.5258	1.03364	0.516819	−	0.856095i	$-0.327116\pi$
$563$	24.5258	1.03364	0.516819	+	0.856095i	$0.327116\pi$
$564$	11.4422	0.481803
$565$	−66.2420	−2.78682
$566$	13.7997	0.580046
$567$	3.52731	0.148133
$568$	−10.4178	−0.437121
$569$	−28.1209	−1.17889	−0.589445	−	0.807809i	$-0.700653\pi$
$569$	−28.1209	−1.17889	−0.589445	+	0.807809i	$0.700653\pi$
$570$	−8.25978	−0.345964
$571$	−6.20767	−0.259783	−0.129891	−	0.991528i	$-0.541463\pi$
$571$	−6.20767	−0.259783	−0.129891	+	0.991528i	$0.541463\pi$
$572$	3.83921	0.160526
$573$	14.2300	0.594468
$574$	−8.47641	−0.353799
$575$	71.3697	2.97632
$576$	27.0817	1.12840
$577$	14.2116	0.591635	0.295818	−	0.955244i	$-0.404408\pi$
$577$	14.2116	0.591635	0.295818	+	0.955244i	$0.404408\pi$
$578$	34.2814	1.42592
$579$	−2.52785	−0.105054
$580$	8.22717	0.341614
$581$	7.76600	0.322188
$582$	−5.62625	−0.233216
$583$	−12.4424	−0.515313
$584$	−5.42689	−0.224566
$585$	−15.8542	−0.655489
$586$	8.77303	0.362411
$587$	−28.0399	−1.15733	−0.578666	−	0.815565i	$-0.696426\pi$
$587$	−28.0399	−1.15733	−0.578666	+	0.815565i	$0.696426\pi$
$588$	−11.2063	−0.462140
$589$	10.1234	0.417126
$590$	−23.9073	−0.984248
$591$	−14.1911	−0.583745
$592$	−0.619558	−0.0254637
$593$	−11.3399	−0.465672	−0.232836	−	0.972516i	$-0.574801\pi$
$593$	−11.3399	−0.465672	−0.232836	+	0.972516i	$0.574801\pi$
$594$	−8.32704	−0.341663
$595$	2.59592	0.106422
$596$	33.2518	1.36205
$597$	−17.7227	−0.725342
$598$	21.1092	0.863219
$599$	−6.01187	−0.245638	−0.122819	−	0.992429i	$-0.539194\pi$
$599$	−6.01187	−0.245638	−0.122819	+	0.992429i	$0.539194\pi$
$600$	−7.20063	−0.293964
$601$	25.8092	1.05278	0.526390	−	0.850243i	$-0.323545\pi$
$601$	25.8092	1.05278	0.526390	+	0.850243i	$0.323545\pi$
$602$	−13.8352	−0.563880
$603$	−5.50833	−0.224317
$604$	−19.2771	−0.784373
$605$	−4.03444	−0.164023
$606$	−2.52581	−0.102604
$607$	34.0425	1.38174	0.690872	−	0.722978i	$-0.257227\pi$
$607$	34.0425	1.38174	0.690872	+	0.722978i	$0.257227\pi$
$608$	−10.8249	−0.439009
$609$	−0.470666	−0.0190724
$610$	−83.9022	−3.39710
$611$	−10.3726	−0.419631
$612$	4.99379	0.201862
$613$	−28.4260	−1.14812	−0.574058	−	0.818815i	$-0.694632\pi$
$613$	−28.4260	−1.14812	−0.574058	+	0.818815i	$0.694632\pi$
$614$	−45.4552	−1.83442
$615$	−15.2297	−0.614121
$616$	0.681996	0.0274784
$617$	−15.1339	−0.609269	−0.304635	−	0.952469i	$-0.598534\pi$
$617$	−15.1339	−0.609269	−0.304635	+	0.952469i	$0.598534\pi$
$618$	17.8993	0.720016
$619$	−19.8201	−0.796637	−0.398318	−	0.917247i	$-0.630406\pi$
$619$	−19.8201	−0.796637	−0.398318	+	0.917247i	$0.630406\pi$
$620$	73.3975	2.94771
$621$	−25.0676	−1.00593
$622$	15.6338	0.626856
$623$	−4.79608	−0.192151
$624$	3.42298	0.137029
$625$	45.7799	1.83120
$626$	33.8259	1.35196
$627$	0.973811	0.0388903
$628$	36.7500	1.46649
$629$	−0.172991	−0.00689758
$630$	−16.2276	−0.646521
$631$	−41.8880	−1.66754	−0.833768	−	0.552115i	$-0.813821\pi$
$631$	−41.8880	−1.66754	−0.833768	+	0.552115i	$0.813821\pi$
$632$	10.6051	0.421848
$633$	15.3446	0.609894
$634$	−48.6211	−1.93099
$635$	−9.24504	−0.366878
$636$	21.7748	0.863425
$637$	10.1588	0.402505
$638$	−1.77159	−0.0701380
$639$	−29.2249	−1.15612
$640$	−27.8705	−1.10168
$641$	−28.0719	−1.10877	−0.554387	−	0.832259i	$-0.687047\pi$
$641$	−28.0719	−1.10877	−0.554387	+	0.832259i	$0.687047\pi$
$642$	22.9342	0.905139
$643$	−28.1564	−1.11038	−0.555191	−	0.831723i	$-0.687355\pi$
$643$	−28.1564	−1.11038	−0.555191	+	0.831723i	$0.687355\pi$
$644$	11.8297	0.466156
$645$	−24.8579	−0.978779
$646$	−2.35849	−0.0927937
$647$	38.5296	1.51475	0.757377	−	0.652978i	$-0.226481\pi$
$647$	38.5296	1.51475	0.757377	+	0.652978i	$0.226481\pi$
$648$	−4.03249	−0.158411
$649$	2.81862	0.110641
$650$	37.6114	1.47524
$651$	−4.19898	−0.164571
$652$	17.1514	0.671700
$653$	−45.2084	−1.76914	−0.884572	−	0.466404i	$-0.845549\pi$
$653$	−45.2084	−1.76914	−0.884572	+	0.466404i	$0.845549\pi$
$654$	21.8265	0.853485
$655$	1.37220	0.0536164
$656$	−15.5746	−0.608086
$657$	−15.2240	−0.593944
$658$	−10.6169	−0.413890
$659$	43.6152	1.69901	0.849503	−	0.527584i	$-0.176902\pi$
$659$	43.6152	1.69901	0.849503	+	0.527584i	$0.176902\pi$
$660$	7.06043	0.274827
$661$	24.2726	0.944094	0.472047	−	0.881573i	$-0.343515\pi$
$661$	24.2726	0.944094	0.472047	+	0.881573i	$0.343515\pi$
$662$	−59.4530	−2.31071
$663$	0.955750	0.0371182
$664$	−8.87824	−0.344542
$665$	4.19614	0.162719
$666$	1.08139	0.0419031
$667$	−5.33318	−0.206502
$668$	6.63530	0.256727
$669$	−7.87479	−0.304457
$670$	18.8617	0.728691
$671$	9.89190	0.381873
$672$	4.48997	0.173205
$673$	−11.7756	−0.453915	−0.226958	−	0.973905i	$-0.572878\pi$
$673$	−11.7756	−0.453915	−0.226958	+	0.973905i	$0.572878\pi$
$674$	−15.4713	−0.595933
$675$	−44.6643	−1.71913
$676$	−25.3692	−0.975739
$677$	3.24721	0.124800	0.0624001	−	0.998051i	$-0.480125\pi$
$677$	3.24721	0.124800	0.0624001	+	0.998051i	$0.480125\pi$
$678$	−24.9629	−0.958696
$679$	2.85825	0.109690
$680$	−2.96771	−0.113806
$681$	−5.60387	−0.214741
$682$	−15.8050	−0.605205
$683$	6.35942	0.243337	0.121668	−	0.992571i	$-0.461176\pi$
$683$	6.35942	0.243337	0.121668	+	0.992571i	$0.461176\pi$
$684$	8.07214	0.308646
$685$	−51.5231	−1.96860
$686$	21.7647	0.830982
$687$	−11.6509	−0.444508
$688$	−25.4209	−0.969161
$689$	−19.7393	−0.752009
$690$	38.8205	1.47787
$691$	−34.6745	−1.31908	−0.659540	−	0.751669i	$-0.729249\pi$
$691$	−34.6745	−1.31908	−0.659540	+	0.751669i	$0.729249\pi$
$692$	9.67283	0.367706
$693$	1.91320	0.0726763
$694$	−59.1990	−2.24716
$695$	−71.2001	−2.70077
$696$	0.538074	0.0203957
$697$	−4.34868	−0.164718
$698$	−53.5120	−2.02546
$699$	−3.09042	−0.116890
$700$	21.0776	0.796659
$701$	25.8517	0.976405	0.488203	−	0.872730i	$-0.337653\pi$
$701$	25.8517	0.976405	0.488203	+	0.872730i	$0.337653\pi$
$702$	−13.2105	−0.498597
$703$	−0.279628	−0.0105464
$704$	10.9331	0.412056
$705$	−19.0755	−0.718427
$706$	6.93038	0.260828
$707$	1.28316	0.0482584
$708$	−4.93271	−0.185382
$709$	6.10248	0.229183	0.114592	−	0.993413i	$-0.463444\pi$
$709$	6.10248	0.229183	0.114592	+	0.993413i	$0.463444\pi$
$710$	100.072	3.75565
$711$	29.7504	1.11573
$712$	5.48297	0.205483
$713$	−47.5792	−1.78185
$714$	0.978259	0.0366104
$715$	−6.40045	−0.239363
$716$	−44.7134	−1.67102
$717$	−16.6349	−0.621240
$718$	61.4132	2.29192
$719$	39.1680	1.46072	0.730360	−	0.683062i	$-0.239352\pi$
$719$	39.1680	1.46072	0.730360	+	0.683062i	$0.239352\pi$
$720$	−29.8166	−1.11120
$721$	−9.09322	−0.338649
$722$	36.1328	1.34473
$723$	−4.90616	−0.182462
$724$	43.8024	1.62790
$725$	−9.50241	−0.352911
$726$	−1.52035	−0.0564256
$727$	34.6693	1.28581	0.642906	−	0.765945i	$-0.277729\pi$
$727$	34.6693	1.28581	0.642906	+	0.765945i	$0.277729\pi$
$728$	1.08196	0.0401000
$729$	−2.71949	−0.100722
$730$	52.1301	1.92942
$731$	−7.09791	−0.262526
$732$	−17.3112	−0.639842
$733$	10.5245	0.388732	0.194366	−	0.980929i	$-0.437735\pi$
$733$	10.5245	0.388732	0.194366	+	0.980929i	$0.437735\pi$
$734$	−1.74263	−0.0643216
$735$	18.6823	0.689106
$736$	50.8765	1.87533
$737$	−2.22376	−0.0819131
$738$	27.1843	1.00067
$739$	−6.61891	−0.243480	−0.121740	−	0.992562i	$-0.538847\pi$
$739$	−6.61891	−0.243480	−0.121740	+	0.992562i	$0.538847\pi$
$740$	−2.02739	−0.0745283
$741$	1.54491	0.0567536
$742$	−20.2042	−0.741721
$743$	32.2342	1.18256	0.591280	−	0.806466i	$-0.298623\pi$
$743$	32.2342	1.18256	0.591280	+	0.806466i	$0.298623\pi$
$744$	4.80035	0.175989
$745$	−55.4349	−2.03098
$746$	−27.3980	−1.00311
$747$	−24.9060	−0.911264
$748$	2.01603	0.0737134
$749$	−11.6510	−0.425719
$750$	38.4996	1.40581
$751$	−8.33428	−0.304122	−0.152061	−	0.988371i	$-0.548591\pi$
$751$	−8.33428	−0.304122	−0.152061	+	0.988371i	$0.548591\pi$
$752$	−19.5076	−0.711367
$753$	−4.96894	−0.181078
$754$	−2.81055	−0.102354
$755$	32.1373	1.16960
$756$	−7.40322	−0.269253
$757$	28.5814	1.03881	0.519405	−	0.854528i	$-0.326154\pi$
$757$	28.5814	1.03881	0.519405	+	0.854528i	$0.326154\pi$
$758$	−52.9913	−1.92473
$759$	−4.57685	−0.166129
$760$	−4.79711	−0.174009
$761$	−32.9592	−1.19477	−0.597385	−	0.801954i	$-0.703794\pi$
$761$	−32.9592	−1.19477	−0.597385	+	0.801954i	$0.703794\pi$
$762$	−3.48394	−0.126210
$763$	−11.0883	−0.401425
$764$	47.6197	1.72282
$765$	−8.32528	−0.301001
$766$	3.26943	0.118129
$767$	4.47161	0.161461
$768$	5.30987	0.191603
$769$	3.50014	0.126218	0.0631092	−	0.998007i	$-0.479898\pi$
$769$	3.50014	0.126218	0.0631092	+	0.998007i	$0.479898\pi$
$770$	−6.55119	−0.236088
$771$	−20.3846	−0.734133
$772$	−8.45926	−0.304455
$773$	−40.7673	−1.46630	−0.733148	−	0.680069i	$-0.761950\pi$
$773$	−40.7673	−1.46630	−0.733148	+	0.680069i	$0.761950\pi$
$774$	44.3703	1.59486
$775$	−84.7744	−3.04518
$776$	−3.26761	−0.117300
$777$	0.115984	0.00416092
$778$	−76.1625	−2.73056
$779$	−7.02936	−0.251853
$780$	11.2010	0.401062
$781$	−11.7983	−0.422177
$782$	11.0848	0.396391
$783$	3.33759	0.119276
$784$	19.1054	0.682335
$785$	−61.2669	−2.18671
$786$	0.517107	0.0184446
$787$	8.44321	0.300968	0.150484	−	0.988612i	$-0.451917\pi$
$787$	8.44321	0.300968	0.150484	+	0.988612i	$0.451917\pi$
$788$	−47.4895	−1.69174
$789$	−11.2316	−0.399855
$790$	−101.871	−3.62442
$791$	12.6817	0.450909
$792$	−2.18720	−0.0777188
$793$	15.6930	0.557277
$794$	36.4933	1.29510
$795$	−36.3012	−1.28747
$796$	−59.3077	−2.10211
$797$	−31.1391	−1.10300	−0.551501	−	0.834174i	$-0.685945\pi$
$797$	−31.1391	−1.10300	−0.551501	+	0.834174i	$0.685945\pi$
$798$	1.58129	0.0559771
$799$	−5.44682	−0.192695
$800$	90.6493	3.20494
$801$	15.3813	0.543472
$802$	45.3846	1.60259
$803$	−6.14604	−0.216889
$804$	3.89166	0.137248
$805$	−19.7216	−0.695095
$806$	−25.0739	−0.883191
$807$	0.841607	0.0296260
$808$	−1.46694	−0.0516067
$809$	−37.3990	−1.31488	−0.657440	−	0.753507i	$-0.728361\pi$
$809$	−37.3990	−1.31488	−0.657440	+	0.753507i	$0.728361\pi$
$810$	38.7357	1.36103
$811$	−56.0075	−1.96669	−0.983345	−	0.181748i	$-0.941824\pi$
$811$	−56.0075	−1.96669	−0.983345	+	0.181748i	$0.941824\pi$
$812$	−1.57505	−0.0552733
$813$	8.29250	0.290831
$814$	0.436566	0.0153016
$815$	−28.5935	−1.00159
$816$	1.79746	0.0629237
$817$	−11.4733	−0.401400
$818$	17.7565	0.620840
$819$	3.03520	0.106058
$820$	−50.9650	−1.77978
$821$	38.2628	1.33538	0.667691	−	0.744438i	$-0.267283\pi$
$821$	38.2628	1.33538	0.667691	+	0.744438i	$0.267283\pi$
$822$	−19.4162	−0.677218
$823$	10.1966	0.355432	0.177716	−	0.984082i	$-0.443129\pi$
$823$	10.1966	0.355432	0.177716	+	0.984082i	$0.443129\pi$
$824$	10.3955	0.362146
$825$	−8.15482	−0.283914
$826$	4.57693	0.159252
$827$	5.64193	0.196189	0.0980946	−	0.995177i	$-0.468725\pi$
$827$	5.64193	0.196189	0.0980946	+	0.995177i	$0.468725\pi$
$828$	−37.9386	−1.31846
$829$	−29.0276	−1.00817	−0.504085	−	0.863654i	$-0.668170\pi$
$829$	−29.0276	−1.00817	−0.504085	+	0.863654i	$0.668170\pi$
$830$	85.2835	2.96023
$831$	10.0075	0.347156
$832$	17.3448	0.601324
$833$	5.33453	0.184831
$834$	−26.8313	−0.929093
$835$	−11.0619	−0.382812
$836$	3.25878	0.112707
$837$	29.7758	1.02920
$838$	30.9841	1.07033
$839$	−11.4985	−0.396971	−0.198486	−	0.980104i	$-0.563602\pi$
$839$	−11.4985	−0.396971	−0.198486	+	0.980104i	$0.563602\pi$
$840$	1.98975	0.0686529
$841$	−28.2899	−0.975515
$842$	43.3448	1.49376
$843$	−3.01068	−0.103693
$844$	51.3496	1.76753
$845$	42.2936	1.45495
$846$	34.0490	1.17063
$847$	0.772372	0.0265390
$848$	−37.1234	−1.27482
$849$	−4.74672	−0.162907
$850$	19.7503	0.677431
$851$	1.31423	0.0450514
$852$	20.6476	0.707374
$853$	−36.0767	−1.23524	−0.617621	−	0.786476i	$-0.711903\pi$
$853$	−36.0767	−1.23524	−0.617621	+	0.786476i	$0.711903\pi$
$854$	16.0626	0.549652
$855$	−13.4573	−0.460229
$856$	13.3197	0.455257
$857$	−1.62462	−0.0554960	−0.0277480	−	0.999615i	$-0.508834\pi$
$857$	−1.62462	−0.0554960	−0.0277480	+	0.999615i	$0.508834\pi$
$858$	−2.41197	−0.0823434
$859$	−3.04916	−0.104036	−0.0520179	−	0.998646i	$-0.516565\pi$
$859$	−3.04916	−0.104036	−0.0520179	+	0.998646i	$0.516565\pi$
$860$	−83.1850	−2.83659
$861$	2.91565	0.0993650
$862$	45.8954	1.56320
$863$	−7.27785	−0.247741	−0.123870	−	0.992298i	$-0.539531\pi$
$863$	−7.27785	−0.247741	−0.123870	+	0.992298i	$0.539531\pi$
$864$	−31.8393	−1.08320
$865$	−16.1258	−0.548294
$866$	19.1289	0.650026
$867$	−11.7918	−0.400471
$868$	−14.0516	−0.476941
$869$	12.0104	0.407426
$870$	−5.16869	−0.175235
$871$	−3.52789	−0.119538
$872$	12.6764	0.429277
$873$	−9.16658	−0.310242
$874$	17.9178	0.606079
$875$	−19.5586	−0.661202
$876$	10.7558	0.363405
$877$	−28.0963	−0.948744	−0.474372	−	0.880325i	$-0.657325\pi$
$877$	−28.0963	−0.948744	−0.474372	+	0.880325i	$0.657325\pi$
$878$	15.3415	0.517752
$879$	−3.01767	−0.101784
$880$	−12.0372	−0.405774
$881$	−25.5687	−0.861433	−0.430716	−	0.902487i	$-0.641739\pi$
$881$	−25.5687	−0.861433	−0.430716	+	0.902487i	$0.641739\pi$
$882$	−33.3471	−1.12285
$883$	−3.84691	−0.129459	−0.0647295	−	0.997903i	$-0.520618\pi$
$883$	−3.84691	−0.129459	−0.0647295	+	0.997903i	$0.520618\pi$
$884$	3.19834	0.107572
$885$	8.22344	0.276428
$886$	20.4296	0.686347
$887$	−41.9303	−1.40788	−0.703941	−	0.710259i	$-0.748578\pi$
$887$	−41.9303	−1.40788	−0.703941	+	0.710259i	$0.748578\pi$
$888$	−0.132596	−0.00444962
$889$	1.76991	0.0593610
$890$	−52.6689	−1.76546
$891$	−4.56686	−0.152995
$892$	−26.3524	−0.882343
$893$	−8.80443	−0.294629
$894$	−20.8903	−0.698677
$895$	74.5429	2.49169
$896$	5.33567	0.178252
$897$	−7.26097	−0.242437
$898$	42.4336	1.41603
$899$	6.33485	0.211279
$900$	−67.5972	−2.25324
$901$	−10.3654	−0.345323
$902$	10.9745	0.365412
$903$	4.75892	0.158367
$904$	−14.4979	−0.482195
$905$	−73.0240	−2.42740
$906$	12.1108	0.402353
$907$	48.7265	1.61794	0.808969	−	0.587851i	$-0.200026\pi$
$907$	48.7265	1.61794	0.808969	+	0.587851i	$0.200026\pi$
$908$	−18.7529	−0.622338
$909$	−4.11518	−0.136492
$910$	−10.3932	−0.344530
$911$	27.9678	0.926615	0.463307	−	0.886198i	$-0.346663\pi$
$911$	27.9678	0.926615	0.463307	+	0.886198i	$0.346663\pi$
$912$	2.90548	0.0962099
$913$	−10.0547	−0.332764
$914$	20.0601	0.663528
$915$	28.8600	0.954082
$916$	−38.9887	−1.28822
$917$	−0.262701	−0.00867516
$918$	−6.93703	−0.228956
$919$	−20.5644	−0.678357	−0.339178	−	0.940722i	$-0.610149\pi$
$919$	−20.5644	−0.678357	−0.339178	+	0.940722i	$0.610149\pi$
$920$	22.5461	0.743323
$921$	15.6353	0.515201
$922$	64.9702	2.13968
$923$	−18.7175	−0.616094
$924$	−1.35168	−0.0444671
$925$	2.34164	0.0769927
$926$	−43.2670	−1.42184
$927$	29.1625	0.957822
$928$	−6.77387	−0.222363
$929$	−36.2692	−1.18996	−0.594978	−	0.803742i	$-0.702839\pi$
$929$	−36.2692	−1.18996	−0.594978	+	0.803742i	$0.702839\pi$
$930$	−46.1117	−1.51206
$931$	8.62292	0.282605
$932$	−10.3419	−0.338759
$933$	−5.37757	−0.176054
$934$	8.84162	0.289307
$935$	−3.36098	−0.109916
$936$	−3.46990	−0.113417
$937$	−39.8545	−1.30199	−0.650995	−	0.759082i	$-0.725648\pi$
$937$	−39.8545	−1.30199	−0.650995	+	0.759082i	$0.725648\pi$
$938$	−3.61097	−0.117902
$939$	−11.6352	−0.379699
$940$	−63.8348	−2.08206
$941$	9.24555	0.301396	0.150698	−	0.988580i	$-0.451848\pi$
$941$	9.24555	0.301396	0.150698	+	0.988580i	$0.451848\pi$
$942$	−23.0881	−0.752251
$943$	33.0376	1.07585
$944$	8.40968	0.273712
$945$	12.3421	0.401488
$946$	17.9126	0.582389
$947$	49.9386	1.62279	0.811393	−	0.584501i	$-0.198710\pi$
$947$	49.9386	1.62279	0.811393	+	0.584501i	$0.198710\pi$
$948$	−21.0188	−0.682658
$949$	−9.75040	−0.316512
$950$	31.9251	1.03579
$951$	16.7243	0.542322
$952$	0.568152	0.0184139
$953$	48.8027	1.58087	0.790437	−	0.612543i	$-0.209853\pi$
$953$	48.8027	1.58087	0.790437	+	0.612543i	$0.209853\pi$
$954$	64.7961	2.09785
$955$	−79.3880	−2.56894
$956$	−55.6672	−1.80041
$957$	0.609378	0.0196984
$958$	13.1007	0.423265
$959$	9.86383	0.318520
$960$	31.8977	1.02949
$961$	25.5155	0.823080
$962$	0.692593	0.0223301
$963$	37.3655	1.20409
$964$	−16.4181	−0.528791
$965$	14.1026	0.453980
$966$	−7.43198	−0.239120
$967$	4.93802	0.158796	0.0793980	−	0.996843i	$-0.474700\pi$
$967$	4.93802	0.158796	0.0793980	+	0.996843i	$0.474700\pi$
$968$	−0.882990	−0.0283804
$969$	0.811255	0.0260613
$970$	31.3883	1.00782
$971$	24.2151	0.777100	0.388550	−	0.921428i	$-0.372976\pi$
$971$	24.2151	0.777100	0.388550	+	0.921428i	$0.372976\pi$
$972$	36.7473	1.17867
$973$	13.6309	0.436986
$974$	39.6032	1.26897
$975$	−12.9373	−0.414324
$976$	29.5136	0.944707
$977$	−37.9064	−1.21273	−0.606367	−	0.795185i	$-0.707374\pi$
$977$	−37.9064	−1.21273	−0.606367	+	0.795185i	$0.707374\pi$
$978$	−10.7753	−0.344556
$979$	6.20955	0.198458
$980$	62.5188	1.99709
$981$	35.5610	1.13537
$982$	−72.8045	−2.32328
$983$	28.4920	0.908754	0.454377	−	0.890810i	$-0.349862\pi$
$983$	28.4920	0.908754	0.454377	+	0.890810i	$0.349862\pi$
$984$	−3.33322	−0.106259
$985$	79.1710	2.52260
$986$	−1.47587	−0.0470011
$987$	3.65191	0.116242
$988$	5.16991	0.164477
$989$	53.9239	1.71468
$990$	21.0100	0.667743
$991$	−16.9794	−0.539368	−0.269684	−	0.962949i	$-0.586919\pi$
$991$	−16.9794	−0.539368	−0.269684	+	0.962949i	$0.586919\pi$
$992$	−60.4321	−1.91872
$993$	20.4502	0.648966
$994$	−19.1583	−0.607665
$995$	98.8733	3.13450
$996$	17.5962	0.557558
$997$	9.83189	0.311379	0.155690	−	0.987806i	$-0.450240\pi$
$997$	9.83189	0.311379	0.155690	+	0.987806i	$0.450240\pi$
$998$	81.9438	2.59389
$999$	−0.822468	−0.0260218

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.d.1.18	✓	107

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.d.1.18	✓	107	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:	\( N \)	\(=\)	\( 6017 = 11 \cdot 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.10238 q^{2} +0.723159 q^{3} +2.42000 q^{4} -4.03444 q^{5} -1.52035 q^{6} +0.772372 q^{7} -0.882990 q^{8} -2.47704 q^{9} +O(q^{10})\)	\(q-2.10238 q^{2} +0.723159 q^{3} +2.42000 q^{4} -4.03444 q^{5} -1.52035 q^{6} +0.772372 q^{7} -0.882990 q^{8} -2.47704 q^{9} +8.48191 q^{10} -1.00000 q^{11} +1.75004 q^{12} -1.58645 q^{13} -1.62382 q^{14} -2.91754 q^{15} -2.98361 q^{16} -0.833073 q^{17} +5.20768 q^{18} -1.34661 q^{19} -9.76332 q^{20} +0.558547 q^{21} +2.10238 q^{22} +6.32897 q^{23} -0.638542 q^{24} +11.2767 q^{25} +3.33533 q^{26} -3.96077 q^{27} +1.86914 q^{28} -0.842661 q^{29} +6.13377 q^{30} -7.51768 q^{31} +8.03866 q^{32} -0.723159 q^{33} +1.75143 q^{34} -3.11608 q^{35} -5.99443 q^{36} +0.207654 q^{37} +2.83108 q^{38} -1.14726 q^{39} +3.56236 q^{40} +5.22005 q^{41} -1.17428 q^{42} +8.52016 q^{43} -2.42000 q^{44} +9.99346 q^{45} -13.3059 q^{46} +6.53823 q^{47} -2.15763 q^{48} -6.40344 q^{49} -23.7078 q^{50} -0.602444 q^{51} -3.83921 q^{52} +12.4424 q^{53} +8.32704 q^{54} +4.03444 q^{55} -0.681996 q^{56} -0.973811 q^{57} +1.77159 q^{58} -2.81862 q^{59} -7.06043 q^{60} -9.89190 q^{61} +15.8050 q^{62} -1.91320 q^{63} -10.9331 q^{64} +6.40045 q^{65} +1.52035 q^{66} +2.22376 q^{67} -2.01603 q^{68} +4.57685 q^{69} +6.55119 q^{70} +11.7983 q^{71} +2.18720 q^{72} +6.14604 q^{73} -0.436566 q^{74} +8.15482 q^{75} -3.25878 q^{76} -0.772372 q^{77} +2.41197 q^{78} -12.0104 q^{79} +12.0372 q^{80} +4.56686 q^{81} -10.9745 q^{82} +10.0547 q^{83} +1.35168 q^{84} +3.36098 q^{85} -17.9126 q^{86} -0.609378 q^{87} +0.882990 q^{88} -6.20955 q^{89} -21.0100 q^{90} -1.22533 q^{91} +15.3161 q^{92} -5.43648 q^{93} -13.7458 q^{94} +5.43280 q^{95} +5.81323 q^{96} +3.70062 q^{97} +13.4625 q^{98} +2.47704 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 107 q - 3 q^{2} - 18 q^{3} + 91 q^{4} - 15 q^{5} - 54 q^{7} - 3 q^{8} + 95 q^{9}+O(q^{10}) \) 107 * q - 3 * q^2 - 18 * q^3 + 91 * q^4 - 15 * q^5 - 54 * q^7 - 3 * q^8 + 95 * q^9	\( 107 q - 3 q^{2} - 18 q^{3} + 91 q^{4} - 15 q^{5} - 54 q^{7} - 3 q^{8} + 95 q^{9} - 14 q^{10} - 107 q^{11} - 50 q^{12} - 24 q^{13} - 17 q^{14} - 47 q^{15} + 63 q^{16} + 25 q^{17} - 37 q^{18} - 55 q^{19} - 31 q^{20} + 15 q^{21} + 3 q^{22} - 38 q^{23} + 4 q^{24} + 62 q^{25} - 16 q^{26} - 57 q^{27} - 101 q^{28} + 27 q^{29} - 14 q^{30} - 112 q^{31} - 4 q^{32} + 18 q^{33} - 66 q^{34} + 8 q^{35} + 35 q^{36} - 60 q^{37} - 45 q^{38} - 58 q^{39} - 50 q^{40} - 14 q^{41} - 36 q^{42} - 78 q^{43} - 91 q^{44} - 68 q^{45} - 18 q^{46} - 109 q^{47} - 99 q^{48} + 61 q^{49} - 32 q^{50} - 10 q^{51} - 111 q^{52} - 30 q^{53} - 3 q^{54} + 15 q^{55} - 44 q^{56} + q^{57} - 98 q^{58} - 48 q^{59} - 119 q^{60} - 30 q^{61} + 32 q^{62} - 126 q^{63} + 3 q^{64} + 43 q^{65} - 77 q^{67} + 53 q^{68} - 51 q^{69} - 87 q^{70} - 40 q^{71} - 82 q^{72} - 83 q^{73} + 11 q^{74} - 69 q^{75} - 108 q^{76} + 54 q^{77} - 53 q^{78} - 66 q^{79} - 96 q^{80} + 51 q^{81} - 133 q^{82} - 32 q^{83} + 27 q^{84} - 66 q^{85} - 46 q^{86} - 136 q^{87} + 3 q^{88} - 56 q^{89} + 9 q^{90} - 86 q^{91} - 94 q^{92} - 33 q^{93} - 93 q^{94} - 25 q^{95} - 4 q^{96} - 109 q^{97} - 38 q^{98} - 95 q^{99}+O(q^{100}) \) 107 * q - 3 * q^2 - 18 * q^3 + 91 * q^4 - 15 * q^5 - 54 * q^7 - 3 * q^8 + 95 * q^9 - 14 * q^10 - 107 * q^11 - 50 * q^12 - 24 * q^13 - 17 * q^14 - 47 * q^15 + 63 * q^16 + 25 * q^17 - 37 * q^18 - 55 * q^19 - 31 * q^20 + 15 * q^21 + 3 * q^22 - 38 * q^23 + 4 * q^24 + 62 * q^25 - 16 * q^26 - 57 * q^27 - 101 * q^28 + 27 * q^29 - 14 * q^30 - 112 * q^31 - 4 * q^32 + 18 * q^33 - 66 * q^34 + 8 * q^35 + 35 * q^36 - 60 * q^37 - 45 * q^38 - 58 * q^39 - 50 * q^40 - 14 * q^41 - 36 * q^42 - 78 * q^43 - 91 * q^44 - 68 * q^45 - 18 * q^46 - 109 * q^47 - 99 * q^48 + 61 * q^49 - 32 * q^50 - 10 * q^51 - 111 * q^52 - 30 * q^53 - 3 * q^54 + 15 * q^55 - 44 * q^56 + q^57 - 98 * q^58 - 48 * q^59 - 119 * q^60 - 30 * q^61 + 32 * q^62 - 126 * q^63 + 3 * q^64 + 43 * q^65 - 77 * q^67 + 53 * q^68 - 51 * q^69 - 87 * q^70 - 40 * q^71 - 82 * q^72 - 83 * q^73 + 11 * q^74 - 69 * q^75 - 108 * q^76 + 54 * q^77 - 53 * q^78 - 66 * q^79 - 96 * q^80 + 51 * q^81 - 133 * q^82 - 32 * q^83 + 27 * q^84 - 66 * q^85 - 46 * q^86 - 136 * q^87 + 3 * q^88 - 56 * q^89 + 9 * q^90 - 86 * q^91 - 94 * q^92 - 33 * q^93 - 93 * q^94 - 25 * q^95 - 4 * q^96 - 109 * q^97 - 38 * q^98 - 95 * q^99

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