LMFDB - Embedded newform 2671.2.a.a.1.39

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2671,2,Mod(1,2671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2671, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2671.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2671 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2671.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:	$21.3280423799$
Analytic rank:	$1$
Dimension:	$100$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.39
Character	$\chi$	$=$	2671.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.858357 q^{2} -0.469212 q^{3} -1.26322 q^{4} +1.68171 q^{5} +0.402752 q^{6} -4.02447 q^{7} +2.80101 q^{8} -2.77984 q^{9} +O(q^{10})$	\(q-0.858357 q^{2} -0.469212 q^{3} -1.26322 q^{4} +1.68171 q^{5} +0.402752 q^{6} -4.02447 q^{7} +2.80101 q^{8} -2.77984 q^{9} -1.44351 q^{10} -0.0337123 q^{11} +0.592720 q^{12} +3.34673 q^{13} +3.45443 q^{14} -0.789080 q^{15} +0.122180 q^{16} -3.03025 q^{17} +2.38609 q^{18} +6.34055 q^{19} -2.12438 q^{20} +1.88833 q^{21} +0.0289372 q^{22} +0.528443 q^{23} -1.31427 q^{24} -2.17185 q^{25} -2.87269 q^{26} +2.71197 q^{27} +5.08380 q^{28} +7.01201 q^{29} +0.677312 q^{30} -8.04972 q^{31} -5.70689 q^{32} +0.0158182 q^{33} +2.60104 q^{34} -6.76799 q^{35} +3.51156 q^{36} +5.86142 q^{37} -5.44245 q^{38} -1.57033 q^{39} +4.71049 q^{40} +1.97624 q^{41} -1.62086 q^{42} +7.73584 q^{43} +0.0425861 q^{44} -4.67489 q^{45} -0.453592 q^{46} +6.39687 q^{47} -0.0573284 q^{48} +9.19633 q^{49} +1.86422 q^{50} +1.42183 q^{51} -4.22767 q^{52} -9.63352 q^{53} -2.32784 q^{54} -0.0566943 q^{55} -11.2726 q^{56} -2.97506 q^{57} -6.01881 q^{58} +3.41133 q^{59} +0.996784 q^{60} -14.2603 q^{61} +6.90954 q^{62} +11.1874 q^{63} +4.65419 q^{64} +5.62824 q^{65} -0.0135777 q^{66} -5.17647 q^{67} +3.82788 q^{68} -0.247952 q^{69} +5.80935 q^{70} -5.30495 q^{71} -7.78636 q^{72} -6.16186 q^{73} -5.03119 q^{74} +1.01906 q^{75} -8.00952 q^{76} +0.135674 q^{77} +1.34790 q^{78} +2.45794 q^{79} +0.205472 q^{80} +7.06703 q^{81} -1.69632 q^{82} -1.25882 q^{83} -2.38538 q^{84} -5.09601 q^{85} -6.64011 q^{86} -3.29012 q^{87} -0.0944284 q^{88} -15.9992 q^{89} +4.01272 q^{90} -13.4688 q^{91} -0.667541 q^{92} +3.77703 q^{93} -5.49080 q^{94} +10.6630 q^{95} +2.67775 q^{96} -13.7720 q^{97} -7.89373 q^{98} +0.0937147 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9}+O(q^{10}) $ 100 * q - 15 * q^2 - 12 * q^3 + 89 * q^4 - 33 * q^5 - 28 * q^6 - 14 * q^7 - 45 * q^8 + 60 * q^9	\( 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9} - 18 q^{10} - 47 q^{11} - 27 q^{12} - 29 q^{13} - 51 q^{14} - 36 q^{15} + 71 q^{16} - 99 q^{17} - 27 q^{18} - 45 q^{19} - 75 q^{20} - 79 q^{21} - 2 q^{22} - 25 q^{23} - 66 q^{24} + 67 q^{25} - 73 q^{26} - 42 q^{27} - 31 q^{28} - 78 q^{29} - 29 q^{30} - 41 q^{31} - 95 q^{32} - 83 q^{33} - 44 q^{34} - 45 q^{35} + 23 q^{36} - 16 q^{37} - 29 q^{38} - 42 q^{39} - 37 q^{40} - 235 q^{41} + 16 q^{42} - 6 q^{43} - 122 q^{44} - 79 q^{45} - 17 q^{46} - 67 q^{47} - 25 q^{48} + 30 q^{49} - 68 q^{50} - 18 q^{51} - 41 q^{52} - 69 q^{53} - 63 q^{54} - 32 q^{55} - 120 q^{56} - 63 q^{57} - 7 q^{58} - 118 q^{59} - 49 q^{60} - 60 q^{61} - 23 q^{62} - 43 q^{63} + 43 q^{64} - 181 q^{65} - 4 q^{66} - 18 q^{67} - 130 q^{68} - 80 q^{69} + 12 q^{70} - 77 q^{71} - 40 q^{72} - 64 q^{73} - 48 q^{74} - 18 q^{75} - 134 q^{76} - 87 q^{77} + 65 q^{78} - 48 q^{79} - 95 q^{80} - 20 q^{81} + 45 q^{82} - 108 q^{83} - 97 q^{84} - 21 q^{85} - 73 q^{86} - 3 q^{87} + 23 q^{88} - 325 q^{89} + 6 q^{90} - 17 q^{91} - 19 q^{92} + 2 q^{93} - 5 q^{94} - 54 q^{95} - 105 q^{96} - 81 q^{97} - 61 q^{98} - 76 q^{99}+O(q^{100}) \) 100 * q - 15 * q^2 - 12 * q^3 + 89 * q^4 - 33 * q^5 - 28 * q^6 - 14 * q^7 - 45 * q^8 + 60 * q^9 - 18 * q^10 - 47 * q^11 - 27 * q^12 - 29 * q^13 - 51 * q^14 - 36 * q^15 + 71 * q^16 - 99 * q^17 - 27 * q^18 - 45 * q^19 - 75 * q^20 - 79 * q^21 - 2 * q^22 - 25 * q^23 - 66 * q^24 + 67 * q^25 - 73 * q^26 - 42 * q^27 - 31 * q^28 - 78 * q^29 - 29 * q^30 - 41 * q^31 - 95 * q^32 - 83 * q^33 - 44 * q^34 - 45 * q^35 + 23 * q^36 - 16 * q^37 - 29 * q^38 - 42 * q^39 - 37 * q^40 - 235 * q^41 + 16 * q^42 - 6 * q^43 - 122 * q^44 - 79 * q^45 - 17 * q^46 - 67 * q^47 - 25 * q^48 + 30 * q^49 - 68 * q^50 - 18 * q^51 - 41 * q^52 - 69 * q^53 - 63 * q^54 - 32 * q^55 - 120 * q^56 - 63 * q^57 - 7 * q^58 - 118 * q^59 - 49 * q^60 - 60 * q^61 - 23 * q^62 - 43 * q^63 + 43 * q^64 - 181 * q^65 - 4 * q^66 - 18 * q^67 - 130 * q^68 - 80 * q^69 + 12 * q^70 - 77 * q^71 - 40 * q^72 - 64 * q^73 - 48 * q^74 - 18 * q^75 - 134 * q^76 - 87 * q^77 + 65 * q^78 - 48 * q^79 - 95 * q^80 - 20 * q^81 + 45 * q^82 - 108 * q^83 - 97 * q^84 - 21 * q^85 - 73 * q^86 - 3 * q^87 + 23 * q^88 - 325 * q^89 + 6 * q^90 - 17 * q^91 - 19 * q^92 + 2 * q^93 - 5 * q^94 - 54 * q^95 - 105 * q^96 - 81 * q^97 - 61 * q^98 - 76 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−0.858357	−0.606950	−0.303475	−	0.952839i	$-0.598147\pi$
$2$	−0.858357	−0.606950	−0.303475	+	0.952839i	$0.598147\pi$
$3$	−0.469212	−0.270900	−0.135450	−	0.990784i	$-0.543248\pi$
$3$	−0.469212	−0.270900	−0.135450	+	0.990784i	$0.543248\pi$
$4$	−1.26322	−0.631612
$5$	1.68171	0.752084	0.376042	−	0.926603i	$-0.377285\pi$
$5$	1.68171	0.752084	0.376042	+	0.926603i	$0.377285\pi$
$6$	0.402752	0.164423
$7$	−4.02447	−1.52111	−0.760553	−	0.649276i	$-0.775072\pi$
$7$	−4.02447	−1.52111	−0.760553	+	0.649276i	$0.775072\pi$
$8$	2.80101	0.990307
$9$	−2.77984	−0.926613
$10$	−1.44351	−0.456477
$11$	−0.0337123	−0.0101646	−0.00508232	−	0.999987i	$-0.501618\pi$
$11$	−0.0337123	−0.0101646	−0.00508232	+	0.999987i	$0.501618\pi$
$12$	0.592720	0.171104
$13$	3.34673	0.928217	0.464109	−	0.885778i	$-0.346375\pi$
$13$	3.34673	0.928217	0.464109	+	0.885778i	$0.346375\pi$
$14$	3.45443	0.923235
$15$	−0.789080	−0.203740
$16$	0.122180	0.0305450
$17$	−3.03025	−0.734944	−0.367472	−	0.930035i	$-0.619777\pi$
$17$	−3.03025	−0.734944	−0.367472	+	0.930035i	$0.619777\pi$
$18$	2.38609	0.562408
$19$	6.34055	1.45462	0.727310	−	0.686309i	$-0.240770\pi$
$19$	6.34055	1.45462	0.727310	+	0.686309i	$0.240770\pi$
$20$	−2.12438	−0.475025
$21$	1.88833	0.412067
$22$	0.0289372	0.00616942
$23$	0.528443	0.110188	0.0550940	−	0.998481i	$-0.482454\pi$
$23$	0.528443	0.110188	0.0550940	+	0.998481i	$0.482454\pi$
$24$	−1.31427	−0.268274
$25$	−2.17185	−0.434370
$26$	−2.87269	−0.563381
$27$	2.71197	0.521919
$28$	5.08380	0.960748
$29$	7.01201	1.30210	0.651049	−	0.759036i	$-0.274329\pi$
$29$	7.01201	1.30210	0.651049	+	0.759036i	$0.274329\pi$
$30$	0.677312	0.123660
$31$	−8.04972	−1.44577	−0.722887	−	0.690967i	$-0.757185\pi$
$31$	−8.04972	−1.44577	−0.722887	+	0.690967i	$0.757185\pi$
$32$	−5.70689	−1.00885
$33$	0.0158182	0.00275360
$34$	2.60104	0.446074
$35$	−6.76799	−1.14400
$36$	3.51156	0.585260
$37$	5.86142	0.963612	0.481806	−	0.876278i	$-0.339981\pi$
$37$	5.86142	0.963612	0.481806	+	0.876278i	$0.339981\pi$
$38$	−5.44245	−0.882882
$39$	−1.57033	−0.251454
$40$	4.71049	0.744794
$41$	1.97624	0.308637	0.154318	−	0.988021i	$-0.450682\pi$
$41$	1.97624	0.308637	0.154318	+	0.988021i	$0.450682\pi$
$42$	−1.62086	−0.250104
$43$	7.73584	1.17970	0.589852	−	0.807511i	$-0.299186\pi$
$43$	7.73584	1.17970	0.589852	+	0.807511i	$0.299186\pi$
$44$	0.0425861	0.00642010
$45$	−4.67489	−0.696891
$46$	−0.453592	−0.0668786
$47$	6.39687	0.933080	0.466540	−	0.884500i	$-0.345500\pi$
$47$	6.39687	0.933080	0.466540	+	0.884500i	$0.345500\pi$
$48$	−0.0573284	−0.00827465
$49$	9.19633	1.31376
$50$	1.86422	0.263641
$51$	1.42183	0.199096
$52$	−4.22767	−0.586273
$53$	−9.63352	−1.32327	−0.661633	−	0.749828i	$-0.730136\pi$
$53$	−9.63352	−1.32327	−0.661633	+	0.749828i	$0.730136\pi$
$54$	−2.32784	−0.316779
$55$	−0.0566943	−0.00764466
$56$	−11.2726	−1.50636
$57$	−2.97506	−0.394057
$58$	−6.01881	−0.790308
$59$	3.41133	0.444117	0.222059	−	0.975033i	$-0.428722\pi$
$59$	3.41133	0.444117	0.222059	+	0.975033i	$0.428722\pi$
$60$	0.996784	0.128684
$61$	−14.2603	−1.82584	−0.912922	−	0.408134i	$-0.866180\pi$
$61$	−14.2603	−1.82584	−0.912922	+	0.408134i	$0.866180\pi$
$62$	6.90954	0.877512
$63$	11.1874	1.40948
$64$	4.65419	0.581774
$65$	5.62824	0.698097
$66$	−0.0135777	−0.00167130
$67$	−5.17647	−0.632406	−0.316203	−	0.948692i	$-0.602408\pi$
$67$	−5.17647	−0.632406	−0.316203	+	0.948692i	$0.602408\pi$
$68$	3.82788	0.464199
$69$	−0.247952	−0.0298499
$70$	5.80935	0.694350
$71$	−5.30495	−0.629581	−0.314791	−	0.949161i	$-0.601934\pi$
$71$	−5.30495	−0.629581	−0.314791	+	0.949161i	$0.601934\pi$
$72$	−7.78636	−0.917631
$73$	−6.16186	−0.721191	−0.360596	−	0.932722i	$-0.617427\pi$
$73$	−6.16186	−0.721191	−0.360596	+	0.932722i	$0.617427\pi$
$74$	−5.03119	−0.584864
$75$	1.01906	0.117671
$76$	−8.00952	−0.918756
$77$	0.135674	0.0154615
$78$	1.34790	0.152620
$79$	2.45794	0.276540	0.138270	−	0.990395i	$-0.455846\pi$
$79$	2.45794	0.276540	0.138270	+	0.990395i	$0.455846\pi$
$80$	0.205472	0.0229724
$81$	7.06703	0.785225
$82$	−1.69632	−0.187327
$83$	−1.25882	−0.138173	−0.0690865	−	0.997611i	$-0.522008\pi$
$83$	−1.25882	−0.138173	−0.0690865	+	0.997611i	$0.522008\pi$
$84$	−2.38538	−0.260266
$85$	−5.09601	−0.552740
$86$	−6.64011	−0.716022
$87$	−3.29012	−0.352738
$88$	−0.0944284	−0.0100661
$89$	−15.9992	−1.69591	−0.847957	−	0.530065i	$-0.822168\pi$
$89$	−15.9992	−1.69591	−0.847957	+	0.530065i	$0.822168\pi$
$90$	4.01272	0.422978
$91$	−13.4688	−1.41192
$92$	−0.667541	−0.0695960
$93$	3.77703	0.391660
$94$	−5.49080	−0.566333
$95$	10.6630	1.09400
$96$	2.67775	0.273296
$97$	−13.7720	−1.39833	−0.699166	−	0.714959i	$-0.746445\pi$
$97$	−13.7720	−1.39833	−0.699166	+	0.714959i	$0.746445\pi$
$98$	−7.89373	−0.797387
$99$	0.0937147	0.00941868
$100$	2.74353	0.274353
$101$	18.1232	1.80332	0.901661	−	0.432444i	$-0.142349\pi$
$101$	18.1232	1.80332	0.901661	+	0.432444i	$0.142349\pi$
$102$	−1.22044	−0.120841
$103$	−0.745468	−0.0734531	−0.0367266	−	0.999325i	$-0.511693\pi$
$103$	−0.745468	−0.0734531	−0.0367266	+	0.999325i	$0.511693\pi$
$104$	9.37424	0.919220
$105$	3.17562	0.309909
$106$	8.26900	0.803156
$107$	9.68418	0.936205	0.468102	−	0.883674i	$-0.344938\pi$
$107$	9.68418	0.936205	0.468102	+	0.883674i	$0.344938\pi$
$108$	−3.42583	−0.329650
$109$	−16.9218	−1.62081	−0.810407	−	0.585867i	$-0.800754\pi$
$109$	−16.9218	−1.62081	−0.810407	+	0.585867i	$0.800754\pi$
$110$	0.0486640	0.00463993
$111$	−2.75025	−0.261042
$112$	−0.491710	−0.0464622
$113$	−9.98979	−0.939760	−0.469880	−	0.882730i	$-0.655703\pi$
$113$	−9.98979	−0.939760	−0.469880	+	0.882730i	$0.655703\pi$
$114$	2.55367	0.239173
$115$	0.888688	0.0828706
$116$	−8.85773	−0.822420
$117$	−9.30339	−0.860098
$118$	−2.92814	−0.269557
$119$	12.1951	1.11793
$120$	−2.21022	−0.201765
$121$	−10.9989	−0.999897
$122$	12.2404	1.10820
$123$	−0.927276	−0.0836096
$124$	10.1686	0.913167
$125$	−12.0610	−1.07877
$126$	−9.60276	−0.855482
$127$	7.09961	0.629988	0.314994	−	0.949094i	$-0.397997\pi$
$127$	7.09961	0.629988	0.314994	+	0.949094i	$0.397997\pi$
$128$	7.41883	0.655738
$129$	−3.62975	−0.319582
$130$	−4.83104	−0.423710
$131$	4.04122	0.353083	0.176542	−	0.984293i	$-0.443509\pi$
$131$	4.04122	0.353083	0.176542	+	0.984293i	$0.443509\pi$
$132$	−0.0199819	−0.00173921
$133$	−25.5173	−2.21263
$134$	4.44326	0.383839
$135$	4.56075	0.392527
$136$	−8.48776	−0.727820
$137$	5.17953	0.442517	0.221258	−	0.975215i	$-0.428984\pi$
$137$	5.17953	0.442517	0.221258	+	0.975215i	$0.428984\pi$
$138$	0.212831	0.0181174
$139$	17.0651	1.44745	0.723723	−	0.690091i	$-0.242429\pi$
$139$	17.0651	1.44745	0.723723	+	0.690091i	$0.242429\pi$
$140$	8.54948	0.722563
$141$	−3.00149	−0.252771
$142$	4.55354	0.382124
$143$	−0.112826	−0.00943499
$144$	−0.339641	−0.0283034
$145$	11.7922	0.979287
$146$	5.28908	0.437727
$147$	−4.31503	−0.355898
$148$	−7.40429	−0.608628
$149$	20.3905	1.67046	0.835228	−	0.549903i	$-0.185335\pi$
$149$	20.3905	1.67046	0.835228	+	0.549903i	$0.185335\pi$
$150$	−0.874715	−0.0714202
$151$	−16.6262	−1.35302	−0.676512	−	0.736432i	$-0.736509\pi$
$151$	−16.6262	−1.35302	−0.676512	+	0.736432i	$0.736509\pi$
$152$	17.7599	1.44052
$153$	8.42361	0.681009
$154$	−0.116457	−0.00938434
$155$	−13.5373	−1.08734
$156$	1.98368	0.158821
$157$	−0.495221	−0.0395229	−0.0197615	−	0.999805i	$-0.506291\pi$
$157$	−0.495221	−0.0395229	−0.0197615	+	0.999805i	$0.506291\pi$
$158$	−2.10979	−0.167846
$159$	4.52017	0.358473
$160$	−9.59735	−0.758737
$161$	−2.12670	−0.167607
$162$	−6.06603	−0.476593
$163$	16.4161	1.28580	0.642902	−	0.765948i	$-0.277730\pi$
$163$	16.4161	1.28580	0.642902	+	0.765948i	$0.277730\pi$
$164$	−2.49643	−0.194938
$165$	0.0266017	0.00207094
$166$	1.08051	0.0838641
$167$	−14.9447	−1.15646	−0.578230	−	0.815874i	$-0.696256\pi$
$167$	−14.9447	−1.15646	−0.578230	+	0.815874i	$0.696256\pi$
$168$	5.28923	0.408073
$169$	−1.79936	−0.138413
$170$	4.37419	0.335485
$171$	−17.6257	−1.34787
$172$	−9.77209	−0.745115
$173$	−8.13833	−0.618746	−0.309373	−	0.950941i	$-0.600119\pi$
$173$	−8.13833	−0.618746	−0.309373	+	0.950941i	$0.600119\pi$
$174$	2.82410	0.214094
$175$	8.74053	0.660722
$176$	−0.00411897	−0.000310479 0
$177$	−1.60064	−0.120311
$178$	13.7330	1.02934
$179$	−24.8789	−1.85953	−0.929767	−	0.368149i	$-0.879992\pi$
$179$	−24.8789	−1.85953	−0.929767	+	0.368149i	$0.879992\pi$
$180$	5.90543	0.440165
$181$	−3.83886	−0.285340	−0.142670	−	0.989770i	$-0.545569\pi$
$181$	−3.83886	−0.285340	−0.142670	+	0.989770i	$0.545569\pi$
$182$	11.5611	0.856962
$183$	6.69111	0.494621
$184$	1.48017	0.109120
$185$	9.85722	0.724717
$186$	−3.24204	−0.237718
$187$	0.102157	0.00747043
$188$	−8.08068	−0.589344
$189$	−10.9142	−0.793894
$190$	−9.15263	−0.664002
$191$	19.8241	1.43442	0.717212	−	0.696855i	$-0.245418\pi$
$191$	19.8241	1.43442	0.717212	+	0.696855i	$0.245418\pi$
$192$	−2.18380	−0.157603
$193$	−25.0640	−1.80414	−0.902071	−	0.431587i	$-0.857954\pi$
$193$	−25.0640	−1.80414	−0.902071	+	0.431587i	$0.857954\pi$
$194$	11.8213	0.848717
$195$	−2.64084	−0.189115
$196$	−11.6170	−0.829787
$197$	−4.53183	−0.322879	−0.161440	−	0.986883i	$-0.551614\pi$
$197$	−4.53183	−0.322879	−0.161440	+	0.986883i	$0.551614\pi$
$198$	−0.0804407	−0.00571667
$199$	−14.4186	−1.02211	−0.511054	−	0.859549i	$-0.670745\pi$
$199$	−14.4186	−1.02211	−0.511054	+	0.859549i	$0.670745\pi$
$200$	−6.08337	−0.430159
$201$	2.42886	0.171319
$202$	−15.5561	−1.09453
$203$	−28.2196	−1.98063
$204$	−1.79609	−0.125751
$205$	3.32346	0.232121
$206$	0.639877	0.0445824
$207$	−1.46899	−0.102102
$208$	0.408905	0.0283524
$209$	−0.213754	−0.0147857
$210$	−2.72582	−0.188099
$211$	−13.4364	−0.925002	−0.462501	−	0.886619i	$-0.653048\pi$
$211$	−13.4364	−0.925002	−0.462501	+	0.886619i	$0.653048\pi$
$212$	12.1693	0.835790
$213$	2.48915	0.170554
$214$	−8.31248	−0.568230
$215$	13.0094	0.887237
$216$	7.59626	0.516860
$217$	32.3958	2.19917
$218$	14.5249	0.983753
$219$	2.89122	0.195371
$220$	0.0716176	0.00482846
$221$	−10.1414	−0.682188
$222$	2.36070	0.158440
$223$	−6.10002	−0.408487	−0.204244	−	0.978920i	$-0.565473\pi$
$223$	−6.10002	−0.408487	−0.204244	+	0.978920i	$0.565473\pi$
$224$	22.9672	1.53456
$225$	6.03739	0.402493
$226$	8.57480	0.570387
$227$	−24.2684	−1.61075	−0.805376	−	0.592765i	$-0.798036\pi$
$227$	−24.2684	−1.61075	−0.805376	+	0.592765i	$0.798036\pi$
$228$	3.75817	0.248891
$229$	−23.9157	−1.58039	−0.790196	−	0.612854i	$-0.790021\pi$
$229$	−23.9157	−1.58039	−0.790196	+	0.612854i	$0.790021\pi$
$230$	−0.762811	−0.0502983
$231$	−0.0636599	−0.00418851
$232$	19.6407	1.28948
$233$	16.4020	1.07453	0.537264	−	0.843414i	$-0.319458\pi$
$233$	16.4020	1.07453	0.537264	+	0.843414i	$0.319458\pi$
$234$	7.98563	0.522037
$235$	10.7577	0.701755
$236$	−4.30927	−0.280510
$237$	−1.15330	−0.0749147
$238$	−10.4678	−0.678526
$239$	−3.98857	−0.257999	−0.129000	−	0.991645i	$-0.541177\pi$
$239$	−3.98857	−0.257999	−0.129000	+	0.991645i	$0.541177\pi$
$240$	−0.0964099	−0.00622323
$241$	12.4315	0.800785	0.400393	−	0.916344i	$-0.368874\pi$
$241$	12.4315	0.800785	0.400393	+	0.916344i	$0.368874\pi$
$242$	9.44095	0.606887
$243$	−11.4519	−0.734637
$244$	18.0139	1.15322
$245$	15.4656	0.988059
$246$	0.795933	0.0507469
$247$	21.2201	1.35020
$248$	−22.5474	−1.43176
$249$	0.590652	0.0374310
$250$	10.3526	0.654757
$251$	−19.3223	−1.21961	−0.609806	−	0.792550i	$-0.708753\pi$
$251$	−19.3223	−1.21961	−0.609806	+	0.792550i	$0.708753\pi$
$252$	−14.1321	−0.890242
$253$	−0.0178150	−0.00112002
$254$	−6.09400	−0.382371
$255$	2.39111	0.149737
$256$	−15.6764	−0.979774
$257$	−25.6591	−1.60057	−0.800285	−	0.599620i	$-0.795319\pi$
$257$	−25.6591	−1.60057	−0.800285	+	0.599620i	$0.795319\pi$
$258$	3.11562	0.193970
$259$	−23.5891	−1.46575
$260$	−7.10973	−0.440927
$261$	−19.4923	−1.20654
$262$	−3.46881	−0.214304
$263$	15.5373	0.958071	0.479036	−	0.877796i	$-0.340986\pi$
$263$	15.5373	0.958071	0.479036	+	0.877796i	$0.340986\pi$
$264$	0.0443070	0.00272691
$265$	−16.2008	−0.995207
$266$	21.9030	1.34296
$267$	7.50703	0.459423
$268$	6.53903	0.399435
$269$	−19.6577	−1.19855	−0.599275	−	0.800543i	$-0.704544\pi$
$269$	−19.6577	−1.19855	−0.599275	+	0.800543i	$0.704544\pi$
$270$	−3.91476	−0.238244
$271$	−21.6265	−1.31372	−0.656860	−	0.754013i	$-0.728116\pi$
$271$	−21.6265	−1.31372	−0.656860	+	0.754013i	$0.728116\pi$
$272$	−0.370236	−0.0224489
$273$	6.31974	0.382488
$274$	−4.44588	−0.268586
$275$	0.0732179	0.00441521
$276$	0.313219	0.0188535
$277$	15.3778	0.923964	0.461982	−	0.886889i	$-0.347138\pi$
$277$	15.3778	0.923964	0.461982	+	0.886889i	$0.347138\pi$
$278$	−14.6480	−0.878527
$279$	22.3769	1.33967
$280$	−18.9572	−1.13291
$281$	−24.2407	−1.44608	−0.723039	−	0.690807i	$-0.757256\pi$
$281$	−24.2407	−1.44608	−0.723039	+	0.690807i	$0.757256\pi$
$282$	2.57635	0.153420
$283$	−1.72124	−0.102317	−0.0511586	−	0.998691i	$-0.516291\pi$
$283$	−1.72124	−0.102317	−0.0511586	+	0.998691i	$0.516291\pi$
$284$	6.70133	0.397651
$285$	−5.00320	−0.296364
$286$	0.0968450	0.00572657
$287$	−7.95330	−0.469469
$288$	15.8643	0.934810
$289$	−7.81758	−0.459858
$290$	−10.1219	−0.594378
$291$	6.46198	0.378808
$292$	7.78381	0.455513
$293$	−15.9929	−0.934317	−0.467158	−	0.884174i	$-0.654722\pi$
$293$	−15.9929	−0.934317	−0.467158	+	0.884174i	$0.654722\pi$
$294$	3.70384	0.216012
$295$	5.73687	0.334014
$296$	16.4179	0.954271
$297$	−0.0914268	−0.00530512
$298$	−17.5023	−1.01388
$299$	1.76856	0.102278
$300$	−1.28730	−0.0743222
$301$	−31.1326	−1.79445
$302$	14.2712	0.821218
$303$	−8.50361	−0.488520
$304$	0.774689	0.0444314
$305$	−23.9817	−1.37319
$306$	−7.23047	−0.413338
$307$	12.9250	0.737668	0.368834	−	0.929495i	$-0.379757\pi$
$307$	12.9250	0.737668	0.368834	+	0.929495i	$0.379757\pi$
$308$	−0.171386	−0.00976565
$309$	0.349783	0.0198984
$310$	11.6198	0.659963
$311$	11.5927	0.657361	0.328680	−	0.944441i	$-0.393396\pi$
$311$	11.5927	0.657361	0.328680	+	0.944441i	$0.393396\pi$
$312$	−4.39851	−0.249017
$313$	−8.42275	−0.476082	−0.238041	−	0.971255i	$-0.576505\pi$
$313$	−8.42275	−0.476082	−0.238041	+	0.971255i	$0.576505\pi$
$314$	0.425076	0.0239884
$315$	18.8139	1.06004
$316$	−3.10493	−0.174666
$317$	15.9519	0.895949	0.447975	−	0.894046i	$-0.352145\pi$
$317$	15.9519	0.895949	0.447975	+	0.894046i	$0.352145\pi$
$318$	−3.87992	−0.217575
$319$	−0.236391	−0.0132353
$320$	7.82701	0.437543
$321$	−4.54394	−0.253618
$322$	1.82547	0.101729
$323$	−19.2134	−1.06906
$324$	−8.92723	−0.495957
$325$	−7.26860	−0.403189
$326$	−14.0908	−0.780419
$327$	7.93992	0.439079
$328$	5.53546	0.305645
$329$	−25.7440	−1.41931
$330$	−0.0228337	−0.00125696
$331$	−16.6183	−0.913424	−0.456712	−	0.889615i	$-0.650973\pi$
$331$	−16.6183	−0.913424	−0.456712	+	0.889615i	$0.650973\pi$
$332$	1.59017	0.0872717
$333$	−16.2938	−0.892895
$334$	12.8279	0.701913
$335$	−8.70532	−0.475623
$336$	0.230716	0.0125866
$337$	20.3575	1.10895	0.554473	−	0.832202i	$-0.312920\pi$
$337$	20.3575	1.10895	0.554473	+	0.832202i	$0.312920\pi$
$338$	1.54450	0.0840096
$339$	4.68733	0.254581
$340$	6.43739	0.349117
$341$	0.271375	0.0146958
$342$	15.1291	0.818090
$343$	−8.83904	−0.477263
$344$	21.6682	1.16827
$345$	−0.416983	−0.0224496
$346$	6.98559	0.375548
$347$	−7.31047	−0.392446	−0.196223	−	0.980559i	$-0.562868\pi$
$347$	−7.31047	−0.392446	−0.196223	+	0.980559i	$0.562868\pi$
$348$	4.15616	0.222794
$349$	8.64268	0.462632	0.231316	−	0.972879i	$-0.425697\pi$
$349$	8.64268	0.462632	0.231316	+	0.972879i	$0.425697\pi$
$350$	−7.50249	−0.401025
$351$	9.07625	0.484455
$352$	0.192392	0.0102546
$353$	8.90676	0.474059	0.237030	−	0.971502i	$-0.423826\pi$
$353$	8.90676	0.474059	0.237030	+	0.971502i	$0.423826\pi$
$354$	1.37392	0.0730230
$355$	−8.92139	−0.473498
$356$	20.2106	1.07116
$357$	−5.72211	−0.302846
$358$	21.3549	1.12864
$359$	−4.12824	−0.217880	−0.108940	−	0.994048i	$-0.534746\pi$
$359$	−4.12824	−0.217880	−0.108940	+	0.994048i	$0.534746\pi$
$360$	−13.0944	−0.690136
$361$	21.2025	1.11592
$362$	3.29511	0.173187
$363$	5.16080	0.270872
$364$	17.0141	0.891783
$365$	−10.3625	−0.542397
$366$	−5.74336	−0.300210
$367$	−2.76137	−0.144142	−0.0720711	−	0.997399i	$-0.522961\pi$
$367$	−2.76137	−0.144142	−0.0720711	+	0.997399i	$0.522961\pi$
$368$	0.0645652	0.00336569
$369$	−5.49363	−0.285987
$370$	−8.46101	−0.439867
$371$	38.7698	2.01283
$372$	−4.77123	−0.247377
$373$	−10.5881	−0.548231	−0.274116	−	0.961697i	$-0.588385\pi$
$373$	−10.5881	−0.548231	−0.274116	+	0.961697i	$0.588385\pi$
$374$	−0.0876869	−0.00453418
$375$	5.65916	0.292238
$376$	17.9177	0.924035
$377$	23.4673	1.20863
$378$	9.36831	0.481854
$379$	25.0019	1.28426	0.642131	−	0.766595i	$-0.278050\pi$
$379$	25.0019	1.28426	0.642131	+	0.766595i	$0.278050\pi$
$380$	−13.4697	−0.690981
$381$	−3.33122	−0.170664
$382$	−17.0162	−0.870624
$383$	−10.9704	−0.560561	−0.280281	−	0.959918i	$-0.590427\pi$
$383$	−10.9704	−0.560561	−0.280281	+	0.959918i	$0.590427\pi$
$384$	−3.48101	−0.177639
$385$	0.228164	0.0116283
$386$	21.5138	1.09502
$387$	−21.5044	−1.09313
$388$	17.3971	0.883203
$389$	−17.4748	−0.886006	−0.443003	−	0.896520i	$-0.646087\pi$
$389$	−17.4748	−0.886006	−0.443003	+	0.896520i	$0.646087\pi$
$390$	2.26678	0.114783
$391$	−1.60131	−0.0809819
$392$	25.7590	1.30103
$393$	−1.89619	−0.0956502
$394$	3.88993	0.195972
$395$	4.13355	0.207982
$396$	−0.118383	−0.00594895
$397$	1.31232	0.0658633	0.0329317	−	0.999458i	$-0.489516\pi$
$397$	1.31232	0.0658633	0.0329317	+	0.999458i	$0.489516\pi$
$398$	12.3763	0.620368
$399$	11.9730	0.599402
$400$	−0.265357	−0.0132678
$401$	−18.7406	−0.935862	−0.467931	−	0.883765i	$-0.655000\pi$
$401$	−18.7406	−0.935862	−0.467931	+	0.883765i	$0.655000\pi$
$402$	−2.08483	−0.103982
$403$	−26.9403	−1.34199
$404$	−22.8936	−1.13900
$405$	11.8847	0.590555
$406$	24.2225	1.20214
$407$	−0.197602	−0.00979476
$408$	3.98256	0.197166
$409$	31.0463	1.53514	0.767570	−	0.640965i	$-0.221466\pi$
$409$	31.0463	1.53514	0.767570	+	0.640965i	$0.221466\pi$
$410$	−2.85272	−0.140886
$411$	−2.43030	−0.119878
$412$	0.941692	0.0463938
$413$	−13.7288	−0.675549
$414$	1.26091	0.0619706
$415$	−2.11696	−0.103918
$416$	−19.0995	−0.936428
$417$	−8.00717	−0.392113
$418$	0.183477	0.00897417
$419$	26.6167	1.30031	0.650156	−	0.759801i	$-0.274704\pi$
$419$	26.6167	1.30031	0.650156	+	0.759801i	$0.274704\pi$
$420$	−4.01152	−0.195742
$421$	15.1680	0.739242	0.369621	−	0.929183i	$-0.379488\pi$
$421$	15.1680	0.739242	0.369621	+	0.929183i	$0.379488\pi$
$422$	11.5333	0.561430
$423$	−17.7823	−0.864604
$424$	−26.9836	−1.31044
$425$	6.58124	0.319237
$426$	−2.13658	−0.103517
$427$	57.3901	2.77730
$428$	−12.2333	−0.591318
$429$	0.0529394	0.00255594
$430$	−11.1668	−0.538509
$431$	14.4056	0.693894	0.346947	−	0.937885i	$-0.387218\pi$
$431$	14.4056	0.693894	0.346947	+	0.937885i	$0.387218\pi$
$432$	0.331349	0.0159420
$433$	24.2883	1.16722	0.583610	−	0.812034i	$-0.301640\pi$
$433$	24.2883	1.16722	0.583610	+	0.812034i	$0.301640\pi$
$434$	−27.8072	−1.33479
$435$	−5.53303	−0.265289
$436$	21.3760	1.02373
$437$	3.35061	0.160282
$438$	−2.48170	−0.118580
$439$	23.0051	1.09797	0.548987	−	0.835831i	$-0.315014\pi$
$439$	23.0051	1.09797	0.548987	+	0.835831i	$0.315014\pi$
$440$	−0.158801	−0.00757056
$441$	−25.5643	−1.21735
$442$	8.70498	0.414054
$443$	−6.03297	−0.286635	−0.143318	−	0.989677i	$-0.545777\pi$
$443$	−6.03297	−0.286635	−0.143318	+	0.989677i	$0.545777\pi$
$444$	3.47418	0.164877
$445$	−26.9061	−1.27547
$446$	5.23599	0.247931
$447$	−9.56749	−0.452527
$448$	−18.7306	−0.884940
$449$	7.49404	0.353666	0.176833	−	0.984241i	$-0.443415\pi$
$449$	7.49404	0.353666	0.176833	+	0.984241i	$0.443415\pi$
$450$	−5.18223	−0.244293
$451$	−0.0666235	−0.00313718
$452$	12.6193	0.593564
$453$	7.80124	0.366534
$454$	20.8310	0.977646
$455$	−22.6507	−1.06188
$456$	−8.33318	−0.390237
$457$	20.5950	0.963394	0.481697	−	0.876338i	$-0.340021\pi$
$457$	20.5950	0.963394	0.481697	+	0.876338i	$0.340021\pi$
$458$	20.5282	0.959219
$459$	−8.21796	−0.383581
$460$	−1.12261	−0.0523420
$461$	−5.95304	−0.277261	−0.138630	−	0.990344i	$-0.544270\pi$
$461$	−5.95304	−0.277261	−0.138630	+	0.990344i	$0.544270\pi$
$462$	0.0546429	0.00254222
$463$	−33.8859	−1.57481	−0.787406	−	0.616435i	$-0.788576\pi$
$463$	−33.8859	−1.57481	−0.787406	+	0.616435i	$0.788576\pi$
$464$	0.856728	0.0397726
$465$	6.35187	0.294561
$466$	−14.0787	−0.652185
$467$	21.8957	1.01321	0.506607	−	0.862177i	$-0.330899\pi$
$467$	21.8957	1.01321	0.506607	+	0.862177i	$0.330899\pi$
$468$	11.7523	0.543248
$469$	20.8325	0.961956
$470$	−9.23394	−0.425930
$471$	0.232364	0.0107068
$472$	9.55517	0.439812
$473$	−0.260793	−0.0119913
$474$	0.989941	0.0454695
$475$	−13.7707	−0.631843
$476$	−15.4052	−0.706096
$477$	26.7796	1.22616
$478$	3.42362	0.156593
$479$	24.9248	1.13884	0.569422	−	0.822045i	$-0.307167\pi$
$479$	24.9248	1.13884	0.569422	+	0.822045i	$0.307167\pi$
$480$	4.50320	0.205542
$481$	19.6166	0.894441
$482$	−10.6707	−0.486037
$483$	0.997874	0.0454048
$484$	13.8940	0.631546
$485$	−23.1605	−1.05166
$486$	9.82978	0.445888
$487$	30.2492	1.37072	0.685361	−	0.728203i	$-0.259644\pi$
$487$	30.2492	1.37072	0.685361	+	0.728203i	$0.259644\pi$
$488$	−39.9432	−1.80815
$489$	−7.70262	−0.348324
$490$	−13.2750	−0.599702
$491$	−10.9578	−0.494520	−0.247260	−	0.968949i	$-0.579530\pi$
$491$	−10.9578	−0.494520	−0.247260	+	0.968949i	$0.579530\pi$
$492$	1.17136	0.0528088
$493$	−21.2481	−0.956968
$494$	−18.2144	−0.819506
$495$	0.157601	0.00708364
$496$	−0.983516	−0.0441612
$497$	21.3496	0.957659
$498$	−0.506990	−0.0227188
$499$	0.528984	0.0236806	0.0118403	−	0.999930i	$-0.496231\pi$
$499$	0.528984	0.0236806	0.0118403	+	0.999930i	$0.496231\pi$
$500$	15.2357	0.681362
$501$	7.01226	0.313285
$502$	16.5854	0.740244
$503$	31.2325	1.39259	0.696294	−	0.717756i	$-0.254831\pi$
$503$	31.2325	1.39259	0.696294	+	0.717756i	$0.254831\pi$
$504$	31.3359	1.39581
$505$	30.4779	1.35625
$506$	0.0152916	0.000679796 0
$507$	0.844284	0.0374960
$508$	−8.96839	−0.397908
$509$	−16.0594	−0.711821	−0.355911	−	0.934520i	$-0.615829\pi$
$509$	−16.0594	−0.711821	−0.355911	+	0.934520i	$0.615829\pi$
$510$	−2.05243	−0.0908829
$511$	24.7982	1.09701
$512$	−1.38172	−0.0610642
$513$	17.1954	0.759195
$514$	22.0247	0.971466
$515$	−1.25366	−0.0552429
$516$	4.58519	0.201852
$517$	−0.215653	−0.00948442
$518$	20.2479	0.889640
$519$	3.81860	0.167618
$520$	15.7648	0.691331
$521$	25.6513	1.12380	0.561901	−	0.827204i	$-0.310070\pi$
$521$	25.6513	1.12380	0.561901	+	0.827204i	$0.310070\pi$
$522$	16.7313	0.732310
$523$	4.20038	0.183670	0.0918349	−	0.995774i	$-0.470727\pi$
$523$	4.20038	0.183670	0.0918349	+	0.995774i	$0.470727\pi$
$524$	−5.10496	−0.223011
$525$	−4.10116	−0.178989
$526$	−13.3366	−0.581501
$527$	24.3927	1.06256
$528$	0.00193267	8.41088e−5 0
$529$	−22.7207	−0.987859
$530$	13.9061	0.604041
$531$	−9.48295	−0.411525
$532$	32.2341	1.39752
$533$	6.61395	0.286482
$534$	−6.44371	−0.278847
$535$	16.2860	0.704105
$536$	−14.4993	−0.626276
$537$	11.6735	0.503748
$538$	16.8733	0.727460
$539$	−0.310029	−0.0133539
$540$	−5.76125	−0.247925
$541$	−7.71669	−0.331767	−0.165883	−	0.986145i	$-0.553047\pi$
$541$	−7.71669	−0.331767	−0.165883	+	0.986145i	$0.553047\pi$
$542$	18.5633	0.797362
$543$	1.80124	0.0772985
$544$	17.2933	0.741445
$545$	−28.4576	−1.21899
$546$	−5.42459	−0.232151
$547$	−33.5372	−1.43395	−0.716973	−	0.697101i	$-0.754473\pi$
$547$	−33.5372	−1.43395	−0.716973	+	0.697101i	$0.754473\pi$
$548$	−6.54290	−0.279499
$549$	39.6413	1.69185
$550$	−0.0628471	−0.00267981
$551$	44.4600	1.89406
$552$	−0.694516	−0.0295606
$553$	−9.89191	−0.420647
$554$	−13.1997	−0.560800
$555$	−4.62513	−0.196326
$556$	−21.5571	−0.914224
$557$	0.808570	0.0342602	0.0171301	−	0.999853i	$-0.494547\pi$
$557$	0.808570	0.0342602	0.0171301	+	0.999853i	$0.494547\pi$
$558$	−19.2074	−0.813114
$559$	25.8898	1.09502
$560$	−0.826914	−0.0349435
$561$	−0.0479332	−0.00202374
$562$	20.8072	0.877698
$563$	−14.0686	−0.592922	−0.296461	−	0.955045i	$-0.595806\pi$
$563$	−14.0686	−0.592922	−0.296461	+	0.955045i	$0.595806\pi$
$564$	3.79156	0.159653
$565$	−16.7999	−0.706779
$566$	1.47744	0.0621014
$567$	−28.4410	−1.19441
$568$	−14.8592	−0.623479
$569$	−24.3866	−1.02234	−0.511171	−	0.859479i	$-0.670788\pi$
$569$	−24.3866	−1.02234	−0.511171	+	0.859479i	$0.670788\pi$
$570$	4.29453	0.179878
$571$	3.87673	0.162236	0.0811181	−	0.996704i	$-0.474151\pi$
$571$	3.87673	0.162236	0.0811181	+	0.996704i	$0.474151\pi$
$572$	0.142525	0.00595925
$573$	−9.30173	−0.388585
$574$	6.82677	0.284944
$575$	−1.14770	−0.0478623
$576$	−12.9379	−0.539080
$577$	−12.7616	−0.531273	−0.265636	−	0.964073i	$-0.585582\pi$
$577$	−12.7616	−0.531273	−0.265636	+	0.964073i	$0.585582\pi$
$578$	6.71027	0.279111
$579$	11.7603	0.488742
$580$	−14.8962	−0.618529
$581$	5.06606	0.210176
$582$	−5.54669	−0.229918
$583$	0.324768	0.0134505
$584$	−17.2594	−0.714201
$585$	−15.6456	−0.646866
$586$	13.7276	0.567083
$587$	−13.1945	−0.544596	−0.272298	−	0.962213i	$-0.587784\pi$
$587$	−13.1945	−0.544596	−0.272298	+	0.962213i	$0.587784\pi$
$588$	5.45085	0.224789
$589$	−51.0396	−2.10305
$590$	−4.92428	−0.202730
$591$	2.12639	0.0874680
$592$	0.716149	0.0294336
$593$	−15.7053	−0.644939	−0.322469	−	0.946580i	$-0.604513\pi$
$593$	−15.7053	−0.644939	−0.322469	+	0.946580i	$0.604513\pi$
$594$	0.0784768	0.00321994
$595$	20.5087	0.840775
$596$	−25.7578	−1.05508
$597$	6.76539	0.276889
$598$	−1.51805	−0.0620778
$599$	2.25712	0.0922232	0.0461116	−	0.998936i	$-0.485317\pi$
$599$	2.25712	0.0922232	0.0461116	+	0.998936i	$0.485317\pi$
$600$	2.85439	0.116530
$601$	8.89084	0.362665	0.181332	−	0.983422i	$-0.441959\pi$
$601$	8.89084	0.362665	0.181332	+	0.983422i	$0.441959\pi$
$602$	26.7229	1.08914
$603$	14.3897	0.585996
$604$	21.0026	0.854586
$605$	−18.4969	−0.752006
$606$	7.29913	0.296507
$607$	−44.8087	−1.81873	−0.909364	−	0.416001i	$-0.863431\pi$
$607$	−44.8087	−1.81873	−0.909364	+	0.416001i	$0.863431\pi$
$608$	−36.1848	−1.46749
$609$	13.2410	0.536552
$610$	20.5849	0.833457
$611$	21.4086	0.866101
$612$	−10.6409	−0.430133
$613$	23.9196	0.966104	0.483052	−	0.875592i	$-0.339528\pi$
$613$	23.9196	0.966104	0.483052	+	0.875592i	$0.339528\pi$
$614$	−11.0943	−0.447728
$615$	−1.55941	−0.0628815
$616$	0.380024	0.0153116
$617$	23.3448	0.939827	0.469913	−	0.882713i	$-0.344285\pi$
$617$	23.3448	0.939827	0.469913	+	0.882713i	$0.344285\pi$
$618$	−0.300238	−0.0120774
$619$	45.6318	1.83410	0.917048	−	0.398776i	$-0.130565\pi$
$619$	45.6318	1.83410	0.917048	+	0.398776i	$0.130565\pi$
$620$	17.1006	0.686779
$621$	1.43312	0.0575092
$622$	−9.95066	−0.398985
$623$	64.3883	2.57966
$624$	−0.191863	−0.00768067
$625$	−9.42384	−0.376954
$626$	7.22972	0.288958
$627$	0.100296	0.00400544
$628$	0.625575	0.0249631
$629$	−17.7616	−0.708201
$630$	−16.1491	−0.643394
$631$	10.4709	0.416840	0.208420	−	0.978039i	$-0.433168\pi$
$631$	10.4709	0.416840	0.208420	+	0.978039i	$0.433168\pi$
$632$	6.88473	0.273860
$633$	6.30454	0.250583
$634$	−13.6924	−0.543797
$635$	11.9395	0.473804
$636$	−5.70998	−0.226415
$637$	30.7777	1.21946
$638$	0.202908	0.00803319
$639$	14.7469	0.583378
$640$	12.4763	0.493170
$641$	−33.7444	−1.33282	−0.666411	−	0.745585i	$-0.732170\pi$
$641$	−33.7444	−1.33282	−0.666411	+	0.745585i	$0.732170\pi$
$642$	3.90032	0.153933
$643$	−42.2502	−1.66619	−0.833093	−	0.553133i	$-0.813432\pi$
$643$	−42.2502	−1.66619	−0.833093	+	0.553133i	$0.813432\pi$
$644$	2.68650	0.105863
$645$	−6.10419	−0.240352
$646$	16.4920	0.648869
$647$	−0.737034	−0.0289758	−0.0144879	−	0.999895i	$-0.504612\pi$
$647$	−0.737034	−0.0289758	−0.0144879	+	0.999895i	$0.504612\pi$
$648$	19.7948	0.777614
$649$	−0.115004	−0.00451429
$650$	6.23905	0.244716
$651$	−15.2005	−0.595756
$652$	−20.7371	−0.812129
$653$	−24.5106	−0.959173	−0.479586	−	0.877495i	$-0.659213\pi$
$653$	−24.5106	−0.959173	−0.479586	+	0.877495i	$0.659213\pi$
$654$	−6.81528	−0.266499
$655$	6.79616	0.265548
$656$	0.241457	0.00942731
$657$	17.1290	0.668265
$658$	22.0975	0.861452
$659$	−10.1868	−0.396820	−0.198410	−	0.980119i	$-0.563578\pi$
$659$	−10.1868	−0.396820	−0.198410	+	0.980119i	$0.563578\pi$
$660$	−0.0336039	−0.00130803
$661$	−6.53218	−0.254072	−0.127036	−	0.991898i	$-0.540546\pi$
$661$	−6.53218	−0.254072	−0.127036	+	0.991898i	$0.540546\pi$
$662$	14.2644	0.554403
$663$	4.75849	0.184805
$664$	−3.52596	−0.136834
$665$	−42.9127	−1.66408
$666$	13.9859	0.541943
$667$	3.70545	0.143475
$668$	18.8786	0.730433
$669$	2.86220	0.110659
$670$	7.47227	0.288679
$671$	0.480747	0.0185590
$672$	−10.7765	−0.415712
$673$	46.8205	1.80480	0.902398	−	0.430903i	$-0.141805\pi$
$673$	46.8205	1.80480	0.902398	+	0.430903i	$0.141805\pi$
$674$	−17.4740	−0.673075
$675$	−5.88999	−0.226706
$676$	2.27300	0.0874231
$677$	−29.0480	−1.11641	−0.558204	−	0.829704i	$-0.688509\pi$
$677$	−29.0480	−1.11641	−0.558204	+	0.829704i	$0.688509\pi$
$678$	−4.02340	−0.154518
$679$	55.4248	2.12701
$680$	−14.2740	−0.547382
$681$	11.3870	0.436352
$682$	−0.232936	−0.00891959
$683$	15.6068	0.597176	0.298588	−	0.954382i	$-0.403484\pi$
$683$	15.6068	0.597176	0.298588	+	0.954382i	$0.403484\pi$
$684$	22.2652	0.851331
$685$	8.71047	0.332810
$686$	7.58705	0.289675
$687$	11.2215	0.428128
$688$	0.945166	0.0360341
$689$	−32.2408	−1.22828
$690$	0.357921	0.0136258
$691$	19.7681	0.752015	0.376007	−	0.926617i	$-0.377297\pi$
$691$	19.7681	0.752015	0.376007	+	0.926617i	$0.377297\pi$
$692$	10.2805	0.390807
$693$	−0.377152	−0.0143268
$694$	6.27499	0.238195
$695$	28.6986	1.08860
$696$	−9.21567	−0.349319
$697$	−5.98850	−0.226831
$698$	−7.41851	−0.280795
$699$	−7.69600	−0.291090
$700$	−11.0412	−0.417320
$701$	−13.1074	−0.495059	−0.247529	−	0.968880i	$-0.579619\pi$
$701$	−13.1074	−0.495059	−0.247529	+	0.968880i	$0.579619\pi$
$702$	−7.79067	−0.294040
$703$	37.1646	1.40169
$704$	−0.156903	−0.00591352
$705$	−5.04764	−0.190105
$706$	−7.64518	−0.287730
$707$	−72.9360	−2.74304
$708$	2.02196	0.0759900
$709$	−27.5875	−1.03607	−0.518035	−	0.855359i	$-0.673336\pi$
$709$	−27.5875	−1.03607	−0.518035	+	0.855359i	$0.673336\pi$
$710$	7.65773	0.287390
$711$	−6.83269	−0.256246
$712$	−44.8140	−1.67948
$713$	−4.25382	−0.159307
$714$	4.91161	0.183813
$715$	−0.189741	−0.00709591
$716$	31.4276	1.17450
$717$	1.87149	0.0698919
$718$	3.54350	0.132242
$719$	−29.8571	−1.11348	−0.556740	−	0.830687i	$-0.687948\pi$
$719$	−29.8571	−1.11348	−0.556740	+	0.830687i	$0.687948\pi$
$720$	−0.571178	−0.0212866
$721$	3.00011	0.111730
$722$	−18.1993	−0.677309
$723$	−5.83303	−0.216933
$724$	4.84933	0.180224
$725$	−15.2290	−0.565591
$726$	−4.42981	−0.164406
$727$	16.6429	0.617251	0.308625	−	0.951184i	$-0.400131\pi$
$727$	16.6429	0.617251	0.308625	+	0.951184i	$0.400131\pi$
$728$	−37.7263	−1.39823
$729$	−15.8277	−0.586212
$730$	8.89470	0.329208
$731$	−23.4415	−0.867017
$732$	−8.45237	−0.312408
$733$	−17.8922	−0.660863	−0.330431	−	0.943830i	$-0.607194\pi$
$733$	−17.8922	−0.660863	−0.330431	+	0.943830i	$0.607194\pi$
$734$	2.37024	0.0874871
$735$	−7.25663	−0.267665
$736$	−3.01577	−0.111163
$737$	0.174511	0.00642818
$738$	4.71549	0.173580
$739$	−6.32363	−0.232619	−0.116309	−	0.993213i	$-0.537106\pi$
$739$	−6.32363	−0.232619	−0.116309	+	0.993213i	$0.537106\pi$
$740$	−12.4519	−0.457740
$741$	−9.95675	−0.365770
$742$	−33.2783	−1.22168
$743$	−39.4846	−1.44855	−0.724274	−	0.689512i	$-0.757825\pi$
$743$	−39.4846	−1.44855	−0.724274	+	0.689512i	$0.757825\pi$
$744$	10.5795	0.387863
$745$	34.2910	1.25632
$746$	9.08837	0.332749
$747$	3.49931	0.128033
$748$	−0.129047	−0.00471841
$749$	−38.9736	−1.42407
$750$	−4.85758	−0.177374
$751$	−7.65919	−0.279488	−0.139744	−	0.990188i	$-0.544628\pi$
$751$	−7.65919	−0.279488	−0.139744	+	0.990188i	$0.544628\pi$
$752$	0.781571	0.0285010
$753$	9.06626	0.330393
$754$	−20.1434	−0.733578
$755$	−27.9605	−1.01759
$756$	13.7871	0.501433
$757$	−21.0616	−0.765496	−0.382748	−	0.923853i	$-0.625022\pi$
$757$	−21.0616	−0.765496	−0.382748	+	0.923853i	$0.625022\pi$
$758$	−21.4606	−0.779483
$759$	0.00835902	0.000303413 0
$760$	29.8671	1.08339
$761$	5.72276	0.207450	0.103725	−	0.994606i	$-0.466924\pi$
$761$	5.72276	0.207450	0.103725	+	0.994606i	$0.466924\pi$
$762$	2.85938	0.103584
$763$	68.1012	2.46543
$764$	−25.0423	−0.905999
$765$	14.1661	0.512176
$766$	9.41652	0.340233
$767$	11.4168	0.412237
$768$	7.35556	0.265421
$769$	10.2539	0.369765	0.184883	−	0.982761i	$-0.440810\pi$
$769$	10.2539	0.369765	0.184883	+	0.982761i	$0.440810\pi$
$770$	−0.195846	−0.00705782
$771$	12.0396	0.433594
$772$	31.6614	1.13952
$773$	−8.77762	−0.315709	−0.157855	−	0.987462i	$-0.550458\pi$
$773$	−8.77762	−0.315709	−0.157855	+	0.987462i	$0.550458\pi$
$774$	18.4584	0.663475
$775$	17.4828	0.628000
$776$	−38.5754	−1.38478
$777$	11.0683	0.397073
$778$	14.9996	0.537761
$779$	12.5304	0.448949
$780$	3.33597	0.119447
$781$	0.178842	0.00639946
$782$	1.37450	0.0491520
$783$	19.0164	0.679590
$784$	1.12361	0.0401289
$785$	−0.832819	−0.0297246
$786$	1.62761	0.0580549
$787$	44.2940	1.57891	0.789455	−	0.613808i	$-0.210363\pi$
$787$	44.2940	1.57891	0.789455	+	0.613808i	$0.210363\pi$
$788$	5.72471	0.203934
$789$	−7.29030	−0.259541
$790$	−3.54806	−0.126234
$791$	40.2036	1.42947
$792$	0.262496	0.00932739
$793$	−47.7254	−1.69478
$794$	−1.12644	−0.0399757
$795$	7.60162	0.269602
$796$	18.2139	0.645575
$797$	−24.7053	−0.875107	−0.437554	−	0.899192i	$-0.644155\pi$
$797$	−24.7053	−0.875107	−0.437554	+	0.899192i	$0.644155\pi$
$798$	−10.2771	−0.363807
$799$	−19.3841	−0.685761
$800$	12.3945	0.438212
$801$	44.4753	1.57146
$802$	16.0861	0.568021
$803$	0.207730	0.00733065
$804$	−3.06820	−0.108207
$805$	−3.57649	−0.126055
$806$	23.1244	0.814522
$807$	9.22363	0.324687
$808$	50.7631	1.78584
$809$	41.9274	1.47409	0.737044	−	0.675845i	$-0.236221\pi$
$809$	41.9274	1.47409	0.737044	+	0.675845i	$0.236221\pi$
$810$	−10.2013	−0.358438
$811$	−27.5697	−0.968103	−0.484051	−	0.875040i	$-0.660835\pi$
$811$	−27.5697	−0.968103	−0.484051	+	0.875040i	$0.660835\pi$
$812$	35.6477	1.25099
$813$	10.1474	0.355886
$814$	0.169613	0.00594493
$815$	27.6071	0.967033
$816$	0.173720	0.00608140
$817$	49.0494	1.71602
$818$	−26.6488	−0.931754
$819$	37.4412	1.30830
$820$	−4.19828	−0.146610
$821$	−50.0903	−1.74816	−0.874082	−	0.485779i	$-0.838536\pi$
$821$	−50.0903	−1.74816	−0.874082	+	0.485779i	$0.838536\pi$
$822$	2.08606	0.0727598
$823$	32.2627	1.12461	0.562304	−	0.826931i	$-0.309915\pi$
$823$	32.2627	1.12461	0.562304	+	0.826931i	$0.309915\pi$
$824$	−2.08806	−0.0727411
$825$	−0.0343548	−0.00119608
$826$	11.7842	0.410025
$827$	−18.1097	−0.629737	−0.314868	−	0.949135i	$-0.601960\pi$
$827$	−18.1097	−0.629737	−0.314868	+	0.949135i	$0.601960\pi$
$828$	1.85566	0.0644886
$829$	−42.4454	−1.47419	−0.737094	−	0.675790i	$-0.763803\pi$
$829$	−42.4454	−1.47419	−0.737094	+	0.675790i	$0.763803\pi$
$830$	1.81711	0.0630728
$831$	−7.21547	−0.250302
$832$	15.5763	0.540013
$833$	−27.8672	−0.965540
$834$	6.87301	0.237993
$835$	−25.1327	−0.869755
$836$	0.270019	0.00933881
$837$	−21.8306	−0.754577
$838$	−22.8466	−0.789224
$839$	34.7777	1.20066	0.600330	−	0.799752i	$-0.295036\pi$
$839$	34.7777	1.20066	0.600330	+	0.799752i	$0.295036\pi$
$840$	8.89496	0.306905
$841$	20.1683	0.695458
$842$	−13.0195	−0.448683
$843$	11.3740	0.391743
$844$	16.9732	0.584242
$845$	−3.02601	−0.104098
$846$	15.2635	0.524771
$847$	44.2646	1.52095
$848$	−1.17702	−0.0404192
$849$	0.807628	0.0277177
$850$	−5.64906	−0.193761
$851$	3.09743	0.106178
$852$	−3.14435	−0.107724
$853$	33.0642	1.13210	0.566048	−	0.824372i	$-0.308472\pi$
$853$	33.0642	1.13210	0.566048	+	0.824372i	$0.308472\pi$
$854$	−49.2612	−1.68568
$855$	−29.6413	−1.01371
$856$	27.1255	0.927130
$857$	43.7197	1.49344	0.746719	−	0.665140i	$-0.231628\pi$
$857$	43.7197	1.49344	0.746719	+	0.665140i	$0.231628\pi$
$858$	−0.0454409	−0.00155133
$859$	−1.12355	−0.0383352	−0.0191676	−	0.999816i	$-0.506102\pi$
$859$	−1.12355	−0.0383352	−0.0191676	+	0.999816i	$0.506102\pi$
$860$	−16.4338	−0.560389
$861$	3.73179	0.127179
$862$	−12.3652	−0.421159
$863$	−0.582455	−0.0198270	−0.00991350	−	0.999951i	$-0.503156\pi$
$863$	−0.582455	−0.0198270	−0.00991350	+	0.999951i	$0.503156\pi$
$864$	−15.4769	−0.526536
$865$	−13.6863	−0.465349
$866$	−20.8480	−0.708444
$867$	3.66811	0.124575
$868$	−40.9232	−1.38902
$869$	−0.0828629	−0.00281093
$870$	4.74932	0.161017
$871$	−17.3243	−0.587010
$872$	−47.3981	−1.60510
$873$	38.2839	1.29571
$874$	−2.87602	−0.0972829
$875$	48.5390	1.64092
$876$	−3.65226	−0.123398
$877$	44.5547	1.50450	0.752252	−	0.658875i	$-0.228968\pi$
$877$	44.5547	1.50450	0.752252	+	0.658875i	$0.228968\pi$
$878$	−19.7466	−0.666415
$879$	7.50408	0.253106
$880$	−0.00692692	−0.000233506 0
$881$	3.95973	0.133407	0.0667034	−	0.997773i	$-0.478752\pi$
$881$	3.95973	0.133407	0.0667034	+	0.997773i	$0.478752\pi$
$882$	21.9433	0.738869
$883$	36.0206	1.21219	0.606094	−	0.795393i	$-0.292736\pi$
$883$	36.0206	1.21219	0.606094	+	0.795393i	$0.292736\pi$
$884$	12.8109	0.430878
$885$	−2.69181	−0.0904842
$886$	5.17845	0.173973
$887$	56.7087	1.90409	0.952046	−	0.305955i	$-0.0989757\pi$
$887$	56.7087	1.90409	0.952046	+	0.305955i	$0.0989757\pi$
$888$	−7.70348	−0.258512
$889$	−28.5721	−0.958279
$890$	23.0950	0.774147
$891$	−0.238246	−0.00798153
$892$	7.70568	0.258005
$893$	40.5597	1.35728
$894$	8.21232	0.274661
$895$	−41.8391	−1.39853
$896$	−29.8568	−0.997447
$897$	−0.829829	−0.0277072
$898$	−6.43256	−0.214657
$899$	−56.4447	−1.88254
$900$	−7.62657	−0.254219
$901$	29.1920	0.972526
$902$	0.0571867	0.00190411
$903$	14.6078	0.486118
$904$	−27.9815	−0.930651
$905$	−6.45585	−0.214600
$906$	−6.69624	−0.222468
$907$	15.1223	0.502127	0.251064	−	0.967971i	$-0.419220\pi$
$907$	15.1223	0.502127	0.251064	+	0.967971i	$0.419220\pi$
$908$	30.6564	1.01737
$909$	−50.3795	−1.67098
$910$	19.4424	0.644508
$911$	−40.3798	−1.33784	−0.668921	−	0.743333i	$-0.733244\pi$
$911$	−40.3798	−1.33784	−0.668921	+	0.743333i	$0.733244\pi$
$912$	−0.363494	−0.0120365
$913$	0.0424375	0.00140448
$914$	−17.6779	−0.584732
$915$	11.2525	0.371997
$916$	30.2108	0.998194
$917$	−16.2638	−0.537076
$918$	7.05394	0.232815
$919$	−20.4714	−0.675290	−0.337645	−	0.941273i	$-0.609630\pi$
$919$	−20.4714	−0.675290	−0.337645	+	0.941273i	$0.609630\pi$
$920$	2.48922	0.0820673
$921$	−6.06457	−0.199834
$922$	5.10984	0.168283
$923$	−17.7542	−0.584388
$924$	0.0804167	0.00264551
$925$	−12.7301	−0.418564
$926$	29.0862	0.955832
$927$	2.07228	0.0680626
$928$	−40.0168	−1.31362
$929$	−17.9849	−0.590064	−0.295032	−	0.955487i	$-0.595330\pi$
$929$	−17.9849	−0.590064	−0.295032	+	0.955487i	$0.595330\pi$
$930$	−5.45218	−0.178784
$931$	58.3097	1.91102
$932$	−20.7193	−0.678684
$933$	−5.43943	−0.178079
$934$	−18.7944	−0.614970
$935$	0.171798	0.00561840
$936$	−26.0589	−0.851761
$937$	−20.3859	−0.665980	−0.332990	−	0.942930i	$-0.608057\pi$
$937$	−20.3859	−0.665980	−0.332990	+	0.942930i	$0.608057\pi$
$938$	−17.8817	−0.583859
$939$	3.95206	0.128971
$940$	−13.5894	−0.443236
$941$	−45.0460	−1.46846	−0.734228	−	0.678902i	$-0.762456\pi$
$941$	−45.0460	−1.46846	−0.734228	+	0.678902i	$0.762456\pi$
$942$	−0.199451	−0.00649847
$943$	1.04433	0.0340080
$944$	0.416797	0.0135656
$945$	−18.3546	−0.597075
$946$	0.223853	0.00727810
$947$	20.7628	0.674700	0.337350	−	0.941379i	$-0.390469\pi$
$947$	20.7628	0.674700	0.337350	+	0.941379i	$0.390469\pi$
$948$	1.45687	0.0473170
$949$	−20.6221	−0.669422
$950$	11.8202	0.383497
$951$	−7.48484	−0.242713
$952$	34.1587	1.10709
$953$	−7.76824	−0.251638	−0.125819	−	0.992053i	$-0.540156\pi$
$953$	−7.76824	−0.251638	−0.125819	+	0.992053i	$0.540156\pi$
$954$	−22.9865	−0.744215
$955$	33.3385	1.07881
$956$	5.03845	0.162955
$957$	0.110918	0.00358545
$958$	−21.3944	−0.691222
$959$	−20.8448	−0.673115
$960$	−3.67253	−0.118530
$961$	33.7981	1.09026
$962$	−16.8381	−0.542881
$963$	−26.9205	−0.867500
$964$	−15.7038	−0.505785
$965$	−42.1503	−1.35687
$966$	−0.856532	−0.0275585
$967$	−1.06738	−0.0343247	−0.0171623	−	0.999853i	$-0.505463\pi$
$967$	−1.06738	−0.0343247	−0.0171623	+	0.999853i	$0.505463\pi$
$968$	−30.8079	−0.990204
$969$	9.01519	0.289609
$970$	19.8800	0.638307
$971$	−44.4319	−1.42589	−0.712944	−	0.701221i	$-0.752639\pi$
$971$	−44.4319	−1.42589	−0.712944	+	0.701221i	$0.752639\pi$
$972$	14.4663	0.464005
$973$	−68.6780	−2.20172
$974$	−25.9646	−0.831960
$975$	3.41052	0.109224
$976$	−1.74233	−0.0557705
$977$	−40.4014	−1.29255	−0.646277	−	0.763103i	$-0.723675\pi$
$977$	−40.4014	−1.29255	−0.646277	+	0.763103i	$0.723675\pi$
$978$	6.61159	0.211415
$979$	0.539370	0.0172383
$980$	−19.5365	−0.624069
$981$	47.0399	1.50187
$982$	9.40573	0.300149
$983$	−47.4284	−1.51273	−0.756365	−	0.654149i	$-0.773027\pi$
$983$	−47.4284	−1.51273	−0.756365	+	0.654149i	$0.773027\pi$
$984$	−2.59731	−0.0827992
$985$	−7.62123	−0.242832
$986$	18.2385	0.580832
$987$	12.0794	0.384492
$988$	−26.8058	−0.852805
$989$	4.08795	0.129989
$990$	−0.135278	−0.00429942
$991$	−36.1665	−1.14887	−0.574433	−	0.818551i	$-0.694778\pi$
$991$	−36.1665	−1.14887	−0.574433	+	0.818551i	$0.694778\pi$
$992$	45.9389	1.45856
$993$	7.79751	0.247446
$994$	−18.3256	−0.581251
$995$	−24.2479	−0.768711
$996$	−0.746125	−0.0236419
$997$	58.4704	1.85178	0.925888	−	0.377797i	$-0.123318\pi$
$997$	58.4704	1.85178	0.925888	+	0.377797i	$0.123318\pi$
$998$	−0.454057	−0.0143729
$999$	15.8960	0.502928

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2671.2.a.a.1.39	✓	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2671.2.a.a.1.39	✓	100	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:	\( N \)	\(=\)	\( 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2671.a (trivial)

\(f(q)\)	\(=\)	\(q-0.858357 q^{2} -0.469212 q^{3} -1.26322 q^{4} +1.68171 q^{5} +0.402752 q^{6} -4.02447 q^{7} +2.80101 q^{8} -2.77984 q^{9} +O(q^{10})\)	\(q-0.858357 q^{2} -0.469212 q^{3} -1.26322 q^{4} +1.68171 q^{5} +0.402752 q^{6} -4.02447 q^{7} +2.80101 q^{8} -2.77984 q^{9} -1.44351 q^{10} -0.0337123 q^{11} +0.592720 q^{12} +3.34673 q^{13} +3.45443 q^{14} -0.789080 q^{15} +0.122180 q^{16} -3.03025 q^{17} +2.38609 q^{18} +6.34055 q^{19} -2.12438 q^{20} +1.88833 q^{21} +0.0289372 q^{22} +0.528443 q^{23} -1.31427 q^{24} -2.17185 q^{25} -2.87269 q^{26} +2.71197 q^{27} +5.08380 q^{28} +7.01201 q^{29} +0.677312 q^{30} -8.04972 q^{31} -5.70689 q^{32} +0.0158182 q^{33} +2.60104 q^{34} -6.76799 q^{35} +3.51156 q^{36} +5.86142 q^{37} -5.44245 q^{38} -1.57033 q^{39} +4.71049 q^{40} +1.97624 q^{41} -1.62086 q^{42} +7.73584 q^{43} +0.0425861 q^{44} -4.67489 q^{45} -0.453592 q^{46} +6.39687 q^{47} -0.0573284 q^{48} +9.19633 q^{49} +1.86422 q^{50} +1.42183 q^{51} -4.22767 q^{52} -9.63352 q^{53} -2.32784 q^{54} -0.0566943 q^{55} -11.2726 q^{56} -2.97506 q^{57} -6.01881 q^{58} +3.41133 q^{59} +0.996784 q^{60} -14.2603 q^{61} +6.90954 q^{62} +11.1874 q^{63} +4.65419 q^{64} +5.62824 q^{65} -0.0135777 q^{66} -5.17647 q^{67} +3.82788 q^{68} -0.247952 q^{69} +5.80935 q^{70} -5.30495 q^{71} -7.78636 q^{72} -6.16186 q^{73} -5.03119 q^{74} +1.01906 q^{75} -8.00952 q^{76} +0.135674 q^{77} +1.34790 q^{78} +2.45794 q^{79} +0.205472 q^{80} +7.06703 q^{81} -1.69632 q^{82} -1.25882 q^{83} -2.38538 q^{84} -5.09601 q^{85} -6.64011 q^{86} -3.29012 q^{87} -0.0944284 q^{88} -15.9992 q^{89} +4.01272 q^{90} -13.4688 q^{91} -0.667541 q^{92} +3.77703 q^{93} -5.49080 q^{94} +10.6630 q^{95} +2.67775 q^{96} -13.7720 q^{97} -7.89373 q^{98} +0.0937147 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9}+O(q^{10}) \) 100 * q - 15 * q^2 - 12 * q^3 + 89 * q^4 - 33 * q^5 - 28 * q^6 - 14 * q^7 - 45 * q^8 + 60 * q^9	\( 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9} - 18 q^{10} - 47 q^{11} - 27 q^{12} - 29 q^{13} - 51 q^{14} - 36 q^{15} + 71 q^{16} - 99 q^{17} - 27 q^{18} - 45 q^{19} - 75 q^{20} - 79 q^{21} - 2 q^{22} - 25 q^{23} - 66 q^{24} + 67 q^{25} - 73 q^{26} - 42 q^{27} - 31 q^{28} - 78 q^{29} - 29 q^{30} - 41 q^{31} - 95 q^{32} - 83 q^{33} - 44 q^{34} - 45 q^{35} + 23 q^{36} - 16 q^{37} - 29 q^{38} - 42 q^{39} - 37 q^{40} - 235 q^{41} + 16 q^{42} - 6 q^{43} - 122 q^{44} - 79 q^{45} - 17 q^{46} - 67 q^{47} - 25 q^{48} + 30 q^{49} - 68 q^{50} - 18 q^{51} - 41 q^{52} - 69 q^{53} - 63 q^{54} - 32 q^{55} - 120 q^{56} - 63 q^{57} - 7 q^{58} - 118 q^{59} - 49 q^{60} - 60 q^{61} - 23 q^{62} - 43 q^{63} + 43 q^{64} - 181 q^{65} - 4 q^{66} - 18 q^{67} - 130 q^{68} - 80 q^{69} + 12 q^{70} - 77 q^{71} - 40 q^{72} - 64 q^{73} - 48 q^{74} - 18 q^{75} - 134 q^{76} - 87 q^{77} + 65 q^{78} - 48 q^{79} - 95 q^{80} - 20 q^{81} + 45 q^{82} - 108 q^{83} - 97 q^{84} - 21 q^{85} - 73 q^{86} - 3 q^{87} + 23 q^{88} - 325 q^{89} + 6 q^{90} - 17 q^{91} - 19 q^{92} + 2 q^{93} - 5 q^{94} - 54 q^{95} - 105 q^{96} - 81 q^{97} - 61 q^{98} - 76 q^{99}+O(q^{100}) \) 100 * q - 15 * q^2 - 12 * q^3 + 89 * q^4 - 33 * q^5 - 28 * q^6 - 14 * q^7 - 45 * q^8 + 60 * q^9 - 18 * q^10 - 47 * q^11 - 27 * q^12 - 29 * q^13 - 51 * q^14 - 36 * q^15 + 71 * q^16 - 99 * q^17 - 27 * q^18 - 45 * q^19 - 75 * q^20 - 79 * q^21 - 2 * q^22 - 25 * q^23 - 66 * q^24 + 67 * q^25 - 73 * q^26 - 42 * q^27 - 31 * q^28 - 78 * q^29 - 29 * q^30 - 41 * q^31 - 95 * q^32 - 83 * q^33 - 44 * q^34 - 45 * q^35 + 23 * q^36 - 16 * q^37 - 29 * q^38 - 42 * q^39 - 37 * q^40 - 235 * q^41 + 16 * q^42 - 6 * q^43 - 122 * q^44 - 79 * q^45 - 17 * q^46 - 67 * q^47 - 25 * q^48 + 30 * q^49 - 68 * q^50 - 18 * q^51 - 41 * q^52 - 69 * q^53 - 63 * q^54 - 32 * q^55 - 120 * q^56 - 63 * q^57 - 7 * q^58 - 118 * q^59 - 49 * q^60 - 60 * q^61 - 23 * q^62 - 43 * q^63 + 43 * q^64 - 181 * q^65 - 4 * q^66 - 18 * q^67 - 130 * q^68 - 80 * q^69 + 12 * q^70 - 77 * q^71 - 40 * q^72 - 64 * q^73 - 48 * q^74 - 18 * q^75 - 134 * q^76 - 87 * q^77 + 65 * q^78 - 48 * q^79 - 95 * q^80 - 20 * q^81 + 45 * q^82 - 108 * q^83 - 97 * q^84 - 21 * q^85 - 73 * q^86 - 3 * q^87 + 23 * q^88 - 325 * q^89 + 6 * q^90 - 17 * q^91 - 19 * q^92 + 2 * q^93 - 5 * q^94 - 54 * q^95 - 105 * q^96 - 81 * q^97 - 61 * q^98 - 76 * q^99

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