LMFDB - Embedded newform 4017.2.a.e.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 21 x^{14} - 3 x^{13} + 177 x^{12} + 45 x^{11} - 763 x^{10} - 251 x^{9} + 1771 x^{8} + 639 x^{7} + \cdots + 7 $ x^16 - 21x^14 - 3x^13 + 177x^12 + 45x^11 - 763x^10 - 251x^9 + 1771x^8 + 639x^7 - 2118x^6 - 710x^5 + 1113x^4 + 243x^3 - 183x^2 - 10x + 7
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$1.56390$ of defining polynomial
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.56390 q^{2} +1.00000 q^{3} +0.445771 q^{4} +0.640434 q^{5} -1.56390 q^{6} +3.30522 q^{7} +2.43065 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.56390 q^{2} +1.00000 q^{3} +0.445771 q^{4} +0.640434 q^{5} -1.56390 q^{6} +3.30522 q^{7} +2.43065 q^{8} +1.00000 q^{9} -1.00157 q^{10} -4.71212 q^{11} +0.445771 q^{12} -1.00000 q^{13} -5.16902 q^{14} +0.640434 q^{15} -4.69283 q^{16} +3.70018 q^{17} -1.56390 q^{18} +1.83807 q^{19} +0.285487 q^{20} +3.30522 q^{21} +7.36927 q^{22} -4.83349 q^{23} +2.43065 q^{24} -4.58984 q^{25} +1.56390 q^{26} +1.00000 q^{27} +1.47337 q^{28} +3.49494 q^{29} -1.00157 q^{30} -8.89632 q^{31} +2.47779 q^{32} -4.71212 q^{33} -5.78670 q^{34} +2.11678 q^{35} +0.445771 q^{36} -9.16395 q^{37} -2.87455 q^{38} -1.00000 q^{39} +1.55667 q^{40} +3.86756 q^{41} -5.16902 q^{42} -8.55229 q^{43} -2.10053 q^{44} +0.640434 q^{45} +7.55907 q^{46} +0.198343 q^{47} -4.69283 q^{48} +3.92448 q^{49} +7.17804 q^{50} +3.70018 q^{51} -0.445771 q^{52} -2.01297 q^{53} -1.56390 q^{54} -3.01780 q^{55} +8.03384 q^{56} +1.83807 q^{57} -5.46572 q^{58} -1.76350 q^{59} +0.285487 q^{60} -14.2438 q^{61} +13.9129 q^{62} +3.30522 q^{63} +5.51065 q^{64} -0.640434 q^{65} +7.36927 q^{66} +11.5578 q^{67} +1.64943 q^{68} -4.83349 q^{69} -3.31042 q^{70} -2.02977 q^{71} +2.43065 q^{72} -8.31643 q^{73} +14.3315 q^{74} -4.58984 q^{75} +0.819357 q^{76} -15.5746 q^{77} +1.56390 q^{78} -10.4360 q^{79} -3.00545 q^{80} +1.00000 q^{81} -6.04847 q^{82} -9.67462 q^{83} +1.47337 q^{84} +2.36972 q^{85} +13.3749 q^{86} +3.49494 q^{87} -11.4535 q^{88} -12.3627 q^{89} -1.00157 q^{90} -3.30522 q^{91} -2.15463 q^{92} -8.89632 q^{93} -0.310187 q^{94} +1.17716 q^{95} +2.47779 q^{96} +12.4092 q^{97} -6.13747 q^{98} -4.71212 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{3} + 10 q^{4} - 6 q^{5} - 13 q^{7} - 9 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q + 16 * q^3 + 10 * q^4 - 6 * q^5 - 13 * q^7 - 9 * q^8 + 16 * q^9	\( 16 q + 16 q^{3} + 10 q^{4} - 6 q^{5} - 13 q^{7} - 9 q^{8} + 16 q^{9} - 8 q^{10} - 5 q^{11} + 10 q^{12} - 16 q^{13} - 8 q^{14} - 6 q^{15} - 14 q^{16} - q^{17} + 6 q^{19} - 4 q^{20} - 13 q^{21} - 11 q^{22} - 21 q^{23} - 9 q^{24} - 10 q^{25} + 16 q^{27} - 10 q^{28} - 17 q^{29} - 8 q^{30} - 33 q^{31} - 18 q^{32} - 5 q^{33} - 5 q^{34} - 4 q^{35} + 10 q^{36} - 23 q^{37} - 28 q^{38} - 16 q^{39} - 12 q^{40} + 7 q^{41} - 8 q^{42} - 33 q^{43} + 11 q^{44} - 6 q^{45} - 15 q^{46} - 13 q^{47} - 14 q^{48} - 17 q^{49} + 35 q^{50} - q^{51} - 10 q^{52} - 20 q^{53} - 54 q^{55} + 12 q^{56} + 6 q^{57} - 33 q^{58} + 6 q^{59} - 4 q^{60} - 49 q^{61} - 13 q^{62} - 13 q^{63} - 35 q^{64} + 6 q^{65} - 11 q^{66} - 4 q^{67} - 14 q^{68} - 21 q^{69} - 33 q^{70} - 29 q^{71} - 9 q^{72} - 21 q^{73} + 22 q^{74} - 10 q^{75} + 10 q^{76} - 21 q^{77} - 70 q^{79} - 8 q^{80} + 16 q^{81} - 10 q^{82} + 5 q^{83} - 10 q^{84} + 14 q^{85} + 29 q^{86} - 17 q^{87} - 45 q^{88} - 8 q^{89} - 8 q^{90} + 13 q^{91} - 29 q^{92} - 33 q^{93} + 12 q^{94} - 45 q^{95} - 18 q^{96} - 30 q^{97} + 15 q^{98} - 5 q^{99}+O(q^{100}) \) 16 * q + 16 * q^3 + 10 * q^4 - 6 * q^5 - 13 * q^7 - 9 * q^8 + 16 * q^9 - 8 * q^10 - 5 * q^11 + 10 * q^12 - 16 * q^13 - 8 * q^14 - 6 * q^15 - 14 * q^16 - q^17 + 6 * q^19 - 4 * q^20 - 13 * q^21 - 11 * q^22 - 21 * q^23 - 9 * q^24 - 10 * q^25 + 16 * q^27 - 10 * q^28 - 17 * q^29 - 8 * q^30 - 33 * q^31 - 18 * q^32 - 5 * q^33 - 5 * q^34 - 4 * q^35 + 10 * q^36 - 23 * q^37 - 28 * q^38 - 16 * q^39 - 12 * q^40 + 7 * q^41 - 8 * q^42 - 33 * q^43 + 11 * q^44 - 6 * q^45 - 15 * q^46 - 13 * q^47 - 14 * q^48 - 17 * q^49 + 35 * q^50 - q^51 - 10 * q^52 - 20 * q^53 - 54 * q^55 + 12 * q^56 + 6 * q^57 - 33 * q^58 + 6 * q^59 - 4 * q^60 - 49 * q^61 - 13 * q^62 - 13 * q^63 - 35 * q^64 + 6 * q^65 - 11 * q^66 - 4 * q^67 - 14 * q^68 - 21 * q^69 - 33 * q^70 - 29 * q^71 - 9 * q^72 - 21 * q^73 + 22 * q^74 - 10 * q^75 + 10 * q^76 - 21 * q^77 - 70 * q^79 - 8 * q^80 + 16 * q^81 - 10 * q^82 + 5 * q^83 - 10 * q^84 + 14 * q^85 + 29 * q^86 - 17 * q^87 - 45 * q^88 - 8 * q^89 - 8 * q^90 + 13 * q^91 - 29 * q^92 - 33 * q^93 + 12 * q^94 - 45 * q^95 - 18 * q^96 - 30 * q^97 + 15 * q^98 - 5 * 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 $

$2$	−1.56390	−1.10584	−0.552921	−	0.833234i	$-0.686487\pi$
$2$	−1.56390	−1.10584	−0.552921	+	0.833234i	$0.686487\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.445771	0.222885
$5$	0.640434	0.286411	0.143205	−	0.989693i	$-0.454259\pi$
$5$	0.640434	0.286411	0.143205	+	0.989693i	$0.454259\pi$
$6$	−1.56390	−0.638458
$7$	3.30522	1.24926	0.624628	−	0.780923i	$-0.285251\pi$
$7$	3.30522	1.24926	0.624628	+	0.780923i	$0.285251\pi$
$8$	2.43065	0.859365
$9$	1.00000	0.333333
$10$	−1.00157	−0.316725
$11$	−4.71212	−1.42076	−0.710379	−	0.703819i	$-0.751476\pi$
$11$	−4.71212	−1.42076	−0.710379	+	0.703819i	$0.751476\pi$
$12$	0.445771	0.128683
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−5.16902	−1.38148
$15$	0.640434	0.165359
$16$	−4.69283	−1.17321
$17$	3.70018	0.897425	0.448713	−	0.893676i	$-0.351883\pi$
$17$	3.70018	0.897425	0.448713	+	0.893676i	$0.351883\pi$
$18$	−1.56390	−0.368614
$19$	1.83807	0.421682	0.210841	−	0.977520i	$-0.432380\pi$
$19$	1.83807	0.421682	0.210841	+	0.977520i	$0.432380\pi$
$20$	0.285487	0.0638368
$21$	3.30522	0.721258
$22$	7.36927	1.57113
$23$	−4.83349	−1.00785	−0.503926	−	0.863747i	$-0.668112\pi$
$23$	−4.83349	−1.00785	−0.503926	+	0.863747i	$0.668112\pi$
$24$	2.43065	0.496155
$25$	−4.58984	−0.917969
$26$	1.56390	0.306705
$27$	1.00000	0.192450
$28$	1.47337	0.278441
$29$	3.49494	0.648994	0.324497	−	0.945887i	$-0.394805\pi$
$29$	3.49494	0.648994	0.324497	+	0.945887i	$0.394805\pi$
$30$	−1.00157	−0.182861
$31$	−8.89632	−1.59783	−0.798913	−	0.601446i	$-0.794591\pi$
$31$	−8.89632	−1.59783	−0.798913	+	0.601446i	$0.794591\pi$
$32$	2.47779	0.438016
$33$	−4.71212	−0.820275
$34$	−5.78670	−0.992410
$35$	2.11678	0.357800
$36$	0.445771	0.0742952
$37$	−9.16395	−1.50654	−0.753272	−	0.657709i	$-0.771526\pi$
$37$	−9.16395	−1.50654	−0.753272	+	0.657709i	$0.771526\pi$
$38$	−2.87455	−0.466313
$39$	−1.00000	−0.160128
$40$	1.55667	0.246132
$41$	3.86756	0.604012	0.302006	−	0.953306i	$-0.402344\pi$
$41$	3.86756	0.604012	0.302006	+	0.953306i	$0.402344\pi$
$42$	−5.16902	−0.797597
$43$	−8.55229	−1.30421	−0.652106	−	0.758128i	$-0.726114\pi$
$43$	−8.55229	−1.30421	−0.652106	+	0.758128i	$0.726114\pi$
$44$	−2.10053	−0.316666
$45$	0.640434	0.0954703
$46$	7.55907	1.11452
$47$	0.198343	0.0289312	0.0144656	−	0.999895i	$-0.495395\pi$
$47$	0.198343	0.0289312	0.0144656	+	0.999895i	$0.495395\pi$
$48$	−4.69283	−0.677352
$49$	3.92448	0.560640
$50$	7.17804	1.01513
$51$	3.70018	0.518129
$52$	−0.445771	−0.0618173
$53$	−2.01297	−0.276503	−0.138251	−	0.990397i	$-0.544148\pi$
$53$	−2.01297	−0.276503	−0.138251	+	0.990397i	$0.544148\pi$
$54$	−1.56390	−0.212819
$55$	−3.01780	−0.406921
$56$	8.03384	1.07357
$57$	1.83807	0.243458
$58$	−5.46572	−0.717684
$59$	−1.76350	−0.229588	−0.114794	−	0.993389i	$-0.536621\pi$
$59$	−1.76350	−0.229588	−0.114794	+	0.993389i	$0.536621\pi$
$60$	0.285487	0.0368562
$61$	−14.2438	−1.82373	−0.911863	−	0.410495i	$-0.865356\pi$
$61$	−14.2438	−1.82373	−0.911863	+	0.410495i	$0.865356\pi$
$62$	13.9129	1.76694
$63$	3.30522	0.416419
$64$	5.51065	0.688831
$65$	−0.640434	−0.0794361
$66$	7.36927	0.907094
$67$	11.5578	1.41201	0.706005	−	0.708207i	$-0.250496\pi$
$67$	11.5578	1.41201	0.706005	+	0.708207i	$0.250496\pi$
$68$	1.64943	0.200023
$69$	−4.83349	−0.581884
$70$	−3.31042	−0.395671
$71$	−2.02977	−0.240890	−0.120445	−	0.992720i	$-0.538432\pi$
$71$	−2.02977	−0.240890	−0.120445	+	0.992720i	$0.538432\pi$
$72$	2.43065	0.286455
$73$	−8.31643	−0.973364	−0.486682	−	0.873579i	$-0.661793\pi$
$73$	−8.31643	−0.973364	−0.486682	+	0.873579i	$0.661793\pi$
$74$	14.3315	1.66600
$75$	−4.58984	−0.529990
$76$	0.819357	0.0939867
$77$	−15.5746	−1.77489
$78$	1.56390	0.177076
$79$	−10.4360	−1.17414	−0.587071	−	0.809536i	$-0.699719\pi$
$79$	−10.4360	−1.17414	−0.587071	+	0.809536i	$0.699719\pi$
$80$	−3.00545	−0.336019
$81$	1.00000	0.111111
$82$	−6.04847	−0.667942
$83$	−9.67462	−1.06193	−0.530964	−	0.847394i	$-0.678170\pi$
$83$	−9.67462	−1.06193	−0.530964	+	0.847394i	$0.678170\pi$
$84$	1.47337	0.160758
$85$	2.36972	0.257032
$86$	13.3749	1.44225
$87$	3.49494	0.374697
$88$	−11.4535	−1.22095
$89$	−12.3627	−1.31044	−0.655221	−	0.755438i	$-0.727424\pi$
$89$	−12.3627	−1.31044	−0.655221	+	0.755438i	$0.727424\pi$
$90$	−1.00157	−0.105575
$91$	−3.30522	−0.346481
$92$	−2.15463	−0.224636
$93$	−8.89632	−0.922506
$94$	−0.310187	−0.0319934
$95$	1.17716	0.120774
$96$	2.47779	0.252889
$97$	12.4092	1.25997	0.629984	−	0.776608i	$-0.283061\pi$
$97$	12.4092	1.25997	0.629984	+	0.776608i	$0.283061\pi$
$98$	−6.13747	−0.619978
$99$	−4.71212	−0.473586
$100$	−2.04602	−0.204602
$101$	5.20306	0.517723	0.258862	−	0.965914i	$-0.416653\pi$
$101$	5.20306	0.517723	0.258862	+	0.965914i	$0.416653\pi$
$102$	−5.78670	−0.572968
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−2.43065	−0.238345
$105$	2.11678	0.206576
$106$	3.14808	0.305768
$107$	−0.442250	−0.0427539	−0.0213769	−	0.999771i	$-0.506805\pi$
$107$	−0.442250	−0.0427539	−0.0213769	+	0.999771i	$0.506805\pi$
$108$	0.445771	0.0428943
$109$	−8.16940	−0.782486	−0.391243	−	0.920287i	$-0.627955\pi$
$109$	−8.16940	−0.782486	−0.391243	+	0.920287i	$0.627955\pi$
$110$	4.71953	0.449990
$111$	−9.16395	−0.869804
$112$	−15.5108	−1.46564
$113$	7.02913	0.661245	0.330622	−	0.943763i	$-0.392741\pi$
$113$	7.02913	0.661245	0.330622	+	0.943763i	$0.392741\pi$
$114$	−2.87455	−0.269226
$115$	−3.09553	−0.288660
$116$	1.55794	0.144651
$117$	−1.00000	−0.0924500
$118$	2.75793	0.253888
$119$	12.2299	1.12111
$120$	1.55667	0.142104
$121$	11.2041	1.01855
$122$	22.2757	2.01675
$123$	3.86756	0.348726
$124$	−3.96572	−0.356132
$125$	−6.14166	−0.549327
$126$	−5.16902	−0.460493
$127$	−4.51886	−0.400984	−0.200492	−	0.979695i	$-0.564254\pi$
$127$	−4.51886	−0.400984	−0.200492	+	0.979695i	$0.564254\pi$
$128$	−13.5737	−1.19975
$129$	−8.55229	−0.752987
$130$	1.00157	0.0878437
$131$	5.97461	0.522004	0.261002	−	0.965338i	$-0.415947\pi$
$131$	5.97461	0.522004	0.261002	+	0.965338i	$0.415947\pi$
$132$	−2.10053	−0.182827
$133$	6.07522	0.526788
$134$	−18.0752	−1.56146
$135$	0.640434	0.0551198
$136$	8.99385	0.771216
$137$	18.2325	1.55771	0.778855	−	0.627204i	$-0.215801\pi$
$137$	18.2325	1.55771	0.778855	+	0.627204i	$0.215801\pi$
$138$	7.55907	0.643471
$139$	16.2091	1.37484	0.687419	−	0.726261i	$-0.258743\pi$
$139$	16.2091	1.37484	0.687419	+	0.726261i	$0.258743\pi$
$140$	0.943597	0.0797485
$141$	0.198343	0.0167035
$142$	3.17435	0.266386
$143$	4.71212	0.394047
$144$	−4.69283	−0.391069
$145$	2.23828	0.185879
$146$	13.0060	1.07639
$147$	3.92448	0.323685
$148$	−4.08502	−0.335787
$149$	4.59980	0.376830	0.188415	−	0.982090i	$-0.439665\pi$
$149$	4.59980	0.376830	0.188415	+	0.982090i	$0.439665\pi$
$150$	7.17804	0.586084
$151$	−14.3640	−1.16893	−0.584464	−	0.811419i	$-0.698695\pi$
$151$	−14.3640	−1.16893	−0.584464	+	0.811419i	$0.698695\pi$
$152$	4.46771	0.362379
$153$	3.70018	0.299142
$154$	24.3570	1.96275
$155$	−5.69751	−0.457635
$156$	−0.445771	−0.0356902
$157$	22.7515	1.81577	0.907884	−	0.419220i	$-0.137697\pi$
$157$	22.7515	1.81577	0.907884	+	0.419220i	$0.137697\pi$
$158$	16.3208	1.29841
$159$	−2.01297	−0.159639
$160$	1.58686	0.125453
$161$	−15.9757	−1.25906
$162$	−1.56390	−0.122871
$163$	−9.29498	−0.728039	−0.364019	−	0.931391i	$-0.618596\pi$
$163$	−9.29498	−0.728039	−0.364019	+	0.931391i	$0.618596\pi$
$164$	1.72405	0.134626
$165$	−3.01780	−0.234936
$166$	15.1301	1.17432
$167$	−6.39385	−0.494771	−0.247385	−	0.968917i	$-0.579571\pi$
$167$	−6.39385	−0.494771	−0.247385	+	0.968917i	$0.579571\pi$
$168$	8.03384	0.619824
$169$	1.00000	0.0769231
$170$	−3.70600	−0.284237
$171$	1.83807	0.140561
$172$	−3.81236	−0.290690
$173$	4.30340	0.327181	0.163591	−	0.986528i	$-0.447692\pi$
$173$	4.30340	0.327181	0.163591	+	0.986528i	$0.447692\pi$
$174$	−5.46572	−0.414355
$175$	−15.1704	−1.14678
$176$	22.1132	1.66684
$177$	−1.76350	−0.132553
$178$	19.3339	1.44914
$179$	8.82604	0.659689	0.329845	−	0.944035i	$-0.393004\pi$
$179$	8.82604	0.659689	0.329845	+	0.944035i	$0.393004\pi$
$180$	0.285487	0.0212789
$181$	2.24995	0.167238	0.0836188	−	0.996498i	$-0.473352\pi$
$181$	2.24995	0.167238	0.0836188	+	0.996498i	$0.473352\pi$
$182$	5.16902	0.383153
$183$	−14.2438	−1.05293
$184$	−11.7485	−0.866113
$185$	−5.86891	−0.431491
$186$	13.9129	1.02015
$187$	−17.4357	−1.27502
$188$	0.0884154	0.00644835
$189$	3.30522	0.240419
$190$	−1.84096	−0.133557
$191$	−25.1973	−1.82321	−0.911606	−	0.411064i	$-0.865157\pi$
$191$	−25.1973	−1.82321	−0.911606	+	0.411064i	$0.865157\pi$
$192$	5.51065	0.397697
$193$	21.9600	1.58072	0.790359	−	0.612644i	$-0.209894\pi$
$193$	21.9600	1.58072	0.790359	+	0.612644i	$0.209894\pi$
$194$	−19.4068	−1.39332
$195$	−0.640434	−0.0458624
$196$	1.74942	0.124958
$197$	22.2513	1.58534	0.792671	−	0.609650i	$-0.208690\pi$
$197$	22.2513	1.58534	0.792671	+	0.609650i	$0.208690\pi$
$198$	7.36927	0.523711
$199$	−16.9165	−1.19918	−0.599589	−	0.800308i	$-0.704669\pi$
$199$	−16.9165	−1.19918	−0.599589	+	0.800308i	$0.704669\pi$
$200$	−11.1563	−0.788871
$201$	11.5578	0.815224
$202$	−8.13704	−0.572520
$203$	11.5515	0.810759
$204$	1.64943	0.115483
$205$	2.47692	0.172996
$206$	−1.56390	−0.108962
$207$	−4.83349	−0.335951
$208$	4.69283	0.325389
$209$	−8.66120	−0.599108
$210$	−3.31042	−0.228441
$211$	−11.6532	−0.802241	−0.401120	−	0.916025i	$-0.631379\pi$
$211$	−11.6532	−0.802241	−0.401120	+	0.916025i	$0.631379\pi$
$212$	−0.897324	−0.0616284
$213$	−2.02977	−0.139078
$214$	0.691632	0.0472790
$215$	−5.47718	−0.373541
$216$	2.43065	0.165385
$217$	−29.4043	−1.99609
$218$	12.7761	0.865306
$219$	−8.31643	−0.561972
$220$	−1.34525	−0.0906967
$221$	−3.70018	−0.248901
$222$	14.3315	0.961865
$223$	−15.2620	−1.02202	−0.511010	−	0.859575i	$-0.670729\pi$
$223$	−15.2620	−1.02202	−0.511010	+	0.859575i	$0.670729\pi$
$224$	8.18965	0.547194
$225$	−4.58984	−0.305990
$226$	−10.9928	−0.731232
$227$	26.4919	1.75833	0.879165	−	0.476518i	$-0.158101\pi$
$227$	26.4919	1.75833	0.879165	+	0.476518i	$0.158101\pi$
$228$	0.819357	0.0542633
$229$	−3.42996	−0.226658	−0.113329	−	0.993558i	$-0.536151\pi$
$229$	−3.42996	−0.226658	−0.113329	+	0.993558i	$0.536151\pi$
$230$	4.84109	0.319212
$231$	−15.5746	−1.02473
$232$	8.49498	0.557723
$233$	−20.9642	−1.37341	−0.686706	−	0.726935i	$-0.740944\pi$
$233$	−20.9642	−1.37341	−0.686706	+	0.726935i	$0.740944\pi$
$234$	1.56390	0.102235
$235$	0.127025	0.00828622
$236$	−0.786117	−0.0511719
$237$	−10.4360	−0.677891
$238$	−19.1263	−1.23977
$239$	18.7477	1.21269	0.606345	−	0.795202i	$-0.292635\pi$
$239$	18.7477	1.21269	0.606345	+	0.795202i	$0.292635\pi$
$240$	−3.00545	−0.194001
$241$	5.35043	0.344652	0.172326	−	0.985040i	$-0.444872\pi$
$241$	5.35043	0.344652	0.172326	+	0.985040i	$0.444872\pi$
$242$	−17.5220	−1.12636
$243$	1.00000	0.0641500
$244$	−6.34945	−0.406482
$245$	2.51337	0.160573
$246$	−6.04847	−0.385636
$247$	−1.83807	−0.116953
$248$	−21.6239	−1.37312
$249$	−9.67462	−0.613104
$250$	9.60493	0.607469
$251$	−6.50721	−0.410732	−0.205366	−	0.978685i	$-0.565838\pi$
$251$	−6.50721	−0.410732	−0.205366	+	0.978685i	$0.565838\pi$
$252$	1.47337	0.0928137
$253$	22.7760	1.43191
$254$	7.06703	0.443425
$255$	2.36972	0.148398
$256$	10.2065	0.637907
$257$	17.0683	1.06469	0.532346	−	0.846527i	$-0.321311\pi$
$257$	17.0683	1.06469	0.532346	+	0.846527i	$0.321311\pi$
$258$	13.3749	0.832684
$259$	−30.2889	−1.88206
$260$	−0.285487	−0.0177052
$261$	3.49494	0.216331
$262$	−9.34367	−0.577254
$263$	−1.51401	−0.0933580	−0.0466790	−	0.998910i	$-0.514864\pi$
$263$	−1.51401	−0.0933580	−0.0466790	+	0.998910i	$0.514864\pi$
$264$	−11.4535	−0.704916
$265$	−1.28918	−0.0791934
$266$	−9.50101	−0.582544
$267$	−12.3627	−0.756584
$268$	5.15213	0.314716
$269$	−19.2476	−1.17355	−0.586774	−	0.809751i	$-0.699602\pi$
$269$	−19.2476	−1.17355	−0.586774	+	0.809751i	$0.699602\pi$
$270$	−1.00157	−0.0609538
$271$	−4.92779	−0.299342	−0.149671	−	0.988736i	$-0.547821\pi$
$271$	−4.92779	−0.299342	−0.149671	+	0.988736i	$0.547821\pi$
$272$	−17.3643	−1.05287
$273$	−3.30522	−0.200041
$274$	−28.5138	−1.72258
$275$	21.6279	1.30421
$276$	−2.15463	−0.129693
$277$	−12.1196	−0.728196	−0.364098	−	0.931361i	$-0.618623\pi$
$277$	−12.1196	−0.728196	−0.364098	+	0.931361i	$0.618623\pi$
$278$	−25.3494	−1.52035
$279$	−8.89632	−0.532609
$280$	5.14515	0.307481
$281$	−20.7992	−1.24078	−0.620389	−	0.784295i	$-0.713025\pi$
$281$	−20.7992	−1.24078	−0.620389	+	0.784295i	$0.713025\pi$
$282$	−0.310187	−0.0184714
$283$	6.21623	0.369517	0.184758	−	0.982784i	$-0.440850\pi$
$283$	6.21623	0.369517	0.184758	+	0.982784i	$0.440850\pi$
$284$	−0.904814	−0.0536908
$285$	1.17716	0.0697290
$286$	−7.36927	−0.435754
$287$	12.7831	0.754565
$288$	2.47779	0.146005
$289$	−3.30867	−0.194628
$290$	−3.50043	−0.205553
$291$	12.4092	0.727443
$292$	−3.70722	−0.216949
$293$	15.0560	0.879579	0.439789	−	0.898101i	$-0.355053\pi$
$293$	15.0560	0.879579	0.439789	+	0.898101i	$0.355053\pi$
$294$	−6.13747	−0.357945
$295$	−1.12941	−0.0657565
$296$	−22.2744	−1.29467
$297$	−4.71212	−0.273425
$298$	−7.19360	−0.416714
$299$	4.83349	0.279528
$300$	−2.04602	−0.118127
$301$	−28.2672	−1.62929
$302$	22.4639	1.29265
$303$	5.20306	0.298908
$304$	−8.62574	−0.494720
$305$	−9.12219	−0.522335
$306$	−5.78670	−0.330803
$307$	−22.8323	−1.30311	−0.651555	−	0.758601i	$-0.725883\pi$
$307$	−22.8323	−1.30311	−0.651555	+	0.758601i	$0.725883\pi$
$308$	−6.94270	−0.395597
$309$	1.00000	0.0568880
$310$	8.91031	0.506072
$311$	23.1092	1.31040	0.655202	−	0.755454i	$-0.272584\pi$
$311$	23.1092	1.31040	0.655202	+	0.755454i	$0.272584\pi$
$312$	−2.43065	−0.137609
$313$	21.0374	1.18910	0.594552	−	0.804057i	$-0.297330\pi$
$313$	21.0374	1.18910	0.594552	+	0.804057i	$0.297330\pi$
$314$	−35.5810	−2.00795
$315$	2.11678	0.119267
$316$	−4.65206	−0.261699
$317$	−10.9399	−0.614448	−0.307224	−	0.951637i	$-0.599400\pi$
$317$	−10.9399	−0.614448	−0.307224	+	0.951637i	$0.599400\pi$
$318$	3.14808	0.176535
$319$	−16.4686	−0.922063
$320$	3.52921	0.197289
$321$	−0.442250	−0.0246840
$322$	24.9844	1.39233
$323$	6.80118	0.378428
$324$	0.445771	0.0247651
$325$	4.58984	0.254599
$326$	14.5364	0.805095
$327$	−8.16940	−0.451769
$328$	9.40070	0.519067
$329$	0.655566	0.0361425
$330$	4.71953	0.259802
$331$	2.65805	0.146100	0.0730498	−	0.997328i	$-0.476727\pi$
$331$	2.65805	0.146100	0.0730498	+	0.997328i	$0.476727\pi$
$332$	−4.31267	−0.236688
$333$	−9.16395	−0.502181
$334$	9.99931	0.547138
$335$	7.40201	0.404415
$336$	−15.5108	−0.846185
$337$	−17.9354	−0.977003	−0.488501	−	0.872563i	$-0.662456\pi$
$337$	−17.9354	−0.977003	−0.488501	+	0.872563i	$0.662456\pi$
$338$	−1.56390	−0.0850647
$339$	7.02913	0.381770
$340$	1.05635	0.0572888
$341$	41.9205	2.27012
$342$	−2.87455	−0.155438
$343$	−10.1653	−0.548874
$344$	−20.7876	−1.12079
$345$	−3.09553	−0.166658
$346$	−6.73007	−0.361811
$347$	−3.48104	−0.186872	−0.0934360	−	0.995625i	$-0.529785\pi$
$347$	−3.48104	−0.186872	−0.0934360	+	0.995625i	$0.529785\pi$
$348$	1.55794	0.0835145
$349$	−27.8482	−1.49068	−0.745341	−	0.666684i	$-0.767713\pi$
$349$	−27.8482	−1.49068	−0.745341	+	0.666684i	$0.767713\pi$
$350$	23.7250	1.26815
$351$	−1.00000	−0.0533761
$352$	−11.6757	−0.622315
$353$	20.6774	1.10055	0.550275	−	0.834984i	$-0.314523\pi$
$353$	20.6774	1.10055	0.550275	+	0.834984i	$0.314523\pi$
$354$	2.75793	0.146582
$355$	−1.29994	−0.0689935
$356$	−5.51092	−0.292078
$357$	12.2299	0.647275
$358$	−13.8030	−0.729512
$359$	1.20843	0.0637787	0.0318894	−	0.999491i	$-0.489848\pi$
$359$	1.20843	0.0637787	0.0318894	+	0.999491i	$0.489848\pi$
$360$	1.55667	0.0820439
$361$	−15.6215	−0.822185
$362$	−3.51869	−0.184938
$363$	11.2041	0.588062
$364$	−1.47337	−0.0772256
$365$	−5.32612	−0.278782
$366$	22.2757	1.16437
$367$	0.754202	0.0393690	0.0196845	−	0.999806i	$-0.493734\pi$
$367$	0.754202	0.0393690	0.0196845	+	0.999806i	$0.493734\pi$
$368$	22.6827	1.18242
$369$	3.86756	0.201337
$370$	9.17836	0.477160
$371$	−6.65331	−0.345423
$372$	−3.96572	−0.205613
$373$	−24.8674	−1.28758	−0.643791	−	0.765201i	$-0.722640\pi$
$373$	−24.8674	−1.28758	−0.643791	+	0.765201i	$0.722640\pi$
$374$	27.2676	1.40997
$375$	−6.14166	−0.317154
$376$	0.482102	0.0248625
$377$	−3.49494	−0.179998
$378$	−5.16902	−0.265866
$379$	29.0388	1.49162	0.745812	−	0.666157i	$-0.232062\pi$
$379$	29.0388	1.49162	0.745812	+	0.666157i	$0.232062\pi$
$380$	0.524745	0.0269188
$381$	−4.51886	−0.231508
$382$	39.4060	2.01618
$383$	10.1928	0.520826	0.260413	−	0.965497i	$-0.416141\pi$
$383$	10.1928	0.520826	0.260413	+	0.965497i	$0.416141\pi$
$384$	−13.5737	−0.692678
$385$	−9.97450	−0.508348
$386$	−34.3432	−1.74802
$387$	−8.55229	−0.434737
$388$	5.53168	0.280829
$389$	−6.09553	−0.309056	−0.154528	−	0.987988i	$-0.549386\pi$
$389$	−6.09553	−0.309056	−0.154528	+	0.987988i	$0.549386\pi$
$390$	1.00157	0.0507166
$391$	−17.8848	−0.904472
$392$	9.53904	0.481794
$393$	5.97461	0.301379
$394$	−34.7988	−1.75314
$395$	−6.68357	−0.336287
$396$	−2.10053	−0.105555
$397$	−8.91301	−0.447331	−0.223666	−	0.974666i	$-0.571802\pi$
$397$	−8.91301	−0.447331	−0.223666	+	0.974666i	$0.571802\pi$
$398$	26.4556	1.32610
$399$	6.07522	0.304141
$400$	21.5394	1.07697
$401$	−14.0772	−0.702983	−0.351492	−	0.936191i	$-0.614325\pi$
$401$	−14.0772	−0.702983	−0.351492	+	0.936191i	$0.614325\pi$
$402$	−18.0752	−0.901508
$403$	8.89632	0.443157
$404$	2.31937	0.115393
$405$	0.640434	0.0318234
$406$	−18.0654	−0.896571
$407$	43.1816	2.14043
$408$	8.99385	0.445262
$409$	14.5978	0.721816	0.360908	−	0.932601i	$-0.382467\pi$
$409$	14.5978	0.721816	0.360908	+	0.932601i	$0.382467\pi$
$410$	−3.87365	−0.191306
$411$	18.2325	0.899344
$412$	0.445771	0.0219616
$413$	−5.82875	−0.286814
$414$	7.55907	0.371508
$415$	−6.19596	−0.304148
$416$	−2.47779	−0.121484
$417$	16.2091	0.793764
$418$	13.5452	0.662518
$419$	−13.2590	−0.647746	−0.323873	−	0.946101i	$-0.604985\pi$
$419$	−13.2590	−0.647746	−0.323873	+	0.946101i	$0.604985\pi$
$420$	0.943597	0.0460428
$421$	8.05295	0.392477	0.196238	−	0.980556i	$-0.437127\pi$
$421$	8.05295	0.392477	0.196238	+	0.980556i	$0.437127\pi$
$422$	18.2244	0.887151
$423$	0.198343	0.00964375
$424$	−4.89283	−0.237617
$425$	−16.9832	−0.823809
$426$	3.17435	0.153798
$427$	−47.0787	−2.27830
$428$	−0.197142	−0.00952922
$429$	4.71212	0.227503
$430$	8.56574	0.413077
$431$	−8.42127	−0.405638	−0.202819	−	0.979216i	$-0.565010\pi$
$431$	−8.42127	−0.405638	−0.202819	+	0.979216i	$0.565010\pi$
$432$	−4.69283	−0.225784
$433$	−31.6660	−1.52177	−0.760885	−	0.648886i	$-0.775235\pi$
$433$	−31.6660	−1.52177	−0.760885	+	0.648886i	$0.775235\pi$
$434$	45.9853	2.20736
$435$	2.23828	0.107317
$436$	−3.64168	−0.174405
$437$	−8.88428	−0.424993
$438$	13.0060	0.621452
$439$	−21.3825	−1.02053	−0.510265	−	0.860017i	$-0.670453\pi$
$439$	−21.3825	−1.02053	−0.510265	+	0.860017i	$0.670453\pi$
$440$	−7.33523	−0.349693
$441$	3.92448	0.186880
$442$	5.78670	0.275245
$443$	−15.6297	−0.742588	−0.371294	−	0.928515i	$-0.621086\pi$
$443$	−15.6297	−0.742588	−0.371294	+	0.928515i	$0.621086\pi$
$444$	−4.08502	−0.193867
$445$	−7.91748	−0.375325
$446$	23.8682	1.13019
$447$	4.59980	0.217563
$448$	18.2139	0.860526
$449$	−25.6841	−1.21211	−0.606053	−	0.795424i	$-0.707248\pi$
$449$	−25.6841	−1.21211	−0.606053	+	0.795424i	$0.707248\pi$
$450$	7.17804	0.338376
$451$	−18.2244	−0.858155
$452$	3.13338	0.147382
$453$	−14.3640	−0.674881
$454$	−41.4306	−1.94443
$455$	−2.11678	−0.0992360
$456$	4.46771	0.209219
$457$	−16.5212	−0.772827	−0.386413	−	0.922326i	$-0.626286\pi$
$457$	−16.5212	−0.772827	−0.386413	+	0.922326i	$0.626286\pi$
$458$	5.36409	0.250648
$459$	3.70018	0.172710
$460$	−1.37990	−0.0643381
$461$	−26.0400	−1.21280	−0.606402	−	0.795158i	$-0.707388\pi$
$461$	−26.0400	−1.21280	−0.606402	+	0.795158i	$0.707388\pi$
$462$	24.3570	1.13319
$463$	22.2123	1.03230	0.516148	−	0.856500i	$-0.327366\pi$
$463$	22.2123	1.03230	0.516148	+	0.856500i	$0.327366\pi$
$464$	−16.4012	−0.761404
$465$	−5.69751	−0.264216
$466$	32.7859	1.51878
$467$	19.7268	0.912848	0.456424	−	0.889762i	$-0.349130\pi$
$467$	19.7268	0.912848	0.456424	+	0.889762i	$0.349130\pi$
$468$	−0.445771	−0.0206058
$469$	38.2010	1.76396
$470$	−0.198655	−0.00916325
$471$	22.7515	1.04833
$472$	−4.28645	−0.197300
$473$	40.2994	1.85297
$474$	16.3208	0.749640
$475$	−8.43645	−0.387091
$476$	5.45174	0.249880
$477$	−2.01297	−0.0921676
$478$	−29.3195	−1.34104
$479$	−2.60139	−0.118861	−0.0594303	−	0.998232i	$-0.518928\pi$
$479$	−2.60139	−0.118861	−0.0594303	+	0.998232i	$0.518928\pi$
$480$	1.58686	0.0724301
$481$	9.16395	0.417840
$482$	−8.36752	−0.381130
$483$	−15.9757	−0.726921
$484$	4.99446	0.227021
$485$	7.94731	0.360869
$486$	−1.56390	−0.0709398
$487$	15.4746	0.701220	0.350610	−	0.936522i	$-0.385974\pi$
$487$	15.4746	0.701220	0.350610	+	0.936522i	$0.385974\pi$
$488$	−34.6216	−1.56725
$489$	−9.29498	−0.420333
$490$	−3.93065	−0.177569
$491$	−31.1025	−1.40364	−0.701818	−	0.712356i	$-0.747628\pi$
$491$	−31.1025	−1.40364	−0.701818	+	0.712356i	$0.747628\pi$
$492$	1.72405	0.0777261
$493$	12.9319	0.582424
$494$	2.87455	0.129332
$495$	−3.01780	−0.135640
$496$	41.7489	1.87458
$497$	−6.70885	−0.300933
$498$	15.1301	0.677996
$499$	2.49965	0.111900	0.0559499	−	0.998434i	$-0.482181\pi$
$499$	2.49965	0.111900	0.0559499	+	0.998434i	$0.482181\pi$
$500$	−2.73778	−0.122437
$501$	−6.39385	−0.285656
$502$	10.1766	0.454204
$503$	3.63209	0.161947	0.0809735	−	0.996716i	$-0.474197\pi$
$503$	3.63209	0.161947	0.0809735	+	0.996716i	$0.474197\pi$
$504$	8.03384	0.357856
$505$	3.33222	0.148282
$506$	−35.6193	−1.58347
$507$	1.00000	0.0444116
$508$	−2.01438	−0.0893735
$509$	32.5621	1.44329	0.721645	−	0.692264i	$-0.243386\pi$
$509$	32.5621	1.44329	0.721645	+	0.692264i	$0.243386\pi$
$510$	−3.70600	−0.164104
$511$	−27.4876	−1.21598
$512$	11.1854	0.494330
$513$	1.83807	0.0811527
$514$	−26.6931	−1.17738
$515$	0.640434	0.0282209
$516$	−3.81236	−0.167830
$517$	−0.934614	−0.0411043
$518$	47.3686	2.08126
$519$	4.30340	0.188898
$520$	−1.55667	−0.0682646
$521$	4.16831	0.182617	0.0913086	−	0.995823i	$-0.470895\pi$
$521$	4.16831	0.182617	0.0913086	+	0.995823i	$0.470895\pi$
$522$	−5.46572	−0.239228
$523$	21.7575	0.951389	0.475695	−	0.879611i	$-0.342197\pi$
$523$	21.7575	0.951389	0.475695	+	0.879611i	$0.342197\pi$
$524$	2.66331	0.116347
$525$	−15.1704	−0.662092
$526$	2.36776	0.103239
$527$	−32.9180	−1.43393
$528$	22.1132	0.962353
$529$	0.362617	0.0157660
$530$	2.01614	0.0875753
$531$	−1.76350	−0.0765294
$532$	2.70816	0.117413
$533$	−3.86756	−0.167523
$534$	19.3339	0.836661
$535$	−0.283232	−0.0122452
$536$	28.0930	1.21343
$537$	8.82604	0.380872
$538$	30.1013	1.29776
$539$	−18.4926	−0.796533
$540$	0.285487	0.0122854
$541$	41.4245	1.78098	0.890490	−	0.455003i	$-0.150362\pi$
$541$	41.4245	1.78098	0.890490	+	0.455003i	$0.150362\pi$
$542$	7.70655	0.331025
$543$	2.24995	0.0965546
$544$	9.16828	0.393087
$545$	−5.23196	−0.224113
$546$	5.16902	0.221214
$547$	18.5123	0.791529	0.395765	−	0.918352i	$-0.370480\pi$
$547$	18.5123	0.791529	0.395765	+	0.918352i	$0.370480\pi$
$548$	8.12753	0.347191
$549$	−14.2438	−0.607909
$550$	−33.8238	−1.44225
$551$	6.42393	0.273669
$552$	−11.7485	−0.500051
$553$	−34.4933	−1.46680
$554$	18.9538	0.805270
$555$	−5.86891	−0.249121
$556$	7.22555	0.306432
$557$	2.12047	0.0898473	0.0449236	−	0.998990i	$-0.485696\pi$
$557$	2.12047	0.0898473	0.0449236	+	0.998990i	$0.485696\pi$
$558$	13.9129	0.588981
$559$	8.55229	0.361723
$560$	−9.93367	−0.419774
$561$	−17.4357	−0.736136
$562$	32.5278	1.37210
$563$	0.431077	0.0181677	0.00908386	−	0.999959i	$-0.497108\pi$
$563$	0.431077	0.0181677	0.00908386	+	0.999959i	$0.497108\pi$
$564$	0.0884154	0.00372296
$565$	4.50170	0.189388
$566$	−9.72154	−0.408627
$567$	3.30522	0.138806
$568$	−4.93367	−0.207012
$569$	−37.9641	−1.59154	−0.795769	−	0.605600i	$-0.792933\pi$
$569$	−37.9641	−1.59154	−0.795769	+	0.605600i	$0.792933\pi$
$570$	−1.84096	−0.0771093
$571$	−16.9469	−0.709204	−0.354602	−	0.935017i	$-0.615384\pi$
$571$	−16.9469	−0.709204	−0.354602	+	0.935017i	$0.615384\pi$
$572$	2.10053	0.0878274
$573$	−25.1973	−1.05263
$574$	−19.9915	−0.834430
$575$	22.1850	0.925177
$576$	5.51065	0.229610
$577$	20.1515	0.838919	0.419459	−	0.907774i	$-0.362220\pi$
$577$	20.1515	0.838919	0.419459	+	0.907774i	$0.362220\pi$
$578$	5.17442	0.215227
$579$	21.9600	0.912628
$580$	0.997760	0.0414297
$581$	−31.9768	−1.32662
$582$	−19.4068	−0.804436
$583$	9.48536	0.392843
$584$	−20.2143	−0.836476
$585$	−0.640434	−0.0264787
$586$	−23.5460	−0.972675
$587$	−3.68014	−0.151896	−0.0759478	−	0.997112i	$-0.524198\pi$
$587$	−3.68014	−0.151896	−0.0759478	+	0.997112i	$0.524198\pi$
$588$	1.74942	0.0721448
$589$	−16.3520	−0.673774
$590$	1.76627	0.0727163
$591$	22.2513	0.915297
$592$	43.0049	1.76749
$593$	−38.4045	−1.57709	−0.788543	−	0.614980i	$-0.789164\pi$
$593$	−38.4045	−1.57709	−0.788543	+	0.614980i	$0.789164\pi$
$594$	7.36927	0.302365
$595$	7.83245	0.321099
$596$	2.05046	0.0839899
$597$	−16.9165	−0.692346
$598$	−7.55907	−0.309114
$599$	−30.4717	−1.24504	−0.622521	−	0.782603i	$-0.713891\pi$
$599$	−30.4717	−1.24504	−0.622521	+	0.782603i	$0.713891\pi$
$600$	−11.1563	−0.455455
$601$	−2.37522	−0.0968873	−0.0484437	−	0.998826i	$-0.515426\pi$
$601$	−2.37522	−0.0968873	−0.0484437	+	0.998826i	$0.515426\pi$
$602$	44.2070	1.80174
$603$	11.5578	0.470670
$604$	−6.40307	−0.260537
$605$	7.17548	0.291725
$606$	−8.13704	−0.330545
$607$	−48.3408	−1.96209	−0.981046	−	0.193776i	$-0.937926\pi$
$607$	−48.3408	−1.96209	−0.981046	+	0.193776i	$0.937926\pi$
$608$	4.55435	0.184703
$609$	11.5515	0.468092
$610$	14.2662	0.577620
$611$	−0.198343	−0.00802408
$612$	1.64943	0.0666744
$613$	−20.7590	−0.838447	−0.419223	−	0.907883i	$-0.637698\pi$
$613$	−20.7590	−0.838447	−0.419223	+	0.907883i	$0.637698\pi$
$614$	35.7074	1.44103
$615$	2.47692	0.0998791
$616$	−37.8564	−1.52528
$617$	17.4255	0.701526	0.350763	−	0.936464i	$-0.385922\pi$
$617$	17.4255	0.701526	0.350763	+	0.936464i	$0.385922\pi$
$618$	−1.56390	−0.0629091
$619$	17.1855	0.690744	0.345372	−	0.938466i	$-0.387753\pi$
$619$	17.1855	0.690744	0.345372	+	0.938466i	$0.387753\pi$
$620$	−2.53978	−0.102000
$621$	−4.83349	−0.193961
$622$	−36.1404	−1.44910
$623$	−40.8614	−1.63708
$624$	4.69283	0.187864
$625$	19.0159	0.760636
$626$	−32.9003	−1.31496
$627$	−8.66120	−0.345895
$628$	10.1420	0.404709
$629$	−33.9083	−1.35201
$630$	−3.31042	−0.131890
$631$	2.60033	0.103518	0.0517588	−	0.998660i	$-0.483517\pi$
$631$	2.60033	0.103518	0.0517588	+	0.998660i	$0.483517\pi$
$632$	−25.3663	−1.00902
$633$	−11.6532	−0.463174
$634$	17.1089	0.679482
$635$	−2.89403	−0.114846
$636$	−0.897324	−0.0355812
$637$	−3.92448	−0.155493
$638$	25.7551	1.01966
$639$	−2.02977	−0.0802966
$640$	−8.69304	−0.343623
$641$	45.1562	1.78356	0.891781	−	0.452466i	$-0.149456\pi$
$641$	45.1562	1.78356	0.891781	+	0.452466i	$0.149456\pi$
$642$	0.691632	0.0272966
$643$	−44.7336	−1.76412	−0.882060	−	0.471136i	$-0.843844\pi$
$643$	−44.7336	−1.76412	−0.882060	+	0.471136i	$0.843844\pi$
$644$	−7.12152	−0.280627
$645$	−5.47718	−0.215664
$646$	−10.6363	−0.418481
$647$	24.7176	0.971748	0.485874	−	0.874029i	$-0.338501\pi$
$647$	24.7176	0.971748	0.485874	+	0.874029i	$0.338501\pi$
$648$	2.43065	0.0954851
$649$	8.30982	0.326189
$650$	−7.17804	−0.281546
$651$	−29.4043	−1.15245
$652$	−4.14343	−0.162269
$653$	1.79247	0.0701447	0.0350723	−	0.999385i	$-0.488834\pi$
$653$	1.79247	0.0701447	0.0350723	+	0.999385i	$0.488834\pi$
$654$	12.7761	0.499585
$655$	3.82635	0.149508
$656$	−18.1498	−0.708631
$657$	−8.31643	−0.324455
$658$	−1.02524	−0.0399679
$659$	13.5073	0.526170	0.263085	−	0.964773i	$-0.415260\pi$
$659$	13.5073	0.526170	0.263085	+	0.964773i	$0.415260\pi$
$660$	−1.34525	−0.0523638
$661$	−6.83012	−0.265661	−0.132830	−	0.991139i	$-0.542407\pi$
$661$	−6.83012	−0.265661	−0.132830	+	0.991139i	$0.542407\pi$
$662$	−4.15691	−0.161563
$663$	−3.70018	−0.143703
$664$	−23.5156	−0.912584
$665$	3.89078	0.150878
$666$	14.3315	0.555333
$667$	−16.8927	−0.654090
$668$	−2.85019	−0.110277
$669$	−15.2620	−0.590064
$670$	−11.5760	−0.447219
$671$	67.1183	2.59107
$672$	8.18965	0.315923
$673$	40.4803	1.56040	0.780201	−	0.625528i	$-0.215117\pi$
$673$	40.4803	1.56040	0.780201	+	0.625528i	$0.215117\pi$
$674$	28.0491	1.08041
$675$	−4.58984	−0.176663
$676$	0.445771	0.0171450
$677$	−2.86611	−0.110154	−0.0550768	−	0.998482i	$-0.517540\pi$
$677$	−2.86611	−0.110154	−0.0550768	+	0.998482i	$0.517540\pi$
$678$	−10.9928	−0.422177
$679$	41.0153	1.57402
$680$	5.75997	0.220885
$681$	26.4919	1.01517
$682$	−65.5594	−2.51040
$683$	15.4920	0.592784	0.296392	−	0.955066i	$-0.404216\pi$
$683$	15.4920	0.592784	0.296392	+	0.955066i	$0.404216\pi$
$684$	0.819357	0.0313289
$685$	11.6767	0.446145
$686$	15.8974	0.606967
$687$	−3.42996	−0.130861
$688$	40.1344	1.53011
$689$	2.01297	0.0766881
$690$	4.84109	0.184297
$691$	−13.3060	−0.506185	−0.253093	−	0.967442i	$-0.581448\pi$
$691$	−13.3060	−0.506185	−0.253093	+	0.967442i	$0.581448\pi$
$692$	1.91833	0.0729239
$693$	−15.5746	−0.591630
$694$	5.44398	0.206651
$695$	10.3809	0.393769
$696$	8.49498	0.322001
$697$	14.3107	0.542056
$698$	43.5517	1.64846
$699$	−20.9642	−0.792940
$700$	−6.76254	−0.255600
$701$	−7.33168	−0.276914	−0.138457	−	0.990368i	$-0.544214\pi$
$701$	−7.33168	−0.276914	−0.138457	+	0.990368i	$0.544214\pi$
$702$	1.56390	0.0590255
$703$	−16.8440	−0.635282
$704$	−25.9668	−0.978662
$705$	0.127025	0.00478405
$706$	−32.3374	−1.21703
$707$	17.1972	0.646769
$708$	−0.786117	−0.0295441
$709$	15.9497	0.599003	0.299502	−	0.954096i	$-0.403180\pi$
$709$	15.9497	0.599003	0.299502	+	0.954096i	$0.403180\pi$
$710$	2.03297	0.0762958
$711$	−10.4360	−0.391380
$712$	−30.0494	−1.12615
$713$	43.0003	1.61037
$714$	−19.1263	−0.715784
$715$	3.01780	0.112859
$716$	3.93439	0.147035
$717$	18.7477	0.700147
$718$	−1.88987	−0.0705291
$719$	−25.3119	−0.943974	−0.471987	−	0.881606i	$-0.656463\pi$
$719$	−25.3119	−0.943974	−0.471987	+	0.881606i	$0.656463\pi$
$720$	−3.00545	−0.112006
$721$	3.30522	0.123093
$722$	24.4304	0.909206
$723$	5.35043	0.198985
$724$	1.00296	0.0372748
$725$	−16.0412	−0.595756
$726$	−17.5220	−0.650303
$727$	−3.02965	−0.112363	−0.0561817	−	0.998421i	$-0.517893\pi$
$727$	−3.02965	−0.112363	−0.0561817	+	0.998421i	$0.517893\pi$
$728$	−8.03384	−0.297754
$729$	1.00000	0.0370370
$730$	8.32951	0.308289
$731$	−31.6450	−1.17043
$732$	−6.34945	−0.234682
$733$	17.8813	0.660462	0.330231	−	0.943900i	$-0.392873\pi$
$733$	17.8813	0.660462	0.330231	+	0.943900i	$0.392873\pi$
$734$	−1.17949	−0.0435359
$735$	2.51337	0.0927070
$736$	−11.9764	−0.441456
$737$	−54.4617	−2.00612
$738$	−6.04847	−0.222647
$739$	50.9354	1.87369	0.936845	−	0.349745i	$-0.113732\pi$
$739$	50.9354	1.87369	0.936845	+	0.349745i	$0.113732\pi$
$740$	−2.61619	−0.0961730
$741$	−1.83807	−0.0675231
$742$	10.4051	0.381983
$743$	33.8731	1.24268	0.621341	−	0.783540i	$-0.286588\pi$
$743$	33.8731	1.24268	0.621341	+	0.783540i	$0.286588\pi$
$744$	−21.6239	−0.792770
$745$	2.94587	0.107928
$746$	38.8900	1.42386
$747$	−9.67462	−0.353976
$748$	−7.77233	−0.284184
$749$	−1.46173	−0.0534105
$750$	9.60493	0.350722
$751$	4.52903	0.165267	0.0826333	−	0.996580i	$-0.473667\pi$
$751$	4.52903	0.165267	0.0826333	+	0.996580i	$0.473667\pi$
$752$	−0.930788	−0.0339424
$753$	−6.50721	−0.237136
$754$	5.46572	0.199050
$755$	−9.19922	−0.334794
$756$	1.47337	0.0535860
$757$	29.3189	1.06561	0.532807	−	0.846237i	$-0.321137\pi$
$757$	29.3189	1.06561	0.532807	+	0.846237i	$0.321137\pi$
$758$	−45.4137	−1.64950
$759$	22.7760	0.826716
$760$	2.86127	0.103789
$761$	12.8832	0.467015	0.233508	−	0.972355i	$-0.424980\pi$
$761$	12.8832	0.467015	0.233508	+	0.972355i	$0.424980\pi$
$762$	7.06703	0.256011
$763$	−27.0016	−0.977525
$764$	−11.2322	−0.406368
$765$	2.36972	0.0856775
$766$	−15.9404	−0.575951
$767$	1.76350	0.0636763
$768$	10.2065	0.368296
$769$	−43.0290	−1.55166	−0.775832	−	0.630939i	$-0.782670\pi$
$769$	−43.0290	−1.55166	−0.775832	+	0.630939i	$0.782670\pi$
$770$	15.5991	0.562152
$771$	17.0683	0.614700
$772$	9.78915	0.352319
$773$	−42.4614	−1.52723	−0.763614	−	0.645673i	$-0.776577\pi$
$773$	−42.4614	−1.52723	−0.763614	+	0.645673i	$0.776577\pi$
$774$	13.3749	0.480751
$775$	40.8327	1.46676
$776$	30.1626	1.08277
$777$	−30.2889	−1.08661
$778$	9.53277	0.341766
$779$	7.10885	0.254701
$780$	−0.285487	−0.0102221
$781$	9.56454	0.342246
$782$	27.9699	1.00020
$783$	3.49494	0.124899
$784$	−18.4169	−0.657747
$785$	14.5709	0.520056
$786$	−9.34367	−0.333278
$787$	27.9921	0.997810	0.498905	−	0.866657i	$-0.333736\pi$
$787$	27.9921	0.997810	0.498905	+	0.866657i	$0.333736\pi$
$788$	9.91900	0.353350
$789$	−1.51401	−0.0539003
$790$	10.4524	0.371880
$791$	23.2328	0.826064
$792$	−11.4535	−0.406983
$793$	14.2438	0.505810
$794$	13.9390	0.494677
$795$	−1.28918	−0.0457223
$796$	−7.54088	−0.267280
$797$	−9.23559	−0.327141	−0.163571	−	0.986532i	$-0.552301\pi$
$797$	−9.23559	−0.327141	−0.163571	+	0.986532i	$0.552301\pi$
$798$	−9.50101	−0.336332
$799$	0.733903	0.0259636
$800$	−11.3727	−0.402085
$801$	−12.3627	−0.436814
$802$	22.0153	0.777388
$803$	39.1880	1.38291
$804$	5.15213	0.181702
$805$	−10.2314	−0.360610
$806$	−13.9129	−0.490062
$807$	−19.2476	−0.677548
$808$	12.6468	0.444914
$809$	34.5408	1.21439	0.607195	−	0.794553i	$-0.292295\pi$
$809$	34.5408	1.21439	0.607195	+	0.794553i	$0.292295\pi$
$810$	−1.00157	−0.0351917
$811$	−12.3669	−0.434262	−0.217131	−	0.976142i	$-0.569670\pi$
$811$	−12.3669	−0.434262	−0.217131	+	0.976142i	$0.569670\pi$
$812$	5.14934	0.180706
$813$	−4.92779	−0.172825
$814$	−67.5316	−2.36698
$815$	−5.95282	−0.208518
$816$	−17.3643	−0.607873
$817$	−15.7197	−0.549962
$818$	−22.8295	−0.798214
$819$	−3.30522	−0.115494
$820$	1.10414	0.0385582
$821$	46.6258	1.62725	0.813625	−	0.581389i	$-0.197491\pi$
$821$	46.6258	1.62725	0.813625	+	0.581389i	$0.197491\pi$
$822$	−28.5138	−0.994532
$823$	−0.688876	−0.0240127	−0.0120063	−	0.999928i	$-0.503822\pi$
$823$	−0.688876	−0.0240127	−0.0120063	+	0.999928i	$0.503822\pi$
$824$	2.43065	0.0846758
$825$	21.6279	0.752987
$826$	9.11556	0.317171
$827$	−28.8244	−1.00232	−0.501162	−	0.865354i	$-0.667094\pi$
$827$	−28.8244	−1.00232	−0.501162	+	0.865354i	$0.667094\pi$
$828$	−2.15463	−0.0748785
$829$	−31.1655	−1.08242	−0.541212	−	0.840886i	$-0.682034\pi$
$829$	−31.1655	−1.08242	−0.541212	+	0.840886i	$0.682034\pi$
$830$	9.68984	0.336339
$831$	−12.1196	−0.420424
$832$	−5.51065	−0.191047
$833$	14.5213	0.503132
$834$	−25.3494	−0.877777
$835$	−4.09484	−0.141708
$836$	−3.86091	−0.133532
$837$	−8.89632	−0.307502
$838$	20.7358	0.716305
$839$	43.2667	1.49373	0.746866	−	0.664975i	$-0.231558\pi$
$839$	43.2667	1.49373	0.746866	+	0.664975i	$0.231558\pi$
$840$	5.14515	0.177524
$841$	−16.7854	−0.578807
$842$	−12.5940	−0.434017
$843$	−20.7992	−0.716363
$844$	−5.19467	−0.178808
$845$	0.640434	0.0220316
$846$	−0.310187	−0.0106645
$847$	37.0320	1.27243
$848$	9.44653	0.324395
$849$	6.21623	0.213340
$850$	26.5600	0.911002
$851$	44.2939	1.51837
$852$	−0.904814	−0.0309984
$853$	−2.79029	−0.0955376	−0.0477688	−	0.998858i	$-0.515211\pi$
$853$	−2.79029	−0.0955376	−0.0477688	+	0.998858i	$0.515211\pi$
$854$	73.6262	2.51944
$855$	1.17716	0.0402581
$856$	−1.07496	−0.0367412
$857$	−55.6817	−1.90205	−0.951026	−	0.309112i	$-0.899968\pi$
$857$	−55.6817	−1.90205	−0.951026	+	0.309112i	$0.899968\pi$
$858$	−7.36927	−0.251583
$859$	−39.3231	−1.34169	−0.670843	−	0.741599i	$-0.734068\pi$
$859$	−39.3231	−1.34169	−0.670843	+	0.741599i	$0.734068\pi$
$860$	−2.44157	−0.0832568
$861$	12.7831	0.435648
$862$	13.1700	0.448572
$863$	46.4910	1.58257	0.791287	−	0.611445i	$-0.209412\pi$
$863$	46.4910	1.58257	0.791287	+	0.611445i	$0.209412\pi$
$864$	2.47779	0.0842962
$865$	2.75604	0.0937083
$866$	49.5223	1.68284
$867$	−3.30867	−0.112368
$868$	−13.1076	−0.444900
$869$	49.1757	1.66817
$870$	−3.50043	−0.118676
$871$	−11.5578	−0.391621
$872$	−19.8570	−0.672442
$873$	12.4092	0.419989
$874$	13.8941	0.469975
$875$	−20.2996	−0.686250
$876$	−3.70722	−0.125255
$877$	16.2336	0.548169	0.274084	−	0.961706i	$-0.411625\pi$
$877$	16.2336	0.548169	0.274084	+	0.961706i	$0.411625\pi$
$878$	33.4399	1.12854
$879$	15.0560	0.507825
$880$	14.1620	0.477402
$881$	−57.3020	−1.93055	−0.965276	−	0.261231i	$-0.915872\pi$
$881$	−57.3020	−1.93055	−0.965276	+	0.261231i	$0.915872\pi$
$882$	−6.13747	−0.206659
$883$	−0.808660	−0.0272136	−0.0136068	−	0.999907i	$-0.504331\pi$
$883$	−0.808660	−0.0272136	−0.0136068	+	0.999907i	$0.504331\pi$
$884$	−1.64943	−0.0554764
$885$	−1.12941	−0.0379646
$886$	24.4432	0.821184
$887$	−1.67183	−0.0561345	−0.0280672	−	0.999606i	$-0.508935\pi$
$887$	−1.67183	−0.0561345	−0.0280672	+	0.999606i	$0.508935\pi$
$888$	−22.2744	−0.747479
$889$	−14.9358	−0.500931
$890$	12.3821	0.415050
$891$	−4.71212	−0.157862
$892$	−6.80337	−0.227794
$893$	0.364567	0.0121998
$894$	−7.19360	−0.240590
$895$	5.65250	0.188942
$896$	−44.8640	−1.49880
$897$	4.83349	0.161386
$898$	40.1672	1.34040
$899$	−31.0921	−1.03698
$900$	−2.04602	−0.0682006
$901$	−7.44835	−0.248141
$902$	28.5011	0.948983
$903$	−28.2672	−0.940673
$904$	17.0854	0.568251
$905$	1.44095	0.0478986
$906$	22.4639	0.746312
$907$	−37.4032	−1.24195	−0.620977	−	0.783829i	$-0.713264\pi$
$907$	−37.4032	−1.24195	−0.620977	+	0.783829i	$0.713264\pi$
$908$	11.8093	0.391906
$909$	5.20306	0.172574
$910$	3.31042	0.109739
$911$	−40.6084	−1.34541	−0.672707	−	0.739909i	$-0.734869\pi$
$911$	−40.6084	−1.34541	−0.672707	+	0.739909i	$0.734869\pi$
$912$	−8.62574	−0.285627
$913$	45.5880	1.50874
$914$	25.8374	0.854624
$915$	−9.12219	−0.301570
$916$	−1.52897	−0.0505188
$917$	19.7474	0.652117
$918$	−5.78670	−0.190989
$919$	15.4547	0.509802	0.254901	−	0.966967i	$-0.417957\pi$
$919$	15.4547	0.509802	0.254901	+	0.966967i	$0.417957\pi$
$920$	−7.52416	−0.248064
$921$	−22.8323	−0.752351
$922$	40.7239	1.34117
$923$	2.02977	0.0668108
$924$	−6.94270	−0.228398
$925$	42.0611	1.38296
$926$	−34.7378	−1.14156
$927$	1.00000	0.0328443
$928$	8.65974	0.284270
$929$	23.6164	0.774828	0.387414	−	0.921906i	$-0.373368\pi$
$929$	23.6164	0.774828	0.387414	+	0.921906i	$0.373368\pi$
$930$	8.91031	0.292181
$931$	7.21346	0.236411
$932$	−9.34525	−0.306114
$933$	23.1092	0.756562
$934$	−30.8507	−1.00947
$935$	−11.1664	−0.365181
$936$	−2.43065	−0.0794484
$937$	15.0805	0.492660	0.246330	−	0.969186i	$-0.420775\pi$
$937$	15.0805	0.492660	0.246330	+	0.969186i	$0.420775\pi$
$938$	−59.7425	−1.95066
$939$	21.0374	0.686529
$940$	0.0566242	0.00184688
$941$	18.0406	0.588107	0.294053	−	0.955789i	$-0.404996\pi$
$941$	18.0406	0.588107	0.294053	+	0.955789i	$0.404996\pi$
$942$	−35.5810	−1.15929
$943$	−18.6938	−0.608755
$944$	8.27580	0.269354
$945$	2.11678	0.0688587
$946$	−63.0241	−2.04909
$947$	19.9206	0.647332	0.323666	−	0.946171i	$-0.395085\pi$
$947$	19.9206	0.647332	0.323666	+	0.946171i	$0.395085\pi$
$948$	−4.65206	−0.151092
$949$	8.31643	0.269963
$950$	13.1937	0.428061
$951$	−10.9399	−0.354752
$952$	29.7267	0.963446
$953$	−24.9802	−0.809188	−0.404594	−	0.914496i	$-0.632587\pi$
$953$	−24.9802	−0.809188	−0.404594	+	0.914496i	$0.632587\pi$
$954$	3.14808	0.101923
$955$	−16.1372	−0.522188
$956$	8.35719	0.270291
$957$	−16.4686	−0.532353
$958$	4.06831	0.131441
$959$	60.2625	1.94598
$960$	3.52921	0.113905
$961$	48.1446	1.55305
$962$	−14.3315	−0.462065
$963$	−0.442250	−0.0142513
$964$	2.38507	0.0768179
$965$	14.0640	0.452735
$966$	24.9844	0.803860
$967$	−18.2220	−0.585979	−0.292989	−	0.956116i	$-0.594650\pi$
$967$	−18.2220	−0.585979	−0.292989	+	0.956116i	$0.594650\pi$
$968$	27.2332	0.875309
$969$	6.80118	0.218485
$970$	−12.4288	−0.399063
$971$	23.9290	0.767917	0.383959	−	0.923350i	$-0.374561\pi$
$971$	23.9290	0.767917	0.383959	+	0.923350i	$0.374561\pi$
$972$	0.445771	0.0142981
$973$	53.5747	1.71752
$974$	−24.2006	−0.775438
$975$	4.58984	0.146993
$976$	66.8435	2.13961
$977$	45.8746	1.46766	0.733830	−	0.679334i	$-0.237731\pi$
$977$	45.8746	1.46766	0.733830	+	0.679334i	$0.237731\pi$
$978$	14.5364	0.464822
$979$	58.2544	1.86182
$980$	1.12039	0.0357895
$981$	−8.16940	−0.260829
$982$	48.6411	1.55220
$983$	−5.79987	−0.184987	−0.0924935	−	0.995713i	$-0.529484\pi$
$983$	−5.79987	−0.184987	−0.0924935	+	0.995713i	$0.529484\pi$
$984$	9.40070	0.299683
$985$	14.2505	0.454059
$986$	−20.2241	−0.644068
$987$	0.655566	0.0208669
$988$	−0.819357	−0.0260672
$989$	41.3374	1.31445
$990$	4.71953	0.149997
$991$	19.2493	0.611476	0.305738	−	0.952116i	$-0.401097\pi$
$991$	19.2493	0.611476	0.305738	+	0.952116i	$0.401097\pi$
$992$	−22.0432	−0.699874
$993$	2.65805	0.0843506
$994$	10.4919	0.332784
$995$	−10.8339	−0.343458
$996$	−4.31267	−0.136652
$997$	44.4575	1.40798	0.703991	−	0.710209i	$-0.251399\pi$
$997$	44.4575	1.40798	0.703991	+	0.710209i	$0.251399\pi$
$998$	−3.90920	−0.123743
$999$	−9.16395	−0.289935

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.e.1.5	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.e.1.5	✓	16	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q-1.56390 q^{2} +1.00000 q^{3} +0.445771 q^{4} +0.640434 q^{5} -1.56390 q^{6} +3.30522 q^{7} +2.43065 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.56390 q^{2} +1.00000 q^{3} +0.445771 q^{4} +0.640434 q^{5} -1.56390 q^{6} +3.30522 q^{7} +2.43065 q^{8} +1.00000 q^{9} -1.00157 q^{10} -4.71212 q^{11} +0.445771 q^{12} -1.00000 q^{13} -5.16902 q^{14} +0.640434 q^{15} -4.69283 q^{16} +3.70018 q^{17} -1.56390 q^{18} +1.83807 q^{19} +0.285487 q^{20} +3.30522 q^{21} +7.36927 q^{22} -4.83349 q^{23} +2.43065 q^{24} -4.58984 q^{25} +1.56390 q^{26} +1.00000 q^{27} +1.47337 q^{28} +3.49494 q^{29} -1.00157 q^{30} -8.89632 q^{31} +2.47779 q^{32} -4.71212 q^{33} -5.78670 q^{34} +2.11678 q^{35} +0.445771 q^{36} -9.16395 q^{37} -2.87455 q^{38} -1.00000 q^{39} +1.55667 q^{40} +3.86756 q^{41} -5.16902 q^{42} -8.55229 q^{43} -2.10053 q^{44} +0.640434 q^{45} +7.55907 q^{46} +0.198343 q^{47} -4.69283 q^{48} +3.92448 q^{49} +7.17804 q^{50} +3.70018 q^{51} -0.445771 q^{52} -2.01297 q^{53} -1.56390 q^{54} -3.01780 q^{55} +8.03384 q^{56} +1.83807 q^{57} -5.46572 q^{58} -1.76350 q^{59} +0.285487 q^{60} -14.2438 q^{61} +13.9129 q^{62} +3.30522 q^{63} +5.51065 q^{64} -0.640434 q^{65} +7.36927 q^{66} +11.5578 q^{67} +1.64943 q^{68} -4.83349 q^{69} -3.31042 q^{70} -2.02977 q^{71} +2.43065 q^{72} -8.31643 q^{73} +14.3315 q^{74} -4.58984 q^{75} +0.819357 q^{76} -15.5746 q^{77} +1.56390 q^{78} -10.4360 q^{79} -3.00545 q^{80} +1.00000 q^{81} -6.04847 q^{82} -9.67462 q^{83} +1.47337 q^{84} +2.36972 q^{85} +13.3749 q^{86} +3.49494 q^{87} -11.4535 q^{88} -12.3627 q^{89} -1.00157 q^{90} -3.30522 q^{91} -2.15463 q^{92} -8.89632 q^{93} -0.310187 q^{94} +1.17716 q^{95} +2.47779 q^{96} +12.4092 q^{97} -6.13747 q^{98} -4.71212 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{3} + 10 q^{4} - 6 q^{5} - 13 q^{7} - 9 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q + 16 * q^3 + 10 * q^4 - 6 * q^5 - 13 * q^7 - 9 * q^8 + 16 * q^9	\( 16 q + 16 q^{3} + 10 q^{4} - 6 q^{5} - 13 q^{7} - 9 q^{8} + 16 q^{9} - 8 q^{10} - 5 q^{11} + 10 q^{12} - 16 q^{13} - 8 q^{14} - 6 q^{15} - 14 q^{16} - q^{17} + 6 q^{19} - 4 q^{20} - 13 q^{21} - 11 q^{22} - 21 q^{23} - 9 q^{24} - 10 q^{25} + 16 q^{27} - 10 q^{28} - 17 q^{29} - 8 q^{30} - 33 q^{31} - 18 q^{32} - 5 q^{33} - 5 q^{34} - 4 q^{35} + 10 q^{36} - 23 q^{37} - 28 q^{38} - 16 q^{39} - 12 q^{40} + 7 q^{41} - 8 q^{42} - 33 q^{43} + 11 q^{44} - 6 q^{45} - 15 q^{46} - 13 q^{47} - 14 q^{48} - 17 q^{49} + 35 q^{50} - q^{51} - 10 q^{52} - 20 q^{53} - 54 q^{55} + 12 q^{56} + 6 q^{57} - 33 q^{58} + 6 q^{59} - 4 q^{60} - 49 q^{61} - 13 q^{62} - 13 q^{63} - 35 q^{64} + 6 q^{65} - 11 q^{66} - 4 q^{67} - 14 q^{68} - 21 q^{69} - 33 q^{70} - 29 q^{71} - 9 q^{72} - 21 q^{73} + 22 q^{74} - 10 q^{75} + 10 q^{76} - 21 q^{77} - 70 q^{79} - 8 q^{80} + 16 q^{81} - 10 q^{82} + 5 q^{83} - 10 q^{84} + 14 q^{85} + 29 q^{86} - 17 q^{87} - 45 q^{88} - 8 q^{89} - 8 q^{90} + 13 q^{91} - 29 q^{92} - 33 q^{93} + 12 q^{94} - 45 q^{95} - 18 q^{96} - 30 q^{97} + 15 q^{98} - 5 q^{99}+O(q^{100}) \) 16 * q + 16 * q^3 + 10 * q^4 - 6 * q^5 - 13 * q^7 - 9 * q^8 + 16 * q^9 - 8 * q^10 - 5 * q^11 + 10 * q^12 - 16 * q^13 - 8 * q^14 - 6 * q^15 - 14 * q^16 - q^17 + 6 * q^19 - 4 * q^20 - 13 * q^21 - 11 * q^22 - 21 * q^23 - 9 * q^24 - 10 * q^25 + 16 * q^27 - 10 * q^28 - 17 * q^29 - 8 * q^30 - 33 * q^31 - 18 * q^32 - 5 * q^33 - 5 * q^34 - 4 * q^35 + 10 * q^36 - 23 * q^37 - 28 * q^38 - 16 * q^39 - 12 * q^40 + 7 * q^41 - 8 * q^42 - 33 * q^43 + 11 * q^44 - 6 * q^45 - 15 * q^46 - 13 * q^47 - 14 * q^48 - 17 * q^49 + 35 * q^50 - q^51 - 10 * q^52 - 20 * q^53 - 54 * q^55 + 12 * q^56 + 6 * q^57 - 33 * q^58 + 6 * q^59 - 4 * q^60 - 49 * q^61 - 13 * q^62 - 13 * q^63 - 35 * q^64 + 6 * q^65 - 11 * q^66 - 4 * q^67 - 14 * q^68 - 21 * q^69 - 33 * q^70 - 29 * q^71 - 9 * q^72 - 21 * q^73 + 22 * q^74 - 10 * q^75 + 10 * q^76 - 21 * q^77 - 70 * q^79 - 8 * q^80 + 16 * q^81 - 10 * q^82 + 5 * q^83 - 10 * q^84 + 14 * q^85 + 29 * q^86 - 17 * q^87 - 45 * q^88 - 8 * q^89 - 8 * q^90 + 13 * q^91 - 29 * q^92 - 33 * q^93 + 12 * q^94 - 45 * q^95 - 18 * q^96 - 30 * q^97 + 15 * q^98 - 5 * q^99

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