LMFDB - Embedded newform 6038.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6038,2,Mod(1,6038)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6038, 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("6038.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6038 = 2 \cdot 3019 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6038.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.2136727404$
Analytic rank:	$2$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	6038.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.61803 q^{3} +1.00000 q^{4} -1.38197 q^{5} -2.61803 q^{6} -3.00000 q^{7} +1.00000 q^{8} +3.85410 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.61803 q^{3} +1.00000 q^{4} -1.38197 q^{5} -2.61803 q^{6} -3.00000 q^{7} +1.00000 q^{8} +3.85410 q^{9} -1.38197 q^{10} -2.38197 q^{11} -2.61803 q^{12} -3.00000 q^{13} -3.00000 q^{14} +3.61803 q^{15} +1.00000 q^{16} -7.47214 q^{17} +3.85410 q^{18} -3.00000 q^{19} -1.38197 q^{20} +7.85410 q^{21} -2.38197 q^{22} +1.47214 q^{23} -2.61803 q^{24} -3.09017 q^{25} -3.00000 q^{26} -2.23607 q^{27} -3.00000 q^{28} -9.23607 q^{29} +3.61803 q^{30} -6.09017 q^{31} +1.00000 q^{32} +6.23607 q^{33} -7.47214 q^{34} +4.14590 q^{35} +3.85410 q^{36} -1.85410 q^{37} -3.00000 q^{38} +7.85410 q^{39} -1.38197 q^{40} +11.1803 q^{41} +7.85410 q^{42} -9.23607 q^{43} -2.38197 q^{44} -5.32624 q^{45} +1.47214 q^{46} +11.5623 q^{47} -2.61803 q^{48} +2.00000 q^{49} -3.09017 q^{50} +19.5623 q^{51} -3.00000 q^{52} -9.00000 q^{53} -2.23607 q^{54} +3.29180 q^{55} -3.00000 q^{56} +7.85410 q^{57} -9.23607 q^{58} -9.76393 q^{59} +3.61803 q^{60} -2.38197 q^{61} -6.09017 q^{62} -11.5623 q^{63} +1.00000 q^{64} +4.14590 q^{65} +6.23607 q^{66} +1.85410 q^{67} -7.47214 q^{68} -3.85410 q^{69} +4.14590 q^{70} -11.9443 q^{71} +3.85410 q^{72} +0.708204 q^{73} -1.85410 q^{74} +8.09017 q^{75} -3.00000 q^{76} +7.14590 q^{77} +7.85410 q^{78} -1.85410 q^{79} -1.38197 q^{80} -5.70820 q^{81} +11.1803 q^{82} -1.94427 q^{83} +7.85410 q^{84} +10.3262 q^{85} -9.23607 q^{86} +24.1803 q^{87} -2.38197 q^{88} -16.7984 q^{89} -5.32624 q^{90} +9.00000 q^{91} +1.47214 q^{92} +15.9443 q^{93} +11.5623 q^{94} +4.14590 q^{95} -2.61803 q^{96} +13.7639 q^{97} +2.00000 q^{98} -9.18034 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} - 5 q^{5} - 3 q^{6} - 6 q^{7} + 2 q^{8} + q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 3 * q^3 + 2 * q^4 - 5 * q^5 - 3 * q^6 - 6 * q^7 + 2 * q^8 + q^9	\( 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} - 5 q^{5} - 3 q^{6} - 6 q^{7} + 2 q^{8} + q^{9} - 5 q^{10} - 7 q^{11} - 3 q^{12} - 6 q^{13} - 6 q^{14} + 5 q^{15} + 2 q^{16} - 6 q^{17} + q^{18} - 6 q^{19} - 5 q^{20} + 9 q^{21} - 7 q^{22} - 6 q^{23} - 3 q^{24} + 5 q^{25} - 6 q^{26} - 6 q^{28} - 14 q^{29} + 5 q^{30} - q^{31} + 2 q^{32} + 8 q^{33} - 6 q^{34} + 15 q^{35} + q^{36} + 3 q^{37} - 6 q^{38} + 9 q^{39} - 5 q^{40} + 9 q^{42} - 14 q^{43} - 7 q^{44} + 5 q^{45} - 6 q^{46} + 3 q^{47} - 3 q^{48} + 4 q^{49} + 5 q^{50} + 19 q^{51} - 6 q^{52} - 18 q^{53} + 20 q^{55} - 6 q^{56} + 9 q^{57} - 14 q^{58} - 24 q^{59} + 5 q^{60} - 7 q^{61} - q^{62} - 3 q^{63} + 2 q^{64} + 15 q^{65} + 8 q^{66} - 3 q^{67} - 6 q^{68} - q^{69} + 15 q^{70} - 6 q^{71} + q^{72} - 12 q^{73} + 3 q^{74} + 5 q^{75} - 6 q^{76} + 21 q^{77} + 9 q^{78} + 3 q^{79} - 5 q^{80} + 2 q^{81} + 14 q^{83} + 9 q^{84} + 5 q^{85} - 14 q^{86} + 26 q^{87} - 7 q^{88} - 9 q^{89} + 5 q^{90} + 18 q^{91} - 6 q^{92} + 14 q^{93} + 3 q^{94} + 15 q^{95} - 3 q^{96} + 32 q^{97} + 4 q^{98} + 4 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 3 * q^3 + 2 * q^4 - 5 * q^5 - 3 * q^6 - 6 * q^7 + 2 * q^8 + q^9 - 5 * q^10 - 7 * q^11 - 3 * q^12 - 6 * q^13 - 6 * q^14 + 5 * q^15 + 2 * q^16 - 6 * q^17 + q^18 - 6 * q^19 - 5 * q^20 + 9 * q^21 - 7 * q^22 - 6 * q^23 - 3 * q^24 + 5 * q^25 - 6 * q^26 - 6 * q^28 - 14 * q^29 + 5 * q^30 - q^31 + 2 * q^32 + 8 * q^33 - 6 * q^34 + 15 * q^35 + q^36 + 3 * q^37 - 6 * q^38 + 9 * q^39 - 5 * q^40 + 9 * q^42 - 14 * q^43 - 7 * q^44 + 5 * q^45 - 6 * q^46 + 3 * q^47 - 3 * q^48 + 4 * q^49 + 5 * q^50 + 19 * q^51 - 6 * q^52 - 18 * q^53 + 20 * q^55 - 6 * q^56 + 9 * q^57 - 14 * q^58 - 24 * q^59 + 5 * q^60 - 7 * q^61 - q^62 - 3 * q^63 + 2 * q^64 + 15 * q^65 + 8 * q^66 - 3 * q^67 - 6 * q^68 - q^69 + 15 * q^70 - 6 * q^71 + q^72 - 12 * q^73 + 3 * q^74 + 5 * q^75 - 6 * q^76 + 21 * q^77 + 9 * q^78 + 3 * q^79 - 5 * q^80 + 2 * q^81 + 14 * q^83 + 9 * q^84 + 5 * q^85 - 14 * q^86 + 26 * q^87 - 7 * q^88 - 9 * q^89 + 5 * q^90 + 18 * q^91 - 6 * q^92 + 14 * q^93 + 3 * q^94 + 15 * q^95 - 3 * q^96 + 32 * q^97 + 4 * q^98 + 4 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.61803	−1.51152	−0.755761	−	0.654847i	$-0.772733\pi$
$3$	−2.61803	−1.51152	−0.755761	+	0.654847i	$0.772733\pi$
$4$	1.00000	0.500000
$5$	−1.38197	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$5$	−1.38197	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$6$	−2.61803	−1.06881
$7$	−3.00000	−1.13389	−0.566947	−	0.823754i	$-0.691875\pi$
$7$	−3.00000	−1.13389	−0.566947	+	0.823754i	$0.691875\pi$
$8$	1.00000	0.353553
$9$	3.85410	1.28470
$10$	−1.38197	−0.437016
$11$	−2.38197	−0.718190	−0.359095	−	0.933301i	$-0.616915\pi$
$11$	−2.38197	−0.718190	−0.359095	+	0.933301i	$0.616915\pi$
$12$	−2.61803	−0.755761
$13$	−3.00000	−0.832050	−0.416025	−	0.909353i	$-0.636577\pi$
$13$	−3.00000	−0.832050	−0.416025	+	0.909353i	$0.636577\pi$
$14$	−3.00000	−0.801784
$15$	3.61803	0.934172
$16$	1.00000	0.250000
$17$	−7.47214	−1.81226	−0.906130	−	0.423000i	$-0.860977\pi$
$17$	−7.47214	−1.81226	−0.906130	+	0.423000i	$0.860977\pi$
$18$	3.85410	0.908421
$19$	−3.00000	−0.688247	−0.344124	−	0.938924i	$-0.611824\pi$
$19$	−3.00000	−0.688247	−0.344124	+	0.938924i	$0.611824\pi$
$20$	−1.38197	−0.309017
$21$	7.85410	1.71391
$22$	−2.38197	−0.507837
$23$	1.47214	0.306962	0.153481	−	0.988152i	$-0.450952\pi$
$23$	1.47214	0.306962	0.153481	+	0.988152i	$0.450952\pi$
$24$	−2.61803	−0.534404
$25$	−3.09017	−0.618034
$26$	−3.00000	−0.588348
$27$	−2.23607	−0.430331
$28$	−3.00000	−0.566947
$29$	−9.23607	−1.71509	−0.857547	−	0.514405i	$-0.828013\pi$
$29$	−9.23607	−1.71509	−0.857547	+	0.514405i	$0.828013\pi$
$30$	3.61803	0.660560
$31$	−6.09017	−1.09383	−0.546913	−	0.837189i	$-0.684197\pi$
$31$	−6.09017	−1.09383	−0.546913	+	0.837189i	$0.684197\pi$
$32$	1.00000	0.176777
$33$	6.23607	1.08556
$34$	−7.47214	−1.28146
$35$	4.14590	0.700785
$36$	3.85410	0.642350
$37$	−1.85410	−0.304812	−0.152406	−	0.988318i	$-0.548702\pi$
$37$	−1.85410	−0.304812	−0.152406	+	0.988318i	$0.548702\pi$
$38$	−3.00000	−0.486664
$39$	7.85410	1.25766
$40$	−1.38197	−0.218508
$41$	11.1803	1.74608	0.873038	−	0.487652i	$-0.162147\pi$
$41$	11.1803	1.74608	0.873038	+	0.487652i	$0.162147\pi$
$42$	7.85410	1.21191
$43$	−9.23607	−1.40849	−0.704244	−	0.709958i	$-0.748714\pi$
$43$	−9.23607	−1.40849	−0.704244	+	0.709958i	$0.748714\pi$
$44$	−2.38197	−0.359095
$45$	−5.32624	−0.793989
$46$	1.47214	0.217055
$47$	11.5623	1.68654	0.843268	−	0.537494i	$-0.180629\pi$
$47$	11.5623	1.68654	0.843268	+	0.537494i	$0.180629\pi$
$48$	−2.61803	−0.377881
$49$	2.00000	0.285714
$50$	−3.09017	−0.437016
$51$	19.5623	2.73927
$52$	−3.00000	−0.416025
$53$	−9.00000	−1.23625	−0.618123	−	0.786082i	$-0.712106\pi$
$53$	−9.00000	−1.23625	−0.618123	+	0.786082i	$0.712106\pi$
$54$	−2.23607	−0.304290
$55$	3.29180	0.443866
$56$	−3.00000	−0.400892
$57$	7.85410	1.04030
$58$	−9.23607	−1.21276
$59$	−9.76393	−1.27116	−0.635578	−	0.772037i	$-0.719238\pi$
$59$	−9.76393	−1.27116	−0.635578	+	0.772037i	$0.719238\pi$
$60$	3.61803	0.467086
$61$	−2.38197	−0.304979	−0.152490	−	0.988305i	$-0.548729\pi$
$61$	−2.38197	−0.304979	−0.152490	+	0.988305i	$0.548729\pi$
$62$	−6.09017	−0.773452
$63$	−11.5623	−1.45671
$64$	1.00000	0.125000
$65$	4.14590	0.514235
$66$	6.23607	0.767607
$67$	1.85410	0.226515	0.113257	−	0.993566i	$-0.463872\pi$
$67$	1.85410	0.226515	0.113257	+	0.993566i	$0.463872\pi$
$68$	−7.47214	−0.906130
$69$	−3.85410	−0.463979
$70$	4.14590	0.495530
$71$	−11.9443	−1.41752	−0.708762	−	0.705448i	$-0.750746\pi$
$71$	−11.9443	−1.41752	−0.708762	+	0.705448i	$0.750746\pi$
$72$	3.85410	0.454210
$73$	0.708204	0.0828890	0.0414445	−	0.999141i	$-0.486804\pi$
$73$	0.708204	0.0828890	0.0414445	+	0.999141i	$0.486804\pi$
$74$	−1.85410	−0.215535
$75$	8.09017	0.934172
$76$	−3.00000	−0.344124
$77$	7.14590	0.814351
$78$	7.85410	0.889302
$79$	−1.85410	−0.208603	−0.104301	−	0.994546i	$-0.533261\pi$
$79$	−1.85410	−0.208603	−0.104301	+	0.994546i	$0.533261\pi$
$80$	−1.38197	−0.154508
$81$	−5.70820	−0.634245
$82$	11.1803	1.23466
$83$	−1.94427	−0.213412	−0.106706	−	0.994291i	$-0.534030\pi$
$83$	−1.94427	−0.213412	−0.106706	+	0.994291i	$0.534030\pi$
$84$	7.85410	0.856953
$85$	10.3262	1.12004
$86$	−9.23607	−0.995951
$87$	24.1803	2.59240
$88$	−2.38197	−0.253918
$89$	−16.7984	−1.78062	−0.890312	−	0.455351i	$-0.849514\pi$
$89$	−16.7984	−1.78062	−0.890312	+	0.455351i	$0.849514\pi$
$90$	−5.32624	−0.561435
$91$	9.00000	0.943456
$92$	1.47214	0.153481
$93$	15.9443	1.65334
$94$	11.5623	1.19256
$95$	4.14590	0.425360
$96$	−2.61803	−0.267202
$97$	13.7639	1.39752	0.698758	−	0.715358i	$-0.253737\pi$
$97$	13.7639	1.39752	0.698758	+	0.715358i	$0.253737\pi$
$98$	2.00000	0.202031
$99$	−9.18034	−0.922659
$100$	−3.09017	−0.309017
$101$	5.23607	0.521008	0.260504	−	0.965473i	$-0.416111\pi$
$101$	5.23607	0.521008	0.260504	+	0.965473i	$0.416111\pi$
$102$	19.5623	1.93696
$103$	5.14590	0.507040	0.253520	−	0.967330i	$-0.418412\pi$
$103$	5.14590	0.507040	0.253520	+	0.967330i	$0.418412\pi$
$104$	−3.00000	−0.294174
$105$	−10.8541	−1.05925
$106$	−9.00000	−0.874157
$107$	−3.76393	−0.363873	−0.181937	−	0.983310i	$-0.558237\pi$
$107$	−3.76393	−0.363873	−0.181937	+	0.983310i	$0.558237\pi$
$108$	−2.23607	−0.215166
$109$	−9.47214	−0.907266	−0.453633	−	0.891189i	$-0.649872\pi$
$109$	−9.47214	−0.907266	−0.453633	+	0.891189i	$0.649872\pi$
$110$	3.29180	0.313860
$111$	4.85410	0.460731
$112$	−3.00000	−0.283473
$113$	−4.38197	−0.412221	−0.206110	−	0.978529i	$-0.566081\pi$
$113$	−4.38197	−0.412221	−0.206110	+	0.978529i	$0.566081\pi$
$114$	7.85410	0.735604
$115$	−2.03444	−0.189713
$116$	−9.23607	−0.857547
$117$	−11.5623	−1.06894
$118$	−9.76393	−0.898843
$119$	22.4164	2.05491
$120$	3.61803	0.330280
$121$	−5.32624	−0.484203
$122$	−2.38197	−0.215653
$123$	−29.2705	−2.63923
$124$	−6.09017	−0.546913
$125$	11.1803	1.00000
$126$	−11.5623	−1.03005
$127$	−12.4164	−1.10178	−0.550889	−	0.834579i	$-0.685711\pi$
$127$	−12.4164	−1.10178	−0.550889	+	0.834579i	$0.685711\pi$
$128$	1.00000	0.0883883
$129$	24.1803	2.12896
$130$	4.14590	0.363619
$131$	21.6180	1.88878	0.944388	−	0.328833i	$-0.106655\pi$
$131$	21.6180	1.88878	0.944388	+	0.328833i	$0.106655\pi$
$132$	6.23607	0.542780
$133$	9.00000	0.780399
$134$	1.85410	0.160170
$135$	3.09017	0.265959
$136$	−7.47214	−0.640730
$137$	8.56231	0.731527	0.365764	−	0.930708i	$-0.380808\pi$
$137$	8.56231	0.731527	0.365764	+	0.930708i	$0.380808\pi$
$138$	−3.85410	−0.328083
$139$	−15.4721	−1.31233	−0.656165	−	0.754618i	$-0.727822\pi$
$139$	−15.4721	−1.31233	−0.656165	+	0.754618i	$0.727822\pi$
$140$	4.14590	0.350392
$141$	−30.2705	−2.54924
$142$	−11.9443	−1.00234
$143$	7.14590	0.597570
$144$	3.85410	0.321175
$145$	12.7639	1.05999
$146$	0.708204	0.0586114
$147$	−5.23607	−0.431864
$148$	−1.85410	−0.152406
$149$	−2.23607	−0.183186	−0.0915929	−	0.995797i	$-0.529196\pi$
$149$	−2.23607	−0.183186	−0.0915929	+	0.995797i	$0.529196\pi$
$150$	8.09017	0.660560
$151$	−9.79837	−0.797380	−0.398690	−	0.917086i	$-0.630535\pi$
$151$	−9.79837	−0.797380	−0.398690	+	0.917086i	$0.630535\pi$
$152$	−3.00000	−0.243332
$153$	−28.7984	−2.32821
$154$	7.14590	0.575833
$155$	8.41641	0.676022
$156$	7.85410	0.628831
$157$	8.09017	0.645666	0.322833	−	0.946456i	$-0.395365\pi$
$157$	8.09017	0.645666	0.322833	+	0.946456i	$0.395365\pi$
$158$	−1.85410	−0.147504
$159$	23.5623	1.86861
$160$	−1.38197	−0.109254
$161$	−4.41641	−0.348062
$162$	−5.70820	−0.448479
$163$	0.854102	0.0668984	0.0334492	−	0.999440i	$-0.489351\pi$
$163$	0.854102	0.0668984	0.0334492	+	0.999440i	$0.489351\pi$
$164$	11.1803	0.873038
$165$	−8.61803	−0.670913
$166$	−1.94427	−0.150905
$167$	−5.23607	−0.405179	−0.202590	−	0.979264i	$-0.564936\pi$
$167$	−5.23607	−0.405179	−0.202590	+	0.979264i	$0.564936\pi$
$168$	7.85410	0.605957
$169$	−4.00000	−0.307692
$170$	10.3262	0.791986
$171$	−11.5623	−0.884192
$172$	−9.23607	−0.704244
$173$	−7.67376	−0.583425	−0.291713	−	0.956506i	$-0.594225\pi$
$173$	−7.67376	−0.583425	−0.291713	+	0.956506i	$0.594225\pi$
$174$	24.1803	1.83311
$175$	9.27051	0.700785
$176$	−2.38197	−0.179547
$177$	25.5623	1.92138
$178$	−16.7984	−1.25909
$179$	−9.00000	−0.672692	−0.336346	−	0.941739i	$-0.609191\pi$
$179$	−9.00000	−0.672692	−0.336346	+	0.941739i	$0.609191\pi$
$180$	−5.32624	−0.396994
$181$	−18.0000	−1.33793	−0.668965	−	0.743294i	$-0.733262\pi$
$181$	−18.0000	−1.33793	−0.668965	+	0.743294i	$0.733262\pi$
$182$	9.00000	0.667124
$183$	6.23607	0.460983
$184$	1.47214	0.108527
$185$	2.56231	0.188384
$186$	15.9443	1.16909
$187$	17.7984	1.30155
$188$	11.5623	0.843268
$189$	6.70820	0.487950
$190$	4.14590	0.300775
$191$	22.3607	1.61796	0.808981	−	0.587835i	$-0.200019\pi$
$191$	22.3607	1.61796	0.808981	+	0.587835i	$0.200019\pi$
$192$	−2.61803	−0.188940
$193$	3.14590	0.226447	0.113223	−	0.993570i	$-0.463882\pi$
$193$	3.14590	0.226447	0.113223	+	0.993570i	$0.463882\pi$
$194$	13.7639	0.988193
$195$	−10.8541	−0.777278
$196$	2.00000	0.142857
$197$	−2.79837	−0.199376	−0.0996879	−	0.995019i	$-0.531784\pi$
$197$	−2.79837	−0.199376	−0.0996879	+	0.995019i	$0.531784\pi$
$198$	−9.18034	−0.652418
$199$	21.2705	1.50783	0.753913	−	0.656974i	$-0.228164\pi$
$199$	21.2705	1.50783	0.753913	+	0.656974i	$0.228164\pi$
$200$	−3.09017	−0.218508
$201$	−4.85410	−0.342382
$202$	5.23607	0.368408
$203$	27.7082	1.94473
$204$	19.5623	1.36964
$205$	−15.4508	−1.07913
$206$	5.14590	0.358532
$207$	5.67376	0.394354
$208$	−3.00000	−0.208013
$209$	7.14590	0.494292
$210$	−10.8541	−0.749004
$211$	17.8541	1.22913	0.614564	−	0.788867i	$-0.289332\pi$
$211$	17.8541	1.22913	0.614564	+	0.788867i	$0.289332\pi$
$212$	−9.00000	−0.618123
$213$	31.2705	2.14262
$214$	−3.76393	−0.257297
$215$	12.7639	0.870493
$216$	−2.23607	−0.152145
$217$	18.2705	1.24028
$218$	−9.47214	−0.641534
$219$	−1.85410	−0.125289
$220$	3.29180	0.221933
$221$	22.4164	1.50789
$222$	4.85410	0.325786
$223$	−1.58359	−0.106045	−0.0530226	−	0.998593i	$-0.516886\pi$
$223$	−1.58359	−0.106045	−0.0530226	+	0.998593i	$0.516886\pi$
$224$	−3.00000	−0.200446
$225$	−11.9098	−0.793989
$226$	−4.38197	−0.291484
$227$	13.8541	0.919529	0.459765	−	0.888041i	$-0.347934\pi$
$227$	13.8541	0.919529	0.459765	+	0.888041i	$0.347934\pi$
$228$	7.85410	0.520151
$229$	26.5967	1.75756	0.878781	−	0.477225i	$-0.158357\pi$
$229$	26.5967	1.75756	0.878781	+	0.477225i	$0.158357\pi$
$230$	−2.03444	−0.134147
$231$	−18.7082	−1.23091
$232$	−9.23607	−0.606378
$233$	4.14590	0.271607	0.135803	−	0.990736i	$-0.456638\pi$
$233$	4.14590	0.271607	0.135803	+	0.990736i	$0.456638\pi$
$234$	−11.5623	−0.755852
$235$	−15.9787	−1.04234
$236$	−9.76393	−0.635578
$237$	4.85410	0.315308
$238$	22.4164	1.45304
$239$	3.70820	0.239864	0.119932	−	0.992782i	$-0.461732\pi$
$239$	3.70820	0.239864	0.119932	+	0.992782i	$0.461732\pi$
$240$	3.61803	0.233543
$241$	−10.4164	−0.670980	−0.335490	−	0.942044i	$-0.608902\pi$
$241$	−10.4164	−0.670980	−0.335490	+	0.942044i	$0.608902\pi$
$242$	−5.32624	−0.342384
$243$	21.6525	1.38901
$244$	−2.38197	−0.152490
$245$	−2.76393	−0.176581
$246$	−29.2705	−1.86622
$247$	9.00000	0.572656
$248$	−6.09017	−0.386726
$249$	5.09017	0.322576
$250$	11.1803	0.707107
$251$	0.944272	0.0596019	0.0298010	−	0.999556i	$-0.490513\pi$
$251$	0.944272	0.0596019	0.0298010	+	0.999556i	$0.490513\pi$
$252$	−11.5623	−0.728357
$253$	−3.50658	−0.220457
$254$	−12.4164	−0.779075
$255$	−27.0344	−1.69296
$256$	1.00000	0.0625000
$257$	−1.58359	−0.0987818	−0.0493909	−	0.998780i	$-0.515728\pi$
$257$	−1.58359	−0.0987818	−0.0493909	+	0.998780i	$0.515728\pi$
$258$	24.1803	1.50540
$259$	5.56231	0.345625
$260$	4.14590	0.257118
$261$	−35.5967	−2.20338
$262$	21.6180	1.33557
$263$	18.3607	1.13217	0.566084	−	0.824348i	$-0.308458\pi$
$263$	18.3607	1.13217	0.566084	+	0.824348i	$0.308458\pi$
$264$	6.23607	0.383803
$265$	12.4377	0.764041
$266$	9.00000	0.551825
$267$	43.9787	2.69145
$268$	1.85410	0.113257
$269$	−5.56231	−0.339140	−0.169570	−	0.985518i	$-0.554238\pi$
$269$	−5.56231	−0.339140	−0.169570	+	0.985518i	$0.554238\pi$
$270$	3.09017	0.188062
$271$	−6.61803	−0.402017	−0.201008	−	0.979590i	$-0.564422\pi$
$271$	−6.61803	−0.402017	−0.201008	+	0.979590i	$0.564422\pi$
$272$	−7.47214	−0.453065
$273$	−23.5623	−1.42606
$274$	8.56231	0.517268
$275$	7.36068	0.443866
$276$	−3.85410	−0.231990
$277$	−20.5623	−1.23547	−0.617735	−	0.786387i	$-0.711949\pi$
$277$	−20.5623	−1.23547	−0.617735	+	0.786387i	$0.711949\pi$
$278$	−15.4721	−0.927957
$279$	−23.4721	−1.40524
$280$	4.14590	0.247765
$281$	−25.3607	−1.51289	−0.756446	−	0.654057i	$-0.773066\pi$
$281$	−25.3607	−1.51289	−0.756446	+	0.654057i	$0.773066\pi$
$282$	−30.2705	−1.80258
$283$	10.7082	0.636537	0.318268	−	0.948001i	$-0.396899\pi$
$283$	10.7082	0.636537	0.318268	+	0.948001i	$0.396899\pi$
$284$	−11.9443	−0.708762
$285$	−10.8541	−0.642942
$286$	7.14590	0.422546
$287$	−33.5410	−1.97986
$288$	3.85410	0.227105
$289$	38.8328	2.28428
$290$	12.7639	0.749524
$291$	−36.0344	−2.11238
$292$	0.708204	0.0414445
$293$	−32.0902	−1.87473	−0.937364	−	0.348352i	$-0.886741\pi$
$293$	−32.0902	−1.87473	−0.937364	+	0.348352i	$0.886741\pi$
$294$	−5.23607	−0.305374
$295$	13.4934	0.785617
$296$	−1.85410	−0.107767
$297$	5.32624	0.309060
$298$	−2.23607	−0.129532
$299$	−4.41641	−0.255407
$300$	8.09017	0.467086
$301$	27.7082	1.59707
$302$	−9.79837	−0.563833
$303$	−13.7082	−0.787516
$304$	−3.00000	−0.172062
$305$	3.29180	0.188488
$306$	−28.7984	−1.64629
$307$	3.90983	0.223146	0.111573	−	0.993756i	$-0.464411\pi$
$307$	3.90983	0.223146	0.111573	+	0.993756i	$0.464411\pi$
$308$	7.14590	0.407175
$309$	−13.4721	−0.766403
$310$	8.41641	0.478020
$311$	24.7639	1.40423	0.702117	−	0.712062i	$-0.252238\pi$
$311$	24.7639	1.40423	0.702117	+	0.712062i	$0.252238\pi$
$312$	7.85410	0.444651
$313$	32.7426	1.85072	0.925362	−	0.379085i	$-0.123761\pi$
$313$	32.7426	1.85072	0.925362	+	0.379085i	$0.123761\pi$
$314$	8.09017	0.456555
$315$	15.9787	0.900299
$316$	−1.85410	−0.104301
$317$	−10.6180	−0.596368	−0.298184	−	0.954508i	$-0.596381\pi$
$317$	−10.6180	−0.596368	−0.298184	+	0.954508i	$0.596381\pi$
$318$	23.5623	1.32131
$319$	22.0000	1.23176
$320$	−1.38197	−0.0772542
$321$	9.85410	0.550002
$322$	−4.41641	−0.246117
$323$	22.4164	1.24728
$324$	−5.70820	−0.317122
$325$	9.27051	0.514235
$326$	0.854102	0.0473043
$327$	24.7984	1.37135
$328$	11.1803	0.617331
$329$	−34.6869	−1.91235
$330$	−8.61803	−0.474407
$331$	−5.43769	−0.298883	−0.149441	−	0.988771i	$-0.547748\pi$
$331$	−5.43769	−0.298883	−0.149441	+	0.988771i	$0.547748\pi$
$332$	−1.94427	−0.106706
$333$	−7.14590	−0.391593
$334$	−5.23607	−0.286505
$335$	−2.56231	−0.139994
$336$	7.85410	0.428476
$337$	4.61803	0.251560	0.125780	−	0.992058i	$-0.459857\pi$
$337$	4.61803	0.251560	0.125780	+	0.992058i	$0.459857\pi$
$338$	−4.00000	−0.217571
$339$	11.4721	0.623081
$340$	10.3262	0.560019
$341$	14.5066	0.785575
$342$	−11.5623	−0.625218
$343$	15.0000	0.809924
$344$	−9.23607	−0.497975
$345$	5.32624	0.286755
$346$	−7.67376	−0.412544
$347$	−8.67376	−0.465632	−0.232816	−	0.972521i	$-0.574794\pi$
$347$	−8.67376	−0.465632	−0.232816	+	0.972521i	$0.574794\pi$
$348$	24.1803	1.29620
$349$	−22.7082	−1.21554	−0.607771	−	0.794112i	$-0.707936\pi$
$349$	−22.7082	−1.21554	−0.607771	+	0.794112i	$0.707936\pi$
$350$	9.27051	0.495530
$351$	6.70820	0.358057
$352$	−2.38197	−0.126959
$353$	−6.81966	−0.362974	−0.181487	−	0.983393i	$-0.558091\pi$
$353$	−6.81966	−0.362974	−0.181487	+	0.983393i	$0.558091\pi$
$354$	25.5623	1.35862
$355$	16.5066	0.876078
$356$	−16.7984	−0.890312
$357$	−58.6869	−3.10604
$358$	−9.00000	−0.475665
$359$	−14.5967	−0.770387	−0.385193	−	0.922836i	$-0.625865\pi$
$359$	−14.5967	−0.770387	−0.385193	+	0.922836i	$0.625865\pi$
$360$	−5.32624	−0.280717
$361$	−10.0000	−0.526316
$362$	−18.0000	−0.946059
$363$	13.9443	0.731884
$364$	9.00000	0.471728
$365$	−0.978714	−0.0512282
$366$	6.23607	0.325964
$367$	4.88854	0.255180	0.127590	−	0.991827i	$-0.459276\pi$
$367$	4.88854	0.255180	0.127590	+	0.991827i	$0.459276\pi$
$368$	1.47214	0.0767404
$369$	43.0902	2.24318
$370$	2.56231	0.133208
$371$	27.0000	1.40177
$372$	15.9443	0.826672
$373$	−12.0000	−0.621336	−0.310668	−	0.950518i	$-0.600553\pi$
$373$	−12.0000	−0.621336	−0.310668	+	0.950518i	$0.600553\pi$
$374$	17.7984	0.920332
$375$	−29.2705	−1.51152
$376$	11.5623	0.596280
$377$	27.7082	1.42705
$378$	6.70820	0.345033
$379$	22.8328	1.17284	0.586421	−	0.810006i	$-0.300536\pi$
$379$	22.8328	1.17284	0.586421	+	0.810006i	$0.300536\pi$
$380$	4.14590	0.212680
$381$	32.5066	1.66536
$382$	22.3607	1.14407
$383$	−2.29180	−0.117105	−0.0585527	−	0.998284i	$-0.518649\pi$
$383$	−2.29180	−0.117105	−0.0585527	+	0.998284i	$0.518649\pi$
$384$	−2.61803	−0.133601
$385$	−9.87539	−0.503296
$386$	3.14590	0.160122
$387$	−35.5967	−1.80948
$388$	13.7639	0.698758
$389$	−27.2361	−1.38092	−0.690462	−	0.723369i	$-0.742593\pi$
$389$	−27.2361	−1.38092	−0.690462	+	0.723369i	$0.742593\pi$
$390$	−10.8541	−0.549619
$391$	−11.0000	−0.556294
$392$	2.00000	0.101015
$393$	−56.5967	−2.85493
$394$	−2.79837	−0.140980
$395$	2.56231	0.128924
$396$	−9.18034	−0.461329
$397$	−8.56231	−0.429730	−0.214865	−	0.976644i	$-0.568931\pi$
$397$	−8.56231	−0.429730	−0.214865	+	0.976644i	$0.568931\pi$
$398$	21.2705	1.06619
$399$	−23.5623	−1.17959
$400$	−3.09017	−0.154508
$401$	−14.0557	−0.701910	−0.350955	−	0.936392i	$-0.614143\pi$
$401$	−14.0557	−0.701910	−0.350955	+	0.936392i	$0.614143\pi$
$402$	−4.85410	−0.242101
$403$	18.2705	0.910119
$404$	5.23607	0.260504
$405$	7.88854	0.391985
$406$	27.7082	1.37514
$407$	4.41641	0.218913
$408$	19.5623	0.968478
$409$	−33.4164	−1.65234	−0.826168	−	0.563425i	$-0.809484\pi$
$409$	−33.4164	−1.65234	−0.826168	+	0.563425i	$0.809484\pi$
$410$	−15.4508	−0.763063
$411$	−22.4164	−1.10572
$412$	5.14590	0.253520
$413$	29.2918	1.44136
$414$	5.67376	0.278850
$415$	2.68692	0.131896
$416$	−3.00000	−0.147087
$417$	40.5066	1.98362
$418$	7.14590	0.349517
$419$	0.673762	0.0329154	0.0164577	−	0.999865i	$-0.494761\pi$
$419$	0.673762	0.0329154	0.0164577	+	0.999865i	$0.494761\pi$
$420$	−10.8541	−0.529626
$421$	33.3951	1.62758	0.813789	−	0.581160i	$-0.197401\pi$
$421$	33.3951	1.62758	0.813789	+	0.581160i	$0.197401\pi$
$422$	17.8541	0.869124
$423$	44.5623	2.16669
$424$	−9.00000	−0.437079
$425$	23.0902	1.12004
$426$	31.2705	1.51506
$427$	7.14590	0.345814
$428$	−3.76393	−0.181937
$429$	−18.7082	−0.903241
$430$	12.7639	0.615531
$431$	−24.7639	−1.19284	−0.596418	−	0.802674i	$-0.703410\pi$
$431$	−24.7639	−1.19284	−0.596418	+	0.802674i	$0.703410\pi$
$432$	−2.23607	−0.107583
$433$	5.58359	0.268330	0.134165	−	0.990959i	$-0.457165\pi$
$433$	5.58359	0.268330	0.134165	+	0.990959i	$0.457165\pi$
$434$	18.2705	0.877013
$435$	−33.4164	−1.60219
$436$	−9.47214	−0.453633
$437$	−4.41641	−0.211265
$438$	−1.85410	−0.0885924
$439$	−13.0000	−0.620456	−0.310228	−	0.950662i	$-0.600405\pi$
$439$	−13.0000	−0.620456	−0.310228	+	0.950662i	$0.600405\pi$
$440$	3.29180	0.156930
$441$	7.70820	0.367057
$442$	22.4164	1.06624
$443$	4.52786	0.215125	0.107563	−	0.994198i	$-0.465695\pi$
$443$	4.52786	0.215125	0.107563	+	0.994198i	$0.465695\pi$
$444$	4.85410	0.230365
$445$	23.2148	1.10049
$446$	−1.58359	−0.0749853
$447$	5.85410	0.276890
$448$	−3.00000	−0.141737
$449$	−17.3607	−0.819301	−0.409651	−	0.912243i	$-0.634349\pi$
$449$	−17.3607	−0.819301	−0.409651	+	0.912243i	$0.634349\pi$
$450$	−11.9098	−0.561435
$451$	−26.6312	−1.25401
$452$	−4.38197	−0.206110
$453$	25.6525	1.20526
$454$	13.8541	0.650205
$455$	−12.4377	−0.583088
$456$	7.85410	0.367802
$457$	−41.0344	−1.91951	−0.959755	−	0.280838i	$-0.909388\pi$
$457$	−41.0344	−1.91951	−0.959755	+	0.280838i	$0.909388\pi$
$458$	26.5967	1.24278
$459$	16.7082	0.779872
$460$	−2.03444	−0.0948563
$461$	−2.38197	−0.110939	−0.0554696	−	0.998460i	$-0.517666\pi$
$461$	−2.38197	−0.110939	−0.0554696	+	0.998460i	$0.517666\pi$
$462$	−18.7082	−0.870384
$463$	26.3607	1.22508	0.612542	−	0.790438i	$-0.290147\pi$
$463$	26.3607	1.22508	0.612542	+	0.790438i	$0.290147\pi$
$464$	−9.23607	−0.428774
$465$	−22.0344	−1.02182
$466$	4.14590	0.192055
$467$	31.7984	1.47145	0.735727	−	0.677279i	$-0.236841\pi$
$467$	31.7984	1.47145	0.735727	+	0.677279i	$0.236841\pi$
$468$	−11.5623	−0.534468
$469$	−5.56231	−0.256843
$470$	−15.9787	−0.737043
$471$	−21.1803	−0.975939
$472$	−9.76393	−0.449421
$473$	22.0000	1.01156
$474$	4.85410	0.222956
$475$	9.27051	0.425360
$476$	22.4164	1.02745
$477$	−34.6869	−1.58820
$478$	3.70820	0.169609
$479$	−13.8541	−0.633010	−0.316505	−	0.948591i	$-0.602509\pi$
$479$	−13.8541	−0.633010	−0.316505	+	0.948591i	$0.602509\pi$
$480$	3.61803	0.165140
$481$	5.56231	0.253619
$482$	−10.4164	−0.474454
$483$	11.5623	0.526103
$484$	−5.32624	−0.242102
$485$	−19.0213	−0.863712
$486$	21.6525	0.982176
$487$	15.8885	0.719979	0.359989	−	0.932956i	$-0.382780\pi$
$487$	15.8885	0.719979	0.359989	+	0.932956i	$0.382780\pi$
$488$	−2.38197	−0.107827
$489$	−2.23607	−0.101118
$490$	−2.76393	−0.124862
$491$	−6.27051	−0.282984	−0.141492	−	0.989939i	$-0.545190\pi$
$491$	−6.27051	−0.282984	−0.141492	+	0.989939i	$0.545190\pi$
$492$	−29.2705	−1.31962
$493$	69.0132	3.10820
$494$	9.00000	0.404929
$495$	12.6869	0.570235
$496$	−6.09017	−0.273457
$497$	35.8328	1.60732
$498$	5.09017	0.228096
$499$	−5.65248	−0.253040	−0.126520	−	0.991964i	$-0.540381\pi$
$499$	−5.65248	−0.253040	−0.126520	+	0.991964i	$0.540381\pi$
$500$	11.1803	0.500000
$501$	13.7082	0.612437
$502$	0.944272	0.0421449
$503$	5.29180	0.235950	0.117975	−	0.993017i	$-0.462360\pi$
$503$	5.29180	0.235950	0.117975	+	0.993017i	$0.462360\pi$
$504$	−11.5623	−0.515026
$505$	−7.23607	−0.322001
$506$	−3.50658	−0.155886
$507$	10.4721	0.465084
$508$	−12.4164	−0.550889
$509$	−28.4164	−1.25954	−0.629768	−	0.776784i	$-0.716850\pi$
$509$	−28.4164	−1.25954	−0.629768	+	0.776784i	$0.716850\pi$
$510$	−27.0344	−1.19711
$511$	−2.12461	−0.0939873
$512$	1.00000	0.0441942
$513$	6.70820	0.296174
$514$	−1.58359	−0.0698493
$515$	−7.11146	−0.313368
$516$	24.1803	1.06448
$517$	−27.5410	−1.21125
$518$	5.56231	0.244394
$519$	20.0902	0.881861
$520$	4.14590	0.181810
$521$	−12.6525	−0.554315	−0.277158	−	0.960824i	$-0.589392\pi$
$521$	−12.6525	−0.554315	−0.277158	+	0.960824i	$0.589392\pi$
$522$	−35.5967	−1.55803
$523$	−6.03444	−0.263868	−0.131934	−	0.991259i	$-0.542119\pi$
$523$	−6.03444	−0.263868	−0.131934	+	0.991259i	$0.542119\pi$
$524$	21.6180	0.944388
$525$	−24.2705	−1.05925
$526$	18.3607	0.800564
$527$	45.5066	1.98230
$528$	6.23607	0.271390
$529$	−20.8328	−0.905775
$530$	12.4377	0.540259
$531$	−37.6312	−1.63305
$532$	9.00000	0.390199
$533$	−33.5410	−1.45282
$534$	43.9787	1.90315
$535$	5.20163	0.224886
$536$	1.85410	0.0800850
$537$	23.5623	1.01679
$538$	−5.56231	−0.239808
$539$	−4.76393	−0.205197
$540$	3.09017	0.132980
$541$	−31.7082	−1.36324	−0.681621	−	0.731705i	$-0.738725\pi$
$541$	−31.7082	−1.36324	−0.681621	+	0.731705i	$0.738725\pi$
$542$	−6.61803	−0.284269
$543$	47.1246	2.02231
$544$	−7.47214	−0.320365
$545$	13.0902	0.560721
$546$	−23.5623	−1.00837
$547$	9.94427	0.425186	0.212593	−	0.977141i	$-0.431809\pi$
$547$	9.94427	0.425186	0.212593	+	0.977141i	$0.431809\pi$
$548$	8.56231	0.365764
$549$	−9.18034	−0.391807
$550$	7.36068	0.313860
$551$	27.7082	1.18041
$552$	−3.85410	−0.164041
$553$	5.56231	0.236533
$554$	−20.5623	−0.873609
$555$	−6.70820	−0.284747
$556$	−15.4721	−0.656165
$557$	−7.76393	−0.328968	−0.164484	−	0.986380i	$-0.552596\pi$
$557$	−7.76393	−0.328968	−0.164484	+	0.986380i	$0.552596\pi$
$558$	−23.4721	−0.993655
$559$	27.7082	1.17193
$560$	4.14590	0.175196
$561$	−46.5967	−1.96732
$562$	−25.3607	−1.06978
$563$	−33.2705	−1.40218	−0.701092	−	0.713070i	$-0.747304\pi$
$563$	−33.2705	−1.40218	−0.701092	+	0.713070i	$0.747304\pi$
$564$	−30.2705	−1.27462
$565$	6.05573	0.254766
$566$	10.7082	0.450099
$567$	17.1246	0.719166
$568$	−11.9443	−0.501171
$569$	−13.9656	−0.585467	−0.292733	−	0.956194i	$-0.594565\pi$
$569$	−13.9656	−0.585467	−0.292733	+	0.956194i	$0.594565\pi$
$570$	−10.8541	−0.454628
$571$	−25.0000	−1.04622	−0.523109	−	0.852266i	$-0.675228\pi$
$571$	−25.0000	−1.04622	−0.523109	+	0.852266i	$0.675228\pi$
$572$	7.14590	0.298785
$573$	−58.5410	−2.44559
$574$	−33.5410	−1.39998
$575$	−4.54915	−0.189713
$576$	3.85410	0.160588
$577$	−4.41641	−0.183857	−0.0919287	−	0.995766i	$-0.529303\pi$
$577$	−4.41641	−0.183857	−0.0919287	+	0.995766i	$0.529303\pi$
$578$	38.8328	1.61523
$579$	−8.23607	−0.342279
$580$	12.7639	0.529993
$581$	5.83282	0.241986
$582$	−36.0344	−1.49368
$583$	21.4377	0.887859
$584$	0.708204	0.0293057
$585$	15.9787	0.660639
$586$	−32.0902	−1.32563
$587$	−40.9443	−1.68995	−0.844975	−	0.534805i	$-0.820385\pi$
$587$	−40.9443	−1.68995	−0.844975	+	0.534805i	$0.820385\pi$
$588$	−5.23607	−0.215932
$589$	18.2705	0.752823
$590$	13.4934	0.555515
$591$	7.32624	0.301361
$592$	−1.85410	−0.0762031
$593$	30.2148	1.24077	0.620386	−	0.784296i	$-0.286976\pi$
$593$	30.2148	1.24077	0.620386	+	0.784296i	$0.286976\pi$
$594$	5.32624	0.218538
$595$	−30.9787	−1.27000
$596$	−2.23607	−0.0915929
$597$	−55.6869	−2.27911
$598$	−4.41641	−0.180600
$599$	−16.1459	−0.659704	−0.329852	−	0.944033i	$-0.606999\pi$
$599$	−16.1459	−0.659704	−0.329852	+	0.944033i	$0.606999\pi$
$600$	8.09017	0.330280
$601$	−17.2705	−0.704479	−0.352239	−	0.935910i	$-0.614580\pi$
$601$	−17.2705	−0.704479	−0.352239	+	0.935910i	$0.614580\pi$
$602$	27.7082	1.12930
$603$	7.14590	0.291003
$604$	−9.79837	−0.398690
$605$	7.36068	0.299254
$606$	−13.7082	−0.556858
$607$	6.41641	0.260434	0.130217	−	0.991486i	$-0.458433\pi$
$607$	6.41641	0.260434	0.130217	+	0.991486i	$0.458433\pi$
$608$	−3.00000	−0.121666
$609$	−72.5410	−2.93951
$610$	3.29180	0.133281
$611$	−34.6869	−1.40328
$612$	−28.7984	−1.16411
$613$	23.4164	0.945780	0.472890	−	0.881122i	$-0.343211\pi$
$613$	23.4164	0.945780	0.472890	+	0.881122i	$0.343211\pi$
$614$	3.90983	0.157788
$615$	40.4508	1.63114
$616$	7.14590	0.287916
$617$	21.3262	0.858562	0.429281	−	0.903171i	$-0.358767\pi$
$617$	21.3262	0.858562	0.429281	+	0.903171i	$0.358767\pi$
$618$	−13.4721	−0.541929
$619$	44.8541	1.80284	0.901419	−	0.432947i	$-0.142526\pi$
$619$	44.8541	1.80284	0.901419	+	0.432947i	$0.142526\pi$
$620$	8.41641	0.338011
$621$	−3.29180	−0.132095
$622$	24.7639	0.992943
$623$	50.3951	2.01904
$624$	7.85410	0.314416
$625$	0	0
$626$	32.7426	1.30866
$627$	−18.7082	−0.747134
$628$	8.09017	0.322833
$629$	13.8541	0.552399
$630$	15.9787	0.636607
$631$	15.2705	0.607909	0.303955	−	0.952686i	$-0.401693\pi$
$631$	15.2705	0.607909	0.303955	+	0.952686i	$0.401693\pi$
$632$	−1.85410	−0.0737522
$633$	−46.7426	−1.85785
$634$	−10.6180	−0.421696
$635$	17.1591	0.680936
$636$	23.5623	0.934306
$637$	−6.00000	−0.237729
$638$	22.0000	0.870988
$639$	−46.0344	−1.82109
$640$	−1.38197	−0.0546270
$641$	18.8197	0.743332	0.371666	−	0.928367i	$-0.378787\pi$
$641$	18.8197	0.743332	0.371666	+	0.928367i	$0.378787\pi$
$642$	9.85410	0.388910
$643$	−30.3050	−1.19511	−0.597555	−	0.801828i	$-0.703861\pi$
$643$	−30.3050	−1.19511	−0.597555	+	0.801828i	$0.703861\pi$
$644$	−4.41641	−0.174031
$645$	−33.4164	−1.31577
$646$	22.4164	0.881962
$647$	2.67376	0.105116	0.0525582	−	0.998618i	$-0.483262\pi$
$647$	2.67376	0.105116	0.0525582	+	0.998618i	$0.483262\pi$
$648$	−5.70820	−0.224239
$649$	23.2574	0.912931
$650$	9.27051	0.363619
$651$	−47.8328	−1.87472
$652$	0.854102	0.0334492
$653$	18.0902	0.707923	0.353962	−	0.935260i	$-0.384834\pi$
$653$	18.0902	0.707923	0.353962	+	0.935260i	$0.384834\pi$
$654$	24.7984	0.969693
$655$	−29.8754	−1.16733
$656$	11.1803	0.436519
$657$	2.72949	0.106488
$658$	−34.6869	−1.35224
$659$	2.47214	0.0963007	0.0481504	−	0.998840i	$-0.484667\pi$
$659$	2.47214	0.0963007	0.0481504	+	0.998840i	$0.484667\pi$
$660$	−8.61803	−0.335457
$661$	45.7082	1.77784	0.888922	−	0.458059i	$-0.151455\pi$
$661$	45.7082	1.77784	0.888922	+	0.458059i	$0.151455\pi$
$662$	−5.43769	−0.211342
$663$	−58.6869	−2.27921
$664$	−1.94427	−0.0754524
$665$	−12.4377	−0.482313
$666$	−7.14590	−0.276898
$667$	−13.5967	−0.526468
$668$	−5.23607	−0.202590
$669$	4.14590	0.160290
$670$	−2.56231	−0.0989905
$671$	5.67376	0.219033
$672$	7.85410	0.302979
$673$	−18.5410	−0.714704	−0.357352	−	0.933970i	$-0.616320\pi$
$673$	−18.5410	−0.714704	−0.357352	+	0.933970i	$0.616320\pi$
$674$	4.61803	0.177880
$675$	6.90983	0.265959
$676$	−4.00000	−0.153846
$677$	−22.8885	−0.879678	−0.439839	−	0.898077i	$-0.644965\pi$
$677$	−22.8885	−0.879678	−0.439839	+	0.898077i	$0.644965\pi$
$678$	11.4721	0.440585
$679$	−41.2918	−1.58463
$680$	10.3262	0.395993
$681$	−36.2705	−1.38989
$682$	14.5066	0.555486
$683$	9.38197	0.358991	0.179495	−	0.983759i	$-0.442553\pi$
$683$	9.38197	0.358991	0.179495	+	0.983759i	$0.442553\pi$
$684$	−11.5623	−0.442096
$685$	−11.8328	−0.452109
$686$	15.0000	0.572703
$687$	−69.6312	−2.65660
$688$	−9.23607	−0.352122
$689$	27.0000	1.02862
$690$	5.32624	0.202766
$691$	−15.0902	−0.574057	−0.287029	−	0.957922i	$-0.592667\pi$
$691$	−15.0902	−0.574057	−0.287029	+	0.957922i	$0.592667\pi$
$692$	−7.67376	−0.291713
$693$	27.5410	1.04620
$694$	−8.67376	−0.329252
$695$	21.3820	0.811064
$696$	24.1803	0.916553
$697$	−83.5410	−3.16434
$698$	−22.7082	−0.859518
$699$	−10.8541	−0.410540
$700$	9.27051	0.350392
$701$	−49.2148	−1.85882	−0.929408	−	0.369053i	$-0.879682\pi$
$701$	−49.2148	−1.85882	−0.929408	+	0.369053i	$0.879682\pi$
$702$	6.70820	0.253185
$703$	5.56231	0.209786
$704$	−2.38197	−0.0897737
$705$	41.8328	1.57551
$706$	−6.81966	−0.256661
$707$	−15.7082	−0.590768
$708$	25.5623	0.960690
$709$	−17.0557	−0.640541	−0.320271	−	0.947326i	$-0.603774\pi$
$709$	−17.0557	−0.640541	−0.320271	+	0.947326i	$0.603774\pi$
$710$	16.5066	0.619481
$711$	−7.14590	−0.267992
$712$	−16.7984	−0.629546
$713$	−8.96556	−0.335763
$714$	−58.6869	−2.19630
$715$	−9.87539	−0.369319
$716$	−9.00000	−0.336346
$717$	−9.70820	−0.362560
$718$	−14.5967	−0.544746
$719$	−15.0557	−0.561484	−0.280742	−	0.959783i	$-0.590581\pi$
$719$	−15.0557	−0.561484	−0.280742	+	0.959783i	$0.590581\pi$
$720$	−5.32624	−0.198497
$721$	−15.4377	−0.574930
$722$	−10.0000	−0.372161
$723$	27.2705	1.01420
$724$	−18.0000	−0.668965
$725$	28.5410	1.05999
$726$	13.9443	0.517520
$727$	−2.47214	−0.0916864	−0.0458432	−	0.998949i	$-0.514597\pi$
$727$	−2.47214	−0.0916864	−0.0458432	+	0.998949i	$0.514597\pi$
$728$	9.00000	0.333562
$729$	−39.5623	−1.46527
$730$	−0.978714	−0.0362238
$731$	69.0132	2.55254
$732$	6.23607	0.230492
$733$	−1.11146	−0.0410526	−0.0205263	−	0.999789i	$-0.506534\pi$
$733$	−1.11146	−0.0410526	−0.0205263	+	0.999789i	$0.506534\pi$
$734$	4.88854	0.180439
$735$	7.23607	0.266906
$736$	1.47214	0.0542637
$737$	−4.41641	−0.162680
$738$	43.0902	1.58617
$739$	−38.4721	−1.41522	−0.707610	−	0.706603i	$-0.750227\pi$
$739$	−38.4721	−1.41522	−0.707610	+	0.706603i	$0.750227\pi$
$740$	2.56231	0.0941922
$741$	−23.5623	−0.865583
$742$	27.0000	0.991201
$743$	−12.7639	−0.468263	−0.234132	−	0.972205i	$-0.575225\pi$
$743$	−12.7639	−0.468263	−0.234132	+	0.972205i	$0.575225\pi$
$744$	15.9443	0.584545
$745$	3.09017	0.113215
$746$	−12.0000	−0.439351
$747$	−7.49342	−0.274170
$748$	17.7984	0.650773
$749$	11.2918	0.412593
$750$	−29.2705	−1.06881
$751$	−23.5623	−0.859801	−0.429900	−	0.902876i	$-0.641451\pi$
$751$	−23.5623	−0.859801	−0.429900	+	0.902876i	$0.641451\pi$
$752$	11.5623	0.421634
$753$	−2.47214	−0.0900896
$754$	27.7082	1.00907
$755$	13.5410	0.492808
$756$	6.70820	0.243975
$757$	11.7082	0.425542	0.212771	−	0.977102i	$-0.431751\pi$
$757$	11.7082	0.425542	0.212771	+	0.977102i	$0.431751\pi$
$758$	22.8328	0.829325
$759$	9.18034	0.333225
$760$	4.14590	0.150388
$761$	−3.03444	−0.109998	−0.0549992	−	0.998486i	$-0.517516\pi$
$761$	−3.03444	−0.109998	−0.0549992	+	0.998486i	$0.517516\pi$
$762$	32.5066	1.17759
$763$	28.4164	1.02874
$764$	22.3607	0.808981
$765$	39.7984	1.43891
$766$	−2.29180	−0.0828060
$767$	29.2918	1.05767
$768$	−2.61803	−0.0944702
$769$	−13.4164	−0.483808	−0.241904	−	0.970300i	$-0.577772\pi$
$769$	−13.4164	−0.483808	−0.241904	+	0.970300i	$0.577772\pi$
$770$	−9.87539	−0.355884
$771$	4.14590	0.149311
$772$	3.14590	0.113223
$773$	−41.2361	−1.48316	−0.741579	−	0.670865i	$-0.765923\pi$
$773$	−41.2361	−1.48316	−0.741579	+	0.670865i	$0.765923\pi$
$774$	−35.5967	−1.27950
$775$	18.8197	0.676022
$776$	13.7639	0.494096
$777$	−14.5623	−0.522420
$778$	−27.2361	−0.976460
$779$	−33.5410	−1.20173
$780$	−10.8541	−0.388639
$781$	28.4508	1.01805
$782$	−11.0000	−0.393359
$783$	20.6525	0.738059
$784$	2.00000	0.0714286
$785$	−11.1803	−0.399043
$786$	−56.5967	−2.01874
$787$	−7.94427	−0.283183	−0.141591	−	0.989925i	$-0.545222\pi$
$787$	−7.94427	−0.283183	−0.141591	+	0.989925i	$0.545222\pi$
$788$	−2.79837	−0.0996879
$789$	−48.0689	−1.71130
$790$	2.56231	0.0911628
$791$	13.1459	0.467414
$792$	−9.18034	−0.326209
$793$	7.14590	0.253758
$794$	−8.56231	−0.303865
$795$	−32.5623	−1.15487
$796$	21.2705	0.753913
$797$	−30.9443	−1.09610	−0.548051	−	0.836445i	$-0.684630\pi$
$797$	−30.9443	−1.09610	−0.548051	+	0.836445i	$0.684630\pi$
$798$	−23.5623	−0.834097
$799$	−86.3951	−3.05644
$800$	−3.09017	−0.109254
$801$	−64.7426	−2.28757
$802$	−14.0557	−0.496325
$803$	−1.68692	−0.0595300
$804$	−4.85410	−0.171191
$805$	6.10333	0.215114
$806$	18.2705	0.643551
$807$	14.5623	0.512617
$808$	5.23607	0.184204
$809$	31.1459	1.09503	0.547516	−	0.836795i	$-0.315574\pi$
$809$	31.1459	1.09503	0.547516	+	0.836795i	$0.315574\pi$
$810$	7.88854	0.277175
$811$	−22.9443	−0.805682	−0.402841	−	0.915270i	$-0.631977\pi$
$811$	−22.9443	−0.805682	−0.402841	+	0.915270i	$0.631977\pi$
$812$	27.7082	0.972367
$813$	17.3262	0.607658
$814$	4.41641	0.154795
$815$	−1.18034	−0.0413455
$816$	19.5623	0.684818
$817$	27.7082	0.969387
$818$	−33.4164	−1.16838
$819$	34.6869	1.21206
$820$	−15.4508	−0.539567
$821$	−1.49342	−0.0521208	−0.0260604	−	0.999660i	$-0.508296\pi$
$821$	−1.49342	−0.0521208	−0.0260604	+	0.999660i	$0.508296\pi$
$822$	−22.4164	−0.781862
$823$	19.4164	0.676813	0.338407	−	0.941000i	$-0.390112\pi$
$823$	19.4164	0.676813	0.338407	+	0.941000i	$0.390112\pi$
$824$	5.14590	0.179266
$825$	−19.2705	−0.670913
$826$	29.2918	1.01919
$827$	40.9443	1.42377	0.711886	−	0.702295i	$-0.247841\pi$
$827$	40.9443	1.42377	0.711886	+	0.702295i	$0.247841\pi$
$828$	5.67376	0.197177
$829$	−7.29180	−0.253255	−0.126627	−	0.991950i	$-0.540415\pi$
$829$	−7.29180	−0.253255	−0.126627	+	0.991950i	$0.540415\pi$
$830$	2.68692	0.0932643
$831$	53.8328	1.86744
$832$	−3.00000	−0.104006
$833$	−14.9443	−0.517788
$834$	40.5066	1.40263
$835$	7.23607	0.250414
$836$	7.14590	0.247146
$837$	13.6180	0.470708
$838$	0.673762	0.0232747
$839$	15.3475	0.529855	0.264928	−	0.964268i	$-0.414652\pi$
$839$	15.3475	0.529855	0.264928	+	0.964268i	$0.414652\pi$
$840$	−10.8541	−0.374502
$841$	56.3050	1.94155
$842$	33.3951	1.15087
$843$	66.3951	2.28677
$844$	17.8541	0.614564
$845$	5.52786	0.190164
$846$	44.5623	1.53208
$847$	15.9787	0.549035
$848$	−9.00000	−0.309061
$849$	−28.0344	−0.962140
$850$	23.0902	0.791986
$851$	−2.72949	−0.0935657
$852$	31.2705	1.07131
$853$	13.4377	0.460098	0.230049	−	0.973179i	$-0.426111\pi$
$853$	13.4377	0.460098	0.230049	+	0.973179i	$0.426111\pi$
$854$	7.14590	0.244528
$855$	15.9787	0.546460
$856$	−3.76393	−0.128649
$857$	−32.0902	−1.09618	−0.548090	−	0.836420i	$-0.684645\pi$
$857$	−32.0902	−1.09618	−0.548090	+	0.836420i	$0.684645\pi$
$858$	−18.7082	−0.638688
$859$	16.0557	0.547814	0.273907	−	0.961756i	$-0.411684\pi$
$859$	16.0557	0.547814	0.273907	+	0.961756i	$0.411684\pi$
$860$	12.7639	0.435246
$861$	87.8115	2.99261
$862$	−24.7639	−0.843463
$863$	−44.0132	−1.49823	−0.749113	−	0.662443i	$-0.769520\pi$
$863$	−44.0132	−1.49823	−0.749113	+	0.662443i	$0.769520\pi$
$864$	−2.23607	−0.0760726
$865$	10.6049	0.360577
$866$	5.58359	0.189738
$867$	−101.666	−3.45275
$868$	18.2705	0.620142
$869$	4.41641	0.149816
$870$	−33.4164	−1.13292
$871$	−5.56231	−0.188472
$872$	−9.47214	−0.320767
$873$	53.0476	1.79539
$874$	−4.41641	−0.149387
$875$	−33.5410	−1.13389
$876$	−1.85410	−0.0626443
$877$	−35.1246	−1.18607	−0.593037	−	0.805175i	$-0.702071\pi$
$877$	−35.1246	−1.18607	−0.593037	+	0.805175i	$0.702071\pi$
$878$	−13.0000	−0.438729
$879$	84.0132	2.83369
$880$	3.29180	0.110966
$881$	−57.7214	−1.94468	−0.972341	−	0.233566i	$-0.924961\pi$
$881$	−57.7214	−1.94468	−0.972341	+	0.233566i	$0.924961\pi$
$882$	7.70820	0.259549
$883$	−51.0344	−1.71745	−0.858723	−	0.512440i	$-0.828742\pi$
$883$	−51.0344	−1.71745	−0.858723	+	0.512440i	$0.828742\pi$
$884$	22.4164	0.753945
$885$	−35.3262	−1.18748
$886$	4.52786	0.152117
$887$	−3.70820	−0.124509	−0.0622547	−	0.998060i	$-0.519829\pi$
$887$	−3.70820	−0.124509	−0.0622547	+	0.998060i	$0.519829\pi$
$888$	4.85410	0.162893
$889$	37.2492	1.24930
$890$	23.2148	0.778161
$891$	13.5967	0.455508
$892$	−1.58359	−0.0530226
$893$	−34.6869	−1.16075
$894$	5.85410	0.195790
$895$	12.4377	0.415746
$896$	−3.00000	−0.100223
$897$	11.5623	0.386054
$898$	−17.3607	−0.579333
$899$	56.2492	1.87602
$900$	−11.9098	−0.396994
$901$	67.2492	2.24040
$902$	−26.6312	−0.886722
$903$	−72.5410	−2.41401
$904$	−4.38197	−0.145742
$905$	24.8754	0.826886
$906$	25.6525	0.852246
$907$	−21.4164	−0.711120	−0.355560	−	0.934653i	$-0.615710\pi$
$907$	−21.4164	−0.711120	−0.355560	+	0.934653i	$0.615710\pi$
$908$	13.8541	0.459765
$909$	20.1803	0.669340
$910$	−12.4377	−0.412306
$911$	8.56231	0.283682	0.141841	−	0.989889i	$-0.454698\pi$
$911$	8.56231	0.283682	0.141841	+	0.989889i	$0.454698\pi$
$912$	7.85410	0.260075
$913$	4.63119	0.153270
$914$	−41.0344	−1.35730
$915$	−8.61803	−0.284903
$916$	26.5967	0.878781
$917$	−64.8541	−2.14167
$918$	16.7082	0.551453
$919$	43.7214	1.44223	0.721117	−	0.692813i	$-0.243629\pi$
$919$	43.7214	1.44223	0.721117	+	0.692813i	$0.243629\pi$
$920$	−2.03444	−0.0670736
$921$	−10.2361	−0.337290
$922$	−2.38197	−0.0784459
$923$	35.8328	1.17945
$924$	−18.7082	−0.615455
$925$	5.72949	0.188384
$926$	26.3607	0.866266
$927$	19.8328	0.651395
$928$	−9.23607	−0.303189
$929$	41.8328	1.37249	0.686245	−	0.727370i	$-0.259258\pi$
$929$	41.8328	1.37249	0.686245	+	0.727370i	$0.259258\pi$
$930$	−22.0344	−0.722538
$931$	−6.00000	−0.196642
$932$	4.14590	0.135803
$933$	−64.8328	−2.12253
$934$	31.7984	1.04047
$935$	−24.5967	−0.804400
$936$	−11.5623	−0.377926
$937$	−8.83282	−0.288556	−0.144278	−	0.989537i	$-0.546086\pi$
$937$	−8.83282	−0.288556	−0.144278	+	0.989537i	$0.546086\pi$
$938$	−5.56231	−0.181616
$939$	−85.7214	−2.79741
$940$	−15.9787	−0.521168
$941$	1.79837	0.0586253	0.0293127	−	0.999570i	$-0.490668\pi$
$941$	1.79837	0.0586253	0.0293127	+	0.999570i	$0.490668\pi$
$942$	−21.1803	−0.690093
$943$	16.4590	0.535978
$944$	−9.76393	−0.317789
$945$	−9.27051	−0.301570
$946$	22.0000	0.715282
$947$	−16.2016	−0.526482	−0.263241	−	0.964730i	$-0.584791\pi$
$947$	−16.2016	−0.526482	−0.263241	+	0.964730i	$0.584791\pi$
$948$	4.85410	0.157654
$949$	−2.12461	−0.0689678
$950$	9.27051	0.300775
$951$	27.7984	0.901424
$952$	22.4164	0.726520
$953$	−26.3475	−0.853480	−0.426740	−	0.904374i	$-0.640338\pi$
$953$	−26.3475	−0.853480	−0.426740	+	0.904374i	$0.640338\pi$
$954$	−34.6869	−1.12303
$955$	−30.9017	−0.999956
$956$	3.70820	0.119932
$957$	−57.5967	−1.86184
$958$	−13.8541	−0.447606
$959$	−25.6869	−0.829474
$960$	3.61803	0.116772
$961$	6.09017	0.196457
$962$	5.56231	0.179336
$963$	−14.5066	−0.467468
$964$	−10.4164	−0.335490
$965$	−4.34752	−0.139952
$966$	11.5623	0.372011
$967$	58.8328	1.89194	0.945968	−	0.324260i	$-0.105115\pi$
$967$	58.8328	1.89194	0.945968	+	0.324260i	$0.105115\pi$
$968$	−5.32624	−0.171192
$969$	−58.6869	−1.88530
$970$	−19.0213	−0.610737
$971$	−31.2492	−1.00284	−0.501418	−	0.865205i	$-0.667188\pi$
$971$	−31.2492	−1.00284	−0.501418	+	0.865205i	$0.667188\pi$
$972$	21.6525	0.694503
$973$	46.4164	1.48804
$974$	15.8885	0.509102
$975$	−24.2705	−0.777278
$976$	−2.38197	−0.0762449
$977$	−13.7639	−0.440347	−0.220174	−	0.975461i	$-0.570662\pi$
$977$	−13.7639	−0.440347	−0.220174	+	0.975461i	$0.570662\pi$
$978$	−2.23607	−0.0715016
$979$	40.0132	1.27883
$980$	−2.76393	−0.0882906
$981$	−36.5066	−1.16557
$982$	−6.27051	−0.200100
$983$	−10.7426	−0.342637	−0.171319	−	0.985216i	$-0.554803\pi$
$983$	−10.7426	−0.342637	−0.171319	+	0.985216i	$0.554803\pi$
$984$	−29.2705	−0.933110
$985$	3.86726	0.123221
$986$	69.0132	2.19783
$987$	90.8115	2.89056
$988$	9.00000	0.286328
$989$	−13.5967	−0.432351
$990$	12.6869	0.403217
$991$	−9.30495	−0.295582	−0.147791	−	0.989019i	$-0.547216\pi$
$991$	−9.30495	−0.295582	−0.147791	+	0.989019i	$0.547216\pi$
$992$	−6.09017	−0.193363
$993$	14.2361	0.451768
$994$	35.8328	1.13655
$995$	−29.3951	−0.931888
$996$	5.09017	0.161288
$997$	35.0000	1.10846	0.554231	−	0.832363i	$-0.313013\pi$
$997$	35.0000	1.10846	0.554231	+	0.832363i	$0.313013\pi$
$998$	−5.65248	−0.178926
$999$	4.14590	0.131170

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6038.2.a.a.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6038.2.a.a.1.1	✓	2	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:	\( N \)	\(=\)	\( 6038 = 2 \cdot 3019 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6038.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.61803 q^{3} +1.00000 q^{4} -1.38197 q^{5} -2.61803 q^{6} -3.00000 q^{7} +1.00000 q^{8} +3.85410 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.61803 q^{3} +1.00000 q^{4} -1.38197 q^{5} -2.61803 q^{6} -3.00000 q^{7} +1.00000 q^{8} +3.85410 q^{9} -1.38197 q^{10} -2.38197 q^{11} -2.61803 q^{12} -3.00000 q^{13} -3.00000 q^{14} +3.61803 q^{15} +1.00000 q^{16} -7.47214 q^{17} +3.85410 q^{18} -3.00000 q^{19} -1.38197 q^{20} +7.85410 q^{21} -2.38197 q^{22} +1.47214 q^{23} -2.61803 q^{24} -3.09017 q^{25} -3.00000 q^{26} -2.23607 q^{27} -3.00000 q^{28} -9.23607 q^{29} +3.61803 q^{30} -6.09017 q^{31} +1.00000 q^{32} +6.23607 q^{33} -7.47214 q^{34} +4.14590 q^{35} +3.85410 q^{36} -1.85410 q^{37} -3.00000 q^{38} +7.85410 q^{39} -1.38197 q^{40} +11.1803 q^{41} +7.85410 q^{42} -9.23607 q^{43} -2.38197 q^{44} -5.32624 q^{45} +1.47214 q^{46} +11.5623 q^{47} -2.61803 q^{48} +2.00000 q^{49} -3.09017 q^{50} +19.5623 q^{51} -3.00000 q^{52} -9.00000 q^{53} -2.23607 q^{54} +3.29180 q^{55} -3.00000 q^{56} +7.85410 q^{57} -9.23607 q^{58} -9.76393 q^{59} +3.61803 q^{60} -2.38197 q^{61} -6.09017 q^{62} -11.5623 q^{63} +1.00000 q^{64} +4.14590 q^{65} +6.23607 q^{66} +1.85410 q^{67} -7.47214 q^{68} -3.85410 q^{69} +4.14590 q^{70} -11.9443 q^{71} +3.85410 q^{72} +0.708204 q^{73} -1.85410 q^{74} +8.09017 q^{75} -3.00000 q^{76} +7.14590 q^{77} +7.85410 q^{78} -1.85410 q^{79} -1.38197 q^{80} -5.70820 q^{81} +11.1803 q^{82} -1.94427 q^{83} +7.85410 q^{84} +10.3262 q^{85} -9.23607 q^{86} +24.1803 q^{87} -2.38197 q^{88} -16.7984 q^{89} -5.32624 q^{90} +9.00000 q^{91} +1.47214 q^{92} +15.9443 q^{93} +11.5623 q^{94} +4.14590 q^{95} -2.61803 q^{96} +13.7639 q^{97} +2.00000 q^{98} -9.18034 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} - 5 q^{5} - 3 q^{6} - 6 q^{7} + 2 q^{8} + q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 3 * q^3 + 2 * q^4 - 5 * q^5 - 3 * q^6 - 6 * q^7 + 2 * q^8 + q^9	\( 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} - 5 q^{5} - 3 q^{6} - 6 q^{7} + 2 q^{8} + q^{9} - 5 q^{10} - 7 q^{11} - 3 q^{12} - 6 q^{13} - 6 q^{14} + 5 q^{15} + 2 q^{16} - 6 q^{17} + q^{18} - 6 q^{19} - 5 q^{20} + 9 q^{21} - 7 q^{22} - 6 q^{23} - 3 q^{24} + 5 q^{25} - 6 q^{26} - 6 q^{28} - 14 q^{29} + 5 q^{30} - q^{31} + 2 q^{32} + 8 q^{33} - 6 q^{34} + 15 q^{35} + q^{36} + 3 q^{37} - 6 q^{38} + 9 q^{39} - 5 q^{40} + 9 q^{42} - 14 q^{43} - 7 q^{44} + 5 q^{45} - 6 q^{46} + 3 q^{47} - 3 q^{48} + 4 q^{49} + 5 q^{50} + 19 q^{51} - 6 q^{52} - 18 q^{53} + 20 q^{55} - 6 q^{56} + 9 q^{57} - 14 q^{58} - 24 q^{59} + 5 q^{60} - 7 q^{61} - q^{62} - 3 q^{63} + 2 q^{64} + 15 q^{65} + 8 q^{66} - 3 q^{67} - 6 q^{68} - q^{69} + 15 q^{70} - 6 q^{71} + q^{72} - 12 q^{73} + 3 q^{74} + 5 q^{75} - 6 q^{76} + 21 q^{77} + 9 q^{78} + 3 q^{79} - 5 q^{80} + 2 q^{81} + 14 q^{83} + 9 q^{84} + 5 q^{85} - 14 q^{86} + 26 q^{87} - 7 q^{88} - 9 q^{89} + 5 q^{90} + 18 q^{91} - 6 q^{92} + 14 q^{93} + 3 q^{94} + 15 q^{95} - 3 q^{96} + 32 q^{97} + 4 q^{98} + 4 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 3 * q^3 + 2 * q^4 - 5 * q^5 - 3 * q^6 - 6 * q^7 + 2 * q^8 + q^9 - 5 * q^10 - 7 * q^11 - 3 * q^12 - 6 * q^13 - 6 * q^14 + 5 * q^15 + 2 * q^16 - 6 * q^17 + q^18 - 6 * q^19 - 5 * q^20 + 9 * q^21 - 7 * q^22 - 6 * q^23 - 3 * q^24 + 5 * q^25 - 6 * q^26 - 6 * q^28 - 14 * q^29 + 5 * q^30 - q^31 + 2 * q^32 + 8 * q^33 - 6 * q^34 + 15 * q^35 + q^36 + 3 * q^37 - 6 * q^38 + 9 * q^39 - 5 * q^40 + 9 * q^42 - 14 * q^43 - 7 * q^44 + 5 * q^45 - 6 * q^46 + 3 * q^47 - 3 * q^48 + 4 * q^49 + 5 * q^50 + 19 * q^51 - 6 * q^52 - 18 * q^53 + 20 * q^55 - 6 * q^56 + 9 * q^57 - 14 * q^58 - 24 * q^59 + 5 * q^60 - 7 * q^61 - q^62 - 3 * q^63 + 2 * q^64 + 15 * q^65 + 8 * q^66 - 3 * q^67 - 6 * q^68 - q^69 + 15 * q^70 - 6 * q^71 + q^72 - 12 * q^73 + 3 * q^74 + 5 * q^75 - 6 * q^76 + 21 * q^77 + 9 * q^78 + 3 * q^79 - 5 * q^80 + 2 * q^81 + 14 * q^83 + 9 * q^84 + 5 * q^85 - 14 * q^86 + 26 * q^87 - 7 * q^88 - 9 * q^89 + 5 * q^90 + 18 * q^91 - 6 * q^92 + 14 * q^93 + 3 * q^94 + 15 * q^95 - 3 * q^96 + 32 * q^97 + 4 * q^98 + 4 * q^99

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