LMFDB - Embedded newform 1502.2.a.h.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1502,2,Mod(1,1502)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1502, 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("1502.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1502 = 2 \cdot 751 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1502.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:	$11.9935303836$
Analytic rank:	$0$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 6 x^{18} - 23 x^{17} + 190 x^{16} + 128 x^{15} - 2394 x^{14} + 749 x^{13} + 15539 x^{12} + \cdots + 4222 $ x^19 - 6x^18 - 23x^17 + 190x^16 + 128x^15 - 2394x^14 + 749x^13 + 15539x^12 - 11338x^11 - 56744x^10 + 50183x^9 + 120237x^8 - 102992x^7 - 148539x^6 + 99519x^5 + 104388x^4 - 41081x^3 - 35733x^2 + 5542x + 4222
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			1.14
Root			$2.07470$ of defining polynomial
Character	$\chi$	$=$	1502.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.07470 q^{3} +1.00000 q^{4} +4.37927 q^{5} -2.07470 q^{6} +2.25344 q^{7} -1.00000 q^{8} +1.30439 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.07470 q^{3} +1.00000 q^{4} +4.37927 q^{5} -2.07470 q^{6} +2.25344 q^{7} -1.00000 q^{8} +1.30439 q^{9} -4.37927 q^{10} -0.718588 q^{11} +2.07470 q^{12} +0.598244 q^{13} -2.25344 q^{14} +9.08569 q^{15} +1.00000 q^{16} -4.93400 q^{17} -1.30439 q^{18} -0.00963336 q^{19} +4.37927 q^{20} +4.67522 q^{21} +0.718588 q^{22} -1.90945 q^{23} -2.07470 q^{24} +14.1780 q^{25} -0.598244 q^{26} -3.51788 q^{27} +2.25344 q^{28} +4.64289 q^{29} -9.08569 q^{30} -4.03264 q^{31} -1.00000 q^{32} -1.49086 q^{33} +4.93400 q^{34} +9.86843 q^{35} +1.30439 q^{36} +7.06269 q^{37} +0.00963336 q^{38} +1.24118 q^{39} -4.37927 q^{40} -1.15547 q^{41} -4.67522 q^{42} +4.53899 q^{43} -0.718588 q^{44} +5.71229 q^{45} +1.90945 q^{46} +1.33089 q^{47} +2.07470 q^{48} -1.92200 q^{49} -14.1780 q^{50} -10.2366 q^{51} +0.598244 q^{52} -1.45053 q^{53} +3.51788 q^{54} -3.14689 q^{55} -2.25344 q^{56} -0.0199864 q^{57} -4.64289 q^{58} -1.64570 q^{59} +9.08569 q^{60} +1.92803 q^{61} +4.03264 q^{62} +2.93937 q^{63} +1.00000 q^{64} +2.61987 q^{65} +1.49086 q^{66} +0.314808 q^{67} -4.93400 q^{68} -3.96153 q^{69} -9.86843 q^{70} +5.03821 q^{71} -1.30439 q^{72} -11.1240 q^{73} -7.06269 q^{74} +29.4152 q^{75} -0.00963336 q^{76} -1.61930 q^{77} -1.24118 q^{78} -14.2410 q^{79} +4.37927 q^{80} -11.2117 q^{81} +1.15547 q^{82} -5.32343 q^{83} +4.67522 q^{84} -21.6073 q^{85} -4.53899 q^{86} +9.63261 q^{87} +0.718588 q^{88} -5.52442 q^{89} -5.71229 q^{90} +1.34811 q^{91} -1.90945 q^{92} -8.36654 q^{93} -1.33089 q^{94} -0.0421871 q^{95} -2.07470 q^{96} -10.5612 q^{97} +1.92200 q^{98} -0.937321 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q - 19 q^{2} + 6 q^{3} + 19 q^{4} + 2 q^{5} - 6 q^{6} + 13 q^{7} - 19 q^{8} + 25 q^{9}+O(q^{10}) $ 19 * q - 19 * q^2 + 6 * q^3 + 19 * q^4 + 2 * q^5 - 6 * q^6 + 13 * q^7 - 19 * q^8 + 25 * q^9	\( 19 q - 19 q^{2} + 6 q^{3} + 19 q^{4} + 2 q^{5} - 6 q^{6} + 13 q^{7} - 19 q^{8} + 25 q^{9} - 2 q^{10} - 7 q^{11} + 6 q^{12} + 19 q^{13} - 13 q^{14} + 6 q^{15} + 19 q^{16} + 11 q^{17} - 25 q^{18} + 7 q^{19} + 2 q^{20} + 7 q^{21} + 7 q^{22} + 12 q^{23} - 6 q^{24} + 37 q^{25} - 19 q^{26} + 24 q^{27} + 13 q^{28} - 8 q^{29} - 6 q^{30} + 32 q^{31} - 19 q^{32} + 24 q^{33} - 11 q^{34} - 19 q^{35} + 25 q^{36} + 41 q^{37} - 7 q^{38} - 2 q^{39} - 2 q^{40} + 15 q^{41} - 7 q^{42} + 15 q^{43} - 7 q^{44} + 28 q^{45} - 12 q^{46} - 6 q^{47} + 6 q^{48} + 42 q^{49} - 37 q^{50} + 8 q^{51} + 19 q^{52} + 6 q^{53} - 24 q^{54} + 22 q^{55} - 13 q^{56} + 24 q^{57} + 8 q^{58} - 4 q^{59} + 6 q^{60} + 13 q^{61} - 32 q^{62} + 37 q^{63} + 19 q^{64} + 20 q^{65} - 24 q^{66} + 47 q^{67} + 11 q^{68} + 15 q^{69} + 19 q^{70} - 25 q^{72} + 64 q^{73} - 41 q^{74} - 3 q^{75} + 7 q^{76} - 4 q^{77} + 2 q^{78} + 34 q^{79} + 2 q^{80} + 27 q^{81} - 15 q^{82} + 4 q^{83} + 7 q^{84} + 21 q^{85} - 15 q^{86} + 7 q^{88} + 18 q^{89} - 28 q^{90} + 28 q^{91} + 12 q^{92} + 43 q^{93} + 6 q^{94} - 8 q^{95} - 6 q^{96} + 82 q^{97} - 42 q^{98} - 2 q^{99}+O(q^{100}) \) 19 * q - 19 * q^2 + 6 * q^3 + 19 * q^4 + 2 * q^5 - 6 * q^6 + 13 * q^7 - 19 * q^8 + 25 * q^9 - 2 * q^10 - 7 * q^11 + 6 * q^12 + 19 * q^13 - 13 * q^14 + 6 * q^15 + 19 * q^16 + 11 * q^17 - 25 * q^18 + 7 * q^19 + 2 * q^20 + 7 * q^21 + 7 * q^22 + 12 * q^23 - 6 * q^24 + 37 * q^25 - 19 * q^26 + 24 * q^27 + 13 * q^28 - 8 * q^29 - 6 * q^30 + 32 * q^31 - 19 * q^32 + 24 * q^33 - 11 * q^34 - 19 * q^35 + 25 * q^36 + 41 * q^37 - 7 * q^38 - 2 * q^39 - 2 * q^40 + 15 * q^41 - 7 * q^42 + 15 * q^43 - 7 * q^44 + 28 * q^45 - 12 * q^46 - 6 * q^47 + 6 * q^48 + 42 * q^49 - 37 * q^50 + 8 * q^51 + 19 * q^52 + 6 * q^53 - 24 * q^54 + 22 * q^55 - 13 * q^56 + 24 * q^57 + 8 * q^58 - 4 * q^59 + 6 * q^60 + 13 * q^61 - 32 * q^62 + 37 * q^63 + 19 * q^64 + 20 * q^65 - 24 * q^66 + 47 * q^67 + 11 * q^68 + 15 * q^69 + 19 * q^70 - 25 * q^72 + 64 * q^73 - 41 * q^74 - 3 * q^75 + 7 * q^76 - 4 * q^77 + 2 * q^78 + 34 * q^79 + 2 * q^80 + 27 * q^81 - 15 * q^82 + 4 * q^83 + 7 * q^84 + 21 * q^85 - 15 * q^86 + 7 * q^88 + 18 * q^89 - 28 * q^90 + 28 * q^91 + 12 * q^92 + 43 * q^93 + 6 * q^94 - 8 * q^95 - 6 * q^96 + 82 * q^97 - 42 * q^98 - 2 * 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
$3$	2.07470	1.19783	0.598915	−	0.800812i	$-0.295599\pi$
$3$	2.07470	1.19783	0.598915	+	0.800812i	$0.295599\pi$
$4$	1.00000	0.500000
$5$	4.37927	1.95847	0.979235	−	0.202727i	$-0.0649804\pi$
$5$	4.37927	1.95847	0.979235	+	0.202727i	$0.0649804\pi$
$6$	−2.07470	−0.846994
$7$	2.25344	0.851721	0.425860	−	0.904789i	$-0.359972\pi$
$7$	2.25344	0.851721	0.425860	+	0.904789i	$0.359972\pi$
$8$	−1.00000	−0.353553
$9$	1.30439	0.434798
$10$	−4.37927	−1.38485
$11$	−0.718588	−0.216662	−0.108331	−	0.994115i	$-0.534551\pi$
$11$	−0.718588	−0.216662	−0.108331	+	0.994115i	$0.534551\pi$
$12$	2.07470	0.598915
$13$	0.598244	0.165923	0.0829615	−	0.996553i	$-0.473562\pi$
$13$	0.598244	0.165923	0.0829615	+	0.996553i	$0.473562\pi$
$14$	−2.25344	−0.602257
$15$	9.08569	2.34592
$16$	1.00000	0.250000
$17$	−4.93400	−1.19667	−0.598336	−	0.801246i	$-0.704171\pi$
$17$	−4.93400	−1.19667	−0.598336	+	0.801246i	$0.704171\pi$
$18$	−1.30439	−0.307448
$19$	−0.00963336	−0.00221004	−0.00110502	−	0.999999i	$-0.500352\pi$
$19$	−0.00963336	−0.00221004	−0.00110502	+	0.999999i	$0.500352\pi$
$20$	4.37927	0.979235
$21$	4.67522	1.02022
$22$	0.718588	0.153203
$23$	−1.90945	−0.398147	−0.199074	−	0.979985i	$-0.563793\pi$
$23$	−1.90945	−0.398147	−0.199074	+	0.979985i	$0.563793\pi$
$24$	−2.07470	−0.423497
$25$	14.1780	2.83561
$26$	−0.598244	−0.117325
$27$	−3.51788	−0.677017
$28$	2.25344	0.425860
$29$	4.64289	0.862162	0.431081	−	0.902313i	$-0.358132\pi$
$29$	4.64289	0.862162	0.431081	+	0.902313i	$0.358132\pi$
$30$	−9.08569	−1.65881
$31$	−4.03264	−0.724284	−0.362142	−	0.932123i	$-0.617955\pi$
$31$	−4.03264	−0.724284	−0.362142	+	0.932123i	$0.617955\pi$
$32$	−1.00000	−0.176777
$33$	−1.49086	−0.259525
$34$	4.93400	0.846174
$35$	9.86843	1.66807
$36$	1.30439	0.217399
$37$	7.06269	1.16110	0.580550	−	0.814225i	$-0.302838\pi$
$37$	7.06269	1.16110	0.580550	+	0.814225i	$0.302838\pi$
$38$	0.00963336	0.00156274
$39$	1.24118	0.198748
$40$	−4.37927	−0.692424
$41$	−1.15547	−0.180454	−0.0902270	−	0.995921i	$-0.528759\pi$
$41$	−1.15547	−0.180454	−0.0902270	+	0.995921i	$0.528759\pi$
$42$	−4.67522	−0.721402
$43$	4.53899	0.692189	0.346094	−	0.938200i	$-0.387508\pi$
$43$	4.53899	0.692189	0.346094	+	0.938200i	$0.387508\pi$
$44$	−0.718588	−0.108331
$45$	5.71229	0.851538
$46$	1.90945	0.281532
$47$	1.33089	0.194131	0.0970653	−	0.995278i	$-0.469054\pi$
$47$	1.33089	0.194131	0.0970653	+	0.995278i	$0.469054\pi$
$48$	2.07470	0.299458
$49$	−1.92200	−0.274572
$50$	−14.1780	−2.00508
$51$	−10.2366	−1.43341
$52$	0.598244	0.0829615
$53$	−1.45053	−0.199246	−0.0996229	−	0.995025i	$-0.531764\pi$
$53$	−1.45053	−0.199246	−0.0996229	+	0.995025i	$0.531764\pi$
$54$	3.51788	0.478723
$55$	−3.14689	−0.424327
$56$	−2.25344	−0.301129
$57$	−0.0199864	−0.00264726
$58$	−4.64289	−0.609641
$59$	−1.64570	−0.214252	−0.107126	−	0.994245i	$-0.534165\pi$
$59$	−1.64570	−0.214252	−0.107126	+	0.994245i	$0.534165\pi$
$60$	9.08569	1.17296
$61$	1.92803	0.246859	0.123429	−	0.992353i	$-0.460611\pi$
$61$	1.92803	0.246859	0.123429	+	0.992353i	$0.460611\pi$
$62$	4.03264	0.512146
$63$	2.93937	0.370326
$64$	1.00000	0.125000
$65$	2.61987	0.324955
$66$	1.49086	0.183512
$67$	0.314808	0.0384599	0.0192299	−	0.999815i	$-0.493879\pi$
$67$	0.314808	0.0384599	0.0192299	+	0.999815i	$0.493879\pi$
$68$	−4.93400	−0.598336
$69$	−3.96153	−0.476913
$70$	−9.86843	−1.17950
$71$	5.03821	0.597926	0.298963	−	0.954265i	$-0.403359\pi$
$71$	5.03821	0.597926	0.298963	+	0.954265i	$0.403359\pi$
$72$	−1.30439	−0.153724
$73$	−11.1240	−1.30197	−0.650983	−	0.759092i	$-0.725643\pi$
$73$	−11.1240	−1.30197	−0.650983	+	0.759092i	$0.725643\pi$
$74$	−7.06269	−0.821021
$75$	29.4152	3.39658
$76$	−0.00963336	−0.00110502
$77$	−1.61930	−0.184536
$78$	−1.24118	−0.140536
$79$	−14.2410	−1.60223	−0.801117	−	0.598508i	$-0.795760\pi$
$79$	−14.2410	−1.60223	−0.801117	+	0.598508i	$0.795760\pi$
$80$	4.37927	0.489618
$81$	−11.2117	−1.24575
$82$	1.15547	0.127600
$83$	−5.32343	−0.584323	−0.292161	−	0.956369i	$-0.594374\pi$
$83$	−5.32343	−0.584323	−0.292161	+	0.956369i	$0.594374\pi$
$84$	4.67522	0.510108
$85$	−21.6073	−2.34365
$86$	−4.53899	−0.489451
$87$	9.63261	1.03272
$88$	0.718588	0.0766017
$89$	−5.52442	−0.585587	−0.292793	−	0.956176i	$-0.594585\pi$
$89$	−5.52442	−0.585587	−0.292793	+	0.956176i	$0.594585\pi$
$90$	−5.71229	−0.602129
$91$	1.34811	0.141320
$92$	−1.90945	−0.199074
$93$	−8.36654	−0.867570
$94$	−1.33089	−0.137271
$95$	−0.0421871	−0.00432831
$96$	−2.07470	−0.211749
$97$	−10.5612	−1.07233	−0.536164	−	0.844114i	$-0.680127\pi$
$97$	−10.5612	−1.07233	−0.536164	+	0.844114i	$0.680127\pi$
$98$	1.92200	0.194152
$99$	−0.937321	−0.0942043
$100$	14.1780	1.41780
$101$	−4.69406	−0.467076	−0.233538	−	0.972348i	$-0.575030\pi$
$101$	−4.69406	−0.467076	−0.233538	+	0.972348i	$0.575030\pi$
$102$	10.2366	1.01357
$103$	8.53797	0.841271	0.420636	−	0.907230i	$-0.361807\pi$
$103$	8.53797	0.841271	0.420636	+	0.907230i	$0.361807\pi$
$104$	−0.598244	−0.0586626
$105$	20.4741	1.99806
$106$	1.45053	0.140888
$107$	−4.41210	−0.426534	−0.213267	−	0.976994i	$-0.568410\pi$
$107$	−4.41210	−0.426534	−0.213267	+	0.976994i	$0.568410\pi$
$108$	−3.51788	−0.338508
$109$	12.2207	1.17053	0.585265	−	0.810842i	$-0.300991\pi$
$109$	12.2207	1.17053	0.585265	+	0.810842i	$0.300991\pi$
$110$	3.14689	0.300045
$111$	14.6530	1.39080
$112$	2.25344	0.212930
$113$	8.61050	0.810008	0.405004	−	0.914315i	$-0.367270\pi$
$113$	8.61050	0.810008	0.405004	+	0.914315i	$0.367270\pi$
$114$	0.0199864	0.00187189
$115$	−8.36199	−0.779759
$116$	4.64289	0.431081
$117$	0.780345	0.0721429
$118$	1.64570	0.151499
$119$	−11.1185	−1.01923
$120$	−9.08569	−0.829406
$121$	−10.4836	−0.953057
$122$	−1.92803	−0.174555
$123$	−2.39726	−0.216153
$124$	−4.03264	−0.362142
$125$	40.1931	3.59498
$126$	−2.93937	−0.261860
$127$	1.10137	0.0977310	0.0488655	−	0.998805i	$-0.484439\pi$
$127$	1.10137	0.0977310	0.0488655	+	0.998805i	$0.484439\pi$
$128$	−1.00000	−0.0883883
$129$	9.41705	0.829125
$130$	−2.61987	−0.229778
$131$	−21.8069	−1.90528	−0.952639	−	0.304103i	$-0.901643\pi$
$131$	−21.8069	−1.90528	−0.952639	+	0.304103i	$0.901643\pi$
$132$	−1.49086	−0.129762
$133$	−0.0217082	−0.00188234
$134$	−0.314808	−0.0271952
$135$	−15.4058	−1.32592
$136$	4.93400	0.423087
$137$	−1.35765	−0.115992	−0.0579959	−	0.998317i	$-0.518471\pi$
$137$	−1.35765	−0.115992	−0.0579959	+	0.998317i	$0.518471\pi$
$138$	3.96153	0.337228
$139$	2.64515	0.224359	0.112179	−	0.993688i	$-0.464217\pi$
$139$	2.64515	0.224359	0.112179	+	0.993688i	$0.464217\pi$
$140$	9.86843	0.834035
$141$	2.76121	0.232536
$142$	−5.03821	−0.422797
$143$	−0.429891	−0.0359493
$144$	1.30439	0.108699
$145$	20.3325	1.68852
$146$	11.1240	0.920629
$147$	−3.98759	−0.328891
$148$	7.06269	0.580550
$149$	13.8739	1.13660	0.568298	−	0.822823i	$-0.307602\pi$
$149$	13.8739	1.13660	0.568298	+	0.822823i	$0.307602\pi$
$150$	−29.4152	−2.40174
$151$	14.5396	1.18322	0.591608	−	0.806226i	$-0.298493\pi$
$151$	14.5396	1.18322	0.591608	+	0.806226i	$0.298493\pi$
$152$	0.00963336	0.000781369 0
$153$	−6.43588	−0.520310
$154$	1.61930	0.130487
$155$	−17.6601	−1.41849
$156$	1.24118	0.0993738
$157$	21.6271	1.72603	0.863015	−	0.505178i	$-0.168573\pi$
$157$	21.6271	1.72603	0.863015	+	0.505178i	$0.168573\pi$
$158$	14.2410	1.13295
$159$	−3.00942	−0.238663
$160$	−4.37927	−0.346212
$161$	−4.30282	−0.339110
$162$	11.2117	0.880877
$163$	−12.9832	−1.01693	−0.508463	−	0.861084i	$-0.669786\pi$
$163$	−12.9832	−1.01693	−0.508463	+	0.861084i	$0.669786\pi$
$164$	−1.15547	−0.0902270
$165$	−6.52887	−0.508272
$166$	5.32343	0.413179
$167$	−5.86426	−0.453790	−0.226895	−	0.973919i	$-0.572857\pi$
$167$	−5.86426	−0.453790	−0.226895	+	0.973919i	$0.572857\pi$
$168$	−4.67522	−0.360701
$169$	−12.6421	−0.972470
$170$	21.6073	1.65721
$171$	−0.0125657	−0.000960922 0
$172$	4.53899	0.346094
$173$	−13.6486	−1.03769	−0.518843	−	0.854869i	$-0.673637\pi$
$173$	−13.6486	−1.03769	−0.518843	+	0.854869i	$0.673637\pi$
$174$	−9.63261	−0.730246
$175$	31.9494	2.41514
$176$	−0.718588	−0.0541656
$177$	−3.41434	−0.256638
$178$	5.52442	0.414073
$179$	7.53295	0.563039	0.281520	−	0.959555i	$-0.409162\pi$
$179$	7.53295	0.563039	0.281520	+	0.959555i	$0.409162\pi$
$180$	5.71229	0.425769
$181$	15.7092	1.16765	0.583827	−	0.811878i	$-0.301555\pi$
$181$	15.7092	1.16765	0.583827	+	0.811878i	$0.301555\pi$
$182$	−1.34811	−0.0999283
$183$	4.00008	0.295695
$184$	1.90945	0.140766
$185$	30.9295	2.27398
$186$	8.36654	0.613465
$187$	3.54551	0.259274
$188$	1.33089	0.0970653
$189$	−7.92734	−0.576629
$190$	0.0421871	0.00306057
$191$	−11.1401	−0.806068	−0.403034	−	0.915185i	$-0.632044\pi$
$191$	−11.1401	−0.806068	−0.403034	+	0.915185i	$0.632044\pi$
$192$	2.07470	0.149729
$193$	−14.2247	−1.02392	−0.511960	−	0.859009i	$-0.671080\pi$
$193$	−14.2247	−1.02392	−0.511960	+	0.859009i	$0.671080\pi$
$194$	10.5612	0.758251
$195$	5.43546	0.389241
$196$	−1.92200	−0.137286
$197$	9.63508	0.686471	0.343236	−	0.939249i	$-0.388477\pi$
$197$	9.63508	0.686471	0.343236	+	0.939249i	$0.388477\pi$
$198$	0.937321	0.0666125
$199$	22.2946	1.58042	0.790211	−	0.612835i	$-0.209971\pi$
$199$	22.2946	1.58042	0.790211	+	0.612835i	$0.209971\pi$
$200$	−14.1780	−1.00254
$201$	0.653132	0.0460684
$202$	4.69406	0.330273
$203$	10.4625	0.734321
$204$	−10.2366	−0.716705
$205$	−5.06012	−0.353414
$206$	−8.53797	−0.594869
$207$	−2.49067	−0.173113
$208$	0.598244	0.0414807
$209$	0.00692242	0.000478834 0
$210$	−20.4741	−1.41285
$211$	−3.89401	−0.268075	−0.134037	−	0.990976i	$-0.542794\pi$
$211$	−3.89401	−0.268075	−0.134037	+	0.990976i	$0.542794\pi$
$212$	−1.45053	−0.0996229
$213$	10.4528	0.716213
$214$	4.41210	0.301605
$215$	19.8775	1.35563
$216$	3.51788	0.239361
$217$	−9.08733	−0.616888
$218$	−12.2207	−0.827689
$219$	−23.0790	−1.55953
$220$	−3.14689	−0.212164
$221$	−2.95174	−0.198555
$222$	−14.6530	−0.983444
$223$	0.920418	0.0616357	0.0308179	−	0.999525i	$-0.490189\pi$
$223$	0.920418	0.0616357	0.0308179	+	0.999525i	$0.490189\pi$
$224$	−2.25344	−0.150564
$225$	18.4937	1.23292
$226$	−8.61050	−0.572762
$227$	−25.6007	−1.69917	−0.849587	−	0.527448i	$-0.823149\pi$
$227$	−25.6007	−1.69917	−0.849587	+	0.527448i	$0.823149\pi$
$228$	−0.0199864	−0.00132363
$229$	17.5700	1.16106	0.580529	−	0.814240i	$-0.302846\pi$
$229$	17.5700	1.16106	0.580529	+	0.814240i	$0.302846\pi$
$230$	8.36199	0.551373
$231$	−3.35956	−0.221043
$232$	−4.64289	−0.304820
$233$	−24.5675	−1.60947	−0.804736	−	0.593633i	$-0.797693\pi$
$233$	−24.5675	−1.60947	−0.804736	+	0.593633i	$0.797693\pi$
$234$	−0.780345	−0.0510128
$235$	5.82834	0.380199
$236$	−1.64570	−0.107126
$237$	−29.5458	−1.91920
$238$	11.1185	0.720704
$239$	−19.1325	−1.23758	−0.618789	−	0.785557i	$-0.712377\pi$
$239$	−19.1325	−1.23758	−0.618789	+	0.785557i	$0.712377\pi$
$240$	9.08569	0.586479
$241$	15.6232	1.00638	0.503189	−	0.864176i	$-0.332160\pi$
$241$	15.6232	1.00638	0.503189	+	0.864176i	$0.332160\pi$
$242$	10.4836	0.673913
$243$	−12.7074	−0.815179
$244$	1.92803	0.123429
$245$	−8.41698	−0.537741
$246$	2.39726	0.152844
$247$	−0.00576310	−0.000366697 0
$248$	4.03264	0.256073
$249$	−11.0445	−0.699919
$250$	−40.1931	−2.54204
$251$	20.3543	1.28475	0.642376	−	0.766389i	$-0.277949\pi$
$251$	20.3543	1.28475	0.642376	+	0.766389i	$0.277949\pi$
$252$	2.93937	0.185163
$253$	1.37211	0.0862635
$254$	−1.10137	−0.0691062
$255$	−44.8288	−2.80729
$256$	1.00000	0.0625000
$257$	18.5186	1.15516	0.577580	−	0.816334i	$-0.303997\pi$
$257$	18.5186	1.15516	0.577580	+	0.816334i	$0.303997\pi$
$258$	−9.41705	−0.586280
$259$	15.9154	0.988932
$260$	2.61987	0.162478
$261$	6.05615	0.374866
$262$	21.8069	1.34724
$263$	11.1885	0.689916	0.344958	−	0.938618i	$-0.387893\pi$
$263$	11.1885	0.689916	0.344958	+	0.938618i	$0.387893\pi$
$264$	1.49086	0.0917559
$265$	−6.35228	−0.390217
$266$	0.0217082	0.00133102
$267$	−11.4615	−0.701434
$268$	0.314808	0.0192299
$269$	−6.32919	−0.385898	−0.192949	−	0.981209i	$-0.561805\pi$
$269$	−6.32919	−0.385898	−0.192949	+	0.981209i	$0.561805\pi$
$270$	15.4058	0.937565
$271$	−21.8326	−1.32623	−0.663117	−	0.748516i	$-0.730767\pi$
$271$	−21.8326	−1.32623	−0.663117	+	0.748516i	$0.730767\pi$
$272$	−4.93400	−0.299168
$273$	2.79692	0.169277
$274$	1.35765	0.0820186
$275$	−10.1882	−0.614370
$276$	−3.96153	−0.238456
$277$	3.28443	0.197343	0.0986713	−	0.995120i	$-0.468541\pi$
$277$	3.28443	0.197343	0.0986713	+	0.995120i	$0.468541\pi$
$278$	−2.64515	−0.158645
$279$	−5.26015	−0.314917
$280$	−9.86843	−0.589752
$281$	11.9869	0.715081	0.357541	−	0.933898i	$-0.383615\pi$
$281$	11.9869	0.715081	0.357541	+	0.933898i	$0.383615\pi$
$282$	−2.76121	−0.164427
$283$	12.7174	0.755972	0.377986	−	0.925811i	$-0.376617\pi$
$283$	12.7174	0.755972	0.377986	+	0.925811i	$0.376617\pi$
$284$	5.03821	0.298963
$285$	−0.0875257	−0.00518458
$286$	0.429891	0.0254200
$287$	−2.60378	−0.153696
$288$	−1.30439	−0.0768621
$289$	7.34437	0.432022
$290$	−20.3325	−1.19396
$291$	−21.9114	−1.28447
$292$	−11.1240	−0.650983
$293$	−1.41280	−0.0825367	−0.0412683	−	0.999148i	$-0.513140\pi$
$293$	−1.41280	−0.0825367	−0.0412683	+	0.999148i	$0.513140\pi$
$294$	3.98759	0.232561
$295$	−7.20698	−0.419606
$296$	−7.06269	−0.410511
$297$	2.52791	0.146684
$298$	−13.8739	−0.803695
$299$	−1.14231	−0.0660617
$300$	29.4152	1.69829
$301$	10.2283	0.589551
$302$	−14.5396	−0.836660
$303$	−9.73878	−0.559478
$304$	−0.00963336	−0.000552511 0
$305$	8.44336	0.483465
$306$	6.43588	0.367915
$307$	−2.92797	−0.167108	−0.0835540	−	0.996503i	$-0.526627\pi$
$307$	−2.92797	−0.167108	−0.0835540	+	0.996503i	$0.526627\pi$
$308$	−1.61930	−0.0922679
$309$	17.7138	1.00770
$310$	17.6601	1.00302
$311$	−13.2397	−0.750753	−0.375377	−	0.926872i	$-0.622487\pi$
$311$	−13.2397	−0.750753	−0.375377	+	0.926872i	$0.622487\pi$
$312$	−1.24118	−0.0702679
$313$	31.8373	1.79955	0.899775	−	0.436354i	$-0.143731\pi$
$313$	31.8373	1.79955	0.899775	+	0.436354i	$0.143731\pi$
$314$	−21.6271	−1.22049
$315$	12.8723	0.725273
$316$	−14.2410	−0.801117
$317$	−19.2036	−1.07858	−0.539290	−	0.842120i	$-0.681307\pi$
$317$	−19.2036	−1.07858	−0.539290	+	0.842120i	$0.681307\pi$
$318$	3.00942	0.168760
$319$	−3.33632	−0.186798
$320$	4.37927	0.244809
$321$	−9.15381	−0.510916
$322$	4.30282	0.239787
$323$	0.0475310	0.00264470
$324$	−11.2117	−0.622874
$325$	8.48192	0.470492
$326$	12.9832	0.719075
$327$	25.3543	1.40210
$328$	1.15547	0.0638002
$329$	2.99909	0.165345
$330$	6.52887	0.359402
$331$	4.37995	0.240744	0.120372	−	0.992729i	$-0.461591\pi$
$331$	4.37995	0.240744	0.120372	+	0.992729i	$0.461591\pi$
$332$	−5.32343	−0.292161
$333$	9.21252	0.504843
$334$	5.86426	0.320878
$335$	1.37863	0.0753225
$336$	4.67522	0.255054
$337$	−14.7910	−0.805718	−0.402859	−	0.915262i	$-0.631983\pi$
$337$	−14.7910	−0.805718	−0.402859	+	0.915262i	$0.631983\pi$
$338$	12.6421	0.687640
$339$	17.8642	0.970252
$340$	−21.6073	−1.17182
$341$	2.89781	0.156925
$342$	0.0125657	0.000679474 0
$343$	−20.1052	−1.08558
$344$	−4.53899	−0.244726
$345$	−17.3486	−0.934019
$346$	13.6486	0.733755
$347$	8.35747	0.448652	0.224326	−	0.974514i	$-0.427982\pi$
$347$	8.35747	0.448652	0.224326	+	0.974514i	$0.427982\pi$
$348$	9.63261	0.516362
$349$	11.6907	0.625791	0.312895	−	0.949788i	$-0.398701\pi$
$349$	11.6907	0.625791	0.312895	+	0.949788i	$0.398701\pi$
$350$	−31.9494	−1.70777
$351$	−2.10455	−0.112333
$352$	0.718588	0.0383009
$353$	−15.6442	−0.832656	−0.416328	−	0.909215i	$-0.636683\pi$
$353$	−15.6442	−0.832656	−0.416328	+	0.909215i	$0.636683\pi$
$354$	3.41434	0.181470
$355$	22.0637	1.17102
$356$	−5.52442	−0.292793
$357$	−23.0675	−1.22086
$358$	−7.53295	−0.398129
$359$	2.65745	0.140255	0.0701273	−	0.997538i	$-0.477659\pi$
$359$	2.65745	0.140255	0.0701273	+	0.997538i	$0.477659\pi$
$360$	−5.71229	−0.301064
$361$	−18.9999	−0.999995
$362$	−15.7092	−0.825656
$363$	−21.7504	−1.14160
$364$	1.34811	0.0706600
$365$	−48.7151	−2.54986
$366$	−4.00008	−0.209088
$367$	12.6650	0.661109	0.330555	−	0.943787i	$-0.392764\pi$
$367$	12.6650	0.661109	0.330555	+	0.943787i	$0.392764\pi$
$368$	−1.90945	−0.0995368
$369$	−1.50719	−0.0784610
$370$	−30.9295	−1.60795
$371$	−3.26869	−0.169702
$372$	−8.36654	−0.433785
$373$	−0.715685	−0.0370568	−0.0185284	−	0.999828i	$-0.505898\pi$
$373$	−0.715685	−0.0370568	−0.0185284	+	0.999828i	$0.505898\pi$
$374$	−3.54551	−0.183334
$375$	83.3888	4.30618
$376$	−1.33089	−0.0686355
$377$	2.77758	0.143053
$378$	7.92734	0.407738
$379$	−27.9122	−1.43375	−0.716876	−	0.697201i	$-0.754429\pi$
$379$	−27.9122	−1.43375	−0.716876	+	0.697201i	$0.754429\pi$
$380$	−0.0421871	−0.00216415
$381$	2.28502	0.117065
$382$	11.1401	0.569976
$383$	−38.5323	−1.96891	−0.984454	−	0.175641i	$-0.943800\pi$
$383$	−38.5323	−1.96891	−0.984454	+	0.175641i	$0.943800\pi$
$384$	−2.07470	−0.105874
$385$	−7.09134	−0.361408
$386$	14.2247	0.724021
$387$	5.92062	0.300962
$388$	−10.5612	−0.536164
$389$	−14.6741	−0.744004	−0.372002	−	0.928232i	$-0.621329\pi$
$389$	−14.6741	−0.744004	−0.372002	+	0.928232i	$0.621329\pi$
$390$	−5.43546	−0.275235
$391$	9.42121	0.476451
$392$	1.92200	0.0970759
$393$	−45.2429	−2.28220
$394$	−9.63508	−0.485409
$395$	−62.3651	−3.13793
$396$	−0.937321	−0.0471022
$397$	21.4075	1.07441	0.537205	−	0.843451i	$-0.319480\pi$
$397$	21.4075	1.07441	0.537205	+	0.843451i	$0.319480\pi$
$398$	−22.2946	−1.11753
$399$	−0.0450381	−0.00225472
$400$	14.1780	0.708902
$401$	−7.58417	−0.378735	−0.189368	−	0.981906i	$-0.560644\pi$
$401$	−7.58417	−0.378735	−0.189368	+	0.981906i	$0.560644\pi$
$402$	−0.653132	−0.0325753
$403$	−2.41250	−0.120175
$404$	−4.69406	−0.233538
$405$	−49.0993	−2.43976
$406$	−10.4625	−0.519244
$407$	−5.07517	−0.251567
$408$	10.2366	0.506787
$409$	30.5977	1.51296	0.756480	−	0.654017i	$-0.226918\pi$
$409$	30.5977	1.51296	0.756480	+	0.654017i	$0.226918\pi$
$410$	5.06012	0.249901
$411$	−2.81672	−0.138939
$412$	8.53797	0.420636
$413$	−3.70849	−0.182483
$414$	2.49067	0.122410
$415$	−23.3128	−1.14438
$416$	−0.598244	−0.0293313
$417$	5.48790	0.268744
$418$	−0.00692242	−0.000338586 0
$419$	19.6983	0.962324	0.481162	−	0.876632i	$-0.340215\pi$
$419$	19.6983	0.962324	0.481162	+	0.876632i	$0.340215\pi$
$420$	20.4741	0.999032
$421$	33.5526	1.63525	0.817626	−	0.575750i	$-0.195290\pi$
$421$	33.5526	1.63525	0.817626	+	0.575750i	$0.195290\pi$
$422$	3.89401	0.189557
$423$	1.73601	0.0844076
$424$	1.45053	0.0704441
$425$	−69.9545	−3.39329
$426$	−10.4528	−0.506439
$427$	4.34470	0.210255
$428$	−4.41210	−0.213267
$429$	−0.891896	−0.0430611
$430$	−19.8775	−0.958576
$431$	−34.0450	−1.63989	−0.819946	−	0.572441i	$-0.805997\pi$
$431$	−34.0450	−1.63989	−0.819946	+	0.572441i	$0.805997\pi$
$432$	−3.51788	−0.169254
$433$	0.953744	0.0458340	0.0229170	−	0.999737i	$-0.492705\pi$
$433$	0.953744	0.0458340	0.0229170	+	0.999737i	$0.492705\pi$
$434$	9.08733	0.436206
$435$	42.1838	2.02256
$436$	12.2207	0.585265
$437$	0.0183944	0.000879923 0
$438$	23.0790	1.10276
$439$	−8.41109	−0.401439	−0.200720	−	0.979649i	$-0.564328\pi$
$439$	−8.41109	−0.401439	−0.200720	+	0.979649i	$0.564328\pi$
$440$	3.14689	0.150022
$441$	−2.50705	−0.119383
$442$	2.95174	0.140400
$443$	35.9440	1.70775	0.853876	−	0.520476i	$-0.174246\pi$
$443$	35.9440	1.70775	0.853876	+	0.520476i	$0.174246\pi$
$444$	14.6530	0.695400
$445$	−24.1929	−1.14685
$446$	−0.920418	−0.0435830
$447$	28.7843	1.36145
$448$	2.25344	0.106465
$449$	−3.54951	−0.167512	−0.0837560	−	0.996486i	$-0.526692\pi$
$449$	−3.54951	−0.167512	−0.0837560	+	0.996486i	$0.526692\pi$
$450$	−18.4937	−0.871803
$451$	0.830307	0.0390976
$452$	8.61050	0.405004
$453$	30.1653	1.41729
$454$	25.6007	1.20150
$455$	5.90373	0.276771
$456$	0.0199864	0.000935947 0
$457$	3.66407	0.171398	0.0856989	−	0.996321i	$-0.472688\pi$
$457$	3.66407	0.171398	0.0856989	+	0.996321i	$0.472688\pi$
$458$	−17.5700	−0.820991
$459$	17.3572	0.810166
$460$	−8.36199	−0.389880
$461$	−26.3248	−1.22607	−0.613033	−	0.790057i	$-0.710051\pi$
$461$	−26.3248	−1.22607	−0.613033	+	0.790057i	$0.710051\pi$
$462$	3.35956	0.156301
$463$	−35.7955	−1.66356	−0.831779	−	0.555107i	$-0.812677\pi$
$463$	−35.7955	−1.66356	−0.831779	+	0.555107i	$0.812677\pi$
$464$	4.64289	0.215541
$465$	−36.6394	−1.69911
$466$	24.5675	1.13807
$467$	40.0340	1.85255	0.926276	−	0.376845i	$-0.122991\pi$
$467$	40.0340	1.85255	0.926276	+	0.376845i	$0.122991\pi$
$468$	0.780345	0.0360715
$469$	0.709400	0.0327571
$470$	−5.82834	−0.268841
$471$	44.8698	2.06749
$472$	1.64570	0.0757496
$473$	−3.26166	−0.149971
$474$	29.5458	1.35708
$475$	−0.136582	−0.00626682
$476$	−11.1185	−0.509615
$477$	−1.89206	−0.0866316
$478$	19.1325	0.875100
$479$	−31.3226	−1.43116	−0.715582	−	0.698528i	$-0.753839\pi$
$479$	−31.3226	−1.43116	−0.715582	+	0.698528i	$0.753839\pi$
$480$	−9.08569	−0.414703
$481$	4.22521	0.192653
$482$	−15.6232	−0.711617
$483$	−8.92708	−0.406196
$484$	−10.4836	−0.476529
$485$	−46.2504	−2.10012
$486$	12.7074	0.576419
$487$	26.9937	1.22320	0.611601	−	0.791166i	$-0.290526\pi$
$487$	26.9937	1.22320	0.611601	+	0.791166i	$0.290526\pi$
$488$	−1.92803	−0.0872777
$489$	−26.9364	−1.21810
$490$	8.41698	0.380241
$491$	−27.4761	−1.23998	−0.619990	−	0.784609i	$-0.712864\pi$
$491$	−27.4761	−1.23998	−0.619990	+	0.784609i	$0.712864\pi$
$492$	−2.39726	−0.108077
$493$	−22.9080	−1.03172
$494$	0.00576310	0.000259294 0
$495$	−4.10479	−0.184496
$496$	−4.03264	−0.181071
$497$	11.3533	0.509266
$498$	11.0445	0.494918
$499$	1.07787	0.0482523	0.0241261	−	0.999709i	$-0.492320\pi$
$499$	1.07787	0.0482523	0.0241261	+	0.999709i	$0.492320\pi$
$500$	40.1931	1.79749
$501$	−12.1666	−0.543563
$502$	−20.3543	−0.908457
$503$	−10.7370	−0.478737	−0.239369	−	0.970929i	$-0.576940\pi$
$503$	−10.7370	−0.478737	−0.239369	+	0.970929i	$0.576940\pi$
$504$	−2.93937	−0.130930
$505$	−20.5566	−0.914755
$506$	−1.37211	−0.0609975
$507$	−26.2286	−1.16485
$508$	1.10137	0.0488655
$509$	21.0456	0.932828	0.466414	−	0.884566i	$-0.345546\pi$
$509$	21.0456	0.932828	0.466414	+	0.884566i	$0.345546\pi$
$510$	44.8288	1.98505
$511$	−25.0673	−1.10891
$512$	−1.00000	−0.0441942
$513$	0.0338890	0.00149624
$514$	−18.5186	−0.816822
$515$	37.3901	1.64761
$516$	9.41705	0.414562
$517$	−0.956364	−0.0420608
$518$	−15.9154	−0.699281
$519$	−28.3169	−1.24297
$520$	−2.61987	−0.114889
$521$	−8.81963	−0.386395	−0.193198	−	0.981160i	$-0.561886\pi$
$521$	−8.81963	−0.386395	−0.193198	+	0.981160i	$0.561886\pi$
$522$	−6.05615	−0.265070
$523$	−43.1332	−1.88608	−0.943042	−	0.332673i	$-0.892049\pi$
$523$	−43.1332	−1.88608	−0.943042	+	0.332673i	$0.892049\pi$
$524$	−21.8069	−0.952639
$525$	66.2854	2.89293
$526$	−11.1885	−0.487844
$527$	19.8971	0.866730
$528$	−1.49086	−0.0648812
$529$	−19.3540	−0.841479
$530$	6.35228	0.275925
$531$	−2.14664	−0.0931563
$532$	−0.0217082	−0.000941170 0
$533$	−0.691253	−0.0299415
$534$	11.4615	0.495989
$535$	−19.3218	−0.835355
$536$	−0.314808	−0.0135976
$537$	15.6286	0.674425
$538$	6.32919	0.272871
$539$	1.38113	0.0594895
$540$	−15.4058	−0.662958
$541$	33.4774	1.43931	0.719653	−	0.694334i	$-0.244301\pi$
$541$	33.4774	1.43931	0.719653	+	0.694334i	$0.244301\pi$
$542$	21.8326	0.937788
$543$	32.5919	1.39865
$544$	4.93400	0.211544
$545$	53.5177	2.29245
$546$	−2.79692	−0.119697
$547$	29.2927	1.25247	0.626233	−	0.779636i	$-0.284596\pi$
$547$	29.2927	1.25247	0.626233	+	0.779636i	$0.284596\pi$
$548$	−1.35765	−0.0579959
$549$	2.51491	0.107334
$550$	10.1882	0.434425
$551$	−0.0447266	−0.00190542
$552$	3.96153	0.168614
$553$	−32.0912	−1.36466
$554$	−3.28443	−0.139542
$555$	64.1694	2.72384
$556$	2.64515	0.112179
$557$	19.5876	0.829955	0.414977	−	0.909832i	$-0.363789\pi$
$557$	19.5876	0.829955	0.414977	+	0.909832i	$0.363789\pi$
$558$	5.26015	0.222680
$559$	2.71542	0.114850
$560$	9.86843	0.417017
$561$	7.35589	0.310566
$562$	−11.9869	−0.505639
$563$	−11.0023	−0.463691	−0.231845	−	0.972753i	$-0.574476\pi$
$563$	−11.0023	−0.463691	−0.231845	+	0.972753i	$0.574476\pi$
$564$	2.76121	0.116268
$565$	37.7077	1.58638
$566$	−12.7174	−0.534553
$567$	−25.2650	−1.06103
$568$	−5.03821	−0.211399
$569$	30.8363	1.29273	0.646363	−	0.763030i	$-0.276289\pi$
$569$	30.8363	1.29273	0.646363	+	0.763030i	$0.276289\pi$
$570$	0.0875257	0.00366605
$571$	24.3796	1.02026	0.510128	−	0.860098i	$-0.329598\pi$
$571$	24.3796	1.02026	0.510128	+	0.860098i	$0.329598\pi$
$572$	−0.429891	−0.0179746
$573$	−23.1124	−0.965533
$574$	2.60378	0.108680
$575$	−27.0722	−1.12899
$576$	1.30439	0.0543497
$577$	−20.9489	−0.872115	−0.436057	−	0.899919i	$-0.643626\pi$
$577$	−20.9489	−0.872115	−0.436057	+	0.899919i	$0.643626\pi$
$578$	−7.34437	−0.305486
$579$	−29.5121	−1.22648
$580$	20.3325	0.844260
$581$	−11.9960	−0.497680
$582$	21.9114	0.908256
$583$	1.04233	0.0431691
$584$	11.1240	0.460315
$585$	3.41734	0.141290
$586$	1.41280	0.0583622
$587$	29.5155	1.21823	0.609117	−	0.793081i	$-0.291524\pi$
$587$	29.5155	1.21823	0.609117	+	0.793081i	$0.291524\pi$
$588$	−3.98759	−0.164445
$589$	0.0388479	0.00160070
$590$	7.20698	0.296707
$591$	19.9899	0.822276
$592$	7.06269	0.290275
$593$	31.4058	1.28968	0.644841	−	0.764316i	$-0.276923\pi$
$593$	31.4058	1.28968	0.644841	+	0.764316i	$0.276923\pi$
$594$	−2.52791	−0.103721
$595$	−48.6909	−1.99613
$596$	13.8739	0.568298
$597$	46.2546	1.89308
$598$	1.14231	0.0467127
$599$	6.57505	0.268649	0.134325	−	0.990937i	$-0.457114\pi$
$599$	6.57505	0.268649	0.134325	+	0.990937i	$0.457114\pi$
$600$	−29.4152	−1.20087
$601$	8.86517	0.361618	0.180809	−	0.983518i	$-0.442128\pi$
$601$	8.86517	0.361618	0.180809	+	0.983518i	$0.442128\pi$
$602$	−10.2283	−0.416876
$603$	0.410633	0.0167223
$604$	14.5396	0.591608
$605$	−45.9107	−1.86653
$606$	9.73878	0.395611
$607$	−7.17752	−0.291326	−0.145663	−	0.989334i	$-0.546532\pi$
$607$	−7.17752	−0.291326	−0.145663	+	0.989334i	$0.546532\pi$
$608$	0.00963336	0.000390684 0
$609$	21.7065	0.879592
$610$	−8.44336	−0.341862
$611$	0.796198	0.0322107
$612$	−6.43588	−0.260155
$613$	23.4971	0.949037	0.474518	−	0.880246i	$-0.342622\pi$
$613$	23.4971	0.949037	0.474518	+	0.880246i	$0.342622\pi$
$614$	2.92797	0.118163
$615$	−10.4982	−0.423330
$616$	1.61930	0.0652433
$617$	−30.2547	−1.21801	−0.609005	−	0.793166i	$-0.708431\pi$
$617$	−30.2547	−1.21801	−0.609005	+	0.793166i	$0.708431\pi$
$618$	−17.7138	−0.712552
$619$	16.0077	0.643406	0.321703	−	0.946841i	$-0.395745\pi$
$619$	16.0077	0.643406	0.321703	+	0.946841i	$0.395745\pi$
$620$	−17.6601	−0.709245
$621$	6.71720	0.269552
$622$	13.2397	0.530863
$623$	−12.4489	−0.498756
$624$	1.24118	0.0496869
$625$	105.127	4.20506
$626$	−31.8373	−1.27247
$627$	0.0143620	0.000573561 0
$628$	21.6271	0.863015
$629$	−34.8473	−1.38945
$630$	−12.8723	−0.512845
$631$	−3.36011	−0.133764	−0.0668819	−	0.997761i	$-0.521305\pi$
$631$	−3.36011	−0.133764	−0.0668819	+	0.997761i	$0.521305\pi$
$632$	14.2410	0.566475
$633$	−8.07891	−0.321108
$634$	19.2036	0.762672
$635$	4.82321	0.191403
$636$	−3.00942	−0.119331
$637$	−1.14983	−0.0455578
$638$	3.33632	0.132086
$639$	6.57181	0.259977
$640$	−4.37927	−0.173106
$641$	9.25812	0.365674	0.182837	−	0.983143i	$-0.441472\pi$
$641$	9.25812	0.365674	0.182837	+	0.983143i	$0.441472\pi$
$642$	9.15381	0.361272
$643$	2.17362	0.0857193	0.0428597	−	0.999081i	$-0.486353\pi$
$643$	2.17362	0.0857193	0.0428597	+	0.999081i	$0.486353\pi$
$644$	−4.30282	−0.169555
$645$	41.2398	1.62382
$646$	−0.0475310	−0.00187008
$647$	10.5595	0.415137	0.207568	−	0.978221i	$-0.433445\pi$
$647$	10.5595	0.415137	0.207568	+	0.978221i	$0.433445\pi$
$648$	11.2117	0.440439
$649$	1.18258	0.0464204
$650$	−8.48192	−0.332688
$651$	−18.8535	−0.738927
$652$	−12.9832	−0.508463
$653$	14.5577	0.569686	0.284843	−	0.958574i	$-0.408059\pi$
$653$	14.5577	0.569686	0.284843	+	0.958574i	$0.408059\pi$
$654$	−25.3543	−0.991431
$655$	−95.4984	−3.73143
$656$	−1.15547	−0.0451135
$657$	−14.5101	−0.566092
$658$	−2.99909	−0.116917
$659$	−31.1153	−1.21208	−0.606041	−	0.795433i	$-0.707243\pi$
$659$	−31.1153	−1.21208	−0.606041	+	0.795433i	$0.707243\pi$
$660$	−6.52887	−0.254136
$661$	35.4105	1.37731	0.688655	−	0.725089i	$-0.258202\pi$
$661$	35.4105	1.37731	0.688655	+	0.725089i	$0.258202\pi$
$662$	−4.37995	−0.170232
$663$	−6.12398	−0.237836
$664$	5.32343	0.206589
$665$	−0.0950662	−0.00368651
$666$	−9.21252	−0.356978
$667$	−8.86534	−0.343267
$668$	−5.86426	−0.226895
$669$	1.90959	0.0738292
$670$	−1.37863	−0.0532611
$671$	−1.38546	−0.0534850
$672$	−4.67522	−0.180351
$673$	17.4900	0.674190	0.337095	−	0.941471i	$-0.390556\pi$
$673$	17.4900	0.674190	0.337095	+	0.941471i	$0.390556\pi$
$674$	14.7910	0.569728
$675$	−49.8766	−1.91975
$676$	−12.6421	−0.486235
$677$	−12.0050	−0.461391	−0.230696	−	0.973026i	$-0.574100\pi$
$677$	−12.0050	−0.461391	−0.230696	+	0.973026i	$0.574100\pi$
$678$	−17.8642	−0.686072
$679$	−23.7991	−0.913324
$680$	21.6073	0.828604
$681$	−53.1138	−2.03532
$682$	−2.89781	−0.110963
$683$	26.4744	1.01302	0.506508	−	0.862236i	$-0.330936\pi$
$683$	26.4744	1.01302	0.506508	+	0.862236i	$0.330936\pi$
$684$	−0.0125657	−0.000480461 0
$685$	−5.94552	−0.227167
$686$	20.1052	0.767620
$687$	36.4525	1.39075
$688$	4.53899	0.173047
$689$	−0.867772	−0.0330595
$690$	17.3486	0.660451
$691$	10.5907	0.402888	0.201444	−	0.979500i	$-0.435437\pi$
$691$	10.5907	0.402888	0.201444	+	0.979500i	$0.435437\pi$
$692$	−13.6486	−0.518843
$693$	−2.11220	−0.0802358
$694$	−8.35747	−0.317245
$695$	11.5838	0.439400
$696$	−9.63261	−0.365123
$697$	5.70109	0.215944
$698$	−11.6907	−0.442501
$699$	−50.9703	−1.92787
$700$	31.9494	1.20757
$701$	38.4231	1.45122	0.725611	−	0.688106i	$-0.241557\pi$
$701$	38.4231	1.45122	0.725611	+	0.688106i	$0.241557\pi$
$702$	2.10455	0.0794311
$703$	−0.0680374	−0.00256608
$704$	−0.718588	−0.0270828
$705$	12.0921	0.455414
$706$	15.6442	0.588777
$707$	−10.5778	−0.397818
$708$	−3.41434	−0.128319
$709$	−20.8395	−0.782645	−0.391322	−	0.920254i	$-0.627982\pi$
$709$	−20.8395	−0.782645	−0.391322	+	0.920254i	$0.627982\pi$
$710$	−22.0637	−0.828036
$711$	−18.5758	−0.696647
$712$	5.52442	0.207036
$713$	7.70012	0.288372
$714$	23.0675	0.863281
$715$	−1.88261	−0.0704056
$716$	7.53295	0.281520
$717$	−39.6943	−1.48241
$718$	−2.65745	−0.0991750
$719$	−39.3183	−1.46632	−0.733162	−	0.680054i	$-0.761956\pi$
$719$	−39.3183	−1.46632	−0.733162	+	0.680054i	$0.761956\pi$
$720$	5.71229	0.212885
$721$	19.2398	0.716528
$722$	18.9999	0.707103
$723$	32.4135	1.20547
$724$	15.7092	0.583827
$725$	65.8270	2.44475
$726$	21.7504	0.807234
$727$	26.2045	0.971871	0.485935	−	0.873995i	$-0.338479\pi$
$727$	26.2045	0.971871	0.485935	+	0.873995i	$0.338479\pi$
$728$	−1.34811	−0.0499642
$729$	7.27116	0.269302
$730$	48.7151	1.80303
$731$	−22.3954	−0.828322
$732$	4.00008	0.147847
$733$	47.8046	1.76570	0.882852	−	0.469651i	$-0.155620\pi$
$733$	47.8046	1.76570	0.882852	+	0.469651i	$0.155620\pi$
$734$	−12.6650	−0.467475
$735$	−17.4627	−0.644123
$736$	1.90945	0.0703831
$737$	−0.226217	−0.00833281
$738$	1.50719	0.0554803
$739$	−16.2107	−0.596319	−0.298160	−	0.954516i	$-0.596373\pi$
$739$	−16.2107	−0.596319	−0.298160	+	0.954516i	$0.596373\pi$
$740$	30.9295	1.13699
$741$	−0.0119567	−0.000439241 0
$742$	3.26869	0.119997
$743$	−12.1662	−0.446334	−0.223167	−	0.974780i	$-0.571640\pi$
$743$	−12.1662	−0.446334	−0.223167	+	0.974780i	$0.571640\pi$
$744$	8.36654	0.306732
$745$	60.7577	2.22599
$746$	0.715685	0.0262031
$747$	−6.94385	−0.254062
$748$	3.54551	0.129637
$749$	−9.94242	−0.363288
$750$	−83.3888	−3.04493
$751$	1.00000	0.0364905
$751$	1.00000	0.0364905
$752$	1.33089	0.0485327
$753$	42.2292	1.53892
$754$	−2.77758	−0.101153
$755$	63.6729	2.31729
$756$	−7.92734	−0.288314
$757$	−1.11982	−0.0407007	−0.0203503	−	0.999793i	$-0.506478\pi$
$757$	−1.11982	−0.0407007	−0.0203503	+	0.999793i	$0.506478\pi$
$758$	27.9122	1.01382
$759$	2.84671	0.103329
$760$	0.0421871	0.00153029
$761$	−37.1289	−1.34592	−0.672961	−	0.739678i	$-0.734978\pi$
$761$	−37.1289	−1.34592	−0.672961	+	0.739678i	$0.734978\pi$
$762$	−2.28502	−0.0827775
$763$	27.5386	0.996964
$764$	−11.1401	−0.403034
$765$	−28.1845	−1.01901
$766$	38.5323	1.39223
$767$	−0.984531	−0.0355493
$768$	2.07470	0.0748644
$769$	−6.75944	−0.243751	−0.121876	−	0.992545i	$-0.538891\pi$
$769$	−6.75944	−0.243751	−0.121876	+	0.992545i	$0.538891\pi$
$770$	7.09134	0.255554
$771$	38.4207	1.38369
$772$	−14.2247	−0.511960
$773$	17.2654	0.620995	0.310497	−	0.950574i	$-0.399504\pi$
$773$	17.2654	0.620995	0.310497	+	0.950574i	$0.399504\pi$
$774$	−5.92062	−0.212812
$775$	−57.1750	−2.05379
$776$	10.5612	0.379125
$777$	33.0196	1.18457
$778$	14.6741	0.526090
$779$	0.0111311	0.000398811 0
$780$	5.43546	0.194621
$781$	−3.62040	−0.129548
$782$	−9.42121	−0.336902
$783$	−16.3331	−0.583698
$784$	−1.92200	−0.0686430
$785$	94.7110	3.38038
$786$	45.2429	1.61376
$787$	35.1226	1.25199	0.625993	−	0.779828i	$-0.284694\pi$
$787$	35.1226	1.25199	0.625993	+	0.779828i	$0.284694\pi$
$788$	9.63508	0.343236
$789$	23.2129	0.826402
$790$	62.3651	2.21885
$791$	19.4033	0.689900
$792$	0.937321	0.0333063
$793$	1.15343	0.0409595
$794$	−21.4075	−0.759723
$795$	−13.1791	−0.467414
$796$	22.2946	0.790211
$797$	42.7455	1.51412	0.757062	−	0.653343i	$-0.226634\pi$
$797$	42.7455	1.51412	0.757062	+	0.653343i	$0.226634\pi$
$798$	0.0450381	0.00159433
$799$	−6.56663	−0.232311
$800$	−14.1780	−0.501269
$801$	−7.20601	−0.254612
$802$	7.58417	0.267806
$803$	7.99358	0.282087
$804$	0.653132	0.0230342
$805$	−18.8432	−0.664137
$806$	2.41250	0.0849769
$807$	−13.1312	−0.462240
$808$	4.69406	0.165136
$809$	−4.10081	−0.144177	−0.0720883	−	0.997398i	$-0.522966\pi$
$809$	−4.10081	−0.144177	−0.0720883	+	0.997398i	$0.522966\pi$
$810$	49.0993	1.72517
$811$	19.2667	0.676545	0.338272	−	0.941048i	$-0.390157\pi$
$811$	19.2667	0.676545	0.338272	+	0.941048i	$0.390157\pi$
$812$	10.4625	0.367161
$813$	−45.2961	−1.58860
$814$	5.07517	0.177884
$815$	−56.8572	−1.99162
$816$	−10.2366	−0.358352
$817$	−0.0437257	−0.00152977
$818$	−30.5977	−1.06982
$819$	1.75846	0.0614456
$820$	−5.06012	−0.176707
$821$	−54.8551	−1.91446	−0.957228	−	0.289333i	$-0.906566\pi$
$821$	−54.8551	−1.91446	−0.957228	+	0.289333i	$0.906566\pi$
$822$	2.81672	0.0982444
$823$	−32.5351	−1.13410	−0.567052	−	0.823682i	$-0.691916\pi$
$823$	−32.5351	−1.13410	−0.567052	+	0.823682i	$0.691916\pi$
$824$	−8.53797	−0.297434
$825$	−21.1374	−0.735911
$826$	3.70849	0.129035
$827$	11.9341	0.414989	0.207494	−	0.978236i	$-0.433469\pi$
$827$	11.9341	0.414989	0.207494	+	0.978236i	$0.433469\pi$
$828$	−2.49067	−0.0865567
$829$	−38.4421	−1.33515	−0.667574	−	0.744543i	$-0.732667\pi$
$829$	−38.4421	−1.33515	−0.667574	+	0.744543i	$0.732667\pi$
$830$	23.3128	0.809198
$831$	6.81423	0.236383
$832$	0.598244	0.0207404
$833$	9.48317	0.328573
$834$	−5.48790	−0.190030
$835$	−25.6812	−0.888734
$836$	0.00692242	0.000239417 0
$837$	14.1864	0.490352
$838$	−19.6983	−0.680466
$839$	−52.3055	−1.80579	−0.902893	−	0.429865i	$-0.858561\pi$
$839$	−52.3055	−1.80579	−0.902893	+	0.429865i	$0.858561\pi$
$840$	−20.4741	−0.706423
$841$	−7.44361	−0.256676
$842$	−33.5526	−1.15630
$843$	24.8694	0.856546
$844$	−3.89401	−0.134037
$845$	−55.3632	−1.90455
$846$	−1.73601	−0.0596852
$847$	−23.6242	−0.811739
$848$	−1.45053	−0.0498115
$849$	26.3849	0.905527
$850$	69.9545	2.39942
$851$	−13.4858	−0.462288
$852$	10.4528	0.358107
$853$	29.5181	1.01068	0.505340	−	0.862920i	$-0.331367\pi$
$853$	29.5181	1.01068	0.505340	+	0.862920i	$0.331367\pi$
$854$	−4.34470	−0.148672
$855$	−0.0550286	−0.00188194
$856$	4.41210	0.150803
$857$	38.6314	1.31962	0.659811	−	0.751431i	$-0.270636\pi$
$857$	38.6314	1.31962	0.659811	+	0.751431i	$0.270636\pi$
$858$	0.891896	0.0304488
$859$	−33.9703	−1.15905	−0.579527	−	0.814953i	$-0.696762\pi$
$859$	−33.9703	−1.15905	−0.579527	+	0.814953i	$0.696762\pi$
$860$	19.8775	0.677816
$861$	−5.40208	−0.184102
$862$	34.0450	1.15958
$863$	−45.5192	−1.54949	−0.774745	−	0.632274i	$-0.782122\pi$
$863$	−45.5192	−1.54949	−0.774745	+	0.632274i	$0.782122\pi$
$864$	3.51788	0.119681
$865$	−59.7711	−2.03228
$866$	−0.953744	−0.0324095
$867$	15.2374	0.517489
$868$	−9.08733	−0.308444
$869$	10.2334	0.347144
$870$	−42.1838	−1.43017
$871$	0.188332	0.00638138
$872$	−12.2207	−0.413845
$873$	−13.7760	−0.466246
$874$	−0.0183944	−0.000622199 0
$875$	90.5728	3.06192
$876$	−23.0790	−0.779767
$877$	56.7841	1.91746	0.958732	−	0.284311i	$-0.0917649\pi$
$877$	56.7841	1.91746	0.958732	+	0.284311i	$0.0917649\pi$
$878$	8.41109	0.283861
$879$	−2.93114	−0.0988649
$880$	−3.14689	−0.106082
$881$	44.4919	1.49897	0.749486	−	0.662020i	$-0.230301\pi$
$881$	44.4919	1.49897	0.749486	+	0.662020i	$0.230301\pi$
$882$	2.50705	0.0844167
$883$	−0.195472	−0.00657815	−0.00328907	−	0.999995i	$-0.501047\pi$
$883$	−0.195472	−0.00657815	−0.00328907	+	0.999995i	$0.501047\pi$
$884$	−2.95174	−0.0992776
$885$	−14.9523	−0.502617
$886$	−35.9440	−1.20756
$887$	53.6735	1.80218	0.901089	−	0.433634i	$-0.142769\pi$
$887$	53.6735	1.80218	0.901089	+	0.433634i	$0.142769\pi$
$888$	−14.6530	−0.491722
$889$	2.48188	0.0832395
$890$	24.1929	0.810949
$891$	8.05662	0.269907
$892$	0.920418	0.0308179
$893$	−0.0128210	−0.000429037 0
$894$	−28.7843	−0.962690
$895$	32.9888	1.10270
$896$	−2.25344	−0.0752822
$897$	−2.36996	−0.0791308
$898$	3.54951	0.118449
$899$	−18.7231	−0.624451
$900$	18.4937	0.616458
$901$	7.15693	0.238432
$902$	−0.830307	−0.0276462
$903$	21.2208	0.706183
$904$	−8.61050	−0.286381
$905$	68.7948	2.28682
$906$	−30.1653	−1.00218
$907$	47.6152	1.58104	0.790519	−	0.612438i	$-0.209811\pi$
$907$	47.6152	1.58104	0.790519	+	0.612438i	$0.209811\pi$
$908$	−25.6007	−0.849587
$909$	−6.12290	−0.203084
$910$	−5.90373	−0.195707
$911$	45.3399	1.50218	0.751089	−	0.660201i	$-0.229529\pi$
$911$	45.3399	1.50218	0.751089	+	0.660201i	$0.229529\pi$
$912$	−0.0199864	−0.000661814 0
$913$	3.82536	0.126601
$914$	−3.66407	−0.121197
$915$	17.5175	0.579109
$916$	17.5700	0.580529
$917$	−49.1406	−1.62276
$918$	−17.3572	−0.572874
$919$	−41.9327	−1.38323	−0.691617	−	0.722265i	$-0.743101\pi$
$919$	−41.9327	−1.38323	−0.691617	+	0.722265i	$0.743101\pi$
$920$	8.36199	0.275687
$921$	−6.07467	−0.200167
$922$	26.3248	0.866960
$923$	3.01408	0.0992096
$924$	−3.35956	−0.110521
$925$	100.135	3.29242
$926$	35.7955	1.17631
$927$	11.1369	0.365783
$928$	−4.64289	−0.152410
$929$	−10.8384	−0.355596	−0.177798	−	0.984067i	$-0.556897\pi$
$929$	−10.8384	−0.355596	−0.177798	+	0.984067i	$0.556897\pi$
$930$	36.6394	1.20145
$931$	0.0185154	0.000606816 0
$932$	−24.5675	−0.804736
$933$	−27.4684	−0.899275
$934$	−40.0340	−1.30995
$935$	15.5268	0.507780
$936$	−0.780345	−0.0255064
$937$	31.3732	1.02492	0.512459	−	0.858712i	$-0.328735\pi$
$937$	31.3732	1.02492	0.512459	+	0.858712i	$0.328735\pi$
$938$	−0.709400	−0.0231627
$939$	66.0529	2.15556
$940$	5.82834	0.190100
$941$	36.7754	1.19885	0.599423	−	0.800433i	$-0.295397\pi$
$941$	36.7754	1.19885	0.599423	+	0.800433i	$0.295397\pi$
$942$	−44.8698	−1.46194
$943$	2.20631	0.0718473
$944$	−1.64570	−0.0535630
$945$	−34.7160	−1.12931
$946$	3.26166	0.106046
$947$	−14.2135	−0.461876	−0.230938	−	0.972968i	$-0.574179\pi$
$947$	−14.2135	−0.461876	−0.230938	+	0.972968i	$0.574179\pi$
$948$	−29.5458	−0.959602
$949$	−6.65487	−0.216026
$950$	0.136582	0.00443131
$951$	−39.8417	−1.29196
$952$	11.1185	0.360352
$953$	−6.51380	−0.211003	−0.105501	−	0.994419i	$-0.533645\pi$
$953$	−6.51380	−0.211003	−0.105501	+	0.994419i	$0.533645\pi$
$954$	1.89206	0.0612578
$955$	−48.7855	−1.57866
$956$	−19.1325	−0.618789
$957$	−6.92188	−0.223753
$958$	31.3226	1.01199
$959$	−3.05938	−0.0987926
$960$	9.08569	0.293239
$961$	−14.7378	−0.475412
$962$	−4.22521	−0.136226
$963$	−5.75512	−0.185456
$964$	15.6232	0.503189
$965$	−62.2941	−2.00532
$966$	8.92708	0.287224
$967$	−54.8007	−1.76227	−0.881136	−	0.472862i	$-0.843221\pi$
$967$	−54.8007	−1.76227	−0.881136	+	0.472862i	$0.843221\pi$
$968$	10.4836	0.336957
$969$	0.0986127	0.00316790
$970$	46.2504	1.48501
$971$	−31.4947	−1.01071	−0.505357	−	0.862911i	$-0.668639\pi$
$971$	−31.4947	−1.01071	−0.505357	+	0.862911i	$0.668639\pi$
$972$	−12.7074	−0.407590
$973$	5.96069	0.191091
$974$	−26.9937	−0.864934
$975$	17.5975	0.563570
$976$	1.92803	0.0617146
$977$	−46.9853	−1.50319	−0.751597	−	0.659623i	$-0.770716\pi$
$977$	−46.9853	−1.50319	−0.751597	+	0.659623i	$0.770716\pi$
$978$	26.9364	0.861330
$979$	3.96978	0.126875
$980$	−8.41698	−0.268871
$981$	15.9406	0.508944
$982$	27.4761	0.876799
$983$	6.40623	0.204327	0.102163	−	0.994768i	$-0.467424\pi$
$983$	6.40623	0.204327	0.102163	+	0.994768i	$0.467424\pi$
$984$	2.39726	0.0764218
$985$	42.1947	1.34443
$986$	22.9080	0.729539
$987$	6.22222	0.198055
$988$	−0.00576310	−0.000183349 0
$989$	−8.66695	−0.275593
$990$	4.10479	0.130459
$991$	18.5035	0.587783	0.293892	−	0.955839i	$-0.405050\pi$
$991$	18.5035	0.587783	0.293892	+	0.955839i	$0.405050\pi$
$992$	4.03264	0.128037
$993$	9.08709	0.288370
$994$	−11.3533	−0.360105
$995$	97.6341	3.09521
$996$	−11.0445	−0.349960
$997$	−38.3262	−1.21380	−0.606902	−	0.794777i	$-0.707588\pi$
$997$	−38.3262	−1.21380	−0.606902	+	0.794777i	$0.707588\pi$
$998$	−1.07787	−0.0341195
$999$	−24.8457	−0.786083

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1502.2.a.h.1.14	✓	19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1502.2.a.h.1.14	✓	19	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:	\( N \)	\(=\)	\( 1502 = 2 \cdot 751 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1502.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.07470 q^{3} +1.00000 q^{4} +4.37927 q^{5} -2.07470 q^{6} +2.25344 q^{7} -1.00000 q^{8} +1.30439 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.07470 q^{3} +1.00000 q^{4} +4.37927 q^{5} -2.07470 q^{6} +2.25344 q^{7} -1.00000 q^{8} +1.30439 q^{9} -4.37927 q^{10} -0.718588 q^{11} +2.07470 q^{12} +0.598244 q^{13} -2.25344 q^{14} +9.08569 q^{15} +1.00000 q^{16} -4.93400 q^{17} -1.30439 q^{18} -0.00963336 q^{19} +4.37927 q^{20} +4.67522 q^{21} +0.718588 q^{22} -1.90945 q^{23} -2.07470 q^{24} +14.1780 q^{25} -0.598244 q^{26} -3.51788 q^{27} +2.25344 q^{28} +4.64289 q^{29} -9.08569 q^{30} -4.03264 q^{31} -1.00000 q^{32} -1.49086 q^{33} +4.93400 q^{34} +9.86843 q^{35} +1.30439 q^{36} +7.06269 q^{37} +0.00963336 q^{38} +1.24118 q^{39} -4.37927 q^{40} -1.15547 q^{41} -4.67522 q^{42} +4.53899 q^{43} -0.718588 q^{44} +5.71229 q^{45} +1.90945 q^{46} +1.33089 q^{47} +2.07470 q^{48} -1.92200 q^{49} -14.1780 q^{50} -10.2366 q^{51} +0.598244 q^{52} -1.45053 q^{53} +3.51788 q^{54} -3.14689 q^{55} -2.25344 q^{56} -0.0199864 q^{57} -4.64289 q^{58} -1.64570 q^{59} +9.08569 q^{60} +1.92803 q^{61} +4.03264 q^{62} +2.93937 q^{63} +1.00000 q^{64} +2.61987 q^{65} +1.49086 q^{66} +0.314808 q^{67} -4.93400 q^{68} -3.96153 q^{69} -9.86843 q^{70} +5.03821 q^{71} -1.30439 q^{72} -11.1240 q^{73} -7.06269 q^{74} +29.4152 q^{75} -0.00963336 q^{76} -1.61930 q^{77} -1.24118 q^{78} -14.2410 q^{79} +4.37927 q^{80} -11.2117 q^{81} +1.15547 q^{82} -5.32343 q^{83} +4.67522 q^{84} -21.6073 q^{85} -4.53899 q^{86} +9.63261 q^{87} +0.718588 q^{88} -5.52442 q^{89} -5.71229 q^{90} +1.34811 q^{91} -1.90945 q^{92} -8.36654 q^{93} -1.33089 q^{94} -0.0421871 q^{95} -2.07470 q^{96} -10.5612 q^{97} +1.92200 q^{98} -0.937321 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q - 19 q^{2} + 6 q^{3} + 19 q^{4} + 2 q^{5} - 6 q^{6} + 13 q^{7} - 19 q^{8} + 25 q^{9}+O(q^{10}) \) 19 * q - 19 * q^2 + 6 * q^3 + 19 * q^4 + 2 * q^5 - 6 * q^6 + 13 * q^7 - 19 * q^8 + 25 * q^9	\( 19 q - 19 q^{2} + 6 q^{3} + 19 q^{4} + 2 q^{5} - 6 q^{6} + 13 q^{7} - 19 q^{8} + 25 q^{9} - 2 q^{10} - 7 q^{11} + 6 q^{12} + 19 q^{13} - 13 q^{14} + 6 q^{15} + 19 q^{16} + 11 q^{17} - 25 q^{18} + 7 q^{19} + 2 q^{20} + 7 q^{21} + 7 q^{22} + 12 q^{23} - 6 q^{24} + 37 q^{25} - 19 q^{26} + 24 q^{27} + 13 q^{28} - 8 q^{29} - 6 q^{30} + 32 q^{31} - 19 q^{32} + 24 q^{33} - 11 q^{34} - 19 q^{35} + 25 q^{36} + 41 q^{37} - 7 q^{38} - 2 q^{39} - 2 q^{40} + 15 q^{41} - 7 q^{42} + 15 q^{43} - 7 q^{44} + 28 q^{45} - 12 q^{46} - 6 q^{47} + 6 q^{48} + 42 q^{49} - 37 q^{50} + 8 q^{51} + 19 q^{52} + 6 q^{53} - 24 q^{54} + 22 q^{55} - 13 q^{56} + 24 q^{57} + 8 q^{58} - 4 q^{59} + 6 q^{60} + 13 q^{61} - 32 q^{62} + 37 q^{63} + 19 q^{64} + 20 q^{65} - 24 q^{66} + 47 q^{67} + 11 q^{68} + 15 q^{69} + 19 q^{70} - 25 q^{72} + 64 q^{73} - 41 q^{74} - 3 q^{75} + 7 q^{76} - 4 q^{77} + 2 q^{78} + 34 q^{79} + 2 q^{80} + 27 q^{81} - 15 q^{82} + 4 q^{83} + 7 q^{84} + 21 q^{85} - 15 q^{86} + 7 q^{88} + 18 q^{89} - 28 q^{90} + 28 q^{91} + 12 q^{92} + 43 q^{93} + 6 q^{94} - 8 q^{95} - 6 q^{96} + 82 q^{97} - 42 q^{98} - 2 q^{99}+O(q^{100}) \) 19 * q - 19 * q^2 + 6 * q^3 + 19 * q^4 + 2 * q^5 - 6 * q^6 + 13 * q^7 - 19 * q^8 + 25 * q^9 - 2 * q^10 - 7 * q^11 + 6 * q^12 + 19 * q^13 - 13 * q^14 + 6 * q^15 + 19 * q^16 + 11 * q^17 - 25 * q^18 + 7 * q^19 + 2 * q^20 + 7 * q^21 + 7 * q^22 + 12 * q^23 - 6 * q^24 + 37 * q^25 - 19 * q^26 + 24 * q^27 + 13 * q^28 - 8 * q^29 - 6 * q^30 + 32 * q^31 - 19 * q^32 + 24 * q^33 - 11 * q^34 - 19 * q^35 + 25 * q^36 + 41 * q^37 - 7 * q^38 - 2 * q^39 - 2 * q^40 + 15 * q^41 - 7 * q^42 + 15 * q^43 - 7 * q^44 + 28 * q^45 - 12 * q^46 - 6 * q^47 + 6 * q^48 + 42 * q^49 - 37 * q^50 + 8 * q^51 + 19 * q^52 + 6 * q^53 - 24 * q^54 + 22 * q^55 - 13 * q^56 + 24 * q^57 + 8 * q^58 - 4 * q^59 + 6 * q^60 + 13 * q^61 - 32 * q^62 + 37 * q^63 + 19 * q^64 + 20 * q^65 - 24 * q^66 + 47 * q^67 + 11 * q^68 + 15 * q^69 + 19 * q^70 - 25 * q^72 + 64 * q^73 - 41 * q^74 - 3 * q^75 + 7 * q^76 - 4 * q^77 + 2 * q^78 + 34 * q^79 + 2 * q^80 + 27 * q^81 - 15 * q^82 + 4 * q^83 + 7 * q^84 + 21 * q^85 - 15 * q^86 + 7 * q^88 + 18 * q^89 - 28 * q^90 + 28 * q^91 + 12 * q^92 + 43 * q^93 + 6 * q^94 - 8 * q^95 - 6 * q^96 + 82 * q^97 - 42 * q^98 - 2 * q^99

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