LMFDB - Embedded newform 4001.2.a.a.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4001,2,Mod(1,4001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4001, 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("4001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4001.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:	$31.9481458487$
Analytic rank:	$1$
Dimension:	$149$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	4001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.45256 q^{2} +0.529200 q^{3} +4.01507 q^{4} +2.50676 q^{5} -1.29790 q^{6} -0.602620 q^{7} -4.94208 q^{8} -2.71995 q^{9} +O(q^{10})$	\(q-2.45256 q^{2} +0.529200 q^{3} +4.01507 q^{4} +2.50676 q^{5} -1.29790 q^{6} -0.602620 q^{7} -4.94208 q^{8} -2.71995 q^{9} -6.14798 q^{10} +1.28953 q^{11} +2.12477 q^{12} -0.0840546 q^{13} +1.47796 q^{14} +1.32658 q^{15} +4.09063 q^{16} -6.64038 q^{17} +6.67084 q^{18} +1.18824 q^{19} +10.0648 q^{20} -0.318906 q^{21} -3.16265 q^{22} +1.20517 q^{23} -2.61535 q^{24} +1.28383 q^{25} +0.206149 q^{26} -3.02700 q^{27} -2.41956 q^{28} -2.21157 q^{29} -3.25351 q^{30} +3.29916 q^{31} -0.148365 q^{32} +0.682417 q^{33} +16.2859 q^{34} -1.51062 q^{35} -10.9208 q^{36} -6.83528 q^{37} -2.91422 q^{38} -0.0444817 q^{39} -12.3886 q^{40} +5.64435 q^{41} +0.782138 q^{42} +7.53358 q^{43} +5.17754 q^{44} -6.81825 q^{45} -2.95575 q^{46} +9.02679 q^{47} +2.16476 q^{48} -6.63685 q^{49} -3.14868 q^{50} -3.51409 q^{51} -0.337485 q^{52} +9.70487 q^{53} +7.42390 q^{54} +3.23253 q^{55} +2.97820 q^{56} +0.628814 q^{57} +5.42401 q^{58} -3.24115 q^{59} +5.32629 q^{60} -1.23812 q^{61} -8.09141 q^{62} +1.63909 q^{63} -7.81738 q^{64} -0.210704 q^{65} -1.67367 q^{66} +1.76820 q^{67} -26.6616 q^{68} +0.637774 q^{69} +3.70490 q^{70} -11.8657 q^{71} +13.4422 q^{72} +6.48172 q^{73} +16.7640 q^{74} +0.679403 q^{75} +4.77084 q^{76} -0.777095 q^{77} +0.109094 q^{78} -7.93098 q^{79} +10.2542 q^{80} +6.55796 q^{81} -13.8431 q^{82} -9.68320 q^{83} -1.28043 q^{84} -16.6458 q^{85} -18.4766 q^{86} -1.17036 q^{87} -6.37294 q^{88} -8.35044 q^{89} +16.7222 q^{90} +0.0506530 q^{91} +4.83882 q^{92} +1.74592 q^{93} -22.1388 q^{94} +2.97862 q^{95} -0.0785145 q^{96} -5.76190 q^{97} +16.2773 q^{98} -3.50745 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 149 q - 6 q^{2} - 28 q^{3} + 116 q^{4} - 19 q^{5} - 31 q^{6} - 47 q^{7} - 15 q^{8} + 115 q^{9}+O(q^{10}) $ 149 * q - 6 * q^2 - 28 * q^3 + 116 * q^4 - 19 * q^5 - 31 * q^6 - 47 * q^7 - 15 * q^8 + 115 * q^9	\( 149 q - 6 q^{2} - 28 q^{3} + 116 q^{4} - 19 q^{5} - 31 q^{6} - 47 q^{7} - 15 q^{8} + 115 q^{9} - 48 q^{10} - 31 q^{11} - 61 q^{12} - 54 q^{13} - 44 q^{14} - 65 q^{15} + 58 q^{16} - 26 q^{17} - 23 q^{18} - 86 q^{19} - 52 q^{20} - 30 q^{21} - 56 q^{22} - 63 q^{23} - 90 q^{24} + 92 q^{25} - 38 q^{26} - 103 q^{27} - 77 q^{28} - 51 q^{29} - 22 q^{30} - 256 q^{31} - 21 q^{32} - 36 q^{33} - 124 q^{34} - 50 q^{35} + 45 q^{36} - 42 q^{37} - 14 q^{38} - 119 q^{39} - 131 q^{40} - 55 q^{41} - 5 q^{42} - 55 q^{43} - 54 q^{44} - 68 q^{45} - 59 q^{46} - 82 q^{47} - 89 q^{48} + 30 q^{49} + 13 q^{50} - 83 q^{51} - 126 q^{52} - 23 q^{53} - 83 q^{54} - 244 q^{55} - 94 q^{56} - 14 q^{57} - 60 q^{58} - 93 q^{59} - 70 q^{60} - 139 q^{61} - 10 q^{62} - 120 q^{63} - 45 q^{64} - 37 q^{65} - 28 q^{66} - 110 q^{67} - 27 q^{68} - 79 q^{69} - 78 q^{70} - 123 q^{71} - 74 q^{73} - 25 q^{74} - 146 q^{75} - 192 q^{76} - q^{77} + 26 q^{78} - 273 q^{79} - 51 q^{80} + 41 q^{81} - 120 q^{82} - 27 q^{83} - 14 q^{84} - 71 q^{85} + 3 q^{86} - 98 q^{87} - 143 q^{88} - 70 q^{89} - 24 q^{90} - 256 q^{91} - 47 q^{92} + 16 q^{93} - 151 q^{94} - 83 q^{95} - 137 q^{96} - 108 q^{97} + 17 q^{98} - 131 q^{99}+O(q^{100}) \) 149 * q - 6 * q^2 - 28 * q^3 + 116 * q^4 - 19 * q^5 - 31 * q^6 - 47 * q^7 - 15 * q^8 + 115 * q^9 - 48 * q^10 - 31 * q^11 - 61 * q^12 - 54 * q^13 - 44 * q^14 - 65 * q^15 + 58 * q^16 - 26 * q^17 - 23 * q^18 - 86 * q^19 - 52 * q^20 - 30 * q^21 - 56 * q^22 - 63 * q^23 - 90 * q^24 + 92 * q^25 - 38 * q^26 - 103 * q^27 - 77 * q^28 - 51 * q^29 - 22 * q^30 - 256 * q^31 - 21 * q^32 - 36 * q^33 - 124 * q^34 - 50 * q^35 + 45 * q^36 - 42 * q^37 - 14 * q^38 - 119 * q^39 - 131 * q^40 - 55 * q^41 - 5 * q^42 - 55 * q^43 - 54 * q^44 - 68 * q^45 - 59 * q^46 - 82 * q^47 - 89 * q^48 + 30 * q^49 + 13 * q^50 - 83 * q^51 - 126 * q^52 - 23 * q^53 - 83 * q^54 - 244 * q^55 - 94 * q^56 - 14 * q^57 - 60 * q^58 - 93 * q^59 - 70 * q^60 - 139 * q^61 - 10 * q^62 - 120 * q^63 - 45 * q^64 - 37 * q^65 - 28 * q^66 - 110 * q^67 - 27 * q^68 - 79 * q^69 - 78 * q^70 - 123 * q^71 - 74 * q^73 - 25 * q^74 - 146 * q^75 - 192 * q^76 - q^77 + 26 * q^78 - 273 * q^79 - 51 * q^80 + 41 * q^81 - 120 * q^82 - 27 * q^83 - 14 * q^84 - 71 * q^85 + 3 * q^86 - 98 * q^87 - 143 * q^88 - 70 * q^89 - 24 * q^90 - 256 * q^91 - 47 * q^92 + 16 * q^93 - 151 * q^94 - 83 * q^95 - 137 * q^96 - 108 * q^97 + 17 * q^98 - 131 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.45256	−1.73422	−0.867112	−	0.498113i	$-0.834026\pi$
$2$	−2.45256	−1.73422	−0.867112	+	0.498113i	$0.834026\pi$
$3$	0.529200	0.305534	0.152767	−	0.988262i	$-0.451182\pi$
$3$	0.529200	0.305534	0.152767	+	0.988262i	$0.451182\pi$
$4$	4.01507	2.00753
$5$	2.50676	1.12106	0.560528	−	0.828136i	$-0.310598\pi$
$5$	2.50676	1.12106	0.560528	+	0.828136i	$0.310598\pi$
$6$	−1.29790	−0.529864
$7$	−0.602620	−0.227769	−0.113884	−	0.993494i	$-0.536329\pi$
$7$	−0.602620	−0.227769	−0.113884	+	0.993494i	$0.536329\pi$
$8$	−4.94208	−1.74729
$9$	−2.71995	−0.906649
$10$	−6.14798	−1.94416
$11$	1.28953	0.388807	0.194404	−	0.980922i	$-0.437723\pi$
$11$	1.28953	0.388807	0.194404	+	0.980922i	$0.437723\pi$
$12$	2.12477	0.613369
$13$	−0.0840546	−0.0233126	−0.0116563	−	0.999932i	$-0.503710\pi$
$13$	−0.0840546	−0.0233126	−0.0116563	+	0.999932i	$0.503710\pi$
$14$	1.47796	0.395002
$15$	1.32658	0.342520
$16$	4.09063	1.02266
$17$	−6.64038	−1.61053	−0.805264	−	0.592916i	$-0.797977\pi$
$17$	−6.64038	−1.61053	−0.805264	+	0.592916i	$0.797977\pi$
$18$	6.67084	1.57233
$19$	1.18824	0.272600	0.136300	−	0.990668i	$-0.456479\pi$
$19$	1.18824	0.272600	0.136300	+	0.990668i	$0.456479\pi$
$20$	10.0648	2.25056
$21$	−0.318906	−0.0695911
$22$	−3.16265	−0.674278
$23$	1.20517	0.251295	0.125647	−	0.992075i	$-0.459899\pi$
$23$	1.20517	0.251295	0.125647	+	0.992075i	$0.459899\pi$
$24$	−2.61535	−0.533855
$25$	1.28383	0.256766
$26$	0.206149	0.0404292
$27$	−3.02700	−0.582545
$28$	−2.41956	−0.457254
$29$	−2.21157	−0.410678	−0.205339	−	0.978691i	$-0.565830\pi$
$29$	−2.21157	−0.410678	−0.205339	+	0.978691i	$0.565830\pi$
$30$	−3.25351	−0.594007
$31$	3.29916	0.592547	0.296274	−	0.955103i	$-0.404256\pi$
$31$	3.29916	0.592547	0.296274	+	0.955103i	$0.404256\pi$
$32$	−0.148365	−0.0262274
$33$	0.682417	0.118794
$34$	16.2859	2.79302
$35$	−1.51062	−0.255342
$36$	−10.9208	−1.82013
$37$	−6.83528	−1.12371	−0.561857	−	0.827235i	$-0.689913\pi$
$37$	−6.83528	−1.12371	−0.561857	+	0.827235i	$0.689913\pi$
$38$	−2.91422	−0.472749
$39$	−0.0444817	−0.00712277
$40$	−12.3886	−1.95881
$41$	5.64435	0.881499	0.440749	−	0.897630i	$-0.354713\pi$
$41$	5.64435	0.881499	0.440749	+	0.897630i	$0.354713\pi$
$42$	0.782138	0.120687
$43$	7.53358	1.14886	0.574430	−	0.818554i	$-0.305224\pi$
$43$	7.53358	1.14886	0.574430	+	0.818554i	$0.305224\pi$
$44$	5.17754	0.780543
$45$	−6.81825	−1.01640
$46$	−2.95575	−0.435801
$47$	9.02679	1.31669	0.658346	−	0.752715i	$-0.271256\pi$
$47$	9.02679	1.31669	0.658346	+	0.752715i	$0.271256\pi$
$48$	2.16476	0.312456
$49$	−6.63685	−0.948121
$50$	−3.14868	−0.445290
$51$	−3.51409	−0.492071
$52$	−0.337485	−0.0468007
$53$	9.70487	1.33307	0.666533	−	0.745475i	$-0.267777\pi$
$53$	9.70487	1.33307	0.666533	+	0.745475i	$0.267777\pi$
$54$	7.42390	1.01026
$55$	3.23253	0.435874
$56$	2.97820	0.397978
$57$	0.628814	0.0832884
$58$	5.42401	0.712208
$59$	−3.24115	−0.421962	−0.210981	−	0.977490i	$-0.567666\pi$
$59$	−3.24115	−0.421962	−0.210981	+	0.977490i	$0.567666\pi$
$60$	5.32629	0.687621
$61$	−1.23812	−0.158525	−0.0792623	−	0.996854i	$-0.525256\pi$
$61$	−1.23812	−0.158525	−0.0792623	+	0.996854i	$0.525256\pi$
$62$	−8.09141	−1.02761
$63$	1.63909	0.206507
$64$	−7.81738	−0.977173
$65$	−0.210704	−0.0261347
$66$	−1.67367	−0.206015
$67$	1.76820	0.216020	0.108010	−	0.994150i	$-0.465552\pi$
$67$	1.76820	0.216020	0.108010	+	0.994150i	$0.465552\pi$
$68$	−26.6616	−3.23319
$69$	0.637774	0.0767789
$70$	3.70490	0.442820
$71$	−11.8657	−1.40820	−0.704102	−	0.710099i	$-0.748650\pi$
$71$	−11.8657	−1.40820	−0.704102	+	0.710099i	$0.748650\pi$
$72$	13.4422	1.58418
$73$	6.48172	0.758628	0.379314	−	0.925268i	$-0.376160\pi$
$73$	6.48172	0.758628	0.379314	+	0.925268i	$0.376160\pi$
$74$	16.7640	1.94877
$75$	0.679403	0.0784507
$76$	4.77084	0.547253
$77$	−0.777095	−0.0885582
$78$	0.109094	0.0123525
$79$	−7.93098	−0.892305	−0.446152	−	0.894957i	$-0.647206\pi$
$79$	−7.93098	−0.892305	−0.446152	+	0.894957i	$0.647206\pi$
$80$	10.2542	1.14646
$81$	6.55796	0.728662
$82$	−13.8431	−1.52872
$83$	−9.68320	−1.06287	−0.531435	−	0.847099i	$-0.678347\pi$
$83$	−9.68320	−1.06287	−0.531435	+	0.847099i	$0.678347\pi$
$84$	−1.28043	−0.139706
$85$	−16.6458	−1.80549
$86$	−18.4766	−1.99238
$87$	−1.17036	−0.125476
$88$	−6.37294	−0.679358
$89$	−8.35044	−0.885145	−0.442573	−	0.896733i	$-0.645934\pi$
$89$	−8.35044	−0.885145	−0.442573	+	0.896733i	$0.645934\pi$
$90$	16.7222	1.76267
$91$	0.0506530	0.00530988
$92$	4.83882	0.504482
$93$	1.74592	0.181043
$94$	−22.1388	−2.28344
$95$	2.97862	0.305600
$96$	−0.0785145	−0.00801335
$97$	−5.76190	−0.585032	−0.292516	−	0.956261i	$-0.594492\pi$
$97$	−5.76190	−0.585032	−0.292516	+	0.956261i	$0.594492\pi$
$98$	16.2773	1.64425
$99$	−3.50745	−0.352512
$100$	5.15467	0.515467
$101$	−9.62031	−0.957256	−0.478628	−	0.878018i	$-0.658866\pi$
$101$	−9.62031	−0.957256	−0.478628	+	0.878018i	$0.658866\pi$
$102$	8.61852	0.853361
$103$	−14.5252	−1.43121	−0.715603	−	0.698507i	$-0.753848\pi$
$103$	−14.5252	−1.43121	−0.715603	+	0.698507i	$0.753848\pi$
$104$	0.415404	0.0407338
$105$	−0.799421	−0.0780155
$106$	−23.8018	−2.31184
$107$	8.03707	0.776973	0.388486	−	0.921454i	$-0.372998\pi$
$107$	8.03707	0.776973	0.388486	+	0.921454i	$0.372998\pi$
$108$	−12.1536	−1.16948
$109$	−2.49112	−0.238606	−0.119303	−	0.992858i	$-0.538066\pi$
$109$	−2.49112	−0.238606	−0.119303	+	0.992858i	$0.538066\pi$
$110$	−7.92799	−0.755904
$111$	−3.61723	−0.343332
$112$	−2.46509	−0.232929
$113$	−3.30382	−0.310798	−0.155399	−	0.987852i	$-0.549666\pi$
$113$	−3.30382	−0.310798	−0.155399	+	0.987852i	$0.549666\pi$
$114$	−1.54221	−0.144441
$115$	3.02106	0.281715
$116$	−8.87960	−0.824450
$117$	0.228624	0.0211363
$118$	7.94913	0.731777
$119$	4.00162	0.366828
$120$	−6.55604	−0.598482
$121$	−9.33712	−0.848829
$122$	3.03656	0.274917
$123$	2.98699	0.269327
$124$	13.2464	1.18956
$125$	−9.31553	−0.833207
$126$	−4.01998	−0.358129
$127$	4.55107	0.403842	0.201921	−	0.979402i	$-0.435282\pi$
$127$	4.55107	0.403842	0.201921	+	0.979402i	$0.435282\pi$
$128$	19.4693	1.72086
$129$	3.98677	0.351015
$130$	0.516766	0.0453234
$131$	−19.7550	−1.72601	−0.863003	−	0.505199i	$-0.831419\pi$
$131$	−19.7550	−1.72601	−0.863003	+	0.505199i	$0.831419\pi$
$132$	2.73995	0.238482
$133$	−0.716054	−0.0620898
$134$	−4.33662	−0.374627
$135$	−7.58794	−0.653066
$136$	32.8173	2.81406
$137$	−17.9930	−1.53725	−0.768625	−	0.639700i	$-0.779059\pi$
$137$	−17.9930	−1.53725	−0.768625	+	0.639700i	$0.779059\pi$
$138$	−1.56418	−0.133152
$139$	19.0012	1.61166	0.805832	−	0.592144i	$-0.201719\pi$
$139$	19.0012	1.61166	0.805832	+	0.592144i	$0.201719\pi$
$140$	−6.06525	−0.512607
$141$	4.77698	0.402294
$142$	29.1015	2.44214
$143$	−0.108391	−0.00906408
$144$	−11.1263	−0.927191
$145$	−5.54387	−0.460393
$146$	−15.8968	−1.31563
$147$	−3.51222	−0.289683
$148$	−27.4441	−2.25589
$149$	−3.96794	−0.325066	−0.162533	−	0.986703i	$-0.551966\pi$
$149$	−3.96794	−0.325066	−0.162533	+	0.986703i	$0.551966\pi$
$150$	−1.66628	−0.136051
$151$	−10.8926	−0.886429	−0.443215	−	0.896415i	$-0.646162\pi$
$151$	−10.8926	−0.886429	−0.443215	+	0.896415i	$0.646162\pi$
$152$	−5.87235	−0.476311
$153$	18.0615	1.46018
$154$	1.90587	0.153580
$155$	8.27020	0.664279
$156$	−0.178597	−0.0142992
$157$	−12.0577	−0.962312	−0.481156	−	0.876635i	$-0.659783\pi$
$157$	−12.0577	−0.962312	−0.481156	+	0.876635i	$0.659783\pi$
$158$	19.4512	1.54746
$159$	5.13582	0.407297
$160$	−0.371914	−0.0294024
$161$	−0.726257	−0.0572371
$162$	−16.0838	−1.26366
$163$	−16.4475	−1.28827	−0.644134	−	0.764912i	$-0.722782\pi$
$163$	−16.4475	−1.28827	−0.644134	+	0.764912i	$0.722782\pi$
$164$	22.6624	1.76964
$165$	1.71065	0.133174
$166$	23.7487	1.84325
$167$	6.78598	0.525115	0.262557	−	0.964916i	$-0.415434\pi$
$167$	6.78598	0.525115	0.262557	+	0.964916i	$0.415434\pi$
$168$	1.57606	0.121596
$169$	−12.9929	−0.999457
$170$	40.8249	3.13113
$171$	−3.23194	−0.247152
$172$	30.2478	2.30637
$173$	21.6382	1.64512	0.822560	−	0.568678i	$-0.192545\pi$
$173$	21.6382	1.64512	0.822560	+	0.568678i	$0.192545\pi$
$174$	2.87039	0.217603
$175$	−0.773662	−0.0584834
$176$	5.27497	0.397616
$177$	−1.71522	−0.128924
$178$	20.4800	1.53504
$179$	9.10103	0.680243	0.340121	−	0.940382i	$-0.389532\pi$
$179$	9.10103	0.680243	0.340121	+	0.940382i	$0.389532\pi$
$180$	−27.3757	−2.04047
$181$	−18.3174	−1.36152	−0.680762	−	0.732504i	$-0.738351\pi$
$181$	−18.3174	−1.36152	−0.680762	+	0.732504i	$0.738351\pi$
$182$	−0.124230	−0.00920851
$183$	−0.655211	−0.0484346
$184$	−5.95603	−0.439084
$185$	−17.1344	−1.25975
$186$	−4.28197	−0.313969
$187$	−8.56295	−0.626185
$188$	36.2432	2.64330
$189$	1.82413	0.132686
$190$	−7.30525	−0.529978
$191$	19.4938	1.41052	0.705262	−	0.708947i	$-0.250829\pi$
$191$	19.4938	1.41052	0.705262	+	0.708947i	$0.250829\pi$
$192$	−4.13696	−0.298559
$193$	−3.42081	−0.246235	−0.123118	−	0.992392i	$-0.539289\pi$
$193$	−3.42081	−0.246235	−0.123118	+	0.992392i	$0.539289\pi$
$194$	14.1314	1.01458
$195$	−0.111505	−0.00798502
$196$	−26.6474	−1.90339
$197$	14.1719	1.00970	0.504851	−	0.863206i	$-0.331547\pi$
$197$	14.1719	1.00970	0.504851	+	0.863206i	$0.331547\pi$
$198$	8.60223	0.611334
$199$	0.491565	0.0348461	0.0174230	−	0.999848i	$-0.494454\pi$
$199$	0.491565	0.0348461	0.0174230	+	0.999848i	$0.494454\pi$
$200$	−6.34479	−0.448645
$201$	0.935730	0.0660013
$202$	23.5944	1.66010
$203$	1.33274	0.0935397
$204$	−14.1093	−0.987848
$205$	14.1490	0.988209
$206$	35.6239	2.48203
$207$	−3.27799	−0.227836
$208$	−0.343836	−0.0238407
$209$	1.53226	0.105989
$210$	1.96063	0.135296
$211$	−3.11668	−0.214561	−0.107280	−	0.994229i	$-0.534214\pi$
$211$	−3.11668	−0.214561	−0.107280	+	0.994229i	$0.534214\pi$
$212$	38.9657	2.67618
$213$	−6.27935	−0.430254
$214$	−19.7114	−1.34744
$215$	18.8848	1.28794
$216$	14.9596	1.01788
$217$	−1.98814	−0.134964
$218$	6.10963	0.413797
$219$	3.43013	0.231786
$220$	12.9788	0.875032
$221$	0.558154	0.0375455
$222$	8.87148	0.595415
$223$	−3.90510	−0.261505	−0.130752	−	0.991415i	$-0.541739\pi$
$223$	−3.90510	−0.261505	−0.130752	+	0.991415i	$0.541739\pi$
$224$	0.0894074	0.00597378
$225$	−3.49195	−0.232797
$226$	8.10284	0.538993
$227$	−10.4299	−0.692256	−0.346128	−	0.938187i	$-0.612504\pi$
$227$	−10.4299	−0.692256	−0.346128	+	0.938187i	$0.612504\pi$
$228$	2.52473	0.167204
$229$	−17.3314	−1.14529	−0.572645	−	0.819804i	$-0.694083\pi$
$229$	−17.3314	−1.14529	−0.572645	+	0.819804i	$0.694083\pi$
$230$	−7.40934	−0.488557
$231$	−0.411238	−0.0270575
$232$	10.9297	0.717573
$233$	6.83504	0.447778	0.223889	−	0.974615i	$-0.428125\pi$
$233$	6.83504	0.447778	0.223889	+	0.974615i	$0.428125\pi$
$234$	−0.560715	−0.0366551
$235$	22.6280	1.47609
$236$	−13.0134	−0.847103
$237$	−4.19707	−0.272629
$238$	−9.81424	−0.636163
$239$	−11.0014	−0.711623	−0.355811	−	0.934558i	$-0.615795\pi$
$239$	−11.0014	−0.711623	−0.355811	+	0.934558i	$0.615795\pi$
$240$	5.42652	0.350281
$241$	−19.8282	−1.27725	−0.638623	−	0.769520i	$-0.720495\pi$
$241$	−19.8282	−1.27725	−0.638623	+	0.769520i	$0.720495\pi$
$242$	22.8999	1.47206
$243$	12.5515	0.805176
$244$	−4.97112	−0.318244
$245$	−16.6370	−1.06290
$246$	−7.32577	−0.467074
$247$	−0.0998766	−0.00635500
$248$	−16.3047	−1.03535
$249$	−5.12435	−0.324742
$250$	22.8469	1.44497
$251$	18.1225	1.14388	0.571941	−	0.820295i	$-0.306191\pi$
$251$	18.1225	1.14388	0.571941	+	0.820295i	$0.306191\pi$
$252$	6.58108	0.414569
$253$	1.55409	0.0977051
$254$	−11.1618	−0.700353
$255$	−8.80896	−0.551639
$256$	−32.1151	−2.00719
$257$	−4.35004	−0.271348	−0.135674	−	0.990754i	$-0.543320\pi$
$257$	−4.35004	−0.271348	−0.135674	+	0.990754i	$0.543320\pi$
$258$	−9.77780	−0.608739
$259$	4.11908	0.255947
$260$	−0.845992	−0.0524662
$261$	6.01535	0.372341
$262$	48.4505	2.99328
$263$	−11.8853	−0.732882	−0.366441	−	0.930441i	$-0.619424\pi$
$263$	−11.8853	−0.732882	−0.366441	+	0.930441i	$0.619424\pi$
$264$	−3.37256	−0.207567
$265$	24.3278	1.49444
$266$	1.75617	0.107678
$267$	−4.41905	−0.270442
$268$	7.09943	0.433667
$269$	21.6589	1.32057	0.660283	−	0.751017i	$-0.270436\pi$
$269$	21.6589	1.32057	0.660283	+	0.751017i	$0.270436\pi$
$270$	18.6099	1.13256
$271$	1.27973	0.0777380	0.0388690	−	0.999244i	$-0.487624\pi$
$271$	1.27973	0.0777380	0.0388690	+	0.999244i	$0.487624\pi$
$272$	−27.1633	−1.64702
$273$	0.0268055	0.00162235
$274$	44.1291	2.66593
$275$	1.65553	0.0998325
$276$	2.56070	0.154136
$277$	22.7902	1.36933	0.684665	−	0.728858i	$-0.259948\pi$
$277$	22.7902	1.36933	0.684665	+	0.728858i	$0.259948\pi$
$278$	−46.6017	−2.79499
$279$	−8.97355	−0.537233
$280$	7.46561	0.446156
$281$	−4.29622	−0.256291	−0.128146	−	0.991755i	$-0.540902\pi$
$281$	−4.29622	−0.256291	−0.128146	+	0.991755i	$0.540902\pi$
$282$	−11.7158	−0.697668
$283$	−0.403419	−0.0239808	−0.0119904	−	0.999928i	$-0.503817\pi$
$283$	−0.403419	−0.0239808	−0.0119904	+	0.999928i	$0.503817\pi$
$284$	−47.6417	−2.82702
$285$	1.57628	0.0933710
$286$	0.265835	0.0157192
$287$	−3.40140	−0.200778
$288$	0.403544	0.0237790
$289$	27.0946	1.59380
$290$	13.5967	0.798425
$291$	−3.04919	−0.178747
$292$	26.0245	1.52297
$293$	0.643778	0.0376099	0.0188049	−	0.999823i	$-0.494014\pi$
$293$	0.643778	0.0376099	0.0188049	+	0.999823i	$0.494014\pi$
$294$	8.61394	0.502375
$295$	−8.12478	−0.473043
$296$	33.7805	1.96345
$297$	−3.90339	−0.226498
$298$	9.73163	0.563738
$299$	−0.101300	−0.00585832
$300$	2.72785	0.157492
$301$	−4.53988	−0.261675
$302$	26.7149	1.53727
$303$	−5.09106	−0.292474
$304$	4.86063	0.278776
$305$	−3.10366	−0.177715
$306$	−44.2969	−2.53229
$307$	−22.3859	−1.27763	−0.638815	−	0.769360i	$-0.720575\pi$
$307$	−22.3859	−1.27763	−0.638815	+	0.769360i	$0.720575\pi$
$308$	−3.12009	−0.177783
$309$	−7.68671	−0.437281
$310$	−20.2832	−1.15201
$311$	−12.5846	−0.713605	−0.356803	−	0.934180i	$-0.616133\pi$
$311$	−12.5846	−0.713605	−0.356803	+	0.934180i	$0.616133\pi$
$312$	0.219832	0.0124455
$313$	9.02303	0.510012	0.255006	−	0.966940i	$-0.417923\pi$
$313$	9.02303	0.510012	0.255006	+	0.966940i	$0.417923\pi$
$314$	29.5724	1.66887
$315$	4.10881	0.231505
$316$	−31.8434	−1.79133
$317$	0.218431	0.0122683	0.00613416	−	0.999981i	$-0.498047\pi$
$317$	0.218431	0.0122683	0.00613416	+	0.999981i	$0.498047\pi$
$318$	−12.5959	−0.706344
$319$	−2.85188	−0.159675
$320$	−19.5963	−1.09547
$321$	4.25322	0.237391
$322$	1.78119	0.0992619
$323$	−7.89033	−0.439030
$324$	26.3306	1.46281
$325$	−0.107912	−0.00598587
$326$	40.3386	2.23415
$327$	−1.31830	−0.0729022
$328$	−27.8948	−1.54023
$329$	−5.43972	−0.299902
$330$	−4.19549	−0.230954
$331$	−12.9378	−0.711124	−0.355562	−	0.934653i	$-0.615711\pi$
$331$	−12.9378	−0.711124	−0.355562	+	0.934653i	$0.615711\pi$
$332$	−38.8787	−2.13375
$333$	18.5916	1.01881
$334$	−16.6430	−0.910667
$335$	4.43244	0.242170
$336$	−1.30453	−0.0711678
$337$	−34.1758	−1.86168	−0.930838	−	0.365432i	$-0.880921\pi$
$337$	−34.1758	−1.86168	−0.930838	+	0.365432i	$0.880921\pi$
$338$	31.8660	1.73328
$339$	−1.74838	−0.0949591
$340$	−66.8341	−3.62459
$341$	4.25436	0.230387
$342$	7.92653	0.428618
$343$	8.21784	0.443722
$344$	−37.2315	−2.00739
$345$	1.59874	0.0860735
$346$	−53.0690	−2.85301
$347$	21.7658	1.16845	0.584224	−	0.811592i	$-0.301399\pi$
$347$	21.7658	1.16845	0.584224	+	0.811592i	$0.301399\pi$
$348$	−4.69908	−0.251897
$349$	4.08481	0.218655	0.109327	−	0.994006i	$-0.465130\pi$
$349$	4.08481	0.218655	0.109327	+	0.994006i	$0.465130\pi$
$350$	1.89746	0.101423
$351$	0.254433	0.0135806
$352$	−0.191320	−0.0101974
$353$	−13.1497	−0.699890	−0.349945	−	0.936770i	$-0.613800\pi$
$353$	−13.1497	−0.699890	−0.349945	+	0.936770i	$0.613800\pi$
$354$	4.20668	0.223582
$355$	−29.7445	−1.57868
$356$	−33.5276	−1.77696
$357$	2.11766	0.112078
$358$	−22.3208	−1.17969
$359$	−3.30962	−0.174675	−0.0873374	−	0.996179i	$-0.527836\pi$
$359$	−3.30962	−0.174675	−0.0873374	+	0.996179i	$0.527836\pi$
$360$	33.6963	1.77595
$361$	−17.5881	−0.925689
$362$	44.9247	2.36119
$363$	−4.94120	−0.259346
$364$	0.203375	0.0106598
$365$	16.2481	0.850464
$366$	1.60695	0.0839965
$367$	−6.10144	−0.318492	−0.159246	−	0.987239i	$-0.550906\pi$
$367$	−6.10144	−0.318492	−0.159246	+	0.987239i	$0.550906\pi$
$368$	4.92989	0.256988
$369$	−15.3523	−0.799210
$370$	42.0232	2.18468
$371$	−5.84835	−0.303631
$372$	7.00997	0.363450
$373$	−3.40357	−0.176230	−0.0881151	−	0.996110i	$-0.528084\pi$
$373$	−3.40357	−0.176230	−0.0881151	+	0.996110i	$0.528084\pi$
$374$	21.0012	1.08594
$375$	−4.92978	−0.254573
$376$	−44.6111	−2.30064
$377$	0.185893	0.00957396
$378$	−4.47379	−0.230107
$379$	25.9216	1.33150	0.665751	−	0.746174i	$-0.268111\pi$
$379$	25.9216	1.33150	0.665751	+	0.746174i	$0.268111\pi$
$380$	11.9593	0.613502
$381$	2.40843	0.123387
$382$	−47.8098	−2.44616
$383$	6.47423	0.330818	0.165409	−	0.986225i	$-0.447106\pi$
$383$	6.47423	0.330818	0.165409	+	0.986225i	$0.447106\pi$
$384$	10.3032	0.525782
$385$	−1.94799	−0.0992786
$386$	8.38976	0.427027
$387$	−20.4909	−1.04161
$388$	−23.1344	−1.17447
$389$	−22.6069	−1.14622	−0.573108	−	0.819480i	$-0.694262\pi$
$389$	−22.6069	−1.14622	−0.573108	+	0.819480i	$0.694262\pi$
$390$	0.273472	0.0138478
$391$	−8.00276	−0.404717
$392$	32.7998	1.65664
$393$	−10.4544	−0.527353
$394$	−34.7574	−1.75105
$395$	−19.8810	−1.00032
$396$	−14.0826	−0.707679
$397$	−29.4104	−1.47607	−0.738033	−	0.674764i	$-0.764245\pi$
$397$	−29.4104	−1.47607	−0.738033	+	0.674764i	$0.764245\pi$
$398$	−1.20559	−0.0604309
$399$	−0.378936	−0.0189705
$400$	5.25167	0.262584
$401$	−0.857514	−0.0428222	−0.0214111	−	0.999771i	$-0.506816\pi$
$401$	−0.857514	−0.0428222	−0.0214111	+	0.999771i	$0.506816\pi$
$402$	−2.29494	−0.114461
$403$	−0.277310	−0.0138138
$404$	−38.6262	−1.92172
$405$	16.4392	0.816871
$406$	−3.26862	−0.162219
$407$	−8.81428	−0.436908
$408$	17.3669	0.859789
$409$	15.1963	0.751408	0.375704	−	0.926740i	$-0.377401\pi$
$409$	15.1963	0.751408	0.375704	+	0.926740i	$0.377401\pi$
$410$	−34.7013	−1.71378
$411$	−9.52191	−0.469681
$412$	−58.3194	−2.87319
$413$	1.95318	0.0961099
$414$	8.03948	0.395119
$415$	−24.2734	−1.19154
$416$	0.0124707	0.000611427 0
$417$	10.0554	0.492417
$418$	−3.75797	−0.183808
$419$	−16.0944	−0.786263	−0.393132	−	0.919482i	$-0.628608\pi$
$419$	−16.0944	−0.786263	−0.393132	+	0.919482i	$0.628608\pi$
$420$	−3.20973	−0.156619
$421$	−27.4928	−1.33992	−0.669958	−	0.742399i	$-0.733688\pi$
$421$	−27.4928	−1.33992	−0.669958	+	0.742399i	$0.733688\pi$
$422$	7.64385	0.372097
$423$	−24.5524	−1.19378
$424$	−47.9622	−2.32925
$425$	−8.52512	−0.413529
$426$	15.4005	0.746156
$427$	0.746114	0.0361070
$428$	32.2694	1.55980
$429$	−0.0573603	−0.00276938
$430$	−46.3163	−2.23357
$431$	−24.4311	−1.17681	−0.588403	−	0.808568i	$-0.700243\pi$
$431$	−24.4311	−1.17681	−0.588403	+	0.808568i	$0.700243\pi$
$432$	−12.3823	−0.595744
$433$	6.41350	0.308213	0.154107	−	0.988054i	$-0.450750\pi$
$433$	6.41350	0.308213	0.154107	+	0.988054i	$0.450750\pi$
$434$	4.87604	0.234058
$435$	−2.93381	−0.140666
$436$	−10.0020	−0.479010
$437$	1.43202	0.0685029
$438$	−8.41260	−0.401970
$439$	−0.877723	−0.0418914	−0.0209457	−	0.999781i	$-0.506668\pi$
$439$	−0.877723	−0.0418914	−0.0209457	+	0.999781i	$0.506668\pi$
$440$	−15.9754	−0.761598
$441$	18.0519	0.859613
$442$	−1.36891	−0.0651124
$443$	−3.80199	−0.180638	−0.0903191	−	0.995913i	$-0.528789\pi$
$443$	−3.80199	−0.180638	−0.0903191	+	0.995913i	$0.528789\pi$
$444$	−14.5234	−0.689251
$445$	−20.9325	−0.992297
$446$	9.57750	0.453508
$447$	−2.09983	−0.0993187
$448$	4.71091	0.222570
$449$	38.6895	1.82587	0.912935	−	0.408105i	$-0.133810\pi$
$449$	38.6895	1.82587	0.912935	+	0.408105i	$0.133810\pi$
$450$	8.56423	0.403722
$451$	7.27854	0.342733
$452$	−13.2651	−0.623937
$453$	−5.76438	−0.270834
$454$	25.5800	1.20053
$455$	0.126975	0.00595267
$456$	−3.10765	−0.145529
$457$	6.81579	0.318829	0.159415	−	0.987212i	$-0.449039\pi$
$457$	6.81579	0.318829	0.159415	+	0.987212i	$0.449039\pi$
$458$	42.5063	1.98619
$459$	20.1004	0.938206
$460$	12.1298	0.565553
$461$	24.8079	1.15542	0.577710	−	0.816242i	$-0.303947\pi$
$461$	24.8079	1.15542	0.577710	+	0.816242i	$0.303947\pi$
$462$	1.00859	0.0469238
$463$	23.5562	1.09475	0.547375	−	0.836888i	$-0.315627\pi$
$463$	23.5562	1.09475	0.547375	+	0.836888i	$0.315627\pi$
$464$	−9.04671	−0.419983
$465$	4.37659	0.202959
$466$	−16.7634	−0.776548
$467$	−15.0332	−0.695654	−0.347827	−	0.937559i	$-0.613080\pi$
$467$	−15.0332	−0.695654	−0.347827	+	0.937559i	$0.613080\pi$
$468$	0.917941	0.0424318
$469$	−1.06555	−0.0492026
$470$	−55.4965	−2.55986
$471$	−6.38095	−0.294019
$472$	16.0180	0.737290
$473$	9.71475	0.446685
$474$	10.2936	0.472800
$475$	1.52549	0.0699944
$476$	16.0668	0.736420
$477$	−26.3967	−1.20862
$478$	26.9817	1.23411
$479$	25.3833	1.15979	0.579897	−	0.814690i	$-0.303093\pi$
$479$	25.3833	1.15979	0.579897	+	0.814690i	$0.303093\pi$
$480$	−0.196817	−0.00898341
$481$	0.574537	0.0261966
$482$	48.6299	2.21503
$483$	−0.384335	−0.0174879
$484$	−37.4892	−1.70405
$485$	−14.4437	−0.655853
$486$	−30.7832	−1.39636
$487$	21.9765	0.995852	0.497926	−	0.867220i	$-0.334095\pi$
$487$	21.9765	0.995852	0.497926	+	0.867220i	$0.334095\pi$
$488$	6.11887	0.276988
$489$	−8.70402	−0.393609
$490$	40.8032	1.84330
$491$	−34.8696	−1.57364	−0.786822	−	0.617180i	$-0.788275\pi$
$491$	−34.8696	−1.57364	−0.786822	+	0.617180i	$0.788275\pi$
$492$	11.9929	0.540684
$493$	14.6857	0.661409
$494$	0.244954	0.0110210
$495$	−8.79231	−0.395185
$496$	13.4956	0.605972
$497$	7.15053	0.320745
$498$	12.5678	0.563176
$499$	−32.3328	−1.44741	−0.723707	−	0.690107i	$-0.757563\pi$
$499$	−32.3328	−1.44741	−0.723707	+	0.690107i	$0.757563\pi$
$500$	−37.4025	−1.67269
$501$	3.59114	0.160440
$502$	−44.4466	−1.98375
$503$	31.5707	1.40767	0.703833	−	0.710365i	$-0.251470\pi$
$503$	31.5707	1.40767	0.703833	+	0.710365i	$0.251470\pi$
$504$	−8.10054	−0.360827
$505$	−24.1158	−1.07314
$506$	−3.81151	−0.169442
$507$	−6.87586	−0.305368
$508$	18.2729	0.810727
$509$	−23.4985	−1.04155	−0.520777	−	0.853693i	$-0.674358\pi$
$509$	−23.4985	−1.04155	−0.520777	+	0.853693i	$0.674358\pi$
$510$	21.6045	0.956665
$511$	−3.90601	−0.172792
$512$	39.8255	1.76005
$513$	−3.59678	−0.158802
$514$	10.6687	0.470578
$515$	−36.4110	−1.60446
$516$	16.0071	0.704675
$517$	11.6403	0.511939
$518$	−10.1023	−0.443869
$519$	11.4509	0.502640
$520$	1.04132	0.0456648
$521$	37.6865	1.65107	0.825537	−	0.564347i	$-0.190872\pi$
$521$	37.6865	1.65107	0.825537	+	0.564347i	$0.190872\pi$
$522$	−14.7530	−0.645723
$523$	−3.02865	−0.132434	−0.0662168	−	0.997805i	$-0.521093\pi$
$523$	−3.02865	−0.132434	−0.0662168	+	0.997805i	$0.521093\pi$
$524$	−79.3178	−3.46501
$525$	−0.409422	−0.0178686
$526$	29.1496	1.27098
$527$	−21.9077	−0.954314
$528$	2.79152	0.121485
$529$	−21.5476	−0.936851
$530$	−59.6654	−2.59170
$531$	8.81576	0.382572
$532$	−2.87501	−0.124647
$533$	−0.474433	−0.0205500
$534$	10.8380	0.469006
$535$	20.1470	0.871030
$536$	−8.73857	−0.377449
$537$	4.81626	0.207837
$538$	−53.1198	−2.29016
$539$	−8.55840	−0.368636
$540$	−30.4661	−1.31105
$541$	−22.8146	−0.980875	−0.490438	−	0.871476i	$-0.663163\pi$
$541$	−22.8146	−0.980875	−0.490438	+	0.871476i	$0.663163\pi$
$542$	−3.13862	−0.134815
$543$	−9.69359	−0.415992
$544$	0.985197	0.0422400
$545$	−6.24464	−0.267491
$546$	−0.0657423	−0.00281351
$547$	−25.4783	−1.08937	−0.544686	−	0.838640i	$-0.683351\pi$
$547$	−25.4783	−1.08937	−0.544686	+	0.838640i	$0.683351\pi$
$548$	−72.2433	−3.08608
$549$	3.36761	0.143726
$550$	−4.06030	−0.173132
$551$	−2.62786	−0.111951
$552$	−3.15193	−0.134155
$553$	4.77937	0.203239
$554$	−55.8944	−2.37473
$555$	−9.06751	−0.384895
$556$	76.2912	3.23547
$557$	38.0932	1.61406	0.807031	−	0.590509i	$-0.201073\pi$
$557$	38.0932	1.61406	0.807031	+	0.590509i	$0.201073\pi$
$558$	22.0082	0.931682
$559$	−0.633232	−0.0267828
$560$	−6.17939	−0.261127
$561$	−4.53151	−0.191320
$562$	10.5368	0.444466
$563$	−15.6392	−0.659112	−0.329556	−	0.944136i	$-0.606899\pi$
$563$	−15.6392	−0.659112	−0.329556	+	0.944136i	$0.606899\pi$
$564$	19.1799	0.807618
$565$	−8.28189	−0.348422
$566$	0.989411	0.0415881
$567$	−3.95196	−0.165967
$568$	58.6414	2.46054
$569$	−14.9371	−0.626195	−0.313097	−	0.949721i	$-0.601367\pi$
$569$	−14.9371	−0.626195	−0.313097	+	0.949721i	$0.601367\pi$
$570$	−3.86594	−0.161926
$571$	2.83461	0.118625	0.0593124	−	0.998239i	$-0.481109\pi$
$571$	2.83461	0.118625	0.0593124	+	0.998239i	$0.481109\pi$
$572$	−0.435196	−0.0181965
$573$	10.3161	0.430962
$574$	8.34214	0.348194
$575$	1.54723	0.0645239
$576$	21.2629	0.885953
$577$	−39.9599	−1.66355	−0.831776	−	0.555111i	$-0.812676\pi$
$577$	−39.9599	−1.66355	−0.831776	+	0.555111i	$0.812676\pi$
$578$	−66.4513	−2.76401
$579$	−1.81029	−0.0752332
$580$	−22.2590	−0.924254
$581$	5.83529	0.242089
$582$	7.47834	0.309987
$583$	12.5147	0.518306
$584$	−32.0332	−1.32554
$585$	0.573105	0.0236950
$586$	−1.57891	−0.0652240
$587$	7.93533	0.327526	0.163763	−	0.986500i	$-0.447637\pi$
$587$	7.93533	0.327526	0.163763	+	0.986500i	$0.447637\pi$
$588$	−14.1018	−0.581548
$589$	3.92018	0.161528
$590$	19.9265	0.820363
$591$	7.49974	0.308498
$592$	−27.9606	−1.14917
$593$	22.9216	0.941276	0.470638	−	0.882326i	$-0.344024\pi$
$593$	22.9216	0.941276	0.470638	+	0.882326i	$0.344024\pi$
$594$	9.57332	0.392798
$595$	10.0311	0.411235
$596$	−15.9315	−0.652582
$597$	0.260136	0.0106467
$598$	0.248444	0.0101596
$599$	−14.1030	−0.576234	−0.288117	−	0.957595i	$-0.593029\pi$
$599$	−14.1030	−0.576234	−0.288117	+	0.957595i	$0.593029\pi$
$600$	−3.35766	−0.137076
$601$	15.4198	0.628989	0.314494	−	0.949259i	$-0.398165\pi$
$601$	15.4198	0.628989	0.314494	+	0.949259i	$0.398165\pi$
$602$	11.1344	0.453802
$603$	−4.80941	−0.195854
$604$	−43.7346	−1.77954
$605$	−23.4059	−0.951585
$606$	12.4862	0.507215
$607$	−7.22374	−0.293203	−0.146601	−	0.989196i	$-0.546833\pi$
$607$	−7.22374	−0.293203	−0.146601	+	0.989196i	$0.546833\pi$
$608$	−0.176292	−0.00714958
$609$	0.705284	0.0285795
$610$	7.61192	0.308198
$611$	−0.758743	−0.0306955
$612$	72.5181	2.93137
$613$	35.6159	1.43851	0.719255	−	0.694746i	$-0.244483\pi$
$613$	35.6159	1.43851	0.719255	+	0.694746i	$0.244483\pi$
$614$	54.9028	2.21570
$615$	7.48765	0.301931
$616$	3.84046	0.154737
$617$	−0.0348449	−0.00140280	−0.000701401	−	1.00000i	$-0.500223\pi$
$617$	−0.0348449	−0.00140280	−0.000701401		1.00000i	$0.500223\pi$
$618$	18.8521	0.758344
$619$	−42.3289	−1.70134	−0.850671	−	0.525699i	$-0.823804\pi$
$619$	−42.3289	−1.70134	−0.850671	+	0.525699i	$0.823804\pi$
$620$	33.2054	1.33356
$621$	−3.64803	−0.146390
$622$	30.8644	1.23755
$623$	5.03214	0.201609
$624$	−0.181958	−0.00728415
$625$	−29.7709	−1.19084
$626$	−22.1295	−0.884475
$627$	0.810872	0.0323831
$628$	−48.4126	−1.93187
$629$	45.3888	1.80977
$630$	−10.0771	−0.401482
$631$	−30.2727	−1.20514	−0.602569	−	0.798067i	$-0.705856\pi$
$631$	−30.2727	−1.20514	−0.602569	+	0.798067i	$0.705856\pi$
$632$	39.1955	1.55911
$633$	−1.64934	−0.0655556
$634$	−0.535716	−0.0212760
$635$	11.4084	0.452730
$636$	20.6206	0.817662
$637$	0.557858	0.0221031
$638$	6.99441	0.276911
$639$	32.2742	1.27675
$640$	48.8049	1.92918
$641$	36.2708	1.43261	0.716306	−	0.697786i	$-0.245832\pi$
$641$	36.2708	1.43261	0.716306	+	0.697786i	$0.245832\pi$
$642$	−10.4313	−0.411690
$643$	−24.5756	−0.969169	−0.484584	−	0.874745i	$-0.661029\pi$
$643$	−24.5756	−0.969169	−0.484584	+	0.874745i	$0.661029\pi$
$644$	−2.91597	−0.114905
$645$	9.99386	0.393508
$646$	19.3515	0.761376
$647$	−7.30018	−0.287000	−0.143500	−	0.989650i	$-0.545836\pi$
$647$	−7.30018	−0.287000	−0.143500	+	0.989650i	$0.545836\pi$
$648$	−32.4099	−1.27318
$649$	−4.17955	−0.164062
$650$	0.264661	0.0103808
$651$	−1.05212	−0.0412360
$652$	−66.0378	−2.58624
$653$	8.14980	0.318926	0.159463	−	0.987204i	$-0.449024\pi$
$653$	8.14980	0.318926	0.159463	+	0.987204i	$0.449024\pi$
$654$	3.23322	0.126429
$655$	−49.5211	−1.93495
$656$	23.0889	0.901470
$657$	−17.6299	−0.687810
$658$	13.3413	0.520097
$659$	18.6279	0.725641	0.362821	−	0.931859i	$-0.381814\pi$
$659$	18.6279	0.725641	0.362821	+	0.931859i	$0.381814\pi$
$660$	6.86839	0.267352
$661$	38.6244	1.50231	0.751157	−	0.660123i	$-0.229496\pi$
$661$	38.6244	1.50231	0.751157	+	0.660123i	$0.229496\pi$
$662$	31.7307	1.23325
$663$	0.295375	0.0114714
$664$	47.8551	1.85714
$665$	−1.79497	−0.0696061
$666$	−45.5971	−1.76685
$667$	−2.66531	−0.103201
$668$	27.2462	1.05419
$669$	−2.06658	−0.0798985
$670$	−10.8708	−0.419977
$671$	−1.59659	−0.0616355
$672$	0.0473144	0.00182519
$673$	37.5430	1.44718	0.723589	−	0.690231i	$-0.242491\pi$
$673$	37.5430	1.44718	0.723589	+	0.690231i	$0.242491\pi$
$674$	83.8184	3.22856
$675$	−3.88615	−0.149578
$676$	−52.1675	−2.00644
$677$	−4.26185	−0.163796	−0.0818981	−	0.996641i	$-0.526098\pi$
$677$	−4.26185	−0.163796	−0.0818981	+	0.996641i	$0.526098\pi$
$678$	4.28802	0.164680
$679$	3.47223	0.133252
$680$	82.2649	3.15472
$681$	−5.51950	−0.211508
$682$	−10.4341	−0.399542
$683$	−27.2681	−1.04338	−0.521692	−	0.853134i	$-0.674699\pi$
$683$	−27.2681	−1.04338	−0.521692	+	0.853134i	$0.674699\pi$
$684$	−12.9764	−0.496167
$685$	−45.1042	−1.72334
$686$	−20.1548	−0.769513
$687$	−9.17176	−0.349924
$688$	30.8170	1.17489
$689$	−0.815739	−0.0310772
$690$	−3.92102	−0.149271
$691$	38.5478	1.46643	0.733213	−	0.679999i	$-0.238020\pi$
$691$	38.5478	1.46643	0.733213	+	0.679999i	$0.238020\pi$
$692$	86.8787	3.30263
$693$	2.11366	0.0802912
$694$	−53.3820	−2.02635
$695$	47.6315	1.80676
$696$	5.78402	0.219243
$697$	−37.4806	−1.41968
$698$	−10.0183	−0.379197
$699$	3.61710	0.136811
$700$	−3.10630	−0.117407
$701$	23.4776	0.886738	0.443369	−	0.896339i	$-0.353783\pi$
$701$	23.4776	0.886738	0.443369	+	0.896339i	$0.353783\pi$
$702$	−0.624013	−0.0235518
$703$	−8.12192	−0.306324
$704$	−10.0807	−0.379932
$705$	11.9747	0.450994
$706$	32.2506	1.21377
$707$	5.79739	0.218033
$708$	−6.88671	−0.258818
$709$	−8.49189	−0.318919	−0.159460	−	0.987204i	$-0.550975\pi$
$709$	−8.49189	−0.318919	−0.159460	+	0.987204i	$0.550975\pi$
$710$	72.9503	2.73778
$711$	21.5718	0.809007
$712$	41.2685	1.54660
$713$	3.97604	0.148904
$714$	−5.19369	−0.194369
$715$	−0.271709	−0.0101613
$716$	36.5412	1.36561
$717$	−5.82195	−0.217425
$718$	8.11704	0.302925
$719$	18.5807	0.692944	0.346472	−	0.938060i	$-0.387380\pi$
$719$	18.5807	0.692944	0.346472	+	0.938060i	$0.387380\pi$
$720$	−27.8909	−1.03943
$721$	8.75315	0.325984
$722$	43.1359	1.60535
$723$	−10.4931	−0.390241
$724$	−73.5458	−2.73331
$725$	−2.83928	−0.105448
$726$	12.1186	0.449764
$727$	−6.36173	−0.235943	−0.117972	−	0.993017i	$-0.537639\pi$
$727$	−6.36173	−0.235943	−0.117972	+	0.993017i	$0.537639\pi$
$728$	−0.250331	−0.00927789
$729$	−13.0316	−0.482654
$730$	−39.8495	−1.47490
$731$	−50.0258	−1.85027
$732$	−2.63072	−0.0972341
$733$	24.2533	0.895817	0.447908	−	0.894079i	$-0.352169\pi$
$733$	24.2533	0.895817	0.447908	+	0.894079i	$0.352169\pi$
$734$	14.9642	0.552337
$735$	−8.80428	−0.324751
$736$	−0.178804	−0.00659080
$737$	2.28014	0.0839900
$738$	37.6525	1.38601
$739$	14.4839	0.532799	0.266400	−	0.963863i	$-0.414166\pi$
$739$	14.4839	0.532799	0.266400	+	0.963863i	$0.414166\pi$
$740$	−68.7957	−2.52898
$741$	−0.0528547	−0.00194167
$742$	14.3435	0.526565
$743$	10.4772	0.384370	0.192185	−	0.981359i	$-0.438443\pi$
$743$	10.4772	0.384370	0.192185	+	0.981359i	$0.438443\pi$
$744$	−8.62846	−0.316335
$745$	−9.94666	−0.364418
$746$	8.34747	0.305623
$747$	26.3378	0.963650
$748$	−34.3808	−1.25709
$749$	−4.84330	−0.176970
$750$	12.0906	0.441486
$751$	11.5935	0.423052	0.211526	−	0.977372i	$-0.432157\pi$
$751$	11.5935	0.423052	0.211526	+	0.977372i	$0.432157\pi$
$752$	36.9252	1.34652
$753$	9.59042	0.349494
$754$	−0.455913	−0.0166034
$755$	−27.3052	−0.993737
$756$	7.32399	0.266371
$757$	3.38169	0.122910	0.0614548	−	0.998110i	$-0.480426\pi$
$757$	3.38169	0.122910	0.0614548	+	0.998110i	$0.480426\pi$
$758$	−63.5743	−2.30912
$759$	0.822426	0.0298522
$760$	−14.7206	−0.533971
$761$	−16.8527	−0.610909	−0.305454	−	0.952207i	$-0.598808\pi$
$761$	−16.8527	−0.610909	−0.305454	+	0.952207i	$0.598808\pi$
$762$	−5.90682	−0.213981
$763$	1.50120	0.0543471
$764$	78.2690	2.83167
$765$	45.2757	1.63695
$766$	−15.8785	−0.573712
$767$	0.272434	0.00983701
$768$	−16.9953	−0.613264
$769$	−0.562206	−0.0202737	−0.0101368	−	0.999949i	$-0.503227\pi$
$769$	−0.562206	−0.0202737	−0.0101368	+	0.999949i	$0.503227\pi$
$770$	4.77756	0.172171
$771$	−2.30204	−0.0829059
$772$	−13.7348	−0.494326
$773$	29.9928	1.07877	0.539383	−	0.842061i	$-0.318658\pi$
$773$	29.9928	1.07877	0.539383	+	0.842061i	$0.318658\pi$
$774$	50.2553	1.80639
$775$	4.23557	0.152146
$776$	28.4757	1.02222
$777$	2.17981	0.0782004
$778$	55.4449	1.98780
$779$	6.70681	0.240296
$780$	−0.447699	−0.0160302
$781$	−15.3012	−0.547520
$782$	19.6273	0.701870
$783$	6.69441	0.239239
$784$	−27.1489	−0.969603
$785$	−30.2258	−1.07881
$786$	25.6400	0.914548
$787$	7.07362	0.252147	0.126074	−	0.992021i	$-0.459762\pi$
$787$	7.07362	0.252147	0.126074	+	0.992021i	$0.459762\pi$
$788$	56.9009	2.02701
$789$	−6.28972	−0.223920
$790$	48.7595	1.73479
$791$	1.99095	0.0707901
$792$	17.3341	0.615939
$793$	0.104069	0.00369562
$794$	72.1309	2.55983
$795$	12.8742	0.456602
$796$	1.97366	0.0699547
$797$	−37.3116	−1.32164	−0.660822	−	0.750542i	$-0.729792\pi$
$797$	−37.3116	−1.32164	−0.660822	+	0.750542i	$0.729792\pi$
$798$	0.929364	0.0328991
$799$	−59.9413	−2.12057
$800$	−0.190475	−0.00673431
$801$	22.7128	0.802516
$802$	2.10311	0.0742633
$803$	8.35835	0.294960
$804$	3.75702	0.132500
$805$	−1.82055	−0.0641660
$806$	0.680120	0.0239562
$807$	11.4619	0.403477
$808$	47.5443	1.67260
$809$	3.33734	0.117334	0.0586672	−	0.998278i	$-0.481315\pi$
$809$	3.33734	0.117334	0.0586672	+	0.998278i	$0.481315\pi$
$810$	−40.3182	−1.41664
$811$	−32.0451	−1.12525	−0.562627	−	0.826711i	$-0.690209\pi$
$811$	−32.0451	−1.12525	−0.562627	+	0.826711i	$0.690209\pi$
$812$	5.35102	0.187784
$813$	0.677233	0.0237516
$814$	21.6176	0.757696
$815$	−41.2299	−1.44422
$816$	−14.3748	−0.503219
$817$	8.95166	0.313179
$818$	−37.2699	−1.30311
$819$	−0.137773	−0.00481419
$820$	56.8092	1.98386
$821$	47.8076	1.66850	0.834249	−	0.551389i	$-0.185902\pi$
$821$	47.8076	1.66850	0.834249	+	0.551389i	$0.185902\pi$
$822$	23.3531	0.814533
$823$	47.5297	1.65678	0.828390	−	0.560152i	$-0.189257\pi$
$823$	47.5297	1.65678	0.828390	+	0.560152i	$0.189257\pi$
$824$	71.7844	2.50073
$825$	0.876108	0.0305022
$826$	−4.79031	−0.166676
$827$	9.91342	0.344724	0.172362	−	0.985034i	$-0.444860\pi$
$827$	9.91342	0.344724	0.172362	+	0.985034i	$0.444860\pi$
$828$	−13.1613	−0.457388
$829$	−48.8832	−1.69778	−0.848892	−	0.528566i	$-0.822730\pi$
$829$	−48.8832	−1.69778	−0.848892	+	0.528566i	$0.822730\pi$
$830$	59.5321	2.06639
$831$	12.0606	0.418376
$832$	0.657087	0.0227804
$833$	44.0712	1.52698
$834$	−24.6616	−0.853962
$835$	17.0108	0.588683
$836$	6.15213	0.212776
$837$	−9.98655	−0.345186
$838$	39.4726	1.36356
$839$	49.6361	1.71363	0.856813	−	0.515627i	$-0.172441\pi$
$839$	49.6361	1.71363	0.856813	+	0.515627i	$0.172441\pi$
$840$	3.95080	0.136316
$841$	−24.1090	−0.831343
$842$	67.4278	2.32372
$843$	−2.27356	−0.0783055
$844$	−12.5137	−0.430738
$845$	−32.5701	−1.12045
$846$	60.2163	2.07028
$847$	5.62674	0.193337
$848$	39.6990	1.36327
$849$	−0.213489	−0.00732694
$850$	20.9084	0.717152
$851$	−8.23765	−0.282383
$852$	−25.2120	−0.863749
$853$	11.3712	0.389343	0.194671	−	0.980868i	$-0.437636\pi$
$853$	11.3712	0.389343	0.194671	+	0.980868i	$0.437636\pi$
$854$	−1.82989	−0.0626176
$855$	−8.10168	−0.277072
$856$	−39.7198	−1.35760
$857$	−34.7047	−1.18549	−0.592745	−	0.805390i	$-0.701956\pi$
$857$	−34.7047	−1.18549	−0.592745	+	0.805390i	$0.701956\pi$
$858$	0.140680	0.00480273
$859$	5.98867	0.204331	0.102165	−	0.994767i	$-0.467423\pi$
$859$	5.98867	0.204331	0.102165	+	0.994767i	$0.467423\pi$
$860$	75.8239	2.58557
$861$	−1.80002	−0.0613444
$862$	59.9189	2.04085
$863$	49.0513	1.66973	0.834863	−	0.550457i	$-0.185547\pi$
$863$	49.0513	1.66973	0.834863	+	0.550457i	$0.185547\pi$
$864$	0.449099	0.0152786
$865$	54.2417	1.84427
$866$	−15.7295	−0.534511
$867$	14.3385	0.486960
$868$	−7.98252	−0.270944
$869$	−10.2272	−0.346934
$870$	7.19536	0.243946
$871$	−0.148625	−0.00503597
$872$	12.3113	0.416914
$873$	15.6721	0.530419
$874$	−3.51212	−0.118799
$875$	5.61373	0.189779
$876$	13.7722	0.465319
$877$	−2.10297	−0.0710123	−0.0355062	−	0.999369i	$-0.511304\pi$
$877$	−2.10297	−0.0710123	−0.0355062	+	0.999369i	$0.511304\pi$
$878$	2.15267	0.0726491
$879$	0.340687	0.0114911
$880$	13.2231	0.445750
$881$	33.7365	1.13661	0.568305	−	0.822818i	$-0.307599\pi$
$881$	33.7365	1.13661	0.568305	+	0.822818i	$0.307599\pi$
$882$	−44.2734	−1.49076
$883$	−7.14808	−0.240552	−0.120276	−	0.992740i	$-0.538378\pi$
$883$	−7.14808	−0.240552	−0.120276	+	0.992740i	$0.538378\pi$
$884$	2.24103	0.0753739
$885$	−4.29963	−0.144531
$886$	9.32463	0.313267
$887$	−23.2748	−0.781492	−0.390746	−	0.920498i	$-0.627783\pi$
$887$	−23.2748	−0.781492	−0.390746	+	0.920498i	$0.627783\pi$
$888$	17.8766	0.599900
$889$	−2.74257	−0.0919827
$890$	51.3384	1.72087
$891$	8.45666	0.283309
$892$	−15.6792	−0.524979
$893$	10.7259	0.358930
$894$	5.14997	0.172241
$895$	22.8141	0.762590
$896$	−11.7326	−0.391959
$897$	−0.0536078	−0.00178991
$898$	−94.8884	−3.16647
$899$	−7.29633	−0.243346
$900$	−14.0204	−0.467347
$901$	−64.4440	−2.14694
$902$	−17.8511	−0.594376
$903$	−2.40251	−0.0799504
$904$	16.3278	0.543053
$905$	−45.9174	−1.52635
$906$	14.1375	0.469687
$907$	−30.8974	−1.02593	−0.512965	−	0.858409i	$-0.671453\pi$
$907$	−30.8974	−1.02593	−0.512965	+	0.858409i	$0.671453\pi$
$908$	−41.8767	−1.38973
$909$	26.1667	0.867896
$910$	−0.311414	−0.0103233
$911$	5.50075	0.182248	0.0911239	−	0.995840i	$-0.470954\pi$
$911$	5.50075	0.182248	0.0911239	+	0.995840i	$0.470954\pi$
$912$	2.57224	0.0851755
$913$	−12.4867	−0.413251
$914$	−16.7162	−0.552922
$915$	−1.64246	−0.0542979
$916$	−69.5866	−2.29921
$917$	11.9048	0.393131
$918$	−49.2975	−1.62706
$919$	−59.0626	−1.94830	−0.974148	−	0.225911i	$-0.927464\pi$
$919$	−59.0626	−1.94830	−0.974148	+	0.225911i	$0.927464\pi$
$920$	−14.9303	−0.492238
$921$	−11.8466	−0.390359
$922$	−60.8430	−2.00376
$923$	0.997370	0.0328288
$924$	−1.65115	−0.0543188
$925$	−8.77534	−0.288532
$926$	−57.7730	−1.89854
$927$	39.5076	1.29760
$928$	0.328118	0.0107710
$929$	−50.2303	−1.64800	−0.824002	−	0.566587i	$-0.808263\pi$
$929$	−50.2303	−1.64800	−0.824002	+	0.566587i	$0.808263\pi$
$930$	−10.7339	−0.351977
$931$	−7.88614	−0.258458
$932$	27.4431	0.898930
$933$	−6.65975	−0.218030
$934$	36.8699	1.20642
$935$	−21.4652	−0.701988
$936$	−1.12988	−0.0369312
$937$	23.4844	0.767204	0.383602	−	0.923499i	$-0.374684\pi$
$937$	23.4844	0.767204	0.383602	+	0.923499i	$0.374684\pi$
$938$	2.61333	0.0853283
$939$	4.77498	0.155826
$940$	90.8528	2.96329
$941$	48.4425	1.57918	0.789591	−	0.613634i	$-0.210293\pi$
$941$	48.4425	1.57918	0.789591	+	0.613634i	$0.210293\pi$
$942$	15.6497	0.509895
$943$	6.80237	0.221516
$944$	−13.2583	−0.431522
$945$	4.57265	0.148748
$946$	−23.8260	−0.774651
$947$	5.36696	0.174403	0.0872014	−	0.996191i	$-0.472208\pi$
$947$	5.36696	0.174403	0.0872014	+	0.996191i	$0.472208\pi$
$948$	−16.8515	−0.547312
$949$	−0.544818	−0.0176856
$950$	−3.74137	−0.121386
$951$	0.115594	0.00374838
$952$	−19.7763	−0.640955
$953$	−31.3578	−1.01578	−0.507889	−	0.861423i	$-0.669574\pi$
$953$	−31.3578	−1.01578	−0.507889	+	0.861423i	$0.669574\pi$
$954$	64.7397	2.09602
$955$	48.8663	1.58128
$956$	−44.1714	−1.42861
$957$	−1.50921	−0.0487859
$958$	−62.2543	−2.01134
$959$	10.8430	0.350138
$960$	−10.3703	−0.334701
$961$	−20.1155	−0.648888
$962$	−1.40909	−0.0454308
$963$	−21.8604	−0.704442
$964$	−79.6115	−2.56411
$965$	−8.57514	−0.276044
$966$	0.942606	0.0303279
$967$	−18.7845	−0.604068	−0.302034	−	0.953297i	$-0.597666\pi$
$967$	−18.7845	−0.604068	−0.302034	+	0.953297i	$0.597666\pi$
$968$	46.1448	1.48315
$969$	−4.17556	−0.134138
$970$	35.4240	1.13740
$971$	−0.903351	−0.0289899	−0.0144950	−	0.999895i	$-0.504614\pi$
$971$	−0.903351	−0.0289899	−0.0144950	+	0.999895i	$0.504614\pi$
$972$	50.3949	1.61642
$973$	−11.4505	−0.367087
$974$	−53.8988	−1.72703
$975$	−0.0571069	−0.00182889
$976$	−5.06468	−0.162116
$977$	−22.1604	−0.708973	−0.354486	−	0.935061i	$-0.615344\pi$
$977$	−22.1604	−0.708973	−0.354486	+	0.935061i	$0.615344\pi$
$978$	21.3472	0.682607
$979$	−10.7681	−0.344151
$980$	−66.7985	−2.13380
$981$	6.77572	0.216332
$982$	85.5199	2.72905
$983$	2.06334	0.0658102	0.0329051	−	0.999458i	$-0.489524\pi$
$983$	2.06334	0.0658102	0.0329051	+	0.999458i	$0.489524\pi$
$984$	−14.7619	−0.470593
$985$	35.5254	1.13193
$986$	−36.0175	−1.14703
$987$	−2.87870	−0.0916301
$988$	−0.401011	−0.0127579
$989$	9.07921	0.288702
$990$	21.5637	0.685340
$991$	−12.1290	−0.385290	−0.192645	−	0.981269i	$-0.561707\pi$
$991$	−12.1290	−0.385290	−0.192645	+	0.981269i	$0.561707\pi$
$992$	−0.489479	−0.0155410
$993$	−6.84667	−0.217272
$994$	−17.5371	−0.556244
$995$	1.23223	0.0390644
$996$	−20.5746	−0.651931
$997$	−30.3985	−0.962732	−0.481366	−	0.876520i	$-0.659859\pi$
$997$	−30.3985	−0.962732	−0.481366	+	0.876520i	$0.659859\pi$
$998$	79.2982	2.51014
$999$	20.6904	0.654614

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4001.2.a.a.1.11	✓	149

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4001.2.a.a.1.11	✓	149	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:	\( N \)	\(=\)	\( 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.45256 q^{2} +0.529200 q^{3} +4.01507 q^{4} +2.50676 q^{5} -1.29790 q^{6} -0.602620 q^{7} -4.94208 q^{8} -2.71995 q^{9} +O(q^{10})\)	\(q-2.45256 q^{2} +0.529200 q^{3} +4.01507 q^{4} +2.50676 q^{5} -1.29790 q^{6} -0.602620 q^{7} -4.94208 q^{8} -2.71995 q^{9} -6.14798 q^{10} +1.28953 q^{11} +2.12477 q^{12} -0.0840546 q^{13} +1.47796 q^{14} +1.32658 q^{15} +4.09063 q^{16} -6.64038 q^{17} +6.67084 q^{18} +1.18824 q^{19} +10.0648 q^{20} -0.318906 q^{21} -3.16265 q^{22} +1.20517 q^{23} -2.61535 q^{24} +1.28383 q^{25} +0.206149 q^{26} -3.02700 q^{27} -2.41956 q^{28} -2.21157 q^{29} -3.25351 q^{30} +3.29916 q^{31} -0.148365 q^{32} +0.682417 q^{33} +16.2859 q^{34} -1.51062 q^{35} -10.9208 q^{36} -6.83528 q^{37} -2.91422 q^{38} -0.0444817 q^{39} -12.3886 q^{40} +5.64435 q^{41} +0.782138 q^{42} +7.53358 q^{43} +5.17754 q^{44} -6.81825 q^{45} -2.95575 q^{46} +9.02679 q^{47} +2.16476 q^{48} -6.63685 q^{49} -3.14868 q^{50} -3.51409 q^{51} -0.337485 q^{52} +9.70487 q^{53} +7.42390 q^{54} +3.23253 q^{55} +2.97820 q^{56} +0.628814 q^{57} +5.42401 q^{58} -3.24115 q^{59} +5.32629 q^{60} -1.23812 q^{61} -8.09141 q^{62} +1.63909 q^{63} -7.81738 q^{64} -0.210704 q^{65} -1.67367 q^{66} +1.76820 q^{67} -26.6616 q^{68} +0.637774 q^{69} +3.70490 q^{70} -11.8657 q^{71} +13.4422 q^{72} +6.48172 q^{73} +16.7640 q^{74} +0.679403 q^{75} +4.77084 q^{76} -0.777095 q^{77} +0.109094 q^{78} -7.93098 q^{79} +10.2542 q^{80} +6.55796 q^{81} -13.8431 q^{82} -9.68320 q^{83} -1.28043 q^{84} -16.6458 q^{85} -18.4766 q^{86} -1.17036 q^{87} -6.37294 q^{88} -8.35044 q^{89} +16.7222 q^{90} +0.0506530 q^{91} +4.83882 q^{92} +1.74592 q^{93} -22.1388 q^{94} +2.97862 q^{95} -0.0785145 q^{96} -5.76190 q^{97} +16.2773 q^{98} -3.50745 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 149 q - 6 q^{2} - 28 q^{3} + 116 q^{4} - 19 q^{5} - 31 q^{6} - 47 q^{7} - 15 q^{8} + 115 q^{9}+O(q^{10}) \) 149 * q - 6 * q^2 - 28 * q^3 + 116 * q^4 - 19 * q^5 - 31 * q^6 - 47 * q^7 - 15 * q^8 + 115 * q^9	\( 149 q - 6 q^{2} - 28 q^{3} + 116 q^{4} - 19 q^{5} - 31 q^{6} - 47 q^{7} - 15 q^{8} + 115 q^{9} - 48 q^{10} - 31 q^{11} - 61 q^{12} - 54 q^{13} - 44 q^{14} - 65 q^{15} + 58 q^{16} - 26 q^{17} - 23 q^{18} - 86 q^{19} - 52 q^{20} - 30 q^{21} - 56 q^{22} - 63 q^{23} - 90 q^{24} + 92 q^{25} - 38 q^{26} - 103 q^{27} - 77 q^{28} - 51 q^{29} - 22 q^{30} - 256 q^{31} - 21 q^{32} - 36 q^{33} - 124 q^{34} - 50 q^{35} + 45 q^{36} - 42 q^{37} - 14 q^{38} - 119 q^{39} - 131 q^{40} - 55 q^{41} - 5 q^{42} - 55 q^{43} - 54 q^{44} - 68 q^{45} - 59 q^{46} - 82 q^{47} - 89 q^{48} + 30 q^{49} + 13 q^{50} - 83 q^{51} - 126 q^{52} - 23 q^{53} - 83 q^{54} - 244 q^{55} - 94 q^{56} - 14 q^{57} - 60 q^{58} - 93 q^{59} - 70 q^{60} - 139 q^{61} - 10 q^{62} - 120 q^{63} - 45 q^{64} - 37 q^{65} - 28 q^{66} - 110 q^{67} - 27 q^{68} - 79 q^{69} - 78 q^{70} - 123 q^{71} - 74 q^{73} - 25 q^{74} - 146 q^{75} - 192 q^{76} - q^{77} + 26 q^{78} - 273 q^{79} - 51 q^{80} + 41 q^{81} - 120 q^{82} - 27 q^{83} - 14 q^{84} - 71 q^{85} + 3 q^{86} - 98 q^{87} - 143 q^{88} - 70 q^{89} - 24 q^{90} - 256 q^{91} - 47 q^{92} + 16 q^{93} - 151 q^{94} - 83 q^{95} - 137 q^{96} - 108 q^{97} + 17 q^{98} - 131 q^{99}+O(q^{100}) \) 149 * q - 6 * q^2 - 28 * q^3 + 116 * q^4 - 19 * q^5 - 31 * q^6 - 47 * q^7 - 15 * q^8 + 115 * q^9 - 48 * q^10 - 31 * q^11 - 61 * q^12 - 54 * q^13 - 44 * q^14 - 65 * q^15 + 58 * q^16 - 26 * q^17 - 23 * q^18 - 86 * q^19 - 52 * q^20 - 30 * q^21 - 56 * q^22 - 63 * q^23 - 90 * q^24 + 92 * q^25 - 38 * q^26 - 103 * q^27 - 77 * q^28 - 51 * q^29 - 22 * q^30 - 256 * q^31 - 21 * q^32 - 36 * q^33 - 124 * q^34 - 50 * q^35 + 45 * q^36 - 42 * q^37 - 14 * q^38 - 119 * q^39 - 131 * q^40 - 55 * q^41 - 5 * q^42 - 55 * q^43 - 54 * q^44 - 68 * q^45 - 59 * q^46 - 82 * q^47 - 89 * q^48 + 30 * q^49 + 13 * q^50 - 83 * q^51 - 126 * q^52 - 23 * q^53 - 83 * q^54 - 244 * q^55 - 94 * q^56 - 14 * q^57 - 60 * q^58 - 93 * q^59 - 70 * q^60 - 139 * q^61 - 10 * q^62 - 120 * q^63 - 45 * q^64 - 37 * q^65 - 28 * q^66 - 110 * q^67 - 27 * q^68 - 79 * q^69 - 78 * q^70 - 123 * q^71 - 74 * q^73 - 25 * q^74 - 146 * q^75 - 192 * q^76 - q^77 + 26 * q^78 - 273 * q^79 - 51 * q^80 + 41 * q^81 - 120 * q^82 - 27 * q^83 - 14 * q^84 - 71 * q^85 + 3 * q^86 - 98 * q^87 - 143 * q^88 - 70 * q^89 - 24 * q^90 - 256 * q^91 - 47 * q^92 + 16 * q^93 - 151 * q^94 - 83 * q^95 - 137 * q^96 - 108 * q^97 + 17 * q^98 - 131 * q^99

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