LMFDB - Embedded newform 401.2.a.a.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [401,2,Mod(1,401)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(401, 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("401.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	401.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:	$3.20200112105$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 10 x^{10} + 34 x^{9} + 29 x^{8} - 129 x^{7} - 24 x^{6} + 203 x^{5} + x^{4} + \cdots + 4 $ x^12 - 3x^11 - 10x^10 + 34x^9 + 29x^8 - 129x^7 - 24x^6 + 203x^5 + x^4 - 130x^3 - 5x^2 + 22x + 4
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			1.4
Root			$1.53244$ of defining polynomial
Character	$\chi$	$=$	401.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.53244 q^{2} +1.08207 q^{3} +0.348380 q^{4} +1.17495 q^{5} -1.65820 q^{6} -3.29109 q^{7} +2.53101 q^{8} -1.82913 q^{9} +O(q^{10})$	\(q-1.53244 q^{2} +1.08207 q^{3} +0.348380 q^{4} +1.17495 q^{5} -1.65820 q^{6} -3.29109 q^{7} +2.53101 q^{8} -1.82913 q^{9} -1.80054 q^{10} -4.92363 q^{11} +0.376970 q^{12} +2.28740 q^{13} +5.04341 q^{14} +1.27137 q^{15} -4.57539 q^{16} -7.14077 q^{17} +2.80304 q^{18} +2.39316 q^{19} +0.409329 q^{20} -3.56118 q^{21} +7.54518 q^{22} +3.47110 q^{23} +2.73872 q^{24} -3.61949 q^{25} -3.50531 q^{26} -5.22544 q^{27} -1.14655 q^{28} +5.84371 q^{29} -1.94831 q^{30} -2.98470 q^{31} +1.94950 q^{32} -5.32769 q^{33} +10.9428 q^{34} -3.86687 q^{35} -0.637234 q^{36} -6.96780 q^{37} -3.66738 q^{38} +2.47511 q^{39} +2.97381 q^{40} +3.02886 q^{41} +5.45730 q^{42} -12.7491 q^{43} -1.71529 q^{44} -2.14914 q^{45} -5.31926 q^{46} -2.74783 q^{47} -4.95088 q^{48} +3.83128 q^{49} +5.54666 q^{50} -7.72678 q^{51} +0.796884 q^{52} +9.52601 q^{53} +8.00769 q^{54} -5.78502 q^{55} -8.32979 q^{56} +2.58956 q^{57} -8.95514 q^{58} -13.5768 q^{59} +0.442921 q^{60} -0.828753 q^{61} +4.57389 q^{62} +6.01984 q^{63} +6.16329 q^{64} +2.68758 q^{65} +8.16438 q^{66} +8.58194 q^{67} -2.48770 q^{68} +3.75596 q^{69} +5.92575 q^{70} +7.44012 q^{71} -4.62956 q^{72} -0.288306 q^{73} +10.6778 q^{74} -3.91653 q^{75} +0.833730 q^{76} +16.2041 q^{77} -3.79297 q^{78} -16.0678 q^{79} -5.37586 q^{80} -0.166870 q^{81} -4.64156 q^{82} +3.12661 q^{83} -1.24064 q^{84} -8.39004 q^{85} +19.5372 q^{86} +6.32327 q^{87} -12.4618 q^{88} +6.47104 q^{89} +3.29343 q^{90} -7.52803 q^{91} +1.20926 q^{92} -3.22965 q^{93} +4.21089 q^{94} +2.81184 q^{95} +2.10949 q^{96} +8.37682 q^{97} -5.87121 q^{98} +9.00597 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 5 q^{3} + 5 q^{4} - 7 q^{5} - 9 q^{6} - 20 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 - 5 * q^3 + 5 * q^4 - 7 * q^5 - 9 * q^6 - 20 * q^7 - 3 * q^8 + 3 * q^9	\( 12 q - 3 q^{2} - 5 q^{3} + 5 q^{4} - 7 q^{5} - 9 q^{6} - 20 q^{7} - 3 q^{8} + 3 q^{9} - 11 q^{10} - 11 q^{11} - 9 q^{12} - 11 q^{13} - 3 q^{14} - 11 q^{15} - 9 q^{16} + q^{17} - q^{18} - 34 q^{19} - 5 q^{20} - 3 q^{21} + 3 q^{22} - 7 q^{23} - 9 q^{24} + 7 q^{25} + 6 q^{26} - 2 q^{27} - 23 q^{28} - 6 q^{29} + 23 q^{30} - 52 q^{31} + 11 q^{32} + 4 q^{33} - 5 q^{34} + 12 q^{35} + 16 q^{36} + 3 q^{37} + 25 q^{38} - 24 q^{39} - 25 q^{40} - 16 q^{41} + 47 q^{42} - 2 q^{43} - 2 q^{44} - 23 q^{45} - 16 q^{46} - 3 q^{47} + 24 q^{48} + 6 q^{49} + 27 q^{50} - 16 q^{51} - 5 q^{52} + 19 q^{53} + 5 q^{54} - 43 q^{55} + 7 q^{56} + 11 q^{57} + 11 q^{58} - q^{59} + 30 q^{60} - 24 q^{61} + 39 q^{62} - 11 q^{63} - q^{64} + 13 q^{65} + 14 q^{66} + 6 q^{67} + 32 q^{68} + 29 q^{69} + 47 q^{70} - 15 q^{71} + 32 q^{72} - 20 q^{73} + 25 q^{74} + 31 q^{75} - 42 q^{76} + 38 q^{77} + 52 q^{78} - 53 q^{79} + 23 q^{80} - 8 q^{81} + 4 q^{82} + 17 q^{83} + 35 q^{84} + 7 q^{85} + 28 q^{86} - 5 q^{87} + 38 q^{88} - q^{89} + 58 q^{90} - 6 q^{91} + 46 q^{92} + 44 q^{93} - 4 q^{94} + 34 q^{95} + 28 q^{96} + 12 q^{97} + 27 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 - 5 * q^3 + 5 * q^4 - 7 * q^5 - 9 * q^6 - 20 * q^7 - 3 * q^8 + 3 * q^9 - 11 * q^10 - 11 * q^11 - 9 * q^12 - 11 * q^13 - 3 * q^14 - 11 * q^15 - 9 * q^16 + q^17 - q^18 - 34 * q^19 - 5 * q^20 - 3 * q^21 + 3 * q^22 - 7 * q^23 - 9 * q^24 + 7 * q^25 + 6 * q^26 - 2 * q^27 - 23 * q^28 - 6 * q^29 + 23 * q^30 - 52 * q^31 + 11 * q^32 + 4 * q^33 - 5 * q^34 + 12 * q^35 + 16 * q^36 + 3 * q^37 + 25 * q^38 - 24 * q^39 - 25 * q^40 - 16 * q^41 + 47 * q^42 - 2 * q^43 - 2 * q^44 - 23 * q^45 - 16 * q^46 - 3 * q^47 + 24 * q^48 + 6 * q^49 + 27 * q^50 - 16 * q^51 - 5 * q^52 + 19 * q^53 + 5 * q^54 - 43 * q^55 + 7 * q^56 + 11 * q^57 + 11 * q^58 - q^59 + 30 * q^60 - 24 * q^61 + 39 * q^62 - 11 * q^63 - q^64 + 13 * q^65 + 14 * q^66 + 6 * q^67 + 32 * q^68 + 29 * q^69 + 47 * q^70 - 15 * q^71 + 32 * q^72 - 20 * q^73 + 25 * q^74 + 31 * q^75 - 42 * q^76 + 38 * q^77 + 52 * q^78 - 53 * q^79 + 23 * q^80 - 8 * q^81 + 4 * q^82 + 17 * q^83 + 35 * q^84 + 7 * q^85 + 28 * q^86 - 5 * q^87 + 38 * q^88 - q^89 + 58 * q^90 - 6 * q^91 + 46 * q^92 + 44 * q^93 - 4 * q^94 + 34 * q^95 + 28 * q^96 + 12 * q^97 + 27 * q^98

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 $

$2$	−1.53244	−1.08360	−0.541800	−	0.840507i	$-0.682257\pi$
$2$	−1.53244	−1.08360	−0.541800	+	0.840507i	$0.682257\pi$
$3$	1.08207	0.624731	0.312366	−	0.949962i	$-0.398879\pi$
$3$	1.08207	0.624731	0.312366	+	0.949962i	$0.398879\pi$
$4$	0.348380	0.174190
$5$	1.17495	0.525454	0.262727	−	0.964870i	$-0.415378\pi$
$5$	1.17495	0.525454	0.262727	+	0.964870i	$0.415378\pi$
$6$	−1.65820	−0.676959
$7$	−3.29109	−1.24392	−0.621958	−	0.783051i	$-0.713662\pi$
$7$	−3.29109	−1.24392	−0.621958	+	0.783051i	$0.713662\pi$
$8$	2.53101	0.894848
$9$	−1.82913	−0.609711
$10$	−1.80054	−0.569382
$11$	−4.92363	−1.48453	−0.742265	−	0.670107i	$-0.766248\pi$
$11$	−4.92363	−1.48453	−0.742265	+	0.670107i	$0.766248\pi$
$12$	0.376970	0.108822
$13$	2.28740	0.634410	0.317205	−	0.948357i	$-0.397256\pi$
$13$	2.28740	0.634410	0.317205	+	0.948357i	$0.397256\pi$
$14$	5.04341	1.34791
$15$	1.27137	0.328267
$16$	−4.57539	−1.14385
$17$	−7.14077	−1.73189	−0.865945	−	0.500139i	$-0.833282\pi$
$17$	−7.14077	−1.73189	−0.865945	+	0.500139i	$0.833282\pi$
$18$	2.80304	0.660683
$19$	2.39316	0.549029	0.274514	−	0.961583i	$-0.411483\pi$
$19$	2.39316	0.549029	0.274514	+	0.961583i	$0.411483\pi$
$20$	0.409329	0.0915288
$21$	−3.56118	−0.777112
$22$	7.54518	1.60864
$23$	3.47110	0.723774	0.361887	−	0.932222i	$-0.382133\pi$
$23$	3.47110	0.723774	0.361887	+	0.932222i	$0.382133\pi$
$24$	2.73872	0.559039
$25$	−3.61949	−0.723898
$26$	−3.50531	−0.687447
$27$	−5.22544	−1.00564
$28$	−1.14655	−0.216678
$29$	5.84371	1.08515	0.542574	−	0.840008i	$-0.317450\pi$
$29$	5.84371	1.08515	0.542574	+	0.840008i	$0.317450\pi$
$30$	−1.94831	−0.355710
$31$	−2.98470	−0.536069	−0.268034	−	0.963409i	$-0.586374\pi$
$31$	−2.98470	−0.536069	−0.268034	+	0.963409i	$0.586374\pi$
$32$	1.94950	0.344626
$33$	−5.32769	−0.927431
$34$	10.9428	1.87668
$35$	−3.86687	−0.653620
$36$	−0.637234	−0.106206
$37$	−6.96780	−1.14550	−0.572749	−	0.819730i	$-0.694123\pi$
$37$	−6.96780	−1.14550	−0.572749	+	0.819730i	$0.694123\pi$
$38$	−3.66738	−0.594928
$39$	2.47511	0.396336
$40$	2.97381	0.470201
$41$	3.02886	0.473029	0.236514	−	0.971628i	$-0.423995\pi$
$41$	3.02886	0.473029	0.236514	+	0.971628i	$0.423995\pi$
$42$	5.45730	0.842079
$43$	−12.7491	−1.94421	−0.972107	−	0.234537i	$-0.924643\pi$
$43$	−12.7491	−1.94421	−0.972107	+	0.234537i	$0.924643\pi$
$44$	−1.71529	−0.258590
$45$	−2.14914	−0.320375
$46$	−5.31926	−0.784282
$47$	−2.74783	−0.400812	−0.200406	−	0.979713i	$-0.564226\pi$
$47$	−2.74783	−0.400812	−0.200406	+	0.979713i	$0.564226\pi$
$48$	−4.95088	−0.714597
$49$	3.83128	0.547325
$50$	5.54666	0.784417
$51$	−7.72678	−1.08197
$52$	0.796884	0.110508
$53$	9.52601	1.30850	0.654249	−	0.756279i	$-0.272985\pi$
$53$	9.52601	1.30850	0.654249	+	0.756279i	$0.272985\pi$
$54$	8.00769	1.08971
$55$	−5.78502	−0.780051
$56$	−8.32979	−1.11312
$57$	2.58956	0.342995
$58$	−8.95514	−1.17587
$59$	−13.5768	−1.76755	−0.883774	−	0.467915i	$-0.845005\pi$
$59$	−13.5768	−1.76755	−0.883774	+	0.467915i	$0.845005\pi$
$60$	0.442921	0.0571809
$61$	−0.828753	−0.106111	−0.0530555	−	0.998592i	$-0.516896\pi$
$61$	−0.828753	−0.106111	−0.0530555	+	0.998592i	$0.516896\pi$
$62$	4.57389	0.580884
$63$	6.01984	0.758429
$64$	6.16329	0.770411
$65$	2.68758	0.333353
$66$	8.16438	1.00497
$67$	8.58194	1.04845	0.524225	−	0.851580i	$-0.324355\pi$
$67$	8.58194	1.04845	0.524225	+	0.851580i	$0.324355\pi$
$68$	−2.48770	−0.301678
$69$	3.75596	0.452164
$70$	5.92575	0.708263
$71$	7.44012	0.882980	0.441490	−	0.897266i	$-0.354450\pi$
$71$	7.44012	0.882980	0.441490	+	0.897266i	$0.354450\pi$
$72$	−4.62956	−0.545599
$73$	−0.288306	−0.0337437	−0.0168718	−	0.999858i	$-0.505371\pi$
$73$	−0.288306	−0.0337437	−0.0168718	+	0.999858i	$0.505371\pi$
$74$	10.6778	1.24126
$75$	−3.91653	−0.452242
$76$	0.833730	0.0956353
$77$	16.2041	1.84663
$78$	−3.79297	−0.429469
$79$	−16.0678	−1.80777	−0.903885	−	0.427775i	$-0.859298\pi$
$79$	−16.0678	−1.80777	−0.903885	+	0.427775i	$0.859298\pi$
$80$	−5.37586	−0.601039
$81$	−0.166870	−0.0185411
$82$	−4.64156	−0.512574
$83$	3.12661	0.343190	0.171595	−	0.985168i	$-0.445108\pi$
$83$	3.12661	0.343190	0.171595	+	0.985168i	$0.445108\pi$
$84$	−1.24064	−0.135365
$85$	−8.39004	−0.910028
$86$	19.5372	2.10675
$87$	6.32327	0.677926
$88$	−12.4618	−1.32843
$89$	6.47104	0.685929	0.342964	−	0.939348i	$-0.388569\pi$
$89$	6.47104	0.685929	0.342964	+	0.939348i	$0.388569\pi$
$90$	3.29343	0.347158
$91$	−7.52803	−0.789152
$92$	1.20926	0.126074
$93$	−3.22965	−0.334899
$94$	4.21089	0.434320
$95$	2.81184	0.288489
$96$	2.10949	0.215299
$97$	8.37682	0.850537	0.425269	−	0.905067i	$-0.360180\pi$
$97$	8.37682	0.850537	0.425269	+	0.905067i	$0.360180\pi$
$98$	−5.87121	−0.593082
$99$	9.00597	0.905134
$100$	−1.26096	−0.126096
$101$	5.98337	0.595367	0.297684	−	0.954665i	$-0.403786\pi$
$101$	5.98337	0.595367	0.297684	+	0.954665i	$0.403786\pi$
$102$	11.8408	1.17242
$103$	11.7660	1.15933	0.579667	−	0.814854i	$-0.303183\pi$
$103$	11.7660	1.15933	0.579667	+	0.814854i	$0.303183\pi$
$104$	5.78943	0.567701
$105$	−4.18420	−0.408337
$106$	−14.5981	−1.41789
$107$	10.2574	0.991620	0.495810	−	0.868431i	$-0.334871\pi$
$107$	10.2574	0.991620	0.495810	+	0.868431i	$0.334871\pi$
$108$	−1.82044	−0.175172
$109$	−5.17545	−0.495719	−0.247859	−	0.968796i	$-0.579727\pi$
$109$	−5.17545	−0.495719	−0.247859	+	0.968796i	$0.579727\pi$
$110$	8.86520	0.845264
$111$	−7.53962	−0.715629
$112$	15.0580	1.42285
$113$	17.8151	1.67590	0.837950	−	0.545747i	$-0.183754\pi$
$113$	17.8151	1.67590	0.837950	+	0.545747i	$0.183754\pi$
$114$	−3.96835	−0.371670
$115$	4.07837	0.380310
$116$	2.03583	0.189022
$117$	−4.18396	−0.386807
$118$	20.8056	1.91531
$119$	23.5009	2.15432
$120$	3.21786	0.293749
$121$	13.2421	1.20383
$122$	1.27002	0.114982
$123$	3.27743	0.295516
$124$	−1.03981	−0.0933778
$125$	−10.1275	−0.905829
$126$	−9.22506	−0.821834
$127$	−1.87007	−0.165941	−0.0829707	−	0.996552i	$-0.526441\pi$
$127$	−1.87007	−0.165941	−0.0829707	+	0.996552i	$0.526441\pi$
$128$	−13.3439	−1.17944
$129$	−13.7953	−1.21461
$130$	−4.11856	−0.361222
$131$	12.2680	1.07186	0.535928	−	0.844263i	$-0.319962\pi$
$131$	12.2680	1.07186	0.535928	+	0.844263i	$0.319962\pi$
$132$	−1.85606	−0.161549
$133$	−7.87611	−0.682945
$134$	−13.1513	−1.13610
$135$	−6.13963	−0.528415
$136$	−18.0734	−1.54978
$137$	2.71613	0.232055	0.116027	−	0.993246i	$-0.462984\pi$
$137$	2.71613	0.232055	0.116027	+	0.993246i	$0.462984\pi$
$138$	−5.75579	−0.489965
$139$	−15.4200	−1.30791	−0.653953	−	0.756535i	$-0.726891\pi$
$139$	−15.4200	−1.30791	−0.653953	+	0.756535i	$0.726891\pi$
$140$	−1.34714	−0.113854
$141$	−2.97333	−0.250399
$142$	−11.4016	−0.956797
$143$	−11.2623	−0.941800
$144$	8.36900	0.697417
$145$	6.86606	0.570195
$146$	0.441813	0.0365647
$147$	4.14569	0.341931
$148$	−2.42744	−0.199535
$149$	−18.4640	−1.51263	−0.756316	−	0.654206i	$-0.773003\pi$
$149$	−18.4640	−1.51263	−0.756316	+	0.654206i	$0.773003\pi$
$150$	6.00186	0.490049
$151$	−14.8196	−1.20600	−0.603000	−	0.797741i	$-0.706028\pi$
$151$	−14.8196	−1.20600	−0.603000	+	0.797741i	$0.706028\pi$
$152$	6.05712	0.491297
$153$	13.0614	1.05595
$154$	−24.8319	−2.00101
$155$	−3.50688	−0.281679
$156$	0.862281	0.0690377
$157$	4.70944	0.375854	0.187927	−	0.982183i	$-0.439823\pi$
$157$	4.70944	0.375854	0.187927	+	0.982183i	$0.439823\pi$
$158$	24.6230	1.95890
$159$	10.3078	0.817459
$160$	2.29056	0.181085
$161$	−11.4237	−0.900314
$162$	0.255719	0.0200912
$163$	2.77992	0.217740	0.108870	−	0.994056i	$-0.465277\pi$
$163$	2.77992	0.217740	0.108870	+	0.994056i	$0.465277\pi$
$164$	1.05520	0.0823969
$165$	−6.25977	−0.487322
$166$	−4.79135	−0.371881
$167$	7.16745	0.554634	0.277317	−	0.960778i	$-0.410555\pi$
$167$	7.16745	0.554634	0.277317	+	0.960778i	$0.410555\pi$
$168$	−9.01338	−0.695398
$169$	−7.76781	−0.597524
$170$	12.8573	0.986107
$171$	−4.37741	−0.334749
$172$	−4.44152	−0.338663
$173$	−4.90609	−0.373003	−0.186502	−	0.982455i	$-0.559715\pi$
$173$	−4.90609	−0.373003	−0.186502	+	0.982455i	$0.559715\pi$
$174$	−9.69005	−0.734601
$175$	11.9121	0.900468
$176$	22.5275	1.69808
$177$	−14.6910	−1.10424
$178$	−9.91650	−0.743273
$179$	−21.5954	−1.61412	−0.807058	−	0.590472i	$-0.798942\pi$
$179$	−21.5954	−1.61412	−0.807058	+	0.590472i	$0.798942\pi$
$180$	−0.748718	−0.0558061
$181$	−18.5774	−1.38084	−0.690422	−	0.723407i	$-0.742575\pi$
$181$	−18.5774	−1.38084	−0.690422	+	0.723407i	$0.742575\pi$
$182$	11.5363	0.855126
$183$	−0.896766	−0.0662908
$184$	8.78539	0.647668
$185$	−8.18681	−0.601907
$186$	4.94925	0.362896
$187$	35.1585	2.57104
$188$	−0.957288	−0.0698174
$189$	17.1974	1.25093
$190$	−4.30899	−0.312607
$191$	9.73569	0.704450	0.352225	−	0.935915i	$-0.385425\pi$
$191$	9.73569	0.704450	0.352225	+	0.935915i	$0.385425\pi$
$192$	6.66908	0.481300
$193$	4.51633	0.325092	0.162546	−	0.986701i	$-0.448029\pi$
$193$	4.51633	0.325092	0.162546	+	0.986701i	$0.448029\pi$
$194$	−12.8370	−0.921643
$195$	2.90814	0.208256
$196$	1.33474	0.0953386
$197$	4.48736	0.319711	0.159856	−	0.987140i	$-0.448897\pi$
$197$	4.48736	0.319711	0.159856	+	0.987140i	$0.448897\pi$
$198$	−13.8011	−0.980804
$199$	−3.14152	−0.222696	−0.111348	−	0.993781i	$-0.535517\pi$
$199$	−3.14152	−0.222696	−0.111348	+	0.993781i	$0.535517\pi$
$200$	−9.16098	−0.647779
$201$	9.28622	0.655000
$202$	−9.16917	−0.645140
$203$	−19.2322	−1.34983
$204$	−2.69186	−0.188468
$205$	3.55876	0.248555
$206$	−18.0306	−1.25625
$207$	−6.34910	−0.441293
$208$	−10.4657	−0.725669
$209$	−11.7830	−0.815049
$210$	6.41205	0.442474
$211$	−22.4881	−1.54814	−0.774072	−	0.633098i	$-0.781783\pi$
$211$	−22.4881	−1.54814	−0.774072	+	0.633098i	$0.781783\pi$
$212$	3.31867	0.227927
$213$	8.05070	0.551625
$214$	−15.7189	−1.07452
$215$	−14.9795	−1.02159
$216$	−13.2257	−0.899892
$217$	9.82293	0.666824
$218$	7.93109	0.537161
$219$	−0.311966	−0.0210807
$220$	−2.01538	−0.135877
$221$	−16.3338	−1.09873
$222$	11.5540	0.775456
$223$	−5.26812	−0.352779	−0.176390	−	0.984320i	$-0.556442\pi$
$223$	−5.26812	−0.352779	−0.176390	+	0.984320i	$0.556442\pi$
$224$	−6.41598	−0.428686
$225$	6.62053	0.441369
$226$	−27.3006	−1.81601
$227$	−22.3583	−1.48397	−0.741987	−	0.670414i	$-0.766116\pi$
$227$	−22.3583	−1.48397	−0.741987	+	0.670414i	$0.766116\pi$
$228$	0.902150	0.0597464
$229$	24.8346	1.64112	0.820559	−	0.571562i	$-0.193662\pi$
$229$	24.8346	1.64112	0.820559	+	0.571562i	$0.193662\pi$
$230$	−6.24986	−0.412104
$231$	17.5339	1.15365
$232$	14.7905	0.971043
$233$	−13.5705	−0.889036	−0.444518	−	0.895770i	$-0.646625\pi$
$233$	−13.5705	−0.889036	−0.444518	+	0.895770i	$0.646625\pi$
$234$	6.41167	0.419144
$235$	−3.22856	−0.210608
$236$	−4.72988	−0.307889
$237$	−17.3864	−1.12937
$238$	−36.0138	−2.33443
$239$	−21.0247	−1.35998	−0.679989	−	0.733223i	$-0.738015\pi$
$239$	−21.0247	−1.35998	−0.679989	+	0.733223i	$0.738015\pi$
$240$	−5.81703	−0.375488
$241$	22.8659	1.47292	0.736462	−	0.676479i	$-0.236495\pi$
$241$	22.8659	1.47292	0.736462	+	0.676479i	$0.236495\pi$
$242$	−20.2928	−1.30447
$243$	15.4958	0.994053
$244$	−0.288721	−0.0184835
$245$	4.50156	0.287594
$246$	−5.02247	−0.320221
$247$	5.47411	0.348309
$248$	−7.55432	−0.479700
$249$	3.38320	0.214401
$250$	15.5198	0.981556
$251$	25.5786	1.61451	0.807254	−	0.590204i	$-0.200953\pi$
$251$	25.5786	1.61451	0.807254	+	0.590204i	$0.200953\pi$
$252$	2.09719	0.132111
$253$	−17.0904	−1.07446
$254$	2.86577	0.179814
$255$	−9.07858	−0.568523
$256$	8.12216	0.507635
$257$	−1.45745	−0.0909130	−0.0454565	−	0.998966i	$-0.514474\pi$
$257$	−1.45745	−0.0909130	−0.0454565	+	0.998966i	$0.514474\pi$
$258$	21.1406	1.31615
$259$	22.9317	1.42490
$260$	0.936299	0.0580668
$261$	−10.6889	−0.661627
$262$	−18.7999	−1.16146
$263$	15.9829	0.985546	0.492773	−	0.870158i	$-0.335983\pi$
$263$	15.9829	0.985546	0.492773	+	0.870158i	$0.335983\pi$
$264$	−13.4844	−0.829910
$265$	11.1926	0.687555
$266$	12.0697	0.740040
$267$	7.00209	0.428521
$268$	2.98978	0.182630
$269$	25.9953	1.58496	0.792482	−	0.609895i	$-0.208788\pi$
$269$	25.9953	1.58496	0.792482	+	0.609895i	$0.208788\pi$
$270$	9.40863	0.572591
$271$	−26.3510	−1.60071	−0.800353	−	0.599529i	$-0.795355\pi$
$271$	−26.3510	−1.60071	−0.800353	+	0.599529i	$0.795355\pi$
$272$	32.6718	1.98102
$273$	−8.14583	−0.493008
$274$	−4.16232	−0.251455
$275$	17.8210	1.07465
$276$	1.30850	0.0787625
$277$	−5.96380	−0.358330	−0.179165	−	0.983819i	$-0.557340\pi$
$277$	−5.96380	−0.358330	−0.179165	+	0.983819i	$0.557340\pi$
$278$	23.6303	1.41725
$279$	5.45942	0.326847
$280$	−9.78709	−0.584890
$281$	−13.8634	−0.827021	−0.413510	−	0.910499i	$-0.635697\pi$
$281$	−13.8634	−0.827021	−0.413510	+	0.910499i	$0.635697\pi$
$282$	4.55646	0.271333
$283$	2.56396	0.152411	0.0762057	−	0.997092i	$-0.475719\pi$
$283$	2.56396	0.152411	0.0762057	+	0.997092i	$0.475719\pi$
$284$	2.59199	0.153806
$285$	3.04260	0.180228
$286$	17.2588	1.02054
$287$	−9.96826	−0.588408
$288$	−3.56590	−0.210122
$289$	33.9905	1.99944
$290$	−10.5218	−0.617864
$291$	9.06427	0.531357
$292$	−0.100440	−0.00587782
$293$	−23.3712	−1.36536	−0.682679	−	0.730718i	$-0.739185\pi$
$293$	−23.3712	−1.36536	−0.682679	+	0.730718i	$0.739185\pi$
$294$	−6.35304	−0.370517
$295$	−15.9520	−0.928764
$296$	−17.6356	−1.02505
$297$	25.7281	1.49290
$298$	28.2951	1.63909
$299$	7.93978	0.459169
$300$	−1.36444	−0.0787760
$301$	41.9583	2.41844
$302$	22.7101	1.30682
$303$	6.47440	0.371944
$304$	−10.9496	−0.628005
$305$	−0.973744	−0.0557564
$306$	−20.0159	−1.14423
$307$	−27.8489	−1.58942	−0.794709	−	0.606990i	$-0.792377\pi$
$307$	−27.8489	−1.58942	−0.794709	+	0.606990i	$0.792377\pi$
$308$	5.64519	0.321664
$309$	12.7315	0.724272
$310$	5.37409	0.305228
$311$	−20.4968	−1.16227	−0.581133	−	0.813808i	$-0.697391\pi$
$311$	−20.4968	−1.16227	−0.581133	+	0.813808i	$0.697391\pi$
$312$	6.26455	0.354660
$313$	9.78007	0.552802	0.276401	−	0.961042i	$-0.410858\pi$
$313$	9.78007	0.552802	0.276401	+	0.961042i	$0.410858\pi$
$314$	−7.21695	−0.407276
$315$	7.07302	0.398519
$316$	−5.59771	−0.314896
$317$	0.275044	0.0154480	0.00772401	−	0.999970i	$-0.497541\pi$
$317$	0.275044	0.0154480	0.00772401	+	0.999970i	$0.497541\pi$
$318$	−15.7961	−0.885799
$319$	−28.7722	−1.61094
$320$	7.24155	0.404815
$321$	11.0992	0.619496
$322$	17.5062	0.975580
$323$	−17.0890	−0.950857
$324$	−0.0581342	−0.00322968
$325$	−8.27922	−0.459248
$326$	−4.26007	−0.235943
$327$	−5.60018	−0.309691
$328$	7.66609	0.423289
$329$	9.04334	0.498576
$330$	9.59273	0.528063
$331$	26.8525	1.47594	0.737972	−	0.674831i	$-0.235784\pi$
$331$	26.8525	1.47594	0.737972	+	0.674831i	$0.235784\pi$
$332$	1.08925	0.0597803
$333$	12.7450	0.698423
$334$	−10.9837	−0.601002
$335$	10.0833	0.550912
$336$	16.2938	0.888898
$337$	21.8598	1.19078	0.595390	−	0.803437i	$-0.296998\pi$
$337$	21.8598	1.19078	0.595390	+	0.803437i	$0.296998\pi$
$338$	11.9037	0.647477
$339$	19.2771	1.04699
$340$	−2.92292	−0.158518
$341$	14.6956	0.795809
$342$	6.70813	0.362734
$343$	10.4286	0.563089
$344$	−32.2680	−1.73978
$345$	4.41306	0.237591
$346$	7.51830	0.404186
$347$	−11.4167	−0.612880	−0.306440	−	0.951890i	$-0.599138\pi$
$347$	−11.4167	−0.612880	−0.306440	+	0.951890i	$0.599138\pi$
$348$	2.20290	0.118088
$349$	16.6247	0.889898	0.444949	−	0.895556i	$-0.353222\pi$
$349$	16.6247	0.889898	0.444949	+	0.895556i	$0.353222\pi$
$350$	−18.2546	−0.975748
$351$	−11.9527	−0.637986
$352$	−9.59861	−0.511608
$353$	−3.34008	−0.177775	−0.0888873	−	0.996042i	$-0.528331\pi$
$353$	−3.34008	−0.177775	−0.0888873	+	0.996042i	$0.528331\pi$
$354$	22.5131	1.19656
$355$	8.74177	0.463965
$356$	2.25438	0.119482
$357$	25.4295	1.34587
$358$	33.0937	1.74906
$359$	−4.33261	−0.228666	−0.114333	−	0.993442i	$-0.536473\pi$
$359$	−4.33261	−0.228666	−0.114333	+	0.993442i	$0.536473\pi$
$360$	−5.43950	−0.286687
$361$	−13.2728	−0.698568
$362$	28.4687	1.49628
$363$	14.3288	0.752068
$364$	−2.62262	−0.137463
$365$	−0.338745	−0.0177307
$366$	1.37424	0.0718328
$367$	−3.45929	−0.180574	−0.0902868	−	0.995916i	$-0.528778\pi$
$367$	−3.45929	−0.180574	−0.0902868	+	0.995916i	$0.528778\pi$
$368$	−15.8816	−0.827887
$369$	−5.54019	−0.288411
$370$	12.5458	0.652226
$371$	−31.3510	−1.62766
$372$	−1.12514	−0.0583360
$373$	−7.48551	−0.387585	−0.193793	−	0.981043i	$-0.562079\pi$
$373$	−7.48551	−0.387585	−0.193793	+	0.981043i	$0.562079\pi$
$374$	−53.8783	−2.78598
$375$	−10.9586	−0.565899
$376$	−6.95478	−0.358665
$377$	13.3669	0.688429
$378$	−26.3540	−1.35550
$379$	−28.0099	−1.43877	−0.719386	−	0.694610i	$-0.755577\pi$
$379$	−28.0099	−1.43877	−0.719386	+	0.694610i	$0.755577\pi$
$380$	0.979591	0.0502519
$381$	−2.02353	−0.103669
$382$	−14.9194	−0.763343
$383$	−32.6670	−1.66920	−0.834602	−	0.550854i	$-0.814302\pi$
$383$	−32.6670	−1.66920	−0.834602	+	0.550854i	$0.814302\pi$
$384$	−14.4390	−0.736835
$385$	19.0390	0.970318
$386$	−6.92101	−0.352270
$387$	23.3197	1.18541
$388$	2.91832	0.148155
$389$	−7.83296	−0.397147	−0.198573	−	0.980086i	$-0.563631\pi$
$389$	−7.83296	−0.397147	−0.198573	+	0.980086i	$0.563631\pi$
$390$	−4.45655	−0.225666
$391$	−24.7863	−1.25350
$392$	9.69701	0.489773
$393$	13.2747	0.669622
$394$	−6.87663	−0.346439
$395$	−18.8789	−0.949900
$396$	3.13750	0.157665
$397$	−30.6264	−1.53710	−0.768549	−	0.639791i	$-0.779021\pi$
$397$	−30.6264	−1.53710	−0.768549	+	0.639791i	$0.779021\pi$
$398$	4.81420	0.241314
$399$	−8.52247	−0.426657
$400$	16.5606	0.828030
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−14.2306	−0.709758
$403$	−6.82720	−0.340087
$404$	2.08449	0.103707
$405$	−0.196064	−0.00974250
$406$	29.4722	1.46268
$407$	34.3068	1.70053
$408$	−19.5566	−0.968195
$409$	−24.9819	−1.23528	−0.617638	−	0.786463i	$-0.711910\pi$
$409$	−24.9819	−1.23528	−0.617638	+	0.786463i	$0.711910\pi$
$410$	−5.45360	−0.269334
$411$	2.93904	0.144972
$412$	4.09902	0.201944
$413$	44.6824	2.19868
$414$	9.72963	0.478185
$415$	3.67361	0.180330
$416$	4.45928	0.218634
$417$	−16.6854	−0.817090
$418$	18.0568	0.883188
$419$	−0.476469	−0.0232770	−0.0116385	−	0.999932i	$-0.503705\pi$
$419$	−0.476469	−0.0232770	−0.0116385	+	0.999932i	$0.503705\pi$
$420$	−1.45769	−0.0711282
$421$	−11.1595	−0.543881	−0.271940	−	0.962314i	$-0.587665\pi$
$421$	−11.1595	−0.543881	−0.271940	+	0.962314i	$0.587665\pi$
$422$	34.4617	1.67757
$423$	5.02614	0.244379
$424$	24.1105	1.17091
$425$	25.8459	1.25371
$426$	−12.3372	−0.597741
$427$	2.72750	0.131993
$428$	3.57347	0.172730
$429$	−12.1865	−0.588372
$430$	22.9552	1.10700
$431$	−13.8867	−0.668897	−0.334448	−	0.942414i	$-0.608550\pi$
$431$	−13.8867	−0.668897	−0.334448	+	0.942414i	$0.608550\pi$
$432$	23.9084	1.15030
$433$	2.57855	0.123917	0.0619585	−	0.998079i	$-0.480265\pi$
$433$	2.57855	0.123917	0.0619585	+	0.998079i	$0.480265\pi$
$434$	−15.0531	−0.722571
$435$	7.42953	0.356219
$436$	−1.80303	−0.0863493
$437$	8.30689	0.397373
$438$	0.478071	0.0228431
$439$	3.87809	0.185091	0.0925456	−	0.995708i	$-0.470500\pi$
$439$	3.87809	0.185091	0.0925456	+	0.995708i	$0.470500\pi$
$440$	−14.6419	−0.698027
$441$	−7.00792	−0.333710
$442$	25.0306	1.19058
$443$	−35.4363	−1.68363	−0.841815	−	0.539767i	$-0.818512\pi$
$443$	−35.4363	−1.68363	−0.841815	+	0.539767i	$0.818512\pi$
$444$	−2.62665	−0.124655
$445$	7.60315	0.360424
$446$	8.07309	0.382272
$447$	−19.9793	−0.944988
$448$	−20.2839	−0.958326
$449$	−2.60272	−0.122830	−0.0614149	−	0.998112i	$-0.519561\pi$
$449$	−2.60272	−0.122830	−0.0614149	+	0.998112i	$0.519561\pi$
$450$	−10.1456	−0.478268
$451$	−14.9130	−0.702225
$452$	6.20642	0.291925
$453$	−16.0358	−0.753425
$454$	34.2628	1.60803
$455$	−8.84506	−0.414663
$456$	6.55420	0.306929
$457$	−7.98466	−0.373507	−0.186753	−	0.982407i	$-0.559797\pi$
$457$	−7.98466	−0.373507	−0.186753	+	0.982407i	$0.559797\pi$
$458$	−38.0576	−1.77832
$459$	37.3136	1.74165
$460$	1.42082	0.0662462
$461$	−23.9401	−1.11500	−0.557502	−	0.830176i	$-0.688240\pi$
$461$	−23.9401	−1.11500	−0.557502	+	0.830176i	$0.688240\pi$
$462$	−26.8697	−1.25009
$463$	12.4472	0.578472	0.289236	−	0.957258i	$-0.406599\pi$
$463$	12.4472	0.578472	0.289236	+	0.957258i	$0.406599\pi$
$464$	−26.7372	−1.24125
$465$	−3.79467	−0.175974
$466$	20.7961	0.963359
$467$	41.0558	1.89983	0.949917	−	0.312502i	$-0.101167\pi$
$467$	41.0558	1.89983	0.949917	+	0.312502i	$0.101167\pi$
$468$	−1.45761	−0.0673779
$469$	−28.2439	−1.30418
$470$	4.94758	0.228215
$471$	5.09593	0.234808
$472$	−34.3630	−1.58169
$473$	62.7716	2.88624
$474$	26.6437	1.22379
$475$	−8.66202	−0.397441
$476$	8.18725	0.375262
$477$	−17.4243	−0.797806
$478$	32.2192	1.47367
$479$	15.3446	0.701113	0.350557	−	0.936542i	$-0.385992\pi$
$479$	15.3446	0.701113	0.350557	+	0.936542i	$0.385992\pi$
$480$	2.47854	0.113129
$481$	−15.9381	−0.726716
$482$	−35.0407	−1.59606
$483$	−12.3612	−0.562454
$484$	4.61329	0.209695
$485$	9.84235	0.446918
$486$	−23.7464	−1.07716
$487$	−17.7876	−0.806032	−0.403016	−	0.915193i	$-0.632038\pi$
$487$	−17.7876	−0.806032	−0.403016	+	0.915193i	$0.632038\pi$
$488$	−2.09758	−0.0949532
$489$	3.00806	0.136029
$490$	−6.89838	−0.311637
$491$	22.0952	0.997143	0.498571	−	0.866849i	$-0.333858\pi$
$491$	22.0952	0.997143	0.498571	+	0.866849i	$0.333858\pi$
$492$	1.14179	0.0514759
$493$	−41.7285	−1.87936
$494$	−8.38876	−0.377428
$495$	10.5816	0.475606
$496$	13.6562	0.613181
$497$	−24.4861	−1.09835
$498$	−5.18455	−0.232325
$499$	−1.95143	−0.0873579	−0.0436790	−	0.999046i	$-0.513908\pi$
$499$	−1.95143	−0.0873579	−0.0436790	+	0.999046i	$0.513908\pi$
$500$	−3.52821	−0.157786
$501$	7.75565	0.346497
$502$	−39.1978	−1.74948
$503$	24.0145	1.07076	0.535378	−	0.844613i	$-0.320169\pi$
$503$	24.0145	1.07076	0.535378	+	0.844613i	$0.320169\pi$
$504$	15.2363	0.678679
$505$	7.03016	0.312838
$506$	26.1900	1.16429
$507$	−8.40528	−0.373292
$508$	−0.651494	−0.0289054
$509$	−11.3623	−0.503627	−0.251813	−	0.967776i	$-0.581027\pi$
$509$	−11.3623	−0.503627	−0.251813	+	0.967776i	$0.581027\pi$
$510$	13.9124	0.616051
$511$	0.948842	0.0419743
$512$	14.2410	0.629370
$513$	−12.5053	−0.552123
$514$	2.23345	0.0985133
$515$	13.8244	0.609176
$516$	−4.80602	−0.211573
$517$	13.5293	0.595017
$518$	−35.1414	−1.54403
$519$	−5.30871	−0.233027
$520$	6.80229	0.298300
$521$	−11.9591	−0.523937	−0.261968	−	0.965076i	$-0.584372\pi$
$521$	−11.9591	−0.523937	−0.261968	+	0.965076i	$0.584372\pi$
$522$	16.3802	0.716940
$523$	6.43421	0.281348	0.140674	−	0.990056i	$-0.455073\pi$
$523$	6.43421	0.281348	0.140674	+	0.990056i	$0.455073\pi$
$524$	4.27392	0.186707
$525$	12.8897	0.562551
$526$	−24.4928	−1.06794
$527$	21.3131	0.928412
$528$	24.3763	1.06084
$529$	−10.9515	−0.476151
$530$	−17.1520	−0.745035
$531$	24.8338	1.07769
$532$	−2.74388	−0.118962
$533$	6.92821	0.300094
$534$	−10.7303	−0.464346
$535$	12.0519	0.521050
$536$	21.7210	0.938204
$537$	−23.3676	−1.00839
$538$	−39.8364	−1.71747
$539$	−18.8638	−0.812520
$540$	−2.13893	−0.0920447
$541$	−44.0038	−1.89187	−0.945936	−	0.324353i	$-0.894853\pi$
$541$	−44.0038	−1.89187	−0.945936	+	0.324353i	$0.894853\pi$
$542$	40.3813	1.73453
$543$	−20.1019	−0.862656
$544$	−13.9209	−0.596855
$545$	−6.08090	−0.260477
$546$	12.4830	0.534224
$547$	8.68022	0.371139	0.185570	−	0.982631i	$-0.440587\pi$
$547$	8.68022	0.371139	0.185570	+	0.982631i	$0.440587\pi$
$548$	0.946247	0.0404217
$549$	1.51590	0.0646970
$550$	−27.3097	−1.16449
$551$	13.9849	0.595778
$552$	9.50637	0.404618
$553$	52.8806	2.24871
$554$	9.13918	0.388286
$555$	−8.85867	−0.376030
$556$	−5.37202	−0.227824
$557$	0.945475	0.0400611	0.0200305	−	0.999799i	$-0.493624\pi$
$557$	0.945475	0.0400611	0.0200305	+	0.999799i	$0.493624\pi$
$558$	−8.36625	−0.354172
$559$	−29.1622	−1.23343
$560$	17.6924	0.747642
$561$	38.0438	1.60621
$562$	21.2449	0.896160
$563$	−8.55609	−0.360596	−0.180298	−	0.983612i	$-0.557706\pi$
$563$	−8.55609	−0.360596	−0.180298	+	0.983612i	$0.557706\pi$
$564$	−1.03585	−0.0436171
$565$	20.9318	0.880608
$566$	−3.92912	−0.165153
$567$	0.549184	0.0230636
$568$	18.8310	0.790133
$569$	−26.5337	−1.11235	−0.556176	−	0.831065i	$-0.687732\pi$
$569$	−26.5337	−1.11235	−0.556176	+	0.831065i	$0.687732\pi$
$570$	−4.66261	−0.195295
$571$	−24.5243	−1.02631	−0.513155	−	0.858296i	$-0.671523\pi$
$571$	−24.5243	−1.02631	−0.513155	+	0.858296i	$0.671523\pi$
$572$	−3.92356	−0.164052
$573$	10.5347	0.440092
$574$	15.2758	0.637599
$575$	−12.5636	−0.523939
$576$	−11.2735	−0.469728
$577$	29.3782	1.22303	0.611516	−	0.791232i	$-0.290560\pi$
$577$	29.3782	1.22303	0.611516	+	0.791232i	$0.290560\pi$
$578$	−52.0885	−2.16660
$579$	4.88697	0.203095
$580$	2.39200	0.0993224
$581$	−10.2900	−0.426899
$582$	−13.8905	−0.575779
$583$	−46.9025	−1.94250
$584$	−0.729707	−0.0301955
$585$	−4.91594	−0.203249
$586$	35.8150	1.47950
$587$	1.09143	0.0450481	0.0225241	−	0.999746i	$-0.492830\pi$
$587$	1.09143	0.0450481	0.0225241	+	0.999746i	$0.492830\pi$
$588$	1.44428	0.0595610
$589$	−7.14287	−0.294317
$590$	24.4456	1.00641
$591$	4.85562	0.199734
$592$	31.8804	1.31028
$593$	16.9201	0.694827	0.347413	−	0.937712i	$-0.387060\pi$
$593$	16.9201	0.694827	0.347413	+	0.937712i	$0.387060\pi$
$594$	−39.4269	−1.61770
$595$	27.6124	1.13200
$596$	−6.43250	−0.263486
$597$	−3.39933	−0.139125
$598$	−12.1673	−0.497556
$599$	−4.88615	−0.199643	−0.0998214	−	0.995005i	$-0.531827\pi$
$599$	−4.88615	−0.199643	−0.0998214	+	0.995005i	$0.531827\pi$
$600$	−9.91278	−0.404688
$601$	1.06858	0.0435884	0.0217942	−	0.999762i	$-0.493062\pi$
$601$	1.06858	0.0435884	0.0217942	+	0.999762i	$0.493062\pi$
$602$	−64.2987	−2.62062
$603$	−15.6975	−0.639252
$604$	−5.16285	−0.210073
$605$	15.5588	0.632555
$606$	−9.92164	−0.403039
$607$	6.91019	0.280476	0.140238	−	0.990118i	$-0.455213\pi$
$607$	6.91019	0.280476	0.140238	+	0.990118i	$0.455213\pi$
$608$	4.66547	0.189210
$609$	−20.8105	−0.843283
$610$	1.49221	0.0604177
$611$	−6.28537	−0.254279
$612$	4.55034	0.183937
$613$	36.9784	1.49354	0.746771	−	0.665081i	$-0.231603\pi$
$613$	36.9784	1.49354	0.746771	+	0.665081i	$0.231603\pi$
$614$	42.6768	1.72229
$615$	3.85081	0.155280
$616$	41.0128	1.65245
$617$	−21.9646	−0.884263	−0.442131	−	0.896950i	$-0.645778\pi$
$617$	−21.9646	−0.884263	−0.442131	+	0.896950i	$0.645778\pi$
$618$	−19.5103	−0.784821
$619$	3.68241	0.148009	0.0740043	−	0.997258i	$-0.476422\pi$
$619$	3.68241	0.148009	0.0740043	+	0.997258i	$0.476422\pi$
$620$	−1.22173	−0.0490657
$621$	−18.1380	−0.727854
$622$	31.4102	1.25943
$623$	−21.2968	−0.853237
$624$	−11.3246	−0.453348
$625$	6.19819	0.247928
$626$	−14.9874	−0.599017
$627$	−12.7500	−0.509186
$628$	1.64068	0.0654701
$629$	49.7554	1.98388
$630$	−10.8390	−0.431836
$631$	−8.66380	−0.344901	−0.172450	−	0.985018i	$-0.555168\pi$
$631$	−8.66380	−0.344901	−0.172450	+	0.985018i	$0.555168\pi$
$632$	−40.6678	−1.61768
$633$	−24.3336	−0.967173
$634$	−0.421489	−0.0167395
$635$	−2.19723	−0.0871945
$636$	3.59102	0.142393
$637$	8.76365	0.347229
$638$	44.0918	1.74561
$639$	−13.6090	−0.538363
$640$	−15.6784	−0.619743
$641$	31.5588	1.24650	0.623249	−	0.782024i	$-0.285812\pi$
$641$	31.5588	1.24650	0.623249	+	0.782024i	$0.285812\pi$
$642$	−17.0088	−0.671286
$643$	−27.3319	−1.07787	−0.538933	−	0.842349i	$-0.681172\pi$
$643$	−27.3319	−1.07787	−0.538933	+	0.842349i	$0.681172\pi$
$644$	−3.97979	−0.156826
$645$	−16.2088	−0.638222
$646$	26.1879	1.03035
$647$	38.3246	1.50670	0.753348	−	0.657622i	$-0.228438\pi$
$647$	38.3246	1.50670	0.753348	+	0.657622i	$0.228438\pi$
$648$	−0.422350	−0.0165915
$649$	66.8470	2.62398
$650$	12.6874	0.497642
$651$	10.6291	0.416586
$652$	0.968469	0.0379282
$653$	−13.2275	−0.517632	−0.258816	−	0.965927i	$-0.583332\pi$
$653$	−13.2275	−0.517632	−0.258816	+	0.965927i	$0.583332\pi$
$654$	8.58196	0.335581
$655$	14.4142	0.563211
$656$	−13.8582	−0.541073
$657$	0.527351	0.0205739
$658$	−13.8584	−0.540257
$659$	23.0796	0.899054	0.449527	−	0.893267i	$-0.351593\pi$
$659$	23.0796	0.899054	0.449527	+	0.893267i	$0.351593\pi$
$660$	−2.18078	−0.0848867
$661$	18.9523	0.737161	0.368580	−	0.929596i	$-0.379844\pi$
$661$	18.9523	0.737161	0.368580	+	0.929596i	$0.379844\pi$
$662$	−41.1498	−1.59933
$663$	−17.6742	−0.686410
$664$	7.91349	0.307103
$665$	−9.25403	−0.358856
$666$	−19.5310	−0.756812
$667$	20.2841	0.785403
$668$	2.49700	0.0966117
$669$	−5.70045	−0.220392
$670$	−15.4521	−0.596969
$671$	4.08047	0.157525
$672$	−6.94251	−0.267813
$673$	−1.86070	−0.0717247	−0.0358624	−	0.999357i	$-0.511418\pi$
$673$	−1.86070	−0.0717247	−0.0358624	+	0.999357i	$0.511418\pi$
$674$	−33.4989	−1.29033
$675$	18.9134	0.727979
$676$	−2.70615	−0.104083
$677$	39.6924	1.52550	0.762751	−	0.646692i	$-0.223848\pi$
$677$	39.6924	1.52550	0.762751	+	0.646692i	$0.223848\pi$
$678$	−29.5410	−1.13452
$679$	−27.5689	−1.05800
$680$	−21.2353	−0.814337
$681$	−24.1932	−0.927084
$682$	−22.5201	−0.862340
$683$	−33.3733	−1.27699	−0.638496	−	0.769625i	$-0.720443\pi$
$683$	−33.3733	−1.27699	−0.638496	+	0.769625i	$0.720443\pi$
$684$	−1.52500	−0.0583099
$685$	3.19132	0.121934
$686$	−15.9812	−0.610164
$687$	26.8727	1.02526
$688$	58.3320	2.22389
$689$	21.7898	0.830124
$690$	−6.76276	−0.257454
$691$	3.34299	0.127173	0.0635866	−	0.997976i	$-0.479746\pi$
$691$	3.34299	0.127173	0.0635866	+	0.997976i	$0.479746\pi$
$692$	−1.70918	−0.0649734
$693$	−29.6395	−1.12591
$694$	17.4954	0.664117
$695$	−18.1177	−0.687244
$696$	16.0043	0.606641
$697$	−21.6284	−0.819234
$698$	−25.4764	−0.964294
$699$	−14.6842	−0.555408
$700$	4.14993	0.156853
$701$	20.8063	0.785842	0.392921	−	0.919572i	$-0.371465\pi$
$701$	20.8063	0.785842	0.392921	+	0.919572i	$0.371465\pi$
$702$	18.3168	0.691322
$703$	−16.6751	−0.628912
$704$	−30.3457	−1.14370
$705$	−3.49351	−0.131573
$706$	5.11848	0.192637
$707$	−19.6918	−0.740587
$708$	−5.11805	−0.192348
$709$	15.6446	0.587544	0.293772	−	0.955876i	$-0.405089\pi$
$709$	15.6446	0.587544	0.293772	+	0.955876i	$0.405089\pi$
$710$	−13.3963	−0.502753
$711$	29.3902	1.10222
$712$	16.3783	0.613802
$713$	−10.3602	−0.387992
$714$	−38.9693	−1.45839
$715$	−13.2326	−0.494872
$716$	−7.52341	−0.281163
$717$	−22.7501	−0.849620
$718$	6.63947	0.247783
$719$	−50.1752	−1.87122	−0.935610	−	0.353036i	$-0.885149\pi$
$719$	−50.1752	−1.87122	−0.935610	+	0.353036i	$0.885149\pi$
$720$	9.83316	0.366460
$721$	−38.7228	−1.44211
$722$	20.3398	0.756968
$723$	24.7424	0.920181
$724$	−6.47198	−0.240529
$725$	−21.1512	−0.785538
$726$	−21.9581	−0.814942
$727$	10.4728	0.388416	0.194208	−	0.980960i	$-0.437786\pi$
$727$	10.4728	0.388416	0.194208	+	0.980960i	$0.437786\pi$
$728$	−19.0535	−0.706171
$729$	17.2680	0.639557
$730$	0.519108	0.0192130
$731$	91.0381	3.36717
$732$	−0.312415	−0.0115472
$733$	−0.150425	−0.00555609	−0.00277804	−	0.999996i	$-0.500884\pi$
$733$	−0.150425	−0.00555609	−0.00277804	+	0.999996i	$0.500884\pi$
$734$	5.30116	0.195670
$735$	4.87098	0.179669
$736$	6.76691	0.249431
$737$	−42.2543	−1.55646
$738$	8.49003	0.312522
$739$	−36.6475	−1.34810	−0.674050	−	0.738686i	$-0.735447\pi$
$739$	−36.6475	−1.34810	−0.674050	+	0.738686i	$0.735447\pi$
$740$	−2.85212	−0.104846
$741$	5.92335	0.217600
$742$	48.0436	1.76373
$743$	4.77426	0.175151	0.0875753	−	0.996158i	$-0.472088\pi$
$743$	4.77426	0.175151	0.0875753	+	0.996158i	$0.472088\pi$
$744$	−8.17427	−0.299683
$745$	−21.6943	−0.794818
$746$	11.4711	0.419988
$747$	−5.71898	−0.209247
$748$	12.2485	0.447850
$749$	−33.7580	−1.23349
$750$	16.7934	0.613209
$751$	−22.7314	−0.829481	−0.414741	−	0.909940i	$-0.636128\pi$
$751$	−22.7314	−0.829481	−0.414741	+	0.909940i	$0.636128\pi$
$752$	12.5724	0.458468
$753$	27.6778	1.00863
$754$	−20.4840	−0.745982
$755$	−17.4123	−0.633697
$756$	5.99123	0.217899
$757$	31.2168	1.13460	0.567298	−	0.823513i	$-0.307989\pi$
$757$	31.2168	1.13460	0.567298	+	0.823513i	$0.307989\pi$
$758$	42.9236	1.55905
$759$	−18.4929	−0.671251
$760$	7.11681	0.258154
$761$	4.92998	0.178712	0.0893558	−	0.996000i	$-0.471519\pi$
$761$	4.92998	0.178712	0.0893558	+	0.996000i	$0.471519\pi$
$762$	3.10095	0.112336
$763$	17.0329	0.616632
$764$	3.39172	0.122708
$765$	15.3465	0.554854
$766$	50.0602	1.80875
$767$	−31.0555	−1.12135
$768$	8.78871	0.317135
$769$	18.3772	0.662699	0.331350	−	0.943508i	$-0.392496\pi$
$769$	18.3772	0.662699	0.331350	+	0.943508i	$0.392496\pi$
$770$	−29.1762	−1.05144
$771$	−1.57705	−0.0567961
$772$	1.57340	0.0566279
$773$	−5.91737	−0.212833	−0.106417	−	0.994322i	$-0.533938\pi$
$773$	−5.91737	−0.212833	−0.106417	+	0.994322i	$0.533938\pi$
$774$	−35.7362	−1.28451
$775$	10.8031	0.388059
$776$	21.2018	0.761102
$777$	24.8136	0.890181
$778$	12.0036	0.430349
$779$	7.24855	0.259706
$780$	1.01314	0.0362761
$781$	−36.6324	−1.31081
$782$	37.9836	1.35829
$783$	−30.5359	−1.09127
$784$	−17.5296	−0.626057
$785$	5.53336	0.197494
$786$	−20.3428	−0.725603
$787$	−26.4902	−0.944272	−0.472136	−	0.881526i	$-0.656517\pi$
$787$	−26.4902	−0.944272	−0.472136	+	0.881526i	$0.656517\pi$
$788$	1.56331	0.0556906
$789$	17.2945	0.615701
$790$	28.9308	1.02931
$791$	−58.6310	−2.08468
$792$	22.7942	0.809957
$793$	−1.89569	−0.0673179
$794$	46.9333	1.66560
$795$	12.1111	0.429537
$796$	−1.09444	−0.0387915
$797$	34.3959	1.21836	0.609182	−	0.793030i	$-0.291498\pi$
$797$	34.3959	1.21836	0.609182	+	0.793030i	$0.291498\pi$
$798$	13.0602	0.462326
$799$	19.6216	0.694162
$800$	−7.05620	−0.249474
$801$	−11.8364	−0.418219
$802$	1.53244	0.0541124
$803$	1.41951	0.0500935
$804$	3.23514	0.114094
$805$	−13.4223	−0.473073
$806$	10.4623	0.368519
$807$	28.1287	0.990176
$808$	15.1440	0.532763
$809$	−22.3886	−0.787141	−0.393571	−	0.919294i	$-0.628760\pi$
$809$	−22.3886	−0.787141	−0.393571	+	0.919294i	$0.628760\pi$
$810$	0.300457	0.0105570
$811$	29.6597	1.04149	0.520746	−	0.853711i	$-0.325654\pi$
$811$	29.6597	1.04149	0.520746	+	0.853711i	$0.325654\pi$
$812$	−6.70010	−0.235128
$813$	−28.5135	−1.00001
$814$	−52.5733	−1.84269
$815$	3.26627	0.114412
$816$	35.3530	1.23760
$817$	−30.5106	−1.06743
$818$	38.2833	1.33855
$819$	13.7698	0.481155
$820$	1.23980	0.0432958
$821$	6.47384	0.225938	0.112969	−	0.993598i	$-0.463964\pi$
$821$	6.47384	0.225938	0.112969	+	0.993598i	$0.463964\pi$
$822$	−4.50390	−0.157092
$823$	25.5480	0.890548	0.445274	−	0.895394i	$-0.353106\pi$
$823$	25.5480	0.890548	0.445274	+	0.895394i	$0.353106\pi$
$824$	29.7798	1.03743
$825$	19.2835	0.671366
$826$	−68.4733	−2.38249
$827$	19.9902	0.695129	0.347565	−	0.937656i	$-0.387009\pi$
$827$	19.9902	0.695129	0.347565	+	0.937656i	$0.387009\pi$
$828$	−2.21190	−0.0768689
$829$	7.59197	0.263680	0.131840	−	0.991271i	$-0.457912\pi$
$829$	7.59197	0.263680	0.131840	+	0.991271i	$0.457912\pi$
$830$	−5.62959	−0.195406
$831$	−6.45322	−0.223860
$832$	14.0979	0.488756
$833$	−27.3582	−0.947907
$834$	25.5695	0.885399
$835$	8.42140	0.291434
$836$	−4.10497	−0.141973
$837$	15.5964	0.539090
$838$	0.730161	0.0252230
$839$	25.8406	0.892118	0.446059	−	0.895004i	$-0.352827\pi$
$839$	25.8406	0.892118	0.446059	+	0.895004i	$0.352827\pi$
$840$	−10.5903	−0.365399
$841$	5.14889	0.177548
$842$	17.1013	0.589349
$843$	−15.0011	−0.516666
$844$	−7.83440	−0.269671
$845$	−9.12679	−0.313971
$846$	−7.70227	−0.264810
$847$	−43.5809	−1.49746
$848$	−43.5852	−1.49672
$849$	2.77437	0.0952161
$850$	−39.6074	−1.35852
$851$	−24.1859	−0.829082
$852$	2.80470	0.0960876
$853$	43.3521	1.48435	0.742173	−	0.670208i	$-0.233795\pi$
$853$	43.3521	1.48435	0.742173	+	0.670208i	$0.233795\pi$
$854$	−4.17974	−0.143028
$855$	−5.14324	−0.175895
$856$	25.9616	0.887349
$857$	−17.7983	−0.607977	−0.303989	−	0.952676i	$-0.598318\pi$
$857$	−17.7983	−0.607977	−0.303989	+	0.952676i	$0.598318\pi$
$858$	18.6752	0.637560
$859$	−30.2103	−1.03076	−0.515381	−	0.856961i	$-0.672350\pi$
$859$	−30.2103	−1.03076	−0.515381	+	0.856961i	$0.672350\pi$
$860$	−5.21857	−0.177952
$861$	−10.7863	−0.367596
$862$	21.2805	0.724817
$863$	11.2605	0.383312	0.191656	−	0.981462i	$-0.438614\pi$
$863$	11.2605	0.383312	0.191656	+	0.981462i	$0.438614\pi$
$864$	−10.1870	−0.346569
$865$	−5.76441	−0.195996
$866$	−3.95148	−0.134277
$867$	36.7800	1.24911
$868$	3.42211	0.116154
$869$	79.1119	2.68369
$870$	−11.3853	−0.385999
$871$	19.6303	0.665147
$872$	−13.0991	−0.443593
$873$	−15.3223	−0.518582
$874$	−12.7298	−0.430593
$875$	33.3304	1.12677
$876$	−0.108683	−0.00367205
$877$	−9.06201	−0.306002	−0.153001	−	0.988226i	$-0.548894\pi$
$877$	−9.06201	−0.306002	−0.153001	+	0.988226i	$0.548894\pi$
$878$	−5.94295	−0.200565
$879$	−25.2891	−0.852981
$880$	26.4687	0.892260
$881$	−30.1650	−1.01629	−0.508143	−	0.861273i	$-0.669668\pi$
$881$	−30.1650	−1.01629	−0.508143	+	0.861273i	$0.669668\pi$
$882$	10.7392	0.361609
$883$	36.7260	1.23593	0.617965	−	0.786206i	$-0.287957\pi$
$883$	36.7260	1.23593	0.617965	+	0.786206i	$0.287957\pi$
$884$	−5.69036	−0.191388
$885$	−17.2612	−0.580228
$886$	54.3041	1.82438
$887$	−49.8228	−1.67288	−0.836442	−	0.548055i	$-0.815368\pi$
$887$	−49.8228	−1.67288	−0.836442	+	0.548055i	$0.815368\pi$
$888$	−19.0829	−0.640379
$889$	6.15455	0.206417
$890$	−11.6514	−0.390555
$891$	0.821606	0.0275248
$892$	−1.83531	−0.0614507
$893$	−6.57599	−0.220057
$894$	30.6171	1.02399
$895$	−25.3735	−0.848143
$896$	43.9159	1.46713
$897$	8.59137	0.286857
$898$	3.98852	0.133099
$899$	−17.4417	−0.581714
$900$	2.30646	0.0768821
$901$	−68.0230	−2.26618
$902$	22.8533	0.760931
$903$	45.4017	1.51087
$904$	45.0902	1.49968
$905$	−21.8275	−0.725570
$906$	24.5739	0.816412
$907$	25.0117	0.830499	0.415249	−	0.909708i	$-0.363694\pi$
$907$	25.0117	0.830499	0.415249	+	0.909708i	$0.363694\pi$
$908$	−7.78920	−0.258494
$909$	−10.9444	−0.363002
$910$	13.5545	0.449329
$911$	−12.8027	−0.424172	−0.212086	−	0.977251i	$-0.568026\pi$
$911$	−12.8027	−0.424172	−0.212086	+	0.977251i	$0.568026\pi$
$912$	−11.8482	−0.392334
$913$	−15.3943	−0.509475
$914$	12.2360	0.404732
$915$	−1.05365	−0.0348328
$916$	8.65189	0.285866
$917$	−40.3750	−1.33330
$918$	−57.1810	−1.88725
$919$	14.4645	0.477141	0.238571	−	0.971125i	$-0.423321\pi$
$919$	14.4645	0.477141	0.238571	+	0.971125i	$0.423321\pi$
$920$	10.3224	0.340319
$921$	−30.1343	−0.992959
$922$	36.6869	1.20822
$923$	17.0185	0.560171
$924$	6.10846	0.200954
$925$	25.2199	0.829225
$926$	−19.0747	−0.626833
$927$	−21.5215	−0.706859
$928$	11.3923	0.373971
$929$	0.629705	0.0206599	0.0103300	−	0.999947i	$-0.496712\pi$
$929$	0.629705	0.0206599	0.0103300	+	0.999947i	$0.496712\pi$
$930$	5.81512	0.190685
$931$	9.16886	0.300497
$932$	−4.72771	−0.154861
$933$	−22.1789	−0.726104
$934$	−62.9156	−2.05866
$935$	41.3094	1.35096
$936$	−10.5896	−0.346133
$937$	−20.2251	−0.660726	−0.330363	−	0.943854i	$-0.607171\pi$
$937$	−20.2251	−0.660726	−0.330363	+	0.943854i	$0.607171\pi$
$938$	43.2822	1.41321
$939$	10.5827	0.345353
$940$	−1.12477	−0.0366858
$941$	−4.93275	−0.160803	−0.0804015	−	0.996763i	$-0.525620\pi$
$941$	−4.93275	−0.160803	−0.0804015	+	0.996763i	$0.525620\pi$
$942$	−7.80922	−0.254438
$943$	10.5135	0.342366
$944$	62.1191	2.02181
$945$	20.2061	0.657304
$946$	−96.1939	−3.12754
$947$	−15.2546	−0.495707	−0.247854	−	0.968797i	$-0.579725\pi$
$947$	−15.2546	−0.495707	−0.247854	+	0.968797i	$0.579725\pi$
$948$	−6.05709	−0.196725
$949$	−0.659471	−0.0214073
$950$	13.2741	0.430667
$951$	0.297616	0.00965086
$952$	59.4811	1.92779
$953$	42.7632	1.38524	0.692619	−	0.721304i	$-0.256457\pi$
$953$	42.7632	1.38524	0.692619	+	0.721304i	$0.256457\pi$
$954$	26.7018	0.864503
$955$	11.4390	0.370156
$956$	−7.32460	−0.236895
$957$	−31.1334	−1.00640
$958$	−23.5147	−0.759727
$959$	−8.93904	−0.288657
$960$	7.83584	0.252901
$961$	−22.0915	−0.712631
$962$	24.4243	0.787470
$963$	−18.7621	−0.604602
$964$	7.96603	0.256569
$965$	5.30646	0.170821
$966$	18.9428	0.609475
$967$	16.1985	0.520908	0.260454	−	0.965486i	$-0.416128\pi$
$967$	16.1985	0.520908	0.260454	+	0.965486i	$0.416128\pi$
$968$	33.5159	1.07724
$969$	−18.4914	−0.594030
$970$	−15.0828	−0.484280
$971$	49.0524	1.57417	0.787083	−	0.616847i	$-0.211590\pi$
$971$	49.0524	1.57417	0.787083	+	0.616847i	$0.211590\pi$
$972$	5.39841	0.173154
$973$	50.7486	1.62693
$974$	27.2584	0.873417
$975$	−8.95866	−0.286907
$976$	3.79187	0.121375
$977$	−12.7441	−0.407720	−0.203860	−	0.979000i	$-0.565349\pi$
$977$	−12.7441	−0.407720	−0.203860	+	0.979000i	$0.565349\pi$
$978$	−4.60967	−0.147401
$979$	−31.8610	−1.01828
$980$	1.56825	0.0500960
$981$	9.46660	0.302245
$982$	−33.8596	−1.08050
$983$	−18.1001	−0.577303	−0.288652	−	0.957434i	$-0.593207\pi$
$983$	−18.1001	−0.577303	−0.288652	+	0.957434i	$0.593207\pi$
$984$	8.29521	0.264442
$985$	5.27243	0.167994
$986$	63.9466	2.03647
$987$	9.78549	0.311476
$988$	1.90707	0.0606720
$989$	−44.2533	−1.40717
$990$	−16.2156	−0.515367
$991$	23.9882	0.762010	0.381005	−	0.924573i	$-0.375578\pi$
$991$	23.9882	0.762010	0.381005	+	0.924573i	$0.375578\pi$
$992$	−5.81868	−0.184743
$993$	29.0561	0.922068
$994$	37.5236	1.19017
$995$	−3.69113	−0.117017
$996$	1.17864	0.0373466
$997$	−16.3836	−0.518874	−0.259437	−	0.965760i	$-0.583537\pi$
$997$	−16.3836	−0.518874	−0.259437	+	0.965760i	$0.583537\pi$
$998$	2.99045	0.0946611
$999$	36.4098	1.15196

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	401.2.a.a.1.4	✓	12
3.2	odd	2		3609.2.a.b.1.9		12
4.3	odd	2		6416.2.a.k.1.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
401.2.a.a.1.4	✓	12	1.1	even	1	trivial
3609.2.a.b.1.9		12	3.2	odd	2
6416.2.a.k.1.3		12	4.3	odd	2

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:	\( N \)	\(=\)	\( 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	401.a (trivial)

\(f(q)\)	\(=\)	\(q-1.53244 q^{2} +1.08207 q^{3} +0.348380 q^{4} +1.17495 q^{5} -1.65820 q^{6} -3.29109 q^{7} +2.53101 q^{8} -1.82913 q^{9} +O(q^{10})\)	\(q-1.53244 q^{2} +1.08207 q^{3} +0.348380 q^{4} +1.17495 q^{5} -1.65820 q^{6} -3.29109 q^{7} +2.53101 q^{8} -1.82913 q^{9} -1.80054 q^{10} -4.92363 q^{11} +0.376970 q^{12} +2.28740 q^{13} +5.04341 q^{14} +1.27137 q^{15} -4.57539 q^{16} -7.14077 q^{17} +2.80304 q^{18} +2.39316 q^{19} +0.409329 q^{20} -3.56118 q^{21} +7.54518 q^{22} +3.47110 q^{23} +2.73872 q^{24} -3.61949 q^{25} -3.50531 q^{26} -5.22544 q^{27} -1.14655 q^{28} +5.84371 q^{29} -1.94831 q^{30} -2.98470 q^{31} +1.94950 q^{32} -5.32769 q^{33} +10.9428 q^{34} -3.86687 q^{35} -0.637234 q^{36} -6.96780 q^{37} -3.66738 q^{38} +2.47511 q^{39} +2.97381 q^{40} +3.02886 q^{41} +5.45730 q^{42} -12.7491 q^{43} -1.71529 q^{44} -2.14914 q^{45} -5.31926 q^{46} -2.74783 q^{47} -4.95088 q^{48} +3.83128 q^{49} +5.54666 q^{50} -7.72678 q^{51} +0.796884 q^{52} +9.52601 q^{53} +8.00769 q^{54} -5.78502 q^{55} -8.32979 q^{56} +2.58956 q^{57} -8.95514 q^{58} -13.5768 q^{59} +0.442921 q^{60} -0.828753 q^{61} +4.57389 q^{62} +6.01984 q^{63} +6.16329 q^{64} +2.68758 q^{65} +8.16438 q^{66} +8.58194 q^{67} -2.48770 q^{68} +3.75596 q^{69} +5.92575 q^{70} +7.44012 q^{71} -4.62956 q^{72} -0.288306 q^{73} +10.6778 q^{74} -3.91653 q^{75} +0.833730 q^{76} +16.2041 q^{77} -3.79297 q^{78} -16.0678 q^{79} -5.37586 q^{80} -0.166870 q^{81} -4.64156 q^{82} +3.12661 q^{83} -1.24064 q^{84} -8.39004 q^{85} +19.5372 q^{86} +6.32327 q^{87} -12.4618 q^{88} +6.47104 q^{89} +3.29343 q^{90} -7.52803 q^{91} +1.20926 q^{92} -3.22965 q^{93} +4.21089 q^{94} +2.81184 q^{95} +2.10949 q^{96} +8.37682 q^{97} -5.87121 q^{98} +9.00597 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 5 q^{3} + 5 q^{4} - 7 q^{5} - 9 q^{6} - 20 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 - 5 * q^3 + 5 * q^4 - 7 * q^5 - 9 * q^6 - 20 * q^7 - 3 * q^8 + 3 * q^9	\( 12 q - 3 q^{2} - 5 q^{3} + 5 q^{4} - 7 q^{5} - 9 q^{6} - 20 q^{7} - 3 q^{8} + 3 q^{9} - 11 q^{10} - 11 q^{11} - 9 q^{12} - 11 q^{13} - 3 q^{14} - 11 q^{15} - 9 q^{16} + q^{17} - q^{18} - 34 q^{19} - 5 q^{20} - 3 q^{21} + 3 q^{22} - 7 q^{23} - 9 q^{24} + 7 q^{25} + 6 q^{26} - 2 q^{27} - 23 q^{28} - 6 q^{29} + 23 q^{30} - 52 q^{31} + 11 q^{32} + 4 q^{33} - 5 q^{34} + 12 q^{35} + 16 q^{36} + 3 q^{37} + 25 q^{38} - 24 q^{39} - 25 q^{40} - 16 q^{41} + 47 q^{42} - 2 q^{43} - 2 q^{44} - 23 q^{45} - 16 q^{46} - 3 q^{47} + 24 q^{48} + 6 q^{49} + 27 q^{50} - 16 q^{51} - 5 q^{52} + 19 q^{53} + 5 q^{54} - 43 q^{55} + 7 q^{56} + 11 q^{57} + 11 q^{58} - q^{59} + 30 q^{60} - 24 q^{61} + 39 q^{62} - 11 q^{63} - q^{64} + 13 q^{65} + 14 q^{66} + 6 q^{67} + 32 q^{68} + 29 q^{69} + 47 q^{70} - 15 q^{71} + 32 q^{72} - 20 q^{73} + 25 q^{74} + 31 q^{75} - 42 q^{76} + 38 q^{77} + 52 q^{78} - 53 q^{79} + 23 q^{80} - 8 q^{81} + 4 q^{82} + 17 q^{83} + 35 q^{84} + 7 q^{85} + 28 q^{86} - 5 q^{87} + 38 q^{88} - q^{89} + 58 q^{90} - 6 q^{91} + 46 q^{92} + 44 q^{93} - 4 q^{94} + 34 q^{95} + 28 q^{96} + 12 q^{97} + 27 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 - 5 * q^3 + 5 * q^4 - 7 * q^5 - 9 * q^6 - 20 * q^7 - 3 * q^8 + 3 * q^9 - 11 * q^10 - 11 * q^11 - 9 * q^12 - 11 * q^13 - 3 * q^14 - 11 * q^15 - 9 * q^16 + q^17 - q^18 - 34 * q^19 - 5 * q^20 - 3 * q^21 + 3 * q^22 - 7 * q^23 - 9 * q^24 + 7 * q^25 + 6 * q^26 - 2 * q^27 - 23 * q^28 - 6 * q^29 + 23 * q^30 - 52 * q^31 + 11 * q^32 + 4 * q^33 - 5 * q^34 + 12 * q^35 + 16 * q^36 + 3 * q^37 + 25 * q^38 - 24 * q^39 - 25 * q^40 - 16 * q^41 + 47 * q^42 - 2 * q^43 - 2 * q^44 - 23 * q^45 - 16 * q^46 - 3 * q^47 + 24 * q^48 + 6 * q^49 + 27 * q^50 - 16 * q^51 - 5 * q^52 + 19 * q^53 + 5 * q^54 - 43 * q^55 + 7 * q^56 + 11 * q^57 + 11 * q^58 - q^59 + 30 * q^60 - 24 * q^61 + 39 * q^62 - 11 * q^63 - q^64 + 13 * q^65 + 14 * q^66 + 6 * q^67 + 32 * q^68 + 29 * q^69 + 47 * q^70 - 15 * q^71 + 32 * q^72 - 20 * q^73 + 25 * q^74 + 31 * q^75 - 42 * q^76 + 38 * q^77 + 52 * q^78 - 53 * q^79 + 23 * q^80 - 8 * q^81 + 4 * q^82 + 17 * q^83 + 35 * q^84 + 7 * q^85 + 28 * q^86 - 5 * q^87 + 38 * q^88 - q^89 + 58 * q^90 - 6 * q^91 + 46 * q^92 + 44 * q^93 - 4 * q^94 + 34 * q^95 + 28 * q^96 + 12 * q^97 + 27 * q^98

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