LMFDB - Embedded newform 4010.2.a.i.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4010,2,Mod(1,4010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4010, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4010 = 2 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4010.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.0200112105$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 3x^{9} - 12x^{8} + 34x^{7} + 46x^{6} - 104x^{5} - 90x^{4} + 89x^{3} + 82x^{2} + 12x - 1 $ x^10 - 3x^9 - 12x^8 + 34x^7 + 46x^6 - 104x^5 - 90x^4 + 89x^3 + 82x^2 + 12*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$3.08731$ of defining polynomial
Character	$\chi$	$=$	4010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.13000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.13000 q^{6} +2.49851 q^{7} -1.00000 q^{8} +6.79692 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.13000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.13000 q^{6} +2.49851 q^{7} -1.00000 q^{8} +6.79692 q^{9} -1.00000 q^{10} -1.60279 q^{11} -3.13000 q^{12} -0.554325 q^{13} -2.49851 q^{14} -3.13000 q^{15} +1.00000 q^{16} +5.26951 q^{17} -6.79692 q^{18} -2.32369 q^{19} +1.00000 q^{20} -7.82035 q^{21} +1.60279 q^{22} +4.26393 q^{23} +3.13000 q^{24} +1.00000 q^{25} +0.554325 q^{26} -11.8844 q^{27} +2.49851 q^{28} -2.40114 q^{29} +3.13000 q^{30} -10.2745 q^{31} -1.00000 q^{32} +5.01675 q^{33} -5.26951 q^{34} +2.49851 q^{35} +6.79692 q^{36} -0.359181 q^{37} +2.32369 q^{38} +1.73504 q^{39} -1.00000 q^{40} -2.50682 q^{41} +7.82035 q^{42} +1.01036 q^{43} -1.60279 q^{44} +6.79692 q^{45} -4.26393 q^{46} -6.02260 q^{47} -3.13000 q^{48} -0.757432 q^{49} -1.00000 q^{50} -16.4936 q^{51} -0.554325 q^{52} -11.4646 q^{53} +11.8844 q^{54} -1.60279 q^{55} -2.49851 q^{56} +7.27317 q^{57} +2.40114 q^{58} -5.94415 q^{59} -3.13000 q^{60} +0.692162 q^{61} +10.2745 q^{62} +16.9822 q^{63} +1.00000 q^{64} -0.554325 q^{65} -5.01675 q^{66} -3.85892 q^{67} +5.26951 q^{68} -13.3461 q^{69} -2.49851 q^{70} -6.49192 q^{71} -6.79692 q^{72} +5.75377 q^{73} +0.359181 q^{74} -3.13000 q^{75} -2.32369 q^{76} -4.00460 q^{77} -1.73504 q^{78} +1.29382 q^{79} +1.00000 q^{80} +16.8073 q^{81} +2.50682 q^{82} +2.60037 q^{83} -7.82035 q^{84} +5.26951 q^{85} -1.01036 q^{86} +7.51558 q^{87} +1.60279 q^{88} +9.62868 q^{89} -6.79692 q^{90} -1.38499 q^{91} +4.26393 q^{92} +32.1593 q^{93} +6.02260 q^{94} -2.32369 q^{95} +3.13000 q^{96} +7.34064 q^{97} +0.757432 q^{98} -10.8941 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} - 4 q^{3} + 10 q^{4} + 10 q^{5} + 4 q^{6} - 3 q^{7} - 10 q^{8} + 6 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 - 4 * q^3 + 10 * q^4 + 10 * q^5 + 4 * q^6 - 3 * q^7 - 10 * q^8 + 6 * q^9	\( 10 q - 10 q^{2} - 4 q^{3} + 10 q^{4} + 10 q^{5} + 4 q^{6} - 3 q^{7} - 10 q^{8} + 6 q^{9} - 10 q^{10} - 11 q^{11} - 4 q^{12} + 6 q^{13} + 3 q^{14} - 4 q^{15} + 10 q^{16} + 9 q^{17} - 6 q^{18} - 13 q^{19} + 10 q^{20} - 24 q^{21} + 11 q^{22} - 3 q^{23} + 4 q^{24} + 10 q^{25} - 6 q^{26} - 10 q^{27} - 3 q^{28} - 4 q^{29} + 4 q^{30} - 17 q^{31} - 10 q^{32} - 2 q^{33} - 9 q^{34} - 3 q^{35} + 6 q^{36} - 15 q^{37} + 13 q^{38} - 6 q^{39} - 10 q^{40} - 11 q^{41} + 24 q^{42} - 11 q^{43} - 11 q^{44} + 6 q^{45} + 3 q^{46} + 3 q^{47} - 4 q^{48} - 5 q^{49} - 10 q^{50} - 21 q^{51} + 6 q^{52} + 25 q^{53} + 10 q^{54} - 11 q^{55} + 3 q^{56} + 31 q^{57} + 4 q^{58} - 46 q^{59} - 4 q^{60} - 54 q^{61} + 17 q^{62} - 6 q^{63} + 10 q^{64} + 6 q^{65} + 2 q^{66} - 26 q^{67} + 9 q^{68} - 9 q^{69} + 3 q^{70} - 16 q^{71} - 6 q^{72} + 4 q^{73} + 15 q^{74} - 4 q^{75} - 13 q^{76} + 11 q^{77} + 6 q^{78} - 19 q^{79} + 10 q^{80} - 6 q^{81} + 11 q^{82} + 19 q^{83} - 24 q^{84} + 9 q^{85} + 11 q^{86} + 28 q^{87} + 11 q^{88} - 30 q^{89} - 6 q^{90} - 38 q^{91} - 3 q^{92} - 18 q^{93} - 3 q^{94} - 13 q^{95} + 4 q^{96} - 16 q^{97} + 5 q^{98} - 59 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 - 4 * q^3 + 10 * q^4 + 10 * q^5 + 4 * q^6 - 3 * q^7 - 10 * q^8 + 6 * q^9 - 10 * q^10 - 11 * q^11 - 4 * q^12 + 6 * q^13 + 3 * q^14 - 4 * q^15 + 10 * q^16 + 9 * q^17 - 6 * q^18 - 13 * q^19 + 10 * q^20 - 24 * q^21 + 11 * q^22 - 3 * q^23 + 4 * q^24 + 10 * q^25 - 6 * q^26 - 10 * q^27 - 3 * q^28 - 4 * q^29 + 4 * q^30 - 17 * q^31 - 10 * q^32 - 2 * q^33 - 9 * q^34 - 3 * q^35 + 6 * q^36 - 15 * q^37 + 13 * q^38 - 6 * q^39 - 10 * q^40 - 11 * q^41 + 24 * q^42 - 11 * q^43 - 11 * q^44 + 6 * q^45 + 3 * q^46 + 3 * q^47 - 4 * q^48 - 5 * q^49 - 10 * q^50 - 21 * q^51 + 6 * q^52 + 25 * q^53 + 10 * q^54 - 11 * q^55 + 3 * q^56 + 31 * q^57 + 4 * q^58 - 46 * q^59 - 4 * q^60 - 54 * q^61 + 17 * q^62 - 6 * q^63 + 10 * q^64 + 6 * q^65 + 2 * q^66 - 26 * q^67 + 9 * q^68 - 9 * q^69 + 3 * q^70 - 16 * q^71 - 6 * q^72 + 4 * q^73 + 15 * q^74 - 4 * q^75 - 13 * q^76 + 11 * q^77 + 6 * q^78 - 19 * q^79 + 10 * q^80 - 6 * q^81 + 11 * q^82 + 19 * q^83 - 24 * q^84 + 9 * q^85 + 11 * q^86 + 28 * q^87 + 11 * q^88 - 30 * q^89 - 6 * q^90 - 38 * q^91 - 3 * q^92 - 18 * q^93 - 3 * q^94 - 13 * q^95 + 4 * q^96 - 16 * q^97 + 5 * q^98 - 59 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−3.13000	−1.80711	−0.903554	−	0.428474i	$-0.859051\pi$
$3$	−3.13000	−1.80711	−0.903554	+	0.428474i	$0.859051\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	3.13000	1.27782
$7$	2.49851	0.944349	0.472175	−	0.881505i	$-0.343469\pi$
$7$	2.49851	0.944349	0.472175	+	0.881505i	$0.343469\pi$
$8$	−1.00000	−0.353553
$9$	6.79692	2.26564
$10$	−1.00000	−0.316228
$11$	−1.60279	−0.483260	−0.241630	−	0.970368i	$-0.577682\pi$
$11$	−1.60279	−0.483260	−0.241630	+	0.970368i	$0.577682\pi$
$12$	−3.13000	−0.903554
$13$	−0.554325	−0.153742	−0.0768711	−	0.997041i	$-0.524493\pi$
$13$	−0.554325	−0.153742	−0.0768711	+	0.997041i	$0.524493\pi$
$14$	−2.49851	−0.667756
$15$	−3.13000	−0.808163
$16$	1.00000	0.250000
$17$	5.26951	1.27804	0.639022	−	0.769188i	$-0.279339\pi$
$17$	5.26951	1.27804	0.639022	+	0.769188i	$0.279339\pi$
$18$	−6.79692	−1.60205
$19$	−2.32369	−0.533092	−0.266546	−	0.963822i	$-0.585882\pi$
$19$	−2.32369	−0.533092	−0.266546	+	0.963822i	$0.585882\pi$
$20$	1.00000	0.223607
$21$	−7.82035	−1.70654
$22$	1.60279	0.341717
$23$	4.26393	0.889092	0.444546	−	0.895756i	$-0.353365\pi$
$23$	4.26393	0.889092	0.444546	+	0.895756i	$0.353365\pi$
$24$	3.13000	0.638909
$25$	1.00000	0.200000
$26$	0.554325	0.108712
$27$	−11.8844	−2.28715
$28$	2.49851	0.472175
$29$	−2.40114	−0.445881	−0.222940	−	0.974832i	$-0.571566\pi$
$29$	−2.40114	−0.445881	−0.222940	+	0.974832i	$0.571566\pi$
$30$	3.13000	0.571458
$31$	−10.2745	−1.84536	−0.922680	−	0.385567i	$-0.874006\pi$
$31$	−10.2745	−1.84536	−0.922680	+	0.385567i	$0.874006\pi$
$32$	−1.00000	−0.176777
$33$	5.01675	0.873304
$34$	−5.26951	−0.903714
$35$	2.49851	0.422326
$36$	6.79692	1.13282
$37$	−0.359181	−0.0590490	−0.0295245	−	0.999564i	$-0.509399\pi$
$37$	−0.359181	−0.0590490	−0.0295245	+	0.999564i	$0.509399\pi$
$38$	2.32369	0.376953
$39$	1.73504	0.277829
$40$	−1.00000	−0.158114
$41$	−2.50682	−0.391500	−0.195750	−	0.980654i	$-0.562714\pi$
$41$	−2.50682	−0.391500	−0.195750	+	0.980654i	$0.562714\pi$
$42$	7.82035	1.20671
$43$	1.01036	0.154078	0.0770391	−	0.997028i	$-0.475453\pi$
$43$	1.01036	0.154078	0.0770391	+	0.997028i	$0.475453\pi$
$44$	−1.60279	−0.241630
$45$	6.79692	1.01322
$46$	−4.26393	−0.628683
$47$	−6.02260	−0.878486	−0.439243	−	0.898368i	$-0.644753\pi$
$47$	−6.02260	−0.878486	−0.439243	+	0.898368i	$0.644753\pi$
$48$	−3.13000	−0.451777
$49$	−0.757432	−0.108205
$50$	−1.00000	−0.141421
$51$	−16.4936	−2.30956
$52$	−0.554325	−0.0768711
$53$	−11.4646	−1.57478	−0.787390	−	0.616455i	$-0.788568\pi$
$53$	−11.4646	−1.57478	−0.787390	+	0.616455i	$0.788568\pi$
$54$	11.8844	1.61726
$55$	−1.60279	−0.216121
$56$	−2.49851	−0.333878
$57$	7.27317	0.963354
$58$	2.40114	0.315285
$59$	−5.94415	−0.773862	−0.386931	−	0.922109i	$-0.626465\pi$
$59$	−5.94415	−0.773862	−0.386931	+	0.922109i	$0.626465\pi$
$60$	−3.13000	−0.404082
$61$	0.692162	0.0886223	0.0443111	−	0.999018i	$-0.485891\pi$
$61$	0.692162	0.0886223	0.0443111	+	0.999018i	$0.485891\pi$
$62$	10.2745	1.30487
$63$	16.9822	2.13955
$64$	1.00000	0.125000
$65$	−0.554325	−0.0687556
$66$	−5.01675	−0.617519
$67$	−3.85892	−0.471442	−0.235721	−	0.971821i	$-0.575745\pi$
$67$	−3.85892	−0.471442	−0.235721	+	0.971821i	$0.575745\pi$
$68$	5.26951	0.639022
$69$	−13.3461	−1.60669
$70$	−2.49851	−0.298629
$71$	−6.49192	−0.770449	−0.385224	−	0.922823i	$-0.625876\pi$
$71$	−6.49192	−0.770449	−0.385224	+	0.922823i	$0.625876\pi$
$72$	−6.79692	−0.801025
$73$	5.75377	0.673428	0.336714	−	0.941607i	$-0.390685\pi$
$73$	5.75377	0.673428	0.336714	+	0.941607i	$0.390685\pi$
$74$	0.359181	0.0417540
$75$	−3.13000	−0.361422
$76$	−2.32369	−0.266546
$77$	−4.00460	−0.456367
$78$	−1.73504	−0.196455
$79$	1.29382	0.145566	0.0727829	−	0.997348i	$-0.476812\pi$
$79$	1.29382	0.145566	0.0727829	+	0.997348i	$0.476812\pi$
$80$	1.00000	0.111803
$81$	16.8073	1.86748
$82$	2.50682	0.276832
$83$	2.60037	0.285428	0.142714	−	0.989764i	$-0.454417\pi$
$83$	2.60037	0.285428	0.142714	+	0.989764i	$0.454417\pi$
$84$	−7.82035	−0.853271
$85$	5.26951	0.571559
$86$	−1.01036	−0.108950
$87$	7.51558	0.805755
$88$	1.60279	0.170858
$89$	9.62868	1.02064	0.510319	−	0.859985i	$-0.329527\pi$
$89$	9.62868	1.02064	0.510319	+	0.859985i	$0.329527\pi$
$90$	−6.79692	−0.716458
$91$	−1.38499	−0.145186
$92$	4.26393	0.444546
$93$	32.1593	3.33476
$94$	6.02260	0.621183
$95$	−2.32369	−0.238406
$96$	3.13000	0.319455
$97$	7.34064	0.745329	0.372664	−	0.927966i	$-0.378444\pi$
$97$	7.34064	0.745329	0.372664	+	0.927966i	$0.378444\pi$
$98$	0.757432	0.0765122
$99$	−10.8941	−1.09489
$100$	1.00000	0.100000
$101$	−0.841840	−0.0837662	−0.0418831	−	0.999123i	$-0.513336\pi$
$101$	−0.841840	−0.0837662	−0.0418831	+	0.999123i	$0.513336\pi$
$102$	16.4936	1.63311
$103$	13.3474	1.31516	0.657580	−	0.753385i	$-0.271580\pi$
$103$	13.3474	1.31516	0.657580	+	0.753385i	$0.271580\pi$
$104$	0.554325	0.0543561
$105$	−7.82035	−0.763188
$106$	11.4646	1.11354
$107$	2.35230	0.227405	0.113703	−	0.993515i	$-0.463729\pi$
$107$	2.35230	0.227405	0.113703	+	0.993515i	$0.463729\pi$
$108$	−11.8844	−1.14357
$109$	−1.08799	−0.104210	−0.0521052	−	0.998642i	$-0.516593\pi$
$109$	−1.08799	−0.104210	−0.0521052	+	0.998642i	$0.516593\pi$
$110$	1.60279	0.152820
$111$	1.12424	0.106708
$112$	2.49851	0.236087
$113$	16.3637	1.53937	0.769684	−	0.638426i	$-0.220414\pi$
$113$	16.3637	1.53937	0.769684	+	0.638426i	$0.220414\pi$
$114$	−7.27317	−0.681194
$115$	4.26393	0.397614
$116$	−2.40114	−0.222940
$117$	−3.76770	−0.348324
$118$	5.94415	0.547203
$119$	13.1659	1.20692
$120$	3.13000	0.285729
$121$	−8.43105	−0.766459
$122$	−0.692162	−0.0626654
$123$	7.84637	0.707483
$124$	−10.2745	−0.922680
$125$	1.00000	0.0894427
$126$	−16.9822	−1.51289
$127$	−15.2216	−1.35070	−0.675351	−	0.737497i	$-0.736008\pi$
$127$	−15.2216	−1.35070	−0.675351	+	0.737497i	$0.736008\pi$
$128$	−1.00000	−0.0883883
$129$	−3.16243	−0.278436
$130$	0.554325	0.0486176
$131$	−1.48407	−0.129664	−0.0648319	−	0.997896i	$-0.520651\pi$
$131$	−1.48407	−0.129664	−0.0648319	+	0.997896i	$0.520651\pi$
$132$	5.01675	0.436652
$133$	−5.80578	−0.503425
$134$	3.85892	0.333360
$135$	−11.8844	−1.02284
$136$	−5.26951	−0.451857
$137$	−14.8058	−1.26495	−0.632475	−	0.774581i	$-0.717961\pi$
$137$	−14.8058	−1.26495	−0.632475	+	0.774581i	$0.717961\pi$
$138$	13.3461	1.13610
$139$	−8.84411	−0.750148	−0.375074	−	0.926995i	$-0.622383\pi$
$139$	−8.84411	−0.750148	−0.375074	+	0.926995i	$0.622383\pi$
$140$	2.49851	0.211163
$141$	18.8507	1.58752
$142$	6.49192	0.544790
$143$	0.888469	0.0742975
$144$	6.79692	0.566410
$145$	−2.40114	−0.199404
$146$	−5.75377	−0.476185
$147$	2.37077	0.195537
$148$	−0.359181	−0.0295245
$149$	2.76125	0.226210	0.113105	−	0.993583i	$-0.463920\pi$
$149$	2.76125	0.226210	0.113105	+	0.993583i	$0.463920\pi$
$150$	3.13000	0.255564
$151$	10.9291	0.889395	0.444698	−	0.895681i	$-0.353311\pi$
$151$	10.9291	0.889395	0.444698	+	0.895681i	$0.353311\pi$
$152$	2.32369	0.188476
$153$	35.8164	2.89559
$154$	4.00460	0.322700
$155$	−10.2745	−0.825270
$156$	1.73504	0.138914
$157$	8.69993	0.694330	0.347165	−	0.937804i	$-0.387144\pi$
$157$	8.69993	0.694330	0.347165	+	0.937804i	$0.387144\pi$
$158$	−1.29382	−0.102931
$159$	35.8841	2.84580
$160$	−1.00000	−0.0790569
$161$	10.6535	0.839613
$162$	−16.8073	−1.32051
$163$	−13.4903	−1.05664	−0.528321	−	0.849045i	$-0.677178\pi$
$163$	−13.4903	−1.05664	−0.528321	+	0.849045i	$0.677178\pi$
$164$	−2.50682	−0.195750
$165$	5.01675	0.390553
$166$	−2.60037	−0.201828
$167$	−5.17486	−0.400443	−0.200221	−	0.979751i	$-0.564166\pi$
$167$	−5.17486	−0.400443	−0.200221	+	0.979751i	$0.564166\pi$
$168$	7.82035	0.603353
$169$	−12.6927	−0.976363
$170$	−5.26951	−0.404153
$171$	−15.7940	−1.20779
$172$	1.01036	0.0770391
$173$	16.3903	1.24613	0.623064	−	0.782171i	$-0.285888\pi$
$173$	16.3903	1.24613	0.623064	+	0.782171i	$0.285888\pi$
$174$	−7.51558	−0.569755
$175$	2.49851	0.188870
$176$	−1.60279	−0.120815
$177$	18.6052	1.39845
$178$	−9.62868	−0.721700
$179$	7.00317	0.523442	0.261721	−	0.965144i	$-0.415710\pi$
$179$	7.00317	0.523442	0.261721	+	0.965144i	$0.415710\pi$
$180$	6.79692	0.506612
$181$	−15.4015	−1.14479	−0.572393	−	0.819980i	$-0.693985\pi$
$181$	−15.4015	−1.14479	−0.572393	+	0.819980i	$0.693985\pi$
$182$	1.38499	0.102662
$183$	−2.16647	−0.160150
$184$	−4.26393	−0.314341
$185$	−0.359181	−0.0264075
$186$	−32.1593	−2.35803
$187$	−8.44594	−0.617628
$188$	−6.02260	−0.439243
$189$	−29.6932	−2.15987
$190$	2.32369	0.168578
$191$	−15.8806	−1.14908	−0.574541	−	0.818476i	$-0.694819\pi$
$191$	−15.8806	−1.14908	−0.574541	+	0.818476i	$0.694819\pi$
$192$	−3.13000	−0.225889
$193$	−2.11003	−0.151883	−0.0759416	−	0.997112i	$-0.524196\pi$
$193$	−2.11003	−0.151883	−0.0759416	+	0.997112i	$0.524196\pi$
$194$	−7.34064	−0.527027
$195$	1.73504	0.124249
$196$	−0.757432	−0.0541023
$197$	9.59731	0.683780	0.341890	−	0.939740i	$-0.388933\pi$
$197$	9.59731	0.683780	0.341890	+	0.939740i	$0.388933\pi$
$198$	10.8941	0.774207
$199$	−8.29416	−0.587957	−0.293979	−	0.955812i	$-0.594979\pi$
$199$	−8.29416	−0.587957	−0.293979	+	0.955812i	$0.594979\pi$
$200$	−1.00000	−0.0707107
$201$	12.0784	0.851946
$202$	0.841840	0.0592316
$203$	−5.99928	−0.421067
$204$	−16.4936	−1.15478
$205$	−2.50682	−0.175084
$206$	−13.3474	−0.929958
$207$	28.9816	2.01436
$208$	−0.554325	−0.0384356
$209$	3.72440	0.257622
$210$	7.82035	0.539656
$211$	−24.5118	−1.68746	−0.843729	−	0.536769i	$-0.819645\pi$
$211$	−24.5118	−1.68746	−0.843729	+	0.536769i	$0.819645\pi$
$212$	−11.4646	−0.787390
$213$	20.3197	1.39228
$214$	−2.35230	−0.160800
$215$	1.01036	0.0689059
$216$	11.8844	0.808629
$217$	−25.6710	−1.74266
$218$	1.08799	0.0736878
$219$	−18.0093	−1.21696
$220$	−1.60279	−0.108060
$221$	−2.92102	−0.196489
$222$	−1.12424	−0.0754539
$223$	12.8558	0.860890	0.430445	−	0.902617i	$-0.358357\pi$
$223$	12.8558	0.860890	0.430445	+	0.902617i	$0.358357\pi$
$224$	−2.49851	−0.166939
$225$	6.79692	0.453128
$226$	−16.3637	−1.08850
$227$	4.85991	0.322564	0.161282	−	0.986908i	$-0.448437\pi$
$227$	4.85991	0.322564	0.161282	+	0.986908i	$0.448437\pi$
$228$	7.27317	0.481677
$229$	1.31204	0.0867017	0.0433509	−	0.999060i	$-0.486197\pi$
$229$	1.31204	0.0867017	0.0433509	+	0.999060i	$0.486197\pi$
$230$	−4.26393	−0.281156
$231$	12.5344	0.824704
$232$	2.40114	0.157643
$233$	11.2852	0.739317	0.369658	−	0.929168i	$-0.379475\pi$
$233$	11.2852	0.739317	0.369658	+	0.929168i	$0.379475\pi$
$234$	3.76770	0.246303
$235$	−6.02260	−0.392871
$236$	−5.94415	−0.386931
$237$	−4.04965	−0.263053
$238$	−13.1659	−0.853422
$239$	3.82979	0.247729	0.123864	−	0.992299i	$-0.460471\pi$
$239$	3.82979	0.247729	0.123864	+	0.992299i	$0.460471\pi$
$240$	−3.13000	−0.202041
$241$	−14.3377	−0.923570	−0.461785	−	0.886992i	$-0.652791\pi$
$241$	−14.3377	−0.923570	−0.461785	+	0.886992i	$0.652791\pi$
$242$	8.43105	0.541969
$243$	−16.9539	−1.08760
$244$	0.692162	0.0443111
$245$	−0.757432	−0.0483906
$246$	−7.84637	−0.500266
$247$	1.28808	0.0819587
$248$	10.2745	0.652433
$249$	−8.13917	−0.515799
$250$	−1.00000	−0.0632456
$251$	16.0603	1.01372	0.506858	−	0.862029i	$-0.330807\pi$
$251$	16.0603	1.01372	0.506858	+	0.862029i	$0.330807\pi$
$252$	16.9822	1.06978
$253$	−6.83421	−0.429663
$254$	15.2216	0.955090
$255$	−16.4936	−1.03287
$256$	1.00000	0.0625000
$257$	−5.18645	−0.323522	−0.161761	−	0.986830i	$-0.551717\pi$
$257$	−5.18645	−0.323522	−0.161761	+	0.986830i	$0.551717\pi$
$258$	3.16243	0.196884
$259$	−0.897419	−0.0557629
$260$	−0.554325	−0.0343778
$261$	−16.3204	−1.01021
$262$	1.48407	0.0916861
$263$	−16.6803	−1.02855	−0.514276	−	0.857625i	$-0.671939\pi$
$263$	−16.6803	−1.02855	−0.514276	+	0.857625i	$0.671939\pi$
$264$	−5.01675	−0.308760
$265$	−11.4646	−0.704263
$266$	5.80578	0.355975
$267$	−30.1378	−1.84440
$268$	−3.85892	−0.235721
$269$	−27.5502	−1.67977	−0.839883	−	0.542768i	$-0.817376\pi$
$269$	−27.5502	−1.67977	−0.839883	+	0.542768i	$0.817376\pi$
$270$	11.8844	0.723260
$271$	0.902248	0.0548077	0.0274038	−	0.999624i	$-0.491276\pi$
$271$	0.902248	0.0548077	0.0274038	+	0.999624i	$0.491276\pi$
$272$	5.26951	0.319511
$273$	4.33502	0.262367
$274$	14.8058	0.894454
$275$	−1.60279	−0.0966521
$276$	−13.3461	−0.803343
$277$	−26.1112	−1.56887	−0.784434	−	0.620213i	$-0.787046\pi$
$277$	−26.1112	−1.56887	−0.784434	+	0.620213i	$0.787046\pi$
$278$	8.84411	0.530435
$279$	−69.8351	−4.18092
$280$	−2.49851	−0.149315
$281$	25.6505	1.53018	0.765092	−	0.643921i	$-0.222694\pi$
$281$	25.6505	1.53018	0.765092	+	0.643921i	$0.222694\pi$
$282$	−18.8507	−1.12255
$283$	−22.6307	−1.34525	−0.672627	−	0.739982i	$-0.734834\pi$
$283$	−22.6307	−1.34525	−0.672627	+	0.739982i	$0.734834\pi$
$284$	−6.49192	−0.385224
$285$	7.27317	0.430825
$286$	−0.888469	−0.0525363
$287$	−6.26333	−0.369713
$288$	−6.79692	−0.400512
$289$	10.7678	0.633398
$290$	2.40114	0.141000
$291$	−22.9762	−1.34689
$292$	5.75377	0.336714
$293$	−2.90031	−0.169438	−0.0847190	−	0.996405i	$-0.526999\pi$
$293$	−2.90031	−0.169438	−0.0847190	+	0.996405i	$0.526999\pi$
$294$	−2.37077	−0.138266
$295$	−5.94415	−0.346082
$296$	0.359181	0.0208770
$297$	19.0482	1.10529
$298$	−2.76125	−0.159955
$299$	−2.36361	−0.136691
$300$	−3.13000	−0.180711
$301$	2.52439	0.145504
$302$	−10.9291	−0.628897
$303$	2.63496	0.151375
$304$	−2.32369	−0.133273
$305$	0.692162	0.0396331
$306$	−35.8164	−2.04749
$307$	−19.0094	−1.08492	−0.542462	−	0.840080i	$-0.682508\pi$
$307$	−19.0094	−1.08492	−0.542462	+	0.840080i	$0.682508\pi$
$308$	−4.00460	−0.228183
$309$	−41.7775	−2.37664
$310$	10.2745	0.583554
$311$	23.9786	1.35970	0.679850	−	0.733351i	$-0.262045\pi$
$311$	23.9786	1.35970	0.679850	+	0.733351i	$0.262045\pi$
$312$	−1.73504	−0.0982273
$313$	−1.02820	−0.0581172	−0.0290586	−	0.999578i	$-0.509251\pi$
$313$	−1.02820	−0.0581172	−0.0290586	+	0.999578i	$0.509251\pi$
$314$	−8.69993	−0.490965
$315$	16.9822	0.956838
$316$	1.29382	0.0727829
$317$	−4.13918	−0.232479	−0.116240	−	0.993221i	$-0.537084\pi$
$317$	−4.13918	−0.232479	−0.116240	+	0.993221i	$0.537084\pi$
$318$	−35.8841	−2.01228
$319$	3.84853	0.215477
$320$	1.00000	0.0559017
$321$	−7.36270	−0.410946
$322$	−10.6535	−0.593696
$323$	−12.2447	−0.681315
$324$	16.8073	0.933742
$325$	−0.554325	−0.0307484
$326$	13.4903	0.747158
$327$	3.40540	0.188319
$328$	2.50682	0.138416
$329$	−15.0475	−0.829597
$330$	−5.01675	−0.276163
$331$	−13.6861	−0.752254	−0.376127	−	0.926568i	$-0.622744\pi$
$331$	−13.6861	−0.752254	−0.376127	+	0.926568i	$0.622744\pi$
$332$	2.60037	0.142714
$333$	−2.44133	−0.133784
$334$	5.17486	0.283156
$335$	−3.85892	−0.210835
$336$	−7.82035	−0.426635
$337$	−25.3412	−1.38042	−0.690211	−	0.723608i	$-0.742482\pi$
$337$	−25.3412	−1.38042	−0.690211	+	0.723608i	$0.742482\pi$
$338$	12.6927	0.690393
$339$	−51.2184	−2.78180
$340$	5.26951	0.285779
$341$	16.4679	0.891789
$342$	15.7940	0.854039
$343$	−19.3820	−1.04653
$344$	−1.01036	−0.0544749
$345$	−13.3461	−0.718531
$346$	−16.3903	−0.881145
$347$	−1.18759	−0.0637530	−0.0318765	−	0.999492i	$-0.510148\pi$
$347$	−1.18759	−0.0637530	−0.0318765	+	0.999492i	$0.510148\pi$
$348$	7.51558	0.402877
$349$	12.1807	0.652016	0.326008	−	0.945367i	$-0.394296\pi$
$349$	12.1807	0.652016	0.326008	+	0.945367i	$0.394296\pi$
$350$	−2.49851	−0.133551
$351$	6.58781	0.351631
$352$	1.60279	0.0854292
$353$	13.1057	0.697543	0.348772	−	0.937208i	$-0.386599\pi$
$353$	13.1057	0.697543	0.348772	+	0.937208i	$0.386599\pi$
$354$	−18.6052	−0.988855
$355$	−6.49192	−0.344555
$356$	9.62868	0.510319
$357$	−41.2095	−2.18104
$358$	−7.00317	−0.370129
$359$	−17.1135	−0.903218	−0.451609	−	0.892216i	$-0.649150\pi$
$359$	−17.1135	−0.903218	−0.451609	+	0.892216i	$0.649150\pi$
$360$	−6.79692	−0.358229
$361$	−13.6005	−0.715813
$362$	15.4015	0.809485
$363$	26.3892	1.38507
$364$	−1.38499	−0.0725932
$365$	5.75377	0.301166
$366$	2.16647	0.113243
$367$	2.81757	0.147076	0.0735380	−	0.997292i	$-0.476571\pi$
$367$	2.81757	0.147076	0.0735380	+	0.997292i	$0.476571\pi$
$368$	4.26393	0.222273
$369$	−17.0387	−0.886998
$370$	0.359181	0.0186729
$371$	−28.6444	−1.48714
$372$	32.1593	1.66738
$373$	−35.9524	−1.86155	−0.930773	−	0.365597i	$-0.880865\pi$
$373$	−35.9524	−1.86155	−0.930773	+	0.365597i	$0.880865\pi$
$374$	8.44594	0.436729
$375$	−3.13000	−0.161633
$376$	6.02260	0.310592
$377$	1.33101	0.0685507
$378$	29.6932	1.52726
$379$	−22.1707	−1.13883	−0.569415	−	0.822050i	$-0.692830\pi$
$379$	−22.1707	−1.13883	−0.569415	+	0.822050i	$0.692830\pi$
$380$	−2.32369	−0.119203
$381$	47.6438	2.44086
$382$	15.8806	0.812523
$383$	2.99160	0.152864	0.0764319	−	0.997075i	$-0.475647\pi$
$383$	2.99160	0.152864	0.0764319	+	0.997075i	$0.475647\pi$
$384$	3.13000	0.159727
$385$	−4.00460	−0.204093
$386$	2.11003	0.107398
$387$	6.86733	0.349086
$388$	7.34064	0.372664
$389$	17.2293	0.873562	0.436781	−	0.899568i	$-0.356118\pi$
$389$	17.2293	0.873562	0.436781	+	0.899568i	$0.356118\pi$
$390$	−1.73504	−0.0878572
$391$	22.4689	1.13630
$392$	0.757432	0.0382561
$393$	4.64514	0.234316
$394$	−9.59731	−0.483505
$395$	1.29382	0.0650990
$396$	−10.8941	−0.547447
$397$	38.4232	1.92841	0.964203	−	0.265163i	$-0.0854259\pi$
$397$	38.4232	1.92841	0.964203	+	0.265163i	$0.0854259\pi$
$398$	8.29416	0.415749
$399$	18.1721	0.909743
$400$	1.00000	0.0500000
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−12.0784	−0.602417
$403$	5.69543	0.283710
$404$	−0.841840	−0.0418831
$405$	16.8073	0.835164
$406$	5.99928	0.297739
$407$	0.575693	0.0285361
$408$	16.4936	0.816554
$409$	−15.4432	−0.763618	−0.381809	−	0.924241i	$-0.624699\pi$
$409$	−15.4432	−0.763618	−0.381809	+	0.924241i	$0.624699\pi$
$410$	2.50682	0.123803
$411$	46.3424	2.28590
$412$	13.3474	0.657580
$413$	−14.8515	−0.730796
$414$	−28.9816	−1.42437
$415$	2.60037	0.127647
$416$	0.554325	0.0271780
$417$	27.6821	1.35560
$418$	−3.72440	−0.182166
$419$	−14.4186	−0.704396	−0.352198	−	0.935925i	$-0.614566\pi$
$419$	−14.4186	−0.704396	−0.352198	+	0.935925i	$0.614566\pi$
$420$	−7.82035	−0.381594
$421$	0.880335	0.0429049	0.0214524	−	0.999770i	$-0.493171\pi$
$421$	0.880335	0.0429049	0.0214524	+	0.999770i	$0.493171\pi$
$422$	24.5118	1.19321
$423$	−40.9351	−1.99033
$424$	11.4646	0.556769
$425$	5.26951	0.255609
$426$	−20.3197	−0.984494
$427$	1.72938	0.0836904
$428$	2.35230	0.113703
$429$	−2.78091	−0.134264
$430$	−1.01036	−0.0487238
$431$	23.8006	1.14643	0.573217	−	0.819404i	$-0.305695\pi$
$431$	23.8006	1.14643	0.573217	+	0.819404i	$0.305695\pi$
$432$	−11.8844	−0.571787
$433$	1.78662	0.0858597	0.0429299	−	0.999078i	$-0.486331\pi$
$433$	1.78662	0.0858597	0.0429299	+	0.999078i	$0.486331\pi$
$434$	25.6710	1.23225
$435$	7.51558	0.360345
$436$	−1.08799	−0.0521052
$437$	−9.90807	−0.473967
$438$	18.0093	0.860518
$439$	10.5565	0.503833	0.251917	−	0.967749i	$-0.418939\pi$
$439$	10.5565	0.503833	0.251917	+	0.967749i	$0.418939\pi$
$440$	1.60279	0.0764102
$441$	−5.14821	−0.245153
$442$	2.92102	0.138939
$443$	23.5700	1.11984	0.559922	−	0.828545i	$-0.310831\pi$
$443$	23.5700	1.11984	0.559922	+	0.828545i	$0.310831\pi$
$444$	1.12424	0.0533540
$445$	9.62868	0.456443
$446$	−12.8558	−0.608741
$447$	−8.64271	−0.408786
$448$	2.49851	0.118044
$449$	15.9106	0.750868	0.375434	−	0.926849i	$-0.377494\pi$
$449$	15.9106	0.750868	0.375434	+	0.926849i	$0.377494\pi$
$450$	−6.79692	−0.320410
$451$	4.01792	0.189197
$452$	16.3637	0.769684
$453$	−34.2080	−1.60723
$454$	−4.85991	−0.228087
$455$	−1.38499	−0.0649293
$456$	−7.27317	−0.340597
$457$	11.1245	0.520382	0.260191	−	0.965557i	$-0.416214\pi$
$457$	11.1245	0.520382	0.260191	+	0.965557i	$0.416214\pi$
$458$	−1.31204	−0.0613074
$459$	−62.6248	−2.92308
$460$	4.26393	0.198807
$461$	−19.0227	−0.885978	−0.442989	−	0.896527i	$-0.646082\pi$
$461$	−19.0227	−0.885978	−0.442989	+	0.896527i	$0.646082\pi$
$462$	−12.5344	−0.583154
$463$	16.3268	0.758769	0.379385	−	0.925239i	$-0.376136\pi$
$463$	16.3268	0.758769	0.379385	+	0.925239i	$0.376136\pi$
$464$	−2.40114	−0.111470
$465$	32.1593	1.49135
$466$	−11.2852	−0.522776
$467$	−10.6304	−0.491918	−0.245959	−	0.969280i	$-0.579103\pi$
$467$	−10.6304	−0.491918	−0.245959	+	0.969280i	$0.579103\pi$
$468$	−3.76770	−0.174162
$469$	−9.64155	−0.445206
$470$	6.02260	0.277802
$471$	−27.2308	−1.25473
$472$	5.94415	0.273602
$473$	−1.61940	−0.0744599
$474$	4.04965	0.186007
$475$	−2.32369	−0.106618
$476$	13.1659	0.603460
$477$	−77.9237	−3.56788
$478$	−3.82979	−0.175171
$479$	2.81613	0.128672	0.0643360	−	0.997928i	$-0.479507\pi$
$479$	2.81613	0.128672	0.0643360	+	0.997928i	$0.479507\pi$
$480$	3.13000	0.142864
$481$	0.199103	0.00907833
$482$	14.3377	0.653063
$483$	−33.3455	−1.51727
$484$	−8.43105	−0.383230
$485$	7.34064	0.333321
$486$	16.9539	0.769047
$487$	−31.0010	−1.40479	−0.702395	−	0.711788i	$-0.747886\pi$
$487$	−31.0010	−1.40479	−0.702395	+	0.711788i	$0.747886\pi$
$488$	−0.692162	−0.0313327
$489$	42.2247	1.90946
$490$	0.757432	0.0342173
$491$	−4.69437	−0.211854	−0.105927	−	0.994374i	$-0.533781\pi$
$491$	−4.69437	−0.211854	−0.105927	+	0.994374i	$0.533781\pi$
$492$	7.84637	0.353742
$493$	−12.6528	−0.569856
$494$	−1.28808	−0.0579536
$495$	−10.8941	−0.489651
$496$	−10.2745	−0.461340
$497$	−16.2201	−0.727573
$498$	8.13917	0.364725
$499$	32.5480	1.45705	0.728524	−	0.685021i	$-0.240207\pi$
$499$	32.5480	1.45705	0.728524	+	0.685021i	$0.240207\pi$
$500$	1.00000	0.0447214
$501$	16.1973	0.723643
$502$	−16.0603	−0.716806
$503$	−25.0655	−1.11761	−0.558807	−	0.829298i	$-0.688741\pi$
$503$	−25.0655	−1.11761	−0.558807	+	0.829298i	$0.688741\pi$
$504$	−16.9822	−0.756447
$505$	−0.841840	−0.0374614
$506$	6.83421	0.303818
$507$	39.7283	1.76439
$508$	−15.2216	−0.675351
$509$	16.8920	0.748726	0.374363	−	0.927282i	$-0.377861\pi$
$509$	16.8920	0.748726	0.374363	+	0.927282i	$0.377861\pi$
$510$	16.4936	0.730348
$511$	14.3759	0.635951
$512$	−1.00000	−0.0441942
$513$	27.6156	1.21926
$514$	5.18645	0.228765
$515$	13.3474	0.588157
$516$	−3.16243	−0.139218
$517$	9.65298	0.424537
$518$	0.897419	0.0394303
$519$	−51.3015	−2.25189
$520$	0.554325	0.0243088
$521$	−11.4351	−0.500979	−0.250490	−	0.968119i	$-0.580592\pi$
$521$	−11.4351	−0.500979	−0.250490	+	0.968119i	$0.580592\pi$
$522$	16.3204	0.714323
$523$	−2.75185	−0.120330	−0.0601650	−	0.998188i	$-0.519163\pi$
$523$	−2.75185	−0.120330	−0.0601650	+	0.998188i	$0.519163\pi$
$524$	−1.48407	−0.0648319
$525$	−7.82035	−0.341308
$526$	16.6803	0.727296
$527$	−54.1418	−2.35845
$528$	5.01675	0.218326
$529$	−4.81886	−0.209516
$530$	11.4646	0.497989
$531$	−40.4019	−1.75329
$532$	−5.80578	−0.251712
$533$	1.38960	0.0601901
$534$	30.1378	1.30419
$535$	2.35230	0.101699
$536$	3.85892	0.166680
$537$	−21.9199	−0.945916
$538$	27.5502	1.18777
$539$	1.21401	0.0522910
$540$	−11.8844	−0.511422
$541$	33.4085	1.43635	0.718173	−	0.695865i	$-0.244979\pi$
$541$	33.4085	1.43635	0.718173	+	0.695865i	$0.244979\pi$
$542$	−0.902248	−0.0387549
$543$	48.2068	2.06875
$544$	−5.26951	−0.225928
$545$	−1.08799	−0.0466043
$546$	−4.33502	−0.185522
$547$	−46.1416	−1.97287	−0.986436	−	0.164149i	$-0.947512\pi$
$547$	−46.1416	−1.97287	−0.986436	+	0.164149i	$0.947512\pi$
$548$	−14.8058	−0.632475
$549$	4.70457	0.200786
$550$	1.60279	0.0683433
$551$	5.57952	0.237695
$552$	13.3461	0.568049
$553$	3.23262	0.137465
$554$	26.1112	1.10936
$555$	1.12424	0.0477213
$556$	−8.84411	−0.375074
$557$	22.8300	0.967340	0.483670	−	0.875251i	$-0.339304\pi$
$557$	22.8300	0.967340	0.483670	+	0.875251i	$0.339304\pi$
$558$	69.8351	2.95636
$559$	−0.560068	−0.0236883
$560$	2.49851	0.105581
$561$	26.4358	1.11612
$562$	−25.6505	−1.08200
$563$	−27.4350	−1.15625	−0.578124	−	0.815949i	$-0.696215\pi$
$563$	−27.4350	−1.15625	−0.578124	+	0.815949i	$0.696215\pi$
$564$	18.8507	0.793759
$565$	16.3637	0.688426
$566$	22.6307	0.951238
$567$	41.9934	1.76356
$568$	6.49192	0.272395
$569$	15.3967	0.645464	0.322732	−	0.946490i	$-0.395399\pi$
$569$	15.3967	0.645464	0.322732	+	0.946490i	$0.395399\pi$
$570$	−7.27317	−0.304639
$571$	−6.82895	−0.285783	−0.142891	−	0.989738i	$-0.545640\pi$
$571$	−6.82895	−0.285783	−0.142891	+	0.989738i	$0.545640\pi$
$572$	0.888469	0.0371488
$573$	49.7064	2.07651
$574$	6.26333	0.261427
$575$	4.26393	0.177818
$576$	6.79692	0.283205
$577$	−16.1557	−0.672570	−0.336285	−	0.941760i	$-0.609171\pi$
$577$	−16.1557	−0.672570	−0.336285	+	0.941760i	$0.609171\pi$
$578$	−10.7678	−0.447880
$579$	6.60440	0.274469
$580$	−2.40114	−0.0997020
$581$	6.49706	0.269543
$582$	22.9762	0.952395
$583$	18.3753	0.761029
$584$	−5.75377	−0.238093
$585$	−3.76770	−0.155775
$586$	2.90031	0.119811
$587$	26.0086	1.07349	0.536744	−	0.843745i	$-0.319654\pi$
$587$	26.0086	1.07349	0.536744	+	0.843745i	$0.319654\pi$
$588$	2.37077	0.0977687
$589$	23.8749	0.983746
$590$	5.94415	0.244717
$591$	−30.0396	−1.23566
$592$	−0.359181	−0.0147623
$593$	−25.0795	−1.02989	−0.514946	−	0.857223i	$-0.672188\pi$
$593$	−25.0795	−1.02989	−0.514946	+	0.857223i	$0.672188\pi$
$594$	−19.0482	−0.781557
$595$	13.1659	0.539751
$596$	2.76125	0.113105
$597$	25.9607	1.06250
$598$	2.36361	0.0966551
$599$	38.0130	1.55317	0.776584	−	0.630014i	$-0.216951\pi$
$599$	38.0130	1.55317	0.776584	+	0.630014i	$0.216951\pi$
$600$	3.13000	0.127782
$601$	−30.5002	−1.24413	−0.622065	−	0.782966i	$-0.713706\pi$
$601$	−30.5002	−1.24413	−0.622065	+	0.782966i	$0.713706\pi$
$602$	−2.52439	−0.102887
$603$	−26.2287	−1.06812
$604$	10.9291	0.444698
$605$	−8.43105	−0.342771
$606$	−2.63496	−0.107038
$607$	−27.5176	−1.11690	−0.558452	−	0.829537i	$-0.688604\pi$
$607$	−27.5176	−1.11690	−0.558452	+	0.829537i	$0.688604\pi$
$608$	2.32369	0.0942382
$609$	18.7778	0.760914
$610$	−0.692162	−0.0280248
$611$	3.33848	0.135060
$612$	35.8164	1.44779
$613$	−9.51619	−0.384355	−0.192178	−	0.981360i	$-0.561555\pi$
$613$	−9.51619	−0.384355	−0.192178	+	0.981360i	$0.561555\pi$
$614$	19.0094	0.767157
$615$	7.84637	0.316396
$616$	4.00460	0.161350
$617$	−10.3721	−0.417565	−0.208783	−	0.977962i	$-0.566950\pi$
$617$	−10.3721	−0.417565	−0.208783	+	0.977962i	$0.566950\pi$
$618$	41.7775	1.68054
$619$	−1.99419	−0.0801532	−0.0400766	−	0.999197i	$-0.512760\pi$
$619$	−1.99419	−0.0801532	−0.0400766	+	0.999197i	$0.512760\pi$
$620$	−10.2745	−0.412635
$621$	−50.6742	−2.03348
$622$	−23.9786	−0.961453
$623$	24.0574	0.963839
$624$	1.73504	0.0694572
$625$	1.00000	0.0400000
$626$	1.02820	0.0410951
$627$	−11.6574	−0.465551
$628$	8.69993	0.347165
$629$	−1.89271	−0.0754673
$630$	−16.9822	−0.676587
$631$	−5.45354	−0.217102	−0.108551	−	0.994091i	$-0.534621\pi$
$631$	−5.45354	−0.217102	−0.108551	+	0.994091i	$0.534621\pi$
$632$	−1.29382	−0.0514653
$633$	76.7219	3.04942
$634$	4.13918	0.164388
$635$	−15.2216	−0.604052
$636$	35.8841	1.42290
$637$	0.419864	0.0166356
$638$	−3.84853	−0.152365
$639$	−44.1250	−1.74556
$640$	−1.00000	−0.0395285
$641$	−33.0227	−1.30432	−0.652160	−	0.758081i	$-0.726137\pi$
$641$	−33.0227	−1.30432	−0.652160	+	0.758081i	$0.726137\pi$
$642$	7.36270	0.290583
$643$	−15.8321	−0.624359	−0.312179	−	0.950023i	$-0.601059\pi$
$643$	−15.8321	−0.624359	−0.312179	+	0.950023i	$0.601059\pi$
$644$	10.6535	0.419807
$645$	−3.16243	−0.124520
$646$	12.2447	0.481762
$647$	26.6391	1.04729	0.523645	−	0.851937i	$-0.324572\pi$
$647$	26.6391	1.04729	0.523645	+	0.851937i	$0.324572\pi$
$648$	−16.8073	−0.660255
$649$	9.52724	0.373977
$650$	0.554325	0.0217424
$651$	80.3505	3.14918
$652$	−13.4903	−0.528321
$653$	11.2504	0.440264	0.220132	−	0.975470i	$-0.429351\pi$
$653$	11.2504	0.440264	0.220132	+	0.975470i	$0.429351\pi$
$654$	−3.40540	−0.133162
$655$	−1.48407	−0.0579874
$656$	−2.50682	−0.0978751
$657$	39.1079	1.52574
$658$	15.0475	0.586614
$659$	−27.4914	−1.07091	−0.535456	−	0.844563i	$-0.679860\pi$
$659$	−27.4914	−1.07091	−0.535456	+	0.844563i	$0.679860\pi$
$660$	5.01675	0.195277
$661$	9.44399	0.367329	0.183664	−	0.982989i	$-0.441204\pi$
$661$	9.44399	0.367329	0.183664	+	0.982989i	$0.441204\pi$
$662$	13.6861	0.531924
$663$	9.14282	0.355078
$664$	−2.60037	−0.100914
$665$	−5.80578	−0.225138
$666$	2.44133	0.0945994
$667$	−10.2383	−0.396429
$668$	−5.17486	−0.200221
$669$	−40.2388	−1.55572
$670$	3.85892	0.149083
$671$	−1.10939	−0.0428276
$672$	7.82035	0.301677
$673$	50.7619	1.95673	0.978364	−	0.206890i	$-0.0663343\pi$
$673$	50.7619	1.95673	0.978364	+	0.206890i	$0.0663343\pi$
$674$	25.3412	0.976106
$675$	−11.8844	−0.457429
$676$	−12.6927	−0.488182
$677$	−9.90968	−0.380860	−0.190430	−	0.981701i	$-0.560988\pi$
$677$	−9.90968	−0.380860	−0.190430	+	0.981701i	$0.560988\pi$
$678$	51.2184	1.96703
$679$	18.3407	0.703850
$680$	−5.26951	−0.202077
$681$	−15.2115	−0.582908
$682$	−16.4679	−0.630590
$683$	−24.6540	−0.943358	−0.471679	−	0.881770i	$-0.656352\pi$
$683$	−24.6540	−0.943358	−0.471679	+	0.881770i	$0.656352\pi$
$684$	−15.7940	−0.603897
$685$	−14.8058	−0.565702
$686$	19.3820	0.740010
$687$	−4.10667	−0.156679
$688$	1.01036	0.0385196
$689$	6.35510	0.242110
$690$	13.3461	0.508078
$691$	27.1337	1.03221	0.516107	−	0.856524i	$-0.327381\pi$
$691$	27.1337	1.03221	0.516107	+	0.856524i	$0.327381\pi$
$692$	16.3903	0.623064
$693$	−27.2189	−1.03396
$694$	1.18759	0.0450801
$695$	−8.84411	−0.335476
$696$	−7.51558	−0.284877
$697$	−13.2097	−0.500355
$698$	−12.1807	−0.461045
$699$	−35.3226	−1.33602
$700$	2.49851	0.0944349
$701$	10.8978	0.411604	0.205802	−	0.978594i	$-0.434020\pi$
$701$	10.8978	0.411604	0.205802	+	0.978594i	$0.434020\pi$
$702$	−6.58781	−0.248641
$703$	0.834627	0.0314785
$704$	−1.60279	−0.0604076
$705$	18.8507	0.709960
$706$	−13.1057	−0.493238
$707$	−2.10335	−0.0791045
$708$	18.6052	0.699226
$709$	−33.8638	−1.27178	−0.635890	−	0.771780i	$-0.719367\pi$
$709$	−33.8638	−1.27178	−0.635890	+	0.771780i	$0.719367\pi$
$710$	6.49192	0.243637
$711$	8.79397	0.329800
$712$	−9.62868	−0.360850
$713$	−43.8099	−1.64069
$714$	41.2095	1.54222
$715$	0.888469	0.0332269
$716$	7.00317	0.261721
$717$	−11.9873	−0.447672
$718$	17.1135	0.638671
$719$	−17.2931	−0.644925	−0.322463	−	0.946582i	$-0.604511\pi$
$719$	−17.2931	−0.644925	−0.322463	+	0.946582i	$0.604511\pi$
$720$	6.79692	0.253306
$721$	33.3487	1.24197
$722$	13.6005	0.506156
$723$	44.8769	1.66899
$724$	−15.4015	−0.572393
$725$	−2.40114	−0.0891762
$726$	−26.3892	−0.979396
$727$	31.6920	1.17539	0.587696	−	0.809082i	$-0.300035\pi$
$727$	31.6920	1.17539	0.587696	+	0.809082i	$0.300035\pi$
$728$	1.38499	0.0513311
$729$	2.64387	0.0979210
$730$	−5.75377	−0.212957
$731$	5.32410	0.196919
$732$	−2.16647	−0.0800750
$733$	−24.9775	−0.922565	−0.461282	−	0.887253i	$-0.652611\pi$
$733$	−24.9775	−0.922565	−0.461282	+	0.887253i	$0.652611\pi$
$734$	−2.81757	−0.103998
$735$	2.37077	0.0874470
$736$	−4.26393	−0.157171
$737$	6.18505	0.227829
$738$	17.0387	0.627203
$739$	−23.5856	−0.867609	−0.433805	−	0.901007i	$-0.642829\pi$
$739$	−23.5856	−0.867609	−0.433805	+	0.901007i	$0.642829\pi$
$740$	−0.359181	−0.0132038
$741$	−4.03170	−0.148108
$742$	28.6444	1.05157
$743$	−15.1399	−0.555430	−0.277715	−	0.960664i	$-0.589577\pi$
$743$	−15.1399	−0.555430	−0.277715	+	0.960664i	$0.589577\pi$
$744$	−32.1593	−1.17902
$745$	2.76125	0.101164
$746$	35.9524	1.31631
$747$	17.6745	0.646676
$748$	−8.44594	−0.308814
$749$	5.87725	0.214750
$750$	3.13000	0.114292
$751$	32.7312	1.19438	0.597189	−	0.802100i	$-0.296284\pi$
$751$	32.7312	1.19438	0.597189	+	0.802100i	$0.296284\pi$
$752$	−6.02260	−0.219621
$753$	−50.2687	−1.83189
$754$	−1.33101	−0.0484727
$755$	10.9291	0.397750
$756$	−29.6932	−1.07993
$757$	−50.5083	−1.83576	−0.917878	−	0.396862i	$-0.870099\pi$
$757$	−50.5083	−1.83576	−0.917878	+	0.396862i	$0.870099\pi$
$758$	22.1707	0.805275
$759$	21.3911	0.776447
$760$	2.32369	0.0842892
$761$	−33.1475	−1.20160	−0.600799	−	0.799400i	$-0.705151\pi$
$761$	−33.1475	−1.20160	−0.600799	+	0.799400i	$0.705151\pi$
$762$	−47.6438	−1.72595
$763$	−2.71835	−0.0984109
$764$	−15.8806	−0.574541
$765$	35.8164	1.29495
$766$	−2.99160	−0.108091
$767$	3.29499	0.118975
$768$	−3.13000	−0.112944
$769$	22.8414	0.823682	0.411841	−	0.911256i	$-0.364886\pi$
$769$	22.8414	0.823682	0.411841	+	0.911256i	$0.364886\pi$
$770$	4.00460	0.144316
$771$	16.2336	0.584639
$772$	−2.11003	−0.0759416
$773$	10.5613	0.379864	0.189932	−	0.981797i	$-0.439173\pi$
$773$	10.5613	0.379864	0.189932	+	0.981797i	$0.439173\pi$
$774$	−6.86733	−0.246841
$775$	−10.2745	−0.369072
$776$	−7.34064	−0.263513
$777$	2.80892	0.100770
$778$	−17.2293	−0.617702
$779$	5.82509	0.208706
$780$	1.73504	0.0621244
$781$	10.4052	0.372327
$782$	−22.4689	−0.803485
$783$	28.5361	1.01980
$784$	−0.757432	−0.0270512
$785$	8.69993	0.310514
$786$	−4.64514	−0.165687
$787$	44.5194	1.58694	0.793472	−	0.608607i	$-0.208271\pi$
$787$	44.5194	1.58694	0.793472	+	0.608607i	$0.208271\pi$
$788$	9.59731	0.341890
$789$	52.2094	1.85870
$790$	−1.29382	−0.0460320
$791$	40.8849	1.45370
$792$	10.8941	0.387103
$793$	−0.383683	−0.0136250
$794$	−38.4232	−1.36359
$795$	35.8841	1.27268
$796$	−8.29416	−0.293979
$797$	5.40818	0.191568	0.0957838	−	0.995402i	$-0.469464\pi$
$797$	5.40818	0.191568	0.0957838	+	0.995402i	$0.469464\pi$
$798$	−18.1721	−0.643285
$799$	−31.7361	−1.12274
$800$	−1.00000	−0.0353553
$801$	65.4454	2.31240
$802$	−1.00000	−0.0353112
$803$	−9.22210	−0.325441
$804$	12.0784	0.425973
$805$	10.6535	0.375486
$806$	−5.69543	−0.200613
$807$	86.2322	3.03552
$808$	0.841840	0.0296158
$809$	−28.4191	−0.999161	−0.499580	−	0.866268i	$-0.666512\pi$
$809$	−28.4191	−0.999161	−0.499580	+	0.866268i	$0.666512\pi$
$810$	−16.8073	−0.590550
$811$	30.9856	1.08805	0.544025	−	0.839069i	$-0.316900\pi$
$811$	30.9856	1.08805	0.544025	+	0.839069i	$0.316900\pi$
$812$	−5.99928	−0.210534
$813$	−2.82404	−0.0990434
$814$	−0.575693	−0.0201780
$815$	−13.4903	−0.472544
$816$	−16.4936	−0.577391
$817$	−2.34776	−0.0821378
$818$	15.4432	0.539960
$819$	−9.41366	−0.328940
$820$	−2.50682	−0.0875421
$821$	−32.2652	−1.12606	−0.563032	−	0.826435i	$-0.690365\pi$
$821$	−32.2652	−1.12606	−0.563032	+	0.826435i	$0.690365\pi$
$822$	−46.3424	−1.61638
$823$	−6.94412	−0.242057	−0.121028	−	0.992649i	$-0.538619\pi$
$823$	−6.94412	−0.242057	−0.121028	+	0.992649i	$0.538619\pi$
$824$	−13.3474	−0.464979
$825$	5.01675	0.174661
$826$	14.8515	0.516751
$827$	−36.7619	−1.27834	−0.639169	−	0.769066i	$-0.720722\pi$
$827$	−36.7619	−1.27834	−0.639169	+	0.769066i	$0.720722\pi$
$828$	28.9816	1.00718
$829$	1.75980	0.0611205	0.0305603	−	0.999533i	$-0.490271\pi$
$829$	1.75980	0.0611205	0.0305603	+	0.999533i	$0.490271\pi$
$830$	−2.60037	−0.0902602
$831$	81.7280	2.83511
$832$	−0.554325	−0.0192178
$833$	−3.99130	−0.138290
$834$	−27.6821	−0.958553
$835$	−5.17486	−0.179083
$836$	3.72440	0.128811
$837$	122.106	4.22061
$838$	14.4186	0.498083
$839$	−19.7231	−0.680917	−0.340459	−	0.940259i	$-0.610582\pi$
$839$	−19.7231	−0.680917	−0.340459	+	0.940259i	$0.610582\pi$
$840$	7.82035	0.269828
$841$	−23.2345	−0.801190
$842$	−0.880335	−0.0303383
$843$	−80.2863	−2.76521
$844$	−24.5118	−0.843729
$845$	−12.6927	−0.436643
$846$	40.9351	1.40738
$847$	−21.0651	−0.723805
$848$	−11.4646	−0.393695
$849$	70.8341	2.43102
$850$	−5.26951	−0.180743
$851$	−1.53153	−0.0525000
$852$	20.3197	0.696142
$853$	25.4131	0.870128	0.435064	−	0.900399i	$-0.356726\pi$
$853$	25.4131	0.870128	0.435064	+	0.900399i	$0.356726\pi$
$854$	−1.72938	−0.0591780
$855$	−15.7940	−0.540142
$856$	−2.35230	−0.0803999
$857$	35.0259	1.19646	0.598232	−	0.801323i	$-0.295870\pi$
$857$	35.0259	1.19646	0.598232	+	0.801323i	$0.295870\pi$
$858$	2.78091	0.0949387
$859$	36.0120	1.22871	0.614357	−	0.789028i	$-0.289416\pi$
$859$	36.0120	1.22871	0.614357	+	0.789028i	$0.289416\pi$
$860$	1.01036	0.0344529
$861$	19.6043	0.668111
$862$	−23.8006	−0.810651
$863$	16.5093	0.561984	0.280992	−	0.959710i	$-0.409336\pi$
$863$	16.5093	0.561984	0.280992	+	0.959710i	$0.409336\pi$
$864$	11.8844	0.404314
$865$	16.3903	0.557285
$866$	−1.78662	−0.0607120
$867$	−33.7031	−1.14462
$868$	−25.6710	−0.871332
$869$	−2.07372	−0.0703462
$870$	−7.51558	−0.254802
$871$	2.13910	0.0724805
$872$	1.08799	0.0368439
$873$	49.8937	1.68865
$874$	9.90807	0.335146
$875$	2.49851	0.0844652
$876$	−18.0093	−0.608478
$877$	−9.65863	−0.326149	−0.163074	−	0.986614i	$-0.552141\pi$
$877$	−9.65863	−0.326149	−0.163074	+	0.986614i	$0.552141\pi$
$878$	−10.5565	−0.356264
$879$	9.07798	0.306193
$880$	−1.60279	−0.0540302
$881$	−20.9669	−0.706392	−0.353196	−	0.935549i	$-0.614905\pi$
$881$	−20.9669	−0.706392	−0.353196	+	0.935549i	$0.614905\pi$
$882$	5.14821	0.173349
$883$	−43.3765	−1.45973	−0.729867	−	0.683589i	$-0.760418\pi$
$883$	−43.3765	−1.45973	−0.729867	+	0.683589i	$0.760418\pi$
$884$	−2.92102	−0.0982447
$885$	18.6052	0.625407
$886$	−23.5700	−0.791849
$887$	3.45192	0.115904	0.0579520	−	0.998319i	$-0.481543\pi$
$887$	3.45192	0.115904	0.0579520	+	0.998319i	$0.481543\pi$
$888$	−1.12424	−0.0377270
$889$	−38.0315	−1.27553
$890$	−9.62868	−0.322754
$891$	−26.9387	−0.902481
$892$	12.8558	0.430445
$893$	13.9947	0.468313
$894$	8.64271	0.289055
$895$	7.00317	0.234090
$896$	−2.49851	−0.0834695
$897$	7.39810	0.247015
$898$	−15.9106	−0.530944
$899$	24.6706	0.822811
$900$	6.79692	0.226564
$901$	−60.4127	−2.01264
$902$	−4.01792	−0.133782
$903$	−7.90136	−0.262941
$904$	−16.3637	−0.544248
$905$	−15.4015	−0.511963
$906$	34.2080	1.13649
$907$	−5.38262	−0.178727	−0.0893634	−	0.995999i	$-0.528483\pi$
$907$	−5.38262	−0.178727	−0.0893634	+	0.995999i	$0.528483\pi$
$908$	4.85991	0.161282
$909$	−5.72192	−0.189784
$910$	1.38499	0.0459119
$911$	47.2301	1.56480	0.782402	−	0.622774i	$-0.213995\pi$
$911$	47.2301	1.56480	0.782402	+	0.622774i	$0.213995\pi$
$912$	7.27317	0.240839
$913$	−4.16786	−0.137936
$914$	−11.1245	−0.367966
$915$	−2.16647	−0.0716213
$916$	1.31204	0.0433509
$917$	−3.70797	−0.122448
$918$	62.6248	2.06693
$919$	−44.4070	−1.46485	−0.732426	−	0.680847i	$-0.761612\pi$
$919$	−44.4070	−1.46485	−0.732426	+	0.680847i	$0.761612\pi$
$920$	−4.26393	−0.140578
$921$	59.4995	1.96057
$922$	19.0227	0.626481
$923$	3.59863	0.118451
$924$	12.5344	0.412352
$925$	−0.359181	−0.0118098
$926$	−16.3268	−0.536531
$927$	90.7213	2.97968
$928$	2.40114	0.0788213
$929$	−51.5159	−1.69018	−0.845091	−	0.534623i	$-0.820454\pi$
$929$	−51.5159	−1.69018	−0.845091	+	0.534623i	$0.820454\pi$
$930$	−32.1593	−1.05455
$931$	1.76004	0.0576830
$932$	11.2852	0.369658
$933$	−75.0530	−2.45712
$934$	10.6304	0.347839
$935$	−8.44594	−0.276212
$936$	3.76770	0.123151
$937$	23.2861	0.760722	0.380361	−	0.924838i	$-0.375800\pi$
$937$	23.2861	0.760722	0.380361	+	0.924838i	$0.375800\pi$
$938$	9.64155	0.314808
$939$	3.21827	0.105024
$940$	−6.02260	−0.196435
$941$	−19.9403	−0.650034	−0.325017	−	0.945708i	$-0.605370\pi$
$941$	−19.9403	−0.650034	−0.325017	+	0.945708i	$0.605370\pi$
$942$	27.2308	0.887227
$943$	−10.6889	−0.348080
$944$	−5.94415	−0.193465
$945$	−29.6932	−0.965921
$946$	1.61940	0.0526511
$947$	−3.03046	−0.0984769	−0.0492384	−	0.998787i	$-0.515679\pi$
$947$	−3.03046	−0.0984769	−0.0492384	+	0.998787i	$0.515679\pi$
$948$	−4.04965	−0.131527
$949$	−3.18946	−0.103534
$950$	2.32369	0.0753906
$951$	12.9556	0.420115
$952$	−13.1659	−0.426711
$953$	9.72369	0.314981	0.157491	−	0.987520i	$-0.449660\pi$
$953$	9.72369	0.314981	0.157491	+	0.987520i	$0.449660\pi$
$954$	77.9237	2.52287
$955$	−15.8806	−0.513885
$956$	3.82979	0.123864
$957$	−12.0459	−0.389389
$958$	−2.81613	−0.0909849
$959$	−36.9926	−1.19455
$960$	−3.13000	−0.101020
$961$	74.5660	2.40535
$962$	−0.199103	−0.00641935
$963$	15.9884	0.515218
$964$	−14.3377	−0.461785
$965$	−2.11003	−0.0679243
$966$	33.3455	1.07287
$967$	−15.0536	−0.484090	−0.242045	−	0.970265i	$-0.577818\pi$
$967$	−15.0536	−0.484090	−0.242045	+	0.970265i	$0.577818\pi$
$968$	8.43105	0.270984
$969$	38.3260	1.23121
$970$	−7.34064	−0.235694
$971$	54.2681	1.74155	0.870773	−	0.491684i	$-0.163619\pi$
$971$	54.2681	1.74155	0.870773	+	0.491684i	$0.163619\pi$
$972$	−16.9539	−0.543798
$973$	−22.0971	−0.708402
$974$	31.0010	0.993336
$975$	1.73504	0.0555658
$976$	0.692162	0.0221556
$977$	36.6108	1.17128	0.585641	−	0.810570i	$-0.300843\pi$
$977$	36.6108	1.17128	0.585641	+	0.810570i	$0.300843\pi$
$978$	−42.2247	−1.35020
$979$	−15.4328	−0.493234
$980$	−0.757432	−0.0241953
$981$	−7.39496	−0.236103
$982$	4.69437	0.149804
$983$	3.69731	0.117926	0.0589630	−	0.998260i	$-0.481221\pi$
$983$	3.69731	0.117926	0.0589630	+	0.998260i	$0.481221\pi$
$984$	−7.84637	−0.250133
$985$	9.59731	0.305796
$986$	12.6528	0.402949
$987$	47.0988	1.49917
$988$	1.28808	0.0409793
$989$	4.30810	0.136990
$990$	10.8941	0.346236
$991$	12.9246	0.410565	0.205282	−	0.978703i	$-0.434189\pi$
$991$	12.9246	0.410565	0.205282	+	0.978703i	$0.434189\pi$
$992$	10.2745	0.326217
$993$	42.8374	1.35940
$994$	16.2201	0.514472
$995$	−8.29416	−0.262943
$996$	−8.13917	−0.257899
$997$	14.8534	0.470412	0.235206	−	0.971946i	$-0.424423\pi$
$997$	14.8534	0.470412	0.235206	+	0.971946i	$0.424423\pi$
$998$	−32.5480	−1.03029
$999$	4.26864	0.135054

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.i.1.1	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.i.1.1	✓	10	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:	\( N \)	\(=\)	\( 4010 = 2 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4010.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.13000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.13000 q^{6} +2.49851 q^{7} -1.00000 q^{8} +6.79692 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.13000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +3.13000 q^{6} +2.49851 q^{7} -1.00000 q^{8} +6.79692 q^{9} -1.00000 q^{10} -1.60279 q^{11} -3.13000 q^{12} -0.554325 q^{13} -2.49851 q^{14} -3.13000 q^{15} +1.00000 q^{16} +5.26951 q^{17} -6.79692 q^{18} -2.32369 q^{19} +1.00000 q^{20} -7.82035 q^{21} +1.60279 q^{22} +4.26393 q^{23} +3.13000 q^{24} +1.00000 q^{25} +0.554325 q^{26} -11.8844 q^{27} +2.49851 q^{28} -2.40114 q^{29} +3.13000 q^{30} -10.2745 q^{31} -1.00000 q^{32} +5.01675 q^{33} -5.26951 q^{34} +2.49851 q^{35} +6.79692 q^{36} -0.359181 q^{37} +2.32369 q^{38} +1.73504 q^{39} -1.00000 q^{40} -2.50682 q^{41} +7.82035 q^{42} +1.01036 q^{43} -1.60279 q^{44} +6.79692 q^{45} -4.26393 q^{46} -6.02260 q^{47} -3.13000 q^{48} -0.757432 q^{49} -1.00000 q^{50} -16.4936 q^{51} -0.554325 q^{52} -11.4646 q^{53} +11.8844 q^{54} -1.60279 q^{55} -2.49851 q^{56} +7.27317 q^{57} +2.40114 q^{58} -5.94415 q^{59} -3.13000 q^{60} +0.692162 q^{61} +10.2745 q^{62} +16.9822 q^{63} +1.00000 q^{64} -0.554325 q^{65} -5.01675 q^{66} -3.85892 q^{67} +5.26951 q^{68} -13.3461 q^{69} -2.49851 q^{70} -6.49192 q^{71} -6.79692 q^{72} +5.75377 q^{73} +0.359181 q^{74} -3.13000 q^{75} -2.32369 q^{76} -4.00460 q^{77} -1.73504 q^{78} +1.29382 q^{79} +1.00000 q^{80} +16.8073 q^{81} +2.50682 q^{82} +2.60037 q^{83} -7.82035 q^{84} +5.26951 q^{85} -1.01036 q^{86} +7.51558 q^{87} +1.60279 q^{88} +9.62868 q^{89} -6.79692 q^{90} -1.38499 q^{91} +4.26393 q^{92} +32.1593 q^{93} +6.02260 q^{94} -2.32369 q^{95} +3.13000 q^{96} +7.34064 q^{97} +0.757432 q^{98} -10.8941 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} - 4 q^{3} + 10 q^{4} + 10 q^{5} + 4 q^{6} - 3 q^{7} - 10 q^{8} + 6 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 - 4 * q^3 + 10 * q^4 + 10 * q^5 + 4 * q^6 - 3 * q^7 - 10 * q^8 + 6 * q^9	\( 10 q - 10 q^{2} - 4 q^{3} + 10 q^{4} + 10 q^{5} + 4 q^{6} - 3 q^{7} - 10 q^{8} + 6 q^{9} - 10 q^{10} - 11 q^{11} - 4 q^{12} + 6 q^{13} + 3 q^{14} - 4 q^{15} + 10 q^{16} + 9 q^{17} - 6 q^{18} - 13 q^{19} + 10 q^{20} - 24 q^{21} + 11 q^{22} - 3 q^{23} + 4 q^{24} + 10 q^{25} - 6 q^{26} - 10 q^{27} - 3 q^{28} - 4 q^{29} + 4 q^{30} - 17 q^{31} - 10 q^{32} - 2 q^{33} - 9 q^{34} - 3 q^{35} + 6 q^{36} - 15 q^{37} + 13 q^{38} - 6 q^{39} - 10 q^{40} - 11 q^{41} + 24 q^{42} - 11 q^{43} - 11 q^{44} + 6 q^{45} + 3 q^{46} + 3 q^{47} - 4 q^{48} - 5 q^{49} - 10 q^{50} - 21 q^{51} + 6 q^{52} + 25 q^{53} + 10 q^{54} - 11 q^{55} + 3 q^{56} + 31 q^{57} + 4 q^{58} - 46 q^{59} - 4 q^{60} - 54 q^{61} + 17 q^{62} - 6 q^{63} + 10 q^{64} + 6 q^{65} + 2 q^{66} - 26 q^{67} + 9 q^{68} - 9 q^{69} + 3 q^{70} - 16 q^{71} - 6 q^{72} + 4 q^{73} + 15 q^{74} - 4 q^{75} - 13 q^{76} + 11 q^{77} + 6 q^{78} - 19 q^{79} + 10 q^{80} - 6 q^{81} + 11 q^{82} + 19 q^{83} - 24 q^{84} + 9 q^{85} + 11 q^{86} + 28 q^{87} + 11 q^{88} - 30 q^{89} - 6 q^{90} - 38 q^{91} - 3 q^{92} - 18 q^{93} - 3 q^{94} - 13 q^{95} + 4 q^{96} - 16 q^{97} + 5 q^{98} - 59 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 - 4 * q^3 + 10 * q^4 + 10 * q^5 + 4 * q^6 - 3 * q^7 - 10 * q^8 + 6 * q^9 - 10 * q^10 - 11 * q^11 - 4 * q^12 + 6 * q^13 + 3 * q^14 - 4 * q^15 + 10 * q^16 + 9 * q^17 - 6 * q^18 - 13 * q^19 + 10 * q^20 - 24 * q^21 + 11 * q^22 - 3 * q^23 + 4 * q^24 + 10 * q^25 - 6 * q^26 - 10 * q^27 - 3 * q^28 - 4 * q^29 + 4 * q^30 - 17 * q^31 - 10 * q^32 - 2 * q^33 - 9 * q^34 - 3 * q^35 + 6 * q^36 - 15 * q^37 + 13 * q^38 - 6 * q^39 - 10 * q^40 - 11 * q^41 + 24 * q^42 - 11 * q^43 - 11 * q^44 + 6 * q^45 + 3 * q^46 + 3 * q^47 - 4 * q^48 - 5 * q^49 - 10 * q^50 - 21 * q^51 + 6 * q^52 + 25 * q^53 + 10 * q^54 - 11 * q^55 + 3 * q^56 + 31 * q^57 + 4 * q^58 - 46 * q^59 - 4 * q^60 - 54 * q^61 + 17 * q^62 - 6 * q^63 + 10 * q^64 + 6 * q^65 + 2 * q^66 - 26 * q^67 + 9 * q^68 - 9 * q^69 + 3 * q^70 - 16 * q^71 - 6 * q^72 + 4 * q^73 + 15 * q^74 - 4 * q^75 - 13 * q^76 + 11 * q^77 + 6 * q^78 - 19 * q^79 + 10 * q^80 - 6 * q^81 + 11 * q^82 + 19 * q^83 - 24 * q^84 + 9 * q^85 + 11 * q^86 + 28 * q^87 + 11 * q^88 - 30 * q^89 - 6 * q^90 - 38 * q^91 - 3 * q^92 - 18 * q^93 - 3 * q^94 - 13 * q^95 + 4 * q^96 - 16 * q^97 + 5 * q^98 - 59 * q^99

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