LMFDB - Embedded newform 1045.2.a.j.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,2,Mod(1,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1045.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1045.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:	$8.34436701122$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 2x^{8} - 11x^{7} + 11x^{6} + 34x^{5} - 20x^{4} - 36x^{3} + 13x^{2} + 10x - 2 $ x^9 - 2x^8 - 11x^7 + 11x^6 + 34x^5 - 20x^4 - 36x^3 + 13x^2 + 10x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.56050$ of defining polynomial
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.0815632 q^{2} -0.583675 q^{3} -1.99335 q^{4} -1.00000 q^{5} +0.0476064 q^{6} -3.83288 q^{7} +0.325710 q^{8} -2.65932 q^{9} +O(q^{10})$	\(q-0.0815632 q^{2} -0.583675 q^{3} -1.99335 q^{4} -1.00000 q^{5} +0.0476064 q^{6} -3.83288 q^{7} +0.325710 q^{8} -2.65932 q^{9} +0.0815632 q^{10} -1.00000 q^{11} +1.16347 q^{12} -5.23350 q^{13} +0.312622 q^{14} +0.583675 q^{15} +3.96013 q^{16} +7.76232 q^{17} +0.216903 q^{18} +1.00000 q^{19} +1.99335 q^{20} +2.23715 q^{21} +0.0815632 q^{22} -8.19706 q^{23} -0.190109 q^{24} +1.00000 q^{25} +0.426861 q^{26} +3.30320 q^{27} +7.64026 q^{28} +0.961446 q^{29} -0.0476064 q^{30} +7.54076 q^{31} -0.974421 q^{32} +0.583675 q^{33} -0.633119 q^{34} +3.83288 q^{35} +5.30096 q^{36} +1.60292 q^{37} -0.0815632 q^{38} +3.05466 q^{39} -0.325710 q^{40} -6.12302 q^{41} -0.182469 q^{42} +8.94082 q^{43} +1.99335 q^{44} +2.65932 q^{45} +0.668578 q^{46} -1.51385 q^{47} -2.31143 q^{48} +7.69095 q^{49} -0.0815632 q^{50} -4.53067 q^{51} +10.4322 q^{52} -11.7961 q^{53} -0.269420 q^{54} +1.00000 q^{55} -1.24841 q^{56} -0.583675 q^{57} -0.0784185 q^{58} +3.81964 q^{59} -1.16347 q^{60} -11.3467 q^{61} -0.615048 q^{62} +10.1929 q^{63} -7.84078 q^{64} +5.23350 q^{65} -0.0476064 q^{66} +10.7033 q^{67} -15.4730 q^{68} +4.78442 q^{69} -0.312622 q^{70} +1.57939 q^{71} -0.866168 q^{72} -2.13869 q^{73} -0.130739 q^{74} -0.583675 q^{75} -1.99335 q^{76} +3.83288 q^{77} -0.249148 q^{78} +10.1200 q^{79} -3.96013 q^{80} +6.04997 q^{81} +0.499413 q^{82} -4.18708 q^{83} -4.45943 q^{84} -7.76232 q^{85} -0.729241 q^{86} -0.561172 q^{87} -0.325710 q^{88} +14.1484 q^{89} -0.216903 q^{90} +20.0594 q^{91} +16.3396 q^{92} -4.40135 q^{93} +0.123475 q^{94} -1.00000 q^{95} +0.568745 q^{96} -14.8528 q^{97} -0.627298 q^{98} +2.65932 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 3 q^{2} + 3 q^{3} + 9 q^{4} - 9 q^{5} + 6 q^{6} - 9 q^{7} + 15 q^{8} + 16 q^{9}+O(q^{10}) $ 9 * q + 3 * q^2 + 3 * q^3 + 9 * q^4 - 9 * q^5 + 6 * q^6 - 9 * q^7 + 15 * q^8 + 16 * q^9	\( 9 q + 3 q^{2} + 3 q^{3} + 9 q^{4} - 9 q^{5} + 6 q^{6} - 9 q^{7} + 15 q^{8} + 16 q^{9} - 3 q^{10} - 9 q^{11} + 13 q^{12} - 3 q^{13} + 4 q^{14} - 3 q^{15} + 17 q^{16} + 5 q^{17} + 17 q^{18} + 9 q^{19} - 9 q^{20} - q^{21} - 3 q^{22} + 4 q^{23} + 21 q^{24} + 9 q^{25} + 20 q^{26} + 24 q^{27} - 24 q^{28} + 3 q^{29} - 6 q^{30} - q^{31} + 38 q^{32} - 3 q^{33} + 28 q^{34} + 9 q^{35} + 17 q^{36} + 5 q^{37} + 3 q^{38} - 15 q^{40} - 5 q^{41} - 43 q^{42} - 11 q^{43} - 9 q^{44} - 16 q^{45} + 2 q^{46} + 30 q^{47} + 54 q^{48} + 12 q^{49} + 3 q^{50} + 40 q^{51} - 3 q^{52} - q^{53} + 65 q^{54} + 9 q^{55} - 16 q^{56} + 3 q^{57} - 15 q^{58} + 59 q^{59} - 13 q^{60} - 21 q^{61} - 10 q^{62} - 12 q^{63} + 19 q^{64} + 3 q^{65} - 6 q^{66} - 2 q^{67} - 9 q^{68} - 22 q^{69} - 4 q^{70} + 34 q^{71} + 32 q^{72} - 34 q^{73} - 21 q^{74} + 3 q^{75} + 9 q^{76} + 9 q^{77} - 65 q^{78} - 13 q^{79} - 17 q^{80} + 57 q^{81} + 10 q^{82} + 51 q^{83} - 95 q^{84} - 5 q^{85} - 14 q^{86} + 8 q^{87} - 15 q^{88} + 8 q^{89} - 17 q^{90} + 62 q^{91} + 57 q^{92} - 18 q^{93} + 2 q^{94} - 9 q^{95} + 81 q^{96} - 8 q^{97} - 20 q^{98} - 16 q^{99}+O(q^{100}) \) 9 * q + 3 * q^2 + 3 * q^3 + 9 * q^4 - 9 * q^5 + 6 * q^6 - 9 * q^7 + 15 * q^8 + 16 * q^9 - 3 * q^10 - 9 * q^11 + 13 * q^12 - 3 * q^13 + 4 * q^14 - 3 * q^15 + 17 * q^16 + 5 * q^17 + 17 * q^18 + 9 * q^19 - 9 * q^20 - q^21 - 3 * q^22 + 4 * q^23 + 21 * q^24 + 9 * q^25 + 20 * q^26 + 24 * q^27 - 24 * q^28 + 3 * q^29 - 6 * q^30 - q^31 + 38 * q^32 - 3 * q^33 + 28 * q^34 + 9 * q^35 + 17 * q^36 + 5 * q^37 + 3 * q^38 - 15 * q^40 - 5 * q^41 - 43 * q^42 - 11 * q^43 - 9 * q^44 - 16 * q^45 + 2 * q^46 + 30 * q^47 + 54 * q^48 + 12 * q^49 + 3 * q^50 + 40 * q^51 - 3 * q^52 - q^53 + 65 * q^54 + 9 * q^55 - 16 * q^56 + 3 * q^57 - 15 * q^58 + 59 * q^59 - 13 * q^60 - 21 * q^61 - 10 * q^62 - 12 * q^63 + 19 * q^64 + 3 * q^65 - 6 * q^66 - 2 * q^67 - 9 * q^68 - 22 * q^69 - 4 * q^70 + 34 * q^71 + 32 * q^72 - 34 * q^73 - 21 * q^74 + 3 * q^75 + 9 * q^76 + 9 * q^77 - 65 * q^78 - 13 * q^79 - 17 * q^80 + 57 * q^81 + 10 * q^82 + 51 * q^83 - 95 * q^84 - 5 * q^85 - 14 * q^86 + 8 * q^87 - 15 * q^88 + 8 * q^89 - 17 * q^90 + 62 * q^91 + 57 * q^92 - 18 * q^93 + 2 * q^94 - 9 * q^95 + 81 * q^96 - 8 * q^97 - 20 * q^98 - 16 * 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 $

$2$	−0.0815632	−0.0576739	−0.0288369	−	0.999584i	$-0.509180\pi$
$2$	−0.0815632	−0.0576739	−0.0288369	+	0.999584i	$0.509180\pi$
$3$	−0.583675	−0.336985	−0.168492	−	0.985703i	$-0.553890\pi$
$3$	−0.583675	−0.336985	−0.168492	+	0.985703i	$0.553890\pi$
$4$	−1.99335	−0.996674
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.0476064	0.0194352
$7$	−3.83288	−1.44869	−0.724346	−	0.689437i	$-0.757858\pi$
$7$	−3.83288	−1.44869	−0.724346	+	0.689437i	$0.757858\pi$
$8$	0.325710	0.115156
$9$	−2.65932	−0.886441
$10$	0.0815632	0.0257925
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.16347	0.335864
$13$	−5.23350	−1.45151	−0.725756	−	0.687953i	$-0.758510\pi$
$13$	−5.23350	−1.45151	−0.725756	+	0.687953i	$0.758510\pi$
$14$	0.312622	0.0835516
$15$	0.583675	0.150704
$16$	3.96013	0.990032
$17$	7.76232	1.88264	0.941320	−	0.337516i	$-0.109587\pi$
$17$	7.76232	1.88264	0.941320	+	0.337516i	$0.109587\pi$
$18$	0.216903	0.0511245
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	1.99335	0.445726
$21$	2.23715	0.488187
$22$	0.0815632	0.0173893
$23$	−8.19706	−1.70921	−0.854603	−	0.519282i	$-0.826199\pi$
$23$	−8.19706	−1.70921	−0.854603	+	0.519282i	$0.826199\pi$
$24$	−0.190109	−0.0388058
$25$	1.00000	0.200000
$26$	0.426861	0.0837143
$27$	3.30320	0.635702
$28$	7.64026	1.44387
$29$	0.961446	0.178536	0.0892680	−	0.996008i	$-0.471547\pi$
$29$	0.961446	0.178536	0.0892680	+	0.996008i	$0.471547\pi$
$30$	−0.0476064	−0.00869169
$31$	7.54076	1.35436	0.677180	−	0.735817i	$-0.263202\pi$
$31$	7.54076	1.35436	0.677180	+	0.735817i	$0.263202\pi$
$32$	−0.974421	−0.172255
$33$	0.583675	0.101605
$34$	−0.633119	−0.108579
$35$	3.83288	0.647875
$36$	5.30096	0.883493
$37$	1.60292	0.263519	0.131759	−	0.991282i	$-0.457937\pi$
$37$	1.60292	0.263519	0.131759	+	0.991282i	$0.457937\pi$
$38$	−0.0815632	−0.0132313
$39$	3.05466	0.489137
$40$	−0.325710	−0.0514993
$41$	−6.12302	−0.956256	−0.478128	−	0.878290i	$-0.658684\pi$
$41$	−6.12302	−0.956256	−0.478128	+	0.878290i	$0.658684\pi$
$42$	−0.182469	−0.0281556
$43$	8.94082	1.36346	0.681731	−	0.731603i	$-0.261227\pi$
$43$	8.94082	1.36346	0.681731	+	0.731603i	$0.261227\pi$
$44$	1.99335	0.300508
$45$	2.65932	0.396429
$46$	0.668578	0.0985765
$47$	−1.51385	−0.220818	−0.110409	−	0.993886i	$-0.535216\pi$
$47$	−1.51385	−0.220818	−0.110409	+	0.993886i	$0.535216\pi$
$48$	−2.31143	−0.333626
$49$	7.69095	1.09871
$50$	−0.0815632	−0.0115348
$51$	−4.53067	−0.634421
$52$	10.4322	1.44668
$53$	−11.7961	−1.62032	−0.810160	−	0.586209i	$-0.800620\pi$
$53$	−11.7961	−1.62032	−0.810160	+	0.586209i	$0.800620\pi$
$54$	−0.269420	−0.0366634
$55$	1.00000	0.134840
$56$	−1.24841	−0.166825
$57$	−0.583675	−0.0773096
$58$	−0.0784185	−0.0102969
$59$	3.81964	0.497275	0.248637	−	0.968597i	$-0.420017\pi$
$59$	3.81964	0.497275	0.248637	+	0.968597i	$0.420017\pi$
$60$	−1.16347	−0.150203
$61$	−11.3467	−1.45279	−0.726397	−	0.687275i	$-0.758807\pi$
$61$	−11.3467	−1.45279	−0.726397	+	0.687275i	$0.758807\pi$
$62$	−0.615048	−0.0781112
$63$	10.1929	1.28418
$64$	−7.84078	−0.980098
$65$	5.23350	0.649136
$66$	−0.0476064	−0.00585994
$67$	10.7033	1.30762	0.653811	−	0.756658i	$-0.273169\pi$
$67$	10.7033	1.30762	0.653811	+	0.756658i	$0.273169\pi$
$68$	−15.4730	−1.87638
$69$	4.78442	0.575976
$70$	−0.312622	−0.0373654
$71$	1.57939	0.187439	0.0937193	−	0.995599i	$-0.470124\pi$
$71$	1.57939	0.187439	0.0937193	+	0.995599i	$0.470124\pi$
$72$	−0.866168	−0.102079
$73$	−2.13869	−0.250315	−0.125157	−	0.992137i	$-0.539944\pi$
$73$	−2.13869	−0.250315	−0.125157	+	0.992137i	$0.539944\pi$
$74$	−0.130739	−0.0151982
$75$	−0.583675	−0.0673970
$76$	−1.99335	−0.228653
$77$	3.83288	0.436797
$78$	−0.249148	−0.0282104
$79$	10.1200	1.13859	0.569297	−	0.822132i	$-0.307215\pi$
$79$	10.1200	1.13859	0.569297	+	0.822132i	$0.307215\pi$
$80$	−3.96013	−0.442756
$81$	6.04997	0.672219
$82$	0.499413	0.0551510
$83$	−4.18708	−0.459592	−0.229796	−	0.973239i	$-0.573806\pi$
$83$	−4.18708	−0.459592	−0.229796	+	0.973239i	$0.573806\pi$
$84$	−4.45943	−0.486563
$85$	−7.76232	−0.841942
$86$	−0.729241	−0.0786361
$87$	−0.561172	−0.0601639
$88$	−0.325710	−0.0347208
$89$	14.1484	1.49972	0.749862	−	0.661595i	$-0.230120\pi$
$89$	14.1484	1.49972	0.749862	+	0.661595i	$0.230120\pi$
$90$	−0.216903	−0.0228636
$91$	20.0594	2.10279
$92$	16.3396	1.70352
$93$	−4.40135	−0.456399
$94$	0.123475	0.0127354
$95$	−1.00000	−0.102598
$96$	0.568745	0.0580473
$97$	−14.8528	−1.50808	−0.754039	−	0.656830i	$-0.771897\pi$
$97$	−14.8528	−1.50808	−0.754039	+	0.656830i	$0.771897\pi$
$98$	−0.627298	−0.0633667
$99$	2.65932	0.267272
$100$	−1.99335	−0.199335
$101$	7.55116	0.751368	0.375684	−	0.926748i	$-0.377408\pi$
$101$	7.55116	0.751368	0.375684	+	0.926748i	$0.377408\pi$
$102$	0.369536	0.0365895
$103$	−10.0822	−0.993430	−0.496715	−	0.867914i	$-0.665461\pi$
$103$	−10.0822	−0.993430	−0.496715	+	0.867914i	$0.665461\pi$
$104$	−1.70460	−0.167150
$105$	−2.23715	−0.218324
$106$	0.962128	0.0934501
$107$	14.9036	1.44079	0.720394	−	0.693565i	$-0.243961\pi$
$107$	14.9036	1.44079	0.720394	+	0.693565i	$0.243961\pi$
$108$	−6.58443	−0.633588
$109$	4.54619	0.435446	0.217723	−	0.976011i	$-0.430137\pi$
$109$	4.54619	0.435446	0.217723	+	0.976011i	$0.430137\pi$
$110$	−0.0815632	−0.00777674
$111$	−0.935586	−0.0888019
$112$	−15.1787	−1.43425
$113$	11.7734	1.10754	0.553772	−	0.832668i	$-0.313188\pi$
$113$	11.7734	1.10754	0.553772	+	0.832668i	$0.313188\pi$
$114$	0.0476064	0.00445874
$115$	8.19706	0.764380
$116$	−1.91650	−0.177942
$117$	13.9176	1.28668
$118$	−0.311542	−0.0286797
$119$	−29.7520	−2.72736
$120$	0.190109	0.0173545
$121$	1.00000	0.0909091
$122$	0.925471	0.0837882
$123$	3.57385	0.322244
$124$	−15.0314	−1.34986
$125$	−1.00000	−0.0894427
$126$	−0.831362	−0.0740636
$127$	−16.7247	−1.48408	−0.742039	−	0.670357i	$-0.766141\pi$
$127$	−16.7247	−1.48408	−0.742039	+	0.670357i	$0.766141\pi$
$128$	2.58836	0.228781
$129$	−5.21853	−0.459466
$130$	−0.426861	−0.0374382
$131$	−4.21476	−0.368245	−0.184123	−	0.982903i	$-0.558944\pi$
$131$	−4.21476	−0.368245	−0.184123	+	0.982903i	$0.558944\pi$
$132$	−1.16347	−0.101267
$133$	−3.83288	−0.332353
$134$	−0.872999	−0.0754156
$135$	−3.30320	−0.284295
$136$	2.52827	0.216797
$137$	−10.8385	−0.926000	−0.463000	−	0.886358i	$-0.653227\pi$
$137$	−10.8385	−0.926000	−0.463000	+	0.886358i	$0.653227\pi$
$138$	−0.390232	−0.0332188
$139$	−4.64059	−0.393610	−0.196805	−	0.980443i	$-0.563057\pi$
$139$	−4.64059	−0.393610	−0.196805	+	0.980443i	$0.563057\pi$
$140$	−7.64026	−0.645720
$141$	0.883597	0.0744123
$142$	−0.128820	−0.0108103
$143$	5.23350	0.437647
$144$	−10.5313	−0.877605
$145$	−0.961446	−0.0798437
$146$	0.174438	0.0144366
$147$	−4.48901	−0.370248
$148$	−3.19518	−0.262642
$149$	−4.02841	−0.330020	−0.165010	−	0.986292i	$-0.552766\pi$
$149$	−4.02841	−0.330020	−0.165010	+	0.986292i	$0.552766\pi$
$150$	0.0476064	0.00388704
$151$	16.4088	1.33533	0.667666	−	0.744461i	$-0.267294\pi$
$151$	16.4088	1.33533	0.667666	+	0.744461i	$0.267294\pi$
$152$	0.325710	0.0264186
$153$	−20.6425	−1.66885
$154$	−0.312622	−0.0251918
$155$	−7.54076	−0.605688
$156$	−6.08900	−0.487510
$157$	−6.02740	−0.481039	−0.240519	−	0.970644i	$-0.577318\pi$
$157$	−6.02740	−0.481039	−0.240519	+	0.970644i	$0.577318\pi$
$158$	−0.825423	−0.0656671
$159$	6.88509	0.546023
$160$	0.974421	0.0770347
$161$	31.4183	2.47611
$162$	−0.493455	−0.0387695
$163$	11.4766	0.898916	0.449458	−	0.893301i	$-0.351617\pi$
$163$	11.4766	0.898916	0.449458	+	0.893301i	$0.351617\pi$
$164$	12.2053	0.953075
$165$	−0.583675	−0.0454390
$166$	0.341512	0.0265065
$167$	1.19727	0.0926479	0.0463239	−	0.998926i	$-0.485249\pi$
$167$	1.19727	0.0926479	0.0463239	+	0.998926i	$0.485249\pi$
$168$	0.728664	0.0562176
$169$	14.3895	1.10688
$170$	0.633119	0.0485580
$171$	−2.65932	−0.203364
$172$	−17.8222	−1.35893
$173$	14.1148	1.07313	0.536565	−	0.843859i	$-0.319721\pi$
$173$	14.1148	1.07313	0.536565	+	0.843859i	$0.319721\pi$
$174$	0.0457709	0.00346989
$175$	−3.83288	−0.289738
$176$	−3.96013	−0.298506
$177$	−2.22943	−0.167574
$178$	−1.15399	−0.0864948
$179$	−7.29028	−0.544901	−0.272451	−	0.962170i	$-0.587834\pi$
$179$	−7.29028	−0.544901	−0.272451	+	0.962170i	$0.587834\pi$
$180$	−5.30096	−0.395110
$181$	17.5442	1.30405	0.652024	−	0.758198i	$-0.273920\pi$
$181$	17.5442	1.30405	0.652024	+	0.758198i	$0.273920\pi$
$182$	−1.63610	−0.121276
$183$	6.62277	0.489569
$184$	−2.66987	−0.196825
$185$	−1.60292	−0.117849
$186$	0.358988	0.0263223
$187$	−7.76232	−0.567637
$188$	3.01763	0.220083
$189$	−12.6608	−0.920936
$190$	0.0815632	0.00591721
$191$	22.7184	1.64385	0.821924	−	0.569598i	$-0.192901\pi$
$191$	22.7184	1.64385	0.821924	+	0.569598i	$0.192901\pi$
$192$	4.57647	0.330278
$193$	−14.9737	−1.07783	−0.538916	−	0.842359i	$-0.681166\pi$
$193$	−14.9737	−1.07783	−0.538916	+	0.842359i	$0.681166\pi$
$194$	1.21145	0.0869767
$195$	−3.05466	−0.218749
$196$	−15.3307	−1.09505
$197$	8.31629	0.592511	0.296255	−	0.955109i	$-0.404262\pi$
$197$	8.31629	0.592511	0.296255	+	0.955109i	$0.404262\pi$
$198$	−0.216903	−0.0154146
$199$	−17.3429	−1.22940	−0.614701	−	0.788760i	$-0.710723\pi$
$199$	−17.3429	−1.22940	−0.614701	+	0.788760i	$0.710723\pi$
$200$	0.325710	0.0230312
$201$	−6.24727	−0.440649
$202$	−0.615896	−0.0433343
$203$	−3.68510	−0.258644
$204$	9.03120	0.632311
$205$	6.12302	0.427650
$206$	0.822337	0.0572950
$207$	21.7986	1.51511
$208$	−20.7253	−1.43704
$209$	−1.00000	−0.0691714
$210$	0.182469	0.0125916
$211$	2.19916	0.151396	0.0756982	−	0.997131i	$-0.475881\pi$
$211$	2.19916	0.151396	0.0756982	+	0.997131i	$0.475881\pi$
$212$	23.5137	1.61493
$213$	−0.921848	−0.0631640
$214$	−1.21559	−0.0830958
$215$	−8.94082	−0.609759
$216$	1.07589	0.0732048
$217$	−28.9028	−1.96205
$218$	−0.370802	−0.0251139
$219$	1.24830	0.0843523
$220$	−1.99335	−0.134391
$221$	−40.6241	−2.73267
$222$	0.0763094	0.00512155
$223$	−13.6785	−0.915978	−0.457989	−	0.888958i	$-0.651430\pi$
$223$	−13.6785	−0.915978	−0.457989	+	0.888958i	$0.651430\pi$
$224$	3.73484	0.249544
$225$	−2.65932	−0.177288
$226$	−0.960272	−0.0638763
$227$	−2.17148	−0.144126	−0.0720630	−	0.997400i	$-0.522958\pi$
$227$	−2.17148	−0.144126	−0.0720630	+	0.997400i	$0.522958\pi$
$228$	1.16347	0.0770525
$229$	−5.21077	−0.344337	−0.172169	−	0.985067i	$-0.555077\pi$
$229$	−5.21077	−0.344337	−0.172169	+	0.985067i	$0.555077\pi$
$230$	−0.668578	−0.0440847
$231$	−2.23715	−0.147194
$232$	0.313153	0.0205595
$233$	−8.96199	−0.587120	−0.293560	−	0.955941i	$-0.594840\pi$
$233$	−8.96199	−0.587120	−0.293560	+	0.955941i	$0.594840\pi$
$234$	−1.13516	−0.0742078
$235$	1.51385	0.0987528
$236$	−7.61387	−0.495620
$237$	−5.90681	−0.383689
$238$	2.42667	0.157298
$239$	−18.9159	−1.22357	−0.611783	−	0.791026i	$-0.709547\pi$
$239$	−18.9159	−1.22357	−0.611783	+	0.791026i	$0.709547\pi$
$240$	2.31143	0.149202
$241$	13.1031	0.844042	0.422021	−	0.906586i	$-0.361321\pi$
$241$	13.1031	0.844042	0.422021	+	0.906586i	$0.361321\pi$
$242$	−0.0815632	−0.00524308
$243$	−13.4408	−0.862230
$244$	22.6179	1.44796
$245$	−7.69095	−0.491357
$246$	−0.291495	−0.0185850
$247$	−5.23350	−0.333000
$248$	2.45610	0.155963
$249$	2.44390	0.154876
$250$	0.0815632	0.00515851
$251$	7.31838	0.461932	0.230966	−	0.972962i	$-0.425811\pi$
$251$	7.31838	0.461932	0.230966	+	0.972962i	$0.425811\pi$
$252$	−20.3179	−1.27991
$253$	8.19706	0.515345
$254$	1.36412	0.0855925
$255$	4.53067	0.283722
$256$	15.4704	0.966903
$257$	10.5562	0.658476	0.329238	−	0.944247i	$-0.393208\pi$
$257$	10.5562	0.658476	0.329238	+	0.944247i	$0.393208\pi$
$258$	0.425640	0.0264992
$259$	−6.14381	−0.381758
$260$	−10.4322	−0.646976
$261$	−2.55680	−0.158262
$262$	0.343769	0.0212381
$263$	17.5922	1.08478	0.542390	−	0.840127i	$-0.317519\pi$
$263$	17.5922	1.08478	0.542390	+	0.840127i	$0.317519\pi$
$264$	0.190109	0.0117004
$265$	11.7961	0.724629
$266$	0.312622	0.0191681
$267$	−8.25804	−0.505384
$268$	−21.3355	−1.30327
$269$	1.11106	0.0677427	0.0338714	−	0.999426i	$-0.489216\pi$
$269$	1.11106	0.0677427	0.0338714	+	0.999426i	$0.489216\pi$
$270$	0.269420	0.0163964
$271$	11.0557	0.671588	0.335794	−	0.941935i	$-0.390995\pi$
$271$	11.0557	0.671588	0.335794	+	0.941935i	$0.390995\pi$
$272$	30.7398	1.86387
$273$	−11.7081	−0.708609
$274$	0.884026	0.0534060
$275$	−1.00000	−0.0603023
$276$	−9.53701	−0.574060
$277$	−16.9638	−1.01926	−0.509629	−	0.860394i	$-0.670217\pi$
$277$	−16.9638	−1.01926	−0.509629	+	0.860394i	$0.670217\pi$
$278$	0.378501	0.0227010
$279$	−20.0533	−1.20056
$280$	1.24841	0.0746066
$281$	13.0929	0.781055	0.390528	−	0.920591i	$-0.372293\pi$
$281$	13.0929	0.781055	0.390528	+	0.920591i	$0.372293\pi$
$282$	−0.0720690	−0.00429165
$283$	−12.8142	−0.761725	−0.380862	−	0.924632i	$-0.624373\pi$
$283$	−12.8142	−0.761725	−0.380862	+	0.924632i	$0.624373\pi$
$284$	−3.14826	−0.186815
$285$	0.583675	0.0345739
$286$	−0.426861	−0.0252408
$287$	23.4688	1.38532
$288$	2.59130	0.152694
$289$	43.2536	2.54433
$290$	0.0784185	0.00460490
$291$	8.66923	0.508199
$292$	4.26315	0.249482
$293$	−3.44804	−0.201436	−0.100718	−	0.994915i	$-0.532114\pi$
$293$	−3.44804	−0.201436	−0.100718	+	0.994915i	$0.532114\pi$
$294$	0.366138	0.0213536
$295$	−3.81964	−0.222388
$296$	0.522088	0.0303458
$297$	−3.30320	−0.191671
$298$	0.328570	0.0190335
$299$	42.8993	2.48093
$300$	1.16347	0.0671728
$301$	−34.2691	−1.97524
$302$	−1.33836	−0.0770137
$303$	−4.40742	−0.253200
$304$	3.96013	0.227129
$305$	11.3467	0.649709
$306$	1.68367	0.0962490
$307$	26.6483	1.52090	0.760450	−	0.649397i	$-0.224979\pi$
$307$	26.6483	1.52090	0.760450	+	0.649397i	$0.224979\pi$
$308$	−7.64026	−0.435344
$309$	5.88473	0.334771
$310$	0.615048	0.0349324
$311$	12.9433	0.733949	0.366975	−	0.930231i	$-0.380394\pi$
$311$	12.9433	0.733949	0.366975	+	0.930231i	$0.380394\pi$
$312$	0.994934	0.0563270
$313$	22.5752	1.27602	0.638012	−	0.770026i	$-0.279757\pi$
$313$	22.5752	1.27602	0.638012	+	0.770026i	$0.279757\pi$
$314$	0.491614	0.0277434
$315$	−10.1929	−0.574303
$316$	−20.1728	−1.13481
$317$	−27.0311	−1.51822	−0.759109	−	0.650964i	$-0.774365\pi$
$317$	−27.0311	−1.51822	−0.759109	+	0.650964i	$0.774365\pi$
$318$	−0.561570	−0.0314913
$319$	−0.961446	−0.0538306
$320$	7.84078	0.438313
$321$	−8.69887	−0.485524
$322$	−2.56258	−0.142807
$323$	7.76232	0.431907
$324$	−12.0597	−0.669983
$325$	−5.23350	−0.290302
$326$	−0.936068	−0.0518440
$327$	−2.65350	−0.146739
$328$	−1.99433	−0.110118
$329$	5.80241	0.319897
$330$	0.0476064	0.00262064
$331$	20.2155	1.11114	0.555571	−	0.831469i	$-0.312500\pi$
$331$	20.2155	1.11114	0.555571	+	0.831469i	$0.312500\pi$
$332$	8.34631	0.458063
$333$	−4.26269	−0.233594
$334$	−0.0976535	−0.00534336
$335$	−10.7033	−0.584786
$336$	8.85942	0.483321
$337$	−32.9960	−1.79740	−0.898702	−	0.438559i	$-0.855489\pi$
$337$	−32.9960	−1.79740	−0.898702	+	0.438559i	$0.855489\pi$
$338$	−1.17365	−0.0638383
$339$	−6.87181	−0.373226
$340$	15.4730	0.839141
$341$	−7.54076	−0.408355
$342$	0.216903	0.0117288
$343$	−2.64833	−0.142996
$344$	2.91211	0.157011
$345$	−4.78442	−0.257584
$346$	−1.15125	−0.0618916
$347$	−13.6684	−0.733760	−0.366880	−	0.930268i	$-0.619574\pi$
$347$	−13.6684	−0.733760	−0.366880	+	0.930268i	$0.619574\pi$
$348$	1.11861	0.0599638
$349$	5.02771	0.269127	0.134564	−	0.990905i	$-0.457037\pi$
$349$	5.02771	0.269127	0.134564	+	0.990905i	$0.457037\pi$
$350$	0.312622	0.0167103
$351$	−17.2873	−0.922729
$352$	0.974421	0.0519368
$353$	−16.0093	−0.852087	−0.426043	−	0.904703i	$-0.640093\pi$
$353$	−16.0093	−0.852087	−0.426043	+	0.904703i	$0.640093\pi$
$354$	0.181839	0.00966464
$355$	−1.57939	−0.0838251
$356$	−28.2026	−1.49473
$357$	17.3655	0.919080
$358$	0.594618	0.0314266
$359$	4.50597	0.237816	0.118908	−	0.992905i	$-0.462061\pi$
$359$	4.50597	0.237816	0.118908	+	0.992905i	$0.462061\pi$
$360$	0.866168	0.0456511
$361$	1.00000	0.0526316
$362$	−1.43096	−0.0752095
$363$	−0.583675	−0.0306350
$364$	−39.9853	−2.09580
$365$	2.13869	0.111944
$366$	−0.540174	−0.0282354
$367$	19.0188	0.992773	0.496386	−	0.868102i	$-0.334660\pi$
$367$	19.0188	0.992773	0.496386	+	0.868102i	$0.334660\pi$
$368$	−32.4614	−1.69217
$369$	16.2831	0.847664
$370$	0.130739	0.00679682
$371$	45.2130	2.34734
$372$	8.77342	0.454881
$373$	−19.4212	−1.00559	−0.502797	−	0.864405i	$-0.667696\pi$
$373$	−19.4212	−1.00559	−0.502797	+	0.864405i	$0.667696\pi$
$374$	0.633119	0.0327378
$375$	0.583675	0.0301408
$376$	−0.493077	−0.0254285
$377$	−5.03172	−0.259147
$378$	1.03265	0.0531139
$379$	34.1504	1.75419	0.877094	−	0.480320i	$-0.159479\pi$
$379$	34.1504	1.75419	0.877094	+	0.480320i	$0.159479\pi$
$380$	1.99335	0.102257
$381$	9.76179	0.500111
$382$	−1.85299	−0.0948070
$383$	21.4746	1.09730	0.548649	−	0.836053i	$-0.315142\pi$
$383$	21.4746	1.09730	0.548649	+	0.836053i	$0.315142\pi$
$384$	−1.51076	−0.0770957
$385$	−3.83288	−0.195342
$386$	1.22130	0.0621628
$387$	−23.7765	−1.20863
$388$	29.6069	1.50306
$389$	23.9440	1.21401	0.607004	−	0.794699i	$-0.292371\pi$
$389$	23.9440	1.21401	0.607004	+	0.794699i	$0.292371\pi$
$390$	0.249148	0.0126161
$391$	−63.6282	−3.21782
$392$	2.50502	0.126523
$393$	2.46005	0.124093
$394$	−0.678303	−0.0341724
$395$	−10.1200	−0.509195
$396$	−5.30096	−0.266383
$397$	−5.71668	−0.286912	−0.143456	−	0.989657i	$-0.545822\pi$
$397$	−5.71668	−0.286912	−0.143456	+	0.989657i	$0.545822\pi$
$398$	1.41454	0.0709044
$399$	2.23715	0.111998
$400$	3.96013	0.198006
$401$	11.4372	0.571144	0.285572	−	0.958357i	$-0.407816\pi$
$401$	11.4372	0.571144	0.285572	+	0.958357i	$0.407816\pi$
$402$	0.509547	0.0254139
$403$	−39.4645	−1.96587
$404$	−15.0521	−0.748869
$405$	−6.04997	−0.300626
$406$	0.300569	0.0149170
$407$	−1.60292	−0.0794540
$408$	−1.47569	−0.0730573
$409$	−13.4428	−0.664704	−0.332352	−	0.943155i	$-0.607842\pi$
$409$	−13.4428	−0.664704	−0.332352	+	0.943155i	$0.607842\pi$
$410$	−0.499413	−0.0246643
$411$	6.32619	0.312048
$412$	20.0974	0.990126
$413$	−14.6402	−0.720397
$414$	−1.77797	−0.0873823
$415$	4.18708	0.205536
$416$	5.09963	0.250030
$417$	2.70860	0.132641
$418$	0.0815632	0.00398938
$419$	22.5882	1.10351	0.551754	−	0.834007i	$-0.313959\pi$
$419$	22.5882	1.10351	0.551754	+	0.834007i	$0.313959\pi$
$420$	4.45943	0.217598
$421$	−2.86006	−0.139391	−0.0696953	−	0.997568i	$-0.522203\pi$
$421$	−2.86006	−0.139391	−0.0696953	+	0.997568i	$0.522203\pi$
$422$	−0.179370	−0.00873161
$423$	4.02582	0.195742
$424$	−3.84211	−0.186589
$425$	7.76232	0.376528
$426$	0.0751888	0.00364291
$427$	43.4904	2.10465
$428$	−29.7081	−1.43600
$429$	−3.05466	−0.147480
$430$	0.729241	0.0351671
$431$	14.0087	0.674775	0.337388	−	0.941366i	$-0.390457\pi$
$431$	14.0087	0.674775	0.337388	+	0.941366i	$0.390457\pi$
$432$	13.0811	0.629366
$433$	−5.58484	−0.268390	−0.134195	−	0.990955i	$-0.542845\pi$
$433$	−5.58484	−0.268390	−0.134195	+	0.990955i	$0.542845\pi$
$434$	2.35740	0.113159
$435$	0.561172	0.0269061
$436$	−9.06214	−0.433998
$437$	−8.19706	−0.392119
$438$	−0.101815	−0.00486492
$439$	37.3896	1.78451	0.892254	−	0.451534i	$-0.149123\pi$
$439$	37.3896	1.78451	0.892254	+	0.451534i	$0.149123\pi$
$440$	0.325710	0.0155276
$441$	−20.4527	−0.973939
$442$	3.31343	0.157604
$443$	25.9467	1.23277	0.616383	−	0.787447i	$-0.288597\pi$
$443$	25.9467	1.23277	0.616383	+	0.787447i	$0.288597\pi$
$444$	1.86495	0.0885065
$445$	−14.1484	−0.670697
$446$	1.11566	0.0528280
$447$	2.35128	0.111212
$448$	30.0528	1.41986
$449$	−27.9985	−1.32133	−0.660665	−	0.750681i	$-0.729726\pi$
$449$	−27.9985	−1.32133	−0.660665	+	0.750681i	$0.729726\pi$
$450$	0.216903	0.0102249
$451$	6.12302	0.288322
$452$	−23.4684	−1.10386
$453$	−9.57742	−0.449986
$454$	0.177113	0.00831231
$455$	−20.0594	−0.940397
$456$	−0.190109	−0.00890266
$457$	−7.14624	−0.334287	−0.167143	−	0.985933i	$-0.553454\pi$
$457$	−7.14624	−0.334287	−0.167143	+	0.985933i	$0.553454\pi$
$458$	0.425007	0.0198593
$459$	25.6405	1.19680
$460$	−16.3396	−0.761837
$461$	4.73457	0.220511	0.110255	−	0.993903i	$-0.464833\pi$
$461$	4.73457	0.220511	0.110255	+	0.993903i	$0.464833\pi$
$462$	0.182469	0.00848924
$463$	18.8789	0.877377	0.438689	−	0.898639i	$-0.355443\pi$
$463$	18.8789	0.877377	0.438689	+	0.898639i	$0.355443\pi$
$464$	3.80745	0.176756
$465$	4.40135	0.204108
$466$	0.730968	0.0338615
$467$	17.2014	0.795986	0.397993	−	0.917389i	$-0.369707\pi$
$467$	17.2014	0.795986	0.397993	+	0.917389i	$0.369707\pi$
$468$	−27.7425	−1.28240
$469$	−41.0246	−1.89434
$470$	−0.123475	−0.00569546
$471$	3.51804	0.162103
$472$	1.24409	0.0572641
$473$	−8.94082	−0.411099
$474$	0.481778	0.0221288
$475$	1.00000	0.0458831
$476$	59.3061	2.71829
$477$	31.3697	1.43632
$478$	1.54284	0.0705677
$479$	−11.6850	−0.533900	−0.266950	−	0.963710i	$-0.586016\pi$
$479$	−11.6850	−0.533900	−0.266950	+	0.963710i	$0.586016\pi$
$480$	−0.568745	−0.0259595
$481$	−8.38890	−0.382501
$482$	−1.06873	−0.0486792
$483$	−18.3381	−0.834412
$484$	−1.99335	−0.0906067
$485$	14.8528	0.674433
$486$	1.09628	0.0497281
$487$	0.791919	0.0358853	0.0179426	−	0.999839i	$-0.494288\pi$
$487$	0.791919	0.0358853	0.0179426	+	0.999839i	$0.494288\pi$
$488$	−3.69573	−0.167298
$489$	−6.69860	−0.302921
$490$	0.627298	0.0283384
$491$	6.64462	0.299867	0.149934	−	0.988696i	$-0.452094\pi$
$491$	6.64462	0.299867	0.149934	+	0.988696i	$0.452094\pi$
$492$	−7.12393	−0.321172
$493$	7.46305	0.336119
$494$	0.426861	0.0192054
$495$	−2.65932	−0.119528
$496$	29.8624	1.34086
$497$	−6.05359	−0.271541
$498$	−0.199332	−0.00893227
$499$	−1.89040	−0.0846259	−0.0423130	−	0.999104i	$-0.513473\pi$
$499$	−1.89040	−0.0846259	−0.0423130	+	0.999104i	$0.513473\pi$
$500$	1.99335	0.0891452
$501$	−0.698819	−0.0312209
$502$	−0.596910	−0.0266414
$503$	20.3707	0.908284	0.454142	−	0.890929i	$-0.349946\pi$
$503$	20.3707	0.908284	0.454142	+	0.890929i	$0.349946\pi$
$504$	3.31992	0.147881
$505$	−7.55116	−0.336022
$506$	−0.668578	−0.0297219
$507$	−8.39879	−0.373003
$508$	33.3381	1.47914
$509$	44.6699	1.97996	0.989980	−	0.141210i	$-0.0450994\pi$
$509$	44.6699	1.97996	0.989980	+	0.141210i	$0.0450994\pi$
$510$	−0.369536	−0.0163633
$511$	8.19734	0.362629
$512$	−6.43854	−0.284546
$513$	3.30320	0.145840
$514$	−0.860995	−0.0379769
$515$	10.0822	0.444275
$516$	10.4023	0.457938
$517$	1.51385	0.0665791
$518$	0.501108	0.0220174
$519$	−8.23847	−0.361629
$520$	1.70460	0.0747518
$521$	−1.23457	−0.0540875	−0.0270438	−	0.999634i	$-0.508609\pi$
$521$	−1.23457	−0.0540875	−0.0270438	+	0.999634i	$0.508609\pi$
$522$	0.208540	0.00912756
$523$	−13.9338	−0.609284	−0.304642	−	0.952467i	$-0.598537\pi$
$523$	−13.9338	−0.609284	−0.304642	+	0.952467i	$0.598537\pi$
$524$	8.40148	0.367020
$525$	2.23715	0.0976374
$526$	−1.43487	−0.0625635
$527$	58.5338	2.54977
$528$	2.31143	0.100592
$529$	44.1918	1.92138
$530$	−0.962128	−0.0417922
$531$	−10.1577	−0.440805
$532$	7.64026	0.331247
$533$	32.0448	1.38802
$534$	0.673552	0.0291474
$535$	−14.9036	−0.644340
$536$	3.48619	0.150580
$537$	4.25515	0.183623
$538$	−0.0906218	−0.00390698
$539$	−7.69095	−0.331273
$540$	6.58443	0.283349
$541$	−6.91205	−0.297172	−0.148586	−	0.988899i	$-0.547472\pi$
$541$	−6.91205	−0.297172	−0.148586	+	0.988899i	$0.547472\pi$
$542$	−0.901741	−0.0387331
$543$	−10.2401	−0.439444
$544$	−7.56377	−0.324294
$545$	−4.54619	−0.194738
$546$	0.954953	0.0408682
$547$	−28.6141	−1.22345	−0.611726	−	0.791070i	$-0.709524\pi$
$547$	−28.6141	−1.22345	−0.611726	+	0.791070i	$0.709524\pi$
$548$	21.6050	0.922919
$549$	30.1745	1.28782
$550$	0.0815632	0.00347787
$551$	0.961446	0.0409590
$552$	1.55833	0.0663271
$553$	−38.7889	−1.64947
$554$	1.38362	0.0587845
$555$	0.935586	0.0397134
$556$	9.25031	0.392301
$557$	−11.7312	−0.497068	−0.248534	−	0.968623i	$-0.579949\pi$
$557$	−11.7312	−0.497068	−0.248534	+	0.968623i	$0.579949\pi$
$558$	1.63561	0.0692410
$559$	−46.7918	−1.97908
$560$	15.1787	0.641417
$561$	4.53067	0.191285
$562$	−1.06790	−0.0450465
$563$	25.4376	1.07207	0.536034	−	0.844196i	$-0.319922\pi$
$563$	25.4376	1.07207	0.536034	+	0.844196i	$0.319922\pi$
$564$	−1.76132	−0.0741648
$565$	−11.7734	−0.495309
$566$	1.04517	0.0439316
$567$	−23.1888	−0.973838
$568$	0.514422	0.0215847
$569$	−34.0892	−1.42909	−0.714547	−	0.699587i	$-0.753367\pi$
$569$	−34.0892	−1.42909	−0.714547	+	0.699587i	$0.753367\pi$
$570$	−0.0476064	−0.00199401
$571$	−24.6403	−1.03116	−0.515582	−	0.856840i	$-0.672424\pi$
$571$	−24.6403	−1.03116	−0.515582	+	0.856840i	$0.672424\pi$
$572$	−10.4322	−0.436191
$573$	−13.2602	−0.553952
$574$	−1.91419	−0.0798967
$575$	−8.19706	−0.341841
$576$	20.8512	0.868799
$577$	−17.2926	−0.719902	−0.359951	−	0.932971i	$-0.617207\pi$
$577$	−17.2926	−0.719902	−0.359951	+	0.932971i	$0.617207\pi$
$578$	−3.52790	−0.146741
$579$	8.73979	0.363213
$580$	1.91650	0.0795781
$581$	16.0486	0.665807
$582$	−0.707090	−0.0293098
$583$	11.7961	0.488545
$584$	−0.696593	−0.0288252
$585$	−13.9176	−0.575421
$586$	0.281233	0.0116176
$587$	29.4556	1.21576	0.607882	−	0.794028i	$-0.292019\pi$
$587$	29.4556	1.21576	0.607882	+	0.794028i	$0.292019\pi$
$588$	8.94816	0.369016
$589$	7.54076	0.310712
$590$	0.311542	0.0128260
$591$	−4.85401	−0.199667
$592$	6.34778	0.260892
$593$	43.0574	1.76815	0.884077	−	0.467341i	$-0.154788\pi$
$593$	43.0574	1.76815	0.884077	+	0.467341i	$0.154788\pi$
$594$	0.269420	0.0110544
$595$	29.7520	1.21971
$596$	8.03002	0.328922
$597$	10.1226	0.414290
$598$	−3.49900	−0.143085
$599$	−2.86667	−0.117129	−0.0585645	−	0.998284i	$-0.518652\pi$
$599$	−2.86667	−0.117129	−0.0585645	+	0.998284i	$0.518652\pi$
$600$	−0.190109	−0.00776116
$601$	−41.2216	−1.68146	−0.840732	−	0.541451i	$-0.817875\pi$
$601$	−41.2216	−1.68146	−0.840732	+	0.541451i	$0.817875\pi$
$602$	2.79509	0.113919
$603$	−28.4637	−1.15913
$604$	−32.7085	−1.33089
$605$	−1.00000	−0.0406558
$606$	0.359483	0.0146030
$607$	−4.38511	−0.177986	−0.0889931	−	0.996032i	$-0.528365\pi$
$607$	−4.38511	−0.177986	−0.0889931	+	0.996032i	$0.528365\pi$
$608$	−0.974421	−0.0395180
$609$	2.15090	0.0871589
$610$	−0.925471	−0.0374712
$611$	7.92274	0.320520
$612$	41.1477	1.66330
$613$	34.8551	1.40778	0.703892	−	0.710307i	$-0.251444\pi$
$613$	34.8551	1.40778	0.703892	+	0.710307i	$0.251444\pi$
$614$	−2.17352	−0.0877161
$615$	−3.57385	−0.144112
$616$	1.24841	0.0502997
$617$	32.2889	1.29990	0.649951	−	0.759976i	$-0.274789\pi$
$617$	32.2889	1.29990	0.649951	+	0.759976i	$0.274789\pi$
$618$	−0.479978	−0.0193075
$619$	13.9289	0.559851	0.279925	−	0.960022i	$-0.409690\pi$
$619$	13.9289	0.559851	0.279925	+	0.960022i	$0.409690\pi$
$620$	15.0314	0.603674
$621$	−27.0766	−1.08655
$622$	−1.05570	−0.0423297
$623$	−54.2289	−2.17264
$624$	12.0969	0.484262
$625$	1.00000	0.0400000
$626$	−1.84130	−0.0735933
$627$	0.583675	0.0233097
$628$	12.0147	0.479439
$629$	12.4424	0.496111
$630$	0.831362	0.0331223
$631$	25.3805	1.01038	0.505192	−	0.863007i	$-0.331422\pi$
$631$	25.3805	1.01038	0.505192	+	0.863007i	$0.331422\pi$
$632$	3.29620	0.131116
$633$	−1.28359	−0.0510183
$634$	2.20474	0.0875615
$635$	16.7247	0.663699
$636$	−13.7244	−0.544207
$637$	−40.2506	−1.59479
$638$	0.0784185	0.00310462
$639$	−4.20010	−0.166153
$640$	−2.58836	−0.102314
$641$	−15.0298	−0.593642	−0.296821	−	0.954933i	$-0.595926\pi$
$641$	−15.0298	−0.593642	−0.296821	+	0.954933i	$0.595926\pi$
$642$	0.709507	0.0280020
$643$	31.1435	1.22818	0.614091	−	0.789236i	$-0.289523\pi$
$643$	31.1435	1.22818	0.614091	+	0.789236i	$0.289523\pi$
$644$	−62.6277	−2.46788
$645$	5.21853	0.205479
$646$	−0.633119	−0.0249098
$647$	10.3049	0.405129	0.202565	−	0.979269i	$-0.435072\pi$
$647$	10.3049	0.405129	0.202565	+	0.979269i	$0.435072\pi$
$648$	1.97054	0.0774100
$649$	−3.81964	−0.149934
$650$	0.426861	0.0167429
$651$	16.8698	0.661181
$652$	−22.8768	−0.895926
$653$	50.5511	1.97822	0.989108	−	0.147190i	$-0.0470230\pi$
$653$	50.5511	1.97822	0.989108	+	0.147190i	$0.0470230\pi$
$654$	0.216428	0.00846299
$655$	4.21476	0.164684
$656$	−24.2480	−0.946724
$657$	5.68747	0.221889
$658$	−0.473263	−0.0184497
$659$	−46.4124	−1.80797	−0.903986	−	0.427562i	$-0.859372\pi$
$659$	−46.4124	−1.80797	−0.903986	+	0.427562i	$0.859372\pi$
$660$	1.16347	0.0452879
$661$	31.8352	1.23825	0.619123	−	0.785294i	$-0.287488\pi$
$661$	31.8352	1.23825	0.619123	+	0.785294i	$0.287488\pi$
$662$	−1.64884	−0.0640838
$663$	23.7113	0.920869
$664$	−1.36378	−0.0529247
$665$	3.83288	0.148633
$666$	0.347679	0.0134723
$667$	−7.88103	−0.305155
$668$	−2.38658	−0.0923397
$669$	7.98378	0.308671
$670$	0.872999	0.0337269
$671$	11.3467	0.438034
$672$	−2.17993	−0.0840926
$673$	8.87329	0.342040	0.171020	−	0.985268i	$-0.445294\pi$
$673$	8.87329	0.342040	0.171020	+	0.985268i	$0.445294\pi$
$674$	2.69126	0.103663
$675$	3.30320	0.127140
$676$	−28.6833	−1.10320
$677$	31.1457	1.19703	0.598514	−	0.801112i	$-0.295758\pi$
$677$	31.1457	1.19703	0.598514	+	0.801112i	$0.295758\pi$
$678$	0.560487	0.0215254
$679$	56.9291	2.18474
$680$	−2.52827	−0.0969546
$681$	1.26744	0.0485683
$682$	0.615048	0.0235514
$683$	19.4016	0.742382	0.371191	−	0.928557i	$-0.378950\pi$
$683$	19.4016	0.742382	0.371191	+	0.928557i	$0.378950\pi$
$684$	5.30096	0.202687
$685$	10.8385	0.414120
$686$	0.216006	0.00824714
$687$	3.04139	0.116036
$688$	35.4068	1.34987
$689$	61.7349	2.35191
$690$	0.390232	0.0148559
$691$	35.7317	1.35930	0.679650	−	0.733537i	$-0.262132\pi$
$691$	35.7317	1.35930	0.679650	+	0.733537i	$0.262132\pi$
$692$	−28.1358	−1.06956
$693$	−10.1929	−0.387195
$694$	1.11484	0.0423188
$695$	4.64059	0.176028
$696$	−0.182779	−0.00692823
$697$	−47.5289	−1.80028
$698$	−0.410076	−0.0155216
$699$	5.23089	0.197850
$700$	7.64026	0.288775
$701$	−29.7417	−1.12333	−0.561663	−	0.827366i	$-0.689838\pi$
$701$	−29.7417	−1.12333	−0.561663	+	0.827366i	$0.689838\pi$
$702$	1.41001	0.0532173
$703$	1.60292	0.0604554
$704$	7.84078	0.295511
$705$	−0.883597	−0.0332782
$706$	1.30577	0.0491431
$707$	−28.9427	−1.08850
$708$	4.44402	0.167017
$709$	−48.0091	−1.80302	−0.901510	−	0.432757i	$-0.857541\pi$
$709$	−48.0091	−1.80302	−0.901510	+	0.432757i	$0.857541\pi$
$710$	0.128820	0.00483452
$711$	−26.9125	−1.00930
$712$	4.60826	0.172702
$713$	−61.8121	−2.31488
$714$	−1.41639	−0.0530069
$715$	−5.23350	−0.195722
$716$	14.5321	0.543089
$717$	11.0407	0.412323
$718$	−0.367521	−0.0137158
$719$	−14.4700	−0.539641	−0.269820	−	0.962911i	$-0.586964\pi$
$719$	−14.4700	−0.539641	−0.269820	+	0.962911i	$0.586964\pi$
$720$	10.5313	0.392477
$721$	38.6439	1.43917
$722$	−0.0815632	−0.00303547
$723$	−7.64792	−0.284429
$724$	−34.9716	−1.29971
$725$	0.961446	0.0357072
$726$	0.0476064	0.00176684
$727$	−24.2482	−0.899318	−0.449659	−	0.893200i	$-0.648454\pi$
$727$	−24.2482	−0.899318	−0.449659	+	0.893200i	$0.648454\pi$
$728$	6.53353	0.242149
$729$	−10.3048	−0.381661
$730$	−0.174438	−0.00645625
$731$	69.4015	2.56691
$732$	−13.2015	−0.487941
$733$	10.4456	0.385817	0.192908	−	0.981217i	$-0.438208\pi$
$733$	10.4456	0.385817	0.192908	+	0.981217i	$0.438208\pi$
$734$	−1.55123	−0.0572570
$735$	4.48901	0.165580
$736$	7.98739	0.294419
$737$	−10.7033	−0.394263
$738$	−1.32810	−0.0488881
$739$	−49.4367	−1.81856	−0.909280	−	0.416185i	$-0.863367\pi$
$739$	−49.4367	−1.81856	−0.909280	+	0.416185i	$0.863367\pi$
$740$	3.19518	0.117457
$741$	3.05466	0.112216
$742$	−3.68772	−0.135380
$743$	−36.0952	−1.32421	−0.662103	−	0.749413i	$-0.730336\pi$
$743$	−36.0952	−1.32421	−0.662103	+	0.749413i	$0.730336\pi$
$744$	−1.43356	−0.0525570
$745$	4.02841	0.147589
$746$	1.58406	0.0579965
$747$	11.1348	0.407401
$748$	15.4730	0.565749
$749$	−57.1238	−2.08726
$750$	−0.0476064	−0.00173834
$751$	−9.47552	−0.345767	−0.172883	−	0.984942i	$-0.555308\pi$
$751$	−9.47552	−0.345767	−0.172883	+	0.984942i	$0.555308\pi$
$752$	−5.99505	−0.218617
$753$	−4.27156	−0.155664
$754$	0.410403	0.0149460
$755$	−16.4088	−0.597178
$756$	25.2373	0.917873
$757$	39.4364	1.43334	0.716669	−	0.697413i	$-0.245666\pi$
$757$	39.4364	1.43334	0.716669	+	0.697413i	$0.245666\pi$
$758$	−2.78541	−0.101171
$759$	−4.78442	−0.173663
$760$	−0.325710	−0.0118147
$761$	−41.7515	−1.51349	−0.756745	−	0.653710i	$-0.773212\pi$
$761$	−41.7515	−1.51349	−0.756745	+	0.653710i	$0.773212\pi$
$762$	−0.796202	−0.0288434
$763$	−17.4250	−0.630827
$764$	−45.2857	−1.63838
$765$	20.6425	0.746332
$766$	−1.75153	−0.0632854
$767$	−19.9901	−0.721800
$768$	−9.02971	−0.325832
$769$	6.25422	0.225533	0.112766	−	0.993622i	$-0.464029\pi$
$769$	6.25422	0.225533	0.112766	+	0.993622i	$0.464029\pi$
$770$	0.312622	0.0112661
$771$	−6.16137	−0.221896
$772$	29.8478	1.07425
$773$	−15.5901	−0.560735	−0.280368	−	0.959893i	$-0.590456\pi$
$773$	−15.5901	−0.560735	−0.280368	+	0.959893i	$0.590456\pi$
$774$	1.93929	0.0697063
$775$	7.54076	0.270872
$776$	−4.83772	−0.173664
$777$	3.58599	0.128647
$778$	−1.95295	−0.0700166
$779$	−6.12302	−0.219380
$780$	6.08900	0.218021
$781$	−1.57939	−0.0565149
$782$	5.18972	0.185584
$783$	3.17585	0.113496
$784$	30.4572	1.08776
$785$	6.02740	0.215127
$786$	−0.200649	−0.00715692
$787$	−35.1165	−1.25177	−0.625884	−	0.779916i	$-0.715262\pi$
$787$	−35.1165	−1.25177	−0.625884	+	0.779916i	$0.715262\pi$
$788$	−16.5772	−0.590540
$789$	−10.2681	−0.365554
$790$	0.825423	0.0293672
$791$	−45.1258	−1.60449
$792$	0.866168	0.0307780
$793$	59.3828	2.10875
$794$	0.466271	0.0165473
$795$	−6.88509	−0.244189
$796$	34.5703	1.22531
$797$	5.26227	0.186399	0.0931996	−	0.995647i	$-0.470291\pi$
$797$	5.26227	0.186399	0.0931996	+	0.995647i	$0.470291\pi$
$798$	−0.182469	−0.00645935
$799$	−11.7510	−0.415721
$800$	−0.974421	−0.0344510
$801$	−37.6251	−1.32942
$802$	−0.932850	−0.0329401
$803$	2.13869	0.0754728
$804$	12.4530	0.439183
$805$	−31.4183	−1.10735
$806$	3.21885	0.113379
$807$	−0.648499	−0.0228283
$808$	2.45949	0.0865245
$809$	45.6220	1.60398	0.801991	−	0.597336i	$-0.203774\pi$
$809$	45.6220	1.60398	0.801991	+	0.597336i	$0.203774\pi$
$810$	0.493455	0.0173382
$811$	−19.6106	−0.688621	−0.344311	−	0.938856i	$-0.611887\pi$
$811$	−19.6106	−0.688621	−0.344311	+	0.938856i	$0.611887\pi$
$812$	7.34569	0.257783
$813$	−6.45295	−0.226315
$814$	0.130739	0.00458242
$815$	−11.4766	−0.402008
$816$	−17.9420	−0.628097
$817$	8.94082	0.312800
$818$	1.09644	0.0383361
$819$	−53.3443	−1.86400
$820$	−12.2053	−0.426228
$821$	−11.7521	−0.410152	−0.205076	−	0.978746i	$-0.565744\pi$
$821$	−11.7521	−0.410152	−0.205076	+	0.978746i	$0.565744\pi$
$822$	−0.515984	−0.0179970
$823$	−14.2153	−0.495513	−0.247757	−	0.968822i	$-0.579693\pi$
$823$	−14.2153	−0.495513	−0.247757	+	0.968822i	$0.579693\pi$
$824$	−3.28388	−0.114399
$825$	0.583675	0.0203209
$826$	1.19410	0.0415481
$827$	−28.9068	−1.00519	−0.502593	−	0.864523i	$-0.667621\pi$
$827$	−28.9068	−1.00519	−0.502593	+	0.864523i	$0.667621\pi$
$828$	−43.4523	−1.51007
$829$	−25.9615	−0.901682	−0.450841	−	0.892604i	$-0.648876\pi$
$829$	−25.9615	−0.901682	−0.450841	+	0.892604i	$0.648876\pi$
$830$	−0.341512	−0.0118540
$831$	9.90136	0.343474
$832$	41.0347	1.42262
$833$	59.6996	2.06847
$834$	−0.220922	−0.00764989
$835$	−1.19727	−0.0414334
$836$	1.99335	0.0689414
$837$	24.9087	0.860970
$838$	−1.84237	−0.0636436
$839$	−14.5437	−0.502103	−0.251051	−	0.967974i	$-0.580776\pi$
$839$	−14.5437	−0.502103	−0.251051	+	0.967974i	$0.580776\pi$
$840$	−0.728664	−0.0251413
$841$	−28.0756	−0.968125
$842$	0.233275	0.00803920
$843$	−7.64198	−0.263204
$844$	−4.38369	−0.150893
$845$	−14.3895	−0.495014
$846$	−0.328359	−0.0112892
$847$	−3.83288	−0.131699
$848$	−46.7141	−1.60417
$849$	7.47932	0.256690
$850$	−0.633119	−0.0217158
$851$	−13.1393	−0.450408
$852$	1.83756	0.0629539
$853$	−5.93123	−0.203082	−0.101541	−	0.994831i	$-0.532377\pi$
$853$	−5.93123	−0.203082	−0.101541	+	0.994831i	$0.532377\pi$
$854$	−3.54722	−0.121383
$855$	2.65932	0.0909470
$856$	4.85426	0.165915
$857$	26.2483	0.896625	0.448312	−	0.893877i	$-0.352025\pi$
$857$	26.2483	0.896625	0.448312	+	0.893877i	$0.352025\pi$
$858$	0.249148	0.00850577
$859$	−22.0987	−0.753999	−0.377000	−	0.926213i	$-0.623044\pi$
$859$	−22.0987	−0.753999	−0.377000	+	0.926213i	$0.623044\pi$
$860$	17.8222	0.607730
$861$	−13.6981	−0.466832
$862$	−1.14259	−0.0389169
$863$	36.6731	1.24837	0.624183	−	0.781278i	$-0.285432\pi$
$863$	36.6731	1.24837	0.624183	+	0.781278i	$0.285432\pi$
$864$	−3.21871	−0.109503
$865$	−14.1148	−0.479919
$866$	0.455518	0.0154791
$867$	−25.2461	−0.857401
$868$	57.6133	1.95552
$869$	−10.1200	−0.343299
$870$	−0.0457709	−0.00155178
$871$	−56.0159	−1.89803
$872$	1.48074	0.0501442
$873$	39.4985	1.33682
$874$	0.668578	0.0226150
$875$	3.83288	0.129575
$876$	−2.48830	−0.0840717
$877$	18.3103	0.618296	0.309148	−	0.951014i	$-0.399956\pi$
$877$	18.3103	0.618296	0.309148	+	0.951014i	$0.399956\pi$
$878$	−3.04961	−0.102919
$879$	2.01253	0.0678810
$880$	3.96013	0.133496
$881$	−8.35549	−0.281504	−0.140752	−	0.990045i	$-0.544952\pi$
$881$	−8.35549	−0.281504	−0.140752	+	0.990045i	$0.544952\pi$
$882$	1.66819	0.0561708
$883$	−8.05909	−0.271210	−0.135605	−	0.990763i	$-0.543298\pi$
$883$	−8.05909	−0.271210	−0.135605	+	0.990763i	$0.543298\pi$
$884$	80.9779	2.72358
$885$	2.22943	0.0749413
$886$	−2.11630	−0.0710984
$887$	34.5592	1.16038	0.580192	−	0.814480i	$-0.302978\pi$
$887$	34.5592	1.16038	0.580192	+	0.814480i	$0.302978\pi$
$888$	−0.304730	−0.0102261
$889$	64.1037	2.14997
$890$	1.15399	0.0386817
$891$	−6.04997	−0.202682
$892$	27.2659	0.912931
$893$	−1.51385	−0.0506591
$894$	−0.191778	−0.00641401
$895$	7.29028	0.243687
$896$	−9.92087	−0.331433
$897$	−25.0392	−0.836036
$898$	2.28364	0.0762062
$899$	7.25003	0.241802
$900$	5.30096	0.176699
$901$	−91.5652	−3.05048
$902$	−0.499413	−0.0166286
$903$	20.0020	0.665624
$904$	3.83470	0.127540
$905$	−17.5442	−0.583188
$906$	0.781165	0.0259525
$907$	13.6642	0.453712	0.226856	−	0.973928i	$-0.427155\pi$
$907$	13.6642	0.453712	0.226856	+	0.973928i	$0.427155\pi$
$908$	4.32851	0.143647
$909$	−20.0810	−0.666044
$910$	1.63610	0.0542363
$911$	−12.5065	−0.414360	−0.207180	−	0.978303i	$-0.566429\pi$
$911$	−12.5065	−0.414360	−0.207180	+	0.978303i	$0.566429\pi$
$912$	−2.31143	−0.0765390
$913$	4.18708	0.138572
$914$	0.582870	0.0192796
$915$	−6.62277	−0.218942
$916$	10.3869	0.343192
$917$	16.1547	0.533474
$918$	−2.09132	−0.0690240
$919$	15.2512	0.503091	0.251545	−	0.967846i	$-0.419061\pi$
$919$	15.2512	0.503091	0.251545	+	0.967846i	$0.419061\pi$
$920$	2.66987	0.0880229
$921$	−15.5539	−0.512520
$922$	−0.386167	−0.0127177
$923$	−8.26571	−0.272069
$924$	4.45943	0.146704
$925$	1.60292	0.0527038
$926$	−1.53982	−0.0506017
$927$	26.8119	0.880617
$928$	−0.936853	−0.0307537
$929$	−21.1104	−0.692611	−0.346305	−	0.938122i	$-0.612564\pi$
$929$	−21.1104	−0.692611	−0.346305	+	0.938122i	$0.612564\pi$
$930$	−0.358988	−0.0117717
$931$	7.69095	0.252061
$932$	17.8644	0.585167
$933$	−7.55470	−0.247330
$934$	−1.40300	−0.0459076
$935$	7.76232	0.253855
$936$	4.53309	0.148169
$937$	−39.4478	−1.28870	−0.644351	−	0.764730i	$-0.722873\pi$
$937$	−39.4478	−1.28870	−0.644351	+	0.764730i	$0.722873\pi$
$938$	3.34610	0.109254
$939$	−13.1766	−0.430001
$940$	−3.01763	−0.0984243
$941$	−4.48884	−0.146332	−0.0731660	−	0.997320i	$-0.523310\pi$
$941$	−4.48884	−0.146332	−0.0731660	+	0.997320i	$0.523310\pi$
$942$	−0.286942	−0.00934909
$943$	50.1908	1.63444
$944$	15.1263	0.492318
$945$	12.6608	0.411855
$946$	0.729241	0.0237097
$947$	11.5898	0.376619	0.188310	−	0.982110i	$-0.439699\pi$
$947$	11.5898	0.376619	0.188310	+	0.982110i	$0.439699\pi$
$948$	11.7743	0.382413
$949$	11.1928	0.363335
$950$	−0.0815632	−0.00264626
$951$	15.7774	0.511616
$952$	−9.69053	−0.314072
$953$	−41.8840	−1.35675	−0.678377	−	0.734714i	$-0.737317\pi$
$953$	−41.8840	−1.35675	−0.678377	+	0.734714i	$0.737317\pi$
$954$	−2.55861	−0.0828380
$955$	−22.7184	−0.735151
$956$	37.7059	1.21950
$957$	0.561172	0.0181401
$958$	0.953064	0.0307921
$959$	41.5428	1.34149
$960$	−4.57647	−0.147705
$961$	25.8630	0.834291
$962$	0.684225	0.0220603
$963$	−39.6336	−1.27717
$964$	−26.1189	−0.841234
$965$	14.9737	0.482021
$966$	1.49571	0.0481238
$967$	21.4253	0.688990	0.344495	−	0.938788i	$-0.388050\pi$
$967$	21.4253	0.688990	0.344495	+	0.938788i	$0.388050\pi$
$968$	0.325710	0.0104687
$969$	−4.53067	−0.145546
$970$	−1.21145	−0.0388972
$971$	−20.6993	−0.664271	−0.332136	−	0.943232i	$-0.607769\pi$
$971$	−20.6993	−0.664271	−0.332136	+	0.943232i	$0.607769\pi$
$972$	26.7922	0.859362
$973$	17.7868	0.570219
$974$	−0.0645914	−0.00206964
$975$	3.05466	0.0978274
$976$	−44.9343	−1.43831
$977$	−6.17401	−0.197524	−0.0987620	−	0.995111i	$-0.531488\pi$
$977$	−6.17401	−0.197524	−0.0987620	+	0.995111i	$0.531488\pi$
$978$	0.546359	0.0174706
$979$	−14.1484	−0.452184
$980$	15.3307	0.489722
$981$	−12.0898	−0.385998
$982$	−0.541956	−0.0172945
$983$	6.16460	0.196620	0.0983101	−	0.995156i	$-0.468656\pi$
$983$	6.16460	0.196620	0.0983101	+	0.995156i	$0.468656\pi$
$984$	1.16404	0.0371082
$985$	−8.31629	−0.264979
$986$	−0.608710	−0.0193853
$987$	−3.38672	−0.107800
$988$	10.4322	0.331892
$989$	−73.2884	−2.33044
$990$	0.216903	0.00689363
$991$	−5.69795	−0.181001	−0.0905007	−	0.995896i	$-0.528847\pi$
$991$	−5.69795	−0.181001	−0.0905007	+	0.995896i	$0.528847\pi$
$992$	−7.34787	−0.233295
$993$	−11.7992	−0.374438
$994$	0.493750	0.0156608
$995$	17.3429	0.549806
$996$	−4.87153	−0.154360
$997$	−19.6843	−0.623407	−0.311704	−	0.950179i	$-0.600900\pi$
$997$	−19.6843	−0.623407	−0.311704	+	0.950179i	$0.600900\pi$
$998$	0.154187	0.00488071
$999$	5.29478	0.167520

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.2.a.j.1.4	✓	9
3.2	odd	2		9405.2.a.bi.1.6		9
5.4	even	2		5225.2.a.q.1.6		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.2.a.j.1.4	✓	9	1.1	even	1	trivial
5225.2.a.q.1.6		9	5.4	even	2
9405.2.a.bi.1.6		9	3.2	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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1045.a (trivial)

\(f(q)\)	\(=\)	\(q-0.0815632 q^{2} -0.583675 q^{3} -1.99335 q^{4} -1.00000 q^{5} +0.0476064 q^{6} -3.83288 q^{7} +0.325710 q^{8} -2.65932 q^{9} +O(q^{10})\)	\(q-0.0815632 q^{2} -0.583675 q^{3} -1.99335 q^{4} -1.00000 q^{5} +0.0476064 q^{6} -3.83288 q^{7} +0.325710 q^{8} -2.65932 q^{9} +0.0815632 q^{10} -1.00000 q^{11} +1.16347 q^{12} -5.23350 q^{13} +0.312622 q^{14} +0.583675 q^{15} +3.96013 q^{16} +7.76232 q^{17} +0.216903 q^{18} +1.00000 q^{19} +1.99335 q^{20} +2.23715 q^{21} +0.0815632 q^{22} -8.19706 q^{23} -0.190109 q^{24} +1.00000 q^{25} +0.426861 q^{26} +3.30320 q^{27} +7.64026 q^{28} +0.961446 q^{29} -0.0476064 q^{30} +7.54076 q^{31} -0.974421 q^{32} +0.583675 q^{33} -0.633119 q^{34} +3.83288 q^{35} +5.30096 q^{36} +1.60292 q^{37} -0.0815632 q^{38} +3.05466 q^{39} -0.325710 q^{40} -6.12302 q^{41} -0.182469 q^{42} +8.94082 q^{43} +1.99335 q^{44} +2.65932 q^{45} +0.668578 q^{46} -1.51385 q^{47} -2.31143 q^{48} +7.69095 q^{49} -0.0815632 q^{50} -4.53067 q^{51} +10.4322 q^{52} -11.7961 q^{53} -0.269420 q^{54} +1.00000 q^{55} -1.24841 q^{56} -0.583675 q^{57} -0.0784185 q^{58} +3.81964 q^{59} -1.16347 q^{60} -11.3467 q^{61} -0.615048 q^{62} +10.1929 q^{63} -7.84078 q^{64} +5.23350 q^{65} -0.0476064 q^{66} +10.7033 q^{67} -15.4730 q^{68} +4.78442 q^{69} -0.312622 q^{70} +1.57939 q^{71} -0.866168 q^{72} -2.13869 q^{73} -0.130739 q^{74} -0.583675 q^{75} -1.99335 q^{76} +3.83288 q^{77} -0.249148 q^{78} +10.1200 q^{79} -3.96013 q^{80} +6.04997 q^{81} +0.499413 q^{82} -4.18708 q^{83} -4.45943 q^{84} -7.76232 q^{85} -0.729241 q^{86} -0.561172 q^{87} -0.325710 q^{88} +14.1484 q^{89} -0.216903 q^{90} +20.0594 q^{91} +16.3396 q^{92} -4.40135 q^{93} +0.123475 q^{94} -1.00000 q^{95} +0.568745 q^{96} -14.8528 q^{97} -0.627298 q^{98} +2.65932 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 3 q^{2} + 3 q^{3} + 9 q^{4} - 9 q^{5} + 6 q^{6} - 9 q^{7} + 15 q^{8} + 16 q^{9}+O(q^{10}) \) 9 * q + 3 * q^2 + 3 * q^3 + 9 * q^4 - 9 * q^5 + 6 * q^6 - 9 * q^7 + 15 * q^8 + 16 * q^9	\( 9 q + 3 q^{2} + 3 q^{3} + 9 q^{4} - 9 q^{5} + 6 q^{6} - 9 q^{7} + 15 q^{8} + 16 q^{9} - 3 q^{10} - 9 q^{11} + 13 q^{12} - 3 q^{13} + 4 q^{14} - 3 q^{15} + 17 q^{16} + 5 q^{17} + 17 q^{18} + 9 q^{19} - 9 q^{20} - q^{21} - 3 q^{22} + 4 q^{23} + 21 q^{24} + 9 q^{25} + 20 q^{26} + 24 q^{27} - 24 q^{28} + 3 q^{29} - 6 q^{30} - q^{31} + 38 q^{32} - 3 q^{33} + 28 q^{34} + 9 q^{35} + 17 q^{36} + 5 q^{37} + 3 q^{38} - 15 q^{40} - 5 q^{41} - 43 q^{42} - 11 q^{43} - 9 q^{44} - 16 q^{45} + 2 q^{46} + 30 q^{47} + 54 q^{48} + 12 q^{49} + 3 q^{50} + 40 q^{51} - 3 q^{52} - q^{53} + 65 q^{54} + 9 q^{55} - 16 q^{56} + 3 q^{57} - 15 q^{58} + 59 q^{59} - 13 q^{60} - 21 q^{61} - 10 q^{62} - 12 q^{63} + 19 q^{64} + 3 q^{65} - 6 q^{66} - 2 q^{67} - 9 q^{68} - 22 q^{69} - 4 q^{70} + 34 q^{71} + 32 q^{72} - 34 q^{73} - 21 q^{74} + 3 q^{75} + 9 q^{76} + 9 q^{77} - 65 q^{78} - 13 q^{79} - 17 q^{80} + 57 q^{81} + 10 q^{82} + 51 q^{83} - 95 q^{84} - 5 q^{85} - 14 q^{86} + 8 q^{87} - 15 q^{88} + 8 q^{89} - 17 q^{90} + 62 q^{91} + 57 q^{92} - 18 q^{93} + 2 q^{94} - 9 q^{95} + 81 q^{96} - 8 q^{97} - 20 q^{98} - 16 q^{99}+O(q^{100}) \) 9 * q + 3 * q^2 + 3 * q^3 + 9 * q^4 - 9 * q^5 + 6 * q^6 - 9 * q^7 + 15 * q^8 + 16 * q^9 - 3 * q^10 - 9 * q^11 + 13 * q^12 - 3 * q^13 + 4 * q^14 - 3 * q^15 + 17 * q^16 + 5 * q^17 + 17 * q^18 + 9 * q^19 - 9 * q^20 - q^21 - 3 * q^22 + 4 * q^23 + 21 * q^24 + 9 * q^25 + 20 * q^26 + 24 * q^27 - 24 * q^28 + 3 * q^29 - 6 * q^30 - q^31 + 38 * q^32 - 3 * q^33 + 28 * q^34 + 9 * q^35 + 17 * q^36 + 5 * q^37 + 3 * q^38 - 15 * q^40 - 5 * q^41 - 43 * q^42 - 11 * q^43 - 9 * q^44 - 16 * q^45 + 2 * q^46 + 30 * q^47 + 54 * q^48 + 12 * q^49 + 3 * q^50 + 40 * q^51 - 3 * q^52 - q^53 + 65 * q^54 + 9 * q^55 - 16 * q^56 + 3 * q^57 - 15 * q^58 + 59 * q^59 - 13 * q^60 - 21 * q^61 - 10 * q^62 - 12 * q^63 + 19 * q^64 + 3 * q^65 - 6 * q^66 - 2 * q^67 - 9 * q^68 - 22 * q^69 - 4 * q^70 + 34 * q^71 + 32 * q^72 - 34 * q^73 - 21 * q^74 + 3 * q^75 + 9 * q^76 + 9 * q^77 - 65 * q^78 - 13 * q^79 - 17 * q^80 + 57 * q^81 + 10 * q^82 + 51 * q^83 - 95 * q^84 - 5 * q^85 - 14 * q^86 + 8 * q^87 - 15 * q^88 + 8 * q^89 - 17 * q^90 + 62 * q^91 + 57 * q^92 - 18 * q^93 + 2 * q^94 - 9 * q^95 + 81 * q^96 - 8 * q^97 - 20 * q^98 - 16 * q^99

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