LMFDB - Embedded newform 1335.2.a.h.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1335,2,Mod(1,1335)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1335, 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("1335.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1335 = 3 \cdot 5 \cdot 89 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1335.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:	$10.6600286698$
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} - 4x^{8} - 6x^{7} + 31x^{6} + 13x^{5} - 75x^{4} - 17x^{3} + 52x^{2} + 11x - 1 $ x^9 - 4x^8 - 6x^7 + 31x^6 + 13x^5 - 75x^4 - 17x^3 + 52x^2 + 11x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-1.70432$ of defining polynomial
Character	$\chi$	$=$	1335.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.70432 q^{2} -1.00000 q^{3} +5.31333 q^{4} -1.00000 q^{5} -2.70432 q^{6} +3.91511 q^{7} +8.96030 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.70432 q^{2} -1.00000 q^{3} +5.31333 q^{4} -1.00000 q^{5} -2.70432 q^{6} +3.91511 q^{7} +8.96030 q^{8} +1.00000 q^{9} -2.70432 q^{10} +0.290736 q^{11} -5.31333 q^{12} -2.36069 q^{13} +10.5877 q^{14} +1.00000 q^{15} +13.6048 q^{16} +4.13501 q^{17} +2.70432 q^{18} -7.64191 q^{19} -5.31333 q^{20} -3.91511 q^{21} +0.786242 q^{22} -6.01817 q^{23} -8.96030 q^{24} +1.00000 q^{25} -6.38406 q^{26} -1.00000 q^{27} +20.8023 q^{28} +8.87608 q^{29} +2.70432 q^{30} +7.33038 q^{31} +18.8712 q^{32} -0.290736 q^{33} +11.1824 q^{34} -3.91511 q^{35} +5.31333 q^{36} +0.927874 q^{37} -20.6661 q^{38} +2.36069 q^{39} -8.96030 q^{40} -10.6233 q^{41} -10.5877 q^{42} -9.40345 q^{43} +1.54478 q^{44} -1.00000 q^{45} -16.2751 q^{46} +11.2630 q^{47} -13.6048 q^{48} +8.32807 q^{49} +2.70432 q^{50} -4.13501 q^{51} -12.5431 q^{52} +4.74498 q^{53} -2.70432 q^{54} -0.290736 q^{55} +35.0805 q^{56} +7.64191 q^{57} +24.0037 q^{58} -8.49811 q^{59} +5.31333 q^{60} -2.98630 q^{61} +19.8237 q^{62} +3.91511 q^{63} +23.8239 q^{64} +2.36069 q^{65} -0.786242 q^{66} -7.70384 q^{67} +21.9706 q^{68} +6.01817 q^{69} -10.5877 q^{70} +4.65945 q^{71} +8.96030 q^{72} -11.9200 q^{73} +2.50926 q^{74} -1.00000 q^{75} -40.6040 q^{76} +1.13826 q^{77} +6.38406 q^{78} +13.5279 q^{79} -13.6048 q^{80} +1.00000 q^{81} -28.7288 q^{82} +3.43747 q^{83} -20.8023 q^{84} -4.13501 q^{85} -25.4299 q^{86} -8.87608 q^{87} +2.60508 q^{88} +1.00000 q^{89} -2.70432 q^{90} -9.24237 q^{91} -31.9765 q^{92} -7.33038 q^{93} +30.4587 q^{94} +7.64191 q^{95} -18.8712 q^{96} -6.74861 q^{97} +22.5218 q^{98} +0.290736 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 5 q^{2} - 9 q^{3} + 11 q^{4} - 9 q^{5} - 5 q^{6} - 3 q^{7} + 18 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q + 5 * q^2 - 9 * q^3 + 11 * q^4 - 9 * q^5 - 5 * q^6 - 3 * q^7 + 18 * q^8 + 9 * q^9	\( 9 q + 5 q^{2} - 9 q^{3} + 11 q^{4} - 9 q^{5} - 5 q^{6} - 3 q^{7} + 18 q^{8} + 9 q^{9} - 5 q^{10} + 4 q^{11} - 11 q^{12} + 5 q^{13} - q^{14} + 9 q^{15} + 15 q^{16} + 21 q^{17} + 5 q^{18} - 18 q^{19} - 11 q^{20} + 3 q^{21} + 6 q^{22} + 16 q^{23} - 18 q^{24} + 9 q^{25} + 8 q^{26} - 9 q^{27} + 6 q^{28} + 3 q^{29} + 5 q^{30} - 6 q^{31} + 46 q^{32} - 4 q^{33} + 12 q^{34} + 3 q^{35} + 11 q^{36} + 11 q^{37} + 20 q^{38} - 5 q^{39} - 18 q^{40} - q^{41} + q^{42} - 3 q^{43} + 38 q^{44} - 9 q^{45} + 16 q^{46} + 27 q^{47} - 15 q^{48} + 24 q^{49} + 5 q^{50} - 21 q^{51} + 17 q^{52} + 43 q^{53} - 5 q^{54} - 4 q^{55} + 5 q^{56} + 18 q^{57} + 34 q^{58} + 3 q^{59} + 11 q^{60} - 30 q^{61} + 36 q^{62} - 3 q^{63} + 50 q^{64} - 5 q^{65} - 6 q^{66} - 12 q^{67} + 64 q^{68} - 16 q^{69} + q^{70} - 4 q^{71} + 18 q^{72} + 26 q^{73} + 2 q^{74} - 9 q^{75} - 12 q^{76} + 34 q^{77} - 8 q^{78} + q^{79} - 15 q^{80} + 9 q^{81} - 51 q^{82} + 24 q^{83} - 6 q^{84} - 21 q^{85} + 18 q^{86} - 3 q^{87} + 64 q^{88} + 9 q^{89} - 5 q^{90} - 50 q^{91} + 10 q^{92} + 6 q^{93} - 11 q^{94} + 18 q^{95} - 46 q^{96} - 4 q^{97} + 75 q^{98} + 4 q^{99}+O(q^{100}) \) 9 * q + 5 * q^2 - 9 * q^3 + 11 * q^4 - 9 * q^5 - 5 * q^6 - 3 * q^7 + 18 * q^8 + 9 * q^9 - 5 * q^10 + 4 * q^11 - 11 * q^12 + 5 * q^13 - q^14 + 9 * q^15 + 15 * q^16 + 21 * q^17 + 5 * q^18 - 18 * q^19 - 11 * q^20 + 3 * q^21 + 6 * q^22 + 16 * q^23 - 18 * q^24 + 9 * q^25 + 8 * q^26 - 9 * q^27 + 6 * q^28 + 3 * q^29 + 5 * q^30 - 6 * q^31 + 46 * q^32 - 4 * q^33 + 12 * q^34 + 3 * q^35 + 11 * q^36 + 11 * q^37 + 20 * q^38 - 5 * q^39 - 18 * q^40 - q^41 + q^42 - 3 * q^43 + 38 * q^44 - 9 * q^45 + 16 * q^46 + 27 * q^47 - 15 * q^48 + 24 * q^49 + 5 * q^50 - 21 * q^51 + 17 * q^52 + 43 * q^53 - 5 * q^54 - 4 * q^55 + 5 * q^56 + 18 * q^57 + 34 * q^58 + 3 * q^59 + 11 * q^60 - 30 * q^61 + 36 * q^62 - 3 * q^63 + 50 * q^64 - 5 * q^65 - 6 * q^66 - 12 * q^67 + 64 * q^68 - 16 * q^69 + q^70 - 4 * q^71 + 18 * q^72 + 26 * q^73 + 2 * q^74 - 9 * q^75 - 12 * q^76 + 34 * q^77 - 8 * q^78 + q^79 - 15 * q^80 + 9 * q^81 - 51 * q^82 + 24 * q^83 - 6 * q^84 - 21 * q^85 + 18 * q^86 - 3 * q^87 + 64 * q^88 + 9 * q^89 - 5 * q^90 - 50 * q^91 + 10 * q^92 + 6 * q^93 - 11 * q^94 + 18 * q^95 - 46 * q^96 - 4 * q^97 + 75 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.70432	1.91224	0.956120	−	0.292974i	$-0.0946449\pi$
$2$	2.70432	1.91224	0.956120	+	0.292974i	$0.0946449\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.31333	2.65667
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.70432	−1.10403
$7$	3.91511	1.47977	0.739886	−	0.672732i	$-0.234879\pi$
$7$	3.91511	1.47977	0.739886	+	0.672732i	$0.234879\pi$
$8$	8.96030	3.16794
$9$	1.00000	0.333333
$10$	−2.70432	−0.855180
$11$	0.290736	0.0876602	0.0438301	−	0.999039i	$-0.486044\pi$
$11$	0.290736	0.0876602	0.0438301	+	0.999039i	$0.486044\pi$
$12$	−5.31333	−1.53383
$13$	−2.36069	−0.654738	−0.327369	−	0.944896i	$-0.606162\pi$
$13$	−2.36069	−0.654738	−0.327369	+	0.944896i	$0.606162\pi$
$14$	10.5877	2.82968
$15$	1.00000	0.258199
$16$	13.6048	3.40120
$17$	4.13501	1.00289	0.501443	−	0.865191i	$-0.332803\pi$
$17$	4.13501	1.00289	0.501443	+	0.865191i	$0.332803\pi$
$18$	2.70432	0.637414
$19$	−7.64191	−1.75317	−0.876587	−	0.481244i	$-0.840185\pi$
$19$	−7.64191	−1.75317	−0.876587	+	0.481244i	$0.840185\pi$
$20$	−5.31333	−1.18810
$21$	−3.91511	−0.854347
$22$	0.786242	0.167627
$23$	−6.01817	−1.25488	−0.627438	−	0.778667i	$-0.715896\pi$
$23$	−6.01817	−1.25488	−0.627438	+	0.778667i	$0.715896\pi$
$24$	−8.96030	−1.82901
$25$	1.00000	0.200000
$26$	−6.38406	−1.25202
$27$	−1.00000	−0.192450
$28$	20.8023	3.93126
$29$	8.87608	1.64825	0.824124	−	0.566410i	$-0.191668\pi$
$29$	8.87608	1.64825	0.824124	+	0.566410i	$0.191668\pi$
$30$	2.70432	0.493738
$31$	7.33038	1.31658	0.658288	−	0.752766i	$-0.271281\pi$
$31$	7.33038	1.31658	0.658288	+	0.752766i	$0.271281\pi$
$32$	18.8712	3.33598
$33$	−0.290736	−0.0506106
$34$	11.1824	1.91776
$35$	−3.91511	−0.661774
$36$	5.31333	0.885555
$37$	0.927874	0.152541	0.0762707	−	0.997087i	$-0.475699\pi$
$37$	0.927874	0.152541	0.0762707	+	0.997087i	$0.475699\pi$
$38$	−20.6661	−3.35249
$39$	2.36069	0.378013
$40$	−8.96030	−1.41675
$41$	−10.6233	−1.65908	−0.829541	−	0.558446i	$-0.811398\pi$
$41$	−10.6233	−1.65908	−0.829541	+	0.558446i	$0.811398\pi$
$42$	−10.5877	−1.63372
$43$	−9.40345	−1.43401	−0.717007	−	0.697066i	$-0.754488\pi$
$43$	−9.40345	−1.43401	−0.717007	+	0.697066i	$0.754488\pi$
$44$	1.54478	0.232884
$45$	−1.00000	−0.149071
$46$	−16.2751	−2.39963
$47$	11.2630	1.64288	0.821438	−	0.570298i	$-0.193172\pi$
$47$	11.2630	1.64288	0.821438	+	0.570298i	$0.193172\pi$
$48$	−13.6048	−1.96369
$49$	8.32807	1.18972
$50$	2.70432	0.382448
$51$	−4.13501	−0.579017
$52$	−12.5431	−1.73942
$53$	4.74498	0.651773	0.325887	−	0.945409i	$-0.394337\pi$
$53$	4.74498	0.651773	0.325887	+	0.945409i	$0.394337\pi$
$54$	−2.70432	−0.368011
$55$	−0.290736	−0.0392028
$56$	35.0805	4.68783
$57$	7.64191	1.01220
$58$	24.0037	3.15185
$59$	−8.49811	−1.10636	−0.553180	−	0.833062i	$-0.686586\pi$
$59$	−8.49811	−1.10636	−0.553180	+	0.833062i	$0.686586\pi$
$60$	5.31333	0.685948
$61$	−2.98630	−0.382356	−0.191178	−	0.981555i	$-0.561231\pi$
$61$	−2.98630	−0.382356	−0.191178	+	0.981555i	$0.561231\pi$
$62$	19.8237	2.51761
$63$	3.91511	0.493257
$64$	23.8239	2.97799
$65$	2.36069	0.292808
$66$	−0.786242	−0.0967797
$67$	−7.70384	−0.941174	−0.470587	−	0.882354i	$-0.655958\pi$
$67$	−7.70384	−0.941174	−0.470587	+	0.882354i	$0.655958\pi$
$68$	21.9706	2.66433
$69$	6.01817	0.724503
$70$	−10.5877	−1.26547
$71$	4.65945	0.552975	0.276488	−	0.961017i	$-0.410830\pi$
$71$	4.65945	0.552975	0.276488	+	0.961017i	$0.410830\pi$
$72$	8.96030	1.05598
$73$	−11.9200	−1.39513	−0.697566	−	0.716520i	$-0.745734\pi$
$73$	−11.9200	−1.39513	−0.697566	+	0.716520i	$0.745734\pi$
$74$	2.50926	0.291696
$75$	−1.00000	−0.115470
$76$	−40.6040	−4.65760
$77$	1.13826	0.129717
$78$	6.38406	0.722853
$79$	13.5279	1.52201	0.761004	−	0.648748i	$-0.224707\pi$
$79$	13.5279	1.52201	0.761004	+	0.648748i	$0.224707\pi$
$80$	−13.6048	−1.52107
$81$	1.00000	0.111111
$82$	−28.7288	−3.17257
$83$	3.43747	0.377311	0.188655	−	0.982043i	$-0.439587\pi$
$83$	3.43747	0.377311	0.188655	+	0.982043i	$0.439587\pi$
$84$	−20.8023	−2.26971
$85$	−4.13501	−0.448504
$86$	−25.4299	−2.74218
$87$	−8.87608	−0.951616
$88$	2.60508	0.277702
$89$	1.00000	0.106000
$89$	1.00000	0.106000
$90$	−2.70432	−0.285060
$91$	−9.24237	−0.968864
$92$	−31.9765	−3.33379
$93$	−7.33038	−0.760125
$94$	30.4587	3.14157
$95$	7.64191	0.784043
$96$	−18.8712	−1.92603
$97$	−6.74861	−0.685218	−0.342609	−	0.939478i	$-0.611311\pi$
$97$	−6.74861	−0.685218	−0.342609	+	0.939478i	$0.611311\pi$
$98$	22.5218	2.27504
$99$	0.290736	0.0292201
$100$	5.31333	0.531333
$101$	−2.94829	−0.293366	−0.146683	−	0.989184i	$-0.546860\pi$
$101$	−2.94829	−0.293366	−0.146683	+	0.989184i	$0.546860\pi$
$102$	−11.1824	−1.10722
$103$	−2.72989	−0.268984	−0.134492	−	0.990915i	$-0.542940\pi$
$103$	−2.72989	−0.268984	−0.134492	+	0.990915i	$0.542940\pi$
$104$	−21.1525	−2.07417
$105$	3.91511	0.382075
$106$	12.8319	1.24635
$107$	5.39163	0.521229	0.260614	−	0.965443i	$-0.416075\pi$
$107$	5.39163	0.521229	0.260614	+	0.965443i	$0.416075\pi$
$108$	−5.31333	−0.511275
$109$	−13.3308	−1.27686	−0.638430	−	0.769680i	$-0.720416\pi$
$109$	−13.3308	−1.27686	−0.638430	+	0.769680i	$0.720416\pi$
$110$	−0.786242	−0.0749652
$111$	−0.927874	−0.0880699
$112$	53.2643	5.03301
$113$	−5.75372	−0.541264	−0.270632	−	0.962683i	$-0.587233\pi$
$113$	−5.75372	−0.541264	−0.270632	+	0.962683i	$0.587233\pi$
$114$	20.6661	1.93556
$115$	6.01817	0.561198
$116$	47.1616	4.37884
$117$	−2.36069	−0.218246
$118$	−22.9816	−2.11563
$119$	16.1890	1.48404
$120$	8.96030	0.817959
$121$	−10.9155	−0.992316
$122$	−8.07590	−0.731157
$123$	10.6233	0.957872
$124$	38.9487	3.49770
$125$	−1.00000	−0.0894427
$126$	10.5877	0.943227
$127$	−15.5337	−1.37839	−0.689197	−	0.724574i	$-0.742037\pi$
$127$	−15.5337	−1.37839	−0.689197	+	0.724574i	$0.742037\pi$
$128$	26.6852	2.35866
$129$	9.40345	0.827928
$130$	6.38406	0.559919
$131$	−8.52018	−0.744411	−0.372206	−	0.928150i	$-0.621398\pi$
$131$	−8.52018	−0.744411	−0.372206	+	0.928150i	$0.621398\pi$
$132$	−1.54478	−0.134455
$133$	−29.9189	−2.59430
$134$	−20.8336	−1.79975
$135$	1.00000	0.0860663
$136$	37.0509	3.17709
$137$	11.2125	0.957949	0.478975	−	0.877829i	$-0.341009\pi$
$137$	11.2125	0.957949	0.478975	+	0.877829i	$0.341009\pi$
$138$	16.2751	1.38542
$139$	−20.0296	−1.69889	−0.849446	−	0.527676i	$-0.823064\pi$
$139$	−20.0296	−1.69889	−0.849446	+	0.527676i	$0.823064\pi$
$140$	−20.8023	−1.75811
$141$	−11.2630	−0.948515
$142$	12.6006	1.05742
$143$	−0.686338	−0.0573945
$144$	13.6048	1.13373
$145$	−8.87608	−0.737118
$146$	−32.2355	−2.66783
$147$	−8.32807	−0.686888
$148$	4.93010	0.405252
$149$	16.2201	1.32880	0.664402	−	0.747375i	$-0.268686\pi$
$149$	16.2201	1.32880	0.664402	+	0.747375i	$0.268686\pi$
$150$	−2.70432	−0.220807
$151$	12.8001	1.04166	0.520828	−	0.853662i	$-0.325623\pi$
$151$	12.8001	1.04166	0.520828	+	0.853662i	$0.325623\pi$
$152$	−68.4737	−5.55395
$153$	4.13501	0.334295
$154$	3.07822	0.248050
$155$	−7.33038	−0.588790
$156$	12.5431	1.00426
$157$	1.96635	0.156932	0.0784659	−	0.996917i	$-0.474998\pi$
$157$	1.96635	0.156932	0.0784659	+	0.996917i	$0.474998\pi$
$158$	36.5837	2.91044
$159$	−4.74498	−0.376301
$160$	−18.8712	−1.49190
$161$	−23.5618	−1.85693
$162$	2.70432	0.212471
$163$	0.152079	0.0119117	0.00595586	−	0.999982i	$-0.498104\pi$
$163$	0.152079	0.0119117	0.00595586	+	0.999982i	$0.498104\pi$
$164$	−56.4452	−4.40763
$165$	0.290736	0.0226338
$166$	9.29600	0.721509
$167$	−9.41133	−0.728271	−0.364135	−	0.931346i	$-0.618635\pi$
$167$	−9.41133	−0.728271	−0.364135	+	0.931346i	$0.618635\pi$
$168$	−35.0805	−2.70652
$169$	−7.42713	−0.571318
$170$	−11.1824	−0.857648
$171$	−7.64191	−0.584391
$172$	−49.9637	−3.80969
$173$	−4.96550	−0.377520	−0.188760	−	0.982023i	$-0.560447\pi$
$173$	−4.96550	−0.377520	−0.188760	+	0.982023i	$0.560447\pi$
$174$	−24.0037	−1.81972
$175$	3.91511	0.295954
$176$	3.95541	0.298150
$177$	8.49811	0.638757
$178$	2.70432	0.202697
$179$	−22.0675	−1.64940	−0.824701	−	0.565569i	$-0.808657\pi$
$179$	−22.0675	−1.64940	−0.824701	+	0.565569i	$0.808657\pi$
$180$	−5.31333	−0.396032
$181$	14.3322	1.06530	0.532651	−	0.846335i	$-0.321196\pi$
$181$	14.3322	1.06530	0.532651	+	0.846335i	$0.321196\pi$
$182$	−24.9943	−1.85270
$183$	2.98630	0.220753
$184$	−53.9246	−3.97538
$185$	−0.927874	−0.0682186
$186$	−19.8237	−1.45354
$187$	1.20219	0.0879132
$188$	59.8440	4.36457
$189$	−3.91511	−0.284782
$190$	20.6661	1.49928
$191$	−6.35834	−0.460073	−0.230037	−	0.973182i	$-0.573885\pi$
$191$	−6.35834	−0.460073	−0.230037	+	0.973182i	$0.573885\pi$
$192$	−23.8239	−1.71934
$193$	7.73028	0.556438	0.278219	−	0.960518i	$-0.410256\pi$
$193$	7.73028	0.556438	0.278219	+	0.960518i	$0.410256\pi$
$194$	−18.2504	−1.31030
$195$	−2.36069	−0.169053
$196$	44.2498	3.16070
$197$	16.1717	1.15218	0.576092	−	0.817385i	$-0.304577\pi$
$197$	16.1717	1.15218	0.576092	+	0.817385i	$0.304577\pi$
$198$	0.786242	0.0558758
$199$	6.87573	0.487408	0.243704	−	0.969850i	$-0.421637\pi$
$199$	6.87573	0.487408	0.243704	+	0.969850i	$0.421637\pi$
$200$	8.96030	0.633589
$201$	7.70384	0.543387
$202$	−7.97312	−0.560987
$203$	34.7508	2.43903
$204$	−21.9706	−1.53825
$205$	10.6233	0.741964
$206$	−7.38250	−0.514363
$207$	−6.01817	−0.418292
$208$	−32.1168	−2.22690
$209$	−2.22178	−0.153684
$210$	10.5877	0.730620
$211$	−10.8883	−0.749584	−0.374792	−	0.927109i	$-0.622286\pi$
$211$	−10.8883	−0.749584	−0.374792	+	0.927109i	$0.622286\pi$
$212$	25.2117	1.73154
$213$	−4.65945	−0.319260
$214$	14.5807	0.996715
$215$	9.40345	0.641310
$216$	−8.96030	−0.609671
$217$	28.6992	1.94823
$218$	−36.0507	−2.44166
$219$	11.9200	0.805480
$220$	−1.54478	−0.104149
$221$	−9.76148	−0.656628
$222$	−2.50926	−0.168411
$223$	17.5914	1.17801	0.589003	−	0.808131i	$-0.299521\pi$
$223$	17.5914	1.17801	0.589003	+	0.808131i	$0.299521\pi$
$224$	73.8826	4.93649
$225$	1.00000	0.0666667
$226$	−15.5599	−1.03503
$227$	0.611391	0.0405794	0.0202897	−	0.999794i	$-0.493541\pi$
$227$	0.611391	0.0405794	0.0202897	+	0.999794i	$0.493541\pi$
$228$	40.6040	2.68906
$229$	−3.20075	−0.211512	−0.105756	−	0.994392i	$-0.533726\pi$
$229$	−3.20075	−0.211512	−0.105756	+	0.994392i	$0.533726\pi$
$230$	16.2751	1.07315
$231$	−1.13826	−0.0748922
$232$	79.5323	5.22155
$233$	7.75674	0.508161	0.254080	−	0.967183i	$-0.418227\pi$
$233$	7.75674	0.508161	0.254080	+	0.967183i	$0.418227\pi$
$234$	−6.38406	−0.417339
$235$	−11.2630	−0.734717
$236$	−45.1532	−2.93923
$237$	−13.5279	−0.878731
$238$	43.7802	2.83785
$239$	−28.1059	−1.81802	−0.909011	−	0.416773i	$-0.863161\pi$
$239$	−28.1059	−1.81802	−0.909011	+	0.416773i	$0.863161\pi$
$240$	13.6048	0.878187
$241$	−18.8774	−1.21600	−0.608001	−	0.793937i	$-0.708028\pi$
$241$	−18.8774	−1.21600	−0.608001	+	0.793937i	$0.708028\pi$
$242$	−29.5189	−1.89755
$243$	−1.00000	−0.0641500
$244$	−15.8672	−1.01579
$245$	−8.32807	−0.532061
$246$	28.7288	1.83168
$247$	18.0402	1.14787
$248$	65.6824	4.17084
$249$	−3.43747	−0.217840
$250$	−2.70432	−0.171036
$251$	9.95645	0.628446	0.314223	−	0.949349i	$-0.398256\pi$
$251$	9.95645	0.628446	0.314223	+	0.949349i	$0.398256\pi$
$252$	20.8023	1.31042
$253$	−1.74970	−0.110003
$254$	−42.0081	−2.63582
$255$	4.13501	0.258944
$256$	24.5173	1.53233
$257$	−8.21867	−0.512666	−0.256333	−	0.966588i	$-0.582514\pi$
$257$	−8.21867	−0.512666	−0.256333	+	0.966588i	$0.582514\pi$
$258$	25.4299	1.58320
$259$	3.63273	0.225727
$260$	12.5431	0.777893
$261$	8.87608	0.549416
$262$	−23.0413	−1.42349
$263$	21.1125	1.30186	0.650928	−	0.759140i	$-0.274380\pi$
$263$	21.1125	1.30186	0.650928	+	0.759140i	$0.274380\pi$
$264$	−2.60508	−0.160332
$265$	−4.74498	−0.291482
$266$	−80.9102	−4.96092
$267$	−1.00000	−0.0611990
$268$	−40.9330	−2.50038
$269$	−1.76519	−0.107625	−0.0538126	−	0.998551i	$-0.517137\pi$
$269$	−1.76519	−0.107625	−0.0538126	+	0.998551i	$0.517137\pi$
$270$	2.70432	0.164579
$271$	4.26799	0.259262	0.129631	−	0.991562i	$-0.458621\pi$
$271$	4.26799	0.259262	0.129631	+	0.991562i	$0.458621\pi$
$272$	56.2560	3.41102
$273$	9.24237	0.559374
$274$	30.3222	1.83183
$275$	0.290736	0.0175320
$276$	31.9765	1.92476
$277$	8.15122	0.489760	0.244880	−	0.969553i	$-0.421252\pi$
$277$	8.15122	0.489760	0.244880	+	0.969553i	$0.421252\pi$
$278$	−54.1665	−3.24869
$279$	7.33038	0.438858
$280$	−35.0805	−2.09646
$281$	23.1441	1.38066	0.690330	−	0.723494i	$-0.257465\pi$
$281$	23.1441	1.38066	0.690330	+	0.723494i	$0.257465\pi$
$282$	−30.4587	−1.81379
$283$	0.495284	0.0294416	0.0147208	−	0.999892i	$-0.495314\pi$
$283$	0.495284	0.0294416	0.0147208	+	0.999892i	$0.495314\pi$
$284$	24.7572	1.46907
$285$	−7.64191	−0.452667
$286$	−1.85608	−0.109752
$287$	−41.5914	−2.45506
$288$	18.8712	1.11199
$289$	0.0982690	0.00578053
$290$	−24.0037	−1.40955
$291$	6.74861	0.395611
$292$	−63.3350	−3.70640
$293$	20.8859	1.22017	0.610084	−	0.792337i	$-0.291136\pi$
$293$	20.8859	1.22017	0.610084	+	0.792337i	$0.291136\pi$
$294$	−22.5218	−1.31350
$295$	8.49811	0.494779
$296$	8.31402	0.483243
$297$	−0.290736	−0.0168702
$298$	43.8644	2.54099
$299$	14.2071	0.821616
$300$	−5.31333	−0.306765
$301$	−36.8155	−2.12201
$302$	34.6155	1.99190
$303$	2.94829	0.169375
$304$	−103.967	−5.96290
$305$	2.98630	0.170995
$306$	11.1824	0.639253
$307$	26.2842	1.50012	0.750060	−	0.661370i	$-0.230025\pi$
$307$	26.2842	1.50012	0.750060	+	0.661370i	$0.230025\pi$
$308$	6.04797	0.344615
$309$	2.72989	0.155298
$310$	−19.8237	−1.12591
$311$	8.05572	0.456798	0.228399	−	0.973568i	$-0.426651\pi$
$311$	8.05572	0.456798	0.228399	+	0.973568i	$0.426651\pi$
$312$	21.1525	1.19752
$313$	19.8942	1.12449	0.562245	−	0.826971i	$-0.309938\pi$
$313$	19.8942	1.12449	0.562245	+	0.826971i	$0.309938\pi$
$314$	5.31763	0.300091
$315$	−3.91511	−0.220591
$316$	71.8782	4.04346
$317$	9.08595	0.510318	0.255159	−	0.966899i	$-0.417872\pi$
$317$	9.08595	0.510318	0.255159	+	0.966899i	$0.417872\pi$
$318$	−12.8319	−0.719579
$319$	2.58060	0.144486
$320$	−23.8239	−1.33180
$321$	−5.39163	−0.300932
$322$	−63.7186	−3.55090
$323$	−31.5993	−1.75823
$324$	5.31333	0.295185
$325$	−2.36069	−0.130948
$326$	0.411269	0.0227781
$327$	13.3308	0.737195
$328$	−95.1880	−5.25588
$329$	44.0958	2.43108
$330$	0.786242	0.0432812
$331$	31.7850	1.74706	0.873530	−	0.486771i	$-0.161825\pi$
$331$	31.7850	1.74706	0.873530	+	0.486771i	$0.161825\pi$
$332$	18.2644	1.00239
$333$	0.927874	0.0508472
$334$	−25.4512	−1.39263
$335$	7.70384	0.420906
$336$	−53.2643	−2.90581
$337$	3.71554	0.202398	0.101199	−	0.994866i	$-0.467732\pi$
$337$	3.71554	0.202398	0.101199	+	0.994866i	$0.467732\pi$
$338$	−20.0853	−1.09250
$339$	5.75372	0.312499
$340$	−21.9706	−1.19153
$341$	2.13121	0.115411
$342$	−20.6661	−1.11750
$343$	5.19955	0.280750
$344$	−84.2577	−4.54287
$345$	−6.01817	−0.324008
$346$	−13.4283	−0.721909
$347$	8.95640	0.480805	0.240402	−	0.970673i	$-0.422721\pi$
$347$	8.95640	0.480805	0.240402	+	0.970673i	$0.422721\pi$
$348$	−47.1616	−2.52812
$349$	−6.54543	−0.350369	−0.175185	−	0.984536i	$-0.556052\pi$
$349$	−6.54543	−0.350369	−0.175185	+	0.984536i	$0.556052\pi$
$350$	10.5877	0.565936
$351$	2.36069	0.126004
$352$	5.48652	0.292433
$353$	18.3177	0.974953	0.487476	−	0.873136i	$-0.337918\pi$
$353$	18.3177	0.974953	0.487476	+	0.873136i	$0.337918\pi$
$354$	22.9816	1.22146
$355$	−4.65945	−0.247298
$356$	5.31333	0.281606
$357$	−16.1890	−0.856812
$358$	−59.6775	−3.15406
$359$	11.6477	0.614740	0.307370	−	0.951590i	$-0.400551\pi$
$359$	11.6477	0.614740	0.307370	+	0.951590i	$0.400551\pi$
$360$	−8.96030	−0.472249
$361$	39.3987	2.07362
$362$	38.7587	2.03711
$363$	10.9155	0.572914
$364$	−49.1078	−2.57395
$365$	11.9200	0.623922
$366$	8.07590	0.422134
$367$	−22.7882	−1.18954	−0.594768	−	0.803897i	$-0.702756\pi$
$367$	−22.7882	−1.18954	−0.594768	+	0.803897i	$0.702756\pi$
$368$	−81.8762	−4.26809
$369$	−10.6233	−0.553027
$370$	−2.50926	−0.130450
$371$	18.5771	0.964476
$372$	−38.9487	−2.01940
$373$	19.1659	0.992374	0.496187	−	0.868216i	$-0.334733\pi$
$373$	19.1659	0.992374	0.496187	+	0.868216i	$0.334733\pi$
$374$	3.25112	0.168111
$375$	1.00000	0.0516398
$376$	100.920	5.20454
$377$	−20.9537	−1.07917
$378$	−10.5877	−0.544572
$379$	−36.4928	−1.87451	−0.937255	−	0.348646i	$-0.886642\pi$
$379$	−36.4928	−1.87451	−0.937255	+	0.348646i	$0.886642\pi$
$380$	40.6040	2.08294
$381$	15.5337	0.795816
$382$	−17.1950	−0.879770
$383$	−23.1764	−1.18426	−0.592129	−	0.805843i	$-0.701713\pi$
$383$	−23.1764	−1.18426	−0.592129	+	0.805843i	$0.701713\pi$
$384$	−26.6852	−1.36177
$385$	−1.13826	−0.0580112
$386$	20.9051	1.06404
$387$	−9.40345	−0.478004
$388$	−35.8576	−1.82039
$389$	11.8330	0.599955	0.299978	−	0.953946i	$-0.403021\pi$
$389$	11.8330	0.599955	0.299978	+	0.953946i	$0.403021\pi$
$390$	−6.38406	−0.323270
$391$	−24.8852	−1.25850
$392$	74.6220	3.76898
$393$	8.52018	0.429786
$394$	43.7334	2.20325
$395$	−13.5279	−0.680662
$396$	1.54478	0.0776279
$397$	−6.87506	−0.345050	−0.172525	−	0.985005i	$-0.555192\pi$
$397$	−6.87506	−0.345050	−0.172525	+	0.985005i	$0.555192\pi$
$398$	18.5942	0.932041
$399$	29.9189	1.49782
$400$	13.6048	0.680241
$401$	1.27432	0.0636367	0.0318184	−	0.999494i	$-0.489870\pi$
$401$	1.27432	0.0636367	0.0318184	+	0.999494i	$0.489870\pi$
$402$	20.8336	1.03909
$403$	−17.3048	−0.862013
$404$	−15.6653	−0.779376
$405$	−1.00000	−0.0496904
$406$	93.9772	4.66401
$407$	0.269766	0.0133718
$408$	−37.0509	−1.83429
$409$	28.2287	1.39582	0.697910	−	0.716185i	$-0.254113\pi$
$409$	28.2287	1.39582	0.697910	+	0.716185i	$0.254113\pi$
$410$	28.7288	1.41881
$411$	−11.2125	−0.553072
$412$	−14.5048	−0.714602
$413$	−33.2710	−1.63716
$414$	−16.2751	−0.799875
$415$	−3.43747	−0.168739
$416$	−44.5490	−2.18419
$417$	20.0296	0.980855
$418$	−6.00839	−0.293880
$419$	12.3685	0.604241	0.302121	−	0.953270i	$-0.402305\pi$
$419$	12.3685	0.604241	0.302121	+	0.953270i	$0.402305\pi$
$420$	20.8023	1.01505
$421$	−23.8509	−1.16242	−0.581210	−	0.813754i	$-0.697420\pi$
$421$	−23.8509	−1.16242	−0.581210	+	0.813754i	$0.697420\pi$
$422$	−29.4455	−1.43339
$423$	11.2630	0.547625
$424$	42.5164	2.06478
$425$	4.13501	0.200577
$426$	−12.6006	−0.610503
$427$	−11.6917	−0.565800
$428$	28.6475	1.38473
$429$	0.686338	0.0331367
$430$	25.4299	1.22634
$431$	2.87409	0.138440	0.0692200	−	0.997601i	$-0.477949\pi$
$431$	2.87409	0.138440	0.0692200	+	0.997601i	$0.477949\pi$
$432$	−13.6048	−0.654562
$433$	23.0356	1.10702	0.553510	−	0.832843i	$-0.313288\pi$
$433$	23.0356	1.10702	0.553510	+	0.832843i	$0.313288\pi$
$434$	77.6118	3.72549
$435$	8.87608	0.425576
$436$	−70.8310	−3.39219
$437$	45.9903	2.20002
$438$	32.2355	1.54027
$439$	−7.98024	−0.380876	−0.190438	−	0.981699i	$-0.560991\pi$
$439$	−7.98024	−0.380876	−0.190438	+	0.981699i	$0.560991\pi$
$440$	−2.60508	−0.124192
$441$	8.32807	0.396575
$442$	−26.3981	−1.25563
$443$	7.28163	0.345961	0.172980	−	0.984925i	$-0.444660\pi$
$443$	7.28163	0.345961	0.172980	+	0.984925i	$0.444660\pi$
$444$	−4.93010	−0.233972
$445$	−1.00000	−0.0474045
$446$	47.5727	2.25263
$447$	−16.2201	−0.767185
$448$	93.2733	4.40675
$449$	16.2637	0.767531	0.383765	−	0.923431i	$-0.374627\pi$
$449$	16.2637	0.767531	0.383765	+	0.923431i	$0.374627\pi$
$450$	2.70432	0.127483
$451$	−3.08858	−0.145435
$452$	−30.5714	−1.43796
$453$	−12.8001	−0.601400
$454$	1.65339	0.0775977
$455$	9.24237	0.433289
$456$	68.4737	3.20658
$457$	29.1422	1.36321	0.681607	−	0.731719i	$-0.261282\pi$
$457$	29.1422	1.36321	0.681607	+	0.731719i	$0.261282\pi$
$458$	−8.65585	−0.404461
$459$	−4.13501	−0.193006
$460$	31.9765	1.49091
$461$	7.11329	0.331299	0.165650	−	0.986185i	$-0.447028\pi$
$461$	7.11329	0.331299	0.165650	+	0.986185i	$0.447028\pi$
$462$	−3.07822	−0.143212
$463$	−15.4906	−0.719911	−0.359955	−	0.932969i	$-0.617208\pi$
$463$	−15.4906	−0.719911	−0.359955	+	0.932969i	$0.617208\pi$
$464$	120.757	5.60603
$465$	7.33038	0.339938
$466$	20.9767	0.971726
$467$	29.5394	1.36692	0.683461	−	0.729987i	$-0.260474\pi$
$467$	29.5394	1.36692	0.683461	+	0.729987i	$0.260474\pi$
$468$	−12.5431	−0.579807
$469$	−30.1614	−1.39272
$470$	−30.4587	−1.40495
$471$	−1.96635	−0.0906046
$472$	−76.1455	−3.50488
$473$	−2.73392	−0.125706
$474$	−36.5837	−1.68035
$475$	−7.64191	−0.350635
$476$	86.0175	3.94260
$477$	4.74498	0.217258
$478$	−76.0073	−3.47649
$479$	−4.05176	−0.185129	−0.0925647	−	0.995707i	$-0.529507\pi$
$479$	−4.05176	−0.185129	−0.0925647	+	0.995707i	$0.529507\pi$
$480$	18.8712	0.861346
$481$	−2.19042	−0.0998748
$482$	−51.0505	−2.32529
$483$	23.5618	1.07210
$484$	−57.9975	−2.63625
$485$	6.74861	0.306439
$486$	−2.70432	−0.122670
$487$	−18.7820	−0.851092	−0.425546	−	0.904937i	$-0.639918\pi$
$487$	−18.7820	−0.851092	−0.425546	+	0.904937i	$0.639918\pi$
$488$	−26.7581	−1.21128
$489$	−0.152079	−0.00687723
$490$	−22.5218	−1.01743
$491$	−5.77459	−0.260604	−0.130302	−	0.991474i	$-0.541595\pi$
$491$	−5.77459	−0.260604	−0.130302	+	0.991474i	$0.541595\pi$
$492$	56.4452	2.54474
$493$	36.7026	1.65300
$494$	48.7864	2.19500
$495$	−0.290736	−0.0130676
$496$	99.7285	4.47794
$497$	18.2423	0.818277
$498$	−9.29600	−0.416564
$499$	−25.9609	−1.16217	−0.581086	−	0.813842i	$-0.697372\pi$
$499$	−25.9609	−1.16217	−0.581086	+	0.813842i	$0.697372\pi$
$500$	−5.31333	−0.237619
$501$	9.41133	0.420467
$502$	26.9254	1.20174
$503$	19.4539	0.867407	0.433704	−	0.901056i	$-0.357206\pi$
$503$	19.4539	0.867407	0.433704	+	0.901056i	$0.357206\pi$
$504$	35.0805	1.56261
$505$	2.94829	0.131197
$506$	−4.73174	−0.210352
$507$	7.42713	0.329850
$508$	−82.5358	−3.66193
$509$	6.14500	0.272372	0.136186	−	0.990683i	$-0.456515\pi$
$509$	6.14500	0.272372	0.136186	+	0.990683i	$0.456515\pi$
$510$	11.1824	0.495163
$511$	−46.6682	−2.06448
$512$	12.9322	0.571529
$513$	7.64191	0.337398
$514$	−22.2259	−0.980342
$515$	2.72989	0.120294
$516$	49.9637	2.19953
$517$	3.27456	0.144015
$518$	9.82404	0.431644
$519$	4.96550	0.217961
$520$	21.1525	0.927599
$521$	−10.9960	−0.481742	−0.240871	−	0.970557i	$-0.577433\pi$
$521$	−10.9960	−0.481742	−0.240871	+	0.970557i	$0.577433\pi$
$522$	24.0037	1.05062
$523$	37.9162	1.65796	0.828979	−	0.559280i	$-0.188922\pi$
$523$	37.9162	1.65796	0.828979	+	0.559280i	$0.188922\pi$
$524$	−45.2705	−1.97765
$525$	−3.91511	−0.170869
$526$	57.0950	2.48946
$527$	30.3112	1.32038
$528$	−3.95541	−0.172137
$529$	13.2184	0.574714
$530$	−12.8319	−0.557384
$531$	−8.49811	−0.368786
$532$	−158.969	−6.89218
$533$	25.0784	1.08626
$534$	−2.70432	−0.117027
$535$	−5.39163	−0.233101
$536$	−69.0287	−2.98158
$537$	22.0675	0.952283
$538$	−4.77362	−0.205805
$539$	2.42127	0.104291
$540$	5.31333	0.228649
$541$	3.31521	0.142532	0.0712660	−	0.997457i	$-0.477296\pi$
$541$	3.31521	0.142532	0.0712660	+	0.997457i	$0.477296\pi$
$542$	11.5420	0.495771
$543$	−14.3322	−0.615052
$544$	78.0323	3.34561
$545$	13.3308	0.571029
$546$	24.9943	1.06966
$547$	−19.7730	−0.845432	−0.422716	−	0.906262i	$-0.638923\pi$
$547$	−19.7730	−0.845432	−0.422716	+	0.906262i	$0.638923\pi$
$548$	59.5758	2.54495
$549$	−2.98630	−0.127452
$550$	0.786242	0.0335255
$551$	−67.8302	−2.88966
$552$	53.9246	2.29518
$553$	52.9632	2.25222
$554$	22.0435	0.936538
$555$	0.927874	0.0393860
$556$	−106.424	−4.51339
$557$	17.3478	0.735049	0.367525	−	0.930014i	$-0.380205\pi$
$557$	17.3478	0.735049	0.367525	+	0.930014i	$0.380205\pi$
$558$	19.8237	0.839203
$559$	22.1987	0.938904
$560$	−53.2643	−2.25083
$561$	−1.20219	−0.0507567
$562$	62.5890	2.64016
$563$	−24.6281	−1.03795	−0.518975	−	0.854789i	$-0.673686\pi$
$563$	−24.6281	−1.03795	−0.518975	+	0.854789i	$0.673686\pi$
$564$	−59.8440	−2.51989
$565$	5.75372	0.242061
$566$	1.33940	0.0562993
$567$	3.91511	0.164419
$568$	41.7501	1.75179
$569$	−30.3206	−1.27111	−0.635553	−	0.772057i	$-0.719228\pi$
$569$	−30.3206	−1.27111	−0.635553	+	0.772057i	$0.719228\pi$
$570$	−20.6661	−0.865609
$571$	−9.48083	−0.396760	−0.198380	−	0.980125i	$-0.563568\pi$
$571$	−9.48083	−0.396760	−0.198380	+	0.980125i	$0.563568\pi$
$572$	−3.64674	−0.152478
$573$	6.35834	0.265623
$574$	−112.476	−4.69467
$575$	−6.01817	−0.250975
$576$	23.8239	0.992664
$577$	10.4548	0.435240	0.217620	−	0.976034i	$-0.430171\pi$
$577$	10.4548	0.435240	0.217620	+	0.976034i	$0.430171\pi$
$578$	0.265750	0.0110538
$579$	−7.73028	−0.321259
$580$	−47.1616	−1.95828
$581$	13.4580	0.558334
$582$	18.2504	0.756503
$583$	1.37954	0.0571346
$584$	−106.807	−4.41970
$585$	2.36069	0.0976026
$586$	56.4821	2.33326
$587$	−23.5836	−0.973398	−0.486699	−	0.873570i	$-0.661799\pi$
$587$	−23.5836	−0.973398	−0.486699	+	0.873570i	$0.661799\pi$
$588$	−44.2498	−1.82483
$589$	−56.0181	−2.30819
$590$	22.9816	0.946136
$591$	−16.1717	−0.665214
$592$	12.6236	0.518825
$593$	23.1956	0.952530	0.476265	−	0.879302i	$-0.341990\pi$
$593$	23.1956	0.952530	0.476265	+	0.879302i	$0.341990\pi$
$594$	−0.786242	−0.0322599
$595$	−16.1890	−0.663684
$596$	86.1829	3.53019
$597$	−6.87573	−0.281405
$598$	38.4204	1.57113
$599$	−3.51234	−0.143510	−0.0717551	−	0.997422i	$-0.522860\pi$
$599$	−3.51234	−0.143510	−0.0717551	+	0.997422i	$0.522860\pi$
$600$	−8.96030	−0.365803
$601$	5.13651	0.209522	0.104761	−	0.994497i	$-0.466592\pi$
$601$	5.13651	0.209522	0.104761	+	0.994497i	$0.466592\pi$
$602$	−99.5609	−4.05780
$603$	−7.70384	−0.313725
$604$	68.0110	2.76733
$605$	10.9155	0.443777
$606$	7.97312	0.323886
$607$	3.14756	0.127755	0.0638777	−	0.997958i	$-0.479653\pi$
$607$	3.14756	0.127755	0.0638777	+	0.997958i	$0.479653\pi$
$608$	−144.212	−5.84855
$609$	−34.7508	−1.40817
$610$	8.07590	0.326983
$611$	−26.5885	−1.07565
$612$	21.9706	0.888111
$613$	16.6025	0.670568	0.335284	−	0.942117i	$-0.391168\pi$
$613$	16.6025	0.670568	0.335284	+	0.942117i	$0.391168\pi$
$614$	71.0809	2.86859
$615$	−10.6233	−0.428373
$616$	10.1992	0.410936
$617$	−41.0369	−1.65208	−0.826041	−	0.563610i	$-0.809412\pi$
$617$	−41.0369	−1.65208	−0.826041	+	0.563610i	$0.809412\pi$
$618$	7.38250	0.296968
$619$	11.3158	0.454820	0.227410	−	0.973799i	$-0.426974\pi$
$619$	11.3158	0.454820	0.227410	+	0.973799i	$0.426974\pi$
$620$	−38.9487	−1.56422
$621$	6.01817	0.241501
$622$	21.7852	0.873507
$623$	3.91511	0.156856
$624$	32.1168	1.28570
$625$	1.00000	0.0400000
$626$	53.8004	2.15029
$627$	2.22178	0.0887292
$628$	10.4479	0.416915
$629$	3.83676	0.152982
$630$	−10.5877	−0.421824
$631$	26.0023	1.03514	0.517568	−	0.855642i	$-0.326837\pi$
$631$	26.0023	1.03514	0.517568	+	0.855642i	$0.326837\pi$
$632$	121.214	4.82163
$633$	10.8883	0.432773
$634$	24.5713	0.975851
$635$	15.5337	0.616437
$636$	−25.2117	−0.999707
$637$	−19.6600	−0.778959
$638$	6.97875	0.276291
$639$	4.65945	0.184325
$640$	−26.6852	−1.05482
$641$	34.0199	1.34370	0.671852	−	0.740685i	$-0.265499\pi$
$641$	34.0199	1.34370	0.671852	+	0.740685i	$0.265499\pi$
$642$	−14.5807	−0.575454
$643$	−40.6945	−1.60483	−0.802417	−	0.596763i	$-0.796453\pi$
$643$	−40.6945	−1.60483	−0.802417	+	0.596763i	$0.796453\pi$
$644$	−125.192	−4.93324
$645$	−9.40345	−0.370261
$646$	−85.4546	−3.36217
$647$	40.9166	1.60860	0.804300	−	0.594224i	$-0.202541\pi$
$647$	40.9166	1.60860	0.804300	+	0.594224i	$0.202541\pi$
$648$	8.96030	0.351994
$649$	−2.47070	−0.0969836
$650$	−6.38406	−0.250404
$651$	−28.6992	−1.12481
$652$	0.808044	0.0316454
$653$	24.3197	0.951704	0.475852	−	0.879525i	$-0.342140\pi$
$653$	24.3197	0.951704	0.475852	+	0.879525i	$0.342140\pi$
$654$	36.0507	1.40970
$655$	8.52018	0.332911
$656$	−144.528	−5.64288
$657$	−11.9200	−0.465044
$658$	119.249	4.64881
$659$	33.6065	1.30912	0.654561	−	0.756009i	$-0.272854\pi$
$659$	33.6065	1.30912	0.654561	+	0.756009i	$0.272854\pi$
$660$	1.54478	0.0601303
$661$	−23.4974	−0.913945	−0.456972	−	0.889481i	$-0.651066\pi$
$661$	−23.4974	−0.913945	−0.456972	+	0.889481i	$0.651066\pi$
$662$	85.9566	3.34080
$663$	9.76148	0.379104
$664$	30.8007	1.19530
$665$	29.9189	1.16020
$666$	2.50926	0.0972320
$667$	−53.4178	−2.06835
$668$	−50.0055	−1.93477
$669$	−17.5914	−0.680122
$670$	20.8336	0.804873
$671$	−0.868224	−0.0335174
$672$	−73.8826	−2.85008
$673$	41.5321	1.60094	0.800472	−	0.599370i	$-0.204582\pi$
$673$	41.5321	1.60094	0.800472	+	0.599370i	$0.204582\pi$
$674$	10.0480	0.387034
$675$	−1.00000	−0.0384900
$676$	−39.4628	−1.51780
$677$	20.9719	0.806017	0.403008	−	0.915196i	$-0.367965\pi$
$677$	20.9719	0.806017	0.403008	+	0.915196i	$0.367965\pi$
$678$	15.5599	0.597574
$679$	−26.4215	−1.01397
$680$	−37.0509	−1.42084
$681$	−0.611391	−0.0234285
$682$	5.76345	0.220694
$683$	−45.2377	−1.73097	−0.865486	−	0.500934i	$-0.832990\pi$
$683$	−45.2377	−1.73097	−0.865486	+	0.500934i	$0.832990\pi$
$684$	−40.6040	−1.55253
$685$	−11.2125	−0.428408
$686$	14.0612	0.536861
$687$	3.20075	0.122116
$688$	−127.932	−4.87737
$689$	−11.2014	−0.426741
$690$	−16.2751	−0.619581
$691$	−13.5491	−0.515434	−0.257717	−	0.966220i	$-0.582970\pi$
$691$	−13.5491	−0.515434	−0.257717	+	0.966220i	$0.582970\pi$
$692$	−26.3833	−1.00294
$693$	1.13826	0.0432390
$694$	24.2210	0.919415
$695$	20.0296	0.759767
$696$	−79.5323	−3.01466
$697$	−43.9274	−1.66387
$698$	−17.7009	−0.669990
$699$	−7.75674	−0.293387
$700$	20.8023	0.786252
$701$	−39.1511	−1.47871	−0.739357	−	0.673313i	$-0.764871\pi$
$701$	−39.1511	−1.47871	−0.739357	+	0.673313i	$0.764871\pi$
$702$	6.38406	0.240951
$703$	−7.09072	−0.267432
$704$	6.92648	0.261051
$705$	11.2630	0.424189
$706$	49.5369	1.86434
$707$	−11.5429	−0.434115
$708$	45.1532	1.69696
$709$	38.5042	1.44606	0.723028	−	0.690818i	$-0.242750\pi$
$709$	38.5042	1.44606	0.723028	+	0.690818i	$0.242750\pi$
$710$	−12.6006	−0.472894
$711$	13.5279	0.507336
$712$	8.96030	0.335801
$713$	−44.1155	−1.65214
$714$	−43.7802	−1.63843
$715$	0.686338	0.0256676
$716$	−117.252	−4.38191
$717$	28.1059	1.04963
$718$	31.4990	1.17553
$719$	−10.7708	−0.401682	−0.200841	−	0.979624i	$-0.564367\pi$
$719$	−10.7708	−0.401682	−0.200841	+	0.979624i	$0.564367\pi$
$720$	−13.6048	−0.507022
$721$	−10.6878	−0.398036
$722$	106.547	3.96526
$723$	18.8774	0.702059
$724$	76.1515	2.83015
$725$	8.87608	0.329649
$726$	29.5189	1.09555
$727$	−8.46822	−0.314069	−0.157034	−	0.987593i	$-0.550193\pi$
$727$	−8.46822	−0.314069	−0.157034	+	0.987593i	$0.550193\pi$
$728$	−82.8144	−3.06930
$729$	1.00000	0.0370370
$730$	32.2355	1.19309
$731$	−38.8833	−1.43815
$732$	15.8672	0.586468
$733$	−19.7393	−0.729087	−0.364543	−	0.931186i	$-0.618775\pi$
$733$	−19.7393	−0.729087	−0.364543	+	0.931186i	$0.618775\pi$
$734$	−61.6266	−2.27468
$735$	8.32807	0.307186
$736$	−113.570	−4.18624
$737$	−2.23978	−0.0825035
$738$	−28.7288	−1.05752
$739$	−47.1294	−1.73368	−0.866842	−	0.498583i	$-0.833854\pi$
$739$	−47.1294	−1.73368	−0.866842	+	0.498583i	$0.833854\pi$
$740$	−4.93010	−0.181234
$741$	−18.0402	−0.662723
$742$	50.2384	1.84431
$743$	−4.46755	−0.163899	−0.0819493	−	0.996637i	$-0.526115\pi$
$743$	−4.46755	−0.163899	−0.0819493	+	0.996637i	$0.526115\pi$
$744$	−65.6824	−2.40803
$745$	−16.2201	−0.594259
$746$	51.8307	1.89766
$747$	3.43747	0.125770
$748$	6.38766	0.233556
$749$	21.1088	0.771300
$750$	2.70432	0.0987477
$751$	−34.6927	−1.26595	−0.632977	−	0.774171i	$-0.718167\pi$
$751$	−34.6927	−1.26595	−0.632977	+	0.774171i	$0.718167\pi$
$752$	153.231	5.58776
$753$	−9.95645	−0.362833
$754$	−56.6655	−2.06363
$755$	−12.8001	−0.465842
$756$	−20.8023	−0.756571
$757$	−3.94366	−0.143335	−0.0716674	−	0.997429i	$-0.522832\pi$
$757$	−3.94366	−0.143335	−0.0716674	+	0.997429i	$0.522832\pi$
$758$	−98.6881	−3.58451
$759$	1.74970	0.0635101
$760$	68.4737	2.48380
$761$	−21.1330	−0.766070	−0.383035	−	0.923734i	$-0.625121\pi$
$761$	−21.1330	−0.766070	−0.383035	+	0.923734i	$0.625121\pi$
$762$	42.0081	1.52179
$763$	−52.1916	−1.88946
$764$	−33.7839	−1.22226
$765$	−4.13501	−0.149501
$766$	−62.6763	−2.26459
$767$	20.0614	0.724376
$768$	−24.5173	−0.884692
$769$	18.5773	0.669914	0.334957	−	0.942233i	$-0.391278\pi$
$769$	18.5773	0.669914	0.334957	+	0.942233i	$0.391278\pi$
$770$	−3.07822	−0.110931
$771$	8.21867	0.295988
$772$	41.0735	1.47827
$773$	8.54873	0.307476	0.153738	−	0.988112i	$-0.450869\pi$
$773$	8.54873	0.307476	0.153738	+	0.988112i	$0.450869\pi$
$774$	−25.4299	−0.914060
$775$	7.33038	0.263315
$776$	−60.4696	−2.17073
$777$	−3.63273	−0.130323
$778$	32.0001	1.14726
$779$	81.1823	2.90866
$780$	−12.5431	−0.449117
$781$	1.35467	0.0484739
$782$	−67.2974	−2.40655
$783$	−8.87608	−0.317205
$784$	113.302	4.04650
$785$	−1.96635	−0.0701820
$786$	23.0413	0.821855
$787$	19.6235	0.699502	0.349751	−	0.936843i	$-0.386266\pi$
$787$	19.6235	0.699502	0.349751	+	0.936843i	$0.386266\pi$
$788$	85.9255	3.06097
$789$	−21.1125	−0.751627
$790$	−36.5837	−1.30159
$791$	−22.5264	−0.800948
$792$	2.60508	0.0925675
$793$	7.04973	0.250343
$794$	−18.5924	−0.659818
$795$	4.74498	0.168287
$796$	36.5330	1.29488
$797$	17.9984	0.637534	0.318767	−	0.947833i	$-0.396731\pi$
$797$	17.9984	0.637534	0.318767	+	0.947833i	$0.396731\pi$
$798$	80.9102	2.86419
$799$	46.5725	1.64762
$800$	18.8712	0.667196
$801$	1.00000	0.0353333
$802$	3.44618	0.121689
$803$	−3.46558	−0.122298
$804$	40.9330	1.44360
$805$	23.5618	0.830444
$806$	−46.7976	−1.64838
$807$	1.76519	0.0621375
$808$	−26.4176	−0.929367
$809$	−53.3900	−1.87709	−0.938547	−	0.345153i	$-0.887827\pi$
$809$	−53.3900	−1.87709	−0.938547	+	0.345153i	$0.887827\pi$
$810$	−2.70432	−0.0950200
$811$	41.3617	1.45241	0.726203	−	0.687480i	$-0.241283\pi$
$811$	41.3617	1.45241	0.726203	+	0.687480i	$0.241283\pi$
$812$	184.643	6.47969
$813$	−4.26799	−0.149685
$814$	0.729533	0.0255701
$815$	−0.152079	−0.00532708
$816$	−56.2560	−1.96935
$817$	71.8603	2.51407
$818$	76.3394	2.66915
$819$	−9.24237	−0.322955
$820$	56.4452	1.97115
$821$	−51.9464	−1.81294	−0.906471	−	0.422268i	$-0.861234\pi$
$821$	−51.9464	−1.81294	−0.906471	+	0.422268i	$0.861234\pi$
$822$	−30.3222	−1.05761
$823$	−24.7601	−0.863084	−0.431542	−	0.902093i	$-0.642030\pi$
$823$	−24.7601	−0.863084	−0.431542	+	0.902093i	$0.642030\pi$
$824$	−24.4607	−0.852127
$825$	−0.290736	−0.0101221
$826$	−89.9753	−3.13064
$827$	−5.69603	−0.198070	−0.0990352	−	0.995084i	$-0.531576\pi$
$827$	−5.69603	−0.198070	−0.0990352	+	0.995084i	$0.531576\pi$
$828$	−31.9765	−1.11126
$829$	−30.6160	−1.06334	−0.531669	−	0.846952i	$-0.678435\pi$
$829$	−30.6160	−1.06334	−0.531669	+	0.846952i	$0.678435\pi$
$830$	−9.29600	−0.322669
$831$	−8.15122	−0.282763
$832$	−56.2410	−1.94981
$833$	34.4366	1.19316
$834$	54.1665	1.87563
$835$	9.41133	0.325692
$836$	−11.8050	−0.408286
$837$	−7.33038	−0.253375
$838$	33.4484	1.15546
$839$	7.71064	0.266201	0.133100	−	0.991103i	$-0.457507\pi$
$839$	7.71064	0.266201	0.133100	+	0.991103i	$0.457507\pi$
$840$	35.0805	1.21039
$841$	49.7848	1.71672
$842$	−64.5003	−2.22283
$843$	−23.1441	−0.797125
$844$	−57.8534	−1.99139
$845$	7.42713	0.255501
$846$	30.4587	1.04719
$847$	−42.7353	−1.46840
$848$	64.5546	2.21681
$849$	−0.495284	−0.0169981
$850$	11.1824	0.383552
$851$	−5.58410	−0.191421
$852$	−24.7572	−0.848168
$853$	42.1577	1.44345	0.721727	−	0.692178i	$-0.243349\pi$
$853$	42.1577	1.44345	0.721727	+	0.692178i	$0.243349\pi$
$854$	−31.6180	−1.08195
$855$	7.64191	0.261348
$856$	48.3106	1.65122
$857$	−11.5033	−0.392946	−0.196473	−	0.980509i	$-0.562949\pi$
$857$	−11.5033	−0.392946	−0.196473	+	0.980509i	$0.562949\pi$
$858$	1.85608	0.0633654
$859$	17.0400	0.581399	0.290699	−	0.956814i	$-0.406112\pi$
$859$	17.0400	0.581399	0.290699	+	0.956814i	$0.406112\pi$
$860$	49.9637	1.70375
$861$	41.5914	1.41743
$862$	7.77245	0.264731
$863$	20.0375	0.682083	0.341042	−	0.940048i	$-0.389220\pi$
$863$	20.0375	0.682083	0.341042	+	0.940048i	$0.389220\pi$
$864$	−18.8712	−0.642010
$865$	4.96550	0.168832
$866$	62.2955	2.11689
$867$	−0.0982690	−0.00333739
$868$	152.489	5.17580
$869$	3.93305	0.133419
$870$	24.0037	0.813803
$871$	18.1864	0.616223
$872$	−119.448	−4.04502
$873$	−6.74861	−0.228406
$874$	124.372	4.20696
$875$	−3.91511	−0.132355
$876$	63.3350	2.13989
$877$	31.0620	1.04889	0.524445	−	0.851445i	$-0.324273\pi$
$877$	31.0620	1.04889	0.524445	+	0.851445i	$0.324273\pi$
$878$	−21.5811	−0.728327
$879$	−20.8859	−0.704464
$880$	−3.95541	−0.133337
$881$	−7.02503	−0.236679	−0.118340	−	0.992973i	$-0.537757\pi$
$881$	−7.02503	−0.236679	−0.118340	+	0.992973i	$0.537757\pi$
$882$	22.5218	0.758347
$883$	−14.6289	−0.492303	−0.246151	−	0.969231i	$-0.579166\pi$
$883$	−14.6289	−0.492303	−0.246151	+	0.969231i	$0.579166\pi$
$884$	−51.8660	−1.74444
$885$	−8.49811	−0.285661
$886$	19.6918	0.661560
$887$	45.2292	1.51865	0.759325	−	0.650712i	$-0.225529\pi$
$887$	45.2292	1.51865	0.759325	+	0.650712i	$0.225529\pi$
$888$	−8.31402	−0.279000
$889$	−60.8162	−2.03971
$890$	−2.70432	−0.0906489
$891$	0.290736	0.00974002
$892$	93.4688	3.12957
$893$	−86.0707	−2.88025
$894$	−43.8644	−1.46704
$895$	22.0675	0.737635
$896$	104.475	3.49028
$897$	−14.2071	−0.474360
$898$	43.9822	1.46770
$899$	65.0651	2.17004
$900$	5.31333	0.177111
$901$	19.6205	0.653654
$902$	−8.35249	−0.278108
$903$	36.8155	1.22514
$904$	−51.5550	−1.71469
$905$	−14.3322	−0.476417
$906$	−34.6155	−1.15002
$907$	13.3391	0.442917	0.221459	−	0.975170i	$-0.428918\pi$
$907$	13.3391	0.442917	0.221459	+	0.975170i	$0.428918\pi$
$908$	3.24852	0.107806
$909$	−2.94829	−0.0977887
$910$	24.9943	0.828553
$911$	2.51924	0.0834663	0.0417331	−	0.999129i	$-0.486712\pi$
$911$	2.51924	0.0834663	0.0417331	+	0.999129i	$0.486712\pi$
$912$	103.967	3.44268
$913$	0.999395	0.0330751
$914$	78.8097	2.60679
$915$	−2.98630	−0.0987240
$916$	−17.0067	−0.561916
$917$	−33.3574	−1.10156
$918$	−11.1824	−0.369073
$919$	13.7219	0.452645	0.226322	−	0.974052i	$-0.427330\pi$
$919$	13.7219	0.452645	0.226322	+	0.974052i	$0.427330\pi$
$920$	53.9246	1.77784
$921$	−26.2842	−0.866095
$922$	19.2366	0.633524
$923$	−10.9995	−0.362054
$924$	−6.04797	−0.198963
$925$	0.927874	0.0305083
$926$	−41.8916	−1.37664
$927$	−2.72989	−0.0896615
$928$	167.502	5.49852
$929$	−21.1806	−0.694912	−0.347456	−	0.937696i	$-0.612954\pi$
$929$	−21.1806	−0.694912	−0.347456	+	0.937696i	$0.612954\pi$
$930$	19.8237	0.650044
$931$	−63.6424	−2.08579
$932$	41.2141	1.35001
$933$	−8.05572	−0.263732
$934$	79.8840	2.61388
$935$	−1.20219	−0.0393160
$936$	−21.1525	−0.691391
$937$	0.680210	0.0222215	0.0111107	−	0.999938i	$-0.496463\pi$
$937$	0.680210	0.0222215	0.0111107	+	0.999938i	$0.496463\pi$
$938$	−81.5659	−2.66322
$939$	−19.8942	−0.649224
$940$	−59.8440	−1.95190
$941$	33.5948	1.09516	0.547579	−	0.836754i	$-0.315549\pi$
$941$	33.5948	1.09516	0.547579	+	0.836754i	$0.315549\pi$
$942$	−5.31763	−0.173258
$943$	63.9329	2.08194
$944$	−115.615	−3.76295
$945$	3.91511	0.127358
$946$	−7.39339	−0.240380
$947$	−7.62796	−0.247875	−0.123938	−	0.992290i	$-0.539552\pi$
$947$	−7.62796	−0.247875	−0.123938	+	0.992290i	$0.539552\pi$
$948$	−71.8782	−2.33449
$949$	28.1395	0.913447
$950$	−20.6661	−0.670498
$951$	−9.08595	−0.294632
$952$	145.058	4.70136
$953$	47.5199	1.53932	0.769661	−	0.638453i	$-0.220425\pi$
$953$	47.5199	1.53932	0.769661	+	0.638453i	$0.220425\pi$
$954$	12.8319	0.415449
$955$	6.35834	0.205751
$956$	−149.336	−4.82987
$957$	−2.58060	−0.0834188
$958$	−10.9572	−0.354012
$959$	43.8982	1.41755
$960$	23.8239	0.768914
$961$	22.7345	0.733371
$962$	−5.92360	−0.190985
$963$	5.39163	0.173743
$964$	−100.302	−3.23051
$965$	−7.73028	−0.248847
$966$	63.7186	2.05011
$967$	0.611837	0.0196753	0.00983767	−	0.999952i	$-0.496869\pi$
$967$	0.611837	0.0196753	0.00983767	+	0.999952i	$0.496869\pi$
$968$	−97.8059	−3.14360
$969$	31.5993	1.01512
$970$	18.2504	0.585985
$971$	−61.0779	−1.96008	−0.980041	−	0.198793i	$-0.936298\pi$
$971$	−61.0779	−1.96008	−0.980041	+	0.198793i	$0.936298\pi$
$972$	−5.31333	−0.170425
$973$	−78.4182	−2.51397
$974$	−50.7924	−1.62749
$975$	2.36069	0.0756027
$976$	−40.6280	−1.30047
$977$	6.86858	0.219745	0.109873	−	0.993946i	$-0.464956\pi$
$977$	6.86858	0.219745	0.109873	+	0.993946i	$0.464956\pi$
$978$	−0.411269	−0.0131509
$979$	0.290736	0.00929196
$980$	−44.2498	−1.41351
$981$	−13.3308	−0.425620
$982$	−15.6163	−0.498337
$983$	42.0513	1.34123	0.670615	−	0.741806i	$-0.266030\pi$
$983$	42.0513	1.34123	0.670615	+	0.741806i	$0.266030\pi$
$984$	95.1880	3.03448
$985$	−16.1717	−0.515273
$986$	99.2556	3.16094
$987$	−44.0958	−1.40359
$988$	95.8535	3.04951
$989$	56.5916	1.79951
$990$	−0.786242	−0.0249884
$991$	0.917498	0.0291453	0.0145726	−	0.999894i	$-0.495361\pi$
$991$	0.917498	0.0291453	0.0145726	+	0.999894i	$0.495361\pi$
$992$	138.333	4.39207
$993$	−31.7850	−1.00867
$994$	49.3329	1.56474
$995$	−6.87573	−0.217975
$996$	−18.2644	−0.578729
$997$	−0.150382	−0.00476264	−0.00238132	−	0.999997i	$-0.500758\pi$
$997$	−0.150382	−0.00476264	−0.00238132	+	0.999997i	$0.500758\pi$
$998$	−70.2066	−2.22235
$999$	−0.927874	−0.0293566

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1335.2.a.h.1.8	✓	9
3.2	odd	2		4005.2.a.q.1.2		9
5.4	even	2		6675.2.a.x.1.2		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1335.2.a.h.1.8	✓	9	1.1	even	1	trivial
4005.2.a.q.1.2		9	3.2	odd	2
6675.2.a.x.1.2		9	5.4	even	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:	\( N \)	\(=\)	\( 1335 = 3 \cdot 5 \cdot 89 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1335.a (trivial)

\(f(q)\)	\(=\)	\(q+2.70432 q^{2} -1.00000 q^{3} +5.31333 q^{4} -1.00000 q^{5} -2.70432 q^{6} +3.91511 q^{7} +8.96030 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.70432 q^{2} -1.00000 q^{3} +5.31333 q^{4} -1.00000 q^{5} -2.70432 q^{6} +3.91511 q^{7} +8.96030 q^{8} +1.00000 q^{9} -2.70432 q^{10} +0.290736 q^{11} -5.31333 q^{12} -2.36069 q^{13} +10.5877 q^{14} +1.00000 q^{15} +13.6048 q^{16} +4.13501 q^{17} +2.70432 q^{18} -7.64191 q^{19} -5.31333 q^{20} -3.91511 q^{21} +0.786242 q^{22} -6.01817 q^{23} -8.96030 q^{24} +1.00000 q^{25} -6.38406 q^{26} -1.00000 q^{27} +20.8023 q^{28} +8.87608 q^{29} +2.70432 q^{30} +7.33038 q^{31} +18.8712 q^{32} -0.290736 q^{33} +11.1824 q^{34} -3.91511 q^{35} +5.31333 q^{36} +0.927874 q^{37} -20.6661 q^{38} +2.36069 q^{39} -8.96030 q^{40} -10.6233 q^{41} -10.5877 q^{42} -9.40345 q^{43} +1.54478 q^{44} -1.00000 q^{45} -16.2751 q^{46} +11.2630 q^{47} -13.6048 q^{48} +8.32807 q^{49} +2.70432 q^{50} -4.13501 q^{51} -12.5431 q^{52} +4.74498 q^{53} -2.70432 q^{54} -0.290736 q^{55} +35.0805 q^{56} +7.64191 q^{57} +24.0037 q^{58} -8.49811 q^{59} +5.31333 q^{60} -2.98630 q^{61} +19.8237 q^{62} +3.91511 q^{63} +23.8239 q^{64} +2.36069 q^{65} -0.786242 q^{66} -7.70384 q^{67} +21.9706 q^{68} +6.01817 q^{69} -10.5877 q^{70} +4.65945 q^{71} +8.96030 q^{72} -11.9200 q^{73} +2.50926 q^{74} -1.00000 q^{75} -40.6040 q^{76} +1.13826 q^{77} +6.38406 q^{78} +13.5279 q^{79} -13.6048 q^{80} +1.00000 q^{81} -28.7288 q^{82} +3.43747 q^{83} -20.8023 q^{84} -4.13501 q^{85} -25.4299 q^{86} -8.87608 q^{87} +2.60508 q^{88} +1.00000 q^{89} -2.70432 q^{90} -9.24237 q^{91} -31.9765 q^{92} -7.33038 q^{93} +30.4587 q^{94} +7.64191 q^{95} -18.8712 q^{96} -6.74861 q^{97} +22.5218 q^{98} +0.290736 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 5 q^{2} - 9 q^{3} + 11 q^{4} - 9 q^{5} - 5 q^{6} - 3 q^{7} + 18 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q + 5 * q^2 - 9 * q^3 + 11 * q^4 - 9 * q^5 - 5 * q^6 - 3 * q^7 + 18 * q^8 + 9 * q^9	\( 9 q + 5 q^{2} - 9 q^{3} + 11 q^{4} - 9 q^{5} - 5 q^{6} - 3 q^{7} + 18 q^{8} + 9 q^{9} - 5 q^{10} + 4 q^{11} - 11 q^{12} + 5 q^{13} - q^{14} + 9 q^{15} + 15 q^{16} + 21 q^{17} + 5 q^{18} - 18 q^{19} - 11 q^{20} + 3 q^{21} + 6 q^{22} + 16 q^{23} - 18 q^{24} + 9 q^{25} + 8 q^{26} - 9 q^{27} + 6 q^{28} + 3 q^{29} + 5 q^{30} - 6 q^{31} + 46 q^{32} - 4 q^{33} + 12 q^{34} + 3 q^{35} + 11 q^{36} + 11 q^{37} + 20 q^{38} - 5 q^{39} - 18 q^{40} - q^{41} + q^{42} - 3 q^{43} + 38 q^{44} - 9 q^{45} + 16 q^{46} + 27 q^{47} - 15 q^{48} + 24 q^{49} + 5 q^{50} - 21 q^{51} + 17 q^{52} + 43 q^{53} - 5 q^{54} - 4 q^{55} + 5 q^{56} + 18 q^{57} + 34 q^{58} + 3 q^{59} + 11 q^{60} - 30 q^{61} + 36 q^{62} - 3 q^{63} + 50 q^{64} - 5 q^{65} - 6 q^{66} - 12 q^{67} + 64 q^{68} - 16 q^{69} + q^{70} - 4 q^{71} + 18 q^{72} + 26 q^{73} + 2 q^{74} - 9 q^{75} - 12 q^{76} + 34 q^{77} - 8 q^{78} + q^{79} - 15 q^{80} + 9 q^{81} - 51 q^{82} + 24 q^{83} - 6 q^{84} - 21 q^{85} + 18 q^{86} - 3 q^{87} + 64 q^{88} + 9 q^{89} - 5 q^{90} - 50 q^{91} + 10 q^{92} + 6 q^{93} - 11 q^{94} + 18 q^{95} - 46 q^{96} - 4 q^{97} + 75 q^{98} + 4 q^{99}+O(q^{100}) \) 9 * q + 5 * q^2 - 9 * q^3 + 11 * q^4 - 9 * q^5 - 5 * q^6 - 3 * q^7 + 18 * q^8 + 9 * q^9 - 5 * q^10 + 4 * q^11 - 11 * q^12 + 5 * q^13 - q^14 + 9 * q^15 + 15 * q^16 + 21 * q^17 + 5 * q^18 - 18 * q^19 - 11 * q^20 + 3 * q^21 + 6 * q^22 + 16 * q^23 - 18 * q^24 + 9 * q^25 + 8 * q^26 - 9 * q^27 + 6 * q^28 + 3 * q^29 + 5 * q^30 - 6 * q^31 + 46 * q^32 - 4 * q^33 + 12 * q^34 + 3 * q^35 + 11 * q^36 + 11 * q^37 + 20 * q^38 - 5 * q^39 - 18 * q^40 - q^41 + q^42 - 3 * q^43 + 38 * q^44 - 9 * q^45 + 16 * q^46 + 27 * q^47 - 15 * q^48 + 24 * q^49 + 5 * q^50 - 21 * q^51 + 17 * q^52 + 43 * q^53 - 5 * q^54 - 4 * q^55 + 5 * q^56 + 18 * q^57 + 34 * q^58 + 3 * q^59 + 11 * q^60 - 30 * q^61 + 36 * q^62 - 3 * q^63 + 50 * q^64 - 5 * q^65 - 6 * q^66 - 12 * q^67 + 64 * q^68 - 16 * q^69 + q^70 - 4 * q^71 + 18 * q^72 + 26 * q^73 + 2 * q^74 - 9 * q^75 - 12 * q^76 + 34 * q^77 - 8 * q^78 + q^79 - 15 * q^80 + 9 * q^81 - 51 * q^82 + 24 * q^83 - 6 * q^84 - 21 * q^85 + 18 * q^86 - 3 * q^87 + 64 * q^88 + 9 * q^89 - 5 * q^90 - 50 * q^91 + 10 * q^92 + 6 * q^93 - 11 * q^94 + 18 * q^95 - 46 * q^96 - 4 * q^97 + 75 * q^98 + 4 * q^99

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