LMFDB - Embedded newform 1573.2.a.o.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1573,2,Mod(1,1573)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1573, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1573.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1573 = 11^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1573.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:	$12.5604682379$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	8.8.661518125.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 7x^{6} + 5x^{5} + 15x^{4} - 7x^{3} - 10x^{2} + 2x + 1 $ x^8 - x^7 - 7x^6 + 5x^5 + 15x^4 - 7x^3 - 10x^2 + 2x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.859317$ of defining polynomial
Character	$\chi$	$=$	1573.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.922431 q^{2} +1.04127 q^{3} -1.14912 q^{4} -0.366793 q^{5} -0.960498 q^{6} -1.05586 q^{7} +2.90485 q^{8} -1.91576 q^{9} +O(q^{10})$	\(q-0.922431 q^{2} +1.04127 q^{3} -1.14912 q^{4} -0.366793 q^{5} -0.960498 q^{6} -1.05586 q^{7} +2.90485 q^{8} -1.91576 q^{9} +0.338341 q^{10} -1.19654 q^{12} -1.00000 q^{13} +0.973959 q^{14} -0.381930 q^{15} -0.381277 q^{16} +5.81387 q^{17} +1.76716 q^{18} +1.83365 q^{19} +0.421490 q^{20} -1.09944 q^{21} +1.87405 q^{23} +3.02473 q^{24} -4.86546 q^{25} +0.922431 q^{26} -5.11863 q^{27} +1.21331 q^{28} +4.57993 q^{29} +0.352304 q^{30} +0.406204 q^{31} -5.45799 q^{32} -5.36289 q^{34} +0.387283 q^{35} +2.20144 q^{36} -7.99264 q^{37} -1.69141 q^{38} -1.04127 q^{39} -1.06548 q^{40} -0.000546242 q^{41} +1.01415 q^{42} -11.8466 q^{43} +0.702687 q^{45} -1.72868 q^{46} +2.63645 q^{47} -0.397012 q^{48} -5.88516 q^{49} +4.48805 q^{50} +6.05380 q^{51} +1.14912 q^{52} -12.2719 q^{53} +4.72158 q^{54} -3.06712 q^{56} +1.90932 q^{57} -4.22467 q^{58} -4.95638 q^{59} +0.438884 q^{60} +5.09198 q^{61} -0.374695 q^{62} +2.02278 q^{63} +5.79717 q^{64} +0.366793 q^{65} +4.08687 q^{67} -6.68084 q^{68} +1.95139 q^{69} -0.357242 q^{70} -4.59211 q^{71} -5.56499 q^{72} +2.67351 q^{73} +7.37266 q^{74} -5.06625 q^{75} -2.10708 q^{76} +0.960498 q^{78} -0.698032 q^{79} +0.139850 q^{80} +0.417411 q^{81} +0.000503870 q^{82} -11.8271 q^{83} +1.26339 q^{84} -2.13249 q^{85} +10.9277 q^{86} +4.76893 q^{87} -14.3152 q^{89} -0.648180 q^{90} +1.05586 q^{91} -2.15351 q^{92} +0.422968 q^{93} -2.43194 q^{94} -0.672569 q^{95} -5.68324 q^{96} +15.0592 q^{97} +5.42865 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 5 q^{3} + q^{4} - 5 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} - q^{9}+O(q^{10}) $ 8 * q + q^2 - 5 * q^3 + q^4 - 5 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 - q^9	$ 8 q + q^{2} - 5 q^{3} + q^{4} - 5 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} - q^{9} - 6 q^{10} - 7 q^{12} - 8 q^{13} + 2 q^{14} + 5 q^{15} - 5 q^{16} - 13 q^{17} - 5 q^{18} + 6 q^{19} - 3 q^{20} - 4 q^{21} - 23 q^{23} - q^{24} - q^{25} - q^{26} + q^{27} - 32 q^{28} + 15 q^{29} - 4 q^{30} - 11 q^{31} + 12 q^{32} + 2 q^{34} + 8 q^{35} - 6 q^{36} - 11 q^{37} - 25 q^{38} + 5 q^{39} + 15 q^{40} + 11 q^{41} - 11 q^{42} - 8 q^{43} - 23 q^{45} + 12 q^{46} - 21 q^{47} + 8 q^{48} + 2 q^{49} - 12 q^{50} + 26 q^{51} - q^{52} - 7 q^{53} + 3 q^{54} - 34 q^{56} - 51 q^{57} - 20 q^{58} - 22 q^{59} - 3 q^{60} + 6 q^{61} - q^{62} + 14 q^{63} + 5 q^{64} + 5 q^{65} - 31 q^{67} - q^{68} + 17 q^{69} - 26 q^{70} - 23 q^{71} - 27 q^{72} + 34 q^{73} + 6 q^{74} - 27 q^{75} - 2 q^{76} - 3 q^{78} - 5 q^{79} - 7 q^{80} - 32 q^{81} - 11 q^{82} + 11 q^{83} + 45 q^{84} - 4 q^{85} - 21 q^{86} + 2 q^{87} - 15 q^{89} + 3 q^{90} - 2 q^{91} - 6 q^{92} - 8 q^{93} - 8 q^{94} - 11 q^{95} - 41 q^{96} - 6 q^{97} + 12 q^{98}+O(q^{100}) $ 8 * q + q^2 - 5 * q^3 + q^4 - 5 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 - q^9 - 6 * q^10 - 7 * q^12 - 8 * q^13 + 2 * q^14 + 5 * q^15 - 5 * q^16 - 13 * q^17 - 5 * q^18 + 6 * q^19 - 3 * q^20 - 4 * q^21 - 23 * q^23 - q^24 - q^25 - q^26 + q^27 - 32 * q^28 + 15 * q^29 - 4 * q^30 - 11 * q^31 + 12 * q^32 + 2 * q^34 + 8 * q^35 - 6 * q^36 - 11 * q^37 - 25 * q^38 + 5 * q^39 + 15 * q^40 + 11 * q^41 - 11 * q^42 - 8 * q^43 - 23 * q^45 + 12 * q^46 - 21 * q^47 + 8 * q^48 + 2 * q^49 - 12 * q^50 + 26 * q^51 - q^52 - 7 * q^53 + 3 * q^54 - 34 * q^56 - 51 * q^57 - 20 * q^58 - 22 * q^59 - 3 * q^60 + 6 * q^61 - q^62 + 14 * q^63 + 5 * q^64 + 5 * q^65 - 31 * q^67 - q^68 + 17 * q^69 - 26 * q^70 - 23 * q^71 - 27 * q^72 + 34 * q^73 + 6 * q^74 - 27 * q^75 - 2 * q^76 - 3 * q^78 - 5 * q^79 - 7 * q^80 - 32 * q^81 - 11 * q^82 + 11 * q^83 + 45 * q^84 - 4 * q^85 - 21 * q^86 + 2 * q^87 - 15 * q^89 + 3 * q^90 - 2 * q^91 - 6 * q^92 - 8 * q^93 - 8 * q^94 - 11 * q^95 - 41 * q^96 - 6 * q^97 + 12 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.922431	−0.652257	−0.326129	−	0.945325i	$-0.605744\pi$
$2$	−0.922431	−0.652257	−0.326129	+	0.945325i	$0.605744\pi$
$3$	1.04127	0.601177	0.300588	−	0.953754i	$-0.402817\pi$
$3$	1.04127	0.601177	0.300588	+	0.953754i	$0.402817\pi$
$4$	−1.14912	−0.574561
$5$	−0.366793	−0.164035	−0.0820174	−	0.996631i	$-0.526136\pi$
$5$	−0.366793	−0.164035	−0.0820174	+	0.996631i	$0.526136\pi$
$6$	−0.960498	−0.392122
$7$	−1.05586	−0.399078	−0.199539	−	0.979890i	$-0.563944\pi$
$7$	−1.05586	−0.399078	−0.199539	+	0.979890i	$0.563944\pi$
$8$	2.90485	1.02702
$9$	−1.91576	−0.638586
$10$	0.338341	0.106993
$11$	0	0
$11$	0	0
$12$	−1.19654	−0.345413
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0.973959	0.260302
$15$	−0.381930	−0.0986139
$16$	−0.381277	−0.0953193
$17$	5.81387	1.41007	0.705036	−	0.709172i	$-0.250931\pi$
$17$	5.81387	1.41007	0.705036	+	0.709172i	$0.250931\pi$
$18$	1.76716	0.416523
$19$	1.83365	0.420668	0.210334	−	0.977630i	$-0.432545\pi$
$19$	1.83365	0.420668	0.210334	+	0.977630i	$0.432545\pi$
$20$	0.421490	0.0942480
$21$	−1.09944	−0.239917
$22$	0	0
$23$	1.87405	0.390767	0.195383	−	0.980727i	$-0.437405\pi$
$23$	1.87405	0.390767	0.195383	+	0.980727i	$0.437405\pi$
$24$	3.02473	0.617420
$25$	−4.86546	−0.973093
$26$	0.922431	0.180904
$27$	−5.11863	−0.985080
$28$	1.21331	0.229295
$29$	4.57993	0.850471	0.425235	−	0.905083i	$-0.360191\pi$
$29$	4.57993	0.850471	0.425235	+	0.905083i	$0.360191\pi$
$30$	0.352304	0.0643216
$31$	0.406204	0.0729564	0.0364782	−	0.999334i	$-0.488386\pi$
$31$	0.406204	0.0729564	0.0364782	+	0.999334i	$0.488386\pi$
$32$	−5.45799	−0.964846
$33$	0	0
$34$	−5.36289	−0.919729
$35$	0.387283	0.0654627
$36$	2.20144	0.366907
$37$	−7.99264	−1.31398	−0.656991	−	0.753898i	$-0.728171\pi$
$37$	−7.99264	−1.31398	−0.656991	+	0.753898i	$0.728171\pi$
$38$	−1.69141	−0.274383
$39$	−1.04127	−0.166736
$40$	−1.06548	−0.168467
$41$	−0.000546242 0	−8.53086e−5 0	−4.26543e−5	−	1.00000i	$-0.500014\pi$
$41$	−0.000546242 0	−8.53086e−5 0	−4.26543e−5		1.00000i	$0.500014\pi$
$42$	1.01415	0.156487
$43$	−11.8466	−1.80659	−0.903297	−	0.429015i	$-0.858861\pi$
$43$	−11.8466	−1.80659	−0.903297	+	0.429015i	$0.858861\pi$
$44$	0	0
$45$	0.702687	0.104750
$46$	−1.72868	−0.254880
$47$	2.63645	0.384565	0.192283	−	0.981340i	$-0.438411\pi$
$47$	2.63645	0.384565	0.192283	+	0.981340i	$0.438411\pi$
$48$	−0.397012	−0.0573038
$49$	−5.88516	−0.840737
$50$	4.48805	0.634707
$51$	6.05380	0.847702
$52$	1.14912	0.159354
$53$	−12.2719	−1.68568	−0.842841	−	0.538163i	$-0.819118\pi$
$53$	−12.2719	−1.68568	−0.842841	+	0.538163i	$0.819118\pi$
$54$	4.72158	0.642526
$55$	0	0
$56$	−3.06712	−0.409861
$57$	1.90932	0.252896
$58$	−4.22467	−0.554726
$59$	−4.95638	−0.645265	−0.322633	−	0.946524i	$-0.604568\pi$
$59$	−4.95638	−0.645265	−0.322633	+	0.946524i	$0.604568\pi$
$60$	0.438884	0.0566597
$61$	5.09198	0.651961	0.325981	−	0.945376i	$-0.394306\pi$
$61$	5.09198	0.651961	0.325981	+	0.945376i	$0.394306\pi$
$62$	−0.374695	−0.0475863
$63$	2.02278	0.254846
$64$	5.79717	0.724647
$65$	0.366793	0.0454951
$66$	0	0
$67$	4.08687	0.499290	0.249645	−	0.968337i	$-0.419686\pi$
$67$	4.08687	0.499290	0.249645	+	0.968337i	$0.419686\pi$
$68$	−6.68084	−0.810171
$69$	1.95139	0.234920
$70$	−0.357242	−0.0426985
$71$	−4.59211	−0.544983	−0.272491	−	0.962158i	$-0.587848\pi$
$71$	−4.59211	−0.544983	−0.272491	+	0.962158i	$0.587848\pi$
$72$	−5.56499	−0.655840
$73$	2.67351	0.312910	0.156455	−	0.987685i	$-0.449993\pi$
$73$	2.67351	0.312910	0.156455	+	0.987685i	$0.449993\pi$
$74$	7.37266	0.857054
$75$	−5.06625	−0.585001
$76$	−2.10708	−0.241699
$77$	0	0
$78$	0.960498	0.108755
$79$	−0.698032	−0.0785348	−0.0392674	−	0.999229i	$-0.512502\pi$
$79$	−0.698032	−0.0785348	−0.0392674	+	0.999229i	$0.512502\pi$
$80$	0.139850	0.0156357
$81$	0.417411	0.0463790
$82$	0.000503870 0	5.56432e−5 0
$83$	−11.8271	−1.29820	−0.649098	−	0.760705i	$-0.724854\pi$
$83$	−11.8271	−1.29820	−0.649098	+	0.760705i	$0.724854\pi$
$84$	1.26339	0.137847
$85$	−2.13249	−0.231301
$86$	10.9277	1.17836
$87$	4.76893	0.511283
$88$	0	0
$89$	−14.3152	−1.51741	−0.758704	−	0.651435i	$-0.774167\pi$
$89$	−14.3152	−1.51741	−0.758704	+	0.651435i	$0.774167\pi$
$90$	−0.648180	−0.0683242
$91$	1.05586	0.110684
$92$	−2.15351	−0.224519
$93$	0.422968	0.0438597
$94$	−2.43194	−0.250835
$95$	−0.672569	−0.0690041
$96$	−5.68324	−0.580043
$97$	15.0592	1.52903	0.764513	−	0.644608i	$-0.222979\pi$
$97$	15.0592	1.52903	0.764513	+	0.644608i	$0.222979\pi$
$98$	5.42865	0.548376
$99$	0	0
$100$	5.59101	0.559101
$101$	−12.5810	−1.25186	−0.625928	−	0.779881i	$-0.715279\pi$
$101$	−12.5810	−1.25186	−0.625928	+	0.779881i	$0.715279\pi$
$102$	−5.58421	−0.552920
$103$	−12.8606	−1.26720	−0.633598	−	0.773663i	$-0.718423\pi$
$103$	−12.8606	−1.26720	−0.633598	+	0.773663i	$0.718423\pi$
$104$	−2.90485	−0.284844
$105$	0.403265	0.0393547
$106$	11.3200	1.09950
$107$	12.7199	1.22968	0.614838	−	0.788653i	$-0.289221\pi$
$107$	12.7199	1.22968	0.614838	+	0.788653i	$0.289221\pi$
$108$	5.88192	0.565988
$109$	−10.0078	−0.958575	−0.479288	−	0.877658i	$-0.659105\pi$
$109$	−10.0078	−0.958575	−0.479288	+	0.877658i	$0.659105\pi$
$110$	0	0
$111$	−8.32249	−0.789936
$112$	0.402576	0.0380399
$113$	−4.12892	−0.388416	−0.194208	−	0.980960i	$-0.562214\pi$
$113$	−4.12892	−0.388416	−0.194208	+	0.980960i	$0.562214\pi$
$114$	−1.76122	−0.164953
$115$	−0.687389	−0.0640993
$116$	−5.26289	−0.488647
$117$	1.91576	0.177112
$118$	4.57191	0.420879
$119$	−6.13864	−0.562729
$120$	−1.10945	−0.101278
$121$	0	0
$122$	−4.69700	−0.425246
$123$	−0.000568784 0	−5.12856e−5 0
$124$	−0.466778	−0.0419179
$125$	3.61858	0.323656
$126$	−1.86587	−0.166225
$127$	3.43178	0.304521	0.152261	−	0.988340i	$-0.451345\pi$
$127$	3.43178	0.304521	0.152261	+	0.988340i	$0.451345\pi$
$128$	5.56849	0.492190
$129$	−12.3355	−1.08608
$130$	−0.338341	−0.0296745
$131$	−6.51214	−0.568969	−0.284484	−	0.958681i	$-0.591822\pi$
$131$	−6.51214	−0.568969	−0.284484	+	0.958681i	$0.591822\pi$
$132$	0	0
$133$	−1.93608	−0.167879
$134$	−3.76985	−0.325665
$135$	1.87748	0.161587
$136$	16.8884	1.44817
$137$	4.52628	0.386707	0.193353	−	0.981129i	$-0.438064\pi$
$137$	4.52628	0.386707	0.193353	+	0.981129i	$0.438064\pi$
$138$	−1.80002	−0.153228
$139$	−12.0661	−1.02343	−0.511716	−	0.859155i	$-0.670990\pi$
$139$	−12.0661	−1.02343	−0.511716	+	0.859155i	$0.670990\pi$
$140$	−0.445035	−0.0376123
$141$	2.74525	0.231192
$142$	4.23590	0.355469
$143$	0	0
$144$	0.730435	0.0608696
$145$	−1.67989	−0.139507
$146$	−2.46613	−0.204098
$147$	−6.12803	−0.505431
$148$	9.18451	0.754962
$149$	8.52604	0.698481	0.349240	−	0.937033i	$-0.386440\pi$
$149$	8.52604	0.698481	0.349240	+	0.937033i	$0.386440\pi$
$150$	4.67327	0.381571
$151$	−15.9350	−1.29677	−0.648385	−	0.761313i	$-0.724555\pi$
$151$	−15.9350	−1.29677	−0.648385	+	0.761313i	$0.724555\pi$
$152$	5.32646	0.432033
$153$	−11.1380	−0.900452
$154$	0	0
$155$	−0.148993	−0.0119674
$156$	1.19654	0.0958002
$157$	1.00673	0.0803462	0.0401731	−	0.999193i	$-0.487209\pi$
$157$	1.00673	0.0803462	0.0401731	+	0.999193i	$0.487209\pi$
$158$	0.643887	0.0512249
$159$	−12.7784	−1.01339
$160$	2.00195	0.158268
$161$	−1.97874	−0.155946
$162$	−0.385033	−0.0302510
$163$	1.04293	0.0816889	0.0408445	−	0.999166i	$-0.486995\pi$
$163$	1.04293	0.0816889	0.0408445	+	0.999166i	$0.486995\pi$
$164$	0.000627698 0	4.90150e−5 0
$165$	0	0
$166$	10.9097	0.846758
$167$	8.83304	0.683521	0.341760	−	0.939787i	$-0.388977\pi$
$167$	8.83304	0.683521	0.341760	+	0.939787i	$0.388977\pi$
$168$	−3.19369	−0.246399
$169$	1.00000	0.0769231
$170$	1.96707	0.150868
$171$	−3.51283	−0.268633
$172$	13.6132	1.03800
$173$	−3.93487	−0.299162	−0.149581	−	0.988749i	$-0.547793\pi$
$173$	−3.93487	−0.299162	−0.149581	+	0.988749i	$0.547793\pi$
$174$	−4.39901	−0.333488
$175$	5.13726	0.388340
$176$	0	0
$177$	−5.16092	−0.387918
$178$	13.2048	0.989740
$179$	1.73483	0.129667	0.0648337	−	0.997896i	$-0.479348\pi$
$179$	1.73483	0.129667	0.0648337	+	0.997896i	$0.479348\pi$
$180$	−0.807473	−0.0601855
$181$	−21.2368	−1.57852	−0.789259	−	0.614061i	$-0.789535\pi$
$181$	−21.2368	−1.57852	−0.789259	+	0.614061i	$0.789535\pi$
$182$	−0.973959	−0.0721947
$183$	5.30212	0.391944
$184$	5.44383	0.401324
$185$	2.93165	0.215539
$186$	−0.390158	−0.0286078
$187$	0	0
$188$	−3.02960	−0.220956
$189$	5.40456	0.393124
$190$	0.620398	0.0450084
$191$	21.5603	1.56005	0.780025	−	0.625749i	$-0.215206\pi$
$191$	21.5603	1.56005	0.780025	+	0.625749i	$0.215206\pi$
$192$	6.03642	0.435641
$193$	−6.35334	−0.457323	−0.228662	−	0.973506i	$-0.573435\pi$
$193$	−6.35334	−0.457323	−0.228662	+	0.973506i	$0.573435\pi$
$194$	−13.8910	−0.997319
$195$	0.381930	0.0273506
$196$	6.76276	0.483054
$197$	18.8680	1.34429	0.672143	−	0.740421i	$-0.265374\pi$
$197$	18.8680	1.34429	0.672143	+	0.740421i	$0.265374\pi$
$198$	0	0
$199$	10.5100	0.745038	0.372519	−	0.928025i	$-0.378494\pi$
$199$	10.5100	0.745038	0.372519	+	0.928025i	$0.378494\pi$
$200$	−14.1334	−0.999384
$201$	4.25553	0.300162
$202$	11.6051	0.816531
$203$	−4.83577	−0.339404
$204$	−6.95655	−0.487056
$205$	0.000200358 0	1.39936e−5 0
$206$	11.8630	0.826537
$207$	−3.59023	−0.249538
$208$	0.381277	0.0264368
$209$	0	0
$210$	−0.371984	−0.0256694
$211$	−2.27182	−0.156399	−0.0781994	−	0.996938i	$-0.524917\pi$
$211$	−2.27182	−0.156399	−0.0781994	+	0.996938i	$0.524917\pi$
$212$	14.1020	0.968526
$213$	−4.78162	−0.327631
$214$	−11.7332	−0.802065
$215$	4.34526	0.296344
$216$	−14.8688	−1.01170
$217$	−0.428895	−0.0291153
$218$	9.23152	0.625238
$219$	2.78384	0.188114
$220$	0	0
$221$	−5.81387	−0.391083
$222$	7.67692	0.515241
$223$	13.9568	0.934618	0.467309	−	0.884094i	$-0.345223\pi$
$223$	13.9568	0.934618	0.467309	+	0.884094i	$0.345223\pi$
$224$	5.76288	0.385049
$225$	9.32106	0.621404
$226$	3.80864	0.253347
$227$	−23.3383	−1.54902	−0.774508	−	0.632564i	$-0.782003\pi$
$227$	−23.3383	−1.54902	−0.774508	+	0.632564i	$0.782003\pi$
$228$	−2.19404	−0.145304
$229$	−19.6197	−1.29651	−0.648253	−	0.761425i	$-0.724500\pi$
$229$	−19.6197	−1.29651	−0.648253	+	0.761425i	$0.724500\pi$
$230$	0.634068	0.0418092
$231$	0	0
$232$	13.3040	0.873449
$233$	−8.76982	−0.574530	−0.287265	−	0.957851i	$-0.592746\pi$
$233$	−8.76982	−0.574530	−0.287265	+	0.957851i	$0.592746\pi$
$234$	−1.76716	−0.115523
$235$	−0.967030	−0.0630821
$236$	5.69548	0.370744
$237$	−0.726839	−0.0472133
$238$	5.66247	0.367044
$239$	−14.7917	−0.956796	−0.478398	−	0.878143i	$-0.658782\pi$
$239$	−14.7917	−0.956796	−0.478398	+	0.878143i	$0.658782\pi$
$240$	0.145621	0.00939981
$241$	16.4874	1.06204	0.531022	−	0.847358i	$-0.321808\pi$
$241$	16.4874	1.06204	0.531022	+	0.847358i	$0.321808\pi$
$242$	0	0
$243$	15.7905	1.01296
$244$	−5.85130	−0.374591
$245$	2.15863	0.137910
$246$	0.000524664 0	3.34514e−5 0
$247$	−1.83365	−0.116672
$248$	1.17996	0.0749276
$249$	−12.3152	−0.780446
$250$	−3.33789	−0.211107
$251$	−28.2646	−1.78405	−0.892024	−	0.451988i	$-0.850715\pi$
$251$	−28.2646	−1.78405	−0.892024	+	0.451988i	$0.850715\pi$
$252$	−2.32442	−0.146424
$253$	0	0
$254$	−3.16558	−0.198626
$255$	−2.22049	−0.139053
$256$	−16.7309	−1.04568
$257$	−13.8159	−0.861810	−0.430905	−	0.902397i	$-0.641806\pi$
$257$	−13.8159	−0.861810	−0.430905	+	0.902397i	$0.641806\pi$
$258$	11.3787	0.708405
$259$	8.43912	0.524382
$260$	−0.421490	−0.0261397
$261$	−8.77404	−0.543099
$262$	6.00700	0.371114
$263$	−10.7474	−0.662715	−0.331357	−	0.943505i	$-0.607507\pi$
$263$	−10.7474	−0.662715	−0.331357	+	0.943505i	$0.607507\pi$
$264$	0	0
$265$	4.50126	0.276510
$266$	1.78590	0.109500
$267$	−14.9060	−0.912231
$268$	−4.69630	−0.286872
$269$	19.6484	1.19798	0.598992	−	0.800755i	$-0.295568\pi$
$269$	19.6484	1.19798	0.598992	+	0.800755i	$0.295568\pi$
$270$	−1.73184	−0.105397
$271$	14.8166	0.900044	0.450022	−	0.893018i	$-0.351416\pi$
$271$	14.8166	0.900044	0.450022	+	0.893018i	$0.351416\pi$
$272$	−2.21670	−0.134407
$273$	1.09944	0.0665409
$274$	−4.17518	−0.252232
$275$	0	0
$276$	−2.24238	−0.134976
$277$	−9.26840	−0.556884	−0.278442	−	0.960453i	$-0.589818\pi$
$277$	−9.26840	−0.556884	−0.278442	+	0.960453i	$0.589818\pi$
$278$	11.1301	0.667541
$279$	−0.778189	−0.0465890
$280$	1.12500	0.0672314
$281$	16.3501	0.975363	0.487681	−	0.873022i	$-0.337843\pi$
$281$	16.3501	0.975363	0.487681	+	0.873022i	$0.337843\pi$
$282$	−2.53230	−0.150796
$283$	−14.1316	−0.840038	−0.420019	−	0.907515i	$-0.637977\pi$
$283$	−14.1316	−0.840038	−0.420019	+	0.907515i	$0.637977\pi$
$284$	5.27689	0.313126
$285$	−0.700325	−0.0414837
$286$	0	0
$287$	0.000576756 0	3.40448e−5 0
$288$	10.4562	0.616137
$289$	16.8011	0.988300
$290$	1.54958	0.0909943
$291$	15.6806	0.919216
$292$	−3.07218	−0.179786
$293$	−28.1225	−1.64293	−0.821467	−	0.570256i	$-0.806844\pi$
$293$	−28.1225	−1.64293	−0.821467	+	0.570256i	$0.806844\pi$
$294$	5.65268	0.329671
$295$	1.81796	0.105846
$296$	−23.2174	−1.34948
$297$	0	0
$298$	−7.86469	−0.455589
$299$	−1.87405	−0.108379
$300$	5.82174	0.336118
$301$	12.5084	0.720972
$302$	14.6989	0.845827
$303$	−13.1002	−0.752586
$304$	−0.699128	−0.0400977
$305$	−1.86770	−0.106944
$306$	10.2740	0.587326
$307$	30.2633	1.72722	0.863608	−	0.504163i	$-0.168199\pi$
$307$	30.2633	1.72722	0.863608	+	0.504163i	$0.168199\pi$
$308$	0	0
$309$	−13.3914	−0.761809
$310$	0.137436	0.00780581
$311$	−13.4972	−0.765358	−0.382679	−	0.923881i	$-0.624998\pi$
$311$	−13.4972	−0.765358	−0.382679	+	0.923881i	$0.624998\pi$
$312$	−3.02473	−0.171241
$313$	20.9157	1.18222	0.591112	−	0.806589i	$-0.298689\pi$
$313$	20.9157	1.18222	0.591112	+	0.806589i	$0.298689\pi$
$314$	−0.928643	−0.0524064
$315$	−0.741940	−0.0418036
$316$	0.802124	0.0451230
$317$	−26.2614	−1.47499	−0.737495	−	0.675353i	$-0.763991\pi$
$317$	−26.2614	−1.47499	−0.737495	+	0.675353i	$0.763991\pi$
$318$	11.7872	0.660992
$319$	0	0
$320$	−2.12636	−0.118867
$321$	13.2448	0.739253
$322$	1.82525	0.101717
$323$	10.6606	0.593171
$324$	−0.479656	−0.0266476
$325$	4.86546	0.269887
$326$	−0.962035	−0.0532822
$327$	−10.4208	−0.576273
$328$	−0.00158675	−8.76135e−5 0
$329$	−2.78372	−0.153472
$330$	0	0
$331$	25.2184	1.38613	0.693065	−	0.720875i	$-0.256260\pi$
$331$	25.2184	1.38613	0.693065	+	0.720875i	$0.256260\pi$
$332$	13.5908	0.745893
$333$	15.3120	0.839091
$334$	−8.14786	−0.445831
$335$	−1.49903	−0.0819010
$336$	0.419190	0.0228687
$337$	−4.55229	−0.247979	−0.123989	−	0.992284i	$-0.539569\pi$
$337$	−4.55229	−0.247979	−0.123989	+	0.992284i	$0.539569\pi$
$338$	−0.922431	−0.0501736
$339$	−4.29932	−0.233507
$340$	2.45049	0.132896
$341$	0	0
$342$	3.24034	0.175217
$343$	13.6049	0.734598
$344$	−34.4126	−1.85541
$345$	−0.715756	−0.0385350
$346$	3.62964	0.195131
$347$	5.37024	0.288290	0.144145	−	0.989557i	$-0.453957\pi$
$347$	5.37024	0.288290	0.144145	+	0.989557i	$0.453957\pi$
$348$	−5.48008	−0.293763
$349$	35.3109	1.89015	0.945076	−	0.326851i	$-0.105988\pi$
$349$	35.3109	1.89015	0.945076	+	0.326851i	$0.105988\pi$
$350$	−4.73876	−0.253298
$351$	5.11863	0.273212
$352$	0	0
$353$	−15.4108	−0.820237	−0.410118	−	0.912032i	$-0.634513\pi$
$353$	−15.4108	−0.820237	−0.410118	+	0.912032i	$0.634513\pi$
$354$	4.76059	0.253023
$355$	1.68435	0.0893962
$356$	16.4499	0.871843
$357$	−6.39198	−0.338299
$358$	−1.60026	−0.0845765
$359$	13.5221	0.713669	0.356835	−	0.934168i	$-0.383856\pi$
$359$	13.5221	0.713669	0.356835	+	0.934168i	$0.383856\pi$
$360$	2.04120	0.107581
$361$	−15.6377	−0.823039
$362$	19.5895	1.02960
$363$	0	0
$364$	−1.21331	−0.0635949
$365$	−0.980624	−0.0513282
$366$	−4.89084	−0.255648
$367$	−26.1965	−1.36745	−0.683724	−	0.729741i	$-0.739641\pi$
$367$	−26.1965	−1.36745	−0.683724	+	0.729741i	$0.739641\pi$
$368$	−0.714533	−0.0372476
$369$	0.00104647	5.44769e−5 0
$370$	−2.70424	−0.140587
$371$	12.9575	0.672719
$372$	−0.486041	−0.0252001
$373$	37.1186	1.92193	0.960964	−	0.276674i	$-0.0892323\pi$
$373$	37.1186	1.92193	0.960964	+	0.276674i	$0.0892323\pi$
$374$	0	0
$375$	3.76792	0.194574
$376$	7.65847	0.394956
$377$	−4.57993	−0.235878
$378$	−4.98533	−0.256418
$379$	35.9702	1.84767	0.923834	−	0.382794i	$-0.125038\pi$
$379$	35.9702	1.84767	0.923834	+	0.382794i	$0.125038\pi$
$380$	0.772863	0.0396471
$381$	3.57341	0.183071
$382$	−19.8879	−1.01755
$383$	14.0279	0.716793	0.358396	−	0.933570i	$-0.383324\pi$
$383$	14.0279	0.716793	0.358396	+	0.933570i	$0.383324\pi$
$384$	5.79830	0.295893
$385$	0	0
$386$	5.86052	0.298292
$387$	22.6953	1.15367
$388$	−17.3048	−0.878519
$389$	19.4537	0.986340	0.493170	−	0.869933i	$-0.335838\pi$
$389$	19.4537	0.986340	0.493170	+	0.869933i	$0.335838\pi$
$390$	−0.352304	−0.0178396
$391$	10.8955	0.551009
$392$	−17.0955	−0.863452
$393$	−6.78089	−0.342051
$394$	−17.4044	−0.876820
$395$	0.256033	0.0128824
$396$	0	0
$397$	36.5061	1.83219	0.916094	−	0.400963i	$-0.131324\pi$
$397$	36.5061	1.83219	0.916094	+	0.400963i	$0.131324\pi$
$398$	−9.69479	−0.485956
$399$	−2.01598	−0.100925
$400$	1.85509	0.0927545
$401$	−20.8956	−1.04348	−0.521738	−	0.853106i	$-0.674716\pi$
$401$	−20.8956	−1.04348	−0.521738	+	0.853106i	$0.674716\pi$
$402$	−3.92543	−0.195783
$403$	−0.406204	−0.0202345
$404$	14.4571	0.719267
$405$	−0.153104	−0.00760778
$406$	4.46066	0.221379
$407$	0	0
$408$	17.5854	0.870606
$409$	12.3456	0.610452	0.305226	−	0.952280i	$-0.401268\pi$
$409$	12.3456	0.610452	0.305226	+	0.952280i	$0.401268\pi$
$410$	−0.000184816 0	−9.12742e−6 0
$411$	4.71308	0.232479
$412$	14.7784	0.728081
$413$	5.23325	0.257511
$414$	3.31174	0.162763
$415$	4.33811	0.212949
$416$	5.45799	0.267600
$417$	−12.5640	−0.615264
$418$	0	0
$419$	−25.0848	−1.22547	−0.612737	−	0.790287i	$-0.709932\pi$
$419$	−25.0848	−1.22547	−0.612737	+	0.790287i	$0.709932\pi$
$420$	−0.463401	−0.0226116
$421$	37.8672	1.84554	0.922768	−	0.385355i	$-0.125921\pi$
$421$	37.8672	1.84554	0.922768	+	0.385355i	$0.125921\pi$
$422$	2.09560	0.102012
$423$	−5.05080	−0.245578
$424$	−35.6481	−1.73123
$425$	−28.2872	−1.37213
$426$	4.41071	0.213700
$427$	−5.37643	−0.260183
$428$	−14.6167	−0.706524
$429$	0	0
$430$	−4.00820	−0.193293
$431$	32.6780	1.57404	0.787021	−	0.616926i	$-0.211622\pi$
$431$	32.6780	1.57404	0.787021	+	0.616926i	$0.211622\pi$
$432$	1.95162	0.0938972
$433$	−5.29260	−0.254346	−0.127173	−	0.991881i	$-0.540590\pi$
$433$	−5.29260	−0.254346	−0.127173	+	0.991881i	$0.540590\pi$
$434$	0.395626	0.0189907
$435$	−1.74921	−0.0838683
$436$	11.5002	0.550760
$437$	3.43635	0.164383
$438$	−2.56790	−0.122699
$439$	−20.2668	−0.967281	−0.483640	−	0.875267i	$-0.660686\pi$
$439$	−20.2668	−0.967281	−0.483640	+	0.875267i	$0.660686\pi$
$440$	0	0
$441$	11.2745	0.536883
$442$	5.36289	0.255087
$443$	−10.1489	−0.482190	−0.241095	−	0.970502i	$-0.577507\pi$
$443$	−10.1489	−0.482190	−0.241095	+	0.970502i	$0.577507\pi$
$444$	9.56355	0.453866
$445$	5.25072	0.248908
$446$	−12.8742	−0.609611
$447$	8.87790	0.419910
$448$	−6.12101	−0.289191
$449$	5.43687	0.256582	0.128291	−	0.991737i	$-0.459051\pi$
$449$	5.43687	0.256582	0.128291	+	0.991737i	$0.459051\pi$
$450$	−8.59803	−0.405315
$451$	0	0
$452$	4.74463	0.223169
$453$	−16.5926	−0.779588
$454$	21.5280	1.01036
$455$	−0.387283	−0.0181561
$456$	5.54628	0.259728
$457$	13.1344	0.614401	0.307200	−	0.951645i	$-0.400608\pi$
$457$	13.1344	0.614401	0.307200	+	0.951645i	$0.400608\pi$
$458$	18.0978	0.845655
$459$	−29.7590	−1.38903
$460$	0.789893	0.0368289
$461$	25.7015	1.19704	0.598519	−	0.801108i	$-0.295756\pi$
$461$	25.7015	1.19704	0.598519	+	0.801108i	$0.295756\pi$
$462$	0	0
$463$	14.9544	0.694990	0.347495	−	0.937682i	$-0.387032\pi$
$463$	14.9544	0.694990	0.347495	+	0.937682i	$0.387032\pi$
$464$	−1.74622	−0.0810663
$465$	−0.155142	−0.00719452
$466$	8.08955	0.374741
$467$	7.71161	0.356851	0.178425	−	0.983953i	$-0.442900\pi$
$467$	7.71161	0.356851	0.178425	+	0.983953i	$0.442900\pi$
$468$	−2.20144	−0.101762
$469$	−4.31516	−0.199256
$470$	0.892019	0.0411458
$471$	1.04828	0.0483023
$472$	−14.3975	−0.662699
$473$	0	0
$474$	0.670459	0.0307952
$475$	−8.92154	−0.409348
$476$	7.05405	0.323322
$477$	23.5101	1.07645
$478$	13.6443	0.624077
$479$	3.22236	0.147233	0.0736167	−	0.997287i	$-0.476546\pi$
$479$	3.22236	0.147233	0.0736167	+	0.997287i	$0.476546\pi$
$480$	2.08457	0.0951472
$481$	7.99264	0.364433
$482$	−15.2085	−0.692726
$483$	−2.06040	−0.0937514
$484$	0	0
$485$	−5.52360	−0.250814
$486$	−14.5657	−0.660712
$487$	−23.9288	−1.08432	−0.542158	−	0.840276i	$-0.682393\pi$
$487$	−23.9288	−1.08432	−0.542158	+	0.840276i	$0.682393\pi$
$488$	14.7914	0.669576
$489$	1.08598	0.0491095
$490$	−1.99119	−0.0899528
$491$	−5.81927	−0.262620	−0.131310	−	0.991341i	$-0.541918\pi$
$491$	−5.81927	−0.262620	−0.131310	+	0.991341i	$0.541918\pi$
$492$	0.000653602 0	2.94667e−5 0
$493$	26.6271	1.19922
$494$	1.69141	0.0761003
$495$	0	0
$496$	−0.154876	−0.00695415
$497$	4.84863	0.217491
$498$	11.3599	0.509051
$499$	−27.5026	−1.23119	−0.615593	−	0.788064i	$-0.711084\pi$
$499$	−27.5026	−1.23119	−0.615593	+	0.788064i	$0.711084\pi$
$500$	−4.15819	−0.185960
$501$	9.19756	0.410917
$502$	26.0722	1.16366
$503$	13.5775	0.605390	0.302695	−	0.953087i	$-0.402114\pi$
$503$	13.5775	0.605390	0.302695	+	0.953087i	$0.402114\pi$
$504$	5.87586	0.261731
$505$	4.61462	0.205348
$506$	0	0
$507$	1.04127	0.0462444
$508$	−3.94353	−0.174966
$509$	−10.4461	−0.463014	−0.231507	−	0.972833i	$-0.574366\pi$
$509$	−10.4461	−0.463014	−0.231507	+	0.972833i	$0.574366\pi$
$510$	2.04825	0.0906981
$511$	−2.82285	−0.124876
$512$	4.29611	0.189863
$513$	−9.38576	−0.414391
$514$	12.7442	0.562122
$515$	4.71719	0.207864
$516$	14.1750	0.624020
$517$	0	0
$518$	−7.78451	−0.342032
$519$	−4.09725	−0.179849
$520$	1.06548	0.0467243
$521$	−6.12885	−0.268510	−0.134255	−	0.990947i	$-0.542864\pi$
$521$	−6.12885	−0.268510	−0.134255	+	0.990947i	$0.542864\pi$
$522$	8.09344	0.354240
$523$	0.151470	0.00662331	0.00331166	−	0.999995i	$-0.498946\pi$
$523$	0.151470	0.00662331	0.00331166	+	0.999995i	$0.498946\pi$
$524$	7.48324	0.326907
$525$	5.34926	0.233461
$526$	9.91376	0.432260
$527$	2.36162	0.102874
$528$	0	0
$529$	−19.4879	−0.847302
$530$	−4.15210	−0.180356
$531$	9.49522	0.412058
$532$	2.22479	0.0964568
$533$	0.000546242 0	2.36604e−5 0
$534$	13.7497	0.595009
$535$	−4.66556	−0.201710
$536$	11.8717	0.512780
$537$	1.80643	0.0779531
$538$	−18.1243	−0.781394
$539$	0	0
$540$	−2.15745	−0.0928418
$541$	1.73107	0.0744245	0.0372123	−	0.999307i	$-0.488152\pi$
$541$	1.73107	0.0744245	0.0372123	+	0.999307i	$0.488152\pi$
$542$	−13.6673	−0.587060
$543$	−22.1132	−0.948968
$544$	−31.7321	−1.36050
$545$	3.67080	0.157240
$546$	−1.01415	−0.0434018
$547$	−16.6115	−0.710255	−0.355128	−	0.934818i	$-0.615563\pi$
$547$	−16.6115	−0.710255	−0.355128	+	0.934818i	$0.615563\pi$
$548$	−5.20125	−0.222186
$549$	−9.75501	−0.416334
$550$	0	0
$551$	8.39797	0.357766
$552$	5.66849	0.241267
$553$	0.737026	0.0313415
$554$	8.54946	0.363232
$555$	3.05263	0.129577
$556$	13.8654	0.588024
$557$	−10.7323	−0.454744	−0.227372	−	0.973808i	$-0.573013\pi$
$557$	−10.7323	−0.454744	−0.227372	+	0.973808i	$0.573013\pi$
$558$	0.717826	0.0303880
$559$	11.8466	0.501059
$560$	−0.147662	−0.00623986
$561$	0	0
$562$	−15.0818	−0.636187
$563$	−31.5254	−1.32864	−0.664319	−	0.747449i	$-0.731279\pi$
$563$	−31.5254	−1.32864	−0.664319	+	0.747449i	$0.731279\pi$
$564$	−3.15463	−0.132834
$565$	1.51446	0.0637138
$566$	13.0355	0.547921
$567$	−0.440729	−0.0185089
$568$	−13.3394	−0.559707
$569$	−7.31323	−0.306587	−0.153293	−	0.988181i	$-0.548988\pi$
$569$	−7.31323	−0.306587	−0.153293	+	0.988181i	$0.548988\pi$
$570$	0.646002	0.0270580
$571$	−44.5745	−1.86538	−0.932692	−	0.360674i	$-0.882547\pi$
$571$	−44.5745	−1.86538	−0.932692	+	0.360674i	$0.882547\pi$
$572$	0	0
$573$	22.4501	0.937866
$574$	−0.000532017 0	−2.22060e−5 0
$575$	−9.11812	−0.380252
$576$	−11.1060	−0.462750
$577$	25.5030	1.06170	0.530852	−	0.847464i	$-0.321872\pi$
$577$	25.5030	1.06170	0.530852	+	0.847464i	$0.321872\pi$
$578$	−15.4979	−0.644626
$579$	−6.61553	−0.274932
$580$	1.93039	0.0801552
$581$	12.4878	0.518082
$582$	−14.4643	−0.599565
$583$	0	0
$584$	7.76613	0.321365
$585$	−0.702687	−0.0290525
$586$	25.9411	1.07162
$587$	14.2270	0.587212	0.293606	−	0.955926i	$-0.405145\pi$
$587$	14.2270	0.587212	0.293606	+	0.955926i	$0.405145\pi$
$588$	7.04185	0.290401
$589$	0.744835	0.0306904
$590$	−1.67695	−0.0690388
$591$	19.6466	0.808154
$592$	3.04741	0.125248
$593$	−1.34235	−0.0551235	−0.0275618	−	0.999620i	$-0.508774\pi$
$593$	−1.34235	−0.0551235	−0.0275618	+	0.999620i	$0.508774\pi$
$594$	0	0
$595$	2.25161	0.0923071
$596$	−9.79746	−0.401320
$597$	10.9438	0.447899
$598$	1.72868	0.0706911
$599$	−19.5750	−0.799814	−0.399907	−	0.916556i	$-0.630958\pi$
$599$	−19.5750	−0.799814	−0.399907	+	0.916556i	$0.630958\pi$
$600$	−14.7167	−0.600806
$601$	−4.43564	−0.180933	−0.0904667	−	0.995899i	$-0.528836\pi$
$601$	−4.43564	−0.180933	−0.0904667	+	0.995899i	$0.528836\pi$
$602$	−11.5381	−0.470259
$603$	−7.82945	−0.318840
$604$	18.3112	0.745073
$605$	0	0
$606$	12.0840	0.490880
$607$	36.7283	1.49076	0.745378	−	0.666642i	$-0.232269\pi$
$607$	36.7283	1.49076	0.745378	+	0.666642i	$0.232269\pi$
$608$	−10.0080	−0.405879
$609$	−5.03534	−0.204042
$610$	1.72283	0.0697552
$611$	−2.63645	−0.106659
$612$	12.7989	0.517364
$613$	14.0824	0.568783	0.284392	−	0.958708i	$-0.408208\pi$
$613$	14.0824	0.568783	0.284392	+	0.958708i	$0.408208\pi$
$614$	−27.9158	−1.12659
$615$	0.000208626 0	8.41262e−6 0
$616$	0	0
$617$	−40.1995	−1.61837	−0.809185	−	0.587554i	$-0.800091\pi$
$617$	−40.1995	−1.61837	−0.809185	+	0.587554i	$0.800091\pi$
$618$	12.3526	0.496895
$619$	−43.4852	−1.74782	−0.873909	−	0.486089i	$-0.838423\pi$
$619$	−43.4852	−1.74782	−0.873909	+	0.486089i	$0.838423\pi$
$620$	0.171211	0.00687599
$621$	−9.59256	−0.384936
$622$	12.4503	0.499210
$623$	15.1149	0.605565
$624$	0.397012	0.0158932
$625$	23.0000	0.920002
$626$	−19.2933	−0.771115
$627$	0	0
$628$	−1.15686	−0.0461638
$629$	−46.4682	−1.85281
$630$	0.684389	0.0272667
$631$	36.0670	1.43580	0.717902	−	0.696144i	$-0.245103\pi$
$631$	36.0670	1.43580	0.717902	+	0.696144i	$0.245103\pi$
$632$	−2.02768	−0.0806567
$633$	−2.36558	−0.0940234
$634$	24.2244	0.962073
$635$	−1.25875	−0.0499521
$636$	14.6839	0.582255
$637$	5.88516	0.233178
$638$	0	0
$639$	8.79737	0.348019
$640$	−2.04248	−0.0807363
$641$	19.3973	0.766149	0.383075	−	0.923717i	$-0.374865\pi$
$641$	19.3973	0.766149	0.383075	+	0.923717i	$0.374865\pi$
$642$	−12.2174	−0.482183
$643$	−18.2403	−0.719328	−0.359664	−	0.933082i	$-0.617109\pi$
$643$	−18.2403	−0.719328	−0.359664	+	0.933082i	$0.617109\pi$
$644$	2.27381	0.0896007
$645$	4.52459	0.178155
$646$	−9.83366	−0.386900
$647$	−26.6796	−1.04888	−0.524441	−	0.851447i	$-0.675726\pi$
$647$	−26.6796	−1.04888	−0.524441	+	0.851447i	$0.675726\pi$
$648$	1.21252	0.0476321
$649$	0	0
$650$	−4.48805	−0.176036
$651$	−0.446595	−0.0175034
$652$	−1.19846	−0.0469353
$653$	−22.8050	−0.892427	−0.446214	−	0.894927i	$-0.647228\pi$
$653$	−22.8050	−0.892427	−0.446214	+	0.894927i	$0.647228\pi$
$654$	9.61250	0.375878
$655$	2.38861	0.0933307
$656$	0.000208270 0	8.13156e−6 0
$657$	−5.12180	−0.199820
$658$	2.56779	0.100103
$659$	36.9350	1.43878	0.719392	−	0.694605i	$-0.244421\pi$
$659$	36.9350	1.43878	0.719392	+	0.694605i	$0.244421\pi$
$660$	0	0
$661$	−3.11128	−0.121015	−0.0605074	−	0.998168i	$-0.519272\pi$
$661$	−3.11128	−0.121015	−0.0605074	+	0.998168i	$0.519272\pi$
$662$	−23.2623	−0.904114
$663$	−6.05380	−0.235110
$664$	−34.3560	−1.33327
$665$	0.710140	0.0275380
$666$	−14.1242	−0.547303
$667$	8.58301	0.332336
$668$	−10.1502	−0.392724
$669$	14.5328	0.561871
$670$	1.38275	0.0534205
$671$	0	0
$672$	6.00071	0.231482
$673$	−50.4380	−1.94424	−0.972121	−	0.234478i	$-0.924662\pi$
$673$	−50.4380	−1.94424	−0.972121	+	0.234478i	$0.924662\pi$
$674$	4.19917	0.161746
$675$	24.9045	0.958574
$676$	−1.14912	−0.0441970
$677$	−22.0689	−0.848175	−0.424087	−	0.905621i	$-0.639405\pi$
$677$	−22.0689	−0.848175	−0.424087	+	0.905621i	$0.639405\pi$
$678$	3.96582	0.152306
$679$	−15.9004	−0.610201
$680$	−6.19455	−0.237550
$681$	−24.3014	−0.931233
$682$	0	0
$683$	−16.8808	−0.645925	−0.322963	−	0.946412i	$-0.604679\pi$
$683$	−16.8808	−0.645925	−0.322963	+	0.946412i	$0.604679\pi$
$684$	4.03666	0.154346
$685$	−1.66021	−0.0634333
$686$	−12.5496	−0.479147
$687$	−20.4294	−0.779429
$688$	4.51685	0.172203
$689$	12.2719	0.467524
$690$	0.660236	0.0251347
$691$	−8.56231	−0.325726	−0.162863	−	0.986649i	$-0.552073\pi$
$691$	−8.56231	−0.325726	−0.162863	+	0.986649i	$0.552073\pi$
$692$	4.52164	0.171887
$693$	0	0
$694$	−4.95368	−0.188039
$695$	4.42576	0.167879
$696$	13.8530	0.525097
$697$	−0.00317578	−0.000120291 0
$698$	−32.5719	−1.23286
$699$	−9.13174	−0.345394
$700$	−5.90333	−0.223125
$701$	41.2783	1.55906	0.779530	−	0.626364i	$-0.215458\pi$
$701$	41.2783	1.55906	0.779530	+	0.626364i	$0.215458\pi$
$702$	−4.72158	−0.178205
$703$	−14.6557	−0.552750
$704$	0	0
$705$	−1.00694	−0.0379235
$706$	14.2154	0.535005
$707$	13.2838	0.499588
$708$	5.93052	0.222883
$709$	−37.8390	−1.42107	−0.710537	−	0.703660i	$-0.751548\pi$
$709$	−37.8390	−1.42107	−0.710537	+	0.703660i	$0.751548\pi$
$710$	−1.55370	−0.0583093
$711$	1.33726	0.0501512
$712$	−41.5835	−1.55841
$713$	0.761247	0.0285089
$714$	5.89616	0.220658
$715$	0	0
$716$	−1.99353	−0.0745018
$717$	−15.4021	−0.575204
$718$	−12.4732	−0.465496
$719$	−21.6258	−0.806506	−0.403253	−	0.915089i	$-0.632121\pi$
$719$	−21.6258	−0.806506	−0.403253	+	0.915089i	$0.632121\pi$
$720$	−0.267919	−0.00998474
$721$	13.5790	0.505710
$722$	14.4247	0.536833
$723$	17.1678	0.638477
$724$	24.4036	0.906954
$725$	−22.2835	−0.827587
$726$	0	0
$727$	−22.0230	−0.816789	−0.408395	−	0.912806i	$-0.633911\pi$
$727$	−22.0230	−0.816789	−0.408395	+	0.912806i	$0.633911\pi$
$728$	3.06712	0.113675
$729$	15.1899	0.562590
$730$	0.904558	0.0334792
$731$	−68.8748	−2.54743
$732$	−6.09278	−0.225196
$733$	−7.18641	−0.265436	−0.132718	−	0.991154i	$-0.542370\pi$
$733$	−7.18641	−0.265436	−0.132718	+	0.991154i	$0.542370\pi$
$734$	24.1645	0.891927
$735$	2.24772	0.0829083
$736$	−10.2286	−0.377029
$737$	0	0
$738$	−0.000965294 0	−3.55330e−5 0
$739$	40.8058	1.50107	0.750533	−	0.660833i	$-0.229797\pi$
$739$	40.8058	1.50107	0.750533	+	0.660833i	$0.229797\pi$
$740$	−3.36882	−0.123840
$741$	−1.90932	−0.0701406
$742$	−11.9524	−0.438785
$743$	−33.5569	−1.23108	−0.615541	−	0.788105i	$-0.711063\pi$
$743$	−33.5569	−1.23108	−0.615541	+	0.788105i	$0.711063\pi$
$744$	1.22866	0.0450447
$745$	−3.12729	−0.114575
$746$	−34.2393	−1.25359
$747$	22.6579	0.829011
$748$	0	0
$749$	−13.4304	−0.490737
$750$	−3.47564	−0.126913
$751$	45.4190	1.65736	0.828681	−	0.559721i	$-0.189092\pi$
$751$	45.4190	1.65736	0.828681	+	0.559721i	$0.189092\pi$
$752$	−1.00522	−0.0366565
$753$	−29.4311	−1.07253
$754$	4.22467	0.153853
$755$	5.84484	0.212715
$756$	−6.21050	−0.225874
$757$	27.3245	0.993127	0.496564	−	0.868000i	$-0.334595\pi$
$757$	27.3245	0.993127	0.496564	+	0.868000i	$0.334595\pi$
$758$	−33.1801	−1.20515
$759$	0	0
$760$	−1.95371	−0.0708685
$761$	12.6284	0.457778	0.228889	−	0.973453i	$-0.426491\pi$
$761$	12.6284	0.457778	0.228889	+	0.973453i	$0.426491\pi$
$762$	−3.29622	−0.119409
$763$	10.5669	0.382547
$764$	−24.7754	−0.896343
$765$	4.08533	0.147706
$766$	−12.9398	−0.467533
$767$	4.95638	0.178964
$768$	−17.4214	−0.628639
$769$	44.6860	1.61142	0.805710	−	0.592311i	$-0.201784\pi$
$769$	44.6860	1.61142	0.805710	+	0.592311i	$0.201784\pi$
$770$	0	0
$771$	−14.3860	−0.518100
$772$	7.30076	0.262760
$773$	−25.0037	−0.899319	−0.449659	−	0.893200i	$-0.648455\pi$
$773$	−25.0037	−0.899319	−0.449659	+	0.893200i	$0.648455\pi$
$774$	−20.9348	−0.752487
$775$	−1.97637	−0.0709933
$776$	43.7446	1.57034
$777$	8.78740	0.315246
$778$	−17.9447	−0.643347
$779$	−0.00100161	−3.58866e−5 0
$780$	−0.438884	−0.0157146
$781$	0	0
$782$	−10.0503	−0.359399
$783$	−23.4429	−0.837782
$784$	2.24388	0.0801384
$785$	−0.369263	−0.0131796
$786$	6.25490	0.223105
$787$	10.8697	0.387464	0.193732	−	0.981055i	$-0.437941\pi$
$787$	10.8697	0.387464	0.193732	+	0.981055i	$0.437941\pi$
$788$	−21.6816	−0.772374
$789$	−11.1910	−0.398409
$790$	−0.236173	−0.00840266
$791$	4.35957	0.155008
$792$	0	0
$793$	−5.09198	−0.180821
$794$	−33.6743	−1.19506
$795$	4.68703	0.166232
$796$	−12.0773	−0.428069
$797$	37.7637	1.33766	0.668830	−	0.743416i	$-0.266795\pi$
$797$	37.7637	1.33766	0.668830	+	0.743416i	$0.266795\pi$
$798$	1.85960	0.0658291
$799$	15.3280	0.542264
$800$	26.5557	0.938884
$801$	27.4245	0.968996
$802$	19.2747	0.680614
$803$	0	0
$804$	−4.89012	−0.172461
$805$	0.725787	0.0255806
$806$	0.374695	0.0131981
$807$	20.4593	0.720201
$808$	−36.5458	−1.28568
$809$	27.6341	0.971562	0.485781	−	0.874080i	$-0.338535\pi$
$809$	27.6341	0.971562	0.485781	+	0.874080i	$0.338535\pi$
$810$	0.141227	0.00496223
$811$	−26.0452	−0.914571	−0.457286	−	0.889320i	$-0.651178\pi$
$811$	−26.0452	−0.914571	−0.457286	+	0.889320i	$0.651178\pi$
$812$	5.55689	0.195008
$813$	15.4281	0.541085
$814$	0	0
$815$	−0.382541	−0.0133998
$816$	−2.30818	−0.0808024
$817$	−21.7225	−0.759976
$818$	−11.3880	−0.398172
$819$	−2.02278	−0.0706815
$820$	−0.000230235 0	−8.04016e−6 0
$821$	24.7188	0.862692	0.431346	−	0.902187i	$-0.358039\pi$
$821$	24.7188	0.862692	0.431346	+	0.902187i	$0.358039\pi$
$822$	−4.34749	−0.151636
$823$	−21.6631	−0.755129	−0.377565	−	0.925983i	$-0.623238\pi$
$823$	−21.6631	−0.755129	−0.377565	+	0.925983i	$0.623238\pi$
$824$	−37.3582	−1.30143
$825$	0	0
$826$	−4.82731	−0.167964
$827$	23.5219	0.817935	0.408968	−	0.912549i	$-0.365889\pi$
$827$	23.5219	0.817935	0.408968	+	0.912549i	$0.365889\pi$
$828$	4.12561	0.143375
$829$	4.22276	0.146663	0.0733313	−	0.997308i	$-0.476637\pi$
$829$	4.22276	0.146663	0.0733313	+	0.997308i	$0.476637\pi$
$830$	−4.00161	−0.138898
$831$	−9.65090	−0.334786
$832$	−5.79717	−0.200981
$833$	−34.2155	−1.18550
$834$	11.5895	0.401310
$835$	−3.23990	−0.112121
$836$	0	0
$837$	−2.07921	−0.0718679
$838$	23.1390	0.799325
$839$	−52.4869	−1.81205	−0.906025	−	0.423225i	$-0.860898\pi$
$839$	−52.4869	−1.81205	−0.906025	+	0.423225i	$0.860898\pi$
$840$	1.17142	0.0404180
$841$	−8.02427	−0.276699
$842$	−34.9299	−1.20376
$843$	17.0248	0.586366
$844$	2.61060	0.0898606
$845$	−0.366793	−0.0126181
$846$	4.65901	0.160180
$847$	0	0
$848$	4.67901	0.160678
$849$	−14.7148	−0.505012
$850$	26.0930	0.894981
$851$	−14.9786	−0.513460
$852$	5.49466	0.188244
$853$	17.3001	0.592344	0.296172	−	0.955135i	$-0.404290\pi$
$853$	17.3001	0.592344	0.296172	+	0.955135i	$0.404290\pi$
$854$	4.95938	0.169707
$855$	1.28848	0.0440651
$856$	36.9493	1.26290
$857$	41.9996	1.43468	0.717340	−	0.696723i	$-0.245359\pi$
$857$	41.9996	1.43468	0.717340	+	0.696723i	$0.245359\pi$
$858$	0	0
$859$	−30.7468	−1.04907	−0.524534	−	0.851390i	$-0.675760\pi$
$859$	−30.7468	−1.04907	−0.524534	+	0.851390i	$0.675760\pi$
$860$	−4.99323	−0.170268
$861$	0.000600558 0	2.04670e−5 0
$862$	−30.1432	−1.02668
$863$	26.0836	0.887898	0.443949	−	0.896052i	$-0.353577\pi$
$863$	26.0836	0.887898	0.443949	+	0.896052i	$0.353577\pi$
$864$	27.9374	0.950450
$865$	1.44328	0.0490730
$866$	4.88205	0.165899
$867$	17.4945	0.594143
$868$	0.492853	0.0167285
$869$	0	0
$870$	1.61353	0.0547037
$871$	−4.08687	−0.138478
$872$	−29.0712	−0.984475
$873$	−28.8497	−0.976416
$874$	−3.16979	−0.107220
$875$	−3.82072	−0.129164
$876$	−3.19897	−0.108083
$877$	−2.79554	−0.0943987	−0.0471994	−	0.998885i	$-0.515030\pi$
$877$	−2.79554	−0.0943987	−0.0471994	+	0.998885i	$0.515030\pi$
$878$	18.6947	0.630916
$879$	−29.2831	−0.987694
$880$	0	0
$881$	−25.8280	−0.870168	−0.435084	−	0.900390i	$-0.643281\pi$
$881$	−25.8280	−0.870168	−0.435084	+	0.900390i	$0.643281\pi$
$882$	−10.4000	−0.350186
$883$	−22.4203	−0.754505	−0.377252	−	0.926110i	$-0.623131\pi$
$883$	−22.4203	−0.754505	−0.377252	+	0.926110i	$0.623131\pi$
$884$	6.68084	0.224701
$885$	1.89299	0.0636321
$886$	9.36168	0.314512
$887$	−4.10729	−0.137909	−0.0689546	−	0.997620i	$-0.521966\pi$
$887$	−4.10729	−0.137909	−0.0689546	+	0.997620i	$0.521966\pi$
$888$	−24.1756	−0.811278
$889$	−3.62348	−0.121528
$890$	−4.84342	−0.162352
$891$	0	0
$892$	−16.0381	−0.536995
$893$	4.83431	0.161774
$894$	−8.18925	−0.273890
$895$	−0.636324	−0.0212700
$896$	−5.87956	−0.196422
$897$	−1.95139	−0.0651550
$898$	−5.01514	−0.167357
$899$	1.86038	0.0620473
$900$	−10.7110	−0.357034
$901$	−71.3475	−2.37693
$902$	0	0
$903$	13.0246	0.433432
$904$	−11.9939	−0.398910
$905$	7.78950	0.258932
$906$	15.3055	0.508492
$907$	−17.3561	−0.576299	−0.288150	−	0.957585i	$-0.593040\pi$
$907$	−17.3561	−0.576299	−0.288150	+	0.957585i	$0.593040\pi$
$908$	26.8185	0.890004
$909$	24.1021	0.799418
$910$	0.357242	0.0118424
$911$	8.39001	0.277973	0.138987	−	0.990294i	$-0.455615\pi$
$911$	8.39001	0.277973	0.138987	+	0.990294i	$0.455615\pi$
$912$	−0.727980	−0.0241058
$913$	0	0
$914$	−12.1156	−0.400747
$915$	−1.94478	−0.0642925
$916$	22.5454	0.744921
$917$	6.87592	0.227063
$918$	27.4507	0.906007
$919$	−46.4736	−1.53302	−0.766511	−	0.642231i	$-0.778009\pi$
$919$	−46.4736	−1.53302	−0.766511	+	0.642231i	$0.778009\pi$
$920$	−1.99676	−0.0658312
$921$	31.5122	1.03836
$922$	−23.7079	−0.780777
$923$	4.59211	0.151151
$924$	0	0
$925$	38.8879	1.27863
$926$	−13.7944	−0.453312
$927$	24.6379	0.809214
$928$	−24.9972	−0.820573
$929$	7.85644	0.257761	0.128881	−	0.991660i	$-0.458862\pi$
$929$	7.85644	0.257761	0.128881	+	0.991660i	$0.458862\pi$
$930$	0.143107	0.00469267
$931$	−10.7913	−0.353671
$932$	10.0776	0.330102
$933$	−14.0542	−0.460115
$934$	−7.11343	−0.232759
$935$	0	0
$936$	5.56499	0.181897
$937$	−41.4540	−1.35424	−0.677122	−	0.735870i	$-0.736773\pi$
$937$	−41.4540	−1.35424	−0.677122	+	0.735870i	$0.736773\pi$
$938$	3.98044	0.129966
$939$	21.7789	0.710726
$940$	1.11124	0.0362445
$941$	15.2678	0.497718	0.248859	−	0.968540i	$-0.419945\pi$
$941$	15.2678	0.497718	0.248859	+	0.968540i	$0.419945\pi$
$942$	−0.966967	−0.0315055
$943$	−0.00102368	−3.33358e−5 0
$944$	1.88975	0.0615062
$945$	−1.98236	−0.0644860
$946$	0	0
$947$	−46.6618	−1.51631	−0.758153	−	0.652077i	$-0.773898\pi$
$947$	−46.6618	−1.51631	−0.758153	+	0.652077i	$0.773898\pi$
$948$	0.835227	0.0271269
$949$	−2.67351	−0.0867857
$950$	8.22951	0.267000
$951$	−27.3452	−0.886730
$952$	−17.8318	−0.577933
$953$	2.15113	0.0696819	0.0348410	−	0.999393i	$-0.488908\pi$
$953$	2.15113	0.0696819	0.0348410	+	0.999393i	$0.488908\pi$
$954$	−21.6864	−0.702124
$955$	−7.90817	−0.255902
$956$	16.9975	0.549737
$957$	0	0
$958$	−2.97241	−0.0960341
$959$	−4.77913	−0.154326
$960$	−2.21412	−0.0714603
$961$	−30.8350	−0.994677
$962$	−7.37266	−0.237704
$963$	−24.3682	−0.785254
$964$	−18.9460	−0.610209
$965$	2.33036	0.0750170
$966$	1.90057	0.0611500
$967$	−37.8034	−1.21568	−0.607838	−	0.794061i	$-0.707963\pi$
$967$	−37.8034	−1.21568	−0.607838	+	0.794061i	$0.707963\pi$
$968$	0	0
$969$	11.1005	0.356601
$970$	5.09514	0.163595
$971$	−49.2417	−1.58024	−0.790121	−	0.612951i	$-0.789982\pi$
$971$	−49.2417	−1.58024	−0.790121	+	0.612951i	$0.789982\pi$
$972$	−18.1452	−0.582008
$973$	12.7401	0.408430
$974$	22.0726	0.707253
$975$	5.06625	0.162250
$976$	−1.94146	−0.0621445
$977$	−16.5099	−0.528198	−0.264099	−	0.964496i	$-0.585075\pi$
$977$	−16.5099	−0.528198	−0.264099	+	0.964496i	$0.585075\pi$
$978$	−1.00174	−0.0320320
$979$	0	0
$980$	−2.48053	−0.0792377
$981$	19.1726	0.612133
$982$	5.36787	0.171296
$983$	−45.2659	−1.44376	−0.721879	−	0.692019i	$-0.756721\pi$
$983$	−45.2659	−1.44376	−0.721879	+	0.692019i	$0.756721\pi$
$984$	−0.00165223	−5.26712e−5 0
$985$	−6.92064	−0.220510
$986$	−24.5617	−0.782203
$987$	−2.89860	−0.0922636
$988$	2.10708	0.0670352
$989$	−22.2012	−0.705957
$990$	0	0
$991$	47.4794	1.50823	0.754117	−	0.656740i	$-0.228065\pi$
$991$	47.4794	1.50823	0.754117	+	0.656740i	$0.228065\pi$
$992$	−2.21706	−0.0703917
$993$	26.2592	0.833310
$994$	−4.47252	−0.141860
$995$	−3.85501	−0.122212
$996$	14.1517	0.448413
$997$	−1.08944	−0.0345029	−0.0172515	−	0.999851i	$-0.505492\pi$
$997$	−1.08944	−0.0345029	−0.0172515	+	0.999851i	$0.505492\pi$
$998$	25.3693	0.803050
$999$	40.9113	1.29438

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1573.2.a.o.1.3		8
11.5	even	5		143.2.h.b.14.3	✓	16
11.9	even	5		143.2.h.b.92.3	yes	16
11.10	odd	2		1573.2.a.n.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.h.b.14.3	✓	16	11.5	even	5
143.2.h.b.92.3	yes	16	11.9	even	5
1573.2.a.n.1.6		8	11.10	odd	2
1573.2.a.o.1.3		8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1573 = 11^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1573.a (trivial)

\(f(q)\)	\(=\)	\(q-0.922431 q^{2} +1.04127 q^{3} -1.14912 q^{4} -0.366793 q^{5} -0.960498 q^{6} -1.05586 q^{7} +2.90485 q^{8} -1.91576 q^{9} +O(q^{10})\)	\(q-0.922431 q^{2} +1.04127 q^{3} -1.14912 q^{4} -0.366793 q^{5} -0.960498 q^{6} -1.05586 q^{7} +2.90485 q^{8} -1.91576 q^{9} +0.338341 q^{10} -1.19654 q^{12} -1.00000 q^{13} +0.973959 q^{14} -0.381930 q^{15} -0.381277 q^{16} +5.81387 q^{17} +1.76716 q^{18} +1.83365 q^{19} +0.421490 q^{20} -1.09944 q^{21} +1.87405 q^{23} +3.02473 q^{24} -4.86546 q^{25} +0.922431 q^{26} -5.11863 q^{27} +1.21331 q^{28} +4.57993 q^{29} +0.352304 q^{30} +0.406204 q^{31} -5.45799 q^{32} -5.36289 q^{34} +0.387283 q^{35} +2.20144 q^{36} -7.99264 q^{37} -1.69141 q^{38} -1.04127 q^{39} -1.06548 q^{40} -0.000546242 q^{41} +1.01415 q^{42} -11.8466 q^{43} +0.702687 q^{45} -1.72868 q^{46} +2.63645 q^{47} -0.397012 q^{48} -5.88516 q^{49} +4.48805 q^{50} +6.05380 q^{51} +1.14912 q^{52} -12.2719 q^{53} +4.72158 q^{54} -3.06712 q^{56} +1.90932 q^{57} -4.22467 q^{58} -4.95638 q^{59} +0.438884 q^{60} +5.09198 q^{61} -0.374695 q^{62} +2.02278 q^{63} +5.79717 q^{64} +0.366793 q^{65} +4.08687 q^{67} -6.68084 q^{68} +1.95139 q^{69} -0.357242 q^{70} -4.59211 q^{71} -5.56499 q^{72} +2.67351 q^{73} +7.37266 q^{74} -5.06625 q^{75} -2.10708 q^{76} +0.960498 q^{78} -0.698032 q^{79} +0.139850 q^{80} +0.417411 q^{81} +0.000503870 q^{82} -11.8271 q^{83} +1.26339 q^{84} -2.13249 q^{85} +10.9277 q^{86} +4.76893 q^{87} -14.3152 q^{89} -0.648180 q^{90} +1.05586 q^{91} -2.15351 q^{92} +0.422968 q^{93} -2.43194 q^{94} -0.672569 q^{95} -5.68324 q^{96} +15.0592 q^{97} +5.42865 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 5 q^{3} + q^{4} - 5 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} - q^{9}+O(q^{10}) \) 8 * q + q^2 - 5 * q^3 + q^4 - 5 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 - q^9	\( 8 q + q^{2} - 5 q^{3} + q^{4} - 5 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} - q^{9} - 6 q^{10} - 7 q^{12} - 8 q^{13} + 2 q^{14} + 5 q^{15} - 5 q^{16} - 13 q^{17} - 5 q^{18} + 6 q^{19} - 3 q^{20} - 4 q^{21} - 23 q^{23} - q^{24} - q^{25} - q^{26} + q^{27} - 32 q^{28} + 15 q^{29} - 4 q^{30} - 11 q^{31} + 12 q^{32} + 2 q^{34} + 8 q^{35} - 6 q^{36} - 11 q^{37} - 25 q^{38} + 5 q^{39} + 15 q^{40} + 11 q^{41} - 11 q^{42} - 8 q^{43} - 23 q^{45} + 12 q^{46} - 21 q^{47} + 8 q^{48} + 2 q^{49} - 12 q^{50} + 26 q^{51} - q^{52} - 7 q^{53} + 3 q^{54} - 34 q^{56} - 51 q^{57} - 20 q^{58} - 22 q^{59} - 3 q^{60} + 6 q^{61} - q^{62} + 14 q^{63} + 5 q^{64} + 5 q^{65} - 31 q^{67} - q^{68} + 17 q^{69} - 26 q^{70} - 23 q^{71} - 27 q^{72} + 34 q^{73} + 6 q^{74} - 27 q^{75} - 2 q^{76} - 3 q^{78} - 5 q^{79} - 7 q^{80} - 32 q^{81} - 11 q^{82} + 11 q^{83} + 45 q^{84} - 4 q^{85} - 21 q^{86} + 2 q^{87} - 15 q^{89} + 3 q^{90} - 2 q^{91} - 6 q^{92} - 8 q^{93} - 8 q^{94} - 11 q^{95} - 41 q^{96} - 6 q^{97} + 12 q^{98}+O(q^{100}) \) 8 * q + q^2 - 5 * q^3 + q^4 - 5 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 - q^9 - 6 * q^10 - 7 * q^12 - 8 * q^13 + 2 * q^14 + 5 * q^15 - 5 * q^16 - 13 * q^17 - 5 * q^18 + 6 * q^19 - 3 * q^20 - 4 * q^21 - 23 * q^23 - q^24 - q^25 - q^26 + q^27 - 32 * q^28 + 15 * q^29 - 4 * q^30 - 11 * q^31 + 12 * q^32 + 2 * q^34 + 8 * q^35 - 6 * q^36 - 11 * q^37 - 25 * q^38 + 5 * q^39 + 15 * q^40 + 11 * q^41 - 11 * q^42 - 8 * q^43 - 23 * q^45 + 12 * q^46 - 21 * q^47 + 8 * q^48 + 2 * q^49 - 12 * q^50 + 26 * q^51 - q^52 - 7 * q^53 + 3 * q^54 - 34 * q^56 - 51 * q^57 - 20 * q^58 - 22 * q^59 - 3 * q^60 + 6 * q^61 - q^62 + 14 * q^63 + 5 * q^64 + 5 * q^65 - 31 * q^67 - q^68 + 17 * q^69 - 26 * q^70 - 23 * q^71 - 27 * q^72 + 34 * q^73 + 6 * q^74 - 27 * q^75 - 2 * q^76 - 3 * q^78 - 5 * q^79 - 7 * q^80 - 32 * q^81 - 11 * q^82 + 11 * q^83 + 45 * q^84 - 4 * q^85 - 21 * q^86 + 2 * q^87 - 15 * q^89 + 3 * q^90 - 2 * q^91 - 6 * q^92 - 8 * q^93 - 8 * q^94 - 11 * q^95 - 41 * q^96 - 6 * q^97 + 12 * q^98

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