LMFDB - Embedded newform 2541.2.a.bk.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2541,2,Mod(1,2541)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2541, 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("2541.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2541 = 3 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2541.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:	$20.2899871536$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.7488.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 4x^{2} + 2x + 1 $ x^4 - 2x^3 - 4x^2 + 2*x + 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			1.3
Root			$-1.43091$ of defining polynomial
Character	$\chi$	$=$	2541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.301143 q^{2} -1.00000 q^{3} -1.90931 q^{4} +1.30114 q^{5} +0.301143 q^{6} -1.00000 q^{7} +1.17726 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.301143 q^{2} -1.00000 q^{3} -1.90931 q^{4} +1.30114 q^{5} +0.301143 q^{6} -1.00000 q^{7} +1.17726 q^{8} +1.00000 q^{9} -0.391830 q^{10} +1.90931 q^{12} -3.38772 q^{13} +0.301143 q^{14} -1.30114 q^{15} +3.46410 q^{16} +0.478405 q^{17} -0.301143 q^{18} +1.60817 q^{19} -2.48429 q^{20} +1.00000 q^{21} +3.47841 q^{23} -1.17726 q^{24} -3.30703 q^{25} +1.02019 q^{26} -1.00000 q^{27} +1.90931 q^{28} +0.942507 q^{29} +0.391830 q^{30} -1.17726 q^{31} -3.39771 q^{32} -0.144068 q^{34} -1.30114 q^{35} -1.90931 q^{36} -3.55479 q^{37} -0.484289 q^{38} +3.38772 q^{39} +1.53179 q^{40} +3.94839 q^{41} -0.301143 q^{42} -2.87024 q^{43} +1.30114 q^{45} -1.04750 q^{46} +12.1113 q^{47} -3.46410 q^{48} +1.00000 q^{49} +0.995888 q^{50} -0.478405 q^{51} +6.46821 q^{52} +5.28273 q^{53} +0.301143 q^{54} -1.17726 q^{56} -1.60817 q^{57} -0.283829 q^{58} -9.69345 q^{59} +2.48429 q^{60} +3.00588 q^{61} +0.354524 q^{62} -1.00000 q^{63} -5.90501 q^{64} -4.40791 q^{65} +7.74683 q^{67} -0.913425 q^{68} -3.47841 q^{69} +0.391830 q^{70} -8.46568 q^{71} +1.17726 q^{72} -13.3709 q^{73} +1.07050 q^{74} +3.30703 q^{75} -3.07050 q^{76} -1.02019 q^{78} -8.86612 q^{79} +4.50729 q^{80} +1.00000 q^{81} -1.18903 q^{82} -11.4700 q^{83} -1.90931 q^{84} +0.622473 q^{85} +0.864351 q^{86} -0.942507 q^{87} +7.54068 q^{89} -0.391830 q^{90} +3.38772 q^{91} -6.64136 q^{92} +1.17726 q^{93} -3.64725 q^{94} +2.09246 q^{95} +3.39771 q^{96} -1.71364 q^{97} -0.301143 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 4 q^{3} + 4 q^{4} + 6 q^{5} + 2 q^{6} - 4 q^{7} + 4 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 4 * q^3 + 4 * q^4 + 6 * q^5 + 2 * q^6 - 4 * q^7 + 4 * q^9	$ 4 q - 2 q^{2} - 4 q^{3} + 4 q^{4} + 6 q^{5} + 2 q^{6} - 4 q^{7} + 4 q^{9} - 14 q^{10} - 4 q^{12} + 2 q^{13} + 2 q^{14} - 6 q^{15} - 2 q^{17} - 2 q^{18} - 6 q^{19} + 8 q^{20} + 4 q^{21} + 10 q^{23} - 4 q^{27} - 4 q^{28} - 14 q^{29} + 14 q^{30} - 12 q^{32} - 2 q^{34} - 6 q^{35} + 4 q^{36} - 12 q^{37} + 16 q^{38} - 2 q^{39} - 8 q^{40} - 16 q^{41} - 2 q^{42} - 20 q^{43} + 6 q^{45} - 8 q^{46} + 2 q^{47} + 4 q^{49} - 24 q^{50} + 2 q^{51} + 40 q^{52} - 16 q^{53} + 2 q^{54} + 6 q^{57} - 8 q^{58} + 2 q^{59} - 8 q^{60} - 2 q^{61} - 8 q^{62} - 4 q^{63} - 16 q^{64} + 2 q^{65} - 20 q^{67} - 20 q^{68} - 10 q^{69} + 14 q^{70} - 10 q^{71} + 10 q^{73} + 20 q^{74} - 28 q^{76} - 16 q^{79} + 12 q^{80} + 4 q^{81} + 28 q^{82} - 18 q^{83} + 4 q^{84} + 26 q^{86} + 14 q^{87} - 14 q^{89} - 14 q^{90} - 2 q^{91} - 8 q^{92} + 18 q^{94} - 22 q^{95} + 12 q^{96} + 38 q^{97} - 2 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 4 * q^3 + 4 * q^4 + 6 * q^5 + 2 * q^6 - 4 * q^7 + 4 * q^9 - 14 * q^10 - 4 * q^12 + 2 * q^13 + 2 * q^14 - 6 * q^15 - 2 * q^17 - 2 * q^18 - 6 * q^19 + 8 * q^20 + 4 * q^21 + 10 * q^23 - 4 * q^27 - 4 * q^28 - 14 * q^29 + 14 * q^30 - 12 * q^32 - 2 * q^34 - 6 * q^35 + 4 * q^36 - 12 * q^37 + 16 * q^38 - 2 * q^39 - 8 * q^40 - 16 * q^41 - 2 * q^42 - 20 * q^43 + 6 * q^45 - 8 * q^46 + 2 * q^47 + 4 * q^49 - 24 * q^50 + 2 * q^51 + 40 * q^52 - 16 * q^53 + 2 * q^54 + 6 * q^57 - 8 * q^58 + 2 * q^59 - 8 * q^60 - 2 * q^61 - 8 * q^62 - 4 * q^63 - 16 * q^64 + 2 * q^65 - 20 * q^67 - 20 * q^68 - 10 * q^69 + 14 * q^70 - 10 * q^71 + 10 * q^73 + 20 * q^74 - 28 * q^76 - 16 * q^79 + 12 * q^80 + 4 * q^81 + 28 * q^82 - 18 * q^83 + 4 * q^84 + 26 * q^86 + 14 * q^87 - 14 * q^89 - 14 * q^90 - 2 * q^91 - 8 * q^92 + 18 * q^94 - 22 * q^95 + 12 * q^96 + 38 * q^97 - 2 * 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 $

$2$	−0.301143	−0.212940	−0.106470	−	0.994316i	$-0.533955\pi$
$2$	−0.301143	−0.212940	−0.106470	+	0.994316i	$0.533955\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.90931	−0.954656
$5$	1.30114	0.581889	0.290944	−	0.956740i	$-0.406031\pi$
$5$	1.30114	0.581889	0.290944	+	0.956740i	$0.406031\pi$
$6$	0.301143	0.122941
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.17726	0.416225
$9$	1.00000	0.333333
$10$	−0.391830	−0.123908
$11$	0	0
$11$	0	0
$12$	1.90931	0.551171
$13$	−3.38772	−0.939584	−0.469792	−	0.882777i	$-0.655671\pi$
$13$	−3.38772	−0.939584	−0.469792	+	0.882777i	$0.655671\pi$
$14$	0.301143	0.0804838
$15$	−1.30114	−0.335954
$16$	3.46410	0.866025
$17$	0.478405	0.116030	0.0580151	−	0.998316i	$-0.481523\pi$
$17$	0.478405	0.116030	0.0580151	+	0.998316i	$0.481523\pi$
$18$	−0.301143	−0.0709801
$19$	1.60817	0.368939	0.184470	−	0.982838i	$-0.440943\pi$
$19$	1.60817	0.368939	0.184470	+	0.982838i	$0.440943\pi$
$20$	−2.48429	−0.555504
$21$	1.00000	0.218218
$22$	0	0
$23$	3.47841	0.725298	0.362649	−	0.931926i	$-0.381872\pi$
$23$	3.47841	0.725298	0.362649	+	0.931926i	$0.381872\pi$
$24$	−1.17726	−0.240308
$25$	−3.30703	−0.661405
$26$	1.02019	0.200075
$27$	−1.00000	−0.192450
$28$	1.90931	0.360826
$29$	0.942507	0.175019	0.0875095	−	0.996164i	$-0.472109\pi$
$29$	0.942507	0.175019	0.0875095	+	0.996164i	$0.472109\pi$
$30$	0.391830	0.0715381
$31$	−1.17726	−0.211443	−0.105721	−	0.994396i	$-0.533715\pi$
$31$	−1.17726	−0.211443	−0.105721	+	0.994396i	$0.533715\pi$
$32$	−3.39771	−0.600637
$33$	0	0
$34$	−0.144068	−0.0247075
$35$	−1.30114	−0.219933
$36$	−1.90931	−0.318219
$37$	−3.55479	−0.584404	−0.292202	−	0.956357i	$-0.594388\pi$
$37$	−3.55479	−0.584404	−0.292202	+	0.956357i	$0.594388\pi$
$38$	−0.484289	−0.0785621
$39$	3.38772	0.542469
$40$	1.53179	0.242197
$41$	3.94839	0.616635	0.308318	−	0.951284i	$-0.400234\pi$
$41$	3.94839	0.616635	0.308318	+	0.951284i	$0.400234\pi$
$42$	−0.301143	−0.0464674
$43$	−2.87024	−0.437707	−0.218853	−	0.975758i	$-0.570232\pi$
$43$	−2.87024	−0.437707	−0.218853	+	0.975758i	$0.570232\pi$
$44$	0	0
$45$	1.30114	0.193963
$46$	−1.04750	−0.154445
$47$	12.1113	1.76662	0.883311	−	0.468788i	$-0.155309\pi$
$47$	12.1113	1.76662	0.883311	+	0.468788i	$0.155309\pi$
$48$	−3.46410	−0.500000
$49$	1.00000	0.142857
$50$	0.995888	0.140840
$51$	−0.478405	−0.0669901
$52$	6.46821	0.896980
$53$	5.28273	0.725638	0.362819	−	0.931860i	$-0.381814\pi$
$53$	5.28273	0.725638	0.362819	+	0.931860i	$0.381814\pi$
$54$	0.301143	0.0409804
$55$	0	0
$56$	−1.17726	−0.157318
$57$	−1.60817	−0.213007
$58$	−0.283829	−0.0372686
$59$	−9.69345	−1.26198	−0.630990	−	0.775791i	$-0.717351\pi$
$59$	−9.69345	−1.26198	−0.630990	+	0.775791i	$0.717351\pi$
$60$	2.48429	0.320720
$61$	3.00588	0.384864	0.192432	−	0.981310i	$-0.438363\pi$
$61$	3.00588	0.384864	0.192432	+	0.981310i	$0.438363\pi$
$62$	0.354524	0.0450246
$63$	−1.00000	−0.125988
$64$	−5.90501	−0.738126
$65$	−4.40791	−0.546733
$66$	0	0
$67$	7.74683	0.946426	0.473213	−	0.880948i	$-0.343094\pi$
$67$	7.74683	0.946426	0.473213	+	0.880948i	$0.343094\pi$
$68$	−0.913425	−0.110769
$69$	−3.47841	−0.418751
$70$	0.391830	0.0468326
$71$	−8.46568	−1.00469	−0.502346	−	0.864667i	$-0.667529\pi$
$71$	−8.46568	−1.00469	−0.502346	+	0.864667i	$0.667529\pi$
$72$	1.17726	0.138742
$73$	−13.3709	−1.56494	−0.782472	−	0.622686i	$-0.786041\pi$
$73$	−13.3709	−1.56494	−0.782472	+	0.622686i	$0.786041\pi$
$74$	1.07050	0.124443
$75$	3.30703	0.381863
$76$	−3.07050	−0.352210
$77$	0	0
$78$	−1.02019	−0.115513
$79$	−8.86612	−0.997517	−0.498758	−	0.866741i	$-0.666210\pi$
$79$	−8.86612	−0.997517	−0.498758	+	0.866741i	$0.666210\pi$
$80$	4.50729	0.503931
$81$	1.00000	0.111111
$82$	−1.18903	−0.131306
$83$	−11.4700	−1.25899	−0.629497	−	0.777003i	$-0.716739\pi$
$83$	−11.4700	−1.25899	−0.629497	+	0.777003i	$0.716739\pi$
$84$	−1.90931	−0.208323
$85$	0.622473	0.0675167
$86$	0.864351	0.0932054
$87$	−0.942507	−0.101047
$88$	0	0
$89$	7.54068	0.799311	0.399655	−	0.916666i	$-0.369130\pi$
$89$	7.54068	0.799311	0.399655	+	0.916666i	$0.369130\pi$
$90$	−0.391830	−0.0413025
$91$	3.38772	0.355129
$92$	−6.64136	−0.692410
$93$	1.17726	0.122076
$94$	−3.64725	−0.376185
$95$	2.09246	0.214682
$96$	3.39771	0.346778
$97$	−1.71364	−0.173993	−0.0869967	−	0.996209i	$-0.527727\pi$
$97$	−1.71364	−0.173993	−0.0869967	+	0.996209i	$0.527727\pi$
$98$	−0.301143	−0.0304200
$99$	0	0
$100$	6.31415	0.631415
$101$	9.53637	0.948905	0.474452	−	0.880281i	$-0.342646\pi$
$101$	9.53637	0.948905	0.474452	+	0.880281i	$0.342646\pi$
$102$	0.144068	0.0142649
$103$	−1.22634	−0.120834	−0.0604172	−	0.998173i	$-0.519243\pi$
$103$	−1.22634	−0.120834	−0.0604172	+	0.998173i	$0.519243\pi$
$104$	−3.98823	−0.391078
$105$	1.30114	0.126979
$106$	−1.59086	−0.154518
$107$	−9.16296	−0.885817	−0.442908	−	0.896567i	$-0.646053\pi$
$107$	−9.16296	−0.885817	−0.442908	+	0.896567i	$0.646053\pi$
$108$	1.90931	0.183724
$109$	−16.2268	−1.55425	−0.777123	−	0.629348i	$-0.783322\pi$
$109$	−16.2268	−1.55425	−0.777123	+	0.629348i	$0.783322\pi$
$110$	0	0
$111$	3.55479	0.337406
$112$	−3.46410	−0.327327
$113$	17.4473	1.64130	0.820650	−	0.571431i	$-0.193611\pi$
$113$	17.4473	1.64130	0.820650	+	0.571431i	$0.193611\pi$
$114$	0.484289	0.0453578
$115$	4.52590	0.422043
$116$	−1.79954	−0.167083
$117$	−3.38772	−0.313195
$118$	2.91911	0.268726
$119$	−0.478405	−0.0438553
$120$	−1.53179	−0.139832
$121$	0	0
$122$	−0.905201	−0.0819530
$123$	−3.94839	−0.356014
$124$	2.24776	0.201855
$125$	−10.8086	−0.966753
$126$	0.301143	0.0268279
$127$	−2.60248	−0.230933	−0.115466	−	0.993311i	$-0.536836\pi$
$127$	−2.60248	−0.230933	−0.115466	+	0.993311i	$0.536836\pi$
$128$	8.57368	0.757813
$129$	2.87024	0.252710
$130$	1.32741	0.116422
$131$	−10.2853	−0.898628	−0.449314	−	0.893374i	$-0.648331\pi$
$131$	−10.2853	−0.898628	−0.449314	+	0.893374i	$0.648331\pi$
$132$	0	0
$133$	−1.60817	−0.139446
$134$	−2.33290	−0.201532
$135$	−1.30114	−0.111985
$136$	0.563208	0.0482947
$137$	−19.9098	−1.70101	−0.850504	−	0.525969i	$-0.823703\pi$
$137$	−19.9098	−1.70101	−0.850504	+	0.525969i	$0.823703\pi$
$138$	1.04750	0.0891689
$139$	−4.64089	−0.393635	−0.196818	−	0.980440i	$-0.563061\pi$
$139$	−4.64089	−0.393635	−0.196818	+	0.980440i	$0.563061\pi$
$140$	2.48429	0.209961
$141$	−12.1113	−1.01996
$142$	2.54938	0.213939
$143$	0	0
$144$	3.46410	0.288675
$145$	1.22634	0.101842
$146$	4.02655	0.333239
$147$	−1.00000	−0.0824786
$148$	6.78720	0.557905
$149$	−23.4807	−1.92361	−0.961805	−	0.273736i	$-0.911741\pi$
$149$	−23.4807	−1.92361	−0.961805	+	0.273736i	$0.911741\pi$
$150$	−0.995888	−0.0813139
$151$	−13.3893	−1.08961	−0.544803	−	0.838564i	$-0.683395\pi$
$151$	−13.3893	−1.08961	−0.544803	+	0.838564i	$0.683395\pi$
$152$	1.89324	0.153562
$153$	0.478405	0.0386768
$154$	0	0
$155$	−1.53179	−0.123036
$156$	−6.46821	−0.517872
$157$	12.6414	1.00889	0.504445	−	0.863444i	$-0.331697\pi$
$157$	12.6414	1.00889	0.504445	+	0.863444i	$0.331697\pi$
$158$	2.66997	0.212411
$159$	−5.28273	−0.418948
$160$	−4.42091	−0.349504
$161$	−3.47841	−0.274137
$162$	−0.301143	−0.0236600
$163$	−0.854355	−0.0669183	−0.0334591	−	0.999440i	$-0.510652\pi$
$163$	−0.854355	−0.0669183	−0.0334591	+	0.999440i	$0.510652\pi$
$164$	−7.53871	−0.588675
$165$	0	0
$166$	3.45411	0.268091
$167$	−8.16727	−0.632002	−0.316001	−	0.948759i	$-0.602340\pi$
$167$	−8.16727	−0.632002	−0.316001	+	0.948759i	$0.602340\pi$
$168$	1.17726	0.0908277
$169$	−1.52337	−0.117182
$170$	−0.187453	−0.0143770
$171$	1.60817	0.122980
$172$	5.48018	0.417860
$173$	−20.9111	−1.58984	−0.794920	−	0.606714i	$-0.792487\pi$
$173$	−20.9111	−1.58984	−0.794920	+	0.606714i	$0.792487\pi$
$174$	0.283829	0.0215170
$175$	3.30703	0.249988
$176$	0	0
$177$	9.69345	0.728604
$178$	−2.27082	−0.170205
$179$	8.41230	0.628765	0.314382	−	0.949296i	$-0.398203\pi$
$179$	8.41230	0.628765	0.314382	+	0.949296i	$0.398203\pi$
$180$	−2.48429	−0.185168
$181$	−20.6995	−1.53858	−0.769292	−	0.638898i	$-0.779391\pi$
$181$	−20.6995	−1.53858	−0.769292	+	0.638898i	$0.779391\pi$
$182$	−1.02019	−0.0756213
$183$	−3.00588	−0.222201
$184$	4.09499	0.301887
$185$	−4.62529	−0.340058
$186$	−0.354524	−0.0259950
$187$	0	0
$188$	−23.1244	−1.68652
$189$	1.00000	0.0727393
$190$	−0.630129	−0.0457144
$191$	−14.6830	−1.06242	−0.531211	−	0.847239i	$-0.678263\pi$
$191$	−14.6830	−1.06242	−0.531211	+	0.847239i	$0.678263\pi$
$192$	5.90501	0.426157
$193$	25.2657	1.81866	0.909332	−	0.416071i	$-0.136593\pi$
$193$	25.2657	1.81866	0.909332	+	0.416071i	$0.136593\pi$
$194$	0.516049	0.0370502
$195$	4.40791	0.315657
$196$	−1.90931	−0.136379
$197$	10.3936	0.740513	0.370257	−	0.928929i	$-0.379270\pi$
$197$	10.3936	0.740513	0.370257	+	0.928929i	$0.379270\pi$
$198$	0	0
$199$	11.1704	0.791850	0.395925	−	0.918283i	$-0.370424\pi$
$199$	11.1704	0.791850	0.395925	+	0.918283i	$0.370424\pi$
$200$	−3.89324	−0.275293
$201$	−7.74683	−0.546419
$202$	−2.87181	−0.202060
$203$	−0.942507	−0.0661510
$204$	0.913425	0.0639525
$205$	5.13742	0.358813
$206$	0.369302	0.0257305
$207$	3.47841	0.241766
$208$	−11.7354	−0.813704
$209$	0	0
$210$	−0.391830	−0.0270388
$211$	−11.1918	−0.770478	−0.385239	−	0.922817i	$-0.625881\pi$
$211$	−11.1918	−0.770478	−0.385239	+	0.922817i	$0.625881\pi$
$212$	−10.0864	−0.692735
$213$	8.46568	0.580059
$214$	2.75936	0.188626
$215$	−3.73459	−0.254697
$216$	−1.17726	−0.0801025
$217$	1.17726	0.0799178
$218$	4.88659	0.330962
$219$	13.3709	0.903520
$220$	0	0
$221$	−1.62070	−0.109020
$222$	−1.07050	−0.0718472
$223$	−20.4514	−1.36953	−0.684763	−	0.728766i	$-0.740094\pi$
$223$	−20.4514	−1.36953	−0.684763	+	0.728766i	$0.740094\pi$
$224$	3.39771	0.227019
$225$	−3.30703	−0.220468
$226$	−5.25412	−0.349499
$227$	−28.0554	−1.86210	−0.931052	−	0.364886i	$-0.881108\pi$
$227$	−28.0554	−1.86210	−0.931052	+	0.364886i	$0.881108\pi$
$228$	3.07050	0.203349
$229$	9.82178	0.649041	0.324521	−	0.945879i	$-0.394797\pi$
$229$	9.82178	0.649041	0.324521	+	0.945879i	$0.394797\pi$
$230$	−1.36294	−0.0898698
$231$	0	0
$232$	1.10958	0.0728473
$233$	3.37294	0.220969	0.110484	−	0.993878i	$-0.464760\pi$
$233$	3.37294	0.220969	0.110484	+	0.993878i	$0.464760\pi$
$234$	1.02019	0.0666917
$235$	15.7586	1.02798
$236$	18.5078	1.20476
$237$	8.86612	0.575917
$238$	0.144068	0.00933856
$239$	−25.1604	−1.62749	−0.813746	−	0.581220i	$-0.802575\pi$
$239$	−25.1604	−1.62749	−0.813746	+	0.581220i	$0.802575\pi$
$240$	−4.50729	−0.290944
$241$	12.9077	0.831460	0.415730	−	0.909488i	$-0.363526\pi$
$241$	12.9077	0.831460	0.415730	+	0.909488i	$0.363526\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	−5.73917	−0.367413
$245$	1.30114	0.0831270
$246$	1.18903	0.0758098
$247$	−5.44803	−0.346650
$248$	−1.38595	−0.0880077
$249$	11.4700	0.726881
$250$	3.25494	0.205861
$251$	−10.8704	−0.686135	−0.343068	−	0.939311i	$-0.611466\pi$
$251$	−10.8704	−0.686135	−0.343068	+	0.939311i	$0.611466\pi$
$252$	1.90931	0.120275
$253$	0	0
$254$	0.783719	0.0491749
$255$	−0.622473	−0.0389808
$256$	9.22811	0.576757
$257$	10.1400	0.632513	0.316257	−	0.948674i	$-0.397574\pi$
$257$	10.1400	0.632513	0.316257	+	0.948674i	$0.397574\pi$
$258$	−0.864351	−0.0538122
$259$	3.55479	0.220884
$260$	8.41607	0.521943
$261$	0.942507	0.0583397
$262$	3.09733	0.191354
$263$	−20.7929	−1.28214	−0.641072	−	0.767480i	$-0.721510\pi$
$263$	−20.7929	−1.28214	−0.641072	+	0.767480i	$0.721510\pi$
$264$	0	0
$265$	6.87358	0.422241
$266$	0.484289	0.0296937
$267$	−7.54068	−0.461482
$268$	−14.7911	−0.903512
$269$	−1.24235	−0.0757476	−0.0378738	−	0.999283i	$-0.512058\pi$
$269$	−1.24235	−0.0757476	−0.0378738	+	0.999283i	$0.512058\pi$
$270$	0.391830	0.0238460
$271$	−22.3996	−1.36068	−0.680340	−	0.732897i	$-0.738168\pi$
$271$	−22.3996	−1.36068	−0.680340	+	0.732897i	$0.738168\pi$
$272$	1.65724	0.100485
$273$	−3.38772	−0.205034
$274$	5.99569	0.362213
$275$	0	0
$276$	6.64136	0.399763
$277$	12.7509	0.766130	0.383065	−	0.923721i	$-0.374869\pi$
$277$	12.7509	0.766130	0.383065	+	0.923721i	$0.374869\pi$
$278$	1.39757	0.0838207
$279$	−1.17726	−0.0704808
$280$	−1.53179	−0.0915417
$281$	1.56957	0.0936325	0.0468163	−	0.998904i	$-0.485092\pi$
$281$	1.56957	0.0936325	0.0468163	+	0.998904i	$0.485092\pi$
$282$	3.64725	0.217190
$283$	14.3841	0.855045	0.427522	−	0.904005i	$-0.359387\pi$
$283$	14.3841	0.855045	0.427522	+	0.904005i	$0.359387\pi$
$284$	16.1636	0.959135
$285$	−2.09246	−0.123947
$286$	0	0
$287$	−3.94839	−0.233066
$288$	−3.39771	−0.200212
$289$	−16.7711	−0.986537
$290$	−0.369302	−0.0216862
$291$	1.71364	0.100455
$292$	25.5292	1.49398
$293$	−17.3984	−1.01642	−0.508212	−	0.861232i	$-0.669693\pi$
$293$	−17.3984	−1.01642	−0.508212	+	0.861232i	$0.669693\pi$
$294$	0.301143	0.0175630
$295$	−12.6126	−0.734332
$296$	−4.18492	−0.243243
$297$	0	0
$298$	7.07103	0.409614
$299$	−11.7839	−0.681478
$300$	−6.31415	−0.364548
$301$	2.87024	0.165438
$302$	4.03209	0.232021
$303$	−9.53637	−0.547850
$304$	5.57086	0.319511
$305$	3.91108	0.223948
$306$	−0.144068	−0.00823584
$307$	11.3404	0.647232	0.323616	−	0.946189i	$-0.395101\pi$
$307$	11.3404	0.647232	0.323616	+	0.946189i	$0.395101\pi$
$308$	0	0
$309$	1.22634	0.0697638
$310$	0.461287	0.0261993
$311$	13.7568	0.780078	0.390039	−	0.920798i	$-0.372462\pi$
$311$	13.7568	0.780078	0.390039	+	0.920798i	$0.372462\pi$
$312$	3.98823	0.225789
$313$	6.41359	0.362518	0.181259	−	0.983435i	$-0.441983\pi$
$313$	6.41359	0.362518	0.181259	+	0.983435i	$0.441983\pi$
$314$	−3.80686	−0.214833
$315$	−1.30114	−0.0733111
$316$	16.9282	0.952286
$317$	10.6661	0.599070	0.299535	−	0.954085i	$-0.403168\pi$
$317$	10.6661	0.599070	0.299535	+	0.954085i	$0.403168\pi$
$318$	1.59086	0.0892108
$319$	0	0
$320$	−7.68326	−0.429507
$321$	9.16296	0.511426
$322$	1.04750	0.0583747
$323$	0.769357	0.0428081
$324$	−1.90931	−0.106073
$325$	11.2033	0.621446
$326$	0.257283	0.0142496
$327$	16.2268	0.897345
$328$	4.64829	0.256659
$329$	−12.1113	−0.667720
$330$	0	0
$331$	9.96427	0.547686	0.273843	−	0.961774i	$-0.411705\pi$
$331$	9.96427	0.547686	0.273843	+	0.961774i	$0.411705\pi$
$332$	21.8998	1.20191
$333$	−3.55479	−0.194801
$334$	2.45951	0.134579
$335$	10.0797	0.550715
$336$	3.46410	0.188982
$337$	19.0653	1.03855	0.519276	−	0.854607i	$-0.326202\pi$
$337$	19.0653	1.03855	0.519276	+	0.854607i	$0.326202\pi$
$338$	0.458751	0.0249528
$339$	−17.4473	−0.947605
$340$	−1.18850	−0.0644553
$341$	0	0
$342$	−0.484289	−0.0261874
$343$	−1.00000	−0.0539949
$344$	−3.37902	−0.182184
$345$	−4.52590	−0.243666
$346$	6.29723	0.338541
$347$	−0.262065	−0.0140684	−0.00703420	−	0.999975i	$-0.502239\pi$
$347$	−0.262065	−0.0140684	−0.00703420	+	0.999975i	$0.502239\pi$
$348$	1.79954	0.0964655
$349$	4.96728	0.265892	0.132946	−	0.991123i	$-0.457556\pi$
$349$	4.96728	0.265892	0.132946	+	0.991123i	$0.457556\pi$
$350$	−0.995888	−0.0532324
$351$	3.38772	0.180823
$352$	0	0
$353$	−19.8104	−1.05440	−0.527201	−	0.849741i	$-0.676758\pi$
$353$	−19.8104	−1.05440	−0.527201	+	0.849741i	$0.676758\pi$
$354$	−2.91911	−0.155149
$355$	−11.0151	−0.584619
$356$	−14.3975	−0.763067
$357$	0.478405	0.0253199
$358$	−2.53330	−0.133889
$359$	19.8539	1.04785	0.523924	−	0.851765i	$-0.324468\pi$
$359$	19.8539	1.04785	0.523924	+	0.851765i	$0.324468\pi$
$360$	1.53179	0.0807322
$361$	−16.4138	−0.863884
$362$	6.23352	0.327626
$363$	0	0
$364$	−6.46821	−0.339027
$365$	−17.3974	−0.910623
$366$	0.905201	0.0473156
$367$	30.9087	1.61342	0.806710	−	0.590947i	$-0.201246\pi$
$367$	30.9087	1.61342	0.806710	+	0.590947i	$0.201246\pi$
$368$	12.0495	0.628126
$369$	3.94839	0.205545
$370$	1.39287	0.0724120
$371$	−5.28273	−0.274266
$372$	−2.24776	−0.116541
$373$	37.1879	1.92552	0.962759	−	0.270361i	$-0.0871431\pi$
$373$	37.1879	1.92552	0.962759	+	0.270361i	$0.0871431\pi$
$374$	0	0
$375$	10.8086	0.558155
$376$	14.2582	0.735312
$377$	−3.19295	−0.164445
$378$	−0.301143	−0.0154891
$379$	−19.9729	−1.02594	−0.512969	−	0.858407i	$-0.671454\pi$
$379$	−19.9729	−1.02594	−0.512969	+	0.858407i	$0.671454\pi$
$380$	−3.99516	−0.204947
$381$	2.60248	0.133329
$382$	4.42168	0.226233
$383$	20.3331	1.03897	0.519486	−	0.854479i	$-0.326123\pi$
$383$	20.3331	1.03897	0.519486	+	0.854479i	$0.326123\pi$
$384$	−8.57368	−0.437524
$385$	0	0
$386$	−7.60859	−0.387267
$387$	−2.87024	−0.145902
$388$	3.27187	0.166104
$389$	10.7754	0.546336	0.273168	−	0.961966i	$-0.411928\pi$
$389$	10.7754	0.546336	0.273168	+	0.961966i	$0.411928\pi$
$390$	−1.32741	−0.0672160
$391$	1.66409	0.0841565
$392$	1.17726	0.0594607
$393$	10.2853	0.518823
$394$	−3.12996	−0.157685
$395$	−11.5361	−0.580444
$396$	0	0
$397$	−0.247762	−0.0124348	−0.00621740	−	0.999981i	$-0.501979\pi$
$397$	−0.247762	−0.0124348	−0.00621740	+	0.999981i	$0.501979\pi$
$398$	−3.36389	−0.168617
$399$	1.60817	0.0805092
$400$	−11.4559	−0.572794
$401$	−24.8441	−1.24065	−0.620327	−	0.784343i	$-0.713000\pi$
$401$	−24.8441	−1.24065	−0.620327	+	0.784343i	$0.713000\pi$
$402$	2.33290	0.116355
$403$	3.98823	0.198668
$404$	−18.2079	−0.905878
$405$	1.30114	0.0646543
$406$	0.283829	0.0140862
$407$	0	0
$408$	−0.563208	−0.0278830
$409$	18.5332	0.916409	0.458204	−	0.888847i	$-0.348493\pi$
$409$	18.5332	0.916409	0.458204	+	0.888847i	$0.348493\pi$
$410$	−1.54710	−0.0764057
$411$	19.9098	0.982077
$412$	2.34146	0.115355
$413$	9.69345	0.476983
$414$	−1.04750	−0.0514817
$415$	−14.9241	−0.732595
$416$	11.5105	0.564349
$417$	4.64089	0.227265
$418$	0	0
$419$	−19.5238	−0.953802	−0.476901	−	0.878957i	$-0.658240\pi$
$419$	−19.5238	−0.953802	−0.476901	+	0.878957i	$0.658240\pi$
$420$	−2.48429	−0.121221
$421$	−8.78687	−0.428246	−0.214123	−	0.976807i	$-0.568689\pi$
$421$	−8.78687	−0.428246	−0.214123	+	0.976807i	$0.568689\pi$
$422$	3.37035	0.164066
$423$	12.1113	0.588874
$424$	6.21915	0.302029
$425$	−1.58210	−0.0767430
$426$	−2.54938	−0.123518
$427$	−3.00588	−0.145465
$428$	17.4950	0.845651
$429$	0	0
$430$	1.12464	0.0542352
$431$	18.1532	0.874407	0.437203	−	0.899363i	$-0.355969\pi$
$431$	18.1532	0.874407	0.437203	+	0.899363i	$0.355969\pi$
$432$	−3.46410	−0.166667
$433$	21.3423	1.02564	0.512822	−	0.858495i	$-0.328600\pi$
$433$	21.3423	1.02564	0.512822	+	0.858495i	$0.328600\pi$
$434$	−0.354524	−0.0170177
$435$	−1.22634	−0.0587983
$436$	30.9821	1.48377
$437$	5.59387	0.267591
$438$	−4.02655	−0.192396
$439$	−7.59086	−0.362292	−0.181146	−	0.983456i	$-0.557981\pi$
$439$	−7.59086	−0.362292	−0.181146	+	0.983456i	$0.557981\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	0.488063	0.0232148
$443$	−37.8911	−1.80026	−0.900130	−	0.435621i	$-0.856529\pi$
$443$	−37.8911	−1.80026	−0.900130	+	0.435621i	$0.856529\pi$
$444$	−6.78720	−0.322106
$445$	9.81150	0.465110
$446$	6.15879	0.291627
$447$	23.4807	1.11060
$448$	5.90501	0.278985
$449$	15.2640	0.720354	0.360177	−	0.932884i	$-0.382716\pi$
$449$	15.2640	0.720354	0.360177	+	0.932884i	$0.382716\pi$
$450$	0.995888	0.0469466
$451$	0	0
$452$	−33.3123	−1.56688
$453$	13.3893	0.629084
$454$	8.44870	0.396517
$455$	4.40791	0.206646
$456$	−1.89324	−0.0886590
$457$	−16.7762	−0.784757	−0.392379	−	0.919804i	$-0.628348\pi$
$457$	−16.7762	−0.784757	−0.392379	+	0.919804i	$0.628348\pi$
$458$	−2.95776	−0.138207
$459$	−0.478405	−0.0223300
$460$	−8.64136	−0.402906
$461$	36.0385	1.67848	0.839239	−	0.543763i	$-0.183001\pi$
$461$	36.0385	1.67848	0.839239	+	0.543763i	$0.183001\pi$
$462$	0	0
$463$	−25.7197	−1.19530	−0.597648	−	0.801758i	$-0.703898\pi$
$463$	−25.7197	−1.19530	−0.597648	+	0.801758i	$0.703898\pi$
$464$	3.26494	0.151571
$465$	1.53179	0.0710349
$466$	−1.01574	−0.0470531
$467$	27.6780	1.28079	0.640394	−	0.768047i	$-0.278771\pi$
$467$	27.6780	1.28079	0.640394	+	0.768047i	$0.278771\pi$
$468$	6.46821	0.298993
$469$	−7.74683	−0.357715
$470$	−4.74559	−0.218898
$471$	−12.6414	−0.582483
$472$	−11.4117	−0.525267
$473$	0	0
$474$	−2.66997	−0.122636
$475$	−5.31826	−0.244019
$476$	0.913425	0.0418668
$477$	5.28273	0.241879
$478$	7.57688	0.346559
$479$	−13.8413	−0.632427	−0.316214	−	0.948688i	$-0.602412\pi$
$479$	−13.8413	−0.632427	−0.316214	+	0.948688i	$0.602412\pi$
$480$	4.42091	0.201786
$481$	12.0426	0.549096
$482$	−3.88707	−0.177051
$483$	3.47841	0.158273
$484$	0	0
$485$	−2.22968	−0.101245
$486$	0.301143	0.0136601
$487$	−10.9228	−0.494959	−0.247480	−	0.968893i	$-0.579602\pi$
$487$	−10.9228	−0.494959	−0.247480	+	0.968893i	$0.579602\pi$
$488$	3.53871	0.160190
$489$	0.854355	0.0386353
$490$	−0.391830	−0.0177011
$491$	26.6839	1.20423	0.602114	−	0.798410i	$-0.294325\pi$
$491$	26.6839	1.20423	0.602114	+	0.798410i	$0.294325\pi$
$492$	7.53871	0.339871
$493$	0.450900	0.0203075
$494$	1.64063	0.0738156
$495$	0	0
$496$	−4.07816	−0.183115
$497$	8.46568	0.379738
$498$	−3.45411	−0.154782
$499$	−36.1374	−1.61773	−0.808867	−	0.587992i	$-0.799919\pi$
$499$	−36.1374	−1.61773	−0.808867	+	0.587992i	$0.799919\pi$
$500$	20.6371	0.922917
$501$	8.16727	0.364887
$502$	3.27355	0.146106
$503$	−27.2718	−1.21599	−0.607994	−	0.793942i	$-0.708026\pi$
$503$	−27.2718	−1.21599	−0.607994	+	0.793942i	$0.708026\pi$
$504$	−1.17726	−0.0524394
$505$	12.4082	0.552157
$506$	0	0
$507$	1.52337	0.0676551
$508$	4.96895	0.220462
$509$	35.5186	1.57434	0.787168	−	0.616739i	$-0.211547\pi$
$509$	35.5186	1.57434	0.787168	+	0.616739i	$0.211547\pi$
$510$	0.187453	0.00830058
$511$	13.3709	0.591493
$512$	−19.9263	−0.880628
$513$	−1.60817	−0.0710024
$514$	−3.05358	−0.134687
$515$	−1.59564	−0.0703122
$516$	−5.48018	−0.241251
$517$	0	0
$518$	−1.07050	−0.0470351
$519$	20.9111	0.917895
$520$	−5.18926	−0.227564
$521$	19.1607	0.839446	0.419723	−	0.907652i	$-0.362127\pi$
$521$	19.1607	0.839446	0.419723	+	0.907652i	$0.362127\pi$
$522$	−0.283829	−0.0124229
$523$	−4.44268	−0.194265	−0.0971323	−	0.995271i	$-0.530967\pi$
$523$	−4.44268	−0.194265	−0.0971323	+	0.995271i	$0.530967\pi$
$524$	19.6378	0.857881
$525$	−3.30703	−0.144330
$526$	6.26163	0.273020
$527$	−0.563208	−0.0245337
$528$	0	0
$529$	−10.9007	−0.473943
$530$	−2.06993	−0.0899121
$531$	−9.69345	−0.420660
$532$	3.07050	0.133123
$533$	−13.3760	−0.579380
$534$	2.27082	0.0982681
$535$	−11.9223	−0.515447
$536$	9.12005	0.393926
$537$	−8.41230	−0.363017
$538$	0.374126	0.0161297
$539$	0	0
$540$	2.48429	0.106907
$541$	23.7902	1.02282	0.511411	−	0.859336i	$-0.329123\pi$
$541$	23.7902	1.02282	0.511411	+	0.859336i	$0.329123\pi$
$542$	6.74549	0.289744
$543$	20.6995	0.888302
$544$	−1.62548	−0.0696920
$545$	−21.1134	−0.904399
$546$	1.02019	0.0436600
$547$	22.0421	0.942452	0.471226	−	0.882013i	$-0.343812\pi$
$547$	22.0421	0.942452	0.471226	+	0.882013i	$0.343812\pi$
$548$	38.0140	1.62388
$549$	3.00588	0.128288
$550$	0	0
$551$	1.51571	0.0645715
$552$	−4.09499	−0.174295
$553$	8.86612	0.377026
$554$	−3.83986	−0.163140
$555$	4.62529	0.196333
$556$	8.86091	0.375786
$557$	−29.7068	−1.25872	−0.629359	−	0.777115i	$-0.716682\pi$
$557$	−29.7068	−1.25872	−0.629359	+	0.777115i	$0.716682\pi$
$558$	0.354524	0.0150082
$559$	9.72355	0.411262
$560$	−4.50729	−0.190468
$561$	0	0
$562$	−0.472664	−0.0199381
$563$	−7.06070	−0.297573	−0.148786	−	0.988869i	$-0.547537\pi$
$563$	−7.06070	−0.297573	−0.148786	+	0.988869i	$0.547537\pi$
$564$	23.1244	0.973711
$565$	22.7014	0.955054
$566$	−4.33166	−0.182073
$567$	−1.00000	−0.0419961
$568$	−9.96632	−0.418178
$569$	−22.6262	−0.948538	−0.474269	−	0.880380i	$-0.657288\pi$
$569$	−22.6262	−0.948538	−0.474269	+	0.880380i	$0.657288\pi$
$570$	0.630129	0.0263932
$571$	18.4644	0.772713	0.386356	−	0.922350i	$-0.373733\pi$
$571$	18.4644	0.772713	0.386356	+	0.922350i	$0.373733\pi$
$572$	0	0
$573$	14.6830	0.613390
$574$	1.18903	0.0496292
$575$	−11.5032	−0.479716
$576$	−5.90501	−0.246042
$577$	2.19908	0.0915488	0.0457744	−	0.998952i	$-0.485424\pi$
$577$	2.19908	0.0915488	0.0457744	+	0.998952i	$0.485424\pi$
$578$	5.05051	0.210073
$579$	−25.2657	−1.05001
$580$	−2.34146	−0.0972238
$581$	11.4700	0.475855
$582$	−0.516049	−0.0213909
$583$	0	0
$584$	−15.7410	−0.651368
$585$	−4.40791	−0.182244
$586$	5.23940	0.216438
$587$	−19.1979	−0.792383	−0.396192	−	0.918168i	$-0.629668\pi$
$587$	−19.1979	−0.792383	−0.396192	+	0.918168i	$0.629668\pi$
$588$	1.90931	0.0787387
$589$	−1.89324	−0.0780095
$590$	3.79818	0.156369
$591$	−10.3936	−0.427536
$592$	−12.3141	−0.506108
$593$	19.1328	0.785691	0.392846	−	0.919604i	$-0.371491\pi$
$593$	19.1328	0.785691	0.392846	+	0.919604i	$0.371491\pi$
$594$	0	0
$595$	−0.622473	−0.0255189
$596$	44.8319	1.83639
$597$	−11.1704	−0.457175
$598$	3.54863	0.145114
$599$	−4.42406	−0.180762	−0.0903812	−	0.995907i	$-0.528809\pi$
$599$	−4.42406	−0.180762	−0.0903812	+	0.995907i	$0.528809\pi$
$600$	3.89324	0.158941
$601$	39.9277	1.62869	0.814343	−	0.580384i	$-0.197098\pi$
$601$	39.9277	1.62869	0.814343	+	0.580384i	$0.197098\pi$
$602$	−0.864351	−0.0352283
$603$	7.74683	0.315475
$604$	25.5644	1.04020
$605$	0	0
$606$	2.87181	0.116659
$607$	22.7804	0.924626	0.462313	−	0.886717i	$-0.347020\pi$
$607$	22.7804	0.924626	0.462313	+	0.886717i	$0.347020\pi$
$608$	−5.46410	−0.221599
$609$	0.942507	0.0381923
$610$	−1.17780	−0.0476876
$611$	−41.0298	−1.65989
$612$	−0.913425	−0.0369230
$613$	−40.4017	−1.63181	−0.815904	−	0.578187i	$-0.803760\pi$
$613$	−40.4017	−1.63181	−0.815904	+	0.578187i	$0.803760\pi$
$614$	−3.41509	−0.137822
$615$	−5.13742	−0.207161
$616$	0	0
$617$	21.2137	0.854033	0.427017	−	0.904244i	$-0.359565\pi$
$617$	21.2137	0.854033	0.427017	+	0.904244i	$0.359565\pi$
$618$	−0.369302	−0.0148555
$619$	13.0445	0.524302	0.262151	−	0.965027i	$-0.415568\pi$
$619$	13.0445	0.524302	0.262151	+	0.965027i	$0.415568\pi$
$620$	2.92466	0.117457
$621$	−3.47841	−0.139584
$622$	−4.14277	−0.166110
$623$	−7.54068	−0.302111
$624$	11.7354	0.469792
$625$	2.47156	0.0988625
$626$	−1.93141	−0.0771946
$627$	0	0
$628$	−24.1363	−0.963144
$629$	−1.70063	−0.0678085
$630$	0.391830	0.0156109
$631$	37.0202	1.47375	0.736875	−	0.676029i	$-0.236301\pi$
$631$	37.0202	1.47375	0.736875	+	0.676029i	$0.236301\pi$
$632$	−10.4378	−0.415191
$633$	11.1918	0.444836
$634$	−3.21203	−0.127566
$635$	−3.38620	−0.134377
$636$	10.0864	0.399951
$637$	−3.38772	−0.134226
$638$	0	0
$639$	−8.46568	−0.334897
$640$	11.1556	0.440963
$641$	21.3679	0.843980	0.421990	−	0.906600i	$-0.361332\pi$
$641$	21.3679	0.843980	0.421990	+	0.906600i	$0.361332\pi$
$642$	−2.75936	−0.108903
$643$	18.1845	0.717128	0.358564	−	0.933505i	$-0.383267\pi$
$643$	18.1845	0.717128	0.358564	+	0.933505i	$0.383267\pi$
$644$	6.64136	0.261706
$645$	3.73459	0.147049
$646$	−0.231686	−0.00911558
$647$	−9.43913	−0.371091	−0.185545	−	0.982636i	$-0.559405\pi$
$647$	−9.43913	−0.371091	−0.185545	+	0.982636i	$0.559405\pi$
$648$	1.17726	0.0462472
$649$	0	0
$650$	−3.37379	−0.132331
$651$	−1.17726	−0.0461405
$652$	1.63123	0.0638839
$653$	−21.9975	−0.860827	−0.430414	−	0.902632i	$-0.641632\pi$
$653$	−21.9975	−0.860827	−0.430414	+	0.902632i	$0.641632\pi$
$654$	−4.88659	−0.191081
$655$	−13.3826	−0.522901
$656$	13.6776	0.534022
$657$	−13.3709	−0.521648
$658$	3.64725	0.142185
$659$	−46.9739	−1.82984	−0.914922	−	0.403631i	$-0.867748\pi$
$659$	−46.9739	−1.82984	−0.914922	+	0.403631i	$0.867748\pi$
$660$	0	0
$661$	−11.4368	−0.444840	−0.222420	−	0.974951i	$-0.571396\pi$
$661$	−11.4368	−0.444840	−0.222420	+	0.974951i	$0.571396\pi$
$662$	−3.00067	−0.116624
$663$	1.62070	0.0629428
$664$	−13.5032	−0.524025
$665$	−2.09246	−0.0811421
$666$	1.07050	0.0414810
$667$	3.27842	0.126941
$668$	15.5939	0.603345
$669$	20.4514	0.790696
$670$	−3.03544	−0.117269
$671$	0	0
$672$	−3.39771	−0.131070
$673$	4.68715	0.180676	0.0903381	−	0.995911i	$-0.471205\pi$
$673$	4.68715	0.180676	0.0903381	+	0.995911i	$0.471205\pi$
$674$	−5.74138	−0.221150
$675$	3.30703	0.127288
$676$	2.90858	0.111869
$677$	8.71493	0.334942	0.167471	−	0.985877i	$-0.446440\pi$
$677$	8.71493	0.334942	0.167471	+	0.985877i	$0.446440\pi$
$678$	5.25412	0.201783
$679$	1.71364	0.0657633
$680$	0.732814	0.0281021
$681$	28.0554	1.07509
$682$	0	0
$683$	−39.2999	−1.50377	−0.751884	−	0.659295i	$-0.770855\pi$
$683$	−39.2999	−1.50377	−0.751884	+	0.659295i	$0.770855\pi$
$684$	−3.07050	−0.117403
$685$	−25.9055	−0.989798
$686$	0.301143	0.0114977
$687$	−9.82178	−0.374724
$688$	−9.94279	−0.379065
$689$	−17.8964	−0.681798
$690$	1.36294	0.0518864
$691$	−21.4190	−0.814819	−0.407409	−	0.913246i	$-0.633568\pi$
$691$	−21.4190	−0.814819	−0.407409	+	0.913246i	$0.633568\pi$
$692$	39.9258	1.51775
$693$	0	0
$694$	0.0789191	0.00299573
$695$	−6.03846	−0.229052
$696$	−1.10958	−0.0420584
$697$	1.88893	0.0715483
$698$	−1.49586	−0.0566192
$699$	−3.37294	−0.127576
$700$	−6.31415	−0.238652
$701$	−24.6197	−0.929875	−0.464937	−	0.885344i	$-0.653923\pi$
$701$	−24.6197	−0.929875	−0.464937	+	0.885344i	$0.653923\pi$
$702$	−1.02019	−0.0385045
$703$	−5.71670	−0.215610
$704$	0	0
$705$	−15.7586	−0.593503
$706$	5.96576	0.224524
$707$	−9.53637	−0.358652
$708$	−18.5078	−0.695567
$709$	−10.9882	−0.412672	−0.206336	−	0.978481i	$-0.566154\pi$
$709$	−10.9882	−0.412672	−0.206336	+	0.978481i	$0.566154\pi$
$710$	3.31711	0.124489
$711$	−8.86612	−0.332506
$712$	8.87736	0.332693
$713$	−4.09499	−0.153359
$714$	−0.144068	−0.00539162
$715$	0	0
$716$	−16.0617	−0.600254
$717$	25.1604	0.939633
$718$	−5.97885	−0.223129
$719$	33.4441	1.24725	0.623627	−	0.781722i	$-0.285658\pi$
$719$	33.4441	1.24725	0.623627	+	0.781722i	$0.285658\pi$
$720$	4.50729	0.167977
$721$	1.22634	0.0456711
$722$	4.94290	0.183956
$723$	−12.9077	−0.480044
$724$	39.5219	1.46882
$725$	−3.11690	−0.115759
$726$	0	0
$727$	44.9100	1.66562	0.832810	−	0.553560i	$-0.186731\pi$
$727$	44.9100	1.66562	0.832810	+	0.553560i	$0.186731\pi$
$728$	3.98823	0.147814
$729$	1.00000	0.0370370
$730$	5.23911	0.193908
$731$	−1.37314	−0.0507872
$732$	5.73917	0.212126
$733$	−23.4850	−0.867437	−0.433718	−	0.901048i	$-0.642799\pi$
$733$	−23.4850	−0.867437	−0.433718	+	0.901048i	$0.642799\pi$
$734$	−9.30793	−0.343562
$735$	−1.30114	−0.0479934
$736$	−11.8186	−0.435640
$737$	0	0
$738$	−1.18903	−0.0437688
$739$	−17.2692	−0.635259	−0.317630	−	0.948215i	$-0.602887\pi$
$739$	−17.2692	−0.635259	−0.317630	+	0.948215i	$0.602887\pi$
$740$	8.83112	0.324639
$741$	5.44803	0.200138
$742$	1.59086	0.0584022
$743$	7.15344	0.262434	0.131217	−	0.991354i	$-0.458112\pi$
$743$	7.15344	0.262434	0.131217	+	0.991354i	$0.458112\pi$
$744$	1.38595	0.0508112
$745$	−30.5517	−1.11933
$746$	−11.1989	−0.410020
$747$	−11.4700	−0.419665
$748$	0	0
$749$	9.16296	0.334807
$750$	−3.25494	−0.118854
$751$	−52.3091	−1.90879	−0.954394	−	0.298551i	$-0.903497\pi$
$751$	−52.3091	−1.90879	−0.954394	+	0.298551i	$0.903497\pi$
$752$	41.9549	1.52994
$753$	10.8704	0.396141
$754$	0.961534	0.0350170
$755$	−17.4214	−0.634029
$756$	−1.90931	−0.0694410
$757$	−11.0149	−0.400344	−0.200172	−	0.979761i	$-0.564150\pi$
$757$	−11.0149	−0.400344	−0.200172	+	0.979761i	$0.564150\pi$
$758$	6.01469	0.218464
$759$	0	0
$760$	2.46337	0.0893559
$761$	11.2716	0.408596	0.204298	−	0.978909i	$-0.434509\pi$
$761$	11.2716	0.408596	0.204298	+	0.978909i	$0.434509\pi$
$762$	−0.783719	−0.0283911
$763$	16.2268	0.587450
$764$	28.0344	1.01425
$765$	0.622473	0.0225056
$766$	−6.12317	−0.221239
$767$	32.8387	1.18574
$768$	−9.22811	−0.332991
$769$	1.37733	0.0496678	0.0248339	−	0.999692i	$-0.492094\pi$
$769$	1.37733	0.0496678	0.0248339	+	0.999692i	$0.492094\pi$
$770$	0	0
$771$	−10.1400	−0.365182
$772$	−48.2401	−1.73620
$773$	1.30100	0.0467937	0.0233969	−	0.999726i	$-0.492552\pi$
$773$	1.30100	0.0467937	0.0233969	+	0.999726i	$0.492552\pi$
$774$	0.864351	0.0310685
$775$	3.89324	0.139849
$776$	−2.01740	−0.0724204
$777$	−3.55479	−0.127527
$778$	−3.24495	−0.116337
$779$	6.34968	0.227501
$780$	−8.41607	−0.301344
$781$	0	0
$782$	−0.501128	−0.0179203
$783$	−0.942507	−0.0336824
$784$	3.46410	0.123718
$785$	16.4482	0.587062
$786$	−3.09733	−0.110478
$787$	50.2646	1.79174	0.895871	−	0.444315i	$-0.146553\pi$
$787$	50.2646	1.79174	0.895871	+	0.444315i	$0.146553\pi$
$788$	−19.8446	−0.706936
$789$	20.7929	0.740247
$790$	3.47401	0.123600
$791$	−17.4473	−0.620353
$792$	0	0
$793$	−10.1831	−0.361612
$794$	0.0746117	0.00264787
$795$	−6.87358	−0.243781
$796$	−21.3278	−0.755945
$797$	−7.51222	−0.266096	−0.133048	−	0.991110i	$-0.542477\pi$
$797$	−7.51222	−0.266096	−0.133048	+	0.991110i	$0.542477\pi$
$798$	−0.484289	−0.0171436
$799$	5.79413	0.204982
$800$	11.2363	0.397264
$801$	7.54068	0.266437
$802$	7.48162	0.264185
$803$	0	0
$804$	14.7911	0.521643
$805$	−4.52590	−0.159517
$806$	−1.20103	−0.0423044
$807$	1.24235	0.0437329
$808$	11.2268	0.394958
$809$	−6.79104	−0.238760	−0.119380	−	0.992849i	$-0.538091\pi$
$809$	−6.79104	−0.238760	−0.119380	+	0.992849i	$0.538091\pi$
$810$	−0.391830	−0.0137675
$811$	−32.0227	−1.12447	−0.562235	−	0.826978i	$-0.690058\pi$
$811$	−32.0227	−1.12447	−0.562235	+	0.826978i	$0.690058\pi$
$812$	1.79954	0.0631515
$813$	22.3996	0.785589
$814$	0	0
$815$	−1.11164	−0.0389390
$816$	−1.65724	−0.0580151
$817$	−4.61583	−0.161487
$818$	−5.58115	−0.195140
$819$	3.38772	0.118376
$820$	−9.80894	−0.342543
$821$	35.3145	1.23249	0.616243	−	0.787556i	$-0.288654\pi$
$821$	35.3145	1.23249	0.616243	+	0.787556i	$0.288654\pi$
$822$	−5.99569	−0.209124
$823$	−2.00171	−0.0697753	−0.0348877	−	0.999391i	$-0.511107\pi$
$823$	−2.00171	−0.0697753	−0.0348877	+	0.999391i	$0.511107\pi$
$824$	−1.44372	−0.0502943
$825$	0	0
$826$	−2.91911	−0.101569
$827$	−8.42435	−0.292943	−0.146472	−	0.989215i	$-0.546792\pi$
$827$	−8.42435	−0.292943	−0.146472	+	0.989215i	$0.546792\pi$
$828$	−6.64136	−0.230803
$829$	14.1931	0.492945	0.246473	−	0.969150i	$-0.420728\pi$
$829$	14.1931	0.492945	0.246473	+	0.969150i	$0.420728\pi$
$830$	4.49429	0.155999
$831$	−12.7509	−0.442325
$832$	20.0045	0.693531
$833$	0.478405	0.0165758
$834$	−1.39757	−0.0483939
$835$	−10.6268	−0.367755
$836$	0	0
$837$	1.17726	0.0406921
$838$	5.87947	0.203103
$839$	8.44234	0.291462	0.145731	−	0.989324i	$-0.453447\pi$
$839$	8.44234	0.291462	0.145731	+	0.989324i	$0.453447\pi$
$840$	1.53179	0.0528516
$841$	−28.1117	−0.969368
$842$	2.64610	0.0911907
$843$	−1.56957	−0.0540588
$844$	21.3687	0.735542
$845$	−1.98212	−0.0681869
$846$	−3.64725	−0.125395
$847$	0	0
$848$	18.2999	0.628421
$849$	−14.3841	−0.493660
$850$	0.476438	0.0163417
$851$	−12.3650	−0.423867
$852$	−16.1636	−0.553757
$853$	−57.3123	−1.96234	−0.981168	−	0.193158i	$-0.938127\pi$
$853$	−57.3123	−1.96234	−0.981168	+	0.193158i	$0.938127\pi$
$854$	0.905201	0.0309753
$855$	2.09246	0.0715606
$856$	−10.7872	−0.368699
$857$	−13.5681	−0.463479	−0.231739	−	0.972778i	$-0.574442\pi$
$857$	−13.5681	−0.463479	−0.231739	+	0.972778i	$0.574442\pi$
$858$	0	0
$859$	−15.4832	−0.528280	−0.264140	−	0.964484i	$-0.585088\pi$
$859$	−15.4832	−0.528280	−0.264140	+	0.964484i	$0.585088\pi$
$860$	7.13049	0.243148
$861$	3.94839	0.134561
$862$	−5.46670	−0.186196
$863$	−21.5553	−0.733752	−0.366876	−	0.930270i	$-0.619573\pi$
$863$	−21.5553	−0.733752	−0.366876	+	0.930270i	$0.619573\pi$
$864$	3.39771	0.115593
$865$	−27.2083	−0.925110
$866$	−6.42708	−0.218401
$867$	16.7711	0.569577
$868$	−2.24776	−0.0762940
$869$	0	0
$870$	0.369302	0.0125205
$871$	−26.2441	−0.889246
$872$	−19.1032	−0.646916
$873$	−1.71364	−0.0579978
$874$	−1.68455	−0.0569809
$875$	10.8086	0.365398
$876$	−25.5292	−0.862551
$877$	18.6275	0.629007	0.314504	−	0.949256i	$-0.398162\pi$
$877$	18.6275	0.629007	0.314504	+	0.949256i	$0.398162\pi$
$878$	2.28593	0.0771465
$879$	17.3984	0.586833
$880$	0	0
$881$	13.7010	0.461600	0.230800	−	0.973001i	$-0.425866\pi$
$881$	13.7010	0.461600	0.230800	+	0.973001i	$0.425866\pi$
$882$	−0.301143	−0.0101400
$883$	−29.4327	−0.990489	−0.495244	−	0.868754i	$-0.664921\pi$
$883$	−29.4327	−0.990489	−0.495244	+	0.868754i	$0.664921\pi$
$884$	3.09443	0.104077
$885$	12.6126	0.423967
$886$	11.4106	0.383348
$887$	−14.4530	−0.485283	−0.242641	−	0.970116i	$-0.578014\pi$
$887$	−14.4530	−0.485283	−0.242641	+	0.970116i	$0.578014\pi$
$888$	4.18492	0.140437
$889$	2.60248	0.0872844
$890$	−2.95467	−0.0990406
$891$	0	0
$892$	39.0481	1.30743
$893$	19.4771	0.651777
$894$	−7.07103	−0.236491
$895$	10.9456	0.365871
$896$	−8.57368	−0.286427
$897$	11.7839	0.393451
$898$	−4.59666	−0.153392
$899$	−1.10958	−0.0370065
$900$	6.31415	0.210472
$901$	2.52728	0.0841960
$902$	0	0
$903$	−2.87024	−0.0955154
$904$	20.5400	0.683150
$905$	−26.9330	−0.895285
$906$	−4.03209	−0.133957
$907$	33.5011	1.11239	0.556193	−	0.831053i	$-0.312261\pi$
$907$	33.5011	1.11239	0.556193	+	0.831053i	$0.312261\pi$
$908$	53.5666	1.77767
$909$	9.53637	0.316302
$910$	−1.32741	−0.0440032
$911$	−21.2100	−0.702718	−0.351359	−	0.936241i	$-0.614280\pi$
$911$	−21.2100	−0.702718	−0.351359	+	0.936241i	$0.614280\pi$
$912$	−5.57086	−0.184470
$913$	0	0
$914$	5.05203	0.167106
$915$	−3.91108	−0.129296
$916$	−18.7528	−0.619612
$917$	10.2853	0.339649
$918$	0.144068	0.00475496
$919$	−46.8324	−1.54486	−0.772430	−	0.635100i	$-0.780959\pi$
$919$	−46.8324	−1.54486	−0.772430	+	0.635100i	$0.780959\pi$
$920$	5.32817	0.175665
$921$	−11.3404	−0.373679
$922$	−10.8527	−0.357415
$923$	28.6793	0.943992
$924$	0	0
$925$	11.7558	0.386528
$926$	7.74531	0.254527
$927$	−1.22634	−0.0402782
$928$	−3.20237	−0.105123
$929$	−10.9210	−0.358307	−0.179154	−	0.983821i	$-0.557336\pi$
$929$	−10.9210	−0.358307	−0.179154	+	0.983821i	$0.557336\pi$
$930$	−0.461287	−0.0151262
$931$	1.60817	0.0527056
$932$	−6.44000	−0.210949
$933$	−13.7568	−0.450378
$934$	−8.33505	−0.272731
$935$	0	0
$936$	−3.98823	−0.130359
$937$	−7.85086	−0.256476	−0.128238	−	0.991743i	$-0.540932\pi$
$937$	−7.85086	−0.256476	−0.128238	+	0.991743i	$0.540932\pi$
$938$	2.33290	0.0761720
$939$	−6.41359	−0.209300
$940$	−30.0881	−0.981365
$941$	27.6122	0.900132	0.450066	−	0.892995i	$-0.351401\pi$
$941$	27.6122	0.900132	0.450066	+	0.892995i	$0.351401\pi$
$942$	3.80686	0.124034
$943$	13.7341	0.447244
$944$	−33.5791	−1.09291
$945$	1.30114	0.0423262
$946$	0	0
$947$	56.9267	1.84987	0.924934	−	0.380127i	$-0.124120\pi$
$947$	56.9267	1.84987	0.924934	+	0.380127i	$0.124120\pi$
$948$	−16.9282	−0.549802
$949$	45.2968	1.47040
$950$	1.60156	0.0519614
$951$	−10.6661	−0.345873
$952$	−0.563208	−0.0182537
$953$	25.2881	0.819163	0.409581	−	0.912274i	$-0.365675\pi$
$953$	25.2881	0.819163	0.409581	+	0.912274i	$0.365675\pi$
$954$	−1.59086	−0.0515059
$955$	−19.1047	−0.618212
$956$	48.0391	1.55370
$957$	0	0
$958$	4.16822	0.134669
$959$	19.9098	0.642921
$960$	7.68326	0.247976
$961$	−29.6141	−0.955292
$962$	−3.62655	−0.116925
$963$	−9.16296	−0.295272
$964$	−24.6449	−0.793759
$965$	32.8743	1.05826
$966$	−1.04750	−0.0337027
$967$	19.2122	0.617824	0.308912	−	0.951091i	$-0.400035\pi$
$967$	19.2122	0.617824	0.308912	+	0.951091i	$0.400035\pi$
$968$	0	0
$969$	−0.769357	−0.0247153
$970$	0.671454	0.0215591
$971$	50.9532	1.63517	0.817583	−	0.575811i	$-0.195314\pi$
$971$	50.9532	1.63517	0.817583	+	0.575811i	$0.195314\pi$
$972$	1.90931	0.0612412
$973$	4.64089	0.148780
$974$	3.28932	0.105397
$975$	−11.2033	−0.358792
$976$	10.4127	0.333302
$977$	−54.7278	−1.75090	−0.875449	−	0.483310i	$-0.839435\pi$
$977$	−54.7278	−1.75090	−0.875449	+	0.483310i	$0.839435\pi$
$978$	−0.257283	−0.00822700
$979$	0	0
$980$	−2.48429	−0.0793577
$981$	−16.2268	−0.518082
$982$	−8.03568	−0.256429
$983$	6.20739	0.197985	0.0989924	−	0.995088i	$-0.468438\pi$
$983$	6.20739	0.197985	0.0989924	+	0.995088i	$0.468438\pi$
$984$	−4.64829	−0.148182
$985$	13.5236	0.430897
$986$	−0.135785	−0.00432429
$987$	12.1113	0.385508
$988$	10.4020	0.330931
$989$	−9.98384	−0.317468
$990$	0	0
$991$	−4.64753	−0.147634	−0.0738168	−	0.997272i	$-0.523518\pi$
$991$	−4.64753	−0.147634	−0.0738168	+	0.997272i	$0.523518\pi$
$992$	4.00000	0.127000
$993$	−9.96427	−0.316207
$994$	−2.54938	−0.0808614
$995$	14.5343	0.460769
$996$	−21.8998	−0.693921
$997$	34.0235	1.07754	0.538768	−	0.842454i	$-0.318890\pi$
$997$	34.0235	1.07754	0.538768	+	0.842454i	$0.318890\pi$
$998$	10.8825	0.344480
$999$	3.55479	0.112469

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2541.2.a.bk.1.3	✓	4
3.2	odd	2		7623.2.a.cm.1.2		4
11.10	odd	2		2541.2.a.bo.1.2	yes	4
33.32	even	2		7623.2.a.cf.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2541.2.a.bk.1.3	✓	4	1.1	even	1	trivial
2541.2.a.bo.1.2	yes	4	11.10	odd	2
7623.2.a.cf.1.3		4	33.32	even	2
7623.2.a.cm.1.2		4	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2541 = 3 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2541.a (trivial)

\(f(q)\)	\(=\)	\(q-0.301143 q^{2} -1.00000 q^{3} -1.90931 q^{4} +1.30114 q^{5} +0.301143 q^{6} -1.00000 q^{7} +1.17726 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.301143 q^{2} -1.00000 q^{3} -1.90931 q^{4} +1.30114 q^{5} +0.301143 q^{6} -1.00000 q^{7} +1.17726 q^{8} +1.00000 q^{9} -0.391830 q^{10} +1.90931 q^{12} -3.38772 q^{13} +0.301143 q^{14} -1.30114 q^{15} +3.46410 q^{16} +0.478405 q^{17} -0.301143 q^{18} +1.60817 q^{19} -2.48429 q^{20} +1.00000 q^{21} +3.47841 q^{23} -1.17726 q^{24} -3.30703 q^{25} +1.02019 q^{26} -1.00000 q^{27} +1.90931 q^{28} +0.942507 q^{29} +0.391830 q^{30} -1.17726 q^{31} -3.39771 q^{32} -0.144068 q^{34} -1.30114 q^{35} -1.90931 q^{36} -3.55479 q^{37} -0.484289 q^{38} +3.38772 q^{39} +1.53179 q^{40} +3.94839 q^{41} -0.301143 q^{42} -2.87024 q^{43} +1.30114 q^{45} -1.04750 q^{46} +12.1113 q^{47} -3.46410 q^{48} +1.00000 q^{49} +0.995888 q^{50} -0.478405 q^{51} +6.46821 q^{52} +5.28273 q^{53} +0.301143 q^{54} -1.17726 q^{56} -1.60817 q^{57} -0.283829 q^{58} -9.69345 q^{59} +2.48429 q^{60} +3.00588 q^{61} +0.354524 q^{62} -1.00000 q^{63} -5.90501 q^{64} -4.40791 q^{65} +7.74683 q^{67} -0.913425 q^{68} -3.47841 q^{69} +0.391830 q^{70} -8.46568 q^{71} +1.17726 q^{72} -13.3709 q^{73} +1.07050 q^{74} +3.30703 q^{75} -3.07050 q^{76} -1.02019 q^{78} -8.86612 q^{79} +4.50729 q^{80} +1.00000 q^{81} -1.18903 q^{82} -11.4700 q^{83} -1.90931 q^{84} +0.622473 q^{85} +0.864351 q^{86} -0.942507 q^{87} +7.54068 q^{89} -0.391830 q^{90} +3.38772 q^{91} -6.64136 q^{92} +1.17726 q^{93} -3.64725 q^{94} +2.09246 q^{95} +3.39771 q^{96} -1.71364 q^{97} -0.301143 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 4 q^{3} + 4 q^{4} + 6 q^{5} + 2 q^{6} - 4 q^{7} + 4 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 4 * q^3 + 4 * q^4 + 6 * q^5 + 2 * q^6 - 4 * q^7 + 4 * q^9	\( 4 q - 2 q^{2} - 4 q^{3} + 4 q^{4} + 6 q^{5} + 2 q^{6} - 4 q^{7} + 4 q^{9} - 14 q^{10} - 4 q^{12} + 2 q^{13} + 2 q^{14} - 6 q^{15} - 2 q^{17} - 2 q^{18} - 6 q^{19} + 8 q^{20} + 4 q^{21} + 10 q^{23} - 4 q^{27} - 4 q^{28} - 14 q^{29} + 14 q^{30} - 12 q^{32} - 2 q^{34} - 6 q^{35} + 4 q^{36} - 12 q^{37} + 16 q^{38} - 2 q^{39} - 8 q^{40} - 16 q^{41} - 2 q^{42} - 20 q^{43} + 6 q^{45} - 8 q^{46} + 2 q^{47} + 4 q^{49} - 24 q^{50} + 2 q^{51} + 40 q^{52} - 16 q^{53} + 2 q^{54} + 6 q^{57} - 8 q^{58} + 2 q^{59} - 8 q^{60} - 2 q^{61} - 8 q^{62} - 4 q^{63} - 16 q^{64} + 2 q^{65} - 20 q^{67} - 20 q^{68} - 10 q^{69} + 14 q^{70} - 10 q^{71} + 10 q^{73} + 20 q^{74} - 28 q^{76} - 16 q^{79} + 12 q^{80} + 4 q^{81} + 28 q^{82} - 18 q^{83} + 4 q^{84} + 26 q^{86} + 14 q^{87} - 14 q^{89} - 14 q^{90} - 2 q^{91} - 8 q^{92} + 18 q^{94} - 22 q^{95} + 12 q^{96} + 38 q^{97} - 2 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 4 * q^3 + 4 * q^4 + 6 * q^5 + 2 * q^6 - 4 * q^7 + 4 * q^9 - 14 * q^10 - 4 * q^12 + 2 * q^13 + 2 * q^14 - 6 * q^15 - 2 * q^17 - 2 * q^18 - 6 * q^19 + 8 * q^20 + 4 * q^21 + 10 * q^23 - 4 * q^27 - 4 * q^28 - 14 * q^29 + 14 * q^30 - 12 * q^32 - 2 * q^34 - 6 * q^35 + 4 * q^36 - 12 * q^37 + 16 * q^38 - 2 * q^39 - 8 * q^40 - 16 * q^41 - 2 * q^42 - 20 * q^43 + 6 * q^45 - 8 * q^46 + 2 * q^47 + 4 * q^49 - 24 * q^50 + 2 * q^51 + 40 * q^52 - 16 * q^53 + 2 * q^54 + 6 * q^57 - 8 * q^58 + 2 * q^59 - 8 * q^60 - 2 * q^61 - 8 * q^62 - 4 * q^63 - 16 * q^64 + 2 * q^65 - 20 * q^67 - 20 * q^68 - 10 * q^69 + 14 * q^70 - 10 * q^71 + 10 * q^73 + 20 * q^74 - 28 * q^76 - 16 * q^79 + 12 * q^80 + 4 * q^81 + 28 * q^82 - 18 * q^83 + 4 * q^84 + 26 * q^86 + 14 * q^87 - 14 * q^89 - 14 * q^90 - 2 * q^91 - 8 * q^92 + 18 * q^94 - 22 * q^95 + 12 * q^96 + 38 * q^97 - 2 * q^98

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