LMFDB - Embedded newform 574.2.a.m.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [574,2,Mod(1,574)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(574, 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("574.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 574 = 2 \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	574.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:	$4.58341307602$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.11348.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 5x^{2} + x + 2 $ x^4 - x^3 - 5*x^2 + x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$0.723742$ of defining polynomial
Character	$\chi$	$=$	574.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.76342 q^{3} +1.00000 q^{4} +3.92368 q^{5} -2.76342 q^{6} -1.00000 q^{7} -1.00000 q^{8} +4.63646 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.76342 q^{3} +1.00000 q^{4} +3.92368 q^{5} -2.76342 q^{6} -1.00000 q^{7} -1.00000 q^{8} +4.63646 q^{9} -3.92368 q^{10} +0.839734 q^{11} +2.76342 q^{12} -0.552516 q^{13} +1.00000 q^{14} +10.8428 q^{15} +1.00000 q^{16} -7.71581 q^{17} -4.63646 q^{18} +1.44748 q^{19} +3.92368 q^{20} -2.76342 q^{21} -0.839734 q^{22} +0.552516 q^{23} -2.76342 q^{24} +10.3953 q^{25} +0.552516 q^{26} +4.52223 q^{27} -1.00000 q^{28} -4.00303 q^{29} -10.8428 q^{30} -6.84276 q^{31} -1.00000 q^{32} +2.32053 q^{33} +7.71581 q^{34} -3.92368 q^{35} +4.63646 q^{36} -7.52683 q^{37} -1.44748 q^{38} -1.52683 q^{39} -3.92368 q^{40} +1.00000 q^{41} +2.76342 q^{42} -5.31593 q^{43} +0.839734 q^{44} +18.1920 q^{45} -0.552516 q^{46} -9.92671 q^{47} +2.76342 q^{48} +1.00000 q^{49} -10.3953 q^{50} -21.3220 q^{51} -0.552516 q^{52} +11.6917 q^{53} -4.52223 q^{54} +3.29485 q^{55} +1.00000 q^{56} +4.00000 q^{57} +4.00303 q^{58} +8.91908 q^{59} +10.8428 q^{60} +12.2350 q^{61} +6.84276 q^{62} -4.63646 q^{63} +1.00000 q^{64} -2.16790 q^{65} -2.32053 q^{66} -9.63949 q^{67} -7.71581 q^{68} +1.52683 q^{69} +3.92368 q^{70} +15.2207 q^{71} -4.63646 q^{72} +11.9048 q^{73} +7.52683 q^{74} +28.7265 q^{75} +1.44748 q^{76} -0.839734 q^{77} +1.52683 q^{78} -4.36354 q^{79} +3.92368 q^{80} -1.41260 q^{81} -1.00000 q^{82} -3.39225 q^{83} -2.76342 q^{84} -30.2744 q^{85} +5.31593 q^{86} -11.0620 q^{87} -0.839734 q^{88} +0.836706 q^{89} -18.1920 q^{90} +0.552516 q^{91} +0.552516 q^{92} -18.9094 q^{93} +9.92671 q^{94} +5.67947 q^{95} -2.76342 q^{96} +0.995398 q^{97} -1.00000 q^{98} +3.89339 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - q^{3} + 4 q^{4} + 3 q^{5} + q^{6} - 4 q^{7} - 4 q^{8} + 9 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - q^3 + 4 * q^4 + 3 * q^5 + q^6 - 4 * q^7 - 4 * q^8 + 9 * q^9	\( 4 q - 4 q^{2} - q^{3} + 4 q^{4} + 3 q^{5} + q^{6} - 4 q^{7} - 4 q^{8} + 9 q^{9} - 3 q^{10} + 4 q^{11} - q^{12} - 6 q^{13} + 4 q^{14} + 11 q^{15} + 4 q^{16} - q^{17} - 9 q^{18} + 2 q^{19} + 3 q^{20} + q^{21} - 4 q^{22} + 6 q^{23} + q^{24} + 13 q^{25} + 6 q^{26} - 13 q^{27} - 4 q^{28} + 17 q^{29} - 11 q^{30} + 5 q^{31} - 4 q^{32} + 8 q^{33} + q^{34} - 3 q^{35} + 9 q^{36} - 6 q^{37} - 2 q^{38} + 18 q^{39} - 3 q^{40} + 4 q^{41} - q^{42} - 13 q^{43} + 4 q^{44} + 34 q^{45} - 6 q^{46} + 6 q^{47} - q^{48} + 4 q^{49} - 13 q^{50} - 11 q^{51} - 6 q^{52} + 29 q^{53} + 13 q^{54} - 16 q^{55} + 4 q^{56} + 16 q^{57} - 17 q^{58} + 16 q^{59} + 11 q^{60} + 21 q^{61} - 5 q^{62} - 9 q^{63} + 4 q^{64} + 18 q^{65} - 8 q^{66} + 4 q^{67} - q^{68} - 18 q^{69} + 3 q^{70} + 17 q^{71} - 9 q^{72} + 12 q^{73} + 6 q^{74} + 26 q^{75} + 2 q^{76} - 4 q^{77} - 18 q^{78} - 27 q^{79} + 3 q^{80} + 40 q^{81} - 4 q^{82} - 18 q^{83} + q^{84} - 29 q^{85} + 13 q^{86} - 41 q^{87} - 4 q^{88} + 37 q^{89} - 34 q^{90} + 6 q^{91} + 6 q^{92} - 47 q^{93} - 6 q^{94} + 24 q^{95} + q^{96} - 3 q^{97} - 4 q^{98} - 32 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - q^3 + 4 * q^4 + 3 * q^5 + q^6 - 4 * q^7 - 4 * q^8 + 9 * q^9 - 3 * q^10 + 4 * q^11 - q^12 - 6 * q^13 + 4 * q^14 + 11 * q^15 + 4 * q^16 - q^17 - 9 * q^18 + 2 * q^19 + 3 * q^20 + q^21 - 4 * q^22 + 6 * q^23 + q^24 + 13 * q^25 + 6 * q^26 - 13 * q^27 - 4 * q^28 + 17 * q^29 - 11 * q^30 + 5 * q^31 - 4 * q^32 + 8 * q^33 + q^34 - 3 * q^35 + 9 * q^36 - 6 * q^37 - 2 * q^38 + 18 * q^39 - 3 * q^40 + 4 * q^41 - q^42 - 13 * q^43 + 4 * q^44 + 34 * q^45 - 6 * q^46 + 6 * q^47 - q^48 + 4 * q^49 - 13 * q^50 - 11 * q^51 - 6 * q^52 + 29 * q^53 + 13 * q^54 - 16 * q^55 + 4 * q^56 + 16 * q^57 - 17 * q^58 + 16 * q^59 + 11 * q^60 + 21 * q^61 - 5 * q^62 - 9 * q^63 + 4 * q^64 + 18 * q^65 - 8 * q^66 + 4 * q^67 - q^68 - 18 * q^69 + 3 * q^70 + 17 * q^71 - 9 * q^72 + 12 * q^73 + 6 * q^74 + 26 * q^75 + 2 * q^76 - 4 * q^77 - 18 * q^78 - 27 * q^79 + 3 * q^80 + 40 * q^81 - 4 * q^82 - 18 * q^83 + q^84 - 29 * q^85 + 13 * q^86 - 41 * q^87 - 4 * q^88 + 37 * q^89 - 34 * q^90 + 6 * q^91 + 6 * q^92 - 47 * q^93 - 6 * q^94 + 24 * q^95 + q^96 - 3 * q^97 - 4 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.76342	1.59546	0.797729	−	0.603016i	$-0.206034\pi$
$3$	2.76342	1.59546	0.797729	+	0.603016i	$0.206034\pi$
$4$	1.00000	0.500000
$5$	3.92368	1.75472	0.877362	−	0.479829i	$-0.159301\pi$
$5$	3.92368	1.75472	0.877362	+	0.479829i	$0.159301\pi$
$6$	−2.76342	−1.12816
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	4.63646	1.54549
$10$	−3.92368	−1.24078
$11$	0.839734	0.253189	0.126595	−	0.991955i	$-0.459595\pi$
$11$	0.839734	0.253189	0.126595	+	0.991955i	$0.459595\pi$
$12$	2.76342	0.797729
$13$	−0.552516	−0.153240	−0.0766201	−	0.997060i	$-0.524413\pi$
$13$	−0.552516	−0.153240	−0.0766201	+	0.997060i	$0.524413\pi$
$14$	1.00000	0.267261
$15$	10.8428	2.79959
$16$	1.00000	0.250000
$17$	−7.71581	−1.87136	−0.935679	−	0.352851i	$-0.885212\pi$
$17$	−7.71581	−1.87136	−0.935679	+	0.352851i	$0.885212\pi$
$18$	−4.63646	−1.09282
$19$	1.44748	0.332076	0.166038	−	0.986119i	$-0.446903\pi$
$19$	1.44748	0.332076	0.166038	+	0.986119i	$0.446903\pi$
$20$	3.92368	0.877362
$21$	−2.76342	−0.603027
$22$	−0.839734	−0.179032
$23$	0.552516	0.115207	0.0576037	−	0.998340i	$-0.481654\pi$
$23$	0.552516	0.115207	0.0576037	+	0.998340i	$0.481654\pi$
$24$	−2.76342	−0.564080
$25$	10.3953	2.07906
$26$	0.552516	0.108357
$27$	4.52223	0.870303
$28$	−1.00000	−0.188982
$29$	−4.00303	−0.743344	−0.371672	−	0.928364i	$-0.621215\pi$
$29$	−4.00303	−0.743344	−0.371672	+	0.928364i	$0.621215\pi$
$30$	−10.8428	−1.97961
$31$	−6.84276	−1.22900	−0.614498	−	0.788918i	$-0.710641\pi$
$31$	−6.84276	−1.22900	−0.614498	+	0.788918i	$0.710641\pi$
$32$	−1.00000	−0.176777
$33$	2.32053	0.403953
$34$	7.71581	1.32325
$35$	−3.92368	−0.663223
$36$	4.63646	0.772744
$37$	−7.52683	−1.23740	−0.618702	−	0.785626i	$-0.712341\pi$
$37$	−7.52683	−1.23740	−0.618702	+	0.785626i	$0.712341\pi$
$38$	−1.44748	−0.234813
$39$	−1.52683	−0.244489
$40$	−3.92368	−0.620389
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	2.76342	0.426404
$43$	−5.31593	−0.810672	−0.405336	−	0.914168i	$-0.632845\pi$
$43$	−5.31593	−0.810672	−0.405336	+	0.914168i	$0.632845\pi$
$44$	0.839734	0.126595
$45$	18.1920	2.71190
$46$	−0.552516	−0.0814640
$47$	−9.92671	−1.44796	−0.723980	−	0.689821i	$-0.757689\pi$
$47$	−9.92671	−1.44796	−0.723980	+	0.689821i	$0.757689\pi$
$48$	2.76342	0.398865
$49$	1.00000	0.142857
$50$	−10.3953	−1.47011
$51$	−21.3220	−2.98568
$52$	−0.552516	−0.0766201
$53$	11.6917	1.60598	0.802989	−	0.595994i	$-0.203242\pi$
$53$	11.6917	1.60598	0.802989	+	0.595994i	$0.203242\pi$
$54$	−4.52223	−0.615397
$55$	3.29485	0.444277
$56$	1.00000	0.133631
$57$	4.00000	0.529813
$58$	4.00303	0.525623
$59$	8.91908	1.16117	0.580583	−	0.814201i	$-0.302825\pi$
$59$	8.91908	1.16117	0.580583	+	0.814201i	$0.302825\pi$
$60$	10.8428	1.39979
$61$	12.2350	1.56653	0.783266	−	0.621686i	$-0.213552\pi$
$61$	12.2350	1.56653	0.783266	+	0.621686i	$0.213552\pi$
$62$	6.84276	0.869032
$63$	−4.63646	−0.584140
$64$	1.00000	0.125000
$65$	−2.16790	−0.268894
$66$	−2.32053	−0.285638
$67$	−9.63949	−1.17765	−0.588826	−	0.808260i	$-0.700410\pi$
$67$	−9.63949	−1.17765	−0.588826	+	0.808260i	$0.700410\pi$
$68$	−7.71581	−0.935679
$69$	1.52683	0.183809
$70$	3.92368	0.468970
$71$	15.2207	1.80637	0.903184	−	0.429254i	$-0.141224\pi$
$71$	15.2207	1.80637	0.903184	+	0.429254i	$0.141224\pi$
$72$	−4.63646	−0.546412
$73$	11.9048	1.39335	0.696675	−	0.717387i	$-0.254662\pi$
$73$	11.9048	1.39335	0.696675	+	0.717387i	$0.254662\pi$
$74$	7.52683	0.874976
$75$	28.7265	3.31705
$76$	1.44748	0.166038
$77$	−0.839734	−0.0956965
$78$	1.52683	0.172880
$79$	−4.36354	−0.490936	−0.245468	−	0.969405i	$-0.578942\pi$
$79$	−4.36354	−0.490936	−0.245468	+	0.969405i	$0.578942\pi$
$80$	3.92368	0.438681
$81$	−1.41260	−0.156955
$82$	−1.00000	−0.110432
$83$	−3.39225	−0.372348	−0.186174	−	0.982517i	$-0.559609\pi$
$83$	−3.39225	−0.372348	−0.186174	+	0.982517i	$0.559609\pi$
$84$	−2.76342	−0.301513
$85$	−30.2744	−3.28372
$86$	5.31593	0.573232
$87$	−11.0620	−1.18597
$88$	−0.839734	−0.0895159
$89$	0.836706	0.0886906	0.0443453	−	0.999016i	$-0.485880\pi$
$89$	0.836706	0.0886906	0.0443453	+	0.999016i	$0.485880\pi$
$90$	−18.1920	−1.91761
$91$	0.552516	0.0579194
$92$	0.552516	0.0576037
$93$	−18.9094	−1.96081
$94$	9.92671	1.02386
$95$	5.67947	0.582701
$96$	−2.76342	−0.282040
$97$	0.995398	0.101067	0.0505337	−	0.998722i	$-0.483908\pi$
$97$	0.995398	0.101067	0.0505337	+	0.998722i	$0.483908\pi$
$98$	−1.00000	−0.101015
$99$	3.89339	0.391301
$100$	10.3953	1.03953
$101$	1.76802	0.175924	0.0879621	−	0.996124i	$-0.471965\pi$
$101$	1.76802	0.175924	0.0879621	+	0.996124i	$0.471965\pi$
$102$	21.3220	2.11119
$103$	−2.04300	−0.201303	−0.100652	−	0.994922i	$-0.532093\pi$
$103$	−2.04300	−0.201303	−0.100652	+	0.994922i	$0.532093\pi$
$104$	0.552516	0.0541786
$105$	−10.8428	−1.05815
$106$	−11.6917	−1.13560
$107$	13.8044	1.33452	0.667259	−	0.744826i	$-0.267467\pi$
$107$	13.8044	1.33452	0.667259	+	0.744826i	$0.267467\pi$
$108$	4.52223	0.435152
$109$	9.89339	0.947615	0.473808	−	0.880628i	$-0.342879\pi$
$109$	9.89339	0.947615	0.473808	+	0.880628i	$0.342879\pi$
$110$	−3.29485	−0.314151
$111$	−20.7998	−1.97423
$112$	−1.00000	−0.0944911
$113$	3.86845	0.363913	0.181956	−	0.983307i	$-0.441757\pi$
$113$	3.86845	0.363913	0.181956	+	0.983307i	$0.441757\pi$
$114$	−4.00000	−0.374634
$115$	2.16790	0.202157
$116$	−4.00303	−0.371672
$117$	−2.56172	−0.236831
$118$	−8.91908	−0.821068
$119$	7.71581	0.707307
$120$	−10.8428	−0.989804
$121$	−10.2948	−0.935895
$122$	−12.2350	−1.10771
$123$	2.76342	0.249169
$124$	−6.84276	−0.614498
$125$	21.1693	1.89344
$126$	4.63646	0.413049
$127$	−19.6062	−1.73977	−0.869883	−	0.493257i	$-0.835806\pi$
$127$	−19.6062	−1.73977	−0.869883	+	0.493257i	$0.835806\pi$
$128$	−1.00000	−0.0883883
$129$	−14.6901	−1.29339
$130$	2.16790	0.190137
$131$	3.81405	0.333235	0.166617	−	0.986022i	$-0.446716\pi$
$131$	3.81405	0.333235	0.166617	+	0.986022i	$0.446716\pi$
$132$	2.32053	0.201976
$133$	−1.44748	−0.125513
$134$	9.63949	0.832725
$135$	17.7438	1.52714
$136$	7.71581	0.661625
$137$	14.7331	1.25874	0.629368	−	0.777107i	$-0.283314\pi$
$137$	14.7331	1.25874	0.629368	+	0.777107i	$0.283314\pi$
$138$	−1.52683	−0.129972
$139$	−8.45511	−0.717153	−0.358577	−	0.933500i	$-0.616738\pi$
$139$	−8.45511	−0.717153	−0.358577	+	0.933500i	$0.616738\pi$
$140$	−3.92368	−0.331612
$141$	−27.4316	−2.31016
$142$	−15.2207	−1.27729
$143$	−0.463966	−0.0387988
$144$	4.63646	0.386372
$145$	−15.7066	−1.30436
$146$	−11.9048	−0.985247
$147$	2.76342	0.227923
$148$	−7.52683	−0.618702
$149$	−4.46699	−0.365950	−0.182975	−	0.983118i	$-0.558573\pi$
$149$	−4.46699	−0.365950	−0.182975	+	0.983118i	$0.558573\pi$
$150$	−28.7265	−2.34551
$151$	−18.1595	−1.47780	−0.738901	−	0.673814i	$-0.764655\pi$
$151$	−18.1595	−1.47780	−0.738901	+	0.673814i	$0.764655\pi$
$152$	−1.44748	−0.117406
$153$	−35.7741	−2.89216
$154$	0.839734	0.0676677
$155$	−26.8488	−2.15655
$156$	−1.52683	−0.122244
$157$	−3.18438	−0.254141	−0.127071	−	0.991894i	$-0.540557\pi$
$157$	−3.18438	−0.254141	−0.127071	+	0.991894i	$0.540557\pi$
$158$	4.36354	0.347144
$159$	32.3090	2.56227
$160$	−3.92368	−0.310194
$161$	−0.552516	−0.0435443
$162$	1.41260	0.110984
$163$	11.5843	0.907349	0.453675	−	0.891167i	$-0.350113\pi$
$163$	11.5843	0.907349	0.453675	+	0.891167i	$0.350113\pi$
$164$	1.00000	0.0780869
$165$	9.10503	0.708826
$166$	3.39225	0.263290
$167$	−5.14887	−0.398432	−0.199216	−	0.979956i	$-0.563839\pi$
$167$	−5.14887	−0.398432	−0.199216	+	0.979956i	$0.563839\pi$
$168$	2.76342	0.213202
$169$	−12.6947	−0.976517
$170$	30.2744	2.32194
$171$	6.71121	0.513219
$172$	−5.31593	−0.405336
$173$	10.2924	0.782519	0.391260	−	0.920280i	$-0.372039\pi$
$173$	10.2924	0.782519	0.391260	+	0.920280i	$0.372039\pi$
$174$	11.0620	0.838610
$175$	−10.3953	−0.785809
$176$	0.839734	0.0632973
$177$	24.6471	1.85259
$178$	−0.836706	−0.0627138
$179$	4.68104	0.349877	0.174939	−	0.984579i	$-0.444027\pi$
$179$	4.68104	0.349877	0.174939	+	0.984579i	$0.444027\pi$
$180$	18.1920	1.35595
$181$	−11.7588	−0.874026	−0.437013	−	0.899455i	$-0.643964\pi$
$181$	−11.7588	−0.874026	−0.437013	+	0.899455i	$0.643964\pi$
$182$	−0.552516	−0.0409552
$183$	33.8104	2.49934
$184$	−0.552516	−0.0407320
$185$	−29.5329	−2.17130
$186$	18.9094	1.38650
$187$	−6.47923	−0.473808
$188$	−9.92671	−0.723980
$189$	−4.52223	−0.328944
$190$	−5.67947	−0.412032
$191$	−20.1065	−1.45485	−0.727427	−	0.686185i	$-0.759284\pi$
$191$	−20.1065	−1.45485	−0.727427	+	0.686185i	$0.759284\pi$
$192$	2.76342	0.199432
$193$	7.99080	0.575190	0.287595	−	0.957752i	$-0.407144\pi$
$193$	7.99080	0.575190	0.287595	+	0.957752i	$0.407144\pi$
$194$	−0.995398	−0.0714654
$195$	−5.99080	−0.429010
$196$	1.00000	0.0714286
$197$	23.7522	1.69227	0.846135	−	0.532968i	$-0.178923\pi$
$197$	23.7522	1.69227	0.846135	+	0.532968i	$0.178923\pi$
$198$	−3.89339	−0.276692
$199$	3.75881	0.266455	0.133228	−	0.991085i	$-0.457466\pi$
$199$	3.75881	0.266455	0.133228	+	0.991085i	$0.457466\pi$
$200$	−10.3953	−0.735057
$201$	−26.6379	−1.87889
$202$	−1.76802	−0.124397
$203$	4.00303	0.280957
$204$	−21.3220	−1.49284
$205$	3.92368	0.274042
$206$	2.04300	0.142343
$207$	2.56172	0.178052
$208$	−0.552516	−0.0383101
$209$	1.21550	0.0840780
$210$	10.8428	0.748222
$211$	20.5827	1.41697	0.708485	−	0.705726i	$-0.249379\pi$
$211$	20.5827	1.41697	0.708485	+	0.705726i	$0.249379\pi$
$212$	11.6917	0.802989
$213$	42.0612	2.88198
$214$	−13.8044	−0.943647
$215$	−20.8580	−1.42251
$216$	−4.52223	−0.307699
$217$	6.84276	0.464517
$218$	−9.89339	−0.670065
$219$	32.8979	2.22303
$220$	3.29485	0.222139
$221$	4.26311	0.286768
$222$	20.7998	1.39599
$223$	−18.9532	−1.26920	−0.634601	−	0.772840i	$-0.718836\pi$
$223$	−18.9532	−1.26920	−0.634601	+	0.772840i	$0.718836\pi$
$224$	1.00000	0.0668153
$225$	48.1973	3.21316
$226$	−3.86845	−0.257325
$227$	5.70661	0.378761	0.189380	−	0.981904i	$-0.439352\pi$
$227$	5.70661	0.378761	0.189380	+	0.981904i	$0.439352\pi$
$228$	4.00000	0.264906
$229$	−9.19964	−0.607929	−0.303965	−	0.952683i	$-0.598310\pi$
$229$	−9.19964	−0.607929	−0.303965	+	0.952683i	$0.598310\pi$
$230$	−2.16790	−0.142947
$231$	−2.32053	−0.152680
$232$	4.00303	0.262812
$233$	−25.4316	−1.66608	−0.833040	−	0.553212i	$-0.813402\pi$
$233$	−25.4316	−1.66608	−0.833040	+	0.553212i	$0.813402\pi$
$234$	2.56172	0.167465
$235$	−38.9492	−2.54077
$236$	8.91908	0.580583
$237$	−12.0583	−0.783268
$238$	−7.71581	−0.500142
$239$	0.415743	0.0268922	0.0134461	−	0.999910i	$-0.495720\pi$
$239$	0.415743	0.0268922	0.0134461	+	0.999910i	$0.495720\pi$
$240$	10.8428	0.699897
$241$	19.5268	1.25783	0.628917	−	0.777473i	$-0.283499\pi$
$241$	19.5268	1.25783	0.628917	+	0.777473i	$0.283499\pi$
$242$	10.2948	0.661778
$243$	−17.4703	−1.12072
$244$	12.2350	0.783266
$245$	3.92368	0.250675
$246$	−2.76342	−0.176189
$247$	−0.799758	−0.0508874
$248$	6.84276	0.434516
$249$	−9.37419	−0.594065
$250$	−21.1693	−1.33887
$251$	22.6712	1.43100	0.715498	−	0.698615i	$-0.246200\pi$
$251$	22.6712	1.43100	0.715498	+	0.698615i	$0.246200\pi$
$252$	−4.63646	−0.292070
$253$	0.463966	0.0291693
$254$	19.6062	1.23020
$255$	−83.6607	−5.23904
$256$	1.00000	0.0625000
$257$	−5.68030	−0.354328	−0.177164	−	0.984181i	$-0.556692\pi$
$257$	−5.68030	−0.354328	−0.177164	+	0.984181i	$0.556692\pi$
$258$	14.6901	0.914567
$259$	7.52683	0.467694
$260$	−2.16790	−0.134447
$261$	−18.5599	−1.14883
$262$	−3.81405	−0.235633
$263$	−12.6411	−0.779481	−0.389741	−	0.920925i	$-0.627435\pi$
$263$	−12.6411	−0.779481	−0.389741	+	0.920925i	$0.627435\pi$
$264$	−2.32053	−0.142819
$265$	45.8745	2.81805
$266$	1.44748	0.0887510
$267$	2.31217	0.141502
$268$	−9.63949	−0.588826
$269$	30.1254	1.83678	0.918388	−	0.395680i	$-0.129491\pi$
$269$	30.1254	1.83678	0.918388	+	0.395680i	$0.129491\pi$
$270$	−17.7438	−1.07985
$271$	−13.9048	−0.844656	−0.422328	−	0.906443i	$-0.638787\pi$
$271$	−13.9048	−0.844656	−0.422328	+	0.906443i	$0.638787\pi$
$272$	−7.71581	−0.467840
$273$	1.52683	0.0924080
$274$	−14.7331	−0.890061
$275$	8.72926	0.526394
$276$	1.52683	0.0919044
$277$	22.1647	1.33175	0.665875	−	0.746063i	$-0.268058\pi$
$277$	22.1647	1.33175	0.665875	+	0.746063i	$0.268058\pi$
$278$	8.45511	0.507104
$279$	−31.7262	−1.89940
$280$	3.92368	0.234485
$281$	5.35893	0.319687	0.159844	−	0.987142i	$-0.448901\pi$
$281$	5.35893	0.319687	0.159844	+	0.987142i	$0.448901\pi$
$282$	27.4316	1.63353
$283$	−12.6078	−0.749453	−0.374726	−	0.927135i	$-0.622263\pi$
$283$	−12.6078	−0.749453	−0.374726	+	0.927135i	$0.622263\pi$
$284$	15.2207	0.903184
$285$	15.6947	0.929675
$286$	0.463966	0.0274349
$287$	−1.00000	−0.0590281
$288$	−4.63646	−0.273206
$289$	42.5337	2.50198
$290$	15.7066	0.922324
$291$	2.75070	0.161249
$292$	11.9048	0.696675
$293$	−17.0892	−0.998360	−0.499180	−	0.866498i	$-0.666365\pi$
$293$	−17.0892	−0.998360	−0.499180	+	0.866498i	$0.666365\pi$
$294$	−2.76342	−0.161166
$295$	34.9956	2.03752
$296$	7.52683	0.437488
$297$	3.79747	0.220351
$298$	4.46699	0.258766
$299$	−0.305274	−0.0176544
$300$	28.7265	1.65852
$301$	5.31593	0.306405
$302$	18.1595	1.04496
$303$	4.88577	0.280680
$304$	1.44748	0.0830189
$305$	48.0063	2.74883
$306$	35.7741	2.04507
$307$	−1.87147	−0.106811	−0.0534053	−	0.998573i	$-0.517008\pi$
$307$	−1.87147	−0.106811	−0.0534053	+	0.998573i	$0.517008\pi$
$308$	−0.839734	−0.0478483
$309$	−5.64567	−0.321171
$310$	26.8488	1.52491
$311$	−29.1391	−1.65232	−0.826162	−	0.563432i	$-0.809481\pi$
$311$	−29.1391	−1.65232	−0.826162	+	0.563432i	$0.809481\pi$
$312$	1.52683	0.0864398
$313$	1.66675	0.0942103	0.0471052	−	0.998890i	$-0.485000\pi$
$313$	1.66675	0.0942103	0.0471052	+	0.998890i	$0.485000\pi$
$314$	3.18438	0.179705
$315$	−18.1920	−1.02500
$316$	−4.36354	−0.245468
$317$	−5.27074	−0.296034	−0.148017	−	0.988985i	$-0.547289\pi$
$317$	−5.27074	−0.296034	−0.148017	+	0.988985i	$0.547289\pi$
$318$	−32.3090	−1.81180
$319$	−3.36148	−0.188207
$320$	3.92368	0.219340
$321$	38.1472	2.12917
$322$	0.552516	0.0307905
$323$	−11.1685	−0.621433
$324$	−1.41260	−0.0784775
$325$	−5.74355	−0.318595
$326$	−11.5843	−0.641593
$327$	27.3396	1.51188
$328$	−1.00000	−0.0552158
$329$	9.92671	0.547277
$330$	−9.10503	−0.501215
$331$	20.3380	1.11788	0.558938	−	0.829209i	$-0.311209\pi$
$331$	20.3380	1.11788	0.558938	+	0.829209i	$0.311209\pi$
$332$	−3.39225	−0.186174
$333$	−34.8979	−1.91239
$334$	5.14887	0.281734
$335$	−37.8223	−2.06645
$336$	−2.76342	−0.150757
$337$	−0.690125	−0.0375935	−0.0187967	−	0.999823i	$-0.505984\pi$
$337$	−0.690125	−0.0375935	−0.0187967	+	0.999823i	$0.505984\pi$
$338$	12.6947	0.690502
$339$	10.6901	0.580608
$340$	−30.2744	−1.64186
$341$	−5.74610	−0.311169
$342$	−6.71121	−0.362901
$343$	−1.00000	−0.0539949
$344$	5.31593	0.286616
$345$	5.99080	0.322534
$346$	−10.2924	−0.553325
$347$	31.2523	1.67771	0.838856	−	0.544353i	$-0.183225\pi$
$347$	31.2523	1.67771	0.838856	+	0.544353i	$0.183225\pi$
$348$	−11.0620	−0.592987
$349$	−34.5094	−1.84725	−0.923623	−	0.383303i	$-0.874787\pi$
$349$	−34.5094	−1.84725	−0.923623	+	0.383303i	$0.874787\pi$
$350$	10.3953	0.555651
$351$	−2.49860	−0.133366
$352$	−0.839734	−0.0447580
$353$	26.3840	1.40428	0.702140	−	0.712039i	$-0.252228\pi$
$353$	26.3840	1.40428	0.702140	+	0.712039i	$0.252228\pi$
$354$	−24.6471	−1.30998
$355$	59.7213	3.16968
$356$	0.836706	0.0443453
$357$	21.3220	1.12848
$358$	−4.68104	−0.247401
$359$	−27.8534	−1.47005	−0.735024	−	0.678042i	$-0.762829\pi$
$359$	−27.8534	−1.47005	−0.735024	+	0.678042i	$0.762829\pi$
$360$	−18.1920	−0.958803
$361$	−16.9048	−0.889726
$362$	11.7588	0.618030
$363$	−28.4489	−1.49318
$364$	0.552516	0.0289597
$365$	46.7106	2.44494
$366$	−33.8104	−1.76730
$367$	−9.89037	−0.516273	−0.258136	−	0.966108i	$-0.583108\pi$
$367$	−9.89037	−0.516273	−0.258136	+	0.966108i	$0.583108\pi$
$368$	0.552516	0.0288019
$369$	4.63646	0.241365
$370$	29.5329	1.53534
$371$	−11.6917	−0.607003
$372$	−18.9094	−0.980406
$373$	5.31677	0.275292	0.137646	−	0.990482i	$-0.456046\pi$
$373$	5.31677	0.275292	0.137646	+	0.990482i	$0.456046\pi$
$374$	6.47923	0.335033
$375$	58.4997	3.02091
$376$	9.92671	0.511931
$377$	2.21174	0.113910
$378$	4.52223	0.232598
$379$	14.7340	0.756833	0.378416	−	0.925635i	$-0.376469\pi$
$379$	14.7340	0.756833	0.378416	+	0.925635i	$0.376469\pi$
$380$	5.67947	0.291351
$381$	−54.1800	−2.77573
$382$	20.1065	1.02874
$383$	−4.00000	−0.204390	−0.102195	−	0.994764i	$-0.532587\pi$
$383$	−4.00000	−0.204390	−0.102195	+	0.994764i	$0.532587\pi$
$384$	−2.76342	−0.141020
$385$	−3.29485	−0.167921
$386$	−7.99080	−0.406721
$387$	−24.6471	−1.25288
$388$	0.995398	0.0505337
$389$	7.99080	0.405149	0.202575	−	0.979267i	$-0.435069\pi$
$389$	7.99080	0.405149	0.202575	+	0.979267i	$0.435069\pi$
$390$	5.99080	0.303356
$391$	−4.26311	−0.215595
$392$	−1.00000	−0.0505076
$393$	10.5398	0.531663
$394$	−23.7522	−1.19662
$395$	−17.1211	−0.861457
$396$	3.89339	0.195650
$397$	−6.91689	−0.347149	−0.173574	−	0.984821i	$-0.555532\pi$
$397$	−6.91689	−0.347149	−0.173574	+	0.984821i	$0.555532\pi$
$398$	−3.75881	−0.188412
$399$	−4.00000	−0.200250
$400$	10.3953	0.519764
$401$	−1.15058	−0.0574571	−0.0287286	−	0.999587i	$-0.509146\pi$
$401$	−1.15058	−0.0574571	−0.0287286	+	0.999587i	$0.509146\pi$
$402$	26.6379	1.32858
$403$	3.78073	0.188332
$404$	1.76802	0.0879621
$405$	−5.54257	−0.275413
$406$	−4.00303	−0.198667
$407$	−6.32053	−0.313297
$408$	21.3220	1.05560
$409$	30.5805	1.51211	0.756054	−	0.654509i	$-0.227125\pi$
$409$	30.5805	1.51211	0.756054	+	0.654509i	$0.227125\pi$
$410$	−3.92368	−0.193777
$411$	40.7138	2.00826
$412$	−2.04300	−0.100652
$413$	−8.91908	−0.438879
$414$	−2.56172	−0.125902
$415$	−13.3101	−0.653367
$416$	0.552516	0.0270893
$417$	−23.3650	−1.14419
$418$	−1.21550	−0.0594521
$419$	12.1060	0.591417	0.295708	−	0.955278i	$-0.404444\pi$
$419$	12.1060	0.591417	0.295708	+	0.955278i	$0.404444\pi$
$420$	−10.8428	−0.529073
$421$	−24.4730	−1.19274	−0.596372	−	0.802708i	$-0.703392\pi$
$421$	−24.4730	−1.19274	−0.596372	+	0.802708i	$0.703392\pi$
$422$	−20.5827	−1.00195
$423$	−46.0248	−2.23780
$424$	−11.6917	−0.567799
$425$	−80.2080	−3.89066
$426$	−42.0612	−2.03787
$427$	−12.2350	−0.592094
$428$	13.8044	0.667259
$429$	−1.28213	−0.0619019
$430$	20.8580	1.00586
$431$	22.1942	1.06906	0.534528	−	0.845150i	$-0.320489\pi$
$431$	22.1942	1.06906	0.534528	+	0.845150i	$0.320489\pi$
$432$	4.52223	0.217576
$433$	8.71787	0.418954	0.209477	−	0.977814i	$-0.432824\pi$
$433$	8.71787	0.418954	0.209477	+	0.977814i	$0.432824\pi$
$434$	−6.84276	−0.328463
$435$	−43.4039	−2.08106
$436$	9.89339	0.473808
$437$	0.799758	0.0382576
$438$	−32.8979	−1.57192
$439$	4.09461	0.195425	0.0977124	−	0.995215i	$-0.468847\pi$
$439$	4.09461	0.195425	0.0977124	+	0.995215i	$0.468847\pi$
$440$	−3.29485	−0.157076
$441$	4.63646	0.220784
$442$	−4.26311	−0.202775
$443$	−20.8520	−0.990707	−0.495353	−	0.868692i	$-0.664961\pi$
$443$	−20.8520	−0.990707	−0.495353	+	0.868692i	$0.664961\pi$
$444$	−20.7998	−0.987113
$445$	3.28297	0.155628
$446$	18.9532	0.897462
$447$	−12.3442	−0.583859
$448$	−1.00000	−0.0472456
$449$	−10.8142	−0.510353	−0.255176	−	0.966895i	$-0.582134\pi$
$449$	−10.8142	−0.510353	−0.255176	+	0.966895i	$0.582134\pi$
$450$	−48.1973	−2.27204
$451$	0.839734	0.0395415
$452$	3.86845	0.181956
$453$	−50.1823	−2.35777
$454$	−5.70661	−0.267824
$455$	2.16790	0.101633
$456$	−4.00000	−0.187317
$457$	−20.6861	−0.967657	−0.483828	−	0.875163i	$-0.660754\pi$
$457$	−20.6861	−0.967657	−0.483828	+	0.875163i	$0.660754\pi$
$458$	9.19964	0.429871
$459$	−34.8927	−1.62865
$460$	2.16790	0.101079
$461$	33.0408	1.53886	0.769432	−	0.638728i	$-0.220539\pi$
$461$	33.0408	1.53886	0.769432	+	0.638728i	$0.220539\pi$
$462$	2.32053	0.107961
$463$	−27.8973	−1.29650	−0.648248	−	0.761429i	$-0.724498\pi$
$463$	−27.8973	−1.29650	−0.648248	+	0.761429i	$0.724498\pi$
$464$	−4.00303	−0.185836
$465$	−74.1944	−3.44068
$466$	25.4316	1.17810
$467$	−25.7249	−1.19041	−0.595203	−	0.803575i	$-0.702928\pi$
$467$	−25.7249	−1.19041	−0.595203	+	0.803575i	$0.702928\pi$
$468$	−2.56172	−0.118416
$469$	9.63949	0.445110
$470$	38.9492	1.79659
$471$	−8.79976	−0.405471
$472$	−8.91908	−0.410534
$473$	−4.46397	−0.205253
$474$	12.0583	0.553854
$475$	15.0470	0.690404
$476$	7.71581	0.353654
$477$	54.2081	2.48202
$478$	−0.415743	−0.0190157
$479$	10.5494	0.482013	0.241006	−	0.970524i	$-0.422522\pi$
$479$	10.5494	0.482013	0.241006	+	0.970524i	$0.422522\pi$
$480$	−10.8428	−0.494902
$481$	4.15869	0.189620
$482$	−19.5268	−0.889423
$483$	−1.52683	−0.0694732
$484$	−10.2948	−0.467948
$485$	3.90563	0.177345
$486$	17.4703	0.792468
$487$	16.5989	0.752168	0.376084	−	0.926586i	$-0.377270\pi$
$487$	16.5989	0.752168	0.376084	+	0.926586i	$0.377270\pi$
$488$	−12.2350	−0.553853
$489$	32.0121	1.44764
$490$	−3.92368	−0.177254
$491$	18.4648	0.833305	0.416652	−	0.909066i	$-0.363203\pi$
$491$	18.4648	0.833305	0.416652	+	0.909066i	$0.363203\pi$
$492$	2.76342	0.124584
$493$	30.8866	1.39106
$494$	0.799758	0.0359828
$495$	15.2764	0.686625
$496$	−6.84276	−0.307249
$497$	−15.2207	−0.682743
$498$	9.37419	0.420068
$499$	5.10284	0.228434	0.114217	−	0.993456i	$-0.463564\pi$
$499$	5.10284	0.228434	0.114217	+	0.993456i	$0.463564\pi$
$500$	21.1693	0.946722
$501$	−14.2285	−0.635681
$502$	−22.6712	−1.01187
$503$	−32.1165	−1.43201	−0.716003	−	0.698098i	$-0.754030\pi$
$503$	−32.1165	−1.43201	−0.716003	+	0.698098i	$0.754030\pi$
$504$	4.63646	0.206525
$505$	6.93714	0.308698
$506$	−0.463966	−0.0206258
$507$	−35.0808	−1.55799
$508$	−19.6062	−0.869883
$509$	14.2187	0.630231	0.315116	−	0.949053i	$-0.397957\pi$
$509$	14.2187	0.630231	0.315116	+	0.949053i	$0.397957\pi$
$510$	83.6607	3.70456
$511$	−11.9048	−0.526637
$512$	−1.00000	−0.0441942
$513$	6.54585	0.289007
$514$	5.68030	0.250547
$515$	−8.01610	−0.353231
$516$	−14.6901	−0.646697
$517$	−8.33579	−0.366608
$518$	−7.52683	−0.330710
$519$	28.4423	1.24848
$520$	2.16790	0.0950685
$521$	−15.8889	−0.696106	−0.348053	−	0.937475i	$-0.613157\pi$
$521$	−15.8889	−0.696106	−0.348053	+	0.937475i	$0.613157\pi$
$522$	18.5599	0.812344
$523$	−10.5319	−0.460529	−0.230264	−	0.973128i	$-0.573959\pi$
$523$	−10.5319	−0.460529	−0.230264	+	0.973128i	$0.573959\pi$
$524$	3.81405	0.166617
$525$	−28.7265	−1.25373
$526$	12.6411	0.551177
$527$	52.7974	2.29989
$528$	2.32053	0.100988
$529$	−22.6947	−0.986727
$530$	−45.8745	−1.99266
$531$	41.3530	1.79457
$532$	−1.44748	−0.0627564
$533$	−0.552516	−0.0239321
$534$	−2.31217	−0.100057
$535$	54.1639	2.34171
$536$	9.63949	0.416363
$537$	12.9357	0.558215
$538$	−30.1254	−1.29880
$539$	0.839734	0.0361699
$540$	17.7438	0.763571
$541$	15.1777	0.652541	0.326271	−	0.945276i	$-0.394208\pi$
$541$	15.1777	0.652541	0.326271	+	0.945276i	$0.394208\pi$
$542$	13.9048	0.597262
$543$	−32.4945	−1.39447
$544$	7.71581	0.330813
$545$	38.8185	1.66280
$546$	−1.52683	−0.0653423
$547$	37.2676	1.59345	0.796724	−	0.604344i	$-0.206565\pi$
$547$	37.2676	1.59345	0.796724	+	0.604344i	$0.206565\pi$
$548$	14.7331	0.629368
$549$	56.7272	2.42106
$550$	−8.72926	−0.372217
$551$	−5.79432	−0.246846
$552$	−1.52683	−0.0649862
$553$	4.36354	0.185556
$554$	−22.1647	−0.941690
$555$	−81.6116	−3.46422
$556$	−8.45511	−0.358577
$557$	33.6025	1.42379	0.711893	−	0.702288i	$-0.247838\pi$
$557$	33.6025	1.42379	0.711893	+	0.702288i	$0.247838\pi$
$558$	31.7262	1.34308
$559$	2.93714	0.124228
$560$	−3.92368	−0.165806
$561$	−17.9048	−0.755941
$562$	−5.35893	−0.226053
$563$	−3.65755	−0.154147	−0.0770736	−	0.997025i	$-0.524558\pi$
$563$	−3.65755	−0.154147	−0.0770736	+	0.997025i	$0.524558\pi$
$564$	−27.4316	−1.15508
$565$	15.1786	0.638567
$566$	12.6078	0.529943
$567$	1.41260	0.0593234
$568$	−15.2207	−0.638647
$569$	12.8691	0.539499	0.269750	−	0.962930i	$-0.413059\pi$
$569$	12.8691	0.539499	0.269750	+	0.962930i	$0.413059\pi$
$570$	−15.6947	−0.657380
$571$	33.1632	1.38784	0.693918	−	0.720054i	$-0.255883\pi$
$571$	33.1632	1.38784	0.693918	+	0.720054i	$0.255883\pi$
$572$	−0.463966	−0.0193994
$573$	−55.5626	−2.32116
$574$	1.00000	0.0417392
$575$	5.74355	0.239523
$576$	4.63646	0.193186
$577$	28.9229	1.20408	0.602039	−	0.798467i	$-0.294355\pi$
$577$	28.9229	1.20408	0.602039	+	0.798467i	$0.294355\pi$
$578$	−42.5337	−1.76917
$579$	22.0819	0.917692
$580$	−15.7066	−0.652181
$581$	3.39225	0.140734
$582$	−2.75070	−0.114020
$583$	9.81791	0.406616
$584$	−11.9048	−0.492624
$585$	−10.0514	−0.415573
$586$	17.0892	0.705947
$587$	−12.0271	−0.496413	−0.248207	−	0.968707i	$-0.579841\pi$
$587$	−12.0271	−0.496413	−0.248207	+	0.968707i	$0.579841\pi$
$588$	2.76342	0.113961
$589$	−9.90479	−0.408120
$590$	−34.9956	−1.44075
$591$	65.6371	2.69995
$592$	−7.52683	−0.309351
$593$	12.4454	0.511072	0.255536	−	0.966799i	$-0.417748\pi$
$593$	12.4454	0.511072	0.255536	+	0.966799i	$0.417748\pi$
$594$	−3.79747	−0.155812
$595$	30.2744	1.24113
$596$	−4.46699	−0.182975
$597$	10.3872	0.425118
$598$	0.305274	0.0124836
$599$	18.3704	0.750595	0.375298	−	0.926904i	$-0.377540\pi$
$599$	18.3704	0.750595	0.375298	+	0.926904i	$0.377540\pi$
$600$	−28.7265	−1.17275
$601$	−18.9282	−0.772096	−0.386048	−	0.922479i	$-0.626160\pi$
$601$	−18.9282	−0.772096	−0.386048	+	0.922479i	$0.626160\pi$
$602$	−5.31593	−0.216661
$603$	−44.6932	−1.82005
$604$	−18.1595	−0.738901
$605$	−40.3937	−1.64224
$606$	−4.88577	−0.198471
$607$	−30.1656	−1.22438	−0.612192	−	0.790709i	$-0.709712\pi$
$607$	−30.1656	−1.22438	−0.612192	+	0.790709i	$0.709712\pi$
$608$	−1.44748	−0.0587032
$609$	11.0620	0.448256
$610$	−48.0063	−1.94372
$611$	5.48466	0.221886
$612$	−35.7741	−1.44608
$613$	−34.0499	−1.37526	−0.687631	−	0.726060i	$-0.741349\pi$
$613$	−34.0499	−1.37526	−0.687631	+	0.726060i	$0.741349\pi$
$614$	1.87147	0.0755266
$615$	10.8428	0.437222
$616$	0.839734	0.0338338
$617$	−1.07391	−0.0432339	−0.0216170	−	0.999766i	$-0.506881\pi$
$617$	−1.07391	−0.0432339	−0.0216170	+	0.999766i	$0.506881\pi$
$618$	5.64567	0.227102
$619$	18.6230	0.748522	0.374261	−	0.927323i	$-0.377896\pi$
$619$	18.6230	0.748522	0.374261	+	0.927323i	$0.377896\pi$
$620$	−26.8488	−1.07827
$621$	2.49860	0.100265
$622$	29.1391	1.16837
$623$	−0.836706	−0.0335219
$624$	−1.52683	−0.0611221
$625$	31.0854	1.24342
$626$	−1.66675	−0.0666168
$627$	3.35893	0.134143
$628$	−3.18438	−0.127071
$629$	58.0756	2.31563
$630$	18.1920	0.724787
$631$	44.4059	1.76777	0.883886	−	0.467702i	$-0.154918\pi$
$631$	44.4059	1.76777	0.883886	+	0.467702i	$0.154918\pi$
$632$	4.36354	0.173572
$633$	56.8785	2.26072
$634$	5.27074	0.209328
$635$	−76.9284	−3.05281
$636$	32.3090	1.28114
$637$	−0.552516	−0.0218915
$638$	3.36148	0.133082
$639$	70.5703	2.79172
$640$	−3.92368	−0.155097
$641$	−15.7277	−0.621206	−0.310603	−	0.950540i	$-0.600531\pi$
$641$	−15.7277	−0.621206	−0.310603	+	0.950540i	$0.600531\pi$
$642$	−38.1472	−1.50555
$643$	23.0510	0.909042	0.454521	−	0.890736i	$-0.349810\pi$
$643$	23.0510	0.909042	0.454521	+	0.890736i	$0.349810\pi$
$644$	−0.552516	−0.0217722
$645$	−57.6394	−2.26955
$646$	11.1685	0.439419
$647$	17.3159	0.680759	0.340380	−	0.940288i	$-0.389444\pi$
$647$	17.3159	0.680759	0.340380	+	0.940288i	$0.389444\pi$
$648$	1.41260	0.0554920
$649$	7.48965	0.293995
$650$	5.74355	0.225281
$651$	18.9094	0.741117
$652$	11.5843	0.453675
$653$	−0.193449	−0.00757025	−0.00378512	−	0.999993i	$-0.501205\pi$
$653$	−0.193449	−0.00757025	−0.00378512	+	0.999993i	$0.501205\pi$
$654$	−27.3396	−1.06906
$655$	14.9651	0.584735
$656$	1.00000	0.0390434
$657$	55.1961	2.15341
$658$	−9.92671	−0.386983
$659$	−39.1784	−1.52618	−0.763088	−	0.646295i	$-0.776317\pi$
$659$	−39.1784	−1.52618	−0.763088	+	0.646295i	$0.776317\pi$
$660$	9.10503	0.354413
$661$	36.6046	1.42375	0.711877	−	0.702304i	$-0.247845\pi$
$661$	36.6046	1.42375	0.711877	+	0.702304i	$0.247845\pi$
$662$	−20.3380	−0.790458
$663$	11.7807	0.457526
$664$	3.39225	0.131645
$665$	−5.67947	−0.220240
$666$	34.8979	1.35227
$667$	−2.21174	−0.0856388
$668$	−5.14887	−0.199216
$669$	−52.3756	−2.02496
$670$	37.8223	1.46120
$671$	10.2742	0.396629
$672$	2.76342	0.106601
$673$	24.7106	0.952524	0.476262	−	0.879303i	$-0.341991\pi$
$673$	24.7106	0.952524	0.476262	+	0.879303i	$0.341991\pi$
$674$	0.690125	0.0265826
$675$	47.0098	1.80941
$676$	−12.6947	−0.488259
$677$	−43.6767	−1.67863	−0.839315	−	0.543645i	$-0.817044\pi$
$677$	−43.6767	−1.67863	−0.839315	+	0.543645i	$0.817044\pi$
$678$	−10.6901	−0.410552
$679$	−0.995398	−0.0381999
$680$	30.2744	1.16097
$681$	15.7697	0.604297
$682$	5.74610	0.220029
$683$	37.5368	1.43630	0.718152	−	0.695886i	$-0.244988\pi$
$683$	37.5368	1.43630	0.718152	+	0.695886i	$0.244988\pi$
$684$	6.71121	0.256609
$685$	57.8081	2.20873
$686$	1.00000	0.0381802
$687$	−25.4224	−0.969926
$688$	−5.31593	−0.202668
$689$	−6.45985	−0.246101
$690$	−5.99080	−0.228066
$691$	3.27122	0.124443	0.0622216	−	0.998062i	$-0.480181\pi$
$691$	3.27122	0.124443	0.0622216	+	0.998062i	$0.480181\pi$
$692$	10.2924	0.391260
$693$	−3.89339	−0.147898
$694$	−31.2523	−1.18632
$695$	−33.1752	−1.25841
$696$	11.0620	0.419305
$697$	−7.71581	−0.292257
$698$	34.5094	1.30620
$699$	−70.2781	−2.65816
$700$	−10.3953	−0.392905
$701$	1.47379	0.0556642	0.0278321	−	0.999613i	$-0.491140\pi$
$701$	1.47379	0.0556642	0.0278321	+	0.999613i	$0.491140\pi$
$702$	2.49860	0.0943037
$703$	−10.8950	−0.410912
$704$	0.839734	0.0316487
$705$	−107.633	−4.05369
$706$	−26.3840	−0.992975
$707$	−1.76802	−0.0664931
$708$	24.6471	0.926296
$709$	50.4084	1.89313	0.946563	−	0.322520i	$-0.104530\pi$
$709$	50.4084	1.89313	0.946563	+	0.322520i	$0.104530\pi$
$710$	−59.7213	−2.24130
$711$	−20.2314	−0.758736
$712$	−0.836706	−0.0313569
$713$	−3.78073	−0.141590
$714$	−21.3220	−0.797955
$715$	−1.82046	−0.0680812
$716$	4.68104	0.174939
$717$	1.14887	0.0429054
$718$	27.8534	1.03948
$719$	−7.78073	−0.290172	−0.145086	−	0.989419i	$-0.546346\pi$
$719$	−7.78073	−0.290172	−0.145086	+	0.989419i	$0.546346\pi$
$720$	18.1920	0.677976
$721$	2.04300	0.0760854
$722$	16.9048	0.629131
$723$	53.9607	2.00682
$724$	−11.7588	−0.437013
$725$	−41.6126	−1.54545
$726$	28.4489	1.05584
$727$	−31.8096	−1.17975	−0.589876	−	0.807494i	$-0.700823\pi$
$727$	−31.8096	−1.17975	−0.589876	+	0.807494i	$0.700823\pi$
$728$	−0.552516	−0.0204776
$729$	−44.0398	−1.63110
$730$	−46.7106	−1.72884
$731$	41.0167	1.51706
$732$	33.8104	1.24967
$733$	−29.5670	−1.09208	−0.546042	−	0.837758i	$-0.683866\pi$
$733$	−29.5670	−1.09208	−0.546042	+	0.837758i	$0.683866\pi$
$734$	9.89037	0.365060
$735$	10.8428	0.399941
$736$	−0.552516	−0.0203660
$737$	−8.09461	−0.298169
$738$	−4.63646	−0.170671
$739$	−31.5381	−1.16015	−0.580074	−	0.814564i	$-0.696976\pi$
$739$	−31.5381	−1.16015	−0.580074	+	0.814564i	$0.696976\pi$
$740$	−29.5329	−1.08565
$741$	−2.21006	−0.0811887
$742$	11.6917	0.429216
$743$	25.4830	0.934880	0.467440	−	0.884025i	$-0.345176\pi$
$743$	25.4830	0.934880	0.467440	+	0.884025i	$0.345176\pi$
$744$	18.9094	0.693252
$745$	−17.5271	−0.642142
$746$	−5.31677	−0.194661
$747$	−15.7280	−0.575459
$748$	−6.47923	−0.236904
$749$	−13.8044	−0.504400
$750$	−58.4997	−2.13611
$751$	−13.0251	−0.475292	−0.237646	−	0.971352i	$-0.576376\pi$
$751$	−13.0251	−0.475292	−0.237646	+	0.971352i	$0.576376\pi$
$752$	−9.92671	−0.361990
$753$	62.6500	2.28309
$754$	−2.21174	−0.0805467
$755$	−71.2522	−2.59313
$756$	−4.52223	−0.164472
$757$	−26.1103	−0.948997	−0.474498	−	0.880256i	$-0.657371\pi$
$757$	−26.1103	−0.948997	−0.474498	+	0.880256i	$0.657371\pi$
$758$	−14.7340	−0.535162
$759$	1.28213	0.0465384
$760$	−5.67947	−0.206016
$761$	25.5843	0.927429	0.463714	−	0.885985i	$-0.346516\pi$
$761$	25.5843	0.927429	0.463714	+	0.885985i	$0.346516\pi$
$762$	54.1800	1.96273
$763$	−9.89339	−0.358165
$764$	−20.1065	−0.727427
$765$	−140.366	−5.07495
$766$	4.00000	0.144526
$767$	−4.92793	−0.177937
$768$	2.76342	0.0997162
$769$	23.6356	0.852323	0.426161	−	0.904647i	$-0.359866\pi$
$769$	23.6356	0.852323	0.426161	+	0.904647i	$0.359866\pi$
$770$	3.29485	0.118738
$771$	−15.6970	−0.565315
$772$	7.99080	0.287595
$773$	12.5964	0.453059	0.226530	−	0.974004i	$-0.427262\pi$
$773$	12.5964	0.453059	0.226530	+	0.974004i	$0.427262\pi$
$774$	24.6471	0.885922
$775$	−71.1324	−2.55515
$776$	−0.995398	−0.0357327
$777$	20.7998	0.746187
$778$	−7.99080	−0.286484
$779$	1.44748	0.0518615
$780$	−5.99080	−0.214505
$781$	12.7814	0.457353
$782$	4.26311	0.152448
$783$	−18.1026	−0.646934
$784$	1.00000	0.0357143
$785$	−12.4945	−0.445947
$786$	−10.5398	−0.375942
$787$	−10.4687	−0.373169	−0.186584	−	0.982439i	$-0.559742\pi$
$787$	−10.4687	−0.373169	−0.186584	+	0.982439i	$0.559742\pi$
$788$	23.7522	0.846135
$789$	−34.9325	−1.24363
$790$	17.1211	0.609142
$791$	−3.86845	−0.137546
$792$	−3.89339	−0.138346
$793$	−6.76004	−0.240056
$794$	6.91689	0.245471
$795$	126.770	4.49608
$796$	3.75881	0.133228
$797$	−30.9895	−1.09770	−0.548851	−	0.835920i	$-0.684935\pi$
$797$	−30.9895	−1.09770	−0.548851	+	0.835920i	$0.684935\pi$
$798$	4.00000	0.141598
$799$	76.5926	2.70965
$800$	−10.3953	−0.367529
$801$	3.87936	0.137070
$802$	1.15058	0.0406283
$803$	9.99685	0.352781
$804$	−26.6379	−0.939447
$805$	−2.16790	−0.0764083
$806$	−3.78073	−0.133171
$807$	83.2489	2.93050
$808$	−1.76802	−0.0621986
$809$	12.0213	0.422647	0.211323	−	0.977416i	$-0.432223\pi$
$809$	12.0213	0.422647	0.211323	+	0.977416i	$0.432223\pi$
$810$	5.54257	0.194746
$811$	6.55032	0.230013	0.115007	−	0.993365i	$-0.463311\pi$
$811$	6.55032	0.230013	0.115007	+	0.993365i	$0.463311\pi$
$812$	4.00303	0.140479
$813$	−38.4247	−1.34761
$814$	6.32053	0.221535
$815$	45.4529	1.59215
$816$	−21.3220	−0.746419
$817$	−7.69473	−0.269204
$818$	−30.5805	−1.06922
$819$	2.56172	0.0895137
$820$	3.92368	0.137021
$821$	6.81914	0.237989	0.118995	−	0.992895i	$-0.462033\pi$
$821$	6.81914	0.237989	0.118995	+	0.992895i	$0.462033\pi$
$822$	−40.7138	−1.42006
$823$	−15.9916	−0.557433	−0.278717	−	0.960373i	$-0.589909\pi$
$823$	−15.9916	−0.557433	−0.278717	+	0.960373i	$0.589909\pi$
$824$	2.04300	0.0711714
$825$	24.1226	0.839840
$826$	8.91908	0.310334
$827$	46.7988	1.62735	0.813677	−	0.581317i	$-0.197463\pi$
$827$	46.7988	1.62735	0.813677	+	0.581317i	$0.197463\pi$
$828$	2.56172	0.0890259
$829$	4.54634	0.157901	0.0789505	−	0.996879i	$-0.474843\pi$
$829$	4.54634	0.157901	0.0789505	+	0.996879i	$0.474843\pi$
$830$	13.3101	0.462001
$831$	61.2504	2.12475
$832$	−0.552516	−0.0191550
$833$	−7.71581	−0.267337
$834$	23.3650	0.809063
$835$	−20.2025	−0.699137
$836$	1.21550	0.0420390
$837$	−30.9445	−1.06960
$838$	−12.1060	−0.418195
$839$	−4.69183	−0.161980	−0.0809900	−	0.996715i	$-0.525808\pi$
$839$	−4.69183	−0.161980	−0.0809900	+	0.996715i	$0.525808\pi$
$840$	10.8428	0.374111
$841$	−12.9758	−0.447440
$842$	24.4730	0.843397
$843$	14.8090	0.510048
$844$	20.5827	0.708485
$845$	−49.8101	−1.71352
$846$	46.0248	1.58237
$847$	10.2948	0.353735
$848$	11.6917	0.401495
$849$	−34.8404	−1.19572
$850$	80.2080	2.75111
$851$	−4.15869	−0.142558
$852$	42.0612	1.44099
$853$	34.6098	1.18502	0.592509	−	0.805564i	$-0.298138\pi$
$853$	34.6098	1.18502	0.592509	+	0.805564i	$0.298138\pi$
$854$	12.2350	0.418673
$855$	26.3326	0.900557
$856$	−13.8044	−0.471823
$857$	−24.9204	−0.851265	−0.425632	−	0.904896i	$-0.639948\pi$
$857$	−24.9204	−0.851265	−0.425632	+	0.904896i	$0.639948\pi$
$858$	1.28213	0.0437712
$859$	−46.2572	−1.57827	−0.789137	−	0.614217i	$-0.789472\pi$
$859$	−46.2572	−1.57827	−0.789137	+	0.614217i	$0.789472\pi$
$860$	−20.8580	−0.711253
$861$	−2.76342	−0.0941769
$862$	−22.1942	−0.755937
$863$	36.8979	1.25602	0.628009	−	0.778206i	$-0.283870\pi$
$863$	36.8979	1.25602	0.628009	+	0.778206i	$0.283870\pi$
$864$	−4.52223	−0.153849
$865$	40.3842	1.37311
$866$	−8.71787	−0.296245
$867$	117.538	3.99181
$868$	6.84276	0.232258
$869$	−3.66421	−0.124300
$870$	43.4039	1.47153
$871$	5.32597	0.180464
$872$	−9.89339	−0.335033
$873$	4.61513	0.156198
$874$	−0.799758	−0.0270522
$875$	−21.1693	−0.715655
$876$	32.8979	1.11152
$877$	−37.5542	−1.26812	−0.634058	−	0.773286i	$-0.718612\pi$
$877$	−37.5542	−1.26812	−0.634058	+	0.773286i	$0.718612\pi$
$878$	−4.09461	−0.138186
$879$	−47.2245	−1.59284
$880$	3.29485	0.111069
$881$	−22.1832	−0.747369	−0.373685	−	0.927556i	$-0.621906\pi$
$881$	−22.1832	−0.747369	−0.373685	+	0.927556i	$0.621906\pi$
$882$	−4.63646	−0.156118
$883$	−42.8988	−1.44366	−0.721830	−	0.692070i	$-0.756699\pi$
$883$	−42.8988	−1.44366	−0.721830	+	0.692070i	$0.756699\pi$
$884$	4.26311	0.143384
$885$	96.7075	3.25079
$886$	20.8520	0.700535
$887$	43.5262	1.46147	0.730734	−	0.682663i	$-0.239178\pi$
$887$	43.5262	1.46147	0.730734	+	0.682663i	$0.239178\pi$
$888$	20.7998	0.697994
$889$	19.6062	0.657570
$890$	−3.28297	−0.110045
$891$	−1.18620	−0.0397393
$892$	−18.9532	−0.634601
$893$	−14.3688	−0.480832
$894$	12.3442	0.412850
$895$	18.3669	0.613938
$896$	1.00000	0.0334077
$897$	−0.843598	−0.0281669
$898$	10.8142	0.360874
$899$	27.3918	0.913566
$900$	48.1973	1.60658
$901$	−90.2109	−3.00536
$902$	−0.839734	−0.0279601
$903$	14.6901	0.488857
$904$	−3.86845	−0.128663
$905$	−46.1378	−1.53367
$906$	50.1823	1.66720
$907$	−30.7568	−1.02126	−0.510631	−	0.859800i	$-0.670588\pi$
$907$	−30.7568	−1.02126	−0.510631	+	0.859800i	$0.670588\pi$
$908$	5.70661	0.189380
$909$	8.19735	0.271889
$910$	−2.16790	−0.0718650
$911$	−12.6385	−0.418733	−0.209366	−	0.977837i	$-0.567140\pi$
$911$	−12.6385	−0.418733	−0.209366	+	0.977837i	$0.567140\pi$
$912$	4.00000	0.132453
$913$	−2.84859	−0.0942744
$914$	20.6861	0.684237
$915$	132.661	4.38565
$916$	−9.19964	−0.303965
$917$	−3.81405	−0.125951
$918$	34.8927	1.15163
$919$	−20.7897	−0.685790	−0.342895	−	0.939374i	$-0.611407\pi$
$919$	−20.7897	−0.685790	−0.342895	+	0.939374i	$0.611407\pi$
$920$	−2.16790	−0.0714734
$921$	−5.17166	−0.170412
$922$	−33.0408	−1.08814
$923$	−8.40969	−0.276808
$924$	−2.32053	−0.0763399
$925$	−78.2435	−2.57263
$926$	27.8973	0.916761
$927$	−9.47231	−0.311112
$928$	4.00303	0.131406
$929$	36.7605	1.20607	0.603036	−	0.797714i	$-0.293957\pi$
$929$	36.7605	1.20607	0.603036	+	0.797714i	$0.293957\pi$
$930$	74.1944	2.43293
$931$	1.44748	0.0474394
$932$	−25.4316	−0.833040
$933$	−80.5233	−2.63622
$934$	25.7249	0.841744
$935$	−25.4224	−0.831402
$936$	2.56172	0.0837324
$937$	49.9100	1.63049	0.815244	−	0.579117i	$-0.196603\pi$
$937$	49.9100	1.63049	0.815244	+	0.579117i	$0.196603\pi$
$938$	−9.63949	−0.314741
$939$	4.60592	0.150309
$940$	−38.9492	−1.27038
$941$	−14.0149	−0.456873	−0.228436	−	0.973559i	$-0.573361\pi$
$941$	−14.0149	−0.456873	−0.228436	+	0.973559i	$0.573361\pi$
$942$	8.79976	0.286712
$943$	0.552516	0.0179924
$944$	8.91908	0.290291
$945$	−17.7438	−0.577205
$946$	4.46397	0.145136
$947$	−48.7154	−1.58304	−0.791519	−	0.611144i	$-0.790710\pi$
$947$	−48.7154	−1.58304	−0.791519	+	0.611144i	$0.790710\pi$
$948$	−12.0583	−0.391634
$949$	−6.57758	−0.213517
$950$	−15.0470	−0.488189
$951$	−14.5652	−0.472310
$952$	−7.71581	−0.250071
$953$	46.2971	1.49971	0.749856	−	0.661601i	$-0.230123\pi$
$953$	46.2971	1.49971	0.749856	+	0.661601i	$0.230123\pi$
$954$	−54.2081	−1.75505
$955$	−78.8914	−2.55287
$956$	0.415743	0.0134461
$957$	−9.28916	−0.300276
$958$	−10.5494	−0.340835
$959$	−14.7331	−0.475758
$960$	10.8428	0.349949
$961$	15.8234	0.510432
$962$	−4.15869	−0.134082
$963$	64.0034	2.06248
$964$	19.5268	0.628917
$965$	31.3533	1.00930
$966$	1.52683	0.0491250
$967$	4.67048	0.150193	0.0750963	−	0.997176i	$-0.476074\pi$
$967$	4.67048	0.150193	0.0750963	+	0.997176i	$0.476074\pi$
$968$	10.2948	0.330889
$969$	−30.8632	−0.991470
$970$	−3.90563	−0.125402
$971$	−21.1821	−0.679765	−0.339882	−	0.940468i	$-0.610387\pi$
$971$	−21.1821	−0.679765	−0.339882	+	0.940468i	$0.610387\pi$
$972$	−17.4703	−0.560359
$973$	8.45511	0.271059
$974$	−16.5989	−0.531863
$975$	−15.8718	−0.508305
$976$	12.2350	0.391633
$977$	−59.4486	−1.90193	−0.950964	−	0.309302i	$-0.899905\pi$
$977$	−59.4486	−1.90193	−0.950964	+	0.309302i	$0.899905\pi$
$978$	−32.0121	−1.02363
$979$	0.702610	0.0224555
$980$	3.92368	0.125337
$981$	45.8704	1.46453
$982$	−18.4648	−0.589236
$983$	15.7469	0.502249	0.251125	−	0.967955i	$-0.419200\pi$
$983$	15.7469	0.502249	0.251125	+	0.967955i	$0.419200\pi$
$984$	−2.76342	−0.0880945
$985$	93.1959	2.96947
$986$	−30.8866	−0.983630
$987$	27.4316	0.873158
$988$	−0.799758	−0.0254437
$989$	−2.93714	−0.0933955
$990$	−15.2764	−0.485517
$991$	12.0787	0.383694	0.191847	−	0.981425i	$-0.438552\pi$
$991$	12.0787	0.383694	0.191847	+	0.981425i	$0.438552\pi$
$992$	6.84276	0.217258
$993$	56.2023	1.78353
$994$	15.2207	0.482772
$995$	14.7484	0.467555
$996$	−9.37419	−0.297033
$997$	−15.1194	−0.478837	−0.239418	−	0.970916i	$-0.576957\pi$
$997$	−15.1194	−0.478837	−0.239418	+	0.970916i	$0.576957\pi$
$998$	−5.10284	−0.161528
$999$	−34.0380	−1.07692

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	574.2.a.m.1.4	✓	4
3.2	odd	2		5166.2.a.bx.1.1		4
4.3	odd	2		4592.2.a.ba.1.1		4
7.6	odd	2		4018.2.a.bj.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.a.m.1.4	✓	4	1.1	even	1	trivial
4018.2.a.bj.1.1		4	7.6	odd	2
4592.2.a.ba.1.1		4	4.3	odd	2
5166.2.a.bx.1.1		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:	\( N \)	\(=\)	\( 574 = 2 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	574.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.76342 q^{3} +1.00000 q^{4} +3.92368 q^{5} -2.76342 q^{6} -1.00000 q^{7} -1.00000 q^{8} +4.63646 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.76342 q^{3} +1.00000 q^{4} +3.92368 q^{5} -2.76342 q^{6} -1.00000 q^{7} -1.00000 q^{8} +4.63646 q^{9} -3.92368 q^{10} +0.839734 q^{11} +2.76342 q^{12} -0.552516 q^{13} +1.00000 q^{14} +10.8428 q^{15} +1.00000 q^{16} -7.71581 q^{17} -4.63646 q^{18} +1.44748 q^{19} +3.92368 q^{20} -2.76342 q^{21} -0.839734 q^{22} +0.552516 q^{23} -2.76342 q^{24} +10.3953 q^{25} +0.552516 q^{26} +4.52223 q^{27} -1.00000 q^{28} -4.00303 q^{29} -10.8428 q^{30} -6.84276 q^{31} -1.00000 q^{32} +2.32053 q^{33} +7.71581 q^{34} -3.92368 q^{35} +4.63646 q^{36} -7.52683 q^{37} -1.44748 q^{38} -1.52683 q^{39} -3.92368 q^{40} +1.00000 q^{41} +2.76342 q^{42} -5.31593 q^{43} +0.839734 q^{44} +18.1920 q^{45} -0.552516 q^{46} -9.92671 q^{47} +2.76342 q^{48} +1.00000 q^{49} -10.3953 q^{50} -21.3220 q^{51} -0.552516 q^{52} +11.6917 q^{53} -4.52223 q^{54} +3.29485 q^{55} +1.00000 q^{56} +4.00000 q^{57} +4.00303 q^{58} +8.91908 q^{59} +10.8428 q^{60} +12.2350 q^{61} +6.84276 q^{62} -4.63646 q^{63} +1.00000 q^{64} -2.16790 q^{65} -2.32053 q^{66} -9.63949 q^{67} -7.71581 q^{68} +1.52683 q^{69} +3.92368 q^{70} +15.2207 q^{71} -4.63646 q^{72} +11.9048 q^{73} +7.52683 q^{74} +28.7265 q^{75} +1.44748 q^{76} -0.839734 q^{77} +1.52683 q^{78} -4.36354 q^{79} +3.92368 q^{80} -1.41260 q^{81} -1.00000 q^{82} -3.39225 q^{83} -2.76342 q^{84} -30.2744 q^{85} +5.31593 q^{86} -11.0620 q^{87} -0.839734 q^{88} +0.836706 q^{89} -18.1920 q^{90} +0.552516 q^{91} +0.552516 q^{92} -18.9094 q^{93} +9.92671 q^{94} +5.67947 q^{95} -2.76342 q^{96} +0.995398 q^{97} -1.00000 q^{98} +3.89339 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - q^{3} + 4 q^{4} + 3 q^{5} + q^{6} - 4 q^{7} - 4 q^{8} + 9 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - q^3 + 4 * q^4 + 3 * q^5 + q^6 - 4 * q^7 - 4 * q^8 + 9 * q^9	\( 4 q - 4 q^{2} - q^{3} + 4 q^{4} + 3 q^{5} + q^{6} - 4 q^{7} - 4 q^{8} + 9 q^{9} - 3 q^{10} + 4 q^{11} - q^{12} - 6 q^{13} + 4 q^{14} + 11 q^{15} + 4 q^{16} - q^{17} - 9 q^{18} + 2 q^{19} + 3 q^{20} + q^{21} - 4 q^{22} + 6 q^{23} + q^{24} + 13 q^{25} + 6 q^{26} - 13 q^{27} - 4 q^{28} + 17 q^{29} - 11 q^{30} + 5 q^{31} - 4 q^{32} + 8 q^{33} + q^{34} - 3 q^{35} + 9 q^{36} - 6 q^{37} - 2 q^{38} + 18 q^{39} - 3 q^{40} + 4 q^{41} - q^{42} - 13 q^{43} + 4 q^{44} + 34 q^{45} - 6 q^{46} + 6 q^{47} - q^{48} + 4 q^{49} - 13 q^{50} - 11 q^{51} - 6 q^{52} + 29 q^{53} + 13 q^{54} - 16 q^{55} + 4 q^{56} + 16 q^{57} - 17 q^{58} + 16 q^{59} + 11 q^{60} + 21 q^{61} - 5 q^{62} - 9 q^{63} + 4 q^{64} + 18 q^{65} - 8 q^{66} + 4 q^{67} - q^{68} - 18 q^{69} + 3 q^{70} + 17 q^{71} - 9 q^{72} + 12 q^{73} + 6 q^{74} + 26 q^{75} + 2 q^{76} - 4 q^{77} - 18 q^{78} - 27 q^{79} + 3 q^{80} + 40 q^{81} - 4 q^{82} - 18 q^{83} + q^{84} - 29 q^{85} + 13 q^{86} - 41 q^{87} - 4 q^{88} + 37 q^{89} - 34 q^{90} + 6 q^{91} + 6 q^{92} - 47 q^{93} - 6 q^{94} + 24 q^{95} + q^{96} - 3 q^{97} - 4 q^{98} - 32 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - q^3 + 4 * q^4 + 3 * q^5 + q^6 - 4 * q^7 - 4 * q^8 + 9 * q^9 - 3 * q^10 + 4 * q^11 - q^12 - 6 * q^13 + 4 * q^14 + 11 * q^15 + 4 * q^16 - q^17 - 9 * q^18 + 2 * q^19 + 3 * q^20 + q^21 - 4 * q^22 + 6 * q^23 + q^24 + 13 * q^25 + 6 * q^26 - 13 * q^27 - 4 * q^28 + 17 * q^29 - 11 * q^30 + 5 * q^31 - 4 * q^32 + 8 * q^33 + q^34 - 3 * q^35 + 9 * q^36 - 6 * q^37 - 2 * q^38 + 18 * q^39 - 3 * q^40 + 4 * q^41 - q^42 - 13 * q^43 + 4 * q^44 + 34 * q^45 - 6 * q^46 + 6 * q^47 - q^48 + 4 * q^49 - 13 * q^50 - 11 * q^51 - 6 * q^52 + 29 * q^53 + 13 * q^54 - 16 * q^55 + 4 * q^56 + 16 * q^57 - 17 * q^58 + 16 * q^59 + 11 * q^60 + 21 * q^61 - 5 * q^62 - 9 * q^63 + 4 * q^64 + 18 * q^65 - 8 * q^66 + 4 * q^67 - q^68 - 18 * q^69 + 3 * q^70 + 17 * q^71 - 9 * q^72 + 12 * q^73 + 6 * q^74 + 26 * q^75 + 2 * q^76 - 4 * q^77 - 18 * q^78 - 27 * q^79 + 3 * q^80 + 40 * q^81 - 4 * q^82 - 18 * q^83 + q^84 - 29 * q^85 + 13 * q^86 - 41 * q^87 - 4 * q^88 + 37 * q^89 - 34 * q^90 + 6 * q^91 + 6 * q^92 - 47 * q^93 - 6 * q^94 + 24 * q^95 + q^96 - 3 * q^97 - 4 * q^98 - 32 * q^99

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