LMFDB - Embedded newform 4730.2.a.v.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4730,2,Mod(1,4730)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4730, 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("4730.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4730 = 2 \cdot 5 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4730.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:	$37.7692401561$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.220036.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 5x^{3} + 11x^{2} - 2x - 1 $ x^5 - 2x^4 - 5x^3 + 11x^2 - 2x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.75849$ of defining polynomial
Character	$\chi$	$=$	4730.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.75849 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.75849 q^{6} -2.87831 q^{7} +1.00000 q^{8} +0.0923014 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.75849 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.75849 q^{6} -2.87831 q^{7} +1.00000 q^{8} +0.0923014 q^{9} -1.00000 q^{10} +1.00000 q^{11} +1.75849 q^{12} -6.11317 q^{13} -2.87831 q^{14} -1.75849 q^{15} +1.00000 q^{16} +7.37367 q^{17} +0.0923014 q^{18} +1.00335 q^{19} -1.00000 q^{20} -5.06149 q^{21} +1.00000 q^{22} -2.92081 q^{23} +1.75849 q^{24} +1.00000 q^{25} -6.11317 q^{26} -5.11317 q^{27} -2.87831 q^{28} +0.302996 q^{29} -1.75849 q^{30} -0.117276 q^{31} +1.00000 q^{32} +1.75849 q^{33} +7.37367 q^{34} +2.87831 q^{35} +0.0923014 q^{36} -9.01235 q^{37} +1.00335 q^{38} -10.7500 q^{39} -1.00000 q^{40} -8.87755 q^{41} -5.06149 q^{42} -1.00000 q^{43} +1.00000 q^{44} -0.0923014 q^{45} -2.92081 q^{46} -8.82587 q^{47} +1.75849 q^{48} +1.28467 q^{49} +1.00000 q^{50} +12.9666 q^{51} -6.11317 q^{52} +6.30888 q^{53} -5.11317 q^{54} -1.00000 q^{55} -2.87831 q^{56} +1.76438 q^{57} +0.302996 q^{58} -6.09342 q^{59} -1.75849 q^{60} -7.87501 q^{61} -0.117276 q^{62} -0.265672 q^{63} +1.00000 q^{64} +6.11317 q^{65} +1.75849 q^{66} +7.04775 q^{67} +7.37367 q^{68} -5.13622 q^{69} +2.87831 q^{70} -1.67725 q^{71} +0.0923014 q^{72} +6.08124 q^{73} -9.01235 q^{74} +1.75849 q^{75} +1.00335 q^{76} -2.87831 q^{77} -10.7500 q^{78} -0.246729 q^{79} -1.00000 q^{80} -9.26838 q^{81} -8.87755 q^{82} -11.0924 q^{83} -5.06149 q^{84} -7.37367 q^{85} -1.00000 q^{86} +0.532817 q^{87} +1.00000 q^{88} -5.85080 q^{89} -0.0923014 q^{90} +17.5956 q^{91} -2.92081 q^{92} -0.206229 q^{93} -8.82587 q^{94} -1.00335 q^{95} +1.75849 q^{96} +6.27629 q^{97} +1.28467 q^{98} +0.0923014 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} + 2 q^{3} + 5 q^{4} - 5 q^{5} + 2 q^{6} - 6 q^{7} + 5 q^{8} - q^{9}+O(q^{10}) $ 5 * q + 5 * q^2 + 2 * q^3 + 5 * q^4 - 5 * q^5 + 2 * q^6 - 6 * q^7 + 5 * q^8 - q^9	\( 5 q + 5 q^{2} + 2 q^{3} + 5 q^{4} - 5 q^{5} + 2 q^{6} - 6 q^{7} + 5 q^{8} - q^{9} - 5 q^{10} + 5 q^{11} + 2 q^{12} - 12 q^{13} - 6 q^{14} - 2 q^{15} + 5 q^{16} - 2 q^{17} - q^{18} - 4 q^{19} - 5 q^{20} + 2 q^{21} + 5 q^{22} - 6 q^{23} + 2 q^{24} + 5 q^{25} - 12 q^{26} - 7 q^{27} - 6 q^{28} - 19 q^{29} - 2 q^{30} - 7 q^{31} + 5 q^{32} + 2 q^{33} - 2 q^{34} + 6 q^{35} - q^{36} - q^{37} - 4 q^{38} - 20 q^{39} - 5 q^{40} - 2 q^{41} + 2 q^{42} - 5 q^{43} + 5 q^{44} + q^{45} - 6 q^{46} + 7 q^{47} + 2 q^{48} - 5 q^{49} + 5 q^{50} - 5 q^{51} - 12 q^{52} - 6 q^{53} - 7 q^{54} - 5 q^{55} - 6 q^{56} - 15 q^{57} - 19 q^{58} - 5 q^{59} - 2 q^{60} - 5 q^{61} - 7 q^{62} - 17 q^{63} + 5 q^{64} + 12 q^{65} + 2 q^{66} - 20 q^{67} - 2 q^{68} - 40 q^{69} + 6 q^{70} - 22 q^{71} - q^{72} + 10 q^{73} - q^{74} + 2 q^{75} - 4 q^{76} - 6 q^{77} - 20 q^{78} - 9 q^{79} - 5 q^{80} - 15 q^{81} - 2 q^{82} - 19 q^{83} + 2 q^{84} + 2 q^{85} - 5 q^{86} + 15 q^{87} + 5 q^{88} - 21 q^{89} + q^{90} + 10 q^{91} - 6 q^{92} - 15 q^{93} + 7 q^{94} + 4 q^{95} + 2 q^{96} + 10 q^{97} - 5 q^{98} - q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 + 2 * q^3 + 5 * q^4 - 5 * q^5 + 2 * q^6 - 6 * q^7 + 5 * q^8 - q^9 - 5 * q^10 + 5 * q^11 + 2 * q^12 - 12 * q^13 - 6 * q^14 - 2 * q^15 + 5 * q^16 - 2 * q^17 - q^18 - 4 * q^19 - 5 * q^20 + 2 * q^21 + 5 * q^22 - 6 * q^23 + 2 * q^24 + 5 * q^25 - 12 * q^26 - 7 * q^27 - 6 * q^28 - 19 * q^29 - 2 * q^30 - 7 * q^31 + 5 * q^32 + 2 * q^33 - 2 * q^34 + 6 * q^35 - q^36 - q^37 - 4 * q^38 - 20 * q^39 - 5 * q^40 - 2 * q^41 + 2 * q^42 - 5 * q^43 + 5 * q^44 + q^45 - 6 * q^46 + 7 * q^47 + 2 * q^48 - 5 * q^49 + 5 * q^50 - 5 * q^51 - 12 * q^52 - 6 * q^53 - 7 * q^54 - 5 * q^55 - 6 * q^56 - 15 * q^57 - 19 * q^58 - 5 * q^59 - 2 * q^60 - 5 * q^61 - 7 * q^62 - 17 * q^63 + 5 * q^64 + 12 * q^65 + 2 * q^66 - 20 * q^67 - 2 * q^68 - 40 * q^69 + 6 * q^70 - 22 * q^71 - q^72 + 10 * q^73 - q^74 + 2 * q^75 - 4 * q^76 - 6 * q^77 - 20 * q^78 - 9 * q^79 - 5 * q^80 - 15 * q^81 - 2 * q^82 - 19 * q^83 + 2 * q^84 + 2 * q^85 - 5 * q^86 + 15 * q^87 + 5 * q^88 - 21 * q^89 + q^90 + 10 * q^91 - 6 * q^92 - 15 * q^93 + 7 * q^94 + 4 * q^95 + 2 * q^96 + 10 * q^97 - 5 * q^98 - 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
$3$	1.75849	1.01527	0.507634	−	0.861573i	$-0.330520\pi$
$3$	1.75849	1.01527	0.507634	+	0.861573i	$0.330520\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.75849	0.717902
$7$	−2.87831	−1.08790	−0.543949	−	0.839118i	$-0.683072\pi$
$7$	−2.87831	−1.08790	−0.543949	+	0.839118i	$0.683072\pi$
$8$	1.00000	0.353553
$9$	0.0923014	0.0307671
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.75849	0.507634
$13$	−6.11317	−1.69549	−0.847744	−	0.530405i	$-0.822040\pi$
$13$	−6.11317	−1.69549	−0.847744	+	0.530405i	$0.822040\pi$
$14$	−2.87831	−0.769261
$15$	−1.75849	−0.454041
$16$	1.00000	0.250000
$17$	7.37367	1.78838	0.894189	−	0.447690i	$-0.147753\pi$
$17$	7.37367	1.78838	0.894189	+	0.447690i	$0.147753\pi$
$18$	0.0923014	0.0217556
$19$	1.00335	0.230184	0.115092	−	0.993355i	$-0.463284\pi$
$19$	1.00335	0.230184	0.115092	+	0.993355i	$0.463284\pi$
$20$	−1.00000	−0.223607
$21$	−5.06149	−1.10451
$22$	1.00000	0.213201
$23$	−2.92081	−0.609030	−0.304515	−	0.952508i	$-0.598494\pi$
$23$	−2.92081	−0.609030	−0.304515	+	0.952508i	$0.598494\pi$
$24$	1.75849	0.358951
$25$	1.00000	0.200000
$26$	−6.11317	−1.19889
$27$	−5.11317	−0.984030
$28$	−2.87831	−0.543949
$29$	0.302996	0.0562650	0.0281325	−	0.999604i	$-0.491044\pi$
$29$	0.302996	0.0562650	0.0281325	+	0.999604i	$0.491044\pi$
$30$	−1.75849	−0.321056
$31$	−0.117276	−0.0210634	−0.0105317	−	0.999945i	$-0.503352\pi$
$31$	−0.117276	−0.0210634	−0.0105317	+	0.999945i	$0.503352\pi$
$32$	1.00000	0.176777
$33$	1.75849	0.306115
$34$	7.37367	1.26457
$35$	2.87831	0.486523
$36$	0.0923014	0.0153836
$37$	−9.01235	−1.48162	−0.740811	−	0.671714i	$-0.765558\pi$
$37$	−9.01235	−1.48162	−0.740811	+	0.671714i	$0.765558\pi$
$38$	1.00335	0.162765
$39$	−10.7500	−1.72137
$40$	−1.00000	−0.158114
$41$	−8.87755	−1.38644	−0.693220	−	0.720726i	$-0.743809\pi$
$41$	−8.87755	−1.38644	−0.693220	+	0.720726i	$0.743809\pi$
$42$	−5.06149	−0.781005
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	1.00000	0.150756
$45$	−0.0923014	−0.0137595
$46$	−2.92081	−0.430649
$47$	−8.82587	−1.28739	−0.643693	−	0.765284i	$-0.722599\pi$
$47$	−8.82587	−1.28739	−0.643693	+	0.765284i	$0.722599\pi$
$48$	1.75849	0.253817
$49$	1.28467	0.183524
$50$	1.00000	0.141421
$51$	12.9666	1.81568
$52$	−6.11317	−0.847744
$53$	6.30888	0.866592	0.433296	−	0.901252i	$-0.357350\pi$
$53$	6.30888	0.866592	0.433296	+	0.901252i	$0.357350\pi$
$54$	−5.11317	−0.695814
$55$	−1.00000	−0.134840
$56$	−2.87831	−0.384630
$57$	1.76438	0.233698
$58$	0.302996	0.0397854
$59$	−6.09342	−0.793296	−0.396648	−	0.917971i	$-0.629827\pi$
$59$	−6.09342	−0.793296	−0.396648	+	0.917971i	$0.629827\pi$
$60$	−1.75849	−0.227021
$61$	−7.87501	−1.00829	−0.504146	−	0.863618i	$-0.668193\pi$
$61$	−7.87501	−1.00829	−0.504146	+	0.863618i	$0.668193\pi$
$62$	−0.117276	−0.0148941
$63$	−0.265672	−0.0334715
$64$	1.00000	0.125000
$65$	6.11317	0.758246
$66$	1.75849	0.216456
$67$	7.04775	0.861019	0.430510	−	0.902586i	$-0.358334\pi$
$67$	7.04775	0.861019	0.430510	+	0.902586i	$0.358334\pi$
$68$	7.37367	0.894189
$69$	−5.13622	−0.618328
$70$	2.87831	0.344024
$71$	−1.67725	−0.199053	−0.0995266	−	0.995035i	$-0.531733\pi$
$71$	−1.67725	−0.199053	−0.0995266	+	0.995035i	$0.531733\pi$
$72$	0.0923014	0.0108778
$73$	6.08124	0.711756	0.355878	−	0.934533i	$-0.384182\pi$
$73$	6.08124	0.711756	0.355878	+	0.934533i	$0.384182\pi$
$74$	−9.01235	−1.04766
$75$	1.75849	0.203053
$76$	1.00335	0.115092
$77$	−2.87831	−0.328014
$78$	−10.7500	−1.21719
$79$	−0.246729	−0.0277592	−0.0138796	−	0.999904i	$-0.504418\pi$
$79$	−0.246729	−0.0277592	−0.0138796	+	0.999904i	$0.504418\pi$
$80$	−1.00000	−0.111803
$81$	−9.26838	−1.02982
$82$	−8.87755	−0.980362
$83$	−11.0924	−1.21754	−0.608772	−	0.793345i	$-0.708338\pi$
$83$	−11.0924	−1.21754	−0.608772	+	0.793345i	$0.708338\pi$
$84$	−5.06149	−0.552254
$85$	−7.37367	−0.799787
$86$	−1.00000	−0.107833
$87$	0.532817	0.0571240
$88$	1.00000	0.106600
$89$	−5.85080	−0.620183	−0.310092	−	0.950707i	$-0.600360\pi$
$89$	−5.85080	−0.620183	−0.310092	+	0.950707i	$0.600360\pi$
$90$	−0.0923014	−0.00972942
$91$	17.5956	1.84452
$92$	−2.92081	−0.304515
$93$	−0.206229	−0.0213850
$94$	−8.82587	−0.910319
$95$	−1.00335	−0.102941
$96$	1.75849	0.179476
$97$	6.27629	0.637261	0.318630	−	0.947879i	$-0.396777\pi$
$97$	6.27629	0.637261	0.318630	+	0.947879i	$0.396777\pi$
$98$	1.28467	0.129771
$99$	0.0923014	0.00927664
$100$	1.00000	0.100000
$101$	−5.22081	−0.519490	−0.259745	−	0.965677i	$-0.583639\pi$
$101$	−5.22081	−0.519490	−0.259745	+	0.965677i	$0.583639\pi$
$102$	12.9666	1.28388
$103$	10.8854	1.07257	0.536287	−	0.844036i	$-0.319826\pi$
$103$	10.8854	1.07257	0.536287	+	0.844036i	$0.319826\pi$
$104$	−6.11317	−0.599446
$105$	5.06149	0.493951
$106$	6.30888	0.612773
$107$	−9.84487	−0.951739	−0.475870	−	0.879516i	$-0.657867\pi$
$107$	−9.84487	−0.951739	−0.475870	+	0.879516i	$0.657867\pi$
$108$	−5.11317	−0.492015
$109$	−8.98172	−0.860293	−0.430146	−	0.902759i	$-0.641538\pi$
$109$	−8.98172	−0.860293	−0.430146	+	0.902759i	$0.641538\pi$
$110$	−1.00000	−0.0953463
$111$	−15.8482	−1.50424
$112$	−2.87831	−0.271975
$113$	−15.5047	−1.45856	−0.729281	−	0.684215i	$-0.760145\pi$
$113$	−15.5047	−1.45856	−0.729281	+	0.684215i	$0.760145\pi$
$114$	1.76438	0.165250
$115$	2.92081	0.272367
$116$	0.302996	0.0281325
$117$	−0.564254	−0.0521653
$118$	−6.09342	−0.560945
$119$	−21.2237	−1.94557
$120$	−1.75849	−0.160528
$121$	1.00000	0.0909091
$122$	−7.87501	−0.712970
$123$	−15.6111	−1.40761
$124$	−0.117276	−0.0105317
$125$	−1.00000	−0.0894427
$126$	−0.265672	−0.0236679
$127$	−5.26491	−0.467186	−0.233593	−	0.972335i	$-0.575048\pi$
$127$	−5.26491	−0.467186	−0.233593	+	0.972335i	$0.575048\pi$
$128$	1.00000	0.0883883
$129$	−1.75849	−0.154827
$130$	6.11317	0.536161
$131$	16.0097	1.39877	0.699386	−	0.714745i	$-0.253457\pi$
$131$	16.0097	1.39877	0.699386	+	0.714745i	$0.253457\pi$
$132$	1.75849	0.153057
$133$	−2.88795	−0.250417
$134$	7.04775	0.608833
$135$	5.11317	0.440072
$136$	7.37367	0.632287
$137$	6.51704	0.556788	0.278394	−	0.960467i	$-0.410198\pi$
$137$	6.51704	0.556788	0.278394	+	0.960467i	$0.410198\pi$
$138$	−5.13622	−0.437224
$139$	−0.750610	−0.0636659	−0.0318330	−	0.999493i	$-0.510134\pi$
$139$	−0.750610	−0.0636659	−0.0318330	+	0.999493i	$0.510134\pi$
$140$	2.87831	0.243262
$141$	−15.5202	−1.30704
$142$	−1.67725	−0.140752
$143$	−6.11317	−0.511209
$144$	0.0923014	0.00769178
$145$	−0.302996	−0.0251625
$146$	6.08124	0.503287
$147$	2.25908	0.186326
$148$	−9.01235	−0.740811
$149$	−17.8142	−1.45940	−0.729700	−	0.683768i	$-0.760340\pi$
$149$	−17.8142	−1.45940	−0.729700	+	0.683768i	$0.760340\pi$
$150$	1.75849	0.143580
$151$	5.09012	0.414228	0.207114	−	0.978317i	$-0.433593\pi$
$151$	5.09012	0.414228	0.207114	+	0.978317i	$0.433593\pi$
$152$	1.00335	0.0813823
$153$	0.680600	0.0550233
$154$	−2.87831	−0.231941
$155$	0.117276	0.00941984
$156$	−10.7500	−0.860687
$157$	13.3265	1.06357	0.531786	−	0.846879i	$-0.321521\pi$
$157$	13.3265	1.06357	0.531786	+	0.846879i	$0.321521\pi$
$158$	−0.246729	−0.0196287
$159$	11.0941	0.879822
$160$	−1.00000	−0.0790569
$161$	8.40698	0.662563
$162$	−9.26838	−0.728193
$163$	2.04615	0.160267	0.0801335	−	0.996784i	$-0.474465\pi$
$163$	2.04615	0.160267	0.0801335	+	0.996784i	$0.474465\pi$
$164$	−8.87755	−0.693220
$165$	−1.75849	−0.136899
$166$	−11.0924	−0.860934
$167$	−1.95019	−0.150911	−0.0754553	−	0.997149i	$-0.524041\pi$
$167$	−1.95019	−0.150911	−0.0754553	+	0.997149i	$0.524041\pi$
$168$	−5.06149	−0.390502
$169$	24.3709	1.87468
$170$	−7.37367	−0.565535
$171$	0.0926104	0.00708210
$172$	−1.00000	−0.0762493
$173$	18.9095	1.43766	0.718831	−	0.695185i	$-0.244678\pi$
$173$	18.9095	1.43766	0.718831	+	0.695185i	$0.244678\pi$
$174$	0.532817	0.0403928
$175$	−2.87831	−0.217580
$176$	1.00000	0.0753778
$177$	−10.7152	−0.805407
$178$	−5.85080	−0.438536
$179$	−2.47257	−0.184808	−0.0924041	−	0.995722i	$-0.529455\pi$
$179$	−2.47257	−0.184808	−0.0924041	+	0.995722i	$0.529455\pi$
$180$	−0.0923014	−0.00687974
$181$	−9.12851	−0.678517	−0.339258	−	0.940693i	$-0.610176\pi$
$181$	−9.12851	−0.678517	−0.339258	+	0.940693i	$0.610176\pi$
$182$	17.5956	1.30427
$183$	−13.8482	−1.02369
$184$	−2.92081	−0.215325
$185$	9.01235	0.662601
$186$	−0.206229	−0.0151215
$187$	7.37367	0.539216
$188$	−8.82587	−0.643693
$189$	14.7173	1.07053
$190$	−1.00335	−0.0727905
$191$	−3.45134	−0.249730	−0.124865	−	0.992174i	$-0.539850\pi$
$191$	−3.45134	−0.249730	−0.124865	+	0.992174i	$0.539850\pi$
$192$	1.75849	0.126908
$193$	−15.2283	−1.09615	−0.548077	−	0.836428i	$-0.684640\pi$
$193$	−15.2283	−1.09615	−0.548077	+	0.836428i	$0.684640\pi$
$194$	6.27629	0.450611
$195$	10.7500	0.769822
$196$	1.28467	0.0917619
$197$	14.0812	1.00325	0.501623	−	0.865086i	$-0.332736\pi$
$197$	14.0812	1.00325	0.501623	+	0.865086i	$0.332736\pi$
$198$	0.0923014	0.00655957
$199$	−18.2532	−1.29394	−0.646968	−	0.762517i	$-0.723963\pi$
$199$	−18.2532	−1.29394	−0.646968	+	0.762517i	$0.723963\pi$
$200$	1.00000	0.0707107
$201$	12.3934	0.874165
$202$	−5.22081	−0.367335
$203$	−0.872118	−0.0612107
$204$	12.9666	0.907841
$205$	8.87755	0.620035
$206$	10.8854	0.758424
$207$	−0.269594	−0.0187381
$208$	−6.11317	−0.423872
$209$	1.00335	0.0694030
$210$	5.06149	0.349276
$211$	−1.39128	−0.0957800	−0.0478900	−	0.998853i	$-0.515250\pi$
$211$	−1.39128	−0.0957800	−0.0478900	+	0.998853i	$0.515250\pi$
$212$	6.30888	0.433296
$213$	−2.94944	−0.202092
$214$	−9.84487	−0.672981
$215$	1.00000	0.0681994
$216$	−5.11317	−0.347907
$217$	0.337557	0.0229148
$218$	−8.98172	−0.608319
$219$	10.6938	0.722622
$220$	−1.00000	−0.0674200
$221$	−45.0765	−3.03217
$222$	−15.8482	−1.06366
$223$	11.5694	0.774743	0.387372	−	0.921924i	$-0.373383\pi$
$223$	11.5694	0.774743	0.387372	+	0.921924i	$0.373383\pi$
$224$	−2.87831	−0.192315
$225$	0.0923014	0.00615343
$226$	−15.5047	−1.03136
$227$	24.8235	1.64759	0.823797	−	0.566885i	$-0.191852\pi$
$227$	24.8235	1.64759	0.823797	+	0.566885i	$0.191852\pi$
$228$	1.76438	0.116849
$229$	9.98296	0.659693	0.329846	−	0.944035i	$-0.393003\pi$
$229$	9.98296	0.659693	0.329846	+	0.944035i	$0.393003\pi$
$230$	2.92081	0.192592
$231$	−5.06149	−0.333022
$232$	0.302996	0.0198927
$233$	3.93004	0.257466	0.128733	−	0.991679i	$-0.458909\pi$
$233$	3.93004	0.257466	0.128733	+	0.991679i	$0.458909\pi$
$234$	−0.564254	−0.0368864
$235$	8.82587	0.575736
$236$	−6.09342	−0.396648
$237$	−0.433871	−0.0281830
$238$	−21.2237	−1.37573
$239$	−8.03473	−0.519724	−0.259862	−	0.965646i	$-0.583677\pi$
$239$	−8.03473	−0.519724	−0.259862	+	0.965646i	$0.583677\pi$
$240$	−1.75849	−0.113510
$241$	11.4440	0.737175	0.368588	−	0.929593i	$-0.379841\pi$
$241$	11.4440	0.737175	0.368588	+	0.929593i	$0.379841\pi$
$242$	1.00000	0.0642824
$243$	−0.958887	−0.0615126
$244$	−7.87501	−0.504146
$245$	−1.28467	−0.0820743
$246$	−15.6111	−0.995329
$247$	−6.13364	−0.390274
$248$	−0.117276	−0.00744703
$249$	−19.5058	−1.23613
$250$	−1.00000	−0.0632456
$251$	−21.3745	−1.34915	−0.674574	−	0.738208i	$-0.735672\pi$
$251$	−21.3745	−1.34915	−0.674574	+	0.738208i	$0.735672\pi$
$252$	−0.265672	−0.0167358
$253$	−2.92081	−0.183629
$254$	−5.26491	−0.330350
$255$	−12.9666	−0.811997
$256$	1.00000	0.0625000
$257$	28.4183	1.77268	0.886342	−	0.463031i	$-0.153238\pi$
$257$	28.4183	1.77268	0.886342	+	0.463031i	$0.153238\pi$
$258$	−1.75849	−0.109479
$259$	25.9403	1.61185
$260$	6.11317	0.379123
$261$	0.0279670	0.00173111
$262$	16.0097	0.989081
$263$	−12.0841	−0.745140	−0.372570	−	0.928004i	$-0.621523\pi$
$263$	−12.0841	−0.745140	−0.372570	+	0.928004i	$0.621523\pi$
$264$	1.75849	0.108228
$265$	−6.30888	−0.387552
$266$	−2.88795	−0.177071
$267$	−10.2886	−0.629651
$268$	7.04775	0.430510
$269$	2.31705	0.141273	0.0706365	−	0.997502i	$-0.477497\pi$
$269$	2.31705	0.141273	0.0706365	+	0.997502i	$0.477497\pi$
$270$	5.11317	0.311178
$271$	18.4363	1.11992	0.559962	−	0.828518i	$-0.310816\pi$
$271$	18.4363	1.11992	0.559962	+	0.828518i	$0.310816\pi$
$272$	7.37367	0.447095
$273$	30.9418	1.87268
$274$	6.51704	0.393709
$275$	1.00000	0.0603023
$276$	−5.13622	−0.309164
$277$	10.4719	0.629193	0.314597	−	0.949225i	$-0.398131\pi$
$277$	10.4719	0.629193	0.314597	+	0.949225i	$0.398131\pi$
$278$	−0.750610	−0.0450186
$279$	−0.0108247	−0.000648060 0
$280$	2.87831	0.172012
$281$	1.41051	0.0841442	0.0420721	−	0.999115i	$-0.486604\pi$
$281$	1.41051	0.0841442	0.0420721	+	0.999115i	$0.486604\pi$
$282$	−15.5202	−0.924217
$283$	−7.93645	−0.471773	−0.235887	−	0.971781i	$-0.575799\pi$
$283$	−7.93645	−0.471773	−0.235887	+	0.971781i	$0.575799\pi$
$284$	−1.67725	−0.0995266
$285$	−1.76438	−0.104513
$286$	−6.11317	−0.361479
$287$	25.5523	1.50831
$288$	0.0923014	0.00543891
$289$	37.3710	2.19830
$290$	−0.302996	−0.0177926
$291$	11.0368	0.646990
$292$	6.08124	0.355878
$293$	19.2752	1.12607	0.563035	−	0.826433i	$-0.309634\pi$
$293$	19.2752	1.12607	0.563035	+	0.826433i	$0.309634\pi$
$294$	2.25908	0.131752
$295$	6.09342	0.354773
$296$	−9.01235	−0.523832
$297$	−5.11317	−0.296696
$298$	−17.8142	−1.03195
$299$	17.8554	1.03260
$300$	1.75849	0.101527
$301$	2.87831	0.165903
$302$	5.09012	0.292904
$303$	−9.18076	−0.527421
$304$	1.00335	0.0575460
$305$	7.87501	0.450922
$306$	0.680600	0.0389073
$307$	22.7434	1.29803	0.649016	−	0.760775i	$-0.275181\pi$
$307$	22.7434	1.29803	0.649016	+	0.760775i	$0.275181\pi$
$308$	−2.87831	−0.164007
$309$	19.1420	1.08895
$310$	0.117276	0.00666083
$311$	−18.3887	−1.04273	−0.521363	−	0.853335i	$-0.674576\pi$
$311$	−18.3887	−1.04273	−0.521363	+	0.853335i	$0.674576\pi$
$312$	−10.7500	−0.608597
$313$	−26.7205	−1.51033	−0.755165	−	0.655535i	$-0.772443\pi$
$313$	−26.7205	−1.51033	−0.755165	+	0.655535i	$0.772443\pi$
$314$	13.3265	0.752059
$315$	0.265672	0.0149689
$316$	−0.246729	−0.0138796
$317$	12.6603	0.711071	0.355536	−	0.934663i	$-0.384298\pi$
$317$	12.6603	0.711071	0.355536	+	0.934663i	$0.384298\pi$
$318$	11.0941	0.622128
$319$	0.302996	0.0169645
$320$	−1.00000	−0.0559017
$321$	−17.3121	−0.966269
$322$	8.40698	0.468503
$323$	7.39836	0.411656
$324$	−9.26838	−0.514910
$325$	−6.11317	−0.339098
$326$	2.04615	0.113326
$327$	−15.7943	−0.873427
$328$	−8.87755	−0.490181
$329$	25.4036	1.40055
$330$	−1.75849	−0.0968019
$331$	3.34862	0.184057	0.0920285	−	0.995756i	$-0.470665\pi$
$331$	3.34862	0.184057	0.0920285	+	0.995756i	$0.470665\pi$
$332$	−11.0924	−0.608772
$333$	−0.831852	−0.0455852
$334$	−1.95019	−0.106710
$335$	−7.04775	−0.385060
$336$	−5.06149	−0.276127
$337$	14.9016	0.811741	0.405871	−	0.913931i	$-0.366968\pi$
$337$	14.9016	0.811741	0.405871	+	0.913931i	$0.366968\pi$
$338$	24.3709	1.32560
$339$	−27.2650	−1.48083
$340$	−7.37367	−0.399893
$341$	−0.117276	−0.00635085
$342$	0.0926104	0.00500780
$343$	16.4505	0.888243
$344$	−1.00000	−0.0539164
$345$	5.13622	0.276525
$346$	18.9095	1.01658
$347$	12.4727	0.669568	0.334784	−	0.942295i	$-0.391337\pi$
$347$	12.4727	0.669568	0.334784	+	0.942295i	$0.391337\pi$
$348$	0.532817	0.0285620
$349$	−13.3681	−0.715580	−0.357790	−	0.933802i	$-0.616470\pi$
$349$	−13.3681	−0.715580	−0.357790	+	0.933802i	$0.616470\pi$
$350$	−2.87831	−0.153852
$351$	31.2577	1.66841
$352$	1.00000	0.0533002
$353$	−23.5669	−1.25434	−0.627170	−	0.778882i	$-0.715787\pi$
$353$	−23.5669	−1.25434	−0.627170	+	0.778882i	$0.715787\pi$
$354$	−10.7152	−0.569509
$355$	1.67725	0.0890193
$356$	−5.85080	−0.310092
$357$	−37.3218	−1.97528
$358$	−2.47257	−0.130679
$359$	−32.4228	−1.71121	−0.855606	−	0.517628i	$-0.826815\pi$
$359$	−32.4228	−1.71121	−0.855606	+	0.517628i	$0.826815\pi$
$360$	−0.0923014	−0.00486471
$361$	−17.9933	−0.947015
$362$	−9.12851	−0.479784
$363$	1.75849	0.0922970
$364$	17.5956	0.922260
$365$	−6.08124	−0.318307
$366$	−13.8482	−0.723855
$367$	28.5536	1.49048	0.745242	−	0.666794i	$-0.232334\pi$
$367$	28.5536	1.49048	0.745242	+	0.666794i	$0.232334\pi$
$368$	−2.92081	−0.152258
$369$	−0.819410	−0.0426568
$370$	9.01235	0.468530
$371$	−18.1589	−0.942764
$372$	−0.206229	−0.0106925
$373$	−6.42137	−0.332486	−0.166243	−	0.986085i	$-0.553164\pi$
$373$	−6.42137	−0.332486	−0.166243	+	0.986085i	$0.553164\pi$
$374$	7.37367	0.381283
$375$	−1.75849	−0.0908082
$376$	−8.82587	−0.455160
$377$	−1.85227	−0.0953967
$378$	14.7173	0.756976
$379$	−0.677659	−0.0348090	−0.0174045	−	0.999849i	$-0.505540\pi$
$379$	−0.677659	−0.0348090	−0.0174045	+	0.999849i	$0.505540\pi$
$380$	−1.00335	−0.0514707
$381$	−9.25832	−0.474318
$382$	−3.45134	−0.176586
$383$	−19.4006	−0.991322	−0.495661	−	0.868516i	$-0.665074\pi$
$383$	−19.4006	−0.991322	−0.495661	+	0.868516i	$0.665074\pi$
$384$	1.75849	0.0897378
$385$	2.87831	0.146692
$386$	−15.2283	−0.775098
$387$	−0.0923014	−0.00469194
$388$	6.27629	0.318630
$389$	−22.7919	−1.15560	−0.577799	−	0.816179i	$-0.696088\pi$
$389$	−22.7919	−1.15560	−0.577799	+	0.816179i	$0.696088\pi$
$390$	10.7500	0.544346
$391$	−21.5371	−1.08918
$392$	1.28467	0.0648855
$393$	28.1529	1.42013
$394$	14.0812	0.709403
$395$	0.246729	0.0124143
$396$	0.0923014	0.00463832
$397$	−9.26539	−0.465017	−0.232508	−	0.972594i	$-0.574693\pi$
$397$	−9.26539	−0.465017	−0.232508	+	0.972594i	$0.574693\pi$
$398$	−18.2532	−0.914951
$399$	−5.07844	−0.254240
$400$	1.00000	0.0500000
$401$	−5.89124	−0.294195	−0.147097	−	0.989122i	$-0.546993\pi$
$401$	−5.89124	−0.294195	−0.147097	+	0.989122i	$0.546993\pi$
$402$	12.3934	0.618128
$403$	0.716928	0.0357127
$404$	−5.22081	−0.259745
$405$	9.26838	0.460550
$406$	−0.872118	−0.0432825
$407$	−9.01235	−0.446726
$408$	12.9666	0.641940
$409$	20.6012	1.01866	0.509332	−	0.860570i	$-0.329892\pi$
$409$	20.6012	1.01866	0.509332	+	0.860570i	$0.329892\pi$
$410$	8.87755	0.438431
$411$	11.4602	0.565289
$412$	10.8854	0.536287
$413$	17.5387	0.863025
$414$	−0.269594	−0.0132498
$415$	11.0924	0.544502
$416$	−6.11317	−0.299723
$417$	−1.31994	−0.0646379
$418$	1.00335	0.0490754
$419$	27.8925	1.36264	0.681319	−	0.731987i	$-0.261407\pi$
$419$	27.8925	1.36264	0.681319	+	0.731987i	$0.261407\pi$
$420$	5.06149	0.246975
$421$	2.66284	0.129779	0.0648895	−	0.997892i	$-0.479330\pi$
$421$	2.66284	0.129779	0.0648895	+	0.997892i	$0.479330\pi$
$422$	−1.39128	−0.0677267
$423$	−0.814640	−0.0396092
$424$	6.30888	0.306387
$425$	7.37367	0.357676
$426$	−2.94944	−0.142901
$427$	22.6667	1.09692
$428$	−9.84487	−0.475870
$429$	−10.7500	−0.519014
$430$	1.00000	0.0482243
$431$	19.8330	0.955322	0.477661	−	0.878544i	$-0.341485\pi$
$431$	19.8330	0.955322	0.477661	+	0.878544i	$0.341485\pi$
$432$	−5.11317	−0.246008
$433$	−13.7880	−0.662610	−0.331305	−	0.943524i	$-0.607489\pi$
$433$	−13.7880	−0.662610	−0.331305	+	0.943524i	$0.607489\pi$
$434$	0.337557	0.0162032
$435$	−0.532817	−0.0255466
$436$	−8.98172	−0.430146
$437$	−2.93058	−0.140189
$438$	10.6938	0.510971
$439$	40.2252	1.91984	0.959922	−	0.280266i	$-0.0904227\pi$
$439$	40.2252	1.91984	0.959922	+	0.280266i	$0.0904227\pi$
$440$	−1.00000	−0.0476731
$441$	0.118577	0.00564650
$442$	−45.0765	−2.14407
$443$	6.67693	0.317230	0.158615	−	0.987340i	$-0.449297\pi$
$443$	6.67693	0.317230	0.158615	+	0.987340i	$0.449297\pi$
$444$	−15.8482	−0.752121
$445$	5.85080	0.277354
$446$	11.5694	0.547826
$447$	−31.3262	−1.48168
$448$	−2.87831	−0.135987
$449$	15.0258	0.709110	0.354555	−	0.935035i	$-0.384632\pi$
$449$	15.0258	0.709110	0.354555	+	0.935035i	$0.384632\pi$
$450$	0.0923014	0.00435113
$451$	−8.87755	−0.418028
$452$	−15.5047	−0.729281
$453$	8.95095	0.420552
$454$	24.8235	1.16502
$455$	−17.5956	−0.824894
$456$	1.76438	0.0826248
$457$	−14.1718	−0.662928	−0.331464	−	0.943468i	$-0.607542\pi$
$457$	−14.1718	−0.662928	−0.331464	+	0.943468i	$0.607542\pi$
$458$	9.98296	0.466473
$459$	−37.7028	−1.75982
$460$	2.92081	0.136183
$461$	9.92192	0.462110	0.231055	−	0.972941i	$-0.425782\pi$
$461$	9.92192	0.462110	0.231055	+	0.972941i	$0.425782\pi$
$462$	−5.06149	−0.235482
$463$	−22.3009	−1.03641	−0.518205	−	0.855256i	$-0.673400\pi$
$463$	−22.3009	−1.03641	−0.518205	+	0.855256i	$0.673400\pi$
$464$	0.302996	0.0140663
$465$	0.206229	0.00956365
$466$	3.93004	0.182056
$467$	24.4941	1.13345	0.566726	−	0.823906i	$-0.308210\pi$
$467$	24.4941	1.13345	0.566726	+	0.823906i	$0.308210\pi$
$468$	−0.564254	−0.0260827
$469$	−20.2856	−0.936702
$470$	8.82587	0.407107
$471$	23.4346	1.07981
$472$	−6.09342	−0.280472
$473$	−1.00000	−0.0459800
$474$	−0.433871	−0.0199284
$475$	1.00335	0.0460368
$476$	−21.2237	−0.972787
$477$	0.582319	0.0266625
$478$	−8.03473	−0.367500
$479$	−17.0102	−0.777218	−0.388609	−	0.921403i	$-0.627044\pi$
$479$	−17.0102	−0.777218	−0.388609	+	0.921403i	$0.627044\pi$
$480$	−1.75849	−0.0802639
$481$	55.0940	2.51207
$482$	11.4440	0.521262
$483$	14.7836	0.672678
$484$	1.00000	0.0454545
$485$	−6.27629	−0.284992
$486$	−0.958887	−0.0434960
$487$	−36.1457	−1.63792	−0.818958	−	0.573853i	$-0.805448\pi$
$487$	−36.1457	−1.63792	−0.818958	+	0.573853i	$0.805448\pi$
$488$	−7.87501	−0.356485
$489$	3.59815	0.162714
$490$	−1.28467	−0.0580353
$491$	28.3175	1.27795	0.638975	−	0.769227i	$-0.279359\pi$
$491$	28.3175	1.27795	0.638975	+	0.769227i	$0.279359\pi$
$492$	−15.6111	−0.703804
$493$	2.23420	0.100623
$494$	−6.13364	−0.275965
$495$	−0.0923014	−0.00414864
$496$	−0.117276	−0.00526585
$497$	4.82765	0.216550
$498$	−19.5058	−0.874077
$499$	−24.3532	−1.09020	−0.545099	−	0.838372i	$-0.683508\pi$
$499$	−24.3532	−1.09020	−0.545099	+	0.838372i	$0.683508\pi$
$500$	−1.00000	−0.0447214
$501$	−3.42941	−0.153215
$502$	−21.3745	−0.953991
$503$	−11.6274	−0.518438	−0.259219	−	0.965819i	$-0.583465\pi$
$503$	−11.6274	−0.518438	−0.259219	+	0.965819i	$0.583465\pi$
$504$	−0.265672	−0.0118340
$505$	5.22081	0.232323
$506$	−2.92081	−0.129846
$507$	42.8560	1.90330
$508$	−5.26491	−0.233593
$509$	−15.5004	−0.687044	−0.343522	−	0.939145i	$-0.611620\pi$
$509$	−15.5004	−0.687044	−0.343522	+	0.939145i	$0.611620\pi$
$510$	−12.9666	−0.574169
$511$	−17.5037	−0.774318
$512$	1.00000	0.0441942
$513$	−5.13029	−0.226508
$514$	28.4183	1.25348
$515$	−10.8854	−0.479670
$516$	−1.75849	−0.0774134
$517$	−8.82587	−0.388161
$518$	25.9403	1.13975
$519$	33.2522	1.45961
$520$	6.11317	0.268080
$521$	−15.7083	−0.688193	−0.344096	−	0.938934i	$-0.611815\pi$
$521$	−15.7083	−0.688193	−0.344096	+	0.938934i	$0.611815\pi$
$522$	0.0279670	0.00122408
$523$	−41.8613	−1.83047	−0.915233	−	0.402926i	$-0.867993\pi$
$523$	−41.8613	−1.83047	−0.915233	+	0.402926i	$0.867993\pi$
$524$	16.0097	0.699386
$525$	−5.06149	−0.220902
$526$	−12.0841	−0.526894
$527$	−0.864755	−0.0376693
$528$	1.75849	0.0765286
$529$	−14.4689	−0.629082
$530$	−6.30888	−0.274040
$531$	−0.562431	−0.0244074
$532$	−2.88795	−0.125208
$533$	54.2700	2.35069
$534$	−10.2886	−0.445231
$535$	9.84487	0.425631
$536$	7.04775	0.304416
$537$	−4.34799	−0.187630
$538$	2.31705	0.0998950
$539$	1.28467	0.0553345
$540$	5.11317	0.220036
$541$	39.5168	1.69896	0.849480	−	0.527620i	$-0.176916\pi$
$541$	39.5168	1.69896	0.849480	+	0.527620i	$0.176916\pi$
$542$	18.4363	0.791906
$543$	−16.0524	−0.688876
$544$	7.37367	0.316144
$545$	8.98172	0.384735
$546$	30.9418	1.32418
$547$	19.2902	0.824791	0.412395	−	0.911005i	$-0.364692\pi$
$547$	19.2902	0.824791	0.412395	+	0.911005i	$0.364692\pi$
$548$	6.51704	0.278394
$549$	−0.726875	−0.0310223
$550$	1.00000	0.0426401
$551$	0.304011	0.0129513
$552$	−5.13622	−0.218612
$553$	0.710162	0.0301992
$554$	10.4719	0.444907
$555$	15.8482	0.672717
$556$	−0.750610	−0.0318330
$557$	38.9409	1.64998	0.824989	−	0.565149i	$-0.191181\pi$
$557$	38.9409	1.64998	0.824989	+	0.565149i	$0.191181\pi$
$558$	−0.0108247	−0.000458248 0
$559$	6.11317	0.258560
$560$	2.87831	0.121631
$561$	12.9666	0.547448
$562$	1.41051	0.0594989
$563$	40.9127	1.72426	0.862132	−	0.506683i	$-0.169129\pi$
$563$	40.9127	1.72426	0.862132	+	0.506683i	$0.169129\pi$
$564$	−15.5202	−0.653520
$565$	15.5047	0.652288
$566$	−7.93645	−0.333594
$567$	26.6773	1.12034
$568$	−1.67725	−0.0703759
$569$	19.7648	0.828584	0.414292	−	0.910144i	$-0.364029\pi$
$569$	19.7648	0.828584	0.414292	+	0.910144i	$0.364029\pi$
$570$	−1.76438	−0.0739018
$571$	35.8529	1.50040	0.750199	−	0.661212i	$-0.229958\pi$
$571$	35.8529	1.50040	0.750199	+	0.661212i	$0.229958\pi$
$572$	−6.11317	−0.255605
$573$	−6.06916	−0.253543
$574$	25.5523	1.06653
$575$	−2.92081	−0.121806
$576$	0.0923014	0.00384589
$577$	−39.7095	−1.65313	−0.826564	−	0.562843i	$-0.809708\pi$
$577$	−39.7095	−1.65313	−0.826564	+	0.562843i	$0.809708\pi$
$578$	37.3710	1.55443
$579$	−26.7788	−1.11289
$580$	−0.302996	−0.0125812
$581$	31.9272	1.32456
$582$	11.0368	0.457491
$583$	6.30888	0.261287
$584$	6.08124	0.251644
$585$	0.564254	0.0233290
$586$	19.2752	0.796251
$587$	11.4755	0.473644	0.236822	−	0.971553i	$-0.423894\pi$
$587$	11.4755	0.473644	0.236822	+	0.971553i	$0.423894\pi$
$588$	2.25908	0.0931628
$589$	−0.117669	−0.00484845
$590$	6.09342	0.250862
$591$	24.7618	1.01856
$592$	−9.01235	−0.370405
$593$	16.8427	0.691646	0.345823	−	0.938300i	$-0.387600\pi$
$593$	16.8427	0.691646	0.345823	+	0.938300i	$0.387600\pi$
$594$	−5.11317	−0.209796
$595$	21.2237	0.870087
$596$	−17.8142	−0.729700
$597$	−32.0982	−1.31369
$598$	17.8554	0.730161
$599$	−15.3188	−0.625910	−0.312955	−	0.949768i	$-0.601319\pi$
$599$	−15.3188	−0.625910	−0.312955	+	0.949768i	$0.601319\pi$
$600$	1.75849	0.0717902
$601$	3.31412	0.135186	0.0675928	−	0.997713i	$-0.478468\pi$
$601$	3.31412	0.135186	0.0675928	+	0.997713i	$0.478468\pi$
$602$	2.87831	0.117311
$603$	0.650517	0.0264911
$604$	5.09012	0.207114
$605$	−1.00000	−0.0406558
$606$	−9.18076	−0.372943
$607$	−3.93348	−0.159655	−0.0798276	−	0.996809i	$-0.525437\pi$
$607$	−3.93348	−0.159655	−0.0798276	+	0.996809i	$0.525437\pi$
$608$	1.00335	0.0406911
$609$	−1.53361	−0.0621452
$610$	7.87501	0.318850
$611$	53.9541	2.18275
$612$	0.680600	0.0275116
$613$	−14.6246	−0.590683	−0.295342	−	0.955392i	$-0.595433\pi$
$613$	−14.6246	−0.590683	−0.295342	+	0.955392i	$0.595433\pi$
$614$	22.7434	0.917847
$615$	15.6111	0.629501
$616$	−2.87831	−0.115970
$617$	−4.54410	−0.182939	−0.0914693	−	0.995808i	$-0.529156\pi$
$617$	−4.54410	−0.182939	−0.0914693	+	0.995808i	$0.529156\pi$
$618$	19.1420	0.770003
$619$	22.2242	0.893265	0.446632	−	0.894718i	$-0.352623\pi$
$619$	22.2242	0.893265	0.446632	+	0.894718i	$0.352623\pi$
$620$	0.117276	0.00470992
$621$	14.9346	0.599304
$622$	−18.3887	−0.737319
$623$	16.8404	0.674696
$624$	−10.7500	−0.430343
$625$	1.00000	0.0400000
$626$	−26.7205	−1.06796
$627$	1.76438	0.0704626
$628$	13.3265	0.531786
$629$	−66.4541	−2.64970
$630$	0.265672	0.0105846
$631$	−20.4796	−0.815281	−0.407640	−	0.913143i	$-0.633648\pi$
$631$	−20.4796	−0.815281	−0.407640	+	0.913143i	$0.633648\pi$
$632$	−0.246729	−0.00981435
$633$	−2.44657	−0.0972423
$634$	12.6603	0.502803
$635$	5.26491	0.208932
$636$	11.0941	0.439911
$637$	−7.85339	−0.311163
$638$	0.302996	0.0119957
$639$	−0.154813	−0.00612429
$640$	−1.00000	−0.0395285
$641$	11.1457	0.440229	0.220115	−	0.975474i	$-0.429357\pi$
$641$	11.1457	0.440229	0.220115	+	0.975474i	$0.429357\pi$
$642$	−17.3121	−0.683256
$643$	−43.7713	−1.72617	−0.863086	−	0.505057i	$-0.831472\pi$
$643$	−43.7713	−1.72617	−0.863086	+	0.505057i	$0.831472\pi$
$644$	8.40698	0.331282
$645$	1.75849	0.0692406
$646$	7.39836	0.291085
$647$	−6.99255	−0.274906	−0.137453	−	0.990508i	$-0.543892\pi$
$647$	−6.99255	−0.274906	−0.137453	+	0.990508i	$0.543892\pi$
$648$	−9.26838	−0.364097
$649$	−6.09342	−0.239188
$650$	−6.11317	−0.239778
$651$	0.593591	0.0232647
$652$	2.04615	0.0801335
$653$	−9.56862	−0.374449	−0.187225	−	0.982317i	$-0.559949\pi$
$653$	−9.56862	−0.374449	−0.187225	+	0.982317i	$0.559949\pi$
$654$	−15.7943	−0.617606
$655$	−16.0097	−0.625549
$656$	−8.87755	−0.346610
$657$	0.561307	0.0218987
$658$	25.4036	0.990335
$659$	−42.3110	−1.64820	−0.824101	−	0.566443i	$-0.808319\pi$
$659$	−42.3110	−1.64820	−0.824101	+	0.566443i	$0.808319\pi$
$660$	−1.75849	−0.0684493
$661$	−40.2884	−1.56704	−0.783519	−	0.621368i	$-0.786577\pi$
$661$	−40.2884	−1.56704	−0.783519	+	0.621368i	$0.786577\pi$
$662$	3.34862	0.130148
$663$	−79.2668	−3.07847
$664$	−11.0924	−0.430467
$665$	2.88795	0.111990
$666$	−0.831852	−0.0322336
$667$	−0.884994	−0.0342671
$668$	−1.95019	−0.0754553
$669$	20.3447	0.786571
$670$	−7.04775	−0.272278
$671$	−7.87501	−0.304012
$672$	−5.06149	−0.195251
$673$	−29.1904	−1.12521	−0.562603	−	0.826727i	$-0.690200\pi$
$673$	−29.1904	−1.12521	−0.562603	+	0.826727i	$0.690200\pi$
$674$	14.9016	0.573988
$675$	−5.11317	−0.196806
$676$	24.3709	0.937341
$677$	−19.7904	−0.760607	−0.380304	−	0.924862i	$-0.624181\pi$
$677$	−19.7904	−0.760607	−0.380304	+	0.924862i	$0.624181\pi$
$678$	−27.2650	−1.04710
$679$	−18.0651	−0.693275
$680$	−7.37367	−0.282767
$681$	43.6520	1.67275
$682$	−0.117276	−0.00449073
$683$	−47.1398	−1.80375	−0.901877	−	0.431994i	$-0.857810\pi$
$683$	−47.1398	−1.80375	−0.901877	+	0.431994i	$0.857810\pi$
$684$	0.0926104	0.00354105
$685$	−6.51704	−0.249003
$686$	16.4505	0.628083
$687$	17.5550	0.669764
$688$	−1.00000	−0.0381246
$689$	−38.5673	−1.46930
$690$	5.13622	0.195533
$691$	−7.07816	−0.269266	−0.134633	−	0.990896i	$-0.542986\pi$
$691$	−7.07816	−0.269266	−0.134633	+	0.990896i	$0.542986\pi$
$692$	18.9095	0.718831
$693$	−0.265672	−0.0100920
$694$	12.4727	0.473456
$695$	0.750610	0.0284723
$696$	0.532817	0.0201964
$697$	−65.4602	−2.47948
$698$	−13.3681	−0.505992
$699$	6.91095	0.261396
$700$	−2.87831	−0.108790
$701$	25.7318	0.971878	0.485939	−	0.873993i	$-0.338478\pi$
$701$	25.7318	0.971878	0.485939	+	0.873993i	$0.338478\pi$
$702$	31.2577	1.17975
$703$	−9.04253	−0.341045
$704$	1.00000	0.0376889
$705$	15.5202	0.584526
$706$	−23.5669	−0.886953
$707$	15.0271	0.565153
$708$	−10.7152	−0.402703
$709$	2.78881	0.104736	0.0523680	−	0.998628i	$-0.483323\pi$
$709$	2.78881	0.104736	0.0523680	+	0.998628i	$0.483323\pi$
$710$	1.67725	0.0629461
$711$	−0.0227734	−0.000854070 0
$712$	−5.85080	−0.219268
$713$	0.342540	0.0128282
$714$	−37.3218	−1.39673
$715$	6.11317	0.228620
$716$	−2.47257	−0.0924041
$717$	−14.1290	−0.527658
$718$	−32.4228	−1.21001
$719$	−28.9802	−1.08078	−0.540389	−	0.841415i	$-0.681723\pi$
$719$	−28.9802	−1.08078	−0.540389	+	0.841415i	$0.681723\pi$
$720$	−0.0923014	−0.00343987
$721$	−31.3317	−1.16685
$722$	−17.9933	−0.669641
$723$	20.1243	0.748430
$724$	−9.12851	−0.339258
$725$	0.302996	0.0112530
$726$	1.75849	0.0652638
$727$	30.1464	1.11807	0.559033	−	0.829145i	$-0.311172\pi$
$727$	30.1464	1.11807	0.559033	+	0.829145i	$0.311172\pi$
$728$	17.5956	0.652136
$729$	26.1190	0.967369
$730$	−6.08124	−0.225077
$731$	−7.37367	−0.272725
$732$	−13.8482	−0.511843
$733$	18.8479	0.696162	0.348081	−	0.937464i	$-0.386833\pi$
$733$	18.8479	0.696162	0.348081	+	0.937464i	$0.386833\pi$
$734$	28.5536	1.05393
$735$	−2.25908	−0.0833274
$736$	−2.92081	−0.107662
$737$	7.04775	0.259607
$738$	−0.819410	−0.0301629
$739$	−21.8536	−0.803899	−0.401949	−	0.915662i	$-0.631667\pi$
$739$	−21.8536	−0.803899	−0.401949	+	0.915662i	$0.631667\pi$
$740$	9.01235	0.331301
$741$	−10.7860	−0.396232
$742$	−18.1589	−0.666635
$743$	−47.8603	−1.75582	−0.877912	−	0.478821i	$-0.841064\pi$
$743$	−47.8603	−1.75582	−0.877912	+	0.478821i	$0.841064\pi$
$744$	−0.206229	−0.00756073
$745$	17.8142	0.652663
$746$	−6.42137	−0.235103
$747$	−1.02384	−0.0374603
$748$	7.37367	0.269608
$749$	28.3366	1.03540
$750$	−1.75849	−0.0642111
$751$	7.38256	0.269393	0.134697	−	0.990887i	$-0.456994\pi$
$751$	7.38256	0.269393	0.134697	+	0.990887i	$0.456994\pi$
$752$	−8.82587	−0.321846
$753$	−37.5869	−1.36974
$754$	−1.85227	−0.0674557
$755$	−5.09012	−0.185249
$756$	14.7173	0.535263
$757$	11.7032	0.425360	0.212680	−	0.977122i	$-0.431781\pi$
$757$	11.7032	0.425360	0.212680	+	0.977122i	$0.431781\pi$
$758$	−0.677659	−0.0246137
$759$	−5.13622	−0.186433
$760$	−1.00335	−0.0363953
$761$	−42.4017	−1.53706	−0.768531	−	0.639813i	$-0.779012\pi$
$761$	−42.4017	−1.53706	−0.768531	+	0.639813i	$0.779012\pi$
$762$	−9.25832	−0.335394
$763$	25.8522	0.935912
$764$	−3.45134	−0.124865
$765$	−0.680600	−0.0246071
$766$	−19.4006	−0.700970
$767$	37.2501	1.34502
$768$	1.75849	0.0634542
$769$	−46.6165	−1.68103	−0.840517	−	0.541785i	$-0.817749\pi$
$769$	−46.6165	−1.68103	−0.840517	+	0.541785i	$0.817749\pi$
$770$	2.87831	0.103727
$771$	49.9734	1.79975
$772$	−15.2283	−0.548077
$773$	−25.8827	−0.930935	−0.465468	−	0.885065i	$-0.654114\pi$
$773$	−25.8827	−0.930935	−0.465468	+	0.885065i	$0.654114\pi$
$774$	−0.0923014	−0.00331770
$775$	−0.117276	−0.00421268
$776$	6.27629	0.225306
$777$	45.6159	1.63646
$778$	−22.7919	−0.817131
$779$	−8.90728	−0.319136
$780$	10.7500	0.384911
$781$	−1.67725	−0.0600168
$782$	−21.5371	−0.770164
$783$	−1.54927	−0.0553665
$784$	1.28467	0.0458810
$785$	−13.3265	−0.475644
$786$	28.1529	1.00418
$787$	−21.6513	−0.771787	−0.385893	−	0.922543i	$-0.626107\pi$
$787$	−21.6513	−0.771787	−0.385893	+	0.922543i	$0.626107\pi$
$788$	14.0812	0.501623
$789$	−21.2499	−0.756516
$790$	0.246729	0.00877822
$791$	44.6274	1.58677
$792$	0.0923014	0.00327979
$793$	48.1413	1.70955
$794$	−9.26539	−0.328816
$795$	−11.0941	−0.393468
$796$	−18.2532	−0.646968
$797$	−41.1403	−1.45727	−0.728633	−	0.684904i	$-0.759844\pi$
$797$	−41.1403	−1.45727	−0.728633	+	0.684904i	$0.759844\pi$
$798$	−5.07844	−0.179775
$799$	−65.0791	−2.30233
$800$	1.00000	0.0353553
$801$	−0.540036	−0.0190813
$802$	−5.89124	−0.208027
$803$	6.08124	0.214602
$804$	12.3934	0.437082
$805$	−8.40698	−0.296307
$806$	0.716928	0.0252527
$807$	4.07452	0.143430
$808$	−5.22081	−0.183667
$809$	29.9119	1.05165	0.525823	−	0.850594i	$-0.323758\pi$
$809$	29.9119	1.05165	0.525823	+	0.850594i	$0.323758\pi$
$810$	9.26838	0.325658
$811$	−39.1283	−1.37398	−0.686991	−	0.726666i	$-0.741069\pi$
$811$	−39.1283	−1.37398	−0.686991	+	0.726666i	$0.741069\pi$
$812$	−0.872118	−0.0306053
$813$	32.4201	1.13702
$814$	−9.01235	−0.315883
$815$	−2.04615	−0.0716736
$816$	12.9666	0.453920
$817$	−1.00335	−0.0351027
$818$	20.6012	0.720305
$819$	1.62410	0.0567506
$820$	8.87755	0.310018
$821$	53.7388	1.87550	0.937748	−	0.347316i	$-0.112907\pi$
$821$	53.7388	1.87550	0.937748	+	0.347316i	$0.112907\pi$
$822$	11.4602	0.399720
$823$	−16.3835	−0.571092	−0.285546	−	0.958365i	$-0.592175\pi$
$823$	−16.3835	−0.571092	−0.285546	+	0.958365i	$0.592175\pi$
$824$	10.8854	0.379212
$825$	1.75849	0.0612229
$826$	17.5387	0.610251
$827$	7.49362	0.260579	0.130289	−	0.991476i	$-0.458409\pi$
$827$	7.49362	0.260579	0.130289	+	0.991476i	$0.458409\pi$
$828$	−0.269594	−0.00936905
$829$	−29.7066	−1.03175	−0.515876	−	0.856663i	$-0.672533\pi$
$829$	−29.7066	−1.03175	−0.515876	+	0.856663i	$0.672533\pi$
$830$	11.0924	0.385021
$831$	18.4147	0.638799
$832$	−6.11317	−0.211936
$833$	9.47271	0.328210
$834$	−1.31994	−0.0457059
$835$	1.95019	0.0674893
$836$	1.00335	0.0347015
$837$	0.599652	0.0207270
$838$	27.8925	0.963530
$839$	31.8715	1.10033	0.550163	−	0.835057i	$-0.314566\pi$
$839$	31.8715	1.10033	0.550163	+	0.835057i	$0.314566\pi$
$840$	5.06149	0.174638
$841$	−28.9082	−0.996834
$842$	2.66284	0.0917677
$843$	2.48038	0.0854288
$844$	−1.39128	−0.0478900
$845$	−24.3709	−0.838383
$846$	−0.814640	−0.0280079
$847$	−2.87831	−0.0988999
$848$	6.30888	0.216648
$849$	−13.9562	−0.478976
$850$	7.37367	0.252915
$851$	26.3233	0.902352
$852$	−2.94944	−0.101046
$853$	0.155013	0.00530753	0.00265377	−	0.999996i	$-0.499155\pi$
$853$	0.155013	0.00530753	0.00265377	+	0.999996i	$0.499155\pi$
$854$	22.6667	0.775639
$855$	−0.0926104	−0.00316721
$856$	−9.84487	−0.336491
$857$	53.9075	1.84145	0.920723	−	0.390217i	$-0.127600\pi$
$857$	53.9075	1.84145	0.920723	+	0.390217i	$0.127600\pi$
$858$	−10.7500	−0.366998
$859$	−16.9691	−0.578977	−0.289489	−	0.957181i	$-0.593485\pi$
$859$	−16.9691	−0.578977	−0.289489	+	0.957181i	$0.593485\pi$
$860$	1.00000	0.0340997
$861$	44.9336	1.53133
$862$	19.8330	0.675515
$863$	−33.8618	−1.15267	−0.576334	−	0.817214i	$-0.695517\pi$
$863$	−33.8618	−1.15267	−0.576334	+	0.817214i	$0.695517\pi$
$864$	−5.11317	−0.173954
$865$	−18.9095	−0.642942
$866$	−13.7880	−0.468536
$867$	65.7167	2.23186
$868$	0.337557	0.0114574
$869$	−0.246729	−0.00836970
$870$	−0.532817	−0.0180642
$871$	−43.0841	−1.45985
$872$	−8.98172	−0.304159
$873$	0.579310	0.0196067
$874$	−2.93058	−0.0991285
$875$	2.87831	0.0973046
$876$	10.6938	0.361311
$877$	21.6429	0.730829	0.365415	−	0.930845i	$-0.380927\pi$
$877$	21.6429	0.730829	0.365415	+	0.930845i	$0.380927\pi$
$878$	40.2252	1.35754
$879$	33.8953	1.14326
$880$	−1.00000	−0.0337100
$881$	46.6118	1.57039	0.785196	−	0.619248i	$-0.212562\pi$
$881$	46.6118	1.57039	0.785196	+	0.619248i	$0.212562\pi$
$882$	0.118577	0.00399268
$883$	−1.69841	−0.0571560	−0.0285780	−	0.999592i	$-0.509098\pi$
$883$	−1.69841	−0.0571560	−0.0285780	+	0.999592i	$0.509098\pi$
$884$	−45.0765	−1.51609
$885$	10.7152	0.360189
$886$	6.67693	0.224316
$887$	12.2999	0.412989	0.206495	−	0.978448i	$-0.433794\pi$
$887$	12.2999	0.412989	0.206495	+	0.978448i	$0.433794\pi$
$888$	−15.8482	−0.531830
$889$	15.1541	0.508251
$890$	5.85080	0.196119
$891$	−9.26838	−0.310503
$892$	11.5694	0.387372
$893$	−8.85542	−0.296335
$894$	−31.3262	−1.04771
$895$	2.47257	0.0826488
$896$	−2.87831	−0.0961576
$897$	31.3986	1.04837
$898$	15.0258	0.501416
$899$	−0.0355342	−0.00118513
$900$	0.0923014	0.00307671
$901$	46.5196	1.54979
$902$	−8.87755	−0.295590
$903$	5.06149	0.168436
$904$	−15.5047	−0.515679
$905$	9.12851	0.303442
$906$	8.95095	0.297375
$907$	16.3225	0.541979	0.270990	−	0.962582i	$-0.412649\pi$
$907$	16.3225	0.541979	0.270990	+	0.962582i	$0.412649\pi$
$908$	24.8235	0.823797
$909$	−0.481888	−0.0159832
$910$	−17.5956	−0.583288
$911$	−11.4590	−0.379653	−0.189826	−	0.981818i	$-0.560793\pi$
$911$	−11.4590	−0.379653	−0.189826	+	0.981818i	$0.560793\pi$
$912$	1.76438	0.0584245
$913$	−11.0924	−0.367103
$914$	−14.1718	−0.468761
$915$	13.8482	0.457806
$916$	9.98296	0.329846
$917$	−46.0808	−1.52172
$918$	−37.7028	−1.24438
$919$	20.0942	0.662847	0.331424	−	0.943482i	$-0.392471\pi$
$919$	20.0942	0.662847	0.331424	+	0.943482i	$0.392471\pi$
$920$	2.92081	0.0962961
$921$	39.9941	1.31785
$922$	9.92192	0.326761
$923$	10.2533	0.337492
$924$	−5.06149	−0.166511
$925$	−9.01235	−0.296324
$926$	−22.3009	−0.732853
$927$	1.00474	0.0330000
$928$	0.302996	0.00994635
$929$	−46.9139	−1.53919	−0.769597	−	0.638530i	$-0.779543\pi$
$929$	−46.9139	−1.53919	−0.769597	+	0.638530i	$0.779543\pi$
$930$	0.206229	0.00676252
$931$	1.28897	0.0422442
$932$	3.93004	0.128733
$933$	−32.3364	−1.05865
$934$	24.4941	0.801472
$935$	−7.37367	−0.241145
$936$	−0.564254	−0.0184432
$937$	−20.1611	−0.658635	−0.329317	−	0.944219i	$-0.606819\pi$
$937$	−20.1611	−0.658635	−0.329317	+	0.944219i	$0.606819\pi$
$938$	−20.2856	−0.662348
$939$	−46.9878	−1.53339
$940$	8.82587	0.287868
$941$	−57.6666	−1.87988	−0.939938	−	0.341345i	$-0.889117\pi$
$941$	−57.6666	−1.87988	−0.939938	+	0.341345i	$0.889117\pi$
$942$	23.4346	0.763541
$943$	25.9296	0.844384
$944$	−6.09342	−0.198324
$945$	−14.7173	−0.478753
$946$	−1.00000	−0.0325128
$947$	32.9236	1.06987	0.534937	−	0.844892i	$-0.320335\pi$
$947$	32.9236	1.06987	0.534937	+	0.844892i	$0.320335\pi$
$948$	−0.433871	−0.0140915
$949$	−37.1757	−1.20677
$950$	1.00335	0.0325529
$951$	22.2630	0.721927
$952$	−21.2237	−0.687864
$953$	16.4551	0.533032	0.266516	−	0.963831i	$-0.414127\pi$
$953$	16.4551	0.533032	0.266516	+	0.963831i	$0.414127\pi$
$954$	0.582319	0.0188533
$955$	3.45134	0.111683
$956$	−8.03473	−0.259862
$957$	0.532817	0.0172235
$958$	−17.0102	−0.549576
$959$	−18.7581	−0.605729
$960$	−1.75849	−0.0567552
$961$	−30.9862	−0.999556
$962$	55.0940	1.77630
$963$	−0.908695	−0.0292823
$964$	11.4440	0.368588
$965$	15.2283	0.490215
$966$	14.7836	0.475655
$967$	−2.15962	−0.0694488	−0.0347244	−	0.999397i	$-0.511055\pi$
$967$	−2.15962	−0.0694488	−0.0347244	+	0.999397i	$0.511055\pi$
$968$	1.00000	0.0321412
$969$	13.0100	0.417941
$970$	−6.27629	−0.201520
$971$	42.7771	1.37278	0.686391	−	0.727233i	$-0.259194\pi$
$971$	42.7771	1.37278	0.686391	+	0.727233i	$0.259194\pi$
$972$	−0.958887	−0.0307563
$973$	2.16049	0.0692621
$974$	−36.1457	−1.15818
$975$	−10.7500	−0.344275
$976$	−7.87501	−0.252073
$977$	−50.1432	−1.60422	−0.802112	−	0.597174i	$-0.796290\pi$
$977$	−50.1432	−1.60422	−0.802112	+	0.597174i	$0.796290\pi$
$978$	3.59815	0.115056
$979$	−5.85080	−0.186992
$980$	−1.28467	−0.0410372
$981$	−0.829025	−0.0264687
$982$	28.3175	0.903647
$983$	18.0026	0.574192	0.287096	−	0.957902i	$-0.407310\pi$
$983$	18.0026	0.574192	0.287096	+	0.957902i	$0.407310\pi$
$984$	−15.6111	−0.497664
$985$	−14.0812	−0.448666
$986$	2.23420	0.0711513
$987$	44.6721	1.42193
$988$	−6.13364	−0.195137
$989$	2.92081	0.0928762
$990$	−0.0923014	−0.00293353
$991$	51.0369	1.62124	0.810620	−	0.585572i	$-0.199130\pi$
$991$	51.0369	1.62124	0.810620	+	0.585572i	$0.199130\pi$
$992$	−0.117276	−0.00372352
$993$	5.88853	0.186867
$994$	4.82765	0.153124
$995$	18.2532	0.578666
$996$	−19.5058	−0.618066
$997$	−23.5442	−0.745651	−0.372825	−	0.927901i	$-0.621611\pi$
$997$	−23.5442	−0.745651	−0.372825	+	0.927901i	$0.621611\pi$
$998$	−24.3532	−0.770886
$999$	46.0817	1.45796

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.v.1.4	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.v.1.4	✓	5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4730.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.75849 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.75849 q^{6} -2.87831 q^{7} +1.00000 q^{8} +0.0923014 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.75849 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.75849 q^{6} -2.87831 q^{7} +1.00000 q^{8} +0.0923014 q^{9} -1.00000 q^{10} +1.00000 q^{11} +1.75849 q^{12} -6.11317 q^{13} -2.87831 q^{14} -1.75849 q^{15} +1.00000 q^{16} +7.37367 q^{17} +0.0923014 q^{18} +1.00335 q^{19} -1.00000 q^{20} -5.06149 q^{21} +1.00000 q^{22} -2.92081 q^{23} +1.75849 q^{24} +1.00000 q^{25} -6.11317 q^{26} -5.11317 q^{27} -2.87831 q^{28} +0.302996 q^{29} -1.75849 q^{30} -0.117276 q^{31} +1.00000 q^{32} +1.75849 q^{33} +7.37367 q^{34} +2.87831 q^{35} +0.0923014 q^{36} -9.01235 q^{37} +1.00335 q^{38} -10.7500 q^{39} -1.00000 q^{40} -8.87755 q^{41} -5.06149 q^{42} -1.00000 q^{43} +1.00000 q^{44} -0.0923014 q^{45} -2.92081 q^{46} -8.82587 q^{47} +1.75849 q^{48} +1.28467 q^{49} +1.00000 q^{50} +12.9666 q^{51} -6.11317 q^{52} +6.30888 q^{53} -5.11317 q^{54} -1.00000 q^{55} -2.87831 q^{56} +1.76438 q^{57} +0.302996 q^{58} -6.09342 q^{59} -1.75849 q^{60} -7.87501 q^{61} -0.117276 q^{62} -0.265672 q^{63} +1.00000 q^{64} +6.11317 q^{65} +1.75849 q^{66} +7.04775 q^{67} +7.37367 q^{68} -5.13622 q^{69} +2.87831 q^{70} -1.67725 q^{71} +0.0923014 q^{72} +6.08124 q^{73} -9.01235 q^{74} +1.75849 q^{75} +1.00335 q^{76} -2.87831 q^{77} -10.7500 q^{78} -0.246729 q^{79} -1.00000 q^{80} -9.26838 q^{81} -8.87755 q^{82} -11.0924 q^{83} -5.06149 q^{84} -7.37367 q^{85} -1.00000 q^{86} +0.532817 q^{87} +1.00000 q^{88} -5.85080 q^{89} -0.0923014 q^{90} +17.5956 q^{91} -2.92081 q^{92} -0.206229 q^{93} -8.82587 q^{94} -1.00335 q^{95} +1.75849 q^{96} +6.27629 q^{97} +1.28467 q^{98} +0.0923014 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} + 2 q^{3} + 5 q^{4} - 5 q^{5} + 2 q^{6} - 6 q^{7} + 5 q^{8} - q^{9}+O(q^{10}) \) 5 * q + 5 * q^2 + 2 * q^3 + 5 * q^4 - 5 * q^5 + 2 * q^6 - 6 * q^7 + 5 * q^8 - q^9	\( 5 q + 5 q^{2} + 2 q^{3} + 5 q^{4} - 5 q^{5} + 2 q^{6} - 6 q^{7} + 5 q^{8} - q^{9} - 5 q^{10} + 5 q^{11} + 2 q^{12} - 12 q^{13} - 6 q^{14} - 2 q^{15} + 5 q^{16} - 2 q^{17} - q^{18} - 4 q^{19} - 5 q^{20} + 2 q^{21} + 5 q^{22} - 6 q^{23} + 2 q^{24} + 5 q^{25} - 12 q^{26} - 7 q^{27} - 6 q^{28} - 19 q^{29} - 2 q^{30} - 7 q^{31} + 5 q^{32} + 2 q^{33} - 2 q^{34} + 6 q^{35} - q^{36} - q^{37} - 4 q^{38} - 20 q^{39} - 5 q^{40} - 2 q^{41} + 2 q^{42} - 5 q^{43} + 5 q^{44} + q^{45} - 6 q^{46} + 7 q^{47} + 2 q^{48} - 5 q^{49} + 5 q^{50} - 5 q^{51} - 12 q^{52} - 6 q^{53} - 7 q^{54} - 5 q^{55} - 6 q^{56} - 15 q^{57} - 19 q^{58} - 5 q^{59} - 2 q^{60} - 5 q^{61} - 7 q^{62} - 17 q^{63} + 5 q^{64} + 12 q^{65} + 2 q^{66} - 20 q^{67} - 2 q^{68} - 40 q^{69} + 6 q^{70} - 22 q^{71} - q^{72} + 10 q^{73} - q^{74} + 2 q^{75} - 4 q^{76} - 6 q^{77} - 20 q^{78} - 9 q^{79} - 5 q^{80} - 15 q^{81} - 2 q^{82} - 19 q^{83} + 2 q^{84} + 2 q^{85} - 5 q^{86} + 15 q^{87} + 5 q^{88} - 21 q^{89} + q^{90} + 10 q^{91} - 6 q^{92} - 15 q^{93} + 7 q^{94} + 4 q^{95} + 2 q^{96} + 10 q^{97} - 5 q^{98} - q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 + 2 * q^3 + 5 * q^4 - 5 * q^5 + 2 * q^6 - 6 * q^7 + 5 * q^8 - q^9 - 5 * q^10 + 5 * q^11 + 2 * q^12 - 12 * q^13 - 6 * q^14 - 2 * q^15 + 5 * q^16 - 2 * q^17 - q^18 - 4 * q^19 - 5 * q^20 + 2 * q^21 + 5 * q^22 - 6 * q^23 + 2 * q^24 + 5 * q^25 - 12 * q^26 - 7 * q^27 - 6 * q^28 - 19 * q^29 - 2 * q^30 - 7 * q^31 + 5 * q^32 + 2 * q^33 - 2 * q^34 + 6 * q^35 - q^36 - q^37 - 4 * q^38 - 20 * q^39 - 5 * q^40 - 2 * q^41 + 2 * q^42 - 5 * q^43 + 5 * q^44 + q^45 - 6 * q^46 + 7 * q^47 + 2 * q^48 - 5 * q^49 + 5 * q^50 - 5 * q^51 - 12 * q^52 - 6 * q^53 - 7 * q^54 - 5 * q^55 - 6 * q^56 - 15 * q^57 - 19 * q^58 - 5 * q^59 - 2 * q^60 - 5 * q^61 - 7 * q^62 - 17 * q^63 + 5 * q^64 + 12 * q^65 + 2 * q^66 - 20 * q^67 - 2 * q^68 - 40 * q^69 + 6 * q^70 - 22 * q^71 - q^72 + 10 * q^73 - q^74 + 2 * q^75 - 4 * q^76 - 6 * q^77 - 20 * q^78 - 9 * q^79 - 5 * q^80 - 15 * q^81 - 2 * q^82 - 19 * q^83 + 2 * q^84 + 2 * q^85 - 5 * q^86 + 15 * q^87 + 5 * q^88 - 21 * q^89 + q^90 + 10 * q^91 - 6 * q^92 - 15 * q^93 + 7 * q^94 + 4 * q^95 + 2 * q^96 + 10 * q^97 - 5 * q^98 - q^99

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