LMFDB - Embedded newform 4641.2.a.w.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4641,2,Mod(1,4641)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4641, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4641.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4641 = 3 \cdot 7 \cdot 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4641.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:	$37.0585715781$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 22 x^{12} + 19 x^{11} + 187 x^{10} - 135 x^{9} - 776 x^{8} + 443 x^{7} + 1636 x^{6} + \cdots - 19 $ x^14 - x^13 - 22x^12 + 19x^11 + 187x^10 - 135x^9 - 776x^8 + 443x^7 + 1636x^6 - 648x^5 - 1635x^4 + 306x^3 + 604x^2 + 8x - 19
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$0.170473$ of defining polynomial
Character	$\chi$	$=$	4641.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.170473 q^{2} -1.00000 q^{3} -1.97094 q^{4} -2.73568 q^{5} +0.170473 q^{6} +1.00000 q^{7} +0.676939 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.170473 q^{2} -1.00000 q^{3} -1.97094 q^{4} -2.73568 q^{5} +0.170473 q^{6} +1.00000 q^{7} +0.676939 q^{8} +1.00000 q^{9} +0.466361 q^{10} -0.775866 q^{11} +1.97094 q^{12} +1.00000 q^{13} -0.170473 q^{14} +2.73568 q^{15} +3.82648 q^{16} +1.00000 q^{17} -0.170473 q^{18} +1.76185 q^{19} +5.39187 q^{20} -1.00000 q^{21} +0.132265 q^{22} -1.79600 q^{23} -0.676939 q^{24} +2.48397 q^{25} -0.170473 q^{26} -1.00000 q^{27} -1.97094 q^{28} -3.21837 q^{29} -0.466361 q^{30} +3.63006 q^{31} -2.00619 q^{32} +0.775866 q^{33} -0.170473 q^{34} -2.73568 q^{35} -1.97094 q^{36} -8.41446 q^{37} -0.300348 q^{38} -1.00000 q^{39} -1.85189 q^{40} -9.26232 q^{41} +0.170473 q^{42} +3.56417 q^{43} +1.52918 q^{44} -2.73568 q^{45} +0.306170 q^{46} -4.25776 q^{47} -3.82648 q^{48} +1.00000 q^{49} -0.423450 q^{50} -1.00000 q^{51} -1.97094 q^{52} +5.99347 q^{53} +0.170473 q^{54} +2.12252 q^{55} +0.676939 q^{56} -1.76185 q^{57} +0.548646 q^{58} -5.80984 q^{59} -5.39187 q^{60} -0.903539 q^{61} -0.618829 q^{62} +1.00000 q^{63} -7.31095 q^{64} -2.73568 q^{65} -0.132265 q^{66} -11.1942 q^{67} -1.97094 q^{68} +1.79600 q^{69} +0.466361 q^{70} +4.86405 q^{71} +0.676939 q^{72} +10.8793 q^{73} +1.43444 q^{74} -2.48397 q^{75} -3.47250 q^{76} -0.775866 q^{77} +0.170473 q^{78} -6.90532 q^{79} -10.4680 q^{80} +1.00000 q^{81} +1.57898 q^{82} -13.8820 q^{83} +1.97094 q^{84} -2.73568 q^{85} -0.607595 q^{86} +3.21837 q^{87} -0.525214 q^{88} -4.52832 q^{89} +0.466361 q^{90} +1.00000 q^{91} +3.53981 q^{92} -3.63006 q^{93} +0.725835 q^{94} -4.81986 q^{95} +2.00619 q^{96} +9.48708 q^{97} -0.170473 q^{98} -0.775866 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - q^{2} - 14 q^{3} + 17 q^{4} - q^{5} + q^{6} + 14 q^{7} - 6 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q - q^2 - 14 * q^3 + 17 * q^4 - q^5 + q^6 + 14 * q^7 - 6 * q^8 + 14 * q^9	\( 14 q - q^{2} - 14 q^{3} + 17 q^{4} - q^{5} + q^{6} + 14 q^{7} - 6 q^{8} + 14 q^{9} + 11 q^{10} - 4 q^{11} - 17 q^{12} + 14 q^{13} - q^{14} + q^{15} + 19 q^{16} + 14 q^{17} - q^{18} + 6 q^{19} + q^{20} - 14 q^{21} + 12 q^{22} + 7 q^{23} + 6 q^{24} + 19 q^{25} - q^{26} - 14 q^{27} + 17 q^{28} - 4 q^{29} - 11 q^{30} + 31 q^{31} - 18 q^{32} + 4 q^{33} - q^{34} - q^{35} + 17 q^{36} + 2 q^{37} + 9 q^{38} - 14 q^{39} + 50 q^{40} + 4 q^{41} + q^{42} + 14 q^{43} - 8 q^{44} - q^{45} - 17 q^{46} - q^{47} - 19 q^{48} + 14 q^{49} - 3 q^{50} - 14 q^{51} + 17 q^{52} - 43 q^{53} + q^{54} + 23 q^{55} - 6 q^{56} - 6 q^{57} - 10 q^{58} + 11 q^{59} - q^{60} + 25 q^{61} - 3 q^{62} + 14 q^{63} + 36 q^{64} - q^{65} - 12 q^{66} + 11 q^{67} + 17 q^{68} - 7 q^{69} + 11 q^{70} + 20 q^{71} - 6 q^{72} + 14 q^{73} - 24 q^{74} - 19 q^{75} + 9 q^{76} - 4 q^{77} + q^{78} + 42 q^{79} + 13 q^{80} + 14 q^{81} + 2 q^{82} + 15 q^{83} - 17 q^{84} - q^{85} - 11 q^{86} + 4 q^{87} + 63 q^{88} + 21 q^{89} + 11 q^{90} + 14 q^{91} + 30 q^{92} - 31 q^{93} - 29 q^{94} + 16 q^{95} + 18 q^{96} + 15 q^{97} - q^{98} - 4 q^{99}+O(q^{100}) \) 14 * q - q^2 - 14 * q^3 + 17 * q^4 - q^5 + q^6 + 14 * q^7 - 6 * q^8 + 14 * q^9 + 11 * q^10 - 4 * q^11 - 17 * q^12 + 14 * q^13 - q^14 + q^15 + 19 * q^16 + 14 * q^17 - q^18 + 6 * q^19 + q^20 - 14 * q^21 + 12 * q^22 + 7 * q^23 + 6 * q^24 + 19 * q^25 - q^26 - 14 * q^27 + 17 * q^28 - 4 * q^29 - 11 * q^30 + 31 * q^31 - 18 * q^32 + 4 * q^33 - q^34 - q^35 + 17 * q^36 + 2 * q^37 + 9 * q^38 - 14 * q^39 + 50 * q^40 + 4 * q^41 + q^42 + 14 * q^43 - 8 * q^44 - q^45 - 17 * q^46 - q^47 - 19 * q^48 + 14 * q^49 - 3 * q^50 - 14 * q^51 + 17 * q^52 - 43 * q^53 + q^54 + 23 * q^55 - 6 * q^56 - 6 * q^57 - 10 * q^58 + 11 * q^59 - q^60 + 25 * q^61 - 3 * q^62 + 14 * q^63 + 36 * q^64 - q^65 - 12 * q^66 + 11 * q^67 + 17 * q^68 - 7 * q^69 + 11 * q^70 + 20 * q^71 - 6 * q^72 + 14 * q^73 - 24 * q^74 - 19 * q^75 + 9 * q^76 - 4 * q^77 + q^78 + 42 * q^79 + 13 * q^80 + 14 * q^81 + 2 * q^82 + 15 * q^83 - 17 * q^84 - q^85 - 11 * q^86 + 4 * q^87 + 63 * q^88 + 21 * q^89 + 11 * q^90 + 14 * q^91 + 30 * q^92 - 31 * q^93 - 29 * q^94 + 16 * q^95 + 18 * q^96 + 15 * q^97 - q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.170473	−0.120543	−0.0602714	−	0.998182i	$-0.519197\pi$
$2$	−0.170473	−0.120543	−0.0602714	+	0.998182i	$0.519197\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.97094	−0.985469
$5$	−2.73568	−1.22344	−0.611718	−	0.791076i	$-0.709521\pi$
$5$	−2.73568	−1.22344	−0.611718	+	0.791076i	$0.709521\pi$
$6$	0.170473	0.0695954
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	0.676939	0.239334
$9$	1.00000	0.333333
$10$	0.466361	0.147476
$11$	−0.775866	−0.233932	−0.116966	−	0.993136i	$-0.537317\pi$
$11$	−0.775866	−0.233932	−0.116966	+	0.993136i	$0.537317\pi$
$12$	1.97094	0.568961
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−0.170473	−0.0455609
$15$	2.73568	0.706351
$16$	3.82648	0.956619
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.170473	−0.0401809
$19$	1.76185	0.404196	0.202098	−	0.979365i	$-0.435224\pi$
$19$	1.76185	0.404196	0.202098	+	0.979365i	$0.435224\pi$
$20$	5.39187	1.20566
$21$	−1.00000	−0.218218
$22$	0.132265	0.0281989
$23$	−1.79600	−0.374492	−0.187246	−	0.982313i	$-0.559956\pi$
$23$	−1.79600	−0.374492	−0.187246	+	0.982313i	$0.559956\pi$
$24$	−0.676939	−0.138180
$25$	2.48397	0.496793
$26$	−0.170473	−0.0334326
$27$	−1.00000	−0.192450
$28$	−1.97094	−0.372472
$29$	−3.21837	−0.597636	−0.298818	−	0.954310i	$-0.596592\pi$
$29$	−3.21837	−0.597636	−0.298818	+	0.954310i	$0.596592\pi$
$30$	−0.466361	−0.0851455
$31$	3.63006	0.651978	0.325989	−	0.945374i	$-0.394303\pi$
$31$	3.63006	0.651978	0.325989	+	0.945374i	$0.394303\pi$
$32$	−2.00619	−0.354648
$33$	0.775866	0.135061
$34$	−0.170473	−0.0292359
$35$	−2.73568	−0.462415
$36$	−1.97094	−0.328490
$37$	−8.41446	−1.38333	−0.691665	−	0.722219i	$-0.743122\pi$
$37$	−8.41446	−1.38333	−0.691665	+	0.722219i	$0.743122\pi$
$38$	−0.300348	−0.0487229
$39$	−1.00000	−0.160128
$40$	−1.85189	−0.292810
$41$	−9.26232	−1.44653	−0.723266	−	0.690569i	$-0.757360\pi$
$41$	−9.26232	−1.44653	−0.723266	+	0.690569i	$0.757360\pi$
$42$	0.170473	0.0263046
$43$	3.56417	0.543530	0.271765	−	0.962364i	$-0.412393\pi$
$43$	3.56417	0.543530	0.271765	+	0.962364i	$0.412393\pi$
$44$	1.52918	0.230533
$45$	−2.73568	−0.407812
$46$	0.306170	0.0451423
$47$	−4.25776	−0.621058	−0.310529	−	0.950564i	$-0.600506\pi$
$47$	−4.25776	−0.621058	−0.310529	+	0.950564i	$0.600506\pi$
$48$	−3.82648	−0.552304
$49$	1.00000	0.142857
$50$	−0.423450	−0.0598849
$51$	−1.00000	−0.140028
$52$	−1.97094	−0.273320
$53$	5.99347	0.823266	0.411633	−	0.911350i	$-0.364958\pi$
$53$	5.99347	0.823266	0.411633	+	0.911350i	$0.364958\pi$
$54$	0.170473	0.0231985
$55$	2.12252	0.286201
$56$	0.676939	0.0904598
$57$	−1.76185	−0.233363
$58$	0.548646	0.0720407
$59$	−5.80984	−0.756377	−0.378188	−	0.925729i	$-0.623453\pi$
$59$	−5.80984	−0.756377	−0.378188	+	0.925729i	$0.623453\pi$
$60$	−5.39187	−0.696087
$61$	−0.903539	−0.115686	−0.0578431	−	0.998326i	$-0.518422\pi$
$61$	−0.903539	−0.115686	−0.0578431	+	0.998326i	$0.518422\pi$
$62$	−0.618829	−0.0785913
$63$	1.00000	0.125988
$64$	−7.31095	−0.913869
$65$	−2.73568	−0.339320
$66$	−0.132265	−0.0162806
$67$	−11.1942	−1.36759	−0.683796	−	0.729673i	$-0.739672\pi$
$67$	−11.1942	−1.36759	−0.683796	+	0.729673i	$0.739672\pi$
$68$	−1.97094	−0.239011
$69$	1.79600	0.216213
$70$	0.466361	0.0557408
$71$	4.86405	0.577257	0.288628	−	0.957441i	$-0.406801\pi$
$71$	4.86405	0.577257	0.288628	+	0.957441i	$0.406801\pi$
$72$	0.676939	0.0797780
$73$	10.8793	1.27333	0.636666	−	0.771140i	$-0.280313\pi$
$73$	10.8793	1.27333	0.636666	+	0.771140i	$0.280313\pi$
$74$	1.43444	0.166750
$75$	−2.48397	−0.286824
$76$	−3.47250	−0.398323
$77$	−0.775866	−0.0884182
$78$	0.170473	0.0193023
$79$	−6.90532	−0.776909	−0.388455	−	0.921468i	$-0.626991\pi$
$79$	−6.90532	−0.776909	−0.388455	+	0.921468i	$0.626991\pi$
$80$	−10.4680	−1.17036
$81$	1.00000	0.111111
$82$	1.57898	0.174369
$83$	−13.8820	−1.52375	−0.761876	−	0.647723i	$-0.775721\pi$
$83$	−13.8820	−1.52375	−0.761876	+	0.647723i	$0.775721\pi$
$84$	1.97094	0.215047
$85$	−2.73568	−0.296727
$86$	−0.607595	−0.0655187
$87$	3.21837	0.345045
$88$	−0.525214	−0.0559880
$89$	−4.52832	−0.480001	−0.240001	−	0.970773i	$-0.577148\pi$
$89$	−4.52832	−0.480001	−0.240001	+	0.970773i	$0.577148\pi$
$90$	0.466361	0.0491588
$91$	1.00000	0.104828
$92$	3.53981	0.369050
$93$	−3.63006	−0.376420
$94$	0.725835	0.0748641
$95$	−4.81986	−0.494507
$96$	2.00619	0.204756
$97$	9.48708	0.963267	0.481634	−	0.876373i	$-0.340044\pi$
$97$	9.48708	0.963267	0.481634	+	0.876373i	$0.340044\pi$
$98$	−0.170473	−0.0172204
$99$	−0.775866	−0.0779775
$100$	−4.89575	−0.489575
$101$	−0.243124	−0.0241917	−0.0120959	−	0.999927i	$-0.503850\pi$
$101$	−0.243124	−0.0241917	−0.0120959	+	0.999927i	$0.503850\pi$
$102$	0.170473	0.0168794
$103$	−6.54652	−0.645048	−0.322524	−	0.946561i	$-0.604531\pi$
$103$	−6.54652	−0.645048	−0.322524	+	0.946561i	$0.604531\pi$
$104$	0.676939	0.0663793
$105$	2.73568	0.266975
$106$	−1.02173	−0.0992389
$107$	−2.40028	−0.232044	−0.116022	−	0.993247i	$-0.537014\pi$
$107$	−2.40028	−0.232044	−0.116022	+	0.993247i	$0.537014\pi$
$108$	1.97094	0.189654
$109$	14.8251	1.41999	0.709993	−	0.704209i	$-0.248698\pi$
$109$	14.8251	1.41999	0.709993	+	0.704209i	$0.248698\pi$
$110$	−0.361834	−0.0344995
$111$	8.41446	0.798665
$112$	3.82648	0.361568
$113$	19.2316	1.80916	0.904579	−	0.426306i	$-0.140185\pi$
$113$	19.2316	1.80916	0.904579	+	0.426306i	$0.140185\pi$
$114$	0.300348	0.0281302
$115$	4.91329	0.458167
$116$	6.34320	0.588952
$117$	1.00000	0.0924500
$118$	0.990422	0.0911758
$119$	1.00000	0.0916698
$120$	1.85189	0.169054
$121$	−10.3980	−0.945276
$122$	0.154029	0.0139452
$123$	9.26232	0.835156
$124$	−7.15463	−0.642505
$125$	6.88307	0.615641
$126$	−0.170473	−0.0151870
$127$	16.6123	1.47411	0.737053	−	0.675835i	$-0.236217\pi$
$127$	16.6123	1.47411	0.737053	+	0.675835i	$0.236217\pi$
$128$	5.25870	0.464808
$129$	−3.56417	−0.313807
$130$	0.466361	0.0409026
$131$	14.9992	1.31049	0.655244	−	0.755417i	$-0.272566\pi$
$131$	14.9992	1.31049	0.655244	+	0.755417i	$0.272566\pi$
$132$	−1.52918	−0.133098
$133$	1.76185	0.152772
$134$	1.90832	0.164854
$135$	2.73568	0.235450
$136$	0.676939	0.0580471
$137$	−12.7908	−1.09280	−0.546398	−	0.837526i	$-0.684001\pi$
$137$	−12.7908	−1.09280	−0.546398	+	0.837526i	$0.684001\pi$
$138$	−0.306170	−0.0260629
$139$	9.41450	0.798528	0.399264	−	0.916836i	$-0.369266\pi$
$139$	9.41450	0.798528	0.399264	+	0.916836i	$0.369266\pi$
$140$	5.39187	0.455696
$141$	4.25776	0.358568
$142$	−0.829191	−0.0695842
$143$	−0.775866	−0.0648812
$144$	3.82648	0.318873
$145$	8.80443	0.731168
$146$	−1.85464	−0.153491
$147$	−1.00000	−0.0824786
$148$	16.5844	1.36323
$149$	−15.9080	−1.30324	−0.651619	−	0.758547i	$-0.725910\pi$
$149$	−15.9080	−1.30324	−0.651619	+	0.758547i	$0.725910\pi$
$150$	0.423450	0.0345745
$151$	−10.7720	−0.876616	−0.438308	−	0.898825i	$-0.644422\pi$
$151$	−10.7720	−0.876616	−0.438308	+	0.898825i	$0.644422\pi$
$152$	1.19266	0.0967378
$153$	1.00000	0.0808452
$154$	0.132265	0.0106582
$155$	−9.93070	−0.797653
$156$	1.97094	0.157801
$157$	−17.2868	−1.37964	−0.689820	−	0.723981i	$-0.742310\pi$
$157$	−17.2868	−1.37964	−0.689820	+	0.723981i	$0.742310\pi$
$158$	1.17717	0.0936509
$159$	−5.99347	−0.475313
$160$	5.48830	0.433888
$161$	−1.79600	−0.141545
$162$	−0.170473	−0.0133936
$163$	12.8451	1.00611	0.503053	−	0.864256i	$-0.332210\pi$
$163$	12.8451	1.00611	0.503053	+	0.864256i	$0.332210\pi$
$164$	18.2555	1.42551
$165$	−2.12252	−0.165238
$166$	2.36652	0.183677
$167$	14.7155	1.13872	0.569361	−	0.822087i	$-0.307191\pi$
$167$	14.7155	1.13872	0.569361	+	0.822087i	$0.307191\pi$
$168$	−0.676939	−0.0522270
$169$	1.00000	0.0769231
$170$	0.466361	0.0357683
$171$	1.76185	0.134732
$172$	−7.02476	−0.535633
$173$	−11.9262	−0.906732	−0.453366	−	0.891324i	$-0.649777\pi$
$173$	−11.9262	−0.906732	−0.453366	+	0.891324i	$0.649777\pi$
$174$	−0.548646	−0.0415927
$175$	2.48397	0.187770
$176$	−2.96883	−0.223784
$177$	5.80984	0.436694
$178$	0.771958	0.0578607
$179$	5.56990	0.416314	0.208157	−	0.978095i	$-0.433254\pi$
$179$	5.56990	0.416314	0.208157	+	0.978095i	$0.433254\pi$
$180$	5.39187	0.401886
$181$	9.73598	0.723670	0.361835	−	0.932242i	$-0.382150\pi$
$181$	9.73598	0.723670	0.361835	+	0.932242i	$0.382150\pi$
$182$	−0.170473	−0.0126363
$183$	0.903539	0.0667915
$184$	−1.21578	−0.0896287
$185$	23.0193	1.69241
$186$	0.618829	0.0453747
$187$	−0.775866	−0.0567370
$188$	8.39179	0.612034
$189$	−1.00000	−0.0727393
$190$	0.821658	0.0596093
$191$	−18.2857	−1.32311	−0.661554	−	0.749898i	$-0.730103\pi$
$191$	−18.2857	−1.32311	−0.661554	+	0.749898i	$0.730103\pi$
$192$	7.31095	0.527623
$193$	−4.74306	−0.341413	−0.170707	−	0.985322i	$-0.554605\pi$
$193$	−4.74306	−0.341413	−0.170707	+	0.985322i	$0.554605\pi$
$194$	−1.61729	−0.116115
$195$	2.73568	0.195906
$196$	−1.97094	−0.140781
$197$	21.6355	1.54146	0.770732	−	0.637160i	$-0.219891\pi$
$197$	21.6355	1.54146	0.770732	+	0.637160i	$0.219891\pi$
$198$	0.132265	0.00939963
$199$	23.0437	1.63353	0.816763	−	0.576973i	$-0.195766\pi$
$199$	23.0437	1.63353	0.816763	+	0.576973i	$0.195766\pi$
$200$	1.68149	0.118900
$201$	11.1942	0.789580
$202$	0.0414461	0.00291614
$203$	−3.21837	−0.225885
$204$	1.97094	0.137993
$205$	25.3388	1.76974
$206$	1.11601	0.0777559
$207$	−1.79600	−0.124831
$208$	3.82648	0.265318
$209$	−1.36696	−0.0945545
$210$	−0.466361	−0.0321820
$211$	−6.48386	−0.446368	−0.223184	−	0.974776i	$-0.571645\pi$
$211$	−6.48386	−0.446368	−0.223184	+	0.974776i	$0.571645\pi$
$212$	−11.8128	−0.811304
$213$	−4.86405	−0.333279
$214$	0.409184	0.0279712
$215$	−9.75043	−0.664974
$216$	−0.676939	−0.0460599
$217$	3.63006	0.246425
$218$	−2.52728	−0.171169
$219$	−10.8793	−0.735158
$220$	−4.18337	−0.282043
$221$	1.00000	0.0672673
$222$	−1.43444	−0.0962734
$223$	−19.0016	−1.27244	−0.636219	−	0.771508i	$-0.719503\pi$
$223$	−19.0016	−1.27244	−0.636219	+	0.771508i	$0.719503\pi$
$224$	−2.00619	−0.134044
$225$	2.48397	0.165598
$226$	−3.27848	−0.218081
$227$	−12.7877	−0.848748	−0.424374	−	0.905487i	$-0.639506\pi$
$227$	−12.7877	−0.848748	−0.424374	+	0.905487i	$0.639506\pi$
$228$	3.47250	0.229972
$229$	20.0938	1.32783	0.663917	−	0.747806i	$-0.268893\pi$
$229$	20.0938	1.32783	0.663917	+	0.747806i	$0.268893\pi$
$230$	−0.837585	−0.0552287
$231$	0.775866	0.0510483
$232$	−2.17864	−0.143035
$233$	−15.9007	−1.04169	−0.520845	−	0.853651i	$-0.674383\pi$
$233$	−15.9007	−1.04169	−0.520845	+	0.853651i	$0.674383\pi$
$234$	−0.170473	−0.0111442
$235$	11.6479	0.759825
$236$	11.4508	0.745386
$237$	6.90532	0.448549
$238$	−0.170473	−0.0110501
$239$	18.2176	1.17840	0.589201	−	0.807987i	$-0.299443\pi$
$239$	18.2176	1.17840	0.589201	+	0.807987i	$0.299443\pi$
$240$	10.4680	0.675709
$241$	12.1286	0.781275	0.390637	−	0.920545i	$-0.372255\pi$
$241$	12.1286	0.781275	0.390637	+	0.920545i	$0.372255\pi$
$242$	1.77259	0.113946
$243$	−1.00000	−0.0641500
$244$	1.78082	0.114005
$245$	−2.73568	−0.174776
$246$	−1.57898	−0.100672
$247$	1.76185	0.112104
$248$	2.45733	0.156041
$249$	13.8820	0.879738
$250$	−1.17338	−0.0742111
$251$	2.27569	0.143640	0.0718202	−	0.997418i	$-0.477119\pi$
$251$	2.27569	0.143640	0.0718202	+	0.997418i	$0.477119\pi$
$252$	−1.97094	−0.124157
$253$	1.39346	0.0876059
$254$	−2.83196	−0.177693
$255$	2.73568	0.171315
$256$	13.7254	0.857840
$257$	6.42541	0.400806	0.200403	−	0.979714i	$-0.435775\pi$
$257$	6.42541	0.400806	0.200403	+	0.979714i	$0.435775\pi$
$258$	0.607595	0.0378272
$259$	−8.41446	−0.522849
$260$	5.39187	0.334389
$261$	−3.21837	−0.199212
$262$	−2.55697	−0.157970
$263$	−2.80471	−0.172946	−0.0864729	−	0.996254i	$-0.527560\pi$
$263$	−2.80471	−0.172946	−0.0864729	+	0.996254i	$0.527560\pi$
$264$	0.525214	0.0323247
$265$	−16.3962	−1.00721
$266$	−0.300348	−0.0184155
$267$	4.52832	0.277129
$268$	22.0631	1.34772
$269$	27.4350	1.67274	0.836369	−	0.548166i	$-0.184674\pi$
$269$	27.4350	1.67274	0.836369	+	0.548166i	$0.184674\pi$
$270$	−0.466361	−0.0283818
$271$	16.4693	1.00044	0.500220	−	0.865898i	$-0.333253\pi$
$271$	16.4693	1.00044	0.500220	+	0.865898i	$0.333253\pi$
$272$	3.82648	0.232014
$273$	−1.00000	−0.0605228
$274$	2.18050	0.131729
$275$	−1.92723	−0.116216
$276$	−3.53981	−0.213071
$277$	−10.3769	−0.623486	−0.311743	−	0.950166i	$-0.600913\pi$
$277$	−10.3769	−0.623486	−0.311743	+	0.950166i	$0.600913\pi$
$278$	−1.60492	−0.0962568
$279$	3.63006	0.217326
$280$	−1.85189	−0.110672
$281$	20.8448	1.24349	0.621747	−	0.783218i	$-0.286423\pi$
$281$	20.8448	1.24349	0.621747	+	0.783218i	$0.286423\pi$
$282$	−0.725835	−0.0432228
$283$	−2.24788	−0.133623	−0.0668113	−	0.997766i	$-0.521283\pi$
$283$	−2.24788	−0.133623	−0.0668113	+	0.997766i	$0.521283\pi$
$284$	−9.58675	−0.568869
$285$	4.81986	0.285504
$286$	0.132265	0.00782096
$287$	−9.26232	−0.546738
$288$	−2.00619	−0.118216
$289$	1.00000	0.0588235
$290$	−1.50092	−0.0881371
$291$	−9.48708	−0.556143
$292$	−21.4425	−1.25483
$293$	−5.34885	−0.312483	−0.156241	−	0.987719i	$-0.549938\pi$
$293$	−5.34885	−0.312483	−0.156241	+	0.987719i	$0.549938\pi$
$294$	0.170473	0.00994221
$295$	15.8939	0.925378
$296$	−5.69608	−0.331078
$297$	0.775866	0.0450203
$298$	2.71190	0.157096
$299$	−1.79600	−0.103865
$300$	4.89575	0.282656
$301$	3.56417	0.205435
$302$	1.83635	0.105670
$303$	0.243124	0.0139671
$304$	6.74167	0.386661
$305$	2.47180	0.141535
$306$	−0.170473	−0.00974531
$307$	26.4875	1.51172	0.755861	−	0.654732i	$-0.227218\pi$
$307$	26.4875	1.51172	0.755861	+	0.654732i	$0.227218\pi$
$308$	1.52918	0.0871334
$309$	6.54652	0.372419
$310$	1.69292	0.0961514
$311$	4.45223	0.252463	0.126231	−	0.992001i	$-0.459712\pi$
$311$	4.45223	0.252463	0.126231	+	0.992001i	$0.459712\pi$
$312$	−0.676939	−0.0383241
$313$	10.6894	0.604199	0.302099	−	0.953276i	$-0.402313\pi$
$313$	10.6894	0.604199	0.302099	+	0.953276i	$0.402313\pi$
$314$	2.94694	0.166306
$315$	−2.73568	−0.154138
$316$	13.6100	0.765620
$317$	−26.3194	−1.47824	−0.739121	−	0.673572i	$-0.764759\pi$
$317$	−26.3194	−1.47824	−0.739121	+	0.673572i	$0.764759\pi$
$318$	1.02173	0.0572956
$319$	2.49702	0.139806
$320$	20.0005	1.11806
$321$	2.40028	0.133971
$322$	0.306170	0.0170622
$323$	1.76185	0.0980319
$324$	−1.97094	−0.109497
$325$	2.48397	0.137786
$326$	−2.18975	−0.121279
$327$	−14.8251	−0.819829
$328$	−6.27003	−0.346205
$329$	−4.25776	−0.234738
$330$	0.361834	0.0199183
$331$	−24.5635	−1.35013	−0.675065	−	0.737758i	$-0.735885\pi$
$331$	−24.5635	−1.35013	−0.675065	+	0.737758i	$0.735885\pi$
$332$	27.3606	1.50161
$333$	−8.41446	−0.461110
$334$	−2.50861	−0.137265
$335$	30.6239	1.67316
$336$	−3.82648	−0.208751
$337$	19.0484	1.03763	0.518815	−	0.854886i	$-0.326373\pi$
$337$	19.0484	1.03763	0.518815	+	0.854886i	$0.326373\pi$
$338$	−0.170473	−0.00927253
$339$	−19.2316	−1.04452
$340$	5.39187	0.292415
$341$	−2.81644	−0.152519
$342$	−0.300348	−0.0162410
$343$	1.00000	0.0539949
$344$	2.41272	0.130085
$345$	−4.91329	−0.264523
$346$	2.03310	0.109300
$347$	0.386451	0.0207458	0.0103729	−	0.999946i	$-0.496698\pi$
$347$	0.386451	0.0207458	0.0103729	+	0.999946i	$0.496698\pi$
$348$	−6.34320	−0.340031
$349$	8.57490	0.459004	0.229502	−	0.973308i	$-0.426290\pi$
$349$	8.57490	0.459004	0.229502	+	0.973308i	$0.426290\pi$
$350$	−0.423450	−0.0226344
$351$	−1.00000	−0.0533761
$352$	1.55654	0.0829636
$353$	24.3063	1.29369	0.646846	−	0.762620i	$-0.276088\pi$
$353$	24.3063	1.29369	0.646846	+	0.762620i	$0.276088\pi$
$354$	−0.990422	−0.0526404
$355$	−13.3065	−0.706236
$356$	8.92505	0.473027
$357$	−1.00000	−0.0529256
$358$	−0.949519	−0.0501837
$359$	6.05032	0.319324	0.159662	−	0.987172i	$-0.448960\pi$
$359$	6.05032	0.319324	0.159662	+	0.987172i	$0.448960\pi$
$360$	−1.85189	−0.0976033
$361$	−15.8959	−0.836626
$362$	−1.65973	−0.0872332
$363$	10.3980	0.545755
$364$	−1.97094	−0.103305
$365$	−29.7625	−1.55784
$366$	−0.154029	−0.00805124
$367$	18.8790	0.985474	0.492737	−	0.870178i	$-0.335996\pi$
$367$	18.8790	0.985474	0.492737	+	0.870178i	$0.335996\pi$
$368$	−6.87236	−0.358246
$369$	−9.26232	−0.482177
$370$	−3.92418	−0.204008
$371$	5.99347	0.311165
$372$	7.15463	0.370950
$373$	8.65124	0.447944	0.223972	−	0.974596i	$-0.428098\pi$
$373$	8.65124	0.447944	0.223972	+	0.974596i	$0.428098\pi$
$374$	0.132265	0.00683923
$375$	−6.88307	−0.355440
$376$	−2.88225	−0.148640
$377$	−3.21837	−0.165754
$378$	0.170473	0.00876820
$379$	−34.7156	−1.78322	−0.891610	−	0.452805i	$-0.850424\pi$
$379$	−34.7156	−1.78322	−0.891610	+	0.452805i	$0.850424\pi$
$380$	9.49965	0.487322
$381$	−16.6123	−0.851076
$382$	3.11723	0.159491
$383$	6.55232	0.334808	0.167404	−	0.985888i	$-0.446462\pi$
$383$	6.55232	0.334808	0.167404	+	0.985888i	$0.446462\pi$
$384$	−5.25870	−0.268357
$385$	2.12252	0.108174
$386$	0.808565	0.0411549
$387$	3.56417	0.181177
$388$	−18.6985	−0.949270
$389$	−0.754723	−0.0382660	−0.0191330	−	0.999817i	$-0.506091\pi$
$389$	−0.754723	−0.0382660	−0.0191330	+	0.999817i	$0.506091\pi$
$390$	−0.466361	−0.0236151
$391$	−1.79600	−0.0908277
$392$	0.676939	0.0341906
$393$	−14.9992	−0.756611
$394$	−3.68827	−0.185812
$395$	18.8908	0.950498
$396$	1.52918	0.0768444
$397$	12.9293	0.648903	0.324452	−	0.945902i	$-0.394820\pi$
$397$	12.9293	0.648903	0.324452	+	0.945902i	$0.394820\pi$
$398$	−3.92834	−0.196910
$399$	−1.76185	−0.0882027
$400$	9.50484	0.475242
$401$	−3.67669	−0.183605	−0.0918025	−	0.995777i	$-0.529263\pi$
$401$	−3.67669	−0.183605	−0.0918025	+	0.995777i	$0.529263\pi$
$402$	−1.90832	−0.0951782
$403$	3.63006	0.180826
$404$	0.479182	0.0238402
$405$	−2.73568	−0.135937
$406$	0.548646	0.0272288
$407$	6.52850	0.323606
$408$	−0.676939	−0.0335135
$409$	25.4734	1.25958	0.629789	−	0.776766i	$-0.283141\pi$
$409$	25.4734	1.25958	0.629789	+	0.776766i	$0.283141\pi$
$410$	−4.31959	−0.213329
$411$	12.7908	0.630926
$412$	12.9028	0.635675
$413$	−5.80984	−0.285883
$414$	0.306170	0.0150474
$415$	37.9769	1.86421
$416$	−2.00619	−0.0983616
$417$	−9.41450	−0.461030
$418$	0.233030	0.0113979
$419$	20.0637	0.980175	0.490087	−	0.871673i	$-0.336965\pi$
$419$	20.0637	0.980175	0.490087	+	0.871673i	$0.336965\pi$
$420$	−5.39187	−0.263096
$421$	−34.0249	−1.65827	−0.829137	−	0.559046i	$-0.811168\pi$
$421$	−34.0249	−1.65827	−0.829137	+	0.559046i	$0.811168\pi$
$422$	1.10533	0.0538064
$423$	−4.25776	−0.207019
$424$	4.05721	0.197036
$425$	2.48397	0.120490
$426$	0.829191	0.0401744
$427$	−0.903539	−0.0437253
$428$	4.73080	0.228672
$429$	0.775866	0.0374592
$430$	1.66219	0.0801579
$431$	−25.3249	−1.21986	−0.609930	−	0.792455i	$-0.708802\pi$
$431$	−25.3249	−1.21986	−0.609930	+	0.792455i	$0.708802\pi$
$432$	−3.82648	−0.184101
$433$	10.7097	0.514674	0.257337	−	0.966322i	$-0.417155\pi$
$433$	10.7097	0.514674	0.257337	+	0.966322i	$0.417155\pi$
$434$	−0.618829	−0.0297047
$435$	−8.80443	−0.422140
$436$	−29.2193	−1.39935
$437$	−3.16428	−0.151368
$438$	1.85464	0.0886180
$439$	24.2013	1.15507	0.577533	−	0.816368i	$-0.304016\pi$
$439$	24.2013	1.15507	0.577533	+	0.816368i	$0.304016\pi$
$440$	1.43682	0.0684977
$441$	1.00000	0.0476190
$442$	−0.170473	−0.00810859
$443$	21.1033	1.00265	0.501324	−	0.865260i	$-0.332847\pi$
$443$	21.1033	1.00265	0.501324	+	0.865260i	$0.332847\pi$
$444$	−16.5844	−0.787060
$445$	12.3881	0.587250
$446$	3.23926	0.153383
$447$	15.9080	0.752424
$448$	−7.31095	−0.345410
$449$	25.8076	1.21794	0.608968	−	0.793195i	$-0.291584\pi$
$449$	25.8076	1.21794	0.608968	+	0.793195i	$0.291584\pi$
$450$	−0.423450	−0.0199616
$451$	7.18633	0.338391
$452$	−37.9043	−1.78287
$453$	10.7720	0.506115
$454$	2.17996	0.102311
$455$	−2.73568	−0.128251
$456$	−1.19266	−0.0558516
$457$	23.8538	1.11584	0.557918	−	0.829896i	$-0.311600\pi$
$457$	23.8538	1.11584	0.557918	+	0.829896i	$0.311600\pi$
$458$	−3.42545	−0.160061
$459$	−1.00000	−0.0466760
$460$	−9.68380	−0.451509
$461$	−15.6753	−0.730073	−0.365036	−	0.930993i	$-0.618943\pi$
$461$	−15.6753	−0.730073	−0.365036	+	0.930993i	$0.618943\pi$
$462$	−0.132265	−0.00615350
$463$	26.7945	1.24524	0.622622	−	0.782522i	$-0.286067\pi$
$463$	26.7945	1.24524	0.622622	+	0.782522i	$0.286067\pi$
$464$	−12.3150	−0.571710
$465$	9.93070	0.460525
$466$	2.71065	0.125568
$467$	−17.4715	−0.808483	−0.404241	−	0.914652i	$-0.632464\pi$
$467$	−17.4715	−0.808483	−0.404241	+	0.914652i	$0.632464\pi$
$468$	−1.97094	−0.0911067
$469$	−11.1942	−0.516902
$470$	−1.98565	−0.0915914
$471$	17.2868	0.796535
$472$	−3.93291	−0.181027
$473$	−2.76532	−0.127149
$474$	−1.17717	−0.0540694
$475$	4.37637	0.200802
$476$	−1.97094	−0.0903378
$477$	5.99347	0.274422
$478$	−3.10562	−0.142048
$479$	−33.6546	−1.53772	−0.768859	−	0.639418i	$-0.779175\pi$
$479$	−33.6546	−1.53772	−0.768859	+	0.639418i	$0.779175\pi$
$480$	−5.48830	−0.250506
$481$	−8.41446	−0.383666
$482$	−2.06761	−0.0941771
$483$	1.79600	0.0817209
$484$	20.4939	0.931540
$485$	−25.9537	−1.17849
$486$	0.170473	0.00773283
$487$	−4.21655	−0.191070	−0.0955350	−	0.995426i	$-0.530456\pi$
$487$	−4.21655	−0.191070	−0.0955350	+	0.995426i	$0.530456\pi$
$488$	−0.611641	−0.0276877
$489$	−12.8451	−0.580876
$490$	0.466361	0.0210680
$491$	−0.490506	−0.0221362	−0.0110681	−	0.999939i	$-0.503523\pi$
$491$	−0.490506	−0.0221362	−0.0110681	+	0.999939i	$0.503523\pi$
$492$	−18.2555	−0.823020
$493$	−3.21837	−0.144948
$494$	−0.300348	−0.0135133
$495$	2.12252	0.0954004
$496$	13.8903	0.623695
$497$	4.86405	0.218183
$498$	−2.36652	−0.106046
$499$	41.2564	1.84689	0.923446	−	0.383728i	$-0.125360\pi$
$499$	41.2564	1.84689	0.923446	+	0.383728i	$0.125360\pi$
$500$	−13.5661	−0.606695
$501$	−14.7155	−0.657442
$502$	−0.387945	−0.0173148
$503$	32.6322	1.45500	0.727498	−	0.686109i	$-0.240683\pi$
$503$	32.6322	1.45500	0.727498	+	0.686109i	$0.240683\pi$
$504$	0.676939	0.0301533
$505$	0.665110	0.0295970
$506$	−0.237547	−0.0105603
$507$	−1.00000	−0.0444116
$508$	−32.7419	−1.45269
$509$	−13.0185	−0.577036	−0.288518	−	0.957474i	$-0.593163\pi$
$509$	−13.0185	−0.577036	−0.288518	+	0.957474i	$0.593163\pi$
$510$	−0.466361	−0.0206508
$511$	10.8793	0.481274
$512$	−12.8572	−0.568215
$513$	−1.76185	−0.0777875
$514$	−1.09536	−0.0483143
$515$	17.9092	0.789175
$516$	7.02476	0.309248
$517$	3.30345	0.145286
$518$	1.43444	0.0630257
$519$	11.9262	0.523502
$520$	−1.85189	−0.0812108
$521$	−10.4686	−0.458636	−0.229318	−	0.973352i	$-0.573650\pi$
$521$	−10.4686	−0.458636	−0.229318	+	0.973352i	$0.573650\pi$
$522$	0.548646	0.0240136
$523$	9.95612	0.435351	0.217675	−	0.976021i	$-0.430153\pi$
$523$	9.95612	0.435351	0.217675	+	0.976021i	$0.430153\pi$
$524$	−29.5626	−1.29145
$525$	−2.48397	−0.108409
$526$	0.478128	0.0208474
$527$	3.63006	0.158128
$528$	2.96883	0.129202
$529$	−19.7744	−0.859756
$530$	2.79512	0.121412
$531$	−5.80984	−0.252126
$532$	−3.47250	−0.150552
$533$	−9.26232	−0.401196
$534$	−0.771958	−0.0334059
$535$	6.56640	0.283890
$536$	−7.57781	−0.327312
$537$	−5.56990	−0.240359
$538$	−4.67693	−0.201637
$539$	−0.775866	−0.0334189
$540$	−5.39187	−0.232029
$541$	−44.4177	−1.90967	−0.954833	−	0.297142i	$-0.903967\pi$
$541$	−44.4177	−1.90967	−0.954833	+	0.297142i	$0.903967\pi$
$542$	−2.80758	−0.120596
$543$	−9.73598	−0.417811
$544$	−2.00619	−0.0860147
$545$	−40.5567	−1.73726
$546$	0.170473	0.00729558
$547$	−1.80291	−0.0770868	−0.0385434	−	0.999257i	$-0.512272\pi$
$547$	−1.80291	−0.0770868	−0.0385434	+	0.999257i	$0.512272\pi$
$548$	25.2100	1.07692
$549$	−0.903539	−0.0385621
$550$	0.328541	0.0140090
$551$	−5.67027	−0.241562
$552$	1.21578	0.0517472
$553$	−6.90532	−0.293644
$554$	1.76898	0.0751568
$555$	−23.0193	−0.977115
$556$	−18.5554	−0.786925
$557$	27.6337	1.17088	0.585439	−	0.810717i	$-0.300922\pi$
$557$	27.6337	1.17088	0.585439	+	0.810717i	$0.300922\pi$
$558$	−0.618829	−0.0261971
$559$	3.56417	0.150748
$560$	−10.4680	−0.442355
$561$	0.775866	0.0327571
$562$	−3.55347	−0.149894
$563$	−15.2944	−0.644582	−0.322291	−	0.946641i	$-0.604453\pi$
$563$	−15.2944	−0.644582	−0.322291	+	0.946641i	$0.604453\pi$
$564$	−8.39179	−0.353358
$565$	−52.6116	−2.21339
$566$	0.383204	0.0161072
$567$	1.00000	0.0419961
$568$	3.29267	0.138157
$569$	28.2205	1.18307	0.591533	−	0.806281i	$-0.298523\pi$
$569$	28.2205	1.18307	0.591533	+	0.806281i	$0.298523\pi$
$570$	−0.821658	−0.0344154
$571$	−18.2511	−0.763783	−0.381891	−	0.924207i	$-0.624727\pi$
$571$	−18.2511	−0.763783	−0.381891	+	0.924207i	$0.624727\pi$
$572$	1.52918	0.0639384
$573$	18.2857	0.763896
$574$	1.57898	0.0659053
$575$	−4.46121	−0.186045
$576$	−7.31095	−0.304623
$577$	−2.45339	−0.102136	−0.0510681	−	0.998695i	$-0.516263\pi$
$577$	−2.45339	−0.102136	−0.0510681	+	0.998695i	$0.516263\pi$
$578$	−0.170473	−0.00709076
$579$	4.74306	0.197115
$580$	−17.3530	−0.720544
$581$	−13.8820	−0.575924
$582$	1.61729	0.0670390
$583$	−4.65013	−0.192589
$584$	7.36465	0.304752
$585$	−2.73568	−0.113107
$586$	0.911836	0.0376676
$587$	−19.7928	−0.816938	−0.408469	−	0.912772i	$-0.633937\pi$
$587$	−19.7928	−0.816938	−0.408469	+	0.912772i	$0.633937\pi$
$588$	1.97094	0.0812801
$589$	6.39562	0.263527
$590$	−2.70948	−0.111548
$591$	−21.6355	−0.889964
$592$	−32.1978	−1.32332
$593$	−28.2929	−1.16185	−0.580925	−	0.813957i	$-0.697309\pi$
$593$	−28.2929	−1.16185	−0.580925	+	0.813957i	$0.697309\pi$
$594$	−0.132265	−0.00542688
$595$	−2.73568	−0.112152
$596$	31.3538	1.28430
$597$	−23.0437	−0.943117
$598$	0.306170	0.0125202
$599$	−2.89516	−0.118293	−0.0591466	−	0.998249i	$-0.518838\pi$
$599$	−2.89516	−0.118293	−0.0591466	+	0.998249i	$0.518838\pi$
$600$	−1.68149	−0.0686467
$601$	−19.7992	−0.807628	−0.403814	−	0.914841i	$-0.632316\pi$
$601$	−19.7992	−0.807628	−0.403814	+	0.914841i	$0.632316\pi$
$602$	−0.607595	−0.0247637
$603$	−11.1942	−0.455864
$604$	21.2310	0.863878
$605$	28.4457	1.15648
$606$	−0.0414461	−0.00168363
$607$	36.7340	1.49099	0.745493	−	0.666513i	$-0.232214\pi$
$607$	36.7340	1.49099	0.745493	+	0.666513i	$0.232214\pi$
$608$	−3.53460	−0.143347
$609$	3.21837	0.130415
$610$	−0.421375	−0.0170610
$611$	−4.25776	−0.172251
$612$	−1.97094	−0.0796705
$613$	19.6643	0.794234	0.397117	−	0.917768i	$-0.370011\pi$
$613$	19.6643	0.794234	0.397117	+	0.917768i	$0.370011\pi$
$614$	−4.51542	−0.182227
$615$	−25.3388	−1.02176
$616$	−0.525214	−0.0211615
$617$	−40.3177	−1.62313	−0.811566	−	0.584261i	$-0.801384\pi$
$617$	−40.3177	−1.62313	−0.811566	+	0.584261i	$0.801384\pi$
$618$	−1.11601	−0.0448924
$619$	28.4116	1.14196	0.570980	−	0.820964i	$-0.306563\pi$
$619$	28.4116	1.14196	0.570980	+	0.820964i	$0.306563\pi$
$620$	19.5728	0.786063
$621$	1.79600	0.0720710
$622$	−0.758986	−0.0304326
$623$	−4.52832	−0.181423
$624$	−3.82648	−0.153182
$625$	−31.2497	−1.24999
$626$	−1.82225	−0.0728318
$627$	1.36696	0.0545911
$628$	34.0713	1.35959
$629$	−8.41446	−0.335507
$630$	0.466361	0.0185803
$631$	15.6816	0.624274	0.312137	−	0.950037i	$-0.398955\pi$
$631$	15.6816	0.624274	0.312137	+	0.950037i	$0.398955\pi$
$632$	−4.67448	−0.185941
$633$	6.48386	0.257710
$634$	4.48675	0.178192
$635$	−45.4461	−1.80347
$636$	11.8128	0.468407
$637$	1.00000	0.0396214
$638$	−0.425676	−0.0168527
$639$	4.86405	0.192419
$640$	−14.3862	−0.568663
$641$	38.0700	1.50367	0.751837	−	0.659349i	$-0.229168\pi$
$641$	38.0700	1.50367	0.751837	+	0.659349i	$0.229168\pi$
$642$	−0.409184	−0.0161492
$643$	6.54407	0.258073	0.129036	−	0.991640i	$-0.458812\pi$
$643$	6.54407	0.258073	0.129036	+	0.991640i	$0.458812\pi$
$644$	3.53981	0.139488
$645$	9.75043	0.383923
$646$	−0.300348	−0.0118170
$647$	2.22304	0.0873966	0.0436983	−	0.999045i	$-0.486086\pi$
$647$	2.22304	0.0873966	0.0436983	+	0.999045i	$0.486086\pi$
$648$	0.676939	0.0265927
$649$	4.50766	0.176941
$650$	−0.423450	−0.0166091
$651$	−3.63006	−0.142273
$652$	−25.3169	−0.991487
$653$	−26.5127	−1.03752	−0.518761	−	0.854919i	$-0.673606\pi$
$653$	−26.5127	−1.03752	−0.518761	+	0.854919i	$0.673606\pi$
$654$	2.52728	0.0988245
$655$	−41.0331	−1.60330
$656$	−35.4421	−1.38378
$657$	10.8793	0.424444
$658$	0.725835	0.0282960
$659$	11.3776	0.443207	0.221603	−	0.975137i	$-0.428871\pi$
$659$	11.3776	0.443207	0.221603	+	0.975137i	$0.428871\pi$
$660$	4.18337	0.162837
$661$	15.6479	0.608631	0.304316	−	0.952571i	$-0.401572\pi$
$661$	15.6479	0.608631	0.304316	+	0.952571i	$0.401572\pi$
$662$	4.18742	0.162749
$663$	−1.00000	−0.0388368
$664$	−9.39730	−0.364686
$665$	−4.81986	−0.186906
$666$	1.43444	0.0555835
$667$	5.78019	0.223810
$668$	−29.0034	−1.12218
$669$	19.0016	0.734642
$670$	−5.22055	−0.201688
$671$	0.701025	0.0270628
$672$	2.00619	0.0773905
$673$	−10.5940	−0.408369	−0.204185	−	0.978932i	$-0.565454\pi$
$673$	−10.5940	−0.408369	−0.204185	+	0.978932i	$0.565454\pi$
$674$	−3.24724	−0.125079
$675$	−2.48397	−0.0956079
$676$	−1.97094	−0.0758053
$677$	8.74127	0.335954	0.167977	−	0.985791i	$-0.446276\pi$
$677$	8.74127	0.335954	0.167977	+	0.985791i	$0.446276\pi$
$678$	3.27848	0.125909
$679$	9.48708	0.364081
$680$	−1.85189	−0.0710168
$681$	12.7877	0.490025
$682$	0.480128	0.0183851
$683$	16.9435	0.648326	0.324163	−	0.946001i	$-0.394917\pi$
$683$	16.9435	0.648326	0.324163	+	0.946001i	$0.394917\pi$
$684$	−3.47250	−0.132774
$685$	34.9917	1.33696
$686$	−0.170473	−0.00650870
$687$	−20.0938	−0.766626
$688$	13.6382	0.519952
$689$	5.99347	0.228333
$690$	0.837585	0.0318863
$691$	−6.74911	−0.256748	−0.128374	−	0.991726i	$-0.540976\pi$
$691$	−6.74911	−0.256748	−0.128374	+	0.991726i	$0.540976\pi$
$692$	23.5058	0.893557
$693$	−0.775866	−0.0294727
$694$	−0.0658797	−0.00250076
$695$	−25.7551	−0.976947
$696$	2.17864	0.0825811
$697$	−9.26232	−0.350836
$698$	−1.46179	−0.0553296
$699$	15.9007	0.601421
$700$	−4.89575	−0.185042
$701$	0.693631	0.0261981	0.0130990	−	0.999914i	$-0.495830\pi$
$701$	0.693631	0.0261981	0.0130990	+	0.999914i	$0.495830\pi$
$702$	0.170473	0.00643410
$703$	−14.8250	−0.559136
$704$	5.67232	0.213784
$705$	−11.6479	−0.438685
$706$	−4.14357	−0.155945
$707$	−0.243124	−0.00914362
$708$	−11.4508	−0.430349
$709$	43.9239	1.64960	0.824799	−	0.565426i	$-0.191288\pi$
$709$	43.9239	1.64960	0.824799	+	0.565426i	$0.191288\pi$
$710$	2.26841	0.0851317
$711$	−6.90532	−0.258970
$712$	−3.06540	−0.114881
$713$	−6.51959	−0.244161
$714$	0.170473	0.00637980
$715$	2.12252	0.0793779
$716$	−10.9779	−0.410265
$717$	−18.2176	−0.680350
$718$	−1.03142	−0.0384922
$719$	−23.3011	−0.868983	−0.434491	−	0.900676i	$-0.643072\pi$
$719$	−23.3011	−0.868983	−0.434491	+	0.900676i	$0.643072\pi$
$720$	−10.4680	−0.390121
$721$	−6.54652	−0.243805
$722$	2.70983	0.100849
$723$	−12.1286	−0.451069
$724$	−19.1890	−0.713155
$725$	−7.99431	−0.296901
$726$	−1.77259	−0.0657869
$727$	23.8591	0.884886	0.442443	−	0.896797i	$-0.354112\pi$
$727$	23.8591	0.884886	0.442443	+	0.896797i	$0.354112\pi$
$728$	0.676939	0.0250890
$729$	1.00000	0.0370370
$730$	5.07370	0.187786
$731$	3.56417	0.131825
$732$	−1.78082	−0.0658210
$733$	28.5586	1.05484	0.527418	−	0.849606i	$-0.323160\pi$
$733$	28.5586	1.05484	0.527418	+	0.849606i	$0.323160\pi$
$734$	−3.21836	−0.118792
$735$	2.73568	0.100907
$736$	3.60312	0.132813
$737$	8.68523	0.319924
$738$	1.57898	0.0581230
$739$	−26.2824	−0.966814	−0.483407	−	0.875396i	$-0.660601\pi$
$739$	−26.2824	−0.966814	−0.483407	+	0.875396i	$0.660601\pi$
$740$	−45.3697	−1.66782
$741$	−1.76185	−0.0647231
$742$	−1.02173	−0.0375088
$743$	23.4048	0.858638	0.429319	−	0.903153i	$-0.358754\pi$
$743$	23.4048	0.858638	0.429319	+	0.903153i	$0.358754\pi$
$744$	−2.45733	−0.0900901
$745$	43.5194	1.59443
$746$	−1.47481	−0.0539965
$747$	−13.8820	−0.507917
$748$	1.52918	0.0559125
$749$	−2.40028	−0.0877043
$750$	1.17338	0.0428458
$751$	−6.75881	−0.246632	−0.123316	−	0.992367i	$-0.539353\pi$
$751$	−6.75881	−0.246632	−0.123316	+	0.992367i	$0.539353\pi$
$752$	−16.2922	−0.594117
$753$	−2.27569	−0.0829308
$754$	0.548646	0.0199805
$755$	29.4689	1.07248
$756$	1.97094	0.0716824
$757$	8.84556	0.321497	0.160749	−	0.986995i	$-0.448609\pi$
$757$	8.84556	0.321497	0.160749	+	0.986995i	$0.448609\pi$
$758$	5.91808	0.214954
$759$	−1.39346	−0.0505793
$760$	−3.26275	−0.118352
$761$	−3.13107	−0.113501	−0.0567506	−	0.998388i	$-0.518074\pi$
$761$	−3.13107	−0.113501	−0.0567506	+	0.998388i	$0.518074\pi$
$762$	2.83196	0.102591
$763$	14.8251	0.536704
$764$	36.0400	1.30388
$765$	−2.73568	−0.0989089
$766$	−1.11700	−0.0403587
$767$	−5.80984	−0.209781
$768$	−13.7254	−0.495274
$769$	24.5064	0.883722	0.441861	−	0.897084i	$-0.354318\pi$
$769$	24.5064	0.883722	0.441861	+	0.897084i	$0.354318\pi$
$770$	−0.361834	−0.0130396
$771$	−6.42541	−0.231406
$772$	9.34828	0.336452
$773$	0.452347	0.0162698	0.00813490	−	0.999967i	$-0.497411\pi$
$773$	0.452347	0.0162698	0.00813490	+	0.999967i	$0.497411\pi$
$774$	−0.607595	−0.0218396
$775$	9.01695	0.323898
$776$	6.42218	0.230543
$777$	8.41446	0.301867
$778$	0.128660	0.00461269
$779$	−16.3188	−0.584682
$780$	−5.39187	−0.193060
$781$	−3.77385	−0.135039
$782$	0.306170	0.0109486
$783$	3.21837	0.115015
$784$	3.82648	0.136660
$785$	47.2913	1.68790
$786$	2.55697	0.0912040
$787$	35.0466	1.24927	0.624637	−	0.780915i	$-0.285247\pi$
$787$	35.0466	1.24927	0.624637	+	0.780915i	$0.285247\pi$
$788$	−42.6422	−1.51906
$789$	2.80471	0.0998503
$790$	−3.22037	−0.114576
$791$	19.2316	0.683798
$792$	−0.525214	−0.0186627
$793$	−0.903539	−0.0320856
$794$	−2.20410	−0.0782206
$795$	16.3962	0.581515
$796$	−45.4178	−1.60979
$797$	−16.0776	−0.569497	−0.284748	−	0.958602i	$-0.591910\pi$
$797$	−16.0776	−0.569497	−0.284748	+	0.958602i	$0.591910\pi$
$798$	0.300348	0.0106322
$799$	−4.25776	−0.150629
$800$	−4.98331	−0.176187
$801$	−4.52832	−0.160000
$802$	0.626777	0.0221323
$803$	−8.44092	−0.297874
$804$	−22.0631	−0.778107
$805$	4.91329	0.173171
$806$	−0.618829	−0.0217973
$807$	−27.4350	−0.965756
$808$	−0.164580	−0.00578991
$809$	4.50929	0.158538	0.0792690	−	0.996853i	$-0.474741\pi$
$809$	4.50929	0.158538	0.0792690	+	0.996853i	$0.474741\pi$
$810$	0.466361	0.0163863
$811$	−29.3537	−1.03075	−0.515375	−	0.856965i	$-0.672347\pi$
$811$	−29.3537	−1.03075	−0.515375	+	0.856965i	$0.672347\pi$
$812$	6.34320	0.222603
$813$	−16.4693	−0.577604
$814$	−1.11293	−0.0390083
$815$	−35.1401	−1.23091
$816$	−3.82648	−0.133954
$817$	6.27952	0.219693
$818$	−4.34253	−0.151833
$819$	1.00000	0.0349428
$820$	−49.9412	−1.74402
$821$	−48.3324	−1.68681	−0.843406	−	0.537276i	$-0.819453\pi$
$821$	−48.3324	−1.68681	−0.843406	+	0.537276i	$0.819453\pi$
$822$	−2.18050	−0.0760536
$823$	6.16600	0.214933	0.107467	−	0.994209i	$-0.465726\pi$
$823$	6.16600	0.214933	0.107467	+	0.994209i	$0.465726\pi$
$824$	−4.43160	−0.154382
$825$	1.92723	0.0670974
$826$	0.990422	0.0344612
$827$	−34.4049	−1.19638	−0.598188	−	0.801356i	$-0.704112\pi$
$827$	−34.4049	−1.19638	−0.598188	+	0.801356i	$0.704112\pi$
$828$	3.53981	0.123017
$829$	30.2380	1.05021	0.525104	−	0.851038i	$-0.324026\pi$
$829$	30.2380	1.05021	0.525104	+	0.851038i	$0.324026\pi$
$830$	−6.47404	−0.224717
$831$	10.3769	0.359970
$832$	−7.31095	−0.253462
$833$	1.00000	0.0346479
$834$	1.60492	0.0555739
$835$	−40.2571	−1.39315
$836$	2.69419	0.0931806
$837$	−3.63006	−0.125473
$838$	−3.42032	−0.118153
$839$	12.7957	0.441756	0.220878	−	0.975301i	$-0.429108\pi$
$839$	12.7957	0.441756	0.220878	+	0.975301i	$0.429108\pi$
$840$	1.85189	0.0638963
$841$	−18.6421	−0.642832
$842$	5.80034	0.199893
$843$	−20.8448	−0.717931
$844$	12.7793	0.439882
$845$	−2.73568	−0.0941104
$846$	0.725835	0.0249547
$847$	−10.3980	−0.357281
$848$	22.9339	0.787553
$849$	2.24788	0.0771470
$850$	−0.423450	−0.0145242
$851$	15.1124	0.518046
$852$	9.58675	0.328437
$853$	45.1324	1.54531	0.772653	−	0.634829i	$-0.218929\pi$
$853$	45.1324	1.54531	0.772653	+	0.634829i	$0.218929\pi$
$854$	0.154029	0.00527077
$855$	−4.81986	−0.164836
$856$	−1.62484	−0.0555360
$857$	−35.0561	−1.19749	−0.598746	−	0.800939i	$-0.704334\pi$
$857$	−35.0561	−1.19749	−0.598746	+	0.800939i	$0.704334\pi$
$858$	−0.132265	−0.00451544
$859$	7.86272	0.268273	0.134136	−	0.990963i	$-0.457174\pi$
$859$	7.86272	0.268273	0.134136	+	0.990963i	$0.457174\pi$
$860$	19.2175	0.655312
$861$	9.26232	0.315659
$862$	4.31723	0.147045
$863$	−1.95868	−0.0666743	−0.0333371	−	0.999444i	$-0.510614\pi$
$863$	−1.95868	−0.0666743	−0.0333371	+	0.999444i	$0.510614\pi$
$864$	2.00619	0.0682520
$865$	32.6263	1.10933
$866$	−1.82571	−0.0620402
$867$	−1.00000	−0.0339618
$868$	−7.15463	−0.242844
$869$	5.35761	0.181744
$870$	1.50092	0.0508860
$871$	−11.1942	−0.379302
$872$	10.0357	0.339851
$873$	9.48708	0.321089
$874$	0.539426	0.0182463
$875$	6.88307	0.232690
$876$	21.4425	0.724476
$877$	56.2995	1.90110	0.950550	−	0.310572i	$-0.100520\pi$
$877$	56.2995	1.90110	0.950550	+	0.310572i	$0.100520\pi$
$878$	−4.12568	−0.139235
$879$	5.34885	0.180412
$880$	8.12179	0.273786
$881$	52.4633	1.76753	0.883766	−	0.467929i	$-0.155000\pi$
$881$	52.4633	1.76753	0.883766	+	0.467929i	$0.155000\pi$
$882$	−0.170473	−0.00574014
$883$	−10.7356	−0.361281	−0.180640	−	0.983549i	$-0.557817\pi$
$883$	−10.7356	−0.361281	−0.180640	+	0.983549i	$0.557817\pi$
$884$	−1.97094	−0.0662898
$885$	−15.8939	−0.534267
$886$	−3.59755	−0.120862
$887$	33.2202	1.11543	0.557713	−	0.830034i	$-0.311679\pi$
$887$	33.2202	1.11543	0.557713	+	0.830034i	$0.311679\pi$
$888$	5.69608	0.191148
$889$	16.6123	0.557160
$890$	−2.11183	−0.0707888
$891$	−0.775866	−0.0259925
$892$	37.4509	1.25395
$893$	−7.50153	−0.251029
$894$	−2.71190	−0.0906994
$895$	−15.2375	−0.509333
$896$	5.25870	0.175681
$897$	1.79600	0.0599667
$898$	−4.39950	−0.146813
$899$	−11.6829	−0.389645
$900$	−4.89575	−0.163192
$901$	5.99347	0.199671
$902$	−1.22508	−0.0407906
$903$	−3.56417	−0.118608
$904$	13.0186	0.432993
$905$	−26.6346	−0.885363
$906$	−1.83635	−0.0610085
$907$	8.10886	0.269250	0.134625	−	0.990897i	$-0.457017\pi$
$907$	8.10886	0.269250	0.134625	+	0.990897i	$0.457017\pi$
$908$	25.2037	0.836415
$909$	−0.243124	−0.00806391
$910$	0.466361	0.0154597
$911$	56.2447	1.86347	0.931735	−	0.363140i	$-0.118295\pi$
$911$	56.2447	1.86347	0.931735	+	0.363140i	$0.118295\pi$
$912$	−6.74167	−0.223239
$913$	10.7706	0.356455
$914$	−4.06644	−0.134506
$915$	−2.47180	−0.0817151
$916$	−39.6036	−1.30854
$917$	14.9992	0.495318
$918$	0.170473	0.00562646
$919$	38.7579	1.27851	0.639253	−	0.768997i	$-0.279244\pi$
$919$	38.7579	1.27851	0.639253	+	0.768997i	$0.279244\pi$
$920$	3.32600	0.109655
$921$	−26.4875	−0.872793
$922$	2.67223	0.0880051
$923$	4.86405	0.160102
$924$	−1.52918	−0.0503065
$925$	−20.9012	−0.687229
$926$	−4.56774	−0.150105
$927$	−6.54652	−0.215016
$928$	6.45666	0.211950
$929$	−2.06282	−0.0676788	−0.0338394	−	0.999427i	$-0.510773\pi$
$929$	−2.06282	−0.0676788	−0.0338394	+	0.999427i	$0.510773\pi$
$930$	−1.69292	−0.0555130
$931$	1.76185	0.0577422
$932$	31.3394	1.02655
$933$	−4.45223	−0.145759
$934$	2.97842	0.0974568
$935$	2.12252	0.0694140
$936$	0.676939	0.0221264
$937$	−20.0971	−0.656544	−0.328272	−	0.944583i	$-0.606466\pi$
$937$	−20.0971	−0.656544	−0.328272	+	0.944583i	$0.606466\pi$
$938$	1.90832	0.0623088
$939$	−10.6894	−0.348834
$940$	−22.9573	−0.748784
$941$	−12.3944	−0.404046	−0.202023	−	0.979381i	$-0.564752\pi$
$941$	−12.3944	−0.404046	−0.202023	+	0.979381i	$0.564752\pi$
$942$	−2.94694	−0.0960166
$943$	16.6351	0.541715
$944$	−22.2312	−0.723564
$945$	2.73568	0.0889918
$946$	0.471413	0.0153270
$947$	−4.06829	−0.132202	−0.0661009	−	0.997813i	$-0.521056\pi$
$947$	−4.06829	−0.132202	−0.0661009	+	0.997813i	$0.521056\pi$
$948$	−13.6100	−0.442031
$949$	10.8793	0.353158
$950$	−0.746055	−0.0242052
$951$	26.3194	0.853464
$952$	0.676939	0.0219397
$953$	−6.29671	−0.203970	−0.101985	−	0.994786i	$-0.532519\pi$
$953$	−6.29671	−0.203970	−0.101985	+	0.994786i	$0.532519\pi$
$954$	−1.02173	−0.0330796
$955$	50.0239	1.61874
$956$	−35.9059	−1.16128
$957$	−2.49702	−0.0807172
$958$	5.73721	0.185361
$959$	−12.7908	−0.413038
$960$	−20.0005	−0.645512
$961$	−17.8227	−0.574924
$962$	1.43444	0.0462482
$963$	−2.40028	−0.0773479
$964$	−23.9048	−0.769923
$965$	12.9755	0.417697
$966$	−0.306170	−0.00985087
$967$	−45.0865	−1.44988	−0.724942	−	0.688810i	$-0.758134\pi$
$967$	−45.0865	−1.44988	−0.724942	+	0.688810i	$0.758134\pi$
$968$	−7.03883	−0.226237
$969$	−1.76185	−0.0565987
$970$	4.42441	0.142059
$971$	0.987555	0.0316922	0.0158461	−	0.999874i	$-0.494956\pi$
$971$	0.987555	0.0316922	0.0158461	+	0.999874i	$0.494956\pi$
$972$	1.97094	0.0632179
$973$	9.41450	0.301815
$974$	0.718809	0.0230321
$975$	−2.48397	−0.0795506
$976$	−3.45737	−0.110668
$977$	−49.5496	−1.58523	−0.792615	−	0.609722i	$-0.791281\pi$
$977$	−49.5496	−1.58523	−0.792615	+	0.609722i	$0.791281\pi$
$978$	2.18975	0.0700204
$979$	3.51337	0.112288
$980$	5.39187	0.172237
$981$	14.8251	0.473328
$982$	0.0836182	0.00266836
$983$	29.8965	0.953551	0.476775	−	0.879025i	$-0.341806\pi$
$983$	29.8965	0.953551	0.476775	+	0.879025i	$0.341806\pi$
$984$	6.27003	0.199881
$985$	−59.1878	−1.88588
$986$	0.548646	0.0174724
$987$	4.25776	0.135526
$988$	−3.47250	−0.110475
$989$	−6.40125	−0.203548
$990$	−0.361834	−0.0114998
$991$	10.4294	0.331302	0.165651	−	0.986184i	$-0.447027\pi$
$991$	10.4294	0.331302	0.165651	+	0.986184i	$0.447027\pi$
$992$	−7.28260	−0.231223
$993$	24.5635	0.779498
$994$	−0.829191	−0.0263004
$995$	−63.0403	−1.99851
$996$	−27.3606	−0.866955
$997$	25.7025	0.814006	0.407003	−	0.913427i	$-0.366574\pi$
$997$	25.7025	0.814006	0.407003	+	0.913427i	$0.366574\pi$
$998$	−7.03312	−0.222630
$999$	8.41446	0.266222

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4641.2.a.w.1.7	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4641.2.a.w.1.7	✓	14	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:	\( N \)	\(=\)	\( 4641 = 3 \cdot 7 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4641.a (trivial)

\(f(q)\)	\(=\)	\(q-0.170473 q^{2} -1.00000 q^{3} -1.97094 q^{4} -2.73568 q^{5} +0.170473 q^{6} +1.00000 q^{7} +0.676939 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.170473 q^{2} -1.00000 q^{3} -1.97094 q^{4} -2.73568 q^{5} +0.170473 q^{6} +1.00000 q^{7} +0.676939 q^{8} +1.00000 q^{9} +0.466361 q^{10} -0.775866 q^{11} +1.97094 q^{12} +1.00000 q^{13} -0.170473 q^{14} +2.73568 q^{15} +3.82648 q^{16} +1.00000 q^{17} -0.170473 q^{18} +1.76185 q^{19} +5.39187 q^{20} -1.00000 q^{21} +0.132265 q^{22} -1.79600 q^{23} -0.676939 q^{24} +2.48397 q^{25} -0.170473 q^{26} -1.00000 q^{27} -1.97094 q^{28} -3.21837 q^{29} -0.466361 q^{30} +3.63006 q^{31} -2.00619 q^{32} +0.775866 q^{33} -0.170473 q^{34} -2.73568 q^{35} -1.97094 q^{36} -8.41446 q^{37} -0.300348 q^{38} -1.00000 q^{39} -1.85189 q^{40} -9.26232 q^{41} +0.170473 q^{42} +3.56417 q^{43} +1.52918 q^{44} -2.73568 q^{45} +0.306170 q^{46} -4.25776 q^{47} -3.82648 q^{48} +1.00000 q^{49} -0.423450 q^{50} -1.00000 q^{51} -1.97094 q^{52} +5.99347 q^{53} +0.170473 q^{54} +2.12252 q^{55} +0.676939 q^{56} -1.76185 q^{57} +0.548646 q^{58} -5.80984 q^{59} -5.39187 q^{60} -0.903539 q^{61} -0.618829 q^{62} +1.00000 q^{63} -7.31095 q^{64} -2.73568 q^{65} -0.132265 q^{66} -11.1942 q^{67} -1.97094 q^{68} +1.79600 q^{69} +0.466361 q^{70} +4.86405 q^{71} +0.676939 q^{72} +10.8793 q^{73} +1.43444 q^{74} -2.48397 q^{75} -3.47250 q^{76} -0.775866 q^{77} +0.170473 q^{78} -6.90532 q^{79} -10.4680 q^{80} +1.00000 q^{81} +1.57898 q^{82} -13.8820 q^{83} +1.97094 q^{84} -2.73568 q^{85} -0.607595 q^{86} +3.21837 q^{87} -0.525214 q^{88} -4.52832 q^{89} +0.466361 q^{90} +1.00000 q^{91} +3.53981 q^{92} -3.63006 q^{93} +0.725835 q^{94} -4.81986 q^{95} +2.00619 q^{96} +9.48708 q^{97} -0.170473 q^{98} -0.775866 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - q^{2} - 14 q^{3} + 17 q^{4} - q^{5} + q^{6} + 14 q^{7} - 6 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - q^2 - 14 * q^3 + 17 * q^4 - q^5 + q^6 + 14 * q^7 - 6 * q^8 + 14 * q^9	\( 14 q - q^{2} - 14 q^{3} + 17 q^{4} - q^{5} + q^{6} + 14 q^{7} - 6 q^{8} + 14 q^{9} + 11 q^{10} - 4 q^{11} - 17 q^{12} + 14 q^{13} - q^{14} + q^{15} + 19 q^{16} + 14 q^{17} - q^{18} + 6 q^{19} + q^{20} - 14 q^{21} + 12 q^{22} + 7 q^{23} + 6 q^{24} + 19 q^{25} - q^{26} - 14 q^{27} + 17 q^{28} - 4 q^{29} - 11 q^{30} + 31 q^{31} - 18 q^{32} + 4 q^{33} - q^{34} - q^{35} + 17 q^{36} + 2 q^{37} + 9 q^{38} - 14 q^{39} + 50 q^{40} + 4 q^{41} + q^{42} + 14 q^{43} - 8 q^{44} - q^{45} - 17 q^{46} - q^{47} - 19 q^{48} + 14 q^{49} - 3 q^{50} - 14 q^{51} + 17 q^{52} - 43 q^{53} + q^{54} + 23 q^{55} - 6 q^{56} - 6 q^{57} - 10 q^{58} + 11 q^{59} - q^{60} + 25 q^{61} - 3 q^{62} + 14 q^{63} + 36 q^{64} - q^{65} - 12 q^{66} + 11 q^{67} + 17 q^{68} - 7 q^{69} + 11 q^{70} + 20 q^{71} - 6 q^{72} + 14 q^{73} - 24 q^{74} - 19 q^{75} + 9 q^{76} - 4 q^{77} + q^{78} + 42 q^{79} + 13 q^{80} + 14 q^{81} + 2 q^{82} + 15 q^{83} - 17 q^{84} - q^{85} - 11 q^{86} + 4 q^{87} + 63 q^{88} + 21 q^{89} + 11 q^{90} + 14 q^{91} + 30 q^{92} - 31 q^{93} - 29 q^{94} + 16 q^{95} + 18 q^{96} + 15 q^{97} - q^{98} - 4 q^{99}+O(q^{100}) \) 14 * q - q^2 - 14 * q^3 + 17 * q^4 - q^5 + q^6 + 14 * q^7 - 6 * q^8 + 14 * q^9 + 11 * q^10 - 4 * q^11 - 17 * q^12 + 14 * q^13 - q^14 + q^15 + 19 * q^16 + 14 * q^17 - q^18 + 6 * q^19 + q^20 - 14 * q^21 + 12 * q^22 + 7 * q^23 + 6 * q^24 + 19 * q^25 - q^26 - 14 * q^27 + 17 * q^28 - 4 * q^29 - 11 * q^30 + 31 * q^31 - 18 * q^32 + 4 * q^33 - q^34 - q^35 + 17 * q^36 + 2 * q^37 + 9 * q^38 - 14 * q^39 + 50 * q^40 + 4 * q^41 + q^42 + 14 * q^43 - 8 * q^44 - q^45 - 17 * q^46 - q^47 - 19 * q^48 + 14 * q^49 - 3 * q^50 - 14 * q^51 + 17 * q^52 - 43 * q^53 + q^54 + 23 * q^55 - 6 * q^56 - 6 * q^57 - 10 * q^58 + 11 * q^59 - q^60 + 25 * q^61 - 3 * q^62 + 14 * q^63 + 36 * q^64 - q^65 - 12 * q^66 + 11 * q^67 + 17 * q^68 - 7 * q^69 + 11 * q^70 + 20 * q^71 - 6 * q^72 + 14 * q^73 - 24 * q^74 - 19 * q^75 + 9 * q^76 - 4 * q^77 + q^78 + 42 * q^79 + 13 * q^80 + 14 * q^81 + 2 * q^82 + 15 * q^83 - 17 * q^84 - q^85 - 11 * q^86 + 4 * q^87 + 63 * q^88 + 21 * q^89 + 11 * q^90 + 14 * q^91 + 30 * q^92 - 31 * q^93 - 29 * q^94 + 16 * q^95 + 18 * q^96 + 15 * q^97 - q^98 - 4 * q^99

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