LMFDB - Embedded newform 946.2.a.e.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [946,2,Mod(1,946)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(946, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("946.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 946 = 2 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	946.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:	$7.55384803121$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{13}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 3 $ x^2 - x - 3
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			1.2
Root			$2.30278$ of defining polynomial
Character	$\chi$	$=$	946.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.30278 q^{3} +1.00000 q^{4} +1.30278 q^{5} -2.30278 q^{6} +4.60555 q^{7} -1.00000 q^{8} +2.30278 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.30278 q^{3} +1.00000 q^{4} +1.30278 q^{5} -2.30278 q^{6} +4.60555 q^{7} -1.00000 q^{8} +2.30278 q^{9} -1.30278 q^{10} -1.00000 q^{11} +2.30278 q^{12} -4.00000 q^{13} -4.60555 q^{14} +3.00000 q^{15} +1.00000 q^{16} +4.30278 q^{17} -2.30278 q^{18} +3.30278 q^{19} +1.30278 q^{20} +10.6056 q^{21} +1.00000 q^{22} +1.30278 q^{23} -2.30278 q^{24} -3.30278 q^{25} +4.00000 q^{26} -1.60555 q^{27} +4.60555 q^{28} +10.3028 q^{29} -3.00000 q^{30} -8.30278 q^{31} -1.00000 q^{32} -2.30278 q^{33} -4.30278 q^{34} +6.00000 q^{35} +2.30278 q^{36} -10.9083 q^{37} -3.30278 q^{38} -9.21110 q^{39} -1.30278 q^{40} -7.30278 q^{41} -10.6056 q^{42} +1.00000 q^{43} -1.00000 q^{44} +3.00000 q^{45} -1.30278 q^{46} -0.908327 q^{47} +2.30278 q^{48} +14.2111 q^{49} +3.30278 q^{50} +9.90833 q^{51} -4.00000 q^{52} +11.2111 q^{53} +1.60555 q^{54} -1.30278 q^{55} -4.60555 q^{56} +7.60555 q^{57} -10.3028 q^{58} -5.21110 q^{59} +3.00000 q^{60} +2.00000 q^{61} +8.30278 q^{62} +10.6056 q^{63} +1.00000 q^{64} -5.21110 q^{65} +2.30278 q^{66} -7.39445 q^{67} +4.30278 q^{68} +3.00000 q^{69} -6.00000 q^{70} -2.60555 q^{71} -2.30278 q^{72} -9.21110 q^{73} +10.9083 q^{74} -7.60555 q^{75} +3.30278 q^{76} -4.60555 q^{77} +9.21110 q^{78} -15.7250 q^{79} +1.30278 q^{80} -10.6056 q^{81} +7.30278 q^{82} +13.8167 q^{83} +10.6056 q^{84} +5.60555 q^{85} -1.00000 q^{86} +23.7250 q^{87} +1.00000 q^{88} +12.0000 q^{89} -3.00000 q^{90} -18.4222 q^{91} +1.30278 q^{92} -19.1194 q^{93} +0.908327 q^{94} +4.30278 q^{95} -2.30278 q^{96} +11.1194 q^{97} -14.2111 q^{98} -2.30278 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + q^{3} + 2 q^{4} - q^{5} - q^{6} + 2 q^{7} - 2 q^{8} + q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + q^3 + 2 * q^4 - q^5 - q^6 + 2 * q^7 - 2 * q^8 + q^9	\( 2 q - 2 q^{2} + q^{3} + 2 q^{4} - q^{5} - q^{6} + 2 q^{7} - 2 q^{8} + q^{9} + q^{10} - 2 q^{11} + q^{12} - 8 q^{13} - 2 q^{14} + 6 q^{15} + 2 q^{16} + 5 q^{17} - q^{18} + 3 q^{19} - q^{20} + 14 q^{21} + 2 q^{22} - q^{23} - q^{24} - 3 q^{25} + 8 q^{26} + 4 q^{27} + 2 q^{28} + 17 q^{29} - 6 q^{30} - 13 q^{31} - 2 q^{32} - q^{33} - 5 q^{34} + 12 q^{35} + q^{36} - 11 q^{37} - 3 q^{38} - 4 q^{39} + q^{40} - 11 q^{41} - 14 q^{42} + 2 q^{43} - 2 q^{44} + 6 q^{45} + q^{46} + 9 q^{47} + q^{48} + 14 q^{49} + 3 q^{50} + 9 q^{51} - 8 q^{52} + 8 q^{53} - 4 q^{54} + q^{55} - 2 q^{56} + 8 q^{57} - 17 q^{58} + 4 q^{59} + 6 q^{60} + 4 q^{61} + 13 q^{62} + 14 q^{63} + 2 q^{64} + 4 q^{65} + q^{66} - 22 q^{67} + 5 q^{68} + 6 q^{69} - 12 q^{70} + 2 q^{71} - q^{72} - 4 q^{73} + 11 q^{74} - 8 q^{75} + 3 q^{76} - 2 q^{77} + 4 q^{78} + q^{79} - q^{80} - 14 q^{81} + 11 q^{82} + 6 q^{83} + 14 q^{84} + 4 q^{85} - 2 q^{86} + 15 q^{87} + 2 q^{88} + 24 q^{89} - 6 q^{90} - 8 q^{91} - q^{92} - 13 q^{93} - 9 q^{94} + 5 q^{95} - q^{96} - 3 q^{97} - 14 q^{98} - q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + q^3 + 2 * q^4 - q^5 - q^6 + 2 * q^7 - 2 * q^8 + q^9 + q^10 - 2 * q^11 + q^12 - 8 * q^13 - 2 * q^14 + 6 * q^15 + 2 * q^16 + 5 * q^17 - q^18 + 3 * q^19 - q^20 + 14 * q^21 + 2 * q^22 - q^23 - q^24 - 3 * q^25 + 8 * q^26 + 4 * q^27 + 2 * q^28 + 17 * q^29 - 6 * q^30 - 13 * q^31 - 2 * q^32 - q^33 - 5 * q^34 + 12 * q^35 + q^36 - 11 * q^37 - 3 * q^38 - 4 * q^39 + q^40 - 11 * q^41 - 14 * q^42 + 2 * q^43 - 2 * q^44 + 6 * q^45 + q^46 + 9 * q^47 + q^48 + 14 * q^49 + 3 * q^50 + 9 * q^51 - 8 * q^52 + 8 * q^53 - 4 * q^54 + q^55 - 2 * q^56 + 8 * q^57 - 17 * q^58 + 4 * q^59 + 6 * q^60 + 4 * q^61 + 13 * q^62 + 14 * q^63 + 2 * q^64 + 4 * q^65 + q^66 - 22 * q^67 + 5 * q^68 + 6 * q^69 - 12 * q^70 + 2 * q^71 - q^72 - 4 * q^73 + 11 * q^74 - 8 * q^75 + 3 * q^76 - 2 * q^77 + 4 * q^78 + q^79 - q^80 - 14 * q^81 + 11 * q^82 + 6 * q^83 + 14 * q^84 + 4 * q^85 - 2 * q^86 + 15 * q^87 + 2 * q^88 + 24 * q^89 - 6 * q^90 - 8 * q^91 - q^92 - 13 * q^93 - 9 * q^94 + 5 * q^95 - q^96 - 3 * q^97 - 14 * 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
$3$	2.30278	1.32951	0.664754	−	0.747062i	$-0.268536\pi$
$3$	2.30278	1.32951	0.664754	+	0.747062i	$0.268536\pi$
$4$	1.00000	0.500000
$5$	1.30278	0.582619	0.291309	−	0.956629i	$-0.405909\pi$
$5$	1.30278	0.582619	0.291309	+	0.956629i	$0.405909\pi$
$6$	−2.30278	−0.940104
$7$	4.60555	1.74073	0.870367	−	0.492403i	$-0.163881\pi$
$7$	4.60555	1.74073	0.870367	+	0.492403i	$0.163881\pi$
$8$	−1.00000	−0.353553
$9$	2.30278	0.767592
$10$	−1.30278	−0.411974
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	2.30278	0.664754
$13$	−4.00000	−1.10940	−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000	−1.10940	−0.554700	+	0.832050i	$0.687167\pi$
$14$	−4.60555	−1.23089
$15$	3.00000	0.774597
$16$	1.00000	0.250000
$17$	4.30278	1.04358	0.521788	−	0.853075i	$-0.325265\pi$
$17$	4.30278	1.04358	0.521788	+	0.853075i	$0.325265\pi$
$18$	−2.30278	−0.542769
$19$	3.30278	0.757709	0.378854	−	0.925456i	$-0.376318\pi$
$19$	3.30278	0.757709	0.378854	+	0.925456i	$0.376318\pi$
$20$	1.30278	0.291309
$21$	10.6056	2.31432
$22$	1.00000	0.213201
$23$	1.30278	0.271647	0.135824	−	0.990733i	$-0.456632\pi$
$23$	1.30278	0.271647	0.135824	+	0.990733i	$0.456632\pi$
$24$	−2.30278	−0.470052
$25$	−3.30278	−0.660555
$26$	4.00000	0.784465
$27$	−1.60555	−0.308988
$28$	4.60555	0.870367
$29$	10.3028	1.91318	0.956589	−	0.291441i	$-0.0941348\pi$
$29$	10.3028	1.91318	0.956589	+	0.291441i	$0.0941348\pi$
$30$	−3.00000	−0.547723
$31$	−8.30278	−1.49122	−0.745611	−	0.666381i	$-0.767842\pi$
$31$	−8.30278	−1.49122	−0.745611	+	0.666381i	$0.767842\pi$
$32$	−1.00000	−0.176777
$33$	−2.30278	−0.400862
$34$	−4.30278	−0.737920
$35$	6.00000	1.01419
$36$	2.30278	0.383796
$37$	−10.9083	−1.79332	−0.896659	−	0.442722i	$-0.854013\pi$
$37$	−10.9083	−1.79332	−0.896659	+	0.442722i	$0.854013\pi$
$38$	−3.30278	−0.535781
$39$	−9.21110	−1.47496
$40$	−1.30278	−0.205987
$41$	−7.30278	−1.14050	−0.570251	−	0.821471i	$-0.693154\pi$
$41$	−7.30278	−1.14050	−0.570251	+	0.821471i	$0.693154\pi$
$42$	−10.6056	−1.63647
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−1.00000	−0.150756
$45$	3.00000	0.447214
$46$	−1.30278	−0.192084
$47$	−0.908327	−0.132493	−0.0662465	−	0.997803i	$-0.521102\pi$
$47$	−0.908327	−0.132493	−0.0662465	+	0.997803i	$0.521102\pi$
$48$	2.30278	0.332377
$49$	14.2111	2.03016
$50$	3.30278	0.467083
$51$	9.90833	1.38744
$52$	−4.00000	−0.554700
$53$	11.2111	1.53996	0.769982	−	0.638066i	$-0.220265\pi$
$53$	11.2111	1.53996	0.769982	+	0.638066i	$0.220265\pi$
$54$	1.60555	0.218488
$55$	−1.30278	−0.175666
$56$	−4.60555	−0.615443
$57$	7.60555	1.00738
$58$	−10.3028	−1.35282
$59$	−5.21110	−0.678428	−0.339214	−	0.940709i	$-0.610161\pi$
$59$	−5.21110	−0.678428	−0.339214	+	0.940709i	$0.610161\pi$
$60$	3.00000	0.387298
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	8.30278	1.05445
$63$	10.6056	1.33617
$64$	1.00000	0.125000
$65$	−5.21110	−0.646358
$66$	2.30278	0.283452
$67$	−7.39445	−0.903376	−0.451688	−	0.892176i	$-0.649178\pi$
$67$	−7.39445	−0.903376	−0.451688	+	0.892176i	$0.649178\pi$
$68$	4.30278	0.521788
$69$	3.00000	0.361158
$70$	−6.00000	−0.717137
$71$	−2.60555	−0.309222	−0.154611	−	0.987975i	$-0.549412\pi$
$71$	−2.60555	−0.309222	−0.154611	+	0.987975i	$0.549412\pi$
$72$	−2.30278	−0.271385
$73$	−9.21110	−1.07808	−0.539039	−	0.842281i	$-0.681212\pi$
$73$	−9.21110	−1.07808	−0.539039	+	0.842281i	$0.681212\pi$
$74$	10.9083	1.26807
$75$	−7.60555	−0.878213
$76$	3.30278	0.378854
$77$	−4.60555	−0.524851
$78$	9.21110	1.04295
$79$	−15.7250	−1.76920	−0.884599	−	0.466352i	$-0.845568\pi$
$79$	−15.7250	−1.76920	−0.884599	+	0.466352i	$0.845568\pi$
$80$	1.30278	0.145655
$81$	−10.6056	−1.17839
$82$	7.30278	0.806457
$83$	13.8167	1.51657	0.758287	−	0.651920i	$-0.226036\pi$
$83$	13.8167	1.51657	0.758287	+	0.651920i	$0.226036\pi$
$84$	10.6056	1.15716
$85$	5.60555	0.608007
$86$	−1.00000	−0.107833
$87$	23.7250	2.54358
$88$	1.00000	0.106600
$89$	12.0000	1.27200	0.635999	−	0.771690i	$-0.280588\pi$
$89$	12.0000	1.27200	0.635999	+	0.771690i	$0.280588\pi$
$90$	−3.00000	−0.316228
$91$	−18.4222	−1.93117
$92$	1.30278	0.135824
$93$	−19.1194	−1.98259
$94$	0.908327	0.0936868
$95$	4.30278	0.441455
$96$	−2.30278	−0.235026
$97$	11.1194	1.12901	0.564504	−	0.825431i	$-0.309068\pi$
$97$	11.1194	1.12901	0.564504	+	0.825431i	$0.309068\pi$
$98$	−14.2111	−1.43554
$99$	−2.30278	−0.231438
$100$	−3.30278	−0.330278
$101$	3.39445	0.337760	0.168880	−	0.985637i	$-0.445985\pi$
$101$	3.39445	0.337760	0.168880	+	0.985637i	$0.445985\pi$
$102$	−9.90833	−0.981071
$103$	1.48612	0.146432	0.0732160	−	0.997316i	$-0.476674\pi$
$103$	1.48612	0.146432	0.0732160	+	0.997316i	$0.476674\pi$
$104$	4.00000	0.392232
$105$	13.8167	1.34837
$106$	−11.2111	−1.08892
$107$	8.60555	0.831930	0.415965	−	0.909381i	$-0.363444\pi$
$107$	8.60555	0.831930	0.415965	+	0.909381i	$0.363444\pi$
$108$	−1.60555	−0.154494
$109$	9.81665	0.940265	0.470132	−	0.882596i	$-0.344206\pi$
$109$	9.81665	0.940265	0.470132	+	0.882596i	$0.344206\pi$
$110$	1.30278	0.124215
$111$	−25.1194	−2.38423
$112$	4.60555	0.435184
$113$	−17.2111	−1.61908	−0.809542	−	0.587062i	$-0.800285\pi$
$113$	−17.2111	−1.61908	−0.809542	+	0.587062i	$0.800285\pi$
$114$	−7.60555	−0.712325
$115$	1.69722	0.158267
$116$	10.3028	0.956589
$117$	−9.21110	−0.851567
$118$	5.21110	0.479721
$119$	19.8167	1.81659
$120$	−3.00000	−0.273861
$121$	1.00000	0.0909091
$122$	−2.00000	−0.181071
$123$	−16.8167	−1.51631
$124$	−8.30278	−0.745611
$125$	−10.8167	−0.967471
$126$	−10.6056	−0.944818
$127$	14.1194	1.25290	0.626448	−	0.779463i	$-0.284508\pi$
$127$	14.1194	1.25290	0.626448	+	0.779463i	$0.284508\pi$
$128$	−1.00000	−0.0883883
$129$	2.30278	0.202748
$130$	5.21110	0.457044
$131$	10.3028	0.900158	0.450079	−	0.892989i	$-0.351396\pi$
$131$	10.3028	0.900158	0.450079	+	0.892989i	$0.351396\pi$
$132$	−2.30278	−0.200431
$133$	15.2111	1.31897
$134$	7.39445	0.638783
$135$	−2.09167	−0.180023
$136$	−4.30278	−0.368960
$137$	7.81665	0.667822	0.333911	−	0.942605i	$-0.391632\pi$
$137$	7.81665	0.667822	0.333911	+	0.942605i	$0.391632\pi$
$138$	−3.00000	−0.255377
$139$	−15.2111	−1.29019	−0.645094	−	0.764103i	$-0.723182\pi$
$139$	−15.2111	−1.29019	−0.645094	+	0.764103i	$0.723182\pi$
$140$	6.00000	0.507093
$141$	−2.09167	−0.176151
$142$	2.60555	0.218653
$143$	4.00000	0.334497
$144$	2.30278	0.191898
$145$	13.4222	1.11465
$146$	9.21110	0.762316
$147$	32.7250	2.69911
$148$	−10.9083	−0.896659
$149$	−24.1194	−1.97594	−0.987970	−	0.154644i	$-0.950577\pi$
$149$	−24.1194	−1.97594	−0.987970	+	0.154644i	$0.950577\pi$
$150$	7.60555	0.620991
$151$	11.3944	0.927267	0.463634	−	0.886027i	$-0.346545\pi$
$151$	11.3944	0.927267	0.463634	+	0.886027i	$0.346545\pi$
$152$	−3.30278	−0.267890
$153$	9.90833	0.801041
$154$	4.60555	0.371126
$155$	−10.8167	−0.868815
$156$	−9.21110	−0.737478
$157$	5.11943	0.408575	0.204287	−	0.978911i	$-0.434512\pi$
$157$	5.11943	0.408575	0.204287	+	0.978911i	$0.434512\pi$
$158$	15.7250	1.25101
$159$	25.8167	2.04739
$160$	−1.30278	−0.102993
$161$	6.00000	0.472866
$162$	10.6056	0.833251
$163$	3.30278	0.258693	0.129347	−	0.991599i	$-0.458712\pi$
$163$	3.30278	0.258693	0.129347	+	0.991599i	$0.458712\pi$
$164$	−7.30278	−0.570251
$165$	−3.00000	−0.233550
$166$	−13.8167	−1.07238
$167$	−10.4222	−0.806494	−0.403247	−	0.915091i	$-0.632119\pi$
$167$	−10.4222	−0.806494	−0.403247	+	0.915091i	$0.632119\pi$
$168$	−10.6056	−0.818236
$169$	3.00000	0.230769
$170$	−5.60555	−0.429926
$171$	7.60555	0.581611
$172$	1.00000	0.0762493
$173$	−14.6056	−1.11044	−0.555220	−	0.831704i	$-0.687366\pi$
$173$	−14.6056	−1.11044	−0.555220	+	0.831704i	$0.687366\pi$
$174$	−23.7250	−1.79859
$175$	−15.2111	−1.14985
$176$	−1.00000	−0.0753778
$177$	−12.0000	−0.901975
$178$	−12.0000	−0.899438
$179$	−21.9083	−1.63751	−0.818753	−	0.574146i	$-0.805334\pi$
$179$	−21.9083	−1.63751	−0.818753	+	0.574146i	$0.805334\pi$
$180$	3.00000	0.223607
$181$	7.21110	0.535997	0.267999	−	0.963419i	$-0.413638\pi$
$181$	7.21110	0.535997	0.267999	+	0.963419i	$0.413638\pi$
$182$	18.4222	1.36554
$183$	4.60555	0.340452
$184$	−1.30278	−0.0960419
$185$	−14.2111	−1.04482
$186$	19.1194	1.40190
$187$	−4.30278	−0.314650
$188$	−0.908327	−0.0662465
$189$	−7.39445	−0.537867
$190$	−4.30278	−0.312156
$191$	3.39445	0.245614	0.122807	−	0.992431i	$-0.460810\pi$
$191$	3.39445	0.245614	0.122807	+	0.992431i	$0.460810\pi$
$192$	2.30278	0.166189
$193$	25.7250	1.85172	0.925862	−	0.377861i	$-0.123340\pi$
$193$	25.7250	1.85172	0.925862	+	0.377861i	$0.123340\pi$
$194$	−11.1194	−0.798329
$195$	−12.0000	−0.859338
$196$	14.2111	1.01508
$197$	−15.3944	−1.09681	−0.548405	−	0.836213i	$-0.684765\pi$
$197$	−15.3944	−1.09681	−0.548405	+	0.836213i	$0.684765\pi$
$198$	2.30278	0.163651
$199$	14.0000	0.992434	0.496217	−	0.868199i	$-0.334722\pi$
$199$	14.0000	0.992434	0.496217	+	0.868199i	$0.334722\pi$
$200$	3.30278	0.233542
$201$	−17.0278	−1.20105
$202$	−3.39445	−0.238833
$203$	47.4500	3.33033
$204$	9.90833	0.693722
$205$	−9.51388	−0.664478
$206$	−1.48612	−0.103543
$207$	3.00000	0.208514
$208$	−4.00000	−0.277350
$209$	−3.30278	−0.228458
$210$	−13.8167	−0.953440
$211$	−17.6972	−1.21833	−0.609164	−	0.793045i	$-0.708495\pi$
$211$	−17.6972	−1.21833	−0.609164	+	0.793045i	$0.708495\pi$
$212$	11.2111	0.769982
$213$	−6.00000	−0.411113
$214$	−8.60555	−0.588263
$215$	1.30278	0.0888486
$216$	1.60555	0.109244
$217$	−38.2389	−2.59582
$218$	−9.81665	−0.664868
$219$	−21.2111	−1.43331
$220$	−1.30278	−0.0878331
$221$	−17.2111	−1.15774
$222$	25.1194	1.68591
$223$	−1.39445	−0.0933792	−0.0466896	−	0.998909i	$-0.514867\pi$
$223$	−1.39445	−0.0933792	−0.0466896	+	0.998909i	$0.514867\pi$
$224$	−4.60555	−0.307721
$225$	−7.60555	−0.507037
$226$	17.2111	1.14487
$227$	−7.30278	−0.484702	−0.242351	−	0.970189i	$-0.577919\pi$
$227$	−7.30278	−0.484702	−0.242351	+	0.970189i	$0.577919\pi$
$228$	7.60555	0.503690
$229$	−22.0000	−1.45380	−0.726900	−	0.686743i	$-0.759040\pi$
$229$	−22.0000	−1.45380	−0.726900	+	0.686743i	$0.759040\pi$
$230$	−1.69722	−0.111912
$231$	−10.6056	−0.697794
$232$	−10.3028	−0.676410
$233$	19.8167	1.29823	0.649116	−	0.760689i	$-0.275139\pi$
$233$	19.8167	1.29823	0.649116	+	0.760689i	$0.275139\pi$
$234$	9.21110	0.602149
$235$	−1.18335	−0.0771930
$236$	−5.21110	−0.339214
$237$	−36.2111	−2.35216
$238$	−19.8167	−1.28452
$239$	6.51388	0.421348	0.210674	−	0.977556i	$-0.432434\pi$
$239$	6.51388	0.421348	0.210674	+	0.977556i	$0.432434\pi$
$240$	3.00000	0.193649
$241$	−17.8167	−1.14767	−0.573836	−	0.818970i	$-0.694545\pi$
$241$	−17.8167	−1.14767	−0.573836	+	0.818970i	$0.694545\pi$
$242$	−1.00000	−0.0642824
$243$	−19.6056	−1.25770
$244$	2.00000	0.128037
$245$	18.5139	1.18281
$246$	16.8167	1.07219
$247$	−13.2111	−0.840602
$248$	8.30278	0.527227
$249$	31.8167	2.01630
$250$	10.8167	0.684105
$251$	−3.39445	−0.214256	−0.107128	−	0.994245i	$-0.534165\pi$
$251$	−3.39445	−0.214256	−0.107128	+	0.994245i	$0.534165\pi$
$252$	10.6056	0.668087
$253$	−1.30278	−0.0819048
$254$	−14.1194	−0.885932
$255$	12.9083	0.808351
$256$	1.00000	0.0625000
$257$	−5.21110	−0.325060	−0.162530	−	0.986704i	$-0.551965\pi$
$257$	−5.21110	−0.325060	−0.162530	+	0.986704i	$0.551965\pi$
$258$	−2.30278	−0.143365
$259$	−50.2389	−3.12169
$260$	−5.21110	−0.323179
$261$	23.7250	1.46854
$262$	−10.3028	−0.636508
$263$	−13.0278	−0.803326	−0.401663	−	0.915788i	$-0.631568\pi$
$263$	−13.0278	−0.803326	−0.401663	+	0.915788i	$0.631568\pi$
$264$	2.30278	0.141726
$265$	14.6056	0.897212
$266$	−15.2111	−0.932653
$267$	27.6333	1.69113
$268$	−7.39445	−0.451688
$269$	8.60555	0.524690	0.262345	−	0.964974i	$-0.415504\pi$
$269$	8.60555	0.524690	0.262345	+	0.964974i	$0.415504\pi$
$270$	2.09167	0.127295
$271$	23.9083	1.45233	0.726164	−	0.687522i	$-0.241301\pi$
$271$	23.9083	1.45233	0.726164	+	0.687522i	$0.241301\pi$
$272$	4.30278	0.260894
$273$	−42.4222	−2.56751
$274$	−7.81665	−0.472221
$275$	3.30278	0.199165
$276$	3.00000	0.180579
$277$	−7.90833	−0.475165	−0.237583	−	0.971367i	$-0.576355\pi$
$277$	−7.90833	−0.475165	−0.237583	+	0.971367i	$0.576355\pi$
$278$	15.2111	0.912301
$279$	−19.1194	−1.14465
$280$	−6.00000	−0.358569
$281$	−0.908327	−0.0541862	−0.0270931	−	0.999633i	$-0.508625\pi$
$281$	−0.908327	−0.0541862	−0.0270931	+	0.999633i	$0.508625\pi$
$282$	2.09167	0.124557
$283$	−19.6333	−1.16708	−0.583539	−	0.812085i	$-0.698333\pi$
$283$	−19.6333	−1.16708	−0.583539	+	0.812085i	$0.698333\pi$
$284$	−2.60555	−0.154611
$285$	9.90833	0.586919
$286$	−4.00000	−0.236525
$287$	−33.6333	−1.98531
$288$	−2.30278	−0.135692
$289$	1.51388	0.0890517
$290$	−13.4222	−0.788179
$291$	25.6056	1.50102
$292$	−9.21110	−0.539039
$293$	4.18335	0.244394	0.122197	−	0.992506i	$-0.461006\pi$
$293$	4.18335	0.244394	0.122197	+	0.992506i	$0.461006\pi$
$294$	−32.7250	−1.90856
$295$	−6.78890	−0.395265
$296$	10.9083	0.634034
$297$	1.60555	0.0931635
$298$	24.1194	1.39720
$299$	−5.21110	−0.301366
$300$	−7.60555	−0.439107
$301$	4.60555	0.265460
$302$	−11.3944	−0.655677
$303$	7.81665	0.449055
$304$	3.30278	0.189427
$305$	2.60555	0.149193
$306$	−9.90833	−0.566421
$307$	−10.0000	−0.570730	−0.285365	−	0.958419i	$-0.592115\pi$
$307$	−10.0000	−0.570730	−0.285365	+	0.958419i	$0.592115\pi$
$308$	−4.60555	−0.262426
$309$	3.42221	0.194682
$310$	10.8167	0.614345
$311$	22.4222	1.27145	0.635723	−	0.771917i	$-0.280702\pi$
$311$	22.4222	1.27145	0.635723	+	0.771917i	$0.280702\pi$
$312$	9.21110	0.521476
$313$	−29.0278	−1.64075	−0.820373	−	0.571829i	$-0.806234\pi$
$313$	−29.0278	−1.64075	−0.820373	+	0.571829i	$0.806234\pi$
$314$	−5.11943	−0.288906
$315$	13.8167	0.778480
$316$	−15.7250	−0.884599
$317$	0	0		−	1.00000i	$-0.5\pi$
$317$	0	0			1.00000i	$0.5\pi$
$318$	−25.8167	−1.44773
$319$	−10.3028	−0.576845
$320$	1.30278	0.0728274
$321$	19.8167	1.10606
$322$	−6.00000	−0.334367
$323$	14.2111	0.790727
$324$	−10.6056	−0.589197
$325$	13.2111	0.732820
$326$	−3.30278	−0.182924
$327$	22.6056	1.25009
$328$	7.30278	0.403228
$329$	−4.18335	−0.230635
$330$	3.00000	0.165145
$331$	−4.00000	−0.219860	−0.109930	−	0.993939i	$-0.535063\pi$
$331$	−4.00000	−0.219860	−0.109930	+	0.993939i	$0.535063\pi$
$332$	13.8167	0.758287
$333$	−25.1194	−1.37654
$334$	10.4222	0.570278
$335$	−9.63331	−0.526324
$336$	10.6056	0.578580
$337$	−6.72498	−0.366333	−0.183167	−	0.983082i	$-0.558635\pi$
$337$	−6.72498	−0.366333	−0.183167	+	0.983082i	$0.558635\pi$
$338$	−3.00000	−0.163178
$339$	−39.6333	−2.15259
$340$	5.60555	0.304004
$341$	8.30278	0.449621
$342$	−7.60555	−0.411261
$343$	33.2111	1.79323
$344$	−1.00000	−0.0539164
$345$	3.90833	0.210417
$346$	14.6056	0.785199
$347$	2.09167	0.112287	0.0561434	−	0.998423i	$-0.482120\pi$
$347$	2.09167	0.112287	0.0561434	+	0.998423i	$0.482120\pi$
$348$	23.7250	1.27179
$349$	7.88057	0.421837	0.210919	−	0.977504i	$-0.432354\pi$
$349$	7.88057	0.421837	0.210919	+	0.977504i	$0.432354\pi$
$350$	15.2111	0.813068
$351$	6.42221	0.342792
$352$	1.00000	0.0533002
$353$	−6.00000	−0.319348	−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000	−0.319348	−0.159674	+	0.987170i	$0.551044\pi$
$354$	12.0000	0.637793
$355$	−3.39445	−0.180159
$356$	12.0000	0.635999
$357$	45.6333	2.41517
$358$	21.9083	1.15789
$359$	21.5139	1.13546	0.567730	−	0.823215i	$-0.307822\pi$
$359$	21.5139	1.13546	0.567730	+	0.823215i	$0.307822\pi$
$360$	−3.00000	−0.158114
$361$	−8.09167	−0.425878
$362$	−7.21110	−0.379007
$363$	2.30278	0.120864
$364$	−18.4222	−0.965586
$365$	−12.0000	−0.628109
$366$	−4.60555	−0.240736
$367$	20.9083	1.09141	0.545703	−	0.837979i	$-0.316263\pi$
$367$	20.9083	1.09141	0.545703	+	0.837979i	$0.316263\pi$
$368$	1.30278	0.0679119
$369$	−16.8167	−0.875440
$370$	14.2111	0.738800
$371$	51.6333	2.68067
$372$	−19.1194	−0.991296
$373$	−3.72498	−0.192872	−0.0964361	−	0.995339i	$-0.530744\pi$
$373$	−3.72498	−0.192872	−0.0964361	+	0.995339i	$0.530744\pi$
$374$	4.30278	0.222491
$375$	−24.9083	−1.28626
$376$	0.908327	0.0468434
$377$	−41.2111	−2.12248
$378$	7.39445	0.380329
$379$	−23.8167	−1.22338	−0.611690	−	0.791098i	$-0.709510\pi$
$379$	−23.8167	−1.22338	−0.611690	+	0.791098i	$0.709510\pi$
$380$	4.30278	0.220728
$381$	32.5139	1.66574
$382$	−3.39445	−0.173675
$383$	−14.6056	−0.746309	−0.373154	−	0.927769i	$-0.621724\pi$
$383$	−14.6056	−0.746309	−0.373154	+	0.927769i	$0.621724\pi$
$384$	−2.30278	−0.117513
$385$	−6.00000	−0.305788
$386$	−25.7250	−1.30937
$387$	2.30278	0.117057
$388$	11.1194	0.564504
$389$	−0.788897	−0.0399987	−0.0199993	−	0.999800i	$-0.506366\pi$
$389$	−0.788897	−0.0399987	−0.0199993	+	0.999800i	$0.506366\pi$
$390$	12.0000	0.607644
$391$	5.60555	0.283485
$392$	−14.2111	−0.717769
$393$	23.7250	1.19677
$394$	15.3944	0.775561
$395$	−20.4861	−1.03077
$396$	−2.30278	−0.115719
$397$	3.02776	0.151959	0.0759794	−	0.997109i	$-0.475792\pi$
$397$	3.02776	0.151959	0.0759794	+	0.997109i	$0.475792\pi$
$398$	−14.0000	−0.701757
$399$	35.0278	1.75358
$400$	−3.30278	−0.165139
$401$	24.9083	1.24386	0.621931	−	0.783072i	$-0.286348\pi$
$401$	24.9083	1.24386	0.621931	+	0.783072i	$0.286348\pi$
$402$	17.0278	0.849267
$403$	33.2111	1.65436
$404$	3.39445	0.168880
$405$	−13.8167	−0.686555
$406$	−47.4500	−2.35490
$407$	10.9083	0.540706
$408$	−9.90833	−0.490535
$409$	−11.8167	−0.584296	−0.292148	−	0.956373i	$-0.594370\pi$
$409$	−11.8167	−0.584296	−0.292148	+	0.956373i	$0.594370\pi$
$410$	9.51388	0.469857
$411$	18.0000	0.887875
$412$	1.48612	0.0732160
$413$	−24.0000	−1.18096
$414$	−3.00000	−0.147442
$415$	18.0000	0.883585
$416$	4.00000	0.196116
$417$	−35.0278	−1.71532
$418$	3.30278	0.161544
$419$	29.2111	1.42706	0.713528	−	0.700627i	$-0.247096\pi$
$419$	29.2111	1.42706	0.713528	+	0.700627i	$0.247096\pi$
$420$	13.8167	0.674184
$421$	−3.72498	−0.181544	−0.0907722	−	0.995872i	$-0.528934\pi$
$421$	−3.72498	−0.181544	−0.0907722	+	0.995872i	$0.528934\pi$
$422$	17.6972	0.861487
$423$	−2.09167	−0.101701
$424$	−11.2111	−0.544459
$425$	−14.2111	−0.689340
$426$	6.00000	0.290701
$427$	9.21110	0.445756
$428$	8.60555	0.415965
$429$	9.21110	0.444716
$430$	−1.30278	−0.0628254
$431$	12.9083	0.621772	0.310886	−	0.950447i	$-0.399374\pi$
$431$	12.9083	0.621772	0.310886	+	0.950447i	$0.399374\pi$
$432$	−1.60555	−0.0772471
$433$	9.81665	0.471758	0.235879	−	0.971782i	$-0.424203\pi$
$433$	9.81665	0.471758	0.235879	+	0.971782i	$0.424203\pi$
$434$	38.2389	1.83552
$435$	30.9083	1.48194
$436$	9.81665	0.470132
$437$	4.30278	0.205830
$438$	21.2111	1.01351
$439$	22.4861	1.07320	0.536602	−	0.843835i	$-0.319708\pi$
$439$	22.4861	1.07320	0.536602	+	0.843835i	$0.319708\pi$
$440$	1.30278	0.0621074
$441$	32.7250	1.55833
$442$	17.2111	0.818649
$443$	−9.63331	−0.457692	−0.228846	−	0.973463i	$-0.573495\pi$
$443$	−9.63331	−0.457692	−0.228846	+	0.973463i	$0.573495\pi$
$444$	−25.1194	−1.19212
$445$	15.6333	0.741090
$446$	1.39445	0.0660291
$447$	−55.5416	−2.62703
$448$	4.60555	0.217592
$449$	−39.6333	−1.87041	−0.935206	−	0.354105i	$-0.884786\pi$
$449$	−39.6333	−1.87041	−0.935206	+	0.354105i	$0.884786\pi$
$450$	7.60555	0.358529
$451$	7.30278	0.343874
$452$	−17.2111	−0.809542
$453$	26.2389	1.23281
$454$	7.30278	0.342736
$455$	−24.0000	−1.12514
$456$	−7.60555	−0.356163
$457$	−36.8444	−1.72351	−0.861754	−	0.507326i	$-0.830634\pi$
$457$	−36.8444	−1.72351	−0.861754	+	0.507326i	$0.830634\pi$
$458$	22.0000	1.02799
$459$	−6.90833	−0.322453
$460$	1.69722	0.0791335
$461$	12.0000	0.558896	0.279448	−	0.960161i	$-0.409849\pi$
$461$	12.0000	0.558896	0.279448	+	0.960161i	$0.409849\pi$
$462$	10.6056	0.493415
$463$	33.0278	1.53493	0.767465	−	0.641091i	$-0.221518\pi$
$463$	33.0278	1.53493	0.767465	+	0.641091i	$0.221518\pi$
$464$	10.3028	0.478294
$465$	−24.9083	−1.15510
$466$	−19.8167	−0.917989
$467$	18.9083	0.874973	0.437487	−	0.899225i	$-0.355869\pi$
$467$	18.9083	0.874973	0.437487	+	0.899225i	$0.355869\pi$
$468$	−9.21110	−0.425783
$469$	−34.0555	−1.57254
$470$	1.18335	0.0545837
$471$	11.7889	0.543204
$472$	5.21110	0.239860
$473$	−1.00000	−0.0459800
$474$	36.2111	1.66323
$475$	−10.9083	−0.500508
$476$	19.8167	0.908295
$477$	25.8167	1.18206
$478$	−6.51388	−0.297938
$479$	38.3305	1.75137	0.875683	−	0.482886i	$-0.160411\pi$
$479$	38.3305	1.75137	0.875683	+	0.482886i	$0.160411\pi$
$480$	−3.00000	−0.136931
$481$	43.6333	1.98951
$482$	17.8167	0.811526
$483$	13.8167	0.628680
$484$	1.00000	0.0454545
$485$	14.4861	0.657781
$486$	19.6056	0.889326
$487$	16.0917	0.729183	0.364592	−	0.931168i	$-0.381209\pi$
$487$	16.0917	0.729183	0.364592	+	0.931168i	$0.381209\pi$
$488$	−2.00000	−0.0905357
$489$	7.60555	0.343935
$490$	−18.5139	−0.836372
$491$	2.09167	0.0943959	0.0471979	−	0.998886i	$-0.484971\pi$
$491$	2.09167	0.0943959	0.0471979	+	0.998886i	$0.484971\pi$
$492$	−16.8167	−0.758153
$493$	44.3305	1.99655
$494$	13.2111	0.594396
$495$	−3.00000	−0.134840
$496$	−8.30278	−0.372806
$497$	−12.0000	−0.538274
$498$	−31.8167	−1.42574
$499$	2.90833	0.130195	0.0650973	−	0.997879i	$-0.479264\pi$
$499$	2.90833	0.130195	0.0650973	+	0.997879i	$0.479264\pi$
$500$	−10.8167	−0.483735
$501$	−24.0000	−1.07224
$502$	3.39445	0.151502
$503$	2.60555	0.116176	0.0580879	−	0.998311i	$-0.481500\pi$
$503$	2.60555	0.116176	0.0580879	+	0.998311i	$0.481500\pi$
$504$	−10.6056	−0.472409
$505$	4.42221	0.196786
$506$	1.30278	0.0579154
$507$	6.90833	0.306810
$508$	14.1194	0.626448
$509$	−11.2111	−0.496923	−0.248462	−	0.968642i	$-0.579925\pi$
$509$	−11.2111	−0.496923	−0.248462	+	0.968642i	$0.579925\pi$
$510$	−12.9083	−0.571590
$511$	−42.4222	−1.87665
$512$	−1.00000	−0.0441942
$513$	−5.30278	−0.234123
$514$	5.21110	0.229852
$515$	1.93608	0.0853140
$516$	2.30278	0.101374
$517$	0.908327	0.0399482
$518$	50.2389	2.20737
$519$	−33.6333	−1.47634
$520$	5.21110	0.228522
$521$	−15.6333	−0.684908	−0.342454	−	0.939535i	$-0.611258\pi$
$521$	−15.6333	−0.684908	−0.342454	+	0.939535i	$0.611258\pi$
$522$	−23.7250	−1.03841
$523$	−26.5416	−1.16058	−0.580292	−	0.814408i	$-0.697062\pi$
$523$	−26.5416	−1.16058	−0.580292	+	0.814408i	$0.697062\pi$
$524$	10.3028	0.450079
$525$	−35.0278	−1.52874
$526$	13.0278	0.568037
$527$	−35.7250	−1.55620
$528$	−2.30278	−0.100215
$529$	−21.3028	−0.926208
$530$	−14.6056	−0.634425
$531$	−12.0000	−0.520756
$532$	15.2111	0.659485
$533$	29.2111	1.26527
$534$	−27.6333	−1.19581
$535$	11.2111	0.484698
$536$	7.39445	0.319392
$537$	−50.4500	−2.17708
$538$	−8.60555	−0.371012
$539$	−14.2111	−0.612116
$540$	−2.09167	−0.0900113
$541$	−1.39445	−0.0599520	−0.0299760	−	0.999551i	$-0.509543\pi$
$541$	−1.39445	−0.0599520	−0.0299760	+	0.999551i	$0.509543\pi$
$542$	−23.9083	−1.02695
$543$	16.6056	0.712612
$544$	−4.30278	−0.184480
$545$	12.7889	0.547816
$546$	42.4222	1.81550
$547$	4.60555	0.196919	0.0984596	−	0.995141i	$-0.468608\pi$
$547$	4.60555	0.196919	0.0984596	+	0.995141i	$0.468608\pi$
$548$	7.81665	0.333911
$549$	4.60555	0.196560
$550$	−3.30278	−0.140831
$551$	34.0278	1.44963
$552$	−3.00000	−0.127688
$553$	−72.4222	−3.07971
$554$	7.90833	0.335993
$555$	−32.7250	−1.38910
$556$	−15.2111	−0.645094
$557$	−9.39445	−0.398056	−0.199028	−	0.979994i	$-0.563778\pi$
$557$	−9.39445	−0.398056	−0.199028	+	0.979994i	$0.563778\pi$
$558$	19.1194	0.809390
$559$	−4.00000	−0.169182
$560$	6.00000	0.253546
$561$	−9.90833	−0.418330
$562$	0.908327	0.0383155
$563$	43.8167	1.84665	0.923326	−	0.384017i	$-0.125460\pi$
$563$	43.8167	1.84665	0.923326	+	0.384017i	$0.125460\pi$
$564$	−2.09167	−0.0880753
$565$	−22.4222	−0.943309
$566$	19.6333	0.825249
$567$	−48.8444	−2.05127
$568$	2.60555	0.109327
$569$	−4.42221	−0.185388	−0.0926942	−	0.995695i	$-0.529548\pi$
$569$	−4.42221	−0.185388	−0.0926942	+	0.995695i	$0.529548\pi$
$570$	−9.90833	−0.415014
$571$	44.3583	1.85634	0.928168	−	0.372161i	$-0.121383\pi$
$571$	44.3583	1.85634	0.928168	+	0.372161i	$0.121383\pi$
$572$	4.00000	0.167248
$573$	7.81665	0.326545
$574$	33.6333	1.40383
$575$	−4.30278	−0.179438
$576$	2.30278	0.0959490
$577$	20.2389	0.842555	0.421277	−	0.906932i	$-0.361582\pi$
$577$	20.2389	0.842555	0.421277	+	0.906932i	$0.361582\pi$
$578$	−1.51388	−0.0629690
$579$	59.2389	2.46188
$580$	13.4222	0.557327
$581$	63.6333	2.63995
$582$	−25.6056	−1.06138
$583$	−11.2111	−0.464316
$584$	9.21110	0.381158
$585$	−12.0000	−0.496139
$586$	−4.18335	−0.172812
$587$	−1.57779	−0.0651226	−0.0325613	−	0.999470i	$-0.510366\pi$
$587$	−1.57779	−0.0651226	−0.0325613	+	0.999470i	$0.510366\pi$
$588$	32.7250	1.34956
$589$	−27.4222	−1.12991
$590$	6.78890	0.279494
$591$	−35.4500	−1.45822
$592$	−10.9083	−0.448329
$593$	12.0000	0.492781	0.246390	−	0.969171i	$-0.420755\pi$
$593$	12.0000	0.492781	0.246390	+	0.969171i	$0.420755\pi$
$594$	−1.60555	−0.0658766
$595$	25.8167	1.05838
$596$	−24.1194	−0.987970
$597$	32.2389	1.31945
$598$	5.21110	0.213098
$599$	23.3305	0.953260	0.476630	−	0.879104i	$-0.341858\pi$
$599$	23.3305	0.953260	0.476630	+	0.879104i	$0.341858\pi$
$600$	7.60555	0.310495
$601$	24.4222	0.996203	0.498101	−	0.867119i	$-0.334031\pi$
$601$	24.4222	0.996203	0.498101	+	0.867119i	$0.334031\pi$
$602$	−4.60555	−0.187708
$603$	−17.0278	−0.693424
$604$	11.3944	0.463634
$605$	1.30278	0.0529654
$606$	−7.81665	−0.317530
$607$	25.2111	1.02329	0.511644	−	0.859198i	$-0.329037\pi$
$607$	25.2111	1.02329	0.511644	+	0.859198i	$0.329037\pi$
$608$	−3.30278	−0.133945
$609$	109.267	4.42771
$610$	−2.60555	−0.105496
$611$	3.63331	0.146988
$612$	9.90833	0.400520
$613$	32.2389	1.30212	0.651058	−	0.759028i	$-0.274326\pi$
$613$	32.2389	1.30212	0.651058	+	0.759028i	$0.274326\pi$
$614$	10.0000	0.403567
$615$	−21.9083	−0.883429
$616$	4.60555	0.185563
$617$	−16.6972	−0.672205	−0.336102	−	0.941825i	$-0.609109\pi$
$617$	−16.6972	−0.672205	−0.336102	+	0.941825i	$0.609109\pi$
$618$	−3.42221	−0.137661
$619$	−7.63331	−0.306809	−0.153404	−	0.988164i	$-0.549024\pi$
$619$	−7.63331	−0.306809	−0.153404	+	0.988164i	$0.549024\pi$
$620$	−10.8167	−0.434407
$621$	−2.09167	−0.0839359
$622$	−22.4222	−0.899049
$623$	55.2666	2.21421
$624$	−9.21110	−0.368739
$625$	2.42221	0.0968882
$626$	29.0278	1.16018
$627$	−7.60555	−0.303736
$628$	5.11943	0.204287
$629$	−46.9361	−1.87146
$630$	−13.8167	−0.550469
$631$	−10.2389	−0.407603	−0.203801	−	0.979012i	$-0.565330\pi$
$631$	−10.2389	−0.407603	−0.203801	+	0.979012i	$0.565330\pi$
$632$	15.7250	0.625506
$633$	−40.7527	−1.61978
$634$	0	0
$635$	18.3944	0.729961
$636$	25.8167	1.02370
$637$	−56.8444	−2.25226
$638$	10.3028	0.407891
$639$	−6.00000	−0.237356
$640$	−1.30278	−0.0514967
$641$	40.4222	1.59658	0.798291	−	0.602273i	$-0.205738\pi$
$641$	40.4222	1.59658	0.798291	+	0.602273i	$0.205738\pi$
$642$	−19.8167	−0.782101
$643$	−42.0555	−1.65851	−0.829254	−	0.558872i	$-0.811234\pi$
$643$	−42.0555	−1.65851	−0.829254	+	0.558872i	$0.811234\pi$
$644$	6.00000	0.236433
$645$	3.00000	0.118125
$646$	−14.2111	−0.559128
$647$	−33.6333	−1.32226	−0.661131	−	0.750271i	$-0.729923\pi$
$647$	−33.6333	−1.32226	−0.661131	+	0.750271i	$0.729923\pi$
$648$	10.6056	0.416625
$649$	5.21110	0.204554
$650$	−13.2111	−0.518182
$651$	−88.0555	−3.45117
$652$	3.30278	0.129347
$653$	10.6972	0.418615	0.209307	−	0.977850i	$-0.432879\pi$
$653$	10.6972	0.418615	0.209307	+	0.977850i	$0.432879\pi$
$654$	−22.6056	−0.883947
$655$	13.4222	0.524449
$656$	−7.30278	−0.285125
$657$	−21.2111	−0.827524
$658$	4.18335	0.163084
$659$	50.0555	1.94989	0.974943	−	0.222455i	$-0.0714070\pi$
$659$	50.0555	1.94989	0.974943	+	0.222455i	$0.0714070\pi$
$660$	−3.00000	−0.116775
$661$	1.21110	0.0471064	0.0235532	−	0.999723i	$-0.492502\pi$
$661$	1.21110	0.0471064	0.0235532	+	0.999723i	$0.492502\pi$
$662$	4.00000	0.155464
$663$	−39.6333	−1.53923
$664$	−13.8167	−0.536190
$665$	19.8167	0.768457
$666$	25.1194	0.973358
$667$	13.4222	0.519710
$668$	−10.4222	−0.403247
$669$	−3.21110	−0.124148
$670$	9.63331	0.372167
$671$	−2.00000	−0.0772091
$672$	−10.6056	−0.409118
$673$	23.3944	0.901790	0.450895	−	0.892577i	$-0.351105\pi$
$673$	23.3944	0.901790	0.450895	+	0.892577i	$0.351105\pi$
$674$	6.72498	0.259037
$675$	5.30278	0.204104
$676$	3.00000	0.115385
$677$	−8.09167	−0.310988	−0.155494	−	0.987837i	$-0.549697\pi$
$677$	−8.09167	−0.310988	−0.155494	+	0.987837i	$0.549697\pi$
$678$	39.6333	1.52211
$679$	51.2111	1.96530
$680$	−5.60555	−0.214963
$681$	−16.8167	−0.644416
$682$	−8.30278	−0.317930
$683$	−31.8167	−1.21743	−0.608715	−	0.793389i	$-0.708315\pi$
$683$	−31.8167	−1.21743	−0.608715	+	0.793389i	$0.708315\pi$
$684$	7.60555	0.290806
$685$	10.1833	0.389086
$686$	−33.2111	−1.26801
$687$	−50.6611	−1.93284
$688$	1.00000	0.0381246
$689$	−44.8444	−1.70844
$690$	−3.90833	−0.148787
$691$	13.2111	0.502574	0.251287	−	0.967913i	$-0.419146\pi$
$691$	13.2111	0.502574	0.251287	+	0.967913i	$0.419146\pi$
$692$	−14.6056	−0.555220
$693$	−10.6056	−0.402872
$694$	−2.09167	−0.0793988
$695$	−19.8167	−0.751689
$696$	−23.7250	−0.899293
$697$	−31.4222	−1.19020
$698$	−7.88057	−0.298284
$699$	45.6333	1.72601
$700$	−15.2111	−0.574926
$701$	−12.2389	−0.462255	−0.231128	−	0.972923i	$-0.574242\pi$
$701$	−12.2389	−0.462255	−0.231128	+	0.972923i	$0.574242\pi$
$702$	−6.42221	−0.242391
$703$	−36.0278	−1.35881
$704$	−1.00000	−0.0376889
$705$	−2.72498	−0.102629
$706$	6.00000	0.225813
$707$	15.6333	0.587951
$708$	−12.0000	−0.450988
$709$	3.57779	0.134367	0.0671835	−	0.997741i	$-0.478599\pi$
$709$	3.57779	0.134367	0.0671835	+	0.997741i	$0.478599\pi$
$710$	3.39445	0.127391
$711$	−36.2111	−1.35802
$712$	−12.0000	−0.449719
$713$	−10.8167	−0.405087
$714$	−45.6333	−1.70778
$715$	5.21110	0.194884
$716$	−21.9083	−0.818753
$717$	15.0000	0.560185
$718$	−21.5139	−0.802891
$719$	7.69722	0.287058	0.143529	−	0.989646i	$-0.454155\pi$
$719$	7.69722	0.287058	0.143529	+	0.989646i	$0.454155\pi$
$720$	3.00000	0.111803
$721$	6.84441	0.254899
$722$	8.09167	0.301141
$723$	−41.0278	−1.52584
$724$	7.21110	0.267999
$725$	−34.0278	−1.26376
$726$	−2.30278	−0.0854640
$727$	−8.97224	−0.332762	−0.166381	−	0.986062i	$-0.553208\pi$
$727$	−8.97224	−0.332762	−0.166381	+	0.986062i	$0.553208\pi$
$728$	18.4222	0.682772
$729$	−13.3305	−0.493723
$730$	12.0000	0.444140
$731$	4.30278	0.159144
$732$	4.60555	0.170226
$733$	−5.69722	−0.210432	−0.105216	−	0.994449i	$-0.533553\pi$
$733$	−5.69722	−0.210432	−0.105216	+	0.994449i	$0.533553\pi$
$734$	−20.9083	−0.771740
$735$	42.6333	1.57255
$736$	−1.30278	−0.0480209
$737$	7.39445	0.272378
$738$	16.8167	0.619030
$739$	−12.4861	−0.459309	−0.229655	−	0.973272i	$-0.573760\pi$
$739$	−12.4861	−0.459309	−0.229655	+	0.973272i	$0.573760\pi$
$740$	−14.2111	−0.522411
$741$	−30.4222	−1.11759
$742$	−51.6333	−1.89552
$743$	−6.00000	−0.220119	−0.110059	−	0.993925i	$-0.535104\pi$
$743$	−6.00000	−0.220119	−0.110059	+	0.993925i	$0.535104\pi$
$744$	19.1194	0.700952
$745$	−31.4222	−1.15122
$746$	3.72498	0.136381
$747$	31.8167	1.16411
$748$	−4.30278	−0.157325
$749$	39.6333	1.44817
$750$	24.9083	0.909524
$751$	28.6056	1.04383	0.521916	−	0.852997i	$-0.325218\pi$
$751$	28.6056	1.04383	0.521916	+	0.852997i	$0.325218\pi$
$752$	−0.908327	−0.0331233
$753$	−7.81665	−0.284855
$754$	41.2111	1.50082
$755$	14.8444	0.540243
$756$	−7.39445	−0.268934
$757$	28.7250	1.04403	0.522014	−	0.852937i	$-0.325181\pi$
$757$	28.7250	1.04403	0.522014	+	0.852937i	$0.325181\pi$
$758$	23.8167	0.865060
$759$	−3.00000	−0.108893
$760$	−4.30278	−0.156078
$761$	19.8167	0.718353	0.359177	−	0.933270i	$-0.383058\pi$
$761$	19.8167	0.718353	0.359177	+	0.933270i	$0.383058\pi$
$762$	−32.5139	−1.17785
$763$	45.2111	1.63675
$764$	3.39445	0.122807
$765$	12.9083	0.466702
$766$	14.6056	0.527720
$767$	20.8444	0.752648
$768$	2.30278	0.0830943
$769$	−42.7250	−1.54070	−0.770351	−	0.637620i	$-0.779919\pi$
$769$	−42.7250	−1.54070	−0.770351	+	0.637620i	$0.779919\pi$
$770$	6.00000	0.216225
$771$	−12.0000	−0.432169
$772$	25.7250	0.925862
$773$	−36.3583	−1.30772	−0.653858	−	0.756617i	$-0.726851\pi$
$773$	−36.3583	−1.30772	−0.653858	+	0.756617i	$0.726851\pi$
$774$	−2.30278	−0.0827716
$775$	27.4222	0.985035
$776$	−11.1194	−0.399164
$777$	−115.689	−4.15031
$778$	0.788897	0.0282833
$779$	−24.1194	−0.864168
$780$	−12.0000	−0.429669
$781$	2.60555	0.0932340
$782$	−5.60555	−0.200454
$783$	−16.5416	−0.591150
$784$	14.2111	0.507539
$785$	6.66947	0.238044
$786$	−23.7250	−0.846242
$787$	−11.8167	−0.421218	−0.210609	−	0.977570i	$-0.567545\pi$
$787$	−11.8167	−0.421218	−0.210609	+	0.977570i	$0.567545\pi$
$788$	−15.3944	−0.548405
$789$	−30.0000	−1.06803
$790$	20.4861	0.728864
$791$	−79.2666	−2.81840
$792$	2.30278	0.0818256
$793$	−8.00000	−0.284088
$794$	−3.02776	−0.107451
$795$	33.6333	1.19285
$796$	14.0000	0.496217
$797$	−39.6333	−1.40388	−0.701942	−	0.712234i	$-0.747683\pi$
$797$	−39.6333	−1.40388	−0.701942	+	0.712234i	$0.747683\pi$
$798$	−35.0278	−1.23997
$799$	−3.90833	−0.138267
$800$	3.30278	0.116771
$801$	27.6333	0.976375
$802$	−24.9083	−0.879544
$803$	9.21110	0.325053
$804$	−17.0278	−0.600523
$805$	7.81665	0.275501
$806$	−33.2111	−1.16981
$807$	19.8167	0.697579
$808$	−3.39445	−0.119416
$809$	−12.9083	−0.453833	−0.226916	−	0.973914i	$-0.572864\pi$
$809$	−12.9083	−0.453833	−0.226916	+	0.973914i	$0.572864\pi$
$810$	13.8167	0.485468
$811$	−21.7250	−0.762867	−0.381434	−	0.924396i	$-0.624570\pi$
$811$	−21.7250	−0.762867	−0.381434	+	0.924396i	$0.624570\pi$
$812$	47.4500	1.66517
$813$	55.0555	1.93088
$814$	−10.9083	−0.382337
$815$	4.30278	0.150720
$816$	9.90833	0.346861
$817$	3.30278	0.115549
$818$	11.8167	0.413160
$819$	−42.4222	−1.48235
$820$	−9.51388	−0.332239
$821$	35.4500	1.23721	0.618606	−	0.785701i	$-0.287698\pi$
$821$	35.4500	1.23721	0.618606	+	0.785701i	$0.287698\pi$
$822$	−18.0000	−0.627822
$823$	6.42221	0.223864	0.111932	−	0.993716i	$-0.464296\pi$
$823$	6.42221	0.223864	0.111932	+	0.993716i	$0.464296\pi$
$824$	−1.48612	−0.0517715
$825$	7.60555	0.264791
$826$	24.0000	0.835067
$827$	7.57779	0.263506	0.131753	−	0.991283i	$-0.457939\pi$
$827$	7.57779	0.263506	0.131753	+	0.991283i	$0.457939\pi$
$828$	3.00000	0.104257
$829$	18.5416	0.643978	0.321989	−	0.946743i	$-0.395649\pi$
$829$	18.5416	0.643978	0.321989	+	0.946743i	$0.395649\pi$
$830$	−18.0000	−0.624789
$831$	−18.2111	−0.631736
$832$	−4.00000	−0.138675
$833$	61.1472	2.11862
$834$	35.0278	1.21291
$835$	−13.5778	−0.469879
$836$	−3.30278	−0.114229
$837$	13.3305	0.460771
$838$	−29.2111	−1.00908
$839$	8.60555	0.297097	0.148548	−	0.988905i	$-0.452540\pi$
$839$	8.60555	0.297097	0.148548	+	0.988905i	$0.452540\pi$
$840$	−13.8167	−0.476720
$841$	77.1472	2.66025
$842$	3.72498	0.128371
$843$	−2.09167	−0.0720410
$844$	−17.6972	−0.609164
$845$	3.90833	0.134451
$846$	2.09167	0.0719132
$847$	4.60555	0.158249
$848$	11.2111	0.384991
$849$	−45.2111	−1.55164
$850$	14.2111	0.487437
$851$	−14.2111	−0.487150
$852$	−6.00000	−0.205557
$853$	−22.0000	−0.753266	−0.376633	−	0.926363i	$-0.622918\pi$
$853$	−22.0000	−0.753266	−0.376633	+	0.926363i	$0.622918\pi$
$854$	−9.21110	−0.315197
$855$	9.90833	0.338858
$856$	−8.60555	−0.294132
$857$	−21.9083	−0.748374	−0.374187	−	0.927353i	$-0.622078\pi$
$857$	−21.9083	−0.748374	−0.374187	+	0.927353i	$0.622078\pi$
$858$	−9.21110	−0.314462
$859$	12.6972	0.433224	0.216612	−	0.976258i	$-0.430499\pi$
$859$	12.6972	0.433224	0.216612	+	0.976258i	$0.430499\pi$
$860$	1.30278	0.0444243
$861$	−77.4500	−2.63949
$862$	−12.9083	−0.439659
$863$	48.4777	1.65020	0.825100	−	0.564986i	$-0.191119\pi$
$863$	48.4777	1.65020	0.825100	+	0.564986i	$0.191119\pi$
$864$	1.60555	0.0546220
$865$	−19.0278	−0.646963
$866$	−9.81665	−0.333583
$867$	3.48612	0.118395
$868$	−38.2389	−1.29791
$869$	15.7250	0.533433
$870$	−30.9083	−1.04789
$871$	29.5778	1.00221
$872$	−9.81665	−0.332434
$873$	25.6056	0.866617
$874$	−4.30278	−0.145544
$875$	−49.8167	−1.68411
$876$	−21.2111	−0.716657
$877$	27.5778	0.931236	0.465618	−	0.884986i	$-0.345832\pi$
$877$	27.5778	0.931236	0.465618	+	0.884986i	$0.345832\pi$
$878$	−22.4861	−0.758870
$879$	9.63331	0.324923
$880$	−1.30278	−0.0439166
$881$	33.5139	1.12911	0.564556	−	0.825395i	$-0.309048\pi$
$881$	33.5139	1.12911	0.564556	+	0.825395i	$0.309048\pi$
$882$	−32.7250	−1.10191
$883$	19.4500	0.654543	0.327272	−	0.944930i	$-0.393871\pi$
$883$	19.4500	0.654543	0.327272	+	0.944930i	$0.393871\pi$
$884$	−17.2111	−0.578872
$885$	−15.6333	−0.525508
$886$	9.63331	0.323637
$887$	2.60555	0.0874858	0.0437429	−	0.999043i	$-0.486072\pi$
$887$	2.60555	0.0874858	0.0437429	+	0.999043i	$0.486072\pi$
$888$	25.1194	0.842953
$889$	65.0278	2.18096
$890$	−15.6333	−0.524030
$891$	10.6056	0.355299
$892$	−1.39445	−0.0466896
$893$	−3.00000	−0.100391
$894$	55.5416	1.85759
$895$	−28.5416	−0.954042
$896$	−4.60555	−0.153861
$897$	−12.0000	−0.400668
$898$	39.6333	1.32258
$899$	−85.5416	−2.85297
$900$	−7.60555	−0.253518
$901$	48.2389	1.60707
$902$	−7.30278	−0.243156
$903$	10.6056	0.352931
$904$	17.2111	0.572433
$905$	9.39445	0.312282
$906$	−26.2389	−0.871728
$907$	−60.0555	−1.99411	−0.997055	−	0.0766861i	$-0.975566\pi$
$907$	−60.0555	−1.99411	−0.997055	+	0.0766861i	$0.975566\pi$
$908$	−7.30278	−0.242351
$909$	7.81665	0.259262
$910$	24.0000	0.795592
$911$	1.02776	0.0340511	0.0170255	−	0.999855i	$-0.494580\pi$
$911$	1.02776	0.0340511	0.0170255	+	0.999855i	$0.494580\pi$
$912$	7.60555	0.251845
$913$	−13.8167	−0.457265
$914$	36.8444	1.21870
$915$	6.00000	0.198354
$916$	−22.0000	−0.726900
$917$	47.4500	1.56694
$918$	6.90833	0.228009
$919$	31.3305	1.03350	0.516749	−	0.856137i	$-0.327142\pi$
$919$	31.3305	1.03350	0.516749	+	0.856137i	$0.327142\pi$
$920$	−1.69722	−0.0559558
$921$	−23.0278	−0.758790
$922$	−12.0000	−0.395199
$923$	10.4222	0.343051
$924$	−10.6056	−0.348897
$925$	36.0278	1.18459
$926$	−33.0278	−1.08536
$927$	3.42221	0.112400
$928$	−10.3028	−0.338205
$929$	24.0000	0.787414	0.393707	−	0.919236i	$-0.371192\pi$
$929$	24.0000	0.787414	0.393707	+	0.919236i	$0.371192\pi$
$930$	24.9083	0.816776
$931$	46.9361	1.53827
$932$	19.8167	0.649116
$933$	51.6333	1.69040
$934$	−18.9083	−0.618699
$935$	−5.60555	−0.183321
$936$	9.21110	0.301074
$937$	−30.0555	−0.981871	−0.490935	−	0.871196i	$-0.663345\pi$
$937$	−30.0555	−0.981871	−0.490935	+	0.871196i	$0.663345\pi$
$938$	34.0555	1.11195
$939$	−66.8444	−2.18138
$940$	−1.18335	−0.0385965
$941$	−18.0000	−0.586783	−0.293392	−	0.955992i	$-0.594784\pi$
$941$	−18.0000	−0.586783	−0.293392	+	0.955992i	$0.594784\pi$
$942$	−11.7889	−0.384103
$943$	−9.51388	−0.309815
$944$	−5.21110	−0.169607
$945$	−9.63331	−0.313372
$946$	1.00000	0.0325128
$947$	−35.4500	−1.15197	−0.575984	−	0.817461i	$-0.695381\pi$
$947$	−35.4500	−1.15197	−0.575984	+	0.817461i	$0.695381\pi$
$948$	−36.2111	−1.17608
$949$	36.8444	1.19602
$950$	10.9083	0.353913
$951$	0	0
$952$	−19.8167	−0.642261
$953$	33.6333	1.08949	0.544745	−	0.838602i	$-0.316627\pi$
$953$	33.6333	1.08949	0.544745	+	0.838602i	$0.316627\pi$
$954$	−25.8167	−0.835845
$955$	4.42221	0.143099
$956$	6.51388	0.210674
$957$	−23.7250	−0.766920
$958$	−38.3305	−1.23840
$959$	36.0000	1.16250
$960$	3.00000	0.0968246
$961$	37.9361	1.22374
$962$	−43.6333	−1.40679
$963$	19.8167	0.638583
$964$	−17.8167	−0.573836
$965$	33.5139	1.07885
$966$	−13.8167	−0.444544
$967$	41.1194	1.32231	0.661156	−	0.750249i	$-0.270066\pi$
$967$	41.1194	1.32231	0.661156	+	0.750249i	$0.270066\pi$
$968$	−1.00000	−0.0321412
$969$	32.7250	1.05128
$970$	−14.4861	−0.465121
$971$	3.63331	0.116598	0.0582992	−	0.998299i	$-0.481432\pi$
$971$	3.63331	0.116598	0.0582992	+	0.998299i	$0.481432\pi$
$972$	−19.6056	−0.628848
$973$	−70.0555	−2.24588
$974$	−16.0917	−0.515610
$975$	30.4222	0.974290
$976$	2.00000	0.0640184
$977$	−48.9083	−1.56472	−0.782358	−	0.622829i	$-0.785983\pi$
$977$	−48.9083	−1.56472	−0.782358	+	0.622829i	$0.785983\pi$
$978$	−7.60555	−0.243199
$979$	−12.0000	−0.383522
$980$	18.5139	0.591404
$981$	22.6056	0.721740
$982$	−2.09167	−0.0667480
$983$	40.6611	1.29689	0.648443	−	0.761263i	$-0.275420\pi$
$983$	40.6611	1.29689	0.648443	+	0.761263i	$0.275420\pi$
$984$	16.8167	0.536095
$985$	−20.0555	−0.639022
$986$	−44.3305	−1.41177
$987$	−9.63331	−0.306632
$988$	−13.2111	−0.420301
$989$	1.30278	0.0414259
$990$	3.00000	0.0953463
$991$	31.2111	0.991453	0.495727	−	0.868479i	$-0.334902\pi$
$991$	31.2111	0.991453	0.495727	+	0.868479i	$0.334902\pi$
$992$	8.30278	0.263613
$993$	−9.21110	−0.292306
$994$	12.0000	0.380617
$995$	18.2389	0.578211
$996$	31.8167	1.00815
$997$	−41.6972	−1.32056	−0.660282	−	0.751018i	$-0.729563\pi$
$997$	−41.6972	−1.32056	−0.660282	+	0.751018i	$0.729563\pi$
$998$	−2.90833	−0.0920615
$999$	17.5139	0.554115

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	946.2.a.e.1.2	✓	2
3.2	odd	2		8514.2.a.r.1.1		2
4.3	odd	2		7568.2.a.q.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
946.2.a.e.1.2	✓	2	1.1	even	1	trivial
7568.2.a.q.1.1		2	4.3	odd	2
8514.2.a.r.1.1		2	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 946 = 2 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	946.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.30278 q^{3} +1.00000 q^{4} +1.30278 q^{5} -2.30278 q^{6} +4.60555 q^{7} -1.00000 q^{8} +2.30278 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.30278 q^{3} +1.00000 q^{4} +1.30278 q^{5} -2.30278 q^{6} +4.60555 q^{7} -1.00000 q^{8} +2.30278 q^{9} -1.30278 q^{10} -1.00000 q^{11} +2.30278 q^{12} -4.00000 q^{13} -4.60555 q^{14} +3.00000 q^{15} +1.00000 q^{16} +4.30278 q^{17} -2.30278 q^{18} +3.30278 q^{19} +1.30278 q^{20} +10.6056 q^{21} +1.00000 q^{22} +1.30278 q^{23} -2.30278 q^{24} -3.30278 q^{25} +4.00000 q^{26} -1.60555 q^{27} +4.60555 q^{28} +10.3028 q^{29} -3.00000 q^{30} -8.30278 q^{31} -1.00000 q^{32} -2.30278 q^{33} -4.30278 q^{34} +6.00000 q^{35} +2.30278 q^{36} -10.9083 q^{37} -3.30278 q^{38} -9.21110 q^{39} -1.30278 q^{40} -7.30278 q^{41} -10.6056 q^{42} +1.00000 q^{43} -1.00000 q^{44} +3.00000 q^{45} -1.30278 q^{46} -0.908327 q^{47} +2.30278 q^{48} +14.2111 q^{49} +3.30278 q^{50} +9.90833 q^{51} -4.00000 q^{52} +11.2111 q^{53} +1.60555 q^{54} -1.30278 q^{55} -4.60555 q^{56} +7.60555 q^{57} -10.3028 q^{58} -5.21110 q^{59} +3.00000 q^{60} +2.00000 q^{61} +8.30278 q^{62} +10.6056 q^{63} +1.00000 q^{64} -5.21110 q^{65} +2.30278 q^{66} -7.39445 q^{67} +4.30278 q^{68} +3.00000 q^{69} -6.00000 q^{70} -2.60555 q^{71} -2.30278 q^{72} -9.21110 q^{73} +10.9083 q^{74} -7.60555 q^{75} +3.30278 q^{76} -4.60555 q^{77} +9.21110 q^{78} -15.7250 q^{79} +1.30278 q^{80} -10.6056 q^{81} +7.30278 q^{82} +13.8167 q^{83} +10.6056 q^{84} +5.60555 q^{85} -1.00000 q^{86} +23.7250 q^{87} +1.00000 q^{88} +12.0000 q^{89} -3.00000 q^{90} -18.4222 q^{91} +1.30278 q^{92} -19.1194 q^{93} +0.908327 q^{94} +4.30278 q^{95} -2.30278 q^{96} +11.1194 q^{97} -14.2111 q^{98} -2.30278 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + q^{3} + 2 q^{4} - q^{5} - q^{6} + 2 q^{7} - 2 q^{8} + q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + q^3 + 2 * q^4 - q^5 - q^6 + 2 * q^7 - 2 * q^8 + q^9	\( 2 q - 2 q^{2} + q^{3} + 2 q^{4} - q^{5} - q^{6} + 2 q^{7} - 2 q^{8} + q^{9} + q^{10} - 2 q^{11} + q^{12} - 8 q^{13} - 2 q^{14} + 6 q^{15} + 2 q^{16} + 5 q^{17} - q^{18} + 3 q^{19} - q^{20} + 14 q^{21} + 2 q^{22} - q^{23} - q^{24} - 3 q^{25} + 8 q^{26} + 4 q^{27} + 2 q^{28} + 17 q^{29} - 6 q^{30} - 13 q^{31} - 2 q^{32} - q^{33} - 5 q^{34} + 12 q^{35} + q^{36} - 11 q^{37} - 3 q^{38} - 4 q^{39} + q^{40} - 11 q^{41} - 14 q^{42} + 2 q^{43} - 2 q^{44} + 6 q^{45} + q^{46} + 9 q^{47} + q^{48} + 14 q^{49} + 3 q^{50} + 9 q^{51} - 8 q^{52} + 8 q^{53} - 4 q^{54} + q^{55} - 2 q^{56} + 8 q^{57} - 17 q^{58} + 4 q^{59} + 6 q^{60} + 4 q^{61} + 13 q^{62} + 14 q^{63} + 2 q^{64} + 4 q^{65} + q^{66} - 22 q^{67} + 5 q^{68} + 6 q^{69} - 12 q^{70} + 2 q^{71} - q^{72} - 4 q^{73} + 11 q^{74} - 8 q^{75} + 3 q^{76} - 2 q^{77} + 4 q^{78} + q^{79} - q^{80} - 14 q^{81} + 11 q^{82} + 6 q^{83} + 14 q^{84} + 4 q^{85} - 2 q^{86} + 15 q^{87} + 2 q^{88} + 24 q^{89} - 6 q^{90} - 8 q^{91} - q^{92} - 13 q^{93} - 9 q^{94} + 5 q^{95} - q^{96} - 3 q^{97} - 14 q^{98} - q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + q^3 + 2 * q^4 - q^5 - q^6 + 2 * q^7 - 2 * q^8 + q^9 + q^10 - 2 * q^11 + q^12 - 8 * q^13 - 2 * q^14 + 6 * q^15 + 2 * q^16 + 5 * q^17 - q^18 + 3 * q^19 - q^20 + 14 * q^21 + 2 * q^22 - q^23 - q^24 - 3 * q^25 + 8 * q^26 + 4 * q^27 + 2 * q^28 + 17 * q^29 - 6 * q^30 - 13 * q^31 - 2 * q^32 - q^33 - 5 * q^34 + 12 * q^35 + q^36 - 11 * q^37 - 3 * q^38 - 4 * q^39 + q^40 - 11 * q^41 - 14 * q^42 + 2 * q^43 - 2 * q^44 + 6 * q^45 + q^46 + 9 * q^47 + q^48 + 14 * q^49 + 3 * q^50 + 9 * q^51 - 8 * q^52 + 8 * q^53 - 4 * q^54 + q^55 - 2 * q^56 + 8 * q^57 - 17 * q^58 + 4 * q^59 + 6 * q^60 + 4 * q^61 + 13 * q^62 + 14 * q^63 + 2 * q^64 + 4 * q^65 + q^66 - 22 * q^67 + 5 * q^68 + 6 * q^69 - 12 * q^70 + 2 * q^71 - q^72 - 4 * q^73 + 11 * q^74 - 8 * q^75 + 3 * q^76 - 2 * q^77 + 4 * q^78 + q^79 - q^80 - 14 * q^81 + 11 * q^82 + 6 * q^83 + 14 * q^84 + 4 * q^85 - 2 * q^86 + 15 * q^87 + 2 * q^88 + 24 * q^89 - 6 * q^90 - 8 * q^91 - q^92 - 13 * q^93 - 9 * q^94 + 5 * q^95 - q^96 - 3 * q^97 - 14 * q^98 - q^99

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