LMFDB - Embedded newform 4334.2.a.g.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, 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("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.11321 q^{3} +1.00000 q^{4} +4.02507 q^{5} -2.11321 q^{6} +1.12513 q^{7} +1.00000 q^{8} +1.46567 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.11321 q^{3} +1.00000 q^{4} +4.02507 q^{5} -2.11321 q^{6} +1.12513 q^{7} +1.00000 q^{8} +1.46567 q^{9} +4.02507 q^{10} +1.00000 q^{11} -2.11321 q^{12} +6.85252 q^{13} +1.12513 q^{14} -8.50583 q^{15} +1.00000 q^{16} -3.72317 q^{17} +1.46567 q^{18} +5.98883 q^{19} +4.02507 q^{20} -2.37764 q^{21} +1.00000 q^{22} +9.19847 q^{23} -2.11321 q^{24} +11.2012 q^{25} +6.85252 q^{26} +3.24237 q^{27} +1.12513 q^{28} -8.60809 q^{29} -8.50583 q^{30} -7.66810 q^{31} +1.00000 q^{32} -2.11321 q^{33} -3.72317 q^{34} +4.52873 q^{35} +1.46567 q^{36} -6.37914 q^{37} +5.98883 q^{38} -14.4808 q^{39} +4.02507 q^{40} -0.870279 q^{41} -2.37764 q^{42} -1.99185 q^{43} +1.00000 q^{44} +5.89941 q^{45} +9.19847 q^{46} +9.15848 q^{47} -2.11321 q^{48} -5.73408 q^{49} +11.2012 q^{50} +7.86786 q^{51} +6.85252 q^{52} -2.76731 q^{53} +3.24237 q^{54} +4.02507 q^{55} +1.12513 q^{56} -12.6557 q^{57} -8.60809 q^{58} +1.66534 q^{59} -8.50583 q^{60} +11.4923 q^{61} -7.66810 q^{62} +1.64907 q^{63} +1.00000 q^{64} +27.5819 q^{65} -2.11321 q^{66} +15.4666 q^{67} -3.72317 q^{68} -19.4383 q^{69} +4.52873 q^{70} -11.4785 q^{71} +1.46567 q^{72} -2.11296 q^{73} -6.37914 q^{74} -23.6705 q^{75} +5.98883 q^{76} +1.12513 q^{77} -14.4808 q^{78} +5.22802 q^{79} +4.02507 q^{80} -11.2488 q^{81} -0.870279 q^{82} -16.1767 q^{83} -2.37764 q^{84} -14.9860 q^{85} -1.99185 q^{86} +18.1907 q^{87} +1.00000 q^{88} -18.1881 q^{89} +5.89941 q^{90} +7.70997 q^{91} +9.19847 q^{92} +16.2043 q^{93} +9.15848 q^{94} +24.1054 q^{95} -2.11321 q^{96} -8.03491 q^{97} -5.73408 q^{98} +1.46567 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q + 26 q^{2} + 12 q^{3} + 26 q^{4} + 13 q^{5} + 12 q^{6} + 13 q^{7} + 26 q^{8} + 38 q^{9}+O(q^{10}) $ 26 * q + 26 * q^2 + 12 * q^3 + 26 * q^4 + 13 * q^5 + 12 * q^6 + 13 * q^7 + 26 * q^8 + 38 * q^9	\( 26 q + 26 q^{2} + 12 q^{3} + 26 q^{4} + 13 q^{5} + 12 q^{6} + 13 q^{7} + 26 q^{8} + 38 q^{9} + 13 q^{10} + 26 q^{11} + 12 q^{12} + 24 q^{13} + 13 q^{14} + 12 q^{15} + 26 q^{16} + q^{17} + 38 q^{18} + 24 q^{19} + 13 q^{20} + 5 q^{21} + 26 q^{22} + 19 q^{23} + 12 q^{24} + 35 q^{25} + 24 q^{26} + 39 q^{27} + 13 q^{28} + 5 q^{29} + 12 q^{30} + 34 q^{31} + 26 q^{32} + 12 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} + 15 q^{37} + 24 q^{38} + 3 q^{39} + 13 q^{40} - 9 q^{41} + 5 q^{42} + 6 q^{43} + 26 q^{44} + 22 q^{45} + 19 q^{46} + 34 q^{47} + 12 q^{48} + 53 q^{49} + 35 q^{50} - 2 q^{51} + 24 q^{52} + 6 q^{53} + 39 q^{54} + 13 q^{55} + 13 q^{56} - 16 q^{57} + 5 q^{58} + 50 q^{59} + 12 q^{60} + 26 q^{61} + 34 q^{62} + 2 q^{63} + 26 q^{64} - 5 q^{65} + 12 q^{66} + 18 q^{67} + q^{68} + 15 q^{69} + 14 q^{70} + 23 q^{71} + 38 q^{72} + 37 q^{73} + 15 q^{74} + 18 q^{75} + 24 q^{76} + 13 q^{77} + 3 q^{78} + 10 q^{79} + 13 q^{80} + 50 q^{81} - 9 q^{82} + 7 q^{83} + 5 q^{84} - 7 q^{85} + 6 q^{86} + 16 q^{87} + 26 q^{88} + 3 q^{89} + 22 q^{90} + 31 q^{91} + 19 q^{92} + 52 q^{93} + 34 q^{94} + 9 q^{95} + 12 q^{96} - 9 q^{97} + 53 q^{98} + 38 q^{99}+O(q^{100}) \) 26 * q + 26 * q^2 + 12 * q^3 + 26 * q^4 + 13 * q^5 + 12 * q^6 + 13 * q^7 + 26 * q^8 + 38 * q^9 + 13 * q^10 + 26 * q^11 + 12 * q^12 + 24 * q^13 + 13 * q^14 + 12 * q^15 + 26 * q^16 + q^17 + 38 * q^18 + 24 * q^19 + 13 * q^20 + 5 * q^21 + 26 * q^22 + 19 * q^23 + 12 * q^24 + 35 * q^25 + 24 * q^26 + 39 * q^27 + 13 * q^28 + 5 * q^29 + 12 * q^30 + 34 * q^31 + 26 * q^32 + 12 * q^33 + q^34 + 14 * q^35 + 38 * q^36 + 15 * q^37 + 24 * q^38 + 3 * q^39 + 13 * q^40 - 9 * q^41 + 5 * q^42 + 6 * q^43 + 26 * q^44 + 22 * q^45 + 19 * q^46 + 34 * q^47 + 12 * q^48 + 53 * q^49 + 35 * q^50 - 2 * q^51 + 24 * q^52 + 6 * q^53 + 39 * q^54 + 13 * q^55 + 13 * q^56 - 16 * q^57 + 5 * q^58 + 50 * q^59 + 12 * q^60 + 26 * q^61 + 34 * q^62 + 2 * q^63 + 26 * q^64 - 5 * q^65 + 12 * q^66 + 18 * q^67 + q^68 + 15 * q^69 + 14 * q^70 + 23 * q^71 + 38 * q^72 + 37 * q^73 + 15 * q^74 + 18 * q^75 + 24 * q^76 + 13 * q^77 + 3 * q^78 + 10 * q^79 + 13 * q^80 + 50 * q^81 - 9 * q^82 + 7 * q^83 + 5 * q^84 - 7 * q^85 + 6 * q^86 + 16 * q^87 + 26 * q^88 + 3 * q^89 + 22 * q^90 + 31 * q^91 + 19 * q^92 + 52 * q^93 + 34 * q^94 + 9 * q^95 + 12 * q^96 - 9 * q^97 + 53 * q^98 + 38 * 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
$3$	−2.11321	−1.22006	−0.610032	−	0.792377i	$-0.708843\pi$
$3$	−2.11321	−1.22006	−0.610032	+	0.792377i	$0.708843\pi$
$4$	1.00000	0.500000
$5$	4.02507	1.80007	0.900033	−	0.435821i	$-0.143542\pi$
$5$	4.02507	1.80007	0.900033	+	0.435821i	$0.143542\pi$
$6$	−2.11321	−0.862715
$7$	1.12513	0.425259	0.212630	−	0.977133i	$-0.431797\pi$
$7$	1.12513	0.425259	0.212630	+	0.977133i	$0.431797\pi$
$8$	1.00000	0.353553
$9$	1.46567	0.488556
$10$	4.02507	1.27284
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.11321	−0.610032
$13$	6.85252	1.90055	0.950274	−	0.311416i	$-0.100803\pi$
$13$	6.85252	1.90055	0.950274	+	0.311416i	$0.100803\pi$
$14$	1.12513	0.300704
$15$	−8.50583	−2.19620
$16$	1.00000	0.250000
$17$	−3.72317	−0.903003	−0.451501	−	0.892270i	$-0.649111\pi$
$17$	−3.72317	−0.903003	−0.451501	+	0.892270i	$0.649111\pi$
$18$	1.46567	0.345461
$19$	5.98883	1.37393	0.686965	−	0.726690i	$-0.258942\pi$
$19$	5.98883	1.37393	0.686965	+	0.726690i	$0.258942\pi$
$20$	4.02507	0.900033
$21$	−2.37764	−0.518843
$22$	1.00000	0.213201
$23$	9.19847	1.91801	0.959007	−	0.283382i	$-0.0914563\pi$
$23$	9.19847	1.91801	0.959007	+	0.283382i	$0.0914563\pi$
$24$	−2.11321	−0.431358
$25$	11.2012	2.24024
$26$	6.85252	1.34389
$27$	3.24237	0.623995
$28$	1.12513	0.212630
$29$	−8.60809	−1.59848	−0.799241	−	0.601011i	$-0.794765\pi$
$29$	−8.60809	−1.59848	−0.799241	+	0.601011i	$0.794765\pi$
$30$	−8.50583	−1.55294
$31$	−7.66810	−1.37723	−0.688616	−	0.725126i	$-0.741781\pi$
$31$	−7.66810	−1.37723	−0.688616	+	0.725126i	$0.741781\pi$
$32$	1.00000	0.176777
$33$	−2.11321	−0.367863
$34$	−3.72317	−0.638519
$35$	4.52873	0.765494
$36$	1.46567	0.244278
$37$	−6.37914	−1.04872	−0.524362	−	0.851495i	$-0.675696\pi$
$37$	−6.37914	−1.04872	−0.524362	+	0.851495i	$0.675696\pi$
$38$	5.98883	0.971516
$39$	−14.4808	−2.31879
$40$	4.02507	0.636420
$41$	−0.870279	−0.135915	−0.0679574	−	0.997688i	$-0.521648\pi$
$41$	−0.870279	−0.135915	−0.0679574	+	0.997688i	$0.521648\pi$
$42$	−2.37764	−0.366878
$43$	−1.99185	−0.303755	−0.151877	−	0.988399i	$-0.548532\pi$
$43$	−1.99185	−0.303755	−0.151877	+	0.988399i	$0.548532\pi$
$44$	1.00000	0.150756
$45$	5.89941	0.879433
$46$	9.19847	1.35624
$47$	9.15848	1.33590	0.667951	−	0.744205i	$-0.267172\pi$
$47$	9.15848	1.33590	0.667951	+	0.744205i	$0.267172\pi$
$48$	−2.11321	−0.305016
$49$	−5.73408	−0.819155
$50$	11.2012	1.58409
$51$	7.86786	1.10172
$52$	6.85252	0.950274
$53$	−2.76731	−0.380119	−0.190059	−	0.981773i	$-0.560868\pi$
$53$	−2.76731	−0.380119	−0.190059	+	0.981773i	$0.560868\pi$
$54$	3.24237	0.441231
$55$	4.02507	0.542740
$56$	1.12513	0.150352
$57$	−12.6557	−1.67628
$58$	−8.60809	−1.13030
$59$	1.66534	0.216809	0.108404	−	0.994107i	$-0.465426\pi$
$59$	1.66534	0.216809	0.108404	+	0.994107i	$0.465426\pi$
$60$	−8.50583	−1.09810
$61$	11.4923	1.47144	0.735721	−	0.677284i	$-0.236843\pi$
$61$	11.4923	1.47144	0.735721	+	0.677284i	$0.236843\pi$
$62$	−7.66810	−0.973850
$63$	1.64907	0.207763
$64$	1.00000	0.125000
$65$	27.5819	3.42111
$66$	−2.11321	−0.260118
$67$	15.4666	1.88955	0.944773	−	0.327725i	$-0.106282\pi$
$67$	15.4666	1.88955	0.944773	+	0.327725i	$0.106282\pi$
$68$	−3.72317	−0.451501
$69$	−19.4383	−2.34010
$70$	4.52873	0.541286
$71$	−11.4785	−1.36225	−0.681123	−	0.732169i	$-0.738508\pi$
$71$	−11.4785	−1.36225	−0.681123	+	0.732169i	$0.738508\pi$
$72$	1.46567	0.172731
$73$	−2.11296	−0.247304	−0.123652	−	0.992326i	$-0.539461\pi$
$73$	−2.11296	−0.247304	−0.123652	+	0.992326i	$0.539461\pi$
$74$	−6.37914	−0.741560
$75$	−23.6705	−2.73323
$76$	5.98883	0.686965
$77$	1.12513	0.128220
$78$	−14.4808	−1.63963
$79$	5.22802	0.588198	0.294099	−	0.955775i	$-0.404980\pi$
$79$	5.22802	0.588198	0.294099	+	0.955775i	$0.404980\pi$
$80$	4.02507	0.450017
$81$	−11.2488	−1.24987
$82$	−0.870279	−0.0961063
$83$	−16.1767	−1.77562	−0.887811	−	0.460209i	$-0.847775\pi$
$83$	−16.1767	−1.77562	−0.887811	+	0.460209i	$0.847775\pi$
$84$	−2.37764	−0.259422
$85$	−14.9860	−1.62546
$86$	−1.99185	−0.214787
$87$	18.1907	1.95025
$88$	1.00000	0.106600
$89$	−18.1881	−1.92794	−0.963969	−	0.266014i	$-0.914293\pi$
$89$	−18.1881	−1.92794	−0.963969	+	0.266014i	$0.914293\pi$
$90$	5.89941	0.621853
$91$	7.70997	0.808225
$92$	9.19847	0.959007
$93$	16.2043	1.68031
$94$	9.15848	0.944626
$95$	24.1054	2.47317
$96$	−2.11321	−0.215679
$97$	−8.03491	−0.815822	−0.407911	−	0.913022i	$-0.633743\pi$
$97$	−8.03491	−0.815822	−0.407911	+	0.913022i	$0.633743\pi$
$98$	−5.73408	−0.579230
$99$	1.46567	0.147305
$100$	11.2012	1.12012
$101$	−13.1031	−1.30381	−0.651903	−	0.758302i	$-0.726029\pi$
$101$	−13.1031	−1.30381	−0.651903	+	0.758302i	$0.726029\pi$
$102$	7.86786	0.779034
$103$	−5.39833	−0.531913	−0.265957	−	0.963985i	$-0.585688\pi$
$103$	−5.39833	−0.531913	−0.265957	+	0.963985i	$0.585688\pi$
$104$	6.85252	0.671945
$105$	−9.57016	−0.933952
$106$	−2.76731	−0.268785
$107$	6.42715	0.621336	0.310668	−	0.950519i	$-0.399447\pi$
$107$	6.42715	0.621336	0.310668	+	0.950519i	$0.399447\pi$
$108$	3.24237	0.311997
$109$	−8.19500	−0.784938	−0.392469	−	0.919765i	$-0.628379\pi$
$109$	−8.19500	−0.784938	−0.392469	+	0.919765i	$0.628379\pi$
$110$	4.02507	0.383775
$111$	13.4805	1.27951
$112$	1.12513	0.106315
$113$	5.99125	0.563609	0.281805	−	0.959472i	$-0.409067\pi$
$113$	5.99125	0.563609	0.281805	+	0.959472i	$0.409067\pi$
$114$	−12.6557	−1.18531
$115$	37.0245	3.45255
$116$	−8.60809	−0.799241
$117$	10.0435	0.928523
$118$	1.66534	0.153307
$119$	−4.18905	−0.384010
$120$	−8.50583	−0.776472
$121$	1.00000	0.0909091
$122$	11.4923	1.04047
$123$	1.83908	0.165825
$124$	−7.66810	−0.688616
$125$	24.9602	2.23251
$126$	1.64907	0.146910
$127$	5.18225	0.459850	0.229925	−	0.973208i	$-0.426152\pi$
$127$	5.18225	0.459850	0.229925	+	0.973208i	$0.426152\pi$
$128$	1.00000	0.0883883
$129$	4.20921	0.370600
$130$	27.5819	2.41909
$131$	−13.3239	−1.16411	−0.582056	−	0.813149i	$-0.697751\pi$
$131$	−13.3239	−1.16411	−0.582056	+	0.813149i	$0.697751\pi$
$132$	−2.11321	−0.183932
$133$	6.73821	0.584277
$134$	15.4666	1.33611
$135$	13.0508	1.12323
$136$	−3.72317	−0.319260
$137$	16.5182	1.41124	0.705622	−	0.708588i	$-0.250668\pi$
$137$	16.5182	1.41124	0.705622	+	0.708588i	$0.250668\pi$
$138$	−19.4383	−1.65470
$139$	−0.714402	−0.0605948	−0.0302974	−	0.999541i	$-0.509645\pi$
$139$	−0.714402	−0.0605948	−0.0302974	+	0.999541i	$0.509645\pi$
$140$	4.52873	0.382747
$141$	−19.3538	−1.62989
$142$	−11.4785	−0.963253
$143$	6.85252	0.573037
$144$	1.46567	0.122139
$145$	−34.6482	−2.87737
$146$	−2.11296	−0.174870
$147$	12.1173	0.999421
$148$	−6.37914	−0.524362
$149$	−14.0502	−1.15103	−0.575517	−	0.817790i	$-0.695199\pi$
$149$	−14.0502	−1.15103	−0.575517	+	0.817790i	$0.695199\pi$
$150$	−23.6705	−1.93269
$151$	2.78031	0.226258	0.113129	−	0.993580i	$-0.463913\pi$
$151$	2.78031	0.226258	0.113129	+	0.993580i	$0.463913\pi$
$152$	5.98883	0.485758
$153$	−5.45694	−0.441167
$154$	1.12513	0.0906655
$155$	−30.8647	−2.47911
$156$	−14.4808	−1.15939
$157$	−3.05469	−0.243791	−0.121895	−	0.992543i	$-0.538897\pi$
$157$	−3.05469	−0.243791	−0.121895	+	0.992543i	$0.538897\pi$
$158$	5.22802	0.415919
$159$	5.84791	0.463769
$160$	4.02507	0.318210
$161$	10.3495	0.815653
$162$	−11.2488	−0.883791
$163$	−21.6362	−1.69467	−0.847337	−	0.531055i	$-0.821796\pi$
$163$	−21.6362	−1.69467	−0.847337	+	0.531055i	$0.821796\pi$
$164$	−0.870279	−0.0679574
$165$	−8.50583	−0.662178
$166$	−16.1767	−1.25555
$167$	12.5669	0.972456	0.486228	−	0.873832i	$-0.338372\pi$
$167$	12.5669	0.972456	0.486228	+	0.873832i	$0.338372\pi$
$168$	−2.37764	−0.183439
$169$	33.9570	2.61208
$170$	−14.9860	−1.14938
$171$	8.77763	0.671242
$172$	−1.99185	−0.151877
$173$	6.55504	0.498370	0.249185	−	0.968456i	$-0.419837\pi$
$173$	6.55504	0.498370	0.249185	+	0.968456i	$0.419837\pi$
$174$	18.1907	1.37903
$175$	12.6028	0.952682
$176$	1.00000	0.0753778
$177$	−3.51922	−0.264521
$178$	−18.1881	−1.36326
$179$	−5.67386	−0.424084	−0.212042	−	0.977261i	$-0.568011\pi$
$179$	−5.67386	−0.424084	−0.212042	+	0.977261i	$0.568011\pi$
$180$	5.89941	0.439716
$181$	7.14818	0.531320	0.265660	−	0.964067i	$-0.414410\pi$
$181$	7.14818	0.531320	0.265660	+	0.964067i	$0.414410\pi$
$182$	7.70997	0.571501
$183$	−24.2857	−1.79525
$184$	9.19847	0.678121
$185$	−25.6765	−1.88777
$186$	16.2043	1.18816
$187$	−3.72317	−0.272266
$188$	9.15848	0.667951
$189$	3.64809	0.265359
$190$	24.1054	1.74879
$191$	11.4023	0.825045	0.412522	−	0.910948i	$-0.364648\pi$
$191$	11.4023	0.825045	0.412522	+	0.910948i	$0.364648\pi$
$192$	−2.11321	−0.152508
$193$	−5.85555	−0.421492	−0.210746	−	0.977541i	$-0.567589\pi$
$193$	−5.85555	−0.421492	−0.210746	+	0.977541i	$0.567589\pi$
$194$	−8.03491	−0.576873
$195$	−58.2864	−4.17397
$196$	−5.73408	−0.409577
$197$	1.00000	0.0712470
$197$	1.00000	0.0712470
$198$	1.46567	0.104160
$199$	14.2512	1.01024	0.505120	−	0.863049i	$-0.331448\pi$
$199$	14.2512	1.01024	0.505120	+	0.863049i	$0.331448\pi$
$200$	11.2012	0.792044
$201$	−32.6842	−2.30537
$202$	−13.1031	−0.921931
$203$	−9.68521	−0.679769
$204$	7.86786	0.550860
$205$	−3.50294	−0.244656
$206$	−5.39833	−0.376119
$207$	13.4819	0.937057
$208$	6.85252	0.475137
$209$	5.98883	0.414256
$210$	−9.57016	−0.660404
$211$	9.14640	0.629664	0.314832	−	0.949147i	$-0.398052\pi$
$211$	9.14640	0.629664	0.314832	+	0.949147i	$0.398052\pi$
$212$	−2.76731	−0.190059
$213$	24.2565	1.66203
$214$	6.42715	0.439351
$215$	−8.01735	−0.546779
$216$	3.24237	0.220615
$217$	−8.62761	−0.585680
$218$	−8.19500	−0.555035
$219$	4.46514	0.301726
$220$	4.02507	0.271370
$221$	−25.5131	−1.71620
$222$	13.4805	0.904751
$223$	12.4041	0.830637	0.415319	−	0.909676i	$-0.363670\pi$
$223$	12.4041	0.830637	0.415319	+	0.909676i	$0.363670\pi$
$224$	1.12513	0.0751759
$225$	16.4172	1.09448
$226$	5.99125	0.398532
$227$	−23.5702	−1.56441	−0.782205	−	0.623021i	$-0.785905\pi$
$227$	−23.5702	−1.56441	−0.782205	+	0.623021i	$0.785905\pi$
$228$	−12.6557	−0.838142
$229$	2.86880	0.189576	0.0947879	−	0.995497i	$-0.469783\pi$
$229$	2.86880	0.189576	0.0947879	+	0.995497i	$0.469783\pi$
$230$	37.0245	2.44132
$231$	−2.37764	−0.156437
$232$	−8.60809	−0.565149
$233$	1.60314	0.105025	0.0525126	−	0.998620i	$-0.483277\pi$
$233$	1.60314	0.105025	0.0525126	+	0.998620i	$0.483277\pi$
$234$	10.0435	0.656565
$235$	36.8635	2.40471
$236$	1.66534	0.108404
$237$	−11.0479	−0.717639
$238$	−4.18905	−0.271536
$239$	3.70653	0.239756	0.119878	−	0.992789i	$-0.461750\pi$
$239$	3.70653	0.239756	0.119878	+	0.992789i	$0.461750\pi$
$240$	−8.50583	−0.549049
$241$	22.2405	1.43264	0.716320	−	0.697772i	$-0.245825\pi$
$241$	22.2405	1.43264	0.716320	+	0.697772i	$0.245825\pi$
$242$	1.00000	0.0642824
$243$	14.0440	0.900925
$244$	11.4923	0.735721
$245$	−23.0801	−1.47453
$246$	1.83908	0.117256
$247$	41.0385	2.61122
$248$	−7.66810	−0.486925
$249$	34.1848	2.16637
$250$	24.9602	1.57862
$251$	0.365919	0.0230966	0.0115483	−	0.999933i	$-0.496324\pi$
$251$	0.365919	0.0230966	0.0115483	+	0.999933i	$0.496324\pi$
$252$	1.64907	0.103881
$253$	9.19847	0.578303
$254$	5.18225	0.325163
$255$	31.6687	1.98317
$256$	1.00000	0.0625000
$257$	−9.90518	−0.617868	−0.308934	−	0.951083i	$-0.599972\pi$
$257$	−9.90518	−0.617868	−0.308934	+	0.951083i	$0.599972\pi$
$258$	4.20921	0.262054
$259$	−7.17736	−0.445980
$260$	27.5819	1.71056
$261$	−12.6166	−0.780947
$262$	−13.3239	−0.823151
$263$	11.6895	0.720805	0.360402	−	0.932797i	$-0.382639\pi$
$263$	11.6895	0.720805	0.360402	+	0.932797i	$0.382639\pi$
$264$	−2.11321	−0.130059
$265$	−11.1386	−0.684239
$266$	6.73821	0.413146
$267$	38.4354	2.35221
$268$	15.4666	0.944773
$269$	5.53361	0.337390	0.168695	−	0.985668i	$-0.446045\pi$
$269$	5.53361	0.337390	0.168695	+	0.985668i	$0.446045\pi$
$270$	13.0508	0.794245
$271$	−8.01334	−0.486776	−0.243388	−	0.969929i	$-0.578259\pi$
$271$	−8.01334	−0.486776	−0.243388	+	0.969929i	$0.578259\pi$
$272$	−3.72317	−0.225751
$273$	−16.2928	−0.986086
$274$	16.5182	0.997900
$275$	11.2012	0.675457
$276$	−19.4383	−1.17005
$277$	15.1316	0.909167	0.454584	−	0.890704i	$-0.349788\pi$
$277$	15.1316	0.909167	0.454584	+	0.890704i	$0.349788\pi$
$278$	−0.714402	−0.0428470
$279$	−11.2389	−0.672855
$280$	4.52873	0.270643
$281$	−8.20727	−0.489605	−0.244802	−	0.969573i	$-0.578723\pi$
$281$	−8.20727	−0.489605	−0.244802	+	0.969573i	$0.578723\pi$
$282$	−19.3538	−1.15250
$283$	26.7684	1.59121	0.795607	−	0.605813i	$-0.207152\pi$
$283$	26.7684	1.59121	0.795607	+	0.605813i	$0.207152\pi$
$284$	−11.4785	−0.681123
$285$	−50.9399	−3.01742
$286$	6.85252	0.405198
$287$	−0.979177	−0.0577990
$288$	1.46567	0.0863653
$289$	−3.13797	−0.184586
$290$	−34.6482	−2.03461
$291$	16.9795	0.995355
$292$	−2.11296	−0.123652
$293$	−3.17625	−0.185559	−0.0927793	−	0.995687i	$-0.529575\pi$
$293$	−3.17625	−0.185559	−0.0927793	+	0.995687i	$0.529575\pi$
$294$	12.1173	0.706697
$295$	6.70311	0.390270
$296$	−6.37914	−0.370780
$297$	3.24237	0.188141
$298$	−14.0502	−0.813904
$299$	63.0327	3.64528
$300$	−23.6705	−1.36662
$301$	−2.24109	−0.129174
$302$	2.78031	0.159989
$303$	27.6896	1.59073
$304$	5.98883	0.343483
$305$	46.2575	2.64869
$306$	−5.45694	−0.311952
$307$	−26.7510	−1.52676	−0.763381	−	0.645949i	$-0.776462\pi$
$307$	−26.7510	−1.52676	−0.763381	+	0.645949i	$0.776462\pi$
$308$	1.12513	0.0641102
$309$	11.4078	0.648968
$310$	−30.8647	−1.75299
$311$	23.1203	1.31103	0.655516	−	0.755182i	$-0.272451\pi$
$311$	23.1203	1.31103	0.655516	+	0.755182i	$0.272451\pi$
$312$	−14.4808	−0.819816
$313$	−21.3281	−1.20553	−0.602767	−	0.797918i	$-0.705935\pi$
$313$	−21.3281	−1.20553	−0.602767	+	0.797918i	$0.705935\pi$
$314$	−3.05469	−0.172386
$315$	6.63761	0.373987
$316$	5.22802	0.294099
$317$	−16.4971	−0.926572	−0.463286	−	0.886209i	$-0.653330\pi$
$317$	−16.4971	−0.926572	−0.463286	+	0.886209i	$0.653330\pi$
$318$	5.84791	0.327934
$319$	−8.60809	−0.481960
$320$	4.02507	0.225008
$321$	−13.5819	−0.758069
$322$	10.3495	0.576754
$323$	−22.2974	−1.24066
$324$	−11.2488	−0.624935
$325$	76.7564	4.25768
$326$	−21.6362	−1.19832
$327$	17.3178	0.957675
$328$	−0.870279	−0.0480531
$329$	10.3045	0.568105
$330$	−8.50583	−0.468231
$331$	18.6378	1.02442	0.512212	−	0.858859i	$-0.328826\pi$
$331$	18.6378	1.02442	0.512212	+	0.858859i	$0.328826\pi$
$332$	−16.1767	−0.887811
$333$	−9.34970	−0.512360
$334$	12.5669	0.687630
$335$	62.2542	3.40131
$336$	−2.37764	−0.129711
$337$	−14.0503	−0.765370	−0.382685	−	0.923879i	$-0.625000\pi$
$337$	−14.0503	−0.765370	−0.382685	+	0.923879i	$0.625000\pi$
$338$	33.9570	1.84702
$339$	−12.6608	−0.687639
$340$	−14.9860	−0.812732
$341$	−7.66810	−0.415251
$342$	8.77763	0.474640
$343$	−14.3275	−0.773612
$344$	−1.99185	−0.107394
$345$	−78.2407	−4.21234
$346$	6.55504	0.352401
$347$	21.4513	1.15156	0.575782	−	0.817603i	$-0.304698\pi$
$347$	21.4513	1.15156	0.575782	+	0.817603i	$0.304698\pi$
$348$	18.1907	0.975125
$349$	28.3544	1.51778	0.758889	−	0.651220i	$-0.225743\pi$
$349$	28.3544	1.51778	0.758889	+	0.651220i	$0.225743\pi$
$350$	12.6028	0.673648
$351$	22.2184	1.18593
$352$	1.00000	0.0533002
$353$	27.0780	1.44121	0.720607	−	0.693343i	$-0.243863\pi$
$353$	27.0780	1.44121	0.720607	+	0.693343i	$0.243863\pi$
$354$	−3.51922	−0.187044
$355$	−46.2017	−2.45213
$356$	−18.1881	−0.963969
$357$	8.85236	0.468517
$358$	−5.67386	−0.299873
$359$	−15.5584	−0.821139	−0.410570	−	0.911829i	$-0.634670\pi$
$359$	−15.5584	−0.821139	−0.410570	+	0.911829i	$0.634670\pi$
$360$	5.89941	0.310926
$361$	16.8660	0.887686
$362$	7.14818	0.375700
$363$	−2.11321	−0.110915
$364$	7.70997	0.404112
$365$	−8.50483	−0.445163
$366$	−24.2857	−1.26944
$367$	−17.4499	−0.910878	−0.455439	−	0.890267i	$-0.650518\pi$
$367$	−17.4499	−0.910878	−0.455439	+	0.890267i	$0.650518\pi$
$368$	9.19847	0.479504
$369$	−1.27554	−0.0664019
$370$	−25.6765	−1.33486
$371$	−3.11358	−0.161649
$372$	16.2043	0.840156
$373$	21.1337	1.09426	0.547130	−	0.837048i	$-0.315720\pi$
$373$	21.1337	1.09426	0.547130	+	0.837048i	$0.315720\pi$
$374$	−3.72317	−0.192521
$375$	−52.7463	−2.72381
$376$	9.15848	0.472313
$377$	−58.9871	−3.03799
$378$	3.64809	0.187637
$379$	5.30518	0.272509	0.136254	−	0.990674i	$-0.456494\pi$
$379$	5.30518	0.272509	0.136254	+	0.990674i	$0.456494\pi$
$380$	24.1054	1.23658
$381$	−10.9512	−0.561047
$382$	11.4023	0.583395
$383$	29.0539	1.48459	0.742293	−	0.670076i	$-0.233738\pi$
$383$	29.0539	1.48459	0.742293	+	0.670076i	$0.233738\pi$
$384$	−2.11321	−0.107839
$385$	4.52873	0.230805
$386$	−5.85555	−0.298040
$387$	−2.91939	−0.148401
$388$	−8.03491	−0.407911
$389$	−9.11828	−0.462315	−0.231158	−	0.972916i	$-0.574251\pi$
$389$	−9.11828	−0.462315	−0.231158	+	0.972916i	$0.574251\pi$
$390$	−58.2864	−2.95144
$391$	−34.2475	−1.73197
$392$	−5.73408	−0.289615
$393$	28.1562	1.42029
$394$	1.00000	0.0503793
$395$	21.0431	1.05880
$396$	1.46567	0.0736525
$397$	−32.6280	−1.63755	−0.818775	−	0.574114i	$-0.805347\pi$
$397$	−32.6280	−1.63755	−0.818775	+	0.574114i	$0.805347\pi$
$398$	14.2512	0.714348
$399$	−14.2393	−0.712855
$400$	11.2012	0.560060
$401$	−7.25250	−0.362173	−0.181086	−	0.983467i	$-0.557961\pi$
$401$	−7.25250	−0.362173	−0.181086	+	0.983467i	$0.557961\pi$
$402$	−32.6842	−1.63014
$403$	−52.5458	−2.61749
$404$	−13.1031	−0.651903
$405$	−45.2773	−2.24985
$406$	−9.68521	−0.480669
$407$	−6.37914	−0.316202
$408$	7.86786	0.389517
$409$	−14.8572	−0.734639	−0.367320	−	0.930095i	$-0.619724\pi$
$409$	−14.8572	−0.734639	−0.367320	+	0.930095i	$0.619724\pi$
$410$	−3.50294	−0.172998
$411$	−34.9064	−1.72181
$412$	−5.39833	−0.265957
$413$	1.87372	0.0921999
$414$	13.4819	0.662599
$415$	−65.1123	−3.19624
$416$	6.85252	0.335972
$417$	1.50968	0.0739295
$418$	5.98883	0.292923
$419$	−1.13864	−0.0556264	−0.0278132	−	0.999613i	$-0.508854\pi$
$419$	−1.13864	−0.0556264	−0.0278132	+	0.999613i	$0.508854\pi$
$420$	−9.57016	−0.466976
$421$	22.8350	1.11291	0.556454	−	0.830878i	$-0.312162\pi$
$421$	22.8350	1.11291	0.556454	+	0.830878i	$0.312162\pi$
$422$	9.14640	0.445240
$423$	13.4233	0.652663
$424$	−2.76731	−0.134392
$425$	−41.7040	−2.02294
$426$	24.2565	1.17523
$427$	12.9304	0.625744
$428$	6.42715	0.310668
$429$	−14.4808	−0.699141
$430$	−8.01735	−0.386631
$431$	−3.20207	−0.154238	−0.0771192	−	0.997022i	$-0.524572\pi$
$431$	−3.20207	−0.154238	−0.0771192	+	0.997022i	$0.524572\pi$
$432$	3.24237	0.155999
$433$	1.47630	0.0709467	0.0354733	−	0.999371i	$-0.488706\pi$
$433$	1.47630	0.0709467	0.0354733	+	0.999371i	$0.488706\pi$
$434$	−8.62761	−0.414139
$435$	73.2189	3.51058
$436$	−8.19500	−0.392469
$437$	55.0881	2.63522
$438$	4.46514	0.213353
$439$	−0.802543	−0.0383033	−0.0191516	−	0.999817i	$-0.506097\pi$
$439$	−0.802543	−0.0383033	−0.0191516	+	0.999817i	$0.506097\pi$
$440$	4.02507	0.191888
$441$	−8.40426	−0.400203
$442$	−25.5131	−1.21354
$443$	−17.4918	−0.831063	−0.415531	−	0.909579i	$-0.636404\pi$
$443$	−17.4918	−0.831063	−0.415531	+	0.909579i	$0.636404\pi$
$444$	13.4805	0.639756
$445$	−73.2085	−3.47042
$446$	12.4041	0.587349
$447$	29.6910	1.40434
$448$	1.12513	0.0531574
$449$	−13.1912	−0.622533	−0.311266	−	0.950323i	$-0.600753\pi$
$449$	−13.1912	−0.622533	−0.311266	+	0.950323i	$0.600753\pi$
$450$	16.4172	0.773915
$451$	−0.870279	−0.0409798
$452$	5.99125	0.281805
$453$	−5.87538	−0.276049
$454$	−23.5702	−1.10621
$455$	31.0332	1.45486
$456$	−12.6557	−0.592656
$457$	37.1568	1.73812	0.869060	−	0.494707i	$-0.164725\pi$
$457$	37.1568	1.73812	0.869060	+	0.494707i	$0.164725\pi$
$458$	2.86880	0.134050
$459$	−12.0719	−0.563469
$460$	37.0245	1.72628
$461$	−4.72758	−0.220185	−0.110093	−	0.993921i	$-0.535115\pi$
$461$	−4.72758	−0.220185	−0.110093	+	0.993921i	$0.535115\pi$
$462$	−2.37764	−0.110618
$463$	−3.04001	−0.141281	−0.0706407	−	0.997502i	$-0.522504\pi$
$463$	−3.04001	−0.141281	−0.0706407	+	0.997502i	$0.522504\pi$
$464$	−8.60809	−0.399620
$465$	65.2236	3.02467
$466$	1.60314	0.0742640
$467$	22.6528	1.04824	0.524122	−	0.851643i	$-0.324393\pi$
$467$	22.6528	1.04824	0.524122	+	0.851643i	$0.324393\pi$
$468$	10.0435	0.464262
$469$	17.4019	0.803547
$470$	36.8635	1.70039
$471$	6.45521	0.297441
$472$	1.66534	0.0766535
$473$	−1.99185	−0.0915855
$474$	−11.0479	−0.507448
$475$	67.0820	3.07793
$476$	−4.18905	−0.192005
$477$	−4.05595	−0.185709
$478$	3.70653	0.169533
$479$	−20.6511	−0.943574	−0.471787	−	0.881713i	$-0.656391\pi$
$479$	−20.6511	−0.943574	−0.471787	+	0.881713i	$0.656391\pi$
$480$	−8.50583	−0.388236
$481$	−43.7132	−1.99315
$482$	22.2405	1.01303
$483$	−21.8706	−0.995149
$484$	1.00000	0.0454545
$485$	−32.3411	−1.46853
$486$	14.0440	0.637050
$487$	−8.05084	−0.364819	−0.182409	−	0.983223i	$-0.558390\pi$
$487$	−8.05084	−0.364819	−0.182409	+	0.983223i	$0.558390\pi$
$488$	11.4923	0.520234
$489$	45.7218	2.06761
$490$	−23.0801	−1.04265
$491$	31.9570	1.44220	0.721099	−	0.692832i	$-0.243637\pi$
$491$	31.9570	1.44220	0.721099	+	0.692832i	$0.243637\pi$
$492$	1.83908	0.0829124
$493$	32.0494	1.44343
$494$	41.0385	1.84641
$495$	5.89941	0.265159
$496$	−7.66810	−0.344308
$497$	−12.9148	−0.579308
$498$	34.1848	1.53186
$499$	−6.04343	−0.270541	−0.135271	−	0.990809i	$-0.543190\pi$
$499$	−6.04343	−0.270541	−0.135271	+	0.990809i	$0.543190\pi$
$500$	24.9602	1.11626
$501$	−26.5565	−1.18646
$502$	0.365919	0.0163318
$503$	−16.5465	−0.737774	−0.368887	−	0.929474i	$-0.620261\pi$
$503$	−16.5465	−0.737774	−0.368887	+	0.929474i	$0.620261\pi$
$504$	1.64907	0.0734552
$505$	−52.7409	−2.34694
$506$	9.19847	0.408922
$507$	−71.7584	−3.18690
$508$	5.18225	0.229925
$509$	−20.2034	−0.895499	−0.447750	−	0.894159i	$-0.647774\pi$
$509$	−20.2034	−0.895499	−0.447750	+	0.894159i	$0.647774\pi$
$510$	31.6687	1.40231
$511$	−2.37736	−0.105168
$512$	1.00000	0.0441942
$513$	19.4180	0.857325
$514$	−9.90518	−0.436899
$515$	−21.7287	−0.957479
$516$	4.20921	0.185300
$517$	9.15848	0.402790
$518$	−7.17736	−0.315355
$519$	−13.8522	−0.608043
$520$	27.5819	1.20955
$521$	13.5392	0.593165	0.296582	−	0.955007i	$-0.404153\pi$
$521$	13.5392	0.593165	0.296582	+	0.955007i	$0.404153\pi$
$522$	−12.6166	−0.552213
$523$	−29.9125	−1.30798	−0.653991	−	0.756502i	$-0.726907\pi$
$523$	−29.9125	−1.30798	−0.653991	+	0.756502i	$0.726907\pi$
$524$	−13.3239	−0.582056
$525$	−26.6324	−1.16233
$526$	11.6895	0.509686
$527$	28.5497	1.24364
$528$	−2.11321	−0.0919658
$529$	61.6119	2.67878
$530$	−11.1386	−0.483830
$531$	2.44083	0.105923
$532$	6.73821	0.292138
$533$	−5.96361	−0.258312
$534$	38.4354	1.66326
$535$	25.8697	1.11845
$536$	15.4666	0.668056
$537$	11.9901	0.517410
$538$	5.53361	0.238571
$539$	−5.73408	−0.246984
$540$	13.0508	0.561616
$541$	−29.5772	−1.27162	−0.635812	−	0.771844i	$-0.719335\pi$
$541$	−29.5772	−1.27162	−0.635812	+	0.771844i	$0.719335\pi$
$542$	−8.01334	−0.344203
$543$	−15.1056	−0.648244
$544$	−3.72317	−0.159630
$545$	−32.9854	−1.41294
$546$	−16.2928	−0.697268
$547$	−23.6796	−1.01247	−0.506233	−	0.862397i	$-0.668962\pi$
$547$	−23.6796	−1.01247	−0.506233	+	0.862397i	$0.668962\pi$
$548$	16.5182	0.705622
$549$	16.8439	0.718882
$550$	11.2012	0.477620
$551$	−51.5523	−2.19620
$552$	−19.4383	−0.827350
$553$	5.88220	0.250137
$554$	15.1316	0.642879
$555$	54.2599	2.30320
$556$	−0.714402	−0.0302974
$557$	−29.4440	−1.24758	−0.623791	−	0.781591i	$-0.714408\pi$
$557$	−29.4440	−1.24758	−0.623791	+	0.781591i	$0.714408\pi$
$558$	−11.2389	−0.475780
$559$	−13.6492	−0.577300
$560$	4.52873	0.191374
$561$	7.86786	0.332181
$562$	−8.20727	−0.346203
$563$	10.5300	0.443788	0.221894	−	0.975071i	$-0.428776\pi$
$563$	10.5300	0.443788	0.221894	+	0.975071i	$0.428776\pi$
$564$	−19.3538	−0.814943
$565$	24.1152	1.01453
$566$	26.7684	1.12516
$567$	−12.6564	−0.531518
$568$	−11.4785	−0.481627
$569$	28.3441	1.18825	0.594123	−	0.804374i	$-0.297499\pi$
$569$	28.3441	1.18825	0.594123	+	0.804374i	$0.297499\pi$
$570$	−50.9399	−2.13364
$571$	−17.0701	−0.714362	−0.357181	−	0.934035i	$-0.616262\pi$
$571$	−17.0701	−0.714362	−0.357181	+	0.934035i	$0.616262\pi$
$572$	6.85252	0.286518
$573$	−24.0956	−1.00661
$574$	−0.979177	−0.0408701
$575$	103.034	4.29681
$576$	1.46567	0.0610695
$577$	8.14695	0.339162	0.169581	−	0.985516i	$-0.445759\pi$
$577$	8.14695	0.339162	0.169581	+	0.985516i	$0.445759\pi$
$578$	−3.13797	−0.130522
$579$	12.3740	0.514247
$580$	−34.6482	−1.43869
$581$	−18.2009	−0.755099
$582$	16.9795	0.703822
$583$	−2.76731	−0.114610
$584$	−2.11296	−0.0874351
$585$	40.4259	1.67140
$586$	−3.17625	−0.131210
$587$	−39.3414	−1.62379	−0.811896	−	0.583802i	$-0.801565\pi$
$587$	−39.3414	−1.62379	−0.811896	+	0.583802i	$0.801565\pi$
$588$	12.1173	0.499711
$589$	−45.9229	−1.89222
$590$	6.70311	0.275963
$591$	−2.11321	−0.0869259
$592$	−6.37914	−0.262181
$593$	0.331340	0.0136065	0.00680326	−	0.999977i	$-0.497834\pi$
$593$	0.331340	0.0136065	0.00680326	+	0.999977i	$0.497834\pi$
$594$	3.24237	0.133036
$595$	−16.8612	−0.691243
$596$	−14.0502	−0.575517
$597$	−30.1158	−1.23256
$598$	63.0327	2.57760
$599$	−43.1164	−1.76169	−0.880845	−	0.473405i	$-0.843025\pi$
$599$	−43.1164	−1.76169	−0.880845	+	0.473405i	$0.843025\pi$
$600$	−23.6705	−0.966344
$601$	−40.7251	−1.66121	−0.830606	−	0.556860i	$-0.812006\pi$
$601$	−40.7251	−1.66121	−0.830606	+	0.556860i	$0.812006\pi$
$602$	−2.24109	−0.0913402
$603$	22.6689	0.923149
$604$	2.78031	0.113129
$605$	4.02507	0.163642
$606$	27.6896	1.12481
$607$	−38.4742	−1.56162	−0.780811	−	0.624768i	$-0.785194\pi$
$607$	−38.4742	−1.56162	−0.780811	+	0.624768i	$0.785194\pi$
$608$	5.98883	0.242879
$609$	20.4669	0.829361
$610$	46.2575	1.87291
$611$	62.7587	2.53895
$612$	−5.45694	−0.220584
$613$	−1.34073	−0.0541514	−0.0270757	−	0.999633i	$-0.508620\pi$
$613$	−1.34073	−0.0541514	−0.0270757	+	0.999633i	$0.508620\pi$
$614$	−26.7510	−1.07958
$615$	7.40245	0.298495
$616$	1.12513	0.0453328
$617$	−26.2921	−1.05848	−0.529240	−	0.848472i	$-0.677523\pi$
$617$	−26.2921	−1.05848	−0.529240	+	0.848472i	$0.677523\pi$
$618$	11.4078	0.458890
$619$	−16.1103	−0.647528	−0.323764	−	0.946138i	$-0.604948\pi$
$619$	−16.1103	−0.647528	−0.323764	+	0.946138i	$0.604948\pi$
$620$	−30.8647	−1.23955
$621$	29.8249	1.19683
$622$	23.1203	0.927039
$623$	−20.4640	−0.819873
$624$	−14.4808	−0.579697
$625$	44.4608	1.77843
$626$	−21.3281	−0.852441
$627$	−12.6557	−0.505418
$628$	−3.05469	−0.121895
$629$	23.7507	0.947001
$630$	6.63761	0.264449
$631$	−26.5819	−1.05821	−0.529104	−	0.848557i	$-0.677472\pi$
$631$	−26.5819	−1.05821	−0.529104	+	0.848557i	$0.677472\pi$
$632$	5.22802	0.207959
$633$	−19.3283	−0.768230
$634$	−16.4971	−0.655185
$635$	20.8589	0.827761
$636$	5.84791	0.231885
$637$	−39.2929	−1.55684
$638$	−8.60809	−0.340797
$639$	−16.8236	−0.665533
$640$	4.02507	0.159105
$641$	4.15035	0.163929	0.0819645	−	0.996635i	$-0.473881\pi$
$641$	4.15035	0.163929	0.0819645	+	0.996635i	$0.473881\pi$
$642$	−13.5819	−0.536036
$643$	39.2771	1.54894	0.774469	−	0.632612i	$-0.218017\pi$
$643$	39.2771	1.54894	0.774469	+	0.632612i	$0.218017\pi$
$644$	10.3495	0.407827
$645$	16.9424	0.667105
$646$	−22.2974	−0.877281
$647$	38.9854	1.53268	0.766338	−	0.642438i	$-0.222077\pi$
$647$	38.9854	1.53268	0.766338	+	0.642438i	$0.222077\pi$
$648$	−11.2488	−0.441895
$649$	1.66534	0.0653703
$650$	76.7564	3.01063
$651$	18.2320	0.714568
$652$	−21.6362	−0.847337
$653$	−12.4326	−0.486526	−0.243263	−	0.969960i	$-0.578218\pi$
$653$	−12.4326	−0.486526	−0.243263	+	0.969960i	$0.578218\pi$
$654$	17.3178	0.677178
$655$	−53.6295	−2.09548
$656$	−0.870279	−0.0339787
$657$	−3.09690	−0.120822
$658$	10.3045	0.401711
$659$	−30.3147	−1.18089	−0.590447	−	0.807077i	$-0.701048\pi$
$659$	−30.3147	−1.18089	−0.590447	+	0.807077i	$0.701048\pi$
$660$	−8.50583	−0.331089
$661$	−12.6571	−0.492306	−0.246153	−	0.969231i	$-0.579166\pi$
$661$	−12.6571	−0.492306	−0.246153	+	0.969231i	$0.579166\pi$
$662$	18.6378	0.724378
$663$	53.9147	2.09387
$664$	−16.1767	−0.627777
$665$	27.1218	1.05174
$666$	−9.34970	−0.362294
$667$	−79.1813	−3.06591
$668$	12.5669	0.486228
$669$	−26.2124	−1.01343
$670$	62.2542	2.40509
$671$	11.4923	0.443657
$672$	−2.37764	−0.0917194
$673$	−18.3185	−0.706125	−0.353062	−	0.935600i	$-0.614860\pi$
$673$	−18.3185	−0.706125	−0.353062	+	0.935600i	$0.614860\pi$
$674$	−14.0503	−0.541198
$675$	36.3184	1.39790
$676$	33.9570	1.30604
$677$	43.4852	1.67127	0.835636	−	0.549284i	$-0.185099\pi$
$677$	43.4852	1.67127	0.835636	+	0.549284i	$0.185099\pi$
$678$	−12.6608	−0.486234
$679$	−9.04032	−0.346936
$680$	−14.9860	−0.574688
$681$	49.8089	1.90868
$682$	−7.66810	−0.293627
$683$	−16.3641	−0.626157	−0.313078	−	0.949727i	$-0.601360\pi$
$683$	−16.3641	−0.626157	−0.313078	+	0.949727i	$0.601360\pi$
$684$	8.77763	0.335621
$685$	66.4869	2.54033
$686$	−14.3275	−0.547026
$687$	−6.06239	−0.231295
$688$	−1.99185	−0.0759387
$689$	−18.9630	−0.722434
$690$	−78.2407	−2.97857
$691$	−10.2159	−0.388629	−0.194315	−	0.980939i	$-0.562248\pi$
$691$	−10.2159	−0.388629	−0.194315	+	0.980939i	$0.562248\pi$
$692$	6.55504	0.249185
$693$	1.64907	0.0626428
$694$	21.4513	0.814279
$695$	−2.87552	−0.109075
$696$	18.1907	0.689517
$697$	3.24020	0.122731
$698$	28.3544	1.07323
$699$	−3.38778	−0.128137
$700$	12.6028	0.476341
$701$	−21.0278	−0.794209	−0.397105	−	0.917773i	$-0.629985\pi$
$701$	−21.0278	−0.794209	−0.397105	+	0.917773i	$0.629985\pi$
$702$	22.2184	0.838580
$703$	−38.2036	−1.44088
$704$	1.00000	0.0376889
$705$	−77.9005	−2.93390
$706$	27.0780	1.01909
$707$	−14.7427	−0.554456
$708$	−3.51922	−0.132260
$709$	−24.6924	−0.927343	−0.463672	−	0.886007i	$-0.653468\pi$
$709$	−24.6924	−0.927343	−0.463672	+	0.886007i	$0.653468\pi$
$710$	−46.2017	−1.73392
$711$	7.66254	0.287368
$712$	−18.1881	−0.681629
$713$	−70.5349	−2.64155
$714$	8.85236	0.331291
$715$	27.5819	1.03150
$716$	−5.67386	−0.212042
$717$	−7.83269	−0.292517
$718$	−15.5584	−0.580633
$719$	21.9393	0.818197	0.409099	−	0.912490i	$-0.365843\pi$
$719$	21.9393	0.818197	0.409099	+	0.912490i	$0.365843\pi$
$720$	5.89941	0.219858
$721$	−6.07382	−0.226201
$722$	16.8660	0.627689
$723$	−46.9990	−1.74791
$724$	7.14818	0.265660
$725$	−96.4208	−3.58098
$726$	−2.11321	−0.0784287
$727$	−2.37240	−0.0879875	−0.0439937	−	0.999032i	$-0.514008\pi$
$727$	−2.37240	−0.0879875	−0.0439937	+	0.999032i	$0.514008\pi$
$728$	7.70997	0.285751
$729$	4.06843	0.150683
$730$	−8.50483	−0.314778
$731$	7.41602	0.274291
$732$	−24.2857	−0.897627
$733$	−1.73248	−0.0639906	−0.0319953	−	0.999488i	$-0.510186\pi$
$733$	−1.73248	−0.0639906	−0.0319953	+	0.999488i	$0.510186\pi$
$734$	−17.4499	−0.644088
$735$	48.7731	1.79902
$736$	9.19847	0.339060
$737$	15.4666	0.569720
$738$	−1.27554	−0.0469533
$739$	7.39273	0.271946	0.135973	−	0.990713i	$-0.456584\pi$
$739$	7.39273	0.271946	0.135973	+	0.990713i	$0.456584\pi$
$740$	−25.6765	−0.943887
$741$	−86.7232	−3.18586
$742$	−3.11358	−0.114303
$743$	27.4889	1.00847	0.504235	−	0.863566i	$-0.331774\pi$
$743$	27.4889	1.00847	0.504235	+	0.863566i	$0.331774\pi$
$744$	16.2043	0.594080
$745$	−56.5529	−2.07194
$746$	21.1337	0.773758
$747$	−23.7096	−0.867490
$748$	−3.72317	−0.136133
$749$	7.23137	0.264229
$750$	−52.7463	−1.92602
$751$	11.0794	0.404292	0.202146	−	0.979355i	$-0.435208\pi$
$751$	11.0794	0.404292	0.202146	+	0.979355i	$0.435208\pi$
$752$	9.15848	0.333976
$753$	−0.773265	−0.0281793
$754$	−58.9871	−2.14818
$755$	11.1909	0.407280
$756$	3.64809	0.132680
$757$	16.6687	0.605834	0.302917	−	0.953017i	$-0.402039\pi$
$757$	16.6687	0.605834	0.302917	+	0.953017i	$0.402039\pi$
$758$	5.30518	0.192693
$759$	−19.4383	−0.705567
$760$	24.1054	0.874396
$761$	−6.60284	−0.239353	−0.119676	−	0.992813i	$-0.538186\pi$
$761$	−6.60284	−0.239353	−0.119676	+	0.992813i	$0.538186\pi$
$762$	−10.9512	−0.396720
$763$	−9.22043	−0.333802
$764$	11.4023	0.412522
$765$	−21.9646	−0.794130
$766$	29.0539	1.04976
$767$	11.4118	0.412055
$768$	−2.11321	−0.0762540
$769$	−12.0978	−0.436258	−0.218129	−	0.975920i	$-0.569995\pi$
$769$	−12.0978	−0.436258	−0.218129	+	0.975920i	$0.569995\pi$
$770$	4.52873	0.163204
$771$	20.9318	0.753839
$772$	−5.85555	−0.210746
$773$	−16.4719	−0.592453	−0.296226	−	0.955118i	$-0.595728\pi$
$773$	−16.4719	−0.592453	−0.296226	+	0.955118i	$0.595728\pi$
$774$	−2.91939	−0.104935
$775$	−85.8919	−3.08533
$776$	−8.03491	−0.288437
$777$	15.1673	0.544124
$778$	−9.11828	−0.326906
$779$	−5.21195	−0.186738
$780$	−58.2864	−2.08699
$781$	−11.4785	−0.410733
$782$	−34.2475	−1.22469
$783$	−27.9106	−0.997444
$784$	−5.73408	−0.204789
$785$	−12.2954	−0.438840
$786$	28.1562	1.00430
$787$	25.9265	0.924181	0.462091	−	0.886833i	$-0.347099\pi$
$787$	25.9265	0.924181	0.462091	+	0.886833i	$0.347099\pi$
$788$	1.00000	0.0356235
$789$	−24.7024	−0.879428
$790$	21.0431	0.748682
$791$	6.74093	0.239680
$792$	1.46567	0.0520802
$793$	78.7514	2.79655
$794$	−32.6280	−1.15792
$795$	23.5382	0.834815
$796$	14.2512	0.505120
$797$	−28.5785	−1.01230	−0.506152	−	0.862444i	$-0.668932\pi$
$797$	−28.5785	−1.01230	−0.506152	+	0.862444i	$0.668932\pi$
$798$	−14.2393	−0.504064
$799$	−34.0986	−1.20632
$800$	11.2012	0.396022
$801$	−26.6578	−0.941905
$802$	−7.25250	−0.256095
$803$	−2.11296	−0.0745649
$804$	−32.6842	−1.15268
$805$	41.6574	1.46823
$806$	−52.5458	−1.85085
$807$	−11.6937	−0.411638
$808$	−13.1031	−0.460965
$809$	39.2805	1.38103	0.690514	−	0.723319i	$-0.257384\pi$
$809$	39.2805	1.38103	0.690514	+	0.723319i	$0.257384\pi$
$810$	−45.2773	−1.59088
$811$	37.0169	1.29984	0.649920	−	0.760002i	$-0.274802\pi$
$811$	37.0169	1.29984	0.649920	+	0.760002i	$0.274802\pi$
$812$	−9.68521	−0.339884
$813$	16.9339	0.593898
$814$	−6.37914	−0.223589
$815$	−87.0870	−3.05053
$816$	7.86786	0.275430
$817$	−11.9289	−0.417338
$818$	−14.8572	−0.519468
$819$	11.3003	0.394863
$820$	−3.50294	−0.122328
$821$	52.8478	1.84440	0.922201	−	0.386712i	$-0.126389\pi$
$821$	52.8478	1.84440	0.922201	+	0.386712i	$0.126389\pi$
$822$	−34.9064	−1.21750
$823$	−38.0527	−1.32644	−0.663218	−	0.748427i	$-0.730810\pi$
$823$	−38.0527	−1.32644	−0.663218	+	0.748427i	$0.730810\pi$
$824$	−5.39833	−0.188060
$825$	−23.6705	−0.824101
$826$	1.87372	0.0651952
$827$	−40.1920	−1.39761	−0.698807	−	0.715311i	$-0.746285\pi$
$827$	−40.1920	−1.39761	−0.698807	+	0.715311i	$0.746285\pi$
$828$	13.4819	0.468529
$829$	−15.1036	−0.524569	−0.262285	−	0.964991i	$-0.584476\pi$
$829$	−15.1036	−0.524569	−0.262285	+	0.964991i	$0.584476\pi$
$830$	−65.1123	−2.26008
$831$	−31.9762	−1.10924
$832$	6.85252	0.237568
$833$	21.3490	0.739699
$834$	1.50968	0.0522761
$835$	50.5827	1.75048
$836$	5.98883	0.207128
$837$	−24.8628	−0.859385
$838$	−1.13864	−0.0393338
$839$	36.3533	1.25505	0.627527	−	0.778595i	$-0.284067\pi$
$839$	36.3533	1.25505	0.627527	+	0.778595i	$0.284067\pi$
$840$	−9.57016	−0.330202
$841$	45.0992	1.55514
$842$	22.8350	0.786945
$843$	17.3437	0.597349
$844$	9.14640	0.314832
$845$	136.679	4.70192
$846$	13.4233	0.461502
$847$	1.12513	0.0386599
$848$	−2.76731	−0.0950297
$849$	−56.5673	−1.94138
$850$	−41.7040	−1.43044
$851$	−58.6784	−2.01147
$852$	24.2565	0.831014
$853$	−40.6170	−1.39070	−0.695350	−	0.718672i	$-0.744750\pi$
$853$	−40.6170	−1.39070	−0.695350	+	0.718672i	$0.744750\pi$
$854$	12.9304	0.442468
$855$	35.3306	1.20828
$856$	6.42715	0.219675
$857$	−16.0623	−0.548676	−0.274338	−	0.961633i	$-0.588459\pi$
$857$	−16.0623	−0.548676	−0.274338	+	0.961633i	$0.588459\pi$
$858$	−14.4808	−0.494367
$859$	−15.0914	−0.514911	−0.257456	−	0.966290i	$-0.582884\pi$
$859$	−15.0914	−0.514911	−0.257456	+	0.966290i	$0.582884\pi$
$860$	−8.01735	−0.273389
$861$	2.06921	0.0705185
$862$	−3.20207	−0.109063
$863$	16.5375	0.562944	0.281472	−	0.959569i	$-0.409177\pi$
$863$	16.5375	0.562944	0.281472	+	0.959569i	$0.409177\pi$
$864$	3.24237	0.110308
$865$	26.3845	0.897099
$866$	1.47630	0.0501669
$867$	6.63119	0.225207
$868$	−8.62761	−0.292840
$869$	5.22802	0.177348
$870$	73.2189	2.48235
$871$	105.985	3.59117
$872$	−8.19500	−0.277518
$873$	−11.7765	−0.398574
$874$	55.0881	1.86338
$875$	28.0835	0.949396
$876$	4.46514	0.150863
$877$	−14.8069	−0.499994	−0.249997	−	0.968247i	$-0.580430\pi$
$877$	−14.8069	−0.499994	−0.249997	+	0.968247i	$0.580430\pi$
$878$	−0.802543	−0.0270845
$879$	6.71210	0.226393
$880$	4.02507	0.135685
$881$	−9.69815	−0.326739	−0.163369	−	0.986565i	$-0.552236\pi$
$881$	−9.69815	−0.326739	−0.163369	+	0.986565i	$0.552236\pi$
$882$	−8.40426	−0.282986
$883$	22.2989	0.750418	0.375209	−	0.926940i	$-0.377571\pi$
$883$	22.2989	0.750418	0.375209	+	0.926940i	$0.377571\pi$
$884$	−25.5131	−0.858099
$885$	−14.1651	−0.476155
$886$	−17.4918	−0.587650
$887$	−11.1805	−0.375403	−0.187702	−	0.982226i	$-0.560104\pi$
$887$	−11.1805	−0.375403	−0.187702	+	0.982226i	$0.560104\pi$
$888$	13.4805	0.452375
$889$	5.83071	0.195556
$890$	−73.2085	−2.45396
$891$	−11.2488	−0.376850
$892$	12.4041	0.415319
$893$	54.8486	1.83544
$894$	29.6910	0.993015
$895$	−22.8377	−0.763379
$896$	1.12513	0.0375879
$897$	−133.202	−4.44747
$898$	−13.1912	−0.440197
$899$	66.0077	2.20148
$900$	16.4172	0.547241
$901$	10.3032	0.343248
$902$	−0.870279	−0.0289771
$903$	4.73591	0.157601
$904$	5.99125	0.199266
$905$	28.7719	0.956411
$906$	−5.87538	−0.195196
$907$	15.9873	0.530850	0.265425	−	0.964131i	$-0.414488\pi$
$907$	15.9873	0.530850	0.265425	+	0.964131i	$0.414488\pi$
$908$	−23.5702	−0.782205
$909$	−19.2048	−0.636982
$910$	31.0332	1.02874
$911$	30.2045	1.00072	0.500360	−	0.865818i	$-0.333201\pi$
$911$	30.2045	1.00072	0.500360	+	0.865818i	$0.333201\pi$
$912$	−12.6557	−0.419071
$913$	−16.1767	−0.535370
$914$	37.1568	1.22904
$915$	−97.7518	−3.23158
$916$	2.86880	0.0947879
$917$	−14.9911	−0.495049
$918$	−12.0719	−0.398433
$919$	−35.3412	−1.16580	−0.582900	−	0.812544i	$-0.698082\pi$
$919$	−35.3412	−1.16580	−0.582900	+	0.812544i	$0.698082\pi$
$920$	37.0245	1.22066
$921$	56.5306	1.86275
$922$	−4.72758	−0.155695
$923$	−78.6566	−2.58901
$924$	−2.37764	−0.0782186
$925$	−71.4540	−2.34939
$926$	−3.04001	−0.0999010
$927$	−7.91215	−0.259869
$928$	−8.60809	−0.282574
$929$	22.7463	0.746281	0.373140	−	0.927775i	$-0.378281\pi$
$929$	22.7463	0.746281	0.373140	+	0.927775i	$0.378281\pi$
$930$	65.2236	2.13877
$931$	−34.3404	−1.12546
$932$	1.60314	0.0525126
$933$	−48.8581	−1.59954
$934$	22.6528	0.741221
$935$	−14.9860	−0.490096
$936$	10.0435	0.328283
$937$	8.97807	0.293301	0.146650	−	0.989188i	$-0.453151\pi$
$937$	8.97807	0.293301	0.146650	+	0.989188i	$0.453151\pi$
$938$	17.4019	0.568193
$939$	45.0707	1.47083
$940$	36.8635	1.20236
$941$	12.9542	0.422295	0.211147	−	0.977454i	$-0.432280\pi$
$941$	12.9542	0.422295	0.211147	+	0.977454i	$0.432280\pi$
$942$	6.45521	0.210322
$943$	−8.00524	−0.260687
$944$	1.66534	0.0542022
$945$	14.6838	0.477664
$946$	−1.99185	−0.0647607
$947$	20.3492	0.661260	0.330630	−	0.943760i	$-0.392739\pi$
$947$	20.3492	0.661260	0.330630	+	0.943760i	$0.392739\pi$
$948$	−11.0479	−0.358820
$949$	−14.4791	−0.470013
$950$	67.0820	2.17643
$951$	34.8620	1.13048
$952$	−4.18905	−0.135768
$953$	−46.4864	−1.50584	−0.752922	−	0.658110i	$-0.771356\pi$
$953$	−46.4864	−1.50584	−0.752922	+	0.658110i	$0.771356\pi$
$954$	−4.05595	−0.131316
$955$	45.8952	1.48513
$956$	3.70653	0.119878
$957$	18.1907	0.588022
$958$	−20.6511	−0.667207
$959$	18.5851	0.600144
$960$	−8.50583	−0.274524
$961$	27.7998	0.896768
$962$	−43.7132	−1.40937
$963$	9.42006	0.303557
$964$	22.2405	0.716320
$965$	−23.5690	−0.758713
$966$	−21.8706	−0.703676
$967$	0.765354	0.0246121	0.0123061	−	0.999924i	$-0.496083\pi$
$967$	0.765354	0.0246121	0.0123061	+	0.999924i	$0.496083\pi$
$968$	1.00000	0.0321412
$969$	47.1192	1.51369
$970$	−32.3411	−1.03841
$971$	−21.9473	−0.704323	−0.352162	−	0.935939i	$-0.614553\pi$
$971$	−21.9473	−0.704323	−0.352162	+	0.935939i	$0.614553\pi$
$972$	14.0440	0.450463
$973$	−0.803795	−0.0257685
$974$	−8.05084	−0.257966
$975$	−162.203	−5.19464
$976$	11.4923	0.367861
$977$	−25.3537	−0.811137	−0.405568	−	0.914065i	$-0.632926\pi$
$977$	−25.3537	−0.811137	−0.405568	+	0.914065i	$0.632926\pi$
$978$	45.7218	1.46202
$979$	−18.1881	−0.581295
$980$	−23.0801	−0.737266
$981$	−12.0111	−0.383486
$982$	31.9570	1.01979
$983$	−14.8598	−0.473955	−0.236978	−	0.971515i	$-0.576157\pi$
$983$	−14.8598	−0.473955	−0.236978	+	0.971515i	$0.576157\pi$
$984$	1.83908	0.0586279
$985$	4.02507	0.128249
$986$	32.0494	1.02066
$987$	−21.7756	−0.693124
$988$	41.0385	1.30561
$989$	−18.3220	−0.582606
$990$	5.89941	0.187496
$991$	−24.5259	−0.779089	−0.389545	−	0.921008i	$-0.627368\pi$
$991$	−24.5259	−0.779089	−0.389545	+	0.921008i	$0.627368\pi$
$992$	−7.66810	−0.243463
$993$	−39.3856	−1.24986
$994$	−12.9148	−0.409632
$995$	57.3620	1.81850
$996$	34.1848	1.08319
$997$	2.66534	0.0844123	0.0422061	−	0.999109i	$-0.486561\pi$
$997$	2.66534	0.0844123	0.0422061	+	0.999109i	$0.486561\pi$
$998$	−6.04343	−0.191302
$999$	−20.6836	−0.654399

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.g.1.4	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.g.1.4	✓	26	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:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.11321 q^{3} +1.00000 q^{4} +4.02507 q^{5} -2.11321 q^{6} +1.12513 q^{7} +1.00000 q^{8} +1.46567 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.11321 q^{3} +1.00000 q^{4} +4.02507 q^{5} -2.11321 q^{6} +1.12513 q^{7} +1.00000 q^{8} +1.46567 q^{9} +4.02507 q^{10} +1.00000 q^{11} -2.11321 q^{12} +6.85252 q^{13} +1.12513 q^{14} -8.50583 q^{15} +1.00000 q^{16} -3.72317 q^{17} +1.46567 q^{18} +5.98883 q^{19} +4.02507 q^{20} -2.37764 q^{21} +1.00000 q^{22} +9.19847 q^{23} -2.11321 q^{24} +11.2012 q^{25} +6.85252 q^{26} +3.24237 q^{27} +1.12513 q^{28} -8.60809 q^{29} -8.50583 q^{30} -7.66810 q^{31} +1.00000 q^{32} -2.11321 q^{33} -3.72317 q^{34} +4.52873 q^{35} +1.46567 q^{36} -6.37914 q^{37} +5.98883 q^{38} -14.4808 q^{39} +4.02507 q^{40} -0.870279 q^{41} -2.37764 q^{42} -1.99185 q^{43} +1.00000 q^{44} +5.89941 q^{45} +9.19847 q^{46} +9.15848 q^{47} -2.11321 q^{48} -5.73408 q^{49} +11.2012 q^{50} +7.86786 q^{51} +6.85252 q^{52} -2.76731 q^{53} +3.24237 q^{54} +4.02507 q^{55} +1.12513 q^{56} -12.6557 q^{57} -8.60809 q^{58} +1.66534 q^{59} -8.50583 q^{60} +11.4923 q^{61} -7.66810 q^{62} +1.64907 q^{63} +1.00000 q^{64} +27.5819 q^{65} -2.11321 q^{66} +15.4666 q^{67} -3.72317 q^{68} -19.4383 q^{69} +4.52873 q^{70} -11.4785 q^{71} +1.46567 q^{72} -2.11296 q^{73} -6.37914 q^{74} -23.6705 q^{75} +5.98883 q^{76} +1.12513 q^{77} -14.4808 q^{78} +5.22802 q^{79} +4.02507 q^{80} -11.2488 q^{81} -0.870279 q^{82} -16.1767 q^{83} -2.37764 q^{84} -14.9860 q^{85} -1.99185 q^{86} +18.1907 q^{87} +1.00000 q^{88} -18.1881 q^{89} +5.89941 q^{90} +7.70997 q^{91} +9.19847 q^{92} +16.2043 q^{93} +9.15848 q^{94} +24.1054 q^{95} -2.11321 q^{96} -8.03491 q^{97} -5.73408 q^{98} +1.46567 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + 26 q^{2} + 12 q^{3} + 26 q^{4} + 13 q^{5} + 12 q^{6} + 13 q^{7} + 26 q^{8} + 38 q^{9}+O(q^{10}) \) 26 * q + 26 * q^2 + 12 * q^3 + 26 * q^4 + 13 * q^5 + 12 * q^6 + 13 * q^7 + 26 * q^8 + 38 * q^9	\( 26 q + 26 q^{2} + 12 q^{3} + 26 q^{4} + 13 q^{5} + 12 q^{6} + 13 q^{7} + 26 q^{8} + 38 q^{9} + 13 q^{10} + 26 q^{11} + 12 q^{12} + 24 q^{13} + 13 q^{14} + 12 q^{15} + 26 q^{16} + q^{17} + 38 q^{18} + 24 q^{19} + 13 q^{20} + 5 q^{21} + 26 q^{22} + 19 q^{23} + 12 q^{24} + 35 q^{25} + 24 q^{26} + 39 q^{27} + 13 q^{28} + 5 q^{29} + 12 q^{30} + 34 q^{31} + 26 q^{32} + 12 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} + 15 q^{37} + 24 q^{38} + 3 q^{39} + 13 q^{40} - 9 q^{41} + 5 q^{42} + 6 q^{43} + 26 q^{44} + 22 q^{45} + 19 q^{46} + 34 q^{47} + 12 q^{48} + 53 q^{49} + 35 q^{50} - 2 q^{51} + 24 q^{52} + 6 q^{53} + 39 q^{54} + 13 q^{55} + 13 q^{56} - 16 q^{57} + 5 q^{58} + 50 q^{59} + 12 q^{60} + 26 q^{61} + 34 q^{62} + 2 q^{63} + 26 q^{64} - 5 q^{65} + 12 q^{66} + 18 q^{67} + q^{68} + 15 q^{69} + 14 q^{70} + 23 q^{71} + 38 q^{72} + 37 q^{73} + 15 q^{74} + 18 q^{75} + 24 q^{76} + 13 q^{77} + 3 q^{78} + 10 q^{79} + 13 q^{80} + 50 q^{81} - 9 q^{82} + 7 q^{83} + 5 q^{84} - 7 q^{85} + 6 q^{86} + 16 q^{87} + 26 q^{88} + 3 q^{89} + 22 q^{90} + 31 q^{91} + 19 q^{92} + 52 q^{93} + 34 q^{94} + 9 q^{95} + 12 q^{96} - 9 q^{97} + 53 q^{98} + 38 q^{99}+O(q^{100}) \) 26 * q + 26 * q^2 + 12 * q^3 + 26 * q^4 + 13 * q^5 + 12 * q^6 + 13 * q^7 + 26 * q^8 + 38 * q^9 + 13 * q^10 + 26 * q^11 + 12 * q^12 + 24 * q^13 + 13 * q^14 + 12 * q^15 + 26 * q^16 + q^17 + 38 * q^18 + 24 * q^19 + 13 * q^20 + 5 * q^21 + 26 * q^22 + 19 * q^23 + 12 * q^24 + 35 * q^25 + 24 * q^26 + 39 * q^27 + 13 * q^28 + 5 * q^29 + 12 * q^30 + 34 * q^31 + 26 * q^32 + 12 * q^33 + q^34 + 14 * q^35 + 38 * q^36 + 15 * q^37 + 24 * q^38 + 3 * q^39 + 13 * q^40 - 9 * q^41 + 5 * q^42 + 6 * q^43 + 26 * q^44 + 22 * q^45 + 19 * q^46 + 34 * q^47 + 12 * q^48 + 53 * q^49 + 35 * q^50 - 2 * q^51 + 24 * q^52 + 6 * q^53 + 39 * q^54 + 13 * q^55 + 13 * q^56 - 16 * q^57 + 5 * q^58 + 50 * q^59 + 12 * q^60 + 26 * q^61 + 34 * q^62 + 2 * q^63 + 26 * q^64 - 5 * q^65 + 12 * q^66 + 18 * q^67 + q^68 + 15 * q^69 + 14 * q^70 + 23 * q^71 + 38 * q^72 + 37 * q^73 + 15 * q^74 + 18 * q^75 + 24 * q^76 + 13 * q^77 + 3 * q^78 + 10 * q^79 + 13 * q^80 + 50 * q^81 - 9 * q^82 + 7 * q^83 + 5 * q^84 - 7 * q^85 + 6 * q^86 + 16 * q^87 + 26 * q^88 + 3 * q^89 + 22 * q^90 + 31 * q^91 + 19 * q^92 + 52 * q^93 + 34 * q^94 + 9 * q^95 + 12 * q^96 - 9 * q^97 + 53 * q^98 + 38 * q^99

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