LMFDB - Embedded newform 4730.2.a.be.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4730, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4730.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$37.7692401561$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 26 x^{10} + 79 x^{9} + 247 x^{8} - 766 x^{7} - 1023 x^{6} + 3281 x^{5} + 1634 x^{4} + \cdots + 392 $ x^12 - 3x^11 - 26x^10 + 79x^9 + 247x^8 - 766x^7 - 1023x^6 + 3281x^5 + 1634x^4 - 5557x^3 - 483x^2 + 1648*x + 392
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$2.72061$ of defining polynomial
Character	$\chi$	$=$	4730.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.72061 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.72061 q^{6} +1.91272 q^{7} +1.00000 q^{8} +4.40172 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.72061 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.72061 q^{6} +1.91272 q^{7} +1.00000 q^{8} +4.40172 q^{9} +1.00000 q^{10} -1.00000 q^{11} +2.72061 q^{12} +1.20875 q^{13} +1.91272 q^{14} +2.72061 q^{15} +1.00000 q^{16} -3.77479 q^{17} +4.40172 q^{18} +5.93546 q^{19} +1.00000 q^{20} +5.20376 q^{21} -1.00000 q^{22} +0.791254 q^{23} +2.72061 q^{24} +1.00000 q^{25} +1.20875 q^{26} +3.81352 q^{27} +1.91272 q^{28} +0.597002 q^{29} +2.72061 q^{30} +7.15695 q^{31} +1.00000 q^{32} -2.72061 q^{33} -3.77479 q^{34} +1.91272 q^{35} +4.40172 q^{36} +1.12735 q^{37} +5.93546 q^{38} +3.28853 q^{39} +1.00000 q^{40} -10.3674 q^{41} +5.20376 q^{42} +1.00000 q^{43} -1.00000 q^{44} +4.40172 q^{45} +0.791254 q^{46} -12.0994 q^{47} +2.72061 q^{48} -3.34151 q^{49} +1.00000 q^{50} -10.2697 q^{51} +1.20875 q^{52} -11.3466 q^{53} +3.81352 q^{54} -1.00000 q^{55} +1.91272 q^{56} +16.1481 q^{57} +0.597002 q^{58} -4.42095 q^{59} +2.72061 q^{60} -2.65531 q^{61} +7.15695 q^{62} +8.41924 q^{63} +1.00000 q^{64} +1.20875 q^{65} -2.72061 q^{66} +15.5544 q^{67} -3.77479 q^{68} +2.15269 q^{69} +1.91272 q^{70} -4.84257 q^{71} +4.40172 q^{72} -2.10242 q^{73} +1.12735 q^{74} +2.72061 q^{75} +5.93546 q^{76} -1.91272 q^{77} +3.28853 q^{78} -0.235281 q^{79} +1.00000 q^{80} -2.83004 q^{81} -10.3674 q^{82} +10.7230 q^{83} +5.20376 q^{84} -3.77479 q^{85} +1.00000 q^{86} +1.62421 q^{87} -1.00000 q^{88} -1.84824 q^{89} +4.40172 q^{90} +2.31199 q^{91} +0.791254 q^{92} +19.4713 q^{93} -12.0994 q^{94} +5.93546 q^{95} +2.72061 q^{96} -0.701016 q^{97} -3.34151 q^{98} -4.40172 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 3 q^{3} + 12 q^{4} + 12 q^{5} + 3 q^{6} + 8 q^{7} + 12 q^{8} + 25 q^{9}+O(q^{10}) $ 12 * q + 12 * q^2 + 3 * q^3 + 12 * q^4 + 12 * q^5 + 3 * q^6 + 8 * q^7 + 12 * q^8 + 25 * q^9	\( 12 q + 12 q^{2} + 3 q^{3} + 12 q^{4} + 12 q^{5} + 3 q^{6} + 8 q^{7} + 12 q^{8} + 25 q^{9} + 12 q^{10} - 12 q^{11} + 3 q^{12} + 16 q^{13} + 8 q^{14} + 3 q^{15} + 12 q^{16} + 18 q^{17} + 25 q^{18} - 4 q^{19} + 12 q^{20} + 4 q^{21} - 12 q^{22} + 8 q^{23} + 3 q^{24} + 12 q^{25} + 16 q^{26} + 6 q^{27} + 8 q^{28} + 20 q^{29} + 3 q^{30} + 5 q^{31} + 12 q^{32} - 3 q^{33} + 18 q^{34} + 8 q^{35} + 25 q^{36} + 19 q^{37} - 4 q^{38} + 6 q^{39} + 12 q^{40} + 16 q^{41} + 4 q^{42} + 12 q^{43} - 12 q^{44} + 25 q^{45} + 8 q^{46} - q^{47} + 3 q^{48} + 52 q^{49} + 12 q^{50} + q^{51} + 16 q^{52} + 11 q^{53} + 6 q^{54} - 12 q^{55} + 8 q^{56} + 9 q^{57} + 20 q^{58} - 11 q^{59} + 3 q^{60} + 18 q^{61} + 5 q^{62} + 15 q^{63} + 12 q^{64} + 16 q^{65} - 3 q^{66} - 10 q^{67} + 18 q^{68} + 8 q^{70} - 2 q^{71} + 25 q^{72} + 29 q^{73} + 19 q^{74} + 3 q^{75} - 4 q^{76} - 8 q^{77} + 6 q^{78} + 2 q^{79} + 12 q^{80} - 8 q^{81} + 16 q^{82} + 26 q^{83} + 4 q^{84} + 18 q^{85} + 12 q^{86} - 4 q^{87} - 12 q^{88} + 41 q^{89} + 25 q^{90} - 4 q^{91} + 8 q^{92} + 5 q^{93} - q^{94} - 4 q^{95} + 3 q^{96} - 7 q^{97} + 52 q^{98} - 25 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 3 * q^3 + 12 * q^4 + 12 * q^5 + 3 * q^6 + 8 * q^7 + 12 * q^8 + 25 * q^9 + 12 * q^10 - 12 * q^11 + 3 * q^12 + 16 * q^13 + 8 * q^14 + 3 * q^15 + 12 * q^16 + 18 * q^17 + 25 * q^18 - 4 * q^19 + 12 * q^20 + 4 * q^21 - 12 * q^22 + 8 * q^23 + 3 * q^24 + 12 * q^25 + 16 * q^26 + 6 * q^27 + 8 * q^28 + 20 * q^29 + 3 * q^30 + 5 * q^31 + 12 * q^32 - 3 * q^33 + 18 * q^34 + 8 * q^35 + 25 * q^36 + 19 * q^37 - 4 * q^38 + 6 * q^39 + 12 * q^40 + 16 * q^41 + 4 * q^42 + 12 * q^43 - 12 * q^44 + 25 * q^45 + 8 * q^46 - q^47 + 3 * q^48 + 52 * q^49 + 12 * q^50 + q^51 + 16 * q^52 + 11 * q^53 + 6 * q^54 - 12 * q^55 + 8 * q^56 + 9 * q^57 + 20 * q^58 - 11 * q^59 + 3 * q^60 + 18 * q^61 + 5 * q^62 + 15 * q^63 + 12 * q^64 + 16 * q^65 - 3 * q^66 - 10 * q^67 + 18 * q^68 + 8 * q^70 - 2 * q^71 + 25 * q^72 + 29 * q^73 + 19 * q^74 + 3 * q^75 - 4 * q^76 - 8 * q^77 + 6 * q^78 + 2 * q^79 + 12 * q^80 - 8 * q^81 + 16 * q^82 + 26 * q^83 + 4 * q^84 + 18 * q^85 + 12 * q^86 - 4 * q^87 - 12 * q^88 + 41 * q^89 + 25 * q^90 - 4 * q^91 + 8 * q^92 + 5 * q^93 - q^94 - 4 * q^95 + 3 * q^96 - 7 * q^97 + 52 * q^98 - 25 * 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
$3$	2.72061	1.57074	0.785372	−	0.619024i	$-0.212471\pi$
$3$	2.72061	1.57074	0.785372	+	0.619024i	$0.212471\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.72061	1.11068
$7$	1.91272	0.722939	0.361469	−	0.932384i	$-0.382275\pi$
$7$	1.91272	0.722939	0.361469	+	0.932384i	$0.382275\pi$
$8$	1.00000	0.353553
$9$	4.40172	1.46724
$10$	1.00000	0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	2.72061	0.785372
$13$	1.20875	0.335246	0.167623	−	0.985851i	$-0.446391\pi$
$13$	1.20875	0.335246	0.167623	+	0.985851i	$0.446391\pi$
$14$	1.91272	0.511195
$15$	2.72061	0.702458
$16$	1.00000	0.250000
$17$	−3.77479	−0.915521	−0.457760	−	0.889076i	$-0.651348\pi$
$17$	−3.77479	−0.915521	−0.457760	+	0.889076i	$0.651348\pi$
$18$	4.40172	1.03749
$19$	5.93546	1.36169	0.680844	−	0.732428i	$-0.261613\pi$
$19$	5.93546	1.36169	0.680844	+	0.732428i	$0.261613\pi$
$20$	1.00000	0.223607
$21$	5.20376	1.13555
$22$	−1.00000	−0.213201
$23$	0.791254	0.164988	0.0824939	−	0.996592i	$-0.473711\pi$
$23$	0.791254	0.164988	0.0824939	+	0.996592i	$0.473711\pi$
$24$	2.72061	0.555342
$25$	1.00000	0.200000
$26$	1.20875	0.237055
$27$	3.81352	0.733913
$28$	1.91272	0.361469
$29$	0.597002	0.110860	0.0554302	−	0.998463i	$-0.482347\pi$
$29$	0.597002	0.110860	0.0554302	+	0.998463i	$0.482347\pi$
$30$	2.72061	0.496713
$31$	7.15695	1.28543	0.642713	−	0.766107i	$-0.277809\pi$
$31$	7.15695	1.28543	0.642713	+	0.766107i	$0.277809\pi$
$32$	1.00000	0.176777
$33$	−2.72061	−0.473597
$34$	−3.77479	−0.647371
$35$	1.91272	0.323308
$36$	4.40172	0.733619
$37$	1.12735	0.185335	0.0926676	−	0.995697i	$-0.470461\pi$
$37$	1.12735	0.185335	0.0926676	+	0.995697i	$0.470461\pi$
$38$	5.93546	0.962859
$39$	3.28853	0.526586
$40$	1.00000	0.158114
$41$	−10.3674	−1.61912	−0.809558	−	0.587039i	$-0.800293\pi$
$41$	−10.3674	−1.61912	−0.809558	+	0.587039i	$0.800293\pi$
$42$	5.20376	0.802957
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−1.00000	−0.150756
$45$	4.40172	0.656169
$46$	0.791254	0.116664
$47$	−12.0994	−1.76488	−0.882439	−	0.470426i	$-0.844100\pi$
$47$	−12.0994	−1.76488	−0.882439	+	0.470426i	$0.844100\pi$
$48$	2.72061	0.392686
$49$	−3.34151	−0.477359
$50$	1.00000	0.141421
$51$	−10.2697	−1.43805
$52$	1.20875	0.167623
$53$	−11.3466	−1.55857	−0.779287	−	0.626667i	$-0.784419\pi$
$53$	−11.3466	−1.55857	−0.779287	+	0.626667i	$0.784419\pi$
$54$	3.81352	0.518955
$55$	−1.00000	−0.134840
$56$	1.91272	0.255598
$57$	16.1481	2.13887
$58$	0.597002	0.0783902
$59$	−4.42095	−0.575558	−0.287779	−	0.957697i	$-0.592917\pi$
$59$	−4.42095	−0.575558	−0.287779	+	0.957697i	$0.592917\pi$
$60$	2.72061	0.351229
$61$	−2.65531	−0.339977	−0.169989	−	0.985446i	$-0.554373\pi$
$61$	−2.65531	−0.339977	−0.169989	+	0.985446i	$0.554373\pi$
$62$	7.15695	0.908933
$63$	8.41924	1.06072
$64$	1.00000	0.125000
$65$	1.20875	0.149926
$66$	−2.72061	−0.334884
$67$	15.5544	1.90027	0.950134	−	0.311841i	$-0.100946\pi$
$67$	15.5544	1.90027	0.950134	+	0.311841i	$0.100946\pi$
$68$	−3.77479	−0.457760
$69$	2.15269	0.259154
$70$	1.91272	0.228613
$71$	−4.84257	−0.574708	−0.287354	−	0.957825i	$-0.592776\pi$
$71$	−4.84257	−0.574708	−0.287354	+	0.957825i	$0.592776\pi$
$72$	4.40172	0.518747
$73$	−2.10242	−0.246069	−0.123035	−	0.992402i	$-0.539263\pi$
$73$	−2.10242	−0.246069	−0.123035	+	0.992402i	$0.539263\pi$
$74$	1.12735	0.131052
$75$	2.72061	0.314149
$76$	5.93546	0.680844
$77$	−1.91272	−0.217974
$78$	3.28853	0.372352
$79$	−0.235281	−0.0264711	−0.0132356	−	0.999912i	$-0.504213\pi$
$79$	−0.235281	−0.0264711	−0.0132356	+	0.999912i	$0.504213\pi$
$80$	1.00000	0.111803
$81$	−2.83004	−0.314449
$82$	−10.3674	−1.14489
$83$	10.7230	1.17700	0.588499	−	0.808498i	$-0.299719\pi$
$83$	10.7230	1.17700	0.588499	+	0.808498i	$0.299719\pi$
$84$	5.20376	0.567776
$85$	−3.77479	−0.409433
$86$	1.00000	0.107833
$87$	1.62421	0.174133
$88$	−1.00000	−0.106600
$89$	−1.84824	−0.195913	−0.0979566	−	0.995191i	$-0.531231\pi$
$89$	−1.84824	−0.195913	−0.0979566	+	0.995191i	$0.531231\pi$
$90$	4.40172	0.463982
$91$	2.31199	0.242362
$92$	0.791254	0.0824939
$93$	19.4713	2.01908
$94$	−12.0994	−1.24796
$95$	5.93546	0.608966
$96$	2.72061	0.277671
$97$	−0.701016	−0.0711774	−0.0355887	−	0.999367i	$-0.511331\pi$
$97$	−0.701016	−0.0711774	−0.0355887	+	0.999367i	$0.511331\pi$
$98$	−3.34151	−0.337544
$99$	−4.40172	−0.442389
$100$	1.00000	0.100000
$101$	−3.90878	−0.388938	−0.194469	−	0.980909i	$-0.562298\pi$
$101$	−3.90878	−0.388938	−0.194469	+	0.980909i	$0.562298\pi$
$102$	−10.2697	−1.01685
$103$	6.85994	0.675930	0.337965	−	0.941159i	$-0.390261\pi$
$103$	6.85994	0.675930	0.337965	+	0.941159i	$0.390261\pi$
$104$	1.20875	0.118527
$105$	5.20376	0.507835
$106$	−11.3466	−1.10208
$107$	11.6856	1.12969	0.564844	−	0.825198i	$-0.308936\pi$
$107$	11.6856	1.12969	0.564844	+	0.825198i	$0.308936\pi$
$108$	3.81352	0.366957
$109$	15.9177	1.52464	0.762321	−	0.647200i	$-0.224060\pi$
$109$	15.9177	1.52464	0.762321	+	0.647200i	$0.224060\pi$
$110$	−1.00000	−0.0953463
$111$	3.06708	0.291114
$112$	1.91272	0.180735
$113$	2.03490	0.191427	0.0957137	−	0.995409i	$-0.469487\pi$
$113$	2.03490	0.191427	0.0957137	+	0.995409i	$0.469487\pi$
$114$	16.1481	1.51241
$115$	0.791254	0.0737848
$116$	0.597002	0.0554302
$117$	5.32056	0.491886
$118$	−4.42095	−0.406981
$119$	−7.22010	−0.661866
$120$	2.72061	0.248357
$121$	1.00000	0.0909091
$122$	−2.65531	−0.240400
$123$	−28.2057	−2.54322
$124$	7.15695	0.642713
$125$	1.00000	0.0894427
$126$	8.41924	0.750045
$127$	8.31619	0.737942	0.368971	−	0.929441i	$-0.379710\pi$
$127$	8.31619	0.737942	0.368971	+	0.929441i	$0.379710\pi$
$128$	1.00000	0.0883883
$129$	2.72061	0.239536
$130$	1.20875	0.106014
$131$	−8.39059	−0.733090	−0.366545	−	0.930400i	$-0.619459\pi$
$131$	−8.39059	−0.733090	−0.366545	+	0.930400i	$0.619459\pi$
$132$	−2.72061	−0.236799
$133$	11.3529	0.984418
$134$	15.5544	1.34369
$135$	3.81352	0.328216
$136$	−3.77479	−0.323686
$137$	−15.8708	−1.35593	−0.677967	−	0.735092i	$-0.737139\pi$
$137$	−15.8708	−1.35593	−0.677967	+	0.735092i	$0.737139\pi$
$138$	2.15269	0.183249
$139$	9.81204	0.832246	0.416123	−	0.909308i	$-0.363389\pi$
$139$	9.81204	0.832246	0.416123	+	0.909308i	$0.363389\pi$
$140$	1.91272	0.161654
$141$	−32.9177	−2.77217
$142$	−4.84257	−0.406380
$143$	−1.20875	−0.101080
$144$	4.40172	0.366810
$145$	0.597002	0.0495783
$146$	−2.10242	−0.173997
$147$	−9.09096	−0.749809
$148$	1.12735	0.0926676
$149$	−3.06332	−0.250957	−0.125478	−	0.992096i	$-0.540047\pi$
$149$	−3.06332	−0.250957	−0.125478	+	0.992096i	$0.540047\pi$
$150$	2.72061	0.222137
$151$	−3.50114	−0.284919	−0.142460	−	0.989801i	$-0.545501\pi$
$151$	−3.50114	−0.284919	−0.142460	+	0.989801i	$0.545501\pi$
$152$	5.93546	0.481430
$153$	−16.6156	−1.34329
$154$	−1.91272	−0.154131
$155$	7.15695	0.574860
$156$	3.28853	0.263293
$157$	−6.52120	−0.520448	−0.260224	−	0.965548i	$-0.583796\pi$
$157$	−6.52120	−0.520448	−0.260224	+	0.965548i	$0.583796\pi$
$158$	−0.235281	−0.0187179
$159$	−30.8696	−2.44812
$160$	1.00000	0.0790569
$161$	1.51345	0.119276
$162$	−2.83004	−0.222349
$163$	−0.0708121	−0.00554643	−0.00277321	−	0.999996i	$-0.500883\pi$
$163$	−0.0708121	−0.00554643	−0.00277321	+	0.999996i	$0.500883\pi$
$164$	−10.3674	−0.809558
$165$	−2.72061	−0.211799
$166$	10.7230	0.832263
$167$	−9.52120	−0.736773	−0.368386	−	0.929673i	$-0.620090\pi$
$167$	−9.52120	−0.736773	−0.368386	+	0.929673i	$0.620090\pi$
$168$	5.20376	0.401478
$169$	−11.5389	−0.887610
$170$	−3.77479	−0.289513
$171$	26.1262	1.99792
$172$	1.00000	0.0762493
$173$	−10.1851	−0.774359	−0.387180	−	0.922004i	$-0.626551\pi$
$173$	−10.1851	−0.774359	−0.387180	+	0.922004i	$0.626551\pi$
$174$	1.62421	0.123131
$175$	1.91272	0.144588
$176$	−1.00000	−0.0753778
$177$	−12.0277	−0.904055
$178$	−1.84824	−0.138532
$179$	16.5986	1.24063	0.620317	−	0.784351i	$-0.287004\pi$
$179$	16.5986	1.24063	0.620317	+	0.784351i	$0.287004\pi$
$180$	4.40172	0.328085
$181$	12.9709	0.964119	0.482060	−	0.876138i	$-0.339889\pi$
$181$	12.9709	0.964119	0.482060	+	0.876138i	$0.339889\pi$
$182$	2.31199	0.171376
$183$	−7.22405	−0.534017
$184$	0.791254	0.0583320
$185$	1.12735	0.0828844
$186$	19.4713	1.42770
$187$	3.77479	0.276040
$188$	−12.0994	−0.882439
$189$	7.29419	0.530574
$190$	5.93546	0.430604
$191$	−4.33138	−0.313408	−0.156704	−	0.987646i	$-0.550087\pi$
$191$	−4.33138	−0.313408	−0.156704	+	0.987646i	$0.550087\pi$
$192$	2.72061	0.196343
$193$	1.94220	0.139802	0.0699012	−	0.997554i	$-0.477732\pi$
$193$	1.94220	0.139802	0.0699012	+	0.997554i	$0.477732\pi$
$194$	−0.701016	−0.0503300
$195$	3.28853	0.235496
$196$	−3.34151	−0.238680
$197$	7.27531	0.518344	0.259172	−	0.965831i	$-0.416550\pi$
$197$	7.27531	0.518344	0.259172	+	0.965831i	$0.416550\pi$
$198$	−4.40172	−0.312816
$199$	−12.3540	−0.875749	−0.437875	−	0.899036i	$-0.644269\pi$
$199$	−12.3540	−0.875749	−0.437875	+	0.899036i	$0.644269\pi$
$200$	1.00000	0.0707107
$201$	42.3174	2.98484
$202$	−3.90878	−0.275021
$203$	1.14190	0.0801453
$204$	−10.2697	−0.719025
$205$	−10.3674	−0.724091
$206$	6.85994	0.477955
$207$	3.48288	0.242077
$208$	1.20875	0.0838114
$209$	−5.93546	−0.410565
$210$	5.20376	0.359093
$211$	−5.49748	−0.378462	−0.189231	−	0.981933i	$-0.560599\pi$
$211$	−5.49748	−0.378462	−0.189231	+	0.981933i	$0.560599\pi$
$212$	−11.3466	−0.779287
$213$	−13.1747	−0.902719
$214$	11.6856	0.798810
$215$	1.00000	0.0681994
$216$	3.81352	0.259477
$217$	13.6892	0.929285
$218$	15.9177	1.07808
$219$	−5.71986	−0.386512
$220$	−1.00000	−0.0674200
$221$	−4.56276	−0.306925
$222$	3.06708	0.205849
$223$	−19.9298	−1.33460	−0.667298	−	0.744791i	$-0.732549\pi$
$223$	−19.9298	−1.33460	−0.667298	+	0.744791i	$0.732549\pi$
$224$	1.91272	0.127799
$225$	4.40172	0.293448
$226$	2.03490	0.135360
$227$	7.77896	0.516307	0.258154	−	0.966104i	$-0.416886\pi$
$227$	7.77896	0.516307	0.258154	+	0.966104i	$0.416886\pi$
$228$	16.1481	1.06943
$229$	−8.96590	−0.592483	−0.296242	−	0.955113i	$-0.595733\pi$
$229$	−8.96590	−0.592483	−0.296242	+	0.955113i	$0.595733\pi$
$230$	0.791254	0.0521738
$231$	−5.20376	−0.342382
$232$	0.597002	0.0391951
$233$	16.7903	1.09997	0.549984	−	0.835175i	$-0.314634\pi$
$233$	16.7903	1.09997	0.549984	+	0.835175i	$0.314634\pi$
$234$	5.32056	0.347816
$235$	−12.0994	−0.789278
$236$	−4.42095	−0.287779
$237$	−0.640107	−0.0415794
$238$	−7.22010	−0.468010
$239$	−8.02935	−0.519375	−0.259688	−	0.965693i	$-0.583620\pi$
$239$	−8.02935	−0.519375	−0.259688	+	0.965693i	$0.583620\pi$
$240$	2.72061	0.175615
$241$	−1.12866	−0.0727034	−0.0363517	−	0.999339i	$-0.511574\pi$
$241$	−1.12866	−0.0727034	−0.0363517	+	0.999339i	$0.511574\pi$
$242$	1.00000	0.0642824
$243$	−19.1400	−1.22783
$244$	−2.65531	−0.169989
$245$	−3.34151	−0.213482
$246$	−28.2057	−1.79833
$247$	7.17447	0.456500
$248$	7.15695	0.454467
$249$	29.1730	1.84876
$250$	1.00000	0.0632456
$251$	−7.67613	−0.484513	−0.242256	−	0.970212i	$-0.577888\pi$
$251$	−7.67613	−0.484513	−0.242256	+	0.970212i	$0.577888\pi$
$252$	8.41924	0.530362
$253$	−0.791254	−0.0497457
$254$	8.31619	0.521804
$255$	−10.2697	−0.643115
$256$	1.00000	0.0625000
$257$	−9.37594	−0.584855	−0.292428	−	0.956288i	$-0.594463\pi$
$257$	−9.37594	−0.584855	−0.292428	+	0.956288i	$0.594463\pi$
$258$	2.72061	0.169378
$259$	2.15630	0.133986
$260$	1.20875	0.0749632
$261$	2.62783	0.162659
$262$	−8.39059	−0.518373
$263$	19.6649	1.21259	0.606296	−	0.795239i	$-0.292655\pi$
$263$	19.6649	1.21259	0.606296	+	0.795239i	$0.292655\pi$
$264$	−2.72061	−0.167442
$265$	−11.3466	−0.697016
$266$	11.3529	0.696089
$267$	−5.02834	−0.307730
$268$	15.5544	0.950134
$269$	2.38473	0.145400	0.0726999	−	0.997354i	$-0.476838\pi$
$269$	2.38473	0.145400	0.0726999	+	0.997354i	$0.476838\pi$
$270$	3.81352	0.232084
$271$	−4.10433	−0.249320	−0.124660	−	0.992199i	$-0.539784\pi$
$271$	−4.10433	−0.249320	−0.124660	+	0.992199i	$0.539784\pi$
$272$	−3.77479	−0.228880
$273$	6.29002	0.380689
$274$	−15.8708	−0.958791
$275$	−1.00000	−0.0603023
$276$	2.15269	0.129577
$277$	−27.0052	−1.62258	−0.811291	−	0.584642i	$-0.801235\pi$
$277$	−27.0052	−1.62258	−0.811291	+	0.584642i	$0.801235\pi$
$278$	9.81204	0.588487
$279$	31.5029	1.88603
$280$	1.91272	0.114307
$281$	−1.83659	−0.109562	−0.0547808	−	0.998498i	$-0.517446\pi$
$281$	−1.83659	−0.109562	−0.0547808	+	0.998498i	$0.517446\pi$
$282$	−32.9177	−1.96022
$283$	−2.44280	−0.145209	−0.0726046	−	0.997361i	$-0.523131\pi$
$283$	−2.44280	−0.145209	−0.0726046	+	0.997361i	$0.523131\pi$
$284$	−4.84257	−0.287354
$285$	16.1481	0.956530
$286$	−1.20875	−0.0714746
$287$	−19.8299	−1.17052
$288$	4.40172	0.259374
$289$	−2.75097	−0.161822
$290$	0.597002	0.0350571
$291$	−1.90719	−0.111801
$292$	−2.10242	−0.123035
$293$	−7.62521	−0.445469	−0.222735	−	0.974879i	$-0.571498\pi$
$293$	−7.62521	−0.445469	−0.222735	+	0.974879i	$0.571498\pi$
$294$	−9.09096	−0.530195
$295$	−4.42095	−0.257397
$296$	1.12735	0.0655259
$297$	−3.81352	−0.221283
$298$	−3.06332	−0.177453
$299$	0.956425	0.0553115
$300$	2.72061	0.157074
$301$	1.91272	0.110247
$302$	−3.50114	−0.201468
$303$	−10.6343	−0.610923
$304$	5.93546	0.340422
$305$	−2.65531	−0.152042
$306$	−16.6156	−0.949848
$307$	−10.9760	−0.626434	−0.313217	−	0.949682i	$-0.601407\pi$
$307$	−10.9760	−0.626434	−0.313217	+	0.949682i	$0.601407\pi$
$308$	−1.91272	−0.108987
$309$	18.6632	1.06171
$310$	7.15695	0.406487
$311$	8.53162	0.483784	0.241892	−	0.970303i	$-0.422232\pi$
$311$	8.53162	0.483784	0.241892	+	0.970303i	$0.422232\pi$
$312$	3.28853	0.186176
$313$	−10.9279	−0.617682	−0.308841	−	0.951114i	$-0.599941\pi$
$313$	−10.9279	−0.617682	−0.308841	+	0.951114i	$0.599941\pi$
$314$	−6.52120	−0.368013
$315$	8.41924	0.474370
$316$	−0.235281	−0.0132356
$317$	5.05291	0.283800	0.141900	−	0.989881i	$-0.454679\pi$
$317$	5.05291	0.283800	0.141900	+	0.989881i	$0.454679\pi$
$318$	−30.8696	−1.73108
$319$	−0.597002	−0.0334257
$320$	1.00000	0.0559017
$321$	31.7919	1.77445
$322$	1.51345	0.0843410
$323$	−22.4051	−1.24665
$324$	−2.83004	−0.157224
$325$	1.20875	0.0670492
$326$	−0.0708121	−0.00392192
$327$	43.3059	2.39482
$328$	−10.3674	−0.572444
$329$	−23.1427	−1.27590
$330$	−2.72061	−0.149765
$331$	31.7736	1.74644	0.873218	−	0.487329i	$-0.162029\pi$
$331$	31.7736	1.74644	0.873218	+	0.487329i	$0.162029\pi$
$332$	10.7230	0.588499
$333$	4.96227	0.271931
$334$	−9.52120	−0.520977
$335$	15.5544	0.849826
$336$	5.20376	0.283888
$337$	16.5299	0.900441	0.450221	−	0.892917i	$-0.351345\pi$
$337$	16.5299	0.900441	0.450221	+	0.892917i	$0.351345\pi$
$338$	−11.5389	−0.627635
$339$	5.53617	0.300683
$340$	−3.77479	−0.204717
$341$	−7.15695	−0.387571
$342$	26.1262	1.41274
$343$	−19.7804	−1.06804
$344$	1.00000	0.0539164
$345$	2.15269	0.115897
$346$	−10.1851	−0.547555
$347$	2.73720	0.146941	0.0734703	−	0.997297i	$-0.476593\pi$
$347$	2.73720	0.146941	0.0734703	+	0.997297i	$0.476593\pi$
$348$	1.62421	0.0870667
$349$	14.0391	0.751498	0.375749	−	0.926722i	$-0.377386\pi$
$349$	14.0391	0.751498	0.375749	+	0.926722i	$0.377386\pi$
$350$	1.91272	0.102239
$351$	4.60958	0.246041
$352$	−1.00000	−0.0533002
$353$	−31.8160	−1.69340	−0.846698	−	0.532074i	$-0.821413\pi$
$353$	−31.8160	−1.69340	−0.846698	+	0.532074i	$0.821413\pi$
$354$	−12.0277	−0.639263
$355$	−4.84257	−0.257017
$356$	−1.84824	−0.0979566
$357$	−19.6431	−1.03962
$358$	16.5986	0.877261
$359$	−3.43246	−0.181158	−0.0905792	−	0.995889i	$-0.528872\pi$
$359$	−3.43246	−0.181158	−0.0905792	+	0.995889i	$0.528872\pi$
$360$	4.40172	0.231991
$361$	16.2297	0.854197
$362$	12.9709	0.681735
$363$	2.72061	0.142795
$364$	2.31199	0.121181
$365$	−2.10242	−0.110046
$366$	−7.22405	−0.377607
$367$	30.7599	1.60566	0.802828	−	0.596211i	$-0.203328\pi$
$367$	30.7599	1.60566	0.802828	+	0.596211i	$0.203328\pi$
$368$	0.791254	0.0412470
$369$	−45.6344	−2.37563
$370$	1.12735	0.0586081
$371$	−21.7028	−1.12675
$372$	19.4713	1.00954
$373$	26.0052	1.34650	0.673250	−	0.739415i	$-0.264898\pi$
$373$	26.0052	1.34650	0.673250	+	0.739415i	$0.264898\pi$
$374$	3.77479	0.195190
$375$	2.72061	0.140492
$376$	−12.0994	−0.623979
$377$	0.721623	0.0371655
$378$	7.29419	0.375173
$379$	−18.6814	−0.959601	−0.479800	−	0.877378i	$-0.659291\pi$
$379$	−18.6814	−0.959601	−0.479800	+	0.877378i	$0.659291\pi$
$380$	5.93546	0.304483
$381$	22.6251	1.15912
$382$	−4.33138	−0.221613
$383$	17.2652	0.882212	0.441106	−	0.897455i	$-0.354586\pi$
$383$	17.2652	0.882212	0.441106	+	0.897455i	$0.354586\pi$
$384$	2.72061	0.138836
$385$	−1.91272	−0.0974811
$386$	1.94220	0.0988552
$387$	4.40172	0.223752
$388$	−0.701016	−0.0355887
$389$	11.3509	0.575513	0.287757	−	0.957704i	$-0.407091\pi$
$389$	11.3509	0.575513	0.287757	+	0.957704i	$0.407091\pi$
$390$	3.28853	0.166521
$391$	−2.98682	−0.151050
$392$	−3.34151	−0.168772
$393$	−22.8275	−1.15150
$394$	7.27531	0.366525
$395$	−0.235281	−0.0118383
$396$	−4.40172	−0.221195
$397$	33.4940	1.68101	0.840507	−	0.541801i	$-0.182257\pi$
$397$	33.4940	1.68101	0.840507	+	0.541801i	$0.182257\pi$
$398$	−12.3540	−0.619248
$399$	30.8867	1.54627
$400$	1.00000	0.0500000
$401$	−10.6671	−0.532691	−0.266345	−	0.963878i	$-0.585816\pi$
$401$	−10.6671	−0.532691	−0.266345	+	0.963878i	$0.585816\pi$
$402$	42.3174	2.11060
$403$	8.65093	0.430934
$404$	−3.90878	−0.194469
$405$	−2.83004	−0.140626
$406$	1.14190	0.0566713
$407$	−1.12735	−0.0558806
$408$	−10.2697	−0.508427
$409$	−5.64176	−0.278967	−0.139483	−	0.990224i	$-0.544544\pi$
$409$	−5.64176	−0.278967	−0.139483	+	0.990224i	$0.544544\pi$
$410$	−10.3674	−0.512010
$411$	−43.1783	−2.12983
$412$	6.85994	0.337965
$413$	−8.45602	−0.416093
$414$	3.48288	0.171174
$415$	10.7230	0.526369
$416$	1.20875	0.0592636
$417$	26.6947	1.30725
$418$	−5.93546	−0.290313
$419$	−12.2933	−0.600566	−0.300283	−	0.953850i	$-0.597081\pi$
$419$	−12.2933	−0.600566	−0.300283	+	0.953850i	$0.597081\pi$
$420$	5.20376	0.253917
$421$	9.99247	0.487003	0.243502	−	0.969900i	$-0.421704\pi$
$421$	9.99247	0.487003	0.243502	+	0.969900i	$0.421704\pi$
$422$	−5.49748	−0.267613
$423$	−53.2581	−2.58950
$424$	−11.3466	−0.551039
$425$	−3.77479	−0.183104
$426$	−13.1747	−0.638319
$427$	−5.07885	−0.245783
$428$	11.6856	0.564844
$429$	−3.28853	−0.158772
$430$	1.00000	0.0482243
$431$	−20.3287	−0.979200	−0.489600	−	0.871947i	$-0.662857\pi$
$431$	−20.3287	−0.979200	−0.489600	+	0.871947i	$0.662857\pi$
$432$	3.81352	0.183478
$433$	−33.7115	−1.62007	−0.810035	−	0.586381i	$-0.800552\pi$
$433$	−33.7115	−1.62007	−0.810035	+	0.586381i	$0.800552\pi$
$434$	13.6892	0.657103
$435$	1.62421	0.0778748
$436$	15.9177	0.762321
$437$	4.69646	0.224662
$438$	−5.71986	−0.273305
$439$	−8.79633	−0.419826	−0.209913	−	0.977720i	$-0.567318\pi$
$439$	−8.79633	−0.419826	−0.209913	+	0.977720i	$0.567318\pi$
$440$	−1.00000	−0.0476731
$441$	−14.7084	−0.700400
$442$	−4.56276	−0.217028
$443$	−20.3959	−0.969040	−0.484520	−	0.874780i	$-0.661006\pi$
$443$	−20.3959	−0.969040	−0.484520	+	0.874780i	$0.661006\pi$
$444$	3.06708	0.145557
$445$	−1.84824	−0.0876150
$446$	−19.9298	−0.943702
$447$	−8.33409	−0.394189
$448$	1.91272	0.0903674
$449$	23.4319	1.10582	0.552910	−	0.833241i	$-0.313517\pi$
$449$	23.4319	1.10582	0.552910	+	0.833241i	$0.313517\pi$
$450$	4.40172	0.207499
$451$	10.3674	0.488182
$452$	2.03490	0.0957137
$453$	−9.52525	−0.447535
$454$	7.77896	0.365084
$455$	2.31199	0.108388
$456$	16.1481	0.756203
$457$	−19.0784	−0.892450	−0.446225	−	0.894921i	$-0.647232\pi$
$457$	−19.0784	−0.892450	−0.446225	+	0.894921i	$0.647232\pi$
$458$	−8.96590	−0.418949
$459$	−14.3953	−0.671913
$460$	0.791254	0.0368924
$461$	34.5032	1.60698	0.803488	−	0.595321i	$-0.202975\pi$
$461$	34.5032	1.60698	0.803488	+	0.595321i	$0.202975\pi$
$462$	−5.20376	−0.242101
$463$	−32.9370	−1.53071	−0.765356	−	0.643607i	$-0.777437\pi$
$463$	−32.9370	−1.53071	−0.765356	+	0.643607i	$0.777437\pi$
$464$	0.597002	0.0277151
$465$	19.4713	0.902958
$466$	16.7903	0.777794
$467$	36.3551	1.68231	0.841156	−	0.540792i	$-0.181875\pi$
$467$	36.3551	1.68231	0.841156	+	0.540792i	$0.181875\pi$
$468$	5.32056	0.245943
$469$	29.7511	1.37378
$470$	−12.0994	−0.558104
$471$	−17.7416	−0.817492
$472$	−4.42095	−0.203490
$473$	−1.00000	−0.0459800
$474$	−0.640107	−0.0294011
$475$	5.93546	0.272338
$476$	−7.22010	−0.330933
$477$	−49.9445	−2.28680
$478$	−8.02935	−0.367254
$479$	8.98706	0.410629	0.205315	−	0.978696i	$-0.434178\pi$
$479$	8.98706	0.410629	0.205315	+	0.978696i	$0.434178\pi$
$480$	2.72061	0.124178
$481$	1.36268	0.0621328
$482$	−1.12866	−0.0514090
$483$	4.11749	0.187352
$484$	1.00000	0.0454545
$485$	−0.701016	−0.0318315
$486$	−19.1400	−0.868208
$487$	−6.66801	−0.302156	−0.151078	−	0.988522i	$-0.548275\pi$
$487$	−6.66801	−0.302156	−0.151078	+	0.988522i	$0.548275\pi$
$488$	−2.65531	−0.120200
$489$	−0.192652	−0.00871202
$490$	−3.34151	−0.150954
$491$	27.9655	1.26206	0.631032	−	0.775757i	$-0.282632\pi$
$491$	27.9655	1.26206	0.631032	+	0.775757i	$0.282632\pi$
$492$	−28.2057	−1.27161
$493$	−2.25356	−0.101495
$494$	7.17447	0.322795
$495$	−4.40172	−0.197842
$496$	7.15695	0.321357
$497$	−9.26247	−0.415479
$498$	29.1730	1.30727
$499$	−27.9426	−1.25088	−0.625442	−	0.780271i	$-0.715081\pi$
$499$	−27.9426	−1.25088	−0.625442	+	0.780271i	$0.715081\pi$
$500$	1.00000	0.0447214
$501$	−25.9035	−1.15728
$502$	−7.67613	−0.342602
$503$	−9.30955	−0.415092	−0.207546	−	0.978225i	$-0.566548\pi$
$503$	−9.30955	−0.415092	−0.207546	+	0.978225i	$0.566548\pi$
$504$	8.41924	0.375023
$505$	−3.90878	−0.173938
$506$	−0.791254	−0.0351755
$507$	−31.3929	−1.39421
$508$	8.31619	0.368971
$509$	−2.82087	−0.125033	−0.0625165	−	0.998044i	$-0.519913\pi$
$509$	−2.82087	−0.125033	−0.0625165	+	0.998044i	$0.519913\pi$
$510$	−10.2697	−0.454751
$511$	−4.02133	−0.177893
$512$	1.00000	0.0441942
$513$	22.6350	0.999361
$514$	−9.37594	−0.413555
$515$	6.85994	0.302285
$516$	2.72061	0.119768
$517$	12.0994	0.532131
$518$	2.15630	0.0947424
$519$	−27.7097	−1.21632
$520$	1.20875	0.0530070
$521$	−17.0892	−0.748692	−0.374346	−	0.927289i	$-0.622133\pi$
$521$	−17.0892	−0.748692	−0.374346	+	0.927289i	$0.622133\pi$
$522$	2.62783	0.115017
$523$	−0.934960	−0.0408830	−0.0204415	−	0.999791i	$-0.506507\pi$
$523$	−0.934960	−0.0408830	−0.0204415	+	0.999791i	$0.506507\pi$
$524$	−8.39059	−0.366545
$525$	5.20376	0.227111
$526$	19.6649	0.857431
$527$	−27.0160	−1.17683
$528$	−2.72061	−0.118399
$529$	−22.3739	−0.972779
$530$	−11.3466	−0.492864
$531$	−19.4597	−0.844481
$532$	11.3529	0.492209
$533$	−12.5316	−0.542802
$534$	−5.02834	−0.217598
$535$	11.6856	0.505212
$536$	15.5544	0.671846
$537$	45.1582	1.94872
$538$	2.38473	0.102813
$539$	3.34151	0.143929
$540$	3.81352	0.164108
$541$	−23.5381	−1.01198	−0.505991	−	0.862539i	$-0.668873\pi$
$541$	−23.5381	−1.01198	−0.505991	+	0.862539i	$0.668873\pi$
$542$	−4.10433	−0.176296
$543$	35.2887	1.51438
$544$	−3.77479	−0.161843
$545$	15.9177	0.681840
$546$	6.29002	0.269188
$547$	21.2179	0.907211	0.453606	−	0.891203i	$-0.350138\pi$
$547$	21.2179	0.907211	0.453606	+	0.891203i	$0.350138\pi$
$548$	−15.8708	−0.677967
$549$	−11.6879	−0.498828
$550$	−1.00000	−0.0426401
$551$	3.54348	0.150957
$552$	2.15269	0.0916247
$553$	−0.450025	−0.0191370
$554$	−27.0052	−1.14734
$555$	3.06708	0.130190
$556$	9.81204	0.416123
$557$	22.9932	0.974254	0.487127	−	0.873331i	$-0.338045\pi$
$557$	22.9932	0.974254	0.487127	+	0.873331i	$0.338045\pi$
$558$	31.5029	1.33362
$559$	1.20875	0.0511245
$560$	1.91272	0.0808270
$561$	10.2697	0.433588
$562$	−1.83659	−0.0774718
$563$	3.75876	0.158413	0.0792065	−	0.996858i	$-0.474761\pi$
$563$	3.75876	0.158413	0.0792065	+	0.996858i	$0.474761\pi$
$564$	−32.9177	−1.38609
$565$	2.03490	0.0856089
$566$	−2.44280	−0.102678
$567$	−5.41306	−0.227327
$568$	−4.84257	−0.203190
$569$	−32.0681	−1.34436	−0.672182	−	0.740386i	$-0.734643\pi$
$569$	−32.0681	−1.34436	−0.672182	+	0.740386i	$0.734643\pi$
$570$	16.1481	0.676369
$571$	29.5503	1.23664	0.618320	−	0.785927i	$-0.287814\pi$
$571$	29.5503	1.23664	0.618320	+	0.785927i	$0.287814\pi$
$572$	−1.20875	−0.0505402
$573$	−11.7840	−0.492284
$574$	−19.8299	−0.827684
$575$	0.791254	0.0329976
$576$	4.40172	0.183405
$577$	−30.9087	−1.28675	−0.643373	−	0.765553i	$-0.722466\pi$
$577$	−30.9087	−1.28675	−0.643373	+	0.765553i	$0.722466\pi$
$578$	−2.75097	−0.114425
$579$	5.28396	0.219594
$580$	0.597002	0.0247891
$581$	20.5100	0.850897
$582$	−1.90719	−0.0790556
$583$	11.3466	0.469928
$584$	−2.10242	−0.0869987
$585$	5.32056	0.219978
$586$	−7.62521	−0.314994
$587$	25.2434	1.04191	0.520953	−	0.853586i	$-0.325577\pi$
$587$	25.2434	1.04191	0.520953	+	0.853586i	$0.325577\pi$
$588$	−9.09096	−0.374905
$589$	42.4798	1.75035
$590$	−4.42095	−0.182007
$591$	19.7933	0.814186
$592$	1.12735	0.0463338
$593$	−3.53476	−0.145155	−0.0725776	−	0.997363i	$-0.523122\pi$
$593$	−3.53476	−0.145155	−0.0725776	+	0.997363i	$0.523122\pi$
$594$	−3.81352	−0.156471
$595$	−7.22010	−0.295995
$596$	−3.06332	−0.125478
$597$	−33.6103	−1.37558
$598$	0.956425	0.0391111
$599$	12.1990	0.498436	0.249218	−	0.968447i	$-0.419826\pi$
$599$	12.1990	0.498436	0.249218	+	0.968447i	$0.419826\pi$
$600$	2.72061	0.111068
$601$	26.4493	1.07889	0.539445	−	0.842021i	$-0.318634\pi$
$601$	26.4493	1.07889	0.539445	+	0.842021i	$0.318634\pi$
$602$	1.91272	0.0779565
$603$	68.4659	2.78815
$604$	−3.50114	−0.142460
$605$	1.00000	0.0406558
$606$	−10.6343	−0.431987
$607$	−9.77084	−0.396586	−0.198293	−	0.980143i	$-0.563540\pi$
$607$	−9.77084	−0.396586	−0.198293	+	0.980143i	$0.563540\pi$
$608$	5.93546	0.240715
$609$	3.10665	0.125888
$610$	−2.65531	−0.107510
$611$	−14.6251	−0.591668
$612$	−16.6156	−0.671644
$613$	−29.1266	−1.17641	−0.588205	−	0.808712i	$-0.700165\pi$
$613$	−29.1266	−1.17641	−0.588205	+	0.808712i	$0.700165\pi$
$614$	−10.9760	−0.442956
$615$	−28.2057	−1.13736
$616$	−1.91272	−0.0770656
$617$	30.5532	1.23003	0.615013	−	0.788517i	$-0.289151\pi$
$617$	30.5532	1.23003	0.615013	+	0.788517i	$0.289151\pi$
$618$	18.6632	0.750745
$619$	18.4567	0.741836	0.370918	−	0.928666i	$-0.379043\pi$
$619$	18.4567	0.741836	0.370918	+	0.928666i	$0.379043\pi$
$620$	7.15695	0.287430
$621$	3.01747	0.121087
$622$	8.53162	0.342087
$623$	−3.53516	−0.141633
$624$	3.28853	0.131646
$625$	1.00000	0.0400000
$626$	−10.9279	−0.436767
$627$	−16.1481	−0.644892
$628$	−6.52120	−0.260224
$629$	−4.25551	−0.169678
$630$	8.41924	0.335430
$631$	−27.1736	−1.08176	−0.540882	−	0.841098i	$-0.681910\pi$
$631$	−27.1736	−1.08176	−0.540882	+	0.841098i	$0.681910\pi$
$632$	−0.235281	−0.00935896
$633$	−14.9565	−0.594467
$634$	5.05291	0.200677
$635$	8.31619	0.330018
$636$	−30.8696	−1.22406
$637$	−4.03904	−0.160033
$638$	−0.597002	−0.0236355
$639$	−21.3156	−0.843233
$640$	1.00000	0.0395285
$641$	−18.7156	−0.739222	−0.369611	−	0.929187i	$-0.620509\pi$
$641$	−18.7156	−0.739222	−0.369611	+	0.929187i	$0.620509\pi$
$642$	31.7919	1.25473
$643$	−22.4437	−0.885094	−0.442547	−	0.896745i	$-0.645925\pi$
$643$	−22.4437	−0.885094	−0.442547	+	0.896745i	$0.645925\pi$
$644$	1.51345	0.0596381
$645$	2.72061	0.107124
$646$	−22.4051	−0.881518
$647$	6.70090	0.263440	0.131720	−	0.991287i	$-0.457950\pi$
$647$	6.70090	0.263440	0.131720	+	0.991287i	$0.457950\pi$
$648$	−2.83004	−0.111174
$649$	4.42095	0.173537
$650$	1.20875	0.0474109
$651$	37.2430	1.45967
$652$	−0.0708121	−0.00277321
$653$	−23.8883	−0.934822	−0.467411	−	0.884040i	$-0.654813\pi$
$653$	−23.8883	−0.934822	−0.467411	+	0.884040i	$0.654813\pi$
$654$	43.3059	1.69339
$655$	−8.39059	−0.327848
$656$	−10.3674	−0.404779
$657$	−9.25425	−0.361043
$658$	−23.1427	−0.902197
$659$	6.89215	0.268480	0.134240	−	0.990949i	$-0.457141\pi$
$659$	6.89215	0.268480	0.134240	+	0.990949i	$0.457141\pi$
$660$	−2.72061	−0.105900
$661$	−34.7551	−1.35182	−0.675908	−	0.736986i	$-0.736248\pi$
$661$	−34.7551	−1.35182	−0.675908	+	0.736986i	$0.736248\pi$
$662$	31.7736	1.23492
$663$	−12.4135	−0.482100
$664$	10.7230	0.416131
$665$	11.3529	0.440245
$666$	4.96227	0.192284
$667$	0.472380	0.0182906
$668$	−9.52120	−0.368386
$669$	−54.2211	−2.09631
$670$	15.5544	0.600918
$671$	2.65531	0.102507
$672$	5.20376	0.200739
$673$	−26.8790	−1.03611	−0.518055	−	0.855347i	$-0.673344\pi$
$673$	−26.8790	−1.03611	−0.518055	+	0.855347i	$0.673344\pi$
$674$	16.5299	0.636708
$675$	3.81352	0.146783
$676$	−11.5389	−0.443805
$677$	−13.6546	−0.524787	−0.262394	−	0.964961i	$-0.584512\pi$
$677$	−13.6546	−0.524787	−0.262394	+	0.964961i	$0.584512\pi$
$678$	5.53617	0.212615
$679$	−1.34084	−0.0514569
$680$	−3.77479	−0.144757
$681$	21.1635	0.810987
$682$	−7.15695	−0.274054
$683$	19.7840	0.757014	0.378507	−	0.925598i	$-0.376438\pi$
$683$	19.7840	0.757014	0.378507	+	0.925598i	$0.376438\pi$
$684$	26.1262	0.998961
$685$	−15.8708	−0.606393
$686$	−19.7804	−0.755219
$687$	−24.3927	−0.930640
$688$	1.00000	0.0381246
$689$	−13.7151	−0.522505
$690$	2.15269	0.0819516
$691$	−24.6686	−0.938437	−0.469218	−	0.883082i	$-0.655464\pi$
$691$	−24.6686	−0.938437	−0.469218	+	0.883082i	$0.655464\pi$
$692$	−10.1851	−0.387180
$693$	−8.41924	−0.319820
$694$	2.73720	0.103903
$695$	9.81204	0.372192
$696$	1.62421	0.0615655
$697$	39.1348	1.48234
$698$	14.0391	0.531389
$699$	45.6798	1.72777
$700$	1.91272	0.0722939
$701$	−0.950137	−0.0358862	−0.0179431	−	0.999839i	$-0.505712\pi$
$701$	−0.950137	−0.0358862	−0.0179431	+	0.999839i	$0.505712\pi$
$702$	4.60958	0.173977
$703$	6.69134	0.252369
$704$	−1.00000	−0.0376889
$705$	−32.9177	−1.23975
$706$	−31.8160	−1.19741
$707$	−7.47639	−0.281179
$708$	−12.0277	−0.452027
$709$	−9.66206	−0.362866	−0.181433	−	0.983403i	$-0.558074\pi$
$709$	−9.66206	−0.362866	−0.181433	+	0.983403i	$0.558074\pi$
$710$	−4.84257	−0.181739
$711$	−1.03564	−0.0388395
$712$	−1.84824	−0.0692658
$713$	5.66297	0.212080
$714$	−19.6431	−0.735124
$715$	−1.20875	−0.0452045
$716$	16.5986	0.620317
$717$	−21.8447	−0.815806
$718$	−3.43246	−0.128098
$719$	30.0475	1.12058	0.560290	−	0.828296i	$-0.310690\pi$
$719$	30.0475	1.12058	0.560290	+	0.828296i	$0.310690\pi$
$720$	4.40172	0.164042
$721$	13.1211	0.488656
$722$	16.2297	0.604008
$723$	−3.07064	−0.114198
$724$	12.9709	0.482060
$725$	0.597002	0.0221721
$726$	2.72061	0.100971
$727$	36.8592	1.36703	0.683515	−	0.729936i	$-0.260450\pi$
$727$	36.8592	1.36703	0.683515	+	0.729936i	$0.260450\pi$
$728$	2.31199	0.0856880
$729$	−43.5824	−1.61416
$730$	−2.10242	−0.0778140
$731$	−3.77479	−0.139616
$732$	−7.22405	−0.267009
$733$	−25.6801	−0.948517	−0.474259	−	0.880386i	$-0.657284\pi$
$733$	−25.6801	−0.948517	−0.474259	+	0.880386i	$0.657284\pi$
$734$	30.7599	1.13537
$735$	−9.09096	−0.335325
$736$	0.791254	0.0291660
$737$	−15.5544	−0.572953
$738$	−45.6344	−1.67982
$739$	−40.8543	−1.50285	−0.751424	−	0.659820i	$-0.770633\pi$
$739$	−40.8543	−1.50285	−0.751424	+	0.659820i	$0.770633\pi$
$740$	1.12735	0.0414422
$741$	19.5189	0.717046
$742$	−21.7028	−0.796735
$743$	48.6927	1.78636	0.893180	−	0.449699i	$-0.148469\pi$
$743$	48.6927	1.78636	0.893180	+	0.449699i	$0.148469\pi$
$744$	19.4713	0.713851
$745$	−3.06332	−0.112231
$746$	26.0052	0.952119
$747$	47.1994	1.72694
$748$	3.77479	0.138020
$749$	22.3512	0.816695
$750$	2.72061	0.0993426
$751$	28.7921	1.05064	0.525319	−	0.850906i	$-0.323946\pi$
$751$	28.7921	1.05064	0.525319	+	0.850906i	$0.323946\pi$
$752$	−12.0994	−0.441220
$753$	−20.8837	−0.761046
$754$	0.721623	0.0262800
$755$	−3.50114	−0.127420
$756$	7.29419	0.265287
$757$	2.21937	0.0806642	0.0403321	−	0.999186i	$-0.487158\pi$
$757$	2.21937	0.0806642	0.0403321	+	0.999186i	$0.487158\pi$
$758$	−18.6814	−0.678540
$759$	−2.15269	−0.0781378
$760$	5.93546	0.215302
$761$	2.96812	0.107594	0.0537972	−	0.998552i	$-0.482868\pi$
$761$	2.96812	0.107594	0.0537972	+	0.998552i	$0.482868\pi$
$762$	22.6251	0.819621
$763$	30.4461	1.10222
$764$	−4.33138	−0.156704
$765$	−16.6156	−0.600737
$766$	17.2652	0.623818
$767$	−5.34380	−0.192953
$768$	2.72061	0.0981715
$769$	−19.5103	−0.703561	−0.351781	−	0.936082i	$-0.614424\pi$
$769$	−19.5103	−0.703561	−0.351781	+	0.936082i	$0.614424\pi$
$770$	−1.91272	−0.0689295
$771$	−25.5083	−0.918658
$772$	1.94220	0.0699012
$773$	−34.3646	−1.23601	−0.618005	−	0.786174i	$-0.712059\pi$
$773$	−34.3646	−1.23601	−0.618005	+	0.786174i	$0.712059\pi$
$774$	4.40172	0.158216
$775$	7.15695	0.257085
$776$	−0.701016	−0.0251650
$777$	5.86645	0.210458
$778$	11.3509	0.406949
$779$	−61.5354	−2.20473
$780$	3.28853	0.117748
$781$	4.84257	0.173281
$782$	−2.98682	−0.106808
$783$	2.27668	0.0813619
$784$	−3.34151	−0.119340
$785$	−6.52120	−0.232752
$786$	−22.8275	−0.814231
$787$	19.7549	0.704186	0.352093	−	0.935965i	$-0.385470\pi$
$787$	19.7549	0.704186	0.352093	+	0.935965i	$0.385470\pi$
$788$	7.27531	0.259172
$789$	53.5006	1.90467
$790$	−0.235281	−0.00837091
$791$	3.89219	0.138390
$792$	−4.40172	−0.156408
$793$	−3.20959	−0.113976
$794$	33.4940	1.18866
$795$	−30.8696	−1.09483
$796$	−12.3540	−0.437875
$797$	−30.6839	−1.08688	−0.543440	−	0.839448i	$-0.682878\pi$
$797$	−30.6839	−1.08688	−0.543440	+	0.839448i	$0.682878\pi$
$798$	30.8867	1.09338
$799$	45.6727	1.61578
$800$	1.00000	0.0353553
$801$	−8.13543	−0.287451
$802$	−10.6671	−0.376669
$803$	2.10242	0.0741927
$804$	42.3174	1.49242
$805$	1.51345	0.0533419
$806$	8.65093	0.304716
$807$	6.48793	0.228386
$808$	−3.90878	−0.137510
$809$	31.2009	1.09697	0.548483	−	0.836162i	$-0.315205\pi$
$809$	31.2009	1.09697	0.548483	+	0.836162i	$0.315205\pi$
$810$	−2.83004	−0.0994374
$811$	30.9511	1.08684	0.543420	−	0.839461i	$-0.317129\pi$
$811$	30.9511	1.08684	0.543420	+	0.839461i	$0.317129\pi$
$812$	1.14190	0.0400727
$813$	−11.1663	−0.391619
$814$	−1.12735	−0.0395136
$815$	−0.0708121	−0.00248044
$816$	−10.2697	−0.359512
$817$	5.93546	0.207656
$818$	−5.64176	−0.197259
$819$	10.1767	0.355603
$820$	−10.3674	−0.362045
$821$	49.2147	1.71761	0.858803	−	0.512306i	$-0.171209\pi$
$821$	49.2147	1.71761	0.858803	+	0.512306i	$0.171209\pi$
$822$	−43.1783	−1.50602
$823$	6.63026	0.231116	0.115558	−	0.993301i	$-0.463134\pi$
$823$	6.63026	0.231116	0.115558	+	0.993301i	$0.463134\pi$
$824$	6.85994	0.238977
$825$	−2.72061	−0.0947195
$826$	−8.45602	−0.294222
$827$	−11.4359	−0.397667	−0.198833	−	0.980033i	$-0.563715\pi$
$827$	−11.4359	−0.397667	−0.198833	+	0.980033i	$0.563715\pi$
$828$	3.48288	0.121038
$829$	32.8379	1.14051	0.570254	−	0.821468i	$-0.306845\pi$
$829$	32.8379	1.14051	0.570254	+	0.821468i	$0.306845\pi$
$830$	10.7230	0.372199
$831$	−73.4705	−2.54866
$832$	1.20875	0.0419057
$833$	12.6135	0.437032
$834$	26.6947	0.924363
$835$	−9.52120	−0.329495
$836$	−5.93546	−0.205282
$837$	27.2932	0.943391
$838$	−12.2933	−0.424664
$839$	17.6411	0.609039	0.304520	−	0.952506i	$-0.401504\pi$
$839$	17.6411	0.609039	0.304520	+	0.952506i	$0.401504\pi$
$840$	5.20376	0.179547
$841$	−28.6436	−0.987710
$842$	9.99247	0.344363
$843$	−4.99664	−0.172093
$844$	−5.49748	−0.189231
$845$	−11.5389	−0.396951
$846$	−53.2581	−1.83105
$847$	1.91272	0.0657217
$848$	−11.3466	−0.389644
$849$	−6.64590	−0.228087
$850$	−3.77479	−0.129474
$851$	0.892020	0.0305781
$852$	−13.1747	−0.451359
$853$	30.5864	1.04726	0.523629	−	0.851946i	$-0.324578\pi$
$853$	30.5864	1.04726	0.523629	+	0.851946i	$0.324578\pi$
$854$	−5.07885	−0.173795
$855$	26.1262	0.893498
$856$	11.6856	0.399405
$857$	48.9983	1.67375	0.836875	−	0.547394i	$-0.184380\pi$
$857$	48.9983	1.67375	0.836875	+	0.547394i	$0.184380\pi$
$858$	−3.28853	−0.112268
$859$	−36.0523	−1.23009	−0.615044	−	0.788493i	$-0.710862\pi$
$859$	−36.0523	−1.23009	−0.615044	+	0.788493i	$0.710862\pi$
$860$	1.00000	0.0340997
$861$	−53.9494	−1.83859
$862$	−20.3287	−0.692399
$863$	40.1399	1.36638	0.683190	−	0.730241i	$-0.260592\pi$
$863$	40.1399	1.36638	0.683190	+	0.730241i	$0.260592\pi$
$864$	3.81352	0.129739
$865$	−10.1851	−0.346304
$866$	−33.7115	−1.14556
$867$	−7.48430	−0.254180
$868$	13.6892	0.464642
$869$	0.235281	0.00798135
$870$	1.62421	0.0550658
$871$	18.8013	0.637057
$872$	15.9177	0.539042
$873$	−3.08567	−0.104434
$874$	4.69646	0.158860
$875$	1.91272	0.0646616
$876$	−5.71986	−0.193256
$877$	58.5488	1.97705	0.988526	−	0.151049i	$-0.0482652\pi$
$877$	58.5488	1.97705	0.988526	+	0.151049i	$0.0482652\pi$
$878$	−8.79633	−0.296862
$879$	−20.7452	−0.699719
$880$	−1.00000	−0.0337100
$881$	49.4346	1.66550	0.832748	−	0.553653i	$-0.186766\pi$
$881$	49.4346	1.66550	0.832748	+	0.553653i	$0.186766\pi$
$882$	−14.7084	−0.495258
$883$	−46.3441	−1.55960	−0.779801	−	0.626028i	$-0.784680\pi$
$883$	−46.3441	−1.55960	−0.779801	+	0.626028i	$0.784680\pi$
$884$	−4.56276	−0.153462
$885$	−12.0277	−0.404306
$886$	−20.3959	−0.685215
$887$	25.9287	0.870602	0.435301	−	0.900285i	$-0.356642\pi$
$887$	25.9287	0.870602	0.435301	+	0.900285i	$0.356642\pi$
$888$	3.06708	0.102924
$889$	15.9065	0.533487
$890$	−1.84824	−0.0619532
$891$	2.83004	0.0948099
$892$	−19.9298	−0.667298
$893$	−71.8156	−2.40322
$894$	−8.33409	−0.278734
$895$	16.5986	0.554829
$896$	1.91272	0.0638994
$897$	2.60206	0.0868802
$898$	23.4319	0.781933
$899$	4.27271	0.142503
$900$	4.40172	0.146724
$901$	42.8310	1.42691
$902$	10.3674	0.345197
$903$	5.20376	0.173170
$904$	2.03490	0.0676798
$905$	12.9709	0.431167
$906$	−9.52525	−0.316455
$907$	−50.9527	−1.69186	−0.845929	−	0.533296i	$-0.820953\pi$
$907$	−50.9527	−1.69186	−0.845929	+	0.533296i	$0.820953\pi$
$908$	7.77896	0.258154
$909$	−17.2053	−0.570665
$910$	2.31199	0.0766417
$911$	−25.6757	−0.850674	−0.425337	−	0.905035i	$-0.639844\pi$
$911$	−25.6757	−0.850674	−0.425337	+	0.905035i	$0.639844\pi$
$912$	16.1481	0.534716
$913$	−10.7230	−0.354878
$914$	−19.0784	−0.631058
$915$	−7.22405	−0.238820
$916$	−8.96590	−0.296242
$917$	−16.0488	−0.529979
$918$	−14.3953	−0.475114
$919$	43.9593	1.45008	0.725042	−	0.688704i	$-0.241820\pi$
$919$	43.9593	1.45008	0.725042	+	0.688704i	$0.241820\pi$
$920$	0.791254	0.0260869
$921$	−29.8615	−0.983969
$922$	34.5032	1.13630
$923$	−5.85344	−0.192668
$924$	−5.20376	−0.171191
$925$	1.12735	0.0370670
$926$	−32.9370	−1.08238
$927$	30.1955	0.991751
$928$	0.597002	0.0195975
$929$	−6.10050	−0.200151	−0.100075	−	0.994980i	$-0.531908\pi$
$929$	−6.10050	−0.200151	−0.100075	+	0.994980i	$0.531908\pi$
$930$	19.4713	0.638488
$931$	−19.8334	−0.650015
$932$	16.7903	0.549984
$933$	23.2112	0.759901
$934$	36.3551	1.18957
$935$	3.77479	0.123449
$936$	5.32056	0.173908
$937$	8.15730	0.266487	0.133244	−	0.991083i	$-0.457461\pi$
$937$	8.15730	0.266487	0.133244	+	0.991083i	$0.457461\pi$
$938$	29.7511	0.971408
$939$	−29.7306	−0.970220
$940$	−12.0994	−0.394639
$941$	−0.279419	−0.00910880	−0.00455440	−	0.999990i	$-0.501450\pi$
$941$	−0.279419	−0.00910880	−0.00455440	+	0.999990i	$0.501450\pi$
$942$	−17.7416	−0.578054
$943$	−8.20325	−0.267135
$944$	−4.42095	−0.143890
$945$	7.29419	0.237280
$946$	−1.00000	−0.0325128
$947$	43.0750	1.39975	0.699875	−	0.714265i	$-0.253239\pi$
$947$	43.0750	1.39975	0.699875	+	0.714265i	$0.253239\pi$
$948$	−0.640107	−0.0207897
$949$	−2.54129	−0.0824937
$950$	5.93546	0.192572
$951$	13.7470	0.445777
$952$	−7.22010	−0.234005
$953$	35.2696	1.14249	0.571247	−	0.820778i	$-0.306460\pi$
$953$	35.2696	1.14249	0.571247	+	0.820778i	$0.306460\pi$
$954$	−49.9445	−1.61701
$955$	−4.33138	−0.140160
$956$	−8.02935	−0.259688
$957$	−1.62421	−0.0525032
$958$	8.98706	0.290359
$959$	−30.3564	−0.980258
$960$	2.72061	0.0878073
$961$	20.2219	0.652320
$962$	1.36268	0.0439345
$963$	51.4366	1.65752
$964$	−1.12866	−0.0363517
$965$	1.94220	0.0625215
$966$	4.11749	0.132478
$967$	−50.2807	−1.61692	−0.808459	−	0.588553i	$-0.799698\pi$
$967$	−50.2807	−1.61692	−0.808459	+	0.588553i	$0.799698\pi$
$968$	1.00000	0.0321412
$969$	−60.9556	−1.95818
$970$	−0.701016	−0.0225083
$971$	38.1828	1.22535	0.612673	−	0.790337i	$-0.290094\pi$
$971$	38.1828	1.22535	0.612673	+	0.790337i	$0.290094\pi$
$972$	−19.1400	−0.613916
$973$	18.7676	0.601663
$974$	−6.66801	−0.213657
$975$	3.28853	0.105317
$976$	−2.65531	−0.0849943
$977$	−14.4882	−0.463520	−0.231760	−	0.972773i	$-0.574448\pi$
$977$	−14.4882	−0.463520	−0.231760	+	0.972773i	$0.574448\pi$
$978$	−0.192652	−0.00616033
$979$	1.84824	0.0590700
$980$	−3.34151	−0.106741
$981$	70.0653	2.23701
$982$	27.9655	0.892413
$983$	−42.9493	−1.36987	−0.684935	−	0.728604i	$-0.740170\pi$
$983$	−42.9493	−1.36987	−0.684935	+	0.728604i	$0.740170\pi$
$984$	−28.2057	−0.899164
$985$	7.27531	0.231811
$986$	−2.25356	−0.0717678
$987$	−62.9623	−2.00411
$988$	7.17447	0.228250
$989$	0.791254	0.0251604
$990$	−4.40172	−0.139896
$991$	23.1905	0.736669	0.368334	−	0.929693i	$-0.379928\pi$
$991$	23.1905	0.736669	0.368334	+	0.929693i	$0.379928\pi$
$992$	7.15695	0.227233
$993$	86.4436	2.74321
$994$	−9.26247	−0.293788
$995$	−12.3540	−0.391647
$996$	29.1730	0.924381
$997$	−33.9549	−1.07536	−0.537681	−	0.843149i	$-0.680699\pi$
$997$	−33.9549	−1.07536	−0.537681	+	0.843149i	$0.680699\pi$
$998$	−27.9426	−0.884508
$999$	4.29918	0.136020

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.be.1.11	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.be.1.11	✓	12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.72061 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.72061 q^{6} +1.91272 q^{7} +1.00000 q^{8} +4.40172 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.72061 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.72061 q^{6} +1.91272 q^{7} +1.00000 q^{8} +4.40172 q^{9} +1.00000 q^{10} -1.00000 q^{11} +2.72061 q^{12} +1.20875 q^{13} +1.91272 q^{14} +2.72061 q^{15} +1.00000 q^{16} -3.77479 q^{17} +4.40172 q^{18} +5.93546 q^{19} +1.00000 q^{20} +5.20376 q^{21} -1.00000 q^{22} +0.791254 q^{23} +2.72061 q^{24} +1.00000 q^{25} +1.20875 q^{26} +3.81352 q^{27} +1.91272 q^{28} +0.597002 q^{29} +2.72061 q^{30} +7.15695 q^{31} +1.00000 q^{32} -2.72061 q^{33} -3.77479 q^{34} +1.91272 q^{35} +4.40172 q^{36} +1.12735 q^{37} +5.93546 q^{38} +3.28853 q^{39} +1.00000 q^{40} -10.3674 q^{41} +5.20376 q^{42} +1.00000 q^{43} -1.00000 q^{44} +4.40172 q^{45} +0.791254 q^{46} -12.0994 q^{47} +2.72061 q^{48} -3.34151 q^{49} +1.00000 q^{50} -10.2697 q^{51} +1.20875 q^{52} -11.3466 q^{53} +3.81352 q^{54} -1.00000 q^{55} +1.91272 q^{56} +16.1481 q^{57} +0.597002 q^{58} -4.42095 q^{59} +2.72061 q^{60} -2.65531 q^{61} +7.15695 q^{62} +8.41924 q^{63} +1.00000 q^{64} +1.20875 q^{65} -2.72061 q^{66} +15.5544 q^{67} -3.77479 q^{68} +2.15269 q^{69} +1.91272 q^{70} -4.84257 q^{71} +4.40172 q^{72} -2.10242 q^{73} +1.12735 q^{74} +2.72061 q^{75} +5.93546 q^{76} -1.91272 q^{77} +3.28853 q^{78} -0.235281 q^{79} +1.00000 q^{80} -2.83004 q^{81} -10.3674 q^{82} +10.7230 q^{83} +5.20376 q^{84} -3.77479 q^{85} +1.00000 q^{86} +1.62421 q^{87} -1.00000 q^{88} -1.84824 q^{89} +4.40172 q^{90} +2.31199 q^{91} +0.791254 q^{92} +19.4713 q^{93} -12.0994 q^{94} +5.93546 q^{95} +2.72061 q^{96} -0.701016 q^{97} -3.34151 q^{98} -4.40172 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 3 q^{3} + 12 q^{4} + 12 q^{5} + 3 q^{6} + 8 q^{7} + 12 q^{8} + 25 q^{9}+O(q^{10}) \) 12 * q + 12 * q^2 + 3 * q^3 + 12 * q^4 + 12 * q^5 + 3 * q^6 + 8 * q^7 + 12 * q^8 + 25 * q^9	\( 12 q + 12 q^{2} + 3 q^{3} + 12 q^{4} + 12 q^{5} + 3 q^{6} + 8 q^{7} + 12 q^{8} + 25 q^{9} + 12 q^{10} - 12 q^{11} + 3 q^{12} + 16 q^{13} + 8 q^{14} + 3 q^{15} + 12 q^{16} + 18 q^{17} + 25 q^{18} - 4 q^{19} + 12 q^{20} + 4 q^{21} - 12 q^{22} + 8 q^{23} + 3 q^{24} + 12 q^{25} + 16 q^{26} + 6 q^{27} + 8 q^{28} + 20 q^{29} + 3 q^{30} + 5 q^{31} + 12 q^{32} - 3 q^{33} + 18 q^{34} + 8 q^{35} + 25 q^{36} + 19 q^{37} - 4 q^{38} + 6 q^{39} + 12 q^{40} + 16 q^{41} + 4 q^{42} + 12 q^{43} - 12 q^{44} + 25 q^{45} + 8 q^{46} - q^{47} + 3 q^{48} + 52 q^{49} + 12 q^{50} + q^{51} + 16 q^{52} + 11 q^{53} + 6 q^{54} - 12 q^{55} + 8 q^{56} + 9 q^{57} + 20 q^{58} - 11 q^{59} + 3 q^{60} + 18 q^{61} + 5 q^{62} + 15 q^{63} + 12 q^{64} + 16 q^{65} - 3 q^{66} - 10 q^{67} + 18 q^{68} + 8 q^{70} - 2 q^{71} + 25 q^{72} + 29 q^{73} + 19 q^{74} + 3 q^{75} - 4 q^{76} - 8 q^{77} + 6 q^{78} + 2 q^{79} + 12 q^{80} - 8 q^{81} + 16 q^{82} + 26 q^{83} + 4 q^{84} + 18 q^{85} + 12 q^{86} - 4 q^{87} - 12 q^{88} + 41 q^{89} + 25 q^{90} - 4 q^{91} + 8 q^{92} + 5 q^{93} - q^{94} - 4 q^{95} + 3 q^{96} - 7 q^{97} + 52 q^{98} - 25 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 3 * q^3 + 12 * q^4 + 12 * q^5 + 3 * q^6 + 8 * q^7 + 12 * q^8 + 25 * q^9 + 12 * q^10 - 12 * q^11 + 3 * q^12 + 16 * q^13 + 8 * q^14 + 3 * q^15 + 12 * q^16 + 18 * q^17 + 25 * q^18 - 4 * q^19 + 12 * q^20 + 4 * q^21 - 12 * q^22 + 8 * q^23 + 3 * q^24 + 12 * q^25 + 16 * q^26 + 6 * q^27 + 8 * q^28 + 20 * q^29 + 3 * q^30 + 5 * q^31 + 12 * q^32 - 3 * q^33 + 18 * q^34 + 8 * q^35 + 25 * q^36 + 19 * q^37 - 4 * q^38 + 6 * q^39 + 12 * q^40 + 16 * q^41 + 4 * q^42 + 12 * q^43 - 12 * q^44 + 25 * q^45 + 8 * q^46 - q^47 + 3 * q^48 + 52 * q^49 + 12 * q^50 + q^51 + 16 * q^52 + 11 * q^53 + 6 * q^54 - 12 * q^55 + 8 * q^56 + 9 * q^57 + 20 * q^58 - 11 * q^59 + 3 * q^60 + 18 * q^61 + 5 * q^62 + 15 * q^63 + 12 * q^64 + 16 * q^65 - 3 * q^66 - 10 * q^67 + 18 * q^68 + 8 * q^70 - 2 * q^71 + 25 * q^72 + 29 * q^73 + 19 * q^74 + 3 * q^75 - 4 * q^76 - 8 * q^77 + 6 * q^78 + 2 * q^79 + 12 * q^80 - 8 * q^81 + 16 * q^82 + 26 * q^83 + 4 * q^84 + 18 * q^85 + 12 * q^86 - 4 * q^87 - 12 * q^88 + 41 * q^89 + 25 * q^90 - 4 * q^91 + 8 * q^92 + 5 * q^93 - q^94 - 4 * q^95 + 3 * q^96 - 7 * q^97 + 52 * q^98 - 25 * q^99

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