LMFDB - Embedded newform 7406.2.a.bt.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7406,2,Mod(1,7406)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7406, 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("7406.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7406 = 2 \cdot 7 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7406.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:	$59.1372077370$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} - 46 x^{18} + 45 x^{17} + 870 x^{16} - 815 x^{15} - 8776 x^{14} + 7663 x^{13} + \cdots - 5819 $ x^20 - x^19 - 46x^18 + 45x^17 + 870x^16 - 815x^15 - 8776x^14 + 7663x^13 + 51400x^12 - 40694x^11 - 178762x^10 + 126834x^9 + 361091x^8 - 236606x^7 - 393143x^6 + 262142x^5 + 192115x^4 - 154253x^3 - 18161x^2 + 31878x - 5819
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 322)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-3.33557$ of defining polynomial
Character	$\chi$	$=$	7406.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.33557 q^{3} +1.00000 q^{4} -3.89939 q^{5} +3.33557 q^{6} +1.00000 q^{7} -1.00000 q^{8} +8.12605 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.33557 q^{3} +1.00000 q^{4} -3.89939 q^{5} +3.33557 q^{6} +1.00000 q^{7} -1.00000 q^{8} +8.12605 q^{9} +3.89939 q^{10} -3.67566 q^{11} -3.33557 q^{12} -3.38059 q^{13} -1.00000 q^{14} +13.0067 q^{15} +1.00000 q^{16} +0.218316 q^{17} -8.12605 q^{18} -3.16946 q^{19} -3.89939 q^{20} -3.33557 q^{21} +3.67566 q^{22} +3.33557 q^{24} +10.2052 q^{25} +3.38059 q^{26} -17.0983 q^{27} +1.00000 q^{28} -4.15301 q^{29} -13.0067 q^{30} -2.33347 q^{31} -1.00000 q^{32} +12.2604 q^{33} -0.218316 q^{34} -3.89939 q^{35} +8.12605 q^{36} +6.20518 q^{37} +3.16946 q^{38} +11.2762 q^{39} +3.89939 q^{40} +6.41562 q^{41} +3.33557 q^{42} -2.09254 q^{43} -3.67566 q^{44} -31.6866 q^{45} -6.78064 q^{47} -3.33557 q^{48} +1.00000 q^{49} -10.2052 q^{50} -0.728210 q^{51} -3.38059 q^{52} -5.64937 q^{53} +17.0983 q^{54} +14.3328 q^{55} -1.00000 q^{56} +10.5720 q^{57} +4.15301 q^{58} +0.211611 q^{59} +13.0067 q^{60} -2.50289 q^{61} +2.33347 q^{62} +8.12605 q^{63} +1.00000 q^{64} +13.1822 q^{65} -12.2604 q^{66} +5.05559 q^{67} +0.218316 q^{68} +3.89939 q^{70} -8.06792 q^{71} -8.12605 q^{72} +7.75777 q^{73} -6.20518 q^{74} -34.0403 q^{75} -3.16946 q^{76} -3.67566 q^{77} -11.2762 q^{78} +6.32402 q^{79} -3.89939 q^{80} +32.6545 q^{81} -6.41562 q^{82} -13.0750 q^{83} -3.33557 q^{84} -0.851301 q^{85} +2.09254 q^{86} +13.8527 q^{87} +3.67566 q^{88} -18.6873 q^{89} +31.6866 q^{90} -3.38059 q^{91} +7.78347 q^{93} +6.78064 q^{94} +12.3590 q^{95} +3.33557 q^{96} -14.3991 q^{97} -1.00000 q^{98} -29.8686 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{2} + q^{3} + 20 q^{4} + q^{5} - q^{6} + 20 q^{7} - 20 q^{8} + 33 q^{9}+O(q^{10}) $ 20 * q - 20 * q^2 + q^3 + 20 * q^4 + q^5 - q^6 + 20 * q^7 - 20 * q^8 + 33 * q^9	$ 20 q - 20 q^{2} + q^{3} + 20 q^{4} + q^{5} - q^{6} + 20 q^{7} - 20 q^{8} + 33 q^{9} - q^{10} + q^{12} + 13 q^{13} - 20 q^{14} + 33 q^{15} + 20 q^{16} - 5 q^{17} - 33 q^{18} - 9 q^{19} + q^{20} + q^{21} - q^{24} + 63 q^{25} - 13 q^{26} - 2 q^{27} + 20 q^{28} + 11 q^{29} - 33 q^{30} + 38 q^{31} - 20 q^{32} - 15 q^{33} + 5 q^{34} + q^{35} + 33 q^{36} + 37 q^{37} + 9 q^{38} + 14 q^{39} - q^{40} + 29 q^{41} - q^{42} + 42 q^{43} - 3 q^{45} - 30 q^{47} + q^{48} + 20 q^{49} - 63 q^{50} - 16 q^{51} + 13 q^{52} - 15 q^{53} + 2 q^{54} + 29 q^{55} - 20 q^{56} + 21 q^{57} - 11 q^{58} - 4 q^{59} + 33 q^{60} - 2 q^{61} - 38 q^{62} + 33 q^{63} + 20 q^{64} - 29 q^{65} + 15 q^{66} + 33 q^{67} - 5 q^{68} - q^{70} - 12 q^{71} - 33 q^{72} + 53 q^{73} - 37 q^{74} + 6 q^{75} - 9 q^{76} - 14 q^{78} + 7 q^{79} + q^{80} + 100 q^{81} - 29 q^{82} + 45 q^{83} + q^{84} + 58 q^{85} - 42 q^{86} - 11 q^{87} + 29 q^{89} + 3 q^{90} + 13 q^{91} + 10 q^{93} + 30 q^{94} - 2 q^{95} - q^{96} - 6 q^{97} - 20 q^{98} + 3 q^{99}+O(q^{100}) $ 20 * q - 20 * q^2 + q^3 + 20 * q^4 + q^5 - q^6 + 20 * q^7 - 20 * q^8 + 33 * q^9 - q^10 + q^12 + 13 * q^13 - 20 * q^14 + 33 * q^15 + 20 * q^16 - 5 * q^17 - 33 * q^18 - 9 * q^19 + q^20 + q^21 - q^24 + 63 * q^25 - 13 * q^26 - 2 * q^27 + 20 * q^28 + 11 * q^29 - 33 * q^30 + 38 * q^31 - 20 * q^32 - 15 * q^33 + 5 * q^34 + q^35 + 33 * q^36 + 37 * q^37 + 9 * q^38 + 14 * q^39 - q^40 + 29 * q^41 - q^42 + 42 * q^43 - 3 * q^45 - 30 * q^47 + q^48 + 20 * q^49 - 63 * q^50 - 16 * q^51 + 13 * q^52 - 15 * q^53 + 2 * q^54 + 29 * q^55 - 20 * q^56 + 21 * q^57 - 11 * q^58 - 4 * q^59 + 33 * q^60 - 2 * q^61 - 38 * q^62 + 33 * q^63 + 20 * q^64 - 29 * q^65 + 15 * q^66 + 33 * q^67 - 5 * q^68 - q^70 - 12 * q^71 - 33 * q^72 + 53 * q^73 - 37 * q^74 + 6 * q^75 - 9 * q^76 - 14 * q^78 + 7 * q^79 + q^80 + 100 * q^81 - 29 * q^82 + 45 * q^83 + q^84 + 58 * q^85 - 42 * q^86 - 11 * q^87 + 29 * q^89 + 3 * q^90 + 13 * q^91 + 10 * q^93 + 30 * q^94 - 2 * q^95 - q^96 - 6 * q^97 - 20 * q^98 + 3 * 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
$3$	−3.33557	−1.92579	−0.962897	−	0.269869i	$-0.913020\pi$
$3$	−3.33557	−1.92579	−0.962897	+	0.269869i	$0.913020\pi$
$4$	1.00000	0.500000
$5$	−3.89939	−1.74386	−0.871930	−	0.489631i	$-0.837131\pi$
$5$	−3.89939	−1.74386	−0.871930	+	0.489631i	$0.837131\pi$
$6$	3.33557	1.36174
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	8.12605	2.70868
$10$	3.89939	1.23309
$11$	−3.67566	−1.10825	−0.554127	−	0.832432i	$-0.686948\pi$
$11$	−3.67566	−1.10825	−0.554127	+	0.832432i	$0.686948\pi$
$12$	−3.33557	−0.962897
$13$	−3.38059	−0.937607	−0.468803	−	0.883303i	$-0.655315\pi$
$13$	−3.38059	−0.937607	−0.468803	+	0.883303i	$0.655315\pi$
$14$	−1.00000	−0.267261
$15$	13.0067	3.35831
$16$	1.00000	0.250000
$17$	0.218316	0.0529495	0.0264748	−	0.999649i	$-0.491572\pi$
$17$	0.218316	0.0529495	0.0264748	+	0.999649i	$0.491572\pi$
$18$	−8.12605	−1.91533
$19$	−3.16946	−0.727124	−0.363562	−	0.931570i	$-0.618440\pi$
$19$	−3.16946	−0.727124	−0.363562	+	0.931570i	$0.618440\pi$
$20$	−3.89939	−0.871930
$21$	−3.33557	−0.727882
$22$	3.67566	0.783654
$23$	0	0
$23$	0	0
$24$	3.33557	0.680871
$25$	10.2052	2.04105
$26$	3.38059	0.662988
$27$	−17.0983	−3.29057
$28$	1.00000	0.188982
$29$	−4.15301	−0.771194	−0.385597	−	0.922667i	$-0.626005\pi$
$29$	−4.15301	−0.771194	−0.385597	+	0.922667i	$0.626005\pi$
$30$	−13.0067	−2.37469
$31$	−2.33347	−0.419104	−0.209552	−	0.977797i	$-0.567201\pi$
$31$	−2.33347	−0.419104	−0.209552	+	0.977797i	$0.567201\pi$
$32$	−1.00000	−0.176777
$33$	12.2604	2.13427
$34$	−0.218316	−0.0374410
$35$	−3.89939	−0.659117
$36$	8.12605	1.35434
$37$	6.20518	1.02013	0.510063	−	0.860137i	$-0.329622\pi$
$37$	6.20518	1.02013	0.510063	+	0.860137i	$0.329622\pi$
$38$	3.16946	0.514154
$39$	11.2762	1.80564
$40$	3.89939	0.616547
$41$	6.41562	1.00195	0.500976	−	0.865461i	$-0.332975\pi$
$41$	6.41562	1.00195	0.500976	+	0.865461i	$0.332975\pi$
$42$	3.33557	0.514690
$43$	−2.09254	−0.319110	−0.159555	−	0.987189i	$-0.551006\pi$
$43$	−2.09254	−0.319110	−0.159555	+	0.987189i	$0.551006\pi$
$44$	−3.67566	−0.554127
$45$	−31.6866	−4.72356
$46$	0	0
$47$	−6.78064	−0.989059	−0.494529	−	0.869161i	$-0.664660\pi$
$47$	−6.78064	−0.989059	−0.494529	+	0.869161i	$0.664660\pi$
$48$	−3.33557	−0.481448
$49$	1.00000	0.142857
$50$	−10.2052	−1.44324
$51$	−0.728210	−0.101970
$52$	−3.38059	−0.468803
$53$	−5.64937	−0.776000	−0.388000	−	0.921659i	$-0.626834\pi$
$53$	−5.64937	−0.776000	−0.388000	+	0.921659i	$0.626834\pi$
$54$	17.0983	2.32678
$55$	14.3328	1.93264
$56$	−1.00000	−0.133631
$57$	10.5720	1.40029
$58$	4.15301	0.545317
$59$	0.211611	0.0275494	0.0137747	−	0.999905i	$-0.495615\pi$
$59$	0.211611	0.0275494	0.0137747	+	0.999905i	$0.495615\pi$
$60$	13.0067	1.67916
$61$	−2.50289	−0.320463	−0.160231	−	0.987079i	$-0.551224\pi$
$61$	−2.50289	−0.320463	−0.160231	+	0.987079i	$0.551224\pi$
$62$	2.33347	0.296351
$63$	8.12605	1.02379
$64$	1.00000	0.125000
$65$	13.1822	1.63505
$66$	−12.2604	−1.50916
$67$	5.05559	0.617639	0.308819	−	0.951121i	$-0.400066\pi$
$67$	5.05559	0.617639	0.308819	+	0.951121i	$0.400066\pi$
$68$	0.218316	0.0264748
$69$	0	0
$70$	3.89939	0.466066
$71$	−8.06792	−0.957486	−0.478743	−	0.877955i	$-0.658907\pi$
$71$	−8.06792	−0.957486	−0.478743	+	0.877955i	$0.658907\pi$
$72$	−8.12605	−0.957664
$73$	7.75777	0.907978	0.453989	−	0.891007i	$-0.350001\pi$
$73$	7.75777	0.907978	0.453989	+	0.891007i	$0.350001\pi$
$74$	−6.20518	−0.721338
$75$	−34.0403	−3.93063
$76$	−3.16946	−0.363562
$77$	−3.67566	−0.418881
$78$	−11.2762	−1.27678
$79$	6.32402	0.711507	0.355754	−	0.934580i	$-0.384224\pi$
$79$	6.32402	0.711507	0.355754	+	0.934580i	$0.384224\pi$
$80$	−3.89939	−0.435965
$81$	32.6545	3.62828
$82$	−6.41562	−0.708487
$83$	−13.0750	−1.43517	−0.717584	−	0.696472i	$-0.754752\pi$
$83$	−13.0750	−1.43517	−0.717584	+	0.696472i	$0.754752\pi$
$84$	−3.33557	−0.363941
$85$	−0.851301	−0.0923365
$86$	2.09254	0.225645
$87$	13.8527	1.48516
$88$	3.67566	0.391827
$89$	−18.6873	−1.98085	−0.990424	−	0.138056i	$-0.955915\pi$
$89$	−18.6873	−1.98085	−0.990424	+	0.138056i	$0.955915\pi$
$90$	31.6866	3.34006
$91$	−3.38059	−0.354382
$92$	0	0
$93$	7.78347	0.807108
$94$	6.78064	0.699370
$95$	12.3590	1.26800
$96$	3.33557	0.340435
$97$	−14.3991	−1.46201	−0.731003	−	0.682375i	$-0.760947\pi$
$97$	−14.3991	−1.46201	−0.731003	+	0.682375i	$0.760947\pi$
$98$	−1.00000	−0.101015
$99$	−29.8686	−3.00191
$100$	10.2052	1.02052
$101$	11.5621	1.15048	0.575238	−	0.817986i	$-0.304910\pi$
$101$	11.5621	1.15048	0.575238	+	0.817986i	$0.304910\pi$
$102$	0.728210	0.0721036
$103$	−8.11593	−0.799686	−0.399843	−	0.916584i	$-0.630935\pi$
$103$	−8.11593	−0.799686	−0.399843	+	0.916584i	$0.630935\pi$
$104$	3.38059	0.331494
$105$	13.0067	1.26932
$106$	5.64937	0.548715
$107$	−8.26149	−0.798668	−0.399334	−	0.916805i	$-0.630759\pi$
$107$	−8.26149	−0.798668	−0.399334	+	0.916805i	$0.630759\pi$
$108$	−17.0983	−1.64529
$109$	5.11429	0.489861	0.244930	−	0.969541i	$-0.421235\pi$
$109$	5.11429	0.489861	0.244930	+	0.969541i	$0.421235\pi$
$110$	−14.3328	−1.36658
$111$	−20.6978	−1.96455
$112$	1.00000	0.0944911
$113$	−7.84309	−0.737816	−0.368908	−	0.929466i	$-0.620268\pi$
$113$	−7.84309	−0.737816	−0.368908	+	0.929466i	$0.620268\pi$
$114$	−10.5720	−0.990155
$115$	0	0
$116$	−4.15301	−0.385597
$117$	−27.4708	−2.53968
$118$	−0.211611	−0.0194803
$119$	0.218316	0.0200130
$120$	−13.0067	−1.18734
$121$	2.51050	0.228227
$122$	2.50289	0.226601
$123$	−21.3998	−1.92955
$124$	−2.33347	−0.209552
$125$	−20.2972	−1.81544
$126$	−8.12605	−0.723926
$127$	−14.2941	−1.26840	−0.634200	−	0.773169i	$-0.718670\pi$
$127$	−14.2941	−1.26840	−0.634200	+	0.773169i	$0.718670\pi$
$128$	−1.00000	−0.0883883
$129$	6.97983	0.614540
$130$	−13.1822	−1.15616
$131$	−5.99622	−0.523892	−0.261946	−	0.965083i	$-0.584364\pi$
$131$	−5.99622	−0.523892	−0.261946	+	0.965083i	$0.584364\pi$
$132$	12.2604	1.06713
$133$	−3.16946	−0.274827
$134$	−5.05559	−0.436737
$135$	66.6729	5.73829
$136$	−0.218316	−0.0187205
$137$	−16.7334	−1.42963	−0.714813	−	0.699315i	$-0.753488\pi$
$137$	−16.7334	−1.42963	−0.714813	+	0.699315i	$0.753488\pi$
$138$	0	0
$139$	−8.62071	−0.731199	−0.365600	−	0.930772i	$-0.619136\pi$
$139$	−8.62071	−0.731199	−0.365600	+	0.930772i	$0.619136\pi$
$140$	−3.89939	−0.329558
$141$	22.6173	1.90472
$142$	8.06792	0.677045
$143$	12.4259	1.03911
$144$	8.12605	0.677171
$145$	16.1942	1.34485
$146$	−7.75777	−0.642037
$147$	−3.33557	−0.275113
$148$	6.20518	0.510063
$149$	−0.932239	−0.0763720	−0.0381860	−	0.999271i	$-0.512158\pi$
$149$	−0.932239	−0.0763720	−0.0381860	+	0.999271i	$0.512158\pi$
$150$	34.0403	2.77938
$151$	2.62397	0.213536	0.106768	−	0.994284i	$-0.465950\pi$
$151$	2.62397	0.213536	0.106768	+	0.994284i	$0.465950\pi$
$152$	3.16946	0.257077
$153$	1.77405	0.143423
$154$	3.67566	0.296193
$155$	9.09912	0.730859
$156$	11.2762	0.902819
$157$	3.10279	0.247630	0.123815	−	0.992305i	$-0.460487\pi$
$157$	3.10279	0.247630	0.123815	+	0.992305i	$0.460487\pi$
$158$	−6.32402	−0.503112
$159$	18.8439	1.49442
$160$	3.89939	0.308274
$161$	0	0
$162$	−32.6545	−2.56558
$163$	−11.8989	−0.931994	−0.465997	−	0.884786i	$-0.654304\pi$
$163$	−11.8989	−0.931994	−0.465997	+	0.884786i	$0.654304\pi$
$164$	6.41562	0.500976
$165$	−47.8082	−3.72187
$166$	13.0750	1.01482
$167$	22.5891	1.74800	0.873998	−	0.485929i	$-0.161519\pi$
$167$	22.5891	1.74800	0.873998	+	0.485929i	$0.161519\pi$
$168$	3.33557	0.257345
$169$	−1.57162	−0.120894
$170$	0.851301	0.0652918
$171$	−25.7552	−1.96955
$172$	−2.09254	−0.159555
$173$	−17.4313	−1.32527	−0.662637	−	0.748940i	$-0.730563\pi$
$173$	−17.4313	−1.32527	−0.662637	+	0.748940i	$0.730563\pi$
$174$	−13.8527	−1.05017
$175$	10.2052	0.771443
$176$	−3.67566	−0.277064
$177$	−0.705843	−0.0530544
$178$	18.6873	1.40067
$179$	−10.3052	−0.770246	−0.385123	−	0.922865i	$-0.625841\pi$
$179$	−10.3052	−0.770246	−0.385123	+	0.922865i	$0.625841\pi$
$180$	−31.6866	−2.36178
$181$	−21.5191	−1.59950	−0.799751	−	0.600332i	$-0.795035\pi$
$181$	−21.5191	−1.59950	−0.799751	+	0.600332i	$0.795035\pi$
$182$	3.38059	0.250586
$183$	8.34858	0.617145
$184$	0	0
$185$	−24.1964	−1.77896
$186$	−7.78347	−0.570712
$187$	−0.802458	−0.0586815
$188$	−6.78064	−0.494529
$189$	−17.0983	−1.24372
$190$	−12.3590	−0.896613
$191$	6.68893	0.483994	0.241997	−	0.970277i	$-0.422198\pi$
$191$	6.68893	0.483994	0.241997	+	0.970277i	$0.422198\pi$
$192$	−3.33557	−0.240724
$193$	−25.1013	−1.80683	−0.903415	−	0.428767i	$-0.858948\pi$
$193$	−25.1013	−1.80683	−0.903415	+	0.428767i	$0.858948\pi$
$194$	14.3991	1.03379
$195$	−43.9703	−3.14878
$196$	1.00000	0.0714286
$197$	−9.42439	−0.671460	−0.335730	−	0.941958i	$-0.608983\pi$
$197$	−9.42439	−0.671460	−0.335730	+	0.941958i	$0.608983\pi$
$198$	29.8686	2.12267
$199$	−9.97178	−0.706881	−0.353440	−	0.935457i	$-0.614988\pi$
$199$	−9.97178	−0.706881	−0.353440	+	0.935457i	$0.614988\pi$
$200$	−10.2052	−0.721619
$201$	−16.8633	−1.18945
$202$	−11.5621	−0.813509
$203$	−4.15301	−0.291484
$204$	−0.728210	−0.0509849
$205$	−25.0170	−1.74726
$206$	8.11593	0.565463
$207$	0	0
$208$	−3.38059	−0.234402
$209$	11.6499	0.805838
$210$	−13.0067	−0.897547
$211$	11.3123	0.778773	0.389386	−	0.921075i	$-0.372687\pi$
$211$	11.3123	0.778773	0.389386	+	0.921075i	$0.372687\pi$
$212$	−5.64937	−0.388000
$213$	26.9111	1.84392
$214$	8.26149	0.564744
$215$	8.15964	0.556483
$216$	17.0983	1.16339
$217$	−2.33347	−0.158406
$218$	−5.11429	−0.346384
$219$	−25.8766	−1.74858
$220$	14.3328	0.966320
$221$	−0.738038	−0.0496458
$222$	20.6978	1.38915
$223$	−23.3277	−1.56214	−0.781069	−	0.624445i	$-0.785325\pi$
$223$	−23.3277	−1.56214	−0.781069	+	0.624445i	$0.785325\pi$
$224$	−1.00000	−0.0668153
$225$	82.9282	5.52854
$226$	7.84309	0.521715
$227$	−7.85276	−0.521206	−0.260603	−	0.965446i	$-0.583921\pi$
$227$	−7.85276	−0.521206	−0.260603	+	0.965446i	$0.583921\pi$
$228$	10.5720	0.700146
$229$	−10.2591	−0.677942	−0.338971	−	0.940797i	$-0.610079\pi$
$229$	−10.2591	−0.677942	−0.338971	+	0.940797i	$0.610079\pi$
$230$	0	0
$231$	12.2604	0.806678
$232$	4.15301	0.272658
$233$	10.7088	0.701559	0.350780	−	0.936458i	$-0.385917\pi$
$233$	10.7088	0.701559	0.350780	+	0.936458i	$0.385917\pi$
$234$	27.4708	1.79582
$235$	26.4404	1.72478
$236$	0.211611	0.0137747
$237$	−21.0942	−1.37022
$238$	−0.218316	−0.0141514
$239$	−10.6940	−0.691739	−0.345869	−	0.938283i	$-0.612416\pi$
$239$	−10.6940	−0.691739	−0.345869	+	0.938283i	$0.612416\pi$
$240$	13.0067	0.839579
$241$	−1.46002	−0.0940481	−0.0470240	−	0.998894i	$-0.514974\pi$
$241$	−1.46002	−0.0940481	−0.0470240	+	0.998894i	$0.514974\pi$
$242$	−2.51050	−0.161381
$243$	−57.6266	−3.69675
$244$	−2.50289	−0.160231
$245$	−3.89939	−0.249123
$246$	21.3998	1.36440
$247$	10.7146	0.681756
$248$	2.33347	0.148176
$249$	43.6126	2.76384
$250$	20.2972	1.28371
$251$	1.94197	0.122576	0.0612881	−	0.998120i	$-0.480479\pi$
$251$	1.94197	0.122576	0.0612881	+	0.998120i	$0.480479\pi$
$252$	8.12605	0.511893
$253$	0	0
$254$	14.2941	0.896894
$255$	2.83958	0.177821
$256$	1.00000	0.0625000
$257$	−23.0882	−1.44020	−0.720102	−	0.693868i	$-0.755905\pi$
$257$	−23.0882	−1.44020	−0.720102	+	0.693868i	$0.755905\pi$
$258$	−6.97983	−0.434545
$259$	6.20518	0.385571
$260$	13.1822	0.817527
$261$	−33.7475	−2.08892
$262$	5.99622	0.370448
$263$	−21.5655	−1.32978	−0.664892	−	0.746939i	$-0.731523\pi$
$263$	−21.5655	−1.32978	−0.664892	+	0.746939i	$0.731523\pi$
$264$	−12.2604	−0.754578
$265$	22.0291	1.35324
$266$	3.16946	0.194332
$267$	62.3328	3.81471
$268$	5.05559	0.308819
$269$	31.8795	1.94373	0.971864	−	0.235543i	$-0.0756868\pi$
$269$	31.8795	1.94373	0.971864	+	0.235543i	$0.0756868\pi$
$270$	−66.6729	−4.05759
$271$	9.12635	0.554387	0.277193	−	0.960814i	$-0.410596\pi$
$271$	9.12635	0.554387	0.277193	+	0.960814i	$0.410596\pi$
$272$	0.218316	0.0132374
$273$	11.2762	0.682467
$274$	16.7334	1.01090
$275$	−37.5110	−2.26200
$276$	0	0
$277$	−1.55360	−0.0933466	−0.0466733	−	0.998910i	$-0.514862\pi$
$277$	−1.55360	−0.0933466	−0.0466733	+	0.998910i	$0.514862\pi$
$278$	8.62071	0.517036
$279$	−18.9619	−1.13522
$280$	3.89939	0.233033
$281$	−9.51001	−0.567320	−0.283660	−	0.958925i	$-0.591549\pi$
$281$	−9.51001	−0.567320	−0.283660	+	0.958925i	$0.591549\pi$
$282$	−22.6173	−1.34684
$283$	8.78321	0.522108	0.261054	−	0.965324i	$-0.415930\pi$
$283$	8.78321	0.522108	0.261054	+	0.965324i	$0.415930\pi$
$284$	−8.06792	−0.478743
$285$	−41.2242	−2.44191
$286$	−12.4259	−0.734759
$287$	6.41562	0.378702
$288$	−8.12605	−0.478832
$289$	−16.9523	−0.997196
$290$	−16.1942	−0.950956
$291$	48.0292	2.81552
$292$	7.75777	0.453989
$293$	−5.71751	−0.334021	−0.167010	−	0.985955i	$-0.553411\pi$
$293$	−5.71751	−0.334021	−0.167010	+	0.985955i	$0.553411\pi$
$294$	3.33557	0.194535
$295$	−0.825152	−0.0480422
$296$	−6.20518	−0.360669
$297$	62.8476	3.64679
$298$	0.932239	0.0540032
$299$	0	0
$300$	−34.0403	−1.96532
$301$	−2.09254	−0.120612
$302$	−2.62397	−0.150993
$303$	−38.5663	−2.21558
$304$	−3.16946	−0.181781
$305$	9.75975	0.558842
$306$	−1.77405	−0.101416
$307$	−20.3143	−1.15940	−0.579701	−	0.814830i	$-0.696830\pi$
$307$	−20.3143	−1.15940	−0.579701	+	0.814830i	$0.696830\pi$
$308$	−3.67566	−0.209440
$309$	27.0713	1.54003
$310$	−9.09912	−0.516795
$311$	−21.0818	−1.19544	−0.597721	−	0.801705i	$-0.703927\pi$
$311$	−21.0818	−1.19544	−0.597721	+	0.801705i	$0.703927\pi$
$312$	−11.2762	−0.638389
$313$	−6.95297	−0.393005	−0.196502	−	0.980503i	$-0.562958\pi$
$313$	−6.95297	−0.393005	−0.196502	+	0.980503i	$0.562958\pi$
$314$	−3.10279	−0.175101
$315$	−31.6866	−1.78534
$316$	6.32402	0.355754
$317$	9.86155	0.553880	0.276940	−	0.960887i	$-0.410680\pi$
$317$	9.86155	0.553880	0.276940	+	0.960887i	$0.410680\pi$
$318$	−18.8439	−1.05671
$319$	15.2651	0.854679
$320$	−3.89939	−0.217982
$321$	27.5568	1.53807
$322$	0	0
$323$	−0.691945	−0.0385009
$324$	32.6545	1.81414
$325$	−34.4997	−1.91370
$326$	11.8989	0.659019
$327$	−17.0591	−0.943370
$328$	−6.41562	−0.354243
$329$	−6.78064	−0.373829
$330$	47.8082	2.63176
$331$	24.6369	1.35416	0.677082	−	0.735907i	$-0.263244\pi$
$331$	24.6369	1.35416	0.677082	+	0.735907i	$0.263244\pi$
$332$	−13.0750	−0.717584
$333$	50.4236	2.76320
$334$	−22.5891	−1.23602
$335$	−19.7137	−1.07708
$336$	−3.33557	−0.181970
$337$	16.4216	0.894541	0.447271	−	0.894399i	$-0.352396\pi$
$337$	16.4216	0.894541	0.447271	+	0.894399i	$0.352396\pi$
$338$	1.57162	0.0854849
$339$	26.1612	1.42088
$340$	−0.851301	−0.0461683
$341$	8.57706	0.464474
$342$	25.7552	1.39268
$343$	1.00000	0.0539949
$344$	2.09254	0.112822
$345$	0	0
$346$	17.4313	0.937111
$347$	25.3217	1.35934	0.679671	−	0.733517i	$-0.262123\pi$
$347$	25.3217	1.35934	0.679671	+	0.733517i	$0.262123\pi$
$348$	13.8527	0.742581
$349$	21.7277	1.16306	0.581529	−	0.813525i	$-0.302455\pi$
$349$	21.7277	1.16306	0.581529	+	0.813525i	$0.302455\pi$
$350$	−10.2052	−0.545492
$351$	57.8023	3.08526
$352$	3.67566	0.195913
$353$	23.4405	1.24761	0.623806	−	0.781580i	$-0.285586\pi$
$353$	23.4405	1.24761	0.623806	+	0.781580i	$0.285586\pi$
$354$	0.705843	0.0375151
$355$	31.4599	1.66972
$356$	−18.6873	−0.990424
$357$	−0.728210	−0.0385410
$358$	10.3052	0.544646
$359$	−29.7516	−1.57023	−0.785115	−	0.619350i	$-0.787396\pi$
$359$	−29.7516	−1.57023	−0.785115	+	0.619350i	$0.787396\pi$
$360$	31.6866	1.67003
$361$	−8.95452	−0.471291
$362$	21.5191	1.13102
$363$	−8.37395	−0.439518
$364$	−3.38059	−0.177191
$365$	−30.2505	−1.58339
$366$	−8.34858	−0.436387
$367$	1.45360	0.0758773	0.0379386	−	0.999280i	$-0.487921\pi$
$367$	1.45360	0.0758773	0.0379386	+	0.999280i	$0.487921\pi$
$368$	0	0
$369$	52.1336	2.71397
$370$	24.1964	1.25791
$371$	−5.64937	−0.293300
$372$	7.78347	0.403554
$373$	4.63067	0.239767	0.119884	−	0.992788i	$-0.461748\pi$
$373$	4.63067	0.239767	0.119884	+	0.992788i	$0.461748\pi$
$374$	0.802458	0.0414941
$375$	67.7028	3.49616
$376$	6.78064	0.349685
$377$	14.0396	0.723077
$378$	17.0983	0.879442
$379$	−13.3491	−0.685699	−0.342850	−	0.939390i	$-0.611392\pi$
$379$	−13.3491	−0.685699	−0.342850	+	0.939390i	$0.611392\pi$
$380$	12.3590	0.634001
$381$	47.6791	2.44268
$382$	−6.68893	−0.342235
$383$	−25.3860	−1.29716	−0.648581	−	0.761146i	$-0.724637\pi$
$383$	−25.3860	−1.29716	−0.648581	+	0.761146i	$0.724637\pi$
$384$	3.33557	0.170218
$385$	14.3328	0.730469
$386$	25.1013	1.27762
$387$	−17.0041	−0.864367
$388$	−14.3991	−0.731003
$389$	22.5306	1.14235	0.571175	−	0.820829i	$-0.306488\pi$
$389$	22.5306	1.14235	0.571175	+	0.820829i	$0.306488\pi$
$390$	43.9703	2.22652
$391$	0	0
$392$	−1.00000	−0.0505076
$393$	20.0008	1.00891
$394$	9.42439	0.474794
$395$	−24.6598	−1.24077
$396$	−29.8686	−1.50095
$397$	3.08810	0.154987	0.0774936	−	0.996993i	$-0.475308\pi$
$397$	3.08810	0.154987	0.0774936	+	0.996993i	$0.475308\pi$
$398$	9.97178	0.499840
$399$	10.5720	0.529260
$400$	10.2052	0.510261
$401$	5.53491	0.276400	0.138200	−	0.990404i	$-0.455868\pi$
$401$	5.53491	0.276400	0.138200	+	0.990404i	$0.455868\pi$
$402$	16.8633	0.841065
$403$	7.88851	0.392955
$404$	11.5621	0.575238
$405$	−127.333	−6.32721
$406$	4.15301	0.206110
$407$	−22.8082	−1.13056
$408$	0.728210	0.0360518
$409$	17.8529	0.882770	0.441385	−	0.897318i	$-0.354487\pi$
$409$	17.8529	0.882770	0.441385	+	0.897318i	$0.354487\pi$
$410$	25.0170	1.23550
$411$	55.8153	2.75317
$412$	−8.11593	−0.399843
$413$	0.211611	0.0104127
$414$	0	0
$415$	50.9845	2.50273
$416$	3.38059	0.165747
$417$	28.7550	1.40814
$418$	−11.6499	−0.569814
$419$	8.02435	0.392015	0.196008	−	0.980602i	$-0.437202\pi$
$419$	8.02435	0.392015	0.196008	+	0.980602i	$0.437202\pi$
$420$	13.0067	0.634662
$421$	21.2293	1.03465	0.517327	−	0.855788i	$-0.326927\pi$
$421$	21.2293	1.03465	0.517327	+	0.855788i	$0.326927\pi$
$422$	−11.3123	−0.550675
$423$	−55.0998	−2.67905
$424$	5.64937	0.274357
$425$	2.22797	0.108072
$426$	−26.9111	−1.30385
$427$	−2.50289	−0.121123
$428$	−8.26149	−0.399334
$429$	−41.4475	−2.00110
$430$	−8.15964	−0.393493
$431$	−30.9834	−1.49242	−0.746208	−	0.665713i	$-0.768128\pi$
$431$	−30.9834	−1.49242	−0.746208	+	0.665713i	$0.768128\pi$
$432$	−17.0983	−0.822643
$433$	4.82180	0.231721	0.115860	−	0.993265i	$-0.463037\pi$
$433$	4.82180	0.231721	0.115860	+	0.993265i	$0.463037\pi$
$434$	2.33347	0.112010
$435$	−54.0169	−2.58991
$436$	5.11429	0.244930
$437$	0	0
$438$	25.8766	1.23643
$439$	−9.85042	−0.470135	−0.235068	−	0.971979i	$-0.575531\pi$
$439$	−9.85042	−0.470135	−0.235068	+	0.971979i	$0.575531\pi$
$440$	−14.3328	−0.683291
$441$	8.12605	0.386955
$442$	0.738038	0.0351049
$443$	1.99563	0.0948153	0.0474076	−	0.998876i	$-0.484904\pi$
$443$	1.99563	0.0948153	0.0474076	+	0.998876i	$0.484904\pi$
$444$	−20.6978	−0.982276
$445$	72.8690	3.45432
$446$	23.3277	1.10460
$447$	3.10955	0.147077
$448$	1.00000	0.0472456
$449$	16.1935	0.764218	0.382109	−	0.924117i	$-0.375198\pi$
$449$	16.1935	0.764218	0.382109	+	0.924117i	$0.375198\pi$
$450$	−82.9282	−3.90927
$451$	−23.5817	−1.11042
$452$	−7.84309	−0.368908
$453$	−8.75245	−0.411226
$454$	7.85276	0.368548
$455$	13.1822	0.617992
$456$	−10.5720	−0.495078
$457$	−17.9750	−0.840837	−0.420418	−	0.907330i	$-0.638117\pi$
$457$	−17.9750	−0.840837	−0.420418	+	0.907330i	$0.638117\pi$
$458$	10.2591	0.479378
$459$	−3.73284	−0.174234
$460$	0	0
$461$	−1.18118	−0.0550129	−0.0275065	−	0.999622i	$-0.508757\pi$
$461$	−1.18118	−0.0550129	−0.0275065	+	0.999622i	$0.508757\pi$
$462$	−12.2604	−0.570407
$463$	−15.6463	−0.727143	−0.363572	−	0.931566i	$-0.618443\pi$
$463$	−15.6463	−0.727143	−0.363572	+	0.931566i	$0.618443\pi$
$464$	−4.15301	−0.192799
$465$	−30.3508	−1.40748
$466$	−10.7088	−0.496077
$467$	21.0792	0.975429	0.487715	−	0.873003i	$-0.337831\pi$
$467$	21.0792	0.975429	0.487715	+	0.873003i	$0.337831\pi$
$468$	−27.4708	−1.26984
$469$	5.05559	0.233446
$470$	−26.4404	−1.21960
$471$	−10.3496	−0.476884
$472$	−0.211611	−0.00974017
$473$	7.69148	0.353655
$474$	21.0942	0.968890
$475$	−32.3451	−1.48409
$476$	0.218316	0.0100065
$477$	−45.9070	−2.10194
$478$	10.6940	0.489133
$479$	16.1223	0.736645	0.368323	−	0.929698i	$-0.379932\pi$
$479$	16.1223	0.736645	0.368323	+	0.929698i	$0.379932\pi$
$480$	−13.0067	−0.593672
$481$	−20.9772	−0.956477
$482$	1.46002	0.0665020
$483$	0	0
$484$	2.51050	0.114114
$485$	56.1476	2.54953
$486$	57.6266	2.61399
$487$	3.92904	0.178042	0.0890209	−	0.996030i	$-0.471626\pi$
$487$	3.92904	0.178042	0.0890209	+	0.996030i	$0.471626\pi$
$488$	2.50289	0.113301
$489$	39.6897	1.79483
$490$	3.89939	0.176156
$491$	−18.7368	−0.845581	−0.422791	−	0.906227i	$-0.638949\pi$
$491$	−18.7368	−0.845581	−0.422791	+	0.906227i	$0.638949\pi$
$492$	−21.3998	−0.964776
$493$	−0.906670	−0.0408344
$494$	−10.7146	−0.482074
$495$	116.469	5.23491
$496$	−2.33347	−0.104776
$497$	−8.06792	−0.361896
$498$	−43.6126	−1.95433
$499$	18.7492	0.839328	0.419664	−	0.907680i	$-0.362148\pi$
$499$	18.7492	0.839328	0.419664	+	0.907680i	$0.362148\pi$
$500$	−20.2972	−0.907719
$501$	−75.3476	−3.36628
$502$	−1.94197	−0.0866745
$503$	−26.0217	−1.16025	−0.580125	−	0.814527i	$-0.696996\pi$
$503$	−26.0217	−1.16025	−0.580125	+	0.814527i	$0.696996\pi$
$504$	−8.12605	−0.361963
$505$	−45.0852	−2.00627
$506$	0	0
$507$	5.24225	0.232817
$508$	−14.2941	−0.634200
$509$	−29.0535	−1.28778	−0.643888	−	0.765120i	$-0.722680\pi$
$509$	−29.0535	−1.28778	−0.643888	+	0.765120i	$0.722680\pi$
$510$	−2.83958	−0.125739
$511$	7.75777	0.343183
$512$	−1.00000	−0.0441942
$513$	54.1924	2.39265
$514$	23.0882	1.01838
$515$	31.6472	1.39454
$516$	6.97983	0.307270
$517$	24.9234	1.09613
$518$	−6.20518	−0.272640
$519$	58.1433	2.55221
$520$	−13.1822	−0.578079
$521$	33.9591	1.48778	0.743888	−	0.668304i	$-0.232979\pi$
$521$	33.9591	1.48778	0.743888	+	0.668304i	$0.232979\pi$
$522$	33.7475	1.47709
$523$	−9.29090	−0.406263	−0.203131	−	0.979151i	$-0.565112\pi$
$523$	−9.29090	−0.406263	−0.203131	+	0.979151i	$0.565112\pi$
$524$	−5.99622	−0.261946
$525$	−34.0403	−1.48564
$526$	21.5655	0.940300
$527$	−0.509436	−0.0221914
$528$	12.2604	0.533567
$529$	0	0
$530$	−22.0291	−0.956882
$531$	1.71956	0.0746225
$532$	−3.16946	−0.137414
$533$	−21.6886	−0.939436
$534$	−62.3328	−2.69740
$535$	32.2148	1.39277
$536$	−5.05559	−0.218368
$537$	34.3737	1.48333
$538$	−31.8795	−1.37442
$539$	−3.67566	−0.158322
$540$	66.6729	2.86915
$541$	−8.54421	−0.367344	−0.183672	−	0.982988i	$-0.558798\pi$
$541$	−8.54421	−0.367344	−0.183672	+	0.982988i	$0.558798\pi$
$542$	−9.12635	−0.392010
$543$	71.7785	3.08031
$544$	−0.218316	−0.00936024
$545$	−19.9426	−0.854248
$546$	−11.2762	−0.482577
$547$	17.4517	0.746182	0.373091	−	0.927795i	$-0.378298\pi$
$547$	17.4517	0.746182	0.373091	+	0.927795i	$0.378298\pi$
$548$	−16.7334	−0.714813
$549$	−20.3386	−0.868031
$550$	37.5110	1.59947
$551$	13.1628	0.560754
$552$	0	0
$553$	6.32402	0.268925
$554$	1.55360	0.0660060
$555$	80.7089	3.42590
$556$	−8.62071	−0.365600
$557$	33.6099	1.42410	0.712049	−	0.702129i	$-0.247767\pi$
$557$	33.6099	1.42410	0.712049	+	0.702129i	$0.247767\pi$
$558$	18.9619	0.802722
$559$	7.07403	0.299199
$560$	−3.89939	−0.164779
$561$	2.67666	0.113009
$562$	9.51001	0.401156
$563$	−12.6494	−0.533108	−0.266554	−	0.963820i	$-0.585885\pi$
$563$	−12.6494	−0.533108	−0.266554	+	0.963820i	$0.585885\pi$
$564$	22.6173	0.952362
$565$	30.5833	1.28665
$566$	−8.78321	−0.369186
$567$	32.6545	1.37136
$568$	8.06792	0.338522
$569$	−28.0881	−1.17751	−0.588757	−	0.808310i	$-0.700382\pi$
$569$	−28.0881	−1.17751	−0.588757	+	0.808310i	$0.700382\pi$
$570$	41.2242	1.72669
$571$	−11.5602	−0.483780	−0.241890	−	0.970304i	$-0.577767\pi$
$571$	−11.5602	−0.483780	−0.241890	+	0.970304i	$0.577767\pi$
$572$	12.4259	0.519553
$573$	−22.3114	−0.932072
$574$	−6.41562	−0.267783
$575$	0	0
$576$	8.12605	0.338585
$577$	5.20512	0.216692	0.108346	−	0.994113i	$-0.465445\pi$
$577$	5.20512	0.216692	0.108346	+	0.994113i	$0.465445\pi$
$578$	16.9523	0.705124
$579$	83.7272	3.47958
$580$	16.1942	0.672427
$581$	−13.0750	−0.542442
$582$	−48.0292	−1.99087
$583$	20.7652	0.860005
$584$	−7.75777	−0.321019
$585$	107.119	4.42884
$586$	5.71751	0.236188
$587$	19.3450	0.798455	0.399228	−	0.916852i	$-0.369278\pi$
$587$	19.3450	0.798455	0.399228	+	0.916852i	$0.369278\pi$
$588$	−3.33557	−0.137557
$589$	7.39585	0.304741
$590$	0.825152	0.0339710
$591$	31.4357	1.29309
$592$	6.20518	0.255032
$593$	0.825201	0.0338869	0.0169435	−	0.999856i	$-0.494606\pi$
$593$	0.825201	0.0338869	0.0169435	+	0.999856i	$0.494606\pi$
$594$	−62.8476	−2.57867
$595$	−0.851301	−0.0348999
$596$	−0.932239	−0.0381860
$597$	33.2616	1.36131
$598$	0	0
$599$	−7.27687	−0.297325	−0.148662	−	0.988888i	$-0.547497\pi$
$599$	−7.27687	−0.297325	−0.148662	+	0.988888i	$0.547497\pi$
$600$	34.0403	1.38969
$601$	30.4515	1.24214	0.621071	−	0.783754i	$-0.286698\pi$
$601$	30.4515	1.24214	0.621071	+	0.783754i	$0.286698\pi$
$602$	2.09254	0.0852857
$603$	41.0820	1.67299
$604$	2.62397	0.106768
$605$	−9.78940	−0.397996
$606$	38.5663	1.56665
$607$	−18.2356	−0.740161	−0.370080	−	0.929000i	$-0.620670\pi$
$607$	−18.2356	−0.740161	−0.370080	+	0.929000i	$0.620670\pi$
$608$	3.16946	0.128539
$609$	13.8527	0.561338
$610$	−9.75975	−0.395161
$611$	22.9226	0.927348
$612$	1.77405	0.0717117
$613$	−19.1304	−0.772668	−0.386334	−	0.922359i	$-0.626259\pi$
$613$	−19.1304	−0.772668	−0.386334	+	0.922359i	$0.626259\pi$
$614$	20.3143	0.819820
$615$	83.4460	3.36487
$616$	3.67566	0.148097
$617$	−36.0315	−1.45057	−0.725287	−	0.688447i	$-0.758293\pi$
$617$	−36.0315	−1.45057	−0.725287	+	0.688447i	$0.758293\pi$
$618$	−27.0713	−1.08897
$619$	0.0583541	0.00234545	0.00117272	−	0.999999i	$-0.499627\pi$
$619$	0.0583541	0.00234545	0.00117272	+	0.999999i	$0.499627\pi$
$620$	9.09912	0.365429
$621$	0	0
$622$	21.0818	0.845305
$623$	−18.6873	−0.748690
$624$	11.2762	0.451409
$625$	28.1206	1.12482
$626$	6.95297	0.277896
$627$	−38.8590	−1.55188
$628$	3.10279	0.123815
$629$	1.35469	0.0540152
$630$	31.6866	1.26242
$631$	0.848623	0.0337831	0.0168916	−	0.999857i	$-0.494623\pi$
$631$	0.848623	0.0337831	0.0168916	+	0.999857i	$0.494623\pi$
$632$	−6.32402	−0.251556
$633$	−37.7331	−1.49976
$634$	−9.86155	−0.391652
$635$	55.7384	2.21191
$636$	18.8439	0.747208
$637$	−3.38059	−0.133944
$638$	−15.2651	−0.604349
$639$	−65.5603	−2.59352
$640$	3.89939	0.154137
$641$	40.7923	1.61120	0.805599	−	0.592462i	$-0.201844\pi$
$641$	40.7923	1.61120	0.805599	+	0.592462i	$0.201844\pi$
$642$	−27.5568	−1.08758
$643$	−23.2323	−0.916191	−0.458095	−	0.888903i	$-0.651468\pi$
$643$	−23.2323	−0.916191	−0.458095	+	0.888903i	$0.651468\pi$
$644$	0	0
$645$	−27.2171	−1.07167
$646$	0.691945	0.0272242
$647$	−11.1773	−0.439427	−0.219713	−	0.975564i	$-0.570512\pi$
$647$	−11.1773	−0.439427	−0.219713	+	0.975564i	$0.570512\pi$
$648$	−32.6545	−1.28279
$649$	−0.777810	−0.0305317
$650$	34.4997	1.35319
$651$	7.78347	0.305058
$652$	−11.8989	−0.465997
$653$	−1.85643	−0.0726477	−0.0363239	−	0.999340i	$-0.511565\pi$
$653$	−1.85643	−0.0726477	−0.0363239	+	0.999340i	$0.511565\pi$
$654$	17.0591	0.667064
$655$	23.3816	0.913594
$656$	6.41562	0.250488
$657$	63.0400	2.45942
$658$	6.78064	0.264337
$659$	−16.5440	−0.644463	−0.322232	−	0.946661i	$-0.604433\pi$
$659$	−16.5440	−0.644463	−0.322232	+	0.946661i	$0.604433\pi$
$660$	−47.8082	−1.86093
$661$	5.02937	0.195620	0.0978098	−	0.995205i	$-0.468816\pi$
$661$	5.02937	0.195620	0.0978098	+	0.995205i	$0.468816\pi$
$662$	−24.6369	−0.957539
$663$	2.46178	0.0956076
$664$	13.0750	0.507408
$665$	12.3590	0.479260
$666$	−50.4236	−1.95388
$667$	0	0
$668$	22.5891	0.873998
$669$	77.8112	3.00835
$670$	19.7137	0.761607
$671$	9.19979	0.355154
$672$	3.33557	0.128673
$673$	45.7362	1.76300	0.881500	−	0.472183i	$-0.156534\pi$
$673$	45.7362	1.76300	0.881500	+	0.472183i	$0.156534\pi$
$674$	−16.4216	−0.632536
$675$	−174.492	−6.71620
$676$	−1.57162	−0.0604469
$677$	−47.5042	−1.82573	−0.912867	−	0.408258i	$-0.866136\pi$
$677$	−47.5042	−1.82573	−0.912867	+	0.408258i	$0.866136\pi$
$678$	−26.1612	−1.00472
$679$	−14.3991	−0.552586
$680$	0.851301	0.0326459
$681$	26.1935	1.00374
$682$	−8.57706	−0.328433
$683$	−4.82156	−0.184492	−0.0922460	−	0.995736i	$-0.529405\pi$
$683$	−4.82156	−0.184492	−0.0922460	+	0.995736i	$0.529405\pi$
$684$	−25.7552	−0.984774
$685$	65.2498	2.49307
$686$	−1.00000	−0.0381802
$687$	34.2201	1.30558
$688$	−2.09254	−0.0797775
$689$	19.0982	0.727583
$690$	0	0
$691$	36.4464	1.38648	0.693242	−	0.720704i	$-0.256182\pi$
$691$	36.4464	1.38648	0.693242	+	0.720704i	$0.256182\pi$
$692$	−17.4313	−0.662637
$693$	−29.8686	−1.13461
$694$	−25.3217	−0.961199
$695$	33.6155	1.27511
$696$	−13.8527	−0.525084
$697$	1.40064	0.0530529
$698$	−21.7277	−0.822407
$699$	−35.7201	−1.35106
$700$	10.2052	0.385721
$701$	−3.41423	−0.128954	−0.0644769	−	0.997919i	$-0.520538\pi$
$701$	−3.41423	−0.128954	−0.0644769	+	0.997919i	$0.520538\pi$
$702$	−57.8023	−2.18161
$703$	−19.6671	−0.741758
$704$	−3.67566	−0.138532
$705$	−88.1938	−3.32157
$706$	−23.4405	−0.882194
$707$	11.5621	0.434839
$708$	−0.705843	−0.0265272
$709$	11.9036	0.447050	0.223525	−	0.974698i	$-0.428244\pi$
$709$	11.9036	0.447050	0.223525	+	0.974698i	$0.428244\pi$
$710$	−31.4599	−1.18067
$711$	51.3893	1.92725
$712$	18.6873	0.700336
$713$	0	0
$714$	0.728210	0.0272526
$715$	−48.4534	−1.81206
$716$	−10.3052	−0.385123
$717$	35.6707	1.33215
$718$	29.7516	1.11032
$719$	48.0078	1.79039	0.895195	−	0.445675i	$-0.147036\pi$
$719$	48.0078	1.79039	0.895195	+	0.445675i	$0.147036\pi$
$720$	−31.6866	−1.18089
$721$	−8.11593	−0.302253
$722$	8.95452	0.333253
$723$	4.87000	0.181117
$724$	−21.5191	−0.799751
$725$	−42.3824	−1.57404
$726$	8.37395	0.310786
$727$	−7.62187	−0.282679	−0.141340	−	0.989961i	$-0.545141\pi$
$727$	−7.62187	−0.282679	−0.141340	+	0.989961i	$0.545141\pi$
$728$	3.38059	0.125293
$729$	94.2541	3.49089
$730$	30.2505	1.11962
$731$	−0.456837	−0.0168967
$732$	8.34858	0.308572
$733$	−20.7733	−0.767280	−0.383640	−	0.923483i	$-0.625330\pi$
$733$	−20.7733	−0.767280	−0.383640	+	0.923483i	$0.625330\pi$
$734$	−1.45360	−0.0536533
$735$	13.0067	0.479759
$736$	0	0
$737$	−18.5827	−0.684501
$738$	−52.1336	−1.91907
$739$	34.4768	1.26825	0.634125	−	0.773231i	$-0.281360\pi$
$739$	34.4768	1.26825	0.634125	+	0.773231i	$0.281360\pi$
$740$	−24.1964	−0.889478
$741$	−35.7395	−1.31292
$742$	5.64937	0.207395
$743$	−46.1235	−1.69211	−0.846053	−	0.533099i	$-0.821027\pi$
$743$	−46.1235	−1.69211	−0.846053	+	0.533099i	$0.821027\pi$
$744$	−7.78347	−0.285356
$745$	3.63516	0.133182
$746$	−4.63067	−0.169541
$747$	−106.248	−3.88741
$748$	−0.802458	−0.0293408
$749$	−8.26149	−0.301868
$750$	−67.7028	−2.47216
$751$	5.97831	0.218152	0.109076	−	0.994033i	$-0.465211\pi$
$751$	5.97831	0.218152	0.109076	+	0.994033i	$0.465211\pi$
$752$	−6.78064	−0.247265
$753$	−6.47759	−0.236057
$754$	−14.0396	−0.511292
$755$	−10.2319	−0.372376
$756$	−17.0983	−0.621859
$757$	5.63124	0.204671	0.102335	−	0.994750i	$-0.467369\pi$
$757$	5.63124	0.204671	0.102335	+	0.994750i	$0.467369\pi$
$758$	13.3491	0.484863
$759$	0	0
$760$	−12.3590	−0.448306
$761$	−20.3384	−0.737267	−0.368633	−	0.929575i	$-0.620174\pi$
$761$	−20.3384	−0.737267	−0.368633	+	0.929575i	$0.620174\pi$
$762$	−47.6791	−1.72723
$763$	5.11429	0.185150
$764$	6.68893	0.241997
$765$	−6.91771	−0.250110
$766$	25.3860	0.917232
$767$	−0.715369	−0.0258305
$768$	−3.33557	−0.120362
$769$	−15.0641	−0.543226	−0.271613	−	0.962407i	$-0.587557\pi$
$769$	−15.0641	−0.543226	−0.271613	+	0.962407i	$0.587557\pi$
$770$	−14.3328	−0.516520
$771$	77.0125	2.77354
$772$	−25.1013	−0.903415
$773$	−7.35480	−0.264534	−0.132267	−	0.991214i	$-0.542226\pi$
$773$	−7.35480	−0.264534	−0.132267	+	0.991214i	$0.542226\pi$
$774$	17.0041	0.611200
$775$	−23.8136	−0.855411
$776$	14.3991	0.516897
$777$	−20.6978	−0.742531
$778$	−22.5306	−0.807763
$779$	−20.3341	−0.728543
$780$	−43.9703	−1.57439
$781$	29.6549	1.06114
$782$	0	0
$783$	71.0094	2.53767
$784$	1.00000	0.0357143
$785$	−12.0990	−0.431831
$786$	−20.0008	−0.713406
$787$	−36.1489	−1.28857	−0.644285	−	0.764785i	$-0.722845\pi$
$787$	−36.1489	−1.28857	−0.644285	+	0.764785i	$0.722845\pi$
$788$	−9.42439	−0.335730
$789$	71.9332	2.56089
$790$	24.6598	0.877356
$791$	−7.84309	−0.278868
$792$	29.8686	1.06133
$793$	8.46125	0.300468
$794$	−3.08810	−0.109593
$795$	−73.4796	−2.60605
$796$	−9.97178	−0.353440
$797$	39.6159	1.40327	0.701634	−	0.712538i	$-0.252454\pi$
$797$	39.6159	1.40327	0.701634	+	0.712538i	$0.252454\pi$
$798$	−10.5720	−0.374244
$799$	−1.48033	−0.0523702
$800$	−10.2052	−0.360809
$801$	−151.854	−5.36549
$802$	−5.53491	−0.195445
$803$	−28.5149	−1.00627
$804$	−16.8633	−0.594723
$805$	0	0
$806$	−7.88851	−0.277861
$807$	−106.336	−3.74322
$808$	−11.5621	−0.406754
$809$	0.477260	0.0167796	0.00838979	−	0.999965i	$-0.497329\pi$
$809$	0.477260	0.0167796	0.00838979	+	0.999965i	$0.497329\pi$
$810$	127.333	4.47401
$811$	−51.8843	−1.82190	−0.910952	−	0.412512i	$-0.864652\pi$
$811$	−51.8843	−1.82190	−0.910952	+	0.412512i	$0.864652\pi$
$812$	−4.15301	−0.145742
$813$	−30.4416	−1.06763
$814$	22.8082	0.799426
$815$	46.3985	1.62527
$816$	−0.728210	−0.0254925
$817$	6.63223	0.232032
$818$	−17.8529	−0.624212
$819$	−27.4708	−0.959908
$820$	−25.0170	−0.873631
$821$	−51.2730	−1.78944	−0.894719	−	0.446629i	$-0.852624\pi$
$821$	−51.2730	−1.78944	−0.894719	+	0.446629i	$0.852624\pi$
$822$	−55.8153	−1.94678
$823$	20.2865	0.707141	0.353571	−	0.935408i	$-0.384967\pi$
$823$	20.2865	0.707141	0.353571	+	0.935408i	$0.384967\pi$
$824$	8.11593	0.282732
$825$	125.121	4.35614
$826$	−0.211611	−0.00736288
$827$	−30.8432	−1.07252	−0.536262	−	0.844052i	$-0.680164\pi$
$827$	−30.8432	−1.07252	−0.536262	+	0.844052i	$0.680164\pi$
$828$	0	0
$829$	39.1185	1.35864	0.679322	−	0.733841i	$-0.262274\pi$
$829$	39.1185	1.35864	0.679322	+	0.733841i	$0.262274\pi$
$830$	−50.9845	−1.76970
$831$	5.18214	0.179766
$832$	−3.38059	−0.117201
$833$	0.218316	0.00756422
$834$	−28.7550	−0.995705
$835$	−88.0837	−3.04826
$836$	11.6499	0.402919
$837$	39.8984	1.37909
$838$	−8.02435	−0.277197
$839$	−24.2132	−0.835933	−0.417967	−	0.908462i	$-0.637257\pi$
$839$	−24.2132	−0.835933	−0.417967	+	0.908462i	$0.637257\pi$
$840$	−13.0067	−0.448774
$841$	−11.7525	−0.405260
$842$	−21.2293	−0.731611
$843$	31.7213	1.09254
$844$	11.3123	0.389386
$845$	6.12836	0.210822
$846$	55.0998	1.89437
$847$	2.51050	0.0862617
$848$	−5.64937	−0.194000
$849$	−29.2970	−1.00547
$850$	−2.22797	−0.0764187
$851$	0	0
$852$	26.9111	0.921960
$853$	−28.0854	−0.961626	−0.480813	−	0.876823i	$-0.659658\pi$
$853$	−28.0854	−0.961626	−0.480813	+	0.876823i	$0.659658\pi$
$854$	2.50289	0.0856472
$855$	100.429	3.43461
$856$	8.26149	0.282372
$857$	−0.0164532	−0.000562029 0	−0.000281015	−	1.00000i	$-0.500089\pi$
$857$	−0.0164532	−0.000562029 0	−0.000281015		1.00000i	$0.500089\pi$
$858$	41.4475	1.41499
$859$	35.4013	1.20788	0.603938	−	0.797031i	$-0.293598\pi$
$859$	35.4013	1.20788	0.603938	+	0.797031i	$0.293598\pi$
$860$	8.15964	0.278241
$861$	−21.3998	−0.729302
$862$	30.9834	1.05530
$863$	−32.8115	−1.11692	−0.558458	−	0.829533i	$-0.688607\pi$
$863$	−32.8115	−1.11692	−0.558458	+	0.829533i	$0.688607\pi$
$864$	17.0983	0.581696
$865$	67.9713	2.31109
$866$	−4.82180	−0.163851
$867$	56.5458	1.92039
$868$	−2.33347	−0.0792032
$869$	−23.2450	−0.788531
$870$	54.0169	1.83134
$871$	−17.0909	−0.579102
$872$	−5.11429	−0.173192
$873$	−117.008	−3.96011
$874$	0	0
$875$	−20.2972	−0.686171
$876$	−25.8766	−0.874289
$877$	16.6273	0.561465	0.280732	−	0.959786i	$-0.409423\pi$
$877$	16.6273	0.561465	0.280732	+	0.959786i	$0.409423\pi$
$878$	9.85042	0.332436
$879$	19.0712	0.643255
$880$	14.3328	0.483160
$881$	3.25404	0.109631	0.0548157	−	0.998496i	$-0.482543\pi$
$881$	3.25404	0.109631	0.0548157	+	0.998496i	$0.482543\pi$
$882$	−8.12605	−0.273618
$883$	−8.16544	−0.274789	−0.137394	−	0.990516i	$-0.543873\pi$
$883$	−8.16544	−0.274789	−0.137394	+	0.990516i	$0.543873\pi$
$884$	−0.738038	−0.0248229
$885$	2.75236	0.0925194
$886$	−1.99563	−0.0670445
$887$	14.1844	0.476265	0.238133	−	0.971233i	$-0.423465\pi$
$887$	14.1844	0.476265	0.238133	+	0.971233i	$0.423465\pi$
$888$	20.6978	0.694574
$889$	−14.2941	−0.479410
$890$	−72.8690	−2.44257
$891$	−120.027	−4.02105
$892$	−23.3277	−0.781069
$893$	21.4910	0.719168
$894$	−3.10955	−0.103999
$895$	40.1839	1.34320
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	−16.1935	−0.540384
$899$	9.69093	0.323211
$900$	82.9282	2.76427
$901$	−1.23335	−0.0410888
$902$	23.5817	0.785183
$903$	6.97983	0.232274
$904$	7.84309	0.260857
$905$	83.9113	2.78931
$906$	8.75245	0.290781
$907$	−45.1100	−1.49785	−0.748926	−	0.662653i	$-0.769430\pi$
$907$	−45.1100	−1.49785	−0.748926	+	0.662653i	$0.769430\pi$
$908$	−7.85276	−0.260603
$909$	93.9544	3.11627
$910$	−13.1822	−0.436987
$911$	9.68056	0.320731	0.160366	−	0.987058i	$-0.448733\pi$
$911$	9.68056	0.320731	0.160366	+	0.987058i	$0.448733\pi$
$912$	10.5720	0.350073
$913$	48.0593	1.59053
$914$	17.9750	0.594561
$915$	−32.5544	−1.07621
$916$	−10.2591	−0.338971
$917$	−5.99622	−0.198013
$918$	3.73284	0.123202
$919$	48.4435	1.59800	0.799002	−	0.601329i	$-0.205362\pi$
$919$	48.4435	1.59800	0.799002	+	0.601329i	$0.205362\pi$
$920$	0	0
$921$	67.7600	2.23277
$922$	1.18118	0.0389000
$923$	27.2743	0.897745
$924$	12.2604	0.403339
$925$	63.3253	2.08212
$926$	15.6463	0.514168
$927$	−65.9504	−2.16610
$928$	4.15301	0.136329
$929$	−3.40553	−0.111732	−0.0558659	−	0.998438i	$-0.517792\pi$
$929$	−3.40553	−0.111732	−0.0558659	+	0.998438i	$0.517792\pi$
$930$	30.3508	0.995241
$931$	−3.16946	−0.103875
$932$	10.7088	0.350780
$933$	70.3200	2.30217
$934$	−21.0792	−0.689733
$935$	3.12909	0.102332
$936$	27.4708	0.897912
$937$	35.3141	1.15366	0.576830	−	0.816864i	$-0.304289\pi$
$937$	35.3141	1.15366	0.576830	+	0.816864i	$0.304289\pi$
$938$	−5.05559	−0.165071
$939$	23.1921	0.756846
$940$	26.4404	0.862390
$941$	13.1319	0.428089	0.214044	−	0.976824i	$-0.431336\pi$
$941$	13.1319	0.428089	0.214044	+	0.976824i	$0.431336\pi$
$942$	10.3496	0.337208
$943$	0	0
$944$	0.211611	0.00688734
$945$	66.6729	2.16887
$946$	−7.69148	−0.250072
$947$	−54.0440	−1.75619	−0.878097	−	0.478482i	$-0.841187\pi$
$947$	−54.0440	−1.75619	−0.878097	+	0.478482i	$0.841187\pi$
$948$	−21.0942	−0.685108
$949$	−26.2258	−0.851326
$950$	32.3451	1.04941
$951$	−32.8939	−1.06666
$952$	−0.218316	−0.00707568
$953$	−32.2791	−1.04562	−0.522812	−	0.852448i	$-0.675117\pi$
$953$	−32.2791	−1.04562	−0.522812	+	0.852448i	$0.675117\pi$
$954$	45.9070	1.48629
$955$	−26.0827	−0.844017
$956$	−10.6940	−0.345869
$957$	−50.9177	−1.64594
$958$	−16.1223	−0.520887
$959$	−16.7334	−0.540348
$960$	13.0067	0.419789
$961$	−25.5549	−0.824352
$962$	20.9772	0.676331
$963$	−67.1332	−2.16334
$964$	−1.46002	−0.0470240
$965$	97.8797	3.15086
$966$	0	0
$967$	−38.4000	−1.23486	−0.617431	−	0.786625i	$-0.711827\pi$
$967$	−38.4000	−1.23486	−0.617431	+	0.786625i	$0.711827\pi$
$968$	−2.51050	−0.0806904
$969$	2.30803	0.0741447
$970$	−56.1476	−1.80279
$971$	−29.3166	−0.940813	−0.470407	−	0.882450i	$-0.655893\pi$
$971$	−29.3166	−0.940813	−0.470407	+	0.882450i	$0.655893\pi$
$972$	−57.6266	−1.84837
$973$	−8.62071	−0.276367
$974$	−3.92904	−0.125895
$975$	115.076	3.68539
$976$	−2.50289	−0.0801156
$977$	−5.16712	−0.165311	−0.0826554	−	0.996578i	$-0.526340\pi$
$977$	−5.16712	−0.165311	−0.0826554	+	0.996578i	$0.526340\pi$
$978$	−39.6897	−1.26914
$979$	68.6882	2.19528
$980$	−3.89939	−0.124561
$981$	41.5590	1.32688
$982$	18.7368	0.597916
$983$	48.0763	1.53340	0.766698	−	0.642009i	$-0.221899\pi$
$983$	48.0763	1.53340	0.766698	+	0.642009i	$0.221899\pi$
$984$	21.3998	0.682200
$985$	36.7494	1.17093
$986$	0.906670	0.0288743
$987$	22.6173	0.719918
$988$	10.7146	0.340878
$989$	0	0
$990$	−116.469	−3.70164
$991$	−46.0939	−1.46422	−0.732111	−	0.681186i	$-0.761465\pi$
$991$	−46.0939	−1.46422	−0.732111	+	0.681186i	$0.761465\pi$
$992$	2.33347	0.0740878
$993$	−82.1781	−2.60784
$994$	8.06792	0.255899
$995$	38.8838	1.23270
$996$	43.6126	1.38192
$997$	46.7875	1.48178	0.740888	−	0.671628i	$-0.234405\pi$
$997$	46.7875	1.48178	0.740888	+	0.671628i	$0.234405\pi$
$998$	−18.7492	−0.593495
$999$	−106.098	−3.35680

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7406.2.a.bt.1.1		20
23.2	even	11		322.2.i.e.211.4	yes	40
23.12	even	11		322.2.i.e.29.4	✓	40
23.22	odd	2		7406.2.a.bs.1.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.i.e.29.4	✓	40	23.12	even	11
322.2.i.e.211.4	yes	40	23.2	even	11
7406.2.a.bs.1.1		20	23.22	odd	2
7406.2.a.bt.1.1		20	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:	\( N \)	\(=\)	\( 7406 = 2 \cdot 7 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7406.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.33557 q^{3} +1.00000 q^{4} -3.89939 q^{5} +3.33557 q^{6} +1.00000 q^{7} -1.00000 q^{8} +8.12605 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.33557 q^{3} +1.00000 q^{4} -3.89939 q^{5} +3.33557 q^{6} +1.00000 q^{7} -1.00000 q^{8} +8.12605 q^{9} +3.89939 q^{10} -3.67566 q^{11} -3.33557 q^{12} -3.38059 q^{13} -1.00000 q^{14} +13.0067 q^{15} +1.00000 q^{16} +0.218316 q^{17} -8.12605 q^{18} -3.16946 q^{19} -3.89939 q^{20} -3.33557 q^{21} +3.67566 q^{22} +3.33557 q^{24} +10.2052 q^{25} +3.38059 q^{26} -17.0983 q^{27} +1.00000 q^{28} -4.15301 q^{29} -13.0067 q^{30} -2.33347 q^{31} -1.00000 q^{32} +12.2604 q^{33} -0.218316 q^{34} -3.89939 q^{35} +8.12605 q^{36} +6.20518 q^{37} +3.16946 q^{38} +11.2762 q^{39} +3.89939 q^{40} +6.41562 q^{41} +3.33557 q^{42} -2.09254 q^{43} -3.67566 q^{44} -31.6866 q^{45} -6.78064 q^{47} -3.33557 q^{48} +1.00000 q^{49} -10.2052 q^{50} -0.728210 q^{51} -3.38059 q^{52} -5.64937 q^{53} +17.0983 q^{54} +14.3328 q^{55} -1.00000 q^{56} +10.5720 q^{57} +4.15301 q^{58} +0.211611 q^{59} +13.0067 q^{60} -2.50289 q^{61} +2.33347 q^{62} +8.12605 q^{63} +1.00000 q^{64} +13.1822 q^{65} -12.2604 q^{66} +5.05559 q^{67} +0.218316 q^{68} +3.89939 q^{70} -8.06792 q^{71} -8.12605 q^{72} +7.75777 q^{73} -6.20518 q^{74} -34.0403 q^{75} -3.16946 q^{76} -3.67566 q^{77} -11.2762 q^{78} +6.32402 q^{79} -3.89939 q^{80} +32.6545 q^{81} -6.41562 q^{82} -13.0750 q^{83} -3.33557 q^{84} -0.851301 q^{85} +2.09254 q^{86} +13.8527 q^{87} +3.67566 q^{88} -18.6873 q^{89} +31.6866 q^{90} -3.38059 q^{91} +7.78347 q^{93} +6.78064 q^{94} +12.3590 q^{95} +3.33557 q^{96} -14.3991 q^{97} -1.00000 q^{98} -29.8686 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{2} + q^{3} + 20 q^{4} + q^{5} - q^{6} + 20 q^{7} - 20 q^{8} + 33 q^{9}+O(q^{10}) \) 20 * q - 20 * q^2 + q^3 + 20 * q^4 + q^5 - q^6 + 20 * q^7 - 20 * q^8 + 33 * q^9	\( 20 q - 20 q^{2} + q^{3} + 20 q^{4} + q^{5} - q^{6} + 20 q^{7} - 20 q^{8} + 33 q^{9} - q^{10} + q^{12} + 13 q^{13} - 20 q^{14} + 33 q^{15} + 20 q^{16} - 5 q^{17} - 33 q^{18} - 9 q^{19} + q^{20} + q^{21} - q^{24} + 63 q^{25} - 13 q^{26} - 2 q^{27} + 20 q^{28} + 11 q^{29} - 33 q^{30} + 38 q^{31} - 20 q^{32} - 15 q^{33} + 5 q^{34} + q^{35} + 33 q^{36} + 37 q^{37} + 9 q^{38} + 14 q^{39} - q^{40} + 29 q^{41} - q^{42} + 42 q^{43} - 3 q^{45} - 30 q^{47} + q^{48} + 20 q^{49} - 63 q^{50} - 16 q^{51} + 13 q^{52} - 15 q^{53} + 2 q^{54} + 29 q^{55} - 20 q^{56} + 21 q^{57} - 11 q^{58} - 4 q^{59} + 33 q^{60} - 2 q^{61} - 38 q^{62} + 33 q^{63} + 20 q^{64} - 29 q^{65} + 15 q^{66} + 33 q^{67} - 5 q^{68} - q^{70} - 12 q^{71} - 33 q^{72} + 53 q^{73} - 37 q^{74} + 6 q^{75} - 9 q^{76} - 14 q^{78} + 7 q^{79} + q^{80} + 100 q^{81} - 29 q^{82} + 45 q^{83} + q^{84} + 58 q^{85} - 42 q^{86} - 11 q^{87} + 29 q^{89} + 3 q^{90} + 13 q^{91} + 10 q^{93} + 30 q^{94} - 2 q^{95} - q^{96} - 6 q^{97} - 20 q^{98} + 3 q^{99}+O(q^{100}) \) 20 * q - 20 * q^2 + q^3 + 20 * q^4 + q^5 - q^6 + 20 * q^7 - 20 * q^8 + 33 * q^9 - q^10 + q^12 + 13 * q^13 - 20 * q^14 + 33 * q^15 + 20 * q^16 - 5 * q^17 - 33 * q^18 - 9 * q^19 + q^20 + q^21 - q^24 + 63 * q^25 - 13 * q^26 - 2 * q^27 + 20 * q^28 + 11 * q^29 - 33 * q^30 + 38 * q^31 - 20 * q^32 - 15 * q^33 + 5 * q^34 + q^35 + 33 * q^36 + 37 * q^37 + 9 * q^38 + 14 * q^39 - q^40 + 29 * q^41 - q^42 + 42 * q^43 - 3 * q^45 - 30 * q^47 + q^48 + 20 * q^49 - 63 * q^50 - 16 * q^51 + 13 * q^52 - 15 * q^53 + 2 * q^54 + 29 * q^55 - 20 * q^56 + 21 * q^57 - 11 * q^58 - 4 * q^59 + 33 * q^60 - 2 * q^61 - 38 * q^62 + 33 * q^63 + 20 * q^64 - 29 * q^65 + 15 * q^66 + 33 * q^67 - 5 * q^68 - q^70 - 12 * q^71 - 33 * q^72 + 53 * q^73 - 37 * q^74 + 6 * q^75 - 9 * q^76 - 14 * q^78 + 7 * q^79 + q^80 + 100 * q^81 - 29 * q^82 + 45 * q^83 + q^84 + 58 * q^85 - 42 * q^86 - 11 * q^87 + 29 * q^89 + 3 * q^90 + 13 * q^91 + 10 * q^93 + 30 * q^94 - 2 * q^95 - q^96 - 6 * q^97 - 20 * q^98 + 3 * q^99

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