LMFDB - Embedded newform 4074.2.a.bf.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4074,2,Mod(1,4074)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4074, 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("4074.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4074 = 2 \cdot 3 \cdot 7 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4074.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:	$32.5310537835$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 3x^{9} - 33x^{8} + 92x^{7} + 330x^{6} - 828x^{5} - 972x^{4} + 2176x^{3} + 152x^{2} - 864x + 32 $ x^10 - 3x^9 - 33x^8 + 92x^7 + 330x^6 - 828x^5 - 972x^4 + 2176x^3 + 152x^2 - 864*x + 32
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$4.16447$ of defining polynomial
Character	$\chi$	$=$	4074.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.16447 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.16447 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +4.16447 q^{10} +5.46637 q^{11} -1.00000 q^{12} -0.925830 q^{13} +1.00000 q^{14} -4.16447 q^{15} +1.00000 q^{16} -6.82330 q^{17} +1.00000 q^{18} -1.06638 q^{19} +4.16447 q^{20} -1.00000 q^{21} +5.46637 q^{22} -3.76064 q^{23} -1.00000 q^{24} +12.3428 q^{25} -0.925830 q^{26} -1.00000 q^{27} +1.00000 q^{28} +7.57431 q^{29} -4.16447 q^{30} +2.98464 q^{31} +1.00000 q^{32} -5.46637 q^{33} -6.82330 q^{34} +4.16447 q^{35} +1.00000 q^{36} -2.14352 q^{37} -1.06638 q^{38} +0.925830 q^{39} +4.16447 q^{40} +3.68047 q^{41} -1.00000 q^{42} +3.82348 q^{43} +5.46637 q^{44} +4.16447 q^{45} -3.76064 q^{46} +7.42662 q^{47} -1.00000 q^{48} +1.00000 q^{49} +12.3428 q^{50} +6.82330 q^{51} -0.925830 q^{52} +13.2402 q^{53} -1.00000 q^{54} +22.7645 q^{55} +1.00000 q^{56} +1.06638 q^{57} +7.57431 q^{58} -10.8798 q^{59} -4.16447 q^{60} -14.0843 q^{61} +2.98464 q^{62} +1.00000 q^{63} +1.00000 q^{64} -3.85559 q^{65} -5.46637 q^{66} +3.24899 q^{67} -6.82330 q^{68} +3.76064 q^{69} +4.16447 q^{70} -15.2324 q^{71} +1.00000 q^{72} -5.84500 q^{73} -2.14352 q^{74} -12.3428 q^{75} -1.06638 q^{76} +5.46637 q^{77} +0.925830 q^{78} -5.65968 q^{79} +4.16447 q^{80} +1.00000 q^{81} +3.68047 q^{82} -6.40160 q^{83} -1.00000 q^{84} -28.4154 q^{85} +3.82348 q^{86} -7.57431 q^{87} +5.46637 q^{88} -0.895375 q^{89} +4.16447 q^{90} -0.925830 q^{91} -3.76064 q^{92} -2.98464 q^{93} +7.42662 q^{94} -4.44091 q^{95} -1.00000 q^{96} +1.00000 q^{97} +1.00000 q^{98} +5.46637 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} - 10 q^{3} + 10 q^{4} + 3 q^{5} - 10 q^{6} + 10 q^{7} + 10 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 10 * q^2 - 10 * q^3 + 10 * q^4 + 3 * q^5 - 10 * q^6 + 10 * q^7 + 10 * q^8 + 10 * q^9	\( 10 q + 10 q^{2} - 10 q^{3} + 10 q^{4} + 3 q^{5} - 10 q^{6} + 10 q^{7} + 10 q^{8} + 10 q^{9} + 3 q^{10} + 12 q^{11} - 10 q^{12} + 6 q^{13} + 10 q^{14} - 3 q^{15} + 10 q^{16} + 4 q^{17} + 10 q^{18} + q^{19} + 3 q^{20} - 10 q^{21} + 12 q^{22} + 10 q^{23} - 10 q^{24} + 25 q^{25} + 6 q^{26} - 10 q^{27} + 10 q^{28} + 10 q^{29} - 3 q^{30} + 3 q^{31} + 10 q^{32} - 12 q^{33} + 4 q^{34} + 3 q^{35} + 10 q^{36} + 15 q^{37} + q^{38} - 6 q^{39} + 3 q^{40} + 10 q^{41} - 10 q^{42} + 17 q^{43} + 12 q^{44} + 3 q^{45} + 10 q^{46} - 10 q^{48} + 10 q^{49} + 25 q^{50} - 4 q^{51} + 6 q^{52} + 13 q^{53} - 10 q^{54} + 10 q^{56} - q^{57} + 10 q^{58} - 20 q^{59} - 3 q^{60} + 9 q^{61} + 3 q^{62} + 10 q^{63} + 10 q^{64} + 22 q^{65} - 12 q^{66} + 26 q^{67} + 4 q^{68} - 10 q^{69} + 3 q^{70} + 18 q^{71} + 10 q^{72} + 6 q^{73} + 15 q^{74} - 25 q^{75} + q^{76} + 12 q^{77} - 6 q^{78} + 12 q^{79} + 3 q^{80} + 10 q^{81} + 10 q^{82} - 10 q^{83} - 10 q^{84} + 16 q^{85} + 17 q^{86} - 10 q^{87} + 12 q^{88} + q^{89} + 3 q^{90} + 6 q^{91} + 10 q^{92} - 3 q^{93} + 18 q^{95} - 10 q^{96} + 10 q^{97} + 10 q^{98} + 12 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 - 10 * q^3 + 10 * q^4 + 3 * q^5 - 10 * q^6 + 10 * q^7 + 10 * q^8 + 10 * q^9 + 3 * q^10 + 12 * q^11 - 10 * q^12 + 6 * q^13 + 10 * q^14 - 3 * q^15 + 10 * q^16 + 4 * q^17 + 10 * q^18 + q^19 + 3 * q^20 - 10 * q^21 + 12 * q^22 + 10 * q^23 - 10 * q^24 + 25 * q^25 + 6 * q^26 - 10 * q^27 + 10 * q^28 + 10 * q^29 - 3 * q^30 + 3 * q^31 + 10 * q^32 - 12 * q^33 + 4 * q^34 + 3 * q^35 + 10 * q^36 + 15 * q^37 + q^38 - 6 * q^39 + 3 * q^40 + 10 * q^41 - 10 * q^42 + 17 * q^43 + 12 * q^44 + 3 * q^45 + 10 * q^46 - 10 * q^48 + 10 * q^49 + 25 * q^50 - 4 * q^51 + 6 * q^52 + 13 * q^53 - 10 * q^54 + 10 * q^56 - q^57 + 10 * q^58 - 20 * q^59 - 3 * q^60 + 9 * q^61 + 3 * q^62 + 10 * q^63 + 10 * q^64 + 22 * q^65 - 12 * q^66 + 26 * q^67 + 4 * q^68 - 10 * q^69 + 3 * q^70 + 18 * q^71 + 10 * q^72 + 6 * q^73 + 15 * q^74 - 25 * q^75 + q^76 + 12 * q^77 - 6 * q^78 + 12 * q^79 + 3 * q^80 + 10 * q^81 + 10 * q^82 - 10 * q^83 - 10 * q^84 + 16 * q^85 + 17 * q^86 - 10 * q^87 + 12 * q^88 + q^89 + 3 * q^90 + 6 * q^91 + 10 * q^92 - 3 * q^93 + 18 * q^95 - 10 * q^96 + 10 * q^97 + 10 * q^98 + 12 * 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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	4.16447	1.86241	0.931204	−	0.364497i	$-0.118759\pi$
$5$	4.16447	1.86241	0.931204	+	0.364497i	$0.118759\pi$
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	4.16447	1.31692
$11$	5.46637	1.64817	0.824086	−	0.566465i	$-0.191689\pi$
$11$	5.46637	1.64817	0.824086	+	0.566465i	$0.191689\pi$
$12$	−1.00000	−0.288675
$13$	−0.925830	−0.256779	−0.128389	−	0.991724i	$-0.540981\pi$
$13$	−0.925830	−0.256779	−0.128389	+	0.991724i	$0.540981\pi$
$14$	1.00000	0.267261
$15$	−4.16447	−1.07526
$16$	1.00000	0.250000
$17$	−6.82330	−1.65489	−0.827446	−	0.561545i	$-0.810207\pi$
$17$	−6.82330	−1.65489	−0.827446	+	0.561545i	$0.810207\pi$
$18$	1.00000	0.235702
$19$	−1.06638	−0.244644	−0.122322	−	0.992490i	$-0.539034\pi$
$19$	−1.06638	−0.244644	−0.122322	+	0.992490i	$0.539034\pi$
$20$	4.16447	0.931204
$21$	−1.00000	−0.218218
$22$	5.46637	1.16543
$23$	−3.76064	−0.784148	−0.392074	−	0.919934i	$-0.628242\pi$
$23$	−3.76064	−0.784148	−0.392074	+	0.919934i	$0.628242\pi$
$24$	−1.00000	−0.204124
$25$	12.3428	2.46857
$26$	−0.925830	−0.181570
$27$	−1.00000	−0.192450
$28$	1.00000	0.188982
$29$	7.57431	1.40651	0.703257	−	0.710936i	$-0.251728\pi$
$29$	7.57431	1.40651	0.703257	+	0.710936i	$0.251728\pi$
$30$	−4.16447	−0.760325
$31$	2.98464	0.536057	0.268029	−	0.963411i	$-0.413628\pi$
$31$	2.98464	0.536057	0.268029	+	0.963411i	$0.413628\pi$
$32$	1.00000	0.176777
$33$	−5.46637	−0.951573
$34$	−6.82330	−1.17019
$35$	4.16447	0.703924
$36$	1.00000	0.166667
$37$	−2.14352	−0.352393	−0.176197	−	0.984355i	$-0.556379\pi$
$37$	−2.14352	−0.352393	−0.176197	+	0.984355i	$0.556379\pi$
$38$	−1.06638	−0.172990
$39$	0.925830	0.148251
$40$	4.16447	0.658461
$41$	3.68047	0.574793	0.287396	−	0.957812i	$-0.407210\pi$
$41$	3.68047	0.574793	0.287396	+	0.957812i	$0.407210\pi$
$42$	−1.00000	−0.154303
$43$	3.82348	0.583075	0.291538	−	0.956559i	$-0.405833\pi$
$43$	3.82348	0.583075	0.291538	+	0.956559i	$0.405833\pi$
$44$	5.46637	0.824086
$45$	4.16447	0.620803
$46$	−3.76064	−0.554476
$47$	7.42662	1.08328	0.541642	−	0.840609i	$-0.317803\pi$
$47$	7.42662	1.08328	0.541642	+	0.840609i	$0.317803\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	12.3428	1.74554
$51$	6.82330	0.955453
$52$	−0.925830	−0.128389
$53$	13.2402	1.81868	0.909338	−	0.416057i	$-0.136588\pi$
$53$	13.2402	1.81868	0.909338	+	0.416057i	$0.136588\pi$
$54$	−1.00000	−0.136083
$55$	22.7645	3.06957
$56$	1.00000	0.133631
$57$	1.06638	0.141246
$58$	7.57431	0.994555
$59$	−10.8798	−1.41643	−0.708213	−	0.705999i	$-0.750498\pi$
$59$	−10.8798	−1.41643	−0.708213	+	0.705999i	$0.750498\pi$
$60$	−4.16447	−0.537631
$61$	−14.0843	−1.80330	−0.901652	−	0.432462i	$-0.857645\pi$
$61$	−14.0843	−1.80330	−0.901652	+	0.432462i	$0.857645\pi$
$62$	2.98464	0.379050
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	−3.85559	−0.478227
$66$	−5.46637	−0.672863
$67$	3.24899	0.396928	0.198464	−	0.980108i	$-0.436405\pi$
$67$	3.24899	0.396928	0.198464	+	0.980108i	$0.436405\pi$
$68$	−6.82330	−0.827446
$69$	3.76064	0.452728
$70$	4.16447	0.497750
$71$	−15.2324	−1.80775	−0.903877	−	0.427791i	$-0.859292\pi$
$71$	−15.2324	−1.80775	−0.903877	+	0.427791i	$0.859292\pi$
$72$	1.00000	0.117851
$73$	−5.84500	−0.684105	−0.342053	−	0.939681i	$-0.611122\pi$
$73$	−5.84500	−0.684105	−0.342053	+	0.939681i	$0.611122\pi$
$74$	−2.14352	−0.249180
$75$	−12.3428	−1.42523
$76$	−1.06638	−0.122322
$77$	5.46637	0.622951
$78$	0.925830	0.104830
$79$	−5.65968	−0.636763	−0.318382	−	0.947963i	$-0.603139\pi$
$79$	−5.65968	−0.636763	−0.318382	+	0.947963i	$0.603139\pi$
$80$	4.16447	0.465602
$81$	1.00000	0.111111
$82$	3.68047	0.406440
$83$	−6.40160	−0.702667	−0.351334	−	0.936250i	$-0.614272\pi$
$83$	−6.40160	−0.702667	−0.351334	+	0.936250i	$0.614272\pi$
$84$	−1.00000	−0.109109
$85$	−28.4154	−3.08209
$86$	3.82348	0.412297
$87$	−7.57431	−0.812051
$88$	5.46637	0.582717
$89$	−0.895375	−0.0949096	−0.0474548	−	0.998873i	$-0.515111\pi$
$89$	−0.895375	−0.0949096	−0.0474548	+	0.998873i	$0.515111\pi$
$90$	4.16447	0.438974
$91$	−0.925830	−0.0970533
$92$	−3.76064	−0.392074
$93$	−2.98464	−0.309493
$94$	7.42662	0.765998
$95$	−4.44091	−0.455628
$96$	−1.00000	−0.102062
$97$	1.00000	0.101535
$97$	1.00000	0.101535
$98$	1.00000	0.101015
$99$	5.46637	0.549391
$100$	12.3428	1.23428
$101$	7.11333	0.707803	0.353901	−	0.935283i	$-0.384855\pi$
$101$	7.11333	0.707803	0.353901	+	0.935283i	$0.384855\pi$
$102$	6.82330	0.675607
$103$	−7.73878	−0.762525	−0.381262	−	0.924467i	$-0.624511\pi$
$103$	−7.73878	−0.762525	−0.381262	+	0.924467i	$0.624511\pi$
$104$	−0.925830	−0.0907851
$105$	−4.16447	−0.406411
$106$	13.2402	1.28600
$107$	3.99663	0.386369	0.193185	−	0.981162i	$-0.438118\pi$
$107$	3.99663	0.386369	0.193185	+	0.981162i	$0.438118\pi$
$108$	−1.00000	−0.0962250
$109$	1.01769	0.0974771	0.0487385	−	0.998812i	$-0.484480\pi$
$109$	1.01769	0.0974771	0.0487385	+	0.998812i	$0.484480\pi$
$110$	22.7645	2.17051
$111$	2.14352	0.203454
$112$	1.00000	0.0944911
$113$	9.00521	0.847139	0.423569	−	0.905864i	$-0.360777\pi$
$113$	9.00521	0.847139	0.423569	+	0.905864i	$0.360777\pi$
$114$	1.06638	0.0998757
$115$	−15.6611	−1.46040
$116$	7.57431	0.703257
$117$	−0.925830	−0.0855930
$118$	−10.8798	−1.00156
$119$	−6.82330	−0.625491
$120$	−4.16447	−0.380163
$121$	18.8812	1.71647
$122$	−14.0843	−1.27513
$123$	−3.68047	−0.331857
$124$	2.98464	0.268029
$125$	30.5790	2.73507
$126$	1.00000	0.0890871
$127$	−13.1936	−1.17074	−0.585371	−	0.810765i	$-0.699051\pi$
$127$	−13.1936	−1.17074	−0.585371	+	0.810765i	$0.699051\pi$
$128$	1.00000	0.0883883
$129$	−3.82348	−0.336639
$130$	−3.85559	−0.338158
$131$	17.7220	1.54838	0.774190	−	0.632953i	$-0.218157\pi$
$131$	17.7220	1.54838	0.774190	+	0.632953i	$0.218157\pi$
$132$	−5.46637	−0.475786
$133$	−1.06638	−0.0924669
$134$	3.24899	0.280670
$135$	−4.16447	−0.358421
$136$	−6.82330	−0.585093
$137$	−17.8070	−1.52135	−0.760677	−	0.649130i	$-0.775133\pi$
$137$	−17.8070	−1.52135	−0.760677	+	0.649130i	$0.775133\pi$
$138$	3.76064	0.320127
$139$	−1.89031	−0.160334	−0.0801670	−	0.996781i	$-0.525545\pi$
$139$	−1.89031	−0.160334	−0.0801670	+	0.996781i	$0.525545\pi$
$140$	4.16447	0.351962
$141$	−7.42662	−0.625434
$142$	−15.2324	−1.27828
$143$	−5.06093	−0.423216
$144$	1.00000	0.0833333
$145$	31.5430	2.61950
$146$	−5.84500	−0.483735
$147$	−1.00000	−0.0824786
$148$	−2.14352	−0.176197
$149$	5.88937	0.482476	0.241238	−	0.970466i	$-0.422447\pi$
$149$	5.88937	0.482476	0.241238	+	0.970466i	$0.422447\pi$
$150$	−12.3428	−1.00779
$151$	−11.7556	−0.956655	−0.478327	−	0.878182i	$-0.658757\pi$
$151$	−11.7556	−0.956655	−0.478327	+	0.878182i	$0.658757\pi$
$152$	−1.06638	−0.0864949
$153$	−6.82330	−0.551631
$154$	5.46637	0.440493
$155$	12.4295	0.998358
$156$	0.925830	0.0741257
$157$	−1.58600	−0.126577	−0.0632884	−	0.997995i	$-0.520159\pi$
$157$	−1.58600	−0.126577	−0.0632884	+	0.997995i	$0.520159\pi$
$158$	−5.65968	−0.450260
$159$	−13.2402	−1.05001
$160$	4.16447	0.329230
$161$	−3.76064	−0.296380
$162$	1.00000	0.0785674
$163$	−6.40549	−0.501717	−0.250858	−	0.968024i	$-0.580713\pi$
$163$	−6.40549	−0.501717	−0.250858	+	0.968024i	$0.580713\pi$
$164$	3.68047	0.287396
$165$	−22.7645	−1.77222
$166$	−6.40160	−0.496861
$167$	7.97322	0.616986	0.308493	−	0.951227i	$-0.400175\pi$
$167$	7.97322	0.616986	0.308493	+	0.951227i	$0.400175\pi$
$168$	−1.00000	−0.0771517
$169$	−12.1428	−0.934065
$170$	−28.4154	−2.17936
$171$	−1.06638	−0.0815482
$172$	3.82348	0.291538
$173$	18.6351	1.41680	0.708402	−	0.705809i	$-0.249416\pi$
$173$	18.6351	1.41680	0.708402	+	0.705809i	$0.249416\pi$
$174$	−7.57431	−0.574207
$175$	12.3428	0.933031
$176$	5.46637	0.412043
$177$	10.8798	0.817774
$178$	−0.895375	−0.0671112
$179$	−2.95347	−0.220753	−0.110377	−	0.993890i	$-0.535206\pi$
$179$	−2.95347	−0.220753	−0.110377	+	0.993890i	$0.535206\pi$
$180$	4.16447	0.310401
$181$	−7.97594	−0.592847	−0.296424	−	0.955057i	$-0.595794\pi$
$181$	−7.97594	−0.592847	−0.296424	+	0.955057i	$0.595794\pi$
$182$	−0.925830	−0.0686271
$183$	14.0843	1.04114
$184$	−3.76064	−0.277238
$185$	−8.92665	−0.656300
$186$	−2.98464	−0.218845
$187$	−37.2987	−2.72755
$188$	7.42662	0.541642
$189$	−1.00000	−0.0727393
$190$	−4.44091	−0.322178
$191$	8.46556	0.612547	0.306273	−	0.951944i	$-0.400918\pi$
$191$	8.46556	0.612547	0.306273	+	0.951944i	$0.400918\pi$
$192$	−1.00000	−0.0721688
$193$	5.88830	0.423849	0.211925	−	0.977286i	$-0.432027\pi$
$193$	5.88830	0.423849	0.211925	+	0.977286i	$0.432027\pi$
$194$	1.00000	0.0717958
$195$	3.85559	0.276105
$196$	1.00000	0.0714286
$197$	19.7375	1.40624	0.703118	−	0.711073i	$-0.251791\pi$
$197$	19.7375	1.40624	0.703118	+	0.711073i	$0.251791\pi$
$198$	5.46637	0.388478
$199$	2.83236	0.200780	0.100390	−	0.994948i	$-0.467991\pi$
$199$	2.83236	0.200780	0.100390	+	0.994948i	$0.467991\pi$
$200$	12.3428	0.872770
$201$	−3.24899	−0.229166
$202$	7.11333	0.500492
$203$	7.57431	0.531612
$204$	6.82330	0.477726
$205$	15.3272	1.07050
$206$	−7.73878	−0.539186
$207$	−3.76064	−0.261383
$208$	−0.925830	−0.0641947
$209$	−5.82923	−0.403216
$210$	−4.16447	−0.287376
$211$	25.3014	1.74182	0.870911	−	0.491441i	$-0.163530\pi$
$211$	25.3014	1.74182	0.870911	+	0.491441i	$0.163530\pi$
$212$	13.2402	0.909338
$213$	15.2324	1.04371
$214$	3.99663	0.273204
$215$	15.9228	1.08592
$216$	−1.00000	−0.0680414
$217$	2.98464	0.202611
$218$	1.01769	0.0689267
$219$	5.84500	0.394968
$220$	22.7645	1.53479
$221$	6.31721	0.424942
$222$	2.14352	0.143864
$223$	−2.83955	−0.190150	−0.0950751	−	0.995470i	$-0.530309\pi$
$223$	−2.83955	−0.190150	−0.0950751	+	0.995470i	$0.530309\pi$
$224$	1.00000	0.0668153
$225$	12.3428	0.822856
$226$	9.00521	0.599018
$227$	−18.5816	−1.23330	−0.616652	−	0.787236i	$-0.711512\pi$
$227$	−18.5816	−1.23330	−0.616652	+	0.787236i	$0.711512\pi$
$228$	1.06638	0.0706228
$229$	18.3680	1.21379	0.606897	−	0.794780i	$-0.292414\pi$
$229$	18.3680	1.21379	0.606897	+	0.794780i	$0.292414\pi$
$230$	−15.6611	−1.03266
$231$	−5.46637	−0.359661
$232$	7.57431	0.497278
$233$	−20.0844	−1.31577	−0.657885	−	0.753118i	$-0.728549\pi$
$233$	−20.0844	−1.31577	−0.657885	+	0.753118i	$0.728549\pi$
$234$	−0.925830	−0.0605234
$235$	30.9280	2.01752
$236$	−10.8798	−0.708213
$237$	5.65968	0.367636
$238$	−6.82330	−0.442289
$239$	−11.7339	−0.759000	−0.379500	−	0.925192i	$-0.623904\pi$
$239$	−11.7339	−0.759000	−0.379500	+	0.925192i	$0.623904\pi$
$240$	−4.16447	−0.268816
$241$	9.07967	0.584873	0.292437	−	0.956285i	$-0.405534\pi$
$241$	9.07967	0.584873	0.292437	+	0.956285i	$0.405534\pi$
$242$	18.8812	1.21373
$243$	−1.00000	−0.0641500
$244$	−14.0843	−0.901652
$245$	4.16447	0.266058
$246$	−3.68047	−0.234658
$247$	0.987287	0.0628196
$248$	2.98464	0.189525
$249$	6.40160	0.405685
$250$	30.5790	1.93399
$251$	−14.4363	−0.911208	−0.455604	−	0.890182i	$-0.650577\pi$
$251$	−14.4363	−0.911208	−0.455604	+	0.890182i	$0.650577\pi$
$252$	1.00000	0.0629941
$253$	−20.5570	−1.29241
$254$	−13.1936	−0.827840
$255$	28.4154	1.77944
$256$	1.00000	0.0625000
$257$	21.3302	1.33054	0.665269	−	0.746603i	$-0.268317\pi$
$257$	21.3302	1.33054	0.665269	+	0.746603i	$0.268317\pi$
$258$	−3.82348	−0.238040
$259$	−2.14352	−0.133192
$260$	−3.85559	−0.239114
$261$	7.57431	0.468838
$262$	17.7220	1.09487
$263$	−12.1853	−0.751378	−0.375689	−	0.926746i	$-0.622594\pi$
$263$	−12.1853	−0.751378	−0.375689	+	0.926746i	$0.622594\pi$
$264$	−5.46637	−0.336432
$265$	55.1383	3.38712
$266$	−1.06638	−0.0653840
$267$	0.895375	0.0547961
$268$	3.24899	0.198464
$269$	−4.04491	−0.246623	−0.123311	−	0.992368i	$-0.539351\pi$
$269$	−4.04491	−0.246623	−0.123311	+	0.992368i	$0.539351\pi$
$270$	−4.16447	−0.253442
$271$	17.2548	1.04815	0.524077	−	0.851671i	$-0.324410\pi$
$271$	17.2548	1.04815	0.524077	+	0.851671i	$0.324410\pi$
$272$	−6.82330	−0.413723
$273$	0.925830	0.0560338
$274$	−17.8070	−1.07576
$275$	67.4705	4.06862
$276$	3.76064	0.226364
$277$	−5.64409	−0.339120	−0.169560	−	0.985520i	$-0.554235\pi$
$277$	−5.64409	−0.339120	−0.169560	+	0.985520i	$0.554235\pi$
$278$	−1.89031	−0.113373
$279$	2.98464	0.178686
$280$	4.16447	0.248875
$281$	−13.8012	−0.823312	−0.411656	−	0.911339i	$-0.635049\pi$
$281$	−13.8012	−0.823312	−0.411656	+	0.911339i	$0.635049\pi$
$282$	−7.42662	−0.442249
$283$	1.41062	0.0838528	0.0419264	−	0.999121i	$-0.486651\pi$
$283$	1.41062	0.0838528	0.0419264	+	0.999121i	$0.486651\pi$
$284$	−15.2324	−0.903877
$285$	4.44091	0.263057
$286$	−5.06093	−0.299259
$287$	3.68047	0.217251
$288$	1.00000	0.0589256
$289$	29.5574	1.73867
$290$	31.5430	1.85227
$291$	−1.00000	−0.0586210
$292$	−5.84500	−0.342053
$293$	−29.7181	−1.73615	−0.868074	−	0.496436i	$-0.834642\pi$
$293$	−29.7181	−1.73615	−0.868074	+	0.496436i	$0.834642\pi$
$294$	−1.00000	−0.0583212
$295$	−45.3085	−2.63797
$296$	−2.14352	−0.124590
$297$	−5.46637	−0.317191
$298$	5.88937	0.341162
$299$	3.48171	0.201353
$300$	−12.3428	−0.712614
$301$	3.82348	0.220382
$302$	−11.7556	−0.676457
$303$	−7.11333	−0.408650
$304$	−1.06638	−0.0611611
$305$	−58.6535	−3.35849
$306$	−6.82330	−0.390062
$307$	−2.65247	−0.151384	−0.0756922	−	0.997131i	$-0.524117\pi$
$307$	−2.65247	−0.151384	−0.0756922	+	0.997131i	$0.524117\pi$
$308$	5.46637	0.311475
$309$	7.73878	0.440244
$310$	12.4295	0.705946
$311$	−24.3770	−1.38229	−0.691145	−	0.722716i	$-0.742893\pi$
$311$	−24.3770	−1.38229	−0.691145	+	0.722716i	$0.742893\pi$
$312$	0.925830	0.0524148
$313$	−8.44233	−0.477189	−0.238594	−	0.971119i	$-0.576687\pi$
$313$	−8.44233	−0.477189	−0.238594	+	0.971119i	$0.576687\pi$
$314$	−1.58600	−0.0895033
$315$	4.16447	0.234641
$316$	−5.65968	−0.318382
$317$	−23.6335	−1.32739	−0.663694	−	0.748005i	$-0.731012\pi$
$317$	−23.6335	−1.32739	−0.663694	+	0.748005i	$0.731012\pi$
$318$	−13.2402	−0.742472
$319$	41.4039	2.31818
$320$	4.16447	0.232801
$321$	−3.99663	−0.223070
$322$	−3.76064	−0.209572
$323$	7.27623	0.404860
$324$	1.00000	0.0555556
$325$	−11.4274	−0.633876
$326$	−6.40549	−0.354767
$327$	−1.01769	−0.0562784
$328$	3.68047	0.203220
$329$	7.42662	0.409443
$330$	−22.7645	−1.25315
$331$	4.78591	0.263057	0.131529	−	0.991312i	$-0.458011\pi$
$331$	4.78591	0.263057	0.131529	+	0.991312i	$0.458011\pi$
$332$	−6.40160	−0.351334
$333$	−2.14352	−0.117464
$334$	7.97322	0.436275
$335$	13.5303	0.739241
$336$	−1.00000	−0.0545545
$337$	−12.2153	−0.665410	−0.332705	−	0.943031i	$-0.607961\pi$
$337$	−12.2153	−0.665410	−0.332705	+	0.943031i	$0.607961\pi$
$338$	−12.1428	−0.660483
$339$	−9.00521	−0.489096
$340$	−28.4154	−1.54104
$341$	16.3151	0.883515
$342$	−1.06638	−0.0576633
$343$	1.00000	0.0539949
$344$	3.82348	0.206148
$345$	15.6611	0.843164
$346$	18.6351	1.00183
$347$	14.5862	0.783028	0.391514	−	0.920172i	$-0.371952\pi$
$347$	14.5862	0.783028	0.391514	+	0.920172i	$0.371952\pi$
$348$	−7.57431	−0.406025
$349$	12.3207	0.659513	0.329756	−	0.944066i	$-0.393033\pi$
$349$	12.3207	0.659513	0.329756	+	0.944066i	$0.393033\pi$
$350$	12.3428	0.659752
$351$	0.925830	0.0494171
$352$	5.46637	0.291358
$353$	−14.9785	−0.797226	−0.398613	−	0.917119i	$-0.630508\pi$
$353$	−14.9785	−0.797226	−0.398613	+	0.917119i	$0.630508\pi$
$354$	10.8798	0.578254
$355$	−63.4350	−3.36678
$356$	−0.895375	−0.0474548
$357$	6.82330	0.361127
$358$	−2.95347	−0.156096
$359$	13.5404	0.714633	0.357317	−	0.933983i	$-0.383692\pi$
$359$	13.5404	0.714633	0.357317	+	0.933983i	$0.383692\pi$
$360$	4.16447	0.219487
$361$	−17.8628	−0.940149
$362$	−7.97594	−0.419206
$363$	−18.8812	−0.991005
$364$	−0.925830	−0.0485267
$365$	−24.3413	−1.27408
$366$	14.0843	0.736196
$367$	−27.7680	−1.44948	−0.724738	−	0.689025i	$-0.758039\pi$
$367$	−27.7680	−1.44948	−0.724738	+	0.689025i	$0.758039\pi$
$368$	−3.76064	−0.196037
$369$	3.68047	0.191598
$370$	−8.92665	−0.464075
$371$	13.2402	0.687395
$372$	−2.98464	−0.154746
$373$	14.9963	0.776479	0.388240	−	0.921558i	$-0.373083\pi$
$373$	14.9963	0.776479	0.388240	+	0.921558i	$0.373083\pi$
$374$	−37.2987	−1.92867
$375$	−30.5790	−1.57909
$376$	7.42662	0.382999
$377$	−7.01252	−0.361163
$378$	−1.00000	−0.0514344
$379$	−19.5673	−1.00510	−0.502552	−	0.864547i	$-0.667605\pi$
$379$	−19.5673	−1.00510	−0.502552	+	0.864547i	$0.667605\pi$
$380$	−4.44091	−0.227814
$381$	13.1936	0.675929
$382$	8.46556	0.433136
$383$	−28.1757	−1.43971	−0.719856	−	0.694123i	$-0.755792\pi$
$383$	−28.1757	−1.43971	−0.719856	+	0.694123i	$0.755792\pi$
$384$	−1.00000	−0.0510310
$385$	22.7645	1.16019
$386$	5.88830	0.299707
$387$	3.82348	0.194358
$388$	1.00000	0.0507673
$389$	33.4611	1.69654	0.848271	−	0.529562i	$-0.177644\pi$
$389$	33.4611	1.69654	0.848271	+	0.529562i	$0.177644\pi$
$390$	3.85559	0.195236
$391$	25.6600	1.29768
$392$	1.00000	0.0505076
$393$	−17.7220	−0.893958
$394$	19.7375	0.994359
$395$	−23.5696	−1.18591
$396$	5.46637	0.274695
$397$	24.6375	1.23652	0.618261	−	0.785973i	$-0.287837\pi$
$397$	24.6375	1.23652	0.618261	+	0.785973i	$0.287837\pi$
$398$	2.83236	0.141973
$399$	1.06638	0.0533858
$400$	12.3428	0.617142
$401$	19.5828	0.977919	0.488959	−	0.872307i	$-0.337377\pi$
$401$	19.5828	0.977919	0.488959	+	0.872307i	$0.337377\pi$
$402$	−3.24899	−0.162045
$403$	−2.76327	−0.137648
$404$	7.11333	0.353901
$405$	4.16447	0.206934
$406$	7.57431	0.375906
$407$	−11.7173	−0.580805
$408$	6.82330	0.337804
$409$	30.4675	1.50652	0.753260	−	0.657723i	$-0.228480\pi$
$409$	30.4675	1.50652	0.753260	+	0.657723i	$0.228480\pi$
$410$	15.3272	0.756957
$411$	17.8070	0.878355
$412$	−7.73878	−0.381262
$413$	−10.8798	−0.535359
$414$	−3.76064	−0.184825
$415$	−26.6593	−1.30865
$416$	−0.925830	−0.0453925
$417$	1.89031	0.0925688
$418$	−5.82923	−0.285117
$419$	−6.37460	−0.311420	−0.155710	−	0.987803i	$-0.549766\pi$
$419$	−6.37460	−0.311420	−0.155710	+	0.987803i	$0.549766\pi$
$420$	−4.16447	−0.203205
$421$	17.1636	0.836500	0.418250	−	0.908332i	$-0.362644\pi$
$421$	17.1636	0.836500	0.418250	+	0.908332i	$0.362644\pi$
$422$	25.3014	1.23165
$423$	7.42662	0.361095
$424$	13.2402	0.642999
$425$	−84.2188	−4.08521
$426$	15.2324	0.738013
$427$	−14.0843	−0.681585
$428$	3.99663	0.193185
$429$	5.06093	0.244344
$430$	15.9228	0.767865
$431$	−1.83380	−0.0883309	−0.0441654	−	0.999024i	$-0.514063\pi$
$431$	−1.83380	−0.0883309	−0.0441654	+	0.999024i	$0.514063\pi$
$432$	−1.00000	−0.0481125
$433$	−32.7356	−1.57317	−0.786586	−	0.617481i	$-0.788153\pi$
$433$	−32.7356	−1.57317	−0.786586	+	0.617481i	$0.788153\pi$
$434$	2.98464	0.143267
$435$	−31.5430	−1.51237
$436$	1.01769	0.0487385
$437$	4.01027	0.191837
$438$	5.84500	0.279285
$439$	−36.2804	−1.73157	−0.865784	−	0.500418i	$-0.833180\pi$
$439$	−36.2804	−1.73157	−0.865784	+	0.500418i	$0.833180\pi$
$440$	22.7645	1.08526
$441$	1.00000	0.0476190
$442$	6.31721	0.300479
$443$	13.3497	0.634266	0.317133	−	0.948381i	$-0.397280\pi$
$443$	13.3497	0.634266	0.317133	+	0.948381i	$0.397280\pi$
$444$	2.14352	0.101727
$445$	−3.72877	−0.176760
$446$	−2.83955	−0.134456
$447$	−5.88937	−0.278558
$448$	1.00000	0.0472456
$449$	20.3178	0.958855	0.479428	−	0.877581i	$-0.340844\pi$
$449$	20.3178	0.958855	0.479428	+	0.877581i	$0.340844\pi$
$450$	12.3428	0.581847
$451$	20.1188	0.947357
$452$	9.00521	0.423569
$453$	11.7556	0.552325
$454$	−18.5816	−0.872078
$455$	−3.85559	−0.180753
$456$	1.06638	0.0499378
$457$	−9.72666	−0.454994	−0.227497	−	0.973779i	$-0.573054\pi$
$457$	−9.72666	−0.454994	−0.227497	+	0.973779i	$0.573054\pi$
$458$	18.3680	0.858282
$459$	6.82330	0.318484
$460$	−15.6611	−0.730202
$461$	20.8266	0.969993	0.484996	−	0.874516i	$-0.338821\pi$
$461$	20.8266	0.969993	0.484996	+	0.874516i	$0.338821\pi$
$462$	−5.46637	−0.254318
$463$	−34.8946	−1.62169	−0.810845	−	0.585261i	$-0.800992\pi$
$463$	−34.8946	−1.62169	−0.810845	+	0.585261i	$0.800992\pi$
$464$	7.57431	0.351628
$465$	−12.4295	−0.576402
$466$	−20.0844	−0.930390
$467$	−23.7496	−1.09900	−0.549501	−	0.835493i	$-0.685182\pi$
$467$	−23.7496	−1.09900	−0.549501	+	0.835493i	$0.685182\pi$
$468$	−0.925830	−0.0427965
$469$	3.24899	0.150025
$470$	30.9280	1.42660
$471$	1.58600	0.0730792
$472$	−10.8798	−0.500782
$473$	20.9006	0.961009
$474$	5.65968	0.259958
$475$	−13.1622	−0.603921
$476$	−6.82330	−0.312745
$477$	13.2402	0.606226
$478$	−11.7339	−0.536694
$479$	−3.30860	−0.151174	−0.0755869	−	0.997139i	$-0.524083\pi$
$479$	−3.30860	−0.151174	−0.0755869	+	0.997139i	$0.524083\pi$
$480$	−4.16447	−0.190081
$481$	1.98454	0.0904872
$482$	9.07967	0.413568
$483$	3.76064	0.171115
$484$	18.8812	0.858236
$485$	4.16447	0.189099
$486$	−1.00000	−0.0453609
$487$	−36.8004	−1.66759	−0.833793	−	0.552077i	$-0.813836\pi$
$487$	−36.8004	−1.66759	−0.833793	+	0.552077i	$0.813836\pi$
$488$	−14.0843	−0.637564
$489$	6.40549	0.289666
$490$	4.16447	0.188132
$491$	4.75066	0.214394	0.107197	−	0.994238i	$-0.465812\pi$
$491$	4.75066	0.214394	0.107197	+	0.994238i	$0.465812\pi$
$492$	−3.68047	−0.165928
$493$	−51.6817	−2.32763
$494$	0.987287	0.0444201
$495$	22.7645	1.02319
$496$	2.98464	0.134014
$497$	−15.2324	−0.683267
$498$	6.40160	0.286863
$499$	33.4986	1.49960	0.749802	−	0.661663i	$-0.230149\pi$
$499$	33.4986	1.49960	0.749802	+	0.661663i	$0.230149\pi$
$500$	30.5790	1.36754
$501$	−7.97322	−0.356217
$502$	−14.4363	−0.644322
$503$	−4.59969	−0.205090	−0.102545	−	0.994728i	$-0.532699\pi$
$503$	−4.59969	−0.205090	−0.102545	+	0.994728i	$0.532699\pi$
$504$	1.00000	0.0445435
$505$	29.6233	1.31822
$506$	−20.5570	−0.913872
$507$	12.1428	0.539282
$508$	−13.1936	−0.585371
$509$	−23.6109	−1.04653	−0.523267	−	0.852169i	$-0.675287\pi$
$509$	−23.6109	−1.04653	−0.523267	+	0.852169i	$0.675287\pi$
$510$	28.4154	1.25826
$511$	−5.84500	−0.258567
$512$	1.00000	0.0441942
$513$	1.06638	0.0470819
$514$	21.3302	0.940833
$515$	−32.2279	−1.42013
$516$	−3.82348	−0.168319
$517$	40.5967	1.78544
$518$	−2.14352	−0.0941811
$519$	−18.6351	−0.817992
$520$	−3.85559	−0.169079
$521$	7.02621	0.307824	0.153912	−	0.988085i	$-0.450813\pi$
$521$	7.02621	0.307824	0.153912	+	0.988085i	$0.450813\pi$
$522$	7.57431	0.331518
$523$	39.9002	1.74472	0.872358	−	0.488868i	$-0.162590\pi$
$523$	39.9002	1.74472	0.872358	+	0.488868i	$0.162590\pi$
$524$	17.7220	0.774190
$525$	−12.3428	−0.538685
$526$	−12.1853	−0.531305
$527$	−20.3651	−0.887118
$528$	−5.46637	−0.237893
$529$	−8.85759	−0.385113
$530$	55.1383	2.39506
$531$	−10.8798	−0.472142
$532$	−1.06638	−0.0462335
$533$	−3.40749	−0.147595
$534$	0.895375	0.0387467
$535$	16.6439	0.719577
$536$	3.24899	0.140335
$537$	2.95347	0.127452
$538$	−4.04491	−0.174389
$539$	5.46637	0.235453
$540$	−4.16447	−0.179210
$541$	22.0768	0.949157	0.474579	−	0.880213i	$-0.342600\pi$
$541$	22.0768	0.949157	0.474579	+	0.880213i	$0.342600\pi$
$542$	17.2548	0.741157
$543$	7.97594	0.342280
$544$	−6.82330	−0.292546
$545$	4.23814	0.181542
$546$	0.925830	0.0396219
$547$	−3.74045	−0.159930	−0.0799650	−	0.996798i	$-0.525481\pi$
$547$	−3.74045	−0.159930	−0.0799650	+	0.996798i	$0.525481\pi$
$548$	−17.8070	−0.760677
$549$	−14.0843	−0.601101
$550$	67.4705	2.87695
$551$	−8.07709	−0.344096
$552$	3.76064	0.160063
$553$	−5.65968	−0.240674
$554$	−5.64409	−0.239794
$555$	8.92665	0.378915
$556$	−1.89031	−0.0801670
$557$	3.09238	0.131028	0.0655142	−	0.997852i	$-0.479131\pi$
$557$	3.09238	0.131028	0.0655142	+	0.997852i	$0.479131\pi$
$558$	2.98464	0.126350
$559$	−3.53989	−0.149722
$560$	4.16447	0.175981
$561$	37.2987	1.57475
$562$	−13.8012	−0.582169
$563$	−29.5232	−1.24426	−0.622128	−	0.782916i	$-0.713732\pi$
$563$	−29.5232	−1.24426	−0.622128	+	0.782916i	$0.713732\pi$
$564$	−7.42662	−0.312717
$565$	37.5019	1.57772
$566$	1.41062	0.0592929
$567$	1.00000	0.0419961
$568$	−15.2324	−0.639138
$569$	−45.8727	−1.92308	−0.961542	−	0.274657i	$-0.911436\pi$
$569$	−45.8727	−1.92308	−0.961542	+	0.274657i	$0.911436\pi$
$570$	4.44091	0.186009
$571$	34.4996	1.44376	0.721881	−	0.692018i	$-0.243278\pi$
$571$	34.4996	1.44376	0.721881	+	0.692018i	$0.243278\pi$
$572$	−5.06093	−0.211608
$573$	−8.46556	−0.353654
$574$	3.68047	0.153620
$575$	−46.4170	−1.93572
$576$	1.00000	0.0416667
$577$	−10.6064	−0.441550	−0.220775	−	0.975325i	$-0.570859\pi$
$577$	−10.6064	−0.441550	−0.220775	+	0.975325i	$0.570859\pi$
$578$	29.5574	1.22943
$579$	−5.88830	−0.244710
$580$	31.5430	1.30975
$581$	−6.40160	−0.265583
$582$	−1.00000	−0.0414513
$583$	72.3756	2.99749
$584$	−5.84500	−0.241868
$585$	−3.85559	−0.159409
$586$	−29.7181	−1.22764
$587$	−13.2422	−0.546565	−0.273282	−	0.961934i	$-0.588109\pi$
$587$	−13.2422	−0.546565	−0.273282	+	0.961934i	$0.588109\pi$
$588$	−1.00000	−0.0412393
$589$	−3.18276	−0.131143
$590$	−45.3085	−1.86532
$591$	−19.7375	−0.811891
$592$	−2.14352	−0.0880983
$593$	25.4181	1.04380	0.521899	−	0.853007i	$-0.325224\pi$
$593$	25.4181	1.04380	0.521899	+	0.853007i	$0.325224\pi$
$594$	−5.46637	−0.224288
$595$	−28.4154	−1.16492
$596$	5.88937	0.241238
$597$	−2.83236	−0.115921
$598$	3.48171	0.142378
$599$	19.8501	0.811052	0.405526	−	0.914083i	$-0.367088\pi$
$599$	19.8501	0.811052	0.405526	+	0.914083i	$0.367088\pi$
$600$	−12.3428	−0.503894
$601$	14.2254	0.580267	0.290134	−	0.956986i	$-0.406300\pi$
$601$	14.2254	0.580267	0.290134	+	0.956986i	$0.406300\pi$
$602$	3.82348	0.155833
$603$	3.24899	0.132309
$604$	−11.7556	−0.478327
$605$	78.6302	3.19677
$606$	−7.11333	−0.288959
$607$	20.2939	0.823703	0.411851	−	0.911251i	$-0.364882\pi$
$607$	20.2939	0.823703	0.411851	+	0.911251i	$0.364882\pi$
$608$	−1.06638	−0.0432474
$609$	−7.57431	−0.306926
$610$	−58.6535	−2.37481
$611$	−6.87579	−0.278165
$612$	−6.82330	−0.275815
$613$	35.8339	1.44732	0.723658	−	0.690158i	$-0.242459\pi$
$613$	35.8339	1.44732	0.723658	+	0.690158i	$0.242459\pi$
$614$	−2.65247	−0.107045
$615$	−15.3272	−0.618053
$616$	5.46637	0.220246
$617$	3.87848	0.156142	0.0780709	−	0.996948i	$-0.475124\pi$
$617$	3.87848	0.156142	0.0780709	+	0.996948i	$0.475124\pi$
$618$	7.73878	0.311299
$619$	−28.4570	−1.14378	−0.571891	−	0.820330i	$-0.693790\pi$
$619$	−28.4570	−1.14378	−0.571891	+	0.820330i	$0.693790\pi$
$620$	12.4295	0.499179
$621$	3.76064	0.150909
$622$	−24.3770	−0.977427
$623$	−0.895375	−0.0358725
$624$	0.925830	0.0370628
$625$	65.6314	2.62525
$626$	−8.44233	−0.337423
$627$	5.82923	0.232797
$628$	−1.58600	−0.0632884
$629$	14.6259	0.583173
$630$	4.16447	0.165917
$631$	11.1714	0.444728	0.222364	−	0.974964i	$-0.428623\pi$
$631$	11.1714	0.444728	0.222364	+	0.974964i	$0.428623\pi$
$632$	−5.65968	−0.225130
$633$	−25.3014	−1.00564
$634$	−23.6335	−0.938604
$635$	−54.9444	−2.18040
$636$	−13.2402	−0.525007
$637$	−0.925830	−0.0366827
$638$	41.4039	1.63920
$639$	−15.2324	−0.602585
$640$	4.16447	0.164615
$641$	12.5880	0.497194	0.248597	−	0.968607i	$-0.420030\pi$
$641$	12.5880	0.497194	0.248597	+	0.968607i	$0.420030\pi$
$642$	−3.99663	−0.157735
$643$	−49.2353	−1.94165	−0.970826	−	0.239785i	$-0.922923\pi$
$643$	−49.2353	−1.94165	−0.970826	+	0.239785i	$0.922923\pi$
$644$	−3.76064	−0.148190
$645$	−15.9228	−0.626959
$646$	7.27623	0.286280
$647$	−41.1690	−1.61852	−0.809260	−	0.587450i	$-0.800132\pi$
$647$	−41.1690	−1.61852	−0.809260	+	0.587450i	$0.800132\pi$
$648$	1.00000	0.0392837
$649$	−59.4729	−2.33451
$650$	−11.4274	−0.448218
$651$	−2.98464	−0.116977
$652$	−6.40549	−0.250858
$653$	−33.0661	−1.29398	−0.646989	−	0.762499i	$-0.723972\pi$
$653$	−33.0661	−1.29398	−0.646989	+	0.762499i	$0.723972\pi$
$654$	−1.01769	−0.0397948
$655$	73.8029	2.88372
$656$	3.68047	0.143698
$657$	−5.84500	−0.228035
$658$	7.42662	0.289520
$659$	−11.5591	−0.450280	−0.225140	−	0.974326i	$-0.572284\pi$
$659$	−11.5591	−0.450280	−0.225140	+	0.974326i	$0.572284\pi$
$660$	−22.7645	−0.886109
$661$	38.1772	1.48492	0.742460	−	0.669890i	$-0.233659\pi$
$661$	38.1772	1.48492	0.742460	+	0.669890i	$0.233659\pi$
$662$	4.78591	0.186010
$663$	−6.31721	−0.245340
$664$	−6.40160	−0.248430
$665$	−4.44091	−0.172211
$666$	−2.14352	−0.0830599
$667$	−28.4842	−1.10291
$668$	7.97322	0.308493
$669$	2.83955	0.109783
$670$	13.5303	0.522723
$671$	−76.9897	−2.97216
$672$	−1.00000	−0.0385758
$673$	13.1734	0.507797	0.253898	−	0.967231i	$-0.418287\pi$
$673$	13.1734	0.507797	0.253898	+	0.967231i	$0.418287\pi$
$674$	−12.2153	−0.470516
$675$	−12.3428	−0.475076
$676$	−12.1428	−0.467032
$677$	36.3715	1.39787	0.698934	−	0.715186i	$-0.253658\pi$
$677$	36.3715	1.39787	0.698934	+	0.715186i	$0.253658\pi$
$678$	−9.00521	−0.345843
$679$	1.00000	0.0383765
$680$	−28.4154	−1.08968
$681$	18.5816	0.712049
$682$	16.3151	0.624739
$683$	0.675240	0.0258374	0.0129187	−	0.999917i	$-0.495888\pi$
$683$	0.675240	0.0258374	0.0129187	+	0.999917i	$0.495888\pi$
$684$	−1.06638	−0.0407741
$685$	−74.1568	−2.83338
$686$	1.00000	0.0381802
$687$	−18.3680	−0.700784
$688$	3.82348	0.145769
$689$	−12.2581	−0.466998
$690$	15.6611	0.596207
$691$	36.4832	1.38788	0.693942	−	0.720031i	$-0.255872\pi$
$691$	36.4832	1.38788	0.693942	+	0.720031i	$0.255872\pi$
$692$	18.6351	0.708402
$693$	5.46637	0.207650
$694$	14.5862	0.553684
$695$	−7.87214	−0.298607
$696$	−7.57431	−0.287103
$697$	−25.1129	−0.951220
$698$	12.3207	0.466346
$699$	20.0844	0.759660
$700$	12.3428	0.466515
$701$	36.0304	1.36085	0.680424	−	0.732818i	$-0.261795\pi$
$701$	36.0304	1.36085	0.680424	+	0.732818i	$0.261795\pi$
$702$	0.925830	0.0349432
$703$	2.28581	0.0862111
$704$	5.46637	0.206022
$705$	−30.9280	−1.16481
$706$	−14.9785	−0.563724
$707$	7.11333	0.267524
$708$	10.8798	0.408887
$709$	−3.45540	−0.129770	−0.0648851	−	0.997893i	$-0.520668\pi$
$709$	−3.45540	−0.129770	−0.0648851	+	0.997893i	$0.520668\pi$
$710$	−63.4350	−2.38067
$711$	−5.65968	−0.212254
$712$	−0.895375	−0.0335556
$713$	−11.2242	−0.420348
$714$	6.82330	0.255356
$715$	−21.0761	−0.788201
$716$	−2.95347	−0.110377
$717$	11.7339	0.438209
$718$	13.5404	0.505322
$719$	−29.7068	−1.10788	−0.553938	−	0.832558i	$-0.686876\pi$
$719$	−29.7068	−1.10788	−0.553938	+	0.832558i	$0.686876\pi$
$720$	4.16447	0.155201
$721$	−7.73878	−0.288207
$722$	−17.8628	−0.664786
$723$	−9.07967	−0.337677
$724$	−7.97594	−0.296424
$725$	93.4884	3.47207
$726$	−18.8812	−0.700746
$727$	−31.5796	−1.17122	−0.585612	−	0.810592i	$-0.699146\pi$
$727$	−31.5796	−1.17122	−0.585612	+	0.810592i	$0.699146\pi$
$728$	−0.925830	−0.0343135
$729$	1.00000	0.0370370
$730$	−24.3413	−0.900913
$731$	−26.0888	−0.964927
$732$	14.0843	0.520569
$733$	19.1850	0.708612	0.354306	−	0.935129i	$-0.384717\pi$
$733$	19.1850	0.708612	0.354306	+	0.935129i	$0.384717\pi$
$734$	−27.7680	−1.02493
$735$	−4.16447	−0.153609
$736$	−3.76064	−0.138619
$737$	17.7602	0.654205
$738$	3.68047	0.135480
$739$	−0.632810	−0.0232783	−0.0116391	−	0.999932i	$-0.503705\pi$
$739$	−0.632810	−0.0232783	−0.0116391	+	0.999932i	$0.503705\pi$
$740$	−8.92665	−0.328150
$741$	−0.987287	−0.0362689
$742$	13.2402	0.486062
$743$	−6.75422	−0.247788	−0.123894	−	0.992295i	$-0.539538\pi$
$743$	−6.75422	−0.247788	−0.123894	+	0.992295i	$0.539538\pi$
$744$	−2.98464	−0.109422
$745$	24.5261	0.898568
$746$	14.9963	0.549054
$747$	−6.40160	−0.234222
$748$	−37.2987	−1.36377
$749$	3.99663	0.146034
$750$	−30.5790	−1.11659
$751$	50.5053	1.84297	0.921483	−	0.388420i	$-0.126979\pi$
$751$	50.5053	1.84297	0.921483	+	0.388420i	$0.126979\pi$
$752$	7.42662	0.270821
$753$	14.4363	0.526086
$754$	−7.01252	−0.255381
$755$	−48.9557	−1.78168
$756$	−1.00000	−0.0363696
$757$	28.3442	1.03019	0.515093	−	0.857134i	$-0.327757\pi$
$757$	28.3442	1.03019	0.515093	+	0.857134i	$0.327757\pi$
$758$	−19.5673	−0.710716
$759$	20.5570	0.746173
$760$	−4.44091	−0.161089
$761$	−19.9148	−0.721910	−0.360955	−	0.932583i	$-0.617549\pi$
$761$	−19.9148	−0.721910	−0.360955	+	0.932583i	$0.617549\pi$
$762$	13.1936	0.477954
$763$	1.01769	0.0368429
$764$	8.46556	0.306273
$765$	−28.4154	−1.02736
$766$	−28.1757	−1.01803
$767$	10.0728	0.363709
$768$	−1.00000	−0.0360844
$769$	−26.0090	−0.937908	−0.468954	−	0.883223i	$-0.655369\pi$
$769$	−26.0090	−0.937908	−0.468954	+	0.883223i	$0.655369\pi$
$770$	22.7645	0.820377
$771$	−21.3302	−0.768187
$772$	5.88830	0.211925
$773$	32.6515	1.17439	0.587196	−	0.809445i	$-0.300232\pi$
$773$	32.6515	1.17439	0.587196	+	0.809445i	$0.300232\pi$
$774$	3.82348	0.137432
$775$	36.8389	1.32329
$776$	1.00000	0.0358979
$777$	2.14352	0.0768985
$778$	33.4611	1.19964
$779$	−3.92478	−0.140620
$780$	3.85559	0.138052
$781$	−83.2660	−2.97949
$782$	25.6600	0.917599
$783$	−7.57431	−0.270684
$784$	1.00000	0.0357143
$785$	−6.60487	−0.235738
$786$	−17.7220	−0.632124
$787$	24.5329	0.874503	0.437251	−	0.899339i	$-0.355952\pi$
$787$	24.5329	0.874503	0.437251	+	0.899339i	$0.355952\pi$
$788$	19.7375	0.703118
$789$	12.1853	0.433809
$790$	−23.5696	−0.838568
$791$	9.00521	0.320188
$792$	5.46637	0.194239
$793$	13.0396	0.463051
$794$	24.6375	0.874353
$795$	−55.1383	−1.95555
$796$	2.83236	0.100390
$797$	−34.4595	−1.22062	−0.610310	−	0.792163i	$-0.708955\pi$
$797$	−34.4595	−1.22062	−0.610310	+	0.792163i	$0.708955\pi$
$798$	1.06638	0.0377495
$799$	−50.6741	−1.79272
$800$	12.3428	0.436385
$801$	−0.895375	−0.0316365
$802$	19.5828	0.691493
$803$	−31.9509	−1.12752
$804$	−3.24899	−0.114583
$805$	−15.6611	−0.551981
$806$	−2.76327	−0.0973320
$807$	4.04491	0.142388
$808$	7.11333	0.250246
$809$	−28.6701	−1.00799	−0.503994	−	0.863707i	$-0.668137\pi$
$809$	−28.6701	−1.00799	−0.503994	+	0.863707i	$0.668137\pi$
$810$	4.16447	0.146325
$811$	−46.5638	−1.63508	−0.817538	−	0.575874i	$-0.804662\pi$
$811$	−46.5638	−1.63508	−0.817538	+	0.575874i	$0.804662\pi$
$812$	7.57431	0.265806
$813$	−17.2548	−0.605152
$814$	−11.7173	−0.410691
$815$	−26.6755	−0.934402
$816$	6.82330	0.238863
$817$	−4.07729	−0.142646
$818$	30.4675	1.06527
$819$	−0.925830	−0.0323511
$820$	15.3272	0.535250
$821$	−23.8937	−0.833897	−0.416949	−	0.908930i	$-0.636900\pi$
$821$	−23.8937	−0.833897	−0.416949	+	0.908930i	$0.636900\pi$
$822$	17.8070	0.621090
$823$	−9.83149	−0.342704	−0.171352	−	0.985210i	$-0.554814\pi$
$823$	−9.83149	−0.342704	−0.171352	+	0.985210i	$0.554814\pi$
$824$	−7.73878	−0.269593
$825$	−67.4705	−2.34902
$826$	−10.8798	−0.378556
$827$	−37.1514	−1.29188	−0.645941	−	0.763387i	$-0.723535\pi$
$827$	−37.1514	−1.29188	−0.645941	+	0.763387i	$0.723535\pi$
$828$	−3.76064	−0.130691
$829$	30.5623	1.06147	0.530736	−	0.847537i	$-0.321916\pi$
$829$	30.5623	1.06147	0.530736	+	0.847537i	$0.321916\pi$
$830$	−26.6593	−0.925358
$831$	5.64409	0.195791
$832$	−0.925830	−0.0320974
$833$	−6.82330	−0.236413
$834$	1.89031	0.0654560
$835$	33.2042	1.14908
$836$	−5.82923	−0.201608
$837$	−2.98464	−0.103164
$838$	−6.37460	−0.220207
$839$	−42.2051	−1.45708	−0.728541	−	0.685003i	$-0.759801\pi$
$839$	−42.2051	−1.45708	−0.728541	+	0.685003i	$0.759801\pi$
$840$	−4.16447	−0.143688
$841$	28.3701	0.978280
$842$	17.1636	0.591495
$843$	13.8012	0.475339
$844$	25.3014	0.870911
$845$	−50.5685	−1.73961
$846$	7.42662	0.255333
$847$	18.8812	0.648765
$848$	13.2402	0.454669
$849$	−1.41062	−0.0484124
$850$	−84.2188	−2.88868
$851$	8.06103	0.276328
$852$	15.2324	0.521854
$853$	47.7917	1.63636	0.818178	−	0.574965i	$-0.194984\pi$
$853$	47.7917	1.63636	0.818178	+	0.574965i	$0.194984\pi$
$854$	−14.0843	−0.481953
$855$	−4.44091	−0.151876
$856$	3.99663	0.136602
$857$	−5.28665	−0.180588	−0.0902942	−	0.995915i	$-0.528781\pi$
$857$	−5.28665	−0.180588	−0.0902942	+	0.995915i	$0.528781\pi$
$858$	5.06093	0.172777
$859$	9.73906	0.332293	0.166146	−	0.986101i	$-0.446868\pi$
$859$	9.73906	0.332293	0.166146	+	0.986101i	$0.446868\pi$
$860$	15.9228	0.542962
$861$	−3.68047	−0.125430
$862$	−1.83380	−0.0624594
$863$	−37.3216	−1.27044	−0.635222	−	0.772330i	$-0.719091\pi$
$863$	−37.3216	−1.27044	−0.635222	+	0.772330i	$0.719091\pi$
$864$	−1.00000	−0.0340207
$865$	77.6056	2.63867
$866$	−32.7356	−1.11240
$867$	−29.5574	−1.00382
$868$	2.98464	0.101305
$869$	−30.9379	−1.04950
$870$	−31.5430	−1.06941
$871$	−3.00801	−0.101923
$872$	1.01769	0.0344633
$873$	1.00000	0.0338449
$874$	4.01027	0.135650
$875$	30.5790	1.03376
$876$	5.84500	0.197484
$877$	−50.8792	−1.71807	−0.859035	−	0.511918i	$-0.828935\pi$
$877$	−50.8792	−1.71807	−0.859035	+	0.511918i	$0.828935\pi$
$878$	−36.2804	−1.22440
$879$	29.7181	1.00236
$880$	22.7645	0.767393
$881$	28.6323	0.964647	0.482324	−	0.875993i	$-0.339793\pi$
$881$	28.6323	0.964647	0.482324	+	0.875993i	$0.339793\pi$
$882$	1.00000	0.0336718
$883$	−14.6733	−0.493795	−0.246898	−	0.969042i	$-0.579411\pi$
$883$	−14.6733	−0.493795	−0.246898	+	0.969042i	$0.579411\pi$
$884$	6.31721	0.212471
$885$	45.3085	1.52303
$886$	13.3497	0.448494
$887$	−29.3701	−0.986152	−0.493076	−	0.869986i	$-0.664127\pi$
$887$	−29.3701	−0.986152	−0.493076	+	0.869986i	$0.664127\pi$
$888$	2.14352	0.0719320
$889$	−13.1936	−0.442499
$890$	−3.72877	−0.124989
$891$	5.46637	0.183130
$892$	−2.83955	−0.0950751
$893$	−7.91961	−0.265020
$894$	−5.88937	−0.196970
$895$	−12.2997	−0.411132
$896$	1.00000	0.0334077
$897$	−3.48171	−0.116251
$898$	20.3178	0.678013
$899$	22.6066	0.753972
$900$	12.3428	0.411428
$901$	−90.3416	−3.00972
$902$	20.1188	0.669883
$903$	−3.82348	−0.127237
$904$	9.00521	0.299509
$905$	−33.2156	−1.10412
$906$	11.7556	0.390553
$907$	−55.7467	−1.85104	−0.925520	−	0.378699i	$-0.876371\pi$
$907$	−55.7467	−1.85104	−0.925520	+	0.378699i	$0.876371\pi$
$908$	−18.5816	−0.616652
$909$	7.11333	0.235934
$910$	−3.85559	−0.127812
$911$	0.0317020	0.00105033	0.000525167	−	1.00000i	$-0.499833\pi$
$911$	0.0317020	0.00105033	0.000525167		1.00000i	$0.499833\pi$
$912$	1.06638	0.0353114
$913$	−34.9935	−1.15812
$914$	−9.72666	−0.321729
$915$	58.6535	1.93903
$916$	18.3680	0.606897
$917$	17.7220	0.585233
$918$	6.82330	0.225202
$919$	−8.69361	−0.286776	−0.143388	−	0.989667i	$-0.545800\pi$
$919$	−8.69361	−0.286776	−0.143388	+	0.989667i	$0.545800\pi$
$920$	−15.6611	−0.516331
$921$	2.65247	0.0874018
$922$	20.8266	0.685888
$923$	14.1026	0.464193
$924$	−5.46637	−0.179830
$925$	−26.4572	−0.869906
$926$	−34.8946	−1.14671
$927$	−7.73878	−0.254175
$928$	7.57431	0.248639
$929$	39.5173	1.29652	0.648261	−	0.761418i	$-0.275497\pi$
$929$	39.5173	1.29652	0.648261	+	0.761418i	$0.275497\pi$
$930$	−12.4295	−0.407578
$931$	−1.06638	−0.0349492
$932$	−20.0844	−0.657885
$933$	24.3770	0.798066
$934$	−23.7496	−0.777112
$935$	−155.329	−5.07981
$936$	−0.925830	−0.0302617
$937$	6.25393	0.204307	0.102153	−	0.994769i	$-0.467427\pi$
$937$	6.25393	0.204307	0.102153	+	0.994769i	$0.467427\pi$
$938$	3.24899	0.106083
$939$	8.44233	0.275505
$940$	30.9280	1.00876
$941$	−50.3898	−1.64266	−0.821330	−	0.570453i	$-0.806768\pi$
$941$	−50.3898	−1.64266	−0.821330	+	0.570453i	$0.806768\pi$
$942$	1.58600	0.0516748
$943$	−13.8409	−0.450722
$944$	−10.8798	−0.354107
$945$	−4.16447	−0.135470
$946$	20.9006	0.679536
$947$	28.0864	0.912687	0.456343	−	0.889804i	$-0.349159\pi$
$947$	28.0864	0.912687	0.456343	+	0.889804i	$0.349159\pi$
$948$	5.65968	0.183818
$949$	5.41147	0.175664
$950$	−13.1622	−0.427037
$951$	23.6335	0.766367
$952$	−6.82330	−0.221144
$953$	11.3441	0.367471	0.183736	−	0.982976i	$-0.441181\pi$
$953$	11.3441	0.367471	0.183736	+	0.982976i	$0.441181\pi$
$954$	13.2402	0.428666
$955$	35.2546	1.14081
$956$	−11.7339	−0.379500
$957$	−41.4039	−1.33840
$958$	−3.30860	−0.106896
$959$	−17.8070	−0.575018
$960$	−4.16447	−0.134408
$961$	−22.0919	−0.712642
$962$	1.98454	0.0639841
$963$	3.99663	0.128790
$964$	9.07967	0.292437
$965$	24.5217	0.789381
$966$	3.76064	0.120997
$967$	−9.46451	−0.304358	−0.152179	−	0.988353i	$-0.548629\pi$
$967$	−9.46451	−0.304358	−0.152179	+	0.988353i	$0.548629\pi$
$968$	18.8812	0.606864
$969$	−7.27623	−0.233746
$970$	4.16447	0.133713
$971$	−7.06730	−0.226801	−0.113400	−	0.993549i	$-0.536174\pi$
$971$	−7.06730	−0.226801	−0.113400	+	0.993549i	$0.536174\pi$
$972$	−1.00000	−0.0320750
$973$	−1.89031	−0.0606005
$974$	−36.8004	−1.17916
$975$	11.4274	0.365968
$976$	−14.0843	−0.450826
$977$	−2.77544	−0.0887942	−0.0443971	−	0.999014i	$-0.514137\pi$
$977$	−2.77544	−0.0887942	−0.0443971	+	0.999014i	$0.514137\pi$
$978$	6.40549	0.204825
$979$	−4.89445	−0.156427
$980$	4.16447	0.133029
$981$	1.01769	0.0324924
$982$	4.75066	0.151600
$983$	60.4200	1.92710	0.963549	−	0.267532i	$-0.0862082\pi$
$983$	60.4200	1.92710	0.963549	+	0.267532i	$0.0862082\pi$
$984$	−3.68047	−0.117329
$985$	82.1961	2.61899
$986$	−51.6817	−1.64588
$987$	−7.42662	−0.236392
$988$	0.987287	0.0314098
$989$	−14.3787	−0.457217
$990$	22.7645	0.723505
$991$	−43.6766	−1.38743	−0.693717	−	0.720248i	$-0.744028\pi$
$991$	−43.6766	−1.38743	−0.693717	+	0.720248i	$0.744028\pi$
$992$	2.98464	0.0947625
$993$	−4.78591	−0.151876
$994$	−15.2324	−0.483143
$995$	11.7953	0.373935
$996$	6.40160	0.202843
$997$	−9.19173	−0.291105	−0.145552	−	0.989351i	$-0.546496\pi$
$997$	−9.19173	−0.291105	−0.145552	+	0.989351i	$0.546496\pi$
$998$	33.4986	1.06038
$999$	2.14352	0.0678181

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4074.2.a.bf.1.10	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4074.2.a.bf.1.10	✓	10	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:	\( N \)	\(=\)	\( 4074 = 2 \cdot 3 \cdot 7 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4074.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.16447 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.16447 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +4.16447 q^{10} +5.46637 q^{11} -1.00000 q^{12} -0.925830 q^{13} +1.00000 q^{14} -4.16447 q^{15} +1.00000 q^{16} -6.82330 q^{17} +1.00000 q^{18} -1.06638 q^{19} +4.16447 q^{20} -1.00000 q^{21} +5.46637 q^{22} -3.76064 q^{23} -1.00000 q^{24} +12.3428 q^{25} -0.925830 q^{26} -1.00000 q^{27} +1.00000 q^{28} +7.57431 q^{29} -4.16447 q^{30} +2.98464 q^{31} +1.00000 q^{32} -5.46637 q^{33} -6.82330 q^{34} +4.16447 q^{35} +1.00000 q^{36} -2.14352 q^{37} -1.06638 q^{38} +0.925830 q^{39} +4.16447 q^{40} +3.68047 q^{41} -1.00000 q^{42} +3.82348 q^{43} +5.46637 q^{44} +4.16447 q^{45} -3.76064 q^{46} +7.42662 q^{47} -1.00000 q^{48} +1.00000 q^{49} +12.3428 q^{50} +6.82330 q^{51} -0.925830 q^{52} +13.2402 q^{53} -1.00000 q^{54} +22.7645 q^{55} +1.00000 q^{56} +1.06638 q^{57} +7.57431 q^{58} -10.8798 q^{59} -4.16447 q^{60} -14.0843 q^{61} +2.98464 q^{62} +1.00000 q^{63} +1.00000 q^{64} -3.85559 q^{65} -5.46637 q^{66} +3.24899 q^{67} -6.82330 q^{68} +3.76064 q^{69} +4.16447 q^{70} -15.2324 q^{71} +1.00000 q^{72} -5.84500 q^{73} -2.14352 q^{74} -12.3428 q^{75} -1.06638 q^{76} +5.46637 q^{77} +0.925830 q^{78} -5.65968 q^{79} +4.16447 q^{80} +1.00000 q^{81} +3.68047 q^{82} -6.40160 q^{83} -1.00000 q^{84} -28.4154 q^{85} +3.82348 q^{86} -7.57431 q^{87} +5.46637 q^{88} -0.895375 q^{89} +4.16447 q^{90} -0.925830 q^{91} -3.76064 q^{92} -2.98464 q^{93} +7.42662 q^{94} -4.44091 q^{95} -1.00000 q^{96} +1.00000 q^{97} +1.00000 q^{98} +5.46637 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} - 10 q^{3} + 10 q^{4} + 3 q^{5} - 10 q^{6} + 10 q^{7} + 10 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 10 * q^2 - 10 * q^3 + 10 * q^4 + 3 * q^5 - 10 * q^6 + 10 * q^7 + 10 * q^8 + 10 * q^9	\( 10 q + 10 q^{2} - 10 q^{3} + 10 q^{4} + 3 q^{5} - 10 q^{6} + 10 q^{7} + 10 q^{8} + 10 q^{9} + 3 q^{10} + 12 q^{11} - 10 q^{12} + 6 q^{13} + 10 q^{14} - 3 q^{15} + 10 q^{16} + 4 q^{17} + 10 q^{18} + q^{19} + 3 q^{20} - 10 q^{21} + 12 q^{22} + 10 q^{23} - 10 q^{24} + 25 q^{25} + 6 q^{26} - 10 q^{27} + 10 q^{28} + 10 q^{29} - 3 q^{30} + 3 q^{31} + 10 q^{32} - 12 q^{33} + 4 q^{34} + 3 q^{35} + 10 q^{36} + 15 q^{37} + q^{38} - 6 q^{39} + 3 q^{40} + 10 q^{41} - 10 q^{42} + 17 q^{43} + 12 q^{44} + 3 q^{45} + 10 q^{46} - 10 q^{48} + 10 q^{49} + 25 q^{50} - 4 q^{51} + 6 q^{52} + 13 q^{53} - 10 q^{54} + 10 q^{56} - q^{57} + 10 q^{58} - 20 q^{59} - 3 q^{60} + 9 q^{61} + 3 q^{62} + 10 q^{63} + 10 q^{64} + 22 q^{65} - 12 q^{66} + 26 q^{67} + 4 q^{68} - 10 q^{69} + 3 q^{70} + 18 q^{71} + 10 q^{72} + 6 q^{73} + 15 q^{74} - 25 q^{75} + q^{76} + 12 q^{77} - 6 q^{78} + 12 q^{79} + 3 q^{80} + 10 q^{81} + 10 q^{82} - 10 q^{83} - 10 q^{84} + 16 q^{85} + 17 q^{86} - 10 q^{87} + 12 q^{88} + q^{89} + 3 q^{90} + 6 q^{91} + 10 q^{92} - 3 q^{93} + 18 q^{95} - 10 q^{96} + 10 q^{97} + 10 q^{98} + 12 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 - 10 * q^3 + 10 * q^4 + 3 * q^5 - 10 * q^6 + 10 * q^7 + 10 * q^8 + 10 * q^9 + 3 * q^10 + 12 * q^11 - 10 * q^12 + 6 * q^13 + 10 * q^14 - 3 * q^15 + 10 * q^16 + 4 * q^17 + 10 * q^18 + q^19 + 3 * q^20 - 10 * q^21 + 12 * q^22 + 10 * q^23 - 10 * q^24 + 25 * q^25 + 6 * q^26 - 10 * q^27 + 10 * q^28 + 10 * q^29 - 3 * q^30 + 3 * q^31 + 10 * q^32 - 12 * q^33 + 4 * q^34 + 3 * q^35 + 10 * q^36 + 15 * q^37 + q^38 - 6 * q^39 + 3 * q^40 + 10 * q^41 - 10 * q^42 + 17 * q^43 + 12 * q^44 + 3 * q^45 + 10 * q^46 - 10 * q^48 + 10 * q^49 + 25 * q^50 - 4 * q^51 + 6 * q^52 + 13 * q^53 - 10 * q^54 + 10 * q^56 - q^57 + 10 * q^58 - 20 * q^59 - 3 * q^60 + 9 * q^61 + 3 * q^62 + 10 * q^63 + 10 * q^64 + 22 * q^65 - 12 * q^66 + 26 * q^67 + 4 * q^68 - 10 * q^69 + 3 * q^70 + 18 * q^71 + 10 * q^72 + 6 * q^73 + 15 * q^74 - 25 * q^75 + q^76 + 12 * q^77 - 6 * q^78 + 12 * q^79 + 3 * q^80 + 10 * q^81 + 10 * q^82 - 10 * q^83 - 10 * q^84 + 16 * q^85 + 17 * q^86 - 10 * q^87 + 12 * q^88 + q^89 + 3 * q^90 + 6 * q^91 + 10 * q^92 - 3 * q^93 + 18 * q^95 - 10 * q^96 + 10 * q^97 + 10 * q^98 + 12 * q^99

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