LMFDB - Embedded newform 2001.2.a.i.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2001,2,Mod(1,2001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2001, 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("2001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2001 = 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2001.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:	$15.9780654445$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 5x^{5} + 18x^{4} + 4x^{3} - 26x^{2} + x + 8 $ x^7 - 3x^6 - 5x^5 + 18x^4 + 4x^3 - 26*x^2 + x + 8
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.22973$ of defining polynomial
Character	$\chi$	$=$	2001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.22973 q^{2} +1.00000 q^{3} +2.97167 q^{4} +0.537118 q^{5} -2.22973 q^{6} -1.88241 q^{7} -2.16657 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.22973 q^{2} +1.00000 q^{3} +2.97167 q^{4} +0.537118 q^{5} -2.22973 q^{6} -1.88241 q^{7} -2.16657 q^{8} +1.00000 q^{9} -1.19762 q^{10} +1.11723 q^{11} +2.97167 q^{12} +1.56781 q^{13} +4.19726 q^{14} +0.537118 q^{15} -1.11250 q^{16} -3.41741 q^{17} -2.22973 q^{18} -2.62638 q^{19} +1.59614 q^{20} -1.88241 q^{21} -2.49110 q^{22} +1.00000 q^{23} -2.16657 q^{24} -4.71150 q^{25} -3.49579 q^{26} +1.00000 q^{27} -5.59392 q^{28} -1.00000 q^{29} -1.19762 q^{30} -2.26219 q^{31} +6.81370 q^{32} +1.11723 q^{33} +7.61989 q^{34} -1.01108 q^{35} +2.97167 q^{36} +1.64906 q^{37} +5.85610 q^{38} +1.56781 q^{39} -1.16370 q^{40} +5.06667 q^{41} +4.19726 q^{42} -10.0332 q^{43} +3.32003 q^{44} +0.537118 q^{45} -2.22973 q^{46} -6.06906 q^{47} -1.11250 q^{48} -3.45652 q^{49} +10.5054 q^{50} -3.41741 q^{51} +4.65903 q^{52} +10.2961 q^{53} -2.22973 q^{54} +0.600081 q^{55} +4.07837 q^{56} -2.62638 q^{57} +2.22973 q^{58} -8.80232 q^{59} +1.59614 q^{60} -3.73087 q^{61} +5.04406 q^{62} -1.88241 q^{63} -12.9677 q^{64} +0.842100 q^{65} -2.49110 q^{66} -7.67562 q^{67} -10.1554 q^{68} +1.00000 q^{69} +2.25442 q^{70} -2.43146 q^{71} -2.16657 q^{72} +1.02242 q^{73} -3.67695 q^{74} -4.71150 q^{75} -7.80475 q^{76} -2.10308 q^{77} -3.49579 q^{78} +1.24162 q^{79} -0.597544 q^{80} +1.00000 q^{81} -11.2973 q^{82} +13.0672 q^{83} -5.59392 q^{84} -1.83555 q^{85} +22.3712 q^{86} -1.00000 q^{87} -2.42054 q^{88} -13.1482 q^{89} -1.19762 q^{90} -2.95127 q^{91} +2.97167 q^{92} -2.26219 q^{93} +13.5323 q^{94} -1.41068 q^{95} +6.81370 q^{96} -7.41766 q^{97} +7.70710 q^{98} +1.11723 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 3 q^{2} + 7 q^{3} + 5 q^{4} - 3 q^{5} - 3 q^{6} - 5 q^{7} - 6 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - 3 * q^2 + 7 * q^3 + 5 * q^4 - 3 * q^5 - 3 * q^6 - 5 * q^7 - 6 * q^8 + 7 * q^9	\( 7 q - 3 q^{2} + 7 q^{3} + 5 q^{4} - 3 q^{5} - 3 q^{6} - 5 q^{7} - 6 q^{8} + 7 q^{9} + 3 q^{10} - 4 q^{11} + 5 q^{12} - 18 q^{13} - 2 q^{14} - 3 q^{15} - 7 q^{16} - 3 q^{17} - 3 q^{18} - 4 q^{19} - 2 q^{20} - 5 q^{21} - 26 q^{22} + 7 q^{23} - 6 q^{24} - 8 q^{25} - 7 q^{26} + 7 q^{27} - 6 q^{28} - 7 q^{29} + 3 q^{30} - 22 q^{31} + 5 q^{32} - 4 q^{33} + 9 q^{34} + 3 q^{35} + 5 q^{36} - 25 q^{37} + 14 q^{38} - 18 q^{39} - 10 q^{40} - 13 q^{41} - 2 q^{42} - 2 q^{43} + 4 q^{44} - 3 q^{45} - 3 q^{46} - 25 q^{47} - 7 q^{48} - 8 q^{49} + 19 q^{50} - 3 q^{51} - 12 q^{52} - 5 q^{53} - 3 q^{54} - 15 q^{55} + 18 q^{56} - 4 q^{57} + 3 q^{58} + 11 q^{59} - 2 q^{60} - 33 q^{61} + 28 q^{62} - 5 q^{63} - 14 q^{64} - 2 q^{65} - 26 q^{66} + 8 q^{67} + 12 q^{68} + 7 q^{69} - 22 q^{70} - 6 q^{71} - 6 q^{72} + 15 q^{73} + 34 q^{74} - 8 q^{75} - 28 q^{76} - q^{77} - 7 q^{78} - 15 q^{79} - 12 q^{80} + 7 q^{81} - 14 q^{82} + 21 q^{83} - 6 q^{84} - 28 q^{85} - 12 q^{86} - 7 q^{87} - 13 q^{88} + 8 q^{89} + 3 q^{90} + 6 q^{91} + 5 q^{92} - 22 q^{93} - 35 q^{94} - 25 q^{95} + 5 q^{96} + 13 q^{97} + q^{98} - 4 q^{99}+O(q^{100}) \) 7 * q - 3 * q^2 + 7 * q^3 + 5 * q^4 - 3 * q^5 - 3 * q^6 - 5 * q^7 - 6 * q^8 + 7 * q^9 + 3 * q^10 - 4 * q^11 + 5 * q^12 - 18 * q^13 - 2 * q^14 - 3 * q^15 - 7 * q^16 - 3 * q^17 - 3 * q^18 - 4 * q^19 - 2 * q^20 - 5 * q^21 - 26 * q^22 + 7 * q^23 - 6 * q^24 - 8 * q^25 - 7 * q^26 + 7 * q^27 - 6 * q^28 - 7 * q^29 + 3 * q^30 - 22 * q^31 + 5 * q^32 - 4 * q^33 + 9 * q^34 + 3 * q^35 + 5 * q^36 - 25 * q^37 + 14 * q^38 - 18 * q^39 - 10 * q^40 - 13 * q^41 - 2 * q^42 - 2 * q^43 + 4 * q^44 - 3 * q^45 - 3 * q^46 - 25 * q^47 - 7 * q^48 - 8 * q^49 + 19 * q^50 - 3 * q^51 - 12 * q^52 - 5 * q^53 - 3 * q^54 - 15 * q^55 + 18 * q^56 - 4 * q^57 + 3 * q^58 + 11 * q^59 - 2 * q^60 - 33 * q^61 + 28 * q^62 - 5 * q^63 - 14 * q^64 - 2 * q^65 - 26 * q^66 + 8 * q^67 + 12 * q^68 + 7 * q^69 - 22 * q^70 - 6 * q^71 - 6 * q^72 + 15 * q^73 + 34 * q^74 - 8 * q^75 - 28 * q^76 - q^77 - 7 * q^78 - 15 * q^79 - 12 * q^80 + 7 * q^81 - 14 * q^82 + 21 * q^83 - 6 * q^84 - 28 * q^85 - 12 * q^86 - 7 * q^87 - 13 * q^88 + 8 * q^89 + 3 * q^90 + 6 * q^91 + 5 * q^92 - 22 * q^93 - 35 * q^94 - 25 * q^95 + 5 * q^96 + 13 * q^97 + q^98 - 4 * 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 $

$2$	−2.22973	−1.57665	−0.788327	−	0.615257i	$-0.789052\pi$
$2$	−2.22973	−1.57665	−0.788327	+	0.615257i	$0.789052\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.97167	1.48584
$5$	0.537118	0.240206	0.120103	−	0.992761i	$-0.461677\pi$
$5$	0.537118	0.240206	0.120103	+	0.992761i	$0.461677\pi$
$6$	−2.22973	−0.910281
$7$	−1.88241	−0.711485	−0.355743	−	0.934584i	$-0.615772\pi$
$7$	−1.88241	−0.711485	−0.355743	+	0.934584i	$0.615772\pi$
$8$	−2.16657	−0.765997
$9$	1.00000	0.333333
$10$	−1.19762	−0.378722
$11$	1.11723	0.336856	0.168428	−	0.985714i	$-0.446131\pi$
$11$	1.11723	0.336856	0.168428	+	0.985714i	$0.446131\pi$
$12$	2.97167	0.857849
$13$	1.56781	0.434833	0.217417	−	0.976079i	$-0.430237\pi$
$13$	1.56781	0.434833	0.217417	+	0.976079i	$0.430237\pi$
$14$	4.19726	1.12177
$15$	0.537118	0.138683
$16$	−1.11250	−0.278125
$17$	−3.41741	−0.828844	−0.414422	−	0.910085i	$-0.636016\pi$
$17$	−3.41741	−0.828844	−0.414422	+	0.910085i	$0.636016\pi$
$18$	−2.22973	−0.525551
$19$	−2.62638	−0.602533	−0.301266	−	0.953540i	$-0.597409\pi$
$19$	−2.62638	−0.602533	−0.301266	+	0.953540i	$0.597409\pi$
$20$	1.59614	0.356908
$21$	−1.88241	−0.410776
$22$	−2.49110	−0.531105
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−2.16657	−0.442249
$25$	−4.71150	−0.942301
$26$	−3.49579	−0.685581
$27$	1.00000	0.192450
$28$	−5.59392	−1.05715
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−1.19762	−0.218655
$31$	−2.26219	−0.406301	−0.203150	−	0.979148i	$-0.565118\pi$
$31$	−2.26219	−0.406301	−0.203150	+	0.979148i	$0.565118\pi$
$32$	6.81370	1.20450
$33$	1.11723	0.194484
$34$	7.61989	1.30680
$35$	−1.01108	−0.170903
$36$	2.97167	0.495279
$37$	1.64906	0.271104	0.135552	−	0.990770i	$-0.456719\pi$
$37$	1.64906	0.271104	0.135552	+	0.990770i	$0.456719\pi$
$38$	5.85610	0.949986
$39$	1.56781	0.251051
$40$	−1.16370	−0.183997
$41$	5.06667	0.791280	0.395640	−	0.918406i	$-0.370523\pi$
$41$	5.06667	0.791280	0.395640	+	0.918406i	$0.370523\pi$
$42$	4.19726	0.647652
$43$	−10.0332	−1.53004	−0.765021	−	0.644005i	$-0.777272\pi$
$43$	−10.0332	−1.53004	−0.765021	+	0.644005i	$0.777272\pi$
$44$	3.32003	0.500513
$45$	0.537118	0.0800688
$46$	−2.22973	−0.328755
$47$	−6.06906	−0.885263	−0.442631	−	0.896704i	$-0.645955\pi$
$47$	−6.06906	−0.885263	−0.442631	+	0.896704i	$0.645955\pi$
$48$	−1.11250	−0.160576
$49$	−3.45652	−0.493789
$50$	10.5054	1.48568
$51$	−3.41741	−0.478533
$52$	4.65903	0.646091
$53$	10.2961	1.41427	0.707137	−	0.707077i	$-0.249987\pi$
$53$	10.2961	1.41427	0.707137	+	0.707077i	$0.249987\pi$
$54$	−2.22973	−0.303427
$55$	0.600081	0.0809150
$56$	4.07837	0.544995
$57$	−2.62638	−0.347872
$58$	2.22973	0.292777
$59$	−8.80232	−1.14596	−0.572982	−	0.819568i	$-0.694214\pi$
$59$	−8.80232	−1.14596	−0.572982	+	0.819568i	$0.694214\pi$
$60$	1.59614	0.206061
$61$	−3.73087	−0.477689	−0.238845	−	0.971058i	$-0.576769\pi$
$61$	−3.73087	−0.477689	−0.238845	+	0.971058i	$0.576769\pi$
$62$	5.04406	0.640596
$63$	−1.88241	−0.237162
$64$	−12.9677	−1.62096
$65$	0.842100	0.104450
$66$	−2.49110	−0.306634
$67$	−7.67562	−0.937726	−0.468863	−	0.883271i	$-0.655336\pi$
$67$	−7.67562	−0.937726	−0.468863	+	0.883271i	$0.655336\pi$
$68$	−10.1554	−1.23153
$69$	1.00000	0.120386
$70$	2.25442	0.269455
$71$	−2.43146	−0.288561	−0.144281	−	0.989537i	$-0.546087\pi$
$71$	−2.43146	−0.288561	−0.144281	+	0.989537i	$0.546087\pi$
$72$	−2.16657	−0.255332
$73$	1.02242	0.119665	0.0598326	−	0.998208i	$-0.480943\pi$
$73$	1.02242	0.119665	0.0598326	+	0.998208i	$0.480943\pi$
$74$	−3.67695	−0.427437
$75$	−4.71150	−0.544038
$76$	−7.80475	−0.895266
$77$	−2.10308	−0.239668
$78$	−3.49579	−0.395821
$79$	1.24162	0.139693	0.0698466	−	0.997558i	$-0.477749\pi$
$79$	1.24162	0.139693	0.0698466	+	0.997558i	$0.477749\pi$
$80$	−0.597544	−0.0668074
$81$	1.00000	0.111111
$82$	−11.2973	−1.24758
$83$	13.0672	1.43432	0.717158	−	0.696910i	$-0.245442\pi$
$83$	13.0672	1.43432	0.717158	+	0.696910i	$0.245442\pi$
$84$	−5.59392	−0.610346
$85$	−1.83555	−0.199094
$86$	22.3712	2.41235
$87$	−1.00000	−0.107211
$88$	−2.42054	−0.258031
$89$	−13.1482	−1.39370	−0.696851	−	0.717216i	$-0.745416\pi$
$89$	−13.1482	−1.39370	−0.696851	+	0.717216i	$0.745416\pi$
$90$	−1.19762	−0.126241
$91$	−2.95127	−0.309377
$92$	2.97167	0.309818
$93$	−2.26219	−0.234578
$94$	13.5323	1.39575
$95$	−1.41068	−0.144732
$96$	6.81370	0.695421
$97$	−7.41766	−0.753149	−0.376575	−	0.926386i	$-0.622898\pi$
$97$	−7.41766	−0.753149	−0.376575	+	0.926386i	$0.622898\pi$
$98$	7.70710	0.778534
$99$	1.11723	0.112285
$100$	−14.0011	−1.40011
$101$	−2.80104	−0.278714	−0.139357	−	0.990242i	$-0.544504\pi$
$101$	−2.80104	−0.278714	−0.139357	+	0.990242i	$0.544504\pi$
$102$	7.61989	0.754481
$103$	10.0128	0.986589	0.493295	−	0.869862i	$-0.335792\pi$
$103$	10.0128	0.986589	0.493295	+	0.869862i	$0.335792\pi$
$104$	−3.39677	−0.333081
$105$	−1.01108	−0.0986710
$106$	−22.9574	−2.22982
$107$	−5.25354	−0.507878	−0.253939	−	0.967220i	$-0.581726\pi$
$107$	−5.25354	−0.507878	−0.253939	+	0.967220i	$0.581726\pi$
$108$	2.97167	0.285950
$109$	−5.08675	−0.487223	−0.243611	−	0.969873i	$-0.578332\pi$
$109$	−5.08675	−0.487223	−0.243611	+	0.969873i	$0.578332\pi$
$110$	−1.33802	−0.127575
$111$	1.64906	0.156522
$112$	2.09418	0.197882
$113$	18.3795	1.72900	0.864500	−	0.502633i	$-0.167635\pi$
$113$	18.3795	1.72900	0.864500	+	0.502633i	$0.167635\pi$
$114$	5.85610	0.548474
$115$	0.537118	0.0500865
$116$	−2.97167	−0.275913
$117$	1.56781	0.144944
$118$	19.6268	1.80679
$119$	6.43298	0.589710
$120$	−1.16370	−0.106231
$121$	−9.75181	−0.886528
$122$	8.31882	0.753151
$123$	5.06667	0.456846
$124$	−6.72249	−0.603697
$125$	−5.21622	−0.466553
$126$	4.19726	0.373922
$127$	4.33301	0.384492	0.192246	−	0.981347i	$-0.438423\pi$
$127$	4.33301	0.384492	0.192246	+	0.981347i	$0.438423\pi$
$128$	15.2870	1.35119
$129$	−10.0332	−0.883371
$130$	−1.87765	−0.164681
$131$	19.3607	1.69155	0.845777	−	0.533537i	$-0.179137\pi$
$131$	19.3607	1.69155	0.845777	+	0.533537i	$0.179137\pi$
$132$	3.32003	0.288971
$133$	4.94393	0.428693
$134$	17.1145	1.47847
$135$	0.537118	0.0462277
$136$	7.40405	0.634892
$137$	−10.2352	−0.874456	−0.437228	−	0.899351i	$-0.644040\pi$
$137$	−10.2352	−0.874456	−0.437228	+	0.899351i	$0.644040\pi$
$138$	−2.22973	−0.189807
$139$	−0.289212	−0.0245306	−0.0122653	−	0.999925i	$-0.503904\pi$
$139$	−0.289212	−0.0245306	−0.0122653	+	0.999925i	$0.503904\pi$
$140$	−3.00459	−0.253934
$141$	−6.06906	−0.511107
$142$	5.42149	0.454961
$143$	1.75160	0.146476
$144$	−1.11250	−0.0927083
$145$	−0.537118	−0.0446052
$146$	−2.27972	−0.188671
$147$	−3.45652	−0.285089
$148$	4.90047	0.402816
$149$	20.1266	1.64884	0.824419	−	0.565979i	$-0.191502\pi$
$149$	20.1266	1.64884	0.824419	+	0.565979i	$0.191502\pi$
$150$	10.5054	0.857759
$151$	0.370644	0.0301626	0.0150813	−	0.999886i	$-0.495199\pi$
$151$	0.370644	0.0301626	0.0150813	+	0.999886i	$0.495199\pi$
$152$	5.69023	0.461538
$153$	−3.41741	−0.276281
$154$	4.68929	0.377874
$155$	−1.21506	−0.0975961
$156$	4.65903	0.373021
$157$	−7.03038	−0.561086	−0.280543	−	0.959842i	$-0.590514\pi$
$157$	−7.03038	−0.561086	−0.280543	+	0.959842i	$0.590514\pi$
$158$	−2.76847	−0.220248
$159$	10.2961	0.816531
$160$	3.65976	0.289330
$161$	−1.88241	−0.148355
$162$	−2.22973	−0.175184
$163$	−19.9434	−1.56209	−0.781044	−	0.624476i	$-0.785312\pi$
$163$	−19.9434	−1.56209	−0.781044	+	0.624476i	$0.785312\pi$
$164$	15.0565	1.17571
$165$	0.600081	0.0467163
$166$	−29.1364	−2.26142
$167$	−12.4215	−0.961201	−0.480601	−	0.876940i	$-0.659581\pi$
$167$	−12.4215	−0.961201	−0.480601	+	0.876940i	$0.659581\pi$
$168$	4.07837	0.314653
$169$	−10.5420	−0.810920
$170$	4.09278	0.313902
$171$	−2.62638	−0.200844
$172$	−29.8153	−2.27339
$173$	−12.5473	−0.953954	−0.476977	−	0.878916i	$-0.658267\pi$
$173$	−12.5473	−0.953954	−0.476977	+	0.878916i	$0.658267\pi$
$174$	2.22973	0.169035
$175$	8.86900	0.670433
$176$	−1.24291	−0.0936881
$177$	−8.80232	−0.661623
$178$	29.3168	2.19739
$179$	−23.4139	−1.75003	−0.875017	−	0.484092i	$-0.839150\pi$
$179$	−23.4139	−1.75003	−0.875017	+	0.484092i	$0.839150\pi$
$180$	1.59614	0.118969
$181$	−10.0534	−0.747263	−0.373632	−	0.927577i	$-0.621888\pi$
$181$	−10.0534	−0.747263	−0.373632	+	0.927577i	$0.621888\pi$
$182$	6.58052	0.487781
$183$	−3.73087	−0.275794
$184$	−2.16657	−0.159721
$185$	0.885740	0.0651209
$186$	5.04406	0.369848
$187$	−3.81802	−0.279201
$188$	−18.0353	−1.31536
$189$	−1.88241	−0.136925
$190$	3.14542	0.228193
$191$	−20.7174	−1.49905	−0.749527	−	0.661973i	$-0.769719\pi$
$191$	−20.7174	−1.49905	−0.749527	+	0.661973i	$0.769719\pi$
$192$	−12.9677	−0.935862
$193$	8.55796	0.616015	0.308008	−	0.951384i	$-0.400338\pi$
$193$	8.55796	0.616015	0.308008	+	0.951384i	$0.400338\pi$
$194$	16.5393	1.18746
$195$	0.842100	0.0603041
$196$	−10.2717	−0.733690
$197$	5.84888	0.416715	0.208358	−	0.978053i	$-0.433188\pi$
$197$	5.84888	0.416715	0.208358	+	0.978053i	$0.433188\pi$
$198$	−2.49110	−0.177035
$199$	9.16433	0.649642	0.324821	−	0.945775i	$-0.394696\pi$
$199$	9.16433	0.649642	0.324821	+	0.945775i	$0.394696\pi$
$200$	10.2078	0.721800
$201$	−7.67562	−0.541396
$202$	6.24555	0.439436
$203$	1.88241	0.132119
$204$	−10.1554	−0.711023
$205$	2.72140	0.190071
$206$	−22.3258	−1.55551
$207$	1.00000	0.0695048
$208$	−1.74419	−0.120938
$209$	−2.93426	−0.202967
$210$	2.25442	0.155570
$211$	−0.0926588	−0.00637889	−0.00318945	−	0.999995i	$-0.501015\pi$
$211$	−0.0926588	−0.00637889	−0.00318945	+	0.999995i	$0.501015\pi$
$212$	30.5966	2.10138
$213$	−2.43146	−0.166601
$214$	11.7139	0.800749
$215$	−5.38899	−0.367526
$216$	−2.16657	−0.147416
$217$	4.25837	0.289077
$218$	11.3421	0.768182
$219$	1.02242	0.0690888
$220$	1.78325	0.120226
$221$	−5.35786	−0.360409
$222$	−3.67695	−0.246781
$223$	−12.8223	−0.858643	−0.429322	−	0.903152i	$-0.641247\pi$
$223$	−12.8223	−0.858643	−0.429322	+	0.903152i	$0.641247\pi$
$224$	−12.8262	−0.856987
$225$	−4.71150	−0.314100
$226$	−40.9813	−2.72603
$227$	14.6393	0.971643	0.485821	−	0.874058i	$-0.338521\pi$
$227$	14.6393	0.971643	0.485821	+	0.874058i	$0.338521\pi$
$228$	−7.80475	−0.516882
$229$	−24.1483	−1.59577	−0.797883	−	0.602812i	$-0.794047\pi$
$229$	−24.1483	−1.59577	−0.797883	+	0.602812i	$0.794047\pi$
$230$	−1.19762	−0.0789691
$231$	−2.10308	−0.138372
$232$	2.16657	0.142242
$233$	16.5564	1.08465	0.542324	−	0.840170i	$-0.317545\pi$
$233$	16.5564	1.08465	0.542324	+	0.840170i	$0.317545\pi$
$234$	−3.49579	−0.228527
$235$	−3.25980	−0.212646
$236$	−26.1576	−1.70272
$237$	1.24162	0.0806519
$238$	−14.3438	−0.929769
$239$	−18.3128	−1.18455	−0.592277	−	0.805735i	$-0.701771\pi$
$239$	−18.3128	−1.18455	−0.592277	+	0.805735i	$0.701771\pi$
$240$	−0.597544	−0.0385713
$241$	16.0413	1.03331	0.516655	−	0.856194i	$-0.327177\pi$
$241$	16.0413	1.03331	0.516655	+	0.856194i	$0.327177\pi$
$242$	21.7439	1.39775
$243$	1.00000	0.0641500
$244$	−11.0869	−0.709768
$245$	−1.85656	−0.118611
$246$	−11.2973	−0.720288
$247$	−4.11767	−0.262001
$248$	4.90118	0.311225
$249$	13.0672	0.828103
$250$	11.6307	0.735593
$251$	−16.2544	−1.02597	−0.512983	−	0.858399i	$-0.671460\pi$
$251$	−16.2544	−1.02597	−0.512983	+	0.858399i	$0.671460\pi$
$252$	−5.59392	−0.352384
$253$	1.11723	0.0702393
$254$	−9.66141	−0.606211
$255$	−1.83555	−0.114947
$256$	−8.15037	−0.509398
$257$	2.52528	0.157523	0.0787613	−	0.996894i	$-0.474904\pi$
$257$	2.52528	0.157523	0.0787613	+	0.996894i	$0.474904\pi$
$258$	22.3712	1.39277
$259$	−3.10421	−0.192886
$260$	2.50245	0.155195
$261$	−1.00000	−0.0618984
$262$	−43.1691	−2.66699
$263$	−28.6908	−1.76915	−0.884575	−	0.466399i	$-0.845551\pi$
$263$	−28.6908	−1.76915	−0.884575	+	0.466399i	$0.845551\pi$
$264$	−2.42054	−0.148974
$265$	5.53020	0.339717
$266$	−11.0236	−0.675901
$267$	−13.1482	−0.804655
$268$	−22.8094	−1.39331
$269$	−18.4710	−1.12620	−0.563099	−	0.826389i	$-0.690391\pi$
$269$	−18.4710	−1.12620	−0.563099	+	0.826389i	$0.690391\pi$
$270$	−1.19762	−0.0728851
$271$	−7.71437	−0.468614	−0.234307	−	0.972163i	$-0.575282\pi$
$271$	−7.71437	−0.468614	−0.234307	+	0.972163i	$0.575282\pi$
$272$	3.80187	0.230522
$273$	−2.95127	−0.178619
$274$	22.8218	1.37871
$275$	−5.26381	−0.317420
$276$	2.97167	0.178874
$277$	−0.702588	−0.0422144	−0.0211072	−	0.999777i	$-0.506719\pi$
$277$	−0.702588	−0.0422144	−0.0211072	+	0.999777i	$0.506719\pi$
$278$	0.644863	0.0386763
$279$	−2.26219	−0.135434
$280$	2.19057	0.130911
$281$	2.46040	0.146775	0.0733876	−	0.997303i	$-0.476619\pi$
$281$	2.46040	0.146775	0.0733876	+	0.997303i	$0.476619\pi$
$282$	13.5323	0.805838
$283$	−15.1893	−0.902908	−0.451454	−	0.892294i	$-0.649095\pi$
$283$	−15.1893	−0.902908	−0.451454	+	0.892294i	$0.649095\pi$
$284$	−7.22551	−0.428755
$285$	−1.41068	−0.0835612
$286$	−3.90559	−0.230942
$287$	−9.53756	−0.562984
$288$	6.81370	0.401501
$289$	−5.32130	−0.313018
$290$	1.19762	0.0703270
$291$	−7.41766	−0.434831
$292$	3.03830	0.177803
$293$	8.84429	0.516689	0.258344	−	0.966053i	$-0.416823\pi$
$293$	8.84429	0.516689	0.258344	+	0.966053i	$0.416823\pi$
$294$	7.70710	0.449487
$295$	−4.72788	−0.275268
$296$	−3.57280	−0.207665
$297$	1.11723	0.0648280
$298$	−44.8769	−2.59965
$299$	1.56781	0.0906690
$300$	−14.0011	−0.808351
$301$	18.8865	1.08860
$302$	−0.826433	−0.0475559
$303$	−2.80104	−0.160916
$304$	2.92185	0.167579
$305$	−2.00392	−0.114744
$306$	7.61989	0.435600
$307$	5.52326	0.315229	0.157614	−	0.987501i	$-0.449620\pi$
$307$	5.52326	0.315229	0.157614	+	0.987501i	$0.449620\pi$
$308$	−6.24966	−0.356108
$309$	10.0128	0.569608
$310$	2.70925	0.153875
$311$	0.0662747	0.00375809	0.00187905	−	0.999998i	$-0.499402\pi$
$311$	0.0662747	0.00375809	0.00187905	+	0.999998i	$0.499402\pi$
$312$	−3.39677	−0.192304
$313$	17.7785	1.00490	0.502450	−	0.864606i	$-0.332432\pi$
$313$	17.7785	1.00490	0.502450	+	0.864606i	$0.332432\pi$
$314$	15.6758	0.884638
$315$	−1.01108	−0.0569677
$316$	3.68969	0.207561
$317$	−8.12451	−0.456318	−0.228159	−	0.973624i	$-0.573271\pi$
$317$	−8.12451	−0.456318	−0.228159	+	0.973624i	$0.573271\pi$
$318$	−22.9574	−1.28739
$319$	−1.11723	−0.0625526
$320$	−6.96517	−0.389365
$321$	−5.25354	−0.293224
$322$	4.19726	0.233904
$323$	8.97542	0.499406
$324$	2.97167	0.165093
$325$	−7.38676	−0.409744
$326$	44.4683	2.46287
$327$	−5.08675	−0.281298
$328$	−10.9773	−0.606118
$329$	11.4245	0.629851
$330$	−1.33802	−0.0736554
$331$	20.2364	1.11229	0.556146	−	0.831085i	$-0.312280\pi$
$331$	20.2364	1.11229	0.556146	+	0.831085i	$0.312280\pi$
$332$	38.8316	2.13116
$333$	1.64906	0.0903680
$334$	27.6964	1.51548
$335$	−4.12271	−0.225248
$336$	2.09418	0.114247
$337$	19.0760	1.03914	0.519568	−	0.854429i	$-0.326093\pi$
$337$	19.0760	1.03914	0.519568	+	0.854429i	$0.326093\pi$
$338$	23.5057	1.27854
$339$	18.3795	0.998238
$340$	−5.45466	−0.295821
$341$	−2.52737	−0.136865
$342$	5.85610	0.316662
$343$	19.6835	1.06281
$344$	21.7375	1.17201
$345$	0.537118	0.0289174
$346$	27.9770	1.50405
$347$	−29.5028	−1.58379	−0.791897	−	0.610655i	$-0.790906\pi$
$347$	−29.5028	−1.58379	−0.791897	+	0.610655i	$0.790906\pi$
$348$	−2.97167	−0.159298
$349$	−11.6279	−0.622426	−0.311213	−	0.950340i	$-0.600735\pi$
$349$	−11.6279	−0.622426	−0.311213	+	0.950340i	$0.600735\pi$
$350$	−19.7754	−1.05704
$351$	1.56781	0.0836837
$352$	7.61244	0.405744
$353$	−0.349829	−0.0186195	−0.00930975	−	0.999957i	$-0.502963\pi$
$353$	−0.349829	−0.0186195	−0.00930975	+	0.999957i	$0.502963\pi$
$354$	19.6268	1.04315
$355$	−1.30598	−0.0693143
$356$	−39.0721	−2.07082
$357$	6.43298	0.340469
$358$	52.2065	2.75920
$359$	−17.4984	−0.923528	−0.461764	−	0.887003i	$-0.652783\pi$
$359$	−17.4984	−0.923528	−0.461764	+	0.887003i	$0.652783\pi$
$360$	−1.16370	−0.0613325
$361$	−12.1021	−0.636954
$362$	22.4163	1.17818
$363$	−9.75181	−0.511837
$364$	−8.77022	−0.459684
$365$	0.549160	0.0287444
$366$	8.31882	0.434832
$367$	−33.9848	−1.77399	−0.886997	−	0.461775i	$-0.847213\pi$
$367$	−33.9848	−1.77399	−0.886997	+	0.461775i	$0.847213\pi$
$368$	−1.11250	−0.0579931
$369$	5.06667	0.263760
$370$	−1.97496	−0.102673
$371$	−19.3814	−1.00623
$372$	−6.72249	−0.348545
$373$	19.9955	1.03533	0.517664	−	0.855584i	$-0.326802\pi$
$373$	19.9955	1.03533	0.517664	+	0.855584i	$0.326802\pi$
$374$	8.51313	0.440203
$375$	−5.21622	−0.269365
$376$	13.1490	0.678109
$377$	−1.56781	−0.0807465
$378$	4.19726	0.215884
$379$	23.0774	1.18541	0.592704	−	0.805420i	$-0.298060\pi$
$379$	23.0774	1.18541	0.592704	+	0.805420i	$0.298060\pi$
$380$	−4.19207	−0.215049
$381$	4.33301	0.221987
$382$	46.1940	2.36349
$383$	32.8565	1.67889	0.839445	−	0.543444i	$-0.182880\pi$
$383$	32.8565	1.67889	0.839445	+	0.543444i	$0.182880\pi$
$384$	15.2870	0.780110
$385$	−1.12960	−0.0575698
$386$	−19.0819	−0.971243
$387$	−10.0332	−0.510014
$388$	−22.0429	−1.11906
$389$	13.9353	0.706547	0.353274	−	0.935520i	$-0.385068\pi$
$389$	13.9353	0.706547	0.353274	+	0.935520i	$0.385068\pi$
$390$	−1.87765	−0.0950786
$391$	−3.41741	−0.172826
$392$	7.48879	0.378241
$393$	19.3607	0.976619
$394$	−13.0414	−0.657016
$395$	0.666896	0.0335552
$396$	3.32003	0.166838
$397$	13.9272	0.698988	0.349494	−	0.936939i	$-0.386353\pi$
$397$	13.9272	0.698988	0.349494	+	0.936939i	$0.386353\pi$
$398$	−20.4339	−1.02426
$399$	4.94393	0.247506
$400$	5.24155	0.262077
$401$	5.07639	0.253503	0.126752	−	0.991935i	$-0.459545\pi$
$401$	5.07639	0.253503	0.126752	+	0.991935i	$0.459545\pi$
$402$	17.1145	0.853595
$403$	−3.54669	−0.176673
$404$	−8.32378	−0.414124
$405$	0.537118	0.0266896
$406$	−4.19726	−0.208307
$407$	1.84237	0.0913230
$408$	7.40405	0.366555
$409$	−20.8607	−1.03150	−0.515748	−	0.856740i	$-0.672486\pi$
$409$	−20.8607	−1.03150	−0.515748	+	0.856740i	$0.672486\pi$
$410$	−6.06797	−0.299676
$411$	−10.2352	−0.504868
$412$	29.7547	1.46591
$413$	16.5696	0.815336
$414$	−2.22973	−0.109585
$415$	7.01865	0.344532
$416$	10.6826	0.523758
$417$	−0.289212	−0.0141628
$418$	6.54259	0.320008
$419$	3.26760	0.159633	0.0798163	−	0.996810i	$-0.474567\pi$
$419$	3.26760	0.159633	0.0798163	+	0.996810i	$0.474567\pi$
$420$	−3.00459	−0.146609
$421$	−1.97217	−0.0961175	−0.0480587	−	0.998845i	$-0.515303\pi$
$421$	−1.97217	−0.0961175	−0.0480587	+	0.998845i	$0.515303\pi$
$422$	0.206604	0.0100573
$423$	−6.06906	−0.295088
$424$	−22.3071	−1.08333
$425$	16.1011	0.781020
$426$	5.42149	0.262672
$427$	7.02304	0.339869
$428$	−15.6118	−0.754625
$429$	1.75160	0.0845681
$430$	12.0160	0.579461
$431$	−3.63225	−0.174959	−0.0874797	−	0.996166i	$-0.527881\pi$
$431$	−3.63225	−0.174959	−0.0874797	+	0.996166i	$0.527881\pi$
$432$	−1.11250	−0.0535252
$433$	−1.31543	−0.0632156	−0.0316078	−	0.999500i	$-0.510063\pi$
$433$	−1.31543	−0.0632156	−0.0316078	+	0.999500i	$0.510063\pi$
$434$	−9.49500	−0.455774
$435$	−0.537118	−0.0257528
$436$	−15.1162	−0.723934
$437$	−2.62638	−0.125637
$438$	−2.27972	−0.108929
$439$	17.1910	0.820480	0.410240	−	0.911978i	$-0.365445\pi$
$439$	17.1910	0.820480	0.410240	+	0.911978i	$0.365445\pi$
$440$	−1.30012	−0.0619806
$441$	−3.45652	−0.164596
$442$	11.9466	0.568240
$443$	−9.59576	−0.455908	−0.227954	−	0.973672i	$-0.573204\pi$
$443$	−9.59576	−0.455908	−0.227954	+	0.973672i	$0.573204\pi$
$444$	4.90047	0.232566
$445$	−7.06211	−0.334776
$446$	28.5902	1.35378
$447$	20.1266	0.951958
$448$	24.4105	1.15329
$449$	19.5494	0.922594	0.461297	−	0.887246i	$-0.347384\pi$
$449$	19.5494	0.922594	0.461297	+	0.887246i	$0.347384\pi$
$450$	10.5054	0.495227
$451$	5.66061	0.266548
$452$	54.6179	2.56901
$453$	0.370644	0.0174144
$454$	−32.6416	−1.53194
$455$	−1.58518	−0.0743144
$456$	5.69023	0.266469
$457$	−12.3018	−0.575453	−0.287726	−	0.957713i	$-0.592899\pi$
$457$	−12.3018	−0.575453	−0.287726	+	0.957713i	$0.592899\pi$
$458$	53.8441	2.51597
$459$	−3.41741	−0.159511
$460$	1.59614	0.0744204
$461$	−33.7959	−1.57403	−0.787016	−	0.616933i	$-0.788375\pi$
$461$	−33.7959	−1.57403	−0.787016	+	0.616933i	$0.788375\pi$
$462$	4.68929	0.218165
$463$	32.9615	1.53185	0.765925	−	0.642930i	$-0.222282\pi$
$463$	32.9615	1.53185	0.765925	+	0.642930i	$0.222282\pi$
$464$	1.11250	0.0516465
$465$	−1.21506	−0.0563471
$466$	−36.9163	−1.71011
$467$	−11.5793	−0.535826	−0.267913	−	0.963443i	$-0.586334\pi$
$467$	−11.5793	−0.535826	−0.267913	+	0.963443i	$0.586334\pi$
$468$	4.65903	0.215364
$469$	14.4487	0.667178
$470$	7.26845	0.335269
$471$	−7.03038	−0.323943
$472$	19.0708	0.877805
$473$	−11.2093	−0.515404
$474$	−2.76847	−0.127160
$475$	12.3742	0.567767
$476$	19.1167	0.876213
$477$	10.2961	0.471424
$478$	40.8324	1.86763
$479$	14.2331	0.650326	0.325163	−	0.945658i	$-0.394581\pi$
$479$	14.2331	0.650326	0.325163	+	0.945658i	$0.394581\pi$
$480$	3.65976	0.167044
$481$	2.58542	0.117885
$482$	−35.7676	−1.62917
$483$	−1.88241	−0.0856527
$484$	−28.9792	−1.31724
$485$	−3.98416	−0.180911
$486$	−2.22973	−0.101142
$487$	25.8118	1.16964	0.584821	−	0.811162i	$-0.301165\pi$
$487$	25.8118	1.16964	0.584821	+	0.811162i	$0.301165\pi$
$488$	8.08318	0.365909
$489$	−19.9434	−0.901872
$490$	4.13962	0.187009
$491$	−35.5608	−1.60484	−0.802419	−	0.596761i	$-0.796454\pi$
$491$	−35.5608	−1.60484	−0.802419	+	0.596761i	$0.796454\pi$
$492$	15.0565	0.678799
$493$	3.41741	0.153912
$494$	9.18128	0.413085
$495$	0.600081	0.0269717
$496$	2.51668	0.113002
$497$	4.57701	0.205307
$498$	−29.1364	−1.30563
$499$	15.5456	0.695918	0.347959	−	0.937510i	$-0.386875\pi$
$499$	15.5456	0.695918	0.347959	+	0.937510i	$0.386875\pi$
$500$	−15.5009	−0.693222
$501$	−12.4215	−0.554950
$502$	36.2428	1.61759
$503$	19.4816	0.868641	0.434321	−	0.900758i	$-0.356989\pi$
$503$	19.4816	0.868641	0.434321	+	0.900758i	$0.356989\pi$
$504$	4.07837	0.181665
$505$	−1.50449	−0.0669489
$506$	−2.49110	−0.110743
$507$	−10.5420	−0.468185
$508$	12.8763	0.571293
$509$	21.8713	0.969428	0.484714	−	0.874673i	$-0.338924\pi$
$509$	21.8713	0.969428	0.484714	+	0.874673i	$0.338924\pi$
$510$	4.09278	0.181231
$511$	−1.92462	−0.0851401
$512$	−12.4009	−0.548046
$513$	−2.62638	−0.115957
$514$	−5.63068	−0.248359
$515$	5.37805	0.236985
$516$	−29.8153	−1.31254
$517$	−6.78050	−0.298206
$518$	6.92154	0.304115
$519$	−12.5473	−0.550765
$520$	−1.82447	−0.0800082
$521$	27.2480	1.19375	0.596877	−	0.802333i	$-0.296408\pi$
$521$	27.2480	1.19375	0.596877	+	0.802333i	$0.296408\pi$
$522$	2.22973	0.0975924
$523$	16.5965	0.725715	0.362858	−	0.931845i	$-0.381801\pi$
$523$	16.5965	0.725715	0.362858	+	0.931845i	$0.381801\pi$
$524$	57.5337	2.51337
$525$	8.86900	0.387075
$526$	63.9726	2.78934
$527$	7.73083	0.336760
$528$	−1.24291	−0.0540908
$529$	1.00000	0.0434783
$530$	−12.3308	−0.535617
$531$	−8.80232	−0.381988
$532$	14.6917	0.636968
$533$	7.94359	0.344075
$534$	29.3168	1.26866
$535$	−2.82177	−0.121996
$536$	16.6297	0.718295
$537$	−23.4139	−1.01038
$538$	41.1853	1.77563
$539$	−3.86171	−0.166336
$540$	1.59614	0.0686869
$541$	−32.7816	−1.40939	−0.704696	−	0.709509i	$-0.748917\pi$
$541$	−32.7816	−1.40939	−0.704696	+	0.709509i	$0.748917\pi$
$542$	17.2009	0.738843
$543$	−10.0534	−0.431433
$544$	−23.2852	−0.998346
$545$	−2.73219	−0.117034
$546$	6.58052	0.281620
$547$	32.1520	1.37472	0.687359	−	0.726318i	$-0.258770\pi$
$547$	32.1520	1.37472	0.687359	+	0.726318i	$0.258770\pi$
$548$	−30.4158	−1.29930
$549$	−3.73087	−0.159230
$550$	11.7369	0.500461
$551$	2.62638	0.111888
$552$	−2.16657	−0.0922152
$553$	−2.33724	−0.0993896
$554$	1.56658	0.0665575
$555$	0.885740	0.0375976
$556$	−0.859444	−0.0364485
$557$	−4.00666	−0.169768	−0.0848839	−	0.996391i	$-0.527052\pi$
$557$	−4.00666	−0.169768	−0.0848839	+	0.996391i	$0.527052\pi$
$558$	5.04406	0.213532
$559$	−15.7301	−0.665313
$560$	1.12482	0.0475325
$561$	−3.81802	−0.161197
$562$	−5.48602	−0.231414
$563$	2.38095	0.100345	0.0501726	−	0.998741i	$-0.484023\pi$
$563$	2.38095	0.100345	0.0501726	+	0.998741i	$0.484023\pi$
$564$	−18.0353	−0.759421
$565$	9.87196	0.415317
$566$	33.8679	1.42357
$567$	−1.88241	−0.0790539
$568$	5.26792	0.221037
$569$	42.7445	1.79194	0.895971	−	0.444113i	$-0.146481\pi$
$569$	42.7445	1.79194	0.895971	+	0.444113i	$0.146481\pi$
$570$	3.14542	0.131747
$571$	−29.5201	−1.23538	−0.617688	−	0.786423i	$-0.711930\pi$
$571$	−29.5201	−1.23538	−0.617688	+	0.786423i	$0.711930\pi$
$572$	5.20519	0.217640
$573$	−20.7174	−0.865480
$574$	21.2661	0.887631
$575$	−4.71150	−0.196483
$576$	−12.9677	−0.540320
$577$	31.3969	1.30707	0.653535	−	0.756896i	$-0.273285\pi$
$577$	31.3969	1.30707	0.653535	+	0.756896i	$0.273285\pi$
$578$	11.8650	0.493521
$579$	8.55796	0.355657
$580$	−1.59614	−0.0662761
$581$	−24.5980	−1.02049
$582$	16.5393	0.685578
$583$	11.5030	0.476406
$584$	−2.21514	−0.0916633
$585$	0.842100	0.0348166
$586$	−19.7203	−0.814640
$587$	44.3332	1.82983	0.914913	−	0.403652i	$-0.132259\pi$
$587$	44.3332	1.82983	0.914913	+	0.403652i	$0.132259\pi$
$588$	−10.2717	−0.423596
$589$	5.94136	0.244810
$590$	10.5419	0.434002
$591$	5.84888	0.240591
$592$	−1.83458	−0.0754008
$593$	−7.80918	−0.320685	−0.160342	−	0.987061i	$-0.551260\pi$
$593$	−7.80918	−0.320685	−0.160342	+	0.987061i	$0.551260\pi$
$594$	−2.49110	−0.102211
$595$	3.45527	0.141652
$596$	59.8098	2.44991
$597$	9.16433	0.375071
$598$	−3.49579	−0.142954
$599$	−26.4951	−1.08256	−0.541280	−	0.840843i	$-0.682060\pi$
$599$	−26.4951	−1.08256	−0.541280	+	0.840843i	$0.682060\pi$
$600$	10.2078	0.416731
$601$	44.4503	1.81317	0.906583	−	0.422027i	$-0.138681\pi$
$601$	44.4503	1.81317	0.906583	+	0.422027i	$0.138681\pi$
$602$	−42.1118	−1.71635
$603$	−7.67562	−0.312575
$604$	1.10143	0.0448166
$605$	−5.23787	−0.212950
$606$	6.24555	0.253708
$607$	−31.2745	−1.26939	−0.634697	−	0.772761i	$-0.718875\pi$
$607$	−31.2745	−1.26939	−0.634697	+	0.772761i	$0.718875\pi$
$608$	−17.8954	−0.725753
$609$	1.88241	0.0762792
$610$	4.46819	0.180912
$611$	−9.51515	−0.384942
$612$	−10.1554	−0.410509
$613$	8.39427	0.339041	0.169521	−	0.985527i	$-0.445778\pi$
$613$	8.39427	0.339041	0.169521	+	0.985527i	$0.445778\pi$
$614$	−12.3153	−0.497007
$615$	2.72140	0.109737
$616$	4.55646	0.183585
$617$	9.87343	0.397489	0.198745	−	0.980051i	$-0.436314\pi$
$617$	9.87343	0.397489	0.198745	+	0.980051i	$0.436314\pi$
$618$	−22.3258	−0.898074
$619$	36.9182	1.48387	0.741935	−	0.670472i	$-0.233908\pi$
$619$	36.9182	1.48387	0.741935	+	0.670472i	$0.233908\pi$
$620$	−3.61077	−0.145012
$621$	1.00000	0.0401286
$622$	−0.147774	−0.00592521
$623$	24.7503	0.991599
$624$	−1.74419	−0.0698236
$625$	20.7558	0.830232
$626$	−39.6411	−1.58438
$627$	−2.93426	−0.117183
$628$	−20.8920	−0.833682
$629$	−5.63552	−0.224703
$630$	2.25442	0.0898184
$631$	15.9457	0.634788	0.317394	−	0.948294i	$-0.397192\pi$
$631$	15.9457	0.634788	0.317394	+	0.948294i	$0.397192\pi$
$632$	−2.69005	−0.107005
$633$	−0.0926588	−0.00368286
$634$	18.1154	0.719455
$635$	2.32734	0.0923575
$636$	30.5966	1.21323
$637$	−5.41918	−0.214716
$638$	2.49110	0.0986238
$639$	−2.43146	−0.0961871
$640$	8.21090	0.324564
$641$	−2.07492	−0.0819542	−0.0409771	−	0.999160i	$-0.513047\pi$
$641$	−2.07492	−0.0819542	−0.0409771	+	0.999160i	$0.513047\pi$
$642$	11.7139	0.462312
$643$	7.94610	0.313364	0.156682	−	0.987649i	$-0.449920\pi$
$643$	7.94610	0.313364	0.156682	+	0.987649i	$0.449920\pi$
$644$	−5.59392	−0.220431
$645$	−5.38899	−0.212191
$646$	−20.0127	−0.787390
$647$	16.9460	0.666217	0.333109	−	0.942888i	$-0.391902\pi$
$647$	16.9460	0.666217	0.333109	+	0.942888i	$0.391902\pi$
$648$	−2.16657	−0.0851108
$649$	−9.83417	−0.386025
$650$	16.4704	0.646024
$651$	4.25837	0.166899
$652$	−59.2653	−2.32101
$653$	21.8874	0.856520	0.428260	−	0.903656i	$-0.359127\pi$
$653$	21.8874	0.856520	0.428260	+	0.903656i	$0.359127\pi$
$654$	11.3421	0.443510
$655$	10.3990	0.406322
$656$	−5.63667	−0.220075
$657$	1.02242	0.0398884
$658$	−25.4734	−0.993057
$659$	28.5542	1.11231	0.556157	−	0.831077i	$-0.312275\pi$
$659$	28.5542	1.11231	0.556157	+	0.831077i	$0.312275\pi$
$660$	1.78325	0.0694128
$661$	−17.1280	−0.666202	−0.333101	−	0.942891i	$-0.608095\pi$
$661$	−17.1280	−0.666202	−0.333101	+	0.942891i	$0.608095\pi$
$662$	−45.1215	−1.75370
$663$	−5.35786	−0.208082
$664$	−28.3111	−1.09868
$665$	2.65547	0.102975
$666$	−3.67695	−0.142479
$667$	−1.00000	−0.0387202
$668$	−36.9125	−1.42819
$669$	−12.8223	−0.495738
$670$	9.19251	0.355138
$671$	−4.16822	−0.160912
$672$	−12.8262	−0.494781
$673$	5.47704	0.211124	0.105562	−	0.994413i	$-0.466336\pi$
$673$	5.47704	0.211124	0.105562	+	0.994413i	$0.466336\pi$
$674$	−42.5342	−1.63836
$675$	−4.71150	−0.181346
$676$	−31.3273	−1.20490
$677$	−42.4886	−1.63297	−0.816485	−	0.577367i	$-0.804080\pi$
$677$	−42.4886	−1.63297	−0.816485	+	0.577367i	$0.804080\pi$
$678$	−40.9813	−1.57388
$679$	13.9631	0.535855
$680$	3.97685	0.152505
$681$	14.6393	0.560978
$682$	5.63535	0.215789
$683$	−25.1897	−0.963857	−0.481929	−	0.876210i	$-0.660064\pi$
$683$	−25.1897	−0.963857	−0.481929	+	0.876210i	$0.660064\pi$
$684$	−7.80475	−0.298422
$685$	−5.49753	−0.210050
$686$	−43.8888	−1.67568
$687$	−24.1483	−0.921316
$688$	11.1619	0.425543
$689$	16.1423	0.614973
$690$	−1.19762	−0.0455928
$691$	5.79765	0.220553	0.110277	−	0.993901i	$-0.464826\pi$
$691$	5.79765	0.220553	0.110277	+	0.993901i	$0.464826\pi$
$692$	−37.2865	−1.41742
$693$	−2.10308	−0.0798893
$694$	65.7832	2.49710
$695$	−0.155341	−0.00589241
$696$	2.16657	0.0821235
$697$	−17.3149	−0.655848
$698$	25.9270	0.981351
$699$	16.5564	0.626221
$700$	26.3558	0.996154
$701$	13.4101	0.506494	0.253247	−	0.967402i	$-0.418501\pi$
$701$	13.4101	0.506494	0.253247	+	0.967402i	$0.418501\pi$
$702$	−3.49579	−0.131940
$703$	−4.33106	−0.163349
$704$	−14.4878	−0.546030
$705$	−3.25980	−0.122771
$706$	0.780022	0.0293565
$707$	5.27271	0.198301
$708$	−26.1576	−0.983064
$709$	−18.0256	−0.676965	−0.338482	−	0.940973i	$-0.609914\pi$
$709$	−18.0256	−0.676965	−0.338482	+	0.940973i	$0.609914\pi$
$710$	2.91198	0.109285
$711$	1.24162	0.0465644
$712$	28.4864	1.06757
$713$	−2.26219	−0.0847196
$714$	−14.3438	−0.536802
$715$	0.940816	0.0351845
$716$	−69.5784	−2.60027
$717$	−18.3128	−0.683902
$718$	39.0165	1.45608
$719$	−20.6072	−0.768518	−0.384259	−	0.923225i	$-0.625543\pi$
$719$	−20.6072	−0.768518	−0.384259	+	0.923225i	$0.625543\pi$
$720$	−0.597544	−0.0222691
$721$	−18.8482	−0.701944
$722$	26.9844	1.00426
$723$	16.0413	0.596581
$724$	−29.8754	−1.11031
$725$	4.71150	0.174981
$726$	21.7439	0.806990
$727$	−8.38118	−0.310841	−0.155420	−	0.987848i	$-0.549673\pi$
$727$	−8.38118	−0.310841	−0.155420	+	0.987848i	$0.549673\pi$
$728$	6.39413	0.236982
$729$	1.00000	0.0370370
$730$	−1.22448	−0.0453199
$731$	34.2874	1.26817
$732$	−11.0869	−0.409785
$733$	−9.51389	−0.351404	−0.175702	−	0.984443i	$-0.556219\pi$
$733$	−9.51389	−0.351404	−0.175702	+	0.984443i	$0.556219\pi$
$734$	75.7768	2.79697
$735$	−1.85656	−0.0684802
$736$	6.81370	0.251156
$737$	−8.57539	−0.315879
$738$	−11.2973	−0.415858
$739$	−31.0800	−1.14330	−0.571648	−	0.820499i	$-0.693696\pi$
$739$	−31.0800	−1.14330	−0.571648	+	0.820499i	$0.693696\pi$
$740$	2.63213	0.0967590
$741$	−4.11767	−0.151267
$742$	43.2153	1.58648
$743$	45.6581	1.67503	0.837517	−	0.546412i	$-0.184007\pi$
$743$	45.6581	1.67503	0.837517	+	0.546412i	$0.184007\pi$
$744$	4.90118	0.179686
$745$	10.8104	0.396062
$746$	−44.5844	−1.63235
$747$	13.0672	0.478106
$748$	−11.3459	−0.414847
$749$	9.88932	0.361348
$750$	11.6307	0.424695
$751$	−30.5101	−1.11333	−0.556664	−	0.830737i	$-0.687919\pi$
$751$	−30.5101	−1.11333	−0.556664	+	0.830737i	$0.687919\pi$
$752$	6.75183	0.246214
$753$	−16.2544	−0.592342
$754$	3.49579	0.127309
$755$	0.199079	0.00724524
$756$	−5.59392	−0.203449
$757$	−30.5168	−1.10915	−0.554576	−	0.832133i	$-0.687120\pi$
$757$	−30.5168	−1.10915	−0.554576	+	0.832133i	$0.687120\pi$
$758$	−51.4563	−1.86898
$759$	1.11723	0.0405527
$760$	3.05632	0.110864
$761$	−20.6725	−0.749377	−0.374689	−	0.927151i	$-0.622250\pi$
$761$	−20.6725	−0.749377	−0.374689	+	0.927151i	$0.622250\pi$
$762$	−9.66141	−0.349996
$763$	9.57537	0.346652
$764$	−61.5652	−2.22735
$765$	−1.83555	−0.0663645
$766$	−73.2611	−2.64703
$767$	−13.8004	−0.498303
$768$	−8.15037	−0.294101
$769$	32.3606	1.16695	0.583476	−	0.812130i	$-0.301692\pi$
$769$	32.3606	1.16695	0.583476	+	0.812130i	$0.301692\pi$
$770$	2.51870	0.0907676
$771$	2.52528	0.0909457
$772$	25.4315	0.915299
$773$	8.63105	0.310437	0.155219	−	0.987880i	$-0.450392\pi$
$773$	8.63105	0.310437	0.155219	+	0.987880i	$0.450392\pi$
$774$	22.3712	0.804116
$775$	10.6583	0.382858
$776$	16.0709	0.576910
$777$	−3.10421	−0.111363
$778$	−31.0719	−1.11398
$779$	−13.3070	−0.476772
$780$	2.50245	0.0896020
$781$	−2.71649	−0.0972037
$782$	7.61989	0.272487
$783$	−1.00000	−0.0357371
$784$	3.84538	0.137335
$785$	−3.77614	−0.134776
$786$	−43.1691	−1.53979
$787$	17.5702	0.626310	0.313155	−	0.949702i	$-0.398614\pi$
$787$	17.5702	0.626310	0.313155	+	0.949702i	$0.398614\pi$
$788$	17.3810	0.619171
$789$	−28.6908	−1.02142
$790$	−1.48700	−0.0529049
$791$	−34.5978	−1.23016
$792$	−2.42054	−0.0860102
$793$	−5.84931	−0.207715
$794$	−31.0539	−1.10206
$795$	5.53020	0.196136
$796$	27.2334	0.965262
$797$	15.4807	0.548355	0.274178	−	0.961679i	$-0.411594\pi$
$797$	15.4807	0.548355	0.274178	+	0.961679i	$0.411594\pi$
$798$	−11.0236	−0.390231
$799$	20.7405	0.733745
$800$	−32.1028	−1.13501
$801$	−13.1482	−0.464568
$802$	−11.3190	−0.399686
$803$	1.14227	0.0403100
$804$	−22.8094	−0.804427
$805$	−1.01108	−0.0356358
$806$	7.90814	0.278552
$807$	−18.4710	−0.650211
$808$	6.06864	0.213494
$809$	−19.9422	−0.701131	−0.350565	−	0.936538i	$-0.614011\pi$
$809$	−19.9422	−0.701131	−0.350565	+	0.936538i	$0.614011\pi$
$810$	−1.19762	−0.0420803
$811$	−24.0964	−0.846139	−0.423069	−	0.906097i	$-0.639047\pi$
$811$	−24.0964	−0.846139	−0.423069	+	0.906097i	$0.639047\pi$
$812$	5.59392	0.196308
$813$	−7.71437	−0.270555
$814$	−4.10798	−0.143985
$815$	−10.7120	−0.375223
$816$	3.80187	0.133092
$817$	26.3509	0.921901
$818$	46.5137	1.62631
$819$	−2.95127	−0.103126
$820$	8.08710	0.282414
$821$	29.8257	1.04092	0.520461	−	0.853885i	$-0.325760\pi$
$821$	29.8257	1.04092	0.520461	+	0.853885i	$0.325760\pi$
$822$	22.8218	0.796001
$823$	−4.38398	−0.152816	−0.0764080	−	0.997077i	$-0.524345\pi$
$823$	−4.38398	−0.152816	−0.0764080	+	0.997077i	$0.524345\pi$
$824$	−21.6934	−0.755725
$825$	−5.26381	−0.183262
$826$	−36.9456	−1.28550
$827$	33.8262	1.17625	0.588126	−	0.808769i	$-0.299866\pi$
$827$	33.8262	1.17625	0.588126	+	0.808769i	$0.299866\pi$
$828$	2.97167	0.103273
$829$	19.9346	0.692358	0.346179	−	0.938169i	$-0.387479\pi$
$829$	19.9346	0.692358	0.346179	+	0.938169i	$0.387479\pi$
$830$	−15.6497	−0.543208
$831$	−0.702588	−0.0243725
$832$	−20.3309	−0.704848
$833$	11.8124	0.409274
$834$	0.644863	0.0223298
$835$	−6.67179	−0.230887
$836$	−8.71966	−0.301576
$837$	−2.26219	−0.0781926
$838$	−7.28584	−0.251685
$839$	−9.52467	−0.328828	−0.164414	−	0.986391i	$-0.552573\pi$
$839$	−9.52467	−0.328828	−0.164414	+	0.986391i	$0.552573\pi$
$840$	2.19057	0.0755817
$841$	1.00000	0.0344828
$842$	4.39739	0.151544
$843$	2.46040	0.0847408
$844$	−0.275352	−0.00947800
$845$	−5.66227	−0.194788
$846$	13.5323	0.465251
$847$	18.3569	0.630751
$848$	−11.4544	−0.393345
$849$	−15.1893	−0.521294
$850$	−35.9011	−1.23140
$851$	1.64906	0.0565291
$852$	−7.22551	−0.247542
$853$	45.9120	1.57200	0.785998	−	0.618229i	$-0.212150\pi$
$853$	45.9120	1.57200	0.785998	+	0.618229i	$0.212150\pi$
$854$	−15.6594	−0.535855
$855$	−1.41068	−0.0482441
$856$	11.3821	0.389033
$857$	54.7299	1.86954	0.934768	−	0.355258i	$-0.115607\pi$
$857$	54.7299	1.86954	0.934768	+	0.355258i	$0.115607\pi$
$858$	−3.90559	−0.133335
$859$	−39.0054	−1.33085	−0.665423	−	0.746466i	$-0.731749\pi$
$859$	−39.0054	−1.33085	−0.665423	+	0.746466i	$0.731749\pi$
$860$	−16.0143	−0.546084
$861$	−9.53756	−0.325039
$862$	8.09892	0.275850
$863$	14.2092	0.483685	0.241843	−	0.970316i	$-0.422248\pi$
$863$	14.2092	0.483685	0.241843	+	0.970316i	$0.422248\pi$
$864$	6.81370	0.231807
$865$	−6.73938	−0.229146
$866$	2.93305	0.0996692
$867$	−5.32130	−0.180721
$868$	12.6545	0.429521
$869$	1.38717	0.0470565
$870$	1.19762	0.0406033
$871$	−12.0339	−0.407754
$872$	11.0208	0.373211
$873$	−7.41766	−0.251050
$874$	5.85610	0.198086
$875$	9.81908	0.331946
$876$	3.03830	0.102655
$877$	17.7516	0.599431	0.299715	−	0.954029i	$-0.403108\pi$
$877$	17.7516	0.599431	0.299715	+	0.954029i	$0.403108\pi$
$878$	−38.3311	−1.29361
$879$	8.84429	0.298311
$880$	−0.667591	−0.0225045
$881$	10.8019	0.363926	0.181963	−	0.983305i	$-0.441755\pi$
$881$	10.8019	0.363926	0.181963	+	0.983305i	$0.441755\pi$
$882$	7.70710	0.259511
$883$	−23.4523	−0.789232	−0.394616	−	0.918846i	$-0.629122\pi$
$883$	−23.4523	−0.789232	−0.394616	+	0.918846i	$0.629122\pi$
$884$	−15.9218	−0.535509
$885$	−4.72788	−0.158926
$886$	21.3959	0.718809
$887$	−39.1075	−1.31310	−0.656550	−	0.754283i	$-0.727985\pi$
$887$	−39.1075	−1.31310	−0.656550	+	0.754283i	$0.727985\pi$
$888$	−3.57280	−0.119895
$889$	−8.15651	−0.273560
$890$	15.7466	0.527826
$891$	1.11723	0.0374284
$892$	−38.1036	−1.27580
$893$	15.9396	0.533400
$894$	−44.8769	−1.50091
$895$	−12.5760	−0.420369
$896$	−28.7764	−0.961351
$897$	1.56781	0.0523478
$898$	−43.5898	−1.45461
$899$	2.26219	0.0754482
$900$	−14.0011	−0.466702
$901$	−35.1859	−1.17221
$902$	−12.6216	−0.420253
$903$	18.8865	0.628505
$904$	−39.8204	−1.32441
$905$	−5.39986	−0.179497
$906$	−0.826433	−0.0274564
$907$	0.854437	0.0283711	0.0141856	−	0.999899i	$-0.495484\pi$
$907$	0.854437	0.0283711	0.0141856	+	0.999899i	$0.495484\pi$
$908$	43.5032	1.44370
$909$	−2.80104	−0.0929047
$910$	3.53452	0.117168
$911$	27.2030	0.901276	0.450638	−	0.892707i	$-0.351197\pi$
$911$	27.2030	0.901276	0.450638	+	0.892707i	$0.351197\pi$
$912$	2.92185	0.0967520
$913$	14.5991	0.483158
$914$	27.4296	0.907290
$915$	−2.00392	−0.0662475
$916$	−71.7609	−2.37105
$917$	−36.4449	−1.20352
$918$	7.61989	0.251494
$919$	−46.5672	−1.53611	−0.768055	−	0.640384i	$-0.778775\pi$
$919$	−46.5672	−1.53611	−0.768055	+	0.640384i	$0.778775\pi$
$920$	−1.16370	−0.0383661
$921$	5.52326	0.181997
$922$	75.3556	2.48170
$923$	−3.81208	−0.125476
$924$	−6.24966	−0.205599
$925$	−7.76956	−0.255461
$926$	−73.4950	−2.41520
$927$	10.0128	0.328863
$928$	−6.81370	−0.223671
$929$	31.6499	1.03840	0.519200	−	0.854653i	$-0.326230\pi$
$929$	31.6499	1.03840	0.519200	+	0.854653i	$0.326230\pi$
$930$	2.70925	0.0888399
$931$	9.07814	0.297524
$932$	49.2003	1.61161
$933$	0.0662747	0.00216974
$934$	25.8186	0.844812
$935$	−2.05072	−0.0670659
$936$	−3.39677	−0.111027
$937$	17.7619	0.580255	0.290128	−	0.956988i	$-0.406302\pi$
$937$	17.7619	0.580255	0.290128	+	0.956988i	$0.406302\pi$
$938$	−32.2166	−1.05191
$939$	17.7785	0.580179
$940$	−9.68706	−0.315957
$941$	52.0711	1.69747	0.848734	−	0.528820i	$-0.177365\pi$
$941$	52.0711	1.69747	0.848734	+	0.528820i	$0.177365\pi$
$942$	15.6758	0.510746
$943$	5.06667	0.164993
$944$	9.79258	0.318721
$945$	−1.01108	−0.0328903
$946$	24.9937	0.812614
$947$	−7.10267	−0.230806	−0.115403	−	0.993319i	$-0.536816\pi$
$947$	−7.10267	−0.230806	−0.115403	+	0.993319i	$0.536816\pi$
$948$	3.68969	0.119836
$949$	1.60296	0.0520344
$950$	−27.5911	−0.895172
$951$	−8.12451	−0.263455
$952$	−13.9375	−0.451716
$953$	11.9585	0.387373	0.193687	−	0.981063i	$-0.437956\pi$
$953$	11.9585	0.387373	0.193687	+	0.981063i	$0.437956\pi$
$954$	−22.9574	−0.743273
$955$	−11.1277	−0.360083
$956$	−54.4195	−1.76005
$957$	−1.11723	−0.0361148
$958$	−31.7359	−1.02534
$959$	19.2670	0.622163
$960$	−6.96517	−0.224800
$961$	−25.8825	−0.834920
$962$	−5.76478	−0.185864
$963$	−5.25354	−0.169293
$964$	47.6694	1.53533
$965$	4.59663	0.147971
$966$	4.19726	0.135045
$967$	10.3118	0.331604	0.165802	−	0.986159i	$-0.446979\pi$
$967$	10.3118	0.331604	0.165802	+	0.986159i	$0.446979\pi$
$968$	21.1279	0.679078
$969$	8.97542	0.288332
$970$	8.88358	0.285234
$971$	−11.4796	−0.368398	−0.184199	−	0.982889i	$-0.558969\pi$
$971$	−11.4796	−0.368398	−0.184199	+	0.982889i	$0.558969\pi$
$972$	2.97167	0.0953165
$973$	0.544416	0.0174532
$974$	−57.5531	−1.84412
$975$	−7.38676	−0.236566
$976$	4.15060	0.132857
$977$	−12.8478	−0.411036	−0.205518	−	0.978653i	$-0.565888\pi$
$977$	−12.8478	−0.411036	−0.205518	+	0.978653i	$0.565888\pi$
$978$	44.4683	1.42194
$979$	−14.6895	−0.469477
$980$	−5.51709	−0.176237
$981$	−5.08675	−0.162408
$982$	79.2909	2.53027
$983$	1.92074	0.0612622	0.0306311	−	0.999531i	$-0.490248\pi$
$983$	1.92074	0.0612622	0.0306311	+	0.999531i	$0.490248\pi$
$984$	−10.9773	−0.349943
$985$	3.14154	0.100098
$986$	−7.61989	−0.242667
$987$	11.4245	0.363645
$988$	−12.2364	−0.389291
$989$	−10.0332	−0.319036
$990$	−1.33802	−0.0425250
$991$	−2.06517	−0.0656022	−0.0328011	−	0.999462i	$-0.510443\pi$
$991$	−2.06517	−0.0656022	−0.0328011	+	0.999462i	$0.510443\pi$
$992$	−15.4139	−0.489391
$993$	20.2364	0.642182
$994$	−10.2055	−0.323698
$995$	4.92232	0.156048
$996$	38.8316	1.23043
$997$	−40.2717	−1.27542	−0.637709	−	0.770277i	$-0.720118\pi$
$997$	−40.2717	−1.27542	−0.637709	+	0.770277i	$0.720118\pi$
$998$	−34.6625	−1.09722
$999$	1.64906	0.0521740

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.i.1.2	✓	7
3.2	odd	2		6003.2.a.j.1.6		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.i.1.2	✓	7	1.1	even	1	trivial
6003.2.a.j.1.6		7	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2001 = 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.22973 q^{2} +1.00000 q^{3} +2.97167 q^{4} +0.537118 q^{5} -2.22973 q^{6} -1.88241 q^{7} -2.16657 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.22973 q^{2} +1.00000 q^{3} +2.97167 q^{4} +0.537118 q^{5} -2.22973 q^{6} -1.88241 q^{7} -2.16657 q^{8} +1.00000 q^{9} -1.19762 q^{10} +1.11723 q^{11} +2.97167 q^{12} +1.56781 q^{13} +4.19726 q^{14} +0.537118 q^{15} -1.11250 q^{16} -3.41741 q^{17} -2.22973 q^{18} -2.62638 q^{19} +1.59614 q^{20} -1.88241 q^{21} -2.49110 q^{22} +1.00000 q^{23} -2.16657 q^{24} -4.71150 q^{25} -3.49579 q^{26} +1.00000 q^{27} -5.59392 q^{28} -1.00000 q^{29} -1.19762 q^{30} -2.26219 q^{31} +6.81370 q^{32} +1.11723 q^{33} +7.61989 q^{34} -1.01108 q^{35} +2.97167 q^{36} +1.64906 q^{37} +5.85610 q^{38} +1.56781 q^{39} -1.16370 q^{40} +5.06667 q^{41} +4.19726 q^{42} -10.0332 q^{43} +3.32003 q^{44} +0.537118 q^{45} -2.22973 q^{46} -6.06906 q^{47} -1.11250 q^{48} -3.45652 q^{49} +10.5054 q^{50} -3.41741 q^{51} +4.65903 q^{52} +10.2961 q^{53} -2.22973 q^{54} +0.600081 q^{55} +4.07837 q^{56} -2.62638 q^{57} +2.22973 q^{58} -8.80232 q^{59} +1.59614 q^{60} -3.73087 q^{61} +5.04406 q^{62} -1.88241 q^{63} -12.9677 q^{64} +0.842100 q^{65} -2.49110 q^{66} -7.67562 q^{67} -10.1554 q^{68} +1.00000 q^{69} +2.25442 q^{70} -2.43146 q^{71} -2.16657 q^{72} +1.02242 q^{73} -3.67695 q^{74} -4.71150 q^{75} -7.80475 q^{76} -2.10308 q^{77} -3.49579 q^{78} +1.24162 q^{79} -0.597544 q^{80} +1.00000 q^{81} -11.2973 q^{82} +13.0672 q^{83} -5.59392 q^{84} -1.83555 q^{85} +22.3712 q^{86} -1.00000 q^{87} -2.42054 q^{88} -13.1482 q^{89} -1.19762 q^{90} -2.95127 q^{91} +2.97167 q^{92} -2.26219 q^{93} +13.5323 q^{94} -1.41068 q^{95} +6.81370 q^{96} -7.41766 q^{97} +7.70710 q^{98} +1.11723 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 3 q^{2} + 7 q^{3} + 5 q^{4} - 3 q^{5} - 3 q^{6} - 5 q^{7} - 6 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - 3 * q^2 + 7 * q^3 + 5 * q^4 - 3 * q^5 - 3 * q^6 - 5 * q^7 - 6 * q^8 + 7 * q^9	\( 7 q - 3 q^{2} + 7 q^{3} + 5 q^{4} - 3 q^{5} - 3 q^{6} - 5 q^{7} - 6 q^{8} + 7 q^{9} + 3 q^{10} - 4 q^{11} + 5 q^{12} - 18 q^{13} - 2 q^{14} - 3 q^{15} - 7 q^{16} - 3 q^{17} - 3 q^{18} - 4 q^{19} - 2 q^{20} - 5 q^{21} - 26 q^{22} + 7 q^{23} - 6 q^{24} - 8 q^{25} - 7 q^{26} + 7 q^{27} - 6 q^{28} - 7 q^{29} + 3 q^{30} - 22 q^{31} + 5 q^{32} - 4 q^{33} + 9 q^{34} + 3 q^{35} + 5 q^{36} - 25 q^{37} + 14 q^{38} - 18 q^{39} - 10 q^{40} - 13 q^{41} - 2 q^{42} - 2 q^{43} + 4 q^{44} - 3 q^{45} - 3 q^{46} - 25 q^{47} - 7 q^{48} - 8 q^{49} + 19 q^{50} - 3 q^{51} - 12 q^{52} - 5 q^{53} - 3 q^{54} - 15 q^{55} + 18 q^{56} - 4 q^{57} + 3 q^{58} + 11 q^{59} - 2 q^{60} - 33 q^{61} + 28 q^{62} - 5 q^{63} - 14 q^{64} - 2 q^{65} - 26 q^{66} + 8 q^{67} + 12 q^{68} + 7 q^{69} - 22 q^{70} - 6 q^{71} - 6 q^{72} + 15 q^{73} + 34 q^{74} - 8 q^{75} - 28 q^{76} - q^{77} - 7 q^{78} - 15 q^{79} - 12 q^{80} + 7 q^{81} - 14 q^{82} + 21 q^{83} - 6 q^{84} - 28 q^{85} - 12 q^{86} - 7 q^{87} - 13 q^{88} + 8 q^{89} + 3 q^{90} + 6 q^{91} + 5 q^{92} - 22 q^{93} - 35 q^{94} - 25 q^{95} + 5 q^{96} + 13 q^{97} + q^{98} - 4 q^{99}+O(q^{100}) \) 7 * q - 3 * q^2 + 7 * q^3 + 5 * q^4 - 3 * q^5 - 3 * q^6 - 5 * q^7 - 6 * q^8 + 7 * q^9 + 3 * q^10 - 4 * q^11 + 5 * q^12 - 18 * q^13 - 2 * q^14 - 3 * q^15 - 7 * q^16 - 3 * q^17 - 3 * q^18 - 4 * q^19 - 2 * q^20 - 5 * q^21 - 26 * q^22 + 7 * q^23 - 6 * q^24 - 8 * q^25 - 7 * q^26 + 7 * q^27 - 6 * q^28 - 7 * q^29 + 3 * q^30 - 22 * q^31 + 5 * q^32 - 4 * q^33 + 9 * q^34 + 3 * q^35 + 5 * q^36 - 25 * q^37 + 14 * q^38 - 18 * q^39 - 10 * q^40 - 13 * q^41 - 2 * q^42 - 2 * q^43 + 4 * q^44 - 3 * q^45 - 3 * q^46 - 25 * q^47 - 7 * q^48 - 8 * q^49 + 19 * q^50 - 3 * q^51 - 12 * q^52 - 5 * q^53 - 3 * q^54 - 15 * q^55 + 18 * q^56 - 4 * q^57 + 3 * q^58 + 11 * q^59 - 2 * q^60 - 33 * q^61 + 28 * q^62 - 5 * q^63 - 14 * q^64 - 2 * q^65 - 26 * q^66 + 8 * q^67 + 12 * q^68 + 7 * q^69 - 22 * q^70 - 6 * q^71 - 6 * q^72 + 15 * q^73 + 34 * q^74 - 8 * q^75 - 28 * q^76 - q^77 - 7 * q^78 - 15 * q^79 - 12 * q^80 + 7 * q^81 - 14 * q^82 + 21 * q^83 - 6 * q^84 - 28 * q^85 - 12 * q^86 - 7 * q^87 - 13 * q^88 + 8 * q^89 + 3 * q^90 + 6 * q^91 + 5 * q^92 - 22 * q^93 - 35 * q^94 - 25 * q^95 + 5 * q^96 + 13 * q^97 + q^98 - 4 * q^99

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