LMFDB - Embedded newform 2001.2.a.i.1.3

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			1.3
Root			$1.44008$ 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)

$f(q)$	$=$	$q-1.44008 q^{2} +1.00000 q^{3} +0.0738306 q^{4} +0.734622 q^{5} -1.44008 q^{6} +3.73618 q^{7} +2.77384 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.44008 q^{2} +1.00000 q^{3} +0.0738306 q^{4} +0.734622 q^{5} -1.44008 q^{6} +3.73618 q^{7} +2.77384 q^{8} +1.00000 q^{9} -1.05791 q^{10} -2.70213 q^{11} +0.0738306 q^{12} -2.87193 q^{13} -5.38039 q^{14} +0.734622 q^{15} -4.14221 q^{16} -2.75120 q^{17} -1.44008 q^{18} -5.54463 q^{19} +0.0542376 q^{20} +3.73618 q^{21} +3.89128 q^{22} +1.00000 q^{23} +2.77384 q^{24} -4.46033 q^{25} +4.13581 q^{26} +1.00000 q^{27} +0.275844 q^{28} -1.00000 q^{29} -1.05791 q^{30} -10.2606 q^{31} +0.417438 q^{32} -2.70213 q^{33} +3.96194 q^{34} +2.74468 q^{35} +0.0738306 q^{36} -11.4951 q^{37} +7.98471 q^{38} -2.87193 q^{39} +2.03772 q^{40} -1.81028 q^{41} -5.38039 q^{42} +0.181163 q^{43} -0.199500 q^{44} +0.734622 q^{45} -1.44008 q^{46} -6.02453 q^{47} -4.14221 q^{48} +6.95901 q^{49} +6.42323 q^{50} -2.75120 q^{51} -0.212037 q^{52} -0.662081 q^{53} -1.44008 q^{54} -1.98504 q^{55} +10.3635 q^{56} -5.54463 q^{57} +1.44008 q^{58} -0.174372 q^{59} +0.0542376 q^{60} -5.37843 q^{61} +14.7760 q^{62} +3.73618 q^{63} +7.68328 q^{64} -2.10978 q^{65} +3.89128 q^{66} +15.9959 q^{67} -0.203123 q^{68} +1.00000 q^{69} -3.95255 q^{70} +12.0047 q^{71} +2.77384 q^{72} +0.990842 q^{73} +16.5538 q^{74} -4.46033 q^{75} -0.409363 q^{76} -10.0956 q^{77} +4.13581 q^{78} -2.96323 q^{79} -3.04296 q^{80} +1.00000 q^{81} +2.60694 q^{82} +1.08995 q^{83} +0.275844 q^{84} -2.02109 q^{85} -0.260889 q^{86} -1.00000 q^{87} -7.49527 q^{88} +5.21337 q^{89} -1.05791 q^{90} -10.7300 q^{91} +0.0738306 q^{92} -10.2606 q^{93} +8.67580 q^{94} -4.07320 q^{95} +0.417438 q^{96} -3.97122 q^{97} -10.0215 q^{98} -2.70213 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.44008	−1.01829	−0.509145	−	0.860681i	$-0.670038\pi$
$2$	−1.44008	−1.01829	−0.509145	+	0.860681i	$0.670038\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.0738306	0.0369153
$5$	0.734622	0.328533	0.164266	−	0.986416i	$-0.447474\pi$
$5$	0.734622	0.328533	0.164266	+	0.986416i	$0.447474\pi$
$6$	−1.44008	−0.587910
$7$	3.73618	1.41214	0.706071	−	0.708141i	$-0.250466\pi$
$7$	3.73618	1.41214	0.706071	+	0.708141i	$0.250466\pi$
$8$	2.77384	0.980700
$9$	1.00000	0.333333
$10$	−1.05791	−0.334542
$11$	−2.70213	−0.814723	−0.407361	−	0.913267i	$-0.633551\pi$
$11$	−2.70213	−0.814723	−0.407361	+	0.913267i	$0.633551\pi$
$12$	0.0738306	0.0213131
$13$	−2.87193	−0.796531	−0.398265	−	0.917270i	$-0.630388\pi$
$13$	−2.87193	−0.796531	−0.398265	+	0.917270i	$0.630388\pi$
$14$	−5.38039	−1.43797
$15$	0.734622	0.189678
$16$	−4.14221	−1.03555
$17$	−2.75120	−0.667263	−0.333632	−	0.942704i	$-0.608274\pi$
$17$	−2.75120	−0.667263	−0.333632	+	0.942704i	$0.608274\pi$
$18$	−1.44008	−0.339430
$19$	−5.54463	−1.27202	−0.636012	−	0.771679i	$-0.719417\pi$
$19$	−5.54463	−1.27202	−0.636012	+	0.771679i	$0.719417\pi$
$20$	0.0542376	0.0121279
$21$	3.73618	0.815300
$22$	3.89128	0.829625
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	2.77384	0.566207
$25$	−4.46033	−0.892066
$26$	4.13581	0.811099
$27$	1.00000	0.192450
$28$	0.275844	0.0521296
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−1.05791	−0.193148
$31$	−10.2606	−1.84285	−0.921425	−	0.388557i	$-0.872974\pi$
$31$	−10.2606	−1.84285	−0.921425	+	0.388557i	$0.872974\pi$
$32$	0.417438	0.0737933
$33$	−2.70213	−0.470380
$34$	3.96194	0.679468
$35$	2.74468	0.463935
$36$	0.0738306	0.0123051
$37$	−11.4951	−1.88978	−0.944888	−	0.327394i	$-0.893829\pi$
$37$	−11.4951	−1.88978	−0.944888	+	0.327394i	$0.893829\pi$
$38$	7.98471	1.29529
$39$	−2.87193	−0.459877
$40$	2.03772	0.322192
$41$	−1.81028	−0.282718	−0.141359	−	0.989958i	$-0.545147\pi$
$41$	−1.81028	−0.282718	−0.141359	+	0.989958i	$0.545147\pi$
$42$	−5.38039	−0.830212
$43$	0.181163	0.0276271	0.0138136	−	0.999905i	$-0.495603\pi$
$43$	0.181163	0.0276271	0.0138136	+	0.999905i	$0.495603\pi$
$44$	−0.199500	−0.0300757
$45$	0.734622	0.109511
$46$	−1.44008	−0.212328
$47$	−6.02453	−0.878768	−0.439384	−	0.898299i	$-0.644803\pi$
$47$	−6.02453	−0.878768	−0.439384	+	0.898299i	$0.644803\pi$
$48$	−4.14221	−0.597877
$49$	6.95901	0.994144
$50$	6.42323	0.908382
$51$	−2.75120	−0.385245
$52$	−0.212037	−0.0294042
$53$	−0.662081	−0.0909438	−0.0454719	−	0.998966i	$-0.514479\pi$
$53$	−0.662081	−0.0909438	−0.0454719	+	0.998966i	$0.514479\pi$
$54$	−1.44008	−0.195970
$55$	−1.98504	−0.267663
$56$	10.3635	1.38489
$57$	−5.54463	−0.734404
$58$	1.44008	0.189092
$59$	−0.174372	−0.0227013	−0.0113506	−	0.999936i	$-0.503613\pi$
$59$	−0.174372	−0.0227013	−0.0113506	+	0.999936i	$0.503613\pi$
$60$	0.0542376	0.00700204
$61$	−5.37843	−0.688637	−0.344318	−	0.938853i	$-0.611890\pi$
$61$	−5.37843	−0.688637	−0.344318	+	0.938853i	$0.611890\pi$
$62$	14.7760	1.87656
$63$	3.73618	0.470714
$64$	7.68328	0.960410
$65$	−2.10978	−0.261686
$66$	3.89128	0.478984
$67$	15.9959	1.95421	0.977106	−	0.212754i	$-0.0682432\pi$
$67$	15.9959	1.95421	0.977106	+	0.212754i	$0.0682432\pi$
$68$	−0.203123	−0.0246322
$69$	1.00000	0.120386
$70$	−3.95255	−0.472420
$71$	12.0047	1.42469	0.712347	−	0.701828i	$-0.247632\pi$
$71$	12.0047	1.42469	0.712347	+	0.701828i	$0.247632\pi$
$72$	2.77384	0.326900
$73$	0.990842	0.115969	0.0579847	−	0.998317i	$-0.481533\pi$
$73$	0.990842	0.115969	0.0579847	+	0.998317i	$0.481533\pi$
$74$	16.5538	1.92434
$75$	−4.46033	−0.515035
$76$	−0.409363	−0.0469572
$77$	−10.0956	−1.15050
$78$	4.13581	0.468288
$79$	−2.96323	−0.333390	−0.166695	−	0.986009i	$-0.553309\pi$
$79$	−2.96323	−0.333390	−0.166695	+	0.986009i	$0.553309\pi$
$80$	−3.04296	−0.340213
$81$	1.00000	0.111111
$82$	2.60694	0.287889
$83$	1.08995	0.119638	0.0598189	−	0.998209i	$-0.480948\pi$
$83$	1.08995	0.119638	0.0598189	+	0.998209i	$0.480948\pi$
$84$	0.275844	0.0300971
$85$	−2.02109	−0.219218
$86$	−0.260889	−0.0281324
$87$	−1.00000	−0.107211
$88$	−7.49527	−0.798999
$89$	5.21337	0.552617	0.276308	−	0.961069i	$-0.410889\pi$
$89$	5.21337	0.552617	0.276308	+	0.961069i	$0.410889\pi$
$90$	−1.05791	−0.111514
$91$	−10.7300	−1.12481
$92$	0.0738306	0.00769737
$93$	−10.2606	−1.06397
$94$	8.67580	0.894841
$95$	−4.07320	−0.417902
$96$	0.417438	0.0426046
$97$	−3.97122	−0.403217	−0.201608	−	0.979466i	$-0.564617\pi$
$97$	−3.97122	−0.403217	−0.201608	+	0.979466i	$0.564617\pi$
$98$	−10.0215	−1.01233
$99$	−2.70213	−0.271574
$100$	−0.329309	−0.0329309
$101$	18.4855	1.83938	0.919688	−	0.392650i	$-0.128442\pi$
$101$	18.4855	1.83938	0.919688	+	0.392650i	$0.128442\pi$
$102$	3.96194	0.392291
$103$	−2.24948	−0.221648	−0.110824	−	0.993840i	$-0.535349\pi$
$103$	−2.24948	−0.221648	−0.110824	+	0.993840i	$0.535349\pi$
$104$	−7.96627	−0.781157
$105$	2.74468	0.267853
$106$	0.953449	0.0926072
$107$	−12.9231	−1.24932	−0.624660	−	0.780897i	$-0.714762\pi$
$107$	−12.9231	−1.24932	−0.624660	+	0.780897i	$0.714762\pi$
$108$	0.0738306	0.00710435
$109$	16.2725	1.55863	0.779313	−	0.626635i	$-0.215568\pi$
$109$	16.2725	1.55863	0.779313	+	0.626635i	$0.215568\pi$
$110$	2.85862	0.272559
$111$	−11.4951	−1.09106
$112$	−15.4760	−1.46235
$113$	−11.3227	−1.06515	−0.532573	−	0.846384i	$-0.678775\pi$
$113$	−11.3227	−1.06515	−0.532573	+	0.846384i	$0.678775\pi$
$114$	7.98471	0.747836
$115$	0.734622	0.0685038
$116$	−0.0738306	−0.00685500
$117$	−2.87193	−0.265510
$118$	0.251109	0.0231165
$119$	−10.2790	−0.942270
$120$	2.03772	0.186018
$121$	−3.69849	−0.336227
$122$	7.74536	0.701232
$123$	−1.81028	−0.163227
$124$	−0.757543	−0.0680294
$125$	−6.94976	−0.621606
$126$	−5.38039	−0.479323
$127$	−9.54485	−0.846968	−0.423484	−	0.905903i	$-0.639193\pi$
$127$	−9.54485	−0.846968	−0.423484	+	0.905903i	$0.639193\pi$
$128$	−11.8994	−1.05177
$129$	0.181163	0.0159505
$130$	3.03826	0.266473
$131$	15.3632	1.34229	0.671146	−	0.741326i	$-0.265803\pi$
$131$	15.3632	1.34229	0.671146	+	0.741326i	$0.265803\pi$
$132$	−0.199500	−0.0173642
$133$	−20.7157	−1.79628
$134$	−23.0354	−1.98995
$135$	0.734622	0.0632262
$136$	−7.63137	−0.654385
$137$	15.4197	1.31739	0.658697	−	0.752408i	$-0.271108\pi$
$137$	15.4197	1.31739	0.658697	+	0.752408i	$0.271108\pi$
$138$	−1.44008	−0.122588
$139$	−16.2808	−1.38092	−0.690461	−	0.723370i	$-0.742592\pi$
$139$	−16.2808	−1.38092	−0.690461	+	0.723370i	$0.742592\pi$
$140$	0.202641	0.0171263
$141$	−6.02453	−0.507357
$142$	−17.2877	−1.45075
$143$	7.76033	0.648952
$144$	−4.14221	−0.345184
$145$	−0.734622	−0.0610070
$146$	−1.42689	−0.118090
$147$	6.95901	0.573969
$148$	−0.848687	−0.0697617
$149$	−11.2442	−0.921159	−0.460580	−	0.887618i	$-0.652358\pi$
$149$	−11.2442	−0.921159	−0.460580	+	0.887618i	$0.652358\pi$
$150$	6.42323	0.524455
$151$	−13.0268	−1.06011	−0.530053	−	0.847965i	$-0.677828\pi$
$151$	−13.0268	−1.06011	−0.530053	+	0.847965i	$0.677828\pi$
$152$	−15.3799	−1.24747
$153$	−2.75120	−0.222421
$154$	14.5385	1.17155
$155$	−7.53762	−0.605436
$156$	−0.212037	−0.0169765
$157$	5.40186	0.431116	0.215558	−	0.976491i	$-0.430843\pi$
$157$	5.40186	0.431116	0.215558	+	0.976491i	$0.430843\pi$
$158$	4.26729	0.339488
$159$	−0.662081	−0.0525064
$160$	0.306659	0.0242435
$161$	3.73618	0.294452
$162$	−1.44008	−0.113143
$163$	5.91249	0.463102	0.231551	−	0.972823i	$-0.425620\pi$
$163$	5.91249	0.463102	0.231551	+	0.972823i	$0.425620\pi$
$164$	−0.133654	−0.0104366
$165$	−1.98504	−0.154535
$166$	−1.56962	−0.121826
$167$	−0.341562	−0.0264308	−0.0132154	−	0.999913i	$-0.504207\pi$
$167$	−0.341562	−0.0264308	−0.0132154	+	0.999913i	$0.504207\pi$
$168$	10.3635	0.799565
$169$	−4.75201	−0.365539
$170$	2.91053	0.223227
$171$	−5.54463	−0.424008
$172$	0.0133754	0.00101986
$173$	13.8093	1.04990	0.524950	−	0.851133i	$-0.324084\pi$
$173$	13.8093	1.04990	0.524950	+	0.851133i	$0.324084\pi$
$174$	1.44008	0.109172
$175$	−16.6646	−1.25972
$176$	11.1928	0.843688
$177$	−0.174372	−0.0131066
$178$	−7.50768	−0.562724
$179$	15.3349	1.14619	0.573093	−	0.819490i	$-0.305743\pi$
$179$	15.3349	1.14619	0.573093	+	0.819490i	$0.305743\pi$
$180$	0.0542376	0.00404263
$181$	−4.64338	−0.345139	−0.172570	−	0.984997i	$-0.555207\pi$
$181$	−4.64338	−0.345139	−0.172570	+	0.984997i	$0.555207\pi$
$182$	15.4521	1.14539
$183$	−5.37843	−0.397585
$184$	2.77384	0.204490
$185$	−8.44452	−0.620853
$186$	14.7760	1.08343
$187$	7.43409	0.543635
$188$	−0.444795	−0.0324400
$189$	3.73618	0.271767
$190$	5.86574	0.425545
$191$	9.85469	0.713060	0.356530	−	0.934284i	$-0.383960\pi$
$191$	9.85469	0.713060	0.356530	+	0.934284i	$0.383960\pi$
$192$	7.68328	0.554493
$193$	−21.2787	−1.53167	−0.765837	−	0.643035i	$-0.777675\pi$
$193$	−21.2787	−1.53167	−0.765837	+	0.643035i	$0.777675\pi$
$194$	5.71888	0.410592
$195$	−2.10978	−0.151085
$196$	0.513788	0.0366991
$197$	9.61747	0.685216	0.342608	−	0.939478i	$-0.388690\pi$
$197$	9.61747	0.685216	0.342608	+	0.939478i	$0.388690\pi$
$198$	3.89128	0.276542
$199$	4.39951	0.311873	0.155936	−	0.987767i	$-0.450161\pi$
$199$	4.39951	0.311873	0.155936	+	0.987767i	$0.450161\pi$
$200$	−12.3722	−0.874849
$201$	15.9959	1.12826
$202$	−26.6206	−1.87302
$203$	−3.73618	−0.262228
$204$	−0.203123	−0.0142214
$205$	−1.32987	−0.0928821
$206$	3.23944	0.225702
$207$	1.00000	0.0695048
$208$	11.8961	0.824849
$209$	14.9823	1.03635
$210$	−3.95255	−0.272752
$211$	1.95120	0.134326	0.0671630	−	0.997742i	$-0.478605\pi$
$211$	1.95120	0.134326	0.0671630	+	0.997742i	$0.478605\pi$
$212$	−0.0488818	−0.00335722
$213$	12.0047	0.822547
$214$	18.6103	1.27217
$215$	0.133086	0.00907641
$216$	2.77384	0.188736
$217$	−38.3352	−2.60236
$218$	−23.4337	−1.58713
$219$	0.990842	0.0669549
$220$	−0.146557	−0.00988087
$221$	7.90125	0.531495
$222$	16.5538	1.11102
$223$	5.60600	0.375406	0.187703	−	0.982226i	$-0.439896\pi$
$223$	5.60600	0.375406	0.187703	+	0.982226i	$0.439896\pi$
$224$	1.55962	0.104207
$225$	−4.46033	−0.297355
$226$	16.3055	1.08463
$227$	−5.99730	−0.398055	−0.199027	−	0.979994i	$-0.563778\pi$
$227$	−5.99730	−0.398055	−0.199027	+	0.979994i	$0.563778\pi$
$228$	−0.409363	−0.0271107
$229$	−14.2127	−0.939199	−0.469599	−	0.882880i	$-0.655602\pi$
$229$	−14.2127	−0.939199	−0.469599	+	0.882880i	$0.655602\pi$
$230$	−1.05791	−0.0697568
$231$	−10.0956	−0.664244
$232$	−2.77384	−0.182111
$233$	−28.3893	−1.85985	−0.929923	−	0.367755i	$-0.880126\pi$
$233$	−28.3893	−1.85985	−0.929923	+	0.367755i	$0.880126\pi$
$234$	4.13581	0.270366
$235$	−4.42575	−0.288704
$236$	−0.0128740	−0.000838024 0
$237$	−2.96323	−0.192483
$238$	14.8025	0.959504
$239$	20.3486	1.31624	0.658121	−	0.752912i	$-0.271352\pi$
$239$	20.3486	1.31624	0.658121	+	0.752912i	$0.271352\pi$
$240$	−3.04296	−0.196422
$241$	19.2101	1.23743	0.618715	−	0.785615i	$-0.287654\pi$
$241$	19.2101	1.23743	0.618715	+	0.785615i	$0.287654\pi$
$242$	5.32613	0.342376
$243$	1.00000	0.0641500
$244$	−0.397093	−0.0254212
$245$	5.11224	0.326609
$246$	2.60694	0.166213
$247$	15.9238	1.01321
$248$	−28.4611	−1.80728
$249$	1.08995	0.0690729
$250$	10.0082	0.632975
$251$	−1.27973	−0.0807761	−0.0403880	−	0.999184i	$-0.512859\pi$
$251$	−1.27973	−0.0807761	−0.0403880	+	0.999184i	$0.512859\pi$
$252$	0.275844	0.0173765
$253$	−2.70213	−0.169881
$254$	13.7453	0.862460
$255$	−2.02109	−0.126565
$256$	1.76955	0.110597
$257$	−21.5611	−1.34494	−0.672472	−	0.740123i	$-0.734767\pi$
$257$	−21.5611	−1.34494	−0.672472	+	0.740123i	$0.734767\pi$
$258$	−0.260889	−0.0162423
$259$	−42.9475	−2.66863
$260$	−0.155767	−0.00966023
$261$	−1.00000	−0.0618984
$262$	−22.1243	−1.36684
$263$	14.7781	0.911258	0.455629	−	0.890170i	$-0.349414\pi$
$263$	14.7781	0.911258	0.455629	+	0.890170i	$0.349414\pi$
$264$	−7.49527	−0.461302
$265$	−0.486379	−0.0298780
$266$	29.8323	1.82913
$267$	5.21337	0.319053
$268$	1.18099	0.0721403
$269$	9.78238	0.596442	0.298221	−	0.954497i	$-0.403607\pi$
$269$	9.78238	0.596442	0.298221	+	0.954497i	$0.403607\pi$
$270$	−1.05791	−0.0643826
$271$	1.60503	0.0974985	0.0487492	−	0.998811i	$-0.484476\pi$
$271$	1.60503	0.0974985	0.0487492	+	0.998811i	$0.484476\pi$
$272$	11.3960	0.690986
$273$	−10.7300	−0.649412
$274$	−22.2056	−1.34149
$275$	12.0524	0.726787
$276$	0.0738306	0.00444408
$277$	2.04019	0.122583	0.0612917	−	0.998120i	$-0.480478\pi$
$277$	2.04019	0.122583	0.0612917	+	0.998120i	$0.480478\pi$
$278$	23.4457	1.40618
$279$	−10.2606	−0.614283
$280$	7.61328	0.454981
$281$	−6.40945	−0.382356	−0.191178	−	0.981555i	$-0.561231\pi$
$281$	−6.40945	−0.382356	−0.191178	+	0.981555i	$0.561231\pi$
$282$	8.67580	0.516636
$283$	−6.25421	−0.371774	−0.185887	−	0.982571i	$-0.559516\pi$
$283$	−6.25421	−0.371774	−0.185887	+	0.982571i	$0.559516\pi$
$284$	0.886313	0.0525930
$285$	−4.07320	−0.241276
$286$	−11.1755	−0.660821
$287$	−6.76351	−0.399238
$288$	0.417438	0.0245978
$289$	−9.43092	−0.554760
$290$	1.05791	0.0621228
$291$	−3.97122	−0.232797
$292$	0.0731545	0.00428104
$293$	−16.3014	−0.952338	−0.476169	−	0.879354i	$-0.657975\pi$
$293$	−16.3014	−0.952338	−0.476169	+	0.879354i	$0.657975\pi$
$294$	−10.0215	−0.584467
$295$	−0.128097	−0.00745811
$296$	−31.8854	−1.85330
$297$	−2.70213	−0.156793
$298$	16.1925	0.938008
$299$	−2.87193	−0.166088
$300$	−0.329309	−0.0190127
$301$	0.676857	0.0390134
$302$	18.7596	1.07949
$303$	18.4855	1.06196
$304$	22.9670	1.31725
$305$	−3.95111	−0.226240
$306$	3.96194	0.226489
$307$	6.13524	0.350157	0.175078	−	0.984555i	$-0.443982\pi$
$307$	6.13524	0.350157	0.175078	+	0.984555i	$0.443982\pi$
$308$	−0.745367	−0.0424712
$309$	−2.24948	−0.127969
$310$	10.8548	0.616510
$311$	−0.302171	−0.0171346	−0.00856728	−	0.999963i	$-0.502727\pi$
$311$	−0.302171	−0.0171346	−0.00856728	+	0.999963i	$0.502727\pi$
$312$	−7.96627	−0.451001
$313$	21.6672	1.22471	0.612353	−	0.790585i	$-0.290223\pi$
$313$	21.6672	1.22471	0.612353	+	0.790585i	$0.290223\pi$
$314$	−7.77912	−0.439001
$315$	2.74468	0.154645
$316$	−0.218777	−0.0123072
$317$	−7.71514	−0.433326	−0.216663	−	0.976247i	$-0.569517\pi$
$317$	−7.71514	−0.433326	−0.216663	+	0.976247i	$0.569517\pi$
$318$	0.953449	0.0534668
$319$	2.70213	0.151290
$320$	5.64430	0.315526
$321$	−12.9231	−0.721295
$322$	−5.38039	−0.299837
$323$	15.2544	0.848775
$324$	0.0738306	0.00410170
$325$	12.8098	0.710558
$326$	−8.51446	−0.471573
$327$	16.2725	0.899873
$328$	−5.02142	−0.277261
$329$	−22.5087	−1.24094
$330$	2.85862	0.157362
$331$	−15.6398	−0.859642	−0.429821	−	0.902914i	$-0.641423\pi$
$331$	−15.6398	−0.859642	−0.429821	+	0.902914i	$0.641423\pi$
$332$	0.0804719	0.00441647
$333$	−11.4951	−0.629925
$334$	0.491876	0.0269143
$335$	11.7509	0.642023
$336$	−15.4760	−0.844286
$337$	22.0539	1.20135	0.600675	−	0.799493i	$-0.294898\pi$
$337$	22.0539	1.20135	0.600675	+	0.799493i	$0.294898\pi$
$338$	6.84327	0.372225
$339$	−11.3227	−0.614962
$340$	−0.149218	−0.00809249
$341$	27.7253	1.50141
$342$	7.98471	0.431764
$343$	−0.153162	−0.00826999
$344$	0.502517	0.0270939
$345$	0.734622	0.0395507
$346$	−19.8865	−1.06910
$347$	−3.22284	−0.173011	−0.0865055	−	0.996251i	$-0.527570\pi$
$347$	−3.22284	−0.173011	−0.0865055	+	0.996251i	$0.527570\pi$
$348$	−0.0738306	−0.00395774
$349$	12.2805	0.657362	0.328681	−	0.944441i	$-0.393396\pi$
$349$	12.2805	0.657362	0.328681	+	0.944441i	$0.393396\pi$
$350$	23.9983	1.28276
$351$	−2.87193	−0.153292
$352$	−1.12797	−0.0601211
$353$	23.4425	1.24772	0.623860	−	0.781536i	$-0.285564\pi$
$353$	23.4425	1.24772	0.623860	+	0.781536i	$0.285564\pi$
$354$	0.251109	0.0133463
$355$	8.81890	0.468058
$356$	0.384907	0.0204000
$357$	−10.2790	−0.544020
$358$	−22.0835	−1.16715
$359$	−3.94790	−0.208362	−0.104181	−	0.994558i	$-0.533222\pi$
$359$	−3.94790	−0.208362	−0.104181	+	0.994558i	$0.533222\pi$
$360$	2.03772	0.107397
$361$	11.7429	0.618047
$362$	6.68683	0.351452
$363$	−3.69849	−0.194121
$364$	−0.792206	−0.0415229
$365$	0.727894	0.0380997
$366$	7.74536	0.404857
$367$	−8.80947	−0.459850	−0.229925	−	0.973208i	$-0.573848\pi$
$367$	−8.80947	−0.459850	−0.229925	+	0.973208i	$0.573848\pi$
$368$	−4.14221	−0.215928
$369$	−1.81028	−0.0942393
$370$	12.1608	0.632209
$371$	−2.47365	−0.128426
$372$	−0.757543	−0.0392768
$373$	15.8227	0.819267	0.409634	−	0.912250i	$-0.365657\pi$
$373$	15.8227	0.819267	0.409634	+	0.912250i	$0.365657\pi$
$374$	−10.7057	−0.553578
$375$	−6.94976	−0.358884
$376$	−16.7111	−0.861807
$377$	2.87193	0.147912
$378$	−5.38039	−0.276737
$379$	10.4466	0.536605	0.268302	−	0.963335i	$-0.413537\pi$
$379$	10.4466	0.536605	0.268302	+	0.963335i	$0.413537\pi$
$380$	−0.300727	−0.0154270
$381$	−9.54485	−0.488997
$382$	−14.1915	−0.726102
$383$	−8.85503	−0.452471	−0.226236	−	0.974073i	$-0.572642\pi$
$383$	−8.85503	−0.452471	−0.226236	+	0.974073i	$0.572642\pi$
$384$	−11.8994	−0.607239
$385$	−7.41647	−0.377978
$386$	30.6430	1.55969
$387$	0.181163	0.00920903
$388$	−0.293198	−0.0148849
$389$	18.5823	0.942158	0.471079	−	0.882091i	$-0.343865\pi$
$389$	18.5823	0.942158	0.471079	+	0.882091i	$0.343865\pi$
$390$	3.03826	0.153848
$391$	−2.75120	−0.139134
$392$	19.3032	0.974957
$393$	15.3632	0.774972
$394$	−13.8499	−0.697749
$395$	−2.17685	−0.109529
$396$	−0.199500	−0.0100252
$397$	−21.6225	−1.08520	−0.542602	−	0.839990i	$-0.682561\pi$
$397$	−21.6225	−1.08520	−0.542602	+	0.839990i	$0.682561\pi$
$398$	−6.33564	−0.317577
$399$	−20.7157	−1.03708
$400$	18.4756	0.923781
$401$	−25.2586	−1.26135	−0.630677	−	0.776045i	$-0.717223\pi$
$401$	−25.2586	−1.26135	−0.630677	+	0.776045i	$0.717223\pi$
$402$	−23.0354	−1.14890
$403$	29.4676	1.46789
$404$	1.36480	0.0679011
$405$	0.734622	0.0365036
$406$	5.38039	0.267024
$407$	31.0611	1.53964
$408$	−7.63137	−0.377809
$409$	2.31715	0.114576	0.0572878	−	0.998358i	$-0.481755\pi$
$409$	2.31715	0.114576	0.0572878	+	0.998358i	$0.481755\pi$
$410$	1.91512	0.0945809
$411$	15.4197	0.760598
$412$	−0.166081	−0.00818221
$413$	−0.651483	−0.0320574
$414$	−1.44008	−0.0707761
$415$	0.800703	0.0393050
$416$	−1.19885	−0.0587787
$417$	−16.2808	−0.797276
$418$	−21.5757	−1.05530
$419$	−6.36432	−0.310917	−0.155459	−	0.987842i	$-0.549686\pi$
$419$	−6.36432	−0.310917	−0.155459	+	0.987842i	$0.549686\pi$
$420$	0.202641	0.00988787
$421$	−5.84235	−0.284739	−0.142369	−	0.989814i	$-0.545472\pi$
$421$	−5.84235	−0.284739	−0.142369	+	0.989814i	$0.545472\pi$
$422$	−2.80988	−0.136783
$423$	−6.02453	−0.292923
$424$	−1.83651	−0.0891886
$425$	12.2712	0.595243
$426$	−17.2877	−0.837592
$427$	−20.0947	−0.972453
$428$	−0.954118	−0.0461190
$429$	7.76033	0.374672
$430$	−0.191655	−0.00924242
$431$	−17.3297	−0.834744	−0.417372	−	0.908736i	$-0.637049\pi$
$431$	−17.3297	−0.834744	−0.417372	+	0.908736i	$0.637049\pi$
$432$	−4.14221	−0.199292
$433$	−13.9592	−0.670835	−0.335417	−	0.942070i	$-0.608877\pi$
$433$	−13.9592	−0.670835	−0.335417	+	0.942070i	$0.608877\pi$
$434$	55.2058	2.64996
$435$	−0.734622	−0.0352224
$436$	1.20141	0.0575371
$437$	−5.54463	−0.265236
$438$	−1.42689	−0.0681795
$439$	14.7239	0.702733	0.351367	−	0.936238i	$-0.385717\pi$
$439$	14.7239	0.702733	0.351367	+	0.936238i	$0.385717\pi$
$440$	−5.50619	−0.262497
$441$	6.95901	0.331381
$442$	−11.3784	−0.541217
$443$	−39.8806	−1.89479	−0.947393	−	0.320073i	$-0.896293\pi$
$443$	−39.8806	−1.89479	−0.947393	+	0.320073i	$0.896293\pi$
$444$	−0.848687	−0.0402769
$445$	3.82986	0.181553
$446$	−8.07309	−0.382272
$447$	−11.2442	−0.531832
$448$	28.7061	1.35623
$449$	13.8427	0.653277	0.326639	−	0.945149i	$-0.394084\pi$
$449$	13.8427	0.653277	0.326639	+	0.945149i	$0.394084\pi$
$450$	6.42323	0.302794
$451$	4.89160	0.230337
$452$	−0.835958	−0.0393202
$453$	−13.0268	−0.612052
$454$	8.63659	0.405335
$455$	−7.88252	−0.369538
$456$	−15.3799	−0.720230
$457$	16.5018	0.771924	0.385962	−	0.922515i	$-0.373870\pi$
$457$	16.5018	0.771924	0.385962	+	0.922515i	$0.373870\pi$
$458$	20.4674	0.956377
$459$	−2.75120	−0.128415
$460$	0.0542376	0.00252884
$461$	32.0920	1.49468	0.747338	−	0.664445i	$-0.231332\pi$
$461$	32.0920	1.49468	0.747338	+	0.664445i	$0.231332\pi$
$462$	14.5385	0.676393
$463$	1.18030	0.0548530	0.0274265	−	0.999624i	$-0.491269\pi$
$463$	1.18030	0.0548530	0.0274265	+	0.999624i	$0.491269\pi$
$464$	4.14221	0.192297
$465$	−7.53762	−0.349549
$466$	40.8829	1.89386
$467$	18.8983	0.874507	0.437254	−	0.899338i	$-0.355951\pi$
$467$	18.8983	0.874507	0.437254	+	0.899338i	$0.355951\pi$
$468$	−0.212037	−0.00980139
$469$	59.7635	2.75962
$470$	6.37343	0.293984
$471$	5.40186	0.248905
$472$	−0.483679	−0.0222631
$473$	−0.489526	−0.0225084
$474$	4.26729	0.196003
$475$	24.7309	1.13473
$476$	−0.758901	−0.0347842
$477$	−0.662081	−0.0303146
$478$	−29.3036	−1.34032
$479$	15.2872	0.698490	0.349245	−	0.937031i	$-0.386438\pi$
$479$	15.2872	0.698490	0.349245	+	0.937031i	$0.386438\pi$
$480$	0.306659	0.0139970
$481$	33.0130	1.50526
$482$	−27.6641	−1.26006
$483$	3.73618	0.170002
$484$	−0.273062	−0.0124119
$485$	−2.91735	−0.132470
$486$	−1.44008	−0.0653234
$487$	−22.1203	−1.00237	−0.501183	−	0.865341i	$-0.667102\pi$
$487$	−22.1203	−1.00237	−0.501183	+	0.865341i	$0.667102\pi$
$488$	−14.9189	−0.675346
$489$	5.91249	0.267372
$490$	−7.36203	−0.332583
$491$	−33.8069	−1.52568	−0.762842	−	0.646585i	$-0.776197\pi$
$491$	−33.8069	−1.52568	−0.762842	+	0.646585i	$0.776197\pi$
$492$	−0.133654	−0.00602558
$493$	2.75120	0.123908
$494$	−22.9315	−1.03174
$495$	−1.98504	−0.0892211
$496$	42.5014	1.90837
$497$	44.8516	2.01187
$498$	−1.56962	−0.0703363
$499$	25.1393	1.12539	0.562695	−	0.826664i	$-0.309764\pi$
$499$	25.1393	1.12539	0.562695	+	0.826664i	$0.309764\pi$
$500$	−0.513105	−0.0229468
$501$	−0.341562	−0.0152599
$502$	1.84292	0.0822535
$503$	−40.7380	−1.81642	−0.908209	−	0.418518i	$-0.862550\pi$
$503$	−40.7380	−1.81642	−0.908209	+	0.418518i	$0.862550\pi$
$504$	10.3635	0.461629
$505$	13.5798	0.604295
$506$	3.89128	0.172989
$507$	−4.75201	−0.211044
$508$	−0.704702	−0.0312661
$509$	25.6947	1.13890	0.569450	−	0.822026i	$-0.307156\pi$
$509$	25.6947	1.13890	0.569450	+	0.822026i	$0.307156\pi$
$510$	2.91053	0.128880
$511$	3.70196	0.163765
$512$	21.2505	0.939149
$513$	−5.54463	−0.244801
$514$	31.0497	1.36954
$515$	−1.65252	−0.0728187
$516$	0.0133754	0.000588818 0
$517$	16.2791	0.715952
$518$	61.8479	2.71744
$519$	13.8093	0.606160
$520$	−5.85220	−0.256636
$521$	−38.8339	−1.70134	−0.850671	−	0.525698i	$-0.823804\pi$
$521$	−38.8339	−1.70134	−0.850671	+	0.525698i	$0.823804\pi$
$522$	1.44008	0.0630306
$523$	27.7980	1.21552	0.607762	−	0.794119i	$-0.292068\pi$
$523$	27.7980	1.21552	0.607762	+	0.794119i	$0.292068\pi$
$524$	1.13428	0.0495511
$525$	−16.6646	−0.727302
$526$	−21.2817	−0.927925
$527$	28.2288	1.22967
$528$	11.1928	0.487104
$529$	1.00000	0.0434783
$530$	0.700425	0.0304245
$531$	−0.174372	−0.00756709
$532$	−1.52945	−0.0663102
$533$	5.19899	0.225193
$534$	−7.50768	−0.324889
$535$	−9.49356	−0.410443
$536$	44.3701	1.91650
$537$	15.3349	0.661751
$538$	−14.0874	−0.607351
$539$	−18.8041	−0.809952
$540$	0.0542376	0.00233401
$541$	−34.1038	−1.46624	−0.733118	−	0.680101i	$-0.761936\pi$
$541$	−34.1038	−1.46624	−0.733118	+	0.680101i	$0.761936\pi$
$542$	−2.31137	−0.0992818
$543$	−4.64338	−0.199266
$544$	−1.14845	−0.0492396
$545$	11.9541	0.512059
$546$	15.4521	0.661290
$547$	9.35076	0.399810	0.199905	−	0.979815i	$-0.435937\pi$
$547$	9.35076	0.399810	0.199905	+	0.979815i	$0.435937\pi$
$548$	1.13845	0.0486320
$549$	−5.37843	−0.229546
$550$	−17.3564	−0.740080
$551$	5.54463	0.236209
$552$	2.77384	0.118062
$553$	−11.0712	−0.470793
$554$	−2.93804	−0.124826
$555$	−8.44452	−0.358450
$556$	−1.20202	−0.0509772
$557$	−12.7997	−0.542341	−0.271170	−	0.962531i	$-0.587411\pi$
$557$	−12.7997	−0.542341	−0.271170	+	0.962531i	$0.587411\pi$
$558$	14.7760	0.625519
$559$	−0.520288	−0.0220058
$560$	−11.3690	−0.480429
$561$	7.43409	0.313868
$562$	9.23012	0.389349
$563$	24.8909	1.04903	0.524513	−	0.851402i	$-0.324247\pi$
$563$	24.8909	1.04903	0.524513	+	0.851402i	$0.324247\pi$
$564$	−0.444795	−0.0187292
$565$	−8.31786	−0.349935
$566$	9.00656	0.378574
$567$	3.73618	0.156905
$568$	33.2990	1.39720
$569$	−36.1179	−1.51414	−0.757072	−	0.653332i	$-0.773371\pi$
$569$	−36.1179	−1.51414	−0.757072	+	0.653332i	$0.773371\pi$
$570$	5.86574	0.245689
$571$	−24.7666	−1.03645	−0.518226	−	0.855244i	$-0.673407\pi$
$571$	−24.7666	−1.03645	−0.518226	+	0.855244i	$0.673407\pi$
$572$	0.572950	0.0239563
$573$	9.85469	0.411686
$574$	9.74000	0.406540
$575$	−4.46033	−0.186009
$576$	7.68328	0.320137
$577$	21.4822	0.894315	0.447157	−	0.894455i	$-0.352436\pi$
$577$	21.4822	0.894315	0.447157	+	0.894455i	$0.352436\pi$
$578$	13.5813	0.564907
$579$	−21.2787	−0.884312
$580$	−0.0542376	−0.00225209
$581$	4.07225	0.168946
$582$	5.71888	0.237055
$583$	1.78903	0.0740940
$584$	2.74844	0.113731
$585$	−2.10978	−0.0872288
$586$	23.4753	0.969756
$587$	47.2043	1.94833	0.974164	−	0.225840i	$-0.0725127\pi$
$587$	47.2043	1.94833	0.974164	+	0.225840i	$0.0725127\pi$
$588$	0.513788	0.0211882
$589$	56.8909	2.34415
$590$	0.184470	0.00759452
$591$	9.61747	0.395610
$592$	47.6149	1.95696
$593$	−30.4167	−1.24906	−0.624532	−	0.780999i	$-0.714710\pi$
$593$	−30.4167	−1.24906	−0.624532	+	0.780999i	$0.714710\pi$
$594$	3.89128	0.159661
$595$	−7.55114	−0.309567
$596$	−0.830165	−0.0340049
$597$	4.39951	0.180060
$598$	4.13581	0.169126
$599$	3.07961	0.125829	0.0629147	−	0.998019i	$-0.479960\pi$
$599$	3.07961	0.125829	0.0629147	+	0.998019i	$0.479960\pi$
$600$	−12.3722	−0.505094
$601$	−22.7054	−0.926171	−0.463086	−	0.886314i	$-0.653258\pi$
$601$	−22.7054	−0.926171	−0.463086	+	0.886314i	$0.653258\pi$
$602$	−0.974728	−0.0397269
$603$	15.9959	0.651404
$604$	−0.961776	−0.0391341
$605$	−2.71699	−0.110461
$606$	−26.6206	−1.08139
$607$	23.3283	0.946868	0.473434	−	0.880829i	$-0.343014\pi$
$607$	23.3283	0.946868	0.473434	+	0.880829i	$0.343014\pi$
$608$	−2.31454	−0.0938670
$609$	−3.73618	−0.151397
$610$	5.68991	0.230378
$611$	17.3020	0.699965
$612$	−0.203123	−0.00821074
$613$	−10.1942	−0.411739	−0.205869	−	0.978579i	$-0.566002\pi$
$613$	−10.1942	−0.411739	−0.205869	+	0.978579i	$0.566002\pi$
$614$	−8.83524	−0.356561
$615$	−1.32987	−0.0536255
$616$	−28.0036	−1.12830
$617$	−35.5944	−1.43298	−0.716489	−	0.697599i	$-0.754252\pi$
$617$	−35.5944	−1.43298	−0.716489	+	0.697599i	$0.754252\pi$
$618$	3.23944	0.130309
$619$	24.9632	1.00336	0.501678	−	0.865055i	$-0.332716\pi$
$619$	24.9632	1.00336	0.501678	+	0.865055i	$0.332716\pi$
$620$	−0.556507	−0.0223499
$621$	1.00000	0.0401286
$622$	0.435151	0.0174480
$623$	19.4781	0.780373
$624$	11.8961	0.476227
$625$	17.1962	0.687848
$626$	−31.2026	−1.24711
$627$	14.9823	0.598336
$628$	0.398823	0.0159148
$629$	31.6252	1.26098
$630$	−3.95255	−0.157473
$631$	−47.0960	−1.87486	−0.937431	−	0.348172i	$-0.886802\pi$
$631$	−47.0960	−1.87486	−0.937431	+	0.348172i	$0.886802\pi$
$632$	−8.21953	−0.326955
$633$	1.95120	0.0775531
$634$	11.1104	0.441251
$635$	−7.01185	−0.278257
$636$	−0.0488818	−0.00193829
$637$	−19.9858	−0.791866
$638$	−3.89128	−0.154057
$639$	12.0047	0.474898
$640$	−8.74156	−0.345541
$641$	−21.9528	−0.867084	−0.433542	−	0.901133i	$-0.642736\pi$
$641$	−21.9528	−0.867084	−0.433542	+	0.901133i	$0.642736\pi$
$642$	18.6103	0.734488
$643$	−40.4333	−1.59454	−0.797268	−	0.603626i	$-0.793722\pi$
$643$	−40.4333	−1.59454	−0.797268	+	0.603626i	$0.793722\pi$
$644$	0.275844	0.0108698
$645$	0.133086	0.00524027
$646$	−21.9675	−0.864300
$647$	7.21645	0.283708	0.141854	−	0.989888i	$-0.454694\pi$
$647$	7.21645	0.283708	0.141854	+	0.989888i	$0.454694\pi$
$648$	2.77384	0.108967
$649$	0.471175	0.0184952
$650$	−18.4471	−0.723554
$651$	−38.3352	−1.50248
$652$	0.436523	0.0170956
$653$	13.4765	0.527377	0.263689	−	0.964608i	$-0.415061\pi$
$653$	13.4765	0.527377	0.263689	+	0.964608i	$0.415061\pi$
$654$	−23.4337	−0.916332
$655$	11.2862	0.440987
$656$	7.49855	0.292769
$657$	0.990842	0.0386564
$658$	32.4143	1.26364
$659$	37.3480	1.45487	0.727435	−	0.686177i	$-0.240712\pi$
$659$	37.3480	1.45487	0.727435	+	0.686177i	$0.240712\pi$
$660$	−0.146557	−0.00570472
$661$	50.2592	1.95486	0.977428	−	0.211268i	$-0.0677592\pi$
$661$	50.2592	1.95486	0.977428	+	0.211268i	$0.0677592\pi$
$662$	22.5226	0.875366
$663$	7.90125	0.306859
$664$	3.02335	0.117329
$665$	−15.2182	−0.590137
$666$	16.5538	0.641447
$667$	−1.00000	−0.0387202
$668$	−0.0252177	−0.000975703 0
$669$	5.60600	0.216740
$670$	−16.9223	−0.653765
$671$	14.5332	0.561048
$672$	1.55962	0.0601637
$673$	−32.0250	−1.23447	−0.617236	−	0.786778i	$-0.711748\pi$
$673$	−32.0250	−1.23447	−0.617236	+	0.786778i	$0.711748\pi$
$674$	−31.7593	−1.22332
$675$	−4.46033	−0.171678
$676$	−0.350844	−0.0134940
$677$	47.4069	1.82200	0.910998	−	0.412412i	$-0.135314\pi$
$677$	47.4069	1.82200	0.910998	+	0.412412i	$0.135314\pi$
$678$	16.3055	0.626210
$679$	−14.8372	−0.569399
$680$	−5.60617	−0.214987
$681$	−5.99730	−0.229817
$682$	−39.9267	−1.52887
$683$	−6.12035	−0.234189	−0.117094	−	0.993121i	$-0.537358\pi$
$683$	−6.12035	−0.234189	−0.117094	+	0.993121i	$0.537358\pi$
$684$	−0.409363	−0.0156524
$685$	11.3276	0.432807
$686$	0.220566	0.00842126
$687$	−14.2127	−0.542247
$688$	−0.750415	−0.0286093
$689$	1.90145	0.0724395
$690$	−1.05791	−0.0402741
$691$	−46.8351	−1.78169	−0.890845	−	0.454307i	$-0.849887\pi$
$691$	−46.8351	−1.78169	−0.890845	+	0.454307i	$0.849887\pi$
$692$	1.01955	0.0387574
$693$	−10.0956	−0.383501
$694$	4.64114	0.176175
$695$	−11.9603	−0.453678
$696$	−2.77384	−0.105142
$697$	4.98043	0.188647
$698$	−17.6850	−0.669386
$699$	−28.3893	−1.07378
$700$	−1.23036	−0.0465031
$701$	−8.62132	−0.325623	−0.162811	−	0.986657i	$-0.552056\pi$
$701$	−8.62132	−0.325623	−0.162811	+	0.986657i	$0.552056\pi$
$702$	4.13581	0.156096
$703$	63.7358	2.40384
$704$	−20.7612	−0.782468
$705$	−4.42575	−0.166683
$706$	−33.7591	−1.27054
$707$	69.0651	2.59746
$708$	−0.0128740	−0.000483834 0
$709$	−23.5240	−0.883463	−0.441731	−	0.897147i	$-0.645636\pi$
$709$	−23.5240	−0.883463	−0.441731	+	0.897147i	$0.645636\pi$
$710$	−12.6999	−0.476619
$711$	−2.96323	−0.111130
$712$	14.4611	0.541951
$713$	−10.2606	−0.384261
$714$	14.8025	0.553970
$715$	5.70091	0.213202
$716$	1.13219	0.0423118
$717$	20.3486	0.759932
$718$	5.68529	0.212173
$719$	−14.1926	−0.529294	−0.264647	−	0.964345i	$-0.585255\pi$
$719$	−14.1926	−0.529294	−0.264647	+	0.964345i	$0.585255\pi$
$720$	−3.04296	−0.113404
$721$	−8.40447	−0.312999
$722$	−16.9107	−0.629351
$723$	19.2101	0.714431
$724$	−0.342823	−0.0127409
$725$	4.46033	0.165653
$726$	5.32613	0.197671
$727$	−4.28230	−0.158822	−0.0794108	−	0.996842i	$-0.525304\pi$
$727$	−4.28230	−0.158822	−0.0794108	+	0.996842i	$0.525304\pi$
$728$	−29.7634	−1.10310
$729$	1.00000	0.0370370
$730$	−1.04823	−0.0387966
$731$	−0.498415	−0.0184345
$732$	−0.397093	−0.0146770
$733$	12.6104	0.465774	0.232887	−	0.972504i	$-0.425183\pi$
$733$	12.6104	0.465774	0.232887	+	0.972504i	$0.425183\pi$
$734$	12.6863	0.468261
$735$	5.11224	0.188568
$736$	0.417438	0.0153870
$737$	−43.2230	−1.59214
$738$	2.60694	0.0959629
$739$	−14.4588	−0.531874	−0.265937	−	0.963990i	$-0.585681\pi$
$739$	−14.4588	−0.531874	−0.265937	+	0.963990i	$0.585681\pi$
$740$	−0.623464	−0.0229190
$741$	15.9238	0.584975
$742$	3.56225	0.130774
$743$	−52.1742	−1.91409	−0.957044	−	0.289944i	$-0.906363\pi$
$743$	−52.1742	−1.91409	−0.957044	+	0.289944i	$0.906363\pi$
$744$	−28.4611	−1.04343
$745$	−8.26022	−0.302631
$746$	−22.7859	−0.834252
$747$	1.08995	0.0398793
$748$	0.548864	0.0200684
$749$	−48.2828	−1.76422
$750$	10.0082	0.365448
$751$	−29.7393	−1.08520	−0.542602	−	0.839990i	$-0.682561\pi$
$751$	−29.7393	−1.08520	−0.542602	+	0.839990i	$0.682561\pi$
$752$	24.9549	0.910010
$753$	−1.27973	−0.0466361
$754$	−4.13581	−0.150617
$755$	−9.56976	−0.348279
$756$	0.275844	0.0100324
$757$	1.08267	0.0393504	0.0196752	−	0.999806i	$-0.493737\pi$
$757$	1.08267	0.0393504	0.0196752	+	0.999806i	$0.493737\pi$
$758$	−15.0439	−0.546419
$759$	−2.70213	−0.0980811
$760$	−11.2984	−0.409836
$761$	−24.7614	−0.897599	−0.448799	−	0.893633i	$-0.648148\pi$
$761$	−24.7614	−0.897599	−0.448799	+	0.893633i	$0.648148\pi$
$762$	13.7453	0.497941
$763$	60.7970	2.20100
$764$	0.727578	0.0263228
$765$	−2.02109	−0.0730726
$766$	12.7520	0.460747
$767$	0.500784	0.0180823
$768$	1.76955	0.0638531
$769$	38.2442	1.37912	0.689560	−	0.724229i	$-0.257804\pi$
$769$	38.2442	1.37912	0.689560	+	0.724229i	$0.257804\pi$
$770$	10.6803	0.384892
$771$	−21.5611	−0.776504
$772$	−1.57102	−0.0565422
$773$	−4.36196	−0.156889	−0.0784444	−	0.996918i	$-0.524995\pi$
$773$	−4.36196	−0.156889	−0.0784444	+	0.996918i	$0.524995\pi$
$774$	−0.260889	−0.00937747
$775$	45.7655	1.64394
$776$	−11.0155	−0.395435
$777$	−42.9475	−1.54073
$778$	−26.7599	−0.959390
$779$	10.0373	0.359624
$780$	−0.155767	−0.00557734
$781$	−32.4382	−1.16073
$782$	3.96194	0.141679
$783$	−1.00000	−0.0357371
$784$	−28.8257	−1.02949
$785$	3.96833	0.141636
$786$	−22.1243	−0.789147
$787$	−54.5403	−1.94415	−0.972076	−	0.234666i	$-0.924600\pi$
$787$	−54.5403	−1.94415	−0.972076	+	0.234666i	$0.924600\pi$
$788$	0.710064	0.0252950
$789$	14.7781	0.526115
$790$	3.13485	0.111533
$791$	−42.3034	−1.50414
$792$	−7.49527	−0.266333
$793$	15.4465	0.548520
$794$	31.1382	1.10505
$795$	−0.486379	−0.0172501
$796$	0.324818	0.0115129
$797$	−14.1584	−0.501518	−0.250759	−	0.968050i	$-0.580680\pi$
$797$	−14.1584	−0.501518	−0.250759	+	0.968050i	$0.580680\pi$
$798$	29.8323	1.05605
$799$	16.5747	0.586369
$800$	−1.86191	−0.0658286
$801$	5.21337	0.184206
$802$	36.3744	1.28442
$803$	−2.67738	−0.0944829
$804$	1.18099	0.0416502
$805$	2.74468	0.0967371
$806$	−42.4357	−1.49473
$807$	9.78238	0.344356
$808$	51.2758	1.80388
$809$	−7.90499	−0.277925	−0.138962	−	0.990298i	$-0.544377\pi$
$809$	−7.90499	−0.277925	−0.138962	+	0.990298i	$0.544377\pi$
$810$	−1.05791	−0.0371713
$811$	−22.0093	−0.772853	−0.386426	−	0.922320i	$-0.626291\pi$
$811$	−22.0093	−0.772853	−0.386426	+	0.922320i	$0.626291\pi$
$812$	−0.275844	−0.00968023
$813$	1.60503	0.0562908
$814$	−44.7305	−1.56780
$815$	4.34345	0.152144
$816$	11.3960	0.398941
$817$	−1.00448	−0.0351424
$818$	−3.33688	−0.116671
$819$	−10.7300	−0.374938
$820$	−0.0981850	−0.00342877
$821$	1.48851	0.0519495	0.0259747	−	0.999663i	$-0.491731\pi$
$821$	1.48851	0.0519495	0.0259747	+	0.999663i	$0.491731\pi$
$822$	−22.2056	−0.774509
$823$	10.8193	0.377138	0.188569	−	0.982060i	$-0.439615\pi$
$823$	10.8193	0.377138	0.188569	+	0.982060i	$0.439615\pi$
$824$	−6.23970	−0.217370
$825$	12.0524	0.419611
$826$	0.938188	0.0326437
$827$	−11.1086	−0.386285	−0.193142	−	0.981171i	$-0.561868\pi$
$827$	−11.1086	−0.386285	−0.193142	+	0.981171i	$0.561868\pi$
$828$	0.0738306	0.00256579
$829$	37.1704	1.29098	0.645490	−	0.763769i	$-0.276653\pi$
$829$	37.1704	1.29098	0.645490	+	0.763769i	$0.276653\pi$
$830$	−1.15308	−0.0400239
$831$	2.04019	0.0707736
$832$	−22.0658	−0.764996
$833$	−19.1456	−0.663355
$834$	23.4457	0.811858
$835$	−0.250919	−0.00868340
$836$	1.10615	0.0382571
$837$	−10.2606	−0.354657
$838$	9.16513	0.316604
$839$	−32.0230	−1.10556	−0.552778	−	0.833328i	$-0.686432\pi$
$839$	−32.0230	−1.10556	−0.552778	+	0.833328i	$0.686432\pi$
$840$	7.61328	0.262683
$841$	1.00000	0.0344828
$842$	8.41345	0.289947
$843$	−6.40945	−0.220753
$844$	0.144058	0.00495869
$845$	−3.49093	−0.120092
$846$	8.67580	0.298280
$847$	−13.8182	−0.474800
$848$	2.74248	0.0941771
$849$	−6.25421	−0.214644
$850$	−17.6716	−0.606130
$851$	−11.4951	−0.394045
$852$	0.886313	0.0303646
$853$	−34.0427	−1.16560	−0.582799	−	0.812616i	$-0.698043\pi$
$853$	−34.0427	−1.16560	−0.582799	+	0.812616i	$0.698043\pi$
$854$	28.9380	0.990239
$855$	−4.07320	−0.139301
$856$	−35.8465	−1.22521
$857$	−8.43886	−0.288266	−0.144133	−	0.989558i	$-0.546039\pi$
$857$	−8.43886	−0.288266	−0.144133	+	0.989558i	$0.546039\pi$
$858$	−11.1755	−0.381525
$859$	9.83616	0.335605	0.167803	−	0.985821i	$-0.446333\pi$
$859$	9.83616	0.335605	0.167803	+	0.985821i	$0.446333\pi$
$860$	0.00982584	0.000335058 0
$861$	−6.76351	−0.230500
$862$	24.9562	0.850012
$863$	−42.6331	−1.45125	−0.725624	−	0.688092i	$-0.758449\pi$
$863$	−42.6331	−1.45125	−0.725624	+	0.688092i	$0.758449\pi$
$864$	0.417438	0.0142015
$865$	10.1446	0.344926
$866$	20.1023	0.683104
$867$	−9.43092	−0.320291
$868$	−2.83031	−0.0960671
$869$	8.00704	0.271620
$870$	1.05791	0.0358666
$871$	−45.9392	−1.55659
$872$	45.1374	1.52854
$873$	−3.97122	−0.134406
$874$	7.98471	0.270087
$875$	−25.9655	−0.877795
$876$	0.0731545	0.00247166
$877$	43.1875	1.45834	0.729170	−	0.684333i	$-0.239906\pi$
$877$	43.1875	1.45834	0.729170	+	0.684333i	$0.239906\pi$
$878$	−21.2036	−0.715587
$879$	−16.3014	−0.549832
$880$	8.22247	0.277179
$881$	5.46060	0.183972	0.0919861	−	0.995760i	$-0.470678\pi$
$881$	5.46060	0.183972	0.0919861	+	0.995760i	$0.470678\pi$
$882$	−10.0215	−0.337442
$883$	17.9095	0.602703	0.301352	−	0.953513i	$-0.402562\pi$
$883$	17.9095	0.602703	0.301352	+	0.953513i	$0.402562\pi$
$884$	0.583354	0.0196203
$885$	−0.128097	−0.00430594
$886$	57.4313	1.92944
$887$	−36.8826	−1.23840	−0.619198	−	0.785235i	$-0.712542\pi$
$887$	−36.8826	−1.23840	−0.619198	+	0.785235i	$0.712542\pi$
$888$	−31.8854	−1.07000
$889$	−35.6612	−1.19604
$890$	−5.51530	−0.184873
$891$	−2.70213	−0.0905248
$892$	0.413894	0.0138582
$893$	33.4038	1.11781
$894$	16.1925	0.541559
$895$	11.2654	0.376560
$896$	−44.4583	−1.48525
$897$	−2.87193	−0.0958910
$898$	−19.9346	−0.665226
$899$	10.2606	0.342209
$900$	−0.329309	−0.0109770
$901$	1.82151	0.0606834
$902$	−7.04430	−0.234550
$903$	0.676857	0.0225244
$904$	−31.4072	−1.04459
$905$	−3.41112	−0.113390
$906$	18.7596	0.623247
$907$	−38.3059	−1.27193	−0.635964	−	0.771719i	$-0.719397\pi$
$907$	−38.3059	−1.27193	−0.635964	+	0.771719i	$0.719397\pi$
$908$	−0.442784	−0.0146943
$909$	18.4855	0.613125
$910$	11.3515	0.376297
$911$	−21.4837	−0.711787	−0.355894	−	0.934526i	$-0.615823\pi$
$911$	−21.4837	−0.711787	−0.355894	+	0.934526i	$0.615823\pi$
$912$	22.9670	0.760514
$913$	−2.94519	−0.0974717
$914$	−23.7640	−0.786042
$915$	−3.95111	−0.130620
$916$	−1.04933	−0.0346708
$917$	57.3997	1.89550
$918$	3.96194	0.130764
$919$	−22.6683	−0.747759	−0.373880	−	0.927477i	$-0.621973\pi$
$919$	−22.6683	−0.747759	−0.373880	+	0.927477i	$0.621973\pi$
$920$	2.03772	0.0671817
$921$	6.13524	0.202163
$922$	−46.2151	−1.52201
$923$	−34.4766	−1.13481
$924$	−0.745367	−0.0245208
$925$	51.2718	1.68581
$926$	−1.69972	−0.0558563
$927$	−2.24948	−0.0738828
$928$	−0.417438	−0.0137031
$929$	−21.5525	−0.707115	−0.353558	−	0.935413i	$-0.615028\pi$
$929$	−21.5525	−0.707115	−0.353558	+	0.935413i	$0.615028\pi$
$930$	10.8548	0.355942
$931$	−38.5851	−1.26458
$932$	−2.09600	−0.0686568
$933$	−0.302171	−0.00989265
$934$	−27.2150	−0.890502
$935$	5.46124	0.178602
$936$	−7.96627	−0.260386
$937$	53.7168	1.75485	0.877425	−	0.479713i	$-0.159259\pi$
$937$	53.7168	1.75485	0.877425	+	0.479713i	$0.159259\pi$
$938$	−86.0643	−2.81010
$939$	21.6672	0.707084
$940$	−0.326756	−0.0106576
$941$	33.2298	1.08326	0.541631	−	0.840617i	$-0.317807\pi$
$941$	33.2298	1.08326	0.541631	+	0.840617i	$0.317807\pi$
$942$	−7.77912	−0.253457
$943$	−1.81028	−0.0589507
$944$	0.722284	0.0235084
$945$	2.74468	0.0892843
$946$	0.704957	0.0229201
$947$	6.93643	0.225404	0.112702	−	0.993629i	$-0.464050\pi$
$947$	6.93643	0.225404	0.112702	+	0.993629i	$0.464050\pi$
$948$	−0.218777	−0.00710556
$949$	−2.84563	−0.0923731
$950$	−35.6144	−1.15548
$951$	−7.71514	−0.250181
$952$	−28.5121	−0.924084
$953$	34.3469	1.11261	0.556303	−	0.830979i	$-0.312219\pi$
$953$	34.3469	1.11261	0.556303	+	0.830979i	$0.312219\pi$
$954$	0.953449	0.0308691
$955$	7.23947	0.234264
$956$	1.50235	0.0485895
$957$	2.70213	0.0873475
$958$	−22.0148	−0.711266
$959$	57.6107	1.86035
$960$	5.64430	0.182169
$961$	74.2789	2.39609
$962$	−47.5414	−1.53280
$963$	−12.9231	−0.416440
$964$	1.41829	0.0456801
$965$	−15.6318	−0.503205
$966$	−5.38039	−0.173111
$967$	22.8151	0.733685	0.366843	−	0.930283i	$-0.380439\pi$
$967$	22.8151	0.733685	0.366843	+	0.930283i	$0.380439\pi$
$968$	−10.2590	−0.329737
$969$	15.2544	0.490041
$970$	4.20121	0.134893
$971$	−43.7200	−1.40304	−0.701521	−	0.712649i	$-0.747495\pi$
$971$	−43.7200	−1.40304	−0.701521	+	0.712649i	$0.747495\pi$
$972$	0.0738306	0.00236812
$973$	−60.8280	−1.95006
$974$	31.8550	1.02070
$975$	12.8098	0.410241
$976$	22.2786	0.713120
$977$	−0.346127	−0.0110736	−0.00553679	−	0.999985i	$-0.501762\pi$
$977$	−0.346127	−0.0110736	−0.00553679	+	0.999985i	$0.501762\pi$
$978$	−8.51446	−0.272263
$979$	−14.0872	−0.450229
$980$	0.377440	0.0120569
$981$	16.2725	0.519542
$982$	48.6846	1.55359
$983$	−3.49735	−0.111548	−0.0557741	−	0.998443i	$-0.517763\pi$
$983$	−3.49735	−0.111548	−0.0557741	+	0.998443i	$0.517763\pi$
$984$	−5.02142	−0.160077
$985$	7.06520	0.225116
$986$	−3.96194	−0.126174
$987$	−22.5087	−0.716459
$988$	1.17566	0.0374028
$989$	0.181163	0.00576065
$990$	2.85862	0.0908529
$991$	−21.4825	−0.682414	−0.341207	−	0.939988i	$-0.610836\pi$
$991$	−21.4825	−0.682414	−0.341207	+	0.939988i	$0.610836\pi$
$992$	−4.28315	−0.135990
$993$	−15.6398	−0.496315
$994$	−64.5899	−2.04867
$995$	3.23197	0.102460
$996$	0.0804719	0.00254985
$997$	15.2460	0.482845	0.241422	−	0.970420i	$-0.422386\pi$
$997$	15.2460	0.482845	0.241422	+	0.970420i	$0.422386\pi$
$998$	−36.2026	−1.14597
$999$	−11.4951	−0.363687

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.i.1.3	✓	7
3.2	odd	2		6003.2.a.j.1.5		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.i.1.3	✓	7	1.1	even	1	trivial
6003.2.a.j.1.5		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)

\(f(q)\)	\(=\)	\(q-1.44008 q^{2} +1.00000 q^{3} +0.0738306 q^{4} +0.734622 q^{5} -1.44008 q^{6} +3.73618 q^{7} +2.77384 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.44008 q^{2} +1.00000 q^{3} +0.0738306 q^{4} +0.734622 q^{5} -1.44008 q^{6} +3.73618 q^{7} +2.77384 q^{8} +1.00000 q^{9} -1.05791 q^{10} -2.70213 q^{11} +0.0738306 q^{12} -2.87193 q^{13} -5.38039 q^{14} +0.734622 q^{15} -4.14221 q^{16} -2.75120 q^{17} -1.44008 q^{18} -5.54463 q^{19} +0.0542376 q^{20} +3.73618 q^{21} +3.89128 q^{22} +1.00000 q^{23} +2.77384 q^{24} -4.46033 q^{25} +4.13581 q^{26} +1.00000 q^{27} +0.275844 q^{28} -1.00000 q^{29} -1.05791 q^{30} -10.2606 q^{31} +0.417438 q^{32} -2.70213 q^{33} +3.96194 q^{34} +2.74468 q^{35} +0.0738306 q^{36} -11.4951 q^{37} +7.98471 q^{38} -2.87193 q^{39} +2.03772 q^{40} -1.81028 q^{41} -5.38039 q^{42} +0.181163 q^{43} -0.199500 q^{44} +0.734622 q^{45} -1.44008 q^{46} -6.02453 q^{47} -4.14221 q^{48} +6.95901 q^{49} +6.42323 q^{50} -2.75120 q^{51} -0.212037 q^{52} -0.662081 q^{53} -1.44008 q^{54} -1.98504 q^{55} +10.3635 q^{56} -5.54463 q^{57} +1.44008 q^{58} -0.174372 q^{59} +0.0542376 q^{60} -5.37843 q^{61} +14.7760 q^{62} +3.73618 q^{63} +7.68328 q^{64} -2.10978 q^{65} +3.89128 q^{66} +15.9959 q^{67} -0.203123 q^{68} +1.00000 q^{69} -3.95255 q^{70} +12.0047 q^{71} +2.77384 q^{72} +0.990842 q^{73} +16.5538 q^{74} -4.46033 q^{75} -0.409363 q^{76} -10.0956 q^{77} +4.13581 q^{78} -2.96323 q^{79} -3.04296 q^{80} +1.00000 q^{81} +2.60694 q^{82} +1.08995 q^{83} +0.275844 q^{84} -2.02109 q^{85} -0.260889 q^{86} -1.00000 q^{87} -7.49527 q^{88} +5.21337 q^{89} -1.05791 q^{90} -10.7300 q^{91} +0.0738306 q^{92} -10.2606 q^{93} +8.67580 q^{94} -4.07320 q^{95} +0.417438 q^{96} -3.97122 q^{97} -10.0215 q^{98} -2.70213 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 3 q^{2} + 7 q^{3} + 5 q^{4} - 3 q^{5} - 3 q^{6} - 5 q^{7} - 6 q^{8} + 7 q^{9}+O(q^{10}) \) 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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