LMFDB - Embedded newform 1001.2.a.n.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1001,2,Mod(1,1001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1001, 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("1001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1001 = 7 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1001.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:	$7.99302524233$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - x^{10} - 18x^{9} + 15x^{8} + 117x^{7} - 78x^{6} - 326x^{5} + 167x^{4} + 348x^{3} - 143x^{2} - 74x + 24 $ x^11 - x^10 - 18x^9 + 15x^8 + 117x^7 - 78x^6 - 326x^5 + 167x^4 + 348x^3 - 143x^2 - 74*x + 24
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-2.37413$ of defining polynomial
Character	$\chi$	$=$	1001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.37413 q^{2} +2.26106 q^{3} +3.63647 q^{4} -2.08089 q^{5} +5.36804 q^{6} +1.00000 q^{7} +3.88519 q^{8} +2.11240 q^{9} +O(q^{10})$	\(q+2.37413 q^{2} +2.26106 q^{3} +3.63647 q^{4} -2.08089 q^{5} +5.36804 q^{6} +1.00000 q^{7} +3.88519 q^{8} +2.11240 q^{9} -4.94030 q^{10} +1.00000 q^{11} +8.22229 q^{12} +1.00000 q^{13} +2.37413 q^{14} -4.70503 q^{15} +1.95099 q^{16} +3.85851 q^{17} +5.01509 q^{18} +1.83860 q^{19} -7.56712 q^{20} +2.26106 q^{21} +2.37413 q^{22} -4.59538 q^{23} +8.78466 q^{24} -0.669881 q^{25} +2.37413 q^{26} -2.00693 q^{27} +3.63647 q^{28} +0.128205 q^{29} -11.1703 q^{30} +3.57479 q^{31} -3.13848 q^{32} +2.26106 q^{33} +9.16060 q^{34} -2.08089 q^{35} +7.68167 q^{36} -3.21606 q^{37} +4.36506 q^{38} +2.26106 q^{39} -8.08468 q^{40} -9.39741 q^{41} +5.36804 q^{42} -2.76421 q^{43} +3.63647 q^{44} -4.39567 q^{45} -10.9100 q^{46} +10.7023 q^{47} +4.41132 q^{48} +1.00000 q^{49} -1.59038 q^{50} +8.72434 q^{51} +3.63647 q^{52} -11.7818 q^{53} -4.76469 q^{54} -2.08089 q^{55} +3.88519 q^{56} +4.15718 q^{57} +0.304375 q^{58} -9.10240 q^{59} -17.1097 q^{60} +4.91974 q^{61} +8.48699 q^{62} +2.11240 q^{63} -11.3531 q^{64} -2.08089 q^{65} +5.36804 q^{66} -10.8810 q^{67} +14.0314 q^{68} -10.3904 q^{69} -4.94030 q^{70} +10.7477 q^{71} +8.20707 q^{72} +4.81845 q^{73} -7.63533 q^{74} -1.51464 q^{75} +6.68601 q^{76} +1.00000 q^{77} +5.36804 q^{78} +4.76289 q^{79} -4.05981 q^{80} -10.8750 q^{81} -22.3106 q^{82} -4.99628 q^{83} +8.22229 q^{84} -8.02916 q^{85} -6.56259 q^{86} +0.289879 q^{87} +3.88519 q^{88} +14.8872 q^{89} -10.4359 q^{90} +1.00000 q^{91} -16.7110 q^{92} +8.08281 q^{93} +25.4086 q^{94} -3.82593 q^{95} -7.09631 q^{96} -6.93934 q^{97} +2.37413 q^{98} +2.11240 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - q^{2} + 2 q^{3} + 15 q^{4} + 7 q^{5} + 3 q^{6} + 11 q^{7} - 6 q^{8} + 15 q^{9}+O(q^{10}) $ 11 * q - q^2 + 2 * q^3 + 15 * q^4 + 7 * q^5 + 3 * q^6 + 11 * q^7 - 6 * q^8 + 15 * q^9	\( 11 q - q^{2} + 2 q^{3} + 15 q^{4} + 7 q^{5} + 3 q^{6} + 11 q^{7} - 6 q^{8} + 15 q^{9} + q^{10} + 11 q^{11} - 5 q^{12} + 11 q^{13} - q^{14} + 4 q^{15} + 15 q^{16} + 7 q^{17} - 17 q^{18} + 22 q^{19} + 6 q^{20} + 2 q^{21} - q^{22} + 3 q^{23} + 17 q^{24} + 10 q^{25} - q^{26} + 2 q^{27} + 15 q^{28} - 6 q^{29} - 40 q^{30} + 28 q^{31} - 23 q^{32} + 2 q^{33} + 19 q^{34} + 7 q^{35} + 48 q^{36} + q^{37} - 20 q^{38} + 2 q^{39} + 16 q^{40} - 4 q^{41} + 3 q^{42} - 8 q^{43} + 15 q^{44} + 12 q^{45} + 2 q^{46} + 22 q^{47} - 30 q^{48} + 11 q^{49} - 24 q^{50} - 27 q^{51} + 15 q^{52} + 9 q^{53} + 36 q^{54} + 7 q^{55} - 6 q^{56} - 34 q^{57} - 8 q^{58} - 2 q^{59} + 25 q^{60} + 8 q^{62} + 15 q^{63} - 10 q^{64} + 7 q^{65} + 3 q^{66} + 23 q^{67} + 24 q^{68} + 7 q^{69} + q^{70} + 3 q^{71} - 76 q^{72} + 29 q^{73} + 15 q^{74} + 36 q^{75} + 62 q^{76} + 11 q^{77} + 3 q^{78} + 26 q^{79} - 16 q^{80} + 7 q^{81} - 16 q^{82} + 9 q^{83} - 5 q^{84} - 31 q^{85} + 28 q^{86} + 13 q^{87} - 6 q^{88} + 9 q^{89} - 26 q^{90} + 11 q^{91} - 58 q^{92} - 24 q^{93} - 34 q^{94} - 14 q^{95} + 56 q^{96} + 40 q^{97} - q^{98} + 15 q^{99}+O(q^{100}) \) 11 * q - q^2 + 2 * q^3 + 15 * q^4 + 7 * q^5 + 3 * q^6 + 11 * q^7 - 6 * q^8 + 15 * q^9 + q^10 + 11 * q^11 - 5 * q^12 + 11 * q^13 - q^14 + 4 * q^15 + 15 * q^16 + 7 * q^17 - 17 * q^18 + 22 * q^19 + 6 * q^20 + 2 * q^21 - q^22 + 3 * q^23 + 17 * q^24 + 10 * q^25 - q^26 + 2 * q^27 + 15 * q^28 - 6 * q^29 - 40 * q^30 + 28 * q^31 - 23 * q^32 + 2 * q^33 + 19 * q^34 + 7 * q^35 + 48 * q^36 + q^37 - 20 * q^38 + 2 * q^39 + 16 * q^40 - 4 * q^41 + 3 * q^42 - 8 * q^43 + 15 * q^44 + 12 * q^45 + 2 * q^46 + 22 * q^47 - 30 * q^48 + 11 * q^49 - 24 * q^50 - 27 * q^51 + 15 * q^52 + 9 * q^53 + 36 * q^54 + 7 * q^55 - 6 * q^56 - 34 * q^57 - 8 * q^58 - 2 * q^59 + 25 * q^60 + 8 * q^62 + 15 * q^63 - 10 * q^64 + 7 * q^65 + 3 * q^66 + 23 * q^67 + 24 * q^68 + 7 * q^69 + q^70 + 3 * q^71 - 76 * q^72 + 29 * q^73 + 15 * q^74 + 36 * q^75 + 62 * q^76 + 11 * q^77 + 3 * q^78 + 26 * q^79 - 16 * q^80 + 7 * q^81 - 16 * q^82 + 9 * q^83 - 5 * q^84 - 31 * q^85 + 28 * q^86 + 13 * q^87 - 6 * q^88 + 9 * q^89 - 26 * q^90 + 11 * q^91 - 58 * q^92 - 24 * q^93 - 34 * q^94 - 14 * q^95 + 56 * q^96 + 40 * q^97 - q^98 + 15 * 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 $

$2$	2.37413	1.67876	0.839380	−	0.543545i	$-0.182918\pi$
$2$	2.37413	1.67876	0.839380	+	0.543545i	$0.182918\pi$
$3$	2.26106	1.30542	0.652712	−	0.757606i	$-0.273631\pi$
$3$	2.26106	1.30542	0.652712	+	0.757606i	$0.273631\pi$
$4$	3.63647	1.81824
$5$	−2.08089	−0.930604	−0.465302	−	0.885152i	$-0.654054\pi$
$5$	−2.08089	−0.930604	−0.465302	+	0.885152i	$0.654054\pi$
$6$	5.36804	2.19149
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	3.88519	1.37362
$9$	2.11240	0.704132
$10$	−4.94030	−1.56226
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	8.22229	2.37357
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	2.37413	0.634512
$15$	−4.70503	−1.21483
$16$	1.95099	0.487748
$17$	3.85851	0.935827	0.467914	−	0.883774i	$-0.345006\pi$
$17$	3.85851	0.935827	0.467914	+	0.883774i	$0.345006\pi$
$18$	5.01509	1.18207
$19$	1.83860	0.421803	0.210902	−	0.977507i	$-0.432360\pi$
$19$	1.83860	0.421803	0.210902	+	0.977507i	$0.432360\pi$
$20$	−7.56712	−1.69206
$21$	2.26106	0.493404
$22$	2.37413	0.506165
$23$	−4.59538	−0.958203	−0.479102	−	0.877759i	$-0.659038\pi$
$23$	−4.59538	−0.958203	−0.479102	+	0.877759i	$0.659038\pi$
$24$	8.78466	1.79316
$25$	−0.669881	−0.133976
$26$	2.37413	0.465604
$27$	−2.00693	−0.386233
$28$	3.63647	0.687229
$29$	0.128205	0.0238071	0.0119035	−	0.999929i	$-0.496211\pi$
$29$	0.128205	0.0238071	0.0119035	+	0.999929i	$0.496211\pi$
$30$	−11.1703	−2.03941
$31$	3.57479	0.642050	0.321025	−	0.947071i	$-0.395973\pi$
$31$	3.57479	0.642050	0.321025	+	0.947071i	$0.395973\pi$
$32$	−3.13848	−0.554811
$33$	2.26106	0.393600
$34$	9.16060	1.57103
$35$	−2.08089	−0.351735
$36$	7.68167	1.28028
$37$	−3.21606	−0.528717	−0.264358	−	0.964425i	$-0.585160\pi$
$37$	−3.21606	−0.528717	−0.264358	+	0.964425i	$0.585160\pi$
$38$	4.36506	0.708106
$39$	2.26106	0.362060
$40$	−8.08468	−1.27830
$41$	−9.39741	−1.46763	−0.733814	−	0.679350i	$-0.762262\pi$
$41$	−9.39741	−1.46763	−0.733814	+	0.679350i	$0.762262\pi$
$42$	5.36804	0.828307
$43$	−2.76421	−0.421539	−0.210769	−	0.977536i	$-0.567597\pi$
$43$	−2.76421	−0.421539	−0.210769	+	0.977536i	$0.567597\pi$
$44$	3.63647	0.548219
$45$	−4.39567	−0.655268
$46$	−10.9100	−1.60859
$47$	10.7023	1.56109	0.780544	−	0.625101i	$-0.214942\pi$
$47$	10.7023	1.56109	0.780544	+	0.625101i	$0.214942\pi$
$48$	4.41132	0.636718
$49$	1.00000	0.142857
$50$	−1.59038	−0.224914
$51$	8.72434	1.22165
$52$	3.63647	0.504288
$53$	−11.7818	−1.61835	−0.809177	−	0.587566i	$-0.800086\pi$
$53$	−11.7818	−1.61835	−0.809177	+	0.587566i	$0.800086\pi$
$54$	−4.76469	−0.648393
$55$	−2.08089	−0.280588
$56$	3.88519	0.519181
$57$	4.15718	0.550632
$58$	0.304375	0.0399664
$59$	−9.10240	−1.18503	−0.592515	−	0.805559i	$-0.701865\pi$
$59$	−9.10240	−1.18503	−0.592515	+	0.805559i	$0.701865\pi$
$60$	−17.1097	−2.20885
$61$	4.91974	0.629909	0.314954	−	0.949107i	$-0.398011\pi$
$61$	4.91974	0.629909	0.314954	+	0.949107i	$0.398011\pi$
$62$	8.48699	1.07785
$63$	2.11240	0.266137
$64$	−11.3531	−1.41914
$65$	−2.08089	−0.258103
$66$	5.36804	0.660760
$67$	−10.8810	−1.32932	−0.664661	−	0.747145i	$-0.731424\pi$
$67$	−10.8810	−1.32932	−0.664661	+	0.747145i	$0.731424\pi$
$68$	14.0314	1.70156
$69$	−10.3904	−1.25086
$70$	−4.94030	−0.590479
$71$	10.7477	1.27552	0.637759	−	0.770236i	$-0.279862\pi$
$71$	10.7477	1.27552	0.637759	+	0.770236i	$0.279862\pi$
$72$	8.20707	0.967213
$73$	4.81845	0.563957	0.281979	−	0.959421i	$-0.409009\pi$
$73$	4.81845	0.563957	0.281979	+	0.959421i	$0.409009\pi$
$74$	−7.63533	−0.887589
$75$	−1.51464	−0.174896
$76$	6.68601	0.766938
$77$	1.00000	0.113961
$78$	5.36804	0.607811
$79$	4.76289	0.535867	0.267933	−	0.963437i	$-0.413659\pi$
$79$	4.76289	0.535867	0.267933	+	0.963437i	$0.413659\pi$
$80$	−4.05981	−0.453901
$81$	−10.8750	−1.20833
$82$	−22.3106	−2.46380
$83$	−4.99628	−0.548413	−0.274206	−	0.961671i	$-0.588415\pi$
$83$	−4.99628	−0.548413	−0.274206	+	0.961671i	$0.588415\pi$
$84$	8.22229	0.897125
$85$	−8.02916	−0.870885
$86$	−6.56259	−0.707663
$87$	0.289879	0.0310783
$88$	3.88519	0.414163
$89$	14.8872	1.57804	0.789022	−	0.614365i	$-0.210588\pi$
$89$	14.8872	1.57804	0.789022	+	0.614365i	$0.210588\pi$
$90$	−10.4359	−1.10004
$91$	1.00000	0.104828
$92$	−16.7110	−1.74224
$93$	8.08281	0.838148
$94$	25.4086	2.62069
$95$	−3.82593	−0.392532
$96$	−7.09631	−0.724264
$97$	−6.93934	−0.704583	−0.352291	−	0.935890i	$-0.614597\pi$
$97$	−6.93934	−0.704583	−0.352291	+	0.935890i	$0.614597\pi$
$98$	2.37413	0.239823
$99$	2.11240	0.212304
$100$	−2.43601	−0.243601
$101$	5.43709	0.541011	0.270505	−	0.962718i	$-0.412809\pi$
$101$	5.43709	0.541011	0.270505	+	0.962718i	$0.412809\pi$
$102$	20.7127	2.05086
$103$	3.29650	0.324814	0.162407	−	0.986724i	$-0.448074\pi$
$103$	3.29650	0.324814	0.162407	+	0.986724i	$0.448074\pi$
$104$	3.88519	0.380975
$105$	−4.70503	−0.459164
$106$	−27.9715	−2.71683
$107$	−4.31949	−0.417581	−0.208790	−	0.977960i	$-0.566953\pi$
$107$	−4.31949	−0.417581	−0.208790	+	0.977960i	$0.566953\pi$
$108$	−7.29813	−0.702263
$109$	14.6179	1.40014	0.700072	−	0.714072i	$-0.253151\pi$
$109$	14.6179	1.40014	0.700072	+	0.714072i	$0.253151\pi$
$110$	−4.94030	−0.471039
$111$	−7.27170	−0.690200
$112$	1.95099	0.184352
$113$	−10.5131	−0.988988	−0.494494	−	0.869181i	$-0.664647\pi$
$113$	−10.5131	−0.988988	−0.494494	+	0.869181i	$0.664647\pi$
$114$	9.86967	0.924379
$115$	9.56250	0.891708
$116$	0.466214	0.0432869
$117$	2.11240	0.195291
$118$	−21.6102	−1.98938
$119$	3.85851	0.353709
$120$	−18.2799	−1.66872
$121$	1.00000	0.0909091
$122$	11.6801	1.05747
$123$	−21.2481	−1.91588
$124$	12.9996	1.16740
$125$	11.7984	1.05528
$126$	5.01509	0.446780
$127$	10.2998	0.913960	0.456980	−	0.889477i	$-0.348931\pi$
$127$	10.2998	0.913960	0.456980	+	0.889477i	$0.348931\pi$
$128$	−20.6768	−1.82759
$129$	−6.25006	−0.550287
$130$	−4.94030	−0.433293
$131$	−15.5821	−1.36141	−0.680707	−	0.732556i	$-0.738327\pi$
$131$	−15.5821	−1.36141	−0.680707	+	0.732556i	$0.738327\pi$
$132$	8.22229	0.715658
$133$	1.83860	0.159427
$134$	−25.8328	−2.23161
$135$	4.17620	0.359430
$136$	14.9911	1.28547
$137$	9.52544	0.813814	0.406907	−	0.913470i	$-0.366607\pi$
$137$	9.52544	0.813814	0.406907	+	0.913470i	$0.366607\pi$
$138$	−24.6682	−2.09990
$139$	−7.44825	−0.631752	−0.315876	−	0.948800i	$-0.602298\pi$
$139$	−7.44825	−0.631752	−0.315876	+	0.948800i	$0.602298\pi$
$140$	−7.56712	−0.639538
$141$	24.1985	2.03788
$142$	25.5164	2.14129
$143$	1.00000	0.0836242
$144$	4.12127	0.343439
$145$	−0.266781	−0.0221550
$146$	11.4396	0.946749
$147$	2.26106	0.186489
$148$	−11.6951	−0.961332
$149$	4.32198	0.354071	0.177035	−	0.984205i	$-0.443349\pi$
$149$	4.32198	0.354071	0.177035	+	0.984205i	$0.443349\pi$
$150$	−3.59595	−0.293608
$151$	−1.21373	−0.0987718	−0.0493859	−	0.998780i	$-0.515726\pi$
$151$	−1.21373	−0.0987718	−0.0493859	+	0.998780i	$0.515726\pi$
$152$	7.14331	0.579399
$153$	8.15071	0.658946
$154$	2.37413	0.191313
$155$	−7.43875	−0.597495
$156$	8.22229	0.658310
$157$	3.71522	0.296507	0.148253	−	0.988949i	$-0.452635\pi$
$157$	3.71522	0.296507	0.148253	+	0.988949i	$0.452635\pi$
$158$	11.3077	0.899592
$159$	−26.6393	−2.11264
$160$	6.53085	0.516309
$161$	−4.59538	−0.362167
$162$	−25.8185	−2.02850
$163$	10.3138	0.807842	0.403921	−	0.914794i	$-0.367647\pi$
$163$	10.3138	0.807842	0.403921	+	0.914794i	$0.367647\pi$
$164$	−34.1734	−2.66850
$165$	−4.70503	−0.366286
$166$	−11.8618	−0.920654
$167$	−9.00596	−0.696902	−0.348451	−	0.937327i	$-0.613292\pi$
$167$	−9.00596	−0.696902	−0.348451	+	0.937327i	$0.613292\pi$
$168$	8.78466	0.677751
$169$	1.00000	0.0769231
$170$	−19.0622	−1.46201
$171$	3.88385	0.297005
$172$	−10.0520	−0.766457
$173$	13.0621	0.993092	0.496546	−	0.868010i	$-0.334601\pi$
$173$	13.0621	0.993092	0.496546	+	0.868010i	$0.334601\pi$
$174$	0.688210	0.0521731
$175$	−0.669881	−0.0506383
$176$	1.95099	0.147062
$177$	−20.5811	−1.54697
$178$	35.3442	2.64916
$179$	−2.63072	−0.196629	−0.0983145	−	0.995155i	$-0.531345\pi$
$179$	−2.63072	−0.196629	−0.0983145	+	0.995155i	$0.531345\pi$
$180$	−15.9847	−1.19143
$181$	10.7315	0.797669	0.398835	−	0.917023i	$-0.369415\pi$
$181$	10.7315	0.797669	0.398835	+	0.917023i	$0.369415\pi$
$182$	2.37413	0.175982
$183$	11.1238	0.822298
$184$	−17.8540	−1.31621
$185$	6.69228	0.492026
$186$	19.1896	1.40705
$187$	3.85851	0.282163
$188$	38.9186	2.83843
$189$	−2.00693	−0.145982
$190$	−9.08323	−0.658967
$191$	2.68265	0.194110	0.0970548	−	0.995279i	$-0.469058\pi$
$191$	2.68265	0.194110	0.0970548	+	0.995279i	$0.469058\pi$
$192$	−25.6702	−1.85258
$193$	24.0654	1.73227	0.866134	−	0.499811i	$-0.166597\pi$
$193$	24.0654	1.73227	0.866134	+	0.499811i	$0.166597\pi$
$194$	−16.4749	−1.18283
$195$	−4.70503	−0.336934
$196$	3.63647	0.259748
$197$	2.95469	0.210513	0.105256	−	0.994445i	$-0.466434\pi$
$197$	2.95469	0.210513	0.105256	+	0.994445i	$0.466434\pi$
$198$	5.01509	0.356407
$199$	14.6510	1.03858	0.519291	−	0.854597i	$-0.326196\pi$
$199$	14.6510	1.03858	0.519291	+	0.854597i	$0.326196\pi$
$200$	−2.60262	−0.184033
$201$	−24.6025	−1.73533
$202$	12.9083	0.908227
$203$	0.128205	0.00899823
$204$	31.7258	2.22125
$205$	19.5550	1.36578
$206$	7.82632	0.545285
$207$	−9.70727	−0.674702
$208$	1.95099	0.135277
$209$	1.83860	0.127178
$210$	−11.1703	−0.770826
$211$	11.0252	0.759005	0.379503	−	0.925191i	$-0.376095\pi$
$211$	11.0252	0.759005	0.379503	+	0.925191i	$0.376095\pi$
$212$	−42.8442	−2.94255
$213$	24.3012	1.66509
$214$	−10.2550	−0.701018
$215$	5.75204	0.392286
$216$	−7.79730	−0.530539
$217$	3.57479	0.242672
$218$	34.7048	2.35051
$219$	10.8948	0.736203
$220$	−7.56712	−0.510175
$221$	3.85851	0.259552
$222$	−17.2639	−1.15868
$223$	10.4809	0.701850	0.350925	−	0.936404i	$-0.385867\pi$
$223$	10.4809	0.701850	0.350925	+	0.936404i	$0.385867\pi$
$224$	−3.13848	−0.209699
$225$	−1.41505	−0.0943370
$226$	−24.9594	−1.66027
$227$	7.06968	0.469231	0.234616	−	0.972088i	$-0.424617\pi$
$227$	7.06968	0.469231	0.234616	+	0.972088i	$0.424617\pi$
$228$	15.1175	1.00118
$229$	28.4421	1.87951	0.939754	−	0.341851i	$-0.111054\pi$
$229$	28.4421	1.87951	0.939754	+	0.341851i	$0.111054\pi$
$230$	22.7026	1.49696
$231$	2.26106	0.148767
$232$	0.498101	0.0327020
$233$	−4.86695	−0.318844	−0.159422	−	0.987210i	$-0.550963\pi$
$233$	−4.86695	−0.318844	−0.159422	+	0.987210i	$0.550963\pi$
$234$	5.01509	0.327847
$235$	−22.2703	−1.45275
$236$	−33.1006	−2.15467
$237$	10.7692	0.699533
$238$	9.16060	0.593794
$239$	−27.2784	−1.76449	−0.882245	−	0.470791i	$-0.843969\pi$
$239$	−27.2784	−1.76449	−0.882245	+	0.470791i	$0.843969\pi$
$240$	−9.17948	−0.592533
$241$	8.15425	0.525261	0.262631	−	0.964896i	$-0.415410\pi$
$241$	8.15425	0.525261	0.262631	+	0.964896i	$0.415410\pi$
$242$	2.37413	0.152615
$243$	−18.5682	−1.19115
$244$	17.8905	1.14532
$245$	−2.08089	−0.132943
$246$	−50.4457	−3.21630
$247$	1.83860	0.116987
$248$	13.8887	0.881936
$249$	−11.2969	−0.715912
$250$	28.0109	1.77157
$251$	12.4020	0.782806	0.391403	−	0.920219i	$-0.371990\pi$
$251$	12.4020	0.782806	0.391403	+	0.920219i	$0.371990\pi$
$252$	7.68167	0.483900
$253$	−4.59538	−0.288909
$254$	24.4530	1.53432
$255$	−18.1544	−1.13687
$256$	−26.3831	−1.64894
$257$	17.7296	1.10594	0.552971	−	0.833200i	$-0.313494\pi$
$257$	17.7296	1.10594	0.552971	+	0.833200i	$0.313494\pi$
$258$	−14.8384	−0.923800
$259$	−3.21606	−0.199836
$260$	−7.56712	−0.469293
$261$	0.270820	0.0167633
$262$	−36.9939	−2.28549
$263$	−13.6351	−0.840779	−0.420389	−	0.907344i	$-0.638107\pi$
$263$	−13.6351	−0.840779	−0.420389	+	0.907344i	$0.638107\pi$
$264$	8.78466	0.540659
$265$	24.5167	1.50605
$266$	4.36506	0.267639
$267$	33.6609	2.06002
$268$	−39.5684	−2.41702
$269$	6.90249	0.420852	0.210426	−	0.977610i	$-0.432515\pi$
$269$	6.90249	0.420852	0.210426	+	0.977610i	$0.432515\pi$
$270$	9.91482	0.603397
$271$	−5.49364	−0.333715	−0.166857	−	0.985981i	$-0.553362\pi$
$271$	−5.49364	−0.333715	−0.166857	+	0.985981i	$0.553362\pi$
$272$	7.52794	0.456448
$273$	2.26106	0.136846
$274$	22.6146	1.36620
$275$	−0.669881	−0.0403954
$276$	−37.7846	−2.27436
$277$	−31.6237	−1.90008	−0.950041	−	0.312124i	$-0.898959\pi$
$277$	−31.6237	−1.90008	−0.950041	+	0.312124i	$0.898959\pi$
$278$	−17.6831	−1.06056
$279$	7.55136	0.452088
$280$	−8.08468	−0.483152
$281$	−5.29433	−0.315833	−0.157916	−	0.987452i	$-0.550478\pi$
$281$	−5.29433	−0.315833	−0.157916	+	0.987452i	$0.550478\pi$
$282$	57.4503	3.42112
$283$	−4.71581	−0.280326	−0.140163	−	0.990128i	$-0.544763\pi$
$283$	−4.71581	−0.280326	−0.140163	+	0.990128i	$0.544763\pi$
$284$	39.0837	2.31919
$285$	−8.65065	−0.512420
$286$	2.37413	0.140385
$287$	−9.39741	−0.554711
$288$	−6.62972	−0.390660
$289$	−2.11186	−0.124227
$290$	−0.633372	−0.0371929
$291$	−15.6903	−0.919779
$292$	17.5222	1.02541
$293$	−11.8415	−0.691789	−0.345895	−	0.938273i	$-0.612425\pi$
$293$	−11.8415	−0.691789	−0.345895	+	0.938273i	$0.612425\pi$
$294$	5.36804	0.313071
$295$	18.9411	1.10279
$296$	−12.4950	−0.726258
$297$	−2.00693	−0.116454
$298$	10.2609	0.594400
$299$	−4.59538	−0.265758
$300$	−5.50796	−0.318002
$301$	−2.76421	−0.159327
$302$	−2.88154	−0.165814
$303$	12.2936	0.706248
$304$	3.58709	0.205734
$305$	−10.2375	−0.586196
$306$	19.3508	1.10621
$307$	17.7656	1.01394	0.506968	−	0.861965i	$-0.330766\pi$
$307$	17.7656	1.01394	0.506968	+	0.861965i	$0.330766\pi$
$308$	3.63647	0.207207
$309$	7.45360	0.424020
$310$	−17.6605	−1.00305
$311$	−31.5620	−1.78971	−0.894857	−	0.446352i	$-0.852723\pi$
$311$	−31.5620	−1.78971	−0.894857	+	0.446352i	$0.852723\pi$
$312$	8.78466	0.497334
$313$	−26.6834	−1.50824	−0.754119	−	0.656738i	$-0.771936\pi$
$313$	−26.6834	−1.50824	−0.754119	+	0.656738i	$0.771936\pi$
$314$	8.82039	0.497763
$315$	−4.39567	−0.247668
$316$	17.3201	0.974333
$317$	−23.4911	−1.31939	−0.659697	−	0.751532i	$-0.729315\pi$
$317$	−23.4911	−1.31939	−0.659697	+	0.751532i	$0.729315\pi$
$318$	−63.2452	−3.54661
$319$	0.128205	0.00717810
$320$	23.6247	1.32066
$321$	−9.76663	−0.545120
$322$	−10.9100	−0.607991
$323$	7.09425	0.394735
$324$	−39.5465	−2.19703
$325$	−0.669881	−0.0371583
$326$	24.4863	1.35617
$327$	33.0521	1.82778
$328$	−36.5108	−2.01597
$329$	10.7023	0.590036
$330$	−11.1703	−0.614906
$331$	2.83531	0.155843	0.0779213	−	0.996960i	$-0.475172\pi$
$331$	2.83531	0.155843	0.0779213	+	0.996960i	$0.475172\pi$
$332$	−18.1688	−0.997145
$333$	−6.79359	−0.372286
$334$	−21.3813	−1.16993
$335$	22.6421	1.23707
$336$	4.41132	0.240657
$337$	−26.9682	−1.46905	−0.734527	−	0.678580i	$-0.762596\pi$
$337$	−26.9682	−1.46905	−0.734527	+	0.678580i	$0.762596\pi$
$338$	2.37413	0.129135
$339$	−23.7707	−1.29105
$340$	−29.1978	−1.58347
$341$	3.57479	0.193585
$342$	9.22074	0.498600
$343$	1.00000	0.0539949
$344$	−10.7395	−0.579036
$345$	21.6214	1.16406
$346$	31.0110	1.66716
$347$	−17.3376	−0.930730	−0.465365	−	0.885119i	$-0.654077\pi$
$347$	−17.3376	−0.930730	−0.465365	+	0.885119i	$0.654077\pi$
$348$	1.05414	0.0565078
$349$	−9.32656	−0.499239	−0.249620	−	0.968344i	$-0.580306\pi$
$349$	−9.32656	−0.499239	−0.249620	+	0.968344i	$0.580306\pi$
$350$	−1.59038	−0.0850095
$351$	−2.00693	−0.107122
$352$	−3.13848	−0.167282
$353$	−30.4825	−1.62242	−0.811209	−	0.584756i	$-0.801190\pi$
$353$	−30.4825	−1.62242	−0.811209	+	0.584756i	$0.801190\pi$
$354$	−48.8621	−2.59699
$355$	−22.3648	−1.18700
$356$	54.1370	2.86926
$357$	8.72434	0.461741
$358$	−6.24565	−0.330093
$359$	36.2754	1.91454	0.957270	−	0.289196i	$-0.0933878\pi$
$359$	36.2754	1.91454	0.957270	+	0.289196i	$0.0933878\pi$
$360$	−17.0780	−0.900092
$361$	−15.6196	−0.822082
$362$	25.4780	1.33910
$363$	2.26106	0.118675
$364$	3.63647	0.190603
$365$	−10.0267	−0.524821
$366$	26.4094	1.38044
$367$	−6.99672	−0.365226	−0.182613	−	0.983185i	$-0.558455\pi$
$367$	−6.99672	−0.365226	−0.182613	+	0.983185i	$0.558455\pi$
$368$	−8.96556	−0.467362
$369$	−19.8510	−1.03340
$370$	15.8883	0.825994
$371$	−11.7818	−0.611680
$372$	29.3929	1.52395
$373$	15.7550	0.815761	0.407881	−	0.913035i	$-0.366268\pi$
$373$	15.7550	0.815761	0.407881	+	0.913035i	$0.366268\pi$
$374$	9.16060	0.473683
$375$	26.6769	1.37759
$376$	41.5804	2.14435
$377$	0.128205	0.00660289
$378$	−4.76469	−0.245069
$379$	19.1046	0.981338	0.490669	−	0.871346i	$-0.336752\pi$
$379$	19.1046	0.981338	0.490669	+	0.871346i	$0.336752\pi$
$380$	−13.9129	−0.713716
$381$	23.2885	1.19311
$382$	6.36895	0.325864
$383$	31.1418	1.59127	0.795636	−	0.605775i	$-0.207137\pi$
$383$	31.1418	1.59127	0.795636	+	0.605775i	$0.207137\pi$
$384$	−46.7516	−2.38578
$385$	−2.08089	−0.106052
$386$	57.1344	2.90806
$387$	−5.83912	−0.296819
$388$	−25.2347	−1.28110
$389$	25.5433	1.29510	0.647549	−	0.762024i	$-0.275794\pi$
$389$	25.5433	1.29510	0.647549	+	0.762024i	$0.275794\pi$
$390$	−11.1703	−0.565632
$391$	−17.7314	−0.896713
$392$	3.88519	0.196232
$393$	−35.2321	−1.77722
$394$	7.01480	0.353400
$395$	−9.91106	−0.498680
$396$	7.68167	0.386019
$397$	18.0153	0.904162	0.452081	−	0.891977i	$-0.350682\pi$
$397$	18.0153	0.904162	0.452081	+	0.891977i	$0.350682\pi$
$398$	34.7833	1.74353
$399$	4.15718	0.208119
$400$	−1.30693	−0.0653467
$401$	15.8891	0.793464	0.396732	−	0.917935i	$-0.370144\pi$
$401$	15.8891	0.793464	0.396732	+	0.917935i	$0.370144\pi$
$402$	−58.4095	−2.91320
$403$	3.57479	0.178073
$404$	19.7718	0.983685
$405$	22.6297	1.12448
$406$	0.304375	0.0151059
$407$	−3.21606	−0.159414
$408$	33.8957	1.67809
$409$	12.7313	0.629522	0.314761	−	0.949171i	$-0.398076\pi$
$409$	12.7313	0.629522	0.314761	+	0.949171i	$0.398076\pi$
$410$	46.4260	2.29282
$411$	21.5376	1.06237
$412$	11.9877	0.590589
$413$	−9.10240	−0.447900
$414$	−23.0463	−1.13266
$415$	10.3967	0.510355
$416$	−3.13848	−0.153877
$417$	−16.8409	−0.824704
$418$	4.36506	0.213502
$419$	6.41767	0.313524	0.156762	−	0.987636i	$-0.449894\pi$
$419$	6.41767	0.313524	0.156762	+	0.987636i	$0.449894\pi$
$420$	−17.1097	−0.834868
$421$	2.32413	0.113271	0.0566356	−	0.998395i	$-0.481963\pi$
$421$	2.32413	0.113271	0.0566356	+	0.998395i	$0.481963\pi$
$422$	26.1752	1.27419
$423$	22.6075	1.09921
$424$	−45.7745	−2.22301
$425$	−2.58475	−0.125379
$426$	57.6941	2.79529
$427$	4.91974	0.238083
$428$	−15.7077	−0.759261
$429$	2.26106	0.109165
$430$	13.6561	0.658554
$431$	6.65129	0.320381	0.160191	−	0.987086i	$-0.448789\pi$
$431$	6.65129	0.320381	0.160191	+	0.987086i	$0.448789\pi$
$432$	−3.91550	−0.188385
$433$	25.3877	1.22006	0.610028	−	0.792380i	$-0.291158\pi$
$433$	25.3877	1.22006	0.610028	+	0.792380i	$0.291158\pi$
$434$	8.48699	0.407389
$435$	−0.603208	−0.0289216
$436$	53.1578	2.54580
$437$	−8.44906	−0.404173
$438$	25.8657	1.23591
$439$	−33.3569	−1.59204	−0.796018	−	0.605273i	$-0.793064\pi$
$439$	−33.3569	−1.59204	−0.796018	+	0.605273i	$0.793064\pi$
$440$	−8.08468	−0.385422
$441$	2.11240	0.100590
$442$	9.16060	0.435725
$443$	−25.9273	−1.23184	−0.615921	−	0.787808i	$-0.711216\pi$
$443$	−25.9273	−1.23184	−0.615921	+	0.787808i	$0.711216\pi$
$444$	−26.4434	−1.25495
$445$	−30.9787	−1.46853
$446$	24.8829	1.17824
$447$	9.77227	0.462212
$448$	−11.3531	−0.536386
$449$	−16.3593	−0.772041	−0.386021	−	0.922490i	$-0.626151\pi$
$449$	−16.3593	−0.772041	−0.386021	+	0.922490i	$0.626151\pi$
$450$	−3.35952	−0.158369
$451$	−9.39741	−0.442507
$452$	−38.2306	−1.79822
$453$	−2.74431	−0.128939
$454$	16.7843	0.787727
$455$	−2.08089	−0.0975538
$456$	16.1515	0.756361
$457$	3.66890	0.171624	0.0858120	−	0.996311i	$-0.472652\pi$
$457$	3.66890	0.171624	0.0858120	+	0.996311i	$0.472652\pi$
$458$	67.5252	3.15524
$459$	−7.74375	−0.361447
$460$	34.7738	1.62134
$461$	−41.9352	−1.95311	−0.976557	−	0.215257i	$-0.930941\pi$
$461$	−41.9352	−1.95311	−0.976557	+	0.215257i	$0.930941\pi$
$462$	5.36804	0.249744
$463$	21.7026	1.00860	0.504302	−	0.863528i	$-0.331750\pi$
$463$	21.7026	1.00860	0.504302	+	0.863528i	$0.331750\pi$
$464$	0.250127	0.0116119
$465$	−16.8195	−0.779984
$466$	−11.5547	−0.535263
$467$	12.6521	0.585468	0.292734	−	0.956194i	$-0.405435\pi$
$467$	12.6521	0.585468	0.292734	+	0.956194i	$0.405435\pi$
$468$	7.68167	0.355085
$469$	−10.8810	−0.502437
$470$	−52.8725	−2.43883
$471$	8.40033	0.387067
$472$	−35.3646	−1.62779
$473$	−2.76421	−0.127099
$474$	25.5674	1.17435
$475$	−1.23164	−0.0565116
$476$	14.0314	0.643128
$477$	−24.8878	−1.13953
$478$	−64.7622	−2.96216
$479$	−10.4477	−0.477368	−0.238684	−	0.971097i	$-0.576716\pi$
$479$	−10.4477	−0.477368	−0.238684	+	0.971097i	$0.576716\pi$
$480$	14.7667	0.674003
$481$	−3.21606	−0.146640
$482$	19.3592	0.881788
$483$	−10.3904	−0.472781
$484$	3.63647	0.165294
$485$	14.4400	0.655687
$486$	−44.0832	−1.99966
$487$	−29.3811	−1.33139	−0.665693	−	0.746226i	$-0.731864\pi$
$487$	−29.3811	−1.33139	−0.665693	+	0.746226i	$0.731864\pi$
$488$	19.1142	0.865258
$489$	23.3202	1.05458
$490$	−4.94030	−0.223180
$491$	−5.97792	−0.269780	−0.134890	−	0.990861i	$-0.543068\pi$
$491$	−5.97792	−0.269780	−0.134890	+	0.990861i	$0.543068\pi$
$492$	−77.2682	−3.48352
$493$	0.494681	0.0222793
$494$	4.36506	0.196393
$495$	−4.39567	−0.197571
$496$	6.97438	0.313159
$497$	10.7477	0.482100
$498$	−26.8202	−1.20184
$499$	31.2904	1.40075	0.700374	−	0.713776i	$-0.253016\pi$
$499$	31.2904	1.40075	0.700374	+	0.713776i	$0.253016\pi$
$500$	42.9046	1.91875
$501$	−20.3630	−0.909752
$502$	29.4438	1.31414
$503$	−12.3031	−0.548570	−0.274285	−	0.961648i	$-0.588441\pi$
$503$	−12.3031	−0.548570	−0.274285	+	0.961648i	$0.588441\pi$
$504$	8.20707	0.365572
$505$	−11.3140	−0.503467
$506$	−10.9100	−0.485009
$507$	2.26106	0.100417
$508$	37.4550	1.66180
$509$	−29.1218	−1.29080	−0.645400	−	0.763845i	$-0.723309\pi$
$509$	−29.1218	−1.29080	−0.645400	+	0.763845i	$0.723309\pi$
$510$	−43.1009	−1.90854
$511$	4.81845	0.213156
$512$	−21.2831	−0.940591
$513$	−3.68993	−0.162914
$514$	42.0923	1.85661
$515$	−6.85968	−0.302273
$516$	−22.7282	−1.00055
$517$	10.7023	0.470686
$518$	−7.63533	−0.335477
$519$	29.5342	1.29641
$520$	−8.08468	−0.354537
$521$	7.69028	0.336917	0.168459	−	0.985709i	$-0.446121\pi$
$521$	7.69028	0.336917	0.168459	+	0.985709i	$0.446121\pi$
$522$	0.642960	0.0281416
$523$	−34.5649	−1.51142	−0.755709	−	0.654907i	$-0.772708\pi$
$523$	−34.5649	−1.51142	−0.755709	+	0.654907i	$0.772708\pi$
$524$	−56.6639	−2.47537
$525$	−1.51464	−0.0661044
$526$	−32.3715	−1.41147
$527$	13.7934	0.600848
$528$	4.41132	0.191978
$529$	−1.88246	−0.0818461
$530$	58.2056	2.52829
$531$	−19.2279	−0.834418
$532$	6.68601	0.289875
$533$	−9.39741	−0.407047
$534$	79.9153	3.45827
$535$	8.98840	0.388602
$536$	−42.2747	−1.82599
$537$	−5.94821	−0.256684
$538$	16.3874	0.706510
$539$	1.00000	0.0430730
$540$	15.1866	0.653529
$541$	−5.51584	−0.237144	−0.118572	−	0.992945i	$-0.537832\pi$
$541$	−5.51584	−0.237144	−0.118572	+	0.992945i	$0.537832\pi$
$542$	−13.0426	−0.560227
$543$	24.2647	1.04130
$544$	−12.1099	−0.519207
$545$	−30.4184	−1.30298
$546$	5.36804	0.229731
$547$	−2.15452	−0.0921207	−0.0460604	−	0.998939i	$-0.514667\pi$
$547$	−2.15452	−0.0921207	−0.0460604	+	0.998939i	$0.514667\pi$
$548$	34.6390	1.47971
$549$	10.3925	0.443539
$550$	−1.59038	−0.0678141
$551$	0.235717	0.0100419
$552$	−40.3689	−1.71821
$553$	4.76289	0.202539
$554$	−75.0786	−3.18978
$555$	15.1316	0.642302
$556$	−27.0853	−1.14867
$557$	0.916260	0.0388232	0.0194116	−	0.999812i	$-0.493821\pi$
$557$	0.916260	0.0388232	0.0194116	+	0.999812i	$0.493821\pi$
$558$	17.9279	0.758948
$559$	−2.76421	−0.116914
$560$	−4.05981	−0.171558
$561$	8.72434	0.368342
$562$	−12.5694	−0.530208
$563$	2.89072	0.121829	0.0609146	−	0.998143i	$-0.480598\pi$
$563$	2.89072	0.121829	0.0609146	+	0.998143i	$0.480598\pi$
$564$	87.9972	3.70535
$565$	21.8766	0.920356
$566$	−11.1959	−0.470599
$567$	−10.8750	−0.456706
$568$	41.7569	1.75208
$569$	6.41458	0.268913	0.134457	−	0.990919i	$-0.457071\pi$
$569$	6.41458	0.268913	0.134457	+	0.990919i	$0.457071\pi$
$570$	−20.5377	−0.860231
$571$	−14.2512	−0.596393	−0.298196	−	0.954505i	$-0.596385\pi$
$571$	−14.2512	−0.596393	−0.298196	+	0.954505i	$0.596385\pi$
$572$	3.63647	0.152049
$573$	6.06563	0.253395
$574$	−22.3106	−0.931228
$575$	3.07836	0.128377
$576$	−23.9823	−0.999264
$577$	−15.8130	−0.658302	−0.329151	−	0.944277i	$-0.606763\pi$
$577$	−15.8130	−0.658302	−0.329151	+	0.944277i	$0.606763\pi$
$578$	−5.01383	−0.208548
$579$	54.4134	2.26135
$580$	−0.970142	−0.0402830
$581$	−4.99628	−0.207281
$582$	−37.2507	−1.54409
$583$	−11.7818	−0.487952
$584$	18.7206	0.774665
$585$	−4.39567	−0.181739
$586$	−28.1133	−1.16135
$587$	30.8162	1.27192	0.635961	−	0.771721i	$-0.280604\pi$
$587$	30.8162	1.27192	0.635961	+	0.771721i	$0.280604\pi$
$588$	8.22229	0.339081
$589$	6.57259	0.270819
$590$	44.9686	1.85133
$591$	6.68073	0.274808
$592$	−6.27451	−0.257881
$593$	29.6107	1.21597	0.607983	−	0.793950i	$-0.291979\pi$
$593$	29.6107	1.21597	0.607983	+	0.793950i	$0.291979\pi$
$594$	−4.76469	−0.195498
$595$	−8.02916	−0.329163
$596$	15.7168	0.643784
$597$	33.1268	1.35579
$598$	−10.9100	−0.446144
$599$	28.3260	1.15737	0.578685	−	0.815551i	$-0.303566\pi$
$599$	28.3260	1.15737	0.578685	+	0.815551i	$0.303566\pi$
$600$	−5.88468	−0.240241
$601$	32.1449	1.31122	0.655608	−	0.755101i	$-0.272412\pi$
$601$	32.1449	1.31122	0.655608	+	0.755101i	$0.272412\pi$
$602$	−6.56259	−0.267471
$603$	−22.9849	−0.936019
$604$	−4.41369	−0.179591
$605$	−2.08089	−0.0846004
$606$	29.1865	1.18562
$607$	10.2077	0.414317	0.207158	−	0.978307i	$-0.433578\pi$
$607$	10.2077	0.414317	0.207158	+	0.978307i	$0.433578\pi$
$608$	−5.77041	−0.234021
$609$	0.289879	0.0117465
$610$	−24.3050	−0.984082
$611$	10.7023	0.432968
$612$	29.6399	1.19812
$613$	−2.95007	−0.119152	−0.0595760	−	0.998224i	$-0.518975\pi$
$613$	−2.95007	−0.119152	−0.0595760	+	0.998224i	$0.518975\pi$
$614$	42.1778	1.70216
$615$	44.2151	1.78292
$616$	3.88519	0.156539
$617$	46.3393	1.86555	0.932774	−	0.360461i	$-0.117381\pi$
$617$	46.3393	1.86555	0.932774	+	0.360461i	$0.117381\pi$
$618$	17.6958	0.711829
$619$	9.74230	0.391576	0.195788	−	0.980646i	$-0.437274\pi$
$619$	9.74230	0.391576	0.195788	+	0.980646i	$0.437274\pi$
$620$	−27.0508	−1.08639
$621$	9.22259	0.370090
$622$	−74.9321	−3.00450
$623$	14.8872	0.596444
$624$	4.41132	0.176594
$625$	−21.2019	−0.848074
$626$	−63.3498	−2.53197
$627$	4.15718	0.166022
$628$	13.5103	0.539119
$629$	−12.4092	−0.494788
$630$	−10.4359	−0.415775
$631$	26.9875	1.07435	0.537177	−	0.843469i	$-0.319491\pi$
$631$	26.9875	1.07435	0.537177	+	0.843469i	$0.319491\pi$
$632$	18.5047	0.736079
$633$	24.9286	0.990823
$634$	−55.7709	−2.21494
$635$	−21.4328	−0.850535
$636$	−96.8733	−3.84127
$637$	1.00000	0.0396214
$638$	0.304375	0.0120503
$639$	22.7034	0.898133
$640$	43.0263	1.70076
$641$	−22.2599	−0.879213	−0.439606	−	0.898191i	$-0.644882\pi$
$641$	−22.2599	−0.879213	−0.439606	+	0.898191i	$0.644882\pi$
$642$	−23.1872	−0.915126
$643$	−44.4299	−1.75214	−0.876072	−	0.482180i	$-0.839845\pi$
$643$	−44.4299	−1.75214	−0.876072	+	0.482180i	$0.839845\pi$
$644$	−16.7110	−0.658505
$645$	13.0057	0.512099
$646$	16.8427	0.662665
$647$	29.0712	1.14291	0.571453	−	0.820635i	$-0.306380\pi$
$647$	29.0712	1.14291	0.571453	+	0.820635i	$0.306380\pi$
$648$	−42.2514	−1.65979
$649$	−9.10240	−0.357300
$650$	−1.59038	−0.0623799
$651$	8.08281	0.316790
$652$	37.5060	1.46885
$653$	5.67765	0.222184	0.111092	−	0.993810i	$-0.464565\pi$
$653$	5.67765	0.222184	0.111092	+	0.993810i	$0.464565\pi$
$654$	78.4697	3.06841
$655$	32.4247	1.26694
$656$	−18.3343	−0.715833
$657$	10.1785	0.397100
$658$	25.4086	0.990529
$659$	11.1307	0.433591	0.216795	−	0.976217i	$-0.430440\pi$
$659$	11.1307	0.433591	0.216795	+	0.976217i	$0.430440\pi$
$660$	−17.1097	−0.665994
$661$	−6.96243	−0.270807	−0.135403	−	0.990791i	$-0.543233\pi$
$661$	−6.96243	−0.270807	−0.135403	+	0.990791i	$0.543233\pi$
$662$	6.73138	0.261622
$663$	8.72434	0.338825
$664$	−19.4115	−0.753313
$665$	−3.82593	−0.148363
$666$	−16.1288	−0.624980
$667$	−0.589151	−0.0228120
$668$	−32.7499	−1.26713
$669$	23.6979	0.916212
$670$	53.7553	2.07675
$671$	4.91974	0.189925
$672$	−7.09631	−0.273746
$673$	40.9320	1.57781	0.788905	−	0.614515i	$-0.210648\pi$
$673$	40.9320	1.57781	0.788905	+	0.614515i	$0.210648\pi$
$674$	−64.0260	−2.46619
$675$	1.34440	0.0517461
$676$	3.63647	0.139864
$677$	24.7383	0.950772	0.475386	−	0.879777i	$-0.342309\pi$
$677$	24.7383	0.950772	0.475386	+	0.879777i	$0.342309\pi$
$678$	−56.4347	−2.16736
$679$	−6.93934	−0.266307
$680$	−31.1948	−1.19627
$681$	15.9850	0.612546
$682$	8.48699	0.324984
$683$	−20.3477	−0.778583	−0.389292	−	0.921115i	$-0.627280\pi$
$683$	−20.3477	−0.778583	−0.389292	+	0.921115i	$0.627280\pi$
$684$	14.1235	0.540026
$685$	−19.8214	−0.757338
$686$	2.37413	0.0906445
$687$	64.3094	2.45356
$688$	−5.39296	−0.205605
$689$	−11.7818	−0.448850
$690$	51.3319	1.95417
$691$	0.761328	0.0289623	0.0144811	−	0.999895i	$-0.495390\pi$
$691$	0.761328	0.0289623	0.0144811	+	0.999895i	$0.495390\pi$
$692$	47.4999	1.80568
$693$	2.11240	0.0802433
$694$	−41.1616	−1.56247
$695$	15.4990	0.587911
$696$	1.12624	0.0426899
$697$	−36.2600	−1.37345
$698$	−22.1424	−0.838103
$699$	−11.0045	−0.416227
$700$	−2.43601	−0.0920724
$701$	−43.2847	−1.63484	−0.817420	−	0.576042i	$-0.804597\pi$
$701$	−43.2847	−1.63484	−0.817420	+	0.576042i	$0.804597\pi$
$702$	−4.76469	−0.179832
$703$	−5.91304	−0.223014
$704$	−11.3531	−0.427888
$705$	−50.3545	−1.89646
$706$	−72.3692	−2.72365
$707$	5.43709	0.204483
$708$	−74.8425	−2.81275
$709$	19.6424	0.737686	0.368843	−	0.929492i	$-0.379754\pi$
$709$	19.6424	0.737686	0.368843	+	0.929492i	$0.379754\pi$
$710$	−53.0969	−1.99269
$711$	10.0611	0.377321
$712$	57.8398	2.16764
$713$	−16.4275	−0.615215
$714$	20.7127	0.775152
$715$	−2.08089	−0.0778210
$716$	−9.56653	−0.357518
$717$	−61.6780	−2.30341
$718$	86.1223	3.21405
$719$	−4.93411	−0.184011	−0.0920056	−	0.995758i	$-0.529328\pi$
$719$	−4.93411	−0.184011	−0.0920056	+	0.995758i	$0.529328\pi$
$720$	−8.57593	−0.319606
$721$	3.29650	0.122768
$722$	−37.0828	−1.38008
$723$	18.4373	0.685689
$724$	39.0250	1.45035
$725$	−0.0858821	−0.00318958
$726$	5.36804	0.199227
$727$	−17.1051	−0.634394	−0.317197	−	0.948360i	$-0.602742\pi$
$727$	−17.1051	−0.634394	−0.317197	+	0.948360i	$0.602742\pi$
$728$	3.88519	0.143995
$729$	−9.35890	−0.346626
$730$	−23.8046	−0.881048
$731$	−10.6658	−0.394487
$732$	40.4516	1.49513
$733$	−9.05182	−0.334336	−0.167168	−	0.985928i	$-0.553462\pi$
$733$	−9.05182	−0.334336	−0.167168	+	0.985928i	$0.553462\pi$
$734$	−16.6111	−0.613127
$735$	−4.70503	−0.173548
$736$	14.4225	0.531622
$737$	−10.8810	−0.400806
$738$	−47.1289	−1.73484
$739$	−8.31072	−0.305715	−0.152857	−	0.988248i	$-0.548848\pi$
$739$	−8.31072	−0.305715	−0.152857	+	0.988248i	$0.548848\pi$
$740$	24.3363	0.894620
$741$	4.15718	0.152718
$742$	−27.9715	−1.02686
$743$	32.8048	1.20349	0.601746	−	0.798687i	$-0.294472\pi$
$743$	32.8048	1.20349	0.601746	+	0.798687i	$0.294472\pi$
$744$	31.4033	1.15130
$745$	−8.99359	−0.329499
$746$	37.4043	1.36947
$747$	−10.5541	−0.386155
$748$	14.0314	0.513038
$749$	−4.31949	−0.157831
$750$	63.3344	2.31265
$751$	−45.3148	−1.65356	−0.826780	−	0.562525i	$-0.809830\pi$
$751$	−45.3148	−1.65356	−0.826780	+	0.562525i	$0.809830\pi$
$752$	20.8801	0.761418
$753$	28.0416	1.02189
$754$	0.304375	0.0110847
$755$	2.52564	0.0919175
$756$	−7.29813	−0.265431
$757$	40.3667	1.46715	0.733576	−	0.679607i	$-0.237850\pi$
$757$	40.3667	1.46715	0.733576	+	0.679607i	$0.237850\pi$
$758$	45.3568	1.64743
$759$	−10.3904	−0.377149
$760$	−14.8645	−0.539191
$761$	−44.4822	−1.61248	−0.806240	−	0.591589i	$-0.798501\pi$
$761$	−44.4822	−1.61248	−0.806240	+	0.591589i	$0.798501\pi$
$762$	55.2898	2.00294
$763$	14.6179	0.529205
$764$	9.75538	0.352937
$765$	−16.9608	−0.613218
$766$	73.9346	2.67136
$767$	−9.10240	−0.328668
$768$	−59.6538	−2.15257
$769$	3.84584	0.138685	0.0693424	−	0.997593i	$-0.477910\pi$
$769$	3.84584	0.138685	0.0693424	+	0.997593i	$0.477910\pi$
$770$	−4.94030	−0.178036
$771$	40.0877	1.44372
$772$	87.5134	3.14967
$773$	−43.6866	−1.57130	−0.785648	−	0.618674i	$-0.787670\pi$
$773$	−43.6866	−1.57130	−0.785648	+	0.618674i	$0.787670\pi$
$774$	−13.8628	−0.498288
$775$	−2.39468	−0.0860195
$776$	−26.9607	−0.967832
$777$	−7.27170	−0.260871
$778$	60.6431	2.17416
$779$	−17.2780	−0.619050
$780$	−17.1097	−0.612626
$781$	10.7477	0.384583
$782$	−42.0965	−1.50537
$783$	−0.257298	−0.00919508
$784$	1.95099	0.0696783
$785$	−7.73097	−0.275930
$786$	−83.6454	−2.98353
$787$	6.34450	0.226157	0.113079	−	0.993586i	$-0.463929\pi$
$787$	6.34450	0.226157	0.113079	+	0.993586i	$0.463929\pi$
$788$	10.7446	0.382762
$789$	−30.8299	−1.09757
$790$	−23.5301	−0.837164
$791$	−10.5131	−0.373802
$792$	8.20707	0.291626
$793$	4.91974	0.174705
$794$	42.7706	1.51787
$795$	55.4336	1.96603
$796$	53.2780	1.88839
$797$	13.7292	0.486314	0.243157	−	0.969987i	$-0.421817\pi$
$797$	13.7292	0.486314	0.243157	+	0.969987i	$0.421817\pi$
$798$	9.86967	0.349383
$799$	41.2949	1.46091
$800$	2.10241	0.0743315
$801$	31.4477	1.11115
$802$	37.7227	1.33204
$803$	4.81845	0.170039
$804$	−89.4665	−3.15524
$805$	9.56250	0.337034
$806$	8.48699	0.298942
$807$	15.6069	0.549390
$808$	21.1241	0.743145
$809$	23.1941	0.815461	0.407730	−	0.913102i	$-0.366320\pi$
$809$	23.1941	0.815461	0.407730	+	0.913102i	$0.366320\pi$
$810$	53.7257	1.88773
$811$	53.3661	1.87394	0.936969	−	0.349411i	$-0.113618\pi$
$811$	53.3661	1.87394	0.936969	+	0.349411i	$0.113618\pi$
$812$	0.466214	0.0163609
$813$	−12.4214	−0.435639
$814$	−7.63533	−0.267618
$815$	−21.4620	−0.751781
$816$	17.0211	0.595859
$817$	−5.08228	−0.177806
$818$	30.2257	1.05682
$819$	2.11240	0.0738131
$820$	71.1113	2.48331
$821$	−48.2804	−1.68500	−0.842499	−	0.538698i	$-0.818917\pi$
$821$	−48.2804	−1.68500	−0.842499	+	0.538698i	$0.818917\pi$
$822$	51.1330	1.78347
$823$	47.9978	1.67310	0.836548	−	0.547893i	$-0.184570\pi$
$823$	47.9978	1.67310	0.836548	+	0.547893i	$0.184570\pi$
$824$	12.8076	0.446173
$825$	−1.51464	−0.0527331
$826$	−21.6102	−0.751916
$827$	−38.9727	−1.35521	−0.677606	−	0.735425i	$-0.736982\pi$
$827$	−38.9727	−1.35521	−0.677606	+	0.735425i	$0.736982\pi$
$828$	−35.3002	−1.22677
$829$	1.44689	0.0502524	0.0251262	−	0.999684i	$-0.492001\pi$
$829$	1.44689	0.0502524	0.0251262	+	0.999684i	$0.492001\pi$
$830$	24.6831	0.856764
$831$	−71.5031	−2.48041
$832$	−11.3531	−0.393599
$833$	3.85851	0.133690
$834$	−39.9825	−1.38448
$835$	18.7404	0.648540
$836$	6.68601	0.231241
$837$	−7.17433	−0.247981
$838$	15.2364	0.526332
$839$	−11.5557	−0.398947	−0.199473	−	0.979903i	$-0.563923\pi$
$839$	−11.5557	−0.398947	−0.199473	+	0.979903i	$0.563923\pi$
$840$	−18.2799	−0.630718
$841$	−28.9836	−0.999433
$842$	5.51778	0.190155
$843$	−11.9708	−0.412296
$844$	40.0928	1.38005
$845$	−2.08089	−0.0715849
$846$	53.6729	1.84531
$847$	1.00000	0.0343604
$848$	−22.9862	−0.789349
$849$	−10.6627	−0.365944
$850$	−6.13652	−0.210481
$851$	14.7790	0.506618
$852$	88.3707	3.02753
$853$	−27.7081	−0.948707	−0.474354	−	0.880334i	$-0.657318\pi$
$853$	−27.7081	−0.948707	−0.474354	+	0.880334i	$0.657318\pi$
$854$	11.6801	0.399685
$855$	−8.08187	−0.276394
$856$	−16.7821	−0.573599
$857$	−29.9977	−1.02470	−0.512351	−	0.858776i	$-0.671225\pi$
$857$	−29.9977	−1.02470	−0.512351	+	0.858776i	$0.671225\pi$
$858$	5.36804	0.183262
$859$	26.4907	0.903853	0.451926	−	0.892055i	$-0.350737\pi$
$859$	26.4907	0.903853	0.451926	+	0.892055i	$0.350737\pi$
$860$	20.9171	0.713268
$861$	−21.2481	−0.724134
$862$	15.7910	0.537843
$863$	−7.60722	−0.258953	−0.129476	−	0.991582i	$-0.541330\pi$
$863$	−7.60722	−0.258953	−0.129476	+	0.991582i	$0.541330\pi$
$864$	6.29871	0.214286
$865$	−27.1808	−0.924175
$866$	60.2737	2.04818
$867$	−4.77505	−0.162169
$868$	12.9996	0.441236
$869$	4.76289	0.161570
$870$	−1.43209	−0.0485525
$871$	−10.8810	−0.368688
$872$	56.7935	1.92327
$873$	−14.6586	−0.496119
$874$	−20.0591	−0.678510
$875$	11.7984	0.398859
$876$	39.6187	1.33859
$877$	8.76120	0.295845	0.147922	−	0.988999i	$-0.452741\pi$
$877$	8.76120	0.295845	0.147922	+	0.988999i	$0.452741\pi$
$878$	−79.1934	−2.67265
$879$	−26.7744	−0.903078
$880$	−4.05981	−0.136856
$881$	−51.4433	−1.73317	−0.866584	−	0.499031i	$-0.833690\pi$
$881$	−51.4433	−1.73317	−0.866584	+	0.499031i	$0.833690\pi$
$882$	5.01509	0.168867
$883$	37.6526	1.26711	0.633555	−	0.773698i	$-0.281595\pi$
$883$	37.6526	1.26711	0.633555	+	0.773698i	$0.281595\pi$
$884$	14.0314	0.471927
$885$	42.8270	1.43961
$886$	−61.5546	−2.06797
$887$	−19.2298	−0.645674	−0.322837	−	0.946455i	$-0.604637\pi$
$887$	−19.2298	−0.645674	−0.322837	+	0.946455i	$0.604637\pi$
$888$	−28.2520	−0.948074
$889$	10.2998	0.345445
$890$	−73.5474	−2.46532
$891$	−10.8750	−0.364325
$892$	38.1134	1.27613
$893$	19.6772	0.658472
$894$	23.2006	0.775944
$895$	5.47424	0.182984
$896$	−20.6768	−0.690764
$897$	−10.3904	−0.346927
$898$	−38.8389	−1.29607
$899$	0.458305	0.0152853
$900$	−5.14581	−0.171527
$901$	−45.4602	−1.51450
$902$	−22.3106	−0.742863
$903$	−6.25006	−0.207989
$904$	−40.8454	−1.35850
$905$	−22.3312	−0.742314
$906$	−6.51535	−0.216458
$907$	1.58499	0.0526289	0.0263144	−	0.999654i	$-0.491623\pi$
$907$	1.58499	0.0526289	0.0263144	+	0.999654i	$0.491623\pi$
$908$	25.7087	0.853173
$909$	11.4853	0.380943
$910$	−4.94030	−0.163769
$911$	−21.7367	−0.720167	−0.360084	−	0.932920i	$-0.617252\pi$
$911$	−21.7367	−0.720167	−0.360084	+	0.932920i	$0.617252\pi$
$912$	8.11063	0.268570
$913$	−4.99628	−0.165353
$914$	8.71044	0.288116
$915$	−23.1475	−0.765234
$916$	103.429	3.41739
$917$	−15.5821	−0.514566
$918$	−18.3846	−0.606784
$919$	35.8856	1.18376	0.591879	−	0.806027i	$-0.298386\pi$
$919$	35.8856	1.18376	0.591879	+	0.806027i	$0.298386\pi$
$920$	37.1522	1.22487
$921$	40.1691	1.32362
$922$	−99.5593	−3.27881
$923$	10.7477	0.353765
$924$	8.22229	0.270493
$925$	2.15438	0.0708355
$926$	51.5246	1.69320
$927$	6.96352	0.228712
$928$	−0.402369	−0.0132084
$929$	43.1698	1.41635	0.708177	−	0.706035i	$-0.249518\pi$
$929$	43.1698	1.41635	0.708177	+	0.706035i	$0.249518\pi$
$930$	−39.9315	−1.30941
$931$	1.83860	0.0602576
$932$	−17.6985	−0.579735
$933$	−71.3635	−2.33634
$934$	30.0376	0.982861
$935$	−8.02916	−0.262582
$936$	8.20707	0.268256
$937$	49.9848	1.63293	0.816466	−	0.577394i	$-0.195930\pi$
$937$	49.9848	1.63293	0.816466	+	0.577394i	$0.195930\pi$
$938$	−25.8328	−0.843471
$939$	−60.3329	−1.96889
$940$	−80.9854	−2.64145
$941$	−10.6703	−0.347843	−0.173922	−	0.984760i	$-0.555644\pi$
$941$	−10.6703	−0.347843	−0.173922	+	0.984760i	$0.555644\pi$
$942$	19.9434	0.649792
$943$	43.1847	1.40629
$944$	−17.7587	−0.577997
$945$	4.17620	0.135852
$946$	−6.56259	−0.213368
$947$	52.5922	1.70902	0.854509	−	0.519436i	$-0.173858\pi$
$947$	52.5922	1.70902	0.854509	+	0.519436i	$0.173858\pi$
$948$	39.1618	1.27192
$949$	4.81845	0.156414
$950$	−2.92407	−0.0948695
$951$	−53.1149	−1.72237
$952$	14.9911	0.485864
$953$	−39.7951	−1.28909	−0.644545	−	0.764566i	$-0.722953\pi$
$953$	−39.7951	−1.28909	−0.644545	+	0.764566i	$0.722953\pi$
$954$	−59.0868	−1.91301
$955$	−5.58231	−0.180639
$956$	−99.1970	−3.20826
$957$	0.289879	0.00937047
$958$	−24.8042	−0.801386
$959$	9.52544	0.307593
$960$	53.4169	1.72402
$961$	−18.2209	−0.587771
$962$	−7.63533	−0.246173
$963$	−9.12448	−0.294032
$964$	29.6527	0.955050
$965$	−50.0776	−1.61206
$966$	−24.6682	−0.793687
$967$	−12.5925	−0.404948	−0.202474	−	0.979288i	$-0.564898\pi$
$967$	−12.5925	−0.404948	−0.202474	+	0.979288i	$0.564898\pi$
$968$	3.88519	0.124875
$969$	16.0405	0.515296
$970$	34.2824	1.10074
$971$	−42.9765	−1.37918	−0.689591	−	0.724199i	$-0.742210\pi$
$971$	−42.9765	−1.37918	−0.689591	+	0.724199i	$0.742210\pi$
$972$	−67.5227	−2.16579
$973$	−7.44825	−0.238780
$974$	−69.7545	−2.23508
$975$	−1.51464	−0.0485074
$976$	9.59839	0.307237
$977$	−23.9644	−0.766690	−0.383345	−	0.923605i	$-0.625228\pi$
$977$	−23.9644	−0.766690	−0.383345	+	0.923605i	$0.625228\pi$
$978$	55.3651	1.77038
$979$	14.8872	0.475798
$980$	−7.56712	−0.241723
$981$	30.8789	0.985887
$982$	−14.1923	−0.452896
$983$	−61.5038	−1.96167	−0.980833	−	0.194848i	$-0.937579\pi$
$983$	−61.5038	−1.96167	−0.980833	+	0.194848i	$0.937579\pi$
$984$	−82.5530	−2.63169
$985$	−6.14839	−0.195904
$986$	1.17443	0.0374016
$987$	24.1985	0.770247
$988$	6.68601	0.212710
$989$	12.7026	0.403920
$990$	−10.4359	−0.331674
$991$	−0.158776	−0.00504369	−0.00252184	−	0.999997i	$-0.500803\pi$
$991$	−0.158776	−0.00504369	−0.00252184	+	0.999997i	$0.500803\pi$
$992$	−11.2194	−0.356217
$993$	6.41080	0.203441
$994$	25.5164	0.809331
$995$	−30.4872	−0.966509
$996$	−41.0809	−1.30170
$997$	−48.9792	−1.55119	−0.775593	−	0.631233i	$-0.782549\pi$
$997$	−48.9792	−1.55119	−0.775593	+	0.631233i	$0.782549\pi$
$998$	74.2872	2.35152
$999$	6.45439	0.204208

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1001.2.a.n.1.10	✓	11
3.2	odd	2		9009.2.a.bs.1.2		11
7.6	odd	2		7007.2.a.w.1.10		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1001.2.a.n.1.10	✓	11	1.1	even	1	trivial
7007.2.a.w.1.10		11	7.6	odd	2
9009.2.a.bs.1.2		11	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:	\( N \)	\(=\)	\( 1001 = 7 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1001.a (trivial)

\(f(q)\)	\(=\)	\(q+2.37413 q^{2} +2.26106 q^{3} +3.63647 q^{4} -2.08089 q^{5} +5.36804 q^{6} +1.00000 q^{7} +3.88519 q^{8} +2.11240 q^{9} +O(q^{10})\)	\(q+2.37413 q^{2} +2.26106 q^{3} +3.63647 q^{4} -2.08089 q^{5} +5.36804 q^{6} +1.00000 q^{7} +3.88519 q^{8} +2.11240 q^{9} -4.94030 q^{10} +1.00000 q^{11} +8.22229 q^{12} +1.00000 q^{13} +2.37413 q^{14} -4.70503 q^{15} +1.95099 q^{16} +3.85851 q^{17} +5.01509 q^{18} +1.83860 q^{19} -7.56712 q^{20} +2.26106 q^{21} +2.37413 q^{22} -4.59538 q^{23} +8.78466 q^{24} -0.669881 q^{25} +2.37413 q^{26} -2.00693 q^{27} +3.63647 q^{28} +0.128205 q^{29} -11.1703 q^{30} +3.57479 q^{31} -3.13848 q^{32} +2.26106 q^{33} +9.16060 q^{34} -2.08089 q^{35} +7.68167 q^{36} -3.21606 q^{37} +4.36506 q^{38} +2.26106 q^{39} -8.08468 q^{40} -9.39741 q^{41} +5.36804 q^{42} -2.76421 q^{43} +3.63647 q^{44} -4.39567 q^{45} -10.9100 q^{46} +10.7023 q^{47} +4.41132 q^{48} +1.00000 q^{49} -1.59038 q^{50} +8.72434 q^{51} +3.63647 q^{52} -11.7818 q^{53} -4.76469 q^{54} -2.08089 q^{55} +3.88519 q^{56} +4.15718 q^{57} +0.304375 q^{58} -9.10240 q^{59} -17.1097 q^{60} +4.91974 q^{61} +8.48699 q^{62} +2.11240 q^{63} -11.3531 q^{64} -2.08089 q^{65} +5.36804 q^{66} -10.8810 q^{67} +14.0314 q^{68} -10.3904 q^{69} -4.94030 q^{70} +10.7477 q^{71} +8.20707 q^{72} +4.81845 q^{73} -7.63533 q^{74} -1.51464 q^{75} +6.68601 q^{76} +1.00000 q^{77} +5.36804 q^{78} +4.76289 q^{79} -4.05981 q^{80} -10.8750 q^{81} -22.3106 q^{82} -4.99628 q^{83} +8.22229 q^{84} -8.02916 q^{85} -6.56259 q^{86} +0.289879 q^{87} +3.88519 q^{88} +14.8872 q^{89} -10.4359 q^{90} +1.00000 q^{91} -16.7110 q^{92} +8.08281 q^{93} +25.4086 q^{94} -3.82593 q^{95} -7.09631 q^{96} -6.93934 q^{97} +2.37413 q^{98} +2.11240 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - q^{2} + 2 q^{3} + 15 q^{4} + 7 q^{5} + 3 q^{6} + 11 q^{7} - 6 q^{8} + 15 q^{9}+O(q^{10}) \) 11 * q - q^2 + 2 * q^3 + 15 * q^4 + 7 * q^5 + 3 * q^6 + 11 * q^7 - 6 * q^8 + 15 * q^9	\( 11 q - q^{2} + 2 q^{3} + 15 q^{4} + 7 q^{5} + 3 q^{6} + 11 q^{7} - 6 q^{8} + 15 q^{9} + q^{10} + 11 q^{11} - 5 q^{12} + 11 q^{13} - q^{14} + 4 q^{15} + 15 q^{16} + 7 q^{17} - 17 q^{18} + 22 q^{19} + 6 q^{20} + 2 q^{21} - q^{22} + 3 q^{23} + 17 q^{24} + 10 q^{25} - q^{26} + 2 q^{27} + 15 q^{28} - 6 q^{29} - 40 q^{30} + 28 q^{31} - 23 q^{32} + 2 q^{33} + 19 q^{34} + 7 q^{35} + 48 q^{36} + q^{37} - 20 q^{38} + 2 q^{39} + 16 q^{40} - 4 q^{41} + 3 q^{42} - 8 q^{43} + 15 q^{44} + 12 q^{45} + 2 q^{46} + 22 q^{47} - 30 q^{48} + 11 q^{49} - 24 q^{50} - 27 q^{51} + 15 q^{52} + 9 q^{53} + 36 q^{54} + 7 q^{55} - 6 q^{56} - 34 q^{57} - 8 q^{58} - 2 q^{59} + 25 q^{60} + 8 q^{62} + 15 q^{63} - 10 q^{64} + 7 q^{65} + 3 q^{66} + 23 q^{67} + 24 q^{68} + 7 q^{69} + q^{70} + 3 q^{71} - 76 q^{72} + 29 q^{73} + 15 q^{74} + 36 q^{75} + 62 q^{76} + 11 q^{77} + 3 q^{78} + 26 q^{79} - 16 q^{80} + 7 q^{81} - 16 q^{82} + 9 q^{83} - 5 q^{84} - 31 q^{85} + 28 q^{86} + 13 q^{87} - 6 q^{88} + 9 q^{89} - 26 q^{90} + 11 q^{91} - 58 q^{92} - 24 q^{93} - 34 q^{94} - 14 q^{95} + 56 q^{96} + 40 q^{97} - q^{98} + 15 q^{99}+O(q^{100}) \) 11 * q - q^2 + 2 * q^3 + 15 * q^4 + 7 * q^5 + 3 * q^6 + 11 * q^7 - 6 * q^8 + 15 * q^9 + q^10 + 11 * q^11 - 5 * q^12 + 11 * q^13 - q^14 + 4 * q^15 + 15 * q^16 + 7 * q^17 - 17 * q^18 + 22 * q^19 + 6 * q^20 + 2 * q^21 - q^22 + 3 * q^23 + 17 * q^24 + 10 * q^25 - q^26 + 2 * q^27 + 15 * q^28 - 6 * q^29 - 40 * q^30 + 28 * q^31 - 23 * q^32 + 2 * q^33 + 19 * q^34 + 7 * q^35 + 48 * q^36 + q^37 - 20 * q^38 + 2 * q^39 + 16 * q^40 - 4 * q^41 + 3 * q^42 - 8 * q^43 + 15 * q^44 + 12 * q^45 + 2 * q^46 + 22 * q^47 - 30 * q^48 + 11 * q^49 - 24 * q^50 - 27 * q^51 + 15 * q^52 + 9 * q^53 + 36 * q^54 + 7 * q^55 - 6 * q^56 - 34 * q^57 - 8 * q^58 - 2 * q^59 + 25 * q^60 + 8 * q^62 + 15 * q^63 - 10 * q^64 + 7 * q^65 + 3 * q^66 + 23 * q^67 + 24 * q^68 + 7 * q^69 + q^70 + 3 * q^71 - 76 * q^72 + 29 * q^73 + 15 * q^74 + 36 * q^75 + 62 * q^76 + 11 * q^77 + 3 * q^78 + 26 * q^79 - 16 * q^80 + 7 * q^81 - 16 * q^82 + 9 * q^83 - 5 * q^84 - 31 * q^85 + 28 * q^86 + 13 * q^87 - 6 * q^88 + 9 * q^89 - 26 * q^90 + 11 * q^91 - 58 * q^92 - 24 * q^93 - 34 * q^94 - 14 * q^95 + 56 * q^96 + 40 * q^97 - q^98 + 15 * q^99

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