LMFDB - Embedded newform 4009.2.a.d.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4009,2,Mod(1,4009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4009, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4009 = 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4009.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.0120261703$
Analytic rank:	$1$
Dimension:	$75$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	4009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.20714 q^{2} +0.00654009 q^{3} +2.87148 q^{4} -3.65103 q^{5} -0.0144349 q^{6} -1.05666 q^{7} -1.92348 q^{8} -2.99996 q^{9} +O(q^{10})$	\(q-2.20714 q^{2} +0.00654009 q^{3} +2.87148 q^{4} -3.65103 q^{5} -0.0144349 q^{6} -1.05666 q^{7} -1.92348 q^{8} -2.99996 q^{9} +8.05835 q^{10} +4.49024 q^{11} +0.0187797 q^{12} -2.04105 q^{13} +2.33220 q^{14} -0.0238781 q^{15} -1.49756 q^{16} +0.705178 q^{17} +6.62133 q^{18} -1.00000 q^{19} -10.4839 q^{20} -0.00691066 q^{21} -9.91059 q^{22} -3.64618 q^{23} -0.0125797 q^{24} +8.33004 q^{25} +4.50489 q^{26} -0.0392402 q^{27} -3.03418 q^{28} +1.37045 q^{29} +0.0527023 q^{30} +6.03596 q^{31} +7.15230 q^{32} +0.0293665 q^{33} -1.55643 q^{34} +3.85791 q^{35} -8.61432 q^{36} -3.41630 q^{37} +2.20714 q^{38} -0.0133486 q^{39} +7.02269 q^{40} -8.06212 q^{41} +0.0152528 q^{42} -0.793266 q^{43} +12.8936 q^{44} +10.9529 q^{45} +8.04763 q^{46} +4.95731 q^{47} -0.00979419 q^{48} -5.88347 q^{49} -18.3856 q^{50} +0.00461193 q^{51} -5.86084 q^{52} +4.83968 q^{53} +0.0866088 q^{54} -16.3940 q^{55} +2.03247 q^{56} -0.00654009 q^{57} -3.02479 q^{58} +0.469255 q^{59} -0.0685654 q^{60} +9.15360 q^{61} -13.3222 q^{62} +3.16994 q^{63} -12.7910 q^{64} +7.45194 q^{65} -0.0648161 q^{66} +10.7657 q^{67} +2.02491 q^{68} -0.0238463 q^{69} -8.51495 q^{70} -9.58984 q^{71} +5.77036 q^{72} +12.8664 q^{73} +7.54026 q^{74} +0.0544791 q^{75} -2.87148 q^{76} -4.74466 q^{77} +0.0294624 q^{78} +11.7519 q^{79} +5.46765 q^{80} +8.99962 q^{81} +17.7943 q^{82} +7.10932 q^{83} -0.0198438 q^{84} -2.57463 q^{85} +1.75085 q^{86} +0.00896288 q^{87} -8.63688 q^{88} -7.68966 q^{89} -24.1747 q^{90} +2.15670 q^{91} -10.4699 q^{92} +0.0394757 q^{93} -10.9415 q^{94} +3.65103 q^{95} +0.0467766 q^{96} +13.5328 q^{97} +12.9856 q^{98} -13.4705 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 75 q - 11 q^{2} - 4 q^{3} + 67 q^{4} - 18 q^{5} - 15 q^{6} - 19 q^{7} - 30 q^{8} + 57 q^{9}+O(q^{10}) $ 75 * q - 11 * q^2 - 4 * q^3 + 67 * q^4 - 18 * q^5 - 15 * q^6 - 19 * q^7 - 30 * q^8 + 57 * q^9	\( 75 q - 11 q^{2} - 4 q^{3} + 67 q^{4} - 18 q^{5} - 15 q^{6} - 19 q^{7} - 30 q^{8} + 57 q^{9} - 48 q^{11} - 14 q^{12} - 3 q^{13} - 4 q^{14} - 39 q^{15} + 59 q^{16} - 23 q^{17} - 24 q^{18} - 75 q^{19} - 62 q^{20} - 3 q^{21} - 6 q^{22} - 73 q^{23} - 64 q^{24} + 57 q^{25} - 46 q^{26} - 22 q^{27} - 26 q^{28} - 39 q^{29} - 14 q^{30} - 44 q^{31} - 71 q^{32} - 3 q^{33} - 9 q^{34} - 49 q^{35} + 20 q^{36} - 12 q^{37} + 11 q^{38} - 90 q^{39} - 8 q^{40} - 42 q^{41} - 45 q^{42} - 24 q^{43} - 120 q^{44} - 63 q^{45} - 39 q^{46} - 59 q^{47} - 4 q^{48} + 48 q^{49} - 100 q^{50} - 55 q^{51} + 2 q^{52} + 13 q^{53} - 87 q^{54} - 36 q^{55} - 12 q^{56} + 4 q^{57} - 17 q^{58} - 47 q^{59} - 45 q^{60} - 35 q^{61} - 40 q^{62} - 69 q^{63} + 26 q^{64} - 44 q^{65} + 33 q^{66} - 39 q^{67} - 63 q^{68} + 42 q^{69} + 40 q^{70} - 154 q^{71} - 51 q^{72} - 29 q^{73} - 95 q^{74} + 37 q^{75} - 67 q^{76} - 24 q^{77} - 19 q^{78} - 95 q^{79} - 146 q^{80} + 23 q^{81} + 7 q^{82} - 52 q^{83} - 72 q^{84} - 36 q^{85} - 44 q^{86} - 103 q^{87} + 67 q^{88} + q^{89} - 2 q^{90} - 64 q^{91} - 183 q^{92} - 49 q^{93} + 5 q^{94} + 18 q^{95} - 69 q^{96} - 7 q^{97} - 23 q^{98} - 100 q^{99}+O(q^{100}) \) 75 * q - 11 * q^2 - 4 * q^3 + 67 * q^4 - 18 * q^5 - 15 * q^6 - 19 * q^7 - 30 * q^8 + 57 * q^9 - 48 * q^11 - 14 * q^12 - 3 * q^13 - 4 * q^14 - 39 * q^15 + 59 * q^16 - 23 * q^17 - 24 * q^18 - 75 * q^19 - 62 * q^20 - 3 * q^21 - 6 * q^22 - 73 * q^23 - 64 * q^24 + 57 * q^25 - 46 * q^26 - 22 * q^27 - 26 * q^28 - 39 * q^29 - 14 * q^30 - 44 * q^31 - 71 * q^32 - 3 * q^33 - 9 * q^34 - 49 * q^35 + 20 * q^36 - 12 * q^37 + 11 * q^38 - 90 * q^39 - 8 * q^40 - 42 * q^41 - 45 * q^42 - 24 * q^43 - 120 * q^44 - 63 * q^45 - 39 * q^46 - 59 * q^47 - 4 * q^48 + 48 * q^49 - 100 * q^50 - 55 * q^51 + 2 * q^52 + 13 * q^53 - 87 * q^54 - 36 * q^55 - 12 * q^56 + 4 * q^57 - 17 * q^58 - 47 * q^59 - 45 * q^60 - 35 * q^61 - 40 * q^62 - 69 * q^63 + 26 * q^64 - 44 * q^65 + 33 * q^66 - 39 * q^67 - 63 * q^68 + 42 * q^69 + 40 * q^70 - 154 * q^71 - 51 * q^72 - 29 * q^73 - 95 * q^74 + 37 * q^75 - 67 * q^76 - 24 * q^77 - 19 * q^78 - 95 * q^79 - 146 * q^80 + 23 * q^81 + 7 * q^82 - 52 * q^83 - 72 * q^84 - 36 * q^85 - 44 * q^86 - 103 * q^87 + 67 * q^88 + q^89 - 2 * q^90 - 64 * q^91 - 183 * q^92 - 49 * q^93 + 5 * q^94 + 18 * q^95 - 69 * q^96 - 7 * q^97 - 23 * q^98 - 100 * 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 $

$2$	−2.20714	−1.56069	−0.780343	−	0.625352i	$-0.784955\pi$
$2$	−2.20714	−1.56069	−0.780343	+	0.625352i	$0.784955\pi$
$3$	0.00654009	0.00377592	0.00188796	−	0.999998i	$-0.499399\pi$
$3$	0.00654009	0.00377592	0.00188796	+	0.999998i	$0.499399\pi$
$4$	2.87148	1.43574
$5$	−3.65103	−1.63279	−0.816396	−	0.577493i	$-0.804031\pi$
$5$	−3.65103	−1.63279	−0.816396	+	0.577493i	$0.804031\pi$
$6$	−0.0144349	−0.00589302
$7$	−1.05666	−0.399381	−0.199690	−	0.979859i	$-0.563994\pi$
$7$	−1.05666	−0.399381	−0.199690	+	0.979859i	$0.563994\pi$
$8$	−1.92348	−0.680053
$9$	−2.99996	−0.999986
$10$	8.05835	2.54827
$11$	4.49024	1.35386	0.676928	−	0.736049i	$-0.263311\pi$
$11$	4.49024	1.35386	0.676928	+	0.736049i	$0.263311\pi$
$12$	0.0187797	0.00542124
$13$	−2.04105	−0.566086	−0.283043	−	0.959107i	$-0.591344\pi$
$13$	−2.04105	−0.566086	−0.283043	+	0.959107i	$0.591344\pi$
$14$	2.33220	0.623308
$15$	−0.0238781	−0.00616529
$16$	−1.49756	−0.374391
$17$	0.705178	0.171031	0.0855154	−	0.996337i	$-0.472746\pi$
$17$	0.705178	0.171031	0.0855154	+	0.996337i	$0.472746\pi$
$18$	6.62133	1.56066
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−10.4839	−2.34426
$21$	−0.00691066	−0.00150803
$22$	−9.91059	−2.11295
$23$	−3.64618	−0.760280	−0.380140	−	0.924929i	$-0.624124\pi$
$23$	−3.64618	−0.760280	−0.380140	+	0.924929i	$0.624124\pi$
$24$	−0.0125797	−0.00256783
$25$	8.33004	1.66601
$26$	4.50489	0.883482
$27$	−0.0392402	−0.00755179
$28$	−3.03418	−0.573407
$29$	1.37045	0.254487	0.127243	−	0.991872i	$-0.459387\pi$
$29$	1.37045	0.254487	0.127243	+	0.991872i	$0.459387\pi$
$30$	0.0527023	0.00962208
$31$	6.03596	1.08409	0.542045	−	0.840350i	$-0.317650\pi$
$31$	6.03596	1.08409	0.542045	+	0.840350i	$0.317650\pi$
$32$	7.15230	1.26436
$33$	0.0293665	0.00511206
$34$	−1.55643	−0.266925
$35$	3.85791	0.652105
$36$	−8.61432	−1.43572
$37$	−3.41630	−0.561636	−0.280818	−	0.959761i	$-0.590606\pi$
$37$	−3.41630	−0.561636	−0.280818	+	0.959761i	$0.590606\pi$
$38$	2.20714	0.358046
$39$	−0.0133486	−0.00213749
$40$	7.02269	1.11038
$41$	−8.06212	−1.25909	−0.629546	−	0.776963i	$-0.716759\pi$
$41$	−8.06212	−1.25909	−0.629546	+	0.776963i	$0.716759\pi$
$42$	0.0152528	0.00235356
$43$	−0.793266	−0.120972	−0.0604860	−	0.998169i	$-0.519265\pi$
$43$	−0.793266	−0.120972	−0.0604860	+	0.998169i	$0.519265\pi$
$44$	12.8936	1.94379
$45$	10.9529	1.63277
$46$	8.04763	1.18656
$47$	4.95731	0.723098	0.361549	−	0.932353i	$-0.382248\pi$
$47$	4.95731	0.723098	0.361549	+	0.932353i	$0.382248\pi$
$48$	−0.00979419	−0.00141367
$49$	−5.88347	−0.840495
$50$	−18.3856	−2.60011
$51$	0.00461193	0.000645799 0
$52$	−5.86084	−0.812752
$53$	4.83968	0.664781	0.332390	−	0.943142i	$-0.392145\pi$
$53$	4.83968	0.664781	0.332390	+	0.943142i	$0.392145\pi$
$54$	0.0866088	0.0117860
$55$	−16.3940	−2.21057
$56$	2.03247	0.271600
$57$	−0.00654009	−0.000866255 0
$58$	−3.02479	−0.397174
$59$	0.469255	0.0610918	0.0305459	−	0.999533i	$-0.490275\pi$
$59$	0.469255	0.0610918	0.0305459	+	0.999533i	$0.490275\pi$
$60$	−0.0685654	−0.00885175
$61$	9.15360	1.17200	0.585999	−	0.810312i	$-0.300702\pi$
$61$	9.15360	1.17200	0.585999	+	0.810312i	$0.300702\pi$
$62$	−13.3222	−1.69192
$63$	3.16994	0.399375
$64$	−12.7910	−1.59888
$65$	7.45194	0.924300
$66$	−0.0648161	−0.00797831
$67$	10.7657	1.31524	0.657619	−	0.753351i	$-0.271564\pi$
$67$	10.7657	1.31524	0.657619	+	0.753351i	$0.271564\pi$
$68$	2.02491	0.245556
$69$	−0.0238463	−0.00287076
$70$	−8.51495	−1.01773
$71$	−9.58984	−1.13810	−0.569052	−	0.822301i	$-0.692690\pi$
$71$	−9.58984	−1.13810	−0.569052	+	0.822301i	$0.692690\pi$
$72$	5.77036	0.680043
$73$	12.8664	1.50589	0.752946	−	0.658082i	$-0.228632\pi$
$73$	12.8664	1.50589	0.752946	+	0.658082i	$0.228632\pi$
$74$	7.54026	0.876538
$75$	0.0544791	0.00629071
$76$	−2.87148	−0.329381
$77$	−4.74466	−0.540704
$78$	0.0294624	0.00333596
$79$	11.7519	1.32219	0.661095	−	0.750302i	$-0.270092\pi$
$79$	11.7519	1.32219	0.661095	+	0.750302i	$0.270092\pi$
$80$	5.46765	0.611302
$81$	8.99962	0.999957
$82$	17.7943	1.96505
$83$	7.10932	0.780349	0.390174	−	0.920741i	$-0.372415\pi$
$83$	7.10932	0.780349	0.390174	+	0.920741i	$0.372415\pi$
$84$	−0.0198438	−0.00216514
$85$	−2.57463	−0.279258
$86$	1.75085	0.188799
$87$	0.00896288	0.000960922 0
$88$	−8.63688	−0.920695
$89$	−7.68966	−0.815102	−0.407551	−	0.913182i	$-0.633617\pi$
$89$	−7.68966	−0.815102	−0.407551	+	0.913182i	$0.633617\pi$
$90$	−24.1747	−2.54824
$91$	2.15670	0.226084
$92$	−10.4699	−1.09156
$93$	0.0394757	0.00409344
$94$	−10.9415	−1.12853
$95$	3.65103	0.374588
$96$	0.0467766	0.00477412
$97$	13.5328	1.37404	0.687022	−	0.726637i	$-0.258918\pi$
$97$	13.5328	1.37404	0.687022	+	0.726637i	$0.258918\pi$
$98$	12.9856	1.31175
$99$	−13.4705	−1.35384
$100$	23.9195	2.39195
$101$	5.13103	0.510557	0.255279	−	0.966868i	$-0.417833\pi$
$101$	5.13103	0.510557	0.255279	+	0.966868i	$0.417833\pi$
$102$	−0.0101792	−0.00100789
$103$	16.3992	1.61586	0.807930	−	0.589278i	$-0.200588\pi$
$103$	16.3992	1.61586	0.807930	+	0.589278i	$0.200588\pi$
$104$	3.92592	0.384968
$105$	0.0252310	0.00246230
$106$	−10.6819	−1.03751
$107$	−6.53986	−0.632233	−0.316116	−	0.948720i	$-0.602379\pi$
$107$	−6.53986	−0.632233	−0.316116	+	0.948720i	$0.602379\pi$
$108$	−0.112678	−0.0108424
$109$	−17.4966	−1.67587	−0.837936	−	0.545769i	$-0.816238\pi$
$109$	−17.4966	−1.67587	−0.837936	+	0.545769i	$0.816238\pi$
$110$	36.1839	3.45000
$111$	−0.0223429	−0.00212069
$112$	1.58242	0.149524
$113$	−21.0682	−1.98193	−0.990965	−	0.134120i	$-0.957179\pi$
$113$	−21.0682	−1.98193	−0.990965	+	0.134120i	$0.957179\pi$
$114$	0.0144349	0.00135195
$115$	13.3123	1.24138
$116$	3.93523	0.365377
$117$	6.12307	0.566078
$118$	−1.03571	−0.0953452
$119$	−0.745135	−0.0683064
$120$	0.0459290	0.00419272
$121$	9.16221	0.832928
$122$	−20.2033	−1.82912
$123$	−0.0527270	−0.00475423
$124$	17.3321	1.55647
$125$	−12.1581	−1.08745
$126$	−6.99651	−0.623299
$127$	17.1118	1.51843	0.759214	−	0.650841i	$-0.225583\pi$
$127$	17.1118	1.51843	0.759214	+	0.650841i	$0.225583\pi$
$128$	13.9270	1.23098
$129$	−0.00518803	−0.000456780 0
$130$	−16.4475	−1.44254
$131$	−16.8068	−1.46842	−0.734210	−	0.678923i	$-0.762447\pi$
$131$	−16.8068	−1.46842	−0.734210	+	0.678923i	$0.762447\pi$
$132$	0.0843254	0.00733958
$133$	1.05666	0.0916242
$134$	−23.7614	−2.05267
$135$	0.143267	0.0123305
$136$	−1.35640	−0.116310
$137$	−0.541245	−0.0462417	−0.0231208	−	0.999733i	$-0.507360\pi$
$137$	−0.541245	−0.0462417	−0.0231208	+	0.999733i	$0.507360\pi$
$138$	0.0526322	0.00448035
$139$	13.6796	1.16028	0.580142	−	0.814515i	$-0.302997\pi$
$139$	13.6796	1.16028	0.580142	+	0.814515i	$0.302997\pi$
$140$	11.0779	0.936254
$141$	0.0324213	0.00273036
$142$	21.1661	1.77622
$143$	−9.16480	−0.766399
$144$	4.49263	0.374385
$145$	−5.00357	−0.415524
$146$	−28.3979	−2.35023
$147$	−0.0384784	−0.00317364
$148$	−9.80984	−0.806364
$149$	−9.72750	−0.796908	−0.398454	−	0.917188i	$-0.630453\pi$
$149$	−9.72750	−0.796908	−0.398454	+	0.917188i	$0.630453\pi$
$150$	−0.120243	−0.00981782
$151$	2.82826	0.230161	0.115080	−	0.993356i	$-0.463287\pi$
$151$	2.82826	0.230161	0.115080	+	0.993356i	$0.463287\pi$
$152$	1.92348	0.156015
$153$	−2.11551	−0.171028
$154$	10.4721	0.843870
$155$	−22.0375	−1.77009
$156$	−0.0383304	−0.00306889
$157$	−2.82602	−0.225541	−0.112771	−	0.993621i	$-0.535972\pi$
$157$	−2.82602	−0.225541	−0.112771	+	0.993621i	$0.535972\pi$
$158$	−25.9381	−2.06352
$159$	0.0316519	0.00251016
$160$	−26.1133	−2.06444
$161$	3.85278	0.303641
$162$	−19.8634	−1.56062
$163$	9.32003	0.730001	0.365001	−	0.931007i	$-0.381069\pi$
$163$	9.32003	0.730001	0.365001	+	0.931007i	$0.381069\pi$
$164$	−23.1502	−1.80773
$165$	−0.107218	−0.00834692
$166$	−15.6913	−1.21788
$167$	−11.0745	−0.856970	−0.428485	−	0.903549i	$-0.640952\pi$
$167$	−11.0745	−0.856970	−0.428485	+	0.903549i	$0.640952\pi$
$168$	0.0132925	0.00102554
$169$	−8.83411	−0.679547
$170$	5.68257	0.435834
$171$	2.99996	0.229412
$172$	−2.27785	−0.173684
$173$	−20.7932	−1.58088	−0.790439	−	0.612540i	$-0.790148\pi$
$173$	−20.7932	−1.58088	−0.790439	+	0.612540i	$0.790148\pi$
$174$	−0.0197824	−0.00149970
$175$	−8.80203	−0.665371
$176$	−6.72441	−0.506872
$177$	0.00306897	0.000230678 0
$178$	16.9722	1.27212
$179$	13.0662	0.976611	0.488305	−	0.872673i	$-0.337615\pi$
$179$	13.0662	0.976611	0.488305	+	0.872673i	$0.337615\pi$
$180$	31.4511	2.34423
$181$	−14.9519	−1.11137	−0.555683	−	0.831394i	$-0.687543\pi$
$181$	−14.9519	−1.11137	−0.555683	+	0.831394i	$0.687543\pi$
$182$	−4.76015	−0.352846
$183$	0.0598653	0.00442537
$184$	7.01335	0.517031
$185$	12.4730	0.917035
$186$	−0.0871284	−0.00638857
$187$	3.16642	0.231551
$188$	14.2348	1.03818
$189$	0.0414637	0.00301604
$190$	−8.05835	−0.584614
$191$	2.34153	0.169427	0.0847136	−	0.996405i	$-0.473002\pi$
$191$	2.34153	0.169427	0.0847136	+	0.996405i	$0.473002\pi$
$192$	−0.0836543	−0.00603723
$193$	16.3721	1.17849	0.589244	−	0.807955i	$-0.299426\pi$
$193$	16.3721	1.17849	0.589244	+	0.807955i	$0.299426\pi$
$194$	−29.8687	−2.14445
$195$	0.0487363	0.00349008
$196$	−16.8943	−1.20673
$197$	−1.44046	−0.102629	−0.0513143	−	0.998683i	$-0.516341\pi$
$197$	−1.44046	−0.102629	−0.0513143	+	0.998683i	$0.516341\pi$
$198$	29.7313	2.11291
$199$	−26.3442	−1.86749	−0.933744	−	0.357940i	$-0.883479\pi$
$199$	−26.3442	−1.86749	−0.933744	+	0.357940i	$0.883479\pi$
$200$	−16.0227	−1.13297
$201$	0.0704085	0.00496623
$202$	−11.3249	−0.796819
$203$	−1.44811	−0.101637
$204$	0.0132431	0.000927199 0
$205$	29.4351	2.05583
$206$	−36.1954	−2.52185
$207$	10.9384	0.760269
$208$	3.05660	0.211937
$209$	−4.49024	−0.310596
$210$	−0.0556885	−0.00384287
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	13.8970	0.954452
$213$	−0.0627184	−0.00429739
$214$	14.4344	0.986716
$215$	2.89624	0.197522
$216$	0.0754778	0.00513562
$217$	−6.37797	−0.432965
$218$	38.6175	2.61551
$219$	0.0841471	0.00568613
$220$	−47.0750	−3.17380
$221$	−1.43931	−0.0968181
$222$	0.0493140	0.00330974
$223$	17.2786	1.15706	0.578531	−	0.815660i	$-0.303626\pi$
$223$	17.2786	1.15706	0.578531	+	0.815660i	$0.303626\pi$
$224$	−7.55756	−0.504961
$225$	−24.9898	−1.66598
$226$	46.5005	3.09317
$227$	−0.293085	−0.0194527	−0.00972637	−	0.999953i	$-0.503096\pi$
$227$	−0.293085	−0.0194527	−0.00972637	+	0.999953i	$0.503096\pi$
$228$	−0.0187797	−0.00124372
$229$	18.8362	1.24473	0.622367	−	0.782726i	$-0.286171\pi$
$229$	18.8362	1.24473	0.622367	+	0.782726i	$0.286171\pi$
$230$	−29.3822	−1.93740
$231$	−0.0310305	−0.00204166
$232$	−2.63604	−0.173064
$233$	8.00564	0.524467	0.262233	−	0.965004i	$-0.415541\pi$
$233$	8.00564	0.524467	0.262233	+	0.965004i	$0.415541\pi$
$234$	−13.5145	−0.883469
$235$	−18.0993	−1.18067
$236$	1.34746	0.0877120
$237$	0.0768583	0.00499249
$238$	1.64462	0.106605
$239$	0.430943	0.0278754	0.0139377	−	0.999903i	$-0.495563\pi$
$239$	0.430943	0.0278754	0.0139377	+	0.999903i	$0.495563\pi$
$240$	0.0357589	0.00230823
$241$	−23.3525	−1.50427	−0.752135	−	0.659009i	$-0.770976\pi$
$241$	−23.3525	−1.50427	−0.752135	+	0.659009i	$0.770976\pi$
$242$	−20.2223	−1.29994
$243$	0.176579	0.0113275
$244$	26.2844	1.68269
$245$	21.4807	1.37235
$246$	0.116376	0.00741986
$247$	2.04105	0.129869
$248$	−11.6100	−0.737238
$249$	0.0464955	0.00294653
$250$	26.8346	1.69717
$251$	26.0268	1.64279	0.821397	−	0.570356i	$-0.193195\pi$
$251$	26.0268	1.64279	0.821397	+	0.570356i	$0.193195\pi$
$252$	9.10242	0.573399
$253$	−16.3722	−1.02931
$254$	−37.7682	−2.36979
$255$	−0.0168383	−0.00105445
$256$	−5.15686	−0.322304
$257$	−10.5030	−0.655157	−0.327579	−	0.944824i	$-0.606233\pi$
$257$	−10.5030	−0.655157	−0.327579	+	0.944824i	$0.606233\pi$
$258$	0.0114507	0.000712890 0
$259$	3.60987	0.224307
$260$	21.3981	1.32705
$261$	−4.11130	−0.254483
$262$	37.0951	2.29174
$263$	1.74802	0.107788	0.0538939	−	0.998547i	$-0.482837\pi$
$263$	1.74802	0.107788	0.0538939	+	0.998547i	$0.482837\pi$
$264$	−0.0564859	−0.00347647
$265$	−17.6698	−1.08545
$266$	−2.33220	−0.142997
$267$	−0.0502910	−0.00307776
$268$	30.9134	1.88834
$269$	−23.6789	−1.44373	−0.721863	−	0.692036i	$-0.756714\pi$
$269$	−23.6789	−1.44373	−0.721863	+	0.692036i	$0.756714\pi$
$270$	−0.316212	−0.0192440
$271$	−13.1707	−0.800066	−0.400033	−	0.916501i	$-0.631001\pi$
$271$	−13.1707	−0.800066	−0.400033	+	0.916501i	$0.631001\pi$
$272$	−1.05605	−0.0640324
$273$	0.0141050	0.000853674 0
$274$	1.19460	0.0721687
$275$	37.4038	2.25554
$276$	−0.0684742	−0.00412166
$277$	−29.4362	−1.76865	−0.884326	−	0.466870i	$-0.845381\pi$
$277$	−29.4362	−1.76865	−0.884326	+	0.466870i	$0.845381\pi$
$278$	−30.1927	−1.81084
$279$	−18.1076	−1.08407
$280$	−7.42061	−0.443466
$281$	27.7732	1.65681	0.828405	−	0.560130i	$-0.189249\pi$
$281$	27.7732	1.65681	0.828405	+	0.560130i	$0.189249\pi$
$282$	−0.0715583	−0.00426124
$283$	0.341089	0.0202756	0.0101378	−	0.999949i	$-0.496773\pi$
$283$	0.341089	0.0202756	0.0101378	+	0.999949i	$0.496773\pi$
$284$	−27.5370	−1.63402
$285$	0.0238781	0.00141441
$286$	20.2280	1.19611
$287$	8.51894	0.502857
$288$	−21.4566	−1.26434
$289$	−16.5027	−0.970748
$290$	11.0436	0.648502
$291$	0.0885054	0.00518828
$292$	36.9455	2.16207
$293$	−1.05392	−0.0615707	−0.0307854	−	0.999526i	$-0.509801\pi$
$293$	−1.05392	−0.0615707	−0.0307854	+	0.999526i	$0.509801\pi$
$294$	0.0849273	0.00495306
$295$	−1.71327	−0.0997502
$296$	6.57119	0.381942
$297$	−0.176198	−0.0102240
$298$	21.4700	1.24372
$299$	7.44203	0.430384
$300$	0.156436	0.00903182
$301$	0.838214	0.0483139
$302$	−6.24238	−0.359209
$303$	0.0335574	0.00192782
$304$	1.49756	0.0858911
$305$	−33.4201	−1.91363
$306$	4.66922	0.266922
$307$	−9.89024	−0.564466	−0.282233	−	0.959346i	$-0.591075\pi$
$307$	−9.89024	−0.564466	−0.282233	+	0.959346i	$0.591075\pi$
$308$	−13.6242	−0.776311
$309$	0.107252	0.00610136
$310$	48.6398	2.76256
$311$	33.3632	1.89185	0.945926	−	0.324384i	$-0.105157\pi$
$311$	33.3632	1.89185	0.945926	+	0.324384i	$0.105157\pi$
$312$	0.0256759	0.00145361
$313$	−33.5593	−1.89689	−0.948443	−	0.316948i	$-0.897342\pi$
$313$	−33.5593	−1.89689	−0.948443	+	0.316948i	$0.897342\pi$
$314$	6.23743	0.351999
$315$	−11.5736	−0.652096
$316$	33.7453	1.89832
$317$	−4.04909	−0.227420	−0.113710	−	0.993514i	$-0.536273\pi$
$317$	−4.04909	−0.227420	−0.113710	+	0.993514i	$0.536273\pi$
$318$	−0.0698603	−0.00391757
$319$	6.15366	0.344539
$320$	46.7004	2.61063
$321$	−0.0427713	−0.00238726
$322$	−8.50363	−0.473889
$323$	−0.705178	−0.0392372
$324$	25.8422	1.43568
$325$	−17.0020	−0.943103
$326$	−20.5706	−1.13930
$327$	−0.114429	−0.00632796
$328$	15.5073	0.856249
$329$	−5.23821	−0.288792
$330$	0.236646	0.0130269
$331$	−8.52899	−0.468795	−0.234398	−	0.972141i	$-0.575312\pi$
$331$	−8.52899	−0.468795	−0.234398	+	0.972141i	$0.575312\pi$
$332$	20.4143	1.12038
$333$	10.2488	0.561628
$334$	24.4430	1.33746
$335$	−39.3059	−2.14751
$336$	0.0103492	0.000564592 0
$337$	16.5110	0.899410	0.449705	−	0.893177i	$-0.351529\pi$
$337$	16.5110	0.899410	0.449705	+	0.893177i	$0.351529\pi$
$338$	19.4981	1.06056
$339$	−0.137788	−0.00748361
$340$	−7.39300	−0.400941
$341$	27.1029	1.46770
$342$	−6.62133	−0.358041
$343$	13.6135	0.735058
$344$	1.52583	0.0822673
$345$	0.0870636	0.00468735
$346$	45.8936	2.46725
$347$	6.32299	0.339436	0.169718	−	0.985493i	$-0.445714\pi$
$347$	6.32299	0.339436	0.169718	+	0.985493i	$0.445714\pi$
$348$	0.0257367	0.00137963
$349$	11.6269	0.622374	0.311187	−	0.950349i	$-0.399273\pi$
$349$	11.6269	0.622374	0.311187	+	0.950349i	$0.399273\pi$
$350$	19.4273	1.03844
$351$	0.0800913	0.00427496
$352$	32.1155	1.71176
$353$	−27.0231	−1.43829	−0.719146	−	0.694859i	$-0.755467\pi$
$353$	−27.0231	−1.43829	−0.719146	+	0.694859i	$0.755467\pi$
$354$	−0.00677366	−0.000360016 0
$355$	35.0128	1.85829
$356$	−22.0807	−1.17028
$357$	−0.00487325	−0.000257920 0
$358$	−28.8389	−1.52418
$359$	−21.4168	−1.13034	−0.565168	−	0.824976i	$-0.691189\pi$
$359$	−21.4168	−1.13034	−0.565168	+	0.824976i	$0.691189\pi$
$360$	−21.0678	−1.11037
$361$	1.00000	0.0526316
$362$	33.0010	1.73449
$363$	0.0599217	0.00314507
$364$	6.19292	0.324597
$365$	−46.9755	−2.45881
$366$	−0.132131	−0.00690662
$367$	9.20985	0.480750	0.240375	−	0.970680i	$-0.422730\pi$
$367$	9.20985	0.480750	0.240375	+	0.970680i	$0.422730\pi$
$368$	5.46038	0.284642
$369$	24.1860	1.25907
$370$	−27.5297	−1.43120
$371$	−5.11390	−0.265501
$372$	0.113354	0.00587711
$373$	−36.1135	−1.86989	−0.934944	−	0.354795i	$-0.884551\pi$
$373$	−36.1135	−1.86989	−0.934944	+	0.354795i	$0.884551\pi$
$374$	−6.98873	−0.361379
$375$	−0.0795148	−0.00410613
$376$	−9.53530	−0.491745
$377$	−2.79716	−0.144061
$378$	−0.0915162	−0.00470709
$379$	−3.49789	−0.179675	−0.0898373	−	0.995956i	$-0.528635\pi$
$379$	−3.49789	−0.179675	−0.0898373	+	0.995956i	$0.528635\pi$
$380$	10.4839	0.537811
$381$	0.111913	0.00573346
$382$	−5.16809	−0.264423
$383$	−29.2796	−1.49612	−0.748059	−	0.663632i	$-0.769014\pi$
$383$	−29.2796	−1.49612	−0.748059	+	0.663632i	$0.769014\pi$
$384$	0.0910838	0.00464810
$385$	17.3229	0.882857
$386$	−36.1355	−1.83925
$387$	2.37976	0.120970
$388$	38.8591	1.97277
$389$	−23.1601	−1.17427	−0.587133	−	0.809491i	$-0.699743\pi$
$389$	−23.1601	−1.17427	−0.587133	+	0.809491i	$0.699743\pi$
$390$	−0.107568	−0.00544692
$391$	−2.57120	−0.130031
$392$	11.3167	0.571581
$393$	−0.109918	−0.00554463
$394$	3.17930	0.160171
$395$	−42.9065	−2.15886
$396$	−38.6803	−1.94376
$397$	−34.1136	−1.71211	−0.856057	−	0.516881i	$-0.827093\pi$
$397$	−34.1136	−1.71211	−0.856057	+	0.516881i	$0.827093\pi$
$398$	58.1454	2.91456
$399$	0.00691066	0.000345966 0
$400$	−12.4748	−0.623738
$401$	−26.2482	−1.31077	−0.655385	−	0.755295i	$-0.727494\pi$
$401$	−26.2482	−1.31077	−0.655385	+	0.755295i	$0.727494\pi$
$402$	−0.155402	−0.00775073
$403$	−12.3197	−0.613688
$404$	14.7337	0.733027
$405$	−32.8579	−1.63272
$406$	3.19618	0.158624
$407$	−15.3400	−0.760375
$408$	−0.00887095	−0.000439178 0
$409$	4.30004	0.212623	0.106312	−	0.994333i	$-0.466096\pi$
$409$	4.30004	0.212623	0.106312	+	0.994333i	$0.466096\pi$
$410$	−64.9674	−3.20851
$411$	−0.00353979	−0.000174605 0
$412$	47.0899	2.31996
$413$	−0.495844	−0.0243989
$414$	−24.1425	−1.18654
$415$	−25.9563	−1.27415
$416$	−14.5982	−0.715736
$417$	0.0894654	0.00438114
$418$	9.91059	0.484743
$419$	−4.95202	−0.241922	−0.120961	−	0.992657i	$-0.538598\pi$
$419$	−4.95202	−0.241922	−0.120961	+	0.992657i	$0.538598\pi$
$420$	0.0724504	0.00353522
$421$	−22.9588	−1.11894	−0.559472	−	0.828850i	$-0.688996\pi$
$421$	−22.9588	−1.11894	−0.559472	+	0.828850i	$0.688996\pi$
$422$	2.20714	0.107442
$423$	−14.8717	−0.723088
$424$	−9.30903	−0.452086
$425$	5.87416	0.284939
$426$	0.138428	0.00670688
$427$	−9.67226	−0.468074
$428$	−18.7791	−0.907721
$429$	−0.0599386	−0.00289386
$430$	−6.39241	−0.308270
$431$	34.8042	1.67646	0.838229	−	0.545318i	$-0.183591\pi$
$431$	34.8042	1.67646	0.838229	+	0.545318i	$0.183591\pi$
$432$	0.0587647	0.00282732
$433$	34.5846	1.66203	0.831015	−	0.556250i	$-0.187760\pi$
$433$	34.5846	1.66203	0.831015	+	0.556250i	$0.187760\pi$
$434$	14.0771	0.675722
$435$	−0.0327238	−0.00156898
$436$	−50.2412	−2.40612
$437$	3.64618	0.174420
$438$	−0.185725	−0.00887426
$439$	−15.9792	−0.762644	−0.381322	−	0.924442i	$-0.624531\pi$
$439$	−15.9792	−0.762644	−0.381322	+	0.924442i	$0.624531\pi$
$440$	31.5335	1.50330
$441$	17.6501	0.840483
$442$	3.17675	0.151103
$443$	27.1043	1.28776	0.643882	−	0.765125i	$-0.277323\pi$
$443$	27.1043	1.28776	0.643882	+	0.765125i	$0.277323\pi$
$444$	−0.0641572	−0.00304476
$445$	28.0752	1.33089
$446$	−38.1364	−1.80581
$447$	−0.0636187	−0.00300906
$448$	13.5158	0.638561
$449$	−0.432507	−0.0204113	−0.0102056	−	0.999948i	$-0.503249\pi$
$449$	−0.432507	−0.0204113	−0.0102056	+	0.999948i	$0.503249\pi$
$450$	55.1560	2.60008
$451$	−36.2008	−1.70463
$452$	−60.4969	−2.84554
$453$	0.0184971	0.000869069 0
$454$	0.646881	0.0303596
$455$	−7.87419	−0.369148
$456$	0.0125797	0.000589100 0
$457$	23.9406	1.11989	0.559946	−	0.828529i	$-0.310822\pi$
$457$	23.9406	1.11989	0.559946	+	0.828529i	$0.310822\pi$
$458$	−41.5743	−1.94264
$459$	−0.0276714	−0.00129159
$460$	38.2260	1.78230
$461$	−26.2981	−1.22483	−0.612413	−	0.790538i	$-0.709801\pi$
$461$	−26.2981	−1.22483	−0.612413	+	0.790538i	$0.709801\pi$
$462$	0.0684887	0.00318638
$463$	9.04037	0.420142	0.210071	−	0.977686i	$-0.432631\pi$
$463$	9.04037	0.420142	0.210071	+	0.977686i	$0.432631\pi$
$464$	−2.05234	−0.0952775
$465$	−0.144127	−0.00668373
$466$	−17.6696	−0.818528
$467$	−34.0889	−1.57745	−0.788723	−	0.614748i	$-0.789258\pi$
$467$	−34.0889	−1.57745	−0.788723	+	0.614748i	$0.789258\pi$
$468$	17.5823	0.812740
$469$	−11.3757	−0.525281
$470$	39.9478	1.84265
$471$	−0.0184824	−0.000851625 0
$472$	−0.902604	−0.0415457
$473$	−3.56195	−0.163779
$474$	−0.169637	−0.00779170
$475$	−8.33004	−0.382208
$476$	−2.13964	−0.0980703
$477$	−14.5188	−0.664771
$478$	−0.951153	−0.0435047
$479$	−7.49416	−0.342417	−0.171208	−	0.985235i	$-0.554767\pi$
$479$	−7.49416	−0.342417	−0.171208	+	0.985235i	$0.554767\pi$
$480$	−0.170783	−0.00779514
$481$	6.97284	0.317934
$482$	51.5424	2.34769
$483$	0.0251975	0.00114653
$484$	26.3091	1.19587
$485$	−49.4086	−2.24353
$486$	−0.389735	−0.0176787
$487$	−18.9363	−0.858086	−0.429043	−	0.903284i	$-0.641149\pi$
$487$	−18.9363	−0.858086	−0.429043	+	0.903284i	$0.641149\pi$
$488$	−17.6068	−0.797021
$489$	0.0609538	0.00275643
$490$	−47.4110	−2.14181
$491$	−10.7908	−0.486980	−0.243490	−	0.969903i	$-0.578292\pi$
$491$	−10.7908	−0.486980	−0.243490	+	0.969903i	$0.578292\pi$
$492$	−0.151404	−0.00682584
$493$	0.966414	0.0435251
$494$	−4.50489	−0.202685
$495$	49.1813	2.21053
$496$	−9.03922	−0.405873
$497$	10.1332	0.454537
$498$	−0.102622	−0.00459861
$499$	−1.10477	−0.0494562	−0.0247281	−	0.999694i	$-0.507872\pi$
$499$	−1.10477	−0.0494562	−0.0247281	+	0.999694i	$0.507872\pi$
$500$	−34.9117	−1.56130
$501$	−0.0724281	−0.00323585
$502$	−57.4448	−2.56389
$503$	−1.50221	−0.0669804	−0.0334902	−	0.999439i	$-0.510662\pi$
$503$	−1.50221	−0.0669804	−0.0334902	+	0.999439i	$0.510662\pi$
$504$	−6.09732	−0.271596
$505$	−18.7336	−0.833633
$506$	36.1358	1.60643
$507$	−0.0577758	−0.00256592
$508$	49.1362	2.18007
$509$	−1.02223	−0.0453095	−0.0226547	−	0.999743i	$-0.507212\pi$
$509$	−1.02223	−0.0453095	−0.0226547	+	0.999743i	$0.507212\pi$
$510$	0.0371645	0.00164567
$511$	−13.5954	−0.601425
$512$	−16.4721	−0.727970
$513$	0.0392402	0.00173250
$514$	23.1815	1.02249
$515$	−59.8740	−2.63836
$516$	−0.0148973	−0.000655818 0
$517$	22.2595	0.978972
$518$	−7.96751	−0.350072
$519$	−0.135989	−0.00596927
$520$	−14.3337	−0.628573
$521$	−13.2302	−0.579626	−0.289813	−	0.957083i	$-0.593593\pi$
$521$	−13.2302	−0.579626	−0.289813	+	0.957083i	$0.593593\pi$
$522$	9.07423	0.397168
$523$	−5.40952	−0.236542	−0.118271	−	0.992981i	$-0.537735\pi$
$523$	−5.40952	−0.236542	−0.118271	+	0.992981i	$0.537735\pi$
$524$	−48.2605	−2.10827
$525$	−0.0575661	−0.00251239
$526$	−3.85814	−0.168223
$527$	4.25643	0.185413
$528$	−0.0439782	−0.00191391
$529$	−9.70540	−0.421974
$530$	38.9998	1.69404
$531$	−1.40775	−0.0610910
$532$	3.03418	0.131549
$533$	16.4552	0.712754
$534$	0.111000	0.00480342
$535$	23.8773	1.03230
$536$	−20.7076	−0.894432
$537$	0.0854538	0.00368760
$538$	52.2626	2.25320
$539$	−26.4181	−1.13791
$540$	0.411389	0.0177034
$541$	−19.9011	−0.855616	−0.427808	−	0.903870i	$-0.640714\pi$
$541$	−19.9011	−0.855616	−0.427808	+	0.903870i	$0.640714\pi$
$542$	29.0697	1.24865
$543$	−0.0977867	−0.00419643
$544$	5.04365	0.216245
$545$	63.8807	2.73635
$546$	−0.0311318	−0.00133232
$547$	22.9445	0.981034	0.490517	−	0.871432i	$-0.336808\pi$
$547$	22.9445	0.981034	0.490517	+	0.871432i	$0.336808\pi$
$548$	−1.55417	−0.0663910
$549$	−27.4604	−1.17198
$550$	−82.5556	−3.52018
$551$	−1.37045	−0.0583833
$552$	0.0458679	0.00195227
$553$	−12.4178	−0.528057
$554$	64.9700	2.76031
$555$	0.0815746	0.00346265
$556$	39.2806	1.66587
$557$	2.66630	0.112975	0.0564873	−	0.998403i	$-0.482010\pi$
$557$	2.66630	0.112975	0.0564873	+	0.998403i	$0.482010\pi$
$558$	39.9661	1.69190
$559$	1.61910	0.0684805
$560$	−5.77746	−0.244142
$561$	0.0207086	0.000874319 0
$562$	−61.2994	−2.58576
$563$	14.8592	0.626241	0.313121	−	0.949713i	$-0.398626\pi$
$563$	14.8592	0.626241	0.313121	+	0.949713i	$0.398626\pi$
$564$	0.0930970	0.00392009
$565$	76.9207	3.23608
$566$	−0.752831	−0.0316439
$567$	−9.50955	−0.399364
$568$	18.4459	0.773971
$569$	14.1525	0.593302	0.296651	−	0.954986i	$-0.404130\pi$
$569$	14.1525	0.593302	0.296651	+	0.954986i	$0.404130\pi$
$570$	−0.0527023	−0.00220746
$571$	7.07902	0.296248	0.148124	−	0.988969i	$-0.452677\pi$
$571$	7.07902	0.296248	0.148124	+	0.988969i	$0.452677\pi$
$572$	−26.3165	−1.10035
$573$	0.0153138	0.000639744 0
$574$	−18.8025	−0.784802
$575$	−30.3728	−1.26663
$576$	38.3725	1.59885
$577$	−2.43954	−0.101559	−0.0507797	−	0.998710i	$-0.516171\pi$
$577$	−2.43954	−0.101559	−0.0507797	+	0.998710i	$0.516171\pi$
$578$	36.4239	1.51503
$579$	0.107075	0.00444988
$580$	−14.3676	−0.596584
$581$	−7.51215	−0.311656
$582$	−0.195344	−0.00809727
$583$	21.7313	0.900018
$584$	−24.7482	−1.02409
$585$	−22.3555	−0.924287
$586$	2.32615	0.0960925
$587$	40.5453	1.67348	0.836742	−	0.547597i	$-0.184457\pi$
$587$	40.5453	1.67348	0.836742	+	0.547597i	$0.184457\pi$
$588$	−0.110490	−0.00455652
$589$	−6.03596	−0.248707
$590$	3.78142	0.155679
$591$	−0.00942074	−0.000387517 0
$592$	5.11612	0.210271
$593$	−22.7499	−0.934228	−0.467114	−	0.884197i	$-0.654706\pi$
$593$	−22.7499	−0.934228	−0.467114	+	0.884197i	$0.654706\pi$
$594$	0.388894	0.0159565
$595$	2.72051	0.111530
$596$	−27.9323	−1.14415
$597$	−0.172293	−0.00705149
$598$	−16.4256	−0.671694
$599$	−2.55205	−0.104274	−0.0521370	−	0.998640i	$-0.516603\pi$
$599$	−2.55205	−0.104274	−0.0521370	+	0.998640i	$0.516603\pi$
$600$	−0.104790	−0.00427802
$601$	2.76799	0.112909	0.0564543	−	0.998405i	$-0.482020\pi$
$601$	2.76799	0.112909	0.0564543	+	0.998405i	$0.482020\pi$
$602$	−1.85006	−0.0754027
$603$	−32.2966	−1.31522
$604$	8.12130	0.330451
$605$	−33.4515	−1.36000
$606$	−0.0740660	−0.00300873
$607$	21.3081	0.864871	0.432436	−	0.901665i	$-0.357654\pi$
$607$	21.3081	0.864871	0.432436	+	0.901665i	$0.357654\pi$
$608$	−7.15230	−0.290064
$609$	−0.00947074	−0.000383774 0
$610$	73.7629	2.98657
$611$	−10.1181	−0.409336
$612$	−6.07463	−0.245552
$613$	−10.5120	−0.424574	−0.212287	−	0.977207i	$-0.568091\pi$
$613$	−10.5120	−0.424574	−0.212287	+	0.977207i	$0.568091\pi$
$614$	21.8292	0.880954
$615$	0.192508	0.00776266
$616$	9.12626	0.367708
$617$	−15.9691	−0.642894	−0.321447	−	0.946928i	$-0.604169\pi$
$617$	−15.9691	−0.642894	−0.321447	+	0.946928i	$0.604169\pi$
$618$	−0.236721	−0.00952230
$619$	−29.5560	−1.18795	−0.593977	−	0.804482i	$-0.702443\pi$
$619$	−29.5560	−1.18795	−0.593977	+	0.804482i	$0.702443\pi$
$620$	−63.2801	−2.54139
$621$	0.143077	0.00574147
$622$	−73.6373	−2.95259
$623$	8.12537	0.325536
$624$	0.0199904	0.000800258 0
$625$	2.73932	0.109573
$626$	74.0703	2.96044
$627$	−0.0293665	−0.00117279
$628$	−8.11486	−0.323818
$629$	−2.40910	−0.0960571
$630$	25.5445	1.01772
$631$	−33.9718	−1.35240	−0.676199	−	0.736719i	$-0.736374\pi$
$631$	−33.9718	−1.35240	−0.676199	+	0.736719i	$0.736374\pi$
$632$	−22.6045	−0.899160
$633$	−0.00654009	−0.000259945 0
$634$	8.93693	0.354931
$635$	−62.4758	−2.47928
$636$	0.0908878	0.00360394
$637$	12.0085	0.475792
$638$	−13.5820	−0.537716
$639$	28.7691	1.13809
$640$	−50.8479	−2.00994
$641$	16.0156	0.632579	0.316290	−	0.948663i	$-0.397563\pi$
$641$	16.0156	0.632579	0.316290	+	0.948663i	$0.397563\pi$
$642$	0.0944023	0.00372576
$643$	30.8967	1.21845	0.609223	−	0.792999i	$-0.291482\pi$
$643$	30.8967	1.21845	0.609223	+	0.792999i	$0.291482\pi$
$644$	11.0632	0.435950
$645$	0.0189417	0.000745827 0
$646$	1.55643	0.0612369
$647$	−19.5626	−0.769084	−0.384542	−	0.923108i	$-0.625641\pi$
$647$	−19.5626	−0.769084	−0.384542	+	0.923108i	$0.625641\pi$
$648$	−17.3106	−0.680024
$649$	2.10707	0.0827096
$650$	37.5259	1.47189
$651$	−0.0417124	−0.00163484
$652$	26.7623	1.04809
$653$	1.42746	0.0558608	0.0279304	−	0.999610i	$-0.491108\pi$
$653$	1.42746	0.0558608	0.0279304	+	0.999610i	$0.491108\pi$
$654$	0.252562	0.00987595
$655$	61.3623	2.39762
$656$	12.0735	0.471392
$657$	−38.5985	−1.50587
$658$	11.5615	0.450713
$659$	38.1571	1.48639	0.743196	−	0.669074i	$-0.233309\pi$
$659$	38.1571	1.48639	0.743196	+	0.669074i	$0.233309\pi$
$660$	−0.307875	−0.0119840
$661$	−26.3253	−1.02393	−0.511967	−	0.859005i	$-0.671083\pi$
$661$	−26.3253	−1.02393	−0.511967	+	0.859005i	$0.671083\pi$
$662$	18.8247	0.731642
$663$	−0.00941318	−0.000365578 0
$664$	−13.6746	−0.530679
$665$	−3.85791	−0.149603
$666$	−22.6205	−0.876525
$667$	−4.99691	−0.193481
$668$	−31.8002	−1.23039
$669$	0.113004	0.00436898
$670$	86.7537	3.35159
$671$	41.1018	1.58672
$672$	−0.0494271	−0.00190669
$673$	−23.3916	−0.901680	−0.450840	−	0.892605i	$-0.648875\pi$
$673$	−23.3916	−0.901680	−0.450840	+	0.892605i	$0.648875\pi$
$674$	−36.4421	−1.40370
$675$	−0.326873	−0.0125813
$676$	−25.3670	−0.975653
$677$	−12.6185	−0.484967	−0.242483	−	0.970156i	$-0.577962\pi$
$677$	−12.6185	−0.484967	−0.242483	+	0.970156i	$0.577962\pi$
$678$	0.304118	0.0116796
$679$	−14.2996	−0.548767
$680$	4.95225	0.189910
$681$	−0.00191680	−7.34520e−5 0
$682$	−59.8199	−2.29062
$683$	−3.87248	−0.148176	−0.0740881	−	0.997252i	$-0.523605\pi$
$683$	−3.87248	−0.148176	−0.0740881	+	0.997252i	$0.523605\pi$
$684$	8.61432	0.329377
$685$	1.97610	0.0755030
$686$	−30.0469	−1.14719
$687$	0.123191	0.00470002
$688$	1.18797	0.0452908
$689$	−9.87803	−0.376323
$690$	−0.192162	−0.00731548
$691$	1.65948	0.0631296	0.0315648	−	0.999502i	$-0.489951\pi$
$691$	1.65948	0.0631296	0.0315648	+	0.999502i	$0.489951\pi$
$692$	−59.7073	−2.26973
$693$	14.2338	0.540697
$694$	−13.9557	−0.529752
$695$	−49.9445	−1.89450
$696$	−0.0172399	−0.000653478 0
$697$	−5.68523	−0.215344
$698$	−25.6622	−0.971330
$699$	0.0523576	0.00198035
$700$	−25.2749	−0.955300
$701$	41.1230	1.55319	0.776597	−	0.629997i	$-0.216944\pi$
$701$	41.1230	1.55319	0.776597	+	0.629997i	$0.216944\pi$
$702$	−0.176773	−0.00667187
$703$	3.41630	0.128848
$704$	−57.4347	−2.16465
$705$	−0.118371	−0.00445811
$706$	59.6438	2.24472
$707$	−5.42177	−0.203907
$708$	0.00881249	0.000331194 0
$709$	−41.8336	−1.57109	−0.785546	−	0.618803i	$-0.787618\pi$
$709$	−41.8336	−1.57109	−0.785546	+	0.618803i	$0.787618\pi$
$710$	−77.2783	−2.90020
$711$	−35.2552	−1.32217
$712$	14.7909	0.554313
$713$	−22.0082	−0.824212
$714$	0.0107560	0.000402532 0
$715$	33.4610	1.25137
$716$	37.5192	1.40216
$717$	0.00281840	0.000105255 0
$718$	47.2699	1.76410
$719$	−17.0449	−0.635667	−0.317834	−	0.948147i	$-0.602955\pi$
$719$	−17.0449	−0.635667	−0.317834	+	0.948147i	$0.602955\pi$
$720$	−16.4027	−0.611293
$721$	−17.3284	−0.645343
$722$	−2.20714	−0.0821414
$723$	−0.152728	−0.00568000
$724$	−42.9341	−1.59563
$725$	11.4159	0.423977
$726$	−0.132256	−0.00490847
$727$	−26.8471	−0.995703	−0.497852	−	0.867262i	$-0.665878\pi$
$727$	−26.8471	−0.995703	−0.497852	+	0.867262i	$0.665878\pi$
$728$	−4.14837	−0.153749
$729$	−26.9977	−0.999914
$730$	103.682	3.83743
$731$	−0.559394	−0.0206899
$732$	0.171902	0.00635369
$733$	−5.77278	−0.213223	−0.106611	−	0.994301i	$-0.534000\pi$
$733$	−5.77278	−0.213223	−0.106611	+	0.994301i	$0.534000\pi$
$734$	−20.3274	−0.750300
$735$	0.140486	0.00518189
$736$	−26.0785	−0.961267
$737$	48.3405	1.78064
$738$	−53.3820	−1.96502
$739$	33.4467	1.23036	0.615179	−	0.788387i	$-0.289084\pi$
$739$	33.4467	1.23036	0.615179	+	0.788387i	$0.289084\pi$
$740$	35.8160	1.31662
$741$	0.0133486	0.000490375 0
$742$	11.2871	0.414363
$743$	−22.4526	−0.823708	−0.411854	−	0.911250i	$-0.635119\pi$
$743$	−22.4526	−0.823708	−0.411854	+	0.911250i	$0.635119\pi$
$744$	−0.0759307	−0.00278375
$745$	35.5154	1.30118
$746$	79.7078	2.91831
$747$	−21.3276	−0.780338
$748$	9.09230	0.332448
$749$	6.91043	0.252502
$750$	0.175501	0.00640837
$751$	22.9360	0.836945	0.418473	−	0.908229i	$-0.362566\pi$
$751$	22.9360	0.836945	0.418473	+	0.908229i	$0.362566\pi$
$752$	−7.42389	−0.270721
$753$	0.170217	0.00620306
$754$	6.17374	0.224834
$755$	−10.3261	−0.375805
$756$	0.119062	0.00433025
$757$	27.8579	1.01251	0.506256	−	0.862384i	$-0.331029\pi$
$757$	27.8579	1.01251	0.506256	+	0.862384i	$0.331029\pi$
$758$	7.72035	0.280416
$759$	−0.107075	−0.00388659
$760$	−7.02269	−0.254740
$761$	9.73040	0.352727	0.176363	−	0.984325i	$-0.443567\pi$
$761$	9.73040	0.352727	0.176363	+	0.984325i	$0.443567\pi$
$762$	−0.247007	−0.00894814
$763$	18.4880	0.669311
$764$	6.72366	0.243253
$765$	7.72378	0.279254
$766$	64.6243	2.33497
$767$	−0.957774	−0.0345832
$768$	−0.0337263	−0.00121699
$769$	−46.5141	−1.67734	−0.838671	−	0.544638i	$-0.816667\pi$
$769$	−46.5141	−1.67734	−0.838671	+	0.544638i	$0.816667\pi$
$770$	−38.2341	−1.37786
$771$	−0.0686903	−0.00247382
$772$	47.0121	1.69200
$773$	28.0181	1.00774	0.503870	−	0.863779i	$-0.331909\pi$
$773$	28.0181	1.00774	0.503870	+	0.863779i	$0.331909\pi$
$774$	−5.25248	−0.188796
$775$	50.2797	1.80610
$776$	−26.0300	−0.934423
$777$	0.0236089	0.000846964 0
$778$	51.1177	1.83266
$779$	8.06212	0.288855
$780$	0.139945	0.00501085
$781$	−43.0606	−1.54083
$782$	5.67502	0.202938
$783$	−0.0537769	−0.00192183
$784$	8.81086	0.314674
$785$	10.3179	0.368261
$786$	0.242605	0.00865343
$787$	36.0027	1.28336	0.641678	−	0.766974i	$-0.278238\pi$
$787$	36.0027	1.28336	0.641678	+	0.766974i	$0.278238\pi$
$788$	−4.13626	−0.147348
$789$	0.0114322	0.000406998 0
$790$	94.7008	3.36930
$791$	22.2620	0.791545
$792$	25.9103	0.920681
$793$	−18.6830	−0.663452
$794$	75.2937	2.67207
$795$	−0.115562	−0.00409857
$796$	−75.6468	−2.68123
$797$	17.3037	0.612928	0.306464	−	0.951882i	$-0.400854\pi$
$797$	17.3037	0.612928	0.306464	+	0.951882i	$0.400854\pi$
$798$	−0.0152528	−0.000539944 0
$799$	3.49579	0.123672
$800$	59.5789	2.10643
$801$	23.0687	0.815091
$802$	57.9335	2.04570
$803$	57.7730	2.03876
$804$	0.202177	0.00713022
$805$	−14.0666	−0.495783
$806$	27.1913	0.957774
$807$	−0.154862	−0.00545139
$808$	−9.86945	−0.347206
$809$	−49.1918	−1.72949	−0.864745	−	0.502211i	$-0.832520\pi$
$809$	−49.1918	−1.72949	−0.864745	+	0.502211i	$0.832520\pi$
$810$	72.5220	2.54816
$811$	32.5576	1.14325	0.571626	−	0.820514i	$-0.306313\pi$
$811$	32.5576	1.14325	0.571626	+	0.820514i	$0.306313\pi$
$812$	−4.15821	−0.145924
$813$	−0.0861378	−0.00302098
$814$	33.8576	1.18671
$815$	−34.0277	−1.19194
$816$	−0.00690665	−0.000241781 0
$817$	0.793266	0.0277529
$818$	−9.49080	−0.331838
$819$	−6.47001	−0.226081
$820$	84.5222	2.95164
$821$	−37.7775	−1.31844	−0.659222	−	0.751948i	$-0.729114\pi$
$821$	−37.7775	−1.31844	−0.659222	+	0.751948i	$0.729114\pi$
$822$	0.00781282	0.000272503 0
$823$	−7.41329	−0.258411	−0.129206	−	0.991618i	$-0.541243\pi$
$823$	−7.41329	−0.258411	−0.129206	+	0.991618i	$0.541243\pi$
$824$	−31.5435	−1.09887
$825$	0.244624	0.00851672
$826$	1.09440	0.0380790
$827$	−7.56691	−0.263127	−0.131564	−	0.991308i	$-0.542000\pi$
$827$	−7.56691	−0.263127	−0.131564	+	0.991308i	$0.542000\pi$
$828$	31.4093	1.09155
$829$	20.2077	0.701843	0.350921	−	0.936405i	$-0.385868\pi$
$829$	20.2077	0.701843	0.350921	+	0.936405i	$0.385868\pi$
$830$	57.2894	1.98854
$831$	−0.192515	−0.00667829
$832$	26.1071	0.905101
$833$	−4.14889	−0.143751
$834$	−0.197463	−0.00683758
$835$	40.4333	1.39925
$836$	−12.8936	−0.445935
$837$	−0.236852	−0.00818681
$838$	10.9298	0.377565
$839$	−33.3740	−1.15220	−0.576099	−	0.817380i	$-0.695426\pi$
$839$	−33.3740	−1.15220	−0.576099	+	0.817380i	$0.695426\pi$
$840$	−0.0485314	−0.00167449
$841$	−27.1219	−0.935236
$842$	50.6733	1.74632
$843$	0.181639	0.00625598
$844$	−2.87148	−0.0988404
$845$	32.2536	1.10956
$846$	32.8240	1.12851
$847$	−9.68136	−0.332656
$848$	−7.24772	−0.248888
$849$	0.00223075	7.65591e−5 0
$850$	−12.9651	−0.444700
$851$	12.4564	0.427001
$852$	−0.180095	−0.00616994
$853$	−8.87453	−0.303858	−0.151929	−	0.988391i	$-0.548549\pi$
$853$	−8.87453	−0.303858	−0.151929	+	0.988391i	$0.548549\pi$
$854$	21.3481	0.730516
$855$	−10.9529	−0.374583
$856$	12.5793	0.429952
$857$	33.9957	1.16127	0.580636	−	0.814164i	$-0.302804\pi$
$857$	33.9957	1.16127	0.580636	+	0.814164i	$0.302804\pi$
$858$	0.132293	0.00451641
$859$	3.67442	0.125370	0.0626848	−	0.998033i	$-0.480034\pi$
$859$	3.67442	0.125370	0.0626848	+	0.998033i	$0.480034\pi$
$860$	8.31649	0.283590
$861$	0.0557146	0.00189875
$862$	−76.8178	−2.61643
$863$	−15.9961	−0.544515	−0.272258	−	0.962224i	$-0.587770\pi$
$863$	−15.9961	−0.544515	−0.272258	+	0.962224i	$0.587770\pi$
$864$	−0.280658	−0.00954817
$865$	75.9167	2.58124
$866$	−76.3332	−2.59391
$867$	−0.107929	−0.00366547
$868$	−18.3142	−0.621624
$869$	52.7687	1.79006
$870$	0.0722260	0.00244869
$871$	−21.9733	−0.744537
$872$	33.6544	1.13968
$873$	−40.5977	−1.37402
$874$	−8.04763	−0.272215
$875$	12.8470	0.434307
$876$	0.241627	0.00816381
$877$	−43.9472	−1.48399	−0.741996	−	0.670405i	$-0.766121\pi$
$877$	−43.9472	−1.48399	−0.741996	+	0.670405i	$0.766121\pi$
$878$	35.2683	1.19025
$879$	−0.00689273	−0.000232486 0
$880$	24.5510	0.827615
$881$	49.8266	1.67870	0.839350	−	0.543591i	$-0.182936\pi$
$881$	49.8266	1.67870	0.839350	+	0.543591i	$0.182936\pi$
$882$	−38.9564	−1.31173
$883$	34.0753	1.14672	0.573362	−	0.819302i	$-0.305639\pi$
$883$	34.0753	1.14672	0.573362	+	0.819302i	$0.305639\pi$
$884$	−4.13294	−0.139006
$885$	−0.0112049	−0.000376649 0
$886$	−59.8231	−2.00980
$887$	−22.2326	−0.746498	−0.373249	−	0.927731i	$-0.621756\pi$
$887$	−22.2326	−0.746498	−0.373249	+	0.927731i	$0.621756\pi$
$888$	0.0429761	0.00144218
$889$	−18.0814	−0.606431
$890$	−61.9660	−2.07710
$891$	40.4104	1.35380
$892$	49.6152	1.66124
$893$	−4.95731	−0.165890
$894$	0.140416	0.00469620
$895$	−47.7050	−1.59460
$896$	−14.7161	−0.491632
$897$	0.0486715	0.00162509
$898$	0.954605	0.0318556
$899$	8.27199	0.275886
$900$	−71.7576	−2.39192
$901$	3.41284	0.113698
$902$	79.9004	2.66039
$903$	0.00548199	0.000182429 0
$904$	40.5243	1.34782
$905$	54.5899	1.81463
$906$	−0.0408257	−0.00135634
$907$	−10.5784	−0.351249	−0.175625	−	0.984457i	$-0.556195\pi$
$907$	−10.5784	−0.351249	−0.175625	+	0.984457i	$0.556195\pi$
$908$	−0.841588	−0.0279291
$909$	−15.3929	−0.510550
$910$	17.3795	0.576123
$911$	−10.6920	−0.354243	−0.177121	−	0.984189i	$-0.556679\pi$
$911$	−10.6920	−0.354243	−0.177121	+	0.984189i	$0.556679\pi$
$912$	0.00979419	0.000324318 0
$913$	31.9225	1.05648
$914$	−52.8402	−1.74780
$915$	−0.218570	−0.00722571
$916$	54.0879	1.78711
$917$	17.7591	0.586458
$918$	0.0610747	0.00201576
$919$	2.98383	0.0984275	0.0492137	−	0.998788i	$-0.484328\pi$
$919$	2.98383	0.0984275	0.0492137	+	0.998788i	$0.484328\pi$
$920$	−25.6060	−0.844203
$921$	−0.0646830	−0.00213138
$922$	58.0437	1.91157
$923$	19.5733	0.644265
$924$	−0.0891034	−0.00293129
$925$	−28.4579	−0.935690
$926$	−19.9534	−0.655709
$927$	−49.1969	−1.61584
$928$	9.80189	0.321763
$929$	−9.09442	−0.298378	−0.149189	−	0.988809i	$-0.547666\pi$
$929$	−9.09442	−0.298378	−0.149189	+	0.988809i	$0.547666\pi$
$930$	0.318109	0.0104312
$931$	5.88347	0.192823
$932$	22.9880	0.752998
$933$	0.218198	0.00714348
$934$	75.2391	2.46190
$935$	−11.5607	−0.378075
$936$	−11.7776	−0.384963
$937$	−22.2580	−0.727138	−0.363569	−	0.931567i	$-0.618442\pi$
$937$	−22.2580	−0.727138	−0.363569	+	0.931567i	$0.618442\pi$
$938$	25.1078	0.819798
$939$	−0.219481	−0.00716249
$940$	−51.9718	−1.69513
$941$	38.7166	1.26212	0.631062	−	0.775732i	$-0.282619\pi$
$941$	38.7166	1.26212	0.631062	+	0.775732i	$0.282619\pi$
$942$	0.0407933	0.00132912
$943$	29.3959	0.957262
$944$	−0.702740	−0.0228722
$945$	−0.151385	−0.00492456
$946$	7.86173	0.255607
$947$	61.3446	1.99343	0.996716	−	0.0809757i	$-0.0258036\pi$
$947$	61.3446	1.99343	0.996716	+	0.0809757i	$0.0258036\pi$
$948$	0.220697	0.00716791
$949$	−26.2609	−0.852464
$950$	18.3856	0.596507
$951$	−0.0264814	−0.000858719 0
$952$	1.43325	0.0464520
$953$	−1.76834	−0.0572823	−0.0286411	−	0.999590i	$-0.509118\pi$
$953$	−1.76834	−0.0572823	−0.0286411	+	0.999590i	$0.509118\pi$
$954$	32.0451	1.03750
$955$	−8.54901	−0.276639
$956$	1.23744	0.0400218
$957$	0.0402454	0.00130095
$958$	16.5407	0.534405
$959$	0.571913	0.0184680
$960$	0.305425	0.00985754
$961$	5.43276	0.175250
$962$	−15.3901	−0.496195
$963$	19.6193	0.632224
$964$	−67.0564	−2.15974
$965$	−59.7750	−1.92423
$966$	−0.0556144	−0.00178937
$967$	−20.4568	−0.657848	−0.328924	−	0.944356i	$-0.606686\pi$
$967$	−20.4568	−0.657848	−0.328924	+	0.944356i	$0.606686\pi$
$968$	−17.6233	−0.566436
$969$	−0.00461193	−0.000148156 0
$970$	109.052	3.50144
$971$	6.28260	0.201618	0.100809	−	0.994906i	$-0.467857\pi$
$971$	6.28260	0.201618	0.100809	+	0.994906i	$0.467857\pi$
$972$	0.507043	0.0162634
$973$	−14.4547	−0.463395
$974$	41.7952	1.33920
$975$	−0.111195	−0.00356108
$976$	−13.7081	−0.438785
$977$	34.9780	1.11905	0.559523	−	0.828815i	$-0.310984\pi$
$977$	34.9780	1.11905	0.559523	+	0.828815i	$0.310984\pi$
$978$	−0.134534	−0.00430192
$979$	−34.5284	−1.10353
$980$	61.6815	1.97034
$981$	52.4891	1.67585
$982$	23.8168	0.760023
$983$	27.8874	0.889468	0.444734	−	0.895663i	$-0.353298\pi$
$983$	27.8874	0.889468	0.444734	+	0.895663i	$0.353298\pi$
$984$	0.101419	0.00323313
$985$	5.25917	0.167571
$986$	−2.13301	−0.0679290
$987$	−0.0342583	−0.00109045
$988$	5.86084	0.186458
$989$	2.89239	0.0919725
$990$	−108.550	−3.44995
$991$	−52.1076	−1.65525	−0.827626	−	0.561280i	$-0.810309\pi$
$991$	−52.1076	−1.65525	−0.827626	+	0.561280i	$0.810309\pi$
$992$	43.1709	1.37068
$993$	−0.0557803	−0.00177013
$994$	−22.3655	−0.709389
$995$	96.1834	3.04922
$996$	0.133511	0.00423046
$997$	−9.06674	−0.287146	−0.143573	−	0.989640i	$-0.545859\pi$
$997$	−9.06674	−0.287146	−0.143573	+	0.989640i	$0.545859\pi$
$998$	2.43838	0.0771855
$999$	0.134056	0.00424136

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4009.2.a.d.1.11	✓	75

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4009.2.a.d.1.11	✓	75	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4009 = 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4009.a (trivial)

\(f(q)\)	\(=\)	\(q-2.20714 q^{2} +0.00654009 q^{3} +2.87148 q^{4} -3.65103 q^{5} -0.0144349 q^{6} -1.05666 q^{7} -1.92348 q^{8} -2.99996 q^{9} +O(q^{10})\)	\(q-2.20714 q^{2} +0.00654009 q^{3} +2.87148 q^{4} -3.65103 q^{5} -0.0144349 q^{6} -1.05666 q^{7} -1.92348 q^{8} -2.99996 q^{9} +8.05835 q^{10} +4.49024 q^{11} +0.0187797 q^{12} -2.04105 q^{13} +2.33220 q^{14} -0.0238781 q^{15} -1.49756 q^{16} +0.705178 q^{17} +6.62133 q^{18} -1.00000 q^{19} -10.4839 q^{20} -0.00691066 q^{21} -9.91059 q^{22} -3.64618 q^{23} -0.0125797 q^{24} +8.33004 q^{25} +4.50489 q^{26} -0.0392402 q^{27} -3.03418 q^{28} +1.37045 q^{29} +0.0527023 q^{30} +6.03596 q^{31} +7.15230 q^{32} +0.0293665 q^{33} -1.55643 q^{34} +3.85791 q^{35} -8.61432 q^{36} -3.41630 q^{37} +2.20714 q^{38} -0.0133486 q^{39} +7.02269 q^{40} -8.06212 q^{41} +0.0152528 q^{42} -0.793266 q^{43} +12.8936 q^{44} +10.9529 q^{45} +8.04763 q^{46} +4.95731 q^{47} -0.00979419 q^{48} -5.88347 q^{49} -18.3856 q^{50} +0.00461193 q^{51} -5.86084 q^{52} +4.83968 q^{53} +0.0866088 q^{54} -16.3940 q^{55} +2.03247 q^{56} -0.00654009 q^{57} -3.02479 q^{58} +0.469255 q^{59} -0.0685654 q^{60} +9.15360 q^{61} -13.3222 q^{62} +3.16994 q^{63} -12.7910 q^{64} +7.45194 q^{65} -0.0648161 q^{66} +10.7657 q^{67} +2.02491 q^{68} -0.0238463 q^{69} -8.51495 q^{70} -9.58984 q^{71} +5.77036 q^{72} +12.8664 q^{73} +7.54026 q^{74} +0.0544791 q^{75} -2.87148 q^{76} -4.74466 q^{77} +0.0294624 q^{78} +11.7519 q^{79} +5.46765 q^{80} +8.99962 q^{81} +17.7943 q^{82} +7.10932 q^{83} -0.0198438 q^{84} -2.57463 q^{85} +1.75085 q^{86} +0.00896288 q^{87} -8.63688 q^{88} -7.68966 q^{89} -24.1747 q^{90} +2.15670 q^{91} -10.4699 q^{92} +0.0394757 q^{93} -10.9415 q^{94} +3.65103 q^{95} +0.0467766 q^{96} +13.5328 q^{97} +12.9856 q^{98} -13.4705 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 75 q - 11 q^{2} - 4 q^{3} + 67 q^{4} - 18 q^{5} - 15 q^{6} - 19 q^{7} - 30 q^{8} + 57 q^{9}+O(q^{10}) \) 75 * q - 11 * q^2 - 4 * q^3 + 67 * q^4 - 18 * q^5 - 15 * q^6 - 19 * q^7 - 30 * q^8 + 57 * q^9	\( 75 q - 11 q^{2} - 4 q^{3} + 67 q^{4} - 18 q^{5} - 15 q^{6} - 19 q^{7} - 30 q^{8} + 57 q^{9} - 48 q^{11} - 14 q^{12} - 3 q^{13} - 4 q^{14} - 39 q^{15} + 59 q^{16} - 23 q^{17} - 24 q^{18} - 75 q^{19} - 62 q^{20} - 3 q^{21} - 6 q^{22} - 73 q^{23} - 64 q^{24} + 57 q^{25} - 46 q^{26} - 22 q^{27} - 26 q^{28} - 39 q^{29} - 14 q^{30} - 44 q^{31} - 71 q^{32} - 3 q^{33} - 9 q^{34} - 49 q^{35} + 20 q^{36} - 12 q^{37} + 11 q^{38} - 90 q^{39} - 8 q^{40} - 42 q^{41} - 45 q^{42} - 24 q^{43} - 120 q^{44} - 63 q^{45} - 39 q^{46} - 59 q^{47} - 4 q^{48} + 48 q^{49} - 100 q^{50} - 55 q^{51} + 2 q^{52} + 13 q^{53} - 87 q^{54} - 36 q^{55} - 12 q^{56} + 4 q^{57} - 17 q^{58} - 47 q^{59} - 45 q^{60} - 35 q^{61} - 40 q^{62} - 69 q^{63} + 26 q^{64} - 44 q^{65} + 33 q^{66} - 39 q^{67} - 63 q^{68} + 42 q^{69} + 40 q^{70} - 154 q^{71} - 51 q^{72} - 29 q^{73} - 95 q^{74} + 37 q^{75} - 67 q^{76} - 24 q^{77} - 19 q^{78} - 95 q^{79} - 146 q^{80} + 23 q^{81} + 7 q^{82} - 52 q^{83} - 72 q^{84} - 36 q^{85} - 44 q^{86} - 103 q^{87} + 67 q^{88} + q^{89} - 2 q^{90} - 64 q^{91} - 183 q^{92} - 49 q^{93} + 5 q^{94} + 18 q^{95} - 69 q^{96} - 7 q^{97} - 23 q^{98} - 100 q^{99}+O(q^{100}) \) 75 * q - 11 * q^2 - 4 * q^3 + 67 * q^4 - 18 * q^5 - 15 * q^6 - 19 * q^7 - 30 * q^8 + 57 * q^9 - 48 * q^11 - 14 * q^12 - 3 * q^13 - 4 * q^14 - 39 * q^15 + 59 * q^16 - 23 * q^17 - 24 * q^18 - 75 * q^19 - 62 * q^20 - 3 * q^21 - 6 * q^22 - 73 * q^23 - 64 * q^24 + 57 * q^25 - 46 * q^26 - 22 * q^27 - 26 * q^28 - 39 * q^29 - 14 * q^30 - 44 * q^31 - 71 * q^32 - 3 * q^33 - 9 * q^34 - 49 * q^35 + 20 * q^36 - 12 * q^37 + 11 * q^38 - 90 * q^39 - 8 * q^40 - 42 * q^41 - 45 * q^42 - 24 * q^43 - 120 * q^44 - 63 * q^45 - 39 * q^46 - 59 * q^47 - 4 * q^48 + 48 * q^49 - 100 * q^50 - 55 * q^51 + 2 * q^52 + 13 * q^53 - 87 * q^54 - 36 * q^55 - 12 * q^56 + 4 * q^57 - 17 * q^58 - 47 * q^59 - 45 * q^60 - 35 * q^61 - 40 * q^62 - 69 * q^63 + 26 * q^64 - 44 * q^65 + 33 * q^66 - 39 * q^67 - 63 * q^68 + 42 * q^69 + 40 * q^70 - 154 * q^71 - 51 * q^72 - 29 * q^73 - 95 * q^74 + 37 * q^75 - 67 * q^76 - 24 * q^77 - 19 * q^78 - 95 * q^79 - 146 * q^80 + 23 * q^81 + 7 * q^82 - 52 * q^83 - 72 * q^84 - 36 * q^85 - 44 * q^86 - 103 * q^87 + 67 * q^88 + q^89 - 2 * q^90 - 64 * q^91 - 183 * q^92 - 49 * q^93 + 5 * q^94 + 18 * q^95 - 69 * q^96 - 7 * q^97 - 23 * q^98 - 100 * q^99

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