LMFDB - Embedded newform 6037.2.a.a.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6037,2,Mod(1,6037)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6037, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6037.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6037 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6037.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:	$48.2056877002$
Analytic rank:	$1$
Dimension:	$243$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	6037.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.59845 q^{2} +1.70782 q^{3} +4.75194 q^{4} +1.33764 q^{5} -4.43768 q^{6} +4.30824 q^{7} -7.15077 q^{8} -0.0833526 q^{9} +O(q^{10})$	\(q-2.59845 q^{2} +1.70782 q^{3} +4.75194 q^{4} +1.33764 q^{5} -4.43768 q^{6} +4.30824 q^{7} -7.15077 q^{8} -0.0833526 q^{9} -3.47580 q^{10} -2.12921 q^{11} +8.11545 q^{12} +3.40580 q^{13} -11.1947 q^{14} +2.28446 q^{15} +9.07704 q^{16} -7.94313 q^{17} +0.216588 q^{18} -6.05996 q^{19} +6.35640 q^{20} +7.35769 q^{21} +5.53265 q^{22} -6.55475 q^{23} -12.2122 q^{24} -3.21071 q^{25} -8.84981 q^{26} -5.26581 q^{27} +20.4725 q^{28} +2.47288 q^{29} -5.93604 q^{30} +1.47200 q^{31} -9.28468 q^{32} -3.63631 q^{33} +20.6398 q^{34} +5.76289 q^{35} -0.396086 q^{36} +0.312915 q^{37} +15.7465 q^{38} +5.81650 q^{39} -9.56519 q^{40} +4.41207 q^{41} -19.1186 q^{42} -4.75140 q^{43} -10.1179 q^{44} -0.111496 q^{45} +17.0322 q^{46} +3.25914 q^{47} +15.5019 q^{48} +11.5609 q^{49} +8.34286 q^{50} -13.5654 q^{51} +16.1842 q^{52} -5.81088 q^{53} +13.6829 q^{54} -2.84813 q^{55} -30.8072 q^{56} -10.3493 q^{57} -6.42566 q^{58} -10.3138 q^{59} +10.8556 q^{60} -0.906212 q^{61} -3.82491 q^{62} -0.359103 q^{63} +5.97169 q^{64} +4.55576 q^{65} +9.44877 q^{66} -7.76532 q^{67} -37.7453 q^{68} -11.1943 q^{69} -14.9746 q^{70} +15.7949 q^{71} +0.596035 q^{72} +15.6027 q^{73} -0.813094 q^{74} -5.48331 q^{75} -28.7965 q^{76} -9.17316 q^{77} -15.1139 q^{78} -8.64693 q^{79} +12.1418 q^{80} -8.74299 q^{81} -11.4645 q^{82} +2.53380 q^{83} +34.9633 q^{84} -10.6251 q^{85} +12.3463 q^{86} +4.22324 q^{87} +15.2255 q^{88} +4.45910 q^{89} +0.289717 q^{90} +14.6730 q^{91} -31.1478 q^{92} +2.51390 q^{93} -8.46870 q^{94} -8.10607 q^{95} -15.8566 q^{96} +7.98023 q^{97} -30.0404 q^{98} +0.177476 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9}+O(q^{10}) $ 243 * q - 47 * q^2 - 31 * q^3 + 229 * q^4 - 40 * q^5 - 18 * q^6 - 42 * q^7 - 135 * q^8 + 214 * q^9	\( 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9} - 14 q^{10} - 112 q^{11} - 54 q^{12} - 45 q^{13} - 35 q^{14} - 56 q^{15} + 213 q^{16} - 71 q^{17} - 135 q^{18} - 69 q^{19} - 107 q^{20} - 36 q^{21} - 24 q^{22} - 162 q^{23} - 57 q^{24} + 203 q^{25} - 55 q^{26} - 115 q^{27} - 87 q^{28} - 76 q^{29} - 64 q^{30} - 35 q^{31} - 302 q^{32} - 77 q^{33} - 9 q^{34} - 264 q^{35} + 173 q^{36} - 61 q^{37} - 71 q^{38} - 123 q^{39} - 16 q^{40} - 74 q^{41} - 70 q^{42} - 178 q^{43} - 209 q^{44} - 107 q^{45} - 11 q^{46} - 191 q^{47} - 65 q^{48} + 211 q^{49} - 188 q^{50} - 175 q^{51} - 95 q^{52} - 122 q^{53} - 36 q^{54} - 47 q^{55} - 69 q^{56} - 103 q^{57} - 37 q^{58} - 212 q^{59} - 79 q^{60} - 14 q^{61} - 152 q^{62} - 203 q^{63} + 217 q^{64} - 159 q^{65} + 5 q^{66} - 202 q^{67} - 176 q^{68} - 34 q^{69} + 45 q^{70} - 170 q^{71} - 347 q^{72} - 57 q^{73} - 68 q^{74} - 124 q^{75} - 74 q^{76} - 166 q^{77} - 63 q^{78} - 48 q^{79} - 222 q^{80} + 159 q^{81} - 27 q^{82} - 434 q^{83} - 52 q^{84} - 57 q^{85} - 77 q^{86} - 184 q^{87} - 15 q^{88} - 62 q^{89} - 24 q^{90} - 81 q^{91} - 330 q^{92} - 164 q^{93} + 40 q^{94} - 182 q^{95} - 66 q^{96} - 21 q^{97} - 254 q^{98} - 306 q^{99}+O(q^{100}) \) 243 * q - 47 * q^2 - 31 * q^3 + 229 * q^4 - 40 * q^5 - 18 * q^6 - 42 * q^7 - 135 * q^8 + 214 * q^9 - 14 * q^10 - 112 * q^11 - 54 * q^12 - 45 * q^13 - 35 * q^14 - 56 * q^15 + 213 * q^16 - 71 * q^17 - 135 * q^18 - 69 * q^19 - 107 * q^20 - 36 * q^21 - 24 * q^22 - 162 * q^23 - 57 * q^24 + 203 * q^25 - 55 * q^26 - 115 * q^27 - 87 * q^28 - 76 * q^29 - 64 * q^30 - 35 * q^31 - 302 * q^32 - 77 * q^33 - 9 * q^34 - 264 * q^35 + 173 * q^36 - 61 * q^37 - 71 * q^38 - 123 * q^39 - 16 * q^40 - 74 * q^41 - 70 * q^42 - 178 * q^43 - 209 * q^44 - 107 * q^45 - 11 * q^46 - 191 * q^47 - 65 * q^48 + 211 * q^49 - 188 * q^50 - 175 * q^51 - 95 * q^52 - 122 * q^53 - 36 * q^54 - 47 * q^55 - 69 * q^56 - 103 * q^57 - 37 * q^58 - 212 * q^59 - 79 * q^60 - 14 * q^61 - 152 * q^62 - 203 * q^63 + 217 * q^64 - 159 * q^65 + 5 * q^66 - 202 * q^67 - 176 * q^68 - 34 * q^69 + 45 * q^70 - 170 * q^71 - 347 * q^72 - 57 * q^73 - 68 * q^74 - 124 * q^75 - 74 * q^76 - 166 * q^77 - 63 * q^78 - 48 * q^79 - 222 * q^80 + 159 * q^81 - 27 * q^82 - 434 * q^83 - 52 * q^84 - 57 * q^85 - 77 * q^86 - 184 * q^87 - 15 * q^88 - 62 * q^89 - 24 * q^90 - 81 * q^91 - 330 * q^92 - 164 * q^93 + 40 * q^94 - 182 * q^95 - 66 * q^96 - 21 * q^97 - 254 * q^98 - 306 * 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 $

$2$	−2.59845	−1.83738	−0.918690	−	0.394978i	$-0.870752\pi$
$2$	−2.59845	−1.83738	−0.918690	+	0.394978i	$0.870752\pi$
$3$	1.70782	0.986010	0.493005	−	0.870026i	$-0.335898\pi$
$3$	1.70782	0.986010	0.493005	+	0.870026i	$0.335898\pi$
$4$	4.75194	2.37597
$5$	1.33764	0.598213	0.299106	−	0.954220i	$-0.403311\pi$
$5$	1.33764	0.598213	0.299106	+	0.954220i	$0.403311\pi$
$6$	−4.43768	−1.81168
$7$	4.30824	1.62836	0.814180	−	0.580612i	$-0.197187\pi$
$7$	4.30824	1.62836	0.814180	+	0.580612i	$0.197187\pi$
$8$	−7.15077	−2.52818
$9$	−0.0833526	−0.0277842
$10$	−3.47580	−1.09914
$11$	−2.12921	−0.641982	−0.320991	−	0.947082i	$-0.604016\pi$
$11$	−2.12921	−0.641982	−0.320991	+	0.947082i	$0.604016\pi$
$12$	8.11545	2.34273
$13$	3.40580	0.944600	0.472300	−	0.881438i	$-0.343424\pi$
$13$	3.40580	0.944600	0.472300	+	0.881438i	$0.343424\pi$
$14$	−11.1947	−2.99192
$15$	2.28446	0.589844
$16$	9.07704	2.26926
$17$	−7.94313	−1.92649	−0.963246	−	0.268620i	$-0.913432\pi$
$17$	−7.94313	−1.92649	−0.963246	+	0.268620i	$0.913432\pi$
$18$	0.216588	0.0510502
$19$	−6.05996	−1.39025	−0.695125	−	0.718889i	$-0.744651\pi$
$19$	−6.05996	−1.39025	−0.695125	+	0.718889i	$0.744651\pi$
$20$	6.35640	1.42134
$21$	7.35769	1.60558
$22$	5.53265	1.17957
$23$	−6.55475	−1.36676	−0.683380	−	0.730063i	$-0.739491\pi$
$23$	−6.55475	−1.36676	−0.683380	+	0.730063i	$0.739491\pi$
$24$	−12.2122	−2.49281
$25$	−3.21071	−0.642141
$26$	−8.84981	−1.73559
$27$	−5.26581	−1.01341
$28$	20.4725	3.86893
$29$	2.47288	0.459203	0.229602	−	0.973285i	$-0.426258\pi$
$29$	2.47288	0.459203	0.229602	+	0.973285i	$0.426258\pi$
$30$	−5.93604	−1.08377
$31$	1.47200	0.264378	0.132189	−	0.991225i	$-0.457799\pi$
$31$	1.47200	0.264378	0.132189	+	0.991225i	$0.457799\pi$
$32$	−9.28468	−1.64131
$33$	−3.63631	−0.633001
$34$	20.6398	3.53970
$35$	5.76289	0.974106
$36$	−0.396086	−0.0660144
$37$	0.312915	0.0514429	0.0257215	−	0.999669i	$-0.491812\pi$
$37$	0.312915	0.0514429	0.0257215	+	0.999669i	$0.491812\pi$
$38$	15.7465	2.55442
$39$	5.81650	0.931385
$40$	−9.56519	−1.51239
$41$	4.41207	0.689050	0.344525	−	0.938777i	$-0.388040\pi$
$41$	4.41207	0.689050	0.344525	+	0.938777i	$0.388040\pi$
$42$	−19.1186	−2.95006
$43$	−4.75140	−0.724582	−0.362291	−	0.932065i	$-0.618005\pi$
$43$	−4.75140	−0.724582	−0.362291	+	0.932065i	$0.618005\pi$
$44$	−10.1179	−1.52533
$45$	−0.111496	−0.0166209
$46$	17.0322	2.51126
$47$	3.25914	0.475394	0.237697	−	0.971339i	$-0.423607\pi$
$47$	3.25914	0.475394	0.237697	+	0.971339i	$0.423607\pi$
$48$	15.5019	2.23751
$49$	11.5609	1.65156
$50$	8.34286	1.17986
$51$	−13.5654	−1.89954
$52$	16.1842	2.24434
$53$	−5.81088	−0.798185	−0.399093	−	0.916911i	$-0.630675\pi$
$53$	−5.81088	−0.798185	−0.399093	+	0.916911i	$0.630675\pi$
$54$	13.6829	1.86201
$55$	−2.84813	−0.384042
$56$	−30.8072	−4.11679
$57$	−10.3493	−1.37080
$58$	−6.42566	−0.843731
$59$	−10.3138	−1.34274	−0.671371	−	0.741121i	$-0.734294\pi$
$59$	−10.3138	−1.34274	−0.671371	+	0.741121i	$0.734294\pi$
$60$	10.8556	1.40145
$61$	−0.906212	−0.116029	−0.0580143	−	0.998316i	$-0.518477\pi$
$61$	−0.906212	−0.116029	−0.0580143	+	0.998316i	$0.518477\pi$
$62$	−3.82491	−0.485764
$63$	−0.359103	−0.0452427
$64$	5.97169	0.746461
$65$	4.55576	0.565072
$66$	9.44877	1.16306
$67$	−7.76532	−0.948685	−0.474343	−	0.880340i	$-0.657314\pi$
$67$	−7.76532	−0.948685	−0.474343	+	0.880340i	$0.657314\pi$
$68$	−37.7453	−4.57729
$69$	−11.1943	−1.34764
$70$	−14.9746	−1.78980
$71$	15.7949	1.87451	0.937255	−	0.348645i	$-0.113358\pi$
$71$	15.7949	1.87451	0.937255	+	0.348645i	$0.113358\pi$
$72$	0.596035	0.0702434
$73$	15.6027	1.82616	0.913078	−	0.407785i	$-0.133699\pi$
$73$	15.6027	1.82616	0.913078	+	0.407785i	$0.133699\pi$
$74$	−0.813094	−0.0945203
$75$	−5.48331	−0.633158
$76$	−28.7965	−3.30319
$77$	−9.17316	−1.04538
$78$	−15.1139	−1.71131
$79$	−8.64693	−0.972856	−0.486428	−	0.873721i	$-0.661700\pi$
$79$	−8.64693	−0.972856	−0.486428	+	0.873721i	$0.661700\pi$
$80$	12.1418	1.35750
$81$	−8.74299	−0.971444
$82$	−11.4645	−1.26605
$83$	2.53380	0.278121	0.139060	−	0.990284i	$-0.455592\pi$
$83$	2.53380	0.278121	0.139060	+	0.990284i	$0.455592\pi$
$84$	34.9633	3.81481
$85$	−10.6251	−1.15245
$86$	12.3463	1.33133
$87$	4.22324	0.452779
$88$	15.2255	1.62305
$89$	4.45910	0.472664	0.236332	−	0.971672i	$-0.424055\pi$
$89$	4.45910	0.472664	0.236332	+	0.971672i	$0.424055\pi$
$90$	0.289717	0.0305389
$91$	14.6730	1.53815
$92$	−31.1478	−3.24738
$93$	2.51390	0.260680
$94$	−8.46870	−0.873480
$95$	−8.10607	−0.831665
$96$	−15.8566	−1.61835
$97$	7.98023	0.810270	0.405135	−	0.914257i	$-0.367225\pi$
$97$	7.98023	0.810270	0.405135	+	0.914257i	$0.367225\pi$
$98$	−30.0404	−3.03454
$99$	0.177476	0.0178370
$100$	−15.2571	−1.52571
$101$	8.76335	0.871986	0.435993	−	0.899950i	$-0.356397\pi$
$101$	8.76335	0.871986	0.435993	+	0.899950i	$0.356397\pi$
$102$	35.2491	3.49018
$103$	10.8692	1.07098	0.535488	−	0.844543i	$-0.320128\pi$
$103$	10.8692	1.07098	0.535488	+	0.844543i	$0.320128\pi$
$104$	−24.3541	−2.38812
$105$	9.84198	0.960478
$106$	15.0993	1.46657
$107$	−18.6281	−1.80085	−0.900425	−	0.435011i	$-0.856744\pi$
$107$	−18.6281	−1.80085	−0.900425	+	0.435011i	$0.856744\pi$
$108$	−25.0228	−2.40782
$109$	9.78348	0.937088	0.468544	−	0.883440i	$-0.344779\pi$
$109$	9.78348	0.937088	0.468544	+	0.883440i	$0.344779\pi$
$110$	7.40072	0.705631
$111$	0.534403	0.0507233
$112$	39.1060	3.69517
$113$	−15.5523	−1.46303	−0.731517	−	0.681823i	$-0.761187\pi$
$113$	−15.5523	−1.46303	−0.731517	+	0.681823i	$0.761187\pi$
$114$	26.8922	2.51868
$115$	−8.76793	−0.817614
$116$	11.7510	1.09105
$117$	−0.283883	−0.0262450
$118$	26.7999	2.46713
$119$	−34.2209	−3.13702
$120$	−16.3356	−1.49123
$121$	−6.46645	−0.587859
$122$	2.35475	0.213189
$123$	7.53502	0.679410
$124$	6.99484	0.628155
$125$	−10.9830	−0.982350
$126$	0.933110	0.0831281
$127$	−3.31971	−0.294577	−0.147288	−	0.989094i	$-0.547055\pi$
$127$	−3.31971	−0.294577	−0.147288	+	0.989094i	$0.547055\pi$
$128$	3.05223	0.269781
$129$	−8.11454	−0.714445
$130$	−11.8379	−1.03825
$131$	−13.5046	−1.17990	−0.589950	−	0.807440i	$-0.700853\pi$
$131$	−13.5046	−1.17990	−0.589950	+	0.807440i	$0.700853\pi$
$132$	−17.2795	−1.50399
$133$	−26.1077	−2.26383
$134$	20.1778	1.74310
$135$	−7.04378	−0.606232
$136$	56.7995	4.87052
$137$	0.345631	0.0295292	0.0147646	−	0.999891i	$-0.495300\pi$
$137$	0.345631	0.0295292	0.0147646	+	0.999891i	$0.495300\pi$
$138$	29.0879	2.47613
$139$	−9.77960	−0.829495	−0.414747	−	0.909937i	$-0.636130\pi$
$139$	−9.77960	−0.829495	−0.414747	+	0.909937i	$0.636130\pi$
$140$	27.3849	2.31445
$141$	5.56602	0.468743
$142$	−41.0422	−3.44419
$143$	−7.25168	−0.606416
$144$	−0.756595	−0.0630496
$145$	3.30784	0.274701
$146$	−40.5428	−3.35534
$147$	19.7439	1.62845
$148$	1.48695	0.122227
$149$	−11.9578	−0.979622	−0.489811	−	0.871829i	$-0.662934\pi$
$149$	−11.9578	−0.979622	−0.489811	+	0.871829i	$0.662934\pi$
$150$	14.2481	1.16335
$151$	5.31113	0.432214	0.216107	−	0.976370i	$-0.430664\pi$
$151$	5.31113	0.432214	0.216107	+	0.976370i	$0.430664\pi$
$152$	43.3334	3.51480
$153$	0.662081	0.0535261
$154$	23.8360	1.92076
$155$	1.96901	0.158155
$156$	27.6396	2.21294
$157$	22.7223	1.81343	0.906717	−	0.421739i	$-0.138580\pi$
$157$	22.7223	1.81343	0.906717	+	0.421739i	$0.138580\pi$
$158$	22.4686	1.78751
$159$	−9.92393	−0.787019
$160$	−12.4196	−0.981855
$161$	−28.2394	−2.22558
$162$	22.7182	1.78491
$163$	−4.63617	−0.363133	−0.181567	−	0.983379i	$-0.558117\pi$
$163$	−4.63617	−0.363133	−0.181567	+	0.983379i	$0.558117\pi$
$164$	20.9659	1.63716
$165$	−4.86409	−0.378669
$166$	−6.58395	−0.511014
$167$	−15.8705	−1.22810	−0.614050	−	0.789267i	$-0.710461\pi$
$167$	−15.8705	−1.22810	−0.614050	+	0.789267i	$0.710461\pi$
$168$	−52.6132	−4.05919
$169$	−1.40050	−0.107731
$170$	27.6087	2.11749
$171$	0.505113	0.0386270
$172$	−22.5784	−1.72158
$173$	−16.1436	−1.22738	−0.613688	−	0.789549i	$-0.710315\pi$
$173$	−16.1436	−1.22738	−0.613688	+	0.789549i	$0.710315\pi$
$174$	−10.9739	−0.831927
$175$	−13.8325	−1.04564
$176$	−19.3269	−1.45682
$177$	−17.6141	−1.32396
$178$	−11.5867	−0.868463
$179$	−25.7875	−1.92745	−0.963723	−	0.266905i	$-0.913999\pi$
$179$	−25.7875	−1.92745	−0.963723	+	0.266905i	$0.913999\pi$
$180$	−0.529823	−0.0394907
$181$	−13.9473	−1.03670	−0.518348	−	0.855170i	$-0.673453\pi$
$181$	−13.9473	−1.03670	−0.518348	+	0.855170i	$0.673453\pi$
$182$	−38.1271	−2.82617
$183$	−1.54765	−0.114405
$184$	46.8715	3.45541
$185$	0.418569	0.0307738
$186$	−6.53225	−0.478968
$187$	16.9126	1.23677
$188$	15.4872	1.12952
$189$	−22.6864	−1.65019
$190$	21.0632	1.52809
$191$	9.72382	0.703591	0.351796	−	0.936077i	$-0.385571\pi$
$191$	9.72382	0.703591	0.351796	+	0.936077i	$0.385571\pi$
$192$	10.1986	0.736018
$193$	8.33149	0.599714	0.299857	−	0.953984i	$-0.403061\pi$
$193$	8.33149	0.599714	0.299857	+	0.953984i	$0.403061\pi$
$194$	−20.7362	−1.48877
$195$	7.78041	0.557167
$196$	54.9367	3.92405
$197$	−0.243611	−0.0173565	−0.00867827	−	0.999962i	$-0.502762\pi$
$197$	−0.243611	−0.0173565	−0.00867827	+	0.999962i	$0.502762\pi$
$198$	−0.461161	−0.0327733
$199$	−17.9645	−1.27347	−0.636736	−	0.771082i	$-0.719716\pi$
$199$	−17.9645	−1.27347	−0.636736	+	0.771082i	$0.719716\pi$
$200$	22.9590	1.62345
$201$	−13.2618	−0.935413
$202$	−22.7711	−1.60217
$203$	10.6538	0.747748
$204$	−64.4621	−4.51325
$205$	5.90179	0.412199
$206$	−28.2431	−1.96779
$207$	0.546356	0.0379744
$208$	30.9146	2.14354
$209$	12.9029	0.892515
$210$	−25.5739	−1.76476
$211$	−26.6384	−1.83386	−0.916930	−	0.399048i	$-0.869341\pi$
$211$	−26.6384	−1.83386	−0.916930	+	0.399048i	$0.869341\pi$
$212$	−27.6129	−1.89646
$213$	26.9748	1.84829
$214$	48.4043	3.30885
$215$	−6.35569	−0.433454
$216$	37.6546	2.56207
$217$	6.34171	0.430503
$218$	−25.4219	−1.72179
$219$	26.6466	1.80061
$220$	−13.5341	−0.912472
$221$	−27.0527	−1.81976
$222$	−1.38862	−0.0931979
$223$	−16.3924	−1.09772	−0.548858	−	0.835915i	$-0.684937\pi$
$223$	−16.3924	−1.09772	−0.548858	+	0.835915i	$0.684937\pi$
$224$	−40.0006	−2.67265
$225$	0.267621	0.0178414
$226$	40.4118	2.68815
$227$	−4.96106	−0.329277	−0.164638	−	0.986354i	$-0.552646\pi$
$227$	−4.96106	−0.329277	−0.164638	+	0.986354i	$0.552646\pi$
$228$	−49.1793	−3.25698
$229$	−5.24538	−0.346624	−0.173312	−	0.984867i	$-0.555447\pi$
$229$	−5.24538	−0.346624	−0.173312	+	0.984867i	$0.555447\pi$
$230$	22.7830	1.50227
$231$	−15.6661	−1.03075
$232$	−17.6830	−1.16095
$233$	10.5418	0.690615	0.345308	−	0.938490i	$-0.387775\pi$
$233$	10.5418	0.690615	0.345308	+	0.938490i	$0.387775\pi$
$234$	0.737655	0.0482220
$235$	4.35957	0.284387
$236$	−49.0105	−3.19031
$237$	−14.7674	−0.959246
$238$	88.9212	5.76391
$239$	18.0547	1.16786	0.583932	−	0.811802i	$-0.301513\pi$
$239$	18.0547	1.16786	0.583932	+	0.811802i	$0.301513\pi$
$240$	20.7361	1.33851
$241$	−18.2140	−1.17327	−0.586634	−	0.809852i	$-0.699547\pi$
$241$	−18.2140	−1.17327	−0.586634	+	0.809852i	$0.699547\pi$
$242$	16.8027	1.08012
$243$	0.865973	0.0555522
$244$	−4.30627	−0.275680
$245$	15.4644	0.987983
$246$	−19.5794	−1.24834
$247$	−20.6390	−1.31323
$248$	−10.5259	−0.668396
$249$	4.32728	0.274230
$250$	28.5388	1.80495
$251$	−20.8701	−1.31731	−0.658654	−	0.752446i	$-0.728874\pi$
$251$	−20.8701	−1.31731	−0.658654	+	0.752446i	$0.728874\pi$
$252$	−1.70643	−0.107495
$253$	13.9565	0.877436
$254$	8.62610	0.541249
$255$	−18.1457	−1.13633
$256$	−19.8744	−1.24215
$257$	16.8707	1.05236	0.526182	−	0.850372i	$-0.323623\pi$
$257$	16.8707	1.05236	0.526182	+	0.850372i	$0.323623\pi$
$258$	21.0852	1.31271
$259$	1.34811	0.0837676
$260$	21.6487	1.34259
$261$	−0.206121	−0.0127586
$262$	35.0910	2.16793
$263$	12.7738	0.787664	0.393832	−	0.919182i	$-0.371149\pi$
$263$	12.7738	0.787664	0.393832	+	0.919182i	$0.371149\pi$
$264$	26.0024	1.60034
$265$	−7.77289	−0.477485
$266$	67.8396	4.15951
$267$	7.61534	0.466051
$268$	−36.9003	−2.25405
$269$	22.4336	1.36780	0.683900	−	0.729575i	$-0.260282\pi$
$269$	22.4336	1.36780	0.683900	+	0.729575i	$0.260282\pi$
$270$	18.3029	1.11388
$271$	−0.490979	−0.0298248	−0.0149124	−	0.999889i	$-0.504747\pi$
$271$	−0.490979	−0.0298248	−0.0149124	+	0.999889i	$0.504747\pi$
$272$	−72.1001	−4.37171
$273$	25.0589	1.51663
$274$	−0.898104	−0.0542565
$275$	6.83628	0.412243
$276$	−53.1948	−3.20195
$277$	−26.1069	−1.56861	−0.784305	−	0.620375i	$-0.786980\pi$
$277$	−26.1069	−1.56861	−0.784305	+	0.620375i	$0.786980\pi$
$278$	25.4118	1.52410
$279$	−0.122695	−0.00734555
$280$	−41.2091	−2.46271
$281$	−5.24838	−0.313092	−0.156546	−	0.987671i	$-0.550036\pi$
$281$	−5.24838	−0.313092	−0.156546	+	0.987671i	$0.550036\pi$
$282$	−14.4630	−0.861260
$283$	23.6571	1.40627	0.703135	−	0.711056i	$-0.251783\pi$
$283$	23.6571	1.40627	0.703135	+	0.711056i	$0.251783\pi$
$284$	75.0564	4.45378
$285$	−13.8437	−0.820030
$286$	18.8431	1.11422
$287$	19.0083	1.12202
$288$	0.773902	0.0456026
$289$	46.0933	2.71137
$290$	−8.59525	−0.504731
$291$	13.6288	0.798934
$292$	74.1430	4.33889
$293$	3.95046	0.230788	0.115394	−	0.993320i	$-0.463187\pi$
$293$	3.95046	0.230788	0.115394	+	0.993320i	$0.463187\pi$
$294$	−51.3036	−2.99209
$295$	−13.7962	−0.803246
$296$	−2.23758	−0.130057
$297$	11.2120	0.650588
$298$	31.0718	1.79994
$299$	−22.3242	−1.29104
$300$	−26.0563	−1.50436
$301$	−20.4702	−1.17988
$302$	−13.8007	−0.794141
$303$	14.9662	0.859787
$304$	−55.0065	−3.15484
$305$	−1.21219	−0.0694098
$306$	−1.72038	−0.0983478
$307$	6.02960	0.344127	0.172064	−	0.985086i	$-0.444956\pi$
$307$	6.02960	0.344127	0.172064	+	0.985086i	$0.444956\pi$
$308$	−43.5903	−2.48379
$309$	18.5627	1.05599
$310$	−5.11637	−0.290590
$311$	19.6053	1.11172	0.555858	−	0.831277i	$-0.312390\pi$
$311$	19.6053	1.11172	0.555858	+	0.831277i	$0.312390\pi$
$312$	−41.5924	−2.35471
$313$	−0.459494	−0.0259721	−0.0129861	−	0.999916i	$-0.504134\pi$
$313$	−0.459494	−0.0259721	−0.0129861	+	0.999916i	$0.504134\pi$
$314$	−59.0426	−3.33197
$315$	−0.480352	−0.0270648
$316$	−41.0897	−2.31147
$317$	5.74110	0.322452	0.161226	−	0.986917i	$-0.448455\pi$
$317$	5.74110	0.322452	0.161226	+	0.986917i	$0.448455\pi$
$318$	25.7868	1.44605
$319$	−5.26530	−0.294800
$320$	7.98800	0.446543
$321$	−31.8135	−1.77566
$322$	73.3787	4.08924
$323$	48.1350	2.67831
$324$	−41.5462	−2.30812
$325$	−10.9350	−0.606567
$326$	12.0469	0.667214
$327$	16.7084	0.923978
$328$	−31.5497	−1.74204
$329$	14.0411	0.774113
$330$	12.6391	0.695760
$331$	−8.04552	−0.442222	−0.221111	−	0.975249i	$-0.570968\pi$
$331$	−8.04552	−0.442222	−0.221111	+	0.975249i	$0.570968\pi$
$332$	12.0405	0.660806
$333$	−0.0260823	−0.00142930
$334$	41.2388	2.25649
$335$	−10.3872	−0.567516
$336$	66.7860	3.64348
$337$	33.8697	1.84500	0.922500	−	0.385997i	$-0.126143\pi$
$337$	33.8697	1.84500	0.922500	+	0.385997i	$0.126143\pi$
$338$	3.63912	0.197942
$339$	−26.5605	−1.44257
$340$	−50.4897	−2.73819
$341$	−3.13420	−0.169726
$342$	−1.31251	−0.0709725
$343$	19.6494	1.06097
$344$	33.9762	1.83187
$345$	−14.9740	−0.806175
$346$	41.9483	2.25516
$347$	−31.0923	−1.66912	−0.834562	−	0.550914i	$-0.814279\pi$
$347$	−31.0923	−1.66912	−0.834562	+	0.550914i	$0.814279\pi$
$348$	20.0686	1.07579
$349$	−19.3486	−1.03571	−0.517853	−	0.855470i	$-0.673269\pi$
$349$	−19.3486	−1.03571	−0.517853	+	0.855470i	$0.673269\pi$
$350$	35.9430	1.92123
$351$	−17.9343	−0.957263
$352$	19.7691	1.05369
$353$	11.1385	0.592845	0.296422	−	0.955057i	$-0.404206\pi$
$353$	11.1385	0.592845	0.296422	+	0.955057i	$0.404206\pi$
$354$	45.7694	2.43261
$355$	21.1280	1.12136
$356$	21.1894	1.12303
$357$	−58.4431	−3.09314
$358$	67.0074	3.54145
$359$	−6.73669	−0.355549	−0.177775	−	0.984071i	$-0.556890\pi$
$359$	−6.73669	−0.355549	−0.177775	+	0.984071i	$0.556890\pi$
$360$	0.797284	0.0420205
$361$	17.7231	0.932795
$362$	36.2414	1.90481
$363$	−11.0435	−0.579635
$364$	69.7252	3.65460
$365$	20.8708	1.09243
$366$	4.02148	0.210206
$367$	−1.50838	−0.0787367	−0.0393683	−	0.999225i	$-0.512535\pi$
$367$	−1.50838	−0.0787367	−0.0393683	+	0.999225i	$0.512535\pi$
$368$	−59.4977	−3.10153
$369$	−0.367758	−0.0191447
$370$	−1.08763	−0.0565432
$371$	−25.0346	−1.29973
$372$	11.9459	0.619367
$373$	−23.2569	−1.20419	−0.602097	−	0.798423i	$-0.705668\pi$
$373$	−23.2569	−1.20419	−0.602097	+	0.798423i	$0.705668\pi$
$374$	−43.9466	−2.27242
$375$	−18.7570	−0.968607
$376$	−23.3053	−1.20188
$377$	8.42216	0.433763
$378$	58.9493	3.03203
$379$	29.4799	1.51428	0.757141	−	0.653252i	$-0.226596\pi$
$379$	29.4799	1.51428	0.757141	+	0.653252i	$0.226596\pi$
$380$	−38.5195	−1.97601
$381$	−5.66946	−0.290455
$382$	−25.2669	−1.29276
$383$	20.2298	1.03369	0.516847	−	0.856078i	$-0.327106\pi$
$383$	20.2298	1.03369	0.516847	+	0.856078i	$0.327106\pi$
$384$	5.21265	0.266007
$385$	−12.2704	−0.625359
$386$	−21.6489	−1.10190
$387$	0.396042	0.0201319
$388$	37.9216	1.92518
$389$	3.85993	0.195706	0.0978532	−	0.995201i	$-0.468802\pi$
$389$	3.85993	0.195706	0.0978532	+	0.995201i	$0.468802\pi$
$390$	−20.2170	−1.02373
$391$	52.0653	2.63305
$392$	−82.6694	−4.17543
$393$	−23.0634	−1.16339
$394$	0.633010	0.0318906
$395$	−11.5665	−0.581975
$396$	0.843353	0.0423801
$397$	−29.1476	−1.46287	−0.731437	−	0.681909i	$-0.761150\pi$
$397$	−29.1476	−1.46287	−0.731437	+	0.681909i	$0.761150\pi$
$398$	46.6799	2.33985
$399$	−44.5873	−2.23216
$400$	−29.1437	−1.45719
$401$	23.1497	1.15604	0.578020	−	0.816023i	$-0.303826\pi$
$401$	23.1497	1.15604	0.578020	+	0.816023i	$0.303826\pi$
$402$	34.4600	1.71871
$403$	5.01333	0.249732
$404$	41.6429	2.07181
$405$	−11.6950	−0.581130
$406$	−27.6833	−1.37390
$407$	−0.666263	−0.0330254
$408$	97.0033	4.80238
$409$	−24.6834	−1.22051	−0.610257	−	0.792203i	$-0.708934\pi$
$409$	−24.6834	−1.22051	−0.610257	+	0.792203i	$0.708934\pi$
$410$	−15.3355	−0.757366
$411$	0.590275	0.0291161
$412$	51.6498	2.54461
$413$	−44.4343	−2.18647
$414$	−1.41968	−0.0697734
$415$	3.38933	0.166375
$416$	−31.6218	−1.55039
$417$	−16.7018	−0.817890
$418$	−33.5276	−1.63989
$419$	1.76925	0.0864337	0.0432169	−	0.999066i	$-0.486239\pi$
$419$	1.76925	0.0864337	0.0432169	+	0.999066i	$0.486239\pi$
$420$	46.7685	2.28207
$421$	−28.4830	−1.38818	−0.694089	−	0.719889i	$-0.744193\pi$
$421$	−28.4830	−1.38818	−0.694089	+	0.719889i	$0.744193\pi$
$422$	69.2184	3.36950
$423$	−0.271658	−0.0132084
$424$	41.5522	2.01795
$425$	25.5031	1.23708
$426$	−70.0927	−3.39600
$427$	−3.90418	−0.188936
$428$	−88.5198	−4.27876
$429$	−12.3846	−0.597933
$430$	16.5149	0.796421
$431$	22.1718	1.06798	0.533990	−	0.845491i	$-0.320692\pi$
$431$	22.1718	1.06798	0.533990	+	0.845491i	$0.320692\pi$
$432$	−47.7979	−2.29968
$433$	−4.00108	−0.192280	−0.0961399	−	0.995368i	$-0.530650\pi$
$433$	−4.00108	−0.192280	−0.0961399	+	0.995368i	$0.530650\pi$
$434$	−16.4786	−0.790999
$435$	5.64919	0.270858
$436$	46.4905	2.22649
$437$	39.7215	1.90014
$438$	−69.2398	−3.30840
$439$	−23.8824	−1.13984	−0.569922	−	0.821699i	$-0.693027\pi$
$439$	−23.8824	−1.13984	−0.569922	+	0.821699i	$0.693027\pi$
$440$	20.3663	0.970927
$441$	−0.963632	−0.0458872
$442$	70.2952	3.34360
$443$	−10.0312	−0.476598	−0.238299	−	0.971192i	$-0.576590\pi$
$443$	−10.0312	−0.476598	−0.238299	+	0.971192i	$0.576590\pi$
$444$	2.53945	0.120517
$445$	5.96469	0.282754
$446$	42.5948	2.01692
$447$	−20.4218	−0.965917
$448$	25.7274	1.21551
$449$	11.6319	0.548945	0.274472	−	0.961595i	$-0.411497\pi$
$449$	11.6319	0.548945	0.274472	+	0.961595i	$0.411497\pi$
$450$	−0.695399	−0.0327814
$451$	−9.39424	−0.442358
$452$	−73.9034	−3.47612
$453$	9.07046	0.426167
$454$	12.8910	0.605007
$455$	19.6273	0.920141
$456$	74.0056	3.46563
$457$	27.0519	1.26544	0.632718	−	0.774383i	$-0.281939\pi$
$457$	27.0519	1.26544	0.632718	+	0.774383i	$0.281939\pi$
$458$	13.6298	0.636881
$459$	41.8270	1.95232
$460$	−41.6647	−1.94262
$461$	39.0535	1.81890	0.909451	−	0.415810i	$-0.136502\pi$
$461$	39.0535	1.81890	0.909451	+	0.415810i	$0.136502\pi$
$462$	40.7075	1.89389
$463$	−31.8292	−1.47923	−0.739615	−	0.673031i	$-0.764992\pi$
$463$	−31.8292	−1.47923	−0.739615	+	0.673031i	$0.764992\pi$
$464$	22.4465	1.04205
$465$	3.36271	0.155942
$466$	−27.3923	−1.26892
$467$	−6.41817	−0.296998	−0.148499	−	0.988913i	$-0.547444\pi$
$467$	−6.41817	−0.296998	−0.148499	+	0.988913i	$0.547444\pi$
$468$	−1.34899	−0.0623572
$469$	−33.4549	−1.54480
$470$	−11.3281	−0.522527
$471$	38.8055	1.78806
$472$	73.7516	3.39469
$473$	10.1168	0.465169
$474$	38.3723	1.76250
$475$	19.4568	0.892737
$476$	−162.616	−7.45347
$477$	0.484352	0.0221769
$478$	−46.9143	−2.14581
$479$	−4.65251	−0.212579	−0.106289	−	0.994335i	$-0.533897\pi$
$479$	−4.65251	−0.212579	−0.106289	+	0.994335i	$0.533897\pi$
$480$	−21.2104	−0.968119
$481$	1.06573	0.0485930
$482$	47.3282	2.15574
$483$	−48.2278	−2.19444
$484$	−30.7282	−1.39673
$485$	10.6747	0.484714
$486$	−2.25019	−0.102071
$487$	−18.1010	−0.820237	−0.410118	−	0.912032i	$-0.634513\pi$
$487$	−18.1010	−0.820237	−0.410118	+	0.912032i	$0.634513\pi$
$488$	6.48012	0.293341
$489$	−7.91775	−0.358053
$490$	−40.1834	−1.81530
$491$	41.7135	1.88250	0.941251	−	0.337708i	$-0.109651\pi$
$491$	41.7135	1.88250	0.941251	+	0.337708i	$0.109651\pi$
$492$	35.8060	1.61426
$493$	−19.6424	−0.884651
$494$	53.6295	2.41290
$495$	0.237399	0.0106703
$496$	13.3614	0.599943
$497$	68.0482	3.05238
$498$	−11.2442	−0.503865
$499$	40.2130	1.80018	0.900091	−	0.435701i	$-0.143500\pi$
$499$	40.2130	1.80018	0.900091	+	0.435701i	$0.143500\pi$
$500$	−52.1906	−2.33403
$501$	−27.1040	−1.21092
$502$	54.2299	2.42040
$503$	−19.6272	−0.875135	−0.437568	−	0.899185i	$-0.644160\pi$
$503$	−19.6272	−0.875135	−0.437568	+	0.899185i	$0.644160\pi$
$504$	2.56786	0.114382
$505$	11.7223	0.521633
$506$	−36.2652	−1.61218
$507$	−2.39180	−0.106223
$508$	−15.7751	−0.699905
$509$	−9.80866	−0.434761	−0.217381	−	0.976087i	$-0.569751\pi$
$509$	−9.80866	−0.434761	−0.217381	+	0.976087i	$0.569751\pi$
$510$	47.1508	2.08787
$511$	67.2201	2.97364
$512$	45.5382	2.01253
$513$	31.9106	1.40889
$514$	−43.8376	−1.93360
$515$	14.5392	0.640672
$516$	−38.5598	−1.69750
$517$	−6.93940	−0.305194
$518$	−3.50300	−0.153913
$519$	−27.5704	−1.21021
$520$	−32.5772	−1.42860
$521$	−5.47109	−0.239693	−0.119846	−	0.992792i	$-0.538240\pi$
$521$	−5.47109	−0.239693	−0.119846	+	0.992792i	$0.538240\pi$
$522$	0.535596	0.0234424
$523$	−9.92553	−0.434013	−0.217007	−	0.976170i	$-0.569629\pi$
$523$	−9.92553	−0.434013	−0.217007	+	0.976170i	$0.569629\pi$
$524$	−64.1729	−2.80341
$525$	−23.6234	−1.03101
$526$	−33.1920	−1.44724
$527$	−11.6923	−0.509323
$528$	−33.0069	−1.43644
$529$	19.9648	0.868034
$530$	20.1974	0.877321
$531$	0.859682	0.0373070
$532$	−124.062	−5.37878
$533$	15.0267	0.650877
$534$	−19.7881	−0.856314
$535$	−24.9178	−1.07729
$536$	55.5280	2.39845
$537$	−44.0403	−1.90048
$538$	−58.2926	−2.51317
$539$	−24.6156	−1.06027
$540$	−33.4716	−1.44039
$541$	−10.6443	−0.457633	−0.228817	−	0.973470i	$-0.573486\pi$
$541$	−10.6443	−0.457633	−0.228817	+	0.973470i	$0.573486\pi$
$542$	1.27578	0.0547996
$543$	−23.8195	−1.02219
$544$	73.7494	3.16198
$545$	13.0868	0.560578
$546$	−65.1142	−2.78663
$547$	−28.8838	−1.23498	−0.617490	−	0.786579i	$-0.711850\pi$
$547$	−28.8838	−1.23498	−0.617490	+	0.786579i	$0.711850\pi$
$548$	1.64242	0.0701606
$549$	0.0755352	0.00322376
$550$	−17.7637	−0.757448
$551$	−14.9856	−0.638407
$552$	80.0481	3.40707
$553$	−37.2530	−1.58416
$554$	67.8374	2.88213
$555$	0.714841	0.0303433
$556$	−46.4720	−1.97085
$557$	−2.26221	−0.0958531	−0.0479265	−	0.998851i	$-0.515261\pi$
$557$	−2.26221	−0.0958531	−0.0479265	+	0.998851i	$0.515261\pi$
$558$	0.318816	0.0134966
$559$	−16.1823	−0.684440
$560$	52.3100	2.21050
$561$	28.8837	1.21947
$562$	13.6377	0.575270
$563$	−38.8088	−1.63559	−0.817797	−	0.575507i	$-0.804805\pi$
$563$	−38.8088	−1.63559	−0.817797	+	0.575507i	$0.804805\pi$
$564$	26.4494	1.11372
$565$	−20.8034	−0.875206
$566$	−61.4719	−2.58386
$567$	−37.6669	−1.58186
$568$	−112.946	−4.73910
$569$	−25.3501	−1.06273	−0.531366	−	0.847142i	$-0.678321\pi$
$569$	−25.3501	−1.06273	−0.531366	+	0.847142i	$0.678321\pi$
$570$	35.9722	1.50671
$571$	31.4274	1.31520	0.657599	−	0.753368i	$-0.271572\pi$
$571$	31.4274	1.31520	0.657599	+	0.753368i	$0.271572\pi$
$572$	−34.4595	−1.44083
$573$	16.6065	0.693748
$574$	−49.3920	−2.06158
$575$	21.0454	0.877653
$576$	−0.497756	−0.0207398
$577$	33.9291	1.41249	0.706244	−	0.707969i	$-0.250388\pi$
$577$	33.9291	1.41249	0.706244	+	0.707969i	$0.250388\pi$
$578$	−119.771	−4.98182
$579$	14.2287	0.591324
$580$	15.7187	0.652681
$581$	10.9162	0.452881
$582$	−35.4137	−1.46795
$583$	12.3726	0.512420
$584$	−111.571	−4.61685
$585$	−0.379734	−0.0157001
$586$	−10.2651	−0.424046
$587$	−34.8576	−1.43873	−0.719363	−	0.694634i	$-0.755566\pi$
$587$	−34.8576	−1.43873	−0.719363	+	0.694634i	$0.755566\pi$
$588$	93.8219	3.86915
$589$	−8.92024	−0.367552
$590$	35.8487	1.47587
$591$	−0.416043	−0.0171137
$592$	2.84034	0.116737
$593$	−20.7675	−0.852820	−0.426410	−	0.904530i	$-0.640222\pi$
$593$	−20.7675	−0.852820	−0.426410	+	0.904530i	$0.640222\pi$
$594$	−29.1339	−1.19538
$595$	−45.7754	−1.87661
$596$	−56.8228	−2.32755
$597$	−30.6802	−1.25566
$598$	58.0083	2.37214
$599$	13.6107	0.556119	0.278059	−	0.960564i	$-0.410309\pi$
$599$	13.6107	0.556119	0.278059	+	0.960564i	$0.410309\pi$
$600$	39.2099	1.60074
$601$	−14.2258	−0.580281	−0.290141	−	0.956984i	$-0.593702\pi$
$601$	−14.2258	−0.580281	−0.290141	+	0.956984i	$0.593702\pi$
$602$	53.1907	2.16789
$603$	0.647260	0.0263585
$604$	25.2382	1.02693
$605$	−8.64981	−0.351665
$606$	−38.8890	−1.57976
$607$	−2.49600	−0.101310	−0.0506548	−	0.998716i	$-0.516131\pi$
$607$	−2.49600	−0.101310	−0.0506548	+	0.998716i	$0.516131\pi$
$608$	56.2648	2.28184
$609$	18.1947	0.737287
$610$	3.14981	0.127532
$611$	11.1000	0.449057
$612$	3.14617	0.127176
$613$	47.9553	1.93690	0.968448	−	0.249218i	$-0.0801734\pi$
$613$	47.9553	1.93690	0.968448	+	0.249218i	$0.0801734\pi$
$614$	−15.6676	−0.632293
$615$	10.0792	0.406432
$616$	65.5951	2.64290
$617$	−6.39407	−0.257415	−0.128708	−	0.991683i	$-0.541083\pi$
$617$	−6.39407	−0.257415	−0.128708	+	0.991683i	$0.541083\pi$
$618$	−48.2341	−1.94026
$619$	−3.10175	−0.124670	−0.0623350	−	0.998055i	$-0.519855\pi$
$619$	−3.10175	−0.124670	−0.0623350	+	0.998055i	$0.519855\pi$
$620$	9.35661	0.375770
$621$	34.5161	1.38508
$622$	−50.9434	−2.04265
$623$	19.2109	0.769667
$624$	52.7966	2.11355
$625$	1.36217	0.0544869
$626$	1.19397	0.0477207
$627$	22.0359	0.880029
$628$	107.975	4.30866
$629$	−2.48553	−0.0991044
$630$	1.24817	0.0497283
$631$	46.2026	1.83929	0.919647	−	0.392745i	$-0.128474\pi$
$631$	46.2026	1.83929	0.919647	+	0.392745i	$0.128474\pi$
$632$	61.8322	2.45955
$633$	−45.4935	−1.80820
$634$	−14.9180	−0.592468
$635$	−4.44059	−0.176219
$636$	−47.1579	−1.86993
$637$	39.3742	1.56006
$638$	13.6816	0.541660
$639$	−1.31655	−0.0520818
$640$	4.08280	0.161387
$641$	8.15721	0.322190	0.161095	−	0.986939i	$-0.448497\pi$
$641$	8.15721	0.322190	0.161095	+	0.986939i	$0.448497\pi$
$642$	82.6658	3.26256
$643$	6.55259	0.258409	0.129205	−	0.991618i	$-0.458758\pi$
$643$	6.55259	0.258409	0.129205	+	0.991618i	$0.458758\pi$
$644$	−134.192	−5.28790
$645$	−10.8544	−0.427390
$646$	−125.076	−4.92107
$647$	15.3816	0.604714	0.302357	−	0.953195i	$-0.402227\pi$
$647$	15.3816	0.604714	0.302357	+	0.953195i	$0.402227\pi$
$648$	62.5191	2.45598
$649$	21.9603	0.862016
$650$	28.4141	1.11449
$651$	10.8305	0.424481
$652$	−22.0308	−0.862793
$653$	−16.9114	−0.661795	−0.330898	−	0.943667i	$-0.607351\pi$
$653$	−16.9114	−0.661795	−0.330898	+	0.943667i	$0.607351\pi$
$654$	−43.4160	−1.69770
$655$	−18.0643	−0.705832
$656$	40.0485	1.56363
$657$	−1.30052	−0.0507383
$658$	−36.4852	−1.42234
$659$	33.8993	1.32053	0.660264	−	0.751034i	$-0.270444\pi$
$659$	33.8993	1.32053	0.660264	+	0.751034i	$0.270444\pi$
$660$	−23.1139	−0.899706
$661$	45.1392	1.75571	0.877855	−	0.478927i	$-0.158974\pi$
$661$	45.1392	1.75571	0.877855	+	0.478927i	$0.158974\pi$
$662$	20.9059	0.812530
$663$	−46.2012	−1.79431
$664$	−18.1186	−0.703139
$665$	−34.9229	−1.35425
$666$	0.0677735	0.00262617
$667$	−16.2091	−0.627621
$668$	−75.4159	−2.91793
$669$	−27.9953	−1.08236
$670$	26.9907	1.04274
$671$	1.92952	0.0744883
$672$	−68.3138	−2.63526
$673$	9.35180	0.360485	0.180243	−	0.983622i	$-0.442312\pi$
$673$	9.35180	0.360485	0.180243	+	0.983622i	$0.442312\pi$
$674$	−88.0087	−3.38997
$675$	16.9070	0.650750
$676$	−6.65508	−0.255965
$677$	−8.81165	−0.338659	−0.169330	−	0.985559i	$-0.554160\pi$
$677$	−8.81165	−0.338659	−0.169330	+	0.985559i	$0.554160\pi$
$678$	69.0160	2.65054
$679$	34.3807	1.31941
$680$	75.9775	2.91361
$681$	−8.47259	−0.324670
$682$	8.14405	0.311852
$683$	−17.7702	−0.679956	−0.339978	−	0.940433i	$-0.610420\pi$
$683$	−17.7702	−0.679956	−0.339978	+	0.940433i	$0.610420\pi$
$684$	2.40027	0.0917765
$685$	0.462331	0.0176648
$686$	−51.0581	−1.94941
$687$	−8.95816	−0.341775
$688$	−43.1287	−1.64426
$689$	−19.7907	−0.753966
$690$	38.9093	1.48125
$691$	50.5423	1.92272	0.961359	−	0.275298i	$-0.0887765\pi$
$691$	50.5423	1.92272	0.961359	+	0.275298i	$0.0887765\pi$
$692$	−76.7134	−2.91621
$693$	0.764606	0.0290450
$694$	80.7919	3.06682
$695$	−13.0816	−0.496214
$696$	−30.1994	−1.14471
$697$	−35.0457	−1.32745
$698$	50.2763	1.90299
$699$	18.0035	0.680954
$700$	−65.7311	−2.48440
$701$	−21.4984	−0.811985	−0.405992	−	0.913877i	$-0.633074\pi$
$701$	−21.4984	−0.811985	−0.405992	+	0.913877i	$0.633074\pi$
$702$	46.6014	1.75886
$703$	−1.89625	−0.0715185
$704$	−12.7150	−0.479214
$705$	7.44535	0.280408
$706$	−28.9429	−1.08928
$707$	37.7546	1.41991
$708$	−83.7011	−3.14568
$709$	−33.5617	−1.26044	−0.630218	−	0.776418i	$-0.717035\pi$
$709$	−33.5617	−1.26044	−0.630218	+	0.776418i	$0.717035\pi$
$710$	−54.8999	−2.06036
$711$	0.720744	0.0270300
$712$	−31.8860	−1.19498
$713$	−9.64857	−0.361342
$714$	151.861	5.68327
$715$	−9.70018	−0.362766
$716$	−122.540	−4.57955
$717$	30.8342	1.15153
$718$	17.5050	0.653279
$719$	2.39497	0.0893171	0.0446586	−	0.999002i	$-0.485780\pi$
$719$	2.39497	0.0893171	0.0446586	+	0.999002i	$0.485780\pi$
$720$	−1.01205	−0.0377171
$721$	46.8272	1.74393
$722$	−46.0526	−1.71390
$723$	−31.1063	−1.15685
$724$	−66.2768	−2.46316
$725$	−7.93971	−0.294873
$726$	28.6961	1.06501
$727$	4.51375	0.167406	0.0837028	−	0.996491i	$-0.473325\pi$
$727$	4.51375	0.167406	0.0837028	+	0.996491i	$0.473325\pi$
$728$	−104.923	−3.88872
$729$	27.7079	1.02622
$730$	−54.2318	−2.00721
$731$	37.7410	1.39590
$732$	−7.35432	−0.271824
$733$	−46.6349	−1.72250	−0.861249	−	0.508183i	$-0.830317\pi$
$733$	−46.6349	−1.72250	−0.861249	+	0.508183i	$0.830317\pi$
$734$	3.91944	0.144669
$735$	26.4104	0.974161
$736$	60.8588	2.24328
$737$	16.5340	0.609039
$738$	0.955600	0.0351761
$739$	14.1398	0.520139	0.260070	−	0.965590i	$-0.416254\pi$
$739$	14.1398	0.520139	0.260070	+	0.965590i	$0.416254\pi$
$740$	1.98902	0.0731177
$741$	−35.2477	−1.29486
$742$	65.0512	2.38810
$743$	−32.9191	−1.20768	−0.603842	−	0.797104i	$-0.706364\pi$
$743$	−32.9191	−1.20768	−0.603842	+	0.797104i	$0.706364\pi$
$744$	−17.9764	−0.659045
$745$	−15.9953	−0.586022
$746$	60.4318	2.21256
$747$	−0.211199	−0.00772737
$748$	80.3677	2.93853
$749$	−80.2544	−2.93243
$750$	48.7391	1.77970
$751$	24.8283	0.905998	0.452999	−	0.891511i	$-0.350354\pi$
$751$	24.8283	0.905998	0.452999	+	0.891511i	$0.350354\pi$
$752$	29.5833	1.07879
$753$	−35.6424	−1.29888
$754$	−21.8846	−0.796988
$755$	7.10441	0.258556
$756$	−107.804	−3.92080
$757$	47.2740	1.71820	0.859102	−	0.511804i	$-0.171023\pi$
$757$	47.2740	1.71820	0.859102	+	0.511804i	$0.171023\pi$
$758$	−76.6021	−2.78231
$759$	23.8351	0.865160
$760$	57.9647	2.10260
$761$	46.1724	1.67375	0.836874	−	0.547396i	$-0.184381\pi$
$761$	46.1724	1.67375	0.836874	+	0.547396i	$0.184381\pi$
$762$	14.7318	0.533677
$763$	42.1496	1.52592
$764$	46.2070	1.67171
$765$	0.885629	0.0320200
$766$	−52.5661	−1.89929
$767$	−35.1268	−1.26835
$768$	−33.9419	−1.22477
$769$	5.08663	0.183429	0.0917144	−	0.995785i	$-0.470765\pi$
$769$	5.08663	0.183429	0.0917144	+	0.995785i	$0.470765\pi$
$770$	31.8841	1.14902
$771$	28.8121	1.03764
$772$	39.5907	1.42490
$773$	16.6436	0.598628	0.299314	−	0.954155i	$-0.403242\pi$
$773$	16.6436	0.598628	0.299314	+	0.954155i	$0.403242\pi$
$774$	−1.02909	−0.0369900
$775$	−4.72615	−0.169768
$776$	−57.0648	−2.04851
$777$	2.30233	0.0825957
$778$	−10.0298	−0.359587
$779$	−26.7370	−0.957952
$780$	36.9720	1.32381
$781$	−33.6307	−1.20340
$782$	−135.289	−4.83792
$783$	−13.0217	−0.465359
$784$	104.939	3.74781
$785$	30.3943	1.08482
$786$	59.9290	2.13760
$787$	4.69056	0.167200	0.0836001	−	0.996499i	$-0.473358\pi$
$787$	4.69056	0.167200	0.0836001	+	0.996499i	$0.473358\pi$
$788$	−1.15762	−0.0412386
$789$	21.8153	0.776645
$790$	30.0550	1.06931
$791$	−67.0029	−2.38235
$792$	−1.26909	−0.0450950
$793$	−3.08638	−0.109601
$794$	75.7385	2.68786
$795$	−13.2747	−0.470805
$796$	−85.3663	−3.02573
$797$	−19.4786	−0.689966	−0.344983	−	0.938609i	$-0.612115\pi$
$797$	−19.4786	−0.689966	−0.344983	+	0.938609i	$0.612115\pi$
$798$	115.858	4.10132
$799$	−25.8878	−0.915843
$800$	29.8104	1.05396
$801$	−0.371678	−0.0131326
$802$	−60.1533	−2.12409
$803$	−33.2214	−1.17236
$804$	−63.0191	−2.22251
$805$	−37.7743	−1.33137
$806$	−13.0269	−0.458853
$807$	38.3125	1.34867
$808$	−62.6647	−2.20454
$809$	−16.4743	−0.579206	−0.289603	−	0.957147i	$-0.593523\pi$
$809$	−16.4743	−0.579206	−0.289603	+	0.957147i	$0.593523\pi$
$810$	30.3889	1.06776
$811$	−5.48400	−0.192569	−0.0962846	−	0.995354i	$-0.530696\pi$
$811$	−5.48400	−0.192569	−0.0962846	+	0.995354i	$0.530696\pi$
$812$	50.6260	1.77663
$813$	−0.838503	−0.0294076
$814$	1.73125	0.0606803
$815$	−6.20155	−0.217231
$816$	−123.134	−4.31055
$817$	28.7933	1.00735
$818$	64.1385	2.24255
$819$	−1.22303	−0.0427363
$820$	28.0449	0.979371
$821$	−43.3867	−1.51421	−0.757104	−	0.653295i	$-0.773386\pi$
$821$	−43.3867	−1.51421	−0.757104	+	0.653295i	$0.773386\pi$
$822$	−1.53380	−0.0534974
$823$	23.8801	0.832408	0.416204	−	0.909271i	$-0.363360\pi$
$823$	23.8801	0.832408	0.416204	+	0.909271i	$0.363360\pi$
$824$	−77.7233	−2.70762
$825$	11.6751	0.406476
$826$	115.460	4.01738
$827$	23.8707	0.830064	0.415032	−	0.909807i	$-0.363770\pi$
$827$	23.8707	0.830064	0.415032	+	0.909807i	$0.363770\pi$
$828$	2.59625	0.0902259
$829$	−42.7153	−1.48356	−0.741782	−	0.670641i	$-0.766019\pi$
$829$	−42.7153	−1.48356	−0.741782	+	0.670641i	$0.766019\pi$
$830$	−8.80699	−0.305695
$831$	−44.5858	−1.54667
$832$	20.3384	0.705107
$833$	−91.8298	−3.18171
$834$	43.3988	1.50278
$835$	−21.2292	−0.734665
$836$	61.3140	2.12059
$837$	−7.75126	−0.267923
$838$	−4.59732	−0.158812
$839$	−3.72186	−0.128493	−0.0642465	−	0.997934i	$-0.520464\pi$
$839$	−3.72186	−0.128493	−0.0642465	+	0.997934i	$0.520464\pi$
$840$	−70.3777	−2.42826
$841$	−22.8848	−0.789133
$842$	74.0117	2.55061
$843$	−8.96329	−0.308712
$844$	−126.584	−4.35719
$845$	−1.87337	−0.0644458
$846$	0.705888	0.0242689
$847$	−27.8590	−0.957247
$848$	−52.7455	−1.81129
$849$	40.4021	1.38660
$850$	−66.2684	−2.27299
$851$	−2.05108	−0.0703102
$852$	128.183	4.39147
$853$	−2.80621	−0.0960828	−0.0480414	−	0.998845i	$-0.515298\pi$
$853$	−2.80621	−0.0960828	−0.0480414	+	0.998845i	$0.515298\pi$
$854$	10.1448	0.347148
$855$	0.675662	0.0231072
$856$	133.206	4.55287
$857$	−12.2710	−0.419169	−0.209584	−	0.977791i	$-0.567211\pi$
$857$	−12.2710	−0.419169	−0.209584	+	0.977791i	$0.567211\pi$
$858$	32.1807	1.09863
$859$	−31.5680	−1.07709	−0.538543	−	0.842598i	$-0.681025\pi$
$859$	−31.5680	−1.07709	−0.538543	+	0.842598i	$0.681025\pi$
$860$	−30.2018	−1.02987
$861$	32.4627	1.10632
$862$	−57.6124	−1.96229
$863$	−35.8148	−1.21915	−0.609574	−	0.792729i	$-0.708660\pi$
$863$	−35.8148	−1.21915	−0.609574	+	0.792729i	$0.708660\pi$
$864$	48.8913	1.66332
$865$	−21.5944	−0.734232
$866$	10.3966	0.353291
$867$	78.7191	2.67344
$868$	30.1354	1.02286
$869$	18.4112	0.624556
$870$	−14.6791	−0.497670
$871$	−26.4472	−0.896128
$872$	−69.9594	−2.36913
$873$	−0.665173	−0.0225127
$874$	−103.214	−3.49128
$875$	−47.3174	−1.59962
$876$	126.623	4.27819
$877$	4.19093	0.141517	0.0707587	−	0.997493i	$-0.477458\pi$
$877$	4.19093	0.141517	0.0707587	+	0.997493i	$0.477458\pi$
$878$	62.0572	2.09433
$879$	6.74667	0.227560
$880$	−25.8526	−0.871491
$881$	−44.7958	−1.50921	−0.754604	−	0.656180i	$-0.772171\pi$
$881$	−44.7958	−1.50921	−0.754604	+	0.656180i	$0.772171\pi$
$882$	2.50395	0.0843123
$883$	42.3642	1.42567	0.712834	−	0.701332i	$-0.247411\pi$
$883$	42.3642	1.42567	0.712834	+	0.701332i	$0.247411\pi$
$884$	−128.553	−4.32370
$885$	−23.5614	−0.792008
$886$	26.0656	0.875692
$887$	20.8372	0.699645	0.349822	−	0.936816i	$-0.386242\pi$
$887$	20.8372	0.699645	0.349822	+	0.936816i	$0.386242\pi$
$888$	−3.82139	−0.128237
$889$	−14.3021	−0.479677
$890$	−15.4989	−0.519526
$891$	18.6157	0.623649
$892$	−77.8957	−2.60814
$893$	−19.7502	−0.660916
$894$	53.0649	1.77476
$895$	−34.4945	−1.15302
$896$	13.1497	0.439301
$897$	−38.1257	−1.27298
$898$	−30.2250	−1.00862
$899$	3.64008	0.121403
$900$	1.27172	0.0423906
$901$	46.1565	1.53770
$902$	24.4105	0.812780
$903$	−34.9594	−1.16337
$904$	111.211	3.69881
$905$	−18.6566	−0.620165
$906$	−23.5691	−0.783031
$907$	−23.3127	−0.774085	−0.387042	−	0.922062i	$-0.626503\pi$
$907$	−23.3127	−0.774085	−0.387042	+	0.922062i	$0.626503\pi$
$908$	−23.5746	−0.782351
$909$	−0.730448	−0.0242274
$910$	−51.0005	−1.69065
$911$	−6.04248	−0.200196	−0.100098	−	0.994978i	$-0.531916\pi$
$911$	−6.04248	−0.200196	−0.100098	+	0.994978i	$0.531916\pi$
$912$	−93.9411	−3.11070
$913$	−5.39500	−0.178549
$914$	−70.2930	−2.32509
$915$	−2.07020	−0.0684388
$916$	−24.9257	−0.823568
$917$	−58.1809	−1.92130
$918$	−108.685	−3.58715
$919$	−5.47621	−0.180644	−0.0903218	−	0.995913i	$-0.528790\pi$
$919$	−5.47621	−0.180644	−0.0903218	+	0.995913i	$0.528790\pi$
$920$	62.6974	2.06707
$921$	10.2975	0.339313
$922$	−101.479	−3.34202
$923$	53.7943	1.77066
$924$	−74.4443	−2.44904
$925$	−1.00468	−0.0330336
$926$	82.7066	2.71791
$927$	−0.905978	−0.0297562
$928$	−22.9599	−0.753697
$929$	−11.5631	−0.379375	−0.189687	−	0.981845i	$-0.560747\pi$
$929$	−11.5631	−0.379375	−0.189687	+	0.981845i	$0.560747\pi$
$930$	−8.73783	−0.286525
$931$	−70.0586	−2.29608
$932$	50.0939	1.64088
$933$	33.4823	1.09616
$934$	16.6773	0.545698
$935$	22.6231	0.739854
$936$	2.02998	0.0663520
$937$	5.00611	0.163542	0.0817712	−	0.996651i	$-0.473942\pi$
$937$	5.00611	0.163542	0.0817712	+	0.996651i	$0.473942\pi$
$938$	86.9307	2.83839
$939$	−0.784732	−0.0256088
$940$	20.7164	0.675694
$941$	−2.34389	−0.0764087	−0.0382044	−	0.999270i	$-0.512164\pi$
$941$	−2.34389	−0.0764087	−0.0382044	+	0.999270i	$0.512164\pi$
$942$	−100.834	−3.28536
$943$	−28.9200	−0.941766
$944$	−93.6187	−3.04703
$945$	−30.3463	−0.987165
$946$	−26.2879	−0.854692
$947$	20.2968	0.659557	0.329778	−	0.944058i	$-0.393026\pi$
$947$	20.2968	0.659557	0.329778	+	0.944058i	$0.393026\pi$
$948$	−70.1738	−2.27914
$949$	53.1397	1.72499
$950$	−50.5574	−1.64030
$951$	9.80476	0.317941
$952$	244.706	7.93096
$953$	−28.0103	−0.907343	−0.453671	−	0.891169i	$-0.649886\pi$
$953$	−28.0103	−0.907343	−0.453671	+	0.891169i	$0.649886\pi$
$954$	−1.25856	−0.0407475
$955$	13.0070	0.420897
$956$	85.7950	2.77481
$957$	−8.99218	−0.290676
$958$	12.0893	0.390588
$959$	1.48906	0.0480842
$960$	13.6421	0.440295
$961$	−28.8332	−0.930104
$962$	−2.76924	−0.0892839
$963$	1.55270	0.0500352
$964$	−86.5519	−2.78765
$965$	11.1446	0.358756
$966$	125.318	4.03203
$967$	−37.5407	−1.20723	−0.603614	−	0.797276i	$-0.706273\pi$
$967$	−37.5407	−1.20723	−0.603614	+	0.797276i	$0.706273\pi$
$968$	46.2401	1.48621
$969$	82.2060	2.64084
$970$	−27.7377	−0.890604
$971$	30.4822	0.978219	0.489110	−	0.872222i	$-0.337322\pi$
$971$	30.4822	0.978219	0.489110	+	0.872222i	$0.337322\pi$
$972$	4.11505	0.131990
$973$	−42.1328	−1.35072
$974$	47.0346	1.50709
$975$	−18.6751	−0.598081
$976$	−8.22572	−0.263299
$977$	46.0943	1.47469	0.737344	−	0.675518i	$-0.236080\pi$
$977$	46.0943	1.47469	0.737344	+	0.675518i	$0.236080\pi$
$978$	20.5739	0.657880
$979$	−9.49438	−0.303442
$980$	73.4858	2.34742
$981$	−0.815479	−0.0260362
$982$	−108.390	−3.45887
$983$	−15.0582	−0.480283	−0.240141	−	0.970738i	$-0.577194\pi$
$983$	−15.0582	−0.480283	−0.240141	+	0.970738i	$0.577194\pi$
$984$	−53.8812	−1.71767
$985$	−0.325865	−0.0103829
$986$	51.0399	1.62544
$987$	23.9797	0.763283
$988$	−98.0754	−3.12019
$989$	31.1443	0.990330
$990$	−0.616870	−0.0196054
$991$	39.5719	1.25704	0.628521	−	0.777792i	$-0.283660\pi$
$991$	39.5719	1.25704	0.628521	+	0.777792i	$0.283660\pi$
$992$	−13.6670	−0.433928
$993$	−13.7403	−0.436035
$994$	−176.820	−5.60838
$995$	−24.0301	−0.761807
$996$	20.5629	0.651562
$997$	−4.09493	−0.129688	−0.0648439	−	0.997895i	$-0.520655\pi$
$997$	−4.09493	−0.129688	−0.0648439	+	0.997895i	$0.520655\pi$
$998$	−104.492	−3.30762
$999$	−1.64775	−0.0521326

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6037.2.a.a.1.20	✓	243

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6037.2.a.a.1.20	✓	243	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:	\( N \)	\(=\)	\( 6037 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6037.a (trivial)

\(f(q)\)	\(=\)	\(q-2.59845 q^{2} +1.70782 q^{3} +4.75194 q^{4} +1.33764 q^{5} -4.43768 q^{6} +4.30824 q^{7} -7.15077 q^{8} -0.0833526 q^{9} +O(q^{10})\)	\(q-2.59845 q^{2} +1.70782 q^{3} +4.75194 q^{4} +1.33764 q^{5} -4.43768 q^{6} +4.30824 q^{7} -7.15077 q^{8} -0.0833526 q^{9} -3.47580 q^{10} -2.12921 q^{11} +8.11545 q^{12} +3.40580 q^{13} -11.1947 q^{14} +2.28446 q^{15} +9.07704 q^{16} -7.94313 q^{17} +0.216588 q^{18} -6.05996 q^{19} +6.35640 q^{20} +7.35769 q^{21} +5.53265 q^{22} -6.55475 q^{23} -12.2122 q^{24} -3.21071 q^{25} -8.84981 q^{26} -5.26581 q^{27} +20.4725 q^{28} +2.47288 q^{29} -5.93604 q^{30} +1.47200 q^{31} -9.28468 q^{32} -3.63631 q^{33} +20.6398 q^{34} +5.76289 q^{35} -0.396086 q^{36} +0.312915 q^{37} +15.7465 q^{38} +5.81650 q^{39} -9.56519 q^{40} +4.41207 q^{41} -19.1186 q^{42} -4.75140 q^{43} -10.1179 q^{44} -0.111496 q^{45} +17.0322 q^{46} +3.25914 q^{47} +15.5019 q^{48} +11.5609 q^{49} +8.34286 q^{50} -13.5654 q^{51} +16.1842 q^{52} -5.81088 q^{53} +13.6829 q^{54} -2.84813 q^{55} -30.8072 q^{56} -10.3493 q^{57} -6.42566 q^{58} -10.3138 q^{59} +10.8556 q^{60} -0.906212 q^{61} -3.82491 q^{62} -0.359103 q^{63} +5.97169 q^{64} +4.55576 q^{65} +9.44877 q^{66} -7.76532 q^{67} -37.7453 q^{68} -11.1943 q^{69} -14.9746 q^{70} +15.7949 q^{71} +0.596035 q^{72} +15.6027 q^{73} -0.813094 q^{74} -5.48331 q^{75} -28.7965 q^{76} -9.17316 q^{77} -15.1139 q^{78} -8.64693 q^{79} +12.1418 q^{80} -8.74299 q^{81} -11.4645 q^{82} +2.53380 q^{83} +34.9633 q^{84} -10.6251 q^{85} +12.3463 q^{86} +4.22324 q^{87} +15.2255 q^{88} +4.45910 q^{89} +0.289717 q^{90} +14.6730 q^{91} -31.1478 q^{92} +2.51390 q^{93} -8.46870 q^{94} -8.10607 q^{95} -15.8566 q^{96} +7.98023 q^{97} -30.0404 q^{98} +0.177476 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9}+O(q^{10}) \) 243 * q - 47 * q^2 - 31 * q^3 + 229 * q^4 - 40 * q^5 - 18 * q^6 - 42 * q^7 - 135 * q^8 + 214 * q^9	\( 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9} - 14 q^{10} - 112 q^{11} - 54 q^{12} - 45 q^{13} - 35 q^{14} - 56 q^{15} + 213 q^{16} - 71 q^{17} - 135 q^{18} - 69 q^{19} - 107 q^{20} - 36 q^{21} - 24 q^{22} - 162 q^{23} - 57 q^{24} + 203 q^{25} - 55 q^{26} - 115 q^{27} - 87 q^{28} - 76 q^{29} - 64 q^{30} - 35 q^{31} - 302 q^{32} - 77 q^{33} - 9 q^{34} - 264 q^{35} + 173 q^{36} - 61 q^{37} - 71 q^{38} - 123 q^{39} - 16 q^{40} - 74 q^{41} - 70 q^{42} - 178 q^{43} - 209 q^{44} - 107 q^{45} - 11 q^{46} - 191 q^{47} - 65 q^{48} + 211 q^{49} - 188 q^{50} - 175 q^{51} - 95 q^{52} - 122 q^{53} - 36 q^{54} - 47 q^{55} - 69 q^{56} - 103 q^{57} - 37 q^{58} - 212 q^{59} - 79 q^{60} - 14 q^{61} - 152 q^{62} - 203 q^{63} + 217 q^{64} - 159 q^{65} + 5 q^{66} - 202 q^{67} - 176 q^{68} - 34 q^{69} + 45 q^{70} - 170 q^{71} - 347 q^{72} - 57 q^{73} - 68 q^{74} - 124 q^{75} - 74 q^{76} - 166 q^{77} - 63 q^{78} - 48 q^{79} - 222 q^{80} + 159 q^{81} - 27 q^{82} - 434 q^{83} - 52 q^{84} - 57 q^{85} - 77 q^{86} - 184 q^{87} - 15 q^{88} - 62 q^{89} - 24 q^{90} - 81 q^{91} - 330 q^{92} - 164 q^{93} + 40 q^{94} - 182 q^{95} - 66 q^{96} - 21 q^{97} - 254 q^{98} - 306 q^{99}+O(q^{100}) \) 243 * q - 47 * q^2 - 31 * q^3 + 229 * q^4 - 40 * q^5 - 18 * q^6 - 42 * q^7 - 135 * q^8 + 214 * q^9 - 14 * q^10 - 112 * q^11 - 54 * q^12 - 45 * q^13 - 35 * q^14 - 56 * q^15 + 213 * q^16 - 71 * q^17 - 135 * q^18 - 69 * q^19 - 107 * q^20 - 36 * q^21 - 24 * q^22 - 162 * q^23 - 57 * q^24 + 203 * q^25 - 55 * q^26 - 115 * q^27 - 87 * q^28 - 76 * q^29 - 64 * q^30 - 35 * q^31 - 302 * q^32 - 77 * q^33 - 9 * q^34 - 264 * q^35 + 173 * q^36 - 61 * q^37 - 71 * q^38 - 123 * q^39 - 16 * q^40 - 74 * q^41 - 70 * q^42 - 178 * q^43 - 209 * q^44 - 107 * q^45 - 11 * q^46 - 191 * q^47 - 65 * q^48 + 211 * q^49 - 188 * q^50 - 175 * q^51 - 95 * q^52 - 122 * q^53 - 36 * q^54 - 47 * q^55 - 69 * q^56 - 103 * q^57 - 37 * q^58 - 212 * q^59 - 79 * q^60 - 14 * q^61 - 152 * q^62 - 203 * q^63 + 217 * q^64 - 159 * q^65 + 5 * q^66 - 202 * q^67 - 176 * q^68 - 34 * q^69 + 45 * q^70 - 170 * q^71 - 347 * q^72 - 57 * q^73 - 68 * q^74 - 124 * q^75 - 74 * q^76 - 166 * q^77 - 63 * q^78 - 48 * q^79 - 222 * q^80 + 159 * q^81 - 27 * q^82 - 434 * q^83 - 52 * q^84 - 57 * q^85 - 77 * q^86 - 184 * q^87 - 15 * q^88 - 62 * q^89 - 24 * q^90 - 81 * q^91 - 330 * q^92 - 164 * q^93 + 40 * q^94 - 182 * q^95 - 66 * q^96 - 21 * q^97 - 254 * q^98 - 306 * q^99

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