LMFDB - Embedded newform 4017.2.a.j.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.02058 q^{2} -1.00000 q^{3} +2.08276 q^{4} +4.24376 q^{5} -2.02058 q^{6} -1.21618 q^{7} +0.167219 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.02058 q^{2} -1.00000 q^{3} +2.08276 q^{4} +4.24376 q^{5} -2.02058 q^{6} -1.21618 q^{7} +0.167219 q^{8} +1.00000 q^{9} +8.57486 q^{10} +4.05959 q^{11} -2.08276 q^{12} +1.00000 q^{13} -2.45739 q^{14} -4.24376 q^{15} -3.82764 q^{16} -3.43411 q^{17} +2.02058 q^{18} +1.65923 q^{19} +8.83871 q^{20} +1.21618 q^{21} +8.20275 q^{22} +0.620280 q^{23} -0.167219 q^{24} +13.0095 q^{25} +2.02058 q^{26} -1.00000 q^{27} -2.53300 q^{28} +7.32374 q^{29} -8.57486 q^{30} +3.81277 q^{31} -8.06850 q^{32} -4.05959 q^{33} -6.93892 q^{34} -5.16116 q^{35} +2.08276 q^{36} -10.7807 q^{37} +3.35262 q^{38} -1.00000 q^{39} +0.709635 q^{40} -1.65147 q^{41} +2.45739 q^{42} +9.74803 q^{43} +8.45515 q^{44} +4.24376 q^{45} +1.25333 q^{46} +9.90352 q^{47} +3.82764 q^{48} -5.52091 q^{49} +26.2867 q^{50} +3.43411 q^{51} +2.08276 q^{52} +13.2309 q^{53} -2.02058 q^{54} +17.2279 q^{55} -0.203368 q^{56} -1.65923 q^{57} +14.7982 q^{58} -7.24509 q^{59} -8.83871 q^{60} -5.43492 q^{61} +7.70403 q^{62} -1.21618 q^{63} -8.64780 q^{64} +4.24376 q^{65} -8.20275 q^{66} +0.936251 q^{67} -7.15243 q^{68} -0.620280 q^{69} -10.4286 q^{70} +2.07572 q^{71} +0.167219 q^{72} -4.79664 q^{73} -21.7833 q^{74} -13.0095 q^{75} +3.45578 q^{76} -4.93718 q^{77} -2.02058 q^{78} -5.55775 q^{79} -16.2435 q^{80} +1.00000 q^{81} -3.33693 q^{82} +6.01550 q^{83} +2.53300 q^{84} -14.5735 q^{85} +19.6967 q^{86} -7.32374 q^{87} +0.678840 q^{88} -3.23079 q^{89} +8.57486 q^{90} -1.21618 q^{91} +1.29189 q^{92} -3.81277 q^{93} +20.0109 q^{94} +7.04138 q^{95} +8.06850 q^{96} +17.3203 q^{97} -11.1555 q^{98} +4.05959 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9} - 6 q^{10} + 21 q^{11} - 28 q^{12} + 25 q^{13} + 10 q^{14} - 7 q^{15} + 30 q^{16} + 14 q^{17} + 6 q^{18} + 12 q^{19} + 24 q^{20} - 17 q^{21} + 3 q^{22} + 41 q^{23} - 21 q^{24} + 30 q^{25} + 6 q^{26} - 25 q^{27} + 14 q^{28} + 22 q^{29} + 6 q^{30} + 14 q^{31} + 28 q^{32} - 21 q^{33} - 11 q^{34} + 14 q^{35} + 28 q^{36} - 6 q^{37} + 16 q^{38} - 25 q^{39} - 34 q^{40} + 33 q^{41} - 10 q^{42} + 35 q^{43} + 45 q^{44} + 7 q^{45} + 3 q^{46} + 48 q^{47} - 30 q^{48} - 4 q^{49} + 7 q^{50} - 14 q^{51} + 28 q^{52} + 18 q^{53} - 6 q^{54} + 10 q^{55} + 32 q^{56} - 12 q^{57} + 33 q^{58} + 46 q^{59} - 24 q^{60} - 19 q^{61} + 5 q^{62} + 17 q^{63} + 29 q^{64} + 7 q^{65} - 3 q^{66} + 16 q^{67} + 20 q^{68} - 41 q^{69} - 43 q^{70} + 60 q^{71} + 21 q^{72} - 14 q^{73} - 50 q^{74} - 30 q^{75} + 59 q^{77} - 6 q^{78} + 7 q^{79} + 32 q^{80} + 25 q^{81} + 18 q^{82} + 23 q^{83} - 14 q^{84} - 9 q^{85} - 9 q^{86} - 22 q^{87} + 23 q^{88} + 10 q^{89} - 6 q^{90} + 17 q^{91} + 69 q^{92} - 14 q^{93} - 30 q^{94} + 81 q^{95} - 28 q^{96} - 10 q^{97} + 55 q^{98} + 21 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9 - 6 * q^10 + 21 * q^11 - 28 * q^12 + 25 * q^13 + 10 * q^14 - 7 * q^15 + 30 * q^16 + 14 * q^17 + 6 * q^18 + 12 * q^19 + 24 * q^20 - 17 * q^21 + 3 * q^22 + 41 * q^23 - 21 * q^24 + 30 * q^25 + 6 * q^26 - 25 * q^27 + 14 * q^28 + 22 * q^29 + 6 * q^30 + 14 * q^31 + 28 * q^32 - 21 * q^33 - 11 * q^34 + 14 * q^35 + 28 * q^36 - 6 * q^37 + 16 * q^38 - 25 * q^39 - 34 * q^40 + 33 * q^41 - 10 * q^42 + 35 * q^43 + 45 * q^44 + 7 * q^45 + 3 * q^46 + 48 * q^47 - 30 * q^48 - 4 * q^49 + 7 * q^50 - 14 * q^51 + 28 * q^52 + 18 * q^53 - 6 * q^54 + 10 * q^55 + 32 * q^56 - 12 * q^57 + 33 * q^58 + 46 * q^59 - 24 * q^60 - 19 * q^61 + 5 * q^62 + 17 * q^63 + 29 * q^64 + 7 * q^65 - 3 * q^66 + 16 * q^67 + 20 * q^68 - 41 * q^69 - 43 * q^70 + 60 * q^71 + 21 * q^72 - 14 * q^73 - 50 * q^74 - 30 * q^75 + 59 * q^77 - 6 * q^78 + 7 * q^79 + 32 * q^80 + 25 * q^81 + 18 * q^82 + 23 * q^83 - 14 * q^84 - 9 * q^85 - 9 * q^86 - 22 * q^87 + 23 * q^88 + 10 * q^89 - 6 * q^90 + 17 * q^91 + 69 * q^92 - 14 * q^93 - 30 * q^94 + 81 * q^95 - 28 * q^96 - 10 * q^97 + 55 * q^98 + 21 * 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 $

$2$	2.02058	1.42877	0.714384	−	0.699754i	$-0.246707\pi$
$2$	2.02058	1.42877	0.714384	+	0.699754i	$0.246707\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.08276	1.04138
$5$	4.24376	1.89787	0.948933	−	0.315479i	$-0.102165\pi$
$5$	4.24376	1.89787	0.948933	+	0.315479i	$0.102165\pi$
$6$	−2.02058	−0.824900
$7$	−1.21618	−0.459672	−0.229836	−	0.973229i	$-0.573819\pi$
$7$	−1.21618	−0.459672	−0.229836	+	0.973229i	$0.573819\pi$
$8$	0.167219	0.0591208
$9$	1.00000	0.333333
$10$	8.57486	2.71161
$11$	4.05959	1.22401	0.612007	−	0.790853i	$-0.290363\pi$
$11$	4.05959	1.22401	0.612007	+	0.790853i	$0.290363\pi$
$12$	−2.08276	−0.601240
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−2.45739	−0.656764
$15$	−4.24376	−1.09573
$16$	−3.82764	−0.956909
$17$	−3.43411	−0.832895	−0.416448	−	0.909160i	$-0.636725\pi$
$17$	−3.43411	−0.832895	−0.416448	+	0.909160i	$0.636725\pi$
$18$	2.02058	0.476256
$19$	1.65923	0.380654	0.190327	−	0.981721i	$-0.439045\pi$
$19$	1.65923	0.380654	0.190327	+	0.981721i	$0.439045\pi$
$20$	8.83871	1.97640
$21$	1.21618	0.265392
$22$	8.20275	1.74883
$23$	0.620280	0.129337	0.0646686	−	0.997907i	$-0.479401\pi$
$23$	0.620280	0.129337	0.0646686	+	0.997907i	$0.479401\pi$
$24$	−0.167219	−0.0341334
$25$	13.0095	2.60189
$26$	2.02058	0.396269
$27$	−1.00000	−0.192450
$28$	−2.53300	−0.478692
$29$	7.32374	1.35998	0.679992	−	0.733220i	$-0.261983\pi$
$29$	7.32374	1.35998	0.679992	+	0.733220i	$0.261983\pi$
$30$	−8.57486	−1.56555
$31$	3.81277	0.684795	0.342397	−	0.939555i	$-0.388761\pi$
$31$	3.81277	0.684795	0.342397	+	0.939555i	$0.388761\pi$
$32$	−8.06850	−1.42632
$33$	−4.05959	−0.706685
$34$	−6.93892	−1.19001
$35$	−5.16116	−0.872395
$36$	2.08276	0.347126
$37$	−10.7807	−1.77233	−0.886166	−	0.463368i	$-0.846641\pi$
$37$	−10.7807	−1.77233	−0.886166	+	0.463368i	$0.846641\pi$
$38$	3.35262	0.543867
$39$	−1.00000	−0.160128
$40$	0.709635	0.112203
$41$	−1.65147	−0.257916	−0.128958	−	0.991650i	$-0.541163\pi$
$41$	−1.65147	−0.257916	−0.128958	+	0.991650i	$0.541163\pi$
$42$	2.45739	0.379183
$43$	9.74803	1.48656	0.743280	−	0.668980i	$-0.233269\pi$
$43$	9.74803	1.48656	0.743280	+	0.668980i	$0.233269\pi$
$44$	8.45515	1.27466
$45$	4.24376	0.632622
$46$	1.25333	0.184793
$47$	9.90352	1.44458	0.722289	−	0.691592i	$-0.243090\pi$
$47$	9.90352	1.44458	0.722289	+	0.691592i	$0.243090\pi$
$48$	3.82764	0.552472
$49$	−5.52091	−0.788702
$50$	26.2867	3.71750
$51$	3.43411	0.480872
$52$	2.08276	0.288827
$53$	13.2309	1.81740	0.908699	−	0.417452i	$-0.137077\pi$
$53$	13.2309	1.81740	0.908699	+	0.417452i	$0.137077\pi$
$54$	−2.02058	−0.274967
$55$	17.2279	2.32301
$56$	−0.203368	−0.0271761
$57$	−1.65923	−0.219771
$58$	14.7982	1.94310
$59$	−7.24509	−0.943230	−0.471615	−	0.881805i	$-0.656329\pi$
$59$	−7.24509	−0.943230	−0.471615	+	0.881805i	$0.656329\pi$
$60$	−8.83871	−1.14107
$61$	−5.43492	−0.695870	−0.347935	−	0.937519i	$-0.613117\pi$
$61$	−5.43492	−0.695870	−0.347935	+	0.937519i	$0.613117\pi$
$62$	7.70403	0.978413
$63$	−1.21618	−0.153224
$64$	−8.64780	−1.08097
$65$	4.24376	0.526373
$66$	−8.20275	−1.00969
$67$	0.936251	0.114381	0.0571906	−	0.998363i	$-0.481786\pi$
$67$	0.936251	0.114381	0.0571906	+	0.998363i	$0.481786\pi$
$68$	−7.15243	−0.867359
$69$	−0.620280	−0.0746729
$70$	−10.4286	−1.24645
$71$	2.07572	0.246342	0.123171	−	0.992385i	$-0.460694\pi$
$71$	2.07572	0.246342	0.123171	+	0.992385i	$0.460694\pi$
$72$	0.167219	0.0197069
$73$	−4.79664	−0.561404	−0.280702	−	0.959795i	$-0.590567\pi$
$73$	−4.79664	−0.561404	−0.280702	+	0.959795i	$0.590567\pi$
$74$	−21.7833	−2.53225
$75$	−13.0095	−1.50220
$76$	3.45578	0.396405
$77$	−4.93718	−0.562644
$78$	−2.02058	−0.228786
$79$	−5.55775	−0.625295	−0.312648	−	0.949869i	$-0.601216\pi$
$79$	−5.55775	−0.625295	−0.312648	+	0.949869i	$0.601216\pi$
$80$	−16.2435	−1.81608
$81$	1.00000	0.111111
$82$	−3.33693	−0.368502
$83$	6.01550	0.660287	0.330143	−	0.943931i	$-0.392903\pi$
$83$	6.01550	0.660287	0.330143	+	0.943931i	$0.392903\pi$
$84$	2.53300	0.276373
$85$	−14.5735	−1.58072
$86$	19.6967	2.12395
$87$	−7.32374	−0.785187
$88$	0.678840	0.0723646
$89$	−3.23079	−0.342463	−0.171232	−	0.985231i	$-0.554775\pi$
$89$	−3.23079	−0.342463	−0.171232	+	0.985231i	$0.554775\pi$
$90$	8.57486	0.903870
$91$	−1.21618	−0.127490
$92$	1.29189	0.134689
$93$	−3.81277	−0.395366
$94$	20.0109	2.06397
$95$	7.04138	0.722430
$96$	8.06850	0.823487
$97$	17.3203	1.75861	0.879307	−	0.476255i	$-0.158006\pi$
$97$	17.3203	1.75861	0.879307	+	0.476255i	$0.158006\pi$
$98$	−11.1555	−1.12687
$99$	4.05959	0.408004
$100$	27.0956	2.70956
$101$	−15.8533	−1.57746	−0.788732	−	0.614738i	$-0.789262\pi$
$101$	−15.8533	−1.57746	−0.788732	+	0.614738i	$0.789262\pi$
$102$	6.93892	0.687055
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	0.167219	0.0163971
$105$	5.16116	0.503677
$106$	26.7341	2.59664
$107$	0.437524	0.0422971	0.0211485	−	0.999776i	$-0.493268\pi$
$107$	0.437524	0.0422971	0.0211485	+	0.999776i	$0.493268\pi$
$108$	−2.08276	−0.200413
$109$	14.3428	1.37379	0.686895	−	0.726757i	$-0.258973\pi$
$109$	14.3428	1.37379	0.686895	+	0.726757i	$0.258973\pi$
$110$	34.8105	3.31905
$111$	10.7807	1.02326
$112$	4.65508	0.439864
$113$	−18.7081	−1.75991	−0.879957	−	0.475054i	$-0.842429\pi$
$113$	−18.7081	−1.75991	−0.879957	+	0.475054i	$0.842429\pi$
$114$	−3.35262	−0.314002
$115$	2.63232	0.245465
$116$	15.2536	1.41626
$117$	1.00000	0.0924500
$118$	−14.6393	−1.34766
$119$	4.17649	0.382858
$120$	−0.709635	−0.0647806
$121$	5.48030	0.498209
$122$	−10.9817	−0.994238
$123$	1.65147	0.148908
$124$	7.94109	0.713131
$125$	33.9902	3.04017
$126$	−2.45739	−0.218921
$127$	10.8923	0.966531	0.483266	−	0.875474i	$-0.339451\pi$
$127$	10.8923	0.966531	0.483266	+	0.875474i	$0.339451\pi$
$128$	−1.33660	−0.118140
$129$	−9.74803	−0.858266
$130$	8.57486	0.752065
$131$	−6.92135	−0.604721	−0.302360	−	0.953194i	$-0.597775\pi$
$131$	−6.92135	−0.604721	−0.302360	+	0.953194i	$0.597775\pi$
$132$	−8.45515	−0.735926
$133$	−2.01792	−0.174976
$134$	1.89177	0.163424
$135$	−4.24376	−0.365244
$136$	−0.574248	−0.0492414
$137$	−5.63515	−0.481443	−0.240722	−	0.970594i	$-0.577384\pi$
$137$	−5.63515	−0.481443	−0.240722	+	0.970594i	$0.577384\pi$
$138$	−1.25333	−0.106690
$139$	3.33341	0.282737	0.141368	−	0.989957i	$-0.454850\pi$
$139$	3.33341	0.282737	0.141368	+	0.989957i	$0.454850\pi$
$140$	−10.7494	−0.908494
$141$	−9.90352	−0.834027
$142$	4.19416	0.351966
$143$	4.05959	0.339480
$144$	−3.82764	−0.318970
$145$	31.0801	2.58107
$146$	−9.69201	−0.802116
$147$	5.52091	0.455357
$148$	−22.4535	−1.84567
$149$	−7.27603	−0.596076	−0.298038	−	0.954554i	$-0.596332\pi$
$149$	−7.27603	−0.596076	−0.298038	+	0.954554i	$0.596332\pi$
$150$	−26.2867	−2.14630
$151$	−11.2710	−0.917218	−0.458609	−	0.888638i	$-0.651652\pi$
$151$	−11.2710	−0.917218	−0.458609	+	0.888638i	$0.651652\pi$
$152$	0.277455	0.0225046
$153$	−3.43411	−0.277632
$154$	−9.97599	−0.803889
$155$	16.1805	1.29965
$156$	−2.08276	−0.166754
$157$	−2.36191	−0.188501	−0.0942504	−	0.995549i	$-0.530045\pi$
$157$	−2.36191	−0.188501	−0.0942504	+	0.995549i	$0.530045\pi$
$158$	−11.2299	−0.893402
$159$	−13.2309	−1.04928
$160$	−34.2407	−2.70697
$161$	−0.754370	−0.0594527
$162$	2.02058	0.158752
$163$	−2.23181	−0.174809	−0.0874045	−	0.996173i	$-0.527857\pi$
$163$	−2.23181	−0.174809	−0.0874045	+	0.996173i	$0.527857\pi$
$164$	−3.43961	−0.268588
$165$	−17.2279	−1.34119
$166$	12.1548	0.943397
$167$	−12.3389	−0.954812	−0.477406	−	0.878683i	$-0.658423\pi$
$167$	−12.3389	−0.954812	−0.477406	+	0.878683i	$0.658423\pi$
$168$	0.203368	0.0156902
$169$	1.00000	0.0769231
$170$	−29.4471	−2.25849
$171$	1.65923	0.126885
$172$	20.3028	1.54807
$173$	−22.2508	−1.69170	−0.845850	−	0.533421i	$-0.820906\pi$
$173$	−22.2508	−1.69170	−0.845850	+	0.533421i	$0.820906\pi$
$174$	−14.7982	−1.12185
$175$	−15.8218	−1.19602
$176$	−15.5386	−1.17127
$177$	7.24509	0.544574
$178$	−6.52809	−0.489301
$179$	−6.44350	−0.481610	−0.240805	−	0.970574i	$-0.577411\pi$
$179$	−6.44350	−0.481610	−0.240805	+	0.970574i	$0.577411\pi$
$180$	8.83871	0.658799
$181$	11.4170	0.848617	0.424308	−	0.905518i	$-0.360517\pi$
$181$	11.4170	0.848617	0.424308	+	0.905518i	$0.360517\pi$
$182$	−2.45739	−0.182154
$183$	5.43492	0.401761
$184$	0.103722	0.00764652
$185$	−45.7506	−3.36365
$186$	−7.70403	−0.564887
$187$	−13.9411	−1.01947
$188$	20.6266	1.50435
$189$	1.21618	0.0884639
$190$	14.2277	1.03219
$191$	15.7818	1.14193	0.570967	−	0.820973i	$-0.306569\pi$
$191$	15.7818	1.14193	0.570967	+	0.820973i	$0.306569\pi$
$192$	8.64780	0.624101
$193$	7.09373	0.510618	0.255309	−	0.966860i	$-0.417823\pi$
$193$	7.09373	0.510618	0.255309	+	0.966860i	$0.417823\pi$
$194$	34.9972	2.51265
$195$	−4.24376	−0.303902
$196$	−11.4987	−0.821337
$197$	16.5534	1.17938	0.589690	−	0.807630i	$-0.299250\pi$
$197$	16.5534	1.17938	0.589690	+	0.807630i	$0.299250\pi$
$198$	8.20275	0.582944
$199$	15.6146	1.10689	0.553444	−	0.832886i	$-0.313313\pi$
$199$	15.6146	1.10689	0.553444	+	0.832886i	$0.313313\pi$
$200$	2.17543	0.153826
$201$	−0.936251	−0.0660380
$202$	−32.0329	−2.25383
$203$	−8.90696	−0.625146
$204$	7.15243	0.500770
$205$	−7.00842	−0.489489
$206$	−2.02058	−0.140781
$207$	0.620280	0.0431124
$208$	−3.82764	−0.265399
$209$	6.73581	0.465926
$210$	10.4286	0.719638
$211$	19.5473	1.34569	0.672847	−	0.739781i	$-0.265071\pi$
$211$	19.5473	1.34569	0.672847	+	0.739781i	$0.265071\pi$
$212$	27.5567	1.89260
$213$	−2.07572	−0.142226
$214$	0.884054	0.0604327
$215$	41.3682	2.82129
$216$	−0.167219	−0.0113778
$217$	−4.63701	−0.314781
$218$	28.9808	1.96283
$219$	4.79664	0.324127
$220$	35.8816	2.41914
$221$	−3.43411	−0.231004
$222$	21.7833	1.46200
$223$	−6.75149	−0.452113	−0.226057	−	0.974114i	$-0.572583\pi$
$223$	−6.75149	−0.452113	−0.226057	+	0.974114i	$0.572583\pi$
$224$	9.81272	0.655640
$225$	13.0095	0.867297
$226$	−37.8014	−2.51451
$227$	29.9752	1.98952	0.994762	−	0.102218i	$-0.0325941\pi$
$227$	29.9752	1.98952	0.994762	+	0.102218i	$0.0325941\pi$
$228$	−3.45578	−0.228865
$229$	−25.4484	−1.68168	−0.840840	−	0.541284i	$-0.817938\pi$
$229$	−25.4484	−1.68168	−0.840840	+	0.541284i	$0.817938\pi$
$230$	5.31881	0.350712
$231$	4.93718	0.324843
$232$	1.22467	0.0804033
$233$	−9.37422	−0.614125	−0.307063	−	0.951689i	$-0.599346\pi$
$233$	−9.37422	−0.614125	−0.307063	+	0.951689i	$0.599346\pi$
$234$	2.02058	0.132090
$235$	42.0281	2.74161
$236$	−15.0898	−0.982260
$237$	5.55775	0.361014
$238$	8.43895	0.547016
$239$	−12.4151	−0.803063	−0.401532	−	0.915845i	$-0.631522\pi$
$239$	−12.4151	−0.803063	−0.401532	+	0.915845i	$0.631522\pi$
$240$	16.2435	1.04852
$241$	1.93177	0.124436	0.0622181	−	0.998063i	$-0.480183\pi$
$241$	1.93177	0.124436	0.0622181	+	0.998063i	$0.480183\pi$
$242$	11.0734	0.711825
$243$	−1.00000	−0.0641500
$244$	−11.3196	−0.724665
$245$	−23.4294	−1.49685
$246$	3.33693	0.212755
$247$	1.65923	0.105574
$248$	0.637567	0.0404856
$249$	−6.01550	−0.381217
$250$	68.6800	4.34370
$251$	−1.98886	−0.125536	−0.0627679	−	0.998028i	$-0.519993\pi$
$251$	−1.98886	−0.125536	−0.0627679	+	0.998028i	$0.519993\pi$
$252$	−2.53300	−0.159564
$253$	2.51808	0.158311
$254$	22.0087	1.38095
$255$	14.5735	0.912631
$256$	14.5949	0.912179
$257$	−18.0229	−1.12423	−0.562117	−	0.827057i	$-0.690013\pi$
$257$	−18.0229	−1.12423	−0.562117	+	0.827057i	$0.690013\pi$
$258$	−19.6967	−1.22626
$259$	13.1112	0.814691
$260$	8.83871	0.548154
$261$	7.32374	0.453328
$262$	−13.9852	−0.864006
$263$	−19.2621	−1.18775	−0.593876	−	0.804556i	$-0.702403\pi$
$263$	−19.2621	−1.18775	−0.593876	+	0.804556i	$0.702403\pi$
$264$	−0.678840	−0.0417797
$265$	56.1485	3.44918
$266$	−4.07738	−0.250000
$267$	3.23079	0.197721
$268$	1.94998	0.119114
$269$	−24.8531	−1.51532	−0.757662	−	0.652648i	$-0.773658\pi$
$269$	−24.8531	−1.51532	−0.757662	+	0.652648i	$0.773658\pi$
$270$	−8.57486	−0.521849
$271$	−11.1960	−0.680109	−0.340054	−	0.940406i	$-0.610445\pi$
$271$	−11.1960	−0.680109	−0.340054	+	0.940406i	$0.610445\pi$
$272$	13.1445	0.797005
$273$	1.21618	0.0736064
$274$	−11.3863	−0.687871
$275$	52.8131	3.18475
$276$	−1.29189	−0.0777628
$277$	−23.7805	−1.42883	−0.714417	−	0.699720i	$-0.753308\pi$
$277$	−23.7805	−1.42883	−0.714417	+	0.699720i	$0.753308\pi$
$278$	6.73544	0.403965
$279$	3.81277	0.228265
$280$	−0.863042	−0.0515767
$281$	−9.04387	−0.539512	−0.269756	−	0.962929i	$-0.586943\pi$
$281$	−9.04387	−0.539512	−0.269756	+	0.962929i	$0.586943\pi$
$282$	−20.0109	−1.19163
$283$	19.8620	1.18068	0.590338	−	0.807156i	$-0.298995\pi$
$283$	19.8620	1.18068	0.590338	+	0.807156i	$0.298995\pi$
$284$	4.32322	0.256536
$285$	−7.04138	−0.417095
$286$	8.20275	0.485039
$287$	2.00848	0.118557
$288$	−8.06850	−0.475441
$289$	−5.20686	−0.306286
$290$	62.8000	3.68774
$291$	−17.3203	−1.01534
$292$	−9.99024	−0.584634
$293$	17.2871	1.00992	0.504962	−	0.863141i	$-0.331506\pi$
$293$	17.2871	1.00992	0.504962	+	0.863141i	$0.331506\pi$
$294$	11.1555	0.650600
$295$	−30.7464	−1.79012
$296$	−1.80273	−0.104782
$297$	−4.05959	−0.235562
$298$	−14.7018	−0.851654
$299$	0.620280	0.0358717
$300$	−27.0956	−1.56436
$301$	−11.8553	−0.683330
$302$	−22.7739	−1.31049
$303$	15.8533	0.910749
$304$	−6.35094	−0.364251
$305$	−23.0645	−1.32067
$306$	−6.93892	−0.396671
$307$	−8.49426	−0.484793	−0.242397	−	0.970177i	$-0.577934\pi$
$307$	−8.49426	−0.484793	−0.242397	+	0.970177i	$0.577934\pi$
$308$	−10.2830	−0.585926
$309$	1.00000	0.0568880
$310$	32.6940	1.85690
$311$	−8.87599	−0.503311	−0.251655	−	0.967817i	$-0.580975\pi$
$311$	−8.87599	−0.503311	−0.251655	+	0.967817i	$0.580975\pi$
$312$	−0.167219	−0.00946690
$313$	18.2376	1.03085	0.515424	−	0.856935i	$-0.327634\pi$
$313$	18.2376	1.03085	0.515424	+	0.856935i	$0.327634\pi$
$314$	−4.77243	−0.269324
$315$	−5.16116	−0.290798
$316$	−11.5754	−0.651169
$317$	−5.44512	−0.305828	−0.152914	−	0.988239i	$-0.548866\pi$
$317$	−5.44512	−0.305828	−0.152914	+	0.988239i	$0.548866\pi$
$318$	−26.7341	−1.49917
$319$	29.7314	1.66464
$320$	−36.6991	−2.05154
$321$	−0.437524	−0.0244202
$322$	−1.52427	−0.0849441
$323$	−5.69800	−0.317045
$324$	2.08276	0.115709
$325$	13.0095	0.721635
$326$	−4.50956	−0.249761
$327$	−14.3428	−0.793158
$328$	−0.276156	−0.0152482
$329$	−12.0444	−0.664031
$330$	−34.8105	−1.91625
$331$	−3.42791	−0.188415	−0.0942074	−	0.995553i	$-0.530032\pi$
$331$	−3.42791	−0.188415	−0.0942074	+	0.995553i	$0.530032\pi$
$332$	12.5288	0.687609
$333$	−10.7807	−0.590777
$334$	−24.9318	−1.36421
$335$	3.97322	0.217080
$336$	−4.65508	−0.253956
$337$	28.9670	1.57793	0.788966	−	0.614436i	$-0.210617\pi$
$337$	28.9670	1.57793	0.788966	+	0.614436i	$0.210617\pi$
$338$	2.02058	0.109905
$339$	18.7081	1.01609
$340$	−30.3532	−1.64613
$341$	15.4783	0.838198
$342$	3.35262	0.181289
$343$	15.2276	0.822216
$344$	1.63005	0.0878866
$345$	−2.63232	−0.141719
$346$	−44.9597	−2.41705
$347$	−1.48453	−0.0796939	−0.0398469	−	0.999206i	$-0.512687\pi$
$347$	−1.48453	−0.0796939	−0.0398469	+	0.999206i	$0.512687\pi$
$348$	−15.2536	−0.817677
$349$	−22.4737	−1.20299	−0.601494	−	0.798877i	$-0.705428\pi$
$349$	−22.4737	−1.20299	−0.601494	+	0.798877i	$0.705428\pi$
$350$	−31.9693	−1.70883
$351$	−1.00000	−0.0533761
$352$	−32.7548	−1.74584
$353$	10.3080	0.548637	0.274319	−	0.961639i	$-0.411548\pi$
$353$	10.3080	0.548637	0.274319	+	0.961639i	$0.411548\pi$
$354$	14.6393	0.778070
$355$	8.80884	0.467525
$356$	−6.72896	−0.356634
$357$	−4.17649	−0.221043
$358$	−13.0196	−0.688109
$359$	11.4076	0.602070	0.301035	−	0.953613i	$-0.402668\pi$
$359$	11.4076	0.602070	0.301035	+	0.953613i	$0.402668\pi$
$360$	0.709635	0.0374011
$361$	−16.2469	−0.855102
$362$	23.0689	1.21248
$363$	−5.48030	−0.287641
$364$	−2.53300	−0.132765
$365$	−20.3558	−1.06547
$366$	10.9817	0.574023
$367$	−6.08507	−0.317638	−0.158819	−	0.987308i	$-0.550769\pi$
$367$	−6.08507	−0.317638	−0.158819	+	0.987308i	$0.550769\pi$
$368$	−2.37420	−0.123764
$369$	−1.65147	−0.0859719
$370$	−92.4428	−4.80587
$371$	−16.0911	−0.835407
$372$	−7.94109	−0.411726
$373$	−1.97406	−0.102213	−0.0511065	−	0.998693i	$-0.516275\pi$
$373$	−1.97406	−0.102213	−0.0511065	+	0.998693i	$0.516275\pi$
$374$	−28.1692	−1.45659
$375$	−33.9902	−1.75525
$376$	1.65605	0.0854045
$377$	7.32374	0.377192
$378$	2.45739	0.126394
$379$	−15.2851	−0.785142	−0.392571	−	0.919722i	$-0.628414\pi$
$379$	−15.2851	−0.785142	−0.392571	+	0.919722i	$0.628414\pi$
$380$	14.6655	0.752324
$381$	−10.8923	−0.558027
$382$	31.8885	1.63156
$383$	19.3274	0.987584	0.493792	−	0.869580i	$-0.335610\pi$
$383$	19.3274	0.987584	0.493792	+	0.869580i	$0.335610\pi$
$384$	1.33660	0.0682083
$385$	−20.9522	−1.06782
$386$	14.3335	0.729555
$387$	9.74803	0.495520
$388$	36.0741	1.83138
$389$	30.7435	1.55876	0.779379	−	0.626552i	$-0.215535\pi$
$389$	30.7435	1.55876	0.779379	+	0.626552i	$0.215535\pi$
$390$	−8.57486	−0.434205
$391$	−2.13011	−0.107724
$392$	−0.923200	−0.0466287
$393$	6.92135	0.349136
$394$	33.4475	1.68506
$395$	−23.5857	−1.18673
$396$	8.45515	0.424887
$397$	7.25712	0.364224	0.182112	−	0.983278i	$-0.441707\pi$
$397$	7.25712	0.364224	0.182112	+	0.983278i	$0.441707\pi$
$398$	31.5505	1.58149
$399$	2.01792	0.101022
$400$	−49.7955	−2.48977
$401$	−29.5473	−1.47552	−0.737761	−	0.675062i	$-0.764117\pi$
$401$	−29.5473	−1.47552	−0.737761	+	0.675062i	$0.764117\pi$
$402$	−1.89177	−0.0943531
$403$	3.81277	0.189928
$404$	−33.0186	−1.64274
$405$	4.24376	0.210874
$406$	−17.9973	−0.893189
$407$	−43.7652	−2.16936
$408$	0.574248	0.0284295
$409$	−16.2027	−0.801172	−0.400586	−	0.916259i	$-0.631193\pi$
$409$	−16.2027	−0.801172	−0.400586	+	0.916259i	$0.631193\pi$
$410$	−14.1611	−0.699367
$411$	5.63515	0.277962
$412$	−2.08276	−0.102610
$413$	8.81131	0.433576
$414$	1.25333	0.0615977
$415$	25.5283	1.25314
$416$	−8.06850	−0.395591
$417$	−3.33341	−0.163238
$418$	13.6103	0.665700
$419$	−32.2123	−1.57367	−0.786837	−	0.617161i	$-0.788283\pi$
$419$	−32.2123	−1.57367	−0.786837	+	0.617161i	$0.788283\pi$
$420$	10.7494	0.524519
$421$	6.11492	0.298023	0.149011	−	0.988835i	$-0.452391\pi$
$421$	6.11492	0.298023	0.149011	+	0.988835i	$0.452391\pi$
$422$	39.4970	1.92269
$423$	9.90352	0.481526
$424$	2.21245	0.107446
$425$	−44.6760	−2.16710
$426$	−4.19416	−0.203208
$427$	6.60983	0.319872
$428$	0.911257	0.0440473
$429$	−4.05959	−0.195999
$430$	83.5880	4.03097
$431$	−18.6807	−0.899819	−0.449909	−	0.893074i	$-0.648544\pi$
$431$	−18.6807	−0.899819	−0.449909	+	0.893074i	$0.648544\pi$
$432$	3.82764	0.184157
$433$	14.7179	0.707296	0.353648	−	0.935379i	$-0.384941\pi$
$433$	14.7179	0.707296	0.353648	+	0.935379i	$0.384941\pi$
$434$	−9.36946	−0.449749
$435$	−31.0801	−1.49018
$436$	29.8725	1.43063
$437$	1.02919	0.0492328
$438$	9.69201	0.463102
$439$	−26.5916	−1.26915	−0.634574	−	0.772862i	$-0.718824\pi$
$439$	−26.5916	−1.26915	−0.634574	+	0.772862i	$0.718824\pi$
$440$	2.88083	0.137338
$441$	−5.52091	−0.262901
$442$	−6.93892	−0.330051
$443$	34.8003	1.65341	0.826707	−	0.562633i	$-0.190212\pi$
$443$	34.8003	1.65341	0.826707	+	0.562633i	$0.190212\pi$
$444$	22.4535	1.06560
$445$	−13.7107	−0.649949
$446$	−13.6420	−0.645965
$447$	7.27603	0.344144
$448$	10.5173	0.496893
$449$	−21.5453	−1.01678	−0.508392	−	0.861126i	$-0.669760\pi$
$449$	−21.5453	−1.01678	−0.508392	+	0.861126i	$0.669760\pi$
$450$	26.2867	1.23917
$451$	−6.70428	−0.315692
$452$	−38.9645	−1.83274
$453$	11.2710	0.529556
$454$	60.5674	2.84257
$455$	−5.16116	−0.241959
$456$	−0.277455	−0.0129930
$457$	−28.0211	−1.31077	−0.655386	−	0.755294i	$-0.727494\pi$
$457$	−28.0211	−1.31077	−0.655386	+	0.755294i	$0.727494\pi$
$458$	−51.4207	−2.40273
$459$	3.43411	0.160291
$460$	5.48248	0.255622
$461$	−16.3892	−0.763320	−0.381660	−	0.924303i	$-0.624647\pi$
$461$	−16.3892	−0.763320	−0.381660	+	0.924303i	$0.624647\pi$
$462$	9.97599	0.464125
$463$	−18.0571	−0.839184	−0.419592	−	0.907713i	$-0.637827\pi$
$463$	−18.0571	−0.839184	−0.419592	+	0.907713i	$0.637827\pi$
$464$	−28.0326	−1.30138
$465$	−16.1805	−0.750352
$466$	−18.9414	−0.877443
$467$	−6.48507	−0.300093	−0.150047	−	0.988679i	$-0.547942\pi$
$467$	−6.48507	−0.300093	−0.150047	+	0.988679i	$0.547942\pi$
$468$	2.08276	0.0962755
$469$	−1.13865	−0.0525778
$470$	84.9213	3.91713
$471$	2.36191	0.108831
$472$	−1.21151	−0.0557645
$473$	39.5730	1.81957
$474$	11.2299	0.515806
$475$	21.5857	0.990421
$476$	8.69862	0.398701
$477$	13.2309	0.605799
$478$	−25.0857	−1.14739
$479$	20.4016	0.932174	0.466087	−	0.884739i	$-0.345663\pi$
$479$	20.4016	0.932174	0.466087	+	0.884739i	$0.345663\pi$
$480$	34.2407	1.56287
$481$	−10.7807	−0.491557
$482$	3.90330	0.177791
$483$	0.754370	0.0343250
$484$	11.4141	0.518824
$485$	73.5033	3.33761
$486$	−2.02058	−0.0916555
$487$	17.5842	0.796818	0.398409	−	0.917208i	$-0.369562\pi$
$487$	17.5842	0.796818	0.398409	+	0.917208i	$0.369562\pi$
$488$	−0.908821	−0.0411404
$489$	2.23181	0.100926
$490$	−47.3411	−2.13865
$491$	−30.8946	−1.39425	−0.697126	−	0.716949i	$-0.745538\pi$
$491$	−30.8946	−1.39425	−0.697126	+	0.716949i	$0.745538\pi$
$492$	3.43961	0.155069
$493$	−25.1505	−1.13272
$494$	3.35262	0.150841
$495$	17.2279	0.774337
$496$	−14.5939	−0.655286
$497$	−2.52444	−0.113237
$498$	−12.1548	−0.544670
$499$	−10.6668	−0.477513	−0.238756	−	0.971079i	$-0.576740\pi$
$499$	−10.6668	−0.477513	−0.238756	+	0.971079i	$0.576740\pi$
$500$	70.7933	3.16597
$501$	12.3389	0.551261
$502$	−4.01866	−0.179362
$503$	−10.3392	−0.461001	−0.230501	−	0.973072i	$-0.574036\pi$
$503$	−10.3392	−0.461001	−0.230501	+	0.973072i	$0.574036\pi$
$504$	−0.203368	−0.00905871
$505$	−67.2776	−2.99381
$506$	5.08800	0.226189
$507$	−1.00000	−0.0444116
$508$	22.6859	1.00653
$509$	−24.3375	−1.07874	−0.539370	−	0.842069i	$-0.681337\pi$
$509$	−24.3375	−1.07874	−0.539370	+	0.842069i	$0.681337\pi$
$510$	29.4471	1.30394
$511$	5.83356	0.258062
$512$	32.1634	1.42143
$513$	−1.65923	−0.0732569
$514$	−36.4167	−1.60627
$515$	−4.24376	−0.187002
$516$	−20.3028	−0.893780
$517$	40.2043	1.76818
$518$	26.4923	1.16400
$519$	22.2508	0.976704
$520$	0.709635	0.0311196
$521$	−26.3881	−1.15608	−0.578041	−	0.816007i	$-0.696183\pi$
$521$	−26.3881	−1.15608	−0.578041	+	0.816007i	$0.696183\pi$
$522$	14.7982	0.647700
$523$	18.3475	0.802281	0.401141	−	0.916016i	$-0.368614\pi$
$523$	18.3475	0.802281	0.401141	+	0.916016i	$0.368614\pi$
$524$	−14.4155	−0.629743
$525$	15.8218	0.690520
$526$	−38.9207	−1.69702
$527$	−13.0935	−0.570362
$528$	15.5386	0.676233
$529$	−22.6153	−0.983272
$530$	113.453	4.92807
$531$	−7.24509	−0.314410
$532$	−4.20284	−0.182216
$533$	−1.65147	−0.0715330
$534$	6.52809	0.282498
$535$	1.85675	0.0802741
$536$	0.156559	0.00676231
$537$	6.44350	0.278057
$538$	−50.2179	−2.16505
$539$	−22.4127	−0.965382
$540$	−8.83871	−0.380358
$541$	−5.17117	−0.222326	−0.111163	−	0.993802i	$-0.535458\pi$
$541$	−5.17117	−0.222326	−0.111163	+	0.993802i	$0.535458\pi$
$542$	−22.6225	−0.971718
$543$	−11.4170	−0.489949
$544$	27.7081	1.18798
$545$	60.8672	2.60727
$546$	2.45739	0.105166
$547$	−26.5534	−1.13534	−0.567670	−	0.823256i	$-0.692155\pi$
$547$	−26.5534	−1.13534	−0.567670	+	0.823256i	$0.692155\pi$
$548$	−11.7367	−0.501365
$549$	−5.43492	−0.231957
$550$	106.713	4.55027
$551$	12.1518	0.517684
$552$	−0.103722	−0.00441472
$553$	6.75920	0.287431
$554$	−48.0506	−2.04147
$555$	45.7506	1.94200
$556$	6.94269	0.294436
$557$	−0.441419	−0.0187035	−0.00935175	−	0.999956i	$-0.502977\pi$
$557$	−0.441419	−0.0187035	−0.00935175	+	0.999956i	$0.502977\pi$
$558$	7.70403	0.326138
$559$	9.74803	0.412298
$560$	19.7550	0.834803
$561$	13.9411	0.588594
$562$	−18.2739	−0.770838
$563$	29.8132	1.25648	0.628238	−	0.778021i	$-0.283776\pi$
$563$	29.8132	1.25648	0.628238	+	0.778021i	$0.283776\pi$
$564$	−20.6266	−0.868538
$565$	−79.3928	−3.34008
$566$	40.1329	1.68691
$567$	−1.21618	−0.0510746
$568$	0.347099	0.0145639
$569$	−5.42326	−0.227355	−0.113677	−	0.993518i	$-0.536263\pi$
$569$	−5.42326	−0.227355	−0.113677	+	0.993518i	$0.536263\pi$
$570$	−14.2277	−0.595933
$571$	−21.4510	−0.897698	−0.448849	−	0.893608i	$-0.648166\pi$
$571$	−21.4510	−0.897698	−0.448849	+	0.893608i	$0.648166\pi$
$572$	8.45515	0.353528
$573$	−15.7818	−0.659295
$574$	4.05829	0.169390
$575$	8.06950	0.336522
$576$	−8.64780	−0.360325
$577$	−30.4323	−1.26691	−0.633456	−	0.773778i	$-0.718364\pi$
$577$	−30.4323	−1.26691	−0.633456	+	0.773778i	$0.718364\pi$
$578$	−10.5209	−0.437611
$579$	−7.09373	−0.294805
$580$	64.7324	2.68787
$581$	−7.31591	−0.303515
$582$	−34.9972	−1.45068
$583$	53.7119	2.22452
$584$	−0.802088	−0.0331906
$585$	4.24376	0.175458
$586$	34.9301	1.44295
$587$	1.12160	0.0462934	0.0231467	−	0.999732i	$-0.492632\pi$
$587$	1.12160	0.0462934	0.0231467	+	0.999732i	$0.492632\pi$
$588$	11.4987	0.474199
$589$	6.32628	0.260670
$590$	−62.1256	−2.55767
$591$	−16.5534	−0.680915
$592$	41.2645	1.69596
$593$	12.0433	0.494558	0.247279	−	0.968944i	$-0.420464\pi$
$593$	12.0433	0.494558	0.247279	+	0.968944i	$0.420464\pi$
$594$	−8.20275	−0.336563
$595$	17.7240	0.726614
$596$	−15.1542	−0.620741
$597$	−15.6146	−0.639062
$598$	1.25333	0.0512524
$599$	32.3003	1.31975	0.659877	−	0.751373i	$-0.270608\pi$
$599$	32.3003	1.31975	0.659877	+	0.751373i	$0.270608\pi$
$600$	−2.17543	−0.0888114
$601$	21.3067	0.869119	0.434559	−	0.900643i	$-0.356904\pi$
$601$	21.3067	0.869119	0.434559	+	0.900643i	$0.356904\pi$
$602$	−23.9547	−0.976320
$603$	0.936251	0.0381271
$604$	−23.4747	−0.955172
$605$	23.2570	0.945533
$606$	32.0329	1.30125
$607$	−36.9882	−1.50130	−0.750652	−	0.660698i	$-0.770260\pi$
$607$	−36.9882	−1.50130	−0.750652	+	0.660698i	$0.770260\pi$
$608$	−13.3875	−0.542936
$609$	8.90696	0.360928
$610$	−46.6037	−1.88693
$611$	9.90352	0.400654
$612$	−7.15243	−0.289120
$613$	19.1093	0.771816	0.385908	−	0.922537i	$-0.373888\pi$
$613$	19.1093	0.771816	0.385908	+	0.922537i	$0.373888\pi$
$614$	−17.1634	−0.692657
$615$	7.00842	0.282607
$616$	−0.825590	−0.0332640
$617$	−3.65596	−0.147183	−0.0735917	−	0.997288i	$-0.523446\pi$
$617$	−3.65596	−0.147183	−0.0735917	+	0.997288i	$0.523446\pi$
$618$	2.02058	0.0812798
$619$	23.4365	0.941990	0.470995	−	0.882136i	$-0.343895\pi$
$619$	23.4365	0.941990	0.470995	+	0.882136i	$0.343895\pi$
$620$	33.7000	1.35343
$621$	−0.620280	−0.0248910
$622$	−17.9347	−0.719115
$623$	3.92922	0.157421
$624$	3.82764	0.153228
$625$	79.1987	3.16795
$626$	36.8505	1.47284
$627$	−6.73581	−0.269002
$628$	−4.91928	−0.196301
$629$	37.0221	1.47617
$630$	−10.4286	−0.415483
$631$	−37.5569	−1.49511	−0.747557	−	0.664197i	$-0.768774\pi$
$631$	−37.5569	−1.49511	−0.747557	+	0.664197i	$0.768774\pi$
$632$	−0.929360	−0.0369679
$633$	−19.5473	−0.776937
$634$	−11.0023	−0.436958
$635$	46.2241	1.83435
$636$	−27.5567	−1.09269
$637$	−5.52091	−0.218747
$638$	60.0748	2.37838
$639$	2.07572	0.0821141
$640$	−5.67222	−0.224214
$641$	−36.3157	−1.43438	−0.717192	−	0.696875i	$-0.754573\pi$
$641$	−36.3157	−1.43438	−0.717192	+	0.696875i	$0.754573\pi$
$642$	−0.884054	−0.0348908
$643$	−38.3686	−1.51311	−0.756554	−	0.653931i	$-0.773119\pi$
$643$	−38.3686	−1.51311	−0.756554	+	0.653931i	$0.773119\pi$
$644$	−1.57117	−0.0619128
$645$	−41.3682	−1.62887
$646$	−11.5133	−0.452984
$647$	11.2521	0.442365	0.221183	−	0.975232i	$-0.429008\pi$
$647$	11.2521	0.442365	0.221183	+	0.975232i	$0.429008\pi$
$648$	0.167219	0.00656897
$649$	−29.4121	−1.15453
$650$	26.2867	1.03105
$651$	4.63701	0.181739
$652$	−4.64832	−0.182042
$653$	29.2608	1.14506	0.572531	−	0.819883i	$-0.305962\pi$
$653$	29.2608	1.14506	0.572531	+	0.819883i	$0.305962\pi$
$654$	−28.9808	−1.13324
$655$	−29.3725	−1.14768
$656$	6.32121	0.246802
$657$	−4.79664	−0.187135
$658$	−24.3368	−0.948747
$659$	3.94572	0.153703	0.0768516	−	0.997043i	$-0.475513\pi$
$659$	3.94572	0.153703	0.0768516	+	0.997043i	$0.475513\pi$
$660$	−35.8816	−1.39669
$661$	7.62241	0.296477	0.148239	−	0.988952i	$-0.452640\pi$
$661$	7.62241	0.296477	0.148239	+	0.988952i	$0.452640\pi$
$662$	−6.92637	−0.269201
$663$	3.43411	0.133370
$664$	1.00590	0.0390367
$665$	−8.56357	−0.332081
$666$	−21.7833	−0.844084
$667$	4.54276	0.175897
$668$	−25.6989	−0.994321
$669$	6.75149	0.261028
$670$	8.02822	0.310157
$671$	−22.0636	−0.851755
$672$	−9.81272	−0.378534
$673$	−46.1283	−1.77811	−0.889057	−	0.457797i	$-0.848639\pi$
$673$	−46.1283	−1.77811	−0.889057	+	0.457797i	$0.848639\pi$
$674$	58.5302	2.25450
$675$	−13.0095	−0.500734
$676$	2.08276	0.0801061
$677$	−28.9183	−1.11142	−0.555710	−	0.831377i	$-0.687553\pi$
$677$	−28.9183	−1.11142	−0.555710	+	0.831377i	$0.687553\pi$
$678$	37.8014	1.45175
$679$	−21.0646	−0.808385
$680$	−2.43697	−0.0934535
$681$	−29.9752	−1.14865
$682$	31.2752	1.19759
$683$	20.7401	0.793596	0.396798	−	0.917906i	$-0.370121\pi$
$683$	20.7401	0.793596	0.396798	+	0.917906i	$0.370121\pi$
$684$	3.45578	0.132135
$685$	−23.9142	−0.913715
$686$	30.7687	1.17476
$687$	25.4484	0.970918
$688$	−37.3119	−1.42250
$689$	13.2309	0.504056
$690$	−5.31881	−0.202484
$691$	18.4788	0.702966	0.351483	−	0.936194i	$-0.385678\pi$
$691$	18.4788	0.702966	0.351483	+	0.936194i	$0.385678\pi$
$692$	−46.3431	−1.76170
$693$	−4.93718	−0.187548
$694$	−2.99962	−0.113864
$695$	14.1462	0.536596
$696$	−1.22467	−0.0464208
$697$	5.67133	0.214817
$698$	−45.4100	−1.71879
$699$	9.37422	0.354566
$700$	−32.9530	−1.24551
$701$	25.7966	0.974323	0.487162	−	0.873312i	$-0.338032\pi$
$701$	25.7966	0.974323	0.487162	+	0.873312i	$0.338032\pi$
$702$	−2.02058	−0.0762620
$703$	−17.8877	−0.674646
$704$	−35.1065	−1.32313
$705$	−42.0281	−1.58287
$706$	20.8281	0.783876
$707$	19.2804	0.725115
$708$	15.0898	0.567108
$709$	40.5176	1.52167	0.760836	−	0.648944i	$-0.224789\pi$
$709$	40.5176	1.52167	0.760836	+	0.648944i	$0.224789\pi$
$710$	17.7990	0.667984
$711$	−5.55775	−0.208432
$712$	−0.540249	−0.0202467
$713$	2.36499	0.0885695
$714$	−8.43895	−0.315820
$715$	17.2279	0.644288
$716$	−13.4202	−0.501538
$717$	12.4151	0.463649
$718$	23.0500	0.860219
$719$	−20.3243	−0.757970	−0.378985	−	0.925403i	$-0.623727\pi$
$719$	−20.3243	−0.757970	−0.378985	+	0.925403i	$0.623727\pi$
$720$	−16.2435	−0.605361
$721$	1.21618	0.0452928
$722$	−32.8283	−1.22174
$723$	−1.93177	−0.0718433
$724$	23.7788	0.883732
$725$	95.2778	3.53853
$726$	−11.0734	−0.410972
$727$	27.9800	1.03772	0.518860	−	0.854859i	$-0.326356\pi$
$727$	27.9800	1.03772	0.518860	+	0.854859i	$0.326356\pi$
$728$	−0.203368	−0.00753731
$729$	1.00000	0.0370370
$730$	−41.1305	−1.52231
$731$	−33.4758	−1.23815
$732$	11.3196	0.418385
$733$	−11.9413	−0.441060	−0.220530	−	0.975380i	$-0.570779\pi$
$733$	−11.9413	−0.441060	−0.220530	+	0.975380i	$0.570779\pi$
$734$	−12.2954	−0.453831
$735$	23.4294	0.864207
$736$	−5.00472	−0.184477
$737$	3.80080	0.140004
$738$	−3.33693	−0.122834
$739$	20.6859	0.760943	0.380472	−	0.924793i	$-0.375762\pi$
$739$	20.6859	0.760943	0.380472	+	0.924793i	$0.375762\pi$
$740$	−95.2873	−3.50283
$741$	−1.65923	−0.0609535
$742$	−32.5133	−1.19360
$743$	−47.2844	−1.73470	−0.867348	−	0.497702i	$-0.834177\pi$
$743$	−47.2844	−1.73470	−0.867348	+	0.497702i	$0.834177\pi$
$744$	−0.637567	−0.0233744
$745$	−30.8777	−1.13127
$746$	−3.98875	−0.146039
$747$	6.01550	0.220096
$748$	−29.0360	−1.06166
$749$	−0.532107	−0.0194428
$750$	−68.6800	−2.50784
$751$	−26.3475	−0.961433	−0.480717	−	0.876876i	$-0.659623\pi$
$751$	−26.3475	−0.961433	−0.480717	+	0.876876i	$0.659623\pi$
$752$	−37.9071	−1.38233
$753$	1.98886	0.0724782
$754$	14.7982	0.538919
$755$	−47.8312	−1.74076
$756$	2.53300	0.0921244
$757$	−44.7771	−1.62745	−0.813726	−	0.581249i	$-0.802564\pi$
$757$	−44.7771	−1.62745	−0.813726	+	0.581249i	$0.802564\pi$
$758$	−30.8848	−1.12179
$759$	−2.51808	−0.0914006
$760$	1.17745	0.0427106
$761$	−16.9868	−0.615773	−0.307886	−	0.951423i	$-0.599622\pi$
$761$	−16.9868	−0.615773	−0.307886	+	0.951423i	$0.599622\pi$
$762$	−22.0087	−0.797291
$763$	−17.4434	−0.631492
$764$	32.8697	1.18919
$765$	−14.5735	−0.526908
$766$	39.0526	1.41103
$767$	−7.24509	−0.261605
$768$	−14.5949	−0.526647
$769$	2.26014	0.0815028	0.0407514	−	0.999169i	$-0.487025\pi$
$769$	2.26014	0.0815028	0.0407514	+	0.999169i	$0.487025\pi$
$770$	−42.3357	−1.52567
$771$	18.0229	0.649077
$772$	14.7745	0.531747
$773$	−41.3043	−1.48561	−0.742807	−	0.669506i	$-0.766506\pi$
$773$	−41.3043	−1.48561	−0.742807	+	0.669506i	$0.766506\pi$
$774$	19.6967	0.707983
$775$	49.6021	1.78176
$776$	2.89629	0.103971
$777$	−13.1112	−0.470362
$778$	62.1199	2.22711
$779$	−2.74017	−0.0981767
$780$	−8.83871	−0.316477
$781$	8.42657	0.301526
$782$	−4.30407	−0.153913
$783$	−7.32374	−0.261729
$784$	21.1320	0.754716
$785$	−10.0234	−0.357749
$786$	13.9852	0.498834
$787$	40.9492	1.45968	0.729841	−	0.683617i	$-0.239594\pi$
$787$	40.9492	1.45968	0.729841	+	0.683617i	$0.239594\pi$
$788$	34.4767	1.22818
$789$	19.2621	0.685749
$790$	−47.6569	−1.69556
$791$	22.7524	0.808983
$792$	0.678840	0.0241215
$793$	−5.43492	−0.193000
$794$	14.6636	0.520392
$795$	−56.1485	−1.99138
$796$	32.5214	1.15269
$797$	1.80291	0.0638624	0.0319312	−	0.999490i	$-0.489834\pi$
$797$	1.80291	0.0638624	0.0319312	+	0.999490i	$0.489834\pi$
$798$	4.07738	0.144338
$799$	−34.0098	−1.20318
$800$	−104.967	−3.71114
$801$	−3.23079	−0.114154
$802$	−59.7028	−2.10818
$803$	−19.4724	−0.687166
$804$	−1.94998	−0.0687706
$805$	−3.20136	−0.112833
$806$	7.70403	0.271363
$807$	24.8531	0.874872
$808$	−2.65097	−0.0932608
$809$	39.4624	1.38742	0.693712	−	0.720253i	$-0.255974\pi$
$809$	39.4624	1.38742	0.693712	+	0.720253i	$0.255974\pi$
$810$	8.57486	0.301290
$811$	−37.6751	−1.32295	−0.661476	−	0.749966i	$-0.730070\pi$
$811$	−37.6751	−1.32295	−0.661476	+	0.749966i	$0.730070\pi$
$812$	−18.5510	−0.651014
$813$	11.1960	0.392661
$814$	−88.4312	−3.09951
$815$	−9.47126	−0.331764
$816$	−13.1445	−0.460151
$817$	16.1743	0.565865
$818$	−32.7389	−1.14469
$819$	−1.21618	−0.0424967
$820$	−14.5968	−0.509744
$821$	40.6738	1.41953	0.709763	−	0.704441i	$-0.248802\pi$
$821$	40.6738	1.41953	0.709763	+	0.704441i	$0.248802\pi$
$822$	11.3863	0.397143
$823$	43.8682	1.52915	0.764575	−	0.644534i	$-0.222949\pi$
$823$	43.8682	1.52915	0.764575	+	0.644534i	$0.222949\pi$
$824$	−0.167219	−0.00582534
$825$	−52.8131	−1.83872
$826$	17.8040	0.619480
$827$	19.1748	0.666772	0.333386	−	0.942790i	$-0.391809\pi$
$827$	19.1748	0.666772	0.333386	+	0.942790i	$0.391809\pi$
$828$	1.29189	0.0448964
$829$	24.3429	0.845463	0.422732	−	0.906255i	$-0.361071\pi$
$829$	24.3429	0.845463	0.422732	+	0.906255i	$0.361071\pi$
$830$	51.5821	1.79044
$831$	23.7805	0.824938
$832$	−8.64780	−0.299808
$833$	18.9594	0.656906
$834$	−6.73544	−0.233229
$835$	−52.3632	−1.81210
$836$	14.0291	0.485205
$837$	−3.81277	−0.131789
$838$	−65.0877	−2.24842
$839$	−17.5743	−0.606733	−0.303367	−	0.952874i	$-0.598111\pi$
$839$	−17.5743	−0.606733	−0.303367	+	0.952874i	$0.598111\pi$
$840$	0.863042	0.0297778
$841$	24.6371	0.849555
$842$	12.3557	0.425805
$843$	9.04387	0.311487
$844$	40.7124	1.40138
$845$	4.24376	0.145990
$846$	20.0109	0.687989
$847$	−6.66501	−0.229013
$848$	−50.6429	−1.73908
$849$	−19.8620	−0.681663
$850$	−90.2715	−3.09629
$851$	−6.68704	−0.229229
$852$	−4.32322	−0.148111
$853$	6.37049	0.218121	0.109061	−	0.994035i	$-0.465216\pi$
$853$	6.37049	0.218121	0.109061	+	0.994035i	$0.465216\pi$
$854$	13.3557	0.457023
$855$	7.04138	0.240810
$856$	0.0731622	0.00250063
$857$	−5.13585	−0.175437	−0.0877187	−	0.996145i	$-0.527958\pi$
$857$	−5.13585	−0.175437	−0.0877187	+	0.996145i	$0.527958\pi$
$858$	−8.20275	−0.280037
$859$	44.3382	1.51280	0.756400	−	0.654109i	$-0.226956\pi$
$859$	44.3382	1.51280	0.756400	+	0.654109i	$0.226956\pi$
$860$	86.1600	2.93803
$861$	−2.00848	−0.0684487
$862$	−37.7460	−1.28563
$863$	−52.4564	−1.78564	−0.892818	−	0.450418i	$-0.851275\pi$
$863$	−52.4564	−1.78564	−0.892818	+	0.450418i	$0.851275\pi$
$864$	8.06850	0.274496
$865$	−94.4271	−3.21062
$866$	29.7387	1.01056
$867$	5.20686	0.176834
$868$	−9.65777	−0.327806
$869$	−22.5622	−0.765370
$870$	−62.8000	−2.12912
$871$	0.936251	0.0317237
$872$	2.39838	0.0812195
$873$	17.3203	0.586205
$874$	2.07956	0.0703422
$875$	−41.3381	−1.39748
$876$	9.99024	0.337539
$877$	9.30250	0.314123	0.157062	−	0.987589i	$-0.449798\pi$
$877$	9.30250	0.314123	0.157062	+	0.987589i	$0.449798\pi$
$878$	−53.7305	−1.81332
$879$	−17.2871	−0.583080
$880$	−65.9422	−2.22291
$881$	15.7383	0.530236	0.265118	−	0.964216i	$-0.414589\pi$
$881$	15.7383	0.530236	0.265118	+	0.964216i	$0.414589\pi$
$882$	−11.1555	−0.375624
$883$	45.9361	1.54587	0.772937	−	0.634483i	$-0.218787\pi$
$883$	45.9361	1.54587	0.772937	+	0.634483i	$0.218787\pi$
$884$	−7.15243	−0.240562
$885$	30.7464	1.03353
$886$	70.3170	2.36234
$887$	2.85477	0.0958539	0.0479269	−	0.998851i	$-0.484739\pi$
$887$	2.85477	0.0958539	0.0479269	+	0.998851i	$0.484739\pi$
$888$	1.80273	0.0604957
$889$	−13.2469	−0.444287
$890$	−27.7036	−0.928627
$891$	4.05959	0.136001
$892$	−14.0617	−0.470821
$893$	16.4323	0.549884
$894$	14.7018	0.491703
$895$	−27.3446	−0.914030
$896$	1.62555	0.0543058
$897$	−0.620280	−0.0207105
$898$	−43.5340	−1.45275
$899$	27.9238	0.931309
$900$	27.0956	0.903185
$901$	−45.4363	−1.51370
$902$	−13.5466	−0.451051
$903$	11.8553	0.394521
$904$	−3.12835	−0.104047
$905$	48.4508	1.61056
$906$	22.7739	0.756613
$907$	9.72972	0.323070	0.161535	−	0.986867i	$-0.448355\pi$
$907$	9.72972	0.323070	0.161535	+	0.986867i	$0.448355\pi$
$908$	62.4311	2.07185
$909$	−15.8533	−0.525821
$910$	−10.4286	−0.345703
$911$	−11.1063	−0.367969	−0.183985	−	0.982929i	$-0.558900\pi$
$911$	−11.1063	−0.367969	−0.183985	+	0.982929i	$0.558900\pi$
$912$	6.35094	0.210301
$913$	24.4205	0.808200
$914$	−56.6190	−1.87279
$915$	23.0645	0.762488
$916$	−53.0029	−1.75127
$917$	8.41758	0.277973
$918$	6.93892	0.229018
$919$	−37.3887	−1.23334	−0.616669	−	0.787222i	$-0.711518\pi$
$919$	−37.3887	−1.23334	−0.616669	+	0.787222i	$0.711518\pi$
$920$	0.440173	0.0145121
$921$	8.49426	0.279896
$922$	−33.1157	−1.09061
$923$	2.07572	0.0683231
$924$	10.2830	0.338285
$925$	−140.251	−4.61142
$926$	−36.4859	−1.19900
$927$	−1.00000	−0.0328443
$928$	−59.0915	−1.93977
$929$	−29.5395	−0.969159	−0.484580	−	0.874747i	$-0.661027\pi$
$929$	−29.5395	−0.969159	−0.484580	+	0.874747i	$0.661027\pi$
$930$	−32.6940	−1.07208
$931$	−9.16048	−0.300223
$932$	−19.5242	−0.639537
$933$	8.87599	0.290587
$934$	−13.1036	−0.428764
$935$	−59.1627	−1.93483
$936$	0.167219	0.00546572
$937$	−31.9308	−1.04313	−0.521567	−	0.853211i	$-0.674652\pi$
$937$	−31.9308	−1.04313	−0.521567	+	0.853211i	$0.674652\pi$
$938$	−2.30073	−0.0751215
$939$	−18.2376	−0.595160
$940$	87.5344	2.85506
$941$	−16.5704	−0.540179	−0.270090	−	0.962835i	$-0.587053\pi$
$941$	−16.5704	−0.540179	−0.270090	+	0.962835i	$0.587053\pi$
$942$	4.77243	0.155494
$943$	−1.02437	−0.0333581
$944$	27.7316	0.902585
$945$	5.16116	0.167892
$946$	79.9606	2.59974
$947$	30.5313	0.992134	0.496067	−	0.868284i	$-0.334777\pi$
$947$	30.5313	0.992134	0.496067	+	0.868284i	$0.334777\pi$
$948$	11.5754	0.375953
$949$	−4.79664	−0.155705
$950$	43.6158	1.41508
$951$	5.44512	0.176570
$952$	0.698388	0.0226349
$953$	21.5883	0.699314	0.349657	−	0.936878i	$-0.386298\pi$
$953$	21.5883	0.699314	0.349657	+	0.936878i	$0.386298\pi$
$954$	26.7341	0.865547
$955$	66.9742	2.16724
$956$	−25.8576	−0.836293
$957$	−29.7314	−0.961079
$958$	41.2232	1.33186
$959$	6.85334	0.221306
$960$	36.6991	1.18446
$961$	−16.4627	−0.531056
$962$	−21.7833	−0.702320
$963$	0.437524	0.0140990
$964$	4.02341	0.129585
$965$	30.1041	0.969084
$966$	1.52427	0.0490425
$967$	61.1908	1.96776	0.983882	−	0.178820i	$-0.0572279\pi$
$967$	61.1908	1.96776	0.983882	+	0.178820i	$0.0572279\pi$
$968$	0.916409	0.0294545
$969$	5.69800	0.183046
$970$	148.520	4.76868
$971$	−8.70220	−0.279267	−0.139633	−	0.990203i	$-0.544592\pi$
$971$	−8.70220	−0.279267	−0.139633	+	0.990203i	$0.544592\pi$
$972$	−2.08276	−0.0668045
$973$	−4.05402	−0.129966
$974$	35.5304	1.13847
$975$	−13.0095	−0.416636
$976$	20.8029	0.665885
$977$	32.4949	1.03961	0.519803	−	0.854286i	$-0.326006\pi$
$977$	32.4949	1.03961	0.519803	+	0.854286i	$0.326006\pi$
$978$	4.50956	0.144200
$979$	−13.1157	−0.419180
$980$	−48.7978	−1.55879
$981$	14.3428	0.457930
$982$	−62.4250	−1.99206
$983$	−32.0897	−1.02350	−0.511751	−	0.859134i	$-0.671003\pi$
$983$	−32.0897	−1.02350	−0.511751	+	0.859134i	$0.671003\pi$
$984$	0.276156	0.00880354
$985$	70.2485	2.23830
$986$	−50.8188	−1.61840
$987$	12.0444	0.383379
$988$	3.45578	0.109943
$989$	6.04650	0.192268
$990$	34.8105	1.10635
$991$	−43.9747	−1.39690	−0.698451	−	0.715658i	$-0.746127\pi$
$991$	−43.9747	−1.39690	−0.698451	+	0.715658i	$0.746127\pi$
$992$	−30.7634	−0.976737
$993$	3.42791	0.108781
$994$	−5.10084	−0.161789
$995$	66.2644	2.10072
$996$	−12.5288	−0.396991
$997$	21.7999	0.690410	0.345205	−	0.938527i	$-0.387809\pi$
$997$	21.7999	0.690410	0.345205	+	0.938527i	$0.387809\pi$
$998$	−21.5532	−0.682255
$999$	10.7807	0.341086

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.j.1.20	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.j.1.20	✓	25	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q+2.02058 q^{2} -1.00000 q^{3} +2.08276 q^{4} +4.24376 q^{5} -2.02058 q^{6} -1.21618 q^{7} +0.167219 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.02058 q^{2} -1.00000 q^{3} +2.08276 q^{4} +4.24376 q^{5} -2.02058 q^{6} -1.21618 q^{7} +0.167219 q^{8} +1.00000 q^{9} +8.57486 q^{10} +4.05959 q^{11} -2.08276 q^{12} +1.00000 q^{13} -2.45739 q^{14} -4.24376 q^{15} -3.82764 q^{16} -3.43411 q^{17} +2.02058 q^{18} +1.65923 q^{19} +8.83871 q^{20} +1.21618 q^{21} +8.20275 q^{22} +0.620280 q^{23} -0.167219 q^{24} +13.0095 q^{25} +2.02058 q^{26} -1.00000 q^{27} -2.53300 q^{28} +7.32374 q^{29} -8.57486 q^{30} +3.81277 q^{31} -8.06850 q^{32} -4.05959 q^{33} -6.93892 q^{34} -5.16116 q^{35} +2.08276 q^{36} -10.7807 q^{37} +3.35262 q^{38} -1.00000 q^{39} +0.709635 q^{40} -1.65147 q^{41} +2.45739 q^{42} +9.74803 q^{43} +8.45515 q^{44} +4.24376 q^{45} +1.25333 q^{46} +9.90352 q^{47} +3.82764 q^{48} -5.52091 q^{49} +26.2867 q^{50} +3.43411 q^{51} +2.08276 q^{52} +13.2309 q^{53} -2.02058 q^{54} +17.2279 q^{55} -0.203368 q^{56} -1.65923 q^{57} +14.7982 q^{58} -7.24509 q^{59} -8.83871 q^{60} -5.43492 q^{61} +7.70403 q^{62} -1.21618 q^{63} -8.64780 q^{64} +4.24376 q^{65} -8.20275 q^{66} +0.936251 q^{67} -7.15243 q^{68} -0.620280 q^{69} -10.4286 q^{70} +2.07572 q^{71} +0.167219 q^{72} -4.79664 q^{73} -21.7833 q^{74} -13.0095 q^{75} +3.45578 q^{76} -4.93718 q^{77} -2.02058 q^{78} -5.55775 q^{79} -16.2435 q^{80} +1.00000 q^{81} -3.33693 q^{82} +6.01550 q^{83} +2.53300 q^{84} -14.5735 q^{85} +19.6967 q^{86} -7.32374 q^{87} +0.678840 q^{88} -3.23079 q^{89} +8.57486 q^{90} -1.21618 q^{91} +1.29189 q^{92} -3.81277 q^{93} +20.0109 q^{94} +7.04138 q^{95} +8.06850 q^{96} +17.3203 q^{97} -11.1555 q^{98} +4.05959 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9} - 6 q^{10} + 21 q^{11} - 28 q^{12} + 25 q^{13} + 10 q^{14} - 7 q^{15} + 30 q^{16} + 14 q^{17} + 6 q^{18} + 12 q^{19} + 24 q^{20} - 17 q^{21} + 3 q^{22} + 41 q^{23} - 21 q^{24} + 30 q^{25} + 6 q^{26} - 25 q^{27} + 14 q^{28} + 22 q^{29} + 6 q^{30} + 14 q^{31} + 28 q^{32} - 21 q^{33} - 11 q^{34} + 14 q^{35} + 28 q^{36} - 6 q^{37} + 16 q^{38} - 25 q^{39} - 34 q^{40} + 33 q^{41} - 10 q^{42} + 35 q^{43} + 45 q^{44} + 7 q^{45} + 3 q^{46} + 48 q^{47} - 30 q^{48} - 4 q^{49} + 7 q^{50} - 14 q^{51} + 28 q^{52} + 18 q^{53} - 6 q^{54} + 10 q^{55} + 32 q^{56} - 12 q^{57} + 33 q^{58} + 46 q^{59} - 24 q^{60} - 19 q^{61} + 5 q^{62} + 17 q^{63} + 29 q^{64} + 7 q^{65} - 3 q^{66} + 16 q^{67} + 20 q^{68} - 41 q^{69} - 43 q^{70} + 60 q^{71} + 21 q^{72} - 14 q^{73} - 50 q^{74} - 30 q^{75} + 59 q^{77} - 6 q^{78} + 7 q^{79} + 32 q^{80} + 25 q^{81} + 18 q^{82} + 23 q^{83} - 14 q^{84} - 9 q^{85} - 9 q^{86} - 22 q^{87} + 23 q^{88} + 10 q^{89} - 6 q^{90} + 17 q^{91} + 69 q^{92} - 14 q^{93} - 30 q^{94} + 81 q^{95} - 28 q^{96} - 10 q^{97} + 55 q^{98} + 21 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9 - 6 * q^10 + 21 * q^11 - 28 * q^12 + 25 * q^13 + 10 * q^14 - 7 * q^15 + 30 * q^16 + 14 * q^17 + 6 * q^18 + 12 * q^19 + 24 * q^20 - 17 * q^21 + 3 * q^22 + 41 * q^23 - 21 * q^24 + 30 * q^25 + 6 * q^26 - 25 * q^27 + 14 * q^28 + 22 * q^29 + 6 * q^30 + 14 * q^31 + 28 * q^32 - 21 * q^33 - 11 * q^34 + 14 * q^35 + 28 * q^36 - 6 * q^37 + 16 * q^38 - 25 * q^39 - 34 * q^40 + 33 * q^41 - 10 * q^42 + 35 * q^43 + 45 * q^44 + 7 * q^45 + 3 * q^46 + 48 * q^47 - 30 * q^48 - 4 * q^49 + 7 * q^50 - 14 * q^51 + 28 * q^52 + 18 * q^53 - 6 * q^54 + 10 * q^55 + 32 * q^56 - 12 * q^57 + 33 * q^58 + 46 * q^59 - 24 * q^60 - 19 * q^61 + 5 * q^62 + 17 * q^63 + 29 * q^64 + 7 * q^65 - 3 * q^66 + 16 * q^67 + 20 * q^68 - 41 * q^69 - 43 * q^70 + 60 * q^71 + 21 * q^72 - 14 * q^73 - 50 * q^74 - 30 * q^75 + 59 * q^77 - 6 * q^78 + 7 * q^79 + 32 * q^80 + 25 * q^81 + 18 * q^82 + 23 * q^83 - 14 * q^84 - 9 * q^85 - 9 * q^86 - 22 * q^87 + 23 * q^88 + 10 * q^89 - 6 * q^90 + 17 * q^91 + 69 * q^92 - 14 * q^93 - 30 * q^94 + 81 * q^95 - 28 * q^96 - 10 * q^97 + 55 * q^98 + 21 * q^99

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