LMFDB - Embedded newform 4003.2.a.c.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4003,2,Mod(1,4003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4003, 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("4003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4003.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:	$31.9641159291$
Analytic rank:	$0$
Dimension:	$179$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	4003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.63071 q^{2} +2.57872 q^{3} +4.92061 q^{4} -1.88131 q^{5} -6.78385 q^{6} -5.19574 q^{7} -7.68328 q^{8} +3.64979 q^{9} +O(q^{10})$	\(q-2.63071 q^{2} +2.57872 q^{3} +4.92061 q^{4} -1.88131 q^{5} -6.78385 q^{6} -5.19574 q^{7} -7.68328 q^{8} +3.64979 q^{9} +4.94917 q^{10} -2.38632 q^{11} +12.6889 q^{12} -1.49198 q^{13} +13.6685 q^{14} -4.85136 q^{15} +10.3712 q^{16} -1.62869 q^{17} -9.60151 q^{18} -5.84283 q^{19} -9.25719 q^{20} -13.3983 q^{21} +6.27770 q^{22} -1.73420 q^{23} -19.8130 q^{24} -1.46068 q^{25} +3.92496 q^{26} +1.67561 q^{27} -25.5662 q^{28} +6.97607 q^{29} +12.7625 q^{30} -0.537433 q^{31} -11.9171 q^{32} -6.15364 q^{33} +4.28459 q^{34} +9.77478 q^{35} +17.9592 q^{36} +4.57588 q^{37} +15.3708 q^{38} -3.84740 q^{39} +14.4546 q^{40} -10.2985 q^{41} +35.2471 q^{42} -1.45623 q^{43} -11.7421 q^{44} -6.86637 q^{45} +4.56217 q^{46} +5.01724 q^{47} +26.7444 q^{48} +19.9957 q^{49} +3.84262 q^{50} -4.19992 q^{51} -7.34146 q^{52} +9.61811 q^{53} -4.40805 q^{54} +4.48940 q^{55} +39.9203 q^{56} -15.0670 q^{57} -18.3520 q^{58} -2.80946 q^{59} -23.8717 q^{60} -9.67030 q^{61} +1.41383 q^{62} -18.9633 q^{63} +10.6078 q^{64} +2.80688 q^{65} +16.1884 q^{66} -4.15099 q^{67} -8.01413 q^{68} -4.47202 q^{69} -25.7146 q^{70} -9.14923 q^{71} -28.0423 q^{72} -3.83807 q^{73} -12.0378 q^{74} -3.76668 q^{75} -28.7503 q^{76} +12.3987 q^{77} +10.1214 q^{78} +1.17242 q^{79} -19.5114 q^{80} -6.62842 q^{81} +27.0922 q^{82} +16.3741 q^{83} -65.9280 q^{84} +3.06406 q^{85} +3.83092 q^{86} +17.9893 q^{87} +18.3347 q^{88} +15.3462 q^{89} +18.0634 q^{90} +7.75194 q^{91} -8.53334 q^{92} -1.38589 q^{93} -13.1989 q^{94} +10.9922 q^{95} -30.7307 q^{96} +7.15550 q^{97} -52.6027 q^{98} -8.70955 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9}+O(q^{10}) $ 179 * q + 22 * q^2 + 16 * q^3 + 196 * q^4 + 61 * q^5 + 7 * q^6 + 21 * q^7 + 60 * q^8 + 221 * q^9	\( 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9} + 9 q^{10} + 46 q^{11} + 33 q^{12} + 47 q^{13} + 22 q^{14} + 36 q^{15} + 222 q^{16} + 103 q^{17} + 43 q^{18} + 12 q^{19} + 102 q^{20} + 50 q^{21} + 39 q^{22} + 121 q^{23} - 3 q^{24} + 246 q^{25} + 52 q^{26} + 49 q^{27} + 41 q^{28} + 138 q^{29} + 28 q^{30} + 5 q^{31} + 137 q^{32} + 63 q^{33} + 2 q^{34} + 72 q^{35} + 279 q^{36} + 118 q^{37} + 123 q^{38} + q^{39} + 9 q^{40} + 50 q^{41} + 48 q^{42} + 48 q^{43} + 108 q^{44} + 158 q^{45} + 13 q^{46} + 85 q^{47} + 50 q^{48} + 230 q^{49} + 78 q^{50} + 15 q^{51} + 41 q^{52} + 399 q^{53} - 5 q^{54} + 24 q^{55} + 53 q^{56} + 45 q^{57} + 27 q^{58} + 48 q^{59} + 66 q^{60} + 46 q^{61} + 81 q^{62} + 78 q^{63} + 252 q^{64} + 153 q^{65} + 6 q^{66} + 70 q^{67} + 240 q^{68} + 120 q^{69} - 31 q^{70} + 86 q^{71} + 89 q^{72} + 45 q^{73} + 68 q^{74} + 17 q^{75} - 13 q^{76} + 362 q^{77} + 69 q^{78} + 31 q^{79} + 169 q^{80} + 303 q^{81} + 25 q^{82} + 106 q^{83} + 13 q^{84} + 115 q^{85} + 95 q^{86} + 32 q^{87} + 83 q^{88} + 105 q^{89} - 38 q^{90} + 3 q^{91} + 310 q^{92} + 298 q^{93} - 17 q^{94} + 102 q^{95} - 82 q^{96} + 34 q^{97} + 81 q^{98} + 58 q^{99}+O(q^{100}) \) 179 * q + 22 * q^2 + 16 * q^3 + 196 * q^4 + 61 * q^5 + 7 * q^6 + 21 * q^7 + 60 * q^8 + 221 * q^9 + 9 * q^10 + 46 * q^11 + 33 * q^12 + 47 * q^13 + 22 * q^14 + 36 * q^15 + 222 * q^16 + 103 * q^17 + 43 * q^18 + 12 * q^19 + 102 * q^20 + 50 * q^21 + 39 * q^22 + 121 * q^23 - 3 * q^24 + 246 * q^25 + 52 * q^26 + 49 * q^27 + 41 * q^28 + 138 * q^29 + 28 * q^30 + 5 * q^31 + 137 * q^32 + 63 * q^33 + 2 * q^34 + 72 * q^35 + 279 * q^36 + 118 * q^37 + 123 * q^38 + q^39 + 9 * q^40 + 50 * q^41 + 48 * q^42 + 48 * q^43 + 108 * q^44 + 158 * q^45 + 13 * q^46 + 85 * q^47 + 50 * q^48 + 230 * q^49 + 78 * q^50 + 15 * q^51 + 41 * q^52 + 399 * q^53 - 5 * q^54 + 24 * q^55 + 53 * q^56 + 45 * q^57 + 27 * q^58 + 48 * q^59 + 66 * q^60 + 46 * q^61 + 81 * q^62 + 78 * q^63 + 252 * q^64 + 153 * q^65 + 6 * q^66 + 70 * q^67 + 240 * q^68 + 120 * q^69 - 31 * q^70 + 86 * q^71 + 89 * q^72 + 45 * q^73 + 68 * q^74 + 17 * q^75 - 13 * q^76 + 362 * q^77 + 69 * q^78 + 31 * q^79 + 169 * q^80 + 303 * q^81 + 25 * q^82 + 106 * q^83 + 13 * q^84 + 115 * q^85 + 95 * q^86 + 32 * q^87 + 83 * q^88 + 105 * q^89 - 38 * q^90 + 3 * q^91 + 310 * q^92 + 298 * q^93 - 17 * q^94 + 102 * q^95 - 82 * q^96 + 34 * q^97 + 81 * q^98 + 58 * 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 $

$2$	−2.63071	−1.86019	−0.930095	−	0.367319i	$-0.880276\pi$
$2$	−2.63071	−1.86019	−0.930095	+	0.367319i	$0.880276\pi$
$3$	2.57872	1.48882	0.744412	−	0.667721i	$-0.232730\pi$
$3$	2.57872	1.48882	0.744412	+	0.667721i	$0.232730\pi$
$4$	4.92061	2.46031
$5$	−1.88131	−0.841347	−0.420673	−	0.907212i	$-0.638206\pi$
$5$	−1.88131	−0.841347	−0.420673	+	0.907212i	$0.638206\pi$
$6$	−6.78385	−2.76949
$7$	−5.19574	−1.96380	−0.981902	−	0.189392i	$-0.939348\pi$
$7$	−5.19574	−1.96380	−0.981902	+	0.189392i	$0.939348\pi$
$8$	−7.68328	−2.71645
$9$	3.64979	1.21660
$10$	4.94917	1.56506
$11$	−2.38632	−0.719502	−0.359751	−	0.933048i	$-0.617138\pi$
$11$	−2.38632	−0.719502	−0.359751	+	0.933048i	$0.617138\pi$
$12$	12.6889	3.66296
$13$	−1.49198	−0.413801	−0.206901	−	0.978362i	$-0.566338\pi$
$13$	−1.49198	−0.413801	−0.206901	+	0.978362i	$0.566338\pi$
$14$	13.6685	3.65305
$15$	−4.85136	−1.25262
$16$	10.3712	2.59280
$17$	−1.62869	−0.395014	−0.197507	−	0.980301i	$-0.563285\pi$
$17$	−1.62869	−0.395014	−0.197507	+	0.980301i	$0.563285\pi$
$18$	−9.60151	−2.26310
$19$	−5.84283	−1.34044	−0.670218	−	0.742164i	$-0.733800\pi$
$19$	−5.84283	−1.34044	−0.670218	+	0.742164i	$0.733800\pi$
$20$	−9.25719	−2.06997
$21$	−13.3983	−2.92376
$22$	6.27770	1.33841
$23$	−1.73420	−0.361606	−0.180803	−	0.983519i	$-0.557870\pi$
$23$	−1.73420	−0.361606	−0.180803	+	0.983519i	$0.557870\pi$
$24$	−19.8130	−4.04431
$25$	−1.46068	−0.292136
$26$	3.92496	0.769749
$27$	1.67561	0.322472
$28$	−25.5662	−4.83156
$29$	6.97607	1.29542	0.647712	−	0.761886i	$-0.275726\pi$
$29$	6.97607	1.29542	0.647712	+	0.761886i	$0.275726\pi$
$30$	12.7625	2.33011
$31$	−0.537433	−0.0965258	−0.0482629	−	0.998835i	$-0.515369\pi$
$31$	−0.537433	−0.0965258	−0.0482629	+	0.998835i	$0.515369\pi$
$32$	−11.9171	−2.10666
$33$	−6.15364	−1.07121
$34$	4.28459	0.734802
$35$	9.77478	1.65224
$36$	17.9592	2.99320
$37$	4.57588	0.752270	0.376135	−	0.926565i	$-0.377253\pi$
$37$	4.57588	0.752270	0.376135	+	0.926565i	$0.377253\pi$
$38$	15.3708	2.49347
$39$	−3.84740	−0.616077
$40$	14.4546	2.28547
$41$	−10.2985	−1.60835	−0.804175	−	0.594392i	$-0.797393\pi$
$41$	−10.2985	−1.60835	−0.804175	+	0.594392i	$0.797393\pi$
$42$	35.2471	5.43874
$43$	−1.45623	−0.222073	−0.111037	−	0.993816i	$-0.535417\pi$
$43$	−1.45623	−0.222073	−0.111037	+	0.993816i	$0.535417\pi$
$44$	−11.7421	−1.77020
$45$	−6.86637	−1.02358
$46$	4.56217	0.672656
$47$	5.01724	0.731840	0.365920	−	0.930646i	$-0.380754\pi$
$47$	5.01724	0.731840	0.365920	+	0.930646i	$0.380754\pi$
$48$	26.7444	3.86023
$49$	19.9957	2.85652
$50$	3.84262	0.543428
$51$	−4.19992	−0.588107
$52$	−7.34146	−1.01808
$53$	9.61811	1.32115	0.660575	−	0.750760i	$-0.270313\pi$
$53$	9.61811	1.32115	0.660575	+	0.750760i	$0.270313\pi$
$54$	−4.40805	−0.599860
$55$	4.48940	0.605351
$56$	39.9203	5.33457
$57$	−15.0670	−1.99567
$58$	−18.3520	−2.40973
$59$	−2.80946	−0.365761	−0.182881	−	0.983135i	$-0.558542\pi$
$59$	−2.80946	−0.365761	−0.182881	+	0.983135i	$0.558542\pi$
$60$	−23.8717	−3.08182
$61$	−9.67030	−1.23816	−0.619078	−	0.785330i	$-0.712493\pi$
$61$	−9.67030	−1.23816	−0.619078	+	0.785330i	$0.712493\pi$
$62$	1.41383	0.179556
$63$	−18.9633	−2.38915
$64$	10.6078	1.32598
$65$	2.80688	0.348150
$66$	16.1884	1.99266
$67$	−4.15099	−0.507124	−0.253562	−	0.967319i	$-0.581602\pi$
$67$	−4.15099	−0.507124	−0.253562	+	0.967319i	$0.581602\pi$
$68$	−8.01413	−0.971856
$69$	−4.47202	−0.538368
$70$	−25.7146	−3.07348
$71$	−9.14923	−1.08581	−0.542907	−	0.839793i	$-0.682676\pi$
$71$	−9.14923	−1.08581	−0.542907	+	0.839793i	$0.682676\pi$
$72$	−28.0423	−3.30482
$73$	−3.83807	−0.449212	−0.224606	−	0.974450i	$-0.572110\pi$
$73$	−3.83807	−0.449212	−0.224606	+	0.974450i	$0.572110\pi$
$74$	−12.0378	−1.39937
$75$	−3.76668	−0.434939
$76$	−28.7503	−3.29789
$77$	12.3987	1.41296
$78$	10.1214	1.14602
$79$	1.17242	0.131908	0.0659539	−	0.997823i	$-0.478991\pi$
$79$	1.17242	0.131908	0.0659539	+	0.997823i	$0.478991\pi$
$80$	−19.5114	−2.18145
$81$	−6.62842	−0.736491
$82$	27.0922	2.99184
$83$	16.3741	1.79729	0.898647	−	0.438674i	$-0.144552\pi$
$83$	16.3741	1.79729	0.898647	+	0.438674i	$0.144552\pi$
$84$	−65.9280	−7.19334
$85$	3.06406	0.332344
$86$	3.83092	0.413099
$87$	17.9893	1.92866
$88$	18.3347	1.95449
$89$	15.3462	1.62669	0.813345	−	0.581782i	$-0.197644\pi$
$89$	15.3462	1.62669	0.813345	+	0.581782i	$0.197644\pi$
$90$	18.0634	1.90405
$91$	7.75194	0.812624
$92$	−8.53334	−0.889662
$93$	−1.38589	−0.143710
$94$	−13.1989	−1.36136
$95$	10.9922	1.12777
$96$	−30.7307	−3.13644
$97$	7.15550	0.726531	0.363266	−	0.931686i	$-0.381662\pi$
$97$	7.15550	0.726531	0.363266	+	0.931686i	$0.381662\pi$
$98$	−52.6027	−5.31368
$99$	−8.70955	−0.875343
$100$	−7.18743	−0.718743
$101$	−15.0255	−1.49509	−0.747545	−	0.664211i	$-0.768768\pi$
$101$	−15.0255	−1.49509	−0.747545	+	0.664211i	$0.768768\pi$
$102$	11.0488	1.09399
$103$	−16.9391	−1.66906	−0.834531	−	0.550961i	$-0.814261\pi$
$103$	−16.9391	−1.66906	−0.834531	+	0.550961i	$0.814261\pi$
$104$	11.4633	1.12407
$105$	25.2064	2.45989
$106$	−25.3024	−2.45759
$107$	5.15097	0.497963	0.248981	−	0.968508i	$-0.419904\pi$
$107$	5.15097	0.497963	0.248981	+	0.968508i	$0.419904\pi$
$108$	8.24505	0.793381
$109$	−7.31183	−0.700346	−0.350173	−	0.936685i	$-0.613877\pi$
$109$	−7.31183	−0.700346	−0.350173	+	0.936685i	$0.613877\pi$
$110$	−11.8103	−1.12607
$111$	11.7999	1.12000
$112$	−53.8861	−5.09175
$113$	20.8908	1.96525	0.982623	−	0.185614i	$-0.0594274\pi$
$113$	20.8908	1.96525	0.982623	+	0.185614i	$0.0594274\pi$
$114$	39.6369	3.71233
$115$	3.26257	0.304236
$116$	34.3265	3.18714
$117$	−5.44541	−0.503428
$118$	7.39088	0.680385
$119$	8.46222	0.775730
$120$	37.2744	3.40267
$121$	−5.30549	−0.482317
$122$	25.4397	2.30320
$123$	−26.5568	−2.39455
$124$	−2.64450	−0.237483
$125$	12.1545	1.08713
$126$	49.8869	4.44428
$127$	5.18532	0.460122	0.230061	−	0.973176i	$-0.426107\pi$
$127$	5.18532	0.460122	0.230061	+	0.973176i	$0.426107\pi$
$128$	−4.07201	−0.359918
$129$	−3.75521	−0.330628
$130$	−7.38407	−0.647625
$131$	−4.26329	−0.372485	−0.186243	−	0.982504i	$-0.559631\pi$
$131$	−4.26329	−0.372485	−0.186243	+	0.982504i	$0.559631\pi$
$132$	−30.2797	−2.63551
$133$	30.3578	2.63235
$134$	10.9200	0.943347
$135$	−3.15235	−0.271311
$136$	12.5136	1.07304
$137$	−0.905625	−0.0773727	−0.0386864	−	0.999251i	$-0.512317\pi$
$137$	−0.905625	−0.0773727	−0.0386864	+	0.999251i	$0.512317\pi$
$138$	11.7646	1.00147
$139$	11.4149	0.968198	0.484099	−	0.875013i	$-0.339147\pi$
$139$	11.4149	0.968198	0.484099	+	0.875013i	$0.339147\pi$
$140$	48.0979	4.06502
$141$	12.9380	1.08958
$142$	24.0689	2.01982
$143$	3.56034	0.297731
$144$	37.8527	3.15439
$145$	−13.1241	−1.08990
$146$	10.0968	0.835620
$147$	51.5632	4.25286
$148$	22.5161	1.85082
$149$	0.763666	0.0625619	0.0312810	−	0.999511i	$-0.490041\pi$
$149$	0.763666	0.0625619	0.0312810	+	0.999511i	$0.490041\pi$
$150$	9.90902	0.809068
$151$	11.4798	0.934211	0.467105	−	0.884202i	$-0.345297\pi$
$151$	11.4798	0.934211	0.467105	+	0.884202i	$0.345297\pi$
$152$	44.8921	3.64123
$153$	−5.94435	−0.480573
$154$	−32.6173	−2.62837
$155$	1.01108	0.0812117
$156$	−18.9316	−1.51574
$157$	6.40914	0.511505	0.255752	−	0.966742i	$-0.417677\pi$
$157$	6.40914	0.511505	0.255752	+	0.966742i	$0.417677\pi$
$158$	−3.08430	−0.245374
$159$	24.8024	1.96696
$160$	22.4197	1.77243
$161$	9.01045	0.710123
$162$	17.4374	1.37001
$163$	10.0008	0.783320	0.391660	−	0.920110i	$-0.371901\pi$
$163$	10.0008	0.783320	0.391660	+	0.920110i	$0.371901\pi$
$164$	−50.6748	−3.95704
$165$	11.5769	0.901260
$166$	−43.0755	−3.34331
$167$	19.5792	1.51509	0.757544	−	0.652785i	$-0.226399\pi$
$167$	19.5792	1.51509	0.757544	+	0.652785i	$0.226399\pi$
$168$	102.943	7.94223
$169$	−10.7740	−0.828769
$170$	−8.06064	−0.618223
$171$	−21.3251	−1.63077
$172$	−7.16556	−0.546369
$173$	13.3702	1.01652	0.508259	−	0.861204i	$-0.330289\pi$
$173$	13.3702	1.01652	0.508259	+	0.861204i	$0.330289\pi$
$174$	−47.3246	−3.58767
$175$	7.58930	0.573697
$176$	−24.7490	−1.86553
$177$	−7.24482	−0.544554
$178$	−40.3712	−3.02595
$179$	−24.8686	−1.85877	−0.929385	−	0.369113i	$-0.879662\pi$
$179$	−24.8686	−1.85877	−0.929385	+	0.369113i	$0.879662\pi$
$180$	−33.7868	−2.51832
$181$	13.0404	0.969285	0.484643	−	0.874712i	$-0.338950\pi$
$181$	13.0404	0.969285	0.484643	+	0.874712i	$0.338950\pi$
$182$	−20.3931	−1.51163
$183$	−24.9370	−1.84339
$184$	13.3243	0.982284
$185$	−8.60864	−0.632920
$186$	3.64586	0.267328
$187$	3.88656	0.284214
$188$	24.6879	1.80055
$189$	−8.70605	−0.633272
$190$	−28.9171	−2.09787
$191$	0.713105	0.0515985	0.0257992	−	0.999667i	$-0.491787\pi$
$191$	0.713105	0.0515985	0.0257992	+	0.999667i	$0.491787\pi$
$192$	27.3546	1.97415
$193$	−14.0872	−1.01402	−0.507009	−	0.861941i	$-0.669249\pi$
$193$	−14.0872	−1.01402	−0.507009	+	0.861941i	$0.669249\pi$
$194$	−18.8240	−1.35149
$195$	7.23814	0.518334
$196$	98.3909	7.02792
$197$	8.52399	0.607309	0.303655	−	0.952782i	$-0.401793\pi$
$197$	8.52399	0.607309	0.303655	+	0.952782i	$0.401793\pi$
$198$	22.9123	1.62830
$199$	6.81923	0.483402	0.241701	−	0.970351i	$-0.422295\pi$
$199$	6.81923	0.483402	0.241701	+	0.970351i	$0.422295\pi$
$200$	11.2228	0.793572
$201$	−10.7042	−0.755018
$202$	39.5276	2.78115
$203$	−36.2458	−2.54396
$204$	−20.6662	−1.44692
$205$	19.3746	1.35318
$206$	44.5619	3.10477
$207$	−6.32946	−0.439928
$208$	−15.4736	−1.07290
$209$	13.9428	0.964447
$210$	−66.3106	−4.57587
$211$	−4.43404	−0.305252	−0.152626	−	0.988284i	$-0.548773\pi$
$211$	−4.43404	−0.305252	−0.152626	+	0.988284i	$0.548773\pi$
$212$	47.3270	3.25043
$213$	−23.5933	−1.61658
$214$	−13.5507	−0.926305
$215$	2.73962	0.186841
$216$	−12.8742	−0.875979
$217$	2.79236	0.189558
$218$	19.2353	1.30278
$219$	−9.89730	−0.668797
$220$	22.0906	1.48935
$221$	2.42997	0.163457
$222$	−31.0421	−2.08341
$223$	−12.0251	−0.805259	−0.402629	−	0.915363i	$-0.631904\pi$
$223$	−12.0251	−0.805259	−0.402629	+	0.915363i	$0.631904\pi$
$224$	61.9179	4.13706
$225$	−5.33116	−0.355411
$226$	−54.9577	−3.65573
$227$	0.292622	0.0194220	0.00971101	−	0.999953i	$-0.496909\pi$
$227$	0.292622	0.0194220	0.00971101	+	0.999953i	$0.496909\pi$
$228$	−74.1389	−4.90997
$229$	16.8685	1.11470	0.557350	−	0.830277i	$-0.311818\pi$
$229$	16.8685	1.11470	0.557350	+	0.830277i	$0.311818\pi$
$230$	−8.58286	−0.565937
$231$	31.9727	2.10365
$232$	−53.5991	−3.51895
$233$	4.70627	0.308318	0.154159	−	0.988046i	$-0.450733\pi$
$233$	4.70627	0.308318	0.154159	+	0.988046i	$0.450733\pi$
$234$	14.3253	0.936473
$235$	−9.43897	−0.615731
$236$	−13.8243	−0.899885
$237$	3.02335	0.196388
$238$	−22.2616	−1.44301
$239$	−23.0029	−1.48793	−0.743966	−	0.668218i	$-0.767058\pi$
$239$	−23.0029	−1.48793	−0.743966	+	0.668218i	$0.767058\pi$
$240$	−50.3145	−3.24779
$241$	3.72857	0.240179	0.120089	−	0.992763i	$-0.461682\pi$
$241$	3.72857	0.240179	0.120089	+	0.992763i	$0.461682\pi$
$242$	13.9572	0.897201
$243$	−22.1197	−1.41898
$244$	−47.5838	−3.04624
$245$	−37.6180	−2.40333
$246$	69.8633	4.45432
$247$	8.71739	0.554674
$248$	4.12925	0.262207
$249$	42.2242	2.67585
$250$	−31.9750	−2.02228
$251$	−10.8855	−0.687086	−0.343543	−	0.939137i	$-0.611627\pi$
$251$	−10.8855	−0.687086	−0.343543	+	0.939137i	$0.611627\pi$
$252$	−93.3112	−5.87805
$253$	4.13836	0.260176
$254$	−13.6410	−0.855915
$255$	7.90135	0.494801
$256$	−10.5034	−0.656464
$257$	9.52337	0.594052	0.297026	−	0.954869i	$-0.404005\pi$
$257$	9.52337	0.594052	0.297026	+	0.954869i	$0.404005\pi$
$258$	9.87886	0.615031
$259$	−23.7751	−1.47731
$260$	13.8116	0.856556
$261$	25.4612	1.57601
$262$	11.2155	0.692893
$263$	26.4678	1.63207	0.816037	−	0.578000i	$-0.196167\pi$
$263$	26.4678	1.63207	0.816037	+	0.578000i	$0.196167\pi$
$264$	47.2801	2.90989
$265$	−18.0946	−1.11154
$266$	−79.8624	−4.89668
$267$	39.5734	2.42185
$268$	−20.4254	−1.24768
$269$	8.53934	0.520653	0.260327	−	0.965521i	$-0.416170\pi$
$269$	8.53934	0.520653	0.260327	+	0.965521i	$0.416170\pi$
$270$	8.29290	0.504690
$271$	18.2190	1.10673	0.553364	−	0.832940i	$-0.313344\pi$
$271$	18.2190	1.10673	0.553364	+	0.832940i	$0.313344\pi$
$272$	−16.8914	−1.02419
$273$	19.9901	1.20985
$274$	2.38243	0.143928
$275$	3.48564	0.210192
$276$	−22.0051	−1.32455
$277$	−4.46205	−0.268099	−0.134049	−	0.990975i	$-0.542798\pi$
$277$	−4.46205	−0.268099	−0.134049	+	0.990975i	$0.542798\pi$
$278$	−30.0292	−1.80103
$279$	−1.96152	−0.117433
$280$	−75.1023	−4.48822
$281$	−8.84325	−0.527544	−0.263772	−	0.964585i	$-0.584967\pi$
$281$	−8.84325	−0.527544	−0.263772	+	0.964585i	$0.584967\pi$
$282$	−34.0362	−2.02683
$283$	−3.26057	−0.193821	−0.0969104	−	0.995293i	$-0.530896\pi$
$283$	−3.26057	−0.193821	−0.0969104	+	0.995293i	$0.530896\pi$
$284$	−45.0198	−2.67143
$285$	28.3457	1.67905
$286$	−9.36621	−0.553836
$287$	53.5081	3.15848
$288$	−43.4947	−2.56295
$289$	−14.3474	−0.843964
$290$	34.5257	2.02742
$291$	18.4520	1.08168
$292$	−18.8857	−1.10520
$293$	−2.42903	−0.141906	−0.0709528	−	0.997480i	$-0.522604\pi$
$293$	−2.42903	−0.141906	−0.0709528	+	0.997480i	$0.522604\pi$
$294$	−135.648	−7.91113
$295$	5.28547	0.307732
$296$	−35.1578	−2.04350
$297$	−3.99855	−0.232019
$298$	−2.00898	−0.116377
$299$	2.58740	0.149633
$300$	−18.5344	−1.07008
$301$	7.56620	0.436109
$302$	−30.1999	−1.73781
$303$	−38.7464	−2.22592
$304$	−60.5972	−3.47549
$305$	18.1928	1.04172
$306$	15.6378	0.893956
$307$	2.78603	0.159007	0.0795036	−	0.996835i	$-0.474666\pi$
$307$	2.78603	0.159007	0.0795036	+	0.996835i	$0.474666\pi$
$308$	61.0091	3.47632
$309$	−43.6812	−2.48494
$310$	−2.65985	−0.151069
$311$	14.3571	0.814117	0.407058	−	0.913402i	$-0.366555\pi$
$311$	14.3571	0.814117	0.407058	+	0.913402i	$0.366555\pi$
$312$	29.5606	1.67354
$313$	−17.6347	−0.996770	−0.498385	−	0.866956i	$-0.666073\pi$
$313$	−17.6347	−0.996770	−0.498385	+	0.866956i	$0.666073\pi$
$314$	−16.8606	−0.951496
$315$	35.6759	2.01011
$316$	5.76904	0.324534
$317$	29.2835	1.64473	0.822363	−	0.568963i	$-0.192655\pi$
$317$	29.2835	1.64473	0.822363	+	0.568963i	$0.192655\pi$
$318$	−65.2478	−3.65892
$319$	−16.6471	−0.932060
$320$	−19.9566	−1.11561
$321$	13.2829	0.741379
$322$	−23.7038	−1.32096
$323$	9.51613	0.529492
$324$	−32.6159	−1.81199
$325$	2.17930	0.120886
$326$	−26.3090	−1.45712
$327$	−18.8552	−1.04269
$328$	79.1260	4.36900
$329$	−26.0682	−1.43719
$330$	−30.4554	−1.67652
$331$	−13.9913	−0.769032	−0.384516	−	0.923118i	$-0.625632\pi$
$331$	−13.9913	−0.769032	−0.384516	+	0.923118i	$0.625632\pi$
$332$	80.5707	4.42189
$333$	16.7010	0.915209
$334$	−51.5072	−2.81835
$335$	7.80929	0.426667
$336$	−138.957	−7.58072
$337$	−15.6645	−0.853299	−0.426650	−	0.904417i	$-0.640306\pi$
$337$	−15.6645	−0.853299	−0.426650	+	0.904417i	$0.640306\pi$
$338$	28.3432	1.54167
$339$	53.8716	2.92590
$340$	15.0771	0.817668
$341$	1.28249	0.0694505
$342$	56.1000	3.03354
$343$	−67.5220	−3.64585
$344$	11.1886	0.603251
$345$	8.41324	0.452954
$346$	−35.1731	−1.89092
$347$	−14.9588	−0.803031	−0.401515	−	0.915852i	$-0.631516\pi$
$347$	−14.9588	−0.803031	−0.401515	+	0.915852i	$0.631516\pi$
$348$	88.5185	4.74509
$349$	23.1858	1.24111	0.620555	−	0.784163i	$-0.286907\pi$
$349$	23.1858	1.24111	0.620555	+	0.784163i	$0.286907\pi$
$350$	−19.9652	−1.06719
$351$	−2.49999	−0.133439
$352$	28.4379	1.51574
$353$	28.8079	1.53329	0.766645	−	0.642072i	$-0.221925\pi$
$353$	28.8079	1.53329	0.766645	+	0.642072i	$0.221925\pi$
$354$	19.0590	1.01297
$355$	17.2125	0.913546
$356$	75.5125	4.00216
$357$	21.8217	1.15493
$358$	65.4221	3.45766
$359$	16.1183	0.850693	0.425346	−	0.905031i	$-0.360152\pi$
$359$	16.1183	0.850693	0.425346	+	0.905031i	$0.360152\pi$
$360$	52.7562	2.78050
$361$	15.1386	0.796770
$362$	−34.3055	−1.80305
$363$	−13.6814	−0.718085
$364$	38.1443	1.99930
$365$	7.22059	0.377943
$366$	65.6019	3.42906
$367$	−4.14453	−0.216343	−0.108171	−	0.994132i	$-0.534500\pi$
$367$	−4.14453	−0.216343	−0.108171	+	0.994132i	$0.534500\pi$
$368$	−17.9858	−0.937573
$369$	−37.5872	−1.95671
$370$	22.6468	1.17735
$371$	−49.9732	−2.59448
$372$	−6.81942	−0.353570
$373$	0.618856	0.0320432	0.0160216	−	0.999872i	$-0.494900\pi$
$373$	0.618856	0.0320432	0.0160216	+	0.999872i	$0.494900\pi$
$374$	−10.2244	−0.528691
$375$	31.3431	1.61855
$376$	−38.5488	−1.98800
$377$	−10.4082	−0.536048
$378$	22.9031	1.17801
$379$	−34.5814	−1.77633	−0.888163	−	0.459528i	$-0.848018\pi$
$379$	−34.5814	−1.77633	−0.888163	+	0.459528i	$0.848018\pi$
$380$	54.0882	2.77466
$381$	13.3715	0.685041
$382$	−1.87597	−0.0959830
$383$	−26.5601	−1.35716	−0.678579	−	0.734527i	$-0.737404\pi$
$383$	−26.5601	−1.35716	−0.678579	+	0.734527i	$0.737404\pi$
$384$	−10.5006	−0.535855
$385$	−23.3257	−1.18879
$386$	37.0593	1.88627
$387$	−5.31494	−0.270173
$388$	35.2095	1.78749
$389$	10.2333	0.518848	0.259424	−	0.965763i	$-0.416467\pi$
$389$	10.2333	0.518848	0.259424	+	0.965763i	$0.416467\pi$
$390$	−19.0414	−0.964200
$391$	2.82447	0.142840
$392$	−153.632	−7.75960
$393$	−10.9938	−0.554565
$394$	−22.4241	−1.12971
$395$	−2.20569	−0.110980
$396$	−42.8563	−2.15361
$397$	−25.1226	−1.26087	−0.630435	−	0.776242i	$-0.717123\pi$
$397$	−25.1226	−1.26087	−0.630435	+	0.776242i	$0.717123\pi$
$398$	−17.9394	−0.899220
$399$	78.2842	3.91911
$400$	−15.1490	−0.757450
$401$	6.98287	0.348708	0.174354	−	0.984683i	$-0.444216\pi$
$401$	6.98287	0.348708	0.174354	+	0.984683i	$0.444216\pi$
$402$	28.1597	1.40448
$403$	0.801840	0.0399425
$404$	−73.9345	−3.67838
$405$	12.4701	0.619644
$406$	95.3521	4.73224
$407$	−10.9195	−0.541260
$408$	32.2691	1.59756
$409$	19.5955	0.968934	0.484467	−	0.874809i	$-0.339014\pi$
$409$	19.5955	0.968934	0.484467	+	0.874809i	$0.339014\pi$
$410$	−50.9689	−2.51717
$411$	−2.33535	−0.115194
$412$	−83.3509	−4.10640
$413$	14.5972	0.718283
$414$	16.6510	0.818350
$415$	−30.8048	−1.51215
$416$	17.7800	0.871737
$417$	29.4358	1.44148
$418$	−36.6795	−1.79405
$419$	−25.5195	−1.24671	−0.623355	−	0.781939i	$-0.714231\pi$
$419$	−25.5195	−1.24671	−0.623355	+	0.781939i	$0.714231\pi$
$420$	124.031	6.05209
$421$	18.9026	0.921256	0.460628	−	0.887593i	$-0.347624\pi$
$421$	18.9026	0.921256	0.460628	+	0.887593i	$0.347624\pi$
$422$	11.6646	0.567826
$423$	18.3118	0.890353
$424$	−73.8986	−3.58883
$425$	2.37899	0.115398
$426$	62.0670	3.00715
$427$	50.2443	2.43149
$428$	25.3459	1.22514
$429$	9.18111	0.443268
$430$	−7.20714	−0.347559
$431$	−2.12608	−0.102410	−0.0512049	−	0.998688i	$-0.516306\pi$
$431$	−2.12608	−0.102410	−0.0512049	+	0.998688i	$0.516306\pi$
$432$	17.3782	0.836107
$433$	14.4247	0.693205	0.346603	−	0.938012i	$-0.387335\pi$
$433$	14.4247	0.693205	0.346603	+	0.938012i	$0.387335\pi$
$434$	−7.34588	−0.352613
$435$	−33.8434	−1.62267
$436$	−35.9787	−1.72307
$437$	10.1326	0.484710
$438$	26.0369	1.24409
$439$	−5.30809	−0.253341	−0.126671	−	0.991945i	$-0.540429\pi$
$439$	−5.30809	−0.253341	−0.126671	+	0.991945i	$0.540429\pi$
$440$	−34.4933	−1.64440
$441$	72.9799	3.47523
$442$	−6.39253	−0.304062
$443$	−16.2659	−0.772819	−0.386409	−	0.922327i	$-0.626285\pi$
$443$	−16.2659	−0.772819	−0.386409	+	0.922327i	$0.626285\pi$
$444$	58.0628	2.75554
$445$	−28.8709	−1.36861
$446$	31.6344	1.49793
$447$	1.96928	0.0931437
$448$	−55.1156	−2.60397
$449$	32.6158	1.53924	0.769618	−	0.638504i	$-0.220447\pi$
$449$	32.6158	1.53924	0.769618	+	0.638504i	$0.220447\pi$
$450$	14.0247	0.661132
$451$	24.5754	1.15721
$452$	102.796	4.83511
$453$	29.6031	1.39088
$454$	−0.769803	−0.0361286
$455$	−14.5838	−0.683698
$456$	115.764	5.42114
$457$	−37.0849	−1.73476	−0.867380	−	0.497646i	$-0.834198\pi$
$457$	−37.0849	−1.73476	−0.867380	+	0.497646i	$0.834198\pi$
$458$	−44.3760	−2.07355
$459$	−2.72905	−0.127381
$460$	16.0538	0.748514
$461$	−42.0065	−1.95644	−0.978219	−	0.207575i	$-0.933443\pi$
$461$	−42.0065	−1.95644	−0.978219	+	0.207575i	$0.933443\pi$
$462$	−84.1107	−3.91319
$463$	−2.02304	−0.0940187	−0.0470093	−	0.998894i	$-0.514969\pi$
$463$	−2.02304	−0.0940187	−0.0470093	+	0.998894i	$0.514969\pi$
$464$	72.3503	3.35878
$465$	2.60728	0.120910
$466$	−12.3808	−0.573530
$467$	−15.7542	−0.729016	−0.364508	−	0.931200i	$-0.618763\pi$
$467$	−15.7542	−0.729016	−0.364508	+	0.931200i	$0.618763\pi$
$468$	−26.7948	−1.23859
$469$	21.5674	0.995892
$470$	24.8312	1.14538
$471$	16.5274	0.761541
$472$	21.5859	0.993571
$473$	3.47503	0.159782
$474$	−7.95354	−0.365318
$475$	8.53449	0.391589
$476$	41.6393	1.90853
$477$	35.1040	1.60730
$478$	60.5138	2.76784
$479$	25.7390	1.17605	0.588023	−	0.808844i	$-0.299906\pi$
$479$	25.7390	1.17605	0.588023	+	0.808844i	$0.299906\pi$
$480$	57.8140	2.63883
$481$	−6.82713	−0.311290
$482$	−9.80878	−0.446778
$483$	23.2354	1.05725
$484$	−26.1063	−1.18665
$485$	−13.4617	−0.611265
$486$	58.1903	2.63957
$487$	37.7771	1.71184	0.855921	−	0.517107i	$-0.172991\pi$
$487$	37.7771	1.71184	0.855921	+	0.517107i	$0.172991\pi$
$488$	74.2996	3.36338
$489$	25.7891	1.16622
$490$	98.9619	4.47064
$491$	−30.2872	−1.36684	−0.683422	−	0.730024i	$-0.739509\pi$
$491$	−30.2872	−1.36684	−0.683422	+	0.730024i	$0.739509\pi$
$492$	−130.676	−5.89133
$493$	−11.3618	−0.511711
$494$	−22.9329	−1.03180
$495$	16.3853	0.736467
$496$	−5.57383	−0.250272
$497$	47.5370	2.13232
$498$	−111.080	−4.97759
$499$	−39.0529	−1.74825	−0.874125	−	0.485701i	$-0.838564\pi$
$499$	−39.0529	−1.74825	−0.874125	+	0.485701i	$0.838564\pi$
$500$	59.8077	2.67468
$501$	50.4893	2.25570
$502$	28.6365	1.27811
$503$	33.1690	1.47893	0.739465	−	0.673195i	$-0.235078\pi$
$503$	33.1690	1.47893	0.739465	+	0.673195i	$0.235078\pi$
$504$	145.700	6.49001
$505$	28.2675	1.25789
$506$	−10.8868	−0.483977
$507$	−27.7831	−1.23389
$508$	25.5149	1.13204
$509$	2.44491	0.108369	0.0541843	−	0.998531i	$-0.482744\pi$
$509$	2.44491	0.108369	0.0541843	+	0.998531i	$0.482744\pi$
$510$	−20.7861	−0.920425
$511$	19.9416	0.882164
$512$	35.7754	1.58107
$513$	−9.79033	−0.432254
$514$	−25.0532	−1.10505
$515$	31.8677	1.40426
$516$	−18.4780	−0.813447
$517$	−11.9727	−0.526560
$518$	62.5452	2.74808
$519$	34.4780	1.51342
$520$	−21.5660	−0.945732
$521$	−10.0990	−0.442447	−0.221223	−	0.975223i	$-0.571005\pi$
$521$	−10.0990	−0.442447	−0.221223	+	0.975223i	$0.571005\pi$
$522$	−66.9808	−2.93167
$523$	12.5025	0.546697	0.273349	−	0.961915i	$-0.411869\pi$
$523$	12.5025	0.546697	0.273349	+	0.961915i	$0.411869\pi$
$524$	−20.9780	−0.916428
$525$	19.5707	0.854134
$526$	−69.6290	−3.03597
$527$	0.875309	0.0381291
$528$	−63.8207	−2.77744
$529$	−19.9925	−0.869241
$530$	47.6017	2.06768
$531$	−10.2539	−0.444983
$532$	149.379	6.47640
$533$	15.3651	0.665537
$534$	−104.106	−4.50511
$535$	−9.69056	−0.418959
$536$	31.8932	1.37758
$537$	−64.1292	−2.76738
$538$	−22.4645	−0.968514
$539$	−47.7160	−2.05527
$540$	−15.5115	−0.667508
$541$	19.8871	0.855012	0.427506	−	0.904012i	$-0.359392\pi$
$541$	19.8871	0.855012	0.427506	+	0.904012i	$0.359392\pi$
$542$	−47.9289	−2.05872
$543$	33.6275	1.44309
$544$	19.4091	0.832160
$545$	13.7558	0.589234
$546$	−52.5880	−2.25056
$547$	12.4081	0.530532	0.265266	−	0.964175i	$-0.414540\pi$
$547$	12.4081	0.530532	0.265266	+	0.964175i	$0.414540\pi$
$548$	−4.45623	−0.190361
$549$	−35.2945	−1.50633
$550$	−9.16970	−0.390997
$551$	−40.7600	−1.73643
$552$	34.3597	1.46245
$553$	−6.09160	−0.259041
$554$	11.7384	0.498715
$555$	−22.1993	−0.942306
$556$	56.1682	2.38206
$557$	35.1163	1.48792	0.743962	−	0.668222i	$-0.232944\pi$
$557$	35.1163	1.48792	0.743962	+	0.668222i	$0.232944\pi$
$558$	5.16017	0.218447
$559$	2.17267	0.0918942
$560$	101.376	4.28393
$561$	10.0223	0.423144
$562$	23.2640	0.981332
$563$	−22.6183	−0.953247	−0.476624	−	0.879108i	$-0.658140\pi$
$563$	−22.6183	−0.953247	−0.476624	+	0.879108i	$0.658140\pi$
$564$	63.6631	2.68070
$565$	−39.3021	−1.65345
$566$	8.57760	0.360543
$567$	34.4395	1.44632
$568$	70.2960	2.94956
$569$	22.8212	0.956714	0.478357	−	0.878165i	$-0.341232\pi$
$569$	22.8212	0.956714	0.478357	+	0.878165i	$0.341232\pi$
$570$	−74.5691	−3.12336
$571$	31.3680	1.31271	0.656356	−	0.754451i	$-0.272097\pi$
$571$	31.3680	1.31271	0.656356	+	0.754451i	$0.272097\pi$
$572$	17.5191	0.732509
$573$	1.83890	0.0768210
$574$	−140.764	−5.87538
$575$	2.53311	0.105638
$576$	38.7164	1.61318
$577$	−1.13044	−0.0470607	−0.0235303	−	0.999723i	$-0.507491\pi$
$577$	−1.13044	−0.0470607	−0.0235303	+	0.999723i	$0.507491\pi$
$578$	37.7437	1.56993
$579$	−36.3269	−1.50969
$580$	−64.5788	−2.68149
$581$	−85.0756	−3.52953
$582$	−48.5418	−2.01212
$583$	−22.9519	−0.950569
$584$	29.4889	1.22026
$585$	10.2445	0.423558
$586$	6.39007	0.263971
$587$	13.3150	0.549569	0.274785	−	0.961506i	$-0.411393\pi$
$587$	13.3150	0.549569	0.274785	+	0.961506i	$0.411393\pi$
$588$	253.722	10.4633
$589$	3.14013	0.129387
$590$	−13.9045	−0.572440
$591$	21.9810	0.904176
$592$	47.4574	1.95049
$593$	−23.2620	−0.955254	−0.477627	−	0.878563i	$-0.658503\pi$
$593$	−23.2620	−0.955254	−0.477627	+	0.878563i	$0.658503\pi$
$594$	10.5190	0.431600
$595$	−15.9200	−0.652658
$596$	3.75770	0.153922
$597$	17.5849	0.719701
$598$	−6.80668	−0.278346
$599$	−34.6224	−1.41463	−0.707317	−	0.706896i	$-0.750095\pi$
$599$	−34.6224	−1.41463	−0.707317	+	0.706896i	$0.750095\pi$
$600$	28.9404	1.18149
$601$	−5.35627	−0.218487	−0.109243	−	0.994015i	$-0.534843\pi$
$601$	−5.35627	−0.218487	−0.109243	+	0.994015i	$0.534843\pi$
$602$	−19.9044	−0.811245
$603$	−15.1502	−0.616965
$604$	56.4875	2.29845
$605$	9.98126	0.405796
$606$	101.930	4.14064
$607$	−27.1448	−1.10178	−0.550888	−	0.834579i	$-0.685711\pi$
$607$	−27.1448	−1.10178	−0.550888	+	0.834579i	$0.685711\pi$
$608$	69.6293	2.82384
$609$	−93.4677	−3.78750
$610$	−47.8600	−1.93779
$611$	−7.48563	−0.302836
$612$	−29.2499	−1.18236
$613$	12.2180	0.493480	0.246740	−	0.969082i	$-0.420641\pi$
$613$	12.2180	0.493480	0.246740	+	0.969082i	$0.420641\pi$
$614$	−7.32923	−0.295783
$615$	49.9616	2.01465
$616$	−95.2624	−3.83823
$617$	12.2204	0.491975	0.245987	−	0.969273i	$-0.420888\pi$
$617$	12.2204	0.491975	0.245987	+	0.969273i	$0.420888\pi$
$618$	114.912	4.62246
$619$	7.24260	0.291105	0.145552	−	0.989351i	$-0.453504\pi$
$619$	7.24260	0.291105	0.145552	+	0.989351i	$0.453504\pi$
$620$	4.97512	0.199806
$621$	−2.90585	−0.116608
$622$	−37.7693	−1.51441
$623$	−79.7346	−3.19450
$624$	−39.9022	−1.59737
$625$	−15.5630	−0.622521
$626$	46.3916	1.85418
$627$	35.9547	1.43589
$628$	31.5369	1.25846
$629$	−7.45267	−0.297158
$630$	−93.8527	−3.73918
$631$	−22.0512	−0.877844	−0.438922	−	0.898525i	$-0.644640\pi$
$631$	−22.0512	−0.877844	−0.438922	+	0.898525i	$0.644640\pi$
$632$	−9.00805	−0.358321
$633$	−11.4341	−0.454466
$634$	−77.0363	−3.05950
$635$	−9.75518	−0.387123
$636$	122.043	4.83932
$637$	−29.8331	−1.18203
$638$	43.7937	1.73381
$639$	−33.3927	−1.32100
$640$	7.66071	0.302816
$641$	20.8398	0.823123	0.411561	−	0.911382i	$-0.364984\pi$
$641$	20.8398	0.823123	0.411561	+	0.911382i	$0.364984\pi$
$642$	−34.9434	−1.37911
$643$	23.4145	0.923379	0.461689	−	0.887042i	$-0.347243\pi$
$643$	23.4145	0.923379	0.461689	+	0.887042i	$0.347243\pi$
$644$	44.3370	1.74712
$645$	7.06471	0.278173
$646$	−25.0341	−0.984955
$647$	37.6497	1.48016	0.740081	−	0.672518i	$-0.234787\pi$
$647$	37.6497	1.48016	0.740081	+	0.672518i	$0.234787\pi$
$648$	50.9280	2.00064
$649$	6.70428	0.263166
$650$	−5.73311	−0.224871
$651$	7.20071	0.282218
$652$	49.2099	1.92721
$653$	−15.4474	−0.604504	−0.302252	−	0.953228i	$-0.597738\pi$
$653$	−15.4474	−0.604504	−0.302252	+	0.953228i	$0.597738\pi$
$654$	49.6024	1.93961
$655$	8.02056	0.313389
$656$	−106.808	−4.17014
$657$	−14.0081	−0.546509
$658$	68.5779	2.67344
$659$	2.30952	0.0899661	0.0449831	−	0.998988i	$-0.485677\pi$
$659$	2.30952	0.0899661	0.0449831	+	0.998988i	$0.485677\pi$
$660$	56.9654	2.21738
$661$	−4.41238	−0.171622	−0.0858108	−	0.996311i	$-0.527348\pi$
$661$	−4.41238	−0.171622	−0.0858108	+	0.996311i	$0.527348\pi$
$662$	36.8070	1.43055
$663$	6.26620	0.243359
$664$	−125.807	−4.88225
$665$	−57.1124	−2.21472
$666$	−43.9354	−1.70246
$667$	−12.0979	−0.468433
$668$	96.3419	3.72758
$669$	−31.0093	−1.19889
$670$	−20.5439	−0.793682
$671$	23.0764	0.890855
$672$	159.669	6.15935
$673$	20.7020	0.798005	0.399003	−	0.916950i	$-0.369356\pi$
$673$	20.7020	0.798005	0.399003	+	0.916950i	$0.369356\pi$
$674$	41.2087	1.58730
$675$	−2.44753	−0.0942057
$676$	−53.0147	−2.03903
$677$	−40.3643	−1.55133	−0.775663	−	0.631148i	$-0.782584\pi$
$677$	−40.3643	−1.55133	−0.775663	+	0.631148i	$0.782584\pi$
$678$	−141.720	−5.44274
$679$	−37.1781	−1.42676
$680$	−23.5420	−0.902795
$681$	0.754590	0.0289160
$682$	−3.37384	−0.129191
$683$	−30.9344	−1.18367	−0.591837	−	0.806058i	$-0.701597\pi$
$683$	−30.9344	−1.18367	−0.591837	+	0.806058i	$0.701597\pi$
$684$	−104.932	−4.01219
$685$	1.70376	0.0650973
$686$	177.631	6.78197
$687$	43.4991	1.65959
$688$	−15.1029	−0.575793
$689$	−14.3500	−0.546693
$690$	−22.1328	−0.842580
$691$	−19.3918	−0.737700	−0.368850	−	0.929489i	$-0.620248\pi$
$691$	−19.3918	−0.737700	−0.368850	+	0.929489i	$0.620248\pi$
$692$	65.7896	2.50095
$693$	45.2525	1.71900
$694$	39.3522	1.49379
$695$	−21.4749	−0.814590
$696$	−138.217	−5.23910
$697$	16.7730	0.635321
$698$	−60.9951	−2.30870
$699$	12.1361	0.459031
$700$	37.3440	1.41147
$701$	26.5665	1.00340	0.501701	−	0.865041i	$-0.332708\pi$
$701$	26.5665	1.00340	0.501701	+	0.865041i	$0.332708\pi$
$702$	6.57673	0.248223
$703$	−26.7361	−1.00837
$704$	−25.3137	−0.954046
$705$	−24.3405	−0.916714
$706$	−75.7851	−2.85221
$707$	78.0683	2.93606
$708$	−35.6489	−1.33977
$709$	−12.3303	−0.463075	−0.231538	−	0.972826i	$-0.574376\pi$
$709$	−12.3303	−0.463075	−0.231538	+	0.972826i	$0.574376\pi$
$710$	−45.2811	−1.69937
$711$	4.27909	0.160479
$712$	−117.909	−4.41882
$713$	0.932017	0.0349043
$714$	−57.4064	−2.14838
$715$	−6.69810	−0.250495
$716$	−122.369	−4.57314
$717$	−59.3179	−2.21527
$718$	−42.4026	−1.58245
$719$	−3.67714	−0.137134	−0.0685671	−	0.997647i	$-0.521843\pi$
$719$	−3.67714	−0.137134	−0.0685671	+	0.997647i	$0.521843\pi$
$720$	−71.2126	−2.65394
$721$	88.0112	3.27771
$722$	−39.8253	−1.48214
$723$	9.61494	0.357583
$724$	64.1668	2.38474
$725$	−10.1898	−0.378439
$726$	35.9916	1.33577
$727$	−24.6617	−0.914651	−0.457326	−	0.889299i	$-0.651193\pi$
$727$	−24.6617	−0.914651	−0.457326	+	0.889299i	$0.651193\pi$
$728$	−59.5603	−2.20745
$729$	−37.1551	−1.37612
$730$	−18.9953	−0.703046
$731$	2.37175	0.0877222
$732$	−122.705	−4.53532
$733$	25.7280	0.950285	0.475142	−	0.879909i	$-0.342397\pi$
$733$	25.7280	0.950285	0.475142	+	0.879909i	$0.342397\pi$
$734$	10.9031	0.402439
$735$	−97.0062	−3.57813
$736$	20.6666	0.761780
$737$	9.90558	0.364877
$738$	98.8809	3.63986
$739$	45.3275	1.66740	0.833700	−	0.552218i	$-0.186218\pi$
$739$	45.3275	1.66740	0.833700	+	0.552218i	$0.186218\pi$
$740$	−42.3598	−1.55718
$741$	22.4797	0.825812
$742$	131.465	4.82622
$743$	10.1545	0.372533	0.186266	−	0.982499i	$-0.440361\pi$
$743$	10.1545	0.372533	0.186266	+	0.982499i	$0.440361\pi$
$744$	10.6482	0.390381
$745$	−1.43669	−0.0526363
$746$	−1.62803	−0.0596064
$747$	59.7620	2.18658
$748$	19.1243	0.699252
$749$	−26.7631	−0.977901
$750$	−82.4545	−3.01081
$751$	6.70177	0.244551	0.122275	−	0.992496i	$-0.460981\pi$
$751$	6.70177	0.244551	0.122275	+	0.992496i	$0.460981\pi$
$752$	52.0348	1.89752
$753$	−28.0706	−1.02295
$754$	27.3808	0.997150
$755$	−21.5970	−0.785995
$756$	−42.8391	−1.55804
$757$	−11.0870	−0.402963	−0.201482	−	0.979492i	$-0.564576\pi$
$757$	−11.0870	−0.402963	−0.201482	+	0.979492i	$0.564576\pi$
$758$	90.9734	3.30430
$759$	10.6717	0.387356
$760$	−84.4558	−3.06353
$761$	14.2821	0.517725	0.258862	−	0.965914i	$-0.416652\pi$
$761$	14.2821	0.517725	0.258862	+	0.965914i	$0.416652\pi$
$762$	−35.1764	−1.27431
$763$	37.9903	1.37534
$764$	3.50892	0.126948
$765$	11.1832	0.404328
$766$	69.8719	2.52457
$767$	4.19167	0.151352
$768$	−27.0854	−0.977359
$769$	25.9443	0.935574	0.467787	−	0.883841i	$-0.345051\pi$
$769$	25.9443	0.935574	0.467787	+	0.883841i	$0.345051\pi$
$770$	61.3631	2.21137
$771$	24.5581	0.884438
$772$	−69.3176	−2.49480
$773$	41.6109	1.49664	0.748320	−	0.663338i	$-0.230861\pi$
$773$	41.6109	1.49664	0.748320	+	0.663338i	$0.230861\pi$
$774$	13.9820	0.502574
$775$	0.785017	0.0281986
$776$	−54.9777	−1.97358
$777$	−61.3092	−2.19946
$778$	−26.9208	−0.965157
$779$	60.1722	2.15589
$780$	35.6161	1.27526
$781$	21.8330	0.781245
$782$	−7.43035	−0.265709
$783$	11.6892	0.417738
$784$	207.379	7.40640
$785$	−12.0576	−0.430353
$786$	28.9215	1.03160
$787$	−17.0112	−0.606384	−0.303192	−	0.952930i	$-0.598052\pi$
$787$	−17.0112	−0.606384	−0.303192	+	0.952930i	$0.598052\pi$
$788$	41.9433	1.49417
$789$	68.2530	2.42987
$790$	5.80252	0.206444
$791$	−108.543	−3.85936
$792$	66.9179	2.37782
$793$	14.4279	0.512350
$794$	66.0903	2.34546
$795$	−46.6610	−1.65489
$796$	33.5548	1.18932
$797$	−39.9808	−1.41619	−0.708096	−	0.706117i	$-0.750445\pi$
$797$	−39.9808	−1.41619	−0.708096	+	0.706117i	$0.750445\pi$
$798$	−205.943	−7.29029
$799$	−8.17150	−0.289087
$800$	17.4070	0.615430
$801$	56.0102	1.97902
$802$	−18.3699	−0.648663
$803$	9.15885	0.323209
$804$	−52.6714	−1.85758
$805$	−16.9514	−0.597460
$806$	−2.10940	−0.0743006
$807$	22.0206	0.775160
$808$	115.445	4.06133
$809$	41.2774	1.45124	0.725618	−	0.688098i	$-0.241554\pi$
$809$	41.2774	1.45124	0.725618	+	0.688098i	$0.241554\pi$
$810$	−32.8052	−1.15266
$811$	34.4106	1.20832	0.604159	−	0.796864i	$-0.293509\pi$
$811$	34.4106	1.20832	0.604159	+	0.796864i	$0.293509\pi$
$812$	−178.352	−6.25891
$813$	46.9818	1.64772
$814$	28.7260	1.00685
$815$	−18.8145	−0.659043
$816$	−43.5583	−1.52484
$817$	8.50852	0.297675
$818$	−51.5500	−1.80240
$819$	28.2929	0.988634
$820$	95.3349	3.32924
$821$	−45.0807	−1.57333	−0.786663	−	0.617382i	$-0.788193\pi$
$821$	−45.0807	−1.57333	−0.786663	+	0.617382i	$0.788193\pi$
$822$	6.14362	0.214283
$823$	33.9845	1.18462	0.592312	−	0.805709i	$-0.298215\pi$
$823$	33.9845	1.18462	0.592312	+	0.805709i	$0.298215\pi$
$824$	130.148	4.53392
$825$	8.98849	0.312939
$826$	−38.4010	−1.33614
$827$	−39.7893	−1.38361	−0.691804	−	0.722085i	$-0.743184\pi$
$827$	−39.7893	−1.38361	−0.691804	+	0.722085i	$0.743184\pi$
$828$	−31.1448	−1.08236
$829$	−7.96733	−0.276717	−0.138358	−	0.990382i	$-0.544183\pi$
$829$	−7.96733	−0.276717	−0.138358	+	0.990382i	$0.544183\pi$
$830$	81.0383	2.81288
$831$	−11.5064	−0.399152
$832$	−15.8267	−0.548692
$833$	−32.5666	−1.12837
$834$	−77.4369	−2.68142
$835$	−36.8346	−1.27471
$836$	68.6073	2.37283
$837$	−0.900531	−0.0311269
$838$	67.1344	2.31912
$839$	20.5992	0.711163	0.355582	−	0.934645i	$-0.384283\pi$
$839$	20.5992	0.711163	0.355582	+	0.934645i	$0.384283\pi$
$840$	−193.668	−6.68217
$841$	19.6655	0.678122
$842$	−49.7271	−1.71371
$843$	−22.8042	−0.785420
$844$	−21.8182	−0.751013
$845$	20.2692	0.697282
$846$	−48.1731	−1.65622
$847$	27.5659	0.947176
$848$	99.7515	3.42548
$849$	−8.40809	−0.288565
$850$	−6.25841	−0.214662
$851$	−7.93550	−0.272025
$852$	−116.093	−3.97729
$853$	−20.6810	−0.708103	−0.354052	−	0.935226i	$-0.615196\pi$
$853$	−20.6810	−0.708103	−0.354052	+	0.935226i	$0.615196\pi$
$854$	−132.178	−4.52304
$855$	40.1190	1.37204
$856$	−39.5763	−1.35269
$857$	−58.4352	−1.99611	−0.998054	−	0.0623527i	$-0.980140\pi$
$857$	−58.4352	−1.99611	−0.998054	+	0.0623527i	$0.980140\pi$
$858$	−24.1528	−0.824563
$859$	−4.63659	−0.158198	−0.0790992	−	0.996867i	$-0.525204\pi$
$859$	−4.63659	−0.158198	−0.0790992	+	0.996867i	$0.525204\pi$
$860$	13.4806	0.459686
$861$	137.982	4.70243
$862$	5.59310	0.190502
$863$	−11.8668	−0.403951	−0.201976	−	0.979391i	$-0.564736\pi$
$863$	−11.8668	−0.403951	−0.201976	+	0.979391i	$0.564736\pi$
$864$	−19.9684	−0.679339
$865$	−25.1535	−0.855244
$866$	−37.9470	−1.28949
$867$	−36.9979	−1.25651
$868$	13.7401	0.466370
$869$	−2.79777	−0.0949080
$870$	89.0322	3.01847
$871$	6.19320	0.209848
$872$	56.1788	1.90245
$873$	26.1161	0.883894
$874$	−26.6560	−0.901652
$875$	−63.1517	−2.13492
$876$	−48.7008	−1.64545
$877$	49.7547	1.68010	0.840048	−	0.542511i	$-0.182526\pi$
$877$	49.7547	1.68010	0.840048	+	0.542511i	$0.182526\pi$
$878$	13.9640	0.471263
$879$	−6.26379	−0.211272
$880$	46.5605	1.56955
$881$	−24.6769	−0.831385	−0.415693	−	0.909505i	$-0.636461\pi$
$881$	−24.6769	−0.831385	−0.415693	+	0.909505i	$0.636461\pi$
$882$	−191.989	−6.46459
$883$	51.9930	1.74970	0.874851	−	0.484391i	$-0.160959\pi$
$883$	51.9930	1.74970	0.874851	+	0.484391i	$0.160959\pi$
$884$	11.9569	0.402155
$885$	13.6297	0.458159
$886$	42.7909	1.43759
$887$	−52.4095	−1.75974	−0.879869	−	0.475216i	$-0.842370\pi$
$887$	−52.4095	−1.75974	−0.879869	+	0.475216i	$0.842370\pi$
$888$	−90.6619	−3.04242
$889$	−26.9415	−0.903590
$890$	75.9507	2.54587
$891$	15.8175	0.529907
$892$	−59.1708	−1.98118
$893$	−29.3149	−0.980984
$894$	−5.18059	−0.173265
$895$	46.7856	1.56387
$896$	21.1571	0.706809
$897$	6.67216	0.222777
$898$	−85.8027	−2.86327
$899$	−3.74917	−0.125042
$900$	−26.2326	−0.874420
$901$	−15.6649	−0.521873
$902$	−64.6507	−2.15263
$903$	19.5111	0.649289
$904$	−160.510	−5.33849
$905$	−24.5330	−0.815505
$906$	−77.8771	−2.58729
$907$	55.7111	1.84986	0.924928	−	0.380142i	$-0.124125\pi$
$907$	55.7111	1.84986	0.924928	+	0.380142i	$0.124125\pi$
$908$	1.43988	0.0477841
$909$	−54.8397	−1.81892
$910$	38.3657	1.27181
$911$	27.9443	0.925837	0.462918	−	0.886401i	$-0.346802\pi$
$911$	27.9443	0.925837	0.462918	+	0.886401i	$0.346802\pi$
$912$	−156.263	−5.17439
$913$	−39.0739	−1.29316
$914$	97.5596	3.22698
$915$	46.9142	1.55093
$916$	83.0033	2.74251
$917$	22.1509	0.731488
$918$	7.17933	0.236953
$919$	22.5498	0.743850	0.371925	−	0.928263i	$-0.378698\pi$
$919$	22.5498	0.743850	0.371925	+	0.928263i	$0.378698\pi$
$920$	−25.0672	−0.826441
$921$	7.18439	0.236734
$922$	110.507	3.63935
$923$	13.6505	0.449311
$924$	157.325	5.17562
$925$	−6.68389	−0.219765
$926$	5.32202	0.174893
$927$	−61.8242	−2.03057
$928$	−83.1342	−2.72901
$929$	4.20631	0.138005	0.0690023	−	0.997617i	$-0.478018\pi$
$929$	4.20631	0.138005	0.0690023	+	0.997617i	$0.478018\pi$
$930$	−6.85900	−0.224915
$931$	−116.831	−3.82899
$932$	23.1577	0.758556
$933$	37.0229	1.21208
$934$	41.4446	1.35611
$935$	−7.31182	−0.239122
$936$	41.8386	1.36754
$937$	−15.5299	−0.507340	−0.253670	−	0.967291i	$-0.581638\pi$
$937$	−15.5299	−0.507340	−0.253670	+	0.967291i	$0.581638\pi$
$938$	−56.7376	−1.85255
$939$	−45.4748	−1.48401
$940$	−46.4455	−1.51489
$941$	−27.9023	−0.909589	−0.454794	−	0.890596i	$-0.650287\pi$
$941$	−27.9023	−0.909589	−0.454794	+	0.890596i	$0.650287\pi$
$942$	−43.4786	−1.41661
$943$	17.8596	0.581589
$944$	−29.1375	−0.948346
$945$	16.3788	0.532801
$946$	−9.14179	−0.297225
$947$	−18.6431	−0.605819	−0.302909	−	0.953019i	$-0.597958\pi$
$947$	−18.6431	−0.605819	−0.302909	+	0.953019i	$0.597958\pi$
$948$	14.8767	0.483174
$949$	5.72633	0.185884
$950$	−22.4517	−0.728431
$951$	75.5139	2.44871
$952$	−65.0176	−2.10723
$953$	41.7706	1.35308	0.676542	−	0.736404i	$-0.263478\pi$
$953$	41.7706	1.35308	0.676542	+	0.736404i	$0.263478\pi$
$954$	−92.3484	−2.98989
$955$	−1.34157	−0.0434122
$956$	−113.188	−3.66077
$957$	−42.9282	−1.38767
$958$	−67.7118	−2.18767
$959$	4.70539	0.151945
$960$	−51.4625	−1.66095
$961$	−30.7112	−0.990683
$962$	17.9602	0.579059
$963$	18.7999	0.605819
$964$	18.3469	0.590913
$965$	26.5023	0.853141
$966$	−61.1255	−1.96668
$967$	−14.4232	−0.463817	−0.231909	−	0.972738i	$-0.574497\pi$
$967$	−14.4232	−0.463817	−0.231909	+	0.972738i	$0.574497\pi$
$968$	40.7635	1.31019
$969$	24.5394	0.788319
$970$	35.4138	1.13707
$971$	50.8289	1.63118	0.815589	−	0.578632i	$-0.196413\pi$
$971$	50.8289	1.63118	0.815589	+	0.578632i	$0.196413\pi$
$972$	−108.842	−3.49112
$973$	−59.3087	−1.90135
$974$	−99.3803	−3.18435
$975$	5.61981	0.179978
$976$	−100.293	−3.21029
$977$	55.4883	1.77523	0.887614	−	0.460588i	$-0.152361\pi$
$977$	55.4883	1.77523	0.887614	+	0.460588i	$0.152361\pi$
$978$	−67.8436	−2.16940
$979$	−36.6208	−1.17041
$980$	−185.104	−5.91292
$981$	−26.6866	−0.852038
$982$	79.6768	2.54259
$983$	−5.97313	−0.190513	−0.0952566	−	0.995453i	$-0.530367\pi$
$983$	−5.97313	−0.190513	−0.0952566	+	0.995453i	$0.530367\pi$
$984$	204.044	6.50467
$985$	−16.0363	−0.510958
$986$	29.8896	0.951879
$987$	−67.2227	−2.13972
$988$	42.8949	1.36467
$989$	2.52540	0.0803031
$990$	−43.1050	−1.36997
$991$	58.7877	1.86745	0.933726	−	0.357988i	$-0.116537\pi$
$991$	58.7877	1.86745	0.933726	+	0.357988i	$0.116537\pi$
$992$	6.40462	0.203347
$993$	−36.0797	−1.14495
$994$	−125.056	−3.96653
$995$	−12.8291	−0.406709
$996$	207.769	6.58342
$997$	−20.4121	−0.646457	−0.323228	−	0.946321i	$-0.604768\pi$
$997$	−20.4121	−0.646457	−0.323228	+	0.946321i	$0.604768\pi$
$998$	102.737	3.25208
$999$	7.66742	0.242586

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4003.2.a.c.1.5	✓	179

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4003.2.a.c.1.5	✓	179	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:	\( N \)	\(=\)	\( 4003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4003.a (trivial)

\(f(q)\)	\(=\)	\(q-2.63071 q^{2} +2.57872 q^{3} +4.92061 q^{4} -1.88131 q^{5} -6.78385 q^{6} -5.19574 q^{7} -7.68328 q^{8} +3.64979 q^{9} +O(q^{10})\)	\(q-2.63071 q^{2} +2.57872 q^{3} +4.92061 q^{4} -1.88131 q^{5} -6.78385 q^{6} -5.19574 q^{7} -7.68328 q^{8} +3.64979 q^{9} +4.94917 q^{10} -2.38632 q^{11} +12.6889 q^{12} -1.49198 q^{13} +13.6685 q^{14} -4.85136 q^{15} +10.3712 q^{16} -1.62869 q^{17} -9.60151 q^{18} -5.84283 q^{19} -9.25719 q^{20} -13.3983 q^{21} +6.27770 q^{22} -1.73420 q^{23} -19.8130 q^{24} -1.46068 q^{25} +3.92496 q^{26} +1.67561 q^{27} -25.5662 q^{28} +6.97607 q^{29} +12.7625 q^{30} -0.537433 q^{31} -11.9171 q^{32} -6.15364 q^{33} +4.28459 q^{34} +9.77478 q^{35} +17.9592 q^{36} +4.57588 q^{37} +15.3708 q^{38} -3.84740 q^{39} +14.4546 q^{40} -10.2985 q^{41} +35.2471 q^{42} -1.45623 q^{43} -11.7421 q^{44} -6.86637 q^{45} +4.56217 q^{46} +5.01724 q^{47} +26.7444 q^{48} +19.9957 q^{49} +3.84262 q^{50} -4.19992 q^{51} -7.34146 q^{52} +9.61811 q^{53} -4.40805 q^{54} +4.48940 q^{55} +39.9203 q^{56} -15.0670 q^{57} -18.3520 q^{58} -2.80946 q^{59} -23.8717 q^{60} -9.67030 q^{61} +1.41383 q^{62} -18.9633 q^{63} +10.6078 q^{64} +2.80688 q^{65} +16.1884 q^{66} -4.15099 q^{67} -8.01413 q^{68} -4.47202 q^{69} -25.7146 q^{70} -9.14923 q^{71} -28.0423 q^{72} -3.83807 q^{73} -12.0378 q^{74} -3.76668 q^{75} -28.7503 q^{76} +12.3987 q^{77} +10.1214 q^{78} +1.17242 q^{79} -19.5114 q^{80} -6.62842 q^{81} +27.0922 q^{82} +16.3741 q^{83} -65.9280 q^{84} +3.06406 q^{85} +3.83092 q^{86} +17.9893 q^{87} +18.3347 q^{88} +15.3462 q^{89} +18.0634 q^{90} +7.75194 q^{91} -8.53334 q^{92} -1.38589 q^{93} -13.1989 q^{94} +10.9922 q^{95} -30.7307 q^{96} +7.15550 q^{97} -52.6027 q^{98} -8.70955 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9}+O(q^{10}) \) 179 * q + 22 * q^2 + 16 * q^3 + 196 * q^4 + 61 * q^5 + 7 * q^6 + 21 * q^7 + 60 * q^8 + 221 * q^9	\( 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9} + 9 q^{10} + 46 q^{11} + 33 q^{12} + 47 q^{13} + 22 q^{14} + 36 q^{15} + 222 q^{16} + 103 q^{17} + 43 q^{18} + 12 q^{19} + 102 q^{20} + 50 q^{21} + 39 q^{22} + 121 q^{23} - 3 q^{24} + 246 q^{25} + 52 q^{26} + 49 q^{27} + 41 q^{28} + 138 q^{29} + 28 q^{30} + 5 q^{31} + 137 q^{32} + 63 q^{33} + 2 q^{34} + 72 q^{35} + 279 q^{36} + 118 q^{37} + 123 q^{38} + q^{39} + 9 q^{40} + 50 q^{41} + 48 q^{42} + 48 q^{43} + 108 q^{44} + 158 q^{45} + 13 q^{46} + 85 q^{47} + 50 q^{48} + 230 q^{49} + 78 q^{50} + 15 q^{51} + 41 q^{52} + 399 q^{53} - 5 q^{54} + 24 q^{55} + 53 q^{56} + 45 q^{57} + 27 q^{58} + 48 q^{59} + 66 q^{60} + 46 q^{61} + 81 q^{62} + 78 q^{63} + 252 q^{64} + 153 q^{65} + 6 q^{66} + 70 q^{67} + 240 q^{68} + 120 q^{69} - 31 q^{70} + 86 q^{71} + 89 q^{72} + 45 q^{73} + 68 q^{74} + 17 q^{75} - 13 q^{76} + 362 q^{77} + 69 q^{78} + 31 q^{79} + 169 q^{80} + 303 q^{81} + 25 q^{82} + 106 q^{83} + 13 q^{84} + 115 q^{85} + 95 q^{86} + 32 q^{87} + 83 q^{88} + 105 q^{89} - 38 q^{90} + 3 q^{91} + 310 q^{92} + 298 q^{93} - 17 q^{94} + 102 q^{95} - 82 q^{96} + 34 q^{97} + 81 q^{98} + 58 q^{99}+O(q^{100}) \) 179 * q + 22 * q^2 + 16 * q^3 + 196 * q^4 + 61 * q^5 + 7 * q^6 + 21 * q^7 + 60 * q^8 + 221 * q^9 + 9 * q^10 + 46 * q^11 + 33 * q^12 + 47 * q^13 + 22 * q^14 + 36 * q^15 + 222 * q^16 + 103 * q^17 + 43 * q^18 + 12 * q^19 + 102 * q^20 + 50 * q^21 + 39 * q^22 + 121 * q^23 - 3 * q^24 + 246 * q^25 + 52 * q^26 + 49 * q^27 + 41 * q^28 + 138 * q^29 + 28 * q^30 + 5 * q^31 + 137 * q^32 + 63 * q^33 + 2 * q^34 + 72 * q^35 + 279 * q^36 + 118 * q^37 + 123 * q^38 + q^39 + 9 * q^40 + 50 * q^41 + 48 * q^42 + 48 * q^43 + 108 * q^44 + 158 * q^45 + 13 * q^46 + 85 * q^47 + 50 * q^48 + 230 * q^49 + 78 * q^50 + 15 * q^51 + 41 * q^52 + 399 * q^53 - 5 * q^54 + 24 * q^55 + 53 * q^56 + 45 * q^57 + 27 * q^58 + 48 * q^59 + 66 * q^60 + 46 * q^61 + 81 * q^62 + 78 * q^63 + 252 * q^64 + 153 * q^65 + 6 * q^66 + 70 * q^67 + 240 * q^68 + 120 * q^69 - 31 * q^70 + 86 * q^71 + 89 * q^72 + 45 * q^73 + 68 * q^74 + 17 * q^75 - 13 * q^76 + 362 * q^77 + 69 * q^78 + 31 * q^79 + 169 * q^80 + 303 * q^81 + 25 * q^82 + 106 * q^83 + 13 * q^84 + 115 * q^85 + 95 * q^86 + 32 * q^87 + 83 * q^88 + 105 * q^89 - 38 * q^90 + 3 * q^91 + 310 * q^92 + 298 * q^93 - 17 * q^94 + 102 * q^95 - 82 * q^96 + 34 * q^97 + 81 * q^98 + 58 * q^99

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