LMFDB - Embedded newform 4003.2.a.c.1.10

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			1.10
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)

$f(q)$	$=$	$q-2.54699 q^{2} -0.919443 q^{3} +4.48717 q^{4} -0.00498874 q^{5} +2.34182 q^{6} -0.132134 q^{7} -6.33481 q^{8} -2.15462 q^{9} +O(q^{10})$	\(q-2.54699 q^{2} -0.919443 q^{3} +4.48717 q^{4} -0.00498874 q^{5} +2.34182 q^{6} -0.132134 q^{7} -6.33481 q^{8} -2.15462 q^{9} +0.0127063 q^{10} +5.60667 q^{11} -4.12570 q^{12} +4.28134 q^{13} +0.336545 q^{14} +0.00458687 q^{15} +7.16038 q^{16} -5.76338 q^{17} +5.48781 q^{18} -6.95640 q^{19} -0.0223854 q^{20} +0.121490 q^{21} -14.2801 q^{22} +6.39969 q^{23} +5.82450 q^{24} -4.99998 q^{25} -10.9045 q^{26} +4.73938 q^{27} -0.592909 q^{28} +1.11344 q^{29} -0.0116827 q^{30} +6.59694 q^{31} -5.56780 q^{32} -5.15501 q^{33} +14.6793 q^{34} +0.000659184 q^{35} -9.66817 q^{36} +3.65341 q^{37} +17.7179 q^{38} -3.93645 q^{39} +0.0316028 q^{40} -3.61946 q^{41} -0.309434 q^{42} +1.54973 q^{43} +25.1581 q^{44} +0.0107489 q^{45} -16.3000 q^{46} -0.423887 q^{47} -6.58356 q^{48} -6.98254 q^{49} +12.7349 q^{50} +5.29910 q^{51} +19.2111 q^{52} -0.698466 q^{53} -12.0712 q^{54} -0.0279702 q^{55} +0.837046 q^{56} +6.39602 q^{57} -2.83592 q^{58} +0.427629 q^{59} +0.0205821 q^{60} -8.82156 q^{61} -16.8024 q^{62} +0.284700 q^{63} -0.139594 q^{64} -0.0213585 q^{65} +13.1298 q^{66} +14.5095 q^{67} -25.8613 q^{68} -5.88415 q^{69} -0.00167894 q^{70} +11.4271 q^{71} +13.6491 q^{72} -7.78949 q^{73} -9.30520 q^{74} +4.59719 q^{75} -31.2146 q^{76} -0.740833 q^{77} +10.0261 q^{78} +8.90525 q^{79} -0.0357213 q^{80} +2.10628 q^{81} +9.21874 q^{82} +3.14039 q^{83} +0.545146 q^{84} +0.0287520 q^{85} -3.94716 q^{86} -1.02374 q^{87} -35.5172 q^{88} +9.35921 q^{89} -0.0273773 q^{90} -0.565712 q^{91} +28.7165 q^{92} -6.06551 q^{93} +1.07964 q^{94} +0.0347037 q^{95} +5.11928 q^{96} -8.80504 q^{97} +17.7845 q^{98} -12.0803 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.54699	−1.80100	−0.900498	−	0.434860i	$-0.856798\pi$
$2$	−2.54699	−1.80100	−0.900498	+	0.434860i	$0.856798\pi$
$3$	−0.919443	−0.530841	−0.265420	−	0.964133i	$-0.585511\pi$
$3$	−0.919443	−0.530841	−0.265420	+	0.964133i	$0.585511\pi$
$4$	4.48717	2.24359
$5$	−0.00498874	−0.00223103	−0.00111552	−	0.999999i	$-0.500355\pi$
$5$	−0.00498874	−0.00223103	−0.00111552	+	0.999999i	$0.500355\pi$
$6$	2.34182	0.956042
$7$	−0.132134	−0.0499420	−0.0249710	−	0.999688i	$-0.507949\pi$
$7$	−0.132134	−0.0499420	−0.0249710	+	0.999688i	$0.507949\pi$
$8$	−6.33481	−2.23969
$9$	−2.15462	−0.718208
$10$	0.0127063	0.00401808
$11$	5.60667	1.69047	0.845237	−	0.534392i	$-0.179459\pi$
$11$	5.60667	1.69047	0.845237	+	0.534392i	$0.179459\pi$
$12$	−4.12570	−1.19099
$13$	4.28134	1.18743	0.593715	−	0.804675i	$-0.297661\pi$
$13$	4.28134	1.18743	0.593715	+	0.804675i	$0.297661\pi$
$14$	0.336545	0.0899454
$15$	0.00458687	0.00118432
$16$	7.16038	1.79009
$17$	−5.76338	−1.39783	−0.698913	−	0.715207i	$-0.746332\pi$
$17$	−5.76338	−1.39783	−0.698913	+	0.715207i	$0.746332\pi$
$18$	5.48781	1.29349
$19$	−6.95640	−1.59591	−0.797954	−	0.602718i	$-0.794084\pi$
$19$	−6.95640	−1.59591	−0.797954	+	0.602718i	$0.794084\pi$
$20$	−0.0223854	−0.00500552
$21$	0.121490	0.0265113
$22$	−14.2801	−3.04454
$23$	6.39969	1.33443	0.667214	−	0.744866i	$-0.267487\pi$
$23$	6.39969	1.33443	0.667214	+	0.744866i	$0.267487\pi$
$24$	5.82450	1.18892
$25$	−4.99998	−0.999995
$26$	−10.9045	−2.13856
$27$	4.73938	0.912095
$28$	−0.592909	−0.112049
$29$	1.11344	0.206760	0.103380	−	0.994642i	$-0.467034\pi$
$29$	1.11344	0.206760	0.103380	+	0.994642i	$0.467034\pi$
$30$	−0.0116827	−0.00213296
$31$	6.59694	1.18485	0.592423	−	0.805627i	$-0.298172\pi$
$31$	6.59694	1.18485	0.592423	+	0.805627i	$0.298172\pi$
$32$	−5.56780	−0.984258
$33$	−5.15501	−0.897372
$34$	14.6793	2.51748
$35$	0.000659184 0	0.000111422 0
$36$	−9.66817	−1.61136
$37$	3.65341	0.600616	0.300308	−	0.953842i	$-0.402911\pi$
$37$	3.65341	0.600616	0.300308	+	0.953842i	$0.402911\pi$
$38$	17.7179	2.87423
$39$	−3.93645	−0.630336
$40$	0.0316028	0.00499683
$41$	−3.61946	−0.565265	−0.282632	−	0.959228i	$-0.591208\pi$
$41$	−3.61946	−0.565265	−0.282632	+	0.959228i	$0.591208\pi$
$42$	−0.309434	−0.0477467
$43$	1.54973	0.236332	0.118166	−	0.992994i	$-0.462299\pi$
$43$	1.54973	0.236332	0.118166	+	0.992994i	$0.462299\pi$
$44$	25.1581	3.79272
$45$	0.0107489	0.00160235
$46$	−16.3000	−2.40330
$47$	−0.423887	−0.0618303	−0.0309152	−	0.999522i	$-0.509842\pi$
$47$	−0.423887	−0.0618303	−0.0309152	+	0.999522i	$0.509842\pi$
$48$	−6.58356	−0.950255
$49$	−6.98254	−0.997506
$50$	12.7349	1.80099
$51$	5.29910	0.742023
$52$	19.2111	2.66410
$53$	−0.698466	−0.0959417	−0.0479709	−	0.998849i	$-0.515275\pi$
$53$	−0.698466	−0.0959417	−0.0479709	+	0.998849i	$0.515275\pi$
$54$	−12.0712	−1.64268
$55$	−0.0279702	−0.00377150
$56$	0.837046	0.111855
$57$	6.39602	0.847173
$58$	−2.83592	−0.372374
$59$	0.427629	0.0556726	0.0278363	−	0.999612i	$-0.491138\pi$
$59$	0.427629	0.0556726	0.0278363	+	0.999612i	$0.491138\pi$
$60$	0.0205821	0.00265713
$61$	−8.82156	−1.12949	−0.564743	−	0.825267i	$-0.691025\pi$
$61$	−8.82156	−1.12949	−0.564743	+	0.825267i	$0.691025\pi$
$62$	−16.8024	−2.13390
$63$	0.284700	0.0358688
$64$	−0.139594	−0.0174493
$65$	−0.0213585	−0.00264920
$66$	13.1298	1.61616
$67$	14.5095	1.77262	0.886308	−	0.463096i	$-0.153262\pi$
$67$	14.5095	1.77262	0.886308	+	0.463096i	$0.153262\pi$
$68$	−25.8613	−3.13614
$69$	−5.88415	−0.708368
$70$	−0.00167894	−0.000200671 0
$71$	11.4271	1.35615	0.678073	−	0.734994i	$-0.262815\pi$
$71$	11.4271	1.35615	0.678073	+	0.734994i	$0.262815\pi$
$72$	13.6491	1.60857
$73$	−7.78949	−0.911691	−0.455846	−	0.890059i	$-0.650663\pi$
$73$	−7.78949	−0.911691	−0.455846	+	0.890059i	$0.650663\pi$
$74$	−9.30520	−1.08171
$75$	4.59719	0.530838
$76$	−31.2146	−3.58056
$77$	−0.740833	−0.0844257
$78$	10.0261	1.13523
$79$	8.90525	1.00192	0.500960	−	0.865471i	$-0.332981\pi$
$79$	8.90525	1.00192	0.500960	+	0.865471i	$0.332981\pi$
$80$	−0.0357213	−0.00399376
$81$	2.10628	0.234031
$82$	9.21874	1.01804
$83$	3.14039	0.344702	0.172351	−	0.985036i	$-0.444864\pi$
$83$	3.14039	0.344702	0.172351	+	0.985036i	$0.444864\pi$
$84$	0.545146	0.0594803
$85$	0.0287520	0.00311860
$86$	−3.94716	−0.425633
$87$	−1.02374	−0.109757
$88$	−35.5172	−3.78615
$89$	9.35921	0.992074	0.496037	−	0.868301i	$-0.334788\pi$
$89$	9.35921	0.992074	0.496037	+	0.868301i	$0.334788\pi$
$90$	−0.0273773	−0.00288582
$91$	−0.565712	−0.0593027
$92$	28.7165	2.99390
$93$	−6.06551	−0.628964
$94$	1.07964	0.111356
$95$	0.0347037	0.00356053
$96$	5.11928	0.522484
$97$	−8.80504	−0.894016	−0.447008	−	0.894530i	$-0.647510\pi$
$97$	−8.80504	−0.894016	−0.447008	+	0.894530i	$0.647510\pi$
$98$	17.7845	1.79650
$99$	−12.0803	−1.21411
$100$	−22.4358	−2.24358
$101$	3.60218	0.358431	0.179215	−	0.983810i	$-0.442644\pi$
$101$	3.60218	0.358431	0.179215	+	0.983810i	$0.442644\pi$
$102$	−13.4968	−1.33638
$103$	−1.56121	−0.153830	−0.0769151	−	0.997038i	$-0.524507\pi$
$103$	−1.56121	−0.153830	−0.0769151	+	0.997038i	$0.524507\pi$
$104$	−27.1215	−2.65948
$105$	−0.000606082 0	−5.91476e−5 0
$106$	1.77899	0.172791
$107$	9.60061	0.928126	0.464063	−	0.885802i	$-0.346391\pi$
$107$	9.60061	0.928126	0.464063	+	0.885802i	$0.346391\pi$
$108$	21.2664	2.04636
$109$	−13.3335	−1.27712	−0.638559	−	0.769573i	$-0.720469\pi$
$109$	−13.3335	−1.27712	−0.638559	+	0.769573i	$0.720469\pi$
$110$	0.0712400	0.00679246
$111$	−3.35910	−0.318832
$112$	−0.946131	−0.0894010
$113$	5.39416	0.507440	0.253720	−	0.967278i	$-0.418346\pi$
$113$	5.39416	0.507440	0.253720	+	0.967278i	$0.418346\pi$
$114$	−16.2906	−1.52576
$115$	−0.0319264	−0.00297715
$116$	4.99619	0.463884
$117$	−9.22468	−0.852822
$118$	−1.08917	−0.100266
$119$	0.761540	0.0698103
$120$	−0.0290569	−0.00265252
$121$	20.4347	1.85770
$122$	22.4685	2.03420
$123$	3.32789	0.300066
$124$	29.6016	2.65830
$125$	0.0498873	0.00446206
$126$	−0.725128	−0.0645995
$127$	−16.5934	−1.47242	−0.736211	−	0.676752i	$-0.763387\pi$
$127$	−16.5934	−1.47242	−0.736211	+	0.676752i	$0.763387\pi$
$128$	11.4912	1.01568
$129$	−1.42489	−0.125455
$130$	0.0544000	0.00477119
$131$	−18.2276	−1.59255	−0.796275	−	0.604934i	$-0.793199\pi$
$131$	−18.2276	−1.59255	−0.796275	+	0.604934i	$0.793199\pi$
$132$	−23.1314	−2.01333
$133$	0.919179	0.0797029
$134$	−36.9556	−3.19247
$135$	−0.0236436	−0.00203491
$136$	36.5100	3.13070
$137$	13.6741	1.16826	0.584131	−	0.811660i	$-0.301436\pi$
$137$	13.6741	1.16826	0.584131	+	0.811660i	$0.301436\pi$
$138$	14.9869	1.27577
$139$	6.72038	0.570016	0.285008	−	0.958525i	$-0.408004\pi$
$139$	6.72038	0.570016	0.285008	+	0.958525i	$0.408004\pi$
$140$	0.00295787	0.000249986 0
$141$	0.389740	0.0328221
$142$	−29.1047	−2.44241
$143$	24.0041	2.00732
$144$	−15.4279	−1.28566
$145$	−0.00555466	−0.000461289 0
$146$	19.8398	1.64195
$147$	6.42005	0.529517
$148$	16.3935	1.34753
$149$	8.80851	0.721621	0.360810	−	0.932639i	$-0.382500\pi$
$149$	8.80851	0.721621	0.360810	+	0.932639i	$0.382500\pi$
$150$	−11.7090	−0.956037
$151$	3.55247	0.289096	0.144548	−	0.989498i	$-0.453827\pi$
$151$	3.55247	0.289096	0.144548	+	0.989498i	$0.453827\pi$
$152$	44.0675	3.57435
$153$	12.4179	1.00393
$154$	1.88690	0.152050
$155$	−0.0329104	−0.00264343
$156$	−17.6635	−1.41421
$157$	−9.58055	−0.764612	−0.382306	−	0.924036i	$-0.624870\pi$
$157$	−9.58055	−0.764612	−0.382306	+	0.924036i	$0.624870\pi$
$158$	−22.6816	−1.80445
$159$	0.642200	0.0509298
$160$	0.0277764	0.00219591
$161$	−0.845618	−0.0666440
$162$	−5.36468	−0.421489
$163$	18.8960	1.48005	0.740024	−	0.672580i	$-0.234814\pi$
$163$	18.8960	1.48005	0.740024	+	0.672580i	$0.234814\pi$
$164$	−16.2411	−1.26822
$165$	0.0257170	0.00200207
$166$	−7.99855	−0.620808
$167$	−23.5498	−1.82233	−0.911167	−	0.412037i	$-0.864818\pi$
$167$	−23.5498	−1.82233	−0.911167	+	0.412037i	$0.864818\pi$
$168$	−0.769616	−0.0593772
$169$	5.32988	0.409991
$170$	−0.0732312	−0.00561658
$171$	14.9884	1.14619
$172$	6.95392	0.530231
$173$	21.1821	1.61044	0.805221	−	0.592974i	$-0.202046\pi$
$173$	21.1821	1.61044	0.805221	+	0.592974i	$0.202046\pi$
$174$	2.60747	0.197671
$175$	0.660668	0.0499418
$176$	40.1459	3.02611
$177$	−0.393181	−0.0295533
$178$	−23.8378	−1.78672
$179$	−21.2330	−1.58703	−0.793515	−	0.608550i	$-0.791751\pi$
$179$	−21.2330	−1.58703	−0.793515	+	0.608550i	$0.791751\pi$
$180$	0.0482320	0.00359500
$181$	−14.7425	−1.09580	−0.547900	−	0.836544i	$-0.684572\pi$
$181$	−14.7425	−1.09580	−0.547900	+	0.836544i	$0.684572\pi$
$182$	1.44086	0.106804
$183$	8.11092	0.599577
$184$	−40.5408	−2.98871
$185$	−0.0182259	−0.00134000
$186$	15.4488	1.13276
$187$	−32.3134	−2.36299
$188$	−1.90206	−0.138722
$189$	−0.626235	−0.0455519
$190$	−0.0883901	−0.00641249
$191$	−8.37038	−0.605659	−0.302830	−	0.953045i	$-0.597931\pi$
$191$	−8.37038	−0.605659	−0.302830	+	0.953045i	$0.597931\pi$
$192$	0.128349	0.00926280
$193$	5.05503	0.363869	0.181935	−	0.983311i	$-0.441764\pi$
$193$	5.05503	0.363869	0.181935	+	0.983311i	$0.441764\pi$
$194$	22.4264	1.61012
$195$	0.0196379	0.00140630
$196$	−31.3319	−2.23799
$197$	−10.0050	−0.712829	−0.356415	−	0.934328i	$-0.616001\pi$
$197$	−10.0050	−0.712829	−0.356415	+	0.934328i	$0.616001\pi$
$198$	30.7683	2.18661
$199$	−1.14529	−0.0811871	−0.0405936	−	0.999176i	$-0.512925\pi$
$199$	−1.14529	−0.0811871	−0.0405936	+	0.999176i	$0.512925\pi$
$200$	31.6739	2.23968
$201$	−13.3406	−0.940977
$202$	−9.17474	−0.645532
$203$	−0.147123	−0.0103260
$204$	23.7780	1.66479
$205$	0.0180566	0.00126112
$206$	3.97638	0.277047
$207$	−13.7889	−0.958396
$208$	30.6560	2.12561
$209$	−39.0022	−2.69784
$210$	0.00154369	0.000106525 0
$211$	−20.8380	−1.43455	−0.717275	−	0.696791i	$-0.754611\pi$
$211$	−20.8380	−1.43455	−0.717275	+	0.696791i	$0.754611\pi$
$212$	−3.13414	−0.215254
$213$	−10.5066	−0.719898
$214$	−24.4527	−1.67155
$215$	−0.00773122	−0.000527265 0
$216$	−30.0231	−2.04281
$217$	−0.871682	−0.0591736
$218$	33.9603	2.30008
$219$	7.16200	0.483963
$220$	−0.125507	−0.00846170
$221$	−24.6750	−1.65982
$222$	8.55560	0.574214
$223$	14.8917	0.997225	0.498612	−	0.866825i	$-0.333843\pi$
$223$	14.8917	0.997225	0.498612	+	0.866825i	$0.333843\pi$
$224$	0.735698	0.0491559
$225$	10.7731	0.718204
$226$	−13.7389	−0.913897
$227$	16.1586	1.07248	0.536240	−	0.844065i	$-0.319844\pi$
$227$	16.1586	1.07248	0.536240	+	0.844065i	$0.319844\pi$
$228$	28.7000	1.90071
$229$	−4.63145	−0.306055	−0.153027	−	0.988222i	$-0.548902\pi$
$229$	−4.63145	−0.306055	−0.153027	+	0.988222i	$0.548902\pi$
$230$	0.0813163	0.00536184
$231$	0.681154	0.0448166
$232$	−7.05342	−0.463080
$233$	−10.2327	−0.670368	−0.335184	−	0.942153i	$-0.608799\pi$
$233$	−10.2327	−0.670368	−0.335184	+	0.942153i	$0.608799\pi$
$234$	23.4952	1.53593
$235$	0.00211466	0.000137946 0
$236$	1.91885	0.124906
$237$	−8.18787	−0.531860
$238$	−1.93964	−0.125728
$239$	21.4387	1.38675	0.693377	−	0.720575i	$-0.256122\pi$
$239$	21.4387	1.38675	0.693377	+	0.720575i	$0.256122\pi$
$240$	0.0328437	0.00212005
$241$	−4.76917	−0.307209	−0.153605	−	0.988132i	$-0.549088\pi$
$241$	−4.76917	−0.307209	−0.153605	+	0.988132i	$0.549088\pi$
$242$	−52.0471	−3.34571
$243$	−16.1548	−1.03633
$244$	−39.5839	−2.53410
$245$	0.0348341	0.00222547
$246$	−8.47611	−0.540417
$247$	−29.7827	−1.89503
$248$	−41.7904	−2.65369
$249$	−2.88741	−0.182982
$250$	−0.127063	−0.00803615
$251$	−9.18029	−0.579455	−0.289728	−	0.957109i	$-0.593565\pi$
$251$	−9.18029	−0.579455	−0.289728	+	0.957109i	$0.593565\pi$
$252$	1.27750	0.0804747
$253$	35.8809	2.25581
$254$	42.2631	2.65183
$255$	−0.0264359	−0.00165548
$256$	−28.9887	−1.81179
$257$	19.2786	1.20257	0.601284	−	0.799036i	$-0.294656\pi$
$257$	19.2786	1.20257	0.601284	+	0.799036i	$0.294656\pi$
$258$	3.62919	0.225943
$259$	−0.482740	−0.0299960
$260$	−0.0958393	−0.00594370
$261$	−2.39904	−0.148497
$262$	46.4255	2.86818
$263$	9.27487	0.571913	0.285957	−	0.958243i	$-0.407689\pi$
$263$	9.27487	0.571913	0.285957	+	0.958243i	$0.407689\pi$
$264$	32.6560	2.00984
$265$	0.00348447	0.000214049 0
$266$	−2.34114	−0.143545
$267$	−8.60526	−0.526633
$268$	65.1066	3.97702
$269$	16.6379	1.01443	0.507215	−	0.861820i	$-0.330675\pi$
$269$	16.6379	1.01443	0.507215	+	0.861820i	$0.330675\pi$
$270$	0.0602200	0.00366487
$271$	−7.42833	−0.451239	−0.225619	−	0.974216i	$-0.572441\pi$
$271$	−7.42833	−0.451239	−0.225619	+	0.974216i	$0.572441\pi$
$272$	−41.2680	−2.50224
$273$	0.520140	0.0314803
$274$	−34.8280	−2.10403
$275$	−28.0332	−1.69047
$276$	−26.4032	−1.58929
$277$	24.5833	1.47707	0.738534	−	0.674216i	$-0.235518\pi$
$277$	24.5833	1.47707	0.738534	+	0.674216i	$0.235518\pi$
$278$	−17.1168	−1.02660
$279$	−14.2139	−0.850966
$280$	−0.00417581	−0.000249552 0
$281$	3.44674	0.205615	0.102808	−	0.994701i	$-0.467217\pi$
$281$	3.44674	0.205615	0.102808	+	0.994701i	$0.467217\pi$
$282$	−0.992666	−0.0591124
$283$	−13.1816	−0.783567	−0.391784	−	0.920057i	$-0.628142\pi$
$283$	−13.1816	−0.783567	−0.391784	+	0.920057i	$0.628142\pi$
$284$	51.2754	3.04263
$285$	−0.0319081	−0.00189007
$286$	−61.1382	−3.61517
$287$	0.478255	0.0282305
$288$	11.9965	0.706902
$289$	16.2166	0.953917
$290$	0.0141477	0.000830780 0
$291$	8.09573	0.474580
$292$	−34.9528	−2.04546
$293$	14.2934	0.835029	0.417514	−	0.908670i	$-0.362901\pi$
$293$	14.2934	0.835029	0.417514	+	0.908670i	$0.362901\pi$
$294$	−16.3518	−0.953658
$295$	−0.00213333	−0.000124207 0
$296$	−23.1436	−1.34520
$297$	26.5722	1.54187
$298$	−22.4352	−1.29964
$299$	27.3992	1.58454
$300$	20.6284	1.19098
$301$	−0.204773	−0.0118029
$302$	−9.04812	−0.520661
$303$	−3.31200	−0.190270
$304$	−49.8105	−2.85683
$305$	0.0440085	0.00251992
$306$	−31.6284	−1.80807
$307$	−10.0890	−0.575807	−0.287903	−	0.957659i	$-0.592958\pi$
$307$	−10.0890	−0.575807	−0.287903	+	0.957659i	$0.592958\pi$
$308$	−3.32424	−0.189416
$309$	1.43544	0.0816593
$310$	0.0838227	0.00476081
$311$	−13.3890	−0.759221	−0.379611	−	0.925146i	$-0.623942\pi$
$311$	−13.3890	−0.759221	−0.379611	+	0.925146i	$0.623942\pi$
$312$	24.9367	1.41176
$313$	14.1061	0.797323	0.398662	−	0.917098i	$-0.369475\pi$
$313$	14.1061	0.797323	0.398662	+	0.917098i	$0.369475\pi$
$314$	24.4016	1.37706
$315$	−0.00142029	−8.00245e−5 0
$316$	39.9594	2.24789
$317$	15.1958	0.853484	0.426742	−	0.904373i	$-0.359661\pi$
$317$	15.1958	0.853484	0.426742	+	0.904373i	$0.359661\pi$
$318$	−1.63568	−0.0917243
$319$	6.24268	0.349523
$320$	0.000696400 0	3.89300e−5 0
$321$	−8.82722	−0.492687
$322$	2.15378	0.120026
$323$	40.0924	2.23080
$324$	9.45123	0.525069
$325$	−21.4066	−1.18742
$326$	−48.1280	−2.66556
$327$	12.2594	0.677946
$328$	22.9286	1.26602
$329$	0.0560100	0.00308793
$330$	−0.0655011	−0.00360572
$331$	33.0920	1.81890	0.909451	−	0.415811i	$-0.136502\pi$
$331$	33.0920	1.81890	0.909451	+	0.415811i	$0.136502\pi$
$332$	14.0915	0.773370
$333$	−7.87172	−0.431367
$334$	59.9810	3.28202
$335$	−0.0723841	−0.00395477
$336$	0.869914	0.0474577
$337$	9.44809	0.514670	0.257335	−	0.966322i	$-0.417156\pi$
$337$	9.44809	0.514670	0.257335	+	0.966322i	$0.417156\pi$
$338$	−13.5752	−0.738391
$339$	−4.95962	−0.269370
$340$	0.129015	0.00699684
$341$	36.9868	2.00295
$342$	−38.1754	−2.06429
$343$	1.84757	0.0997595
$344$	−9.81727	−0.529312
$345$	0.0293545	0.00158039
$346$	−53.9506	−2.90040
$347$	29.5273	1.58511	0.792554	−	0.609801i	$-0.208751\pi$
$347$	29.5273	1.58511	0.792554	+	0.609801i	$0.208751\pi$
$348$	−4.59371	−0.246249
$349$	−22.2461	−1.19081	−0.595405	−	0.803426i	$-0.703008\pi$
$349$	−22.2461	−1.19081	−0.595405	+	0.803426i	$0.703008\pi$
$350$	−1.68272	−0.0899450
$351$	20.2909	1.08305
$352$	−31.2168	−1.66386
$353$	32.4164	1.72535	0.862674	−	0.505760i	$-0.168788\pi$
$353$	32.4164	1.72535	0.862674	+	0.505760i	$0.168788\pi$
$354$	1.00143	0.0532254
$355$	−0.0570068	−0.00302561
$356$	41.9964	2.22580
$357$	−0.700193	−0.0370581
$358$	54.0804	2.85824
$359$	11.1652	0.589276	0.294638	−	0.955609i	$-0.404801\pi$
$359$	11.1652	0.589276	0.294638	+	0.955609i	$0.404801\pi$
$360$	−0.0680921	−0.00358877
$361$	29.3916	1.54692
$362$	37.5490	1.97353
$363$	−18.7886	−0.986144
$364$	−2.53845	−0.133051
$365$	0.0388598	0.00203401
$366$	−20.6585	−1.07984
$367$	4.41283	0.230348	0.115174	−	0.993345i	$-0.463258\pi$
$367$	4.41283	0.230348	0.115174	+	0.993345i	$0.463258\pi$
$368$	45.8242	2.38875
$369$	7.79858	0.405978
$370$	0.0464213	0.00241333
$371$	0.0922913	0.00479153
$372$	−27.2170	−1.41114
$373$	−30.0648	−1.55670	−0.778348	−	0.627833i	$-0.783942\pi$
$373$	−30.0648	−1.55670	−0.778348	+	0.627833i	$0.783942\pi$
$374$	82.3019	4.25573
$375$	−0.0458685	−0.00236864
$376$	2.68525	0.138481
$377$	4.76701	0.245513
$378$	1.59502	0.0820388
$379$	2.03871	0.104721	0.0523607	−	0.998628i	$-0.483325\pi$
$379$	2.03871	0.104721	0.0523607	+	0.998628i	$0.483325\pi$
$380$	0.155722	0.00798835
$381$	15.2566	0.781622
$382$	21.3193	1.09079
$383$	10.9931	0.561720	0.280860	−	0.959749i	$-0.409380\pi$
$383$	10.9931	0.561720	0.280860	+	0.959749i	$0.409380\pi$
$384$	−10.5655	−0.539167
$385$	0.00369582	0.000188357 0
$386$	−12.8751	−0.655327
$387$	−3.33909	−0.169736
$388$	−39.5097	−2.00580
$389$	33.0476	1.67558	0.837789	−	0.545994i	$-0.183848\pi$
$389$	33.0476	1.67558	0.837789	+	0.545994i	$0.183848\pi$
$390$	−0.0500177	−0.00253274
$391$	−36.8839	−1.86530
$392$	44.2331	2.23411
$393$	16.7592	0.845391
$394$	25.4828	1.28380
$395$	−0.0444260	−0.00223532
$396$	−54.2062	−2.72397
$397$	−30.4586	−1.52867	−0.764337	−	0.644818i	$-0.776933\pi$
$397$	−30.4586	−1.52867	−0.764337	+	0.644818i	$0.776933\pi$
$398$	2.91703	0.146218
$399$	−0.845133	−0.0423096
$400$	−35.8017	−1.79009
$401$	−9.58603	−0.478704	−0.239352	−	0.970933i	$-0.576935\pi$
$401$	−9.58603	−0.478704	−0.239352	+	0.970933i	$0.576935\pi$
$402$	33.9785	1.69470
$403$	28.2437	1.40692
$404$	16.1636	0.804170
$405$	−0.0105077	−0.000522131 0
$406$	0.374722	0.0185971
$407$	20.4834	1.01533
$408$	−33.5688	−1.66190
$409$	8.78053	0.434169	0.217085	−	0.976153i	$-0.430345\pi$
$409$	8.78053	0.434169	0.217085	+	0.976153i	$0.430345\pi$
$410$	−0.0459899	−0.00227128
$411$	−12.5726	−0.620161
$412$	−7.00540	−0.345131
$413$	−0.0565045	−0.00278040
$414$	35.1203	1.72607
$415$	−0.0156666	−0.000769043 0
$416$	−23.8377	−1.16874
$417$	−6.17901	−0.302587
$418$	99.3384	4.85880
$419$	5.01986	0.245236	0.122618	−	0.992454i	$-0.460871\pi$
$419$	5.01986	0.245236	0.122618	+	0.992454i	$0.460871\pi$
$420$	−0.00271960	−0.000132703 0
$421$	−7.15490	−0.348708	−0.174354	−	0.984683i	$-0.555784\pi$
$421$	−7.15490	−0.348708	−0.174354	+	0.984683i	$0.555784\pi$
$422$	53.0743	2.58362
$423$	0.913318	0.0444070
$424$	4.42465	0.214880
$425$	28.8168	1.39782
$426$	26.7601	1.29653
$427$	1.16563	0.0564088
$428$	43.0796	2.08233
$429$	−22.0704	−1.06557
$430$	0.0196914	0.000949602 0
$431$	15.2131	0.732791	0.366395	−	0.930459i	$-0.380592\pi$
$431$	15.2131	0.732791	0.366395	+	0.930459i	$0.380592\pi$
$432$	33.9358	1.63274
$433$	37.7158	1.81251	0.906254	−	0.422734i	$-0.138930\pi$
$433$	37.7158	1.81251	0.906254	+	0.422734i	$0.138930\pi$
$434$	2.22017	0.106571
$435$	0.00510719	0.000244871 0
$436$	−59.8297	−2.86532
$437$	−44.5188	−2.12962
$438$	−18.2416	−0.871615
$439$	−6.55294	−0.312755	−0.156377	−	0.987697i	$-0.549982\pi$
$439$	−6.55294	−0.312755	−0.156377	+	0.987697i	$0.549982\pi$
$440$	0.177186	0.00844702
$441$	15.0448	0.716417
$442$	62.8471	2.98933
$443$	37.4385	1.77876	0.889379	−	0.457171i	$-0.151137\pi$
$443$	37.4385	1.77876	0.889379	+	0.457171i	$0.151137\pi$
$444$	−15.0729	−0.715326
$445$	−0.0466907	−0.00221335
$446$	−37.9292	−1.79600
$447$	−8.09892	−0.383066
$448$	0.0184452	0.000871454 0
$449$	0.596286	0.0281405	0.0140702	−	0.999901i	$-0.495521\pi$
$449$	0.596286	0.0281405	0.0140702	+	0.999901i	$0.495521\pi$
$450$	−27.4389	−1.29348
$451$	−20.2931	−0.955565
$452$	24.2045	1.13849
$453$	−3.26630	−0.153464
$454$	−41.1557	−1.93153
$455$	0.00282219	0.000132306 0
$456$	−40.5176	−1.89741
$457$	36.3978	1.70262	0.851309	−	0.524664i	$-0.175809\pi$
$457$	36.3978	1.70262	0.851309	+	0.524664i	$0.175809\pi$
$458$	11.7963	0.551203
$459$	−27.3149	−1.27495
$460$	−0.143259	−0.00667950
$461$	−36.4399	−1.69718	−0.848589	−	0.529053i	$-0.822547\pi$
$461$	−36.4399	−1.69718	−0.848589	+	0.529053i	$0.822547\pi$
$462$	−1.73489	−0.0807145
$463$	38.0092	1.76644	0.883218	−	0.468962i	$-0.155372\pi$
$463$	38.0092	1.76644	0.883218	+	0.468962i	$0.155372\pi$
$464$	7.97263	0.370120
$465$	0.0302593	0.00140324
$466$	26.0627	1.20733
$467$	12.9150	0.597633	0.298816	−	0.954311i	$-0.403408\pi$
$467$	12.9150	0.597633	0.298816	+	0.954311i	$0.403408\pi$
$468$	−41.3927	−1.91338
$469$	−1.91720	−0.0885281
$470$	−0.00538604	−0.000248439 0
$471$	8.80878	0.405887
$472$	−2.70895	−0.124690
$473$	8.68884	0.399513
$474$	20.8545	0.957877
$475$	34.7818	1.59590
$476$	3.41716	0.156625
$477$	1.50493	0.0689061
$478$	−54.6042	−2.49754
$479$	21.7375	0.993211	0.496606	−	0.867976i	$-0.334580\pi$
$479$	21.7375	0.993211	0.496606	+	0.867976i	$0.334580\pi$
$480$	−0.0255388	−0.00116568
$481$	15.6415	0.713190
$482$	12.1471	0.553283
$483$	0.777498	0.0353774
$484$	91.6941	4.16791
$485$	0.0439261	0.00199458
$486$	41.1460	1.86642
$487$	33.8375	1.53332	0.766661	−	0.642052i	$-0.221917\pi$
$487$	33.8375	1.53332	0.766661	+	0.642052i	$0.221917\pi$
$488$	55.8829	2.52970
$489$	−17.3738	−0.785670
$490$	−0.0887222	−0.00400806
$491$	−2.50531	−0.113063	−0.0565315	−	0.998401i	$-0.518004\pi$
$491$	−2.50531	−0.113063	−0.0565315	+	0.998401i	$0.518004\pi$
$492$	14.9328	0.673223
$493$	−6.41717	−0.289015
$494$	75.8564	3.41294
$495$	0.0602653	0.00270872
$496$	47.2366	2.12099
$497$	−1.50991	−0.0677287
$498$	7.35421	0.329550
$499$	18.9020	0.846169	0.423084	−	0.906090i	$-0.360947\pi$
$499$	18.9020	0.846169	0.423084	+	0.906090i	$0.360947\pi$
$500$	0.223853	0.0100110
$501$	21.6527	0.967369
$502$	23.3821	1.04360
$503$	11.4790	0.511824	0.255912	−	0.966700i	$-0.417624\pi$
$503$	11.4790	0.511824	0.255912	+	0.966700i	$0.417624\pi$
$504$	−1.80352	−0.0803351
$505$	−0.0179704	−0.000799671 0
$506$	−91.3885	−4.06271
$507$	−4.90052	−0.217640
$508$	−74.4572	−3.30351
$509$	−3.17455	−0.140709	−0.0703547	−	0.997522i	$-0.522413\pi$
$509$	−3.17455	−0.140709	−0.0703547	+	0.997522i	$0.522413\pi$
$510$	0.0673320	0.00298151
$511$	1.02926	0.0455317
$512$	50.8517	2.24735
$513$	−32.9691	−1.45562
$514$	−49.1025	−2.16582
$515$	0.00778845	0.000343200 0
$516$	−6.39373	−0.281468
$517$	−2.37659	−0.104523
$518$	1.22954	0.0540227
$519$	−19.4757	−0.854889
$520$	0.135302	0.00593339
$521$	9.39862	0.411761	0.205880	−	0.978577i	$-0.433994\pi$
$521$	9.39862	0.411761	0.205880	+	0.978577i	$0.433994\pi$
$522$	6.11034	0.267442
$523$	19.3112	0.844421	0.422211	−	0.906498i	$-0.361254\pi$
$523$	19.3112	0.844421	0.422211	+	0.906498i	$0.361254\pi$
$524$	−81.7903	−3.57303
$525$	−0.607447	−0.0265111
$526$	−23.6230	−1.03001
$527$	−38.0207	−1.65621
$528$	−36.9118	−1.60638
$529$	17.9560	0.780696
$530$	−0.00887492	−0.000385502 0
$531$	−0.921381	−0.0399845
$532$	4.12452	0.178820
$533$	−15.4961	−0.671212
$534$	21.9175	0.948465
$535$	−0.0478950	−0.00207068
$536$	−91.9149	−3.97012
$537$	19.5226	0.842461
$538$	−42.3766	−1.82698
$539$	−39.1488	−1.68626
$540$	−0.106093	−0.00456551
$541$	−3.83761	−0.164992	−0.0824959	−	0.996591i	$-0.526289\pi$
$541$	−3.83761	−0.164992	−0.0824959	+	0.996591i	$0.526289\pi$
$542$	18.9199	0.812679
$543$	13.5549	0.581695
$544$	32.0894	1.37582
$545$	0.0665174	0.00284929
$546$	−1.32479	−0.0566959
$547$	−33.3107	−1.42426	−0.712131	−	0.702047i	$-0.752270\pi$
$547$	−33.3107	−1.42426	−0.712131	+	0.702047i	$0.752270\pi$
$548$	61.3583	2.62110
$549$	19.0071	0.811205
$550$	71.4004	3.04452
$551$	−7.74552	−0.329970
$552$	37.2750	1.58653
$553$	−1.17669	−0.0500379
$554$	−62.6135	−2.66019
$555$	0.0167577	0.000711324 0
$556$	30.1555	1.27888
$557$	−10.9936	−0.465813	−0.232907	−	0.972499i	$-0.574824\pi$
$557$	−10.9936	−0.465813	−0.232907	+	0.972499i	$0.574824\pi$
$558$	36.2028	1.53259
$559$	6.63493	0.280628
$560$	0.00472000	0.000199457 0
$561$	29.7103	1.25437
$562$	−8.77883	−0.370313
$563$	26.2323	1.10556	0.552779	−	0.833328i	$-0.313567\pi$
$563$	26.2323	1.10556	0.552779	+	0.833328i	$0.313567\pi$
$564$	1.74883	0.0736391
$565$	−0.0269101	−0.00113212
$566$	33.5735	1.41120
$567$	−0.278311	−0.0116880
$568$	−72.3885	−3.03735
$569$	1.61722	0.0677972	0.0338986	−	0.999425i	$-0.489208\pi$
$569$	1.61722	0.0677972	0.0338986	+	0.999425i	$0.489208\pi$
$570$	0.0812697	0.00340401
$571$	31.1273	1.30264	0.651318	−	0.758805i	$-0.274216\pi$
$571$	31.1273	1.30264	0.651318	+	0.758805i	$0.274216\pi$
$572$	107.710	4.50360
$573$	7.69609	0.321509
$574$	−1.21811	−0.0508430
$575$	−31.9983	−1.33442
$576$	0.300773	0.0125322
$577$	−29.8247	−1.24162	−0.620808	−	0.783962i	$-0.713195\pi$
$577$	−29.8247	−1.24162	−0.620808	+	0.783962i	$0.713195\pi$
$578$	−41.3035	−1.71800
$579$	−4.64781	−0.193157
$580$	−0.0249247	−0.00103494
$581$	−0.414953	−0.0172151
$582$	−20.6198	−0.854717
$583$	−3.91607	−0.162187
$584$	49.3450	2.04191
$585$	0.0460196	0.00190267
$586$	−36.4052	−1.50388
$587$	−7.69834	−0.317745	−0.158872	−	0.987299i	$-0.550786\pi$
$587$	−7.69834	−0.317745	−0.158872	+	0.987299i	$0.550786\pi$
$588$	28.8079	1.18802
$589$	−45.8910	−1.89091
$590$	0.00543359	0.000223697 0
$591$	9.19906	0.378399
$592$	26.1598	1.07516
$593$	15.4321	0.633722	0.316861	−	0.948472i	$-0.397371\pi$
$593$	15.4321	0.633722	0.316861	+	0.948472i	$0.397371\pi$
$594$	−67.6791	−2.77691
$595$	−0.00379913	−0.000155749 0
$596$	39.5253	1.61902
$597$	1.05303	0.0430974
$598$	−69.7857	−2.85375
$599$	−19.0519	−0.778441	−0.389221	−	0.921145i	$-0.627256\pi$
$599$	−19.0519	−0.778441	−0.389221	+	0.921145i	$0.627256\pi$
$600$	−29.1224	−1.18892
$601$	34.9430	1.42536	0.712678	−	0.701492i	$-0.247482\pi$
$601$	34.9430	1.42536	0.712678	+	0.701492i	$0.247482\pi$
$602$	0.521555	0.0212570
$603$	−31.2625	−1.27311
$604$	15.9406	0.648612
$605$	−0.101944	−0.00414460
$606$	8.43565	0.342675
$607$	−6.67583	−0.270963	−0.135482	−	0.990780i	$-0.543258\pi$
$607$	−6.67583	−0.270963	−0.135482	+	0.990780i	$0.543258\pi$
$608$	38.7319	1.57079
$609$	0.135271	0.00548148
$610$	−0.112089	−0.00453837
$611$	−1.81481	−0.0734192
$612$	55.7214	2.25240
$613$	16.2939	0.658105	0.329052	−	0.944312i	$-0.393271\pi$
$613$	16.2939	0.658105	0.329052	+	0.944312i	$0.393271\pi$
$614$	25.6965	1.03703
$615$	−0.0166020	−0.000669457 0
$616$	4.69304	0.189088
$617$	−41.7478	−1.68070	−0.840352	−	0.542040i	$-0.817652\pi$
$617$	−41.7478	−1.68070	−0.840352	+	0.542040i	$0.817652\pi$
$618$	−3.65605	−0.147068
$619$	9.76112	0.392333	0.196166	−	0.980571i	$-0.437151\pi$
$619$	9.76112	0.392333	0.196166	+	0.980571i	$0.437151\pi$
$620$	−0.147675	−0.00593077
$621$	30.3306	1.21712
$622$	34.1017	1.36735
$623$	−1.23667	−0.0495462
$624$	−28.1865	−1.12836
$625$	24.9996	0.999985
$626$	−35.9281	−1.43598
$627$	35.8603	1.43212
$628$	−42.9896	−1.71547
$629$	−21.0560	−0.839557
$630$	0.00361748	0.000144124 0
$631$	−6.55693	−0.261027	−0.130514	−	0.991447i	$-0.541663\pi$
$631$	−6.55693	−0.261027	−0.130514	+	0.991447i	$0.541663\pi$
$632$	−56.4131	−2.24399
$633$	19.1594	0.761517
$634$	−38.7037	−1.53712
$635$	0.0827800	0.00328502
$636$	2.88166	0.114265
$637$	−29.8946	−1.18447
$638$	−15.9001	−0.629489
$639$	−24.6211	−0.973995
$640$	−0.0573264	−0.00226603
$641$	34.3272	1.35584	0.677922	−	0.735134i	$-0.262881\pi$
$641$	34.3272	1.35584	0.677922	+	0.735134i	$0.262881\pi$
$642$	22.4829	0.887328
$643$	−2.32588	−0.0917238	−0.0458619	−	0.998948i	$-0.514603\pi$
$643$	−2.32588	−0.0917238	−0.0458619	+	0.998948i	$0.514603\pi$
$644$	−3.79443	−0.149522
$645$	0.00710842	0.000279894 0
$646$	−102.115	−4.01767
$647$	−17.8101	−0.700186	−0.350093	−	0.936715i	$-0.613850\pi$
$647$	−17.8101	−0.700186	−0.350093	+	0.936715i	$0.613850\pi$
$648$	−13.3429	−0.524158
$649$	2.39758	0.0941131
$650$	54.5225	2.13855
$651$	0.801462	0.0314118
$652$	84.7896	3.32062
$653$	−37.2591	−1.45806	−0.729031	−	0.684480i	$-0.760029\pi$
$653$	−37.2591	−1.45806	−0.729031	+	0.684480i	$0.760029\pi$
$654$	−31.2246	−1.22098
$655$	0.0909327	0.00355303
$656$	−25.9167	−1.01188
$657$	16.7834	0.654784
$658$	−0.142657	−0.00556135
$659$	−27.8300	−1.08410	−0.542052	−	0.840345i	$-0.682352\pi$
$659$	−27.8300	−1.08410	−0.542052	+	0.840345i	$0.682352\pi$
$660$	0.115397	0.00449181
$661$	22.0184	0.856417	0.428208	−	0.903680i	$-0.359145\pi$
$661$	22.0184	0.856417	0.428208	+	0.903680i	$0.359145\pi$
$662$	−84.2851	−3.27583
$663$	22.6873	0.881100
$664$	−19.8938	−0.772028
$665$	−0.00458555	−0.000177820 0
$666$	20.0492	0.776891
$667$	7.12566	0.275906
$668$	−105.672	−4.08857
$669$	−13.6921	−0.529368
$670$	0.184362	0.00712252
$671$	−49.4596	−1.90937
$672$	−0.676432	−0.0260939
$673$	12.9910	0.500765	0.250383	−	0.968147i	$-0.419444\pi$
$673$	12.9910	0.500765	0.250383	+	0.968147i	$0.419444\pi$
$674$	−24.0642	−0.926919
$675$	−23.6968	−0.912090
$676$	23.9161	0.919849
$677$	19.2858	0.741214	0.370607	−	0.928790i	$-0.379150\pi$
$677$	19.2858	0.741214	0.370607	+	0.928790i	$0.379150\pi$
$678$	12.6321	0.485134
$679$	1.16345	0.0446490
$680$	−0.182139	−0.00698470
$681$	−14.8569	−0.569316
$682$	−94.2052	−3.60731
$683$	3.84053	0.146954	0.0734769	−	0.997297i	$-0.476590\pi$
$683$	3.84053	0.146954	0.0734769	+	0.997297i	$0.476590\pi$
$684$	67.2557	2.57159
$685$	−0.0682168	−0.00260643
$686$	−4.70575	−0.179667
$687$	4.25835	0.162466
$688$	11.0967	0.423057
$689$	−2.99037	−0.113924
$690$	−0.0747657	−0.00284628
$691$	−4.53712	−0.172600	−0.0863001	−	0.996269i	$-0.527504\pi$
$691$	−4.53712	−0.172600	−0.0863001	+	0.996269i	$0.527504\pi$
$692$	95.0476	3.61317
$693$	1.59622	0.0606352
$694$	−75.2058	−2.85477
$695$	−0.0335263	−0.00127172
$696$	6.48522	0.245822
$697$	20.8603	0.790142
$698$	56.6608	2.14464
$699$	9.40841	0.355859
$700$	2.96453	0.112049
$701$	16.3276	0.616686	0.308343	−	0.951275i	$-0.400226\pi$
$701$	16.3276	0.616686	0.308343	+	0.951275i	$0.400226\pi$
$702$	−51.6808	−1.95057
$703$	−25.4146	−0.958529
$704$	−0.782659	−0.0294976
$705$	−0.00194431	−7.32271e−5 0
$706$	−82.5642	−3.10735
$707$	−0.475972	−0.0179008
$708$	−1.76427	−0.0663054
$709$	1.04251	0.0391523	0.0195761	−	0.999808i	$-0.493768\pi$
$709$	1.04251	0.0391523	0.0195761	+	0.999808i	$0.493768\pi$
$710$	0.145196	0.00544911
$711$	−19.1875	−0.719586
$712$	−59.2888	−2.22194
$713$	42.2184	1.58109
$714$	1.78339	0.0667416
$715$	−0.119750	−0.00447840
$716$	−95.2763	−3.56064
$717$	−19.7117	−0.736145
$718$	−28.4376	−1.06128
$719$	21.2837	0.793749	0.396875	−	0.917873i	$-0.370095\pi$
$719$	21.2837	0.793749	0.396875	+	0.917873i	$0.370095\pi$
$720$	0.0769659	0.00286835
$721$	0.206289	0.00768259
$722$	−74.8601	−2.78600
$723$	4.38498	0.163079
$724$	−66.1520	−2.45852
$725$	−5.56716	−0.206759
$726$	47.8543	1.77604
$727$	10.6453	0.394813	0.197406	−	0.980322i	$-0.436748\pi$
$727$	10.6453	0.394813	0.197406	+	0.980322i	$0.436748\pi$
$728$	3.58368	0.132820
$729$	8.53455	0.316094
$730$	−0.0989756	−0.00366325
$731$	−8.93170	−0.330351
$732$	36.3951	1.34520
$733$	49.2118	1.81768	0.908840	−	0.417145i	$-0.136969\pi$
$733$	49.2118	1.81768	0.908840	+	0.417145i	$0.136969\pi$
$734$	−11.2394	−0.414855
$735$	−0.0320280	−0.00118137
$736$	−35.6322	−1.31342
$737$	81.3499	2.99656
$738$	−19.8629	−0.731164
$739$	11.3132	0.416164	0.208082	−	0.978111i	$-0.433278\pi$
$739$	11.3132	0.416164	0.208082	+	0.978111i	$0.433278\pi$
$740$	−0.0817828	−0.00300640
$741$	27.3835	1.00596
$742$	−0.235065	−0.00862952
$743$	30.3159	1.11218	0.556091	−	0.831122i	$-0.312301\pi$
$743$	30.3159	1.11218	0.556091	+	0.831122i	$0.312301\pi$
$744$	38.4239	1.40869
$745$	−0.0439434	−0.00160996
$746$	76.5748	2.80360
$747$	−6.76636	−0.247568
$748$	−144.996	−5.30157
$749$	−1.26857	−0.0463525
$750$	0.116827	0.00426591
$751$	33.8317	1.23454	0.617269	−	0.786752i	$-0.288239\pi$
$751$	33.8317	1.23454	0.617269	+	0.786752i	$0.288239\pi$
$752$	−3.03519	−0.110682
$753$	8.44076	0.307598
$754$	−12.1415	−0.442169
$755$	−0.0177224	−0.000644983 0
$756$	−2.81002	−0.102200
$757$	−32.9599	−1.19795	−0.598975	−	0.800768i	$-0.704425\pi$
$757$	−32.9599	−1.19795	−0.598975	+	0.800768i	$0.704425\pi$
$758$	−5.19257	−0.188603
$759$	−32.9905	−1.19748
$760$	−0.219842	−0.00797449
$761$	37.8923	1.37359	0.686797	−	0.726849i	$-0.259016\pi$
$761$	37.8923	1.37359	0.686797	+	0.726849i	$0.259016\pi$
$762$	−38.8586	−1.40770
$763$	1.76181	0.0637819
$764$	−37.5593	−1.35885
$765$	−0.0619498	−0.00223980
$766$	−27.9993	−1.01165
$767$	1.83083	0.0661073
$768$	26.6535	0.961774
$769$	−13.6451	−0.492057	−0.246028	−	0.969263i	$-0.579126\pi$
$769$	−13.6451	−0.492057	−0.246028	+	0.969263i	$0.579126\pi$
$770$	−0.00941324	−0.000339230 0
$771$	−17.7256	−0.638372
$772$	22.6828	0.816372
$773$	16.3568	0.588312	0.294156	−	0.955757i	$-0.404961\pi$
$773$	16.3568	0.588312	0.294156	+	0.955757i	$0.404961\pi$
$774$	8.50464	0.305693
$775$	−32.9845	−1.18484
$776$	55.7783	2.00232
$777$	0.443852	0.0159231
$778$	−84.1719	−3.01771
$779$	25.1784	0.902111
$780$	0.0881188	0.00315516
$781$	64.0679	2.29253
$782$	93.9429	3.35939
$783$	5.27701	0.188585
$784$	−49.9976	−1.78563
$785$	0.0477949	0.00170587
$786$	−42.6856	−1.52255
$787$	43.2127	1.54037	0.770183	−	0.637823i	$-0.220165\pi$
$787$	43.2127	1.54037	0.770183	+	0.637823i	$0.220165\pi$
$788$	−44.8943	−1.59929
$789$	−8.52772	−0.303595
$790$	0.113153	0.00402579
$791$	−0.712753	−0.0253426
$792$	76.5262	2.71924
$793$	−37.7681	−1.34118
$794$	77.5778	2.75313
$795$	−0.00320377	−0.000113626 0
$796$	−5.13910	−0.182150
$797$	−41.2363	−1.46067	−0.730333	−	0.683091i	$-0.760635\pi$
$797$	−41.2363	−1.46067	−0.730333	+	0.683091i	$0.760635\pi$
$798$	2.15255	0.0761994
$799$	2.44302	0.0864280
$800$	27.8389	0.984253
$801$	−20.1656	−0.712516
$802$	24.4156	0.862143
$803$	−43.6731	−1.54119
$804$	−59.8618	−2.11116
$805$	0.00421857	0.000148685 0
$806$	−71.9366	−2.53386
$807$	−15.2976	−0.538500
$808$	−22.8192	−0.802775
$809$	8.31538	0.292353	0.146177	−	0.989259i	$-0.453303\pi$
$809$	8.31538	0.292353	0.146177	+	0.989259i	$0.453303\pi$
$810$	0.0267630	0.000940356 0
$811$	25.4116	0.892321	0.446160	−	0.894953i	$-0.352791\pi$
$811$	25.4116	0.892321	0.446160	+	0.894953i	$0.352791\pi$
$812$	−0.660168	−0.0231673
$813$	6.82993	0.239536
$814$	−52.1712	−1.82860
$815$	−0.0942673	−0.00330204
$816$	37.9436	1.32829
$817$	−10.7806	−0.377164
$818$	−22.3639	−0.781937
$819$	1.21890	0.0425917
$820$	0.0810229	0.00282944
$821$	−0.188389	−0.00657482	−0.00328741	−	0.999995i	$-0.501046\pi$
$821$	−0.188389	−0.00657482	−0.00328741	+	0.999995i	$0.501046\pi$
$822$	32.0223	1.11691
$823$	2.93960	0.102468	0.0512340	−	0.998687i	$-0.483685\pi$
$823$	2.93960	0.102468	0.0512340	+	0.998687i	$0.483685\pi$
$824$	9.88994	0.344533
$825$	25.7749	0.897368
$826$	0.143917	0.00500750
$827$	5.22540	0.181705	0.0908526	−	0.995864i	$-0.471041\pi$
$827$	5.22540	0.181705	0.0908526	+	0.995864i	$0.471041\pi$
$828$	−61.8733	−2.15025
$829$	12.2304	0.424779	0.212389	−	0.977185i	$-0.431875\pi$
$829$	12.2304	0.424779	0.212389	+	0.977185i	$0.431875\pi$
$830$	0.0399027	0.00138504
$831$	−22.6030	−0.784088
$832$	−0.597651	−0.0207198
$833$	40.2431	1.39434
$834$	15.7379	0.544959
$835$	0.117484	0.00406569
$836$	−175.010	−6.05284
$837$	31.2654	1.08069
$838$	−12.7856	−0.441670
$839$	−34.6254	−1.19540	−0.597700	−	0.801720i	$-0.703919\pi$
$839$	−34.6254	−1.19540	−0.597700	+	0.801720i	$0.703919\pi$
$840$	0.00383942	0.000132472 0
$841$	−27.7603	−0.957250
$842$	18.2235	0.628022
$843$	−3.16908	−0.109149
$844$	−93.5039	−3.21854
$845$	−0.0265894	−0.000914703 0
$846$	−2.32621	−0.0799769
$847$	−2.70013	−0.0927774
$848$	−5.00128	−0.171745
$849$	12.1198	0.415949
$850$	−73.3961	−2.51747
$851$	23.3807	0.801479
$852$	−47.1448	−1.61515
$853$	−41.2028	−1.41076	−0.705379	−	0.708830i	$-0.749223\pi$
$853$	−41.2028	−1.41076	−0.705379	+	0.708830i	$0.749223\pi$
$854$	−2.96885	−0.101592
$855$	−0.0747735	−0.00255720
$856$	−60.8181	−2.07872
$857$	−42.5430	−1.45324	−0.726620	−	0.687040i	$-0.758910\pi$
$857$	−42.5430	−1.45324	−0.726620	+	0.687040i	$0.758910\pi$
$858$	56.2131	1.91908
$859$	−11.8359	−0.403835	−0.201917	−	0.979403i	$-0.564717\pi$
$859$	−11.8359	−0.403835	−0.201917	+	0.979403i	$0.564717\pi$
$860$	−0.0346913	−0.00118296
$861$	−0.439728	−0.0149859
$862$	−38.7477	−1.31975
$863$	−23.3851	−0.796037	−0.398019	−	0.917377i	$-0.630302\pi$
$863$	−23.3851	−0.796037	−0.398019	+	0.917377i	$0.630302\pi$
$864$	−26.3880	−0.897737
$865$	−0.105672	−0.00359295
$866$	−96.0620	−3.26432
$867$	−14.9102	−0.506378
$868$	−3.91139	−0.132761
$869$	49.9288	1.69372
$870$	−0.0130080	−0.000441012 0
$871$	62.1200	2.10486
$872$	84.4652	2.86035
$873$	18.9715	0.642090
$874$	113.389	3.83544
$875$	−0.00659182	−0.000222844 0
$876$	32.1371	1.08581
$877$	3.34805	0.113056	0.0565278	−	0.998401i	$-0.481997\pi$
$877$	3.34805	0.113056	0.0565278	+	0.998401i	$0.481997\pi$
$878$	16.6903	0.563270
$879$	−13.1420	−0.443267
$880$	−0.200277	−0.00675135
$881$	−20.3096	−0.684248	−0.342124	−	0.939655i	$-0.611146\pi$
$881$	−20.3096	−0.684248	−0.342124	+	0.939655i	$0.611146\pi$
$882$	−38.3189	−1.29026
$883$	−53.3092	−1.79400	−0.896999	−	0.442033i	$-0.854257\pi$
$883$	−53.3092	−1.79400	−0.896999	+	0.442033i	$0.854257\pi$
$884$	−110.721	−3.72395
$885$	0.00196148	6.59344e−5 0
$886$	−95.3556	−3.20354
$887$	28.4212	0.954290	0.477145	−	0.878825i	$-0.341672\pi$
$887$	28.4212	0.954290	0.477145	+	0.878825i	$0.341672\pi$
$888$	21.2793	0.714085
$889$	2.19255	0.0735358
$890$	0.118921	0.00398624
$891$	11.8092	0.395623
$892$	66.8218	2.23736
$893$	2.94873	0.0986755
$894$	20.6279	0.689900
$895$	0.105926	0.00354072
$896$	−1.51838	−0.0507254
$897$	−25.1920	−0.841138
$898$	−1.51874	−0.0506809
$899$	7.34528	0.244979
$900$	48.3406	1.61135
$901$	4.02553	0.134110
$902$	51.6864	1.72097
$903$	0.188277	0.00626546
$904$	−34.1710	−1.13651
$905$	0.0735464	0.00244477
$906$	8.31924	0.276388
$907$	−25.8031	−0.856778	−0.428389	−	0.903594i	$-0.640919\pi$
$907$	−25.8031	−0.856778	−0.428389	+	0.903594i	$0.640919\pi$
$908$	72.5062	2.40620
$909$	−7.76135	−0.257428
$910$	−0.00718810	−0.000238283 0
$911$	4.69496	0.155551	0.0777755	−	0.996971i	$-0.475218\pi$
$911$	4.69496	0.155551	0.0777755	+	0.996971i	$0.475218\pi$
$912$	45.7979	1.51652
$913$	17.6071	0.582710
$914$	−92.7050	−3.06641
$915$	−0.0404633	−0.00133768
$916$	−20.7821	−0.686660
$917$	2.40849	0.0795352
$918$	69.5708	2.29618
$919$	0.415191	0.0136959	0.00684794	−	0.999977i	$-0.497820\pi$
$919$	0.415191	0.0136959	0.00684794	+	0.999977i	$0.497820\pi$
$920$	0.202248	0.00666791
$921$	9.27622	0.305662
$922$	92.8123	3.05661
$923$	48.9233	1.61033
$924$	3.05645	0.100550
$925$	−18.2669	−0.600613
$926$	−96.8091	−3.18134
$927$	3.36381	0.110482
$928$	−6.19940	−0.203505
$929$	27.8702	0.914392	0.457196	−	0.889366i	$-0.348854\pi$
$929$	27.8702	0.914392	0.457196	+	0.889366i	$0.348854\pi$
$930$	−0.0770702	−0.00252723
$931$	48.5734	1.59193
$932$	−45.9160	−1.50403
$933$	12.3104	0.403026
$934$	−32.8943	−1.07633
$935$	0.161203	0.00527191
$936$	58.4366	1.91006
$937$	5.72390	0.186992	0.0934959	−	0.995620i	$-0.470196\pi$
$937$	5.72390	0.186992	0.0934959	+	0.995620i	$0.470196\pi$
$938$	4.88309	0.159439
$939$	−12.9697	−0.423252
$940$	0.00948887	0.000309493 0
$941$	14.9870	0.488561	0.244281	−	0.969705i	$-0.421448\pi$
$941$	14.9870	0.488561	0.244281	+	0.969705i	$0.421448\pi$
$942$	−22.4359	−0.731001
$943$	−23.1634	−0.754305
$944$	3.06199	0.0996592
$945$	0.00312413	0.000101628 0
$946$	−22.1304	−0.719521
$947$	17.2751	0.561366	0.280683	−	0.959801i	$-0.409439\pi$
$947$	17.2751	0.561366	0.280683	+	0.959801i	$0.409439\pi$
$948$	−36.7404	−1.19327
$949$	−33.3495	−1.08257
$950$	−88.5891	−2.87421
$951$	−13.9717	−0.453064
$952$	−4.82421	−0.156354
$953$	−21.2276	−0.687631	−0.343815	−	0.939037i	$-0.611719\pi$
$953$	−21.2276	−0.687631	−0.343815	+	0.939037i	$0.611719\pi$
$954$	−3.83305	−0.124100
$955$	0.0417577	0.00135125
$956$	96.1991	3.11130
$957$	−5.73979	−0.185541
$958$	−55.3652	−1.78877
$959$	−1.80682	−0.0583454
$960$	−0.000640301 0	−2.06656e−5 0
$961$	12.5196	0.403859
$962$	−39.8387	−1.28445
$963$	−20.6857	−0.666588
$964$	−21.4001	−0.689251
$965$	−0.0252183	−0.000811804 0
$966$	−1.98028	−0.0637145
$967$	17.7383	0.570426	0.285213	−	0.958464i	$-0.407936\pi$
$967$	17.7383	0.570426	0.285213	+	0.958464i	$0.407936\pi$
$968$	−129.450	−4.16068
$969$	−36.8627	−1.18420
$970$	−0.111879	−0.00359223
$971$	−56.1507	−1.80196	−0.900980	−	0.433860i	$-0.857151\pi$
$971$	−56.1507	−1.80196	−0.900980	+	0.433860i	$0.857151\pi$
$972$	−72.4892	−2.32509
$973$	−0.887993	−0.0284677
$974$	−86.1838	−2.76151
$975$	19.6821	0.630333
$976$	−63.1657	−2.02188
$977$	−17.3861	−0.556230	−0.278115	−	0.960548i	$-0.589710\pi$
$977$	−17.3861	−0.556230	−0.278115	+	0.960548i	$0.589710\pi$
$978$	44.2509	1.41499
$979$	52.4740	1.67708
$980$	0.156307	0.00499303
$981$	28.7287	0.917236
$982$	6.38101	0.203626
$983$	42.6594	1.36062	0.680311	−	0.732924i	$-0.261845\pi$
$983$	42.6594	1.36062	0.680311	+	0.732924i	$0.261845\pi$
$984$	−21.0816	−0.672055
$985$	0.0499126	0.00159035
$986$	16.3445	0.520514
$987$	−0.0514980	−0.00163920
$988$	−133.640	−4.25166
$989$	9.91781	0.315368
$990$	−0.153495	−0.00487840
$991$	3.73568	0.118668	0.0593340	−	0.998238i	$-0.481102\pi$
$991$	3.73568	0.118668	0.0593340	+	0.998238i	$0.481102\pi$
$992$	−36.7305	−1.16619
$993$	−30.4262	−0.965547
$994$	3.84573	0.121979
$995$	0.00571354	0.000181131 0
$996$	−12.9563	−0.410536
$997$	43.5670	1.37978	0.689890	−	0.723914i	$-0.257659\pi$
$997$	43.5670	1.37978	0.689890	+	0.723914i	$0.257659\pi$
$998$	−48.1432	−1.52395
$999$	17.3149	0.547819

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4003.2.a.c.1.10	✓	179

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4003.2.a.c.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-2.54699 q^{2} -0.919443 q^{3} +4.48717 q^{4} -0.00498874 q^{5} +2.34182 q^{6} -0.132134 q^{7} -6.33481 q^{8} -2.15462 q^{9} +O(q^{10})\)	\(q-2.54699 q^{2} -0.919443 q^{3} +4.48717 q^{4} -0.00498874 q^{5} +2.34182 q^{6} -0.132134 q^{7} -6.33481 q^{8} -2.15462 q^{9} +0.0127063 q^{10} +5.60667 q^{11} -4.12570 q^{12} +4.28134 q^{13} +0.336545 q^{14} +0.00458687 q^{15} +7.16038 q^{16} -5.76338 q^{17} +5.48781 q^{18} -6.95640 q^{19} -0.0223854 q^{20} +0.121490 q^{21} -14.2801 q^{22} +6.39969 q^{23} +5.82450 q^{24} -4.99998 q^{25} -10.9045 q^{26} +4.73938 q^{27} -0.592909 q^{28} +1.11344 q^{29} -0.0116827 q^{30} +6.59694 q^{31} -5.56780 q^{32} -5.15501 q^{33} +14.6793 q^{34} +0.000659184 q^{35} -9.66817 q^{36} +3.65341 q^{37} +17.7179 q^{38} -3.93645 q^{39} +0.0316028 q^{40} -3.61946 q^{41} -0.309434 q^{42} +1.54973 q^{43} +25.1581 q^{44} +0.0107489 q^{45} -16.3000 q^{46} -0.423887 q^{47} -6.58356 q^{48} -6.98254 q^{49} +12.7349 q^{50} +5.29910 q^{51} +19.2111 q^{52} -0.698466 q^{53} -12.0712 q^{54} -0.0279702 q^{55} +0.837046 q^{56} +6.39602 q^{57} -2.83592 q^{58} +0.427629 q^{59} +0.0205821 q^{60} -8.82156 q^{61} -16.8024 q^{62} +0.284700 q^{63} -0.139594 q^{64} -0.0213585 q^{65} +13.1298 q^{66} +14.5095 q^{67} -25.8613 q^{68} -5.88415 q^{69} -0.00167894 q^{70} +11.4271 q^{71} +13.6491 q^{72} -7.78949 q^{73} -9.30520 q^{74} +4.59719 q^{75} -31.2146 q^{76} -0.740833 q^{77} +10.0261 q^{78} +8.90525 q^{79} -0.0357213 q^{80} +2.10628 q^{81} +9.21874 q^{82} +3.14039 q^{83} +0.545146 q^{84} +0.0287520 q^{85} -3.94716 q^{86} -1.02374 q^{87} -35.5172 q^{88} +9.35921 q^{89} -0.0273773 q^{90} -0.565712 q^{91} +28.7165 q^{92} -6.06551 q^{93} +1.07964 q^{94} +0.0347037 q^{95} +5.11928 q^{96} -8.80504 q^{97} +17.7845 q^{98} -12.0803 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9}+O(q^{10}) \) 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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