LMFDB - Embedded newform 4003.2.a.c.1.6

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			1.6
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)

$f(q)$	$=$	$q-2.62123 q^{2} +2.13484 q^{3} +4.87085 q^{4} +4.03687 q^{5} -5.59591 q^{6} +2.86410 q^{7} -7.52515 q^{8} +1.55755 q^{9} +O(q^{10})$	\(q-2.62123 q^{2} +2.13484 q^{3} +4.87085 q^{4} +4.03687 q^{5} -5.59591 q^{6} +2.86410 q^{7} -7.52515 q^{8} +1.55755 q^{9} -10.5816 q^{10} +0.867170 q^{11} +10.3985 q^{12} -7.15978 q^{13} -7.50747 q^{14} +8.61809 q^{15} +9.98346 q^{16} +0.681304 q^{17} -4.08269 q^{18} +6.21847 q^{19} +19.6630 q^{20} +6.11440 q^{21} -2.27305 q^{22} -0.0962687 q^{23} -16.0650 q^{24} +11.2964 q^{25} +18.7674 q^{26} -3.07941 q^{27} +13.9506 q^{28} +0.607666 q^{29} -22.5900 q^{30} +5.46088 q^{31} -11.1186 q^{32} +1.85127 q^{33} -1.78585 q^{34} +11.5620 q^{35} +7.58657 q^{36} -6.27561 q^{37} -16.3000 q^{38} -15.2850 q^{39} -30.3781 q^{40} -7.97706 q^{41} -16.0273 q^{42} -3.42647 q^{43} +4.22385 q^{44} +6.28762 q^{45} +0.252343 q^{46} +8.34611 q^{47} +21.3131 q^{48} +1.20308 q^{49} -29.6104 q^{50} +1.45448 q^{51} -34.8742 q^{52} +9.41132 q^{53} +8.07184 q^{54} +3.50066 q^{55} -21.5528 q^{56} +13.2754 q^{57} -1.59283 q^{58} +2.34322 q^{59} +41.9774 q^{60} -4.64538 q^{61} -14.3142 q^{62} +4.46097 q^{63} +9.17758 q^{64} -28.9031 q^{65} -4.85261 q^{66} +12.6045 q^{67} +3.31853 q^{68} -0.205518 q^{69} -30.3067 q^{70} +3.23618 q^{71} -11.7208 q^{72} +14.8508 q^{73} +16.4498 q^{74} +24.1159 q^{75} +30.2892 q^{76} +2.48366 q^{77} +40.0655 q^{78} -5.38099 q^{79} +40.3020 q^{80} -11.2467 q^{81} +20.9097 q^{82} +11.5691 q^{83} +29.7823 q^{84} +2.75034 q^{85} +8.98158 q^{86} +1.29727 q^{87} -6.52559 q^{88} -0.0274887 q^{89} -16.4813 q^{90} -20.5063 q^{91} -0.468910 q^{92} +11.6581 q^{93} -21.8771 q^{94} +25.1032 q^{95} -23.7365 q^{96} -4.26065 q^{97} -3.15354 q^{98} +1.35066 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.62123	−1.85349	−0.926745	−	0.375692i	$-0.877405\pi$
$2$	−2.62123	−1.85349	−0.926745	+	0.375692i	$0.877405\pi$
$3$	2.13484	1.23255	0.616276	−	0.787531i	$-0.288641\pi$
$3$	2.13484	1.23255	0.616276	+	0.787531i	$0.288641\pi$
$4$	4.87085	2.43542
$5$	4.03687	1.80535	0.902673	−	0.430328i	$-0.141602\pi$
$5$	4.03687	1.80535	0.902673	+	0.430328i	$0.141602\pi$
$6$	−5.59591	−2.28452
$7$	2.86410	1.08253	0.541264	−	0.840853i	$-0.317946\pi$
$7$	2.86410	1.08253	0.541264	+	0.840853i	$0.317946\pi$
$8$	−7.52515	−2.66054
$9$	1.55755	0.519182
$10$	−10.5816	−3.34619
$11$	0.867170	0.261462	0.130731	−	0.991418i	$-0.458268\pi$
$11$	0.867170	0.261462	0.130731	+	0.991418i	$0.458268\pi$
$12$	10.3985	3.00178
$13$	−7.15978	−1.98576	−0.992882	−	0.119100i	$-0.961999\pi$
$13$	−7.15978	−1.98576	−0.992882	+	0.119100i	$0.961999\pi$
$14$	−7.50747	−2.00646
$15$	8.61809	2.22518
$16$	9.98346	2.49586
$17$	0.681304	0.165240	0.0826202	−	0.996581i	$-0.473671\pi$
$17$	0.681304	0.165240	0.0826202	+	0.996581i	$0.473671\pi$
$18$	−4.08269	−0.962299
$19$	6.21847	1.42661	0.713307	−	0.700851i	$-0.247196\pi$
$19$	6.21847	1.42661	0.713307	+	0.700851i	$0.247196\pi$
$20$	19.6630	4.39678
$21$	6.11440	1.33427
$22$	−2.27305	−0.484617
$23$	−0.0962687	−0.0200734	−0.0100367	−	0.999950i	$-0.503195\pi$
$23$	−0.0962687	−0.0200734	−0.0100367	+	0.999950i	$0.503195\pi$
$24$	−16.0650	−3.27925
$25$	11.2964	2.25927
$26$	18.7674	3.68059
$27$	−3.07941	−0.592633
$28$	13.9506	2.63642
$29$	0.607666	0.112841	0.0564204	−	0.998407i	$-0.482031\pi$
$29$	0.607666	0.112841	0.0564204	+	0.998407i	$0.482031\pi$
$30$	−22.5900	−4.12435
$31$	5.46088	0.980803	0.490402	−	0.871497i	$-0.336850\pi$
$31$	5.46088	0.980803	0.490402	+	0.871497i	$0.336850\pi$
$32$	−11.1186	−1.96552
$33$	1.85127	0.322265
$34$	−1.78585	−0.306271
$35$	11.5620	1.95434
$36$	7.58657	1.26443
$37$	−6.27561	−1.03170	−0.515852	−	0.856678i	$-0.672524\pi$
$37$	−6.27561	−1.03170	−0.515852	+	0.856678i	$0.672524\pi$
$38$	−16.3000	−2.64422
$39$	−15.2850	−2.44756
$40$	−30.3781	−4.80320
$41$	−7.97706	−1.24581	−0.622904	−	0.782299i	$-0.714047\pi$
$41$	−7.97706	−1.24581	−0.622904	+	0.782299i	$0.714047\pi$
$42$	−16.0273	−2.47306
$43$	−3.42647	−0.522532	−0.261266	−	0.965267i	$-0.584140\pi$
$43$	−3.42647	−0.522532	−0.261266	+	0.965267i	$0.584140\pi$
$44$	4.22385	0.636770
$45$	6.28762	0.937303
$46$	0.252343	0.0372059
$47$	8.34611	1.21740	0.608702	−	0.793399i	$-0.291690\pi$
$47$	8.34611	1.21740	0.608702	+	0.793399i	$0.291690\pi$
$48$	21.3131	3.07628
$49$	1.20308	0.171868
$50$	−29.6104	−4.18754
$51$	1.45448	0.203667
$52$	−34.8742	−4.83618
$53$	9.41132	1.29274	0.646372	−	0.763022i	$-0.276285\pi$
$53$	9.41132	1.29274	0.646372	+	0.763022i	$0.276285\pi$
$54$	8.07184	1.09844
$55$	3.50066	0.472029
$56$	−21.5528	−2.88011
$57$	13.2754	1.75838
$58$	−1.59283	−0.209149
$59$	2.34322	0.305062	0.152531	−	0.988299i	$-0.451258\pi$
$59$	2.34322	0.305062	0.152531	+	0.988299i	$0.451258\pi$
$60$	41.9774	5.41926
$61$	−4.64538	−0.594781	−0.297390	−	0.954756i	$-0.596116\pi$
$61$	−4.64538	−0.594781	−0.297390	+	0.954756i	$0.596116\pi$
$62$	−14.3142	−1.81791
$63$	4.46097	0.562030
$64$	9.17758	1.14720
$65$	−28.9031	−3.58499
$66$	−4.85261	−0.597315
$67$	12.6045	1.53988	0.769941	−	0.638115i	$-0.220286\pi$
$67$	12.6045	1.53988	0.769941	+	0.638115i	$0.220286\pi$
$68$	3.31853	0.402430
$69$	−0.205518	−0.0247415
$70$	−30.3067	−3.62234
$71$	3.23618	0.384064	0.192032	−	0.981389i	$-0.438492\pi$
$71$	3.23618	0.384064	0.192032	+	0.981389i	$0.438492\pi$
$72$	−11.7208	−1.38131
$73$	14.8508	1.73815	0.869077	−	0.494676i	$-0.164713\pi$
$73$	14.8508	1.73815	0.869077	+	0.494676i	$0.164713\pi$
$74$	16.4498	1.91225
$75$	24.1159	2.78467
$76$	30.2892	3.47441
$77$	2.48366	0.283040
$78$	40.0655	4.53652
$79$	−5.38099	−0.605408	−0.302704	−	0.953085i	$-0.597889\pi$
$79$	−5.38099	−0.605408	−0.302704	+	0.953085i	$0.597889\pi$
$80$	40.3020	4.50590
$81$	−11.2467	−1.24963
$82$	20.9097	2.30909
$83$	11.5691	1.26988	0.634939	−	0.772563i	$-0.281025\pi$
$83$	11.5691	1.26988	0.634939	+	0.772563i	$0.281025\pi$
$84$	29.7823	3.24952
$85$	2.75034	0.298316
$86$	8.98158	0.968508
$87$	1.29727	0.139082
$88$	−6.52559	−0.695630
$89$	−0.0274887	−0.00291380	−0.00145690	−	0.999999i	$-0.500464\pi$
$89$	−0.0274887	−0.00291380	−0.00145690	+	0.999999i	$0.500464\pi$
$90$	−16.4813	−1.73728
$91$	−20.5063	−2.14965
$92$	−0.468910	−0.0488873
$93$	11.6581	1.20889
$94$	−21.8771	−2.25645
$95$	25.1032	2.57553
$96$	−23.7365	−2.42260
$97$	−4.26065	−0.432604	−0.216302	−	0.976327i	$-0.569400\pi$
$97$	−4.26065	−0.432604	−0.216302	+	0.976327i	$0.569400\pi$
$98$	−3.15354	−0.318556
$99$	1.35066	0.135746
$100$	55.0228	5.50228
$101$	−4.50233	−0.447999	−0.223999	−	0.974589i	$-0.571911\pi$
$101$	−4.50233	−0.447999	−0.223999	+	0.974589i	$0.571911\pi$
$102$	−3.81251	−0.377495
$103$	11.2744	1.11090	0.555448	−	0.831551i	$-0.312547\pi$
$103$	11.2744	1.11090	0.555448	+	0.831551i	$0.312547\pi$
$104$	53.8784	5.28321
$105$	24.6831	2.40882
$106$	−24.6692	−2.39609
$107$	14.4438	1.39633	0.698165	−	0.715937i	$-0.254000\pi$
$107$	14.4438	1.39633	0.698165	+	0.715937i	$0.254000\pi$
$108$	−14.9993	−1.44331
$109$	−20.4019	−1.95415	−0.977074	−	0.212901i	$-0.931709\pi$
$109$	−20.4019	−1.95415	−0.977074	+	0.212901i	$0.931709\pi$
$110$	−9.17603	−0.874900
$111$	−13.3974	−1.27163
$112$	28.5936	2.70184
$113$	−0.626576	−0.0589433	−0.0294717	−	0.999566i	$-0.509382\pi$
$113$	−0.626576	−0.0589433	−0.0294717	+	0.999566i	$0.509382\pi$
$114$	−34.7980	−3.25913
$115$	−0.388625	−0.0362395
$116$	2.95985	0.274815
$117$	−11.1517	−1.03097
$118$	−6.14213	−0.565429
$119$	1.95132	0.178878
$120$	−64.8524	−5.92019
$121$	−10.2480	−0.931638
$122$	12.1766	1.10242
$123$	−17.0298	−1.53552
$124$	26.5991	2.38867
$125$	25.4176	2.27342
$126$	−11.6932	−1.04172
$127$	2.69938	0.239531	0.119766	−	0.992802i	$-0.461786\pi$
$127$	2.69938	0.239531	0.119766	+	0.992802i	$0.461786\pi$
$128$	−1.81929	−0.160804
$129$	−7.31498	−0.644048
$130$	75.7617	6.64474
$131$	−14.3672	−1.25527	−0.627633	−	0.778509i	$-0.715976\pi$
$131$	−14.3672	−1.25527	−0.627633	+	0.778509i	$0.715976\pi$
$132$	9.01726	0.784852
$133$	17.8103	1.54435
$134$	−33.0392	−2.85415
$135$	−12.4312	−1.06991
$136$	−5.12691	−0.439629
$137$	13.0688	1.11655	0.558273	−	0.829658i	$-0.311464\pi$
$137$	13.0688	1.11655	0.558273	+	0.829658i	$0.311464\pi$
$138$	0.538711	0.0458581
$139$	22.5474	1.91245	0.956224	−	0.292636i	$-0.0945323\pi$
$139$	22.5474	1.91245	0.956224	+	0.292636i	$0.0945323\pi$
$140$	56.3168	4.75964
$141$	17.8176	1.50051
$142$	−8.48278	−0.711859
$143$	−6.20875	−0.519201
$144$	15.5497	1.29581
$145$	2.45307	0.203717
$146$	−38.9274	−3.22165
$147$	2.56838	0.211836
$148$	−30.5675	−2.51263
$149$	22.4243	1.83707	0.918534	−	0.395342i	$-0.129374\pi$
$149$	22.4243	1.83707	0.918534	+	0.395342i	$0.129374\pi$
$150$	−63.2134	−5.16135
$151$	10.8379	0.881972	0.440986	−	0.897514i	$-0.354629\pi$
$151$	10.8379	0.881972	0.440986	+	0.897514i	$0.354629\pi$
$152$	−46.7949	−3.79557
$153$	1.06116	0.0857899
$154$	−6.51026	−0.524611
$155$	22.0449	1.77069
$156$	−74.4508	−5.96084
$157$	0.780391	0.0622820	0.0311410	−	0.999515i	$-0.490086\pi$
$157$	0.780391	0.0622820	0.0311410	+	0.999515i	$0.490086\pi$
$158$	14.1048	1.12212
$159$	20.0917	1.59337
$160$	−44.8845	−3.54843
$161$	−0.275723	−0.0217301
$162$	29.4802	2.31618
$163$	−12.0256	−0.941916	−0.470958	−	0.882156i	$-0.656092\pi$
$163$	−12.0256	−0.941916	−0.470958	+	0.882156i	$0.656092\pi$
$164$	−38.8550	−3.03407
$165$	7.47335	0.581799
$166$	−30.3254	−2.35370
$167$	17.0674	1.32072	0.660358	−	0.750951i	$-0.270405\pi$
$167$	17.0674	1.32072	0.660358	+	0.750951i	$0.270405\pi$
$168$	−46.0118	−3.54989
$169$	38.2624	2.94326
$170$	−7.20927	−0.552926
$171$	9.68556	0.740673
$172$	−16.6898	−1.27259
$173$	0.628992	0.0478214	0.0239107	−	0.999714i	$-0.492388\pi$
$173$	0.628992	0.0478214	0.0239107	+	0.999714i	$0.492388\pi$
$174$	−3.40045	−0.257787
$175$	32.3539	2.44573
$176$	8.65736	0.652573
$177$	5.00241	0.376004
$178$	0.0720542	0.00540069
$179$	−17.7845	−1.32928	−0.664640	−	0.747164i	$-0.731415\pi$
$179$	−17.7845	−1.32928	−0.664640	+	0.747164i	$0.731415\pi$
$180$	30.6260	2.28273
$181$	−16.5715	−1.23175	−0.615877	−	0.787843i	$-0.711198\pi$
$181$	−16.5715	−1.23175	−0.615877	+	0.787843i	$0.711198\pi$
$182$	53.7518	3.98435
$183$	−9.91716	−0.733097
$184$	0.724437	0.0534062
$185$	−25.3338	−1.86258
$186$	−30.5586	−2.24067
$187$	0.590807	0.0432041
$188$	40.6526	2.96490
$189$	−8.81974	−0.641542
$190$	−65.8012	−4.77372
$191$	−9.98762	−0.722679	−0.361339	−	0.932434i	$-0.617680\pi$
$191$	−9.98762	−0.722679	−0.361339	+	0.932434i	$0.617680\pi$
$192$	19.5927	1.41398
$193$	−17.9641	−1.29308	−0.646541	−	0.762880i	$-0.723785\pi$
$193$	−17.9641	−1.29308	−0.646541	+	0.762880i	$0.723785\pi$
$194$	11.1682	0.801827
$195$	−61.7036	−4.41868
$196$	5.86001	0.418572
$197$	−15.6061	−1.11189	−0.555944	−	0.831220i	$-0.687643\pi$
$197$	−15.6061	−1.11189	−0.555944	+	0.831220i	$0.687643\pi$
$198$	−3.54039	−0.251604
$199$	4.87345	0.345469	0.172735	−	0.984968i	$-0.444740\pi$
$199$	4.87345	0.345469	0.172735	+	0.984968i	$0.444740\pi$
$200$	−85.0068	−6.01089
$201$	26.9085	1.89798
$202$	11.8016	0.830361
$203$	1.74042	0.122153
$204$	7.08453	0.496016
$205$	−32.2024	−2.24911
$206$	−29.5527	−2.05903
$207$	−0.149943	−0.0104218
$208$	−71.4793	−4.95620
$209$	5.39247	0.373005
$210$	−64.7000	−4.46473
$211$	−19.7458	−1.35936	−0.679680	−	0.733509i	$-0.737881\pi$
$211$	−19.7458	−1.35936	−0.679680	+	0.733509i	$0.737881\pi$
$212$	45.8411	3.14838
$213$	6.90874	0.473379
$214$	−37.8604	−2.58808
$215$	−13.8322	−0.943352
$216$	23.1730	1.57672
$217$	15.6405	1.06175
$218$	53.4781	3.62199
$219$	31.7041	2.14236
$220$	17.0512	1.14959
$221$	−4.87798	−0.328129
$222$	35.1177	2.35695
$223$	18.5978	1.24540	0.622701	−	0.782460i	$-0.286035\pi$
$223$	18.5978	1.24540	0.622701	+	0.782460i	$0.286035\pi$
$224$	−31.8449	−2.12773
$225$	17.5946	1.17297
$226$	1.64240	0.109251
$227$	−2.36186	−0.156762	−0.0783812	−	0.996923i	$-0.524975\pi$
$227$	−2.36186	−0.156762	−0.0783812	+	0.996923i	$0.524975\pi$
$228$	64.6627	4.28239
$229$	1.85623	0.122663	0.0613315	−	0.998117i	$-0.480465\pi$
$229$	1.85623	0.122663	0.0613315	+	0.998117i	$0.480465\pi$
$230$	1.01868	0.0671695
$231$	5.30223	0.348861
$232$	−4.57278	−0.300218
$233$	−5.30588	−0.347600	−0.173800	−	0.984781i	$-0.555605\pi$
$233$	−5.30588	−0.347600	−0.173800	+	0.984781i	$0.555605\pi$
$234$	29.2311	1.91090
$235$	33.6922	2.19784
$236$	11.4135	0.742955
$237$	−11.4876	−0.746197
$238$	−5.11487	−0.331548
$239$	−3.84156	−0.248490	−0.124245	−	0.992252i	$-0.539651\pi$
$239$	−3.84156	−0.248490	−0.124245	+	0.992252i	$0.539651\pi$
$240$	86.0383	5.55375
$241$	−26.1851	−1.68673	−0.843367	−	0.537339i	$-0.819430\pi$
$241$	−26.1851	−1.68673	−0.843367	+	0.537339i	$0.819430\pi$
$242$	26.8624	1.72678
$243$	−14.7717	−0.947603
$244$	−22.6270	−1.44854
$245$	4.85667	0.310281
$246$	44.6389	2.84607
$247$	−44.5229	−2.83292
$248$	−41.0940	−2.60947
$249$	24.6983	1.56519
$250$	−66.6254	−4.21376
$251$	13.2411	0.835772	0.417886	−	0.908499i	$-0.362771\pi$
$251$	13.2411	0.835772	0.417886	+	0.908499i	$0.362771\pi$
$252$	21.7287	1.36878
$253$	−0.0834814	−0.00524843
$254$	−7.07570	−0.443969
$255$	5.87154	0.367690
$256$	−13.5864	−0.849149
$257$	−4.05989	−0.253249	−0.126625	−	0.991951i	$-0.540414\pi$
$257$	−4.05989	−0.253249	−0.126625	+	0.991951i	$0.540414\pi$
$258$	19.1742	1.19374
$259$	−17.9740	−1.11685
$260$	−140.783	−8.73097
$261$	0.946468	0.0585849
$262$	37.6597	2.32662
$263$	−3.15494	−0.194542	−0.0972709	−	0.995258i	$-0.531011\pi$
$263$	−3.15494	−0.194542	−0.0972709	+	0.995258i	$0.531011\pi$
$264$	−13.9311	−0.857400
$265$	37.9923	2.33385
$266$	−46.6850	−2.86244
$267$	−0.0586840	−0.00359140
$268$	61.3945	3.75026
$269$	0.264077	0.0161010	0.00805052	−	0.999968i	$-0.497437\pi$
$269$	0.264077	0.0161010	0.00805052	+	0.999968i	$0.497437\pi$
$270$	32.5850	1.98306
$271$	−4.27566	−0.259728	−0.129864	−	0.991532i	$-0.541454\pi$
$271$	−4.27566	−0.259728	−0.129864	+	0.991532i	$0.541454\pi$
$272$	6.80177	0.412418
$273$	−43.7777	−2.64955
$274$	−34.2564	−2.06951
$275$	9.79587	0.590713
$276$	−1.00105	−0.0602561
$277$	−7.65067	−0.459684	−0.229842	−	0.973228i	$-0.573821\pi$
$277$	−7.65067	−0.459684	−0.229842	+	0.973228i	$0.573821\pi$
$278$	−59.1020	−3.54470
$279$	8.50558	0.509216
$280$	−87.0059	−5.19960
$281$	−11.2777	−0.672768	−0.336384	−	0.941725i	$-0.609204\pi$
$281$	−11.2777	−0.672768	−0.336384	+	0.941725i	$0.609204\pi$
$282$	−46.7040	−2.78119
$283$	10.0415	0.596904	0.298452	−	0.954425i	$-0.403530\pi$
$283$	10.0415	0.596904	0.298452	+	0.954425i	$0.403530\pi$
$284$	15.7630	0.935359
$285$	53.5913	3.17448
$286$	16.2746	0.962334
$287$	−22.8471	−1.34862
$288$	−17.3178	−1.02046
$289$	−16.5358	−0.972696
$290$	−6.43007	−0.377587
$291$	−9.09582	−0.533206
$292$	72.3360	4.23314
$293$	6.23243	0.364102	0.182051	−	0.983289i	$-0.441726\pi$
$293$	6.23243	0.364102	0.182051	+	0.983289i	$0.441726\pi$
$294$	−6.73231	−0.392636
$295$	9.45930	0.550742
$296$	47.2249	2.74489
$297$	−2.67037	−0.154951
$298$	−58.7792	−3.40499
$299$	0.689263	0.0398611
$300$	117.465	6.78184
$301$	−9.81377	−0.565656
$302$	−28.4085	−1.63473
$303$	−9.61176	−0.552181
$304$	62.0818	3.56064
$305$	−18.7528	−1.07378
$306$	−2.78155	−0.159011
$307$	4.56434	0.260501	0.130250	−	0.991481i	$-0.458422\pi$
$307$	4.56434	0.260501	0.130250	+	0.991481i	$0.458422\pi$
$308$	12.0975	0.689322
$309$	24.0690	1.36924
$310$	−57.7847	−3.28195
$311$	22.7584	1.29051	0.645256	−	0.763966i	$-0.276751\pi$
$311$	22.7584	1.29051	0.645256	+	0.763966i	$0.276751\pi$
$312$	115.022	6.51183
$313$	−22.0003	−1.24353	−0.621764	−	0.783205i	$-0.713584\pi$
$313$	−22.0003	−1.24353	−0.621764	+	0.783205i	$0.713584\pi$
$314$	−2.04558	−0.115439
$315$	18.0084	1.01466
$316$	−26.2100	−1.47443
$317$	−11.1563	−0.626598	−0.313299	−	0.949655i	$-0.601434\pi$
$317$	−11.1563	−0.626598	−0.313299	+	0.949655i	$0.601434\pi$
$318$	−52.6649	−2.95330
$319$	0.526950	0.0295035
$320$	37.0488	2.07109
$321$	30.8351	1.72105
$322$	0.722735	0.0402764
$323$	4.23667	0.235734
$324$	−54.7809	−3.04338
$325$	−80.8794	−4.48638
$326$	31.5218	1.74583
$327$	−43.5548	−2.40859
$328$	60.0286	3.31452
$329$	23.9041	1.31788
$330$	−19.5894	−1.07836
$331$	−15.0550	−0.827497	−0.413749	−	0.910391i	$-0.635781\pi$
$331$	−15.0550	−0.827497	−0.413749	+	0.910391i	$0.635781\pi$
$332$	56.3515	3.09269
$333$	−9.77455	−0.535642
$334$	−44.7376	−2.44793
$335$	50.8827	2.78002
$336$	61.0429	3.33016
$337$	−17.7475	−0.966767	−0.483384	−	0.875409i	$-0.660592\pi$
$337$	−17.7475	−0.966767	−0.483384	+	0.875409i	$0.660592\pi$
$338$	−100.295	−5.45530
$339$	−1.33764	−0.0726507
$340$	13.3965	0.726526
$341$	4.73552	0.256443
$342$	−25.3881	−1.37283
$343$	−16.6030	−0.896476
$344$	25.7847	1.39022
$345$	−0.829652	−0.0446670
$346$	−1.64873	−0.0886365
$347$	0.158237	0.00849461	0.00424731	−	0.999991i	$-0.498648\pi$
$347$	0.158237	0.00849461	0.00424731	+	0.999991i	$0.498648\pi$
$348$	6.31881	0.338724
$349$	−23.8725	−1.27786	−0.638931	−	0.769264i	$-0.720623\pi$
$349$	−23.8725	−1.27786	−0.638931	+	0.769264i	$0.720623\pi$
$350$	−84.8071	−4.53313
$351$	22.0479	1.17683
$352$	−9.64175	−0.513907
$353$	3.10640	0.165337	0.0826684	−	0.996577i	$-0.473656\pi$
$353$	3.10640	0.165337	0.0826684	+	0.996577i	$0.473656\pi$
$354$	−13.1125	−0.696920
$355$	13.0641	0.693369
$356$	−0.133893	−0.00709633
$357$	4.16577	0.220476
$358$	46.6174	2.46381
$359$	−15.8827	−0.838255	−0.419128	−	0.907927i	$-0.637664\pi$
$359$	−15.8827	−0.838255	−0.419128	+	0.907927i	$0.637664\pi$
$360$	−47.3153	−2.49373
$361$	19.6694	1.03523
$362$	43.4378	2.28304
$363$	−21.8779	−1.14829
$364$	−99.8832	−5.23530
$365$	59.9508	3.13797
$366$	25.9952	1.35879
$367$	−25.5600	−1.33422	−0.667110	−	0.744960i	$-0.732469\pi$
$367$	−25.5600	−1.33422	−0.667110	+	0.744960i	$0.732469\pi$
$368$	−0.961095	−0.0501005
$369$	−12.4246	−0.646801
$370$	66.4058	3.45227
$371$	26.9550	1.39943
$372$	56.7849	2.94416
$373$	−27.2007	−1.40840	−0.704198	−	0.710003i	$-0.748693\pi$
$373$	−27.2007	−1.40840	−0.704198	+	0.710003i	$0.748693\pi$
$374$	−1.54864	−0.0800783
$375$	54.2626	2.80211
$376$	−62.8057	−3.23896
$377$	−4.35075	−0.224075
$378$	23.1186	1.18909
$379$	19.3268	0.992749	0.496374	−	0.868109i	$-0.334664\pi$
$379$	19.3268	0.992749	0.496374	+	0.868109i	$0.334664\pi$
$380$	122.274	6.27251
$381$	5.76275	0.295235
$382$	26.1799	1.33948
$383$	26.8329	1.37109	0.685547	−	0.728028i	$-0.259563\pi$
$383$	26.8329	1.37109	0.685547	+	0.728028i	$0.259563\pi$
$384$	−3.88390	−0.198199
$385$	10.0262	0.510985
$386$	47.0879	2.39671
$387$	−5.33689	−0.271290
$388$	−20.7530	−1.05357
$389$	26.4315	1.34013	0.670066	−	0.742302i	$-0.266266\pi$
$389$	26.4315	1.34013	0.670066	+	0.742302i	$0.266266\pi$
$390$	161.739	8.18998
$391$	−0.0655883	−0.00331694
$392$	−9.05334	−0.457263
$393$	−30.6717	−1.54718
$394$	40.9072	2.06087
$395$	−21.7224	−1.09297
$396$	6.57885	0.330600
$397$	20.6008	1.03392	0.516962	−	0.856008i	$-0.327063\pi$
$397$	20.6008	1.03392	0.516962	+	0.856008i	$0.327063\pi$
$398$	−12.7744	−0.640324
$399$	38.0222	1.90349
$400$	112.777	5.63883
$401$	−14.1282	−0.705529	−0.352764	−	0.935712i	$-0.614758\pi$
$401$	−14.1282	−0.705529	−0.352764	+	0.935712i	$0.614758\pi$
$402$	−70.5335	−3.51789
$403$	−39.0987	−1.94764
$404$	−21.9302	−1.09107
$405$	−45.4015	−2.25602
$406$	−4.56204	−0.226410
$407$	−5.44202	−0.269751
$408$	−10.9451	−0.541865
$409$	−22.4868	−1.11190	−0.555951	−	0.831215i	$-0.687646\pi$
$409$	−22.4868	−1.11190	−0.555951	+	0.831215i	$0.687646\pi$
$410$	84.4099	4.16871
$411$	27.8999	1.37620
$412$	54.9157	2.70550
$413$	6.71123	0.330238
$414$	0.393035	0.0193166
$415$	46.7031	2.29257
$416$	79.6069	3.90305
$417$	48.1352	2.35719
$418$	−14.1349	−0.691361
$419$	−20.5411	−1.00350	−0.501748	−	0.865014i	$-0.667310\pi$
$419$	−20.5411	−1.00350	−0.501748	+	0.865014i	$0.667310\pi$
$420$	120.227	5.86650
$421$	−28.3007	−1.37929	−0.689646	−	0.724147i	$-0.742234\pi$
$421$	−28.3007	−1.37929	−0.689646	+	0.724147i	$0.742234\pi$
$422$	51.7584	2.51956
$423$	12.9994	0.632055
$424$	−70.8216	−3.43940
$425$	7.69625	0.373323
$426$	−18.1094	−0.877403
$427$	−13.3049	−0.643867
$428$	70.3533	3.40066
$429$	−13.2547	−0.639942
$430$	36.2575	1.74849
$431$	−0.241676	−0.0116411	−0.00582055	−	0.999983i	$-0.501853\pi$
$431$	−0.241676	−0.0116411	−0.00582055	+	0.999983i	$0.501853\pi$
$432$	−30.7431	−1.47913
$433$	−21.8827	−1.05162	−0.525808	−	0.850603i	$-0.676237\pi$
$433$	−21.8827	−1.05162	−0.525808	+	0.850603i	$0.676237\pi$
$434$	−40.9974	−1.96794
$435$	5.23692	0.251091
$436$	−99.3745	−4.75918
$437$	−0.598644	−0.0286370
$438$	−83.1037	−3.97085
$439$	−13.3774	−0.638471	−0.319235	−	0.947675i	$-0.603426\pi$
$439$	−13.3774	−0.638471	−0.319235	+	0.947675i	$0.603426\pi$
$440$	−26.3430	−1.25585
$441$	1.87385	0.0892309
$442$	12.7863	0.608183
$443$	2.47915	0.117788	0.0588941	−	0.998264i	$-0.481243\pi$
$443$	2.47915	0.117788	0.0588941	+	0.998264i	$0.481243\pi$
$444$	−65.2568	−3.09695
$445$	−0.110968	−0.00526041
$446$	−48.7491	−2.30834
$447$	47.8723	2.26428
$448$	26.2855	1.24187
$449$	2.98680	0.140956	0.0704780	−	0.997513i	$-0.477548\pi$
$449$	2.98680	0.140956	0.0704780	+	0.997513i	$0.477548\pi$
$450$	−46.1195	−2.17409
$451$	−6.91747	−0.325731
$452$	−3.05196	−0.143552
$453$	23.1371	1.08708
$454$	6.19098	0.290557
$455$	−82.7815	−3.88085
$456$	−99.8997	−4.67823
$457$	−38.4570	−1.79894	−0.899472	−	0.436979i	$-0.856048\pi$
$457$	−38.4570	−1.79894	−0.899472	+	0.436979i	$0.856048\pi$
$458$	−4.86560	−0.227355
$459$	−2.09801	−0.0979269
$460$	−1.89293	−0.0882584
$461$	36.7175	1.71010	0.855051	−	0.518543i	$-0.173525\pi$
$461$	36.7175	1.71010	0.855051	+	0.518543i	$0.173525\pi$
$462$	−13.8984	−0.646610
$463$	9.36886	0.435408	0.217704	−	0.976015i	$-0.430143\pi$
$463$	9.36886	0.435408	0.217704	+	0.976015i	$0.430143\pi$
$464$	6.06661	0.281635
$465$	47.0623	2.18246
$466$	13.9079	0.644272
$467$	−22.4781	−1.04016	−0.520080	−	0.854117i	$-0.674098\pi$
$467$	−22.4781	−1.04016	−0.520080	+	0.854117i	$0.674098\pi$
$468$	−54.3181	−2.51086
$469$	36.1005	1.66697
$470$	−88.3150	−4.07367
$471$	1.66601	0.0767657
$472$	−17.6331	−0.811630
$473$	−2.97134	−0.136622
$474$	30.1115	1.38307
$475$	70.2461	3.22311
$476$	9.50460	0.435643
$477$	14.6586	0.671170
$478$	10.0696	0.460573
$479$	26.1358	1.19417	0.597087	−	0.802177i	$-0.296325\pi$
$479$	26.1358	1.19417	0.597087	+	0.802177i	$0.296325\pi$
$480$	−95.8213	−4.37363
$481$	44.9319	2.04872
$482$	68.6373	3.12634
$483$	−0.588626	−0.0267834
$484$	−49.9165	−2.26893
$485$	−17.1997	−0.780999
$486$	38.7199	1.75637
$487$	−9.10139	−0.412423	−0.206212	−	0.978507i	$-0.566114\pi$
$487$	−9.10139	−0.412423	−0.206212	+	0.978507i	$0.566114\pi$
$488$	34.9572	1.58244
$489$	−25.6727	−1.16096
$490$	−12.7305	−0.575103
$491$	7.26704	0.327957	0.163978	−	0.986464i	$-0.447567\pi$
$491$	7.26704	0.327957	0.163978	+	0.986464i	$0.447567\pi$
$492$	−82.9493	−3.73964
$493$	0.414005	0.0186459
$494$	116.705	5.25079
$495$	5.45244	0.245069
$496$	54.5185	2.44795
$497$	9.26876	0.415761
$498$	−64.7398	−2.90106
$499$	−22.0357	−0.986453	−0.493226	−	0.869901i	$-0.664183\pi$
$499$	−22.0357	−0.986453	−0.493226	+	0.869901i	$0.664183\pi$
$500$	123.805	5.53674
$501$	36.4362	1.62785
$502$	−34.7080	−1.54910
$503$	−25.1339	−1.12066	−0.560332	−	0.828268i	$-0.689326\pi$
$503$	−25.1339	−1.12066	−0.560332	+	0.828268i	$0.689326\pi$
$504$	−33.5695	−1.49530
$505$	−18.1754	−0.808793
$506$	0.218824	0.00972791
$507$	81.6841	3.62772
$508$	13.1483	0.583360
$509$	−27.5299	−1.22024	−0.610121	−	0.792308i	$-0.708879\pi$
$509$	−27.5299	−1.22024	−0.610121	+	0.792308i	$0.708879\pi$
$510$	−15.3906	−0.681509
$511$	42.5342	1.88160
$512$	39.2516	1.73469
$513$	−19.1492	−0.845458
$514$	10.6419	0.469395
$515$	45.5132	2.00555
$516$	−35.6301	−1.56853
$517$	7.23750	0.318305
$518$	47.1139	2.07007
$519$	1.34280	0.0589423
$520$	217.500	9.53802
$521$	26.8917	1.17815	0.589073	−	0.808080i	$-0.299493\pi$
$521$	26.8917	1.17815	0.589073	+	0.808080i	$0.299493\pi$
$522$	−2.48091	−0.108587
$523$	5.77766	0.252639	0.126320	−	0.991990i	$-0.459683\pi$
$523$	5.77766	0.252639	0.126320	+	0.991990i	$0.459683\pi$
$524$	−69.9804	−3.05711
$525$	69.0705	3.01448
$526$	8.26982	0.360581
$527$	3.72052	0.162068
$528$	18.4821	0.804329
$529$	−22.9907	−0.999597
$530$	−99.5866	−4.32577
$531$	3.64968	0.158383
$532$	86.7514	3.76115
$533$	57.1139	2.47388
$534$	0.153824	0.00665663
$535$	58.3076	2.52086
$536$	−94.8505	−4.09692
$537$	−37.9672	−1.63841
$538$	−0.692206	−0.0298431
$539$	1.04327	0.0449370
$540$	−60.5504	−2.60568
$541$	−23.8804	−1.02670	−0.513349	−	0.858180i	$-0.671595\pi$
$541$	−23.8804	−1.02670	−0.513349	+	0.858180i	$0.671595\pi$
$542$	11.2075	0.481403
$543$	−35.3776	−1.51820
$544$	−7.57517	−0.324783
$545$	−82.3599	−3.52791
$546$	114.752	4.91091
$547$	−6.55675	−0.280346	−0.140173	−	0.990127i	$-0.544766\pi$
$547$	−6.55675	−0.280346	−0.140173	+	0.990127i	$0.544766\pi$
$548$	63.6563	2.71926
$549$	−7.23540	−0.308799
$550$	−25.6772	−1.09488
$551$	3.77875	0.160980
$552$	1.54656	0.0658259
$553$	−15.4117	−0.655372
$554$	20.0542	0.852020
$555$	−54.0837	−2.29573
$556$	109.825	4.65762
$557$	−28.5175	−1.20833	−0.604163	−	0.796861i	$-0.706492\pi$
$557$	−28.5175	−1.20833	−0.604163	+	0.796861i	$0.706492\pi$
$558$	−22.2951	−0.943826
$559$	24.5328	1.03763
$560$	115.429	4.87776
$561$	1.26128	0.0532512
$562$	29.5613	1.24697
$563$	34.7377	1.46402	0.732010	−	0.681294i	$-0.238582\pi$
$563$	34.7377	1.46402	0.732010	+	0.681294i	$0.238582\pi$
$564$	86.7868	3.65439
$565$	−2.52941	−0.106413
$566$	−26.3210	−1.10635
$567$	−32.2117	−1.35276
$568$	−24.3528	−1.02182
$569$	−37.7861	−1.58407	−0.792037	−	0.610473i	$-0.790979\pi$
$569$	−37.7861	−1.58407	−0.792037	+	0.610473i	$0.790979\pi$
$570$	−140.475	−5.88386
$571$	−18.6846	−0.781928	−0.390964	−	0.920406i	$-0.627858\pi$
$571$	−18.6846	−0.781928	−0.390964	+	0.920406i	$0.627858\pi$
$572$	−30.2419	−1.26448
$573$	−21.3220	−0.890739
$574$	59.8875	2.49966
$575$	−1.08749	−0.0453513
$576$	14.2945	0.595605
$577$	22.3072	0.928662	0.464331	−	0.885662i	$-0.346295\pi$
$577$	22.3072	0.928662	0.464331	+	0.885662i	$0.346295\pi$
$578$	43.3442	1.80288
$579$	−38.3504	−1.59379
$580$	11.9485	0.496136
$581$	33.1352	1.37468
$582$	23.8422	0.988292
$583$	8.16122	0.338003
$584$	−111.754	−4.62443
$585$	−45.0179	−1.86126
$586$	−16.3366	−0.674860
$587$	27.3264	1.12788	0.563941	−	0.825815i	$-0.309284\pi$
$587$	27.3264	1.12788	0.563941	+	0.825815i	$0.309284\pi$
$588$	12.5102	0.515911
$589$	33.9583	1.39923
$590$	−24.7950	−1.02079
$591$	−33.3165	−1.37046
$592$	−62.6522	−2.57499
$593$	11.2956	0.463857	0.231928	−	0.972733i	$-0.425497\pi$
$593$	11.2956	0.463857	0.231928	+	0.972733i	$0.425497\pi$
$594$	6.99966	0.287200
$595$	7.87725	0.322936
$596$	109.225	4.47404
$597$	10.4040	0.425809
$598$	−1.80672	−0.0738821
$599$	13.8204	0.564686	0.282343	−	0.959313i	$-0.408888\pi$
$599$	13.8204	0.564686	0.282343	+	0.959313i	$0.408888\pi$
$600$	−181.476	−7.40873
$601$	−17.7634	−0.724584	−0.362292	−	0.932065i	$-0.618006\pi$
$601$	−17.7634	−0.724584	−0.362292	+	0.932065i	$0.618006\pi$
$602$	25.7242	1.04844
$603$	19.6321	0.799479
$604$	52.7895	2.14798
$605$	−41.3700	−1.68193
$606$	25.1946	1.02346
$607$	−25.1984	−1.02277	−0.511386	−	0.859351i	$-0.670868\pi$
$607$	−25.1984	−1.02277	−0.511386	+	0.859351i	$0.670868\pi$
$608$	−69.1409	−2.80403
$609$	3.71552	0.150560
$610$	49.1555	1.99025
$611$	−59.7562	−2.41748
$612$	5.16876	0.208935
$613$	12.0627	0.487207	0.243603	−	0.969875i	$-0.421670\pi$
$613$	12.0627	0.487207	0.243603	+	0.969875i	$0.421670\pi$
$614$	−11.9642	−0.482835
$615$	−68.7470	−2.77215
$616$	−18.6899	−0.753039
$617$	−4.95127	−0.199331	−0.0996654	−	0.995021i	$-0.531777\pi$
$617$	−4.95127	−0.199331	−0.0996654	+	0.995021i	$0.531777\pi$
$618$	−63.0903	−2.53786
$619$	−5.65952	−0.227475	−0.113738	−	0.993511i	$-0.536282\pi$
$619$	−5.65952	−0.227475	−0.113738	+	0.993511i	$0.536282\pi$
$620$	107.377	4.31238
$621$	0.296451	0.0118962
$622$	−59.6551	−2.39195
$623$	−0.0787304	−0.00315427
$624$	−152.597	−6.10877
$625$	46.1259	1.84504
$626$	57.6677	2.30487
$627$	11.5121	0.459748
$628$	3.80117	0.151683
$629$	−4.27560	−0.170479
$630$	−47.2041	−1.88066
$631$	31.0986	1.23802	0.619009	−	0.785384i	$-0.287535\pi$
$631$	31.0986	1.23802	0.619009	+	0.785384i	$0.287535\pi$
$632$	40.4927	1.61071
$633$	−42.1542	−1.67548
$634$	29.2431	1.16139
$635$	10.8971	0.432437
$636$	97.8635	3.88054
$637$	−8.61377	−0.341290
$638$	−1.38126	−0.0546845
$639$	5.04051	0.199399
$640$	−7.34425	−0.290307
$641$	−19.6792	−0.777284	−0.388642	−	0.921389i	$-0.627056\pi$
$641$	−19.6792	−0.777284	−0.388642	+	0.921389i	$0.627056\pi$
$642$	−80.8260	−3.18995
$643$	27.6655	1.09102	0.545511	−	0.838104i	$-0.316336\pi$
$643$	27.6655	1.09102	0.545511	+	0.838104i	$0.316336\pi$
$644$	−1.34301	−0.0529219
$645$	−29.5297	−1.16273
$646$	−11.1053	−0.436931
$647$	−29.8399	−1.17313	−0.586564	−	0.809903i	$-0.699520\pi$
$647$	−29.8399	−1.17313	−0.586564	+	0.809903i	$0.699520\pi$
$648$	84.6330	3.32470
$649$	2.03197	0.0797620
$650$	212.003	8.31546
$651$	33.3900	1.30866
$652$	−58.5747	−2.29396
$653$	−21.2356	−0.831014	−0.415507	−	0.909590i	$-0.636396\pi$
$653$	−21.2356	−0.831014	−0.415507	+	0.909590i	$0.636396\pi$
$654$	114.167	4.46429
$655$	−57.9985	−2.26619
$656$	−79.6386	−3.10936
$657$	23.1308	0.902419
$658$	−62.6581	−2.44267
$659$	−16.9360	−0.659733	−0.329867	−	0.944028i	$-0.607004\pi$
$659$	−16.9360	−0.659733	−0.329867	+	0.944028i	$0.607004\pi$
$660$	36.4015	1.41693
$661$	−12.5334	−0.487492	−0.243746	−	0.969839i	$-0.578376\pi$
$661$	−12.5334	−0.487492	−0.243746	+	0.969839i	$0.578376\pi$
$662$	39.4626	1.53376
$663$	−10.4137	−0.404435
$664$	−87.0595	−3.37856
$665$	71.8981	2.78809
$666$	25.6213	0.992807
$667$	−0.0584993	−0.00226510
$668$	83.1328	3.21650
$669$	39.7034	1.53502
$670$	−133.375	−5.15273
$671$	−4.02834	−0.155512
$672$	−67.9838	−2.62253
$673$	50.8267	1.95923	0.979613	−	0.200896i	$-0.0643853\pi$
$673$	50.8267	1.95923	0.979613	+	0.200896i	$0.0643853\pi$
$674$	46.5202	1.79189
$675$	−34.7861	−1.33892
$676$	186.370	7.16809
$677$	25.2997	0.972347	0.486173	−	0.873862i	$-0.338392\pi$
$677$	25.2997	0.972347	0.486173	+	0.873862i	$0.338392\pi$
$678$	3.50626	0.134657
$679$	−12.2029	−0.468306
$680$	−20.6967	−0.793683
$681$	−5.04220	−0.193218
$682$	−12.4129	−0.475314
$683$	−33.8433	−1.29498	−0.647489	−	0.762075i	$-0.724181\pi$
$683$	−33.8433	−1.29498	−0.647489	+	0.762075i	$0.724181\pi$
$684$	47.1769	1.80385
$685$	52.7572	2.01575
$686$	43.5202	1.66161
$687$	3.96275	0.151189
$688$	−34.2081	−1.30417
$689$	−67.3830	−2.56709
$690$	2.17471	0.0827898
$691$	7.72893	0.294023	0.147011	−	0.989135i	$-0.453035\pi$
$691$	7.72893	0.294023	0.147011	+	0.989135i	$0.453035\pi$
$692$	3.06373	0.116465
$693$	3.86842	0.146949
$694$	−0.414776	−0.0157447
$695$	91.0212	3.45263
$696$	−9.76216	−0.370034
$697$	−5.43480	−0.205858
$698$	62.5752	2.36851
$699$	−11.3272	−0.428434
$700$	157.591	5.95638
$701$	6.24698	0.235945	0.117973	−	0.993017i	$-0.462361\pi$
$701$	6.24698	0.235945	0.117973	+	0.993017i	$0.462361\pi$
$702$	−57.7926	−2.18124
$703$	−39.0247	−1.47184
$704$	7.95853	0.299948
$705$	71.9275	2.70894
$706$	−8.14258	−0.306450
$707$	−12.8951	−0.484972
$708$	24.3660	0.915729
$709$	20.4179	0.766811	0.383406	−	0.923580i	$-0.374751\pi$
$709$	20.4179	0.766811	0.383406	+	0.923580i	$0.374751\pi$
$710$	−34.2439	−1.28515
$711$	−8.38114	−0.314317
$712$	0.206857	0.00775228
$713$	−0.525712	−0.0196881
$714$	−10.9194	−0.408649
$715$	−25.0639	−0.937338
$716$	−86.6258	−3.23736
$717$	−8.20111	−0.306276
$718$	41.6321	1.55370
$719$	−35.1464	−1.31074	−0.655369	−	0.755309i	$-0.727487\pi$
$719$	−35.1464	−1.31074	−0.655369	+	0.755309i	$0.727487\pi$
$720$	62.7722	2.33938
$721$	32.2909	1.20258
$722$	−51.5579	−1.91879
$723$	−55.9011	−2.07898
$724$	−80.7175	−2.99984
$725$	6.86442	0.254938
$726$	57.3470	2.12835
$727$	12.8903	0.478073	0.239037	−	0.971011i	$-0.423168\pi$
$727$	12.8903	0.478073	0.239037	+	0.971011i	$0.423168\pi$
$728$	154.313	5.71923
$729$	2.20491	0.0816632
$730$	−157.145	−5.81619
$731$	−2.33447	−0.0863435
$732$	−48.3050	−1.78540
$733$	27.8011	1.02686	0.513429	−	0.858132i	$-0.328375\pi$
$733$	27.8011	1.02686	0.513429	+	0.858132i	$0.328375\pi$
$734$	66.9985	2.47296
$735$	10.3682	0.382438
$736$	1.07038	0.0394546
$737$	10.9302	0.402620
$738$	32.5678	1.19884
$739$	−31.9088	−1.17378	−0.586892	−	0.809665i	$-0.699649\pi$
$739$	−31.9088	−1.17378	−0.586892	+	0.809665i	$0.699649\pi$
$740$	−123.397	−4.53617
$741$	−95.0492	−3.49172
$742$	−70.6552	−2.59383
$743$	−11.9823	−0.439590	−0.219795	−	0.975546i	$-0.570539\pi$
$743$	−11.9823	−0.439590	−0.219795	+	0.975546i	$0.570539\pi$
$744$	−87.7291	−3.21630
$745$	90.5240	3.31654
$746$	71.2992	2.61045
$747$	18.0195	0.659298
$748$	2.87773	0.105220
$749$	41.3684	1.51157
$750$	−142.235	−5.19367
$751$	−52.5543	−1.91773	−0.958867	−	0.283856i	$-0.908386\pi$
$751$	−52.5543	−1.91773	−0.958867	+	0.283856i	$0.908386\pi$
$752$	83.3230	3.03848
$753$	28.2677	1.03013
$754$	11.4043	0.415321
$755$	43.7511	1.59226
$756$	−42.9596	−1.56243
$757$	−19.7075	−0.716280	−0.358140	−	0.933668i	$-0.616589\pi$
$757$	−19.7075	−0.716280	−0.358140	+	0.933668i	$0.616589\pi$
$758$	−50.6599	−1.84005
$759$	−0.178220	−0.00646896
$760$	−188.905	−6.85231
$761$	−34.1110	−1.23652	−0.618261	−	0.785973i	$-0.712162\pi$
$761$	−34.1110	−1.23652	−0.618261	+	0.785973i	$0.712162\pi$
$762$	−15.1055	−0.547214
$763$	−58.4331	−2.11542
$764$	−48.6482	−1.76003
$765$	4.28378	0.154880
$766$	−70.3351	−2.54131
$767$	−16.7770	−0.605781
$768$	−29.0048	−1.04662
$769$	11.3929	0.410840	0.205420	−	0.978674i	$-0.434144\pi$
$769$	11.3929	0.410840	0.205420	+	0.978674i	$0.434144\pi$
$770$	−26.2811	−0.947105
$771$	−8.66722	−0.312142
$772$	−87.5002	−3.14920
$773$	−11.0854	−0.398715	−0.199357	−	0.979927i	$-0.563885\pi$
$773$	−11.0854	−0.398715	−0.199357	+	0.979927i	$0.563885\pi$
$774$	13.9892	0.502832
$775$	61.6881	2.21590
$776$	32.0621	1.15096
$777$	−38.3716	−1.37657
$778$	−69.2831	−2.48392
$779$	−49.6051	−1.77729
$780$	−300.549	−10.7614
$781$	2.80632	0.100418
$782$	0.171922	0.00614792
$783$	−1.87125	−0.0668731
$784$	12.0109	0.428960
$785$	3.15034	0.112440
$786$	80.3975	2.86768
$787$	41.9647	1.49588	0.747940	−	0.663766i	$-0.231043\pi$
$787$	41.9647	1.49588	0.747940	+	0.663766i	$0.231043\pi$
$788$	−76.0149	−2.70792
$789$	−6.73529	−0.239783
$790$	56.9393	2.02581
$791$	−1.79458	−0.0638078
$792$	−10.1639	−0.361159
$793$	33.2599	1.18109
$794$	−53.9994	−1.91637
$795$	81.1076	2.87659
$796$	23.7378	0.841364
$797$	−13.2168	−0.468163	−0.234082	−	0.972217i	$-0.575208\pi$
$797$	−13.2168	−0.468163	−0.234082	+	0.972217i	$0.575208\pi$
$798$	−99.6650	−3.52810
$799$	5.68623	0.201164
$800$	−125.600	−4.44063
$801$	−0.0428149	−0.00151279
$802$	37.0333	1.30769
$803$	12.8782	0.454461
$804$	131.067	4.62239
$805$	−1.11306	−0.0392302
$806$	102.487	3.60994
$807$	0.563762	0.0198454
$808$	33.8807	1.19192
$809$	−19.8043	−0.696284	−0.348142	−	0.937442i	$-0.613187\pi$
$809$	−19.8043	−0.696284	−0.348142	+	0.937442i	$0.613187\pi$
$810$	119.008	4.18150
$811$	44.1877	1.55164	0.775820	−	0.630954i	$-0.217336\pi$
$811$	44.1877	1.55164	0.775820	+	0.630954i	$0.217336\pi$
$812$	8.47731	0.297495
$813$	−9.12785	−0.320128
$814$	14.2648	0.499981
$815$	−48.5457	−1.70048
$816$	14.5207	0.508326
$817$	−21.3074	−0.745453
$818$	58.9431	2.06090
$819$	−31.9396	−1.11606
$820$	−156.853	−5.47754
$821$	25.4472	0.888112	0.444056	−	0.895999i	$-0.353539\pi$
$821$	25.4472	0.888112	0.444056	+	0.895999i	$0.353539\pi$
$822$	−73.1320	−2.55077
$823$	6.00165	0.209204	0.104602	−	0.994514i	$-0.466643\pi$
$823$	6.00165	0.209204	0.104602	+	0.994514i	$0.466643\pi$
$824$	−84.8413	−2.95559
$825$	20.9126	0.728084
$826$	−17.5917	−0.612093
$827$	32.3286	1.12418	0.562088	−	0.827077i	$-0.309998\pi$
$827$	32.3286	1.12418	0.562088	+	0.827077i	$0.309998\pi$
$828$	−0.730350	−0.0253814
$829$	43.0539	1.49532	0.747662	−	0.664080i	$-0.231176\pi$
$829$	43.0539	1.49532	0.747662	+	0.664080i	$0.231176\pi$
$830$	−122.420	−4.24925
$831$	−16.3330	−0.566585
$832$	−65.7094	−2.27806
$833$	0.819661	0.0283996
$834$	−126.173	−4.36903
$835$	68.8990	2.38435
$836$	26.2659	0.908426
$837$	−16.8163	−0.581256
$838$	53.8428	1.85997
$839$	−30.5027	−1.05307	−0.526536	−	0.850153i	$-0.676509\pi$
$839$	−30.5027	−1.05307	−0.526536	+	0.850153i	$0.676509\pi$
$840$	−185.744	−6.40877
$841$	−28.6307	−0.987267
$842$	74.1826	2.55650
$843$	−24.0760	−0.829221
$844$	−96.1789	−3.31062
$845$	154.460	5.31360
$846$	−34.0745	−1.17151
$847$	−29.3514	−1.00852
$848$	93.9575	3.22651
$849$	21.4369	0.735714
$850$	−20.1736	−0.691950
$851$	0.604145	0.0207098
$852$	33.6514	1.15288
$853$	−6.93424	−0.237424	−0.118712	−	0.992929i	$-0.537877\pi$
$853$	−6.93424	−0.237424	−0.118712	+	0.992929i	$0.537877\pi$
$854$	34.8751	1.19340
$855$	39.0994	1.33717
$856$	−108.691	−3.71500
$857$	−51.7599	−1.76808	−0.884042	−	0.467408i	$-0.845188\pi$
$857$	−51.7599	−1.76808	−0.884042	+	0.467408i	$0.845188\pi$
$858$	34.7436	1.18613
$859$	−26.2800	−0.896662	−0.448331	−	0.893868i	$-0.647981\pi$
$859$	−26.2800	−0.896662	−0.448331	+	0.893868i	$0.647981\pi$
$860$	−67.3748	−2.29746
$861$	−48.7749	−1.66225
$862$	0.633487	0.0215767
$863$	−8.76982	−0.298528	−0.149264	−	0.988797i	$-0.547690\pi$
$863$	−8.76982	−0.298528	−0.149264	+	0.988797i	$0.547690\pi$
$864$	34.2388	1.16483
$865$	2.53916	0.0863341
$866$	57.3596	1.94916
$867$	−35.3014	−1.19890
$868$	76.1826	2.58580
$869$	−4.66623	−0.158291
$870$	−13.7272	−0.465395
$871$	−90.2452	−3.05784
$872$	153.527	5.19909
$873$	−6.63617	−0.224600
$874$	1.56918	0.0530785
$875$	72.7986	2.46104
$876$	154.426	5.21756
$877$	−37.7607	−1.27509	−0.637545	−	0.770413i	$-0.720050\pi$
$877$	−37.7607	−1.27509	−0.637545	+	0.770413i	$0.720050\pi$
$878$	35.0654	1.18340
$879$	13.3052	0.448775
$880$	34.9487	1.17812
$881$	31.9723	1.07717	0.538587	−	0.842570i	$-0.318958\pi$
$881$	31.9723	1.07717	0.538587	+	0.842570i	$0.318958\pi$
$882$	−4.91179	−0.165389
$883$	−28.4875	−0.958680	−0.479340	−	0.877629i	$-0.659124\pi$
$883$	−28.4875	−0.958680	−0.479340	+	0.877629i	$0.659124\pi$
$884$	−23.7599	−0.799132
$885$	20.1941	0.678817
$886$	−6.49843	−0.218319
$887$	10.5495	0.354218	0.177109	−	0.984191i	$-0.443325\pi$
$887$	10.5495	0.354218	0.177109	+	0.984191i	$0.443325\pi$
$888$	100.818	3.38322
$889$	7.73130	0.259300
$890$	0.290874	0.00975011
$891$	−9.75280	−0.326731
$892$	90.5871	3.03308
$893$	51.9000	1.73677
$894$	−125.484	−4.19682
$895$	−71.7940	−2.39981
$896$	−5.21063	−0.174075
$897$	1.47147	0.0491308
$898$	−7.82910	−0.261260
$899$	3.31839	0.110675
$900$	85.7006	2.85669
$901$	6.41197	0.213614
$902$	18.1323	0.603739
$903$	−20.9508	−0.697200
$904$	4.71508	0.156821
$905$	−66.8973	−2.22374
$906$	−60.6477	−2.01488
$907$	35.9151	1.19254	0.596271	−	0.802783i	$-0.296648\pi$
$907$	35.9151	1.19254	0.596271	+	0.802783i	$0.296648\pi$
$908$	−11.5043	−0.381783
$909$	−7.01259	−0.232593
$910$	216.989	7.19312
$911$	28.4962	0.944122	0.472061	−	0.881566i	$-0.343510\pi$
$911$	28.4962	0.944122	0.472061	+	0.881566i	$0.343510\pi$
$912$	132.535	4.38867
$913$	10.0324	0.332024
$914$	100.805	3.33432
$915$	−40.0343	−1.32349
$916$	9.04141	0.298737
$917$	−41.1491	−1.35886
$918$	5.49938	0.181506
$919$	−18.8041	−0.620291	−0.310146	−	0.950689i	$-0.600378\pi$
$919$	−18.8041	−0.620291	−0.310146	+	0.950689i	$0.600378\pi$
$920$	2.92446	0.0964166
$921$	9.74414	0.321080
$922$	−96.2449	−3.16966
$923$	−23.1703	−0.762661
$924$	25.8263	0.849624
$925$	−70.8915	−2.33090
$926$	−24.5579	−0.807024
$927$	17.5603	0.576757
$928$	−6.75642	−0.221790
$929$	−35.3920	−1.16117	−0.580586	−	0.814199i	$-0.697177\pi$
$929$	−35.3920	−1.16117	−0.580586	+	0.814199i	$0.697177\pi$
$930$	−123.361	−4.04517
$931$	7.48130	0.245190
$932$	−25.8441	−0.846552
$933$	48.5856	1.59062
$934$	58.9202	1.92793
$935$	2.38501	0.0779982
$936$	83.9181	2.74295
$937$	12.4380	0.406332	0.203166	−	0.979144i	$-0.434877\pi$
$937$	12.4380	0.406332	0.203166	+	0.979144i	$0.434877\pi$
$938$	−94.6277	−3.08970
$939$	−46.9670	−1.53271
$940$	164.109	5.35266
$941$	48.4868	1.58062	0.790312	−	0.612704i	$-0.209918\pi$
$941$	48.4868	1.58062	0.790312	+	0.612704i	$0.209918\pi$
$942$	−4.36700	−0.142284
$943$	0.767941	0.0250076
$944$	23.3935	0.761393
$945$	−35.6042	−1.15820
$946$	7.78856	0.253228
$947$	−31.2476	−1.01541	−0.507705	−	0.861531i	$-0.669506\pi$
$947$	−31.2476	−1.01541	−0.507705	+	0.861531i	$0.669506\pi$
$948$	−55.9541	−1.81730
$949$	−106.328	−3.45157
$950$	−184.131	−5.97400
$951$	−23.8168	−0.772314
$952$	−14.6840	−0.475911
$953$	61.0696	1.97824	0.989119	−	0.147119i	$-0.0470001\pi$
$953$	61.0696	1.97824	0.989119	+	0.147119i	$0.0470001\pi$
$954$	−38.4235	−1.24401
$955$	−40.3188	−1.30469
$956$	−18.7116	−0.605177
$957$	1.12495	0.0363646
$958$	−68.5079	−2.21339
$959$	37.4305	1.20869
$960$	79.0932	2.55272
$961$	−1.17877	−0.0380250
$962$	−117.777	−3.79728
$963$	22.4968	0.724950
$964$	−127.544	−4.10791
$965$	−72.5186	−2.33446
$966$	1.54292	0.0496428
$967$	−22.7600	−0.731913	−0.365956	−	0.930632i	$-0.619258\pi$
$967$	−22.7600	−0.731913	−0.365956	+	0.930632i	$0.619258\pi$
$968$	77.1179	2.47866
$969$	9.04461	0.290555
$970$	45.0844	1.44757
$971$	21.2709	0.682616	0.341308	−	0.939951i	$-0.389130\pi$
$971$	21.2709	0.682616	0.341308	+	0.939951i	$0.389130\pi$
$972$	−71.9505	−2.30781
$973$	64.5781	2.07028
$974$	23.8568	0.764422
$975$	−172.665	−5.52969
$976$	−46.3770	−1.48449
$977$	35.5602	1.13767	0.568836	−	0.822451i	$-0.307394\pi$
$977$	35.5602	1.13767	0.568836	+	0.822451i	$0.307394\pi$
$978$	67.2940	2.15183
$979$	−0.0238374	−0.000761846 0
$980$	23.6561	0.755667
$981$	−31.7769	−1.01456
$982$	−19.0486	−0.607865
$983$	−21.8961	−0.698377	−0.349189	−	0.937052i	$-0.613543\pi$
$983$	−21.8961	−0.698377	−0.349189	+	0.937052i	$0.613543\pi$
$984$	128.151	4.08532
$985$	−62.9999	−2.00734
$986$	−1.08520	−0.0345599
$987$	51.0314	1.62435
$988$	−216.864	−6.89936
$989$	0.329862	0.0104890
$990$	−14.2921	−0.454233
$991$	32.9145	1.04556	0.522782	−	0.852466i	$-0.324894\pi$
$991$	32.9145	1.04556	0.522782	+	0.852466i	$0.324894\pi$
$992$	−60.7175	−1.92778
$993$	−32.1400	−1.01993
$994$	−24.2955	−0.770608
$995$	19.6735	0.623692
$996$	120.301	3.81190
$997$	28.7641	0.910969	0.455485	−	0.890244i	$-0.349466\pi$
$997$	28.7641	0.910969	0.455485	+	0.890244i	$0.349466\pi$
$998$	57.7606	1.82838
$999$	19.3252	0.611421

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4003.2.a.c.1.6	✓	179

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4003.2.a.c.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-2.62123 q^{2} +2.13484 q^{3} +4.87085 q^{4} +4.03687 q^{5} -5.59591 q^{6} +2.86410 q^{7} -7.52515 q^{8} +1.55755 q^{9} +O(q^{10})\)	\(q-2.62123 q^{2} +2.13484 q^{3} +4.87085 q^{4} +4.03687 q^{5} -5.59591 q^{6} +2.86410 q^{7} -7.52515 q^{8} +1.55755 q^{9} -10.5816 q^{10} +0.867170 q^{11} +10.3985 q^{12} -7.15978 q^{13} -7.50747 q^{14} +8.61809 q^{15} +9.98346 q^{16} +0.681304 q^{17} -4.08269 q^{18} +6.21847 q^{19} +19.6630 q^{20} +6.11440 q^{21} -2.27305 q^{22} -0.0962687 q^{23} -16.0650 q^{24} +11.2964 q^{25} +18.7674 q^{26} -3.07941 q^{27} +13.9506 q^{28} +0.607666 q^{29} -22.5900 q^{30} +5.46088 q^{31} -11.1186 q^{32} +1.85127 q^{33} -1.78585 q^{34} +11.5620 q^{35} +7.58657 q^{36} -6.27561 q^{37} -16.3000 q^{38} -15.2850 q^{39} -30.3781 q^{40} -7.97706 q^{41} -16.0273 q^{42} -3.42647 q^{43} +4.22385 q^{44} +6.28762 q^{45} +0.252343 q^{46} +8.34611 q^{47} +21.3131 q^{48} +1.20308 q^{49} -29.6104 q^{50} +1.45448 q^{51} -34.8742 q^{52} +9.41132 q^{53} +8.07184 q^{54} +3.50066 q^{55} -21.5528 q^{56} +13.2754 q^{57} -1.59283 q^{58} +2.34322 q^{59} +41.9774 q^{60} -4.64538 q^{61} -14.3142 q^{62} +4.46097 q^{63} +9.17758 q^{64} -28.9031 q^{65} -4.85261 q^{66} +12.6045 q^{67} +3.31853 q^{68} -0.205518 q^{69} -30.3067 q^{70} +3.23618 q^{71} -11.7208 q^{72} +14.8508 q^{73} +16.4498 q^{74} +24.1159 q^{75} +30.2892 q^{76} +2.48366 q^{77} +40.0655 q^{78} -5.38099 q^{79} +40.3020 q^{80} -11.2467 q^{81} +20.9097 q^{82} +11.5691 q^{83} +29.7823 q^{84} +2.75034 q^{85} +8.98158 q^{86} +1.29727 q^{87} -6.52559 q^{88} -0.0274887 q^{89} -16.4813 q^{90} -20.5063 q^{91} -0.468910 q^{92} +11.6581 q^{93} -21.8771 q^{94} +25.1032 q^{95} -23.7365 q^{96} -4.26065 q^{97} -3.15354 q^{98} +1.35066 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9}+O(q^{10}) \) 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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