LMFDB - Embedded newform 4007.2.a.b.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4007,2,Mod(1,4007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4007, 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("4007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4007 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4007.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:	$31.9960560899$
Analytic rank:	$0$
Dimension:	$195$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	4007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.69070 q^{2} -2.66626 q^{3} +5.23985 q^{4} +2.66315 q^{5} +7.17410 q^{6} -3.38912 q^{7} -8.71746 q^{8} +4.10894 q^{9} +O(q^{10})$	\(q-2.69070 q^{2} -2.66626 q^{3} +5.23985 q^{4} +2.66315 q^{5} +7.17410 q^{6} -3.38912 q^{7} -8.71746 q^{8} +4.10894 q^{9} -7.16574 q^{10} -2.71096 q^{11} -13.9708 q^{12} +6.55026 q^{13} +9.11909 q^{14} -7.10065 q^{15} +12.9763 q^{16} +5.30453 q^{17} -11.0559 q^{18} -4.04793 q^{19} +13.9545 q^{20} +9.03627 q^{21} +7.29437 q^{22} +7.39413 q^{23} +23.2430 q^{24} +2.09238 q^{25} -17.6248 q^{26} -2.95671 q^{27} -17.7585 q^{28} +1.78893 q^{29} +19.1057 q^{30} -2.53310 q^{31} -17.4805 q^{32} +7.22811 q^{33} -14.2729 q^{34} -9.02574 q^{35} +21.5302 q^{36} +7.05992 q^{37} +10.8917 q^{38} -17.4647 q^{39} -23.2159 q^{40} -10.2463 q^{41} -24.3139 q^{42} +10.3027 q^{43} -14.2050 q^{44} +10.9427 q^{45} -19.8954 q^{46} -9.80796 q^{47} -34.5983 q^{48} +4.48613 q^{49} -5.62997 q^{50} -14.1433 q^{51} +34.3224 q^{52} +6.63780 q^{53} +7.95562 q^{54} -7.21969 q^{55} +29.5445 q^{56} +10.7928 q^{57} -4.81347 q^{58} +11.2952 q^{59} -37.2064 q^{60} +3.64976 q^{61} +6.81580 q^{62} -13.9257 q^{63} +21.0820 q^{64} +17.4443 q^{65} -19.4487 q^{66} +2.02628 q^{67} +27.7950 q^{68} -19.7147 q^{69} +24.2855 q^{70} +0.124838 q^{71} -35.8195 q^{72} -4.02910 q^{73} -18.9961 q^{74} -5.57883 q^{75} -21.2105 q^{76} +9.18776 q^{77} +46.9922 q^{78} +14.5423 q^{79} +34.5580 q^{80} -4.44345 q^{81} +27.5696 q^{82} +12.6135 q^{83} +47.3487 q^{84} +14.1268 q^{85} -27.7214 q^{86} -4.76975 q^{87} +23.6327 q^{88} -8.21388 q^{89} -29.4436 q^{90} -22.1996 q^{91} +38.7441 q^{92} +6.75389 q^{93} +26.3903 q^{94} -10.7802 q^{95} +46.6075 q^{96} +5.15073 q^{97} -12.0708 q^{98} -11.1392 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 195 q + 14 q^{2} + 22 q^{3} + 220 q^{4} + 14 q^{5} + 13 q^{6} + 48 q^{7} + 39 q^{8} + 245 q^{9}+O(q^{10}) $ 195 * q + 14 * q^2 + 22 * q^3 + 220 * q^4 + 14 * q^5 + 13 * q^6 + 48 * q^7 + 39 * q^8 + 245 * q^9	\( 195 q + 14 q^{2} + 22 q^{3} + 220 q^{4} + 14 q^{5} + 13 q^{6} + 48 q^{7} + 39 q^{8} + 245 q^{9} + 40 q^{10} + 13 q^{11} + 57 q^{12} + 97 q^{13} + 9 q^{14} + 23 q^{15} + 270 q^{16} + 66 q^{17} + 60 q^{18} + 33 q^{19} + 24 q^{20} + 27 q^{21} + 127 q^{22} + 42 q^{23} + 33 q^{24} + 357 q^{25} + 8 q^{26} + 79 q^{27} + 131 q^{28} + 57 q^{29} + 51 q^{30} + 41 q^{31} + 67 q^{32} + 74 q^{33} + 26 q^{34} + 14 q^{35} + 279 q^{36} + 133 q^{37} + 7 q^{38} + 28 q^{39} + 97 q^{40} + 64 q^{41} - q^{42} + 123 q^{43} + 21 q^{44} + 40 q^{45} + 84 q^{46} + 14 q^{47} + 122 q^{48} + 335 q^{49} + 35 q^{50} + 37 q^{51} + 220 q^{52} + 83 q^{53} + 21 q^{54} + 47 q^{55} + q^{56} + 235 q^{57} + 138 q^{58} + 18 q^{59} - 4 q^{60} + 81 q^{61} + 39 q^{62} + 102 q^{63} + 343 q^{64} + 165 q^{65} - 54 q^{66} + 147 q^{67} + 74 q^{68} - 2 q^{69} + 13 q^{70} + 31 q^{71} + 112 q^{72} + 300 q^{73} + 5 q^{74} + 84 q^{75} + 64 q^{76} + 67 q^{77} + 61 q^{78} + 144 q^{79} - 8 q^{80} + 359 q^{81} + 85 q^{82} + 26 q^{83} + 12 q^{84} + 201 q^{85} - 2 q^{86} + 80 q^{87} + 347 q^{88} + 29 q^{89} + 62 q^{90} + 70 q^{91} + 79 q^{92} + 76 q^{93} + 72 q^{94} + 71 q^{95} + 31 q^{96} + 264 q^{97} + 30 q^{98} + 19 q^{99}+O(q^{100}) \) 195 * q + 14 * q^2 + 22 * q^3 + 220 * q^4 + 14 * q^5 + 13 * q^6 + 48 * q^7 + 39 * q^8 + 245 * q^9 + 40 * q^10 + 13 * q^11 + 57 * q^12 + 97 * q^13 + 9 * q^14 + 23 * q^15 + 270 * q^16 + 66 * q^17 + 60 * q^18 + 33 * q^19 + 24 * q^20 + 27 * q^21 + 127 * q^22 + 42 * q^23 + 33 * q^24 + 357 * q^25 + 8 * q^26 + 79 * q^27 + 131 * q^28 + 57 * q^29 + 51 * q^30 + 41 * q^31 + 67 * q^32 + 74 * q^33 + 26 * q^34 + 14 * q^35 + 279 * q^36 + 133 * q^37 + 7 * q^38 + 28 * q^39 + 97 * q^40 + 64 * q^41 - q^42 + 123 * q^43 + 21 * q^44 + 40 * q^45 + 84 * q^46 + 14 * q^47 + 122 * q^48 + 335 * q^49 + 35 * q^50 + 37 * q^51 + 220 * q^52 + 83 * q^53 + 21 * q^54 + 47 * q^55 + q^56 + 235 * q^57 + 138 * q^58 + 18 * q^59 - 4 * q^60 + 81 * q^61 + 39 * q^62 + 102 * q^63 + 343 * q^64 + 165 * q^65 - 54 * q^66 + 147 * q^67 + 74 * q^68 - 2 * q^69 + 13 * q^70 + 31 * q^71 + 112 * q^72 + 300 * q^73 + 5 * q^74 + 84 * q^75 + 64 * q^76 + 67 * q^77 + 61 * q^78 + 144 * q^79 - 8 * q^80 + 359 * q^81 + 85 * q^82 + 26 * q^83 + 12 * q^84 + 201 * q^85 - 2 * q^86 + 80 * q^87 + 347 * q^88 + 29 * q^89 + 62 * q^90 + 70 * q^91 + 79 * q^92 + 76 * q^93 + 72 * q^94 + 71 * q^95 + 31 * q^96 + 264 * q^97 + 30 * q^98 + 19 * 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 $

$2$	−2.69070	−1.90261	−0.951305	−	0.308251i	$-0.900256\pi$
$2$	−2.69070	−1.90261	−0.951305	+	0.308251i	$0.900256\pi$
$3$	−2.66626	−1.53937	−0.769683	−	0.638427i	$-0.779586\pi$
$3$	−2.66626	−1.53937	−0.769683	+	0.638427i	$0.779586\pi$
$4$	5.23985	2.61993
$5$	2.66315	1.19100	0.595499	−	0.803356i	$-0.296954\pi$
$5$	2.66315	1.19100	0.595499	+	0.803356i	$0.296954\pi$
$6$	7.17410	2.92881
$7$	−3.38912	−1.28097	−0.640483	−	0.767972i	$-0.721266\pi$
$7$	−3.38912	−1.28097	−0.640483	+	0.767972i	$0.721266\pi$
$8$	−8.71746	−3.08209
$9$	4.10894	1.36965
$10$	−7.16574	−2.26601
$11$	−2.71096	−0.817384	−0.408692	−	0.912672i	$-0.634015\pi$
$11$	−2.71096	−0.817384	−0.408692	+	0.912672i	$0.634015\pi$
$12$	−13.9708	−4.03302
$13$	6.55026	1.81672	0.908358	−	0.418194i	$-0.137337\pi$
$13$	6.55026	1.81672	0.908358	+	0.418194i	$0.137337\pi$
$14$	9.11909	2.43718
$15$	−7.10065	−1.83338
$16$	12.9763	3.24409
$17$	5.30453	1.28654	0.643269	−	0.765640i	$-0.277578\pi$
$17$	5.30453	1.28654	0.643269	+	0.765640i	$0.277578\pi$
$18$	−11.0559	−2.60590
$19$	−4.04793	−0.928658	−0.464329	−	0.885663i	$-0.653704\pi$
$19$	−4.04793	−0.928658	−0.464329	+	0.885663i	$0.653704\pi$
$20$	13.9545	3.12033
$21$	9.03627	1.97188
$22$	7.29437	1.55516
$23$	7.39413	1.54178	0.770891	−	0.636967i	$-0.219811\pi$
$23$	7.39413	1.54178	0.770891	+	0.636967i	$0.219811\pi$
$24$	23.2430	4.74446
$25$	2.09238	0.418476
$26$	−17.6248	−3.45650
$27$	−2.95671	−0.569020
$28$	−17.7585	−3.35604
$29$	1.78893	0.332196	0.166098	−	0.986109i	$-0.446883\pi$
$29$	1.78893	0.332196	0.166098	+	0.986109i	$0.446883\pi$
$30$	19.1057	3.48821
$31$	−2.53310	−0.454958	−0.227479	−	0.973783i	$-0.573048\pi$
$31$	−2.53310	−0.454958	−0.227479	+	0.973783i	$0.573048\pi$
$32$	−17.4805	−3.09015
$33$	7.22811	1.25825
$34$	−14.2729	−2.44778
$35$	−9.02574	−1.52563
$36$	21.5302	3.58837
$37$	7.05992	1.16064	0.580322	−	0.814387i	$-0.302927\pi$
$37$	7.05992	1.16064	0.580322	+	0.814387i	$0.302927\pi$
$38$	10.8917	1.76687
$39$	−17.4647	−2.79659
$40$	−23.2159	−3.67076
$41$	−10.2463	−1.60020	−0.800100	−	0.599867i	$-0.795220\pi$
$41$	−10.2463	−1.60020	−0.800100	+	0.599867i	$0.795220\pi$
$42$	−24.3139	−3.75171
$43$	10.3027	1.57114	0.785572	−	0.618770i	$-0.212369\pi$
$43$	10.3027	1.57114	0.785572	+	0.618770i	$0.212369\pi$
$44$	−14.2050	−2.14149
$45$	10.9427	1.63125
$46$	−19.8954	−2.93341
$47$	−9.80796	−1.43064	−0.715319	−	0.698798i	$-0.753719\pi$
$47$	−9.80796	−1.43064	−0.715319	+	0.698798i	$0.753719\pi$
$48$	−34.5983	−4.99384
$49$	4.48613	0.640876
$50$	−5.62997	−0.796197
$51$	−14.1433	−1.98045
$52$	34.3224	4.75966
$53$	6.63780	0.911772	0.455886	−	0.890038i	$-0.349322\pi$
$53$	6.63780	0.911772	0.455886	+	0.890038i	$0.349322\pi$
$54$	7.95562	1.08262
$55$	−7.21969	−0.973503
$56$	29.5445	3.94805
$57$	10.7928	1.42954
$58$	−4.81347	−0.632040
$59$	11.2952	1.47052	0.735258	−	0.677788i	$-0.237061\pi$
$59$	11.2952	1.47052	0.735258	+	0.677788i	$0.237061\pi$
$60$	−37.2064	−4.80332
$61$	3.64976	0.467303	0.233652	−	0.972320i	$-0.424932\pi$
$61$	3.64976	0.467303	0.233652	+	0.972320i	$0.424932\pi$
$62$	6.81580	0.865607
$63$	−13.9257	−1.75447
$64$	21.0820	2.63526
$65$	17.4443	2.16370
$66$	−19.4487	−2.39397
$67$	2.02628	0.247549	0.123775	−	0.992310i	$-0.460500\pi$
$67$	2.02628	0.247549	0.123775	+	0.992310i	$0.460500\pi$
$68$	27.7950	3.37063
$69$	−19.7147	−2.37337
$70$	24.2855	2.90268
$71$	0.124838	0.0148155	0.00740775	−	0.999973i	$-0.497642\pi$
$71$	0.124838	0.0148155	0.00740775	+	0.999973i	$0.497642\pi$
$72$	−35.8195	−4.22137
$73$	−4.02910	−0.471571	−0.235785	−	0.971805i	$-0.575766\pi$
$73$	−4.02910	−0.471571	−0.235785	+	0.971805i	$0.575766\pi$
$74$	−18.9961	−2.20825
$75$	−5.57883	−0.644188
$76$	−21.2105	−2.43302
$77$	9.18776	1.04704
$78$	46.9922	5.32082
$79$	14.5423	1.63613	0.818067	−	0.575123i	$-0.195046\pi$
$79$	14.5423	1.63613	0.818067	+	0.575123i	$0.195046\pi$
$80$	34.5580	3.86370
$81$	−4.44345	−0.493716
$82$	27.5696	3.04456
$83$	12.6135	1.38452	0.692258	−	0.721650i	$-0.256616\pi$
$83$	12.6135	1.38452	0.692258	+	0.721650i	$0.256616\pi$
$84$	47.3487	5.16617
$85$	14.1268	1.53226
$86$	−27.7214	−2.98927
$87$	−4.76975	−0.511371
$88$	23.6327	2.51925
$89$	−8.21388	−0.870670	−0.435335	−	0.900269i	$-0.643370\pi$
$89$	−8.21388	−0.870670	−0.435335	+	0.900269i	$0.643370\pi$
$90$	−29.4436	−3.10362
$91$	−22.1996	−2.32715
$92$	38.7441	4.03936
$93$	6.75389	0.700346
$94$	26.3903	2.72195
$95$	−10.7802	−1.10603
$96$	46.6075	4.75686
$97$	5.15073	0.522977	0.261488	−	0.965207i	$-0.415787\pi$
$97$	5.15073	0.522977	0.261488	+	0.965207i	$0.415787\pi$
$98$	−12.0708	−1.21934
$99$	−11.1392	−1.11953
$100$	10.9638	1.09638
$101$	3.70718	0.368878	0.184439	−	0.982844i	$-0.440953\pi$
$101$	3.70718	0.368878	0.184439	+	0.982844i	$0.440953\pi$
$102$	38.0552	3.76803
$103$	−17.1006	−1.68497	−0.842484	−	0.538721i	$-0.818908\pi$
$103$	−17.1006	−1.68497	−0.842484	+	0.538721i	$0.818908\pi$
$104$	−57.1017	−5.59928
$105$	24.0650	2.34850
$106$	−17.8603	−1.73475
$107$	6.03670	0.583590	0.291795	−	0.956481i	$-0.405747\pi$
$107$	6.03670	0.583590	0.291795	+	0.956481i	$0.405747\pi$
$108$	−15.4927	−1.49079
$109$	9.23713	0.884757	0.442378	−	0.896829i	$-0.354135\pi$
$109$	9.23713	0.884757	0.442378	+	0.896829i	$0.354135\pi$
$110$	19.4260	1.85220
$111$	−18.8236	−1.78666
$112$	−43.9784	−4.15557
$113$	−9.06456	−0.852722	−0.426361	−	0.904553i	$-0.640205\pi$
$113$	−9.06456	−0.852722	−0.426361	+	0.904553i	$0.640205\pi$
$114$	−29.0402	−2.71986
$115$	19.6917	1.83626
$116$	9.37373	0.870329
$117$	26.9146	2.48826
$118$	−30.3921	−2.79782
$119$	−17.9777	−1.64801
$120$	61.8997	5.65064
$121$	−3.65071	−0.331883
$122$	−9.82039	−0.889096
$123$	27.3192	2.46329
$124$	−13.2731	−1.19196
$125$	−7.74343	−0.692594
$126$	37.4698	3.33807
$127$	2.12248	0.188340	0.0941698	−	0.995556i	$-0.469980\pi$
$127$	2.12248	0.188340	0.0941698	+	0.995556i	$0.469980\pi$
$128$	−21.7644	−1.92372
$129$	−27.4696	−2.41856
$130$	−46.9375	−4.11669
$131$	−17.9818	−1.57108	−0.785541	−	0.618810i	$-0.787615\pi$
$131$	−17.9818	−1.57108	−0.785541	+	0.618810i	$0.787615\pi$
$132$	37.8743	3.29653
$133$	13.7189	1.18958
$134$	−5.45210	−0.470990
$135$	−7.87418	−0.677702
$136$	−46.2421	−3.96522
$137$	−20.0345	−1.71167	−0.855833	−	0.517252i	$-0.826955\pi$
$137$	−20.0345	−1.71167	−0.855833	+	0.517252i	$0.826955\pi$
$138$	53.0462	4.51559
$139$	3.18927	0.270510	0.135255	−	0.990811i	$-0.456815\pi$
$139$	3.18927	0.270510	0.135255	+	0.990811i	$0.456815\pi$
$140$	−47.2936	−3.99704
$141$	26.1506	2.20227
$142$	−0.335900	−0.0281881
$143$	−17.7575	−1.48495
$144$	53.3190	4.44325
$145$	4.76420	0.395645
$146$	10.8411	0.897215
$147$	−11.9612	−0.986542
$148$	36.9930	3.04080
$149$	2.15826	0.176812	0.0884059	−	0.996085i	$-0.471823\pi$
$149$	2.15826	0.176812	0.0884059	+	0.996085i	$0.471823\pi$
$150$	15.0109	1.22564
$151$	11.5184	0.937350	0.468675	−	0.883371i	$-0.344731\pi$
$151$	11.5184	0.937350	0.468675	+	0.883371i	$0.344731\pi$
$152$	35.2876	2.86221
$153$	21.7960	1.76210
$154$	−24.7215	−1.99211
$155$	−6.74603	−0.541854
$156$	−91.5124	−7.32686
$157$	1.98852	0.158701	0.0793505	−	0.996847i	$-0.474715\pi$
$157$	1.98852	0.158701	0.0793505	+	0.996847i	$0.474715\pi$
$158$	−39.1289	−3.11293
$159$	−17.6981	−1.40355
$160$	−46.5532	−3.68036
$161$	−25.0596	−1.97497
$162$	11.9560	0.939350
$163$	−8.91200	−0.698042	−0.349021	−	0.937115i	$-0.613486\pi$
$163$	−8.91200	−0.698042	−0.349021	+	0.937115i	$0.613486\pi$
$164$	−53.6890	−4.19240
$165$	19.2496	1.49858
$166$	−33.9392	−2.63419
$167$	−9.53061	−0.737500	−0.368750	−	0.929529i	$-0.620214\pi$
$167$	−9.53061	−0.737500	−0.368750	+	0.929529i	$0.620214\pi$
$168$	−78.7733	−6.07750
$169$	29.9059	2.30046
$170$	−38.0109	−2.91530
$171$	−16.6327	−1.27193
$172$	53.9845	4.11628
$173$	−19.1586	−1.45660	−0.728299	−	0.685259i	$-0.759689\pi$
$173$	−19.1586	−1.45660	−0.728299	+	0.685259i	$0.759689\pi$
$174$	12.8340	0.972940
$175$	−7.09133	−0.536054
$176$	−35.1783	−2.65167
$177$	−30.1160	−2.26366
$178$	22.1011	1.65655
$179$	14.9938	1.12069	0.560345	−	0.828259i	$-0.310669\pi$
$179$	14.9938	1.12069	0.560345	+	0.828259i	$0.310669\pi$
$180$	57.3383	4.27374
$181$	−6.64507	−0.493924	−0.246962	−	0.969025i	$-0.579432\pi$
$181$	−6.64507	−0.493924	−0.246962	+	0.969025i	$0.579432\pi$
$182$	59.7325	4.42766
$183$	−9.73119	−0.719351
$184$	−64.4580	−4.75191
$185$	18.8017	1.38233
$186$	−18.1727	−1.33249
$187$	−14.3804	−1.05160
$188$	−51.3923	−3.74817
$189$	10.0207	0.728896
$190$	29.0064	2.10434
$191$	16.3369	1.18210	0.591048	−	0.806637i	$-0.298715\pi$
$191$	16.3369	1.18210	0.591048	+	0.806637i	$0.298715\pi$
$192$	−56.2102	−4.05662
$193$	15.9111	1.14530	0.572652	−	0.819799i	$-0.305915\pi$
$193$	15.9111	1.14530	0.572652	+	0.819799i	$0.305915\pi$
$194$	−13.8590	−0.995021
$195$	−46.5111	−3.33073
$196$	23.5067	1.67905
$197$	5.22287	0.372114	0.186057	−	0.982539i	$-0.440429\pi$
$197$	5.22287	0.372114	0.186057	+	0.982539i	$0.440429\pi$
$198$	29.9721	2.13002
$199$	−10.8342	−0.768018	−0.384009	−	0.923329i	$-0.625457\pi$
$199$	−10.8342	−0.768018	−0.384009	+	0.923329i	$0.625457\pi$
$200$	−18.2403	−1.28978
$201$	−5.40258	−0.381069
$202$	−9.97490	−0.701832
$203$	−6.06290	−0.425532
$204$	−74.1086	−5.18864
$205$	−27.2874	−1.90583
$206$	46.0124	3.20584
$207$	30.3820	2.11170
$208$	84.9985	5.89358
$209$	10.9738	0.759071
$210$	−64.7515	−4.46828
$211$	18.5387	1.27626	0.638129	−	0.769930i	$-0.279709\pi$
$211$	18.5387	1.27626	0.638129	+	0.769930i	$0.279709\pi$
$212$	34.7811	2.38878
$213$	−0.332849	−0.0228065
$214$	−16.2429	−1.11034
$215$	27.4376	1.87123
$216$	25.7750	1.75377
$217$	8.58497	0.582786
$218$	−24.8543	−1.68335
$219$	10.7426	0.725919
$220$	−37.8301	−2.55051
$221$	34.7461	2.33727
$222$	50.6486	3.39931
$223$	17.0072	1.13888	0.569442	−	0.822031i	$-0.307159\pi$
$223$	17.0072	1.13888	0.569442	+	0.822031i	$0.307159\pi$
$224$	59.2435	3.95837
$225$	8.59746	0.573164
$226$	24.3900	1.62240
$227$	−4.22634	−0.280512	−0.140256	−	0.990115i	$-0.544793\pi$
$227$	−4.22634	−0.280512	−0.140256	+	0.990115i	$0.544793\pi$
$228$	56.5528	3.74530
$229$	−5.70834	−0.377218	−0.188609	−	0.982052i	$-0.560398\pi$
$229$	−5.70834	−0.377218	−0.188609	+	0.982052i	$0.560398\pi$
$230$	−52.9844	−3.49369
$231$	−24.4969	−1.61178
$232$	−15.5949	−1.02386
$233$	0.113021	0.00740425	0.00370212	−	0.999993i	$-0.498822\pi$
$233$	0.113021	0.00740425	0.00370212	+	0.999993i	$0.498822\pi$
$234$	−72.4191	−4.73418
$235$	−26.1201	−1.70389
$236$	59.1854	3.85264
$237$	−38.7735	−2.51861
$238$	48.3725	3.13553
$239$	−6.81213	−0.440640	−0.220320	−	0.975428i	$-0.570710\pi$
$239$	−6.81213	−0.440640	−0.220320	+	0.975428i	$0.570710\pi$
$240$	−92.1406	−5.94765
$241$	13.6697	0.880545	0.440272	−	0.897864i	$-0.354882\pi$
$241$	13.6697	0.880545	0.440272	+	0.897864i	$0.354882\pi$
$242$	9.82296	0.631443
$243$	20.7175	1.32903
$244$	19.1242	1.22430
$245$	11.9473	0.763282
$246$	−73.5078	−4.68668
$247$	−26.5150	−1.68711
$248$	22.0822	1.40222
$249$	−33.6310	−2.13128
$250$	20.8352	1.31774
$251$	−2.95454	−0.186489	−0.0932446	−	0.995643i	$-0.529724\pi$
$251$	−2.95454	−0.186489	−0.0932446	+	0.995643i	$0.529724\pi$
$252$	−72.9685	−4.59658
$253$	−20.0452	−1.26023
$254$	−5.71095	−0.358337
$255$	−37.6656	−2.35871
$256$	16.3973	1.02483
$257$	−15.3233	−0.955843	−0.477922	−	0.878403i	$-0.658610\pi$
$257$	−15.3233	−0.955843	−0.477922	+	0.878403i	$0.658610\pi$
$258$	73.9124	4.60159
$259$	−23.9269	−1.48675
$260$	91.4058	5.66875
$261$	7.35060	0.454991
$262$	48.3837	2.98916
$263$	−11.5138	−0.709969	−0.354985	−	0.934872i	$-0.615514\pi$
$263$	−11.5138	−0.709969	−0.354985	+	0.934872i	$0.615514\pi$
$264$	−63.0108	−3.87805
$265$	17.6775	1.08592
$266$	−36.9134	−2.26331
$267$	21.9003	1.34028
$268$	10.6174	0.648561
$269$	−17.5897	−1.07246	−0.536232	−	0.844071i	$-0.680153\pi$
$269$	−17.5897	−1.07246	−0.536232	+	0.844071i	$0.680153\pi$
$270$	21.1870	1.28940
$271$	−16.0703	−0.976202	−0.488101	−	0.872787i	$-0.662310\pi$
$271$	−16.0703	−0.976202	−0.488101	+	0.872787i	$0.662310\pi$
$272$	68.8335	4.17364
$273$	59.1899	3.58234
$274$	53.9069	3.25663
$275$	−5.67236	−0.342056
$276$	−103.302	−6.21805
$277$	7.80129	0.468734	0.234367	−	0.972148i	$-0.424698\pi$
$277$	7.80129	0.468734	0.234367	+	0.972148i	$0.424698\pi$
$278$	−8.58137	−0.514676
$279$	−10.4083	−0.623131
$280$	78.6816	4.70212
$281$	−21.3238	−1.27207	−0.636036	−	0.771659i	$-0.719427\pi$
$281$	−21.3238	−1.27207	−0.636036	+	0.771659i	$0.719427\pi$
$282$	−70.3633	−4.19007
$283$	−18.0040	−1.07022	−0.535112	−	0.844781i	$-0.679731\pi$
$283$	−18.0040	−1.07022	−0.535112	+	0.844781i	$0.679731\pi$
$284$	0.654131	0.0388155
$285$	28.7429	1.70258
$286$	47.7800	2.82529
$287$	34.7258	2.04980
$288$	−71.8263	−4.23240
$289$	11.1381	0.655180
$290$	−12.8190	−0.752758
$291$	−13.7332	−0.805053
$292$	−21.1119	−1.23548
$293$	−9.33849	−0.545561	−0.272780	−	0.962076i	$-0.587943\pi$
$293$	−9.33849	−0.545561	−0.272780	+	0.962076i	$0.587943\pi$
$294$	32.1839	1.87701
$295$	30.0810	1.75138
$296$	−61.5446	−3.57721
$297$	8.01553	0.465108
$298$	−5.80724	−0.336404
$299$	48.4335	2.80098
$300$	−29.2323	−1.68772
$301$	−34.9170	−2.01258
$302$	−30.9924	−1.78341
$303$	−9.88430	−0.567838
$304$	−52.5273	−3.01265
$305$	9.71986	0.556557
$306$	−58.6464	−3.35259
$307$	3.67876	0.209958	0.104979	−	0.994474i	$-0.466522\pi$
$307$	3.67876	0.209958	0.104979	+	0.994474i	$0.466522\pi$
$308$	48.1425	2.74317
$309$	45.5945	2.59378
$310$	18.1515	1.03094
$311$	−27.5148	−1.56022	−0.780111	−	0.625641i	$-0.784838\pi$
$311$	−27.5148	−1.56022	−0.780111	+	0.625641i	$0.784838\pi$
$312$	152.248	8.61933
$313$	−15.5268	−0.877628	−0.438814	−	0.898578i	$-0.644601\pi$
$313$	−15.5268	−0.877628	−0.438814	+	0.898578i	$0.644601\pi$
$314$	−5.35050	−0.301946
$315$	−37.0862	−2.08957
$316$	76.1994	4.28655
$317$	19.1953	1.07812	0.539059	−	0.842268i	$-0.318780\pi$
$317$	19.1953	1.07812	0.539059	+	0.842268i	$0.318780\pi$
$318$	47.6202	2.67041
$319$	−4.84972	−0.271532
$320$	56.1447	3.13858
$321$	−16.0954	−0.898358
$322$	67.4278	3.75760
$323$	−21.4724	−1.19475
$324$	−23.2830	−1.29350
$325$	13.7056	0.760252
$326$	23.9795	1.32810
$327$	−24.6286	−1.36196
$328$	89.3215	4.93196
$329$	33.2404	1.83260
$330$	−51.7948	−2.85121
$331$	−26.5817	−1.46106	−0.730531	−	0.682879i	$-0.760727\pi$
$331$	−26.5817	−1.46106	−0.730531	+	0.682879i	$0.760727\pi$
$332$	66.0931	3.62733
$333$	29.0088	1.58967
$334$	25.6440	1.40318
$335$	5.39629	0.294831
$336$	117.258	6.39694
$337$	18.2995	0.996835	0.498418	−	0.866937i	$-0.333915\pi$
$337$	18.2995	0.996835	0.498418	+	0.866937i	$0.333915\pi$
$338$	−80.4678	−4.37687
$339$	24.1685	1.31265
$340$	74.0222	4.01442
$341$	6.86712	0.371875
$342$	44.7535	2.41999
$343$	8.51980	0.460026
$344$	−89.8132	−4.84240
$345$	−52.5032	−2.82668
$346$	51.5499	2.77134
$347$	19.8666	1.06649	0.533247	−	0.845960i	$-0.320972\pi$
$347$	19.8666	1.06649	0.533247	+	0.845960i	$0.320972\pi$
$348$	−24.9928	−1.33975
$349$	16.1192	0.862839	0.431420	−	0.902151i	$-0.358013\pi$
$349$	16.1192	0.862839	0.431420	+	0.902151i	$0.358013\pi$
$350$	19.0806	1.01990
$351$	−19.3672	−1.03375
$352$	47.3889	2.52584
$353$	21.9146	1.16640	0.583199	−	0.812329i	$-0.301801\pi$
$353$	21.9146	1.16640	0.583199	+	0.812329i	$0.301801\pi$
$354$	81.0332	4.30686
$355$	0.332462	0.0176452
$356$	−43.0395	−2.28109
$357$	47.9332	2.53689
$358$	−40.3438	−2.13224
$359$	−11.3931	−0.601303	−0.300651	−	0.953734i	$-0.597204\pi$
$359$	−11.3931	−0.601303	−0.300651	+	0.953734i	$0.597204\pi$
$360$	−95.3928	−5.02764
$361$	−2.61429	−0.137594
$362$	17.8799	0.939746
$363$	9.73374	0.510889
$364$	−116.323	−6.09697
$365$	−10.7301	−0.561640
$366$	26.1837	1.36864
$367$	27.3354	1.42690	0.713449	−	0.700707i	$-0.247132\pi$
$367$	27.3354	1.42690	0.713449	+	0.700707i	$0.247132\pi$
$368$	95.9488	5.00168
$369$	−42.1013	−2.19171
$370$	−50.5896	−2.63003
$371$	−22.4963	−1.16795
$372$	35.3894	1.83486
$373$	37.8611	1.96037	0.980187	−	0.198076i	$-0.0634694\pi$
$373$	37.8611	1.96037	0.980187	+	0.198076i	$0.0634694\pi$
$374$	38.6932	2.00078
$375$	20.6460	1.06615
$376$	85.5005	4.40935
$377$	11.7180	0.603506
$378$	−26.9626	−1.38680
$379$	21.1247	1.08510	0.542552	−	0.840022i	$-0.317458\pi$
$379$	21.1247	1.08510	0.542552	+	0.840022i	$0.317458\pi$
$380$	−56.4869	−2.89772
$381$	−5.65908	−0.289924
$382$	−43.9576	−2.24907
$383$	10.9078	0.557362	0.278681	−	0.960384i	$-0.410103\pi$
$383$	10.9078	0.557362	0.278681	+	0.960384i	$0.410103\pi$
$384$	58.0295	2.96131
$385$	24.4684	1.24703
$386$	−42.8119	−2.17907
$387$	42.3331	2.15191
$388$	26.9890	1.37016
$389$	−12.5862	−0.638148	−0.319074	−	0.947730i	$-0.603372\pi$
$389$	−12.5862	−0.638148	−0.319074	+	0.947730i	$0.603372\pi$
$390$	125.147	6.33709
$391$	39.2224	1.98356
$392$	−39.1077	−1.97524
$393$	47.9443	2.41847
$394$	−14.0532	−0.707988
$395$	38.7283	1.94863
$396$	−58.3675	−2.93308
$397$	−16.0269	−0.804367	−0.402184	−	0.915559i	$-0.631749\pi$
$397$	−16.0269	−0.804367	−0.402184	+	0.915559i	$0.631749\pi$
$398$	29.1516	1.46124
$399$	−36.5782	−1.83120
$400$	27.1515	1.35757
$401$	0.591233	0.0295248	0.0147624	−	0.999891i	$-0.495301\pi$
$401$	0.591233	0.0295248	0.0147624	+	0.999891i	$0.495301\pi$
$402$	14.5367	0.725026
$403$	−16.5925	−0.826529
$404$	19.4251	0.966434
$405$	−11.8336	−0.588015
$406$	16.3134	0.809622
$407$	−19.1392	−0.948693
$408$	123.293	6.10393
$409$	−28.1377	−1.39132	−0.695660	−	0.718371i	$-0.744888\pi$
$409$	−28.1377	−1.39132	−0.695660	+	0.718371i	$0.744888\pi$
$410$	73.4221	3.62606
$411$	53.4173	2.63488
$412$	−89.6044	−4.41449
$413$	−38.2809	−1.88368
$414$	−81.7488	−4.01773
$415$	33.5918	1.64896
$416$	−114.502	−5.61391
$417$	−8.50342	−0.416414
$418$	−29.5271	−1.44422
$419$	7.95478	0.388617	0.194308	−	0.980941i	$-0.437754\pi$
$419$	7.95478	0.388617	0.194308	+	0.980941i	$0.437754\pi$
$420$	126.097	6.15290
$421$	3.47027	0.169130	0.0845652	−	0.996418i	$-0.473050\pi$
$421$	3.47027	0.169130	0.0845652	+	0.996418i	$0.473050\pi$
$422$	−49.8821	−2.42822
$423$	−40.3003	−1.95947
$424$	−57.8648	−2.81016
$425$	11.0991	0.538386
$426$	0.895597	0.0433918
$427$	−12.3695	−0.598600
$428$	31.6314	1.52896
$429$	47.3460	2.28589
$430$	−73.8263	−3.56022
$431$	0.0836146	0.00402757	0.00201379	−	0.999998i	$-0.499359\pi$
$431$	0.0836146	0.00402757	0.00201379	+	0.999998i	$0.499359\pi$
$432$	−38.3673	−1.84595
$433$	31.9445	1.53515	0.767577	−	0.640956i	$-0.221462\pi$
$433$	31.9445	1.53515	0.767577	+	0.640956i	$0.221462\pi$
$434$	−23.0996	−1.10881
$435$	−12.7026	−0.609042
$436$	48.4012	2.31800
$437$	−29.9309	−1.43179
$438$	−28.9052	−1.38114
$439$	26.8373	1.28087	0.640437	−	0.768011i	$-0.278753\pi$
$439$	26.8373	1.28087	0.640437	+	0.768011i	$0.278753\pi$
$440$	62.9374	3.00042
$441$	18.4332	0.877773
$442$	−93.4912	−4.44692
$443$	−21.6546	−1.02884	−0.514421	−	0.857538i	$-0.671993\pi$
$443$	−21.6546	−1.02884	−0.514421	+	0.857538i	$0.671993\pi$
$444$	−98.6328	−4.68091
$445$	−21.8748	−1.03697
$446$	−45.7612	−2.16685
$447$	−5.75449	−0.272178
$448$	−71.4496	−3.37567
$449$	−19.8996	−0.939123	−0.469561	−	0.882900i	$-0.655588\pi$
$449$	−19.8996	−0.939123	−0.469561	+	0.882900i	$0.655588\pi$
$450$	−23.1332	−1.09051
$451$	27.7772	1.30798
$452$	−47.4969	−2.23407
$453$	−30.7109	−1.44292
$454$	11.3718	0.533705
$455$	−59.1210	−2.77163
$456$	−94.0860	−4.40598
$457$	−8.78833	−0.411101	−0.205550	−	0.978647i	$-0.565898\pi$
$457$	−8.78833	−0.411101	−0.205550	+	0.978647i	$0.565898\pi$
$458$	15.3594	0.717699
$459$	−15.6840	−0.732066
$460$	103.182	4.81087
$461$	34.5609	1.60966	0.804831	−	0.593504i	$-0.202256\pi$
$461$	34.5609	1.60966	0.804831	+	0.593504i	$0.202256\pi$
$462$	65.9139	3.06659
$463$	14.8271	0.689074	0.344537	−	0.938773i	$-0.388036\pi$
$463$	14.8271	0.689074	0.344537	+	0.938773i	$0.388036\pi$
$464$	23.2138	1.07767
$465$	17.9867	0.834111
$466$	−0.304105	−0.0140874
$467$	23.9889	1.11008	0.555038	−	0.831825i	$-0.312704\pi$
$467$	23.9889	1.11008	0.555038	+	0.831825i	$0.312704\pi$
$468$	141.029	6.51905
$469$	−6.86730	−0.317102
$470$	70.2813	3.24183
$471$	−5.30191	−0.244299
$472$	−98.4659	−4.53226
$473$	−27.9301	−1.28423
$474$	104.328	4.79193
$475$	−8.46981	−0.388621
$476$	−94.2005	−4.31767
$477$	27.2743	1.24881
$478$	18.3294	0.838366
$479$	28.6049	1.30699	0.653495	−	0.756931i	$-0.273302\pi$
$479$	28.6049	1.30699	0.653495	+	0.756931i	$0.273302\pi$
$480$	124.123	5.66541
$481$	46.2444	2.10856
$482$	−36.7811	−1.67533
$483$	66.8154	3.04020
$484$	−19.1292	−0.869508
$485$	13.7172	0.622864
$486$	−55.7446	−2.52863
$487$	22.8758	1.03660	0.518301	−	0.855198i	$-0.326565\pi$
$487$	22.8758	1.03660	0.518301	+	0.855198i	$0.326565\pi$
$488$	−31.8166	−1.44027
$489$	23.7617	1.07454
$490$	−32.1464	−1.45223
$491$	−10.6239	−0.479451	−0.239725	−	0.970841i	$-0.577057\pi$
$491$	−10.6239	−0.479451	−0.239725	+	0.970841i	$0.577057\pi$
$492$	143.149	6.45364
$493$	9.48944	0.427383
$494$	71.3438	3.20991
$495$	−29.6653	−1.33335
$496$	−32.8704	−1.47592
$497$	−0.423090	−0.0189782
$498$	90.4908	4.05499
$499$	13.0537	0.584364	0.292182	−	0.956363i	$-0.405619\pi$
$499$	13.0537	0.584364	0.292182	+	0.956363i	$0.405619\pi$
$500$	−40.5744	−1.81454
$501$	25.4111	1.13528
$502$	7.94978	0.354816
$503$	33.2852	1.48412	0.742058	−	0.670336i	$-0.233850\pi$
$503$	33.2852	1.48412	0.742058	+	0.670336i	$0.233850\pi$
$504$	121.397	5.40743
$505$	9.87279	0.439333
$506$	53.9355	2.39772
$507$	−79.7369	−3.54124
$508$	11.1215	0.493436
$509$	9.99095	0.442841	0.221421	−	0.975178i	$-0.428931\pi$
$509$	9.99095	0.442841	0.221421	+	0.975178i	$0.428931\pi$
$510$	101.347	4.48771
$511$	13.6551	0.604066
$512$	−0.591421	−0.0261374
$513$	11.9686	0.528425
$514$	41.2304	1.81860
$515$	−45.5414	−2.00679
$516$	−143.937	−6.33646
$517$	26.5890	1.16938
$518$	64.3801	2.82870
$519$	51.0817	2.24224
$520$	−152.070	−6.66873
$521$	−4.51513	−0.197812	−0.0989058	−	0.995097i	$-0.531534\pi$
$521$	−4.51513	−0.197812	−0.0989058	+	0.995097i	$0.531534\pi$
$522$	−19.7783	−0.865671
$523$	−33.6719	−1.47237	−0.736186	−	0.676780i	$-0.763375\pi$
$523$	−33.6719	−1.47237	−0.736186	+	0.676780i	$0.763375\pi$
$524$	−94.2222	−4.11612
$525$	18.9073	0.825183
$526$	30.9801	1.35079
$527$	−13.4369	−0.585320
$528$	93.7945	4.08188
$529$	31.6732	1.37709
$530$	−47.5648	−2.06608
$531$	46.4114	2.01409
$532$	71.8850	3.11661
$533$	−67.1158	−2.90711
$534$	−58.9272	−2.55003
$535$	16.0767	0.695055
$536$	−17.6640	−0.762969
$537$	−39.9774	−1.72515
$538$	47.3286	2.04048
$539$	−12.1617	−0.523842
$540$	−41.2595	−1.77553
$541$	−8.79763	−0.378240	−0.189120	−	0.981954i	$-0.560563\pi$
$541$	−8.79763	−0.378240	−0.189120	+	0.981954i	$0.560563\pi$
$542$	43.2404	1.85733
$543$	17.7175	0.760330
$544$	−92.7259	−3.97559
$545$	24.5999	1.05374
$546$	−159.262	−6.81579
$547$	10.9898	0.469890	0.234945	−	0.972009i	$-0.424509\pi$
$547$	10.9898	0.469890	0.234945	+	0.972009i	$0.424509\pi$
$548$	−104.978	−4.48444
$549$	14.9966	0.640040
$550$	15.2626	0.650799
$551$	−7.24146	−0.308497
$552$	171.862	7.31493
$553$	−49.2855	−2.09583
$554$	−20.9909	−0.891818
$555$	−50.1301	−2.12790
$556$	16.7113	0.708718
$557$	45.7042	1.93655	0.968276	−	0.249885i	$-0.0803928\pi$
$557$	45.7042	1.93655	0.968276	+	0.249885i	$0.0803928\pi$
$558$	28.0057	1.18558
$559$	67.4852	2.85432
$560$	−117.121	−4.94927
$561$	38.3418	1.61879
$562$	57.3759	2.42026
$563$	42.0838	1.77362	0.886810	−	0.462134i	$-0.152916\pi$
$563$	42.0838	1.77362	0.886810	+	0.462134i	$0.152916\pi$
$564$	137.025	5.76980
$565$	−24.1403	−1.01559
$566$	48.4432	2.03622
$567$	15.0594	0.632434
$568$	−1.08827	−0.0456627
$569$	30.9875	1.29906	0.649532	−	0.760334i	$-0.274965\pi$
$569$	30.9875	1.29906	0.649532	+	0.760334i	$0.274965\pi$
$570$	−77.3385	−3.23935
$571$	11.3726	0.475927	0.237964	−	0.971274i	$-0.423520\pi$
$571$	11.3726	0.475927	0.237964	+	0.971274i	$0.423520\pi$
$572$	−93.0466	−3.89047
$573$	−43.5584	−1.81968
$574$	−93.4367	−3.89997
$575$	15.4713	0.645199
$576$	86.6248	3.60937
$577$	11.0927	0.461794	0.230897	−	0.972978i	$-0.425834\pi$
$577$	11.0927	0.461794	0.230897	+	0.972978i	$0.425834\pi$
$578$	−29.9691	−1.24655
$579$	−42.4230	−1.76304
$580$	24.9637	1.03656
$581$	−42.7488	−1.77352
$582$	36.9518	1.53170
$583$	−17.9948	−0.745269
$584$	35.1235	1.45342
$585$	71.6777	2.96351
$586$	25.1271	1.03799
$587$	−42.0557	−1.73582	−0.867912	−	0.496718i	$-0.834538\pi$
$587$	−42.0557	−1.73582	−0.867912	+	0.496718i	$0.834538\pi$
$588$	−62.6749	−2.58467
$589$	10.2538	0.422500
$590$	−80.9387	−3.33220
$591$	−13.9255	−0.572820
$592$	91.6120	3.76523
$593$	−26.5393	−1.08984	−0.544919	−	0.838489i	$-0.683440\pi$
$593$	−26.5393	−1.08984	−0.544919	+	0.838489i	$0.683440\pi$
$594$	−21.5674	−0.884919
$595$	−47.8773	−1.96278
$596$	11.3090	0.463234
$597$	28.8868	1.18226
$598$	−130.320	−5.32917
$599$	6.19338	0.253055	0.126527	−	0.991963i	$-0.459617\pi$
$599$	6.19338	0.253055	0.126527	+	0.991963i	$0.459617\pi$
$600$	48.6332	1.98544
$601$	29.7936	1.21530	0.607652	−	0.794203i	$-0.292111\pi$
$601$	29.7936	1.21530	0.607652	+	0.794203i	$0.292111\pi$
$602$	93.9511	3.82916
$603$	8.32585	0.339055
$604$	60.3545	2.45579
$605$	−9.72240	−0.395272
$606$	26.5957	1.08038
$607$	16.3284	0.662750	0.331375	−	0.943499i	$-0.392488\pi$
$607$	16.3284	0.662750	0.331375	+	0.943499i	$0.392488\pi$
$608$	70.7598	2.86969
$609$	16.1653	0.655050
$610$	−26.1532	−1.05891
$611$	−64.2447	−2.59906
$612$	114.208	4.61657
$613$	30.4054	1.22806	0.614031	−	0.789282i	$-0.289547\pi$
$613$	30.4054	1.22806	0.614031	+	0.789282i	$0.289547\pi$
$614$	−9.89843	−0.399468
$615$	72.7553	2.93377
$616$	−80.0939	−3.22708
$617$	−0.707549	−0.0284848	−0.0142424	−	0.999899i	$-0.504534\pi$
$617$	−0.707549	−0.0284848	−0.0142424	+	0.999899i	$0.504534\pi$
$618$	−122.681	−4.93496
$619$	38.4728	1.54635	0.773177	−	0.634191i	$-0.218667\pi$
$619$	38.4728	1.54635	0.773177	+	0.634191i	$0.218667\pi$
$620$	−35.3482	−1.41962
$621$	−21.8623	−0.877305
$622$	74.0341	2.96850
$623$	27.8378	1.11530
$624$	−226.628	−9.07238
$625$	−31.0838	−1.24335
$626$	41.7780	1.66978
$627$	−29.2589	−1.16849
$628$	10.4195	0.415785
$629$	37.4496	1.49321
$630$	99.7878	3.97564
$631$	−36.1908	−1.44073	−0.720367	−	0.693593i	$-0.756026\pi$
$631$	−36.1908	−1.44073	−0.720367	+	0.693593i	$0.756026\pi$
$632$	−126.772	−5.04271
$633$	−49.4290	−1.96463
$634$	−51.6489	−2.05124
$635$	5.65249	0.224312
$636$	−92.7355	−3.67720
$637$	29.3853	1.16429
$638$	13.0491	0.516619
$639$	0.512950	0.0202920
$640$	−57.9619	−2.29115
$641$	6.27874	0.247995	0.123998	−	0.992283i	$-0.460428\pi$
$641$	6.27874	0.247995	0.123998	+	0.992283i	$0.460428\pi$
$642$	43.3079	1.70923
$643$	−23.9377	−0.944010	−0.472005	−	0.881596i	$-0.656470\pi$
$643$	−23.9377	−0.944010	−0.472005	+	0.881596i	$0.656470\pi$
$644$	−131.309	−5.17428
$645$	−73.1558	−2.88051
$646$	57.7756	2.27315
$647$	−15.7679	−0.619900	−0.309950	−	0.950753i	$-0.600312\pi$
$647$	−15.7679	−0.619900	−0.309950	+	0.950753i	$0.600312\pi$
$648$	38.7356	1.52168
$649$	−30.6209	−1.20198
$650$	−36.8777	−1.44646
$651$	−22.8898	−0.897120
$652$	−46.6976	−1.82882
$653$	24.1288	0.944232	0.472116	−	0.881536i	$-0.343490\pi$
$653$	24.1288	0.944232	0.472116	+	0.881536i	$0.343490\pi$
$654$	66.2681	2.59129
$655$	−47.8884	−1.87115
$656$	−132.959	−5.19119
$657$	−16.5553	−0.645885
$658$	−89.4397	−3.48672
$659$	−11.7001	−0.455772	−0.227886	−	0.973688i	$-0.573181\pi$
$659$	−11.7001	−0.455772	−0.227886	+	0.973688i	$0.573181\pi$
$660$	100.865	3.92616
$661$	43.6755	1.69878	0.849389	−	0.527767i	$-0.176971\pi$
$661$	43.6755	1.69878	0.849389	+	0.527767i	$0.176971\pi$
$662$	71.5233	2.77983
$663$	−92.6420	−3.59792
$664$	−109.958	−4.26720
$665$	36.5355	1.41679
$666$	−78.0539	−3.02453
$667$	13.2276	0.512174
$668$	−49.9390	−1.93220
$669$	−45.3455	−1.75316
$670$	−14.5198	−0.560948
$671$	−9.89433	−0.381966
$672$	−157.959	−6.09338
$673$	41.5841	1.60295	0.801475	−	0.598029i	$-0.204049\pi$
$673$	41.5841	1.60295	0.801475	+	0.598029i	$0.204049\pi$
$674$	−49.2383	−1.89659
$675$	−6.18657	−0.238121
$676$	156.703	6.02702
$677$	−7.57639	−0.291184	−0.145592	−	0.989345i	$-0.546509\pi$
$677$	−7.57639	−0.291184	−0.145592	+	0.989345i	$0.546509\pi$
$678$	−65.0300	−2.49746
$679$	−17.4564	−0.669916
$680$	−123.150	−4.72257
$681$	11.2685	0.431810
$682$	−18.4773	−0.707534
$683$	−40.2779	−1.54119	−0.770595	−	0.637325i	$-0.780041\pi$
$683$	−40.2779	−1.54119	−0.770595	+	0.637325i	$0.780041\pi$
$684$	−87.1528	−3.33237
$685$	−53.3550	−2.03859
$686$	−22.9242	−0.875250
$687$	15.2199	0.580676
$688$	133.691	5.09693
$689$	43.4793	1.65643
$690$	141.270	5.37806
$691$	7.15676	0.272256	0.136128	−	0.990691i	$-0.456534\pi$
$691$	7.15676	0.272256	0.136128	+	0.990691i	$0.456534\pi$
$692$	−100.388	−3.81618
$693$	37.7519	1.43408
$694$	−53.4549	−2.02912
$695$	8.49352	0.322177
$696$	41.5801	1.57609
$697$	−54.3517	−2.05872
$698$	−43.3718	−1.64165
$699$	−0.301343	−0.0113978
$700$	−37.1575	−1.40442
$701$	5.20264	0.196501	0.0982505	−	0.995162i	$-0.468675\pi$
$701$	5.20264	0.196501	0.0982505	+	0.995162i	$0.468675\pi$
$702$	52.1114	1.96682
$703$	−28.5781	−1.07784
$704$	−57.1525	−2.15402
$705$	69.6429	2.62291
$706$	−58.9657	−2.21920
$707$	−12.5641	−0.472521
$708$	−157.804	−5.93062
$709$	28.8806	1.08464	0.542318	−	0.840174i	$-0.317547\pi$
$709$	28.8806	1.08464	0.542318	+	0.840174i	$0.317547\pi$
$710$	−0.894553	−0.0335720
$711$	59.7533	2.24092
$712$	71.6042	2.68348
$713$	−18.7301	−0.701446
$714$	−128.974	−4.82672
$715$	−47.2909	−1.76858
$716$	78.5654	2.93613
$717$	18.1629	0.678306
$718$	30.6553	1.14404
$719$	21.9268	0.817732	0.408866	−	0.912594i	$-0.365924\pi$
$719$	21.9268	0.817732	0.408866	+	0.912594i	$0.365924\pi$
$720$	141.997	5.29190
$721$	57.9558	2.15839
$722$	7.03428	0.261789
$723$	−36.4470	−1.35548
$724$	−34.8192	−1.29405
$725$	3.74313	0.139016
$726$	−26.1905	−0.972022
$727$	5.41709	0.200909	0.100454	−	0.994942i	$-0.467970\pi$
$727$	5.41709	0.200909	0.100454	+	0.994942i	$0.467970\pi$
$728$	193.524	7.17249
$729$	−41.9079	−1.55215
$730$	28.8715	1.06858
$731$	54.6509	2.02134
$732$	−50.9900	−1.88465
$733$	−35.1063	−1.29668	−0.648341	−	0.761350i	$-0.724537\pi$
$733$	−35.1063	−1.29668	−0.648341	+	0.761350i	$0.724537\pi$
$734$	−73.5514	−2.71483
$735$	−31.8545	−1.17497
$736$	−129.253	−4.76433
$737$	−5.49316	−0.202343
$738$	113.282	4.16996
$739$	48.0139	1.76622	0.883111	−	0.469165i	$-0.155445\pi$
$739$	48.0139	1.76622	0.883111	+	0.469165i	$0.155445\pi$
$740$	98.5179	3.62159
$741$	70.6958	2.59707
$742$	60.5308	2.22215
$743$	32.4899	1.19194	0.595969	−	0.803008i	$-0.296768\pi$
$743$	32.4899	1.19194	0.595969	+	0.803008i	$0.296768\pi$
$744$	−58.8768	−2.15853
$745$	5.74779	0.210583
$746$	−101.873	−3.72983
$747$	51.8282	1.89630
$748$	−75.3510	−2.75510
$749$	−20.4591	−0.747559
$750$	−55.5521	−2.02848
$751$	27.7559	1.01283	0.506414	−	0.862290i	$-0.330971\pi$
$751$	27.7559	1.01283	0.506414	+	0.862290i	$0.330971\pi$
$752$	−127.272	−4.64111
$753$	7.87758	0.287075
$754$	−31.5295	−1.14824
$755$	30.6751	1.11638
$756$	52.5068	1.90965
$757$	−31.2475	−1.13571	−0.567855	−	0.823129i	$-0.692226\pi$
$757$	−31.2475	−1.13571	−0.567855	+	0.823129i	$0.692226\pi$
$758$	−56.8402	−2.06453
$759$	53.4456	1.93995
$760$	93.9764	3.40888
$761$	−43.6645	−1.58284	−0.791419	−	0.611274i	$-0.790657\pi$
$761$	−43.6645	−1.58284	−0.791419	+	0.611274i	$0.790657\pi$
$762$	15.2269	0.551612
$763$	−31.3057	−1.13334
$764$	85.6028	3.09700
$765$	58.0460	2.09866
$766$	−29.3496	−1.06044
$767$	73.9868	2.67151
$768$	−43.7195	−1.57759
$769$	−3.65945	−0.131963	−0.0659816	−	0.997821i	$-0.521018\pi$
$769$	−3.65945	−0.131963	−0.0659816	+	0.997821i	$0.521018\pi$
$770$	−65.8371	−2.37260
$771$	40.8560	1.47139
$772$	83.3716	3.00061
$773$	29.6549	1.06661	0.533306	−	0.845922i	$-0.320949\pi$
$773$	29.6549	1.06661	0.533306	+	0.845922i	$0.320949\pi$
$774$	−113.905	−4.09425
$775$	−5.30021	−0.190389
$776$	−44.9013	−1.61186
$777$	63.7954	2.28865
$778$	33.8658	1.21415
$779$	41.4762	1.48604
$780$	−243.712	−8.72627
$781$	−0.338429	−0.0121100
$782$	−105.536	−3.77395
$783$	−5.28936	−0.189026
$784$	58.2136	2.07906
$785$	5.29573	0.189013
$786$	−129.003	−4.60140
$787$	5.15640	0.183806	0.0919030	−	0.995768i	$-0.470705\pi$
$787$	5.15640	0.183806	0.0919030	+	0.995768i	$0.470705\pi$
$788$	27.3671	0.974912
$789$	30.6987	1.09290
$790$	−104.206	−3.70749
$791$	30.7209	1.09231
$792$	97.1052	3.45048
$793$	23.9069	0.848957
$794$	43.1235	1.53040
$795$	−47.1327	−1.67163
$796$	−56.7697	−2.01215
$797$	7.96776	0.282232	0.141116	−	0.989993i	$-0.454931\pi$
$797$	7.96776	0.282232	0.141116	+	0.989993i	$0.454931\pi$
$798$	98.4207	3.48406
$799$	−52.0266	−1.84057
$800$	−36.5759	−1.29315
$801$	−33.7503	−1.19251
$802$	−1.59083	−0.0561742
$803$	10.9227	0.385454
$804$	−28.3087	−0.998372
$805$	−66.7375	−2.35219
$806$	44.6453	1.57256
$807$	46.8987	1.65091
$808$	−32.3172	−1.13692
$809$	−9.86031	−0.346670	−0.173335	−	0.984863i	$-0.555454\pi$
$809$	−9.86031	−0.346670	−0.173335	+	0.984863i	$0.555454\pi$
$810$	31.8406	1.11876
$811$	−27.7003	−0.972689	−0.486344	−	0.873767i	$-0.661670\pi$
$811$	−27.7003	−0.972689	−0.486344	+	0.873767i	$0.661670\pi$
$812$	−31.7687	−1.11486
$813$	42.8476	1.50273
$814$	51.4977	1.80499
$815$	−23.7340	−0.831367
$816$	−183.528	−6.42476
$817$	−41.7045	−1.45905
$818$	75.7100	2.64714
$819$	−91.2168	−3.18737
$820$	−142.982	−4.99314
$821$	−34.4891	−1.20368	−0.601839	−	0.798617i	$-0.705565\pi$
$821$	−34.4891	−1.20368	−0.601839	+	0.798617i	$0.705565\pi$
$822$	−143.730	−5.01315
$823$	4.64199	0.161809	0.0809047	−	0.996722i	$-0.474219\pi$
$823$	4.64199	0.161809	0.0809047	+	0.996722i	$0.474219\pi$
$824$	149.073	5.19322
$825$	15.1240	0.526549
$826$	103.002	3.58391
$827$	−16.9911	−0.590837	−0.295418	−	0.955368i	$-0.595459\pi$
$827$	−16.9911	−0.590837	−0.295418	+	0.955368i	$0.595459\pi$
$828$	159.197	5.53249
$829$	−35.6059	−1.23665	−0.618323	−	0.785924i	$-0.712188\pi$
$829$	−35.6059	−1.23665	−0.618323	+	0.785924i	$0.712188\pi$
$830$	−90.3853	−3.13732
$831$	−20.8003	−0.721553
$832$	138.093	4.78751
$833$	23.7968	0.824511
$834$	22.8801	0.792275
$835$	−25.3815	−0.878362
$836$	57.5009	1.98871
$837$	7.48965	0.258880
$838$	−21.4039	−0.739386
$839$	14.6603	0.506131	0.253065	−	0.967449i	$-0.418561\pi$
$839$	14.6603	0.506131	0.253065	+	0.967449i	$0.418561\pi$
$840$	−209.785	−7.23829
$841$	−25.7997	−0.889646
$842$	−9.33743	−0.321789
$843$	56.8548	1.95818
$844$	97.1401	3.34370
$845$	79.6440	2.73984
$846$	108.436	3.72810
$847$	12.3727	0.425131
$848$	86.1345	2.95787
$849$	48.0032	1.64747
$850$	−29.8643	−1.02434
$851$	52.2020	1.78946
$852$	−1.74408	−0.0597512
$853$	18.4760	0.632605	0.316302	−	0.948658i	$-0.397559\pi$
$853$	18.4760	0.632605	0.316302	+	0.948658i	$0.397559\pi$
$854$	33.2825	1.13890
$855$	−44.2953	−1.51487
$856$	−52.6247	−1.79868
$857$	1.64359	0.0561441	0.0280721	−	0.999606i	$-0.491063\pi$
$857$	1.64359	0.0561441	0.0280721	+	0.999606i	$0.491063\pi$
$858$	−127.394	−4.34915
$859$	−34.0465	−1.16165	−0.580827	−	0.814027i	$-0.697271\pi$
$859$	−34.0465	−1.16165	−0.580827	+	0.814027i	$0.697271\pi$
$860$	143.769	4.90248
$861$	−92.5881	−3.15539
$862$	−0.224982	−0.00766291
$863$	−41.8260	−1.42377	−0.711887	−	0.702294i	$-0.752159\pi$
$863$	−41.8260	−1.42377	−0.711887	+	0.702294i	$0.752159\pi$
$864$	51.6848	1.75835
$865$	−51.0222	−1.73481
$866$	−85.9530	−2.92080
$867$	−29.6969	−1.00856
$868$	44.9840	1.52686
$869$	−39.4235	−1.33735
$870$	34.1788	1.15877
$871$	13.2727	0.449727
$872$	−80.5243	−2.72690
$873$	21.1640	0.716293
$874$	80.5350	2.72414
$875$	26.2434	0.887189
$876$	56.2898	1.90186
$877$	28.0099	0.945826	0.472913	−	0.881109i	$-0.343202\pi$
$877$	28.0099	0.945826	0.472913	+	0.881109i	$0.343202\pi$
$878$	−72.2110	−2.43700
$879$	24.8988	0.839817
$880$	−93.6853	−3.15813
$881$	28.7042	0.967071	0.483535	−	0.875325i	$-0.339352\pi$
$881$	28.7042	0.967071	0.483535	+	0.875325i	$0.339352\pi$
$882$	−49.5982	−1.67006
$883$	45.3942	1.52764	0.763818	−	0.645432i	$-0.223323\pi$
$883$	45.3942	1.52764	0.763818	+	0.645432i	$0.223323\pi$
$884$	182.064	6.12348
$885$	−80.2036	−2.69602
$886$	58.2661	1.95749
$887$	10.8985	0.365937	0.182968	−	0.983119i	$-0.441429\pi$
$887$	10.8985	0.365937	0.182968	+	0.983119i	$0.441429\pi$
$888$	164.094	5.50663
$889$	−7.19334	−0.241257
$890$	58.8585	1.97294
$891$	12.0460	0.403556
$892$	89.1151	2.98379
$893$	39.7019	1.32857
$894$	15.4836	0.517849
$895$	39.9308	1.33474
$896$	73.7621	2.46422
$897$	−129.136	−4.31173
$898$	53.5439	1.78678
$899$	−4.53154	−0.151135
$900$	45.0494	1.50165
$901$	35.2104	1.17303
$902$	−74.7401	−2.48857
$903$	93.0978	3.09810
$904$	79.0199	2.62816
$905$	−17.6968	−0.588263
$906$	82.6338	2.74532
$907$	−44.8836	−1.49034	−0.745168	−	0.666877i	$-0.767631\pi$
$907$	−44.8836	−1.49034	−0.745168	+	0.666877i	$0.767631\pi$
$908$	−22.1454	−0.734920
$909$	15.2326	0.505233
$910$	159.077	5.27334
$911$	−45.6512	−1.51249	−0.756246	−	0.654288i	$-0.772969\pi$
$911$	−45.6512	−1.51249	−0.756246	+	0.654288i	$0.772969\pi$
$912$	140.051	4.63756
$913$	−34.1948	−1.13168
$914$	23.6467	0.782164
$915$	−25.9157	−0.856745
$916$	−29.9109	−0.988283
$917$	60.9426	2.01250
$918$	42.2009	1.39284
$919$	−24.7959	−0.817942	−0.408971	−	0.912547i	$-0.634112\pi$
$919$	−24.7959	−0.817942	−0.408971	+	0.912547i	$0.634112\pi$
$920$	−171.662	−5.65952
$921$	−9.80853	−0.323202
$922$	−92.9929	−3.06256
$923$	0.817719	0.0269155
$924$	−128.360	−4.22275
$925$	14.7721	0.485702
$926$	−39.8953	−1.31104
$927$	−70.2651	−2.30781
$928$	−31.2714	−1.02653
$929$	−24.3475	−0.798816	−0.399408	−	0.916773i	$-0.630784\pi$
$929$	−24.3475	−0.798816	−0.399408	+	0.916773i	$0.630784\pi$
$930$	−48.3966	−1.58699
$931$	−18.1595	−0.595154
$932$	0.592213	0.0193986
$933$	73.3616	2.40175
$934$	−64.5470	−2.11204
$935$	−38.2971	−1.25245
$936$	−234.627	−7.66903
$937$	13.5949	0.444127	0.222064	−	0.975032i	$-0.428721\pi$
$937$	13.5949	0.444127	0.222064	+	0.975032i	$0.428721\pi$
$938$	18.4778	0.603322
$939$	41.3985	1.35099
$940$	−136.865	−4.46406
$941$	11.9643	0.390025	0.195013	−	0.980801i	$-0.437525\pi$
$941$	11.9643	0.390025	0.195013	+	0.980801i	$0.437525\pi$
$942$	14.2658	0.464806
$943$	−75.7623	−2.46716
$944$	146.571	4.77048
$945$	26.6865	0.868113
$946$	75.1515	2.44339
$947$	−22.6736	−0.736792	−0.368396	−	0.929669i	$-0.620093\pi$
$947$	−22.6736	−0.736792	−0.368396	+	0.929669i	$0.620093\pi$
$948$	−203.167	−6.59857
$949$	−26.3917	−0.856709
$950$	22.7897	0.739395
$951$	−51.1798	−1.65962
$952$	156.720	5.07932
$953$	−32.8206	−1.06316	−0.531582	−	0.847007i	$-0.678402\pi$
$953$	−32.8206	−1.06316	−0.531582	+	0.847007i	$0.678402\pi$
$954$	−73.3869	−2.37599
$955$	43.5076	1.40787
$956$	−35.6945	−1.15444
$957$	12.9306	0.417987
$958$	−76.9670	−2.48669
$959$	67.8995	2.19259
$960$	−149.696	−4.83143
$961$	−24.5834	−0.793013
$962$	−124.430	−4.01177
$963$	24.8044	0.799312
$964$	71.6274	2.30696
$965$	42.3736	1.36405
$966$	−179.780	−5.78432
$967$	57.3303	1.84362	0.921809	−	0.387644i	$-0.126711\pi$
$967$	57.3303	1.84362	0.921809	+	0.387644i	$0.126711\pi$
$968$	31.8249	1.02289
$969$	57.2509	1.83916
$970$	−36.9087	−1.18507
$971$	47.7594	1.53267	0.766336	−	0.642440i	$-0.222078\pi$
$971$	47.7594	1.53267	0.766336	+	0.642440i	$0.222078\pi$
$972$	108.557	3.48196
$973$	−10.8088	−0.346515
$974$	−61.5519	−1.97225
$975$	−36.5428	−1.17031
$976$	47.3605	1.51597
$977$	−21.7768	−0.696702	−0.348351	−	0.937364i	$-0.613258\pi$
$977$	−21.7768	−0.696702	−0.348351	+	0.937364i	$0.613258\pi$
$978$	−63.9356	−2.04443
$979$	22.2675	0.711672
$980$	62.6018	1.99974
$981$	37.9548	1.21180
$982$	28.5858	0.912208
$983$	0.802927	0.0256094	0.0128047	−	0.999918i	$-0.495924\pi$
$983$	0.802927	0.0256094	0.0128047	+	0.999918i	$0.495924\pi$
$984$	−238.154	−7.59208
$985$	13.9093	0.443187
$986$	−25.5332	−0.813143
$987$	−88.6274	−2.82104
$988$	−138.935	−4.42010
$989$	76.1793	2.42236
$990$	79.8203	2.53685
$991$	26.7502	0.849748	0.424874	−	0.905252i	$-0.360318\pi$
$991$	26.7502	0.849748	0.424874	+	0.905252i	$0.360318\pi$
$992$	44.2798	1.40589
$993$	70.8737	2.24911
$994$	1.13841	0.0361080
$995$	−28.8532	−0.914707
$996$	−176.221	−5.58379
$997$	−16.5513	−0.524184	−0.262092	−	0.965043i	$-0.584412\pi$
$997$	−16.5513	−0.524184	−0.262092	+	0.965043i	$0.584412\pi$
$998$	−35.1236	−1.11182
$999$	−20.8742	−0.660430

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4007.2.a.b.1.7	✓	195

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4007.2.a.b.1.7	✓	195	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:	\( N \)	\(=\)	\( 4007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.69070 q^{2} -2.66626 q^{3} +5.23985 q^{4} +2.66315 q^{5} +7.17410 q^{6} -3.38912 q^{7} -8.71746 q^{8} +4.10894 q^{9} +O(q^{10})\)	\(q-2.69070 q^{2} -2.66626 q^{3} +5.23985 q^{4} +2.66315 q^{5} +7.17410 q^{6} -3.38912 q^{7} -8.71746 q^{8} +4.10894 q^{9} -7.16574 q^{10} -2.71096 q^{11} -13.9708 q^{12} +6.55026 q^{13} +9.11909 q^{14} -7.10065 q^{15} +12.9763 q^{16} +5.30453 q^{17} -11.0559 q^{18} -4.04793 q^{19} +13.9545 q^{20} +9.03627 q^{21} +7.29437 q^{22} +7.39413 q^{23} +23.2430 q^{24} +2.09238 q^{25} -17.6248 q^{26} -2.95671 q^{27} -17.7585 q^{28} +1.78893 q^{29} +19.1057 q^{30} -2.53310 q^{31} -17.4805 q^{32} +7.22811 q^{33} -14.2729 q^{34} -9.02574 q^{35} +21.5302 q^{36} +7.05992 q^{37} +10.8917 q^{38} -17.4647 q^{39} -23.2159 q^{40} -10.2463 q^{41} -24.3139 q^{42} +10.3027 q^{43} -14.2050 q^{44} +10.9427 q^{45} -19.8954 q^{46} -9.80796 q^{47} -34.5983 q^{48} +4.48613 q^{49} -5.62997 q^{50} -14.1433 q^{51} +34.3224 q^{52} +6.63780 q^{53} +7.95562 q^{54} -7.21969 q^{55} +29.5445 q^{56} +10.7928 q^{57} -4.81347 q^{58} +11.2952 q^{59} -37.2064 q^{60} +3.64976 q^{61} +6.81580 q^{62} -13.9257 q^{63} +21.0820 q^{64} +17.4443 q^{65} -19.4487 q^{66} +2.02628 q^{67} +27.7950 q^{68} -19.7147 q^{69} +24.2855 q^{70} +0.124838 q^{71} -35.8195 q^{72} -4.02910 q^{73} -18.9961 q^{74} -5.57883 q^{75} -21.2105 q^{76} +9.18776 q^{77} +46.9922 q^{78} +14.5423 q^{79} +34.5580 q^{80} -4.44345 q^{81} +27.5696 q^{82} +12.6135 q^{83} +47.3487 q^{84} +14.1268 q^{85} -27.7214 q^{86} -4.76975 q^{87} +23.6327 q^{88} -8.21388 q^{89} -29.4436 q^{90} -22.1996 q^{91} +38.7441 q^{92} +6.75389 q^{93} +26.3903 q^{94} -10.7802 q^{95} +46.6075 q^{96} +5.15073 q^{97} -12.0708 q^{98} -11.1392 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 195 q + 14 q^{2} + 22 q^{3} + 220 q^{4} + 14 q^{5} + 13 q^{6} + 48 q^{7} + 39 q^{8} + 245 q^{9}+O(q^{10}) \) 195 * q + 14 * q^2 + 22 * q^3 + 220 * q^4 + 14 * q^5 + 13 * q^6 + 48 * q^7 + 39 * q^8 + 245 * q^9	\( 195 q + 14 q^{2} + 22 q^{3} + 220 q^{4} + 14 q^{5} + 13 q^{6} + 48 q^{7} + 39 q^{8} + 245 q^{9} + 40 q^{10} + 13 q^{11} + 57 q^{12} + 97 q^{13} + 9 q^{14} + 23 q^{15} + 270 q^{16} + 66 q^{17} + 60 q^{18} + 33 q^{19} + 24 q^{20} + 27 q^{21} + 127 q^{22} + 42 q^{23} + 33 q^{24} + 357 q^{25} + 8 q^{26} + 79 q^{27} + 131 q^{28} + 57 q^{29} + 51 q^{30} + 41 q^{31} + 67 q^{32} + 74 q^{33} + 26 q^{34} + 14 q^{35} + 279 q^{36} + 133 q^{37} + 7 q^{38} + 28 q^{39} + 97 q^{40} + 64 q^{41} - q^{42} + 123 q^{43} + 21 q^{44} + 40 q^{45} + 84 q^{46} + 14 q^{47} + 122 q^{48} + 335 q^{49} + 35 q^{50} + 37 q^{51} + 220 q^{52} + 83 q^{53} + 21 q^{54} + 47 q^{55} + q^{56} + 235 q^{57} + 138 q^{58} + 18 q^{59} - 4 q^{60} + 81 q^{61} + 39 q^{62} + 102 q^{63} + 343 q^{64} + 165 q^{65} - 54 q^{66} + 147 q^{67} + 74 q^{68} - 2 q^{69} + 13 q^{70} + 31 q^{71} + 112 q^{72} + 300 q^{73} + 5 q^{74} + 84 q^{75} + 64 q^{76} + 67 q^{77} + 61 q^{78} + 144 q^{79} - 8 q^{80} + 359 q^{81} + 85 q^{82} + 26 q^{83} + 12 q^{84} + 201 q^{85} - 2 q^{86} + 80 q^{87} + 347 q^{88} + 29 q^{89} + 62 q^{90} + 70 q^{91} + 79 q^{92} + 76 q^{93} + 72 q^{94} + 71 q^{95} + 31 q^{96} + 264 q^{97} + 30 q^{98} + 19 q^{99}+O(q^{100}) \) 195 * q + 14 * q^2 + 22 * q^3 + 220 * q^4 + 14 * q^5 + 13 * q^6 + 48 * q^7 + 39 * q^8 + 245 * q^9 + 40 * q^10 + 13 * q^11 + 57 * q^12 + 97 * q^13 + 9 * q^14 + 23 * q^15 + 270 * q^16 + 66 * q^17 + 60 * q^18 + 33 * q^19 + 24 * q^20 + 27 * q^21 + 127 * q^22 + 42 * q^23 + 33 * q^24 + 357 * q^25 + 8 * q^26 + 79 * q^27 + 131 * q^28 + 57 * q^29 + 51 * q^30 + 41 * q^31 + 67 * q^32 + 74 * q^33 + 26 * q^34 + 14 * q^35 + 279 * q^36 + 133 * q^37 + 7 * q^38 + 28 * q^39 + 97 * q^40 + 64 * q^41 - q^42 + 123 * q^43 + 21 * q^44 + 40 * q^45 + 84 * q^46 + 14 * q^47 + 122 * q^48 + 335 * q^49 + 35 * q^50 + 37 * q^51 + 220 * q^52 + 83 * q^53 + 21 * q^54 + 47 * q^55 + q^56 + 235 * q^57 + 138 * q^58 + 18 * q^59 - 4 * q^60 + 81 * q^61 + 39 * q^62 + 102 * q^63 + 343 * q^64 + 165 * q^65 - 54 * q^66 + 147 * q^67 + 74 * q^68 - 2 * q^69 + 13 * q^70 + 31 * q^71 + 112 * q^72 + 300 * q^73 + 5 * q^74 + 84 * q^75 + 64 * q^76 + 67 * q^77 + 61 * q^78 + 144 * q^79 - 8 * q^80 + 359 * q^81 + 85 * q^82 + 26 * q^83 + 12 * q^84 + 201 * q^85 - 2 * q^86 + 80 * q^87 + 347 * q^88 + 29 * q^89 + 62 * q^90 + 70 * q^91 + 79 * q^92 + 76 * q^93 + 72 * q^94 + 71 * q^95 + 31 * q^96 + 264 * q^97 + 30 * q^98 + 19 * q^99

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