LMFDB - Embedded newform 4007.2.a.a.1.4

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:	$1$
Dimension:	$139$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
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)

$f(q)$	$=$	$q-2.70090 q^{2} -3.24744 q^{3} +5.29488 q^{4} -0.141100 q^{5} +8.77102 q^{6} +1.56207 q^{7} -8.89915 q^{8} +7.54587 q^{9} +O(q^{10})$	\(q-2.70090 q^{2} -3.24744 q^{3} +5.29488 q^{4} -0.141100 q^{5} +8.77102 q^{6} +1.56207 q^{7} -8.89915 q^{8} +7.54587 q^{9} +0.381096 q^{10} +2.64914 q^{11} -17.1948 q^{12} -2.66298 q^{13} -4.21901 q^{14} +0.458212 q^{15} +13.4460 q^{16} +2.60193 q^{17} -20.3807 q^{18} +6.65660 q^{19} -0.747105 q^{20} -5.07274 q^{21} -7.15507 q^{22} +7.18444 q^{23} +28.8994 q^{24} -4.98009 q^{25} +7.19244 q^{26} -14.7624 q^{27} +8.27099 q^{28} +3.36150 q^{29} -1.23759 q^{30} -10.1275 q^{31} -18.5180 q^{32} -8.60292 q^{33} -7.02757 q^{34} -0.220408 q^{35} +39.9544 q^{36} +0.187764 q^{37} -17.9788 q^{38} +8.64786 q^{39} +1.25567 q^{40} +8.25018 q^{41} +13.7010 q^{42} -3.72128 q^{43} +14.0269 q^{44} -1.06472 q^{45} -19.4045 q^{46} -0.479710 q^{47} -43.6650 q^{48} -4.55992 q^{49} +13.4507 q^{50} -8.44962 q^{51} -14.1001 q^{52} -5.13653 q^{53} +39.8719 q^{54} -0.373792 q^{55} -13.9011 q^{56} -21.6169 q^{57} -9.07907 q^{58} -5.96660 q^{59} +2.42618 q^{60} +7.78820 q^{61} +27.3534 q^{62} +11.7872 q^{63} +23.1233 q^{64} +0.375745 q^{65} +23.2357 q^{66} -12.5636 q^{67} +13.7769 q^{68} -23.3310 q^{69} +0.595300 q^{70} -12.3169 q^{71} -67.1518 q^{72} -15.3914 q^{73} -0.507132 q^{74} +16.1725 q^{75} +35.2459 q^{76} +4.13815 q^{77} -23.3570 q^{78} -10.9598 q^{79} -1.89722 q^{80} +25.3025 q^{81} -22.2829 q^{82} +2.01770 q^{83} -26.8596 q^{84} -0.367131 q^{85} +10.0508 q^{86} -10.9163 q^{87} -23.5751 q^{88} -6.91516 q^{89} +2.87570 q^{90} -4.15977 q^{91} +38.0407 q^{92} +32.8885 q^{93} +1.29565 q^{94} -0.939243 q^{95} +60.1360 q^{96} +5.30369 q^{97} +12.3159 q^{98} +19.9901 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9}+O(q^{10}) $ 139 * q - 13 * q^2 - 22 * q^3 + 113 * q^4 - 16 * q^5 - 15 * q^6 - 44 * q^7 - 36 * q^8 + 87 * q^9	\( 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9} - 40 q^{10} - 17 q^{11} - 59 q^{12} - 89 q^{13} - 15 q^{14} - 29 q^{15} + 73 q^{16} - 58 q^{17} - 51 q^{18} - 37 q^{19} - 24 q^{20} - 37 q^{21} - 99 q^{22} - 42 q^{23} - 27 q^{24} - 11 q^{25} + 2 q^{26} - 73 q^{27} - 113 q^{28} - 57 q^{29} - 29 q^{30} - 51 q^{31} - 80 q^{32} - 78 q^{33} - 28 q^{34} - 34 q^{35} + 28 q^{36} - 117 q^{37} - 31 q^{38} - 36 q^{39} - 107 q^{40} - 60 q^{41} - 41 q^{42} - 109 q^{43} - 21 q^{44} - 62 q^{45} - 92 q^{46} - 26 q^{47} - 90 q^{48} - 7 q^{49} - 22 q^{50} - 47 q^{51} - 182 q^{52} - 83 q^{53} - 19 q^{54} - 53 q^{55} - 23 q^{56} - 201 q^{57} - 112 q^{58} + 14 q^{59} - 64 q^{60} - 73 q^{61} - 21 q^{62} - 94 q^{63} + 14 q^{64} - 123 q^{65} - 10 q^{66} - 135 q^{67} - 84 q^{68} - 50 q^{69} - 35 q^{70} - 29 q^{71} - 143 q^{72} - 266 q^{73} - 53 q^{74} - 32 q^{75} - 66 q^{76} - 69 q^{77} - 59 q^{78} - 124 q^{79} - 20 q^{80} - 33 q^{81} - 93 q^{82} - 28 q^{83} - 4 q^{84} - 179 q^{85} + 6 q^{86} - 40 q^{87} - 259 q^{88} - 41 q^{89} + 2 q^{90} - 50 q^{91} - 77 q^{92} - 60 q^{93} - 48 q^{94} - 37 q^{95} + 3 q^{96} - 220 q^{97} - 9 q^{98} - 35 q^{99}+O(q^{100}) \) 139 * q - 13 * q^2 - 22 * q^3 + 113 * q^4 - 16 * q^5 - 15 * q^6 - 44 * q^7 - 36 * q^8 + 87 * q^9 - 40 * q^10 - 17 * q^11 - 59 * q^12 - 89 * q^13 - 15 * q^14 - 29 * q^15 + 73 * q^16 - 58 * q^17 - 51 * q^18 - 37 * q^19 - 24 * q^20 - 37 * q^21 - 99 * q^22 - 42 * q^23 - 27 * q^24 - 11 * q^25 + 2 * q^26 - 73 * q^27 - 113 * q^28 - 57 * q^29 - 29 * q^30 - 51 * q^31 - 80 * q^32 - 78 * q^33 - 28 * q^34 - 34 * q^35 + 28 * q^36 - 117 * q^37 - 31 * q^38 - 36 * q^39 - 107 * q^40 - 60 * q^41 - 41 * q^42 - 109 * q^43 - 21 * q^44 - 62 * q^45 - 92 * q^46 - 26 * q^47 - 90 * q^48 - 7 * q^49 - 22 * q^50 - 47 * q^51 - 182 * q^52 - 83 * q^53 - 19 * q^54 - 53 * q^55 - 23 * q^56 - 201 * q^57 - 112 * q^58 + 14 * q^59 - 64 * q^60 - 73 * q^61 - 21 * q^62 - 94 * q^63 + 14 * q^64 - 123 * q^65 - 10 * q^66 - 135 * q^67 - 84 * q^68 - 50 * q^69 - 35 * q^70 - 29 * q^71 - 143 * q^72 - 266 * q^73 - 53 * q^74 - 32 * q^75 - 66 * q^76 - 69 * q^77 - 59 * q^78 - 124 * q^79 - 20 * q^80 - 33 * q^81 - 93 * q^82 - 28 * q^83 - 4 * q^84 - 179 * q^85 + 6 * q^86 - 40 * q^87 - 259 * q^88 - 41 * q^89 + 2 * q^90 - 50 * q^91 - 77 * q^92 - 60 * q^93 - 48 * q^94 - 37 * q^95 + 3 * q^96 - 220 * q^97 - 9 * q^98 - 35 * 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 $

$2$	−2.70090	−1.90983	−0.954913	−	0.296884i	$-0.904052\pi$
$2$	−2.70090	−1.90983	−0.954913	+	0.296884i	$0.904052\pi$
$3$	−3.24744	−1.87491	−0.937455	−	0.348106i	$-0.886825\pi$
$3$	−3.24744	−1.87491	−0.937455	+	0.348106i	$0.886825\pi$
$4$	5.29488	2.64744
$5$	−0.141100	−0.0631016	−0.0315508	−	0.999502i	$-0.510045\pi$
$5$	−0.141100	−0.0631016	−0.0315508	+	0.999502i	$0.510045\pi$
$6$	8.77102	3.58075
$7$	1.56207	0.590409	0.295204	−	0.955434i	$-0.404612\pi$
$7$	1.56207	0.590409	0.295204	+	0.955434i	$0.404612\pi$
$8$	−8.89915	−3.14632
$9$	7.54587	2.51529
$10$	0.381096	0.120513
$11$	2.64914	0.798746	0.399373	−	0.916789i	$-0.369228\pi$
$11$	2.64914	0.798746	0.399373	+	0.916789i	$0.369228\pi$
$12$	−17.1948	−4.96371
$13$	−2.66298	−0.738577	−0.369288	−	0.929315i	$-0.620399\pi$
$13$	−2.66298	−0.738577	−0.369288	+	0.929315i	$0.620399\pi$
$14$	−4.21901	−1.12758
$15$	0.458212	0.118310
$16$	13.4460	3.36149
$17$	2.60193	0.631061	0.315531	−	0.948915i	$-0.397817\pi$
$17$	2.60193	0.631061	0.315531	+	0.948915i	$0.397817\pi$
$18$	−20.3807	−4.80377
$19$	6.65660	1.52713	0.763565	−	0.645731i	$-0.223447\pi$
$19$	6.65660	1.52713	0.763565	+	0.645731i	$0.223447\pi$
$20$	−0.747105	−0.167058
$21$	−5.07274	−1.10696
$22$	−7.15507	−1.52547
$23$	7.18444	1.49806	0.749029	−	0.662537i	$-0.230520\pi$
$23$	7.18444	1.49806	0.749029	+	0.662537i	$0.230520\pi$
$24$	28.8994	5.89907
$25$	−4.98009	−0.996018
$26$	7.19244	1.41055
$27$	−14.7624	−2.84103
$28$	8.27099	1.56307
$29$	3.36150	0.624214	0.312107	−	0.950047i	$-0.398965\pi$
$29$	3.36150	0.624214	0.312107	+	0.950047i	$0.398965\pi$
$30$	−1.23759	−0.225951
$31$	−10.1275	−1.81896	−0.909478	−	0.415752i	$-0.863518\pi$
$31$	−10.1275	−1.81896	−0.909478	+	0.415752i	$0.863518\pi$
$32$	−18.5180	−3.27355
$33$	−8.60292	−1.49758
$34$	−7.02757	−1.20522
$35$	−0.220408	−0.0372557
$36$	39.9544	6.65907
$37$	0.187764	0.0308682	0.0154341	−	0.999881i	$-0.495087\pi$
$37$	0.187764	0.0308682	0.0154341	+	0.999881i	$0.495087\pi$
$38$	−17.9788	−2.91655
$39$	8.64786	1.38477
$40$	1.25567	0.198538
$41$	8.25018	1.28846	0.644231	−	0.764831i	$-0.277178\pi$
$41$	8.25018	1.28846	0.644231	+	0.764831i	$0.277178\pi$
$42$	13.7010	2.11411
$43$	−3.72128	−0.567490	−0.283745	−	0.958900i	$-0.591577\pi$
$43$	−3.72128	−0.567490	−0.283745	+	0.958900i	$0.591577\pi$
$44$	14.0269	2.11463
$45$	−1.06472	−0.158719
$46$	−19.4045	−2.86103
$47$	−0.479710	−0.0699730	−0.0349865	−	0.999388i	$-0.511139\pi$
$47$	−0.479710	−0.0699730	−0.0349865	+	0.999388i	$0.511139\pi$
$48$	−43.6650	−6.30250
$49$	−4.55992	−0.651418
$50$	13.4507	1.90222
$51$	−8.44962	−1.18318
$52$	−14.1001	−1.95534
$53$	−5.13653	−0.705557	−0.352779	−	0.935707i	$-0.614763\pi$
$53$	−5.13653	−0.705557	−0.352779	+	0.935707i	$0.614763\pi$
$54$	39.8719	5.42588
$55$	−0.373792	−0.0504022
$56$	−13.9011	−1.85762
$57$	−21.6169	−2.86323
$58$	−9.07907	−1.19214
$59$	−5.96660	−0.776786	−0.388393	−	0.921494i	$-0.626970\pi$
$59$	−5.96660	−0.776786	−0.388393	+	0.921494i	$0.626970\pi$
$60$	2.42618	0.313218
$61$	7.78820	0.997176	0.498588	−	0.866839i	$-0.333852\pi$
$61$	7.78820	0.997176	0.498588	+	0.866839i	$0.333852\pi$
$62$	27.3534	3.47389
$63$	11.7872	1.48505
$64$	23.1233	2.89042
$65$	0.375745	0.0466054
$66$	23.2357	2.86011
$67$	−12.5636	−1.53488	−0.767442	−	0.641118i	$-0.778471\pi$
$67$	−12.5636	−1.53488	−0.767442	+	0.641118i	$0.778471\pi$
$68$	13.7769	1.67070
$69$	−23.3310	−2.80873
$70$	0.595300	0.0711520
$71$	−12.3169	−1.46174	−0.730872	−	0.682515i	$-0.760886\pi$
$71$	−12.3169	−1.46174	−0.730872	+	0.682515i	$0.760886\pi$
$72$	−67.1518	−7.91391
$73$	−15.3914	−1.80143	−0.900715	−	0.434410i	$-0.856957\pi$
$73$	−15.3914	−1.80143	−0.900715	+	0.434410i	$0.856957\pi$
$74$	−0.507132	−0.0589529
$75$	16.1725	1.86744
$76$	35.2459	4.04298
$77$	4.13815	0.471586
$78$	−23.3570	−2.64466
$79$	−10.9598	−1.23307	−0.616536	−	0.787327i	$-0.711464\pi$
$79$	−10.9598	−1.23307	−0.616536	+	0.787327i	$0.711464\pi$
$80$	−1.89722	−0.212116
$81$	25.3025	2.81139
$82$	−22.2829	−2.46074
$83$	2.01770	0.221472	0.110736	−	0.993850i	$-0.464679\pi$
$83$	2.01770	0.221472	0.110736	+	0.993850i	$0.464679\pi$
$84$	−26.8596	−2.93062
$85$	−0.367131	−0.0398210
$86$	10.0508	1.08381
$87$	−10.9163	−1.17035
$88$	−23.5751	−2.51311
$89$	−6.91516	−0.733006	−0.366503	−	0.930417i	$-0.619445\pi$
$89$	−6.91516	−0.733006	−0.366503	+	0.930417i	$0.619445\pi$
$90$	2.87570	0.303125
$91$	−4.15977	−0.436062
$92$	38.0407	3.96602
$93$	32.8885	3.41038
$94$	1.29565	0.133636
$95$	−0.939243	−0.0963643
$96$	60.1360	6.13761
$97$	5.30369	0.538508	0.269254	−	0.963069i	$-0.413223\pi$
$97$	5.30369	0.538508	0.269254	+	0.963069i	$0.413223\pi$
$98$	12.3159	1.24409
$99$	19.9901	2.00908
$100$	−26.3690	−2.63690
$101$	−10.7074	−1.06543	−0.532715	−	0.846295i	$-0.678828\pi$
$101$	−10.7074	−1.06543	−0.532715	+	0.846295i	$0.678828\pi$
$102$	22.8216	2.25968
$103$	−9.24907	−0.911338	−0.455669	−	0.890149i	$-0.650600\pi$
$103$	−9.24907	−0.911338	−0.455669	+	0.890149i	$0.650600\pi$
$104$	23.6982	2.32380
$105$	0.715762	0.0698512
$106$	13.8733	1.34749
$107$	4.86200	0.470028	0.235014	−	0.971992i	$-0.424486\pi$
$107$	4.86200	0.470028	0.235014	+	0.971992i	$0.424486\pi$
$108$	−78.1653	−7.52146
$109$	4.77860	0.457707	0.228853	−	0.973461i	$-0.426502\pi$
$109$	4.77860	0.457707	0.228853	+	0.973461i	$0.426502\pi$
$110$	1.00958	0.0962594
$111$	−0.609752	−0.0578751
$112$	21.0036	1.98466
$113$	−11.1637	−1.05020	−0.525098	−	0.851042i	$-0.675971\pi$
$113$	−11.1637	−1.05020	−0.525098	+	0.851042i	$0.675971\pi$
$114$	58.3852	5.46827
$115$	−1.01372	−0.0945299
$116$	17.7987	1.65257
$117$	−20.0945	−1.85773
$118$	16.1152	1.48353
$119$	4.06441	0.372584
$120$	−4.07770	−0.372241
$121$	−3.98206	−0.362005
$122$	−21.0352	−1.90443
$123$	−26.7920	−2.41575
$124$	−53.6240	−4.81557
$125$	1.40819	0.125952
$126$	−31.8361	−2.83619
$127$	10.0113	0.888361	0.444180	−	0.895937i	$-0.353495\pi$
$127$	10.0113	0.888361	0.444180	+	0.895937i	$0.353495\pi$
$128$	−25.4179	−2.24665
$129$	12.0846	1.06399
$130$	−1.01485	−0.0890082
$131$	16.8757	1.47444	0.737219	−	0.675654i	$-0.236139\pi$
$131$	16.8757	1.47444	0.737219	+	0.675654i	$0.236139\pi$
$132$	−45.5514	−3.96474
$133$	10.3981	0.901630
$134$	33.9330	2.93136
$135$	2.08297	0.179274
$136$	−23.1550	−1.98552
$137$	8.40293	0.717911	0.358955	−	0.933355i	$-0.383133\pi$
$137$	8.40293	0.717911	0.358955	+	0.933355i	$0.383133\pi$
$138$	63.0148	5.36418
$139$	5.56841	0.472307	0.236153	−	0.971716i	$-0.424113\pi$
$139$	5.56841	0.472307	0.236153	+	0.971716i	$0.424113\pi$
$140$	−1.16703	−0.0986323
$141$	1.55783	0.131193
$142$	33.2667	2.79168
$143$	−7.05460	−0.589935
$144$	101.462	8.45513
$145$	−0.474305	−0.0393889
$146$	41.5708	3.44042
$147$	14.8081	1.22135
$148$	0.994187	0.0817217
$149$	−3.38563	−0.277362	−0.138681	−	0.990337i	$-0.544286\pi$
$149$	−3.38563	−0.277362	−0.138681	+	0.990337i	$0.544286\pi$
$150$	−43.6805	−3.56650
$151$	16.6553	1.35539	0.677693	−	0.735345i	$-0.262980\pi$
$151$	16.6553	1.35539	0.677693	+	0.735345i	$0.262980\pi$
$152$	−59.2381	−4.80484
$153$	19.6338	1.58730
$154$	−11.1768	−0.900649
$155$	1.42899	0.114779
$156$	45.7893	3.66608
$157$	−6.12797	−0.489065	−0.244533	−	0.969641i	$-0.578635\pi$
$157$	−6.12797	−0.489065	−0.244533	+	0.969641i	$0.578635\pi$
$158$	29.6013	2.35495
$159$	16.6806	1.32286
$160$	2.61288	0.206566
$161$	11.2226	0.884467
$162$	−68.3396	−5.36927
$163$	−6.40374	−0.501580	−0.250790	−	0.968042i	$-0.580690\pi$
$163$	−6.40374	−0.501580	−0.250790	+	0.968042i	$0.580690\pi$
$164$	43.6837	3.41112
$165$	1.21387	0.0944995
$166$	−5.44962	−0.422973
$167$	20.5001	1.58635	0.793174	−	0.608995i	$-0.208427\pi$
$167$	20.5001	1.58635	0.793174	+	0.608995i	$0.208427\pi$
$168$	45.1431	3.48286
$169$	−5.90856	−0.454504
$170$	0.991586	0.0760512
$171$	50.2298	3.84117
$172$	−19.7037	−1.50240
$173$	9.82850	0.747247	0.373624	−	0.927580i	$-0.378115\pi$
$173$	9.82850	0.747247	0.373624	+	0.927580i	$0.378115\pi$
$174$	29.4837	2.23516
$175$	−7.77927	−0.588058
$176$	35.6203	2.68498
$177$	19.3762	1.45640
$178$	18.6772	1.39991
$179$	−15.9591	−1.19284	−0.596419	−	0.802673i	$-0.703410\pi$
$179$	−15.9591	−1.19284	−0.596419	+	0.802673i	$0.703410\pi$
$180$	−5.63755	−0.420198
$181$	7.01805	0.521647	0.260824	−	0.965386i	$-0.416006\pi$
$181$	7.01805	0.521647	0.260824	+	0.965386i	$0.416006\pi$
$182$	11.2351	0.832803
$183$	−25.2917	−1.86962
$184$	−63.9353	−4.71338
$185$	−0.0264934	−0.00194783
$186$	−88.8287	−6.51323
$187$	6.89288	0.504058
$188$	−2.54001	−0.185249
$189$	−23.0600	−1.67737
$190$	2.53680	0.184039
$191$	10.8784	0.787130	0.393565	−	0.919297i	$-0.371242\pi$
$191$	10.8784	0.787130	0.393565	+	0.919297i	$0.371242\pi$
$192$	−75.0916	−5.41927
$193$	−14.8929	−1.07202	−0.536009	−	0.844212i	$-0.680069\pi$
$193$	−14.8929	−1.07202	−0.536009	+	0.844212i	$0.680069\pi$
$194$	−14.3248	−1.02846
$195$	−1.22021	−0.0873809
$196$	−24.1442	−1.72459
$197$	−5.19526	−0.370147	−0.185073	−	0.982725i	$-0.559252\pi$
$197$	−5.19526	−0.370147	−0.185073	+	0.982725i	$0.559252\pi$
$198$	−53.9912	−3.83699
$199$	−11.4696	−0.813058	−0.406529	−	0.913638i	$-0.633261\pi$
$199$	−11.4696	−0.813058	−0.406529	+	0.913638i	$0.633261\pi$
$200$	44.3186	3.13380
$201$	40.7995	2.87777
$202$	28.9198	2.03479
$203$	5.25091	0.368541
$204$	−44.7397	−3.13241
$205$	−1.16410	−0.0813040
$206$	24.9808	1.74050
$207$	54.2128	3.76805
$208$	−35.8063	−2.48272
$209$	17.6343	1.21979
$210$	−1.93320	−0.133404
$211$	−14.4645	−0.995777	−0.497888	−	0.867241i	$-0.665891\pi$
$211$	−14.4645	−0.995777	−0.497888	+	0.867241i	$0.665891\pi$
$212$	−27.1973	−1.86792
$213$	39.9983	2.74064
$214$	−13.1318	−0.897671
$215$	0.525071	0.0358095
$216$	131.373	8.93880
$217$	−15.8199	−1.07393
$218$	−12.9065	−0.874141
$219$	49.9827	3.37752
$220$	−1.97918	−0.133437
$221$	−6.92888	−0.466087
$222$	1.64688	0.110531
$223$	0.0753591	0.00504642	0.00252321	−	0.999997i	$-0.499197\pi$
$223$	0.0753591	0.00504642	0.00252321	+	0.999997i	$0.499197\pi$
$224$	−28.9265	−1.93273
$225$	−37.5791	−2.50527
$226$	30.1522	2.00569
$227$	20.4439	1.35691	0.678456	−	0.734641i	$-0.262650\pi$
$227$	20.4439	1.35691	0.678456	+	0.734641i	$0.262650\pi$
$228$	−114.459	−7.58023
$229$	−5.20221	−0.343772	−0.171886	−	0.985117i	$-0.554986\pi$
$229$	−5.20221	−0.343772	−0.171886	+	0.985117i	$0.554986\pi$
$230$	2.73796	0.180536
$231$	−13.4384	−0.884182
$232$	−29.9144	−1.96398
$233$	−6.64650	−0.435427	−0.217713	−	0.976013i	$-0.569860\pi$
$233$	−6.64650	−0.435427	−0.217713	+	0.976013i	$0.569860\pi$
$234$	54.2732	3.54795
$235$	0.0676869	0.00441541
$236$	−31.5924	−2.05649
$237$	35.5912	2.31190
$238$	−10.9776	−0.711571
$239$	−23.8440	−1.54234	−0.771171	−	0.636628i	$-0.780329\pi$
$239$	−23.8440	−1.54234	−0.771171	+	0.636628i	$0.780329\pi$
$240$	6.16111	0.397698
$241$	−12.8523	−0.827886	−0.413943	−	0.910303i	$-0.635849\pi$
$241$	−12.8523	−0.827886	−0.413943	+	0.910303i	$0.635849\pi$
$242$	10.7551	0.691367
$243$	−37.8811	−2.43007
$244$	41.2375	2.63996
$245$	0.643403	0.0411055
$246$	72.3625	4.61366
$247$	−17.7264	−1.12790
$248$	90.1263	5.72302
$249$	−6.55237	−0.415240
$250$	−3.80337	−0.240546
$251$	−3.78493	−0.238903	−0.119451	−	0.992840i	$-0.538114\pi$
$251$	−3.78493	−0.238903	−0.119451	+	0.992840i	$0.538114\pi$
$252$	62.4118	3.93158
$253$	19.0326	1.19657
$254$	−27.0396	−1.69662
$255$	1.19224	0.0746608
$256$	22.4047	1.40029
$257$	−12.8977	−0.804534	−0.402267	−	0.915522i	$-0.631778\pi$
$257$	−12.8977	−0.804534	−0.402267	+	0.915522i	$0.631778\pi$
$258$	−32.6394	−2.03204
$259$	0.293301	0.0182249
$260$	1.98952	0.123385
$261$	25.3654	1.57008
$262$	−45.5797	−2.81592
$263$	−28.0197	−1.72777	−0.863884	−	0.503691i	$-0.831975\pi$
$263$	−28.0197	−1.72777	−0.863884	+	0.503691i	$0.831975\pi$
$264$	76.5587	4.71186
$265$	0.724762	0.0445218
$266$	−28.0843	−1.72196
$267$	22.4566	1.37432
$268$	−66.5226	−4.06351
$269$	27.0578	1.64975	0.824873	−	0.565318i	$-0.191247\pi$
$269$	27.0578	1.64975	0.824873	+	0.565318i	$0.191247\pi$
$270$	−5.62590	−0.342382
$271$	24.6519	1.49750	0.748749	−	0.662853i	$-0.230655\pi$
$271$	24.6519	1.49750	0.748749	+	0.662853i	$0.230655\pi$
$272$	34.9855	2.12131
$273$	13.5086	0.817577
$274$	−22.6955	−1.37108
$275$	−13.1930	−0.795565
$276$	−123.535	−7.43593
$277$	−25.2411	−1.51659	−0.758297	−	0.651909i	$-0.773968\pi$
$277$	−25.2411	−1.51659	−0.758297	+	0.651909i	$0.773968\pi$
$278$	−15.0397	−0.902024
$279$	−76.4209	−4.57520
$280$	1.96144	0.117219
$281$	−27.7065	−1.65283	−0.826417	−	0.563059i	$-0.809625\pi$
$281$	−27.7065	−1.65283	−0.826417	+	0.563059i	$0.809625\pi$
$282$	−4.20755	−0.250556
$283$	26.3969	1.56914	0.784568	−	0.620043i	$-0.212885\pi$
$283$	26.3969	1.56914	0.784568	+	0.620043i	$0.212885\pi$
$284$	−65.2163	−3.86988
$285$	3.05014	0.180674
$286$	19.0538	1.12667
$287$	12.8874	0.760719
$288$	−139.734	−8.23392
$289$	−10.2299	−0.601762
$290$	1.28105	0.0752260
$291$	−17.2234	−1.00965
$292$	−81.4957	−4.76918
$293$	−8.48431	−0.495659	−0.247829	−	0.968804i	$-0.579717\pi$
$293$	−8.48431	−0.495659	−0.247829	+	0.968804i	$0.579717\pi$
$294$	−39.9952	−2.33257
$295$	0.841885	0.0490164
$296$	−1.67094	−0.0971213
$297$	−39.1077	−2.26926
$298$	9.14426	0.529713
$299$	−19.1320	−1.10643
$300$	85.6317	4.94395
$301$	−5.81292	−0.335051
$302$	−44.9843	−2.58855
$303$	34.7718	1.99759
$304$	89.5045	5.13344
$305$	−1.09891	−0.0629234
$306$	−53.0291	−3.03147
$307$	26.6215	1.51937	0.759684	−	0.650293i	$-0.225354\pi$
$307$	26.6215	1.51937	0.759684	+	0.650293i	$0.225354\pi$
$308$	21.9110	1.24850
$309$	30.0358	1.70868
$310$	−3.85956	−0.219208
$311$	−30.6800	−1.73970	−0.869851	−	0.493315i	$-0.835785\pi$
$311$	−30.6800	−1.73970	−0.869851	+	0.493315i	$0.835785\pi$
$312$	−76.9585	−4.35692
$313$	−12.5903	−0.711643	−0.355822	−	0.934554i	$-0.615799\pi$
$313$	−12.5903	−0.711643	−0.355822	+	0.934554i	$0.615799\pi$
$314$	16.5511	0.934030
$315$	−1.66317	−0.0937090
$316$	−58.0307	−3.26448
$317$	−10.9630	−0.615742	−0.307871	−	0.951428i	$-0.599616\pi$
$317$	−10.9630	−0.615742	−0.307871	+	0.951428i	$0.599616\pi$
$318$	−45.0526	−2.52643
$319$	8.90507	0.498588
$320$	−3.26269	−0.182390
$321$	−15.7891	−0.881260
$322$	−30.3112	−1.68918
$323$	17.3200	0.963712
$324$	133.974	7.44298
$325$	13.2619	0.735636
$326$	17.2959	0.957930
$327$	−15.5182	−0.858159
$328$	−73.4196	−4.05392
$329$	−0.749343	−0.0413126
$330$	−3.27854	−0.180478
$331$	19.8764	1.09251	0.546254	−	0.837620i	$-0.316053\pi$
$331$	19.8764	1.09251	0.546254	+	0.837620i	$0.316053\pi$
$332$	10.6835	0.586333
$333$	1.41684	0.0776425
$334$	−55.3689	−3.02965
$335$	1.77271	0.0968537
$336$	−68.2080	−3.72105
$337$	−2.65249	−0.144490	−0.0722451	−	0.997387i	$-0.523016\pi$
$337$	−2.65249	−0.144490	−0.0722451	+	0.997387i	$0.523016\pi$
$338$	15.9584	0.868025
$339$	36.2535	1.96902
$340$	−1.94392	−0.105424
$341$	−26.8292	−1.45288
$342$	−135.666	−7.33597
$343$	−18.0575	−0.975011
$344$	33.1162	1.78551
$345$	3.29200	0.177235
$346$	−26.5458	−1.42711
$347$	21.8795	1.17455	0.587277	−	0.809386i	$-0.300200\pi$
$347$	21.8795	1.17455	0.587277	+	0.809386i	$0.300200\pi$
$348$	−57.8002	−3.09842
$349$	12.5191	0.670131	0.335065	−	0.942195i	$-0.391242\pi$
$349$	12.5191	0.670131	0.335065	+	0.942195i	$0.391242\pi$
$350$	21.0111	1.12309
$351$	39.3120	2.09832
$352$	−49.0567	−2.61473
$353$	−23.4079	−1.24588	−0.622940	−	0.782270i	$-0.714062\pi$
$353$	−23.4079	−1.24588	−0.622940	+	0.782270i	$0.714062\pi$
$354$	−52.3332	−2.78148
$355$	1.73790	0.0922384
$356$	−36.6150	−1.94059
$357$	−13.1989	−0.698562
$358$	43.1040	2.27811
$359$	2.77102	0.146249	0.0731243	−	0.997323i	$-0.476703\pi$
$359$	2.77102	0.146249	0.0731243	+	0.997323i	$0.476703\pi$
$360$	9.47508	0.499381
$361$	25.3103	1.33212
$362$	−18.9551	−0.996256
$363$	12.9315	0.678727
$364$	−22.0255	−1.15445
$365$	2.17172	0.113673
$366$	68.3104	3.57064
$367$	17.6415	0.920880	0.460440	−	0.887691i	$-0.347692\pi$
$367$	17.6415	0.920880	0.460440	+	0.887691i	$0.347692\pi$
$368$	96.6017	5.03571
$369$	62.2548	3.24085
$370$	0.0715561	0.00372002
$371$	−8.02365	−0.416567
$372$	174.141	9.02877
$373$	−31.8933	−1.65137	−0.825687	−	0.564128i	$-0.809212\pi$
$373$	−31.8933	−1.65137	−0.825687	+	0.564128i	$0.809212\pi$
$374$	−18.6170	−0.962663
$375$	−4.57300	−0.236149
$376$	4.26901	0.220158
$377$	−8.95158	−0.461030
$378$	62.2829	3.20349
$379$	26.5335	1.36293	0.681467	−	0.731849i	$-0.261342\pi$
$379$	26.5335	1.36293	0.681467	+	0.731849i	$0.261342\pi$
$380$	−4.97318	−0.255119
$381$	−32.5112	−1.66560
$382$	−29.3814	−1.50328
$383$	31.7681	1.62328	0.811638	−	0.584160i	$-0.198576\pi$
$383$	31.7681	1.62328	0.811638	+	0.584160i	$0.198576\pi$
$384$	82.5431	4.21226
$385$	−0.583892	−0.0297579
$386$	40.2244	2.04737
$387$	−28.0803	−1.42740
$388$	28.0824	1.42567
$389$	−35.2843	−1.78899	−0.894493	−	0.447081i	$-0.852464\pi$
$389$	−35.2843	−1.78899	−0.894493	+	0.447081i	$0.852464\pi$
$390$	3.29566	0.166882
$391$	18.6934	0.945367
$392$	40.5794	2.04957
$393$	−54.8028	−2.76444
$394$	14.0319	0.706916
$395$	1.54642	0.0778088
$396$	105.845	5.31891
$397$	−21.1917	−1.06358	−0.531790	−	0.846876i	$-0.678481\pi$
$397$	−21.1917	−1.06358	−0.531790	+	0.846876i	$0.678481\pi$
$398$	30.9783	1.55280
$399$	−33.7672	−1.69048
$400$	−66.9622	−3.34811
$401$	20.1747	1.00748	0.503738	−	0.863857i	$-0.331958\pi$
$401$	20.1747	1.00748	0.503738	+	0.863857i	$0.331958\pi$
$402$	−110.195	−5.49605
$403$	26.9693	1.34344
$404$	−56.6946	−2.82066
$405$	−3.57017	−0.177403
$406$	−14.1822	−0.703850
$407$	0.497413	0.0246558
$408$	75.1944	3.72268
$409$	4.99747	0.247109	0.123555	−	0.992338i	$-0.460571\pi$
$409$	4.99747	0.247109	0.123555	+	0.992338i	$0.460571\pi$
$410$	3.14411	0.155277
$411$	−27.2880	−1.34602
$412$	−48.9727	−2.41271
$413$	−9.32028	−0.458621
$414$	−146.424	−7.19632
$415$	−0.284697	−0.0139752
$416$	49.3130	2.41777
$417$	−18.0831	−0.885532
$418$	−47.6285	−2.32958
$419$	12.9110	0.630742	0.315371	−	0.948968i	$-0.397871\pi$
$419$	12.9110	0.630742	0.315371	+	0.948968i	$0.397871\pi$
$420$	3.78987	0.184927
$421$	−13.0802	−0.637489	−0.318745	−	0.947841i	$-0.603261\pi$
$421$	−13.0802	−0.637489	−0.318745	+	0.947841i	$0.603261\pi$
$422$	39.0672	1.90176
$423$	−3.61983	−0.176002
$424$	45.7108	2.21991
$425$	−12.9579	−0.628549
$426$	−108.032	−5.23414
$427$	12.1657	0.588742
$428$	25.7437	1.24437
$429$	22.9094	1.10608
$430$	−1.41817	−0.0683900
$431$	−5.66956	−0.273093	−0.136547	−	0.990634i	$-0.543600\pi$
$431$	−5.66956	−0.273093	−0.136547	+	0.990634i	$0.543600\pi$
$432$	−198.495	−9.55011
$433$	17.6540	0.848395	0.424197	−	0.905570i	$-0.360556\pi$
$433$	17.6540	0.848395	0.424197	+	0.905570i	$0.360556\pi$
$434$	42.7281	2.05102
$435$	1.54028	0.0738507
$436$	25.3021	1.21175
$437$	47.8239	2.28773
$438$	−134.999	−6.45048
$439$	11.7337	0.560018	0.280009	−	0.959997i	$-0.409663\pi$
$439$	11.7337	0.560018	0.280009	+	0.959997i	$0.409663\pi$
$440$	3.32643	0.158581
$441$	−34.4086	−1.63850
$442$	18.7142	0.890146
$443$	−23.0353	−1.09444	−0.547219	−	0.836990i	$-0.684313\pi$
$443$	−23.0353	−1.09444	−0.547219	+	0.836990i	$0.684313\pi$
$444$	−3.22856	−0.153221
$445$	0.975726	0.0462539
$446$	−0.203538	−0.00963778
$447$	10.9946	0.520028
$448$	36.1204	1.70653
$449$	14.7887	0.697923	0.348961	−	0.937137i	$-0.386534\pi$
$449$	14.7887	0.697923	0.348961	+	0.937137i	$0.386534\pi$
$450$	101.498	4.78464
$451$	21.8559	1.02915
$452$	−59.1106	−2.78033
$453$	−54.0870	−2.54123
$454$	−55.2171	−2.59147
$455$	0.586941	0.0275162
$456$	192.372	9.00865
$457$	38.8054	1.81524	0.907619	−	0.419795i	$-0.137898\pi$
$457$	38.8054	1.81524	0.907619	+	0.419795i	$0.137898\pi$
$458$	14.0507	0.656545
$459$	−38.4108	−1.79286
$460$	−5.36752	−0.250262
$461$	0.857039	0.0399163	0.0199582	−	0.999801i	$-0.493647\pi$
$461$	0.857039	0.0399163	0.0199582	+	0.999801i	$0.493647\pi$
$462$	36.2958	1.68864
$463$	−8.26757	−0.384227	−0.192113	−	0.981373i	$-0.561534\pi$
$463$	−8.26757	−0.384227	−0.192113	+	0.981373i	$0.561534\pi$
$464$	45.1986	2.09829
$465$	−4.64055	−0.215200
$466$	17.9515	0.831589
$467$	20.9766	0.970682	0.485341	−	0.874325i	$-0.338696\pi$
$467$	20.9766	0.970682	0.485341	+	0.874325i	$0.338696\pi$
$468$	−106.398	−4.91824
$469$	−19.6252	−0.906209
$470$	−0.182816	−0.00843266
$471$	19.9002	0.916954
$472$	53.0977	2.44402
$473$	−9.85819	−0.453280
$474$	−96.1284	−4.41533
$475$	−33.1505	−1.52105
$476$	21.5206	0.986394
$477$	−38.7596	−1.77468
$478$	64.4004	2.94561
$479$	−23.7982	−1.08737	−0.543684	−	0.839290i	$-0.682971\pi$
$479$	−23.7982	−1.08737	−0.543684	+	0.839290i	$0.682971\pi$
$480$	−8.48517	−0.387293
$481$	−0.500011	−0.0227985
$482$	34.7127	1.58112
$483$	−36.4448	−1.65830
$484$	−21.0845	−0.958386
$485$	−0.748348	−0.0339807
$486$	102.313	4.64102
$487$	−29.5357	−1.33839	−0.669196	−	0.743086i	$-0.733361\pi$
$487$	−29.5357	−1.33839	−0.669196	+	0.743086i	$0.733361\pi$
$488$	−69.3083	−3.13744
$489$	20.7958	0.940417
$490$	−1.73777	−0.0785044
$491$	−14.2537	−0.643262	−0.321631	−	0.946865i	$-0.604231\pi$
$491$	−14.2537	−0.643262	−0.321631	+	0.946865i	$0.604231\pi$
$492$	−141.860	−6.39555
$493$	8.74638	0.393917
$494$	47.8772	2.15410
$495$	−2.82059	−0.126776
$496$	−136.174	−6.11441
$497$	−19.2399	−0.863026
$498$	17.6973	0.793036
$499$	−24.8489	−1.11239	−0.556195	−	0.831052i	$-0.687739\pi$
$499$	−24.8489	−1.11239	−0.556195	+	0.831052i	$0.687739\pi$
$500$	7.45617	0.333450
$501$	−66.5729	−2.97426
$502$	10.2227	0.456263
$503$	−30.1069	−1.34240	−0.671201	−	0.741275i	$-0.734221\pi$
$503$	−30.1069	−1.34240	−0.671201	+	0.741275i	$0.734221\pi$
$504$	−104.896	−4.67244
$505$	1.51081	0.0672304
$506$	−51.4051	−2.28524
$507$	19.1877	0.852155
$508$	53.0087	2.35188
$509$	−10.2326	−0.453551	−0.226776	−	0.973947i	$-0.572818\pi$
$509$	−10.2326	−0.453551	−0.226776	+	0.973947i	$0.572818\pi$
$510$	−3.22012	−0.142589
$511$	−24.0426	−1.06358
$512$	−9.67697	−0.427666
$513$	−98.2676	−4.33862
$514$	34.8353	1.53652
$515$	1.30504	0.0575069
$516$	63.9867	2.81686
$517$	−1.27082	−0.0558906
$518$	−0.792178	−0.0348063
$519$	−31.9175	−1.40102
$520$	−3.34381	−0.146636
$521$	−29.6719	−1.29995	−0.649976	−	0.759955i	$-0.725221\pi$
$521$	−29.6719	−1.29995	−0.649976	+	0.759955i	$0.725221\pi$
$522$	−68.5095	−2.99858
$523$	−9.25745	−0.404800	−0.202400	−	0.979303i	$-0.564874\pi$
$523$	−9.25745	−0.404800	−0.202400	+	0.979303i	$0.564874\pi$
$524$	89.3548	3.90348
$525$	25.2627	1.10256
$526$	75.6784	3.29974
$527$	−26.3511	−1.14787
$528$	−115.675	−5.03410
$529$	28.6161	1.24418
$530$	−1.95751	−0.0850289
$531$	−45.0232	−1.95384
$532$	55.0567	2.38701
$533$	−21.9700	−0.951628
$534$	−60.6531	−2.62471
$535$	−0.686026	−0.0296595
$536$	111.805	4.82924
$537$	51.8262	2.23646
$538$	−73.0806	−3.15073
$539$	−12.0799	−0.520317
$540$	11.0291	0.474616
$541$	−31.9925	−1.37546	−0.687732	−	0.725964i	$-0.741394\pi$
$541$	−31.9925	−1.37546	−0.687732	+	0.725964i	$0.741394\pi$
$542$	−66.5825	−2.85996
$543$	−22.7907	−0.978042
$544$	−48.1825	−2.06581
$545$	−0.674258	−0.0288820
$546$	−36.4854	−1.56143
$547$	−15.7711	−0.674322	−0.337161	−	0.941447i	$-0.609467\pi$
$547$	−15.7711	−0.674322	−0.337161	+	0.941447i	$0.609467\pi$
$548$	44.4925	1.90062
$549$	58.7687	2.50819
$550$	35.6329	1.51939
$551$	22.3761	0.953255
$552$	207.626	8.83716
$553$	−17.1200	−0.728016
$554$	68.1739	2.89643
$555$	0.0860357	0.00365201
$556$	29.4841	1.25040
$557$	3.16163	0.133963	0.0669813	−	0.997754i	$-0.478663\pi$
$557$	3.16163	0.133963	0.0669813	+	0.997754i	$0.478663\pi$
$558$	206.405	8.73784
$559$	9.90968	0.419135
$560$	−2.96360	−0.125235
$561$	−22.3842	−0.945063
$562$	74.8327	3.15663
$563$	−11.2754	−0.475203	−0.237601	−	0.971363i	$-0.576361\pi$
$563$	−11.2754	−0.475203	−0.237601	+	0.971363i	$0.576361\pi$
$564$	8.24852	0.347326
$565$	1.57520	0.0662690
$566$	−71.2956	−2.99678
$567$	39.5244	1.65987
$568$	109.610	4.59912
$569$	13.0846	0.548537	0.274268	−	0.961653i	$-0.411564\pi$
$569$	13.0846	0.548537	0.274268	+	0.961653i	$0.411564\pi$
$570$	−8.23812	−0.345057
$571$	−9.21443	−0.385612	−0.192806	−	0.981237i	$-0.561759\pi$
$571$	−9.21443	−0.385612	−0.192806	+	0.981237i	$0.561759\pi$
$572$	−37.3532	−1.56182
$573$	−35.3268	−1.47580
$574$	−34.8076	−1.45284
$575$	−35.7791	−1.49209
$576$	174.486	7.27023
$577$	−5.79975	−0.241447	−0.120723	−	0.992686i	$-0.538521\pi$
$577$	−5.79975	−0.241447	−0.120723	+	0.992686i	$0.538521\pi$
$578$	27.6301	1.14926
$579$	48.3639	2.00994
$580$	−2.51139	−0.104280
$581$	3.15180	0.130759
$582$	46.5188	1.92827
$583$	−13.6074	−0.563561
$584$	136.971	5.66788
$585$	2.83532	0.117226
$586$	22.9153	0.946622
$587$	10.8289	0.446955	0.223477	−	0.974709i	$-0.428259\pi$
$587$	10.8289	0.446955	0.223477	+	0.974709i	$0.428259\pi$
$588$	78.4070	3.23345
$589$	−67.4149	−2.77778
$590$	−2.27385	−0.0936129
$591$	16.8713	0.693992
$592$	2.52467	0.103763
$593$	−10.0579	−0.413027	−0.206513	−	0.978444i	$-0.566212\pi$
$593$	−10.0579	−0.413027	−0.206513	+	0.978444i	$0.566212\pi$
$594$	105.626	4.33390
$595$	−0.573487	−0.0235107
$596$	−17.9265	−0.734298
$597$	37.2468	1.52441
$598$	51.6736	2.11309
$599$	10.2623	0.419306	0.209653	−	0.977776i	$-0.432767\pi$
$599$	10.2623	0.419306	0.209653	+	0.977776i	$0.432767\pi$
$600$	−143.922	−5.87558
$601$	6.13007	0.250051	0.125025	−	0.992154i	$-0.460099\pi$
$601$	6.13007	0.250051	0.125025	+	0.992154i	$0.460099\pi$
$602$	15.7001	0.639889
$603$	−94.8031	−3.86068
$604$	88.1876	3.58830
$605$	0.561866	0.0228431
$606$	−93.9152	−3.81504
$607$	37.9600	1.54075	0.770373	−	0.637593i	$-0.220070\pi$
$607$	37.9600	1.54075	0.770373	+	0.637593i	$0.220070\pi$
$608$	−123.267	−4.99913
$609$	−17.0520	−0.690982
$610$	2.96805	0.120173
$611$	1.27746	0.0516804
$612$	103.959	4.20228
$613$	−8.90839	−0.359806	−0.179903	−	0.983684i	$-0.557578\pi$
$613$	−8.90839	−0.359806	−0.179903	+	0.983684i	$0.557578\pi$
$614$	−71.9020	−2.90173
$615$	3.78033	0.152438
$616$	−36.8260	−1.48376
$617$	−7.64787	−0.307892	−0.153946	−	0.988079i	$-0.549198\pi$
$617$	−7.64787	−0.307892	−0.153946	+	0.988079i	$0.549198\pi$
$618$	−81.1238	−3.26328
$619$	15.7662	0.633698	0.316849	−	0.948476i	$-0.397375\pi$
$619$	15.7662	0.633698	0.316849	+	0.948476i	$0.397375\pi$
$620$	7.56632	0.303871
$621$	−106.060	−4.25603
$622$	82.8636	3.32253
$623$	−10.8020	−0.432773
$624$	116.279	4.65488
$625$	24.7018	0.988070
$626$	34.0051	1.35912
$627$	−57.2662	−2.28699
$628$	−32.4469	−1.29477
$629$	0.488549	0.0194797
$630$	4.49206	0.178968
$631$	−27.0442	−1.07661	−0.538306	−	0.842749i	$-0.680936\pi$
$631$	−27.0442	−1.07661	−0.538306	+	0.842749i	$0.680936\pi$
$632$	97.5327	3.87964
$633$	46.9726	1.86699
$634$	29.6099	1.17596
$635$	−1.41259	−0.0560570
$636$	88.3217	3.50218
$637$	12.1430	0.481122
$638$	−24.0517	−0.952217
$639$	−92.9415	−3.67671
$640$	3.58645	0.141767
$641$	−35.8632	−1.41651	−0.708255	−	0.705957i	$-0.750517\pi$
$641$	−35.8632	−1.41651	−0.708255	+	0.705957i	$0.750517\pi$
$642$	42.6447	1.68305
$643$	−23.6209	−0.931518	−0.465759	−	0.884912i	$-0.654219\pi$
$643$	−23.6209	−0.931518	−0.465759	+	0.884912i	$0.654219\pi$
$644$	59.4224	2.34157
$645$	−1.70514	−0.0671397
$646$	−46.7797	−1.84052
$647$	31.9463	1.25594	0.627970	−	0.778238i	$-0.283886\pi$
$647$	31.9463	1.25594	0.627970	+	0.778238i	$0.283886\pi$
$648$	−225.171	−8.84554
$649$	−15.8064	−0.620454
$650$	−35.8190	−1.40494
$651$	51.3743	2.01352
$652$	−33.9070	−1.32790
$653$	33.0366	1.29282	0.646410	−	0.762990i	$-0.276269\pi$
$653$	33.0366	1.29282	0.646410	+	0.762990i	$0.276269\pi$
$654$	41.9132	1.63894
$655$	−2.38115	−0.0930394
$656$	110.932	4.33116
$657$	−116.142	−4.53112
$658$	2.02390	0.0789000
$659$	31.6571	1.23319	0.616594	−	0.787282i	$-0.288512\pi$
$659$	31.6571	1.23319	0.616594	+	0.787282i	$0.288512\pi$
$660$	6.42728	0.250182
$661$	−12.3246	−0.479372	−0.239686	−	0.970850i	$-0.577045\pi$
$661$	−12.3246	−0.479372	−0.239686	+	0.970850i	$0.577045\pi$
$662$	−53.6843	−2.08650
$663$	22.5011	0.873872
$664$	−17.9558	−0.696822
$665$	−1.46717	−0.0568943
$666$	−3.82675	−0.148284
$667$	24.1504	0.935109
$668$	108.546	4.19976
$669$	−0.244724	−0.00946158
$670$	−4.78793	−0.184974
$671$	20.6320	0.796490
$672$	93.9370	3.62370
$673$	−9.86133	−0.380126	−0.190063	−	0.981772i	$-0.560869\pi$
$673$	−9.86133	−0.380126	−0.190063	+	0.981772i	$0.560869\pi$
$674$	7.16411	0.275951
$675$	73.5182	2.82972
$676$	−31.2851	−1.20327
$677$	29.9772	1.15212	0.576058	−	0.817409i	$-0.304590\pi$
$677$	29.9772	1.15212	0.576058	+	0.817409i	$0.304590\pi$
$678$	−97.9173	−3.76049
$679$	8.28476	0.317940
$680$	3.26716	0.125290
$681$	−66.3904	−2.54409
$682$	72.4631	2.77476
$683$	41.0876	1.57217	0.786087	−	0.618116i	$-0.212104\pi$
$683$	41.0876	1.57217	0.786087	+	0.618116i	$0.212104\pi$
$684$	265.961	10.1693
$685$	−1.18565	−0.0453013
$686$	48.7715	1.86210
$687$	16.8939	0.644541
$688$	−50.0362	−1.90761
$689$	13.6785	0.521108
$690$	−8.89136	−0.338488
$691$	10.2007	0.388052	0.194026	−	0.980996i	$-0.437845\pi$
$691$	10.2007	0.388052	0.194026	+	0.980996i	$0.437845\pi$
$692$	52.0407	1.97829
$693$	31.2260	1.18618
$694$	−59.0944	−2.24319
$695$	−0.785700	−0.0298033
$696$	97.1453	3.68228
$697$	21.4664	0.813098
$698$	−33.8128	−1.27983
$699$	21.5841	0.816386
$700$	−41.1903	−1.55685
$701$	−7.90887	−0.298714	−0.149357	−	0.988783i	$-0.547720\pi$
$701$	−7.90887	−0.298714	−0.149357	+	0.988783i	$0.547720\pi$
$702$	−106.178	−4.00743
$703$	1.24987	0.0471397
$704$	61.2569	2.30871
$705$	−0.219809	−0.00827849
$706$	63.2226	2.37941
$707$	−16.7258	−0.629039
$708$	102.595	3.85574
$709$	9.95636	0.373919	0.186960	−	0.982368i	$-0.440137\pi$
$709$	9.95636	0.373919	0.186960	+	0.982368i	$0.440137\pi$
$710$	−4.69391	−0.176159
$711$	−82.7010	−3.10153
$712$	61.5391	2.30627
$713$	−72.7605	−2.72490
$714$	35.6490	1.33413
$715$	0.995400	0.0372259
$716$	−84.5014	−3.15797
$717$	77.4321	2.89175
$718$	−7.48425	−0.279310
$719$	−46.2334	−1.72422	−0.862108	−	0.506725i	$-0.830856\pi$
$719$	−46.2334	−1.72422	−0.862108	+	0.506725i	$0.830856\pi$
$720$	−14.3162	−0.533532
$721$	−14.4477	−0.538062
$722$	−68.3608	−2.54413
$723$	41.7369	1.55221
$724$	37.1597	1.38103
$725$	−16.7406	−0.621729
$726$	−34.9267	−1.29625
$727$	0.186524	0.00691778	0.00345889	−	0.999994i	$-0.498899\pi$
$727$	0.186524	0.00691778	0.00345889	+	0.999994i	$0.498899\pi$
$728$	37.0184	1.37199
$729$	47.1090	1.74478
$730$	−5.86561	−0.217096
$731$	−9.68252	−0.358121
$732$	−133.916	−4.94969
$733$	−15.4413	−0.570338	−0.285169	−	0.958477i	$-0.592050\pi$
$733$	−15.4413	−0.570338	−0.285169	+	0.958477i	$0.592050\pi$
$734$	−47.6480	−1.75872
$735$	−2.08941	−0.0770691
$736$	−133.041	−4.90397
$737$	−33.2827	−1.22598
$738$	−168.144	−6.18947
$739$	43.3339	1.59406	0.797031	−	0.603938i	$-0.206403\pi$
$739$	43.3339	1.59406	0.797031	+	0.603938i	$0.206403\pi$
$740$	−0.140279	−0.00515677
$741$	57.5653	2.11472
$742$	21.6711	0.795571
$743$	51.2136	1.87884	0.939422	−	0.342764i	$-0.111363\pi$
$743$	51.2136	1.87884	0.939422	+	0.342764i	$0.111363\pi$
$744$	−292.680	−10.7302
$745$	0.477711	0.0175020
$746$	86.1408	3.15384
$747$	15.2253	0.557065
$748$	36.4970	1.33446
$749$	7.59481	0.277508
$750$	12.3512	0.451003
$751$	34.9250	1.27443	0.637216	−	0.770686i	$-0.280086\pi$
$751$	34.9250	1.27443	0.637216	+	0.770686i	$0.280086\pi$
$752$	−6.45017	−0.235214
$753$	12.2913	0.447922
$754$	24.1774	0.880487
$755$	−2.35005	−0.0855271
$756$	−122.100	−4.44073
$757$	0.958503	0.0348374	0.0174187	−	0.999848i	$-0.494455\pi$
$757$	0.958503	0.0348374	0.0174187	+	0.999848i	$0.494455\pi$
$758$	−71.6644	−2.60297
$759$	−61.8072	−2.24346
$760$	8.35846	0.303193
$761$	−26.0598	−0.944665	−0.472333	−	0.881420i	$-0.656588\pi$
$761$	−26.0598	−0.944665	−0.472333	+	0.881420i	$0.656588\pi$
$762$	87.8095	3.18100
$763$	7.46453	0.270234
$764$	57.5995	2.08388
$765$	−2.77032	−0.100161
$766$	−85.8027	−3.10018
$767$	15.8889	0.573716
$768$	−72.7578	−2.62542
$769$	−32.1875	−1.16071	−0.580356	−	0.814363i	$-0.697087\pi$
$769$	−32.1875	−1.16071	−0.580356	+	0.814363i	$0.697087\pi$
$770$	1.57703	0.0568324
$771$	41.8844	1.50843
$772$	−78.8563	−2.83810
$773$	12.5333	0.450791	0.225395	−	0.974267i	$-0.427633\pi$
$773$	12.5333	0.450791	0.225395	+	0.974267i	$0.427633\pi$
$774$	75.8421	2.72609
$775$	50.4360	1.81171
$776$	−47.1983	−1.69432
$777$	−0.952478	−0.0341700
$778$	95.2996	3.41666
$779$	54.9182	1.96765
$780$	−6.46085	−0.231336
$781$	−32.6291	−1.16756
$782$	−50.4891	−1.80549
$783$	−49.6238	−1.77341
$784$	−61.3126	−2.18974
$785$	0.864654	0.0308608
$786$	148.017	5.27960
$787$	−22.6975	−0.809080	−0.404540	−	0.914520i	$-0.632568\pi$
$787$	−22.6975	−0.809080	−0.404540	+	0.914520i	$0.632568\pi$
$788$	−27.5082	−0.979941
$789$	90.9922	3.23941
$790$	−4.17673	−0.148601
$791$	−17.4386	−0.620044
$792$	−177.894	−6.32120
$793$	−20.7398	−0.736491
$794$	57.2367	2.03126
$795$	−2.35362	−0.0834744
$796$	−60.7301	−2.15252
$797$	42.6163	1.50955	0.754773	−	0.655986i	$-0.227747\pi$
$797$	42.6163	1.50955	0.754773	+	0.655986i	$0.227747\pi$
$798$	91.2020	3.22852
$799$	−1.24817	−0.0441572
$800$	92.2212	3.26051
$801$	−52.1809	−1.84372
$802$	−54.4898	−1.92410
$803$	−40.7741	−1.43889
$804$	216.028	7.61872
$805$	−1.58351	−0.0558113
$806$	−72.8416	−2.56573
$807$	−87.8687	−3.09313
$808$	95.2871	3.35219
$809$	−46.2759	−1.62697	−0.813486	−	0.581584i	$-0.802433\pi$
$809$	−46.2759	−1.62697	−0.813486	+	0.581584i	$0.802433\pi$
$810$	9.64269	0.338809
$811$	−26.5648	−0.932817	−0.466409	−	0.884569i	$-0.654452\pi$
$811$	−26.5648	−0.932817	−0.466409	+	0.884569i	$0.654452\pi$
$812$	27.8029	0.975691
$813$	−80.0557	−2.80768
$814$	−1.34346	−0.0470884
$815$	0.903564	0.0316505
$816$	−113.613	−3.97726
$817$	−24.7711	−0.866631
$818$	−13.4977	−0.471936
$819$	−31.3891	−1.09682
$820$	−6.16375	−0.215247
$821$	15.6961	0.547799	0.273900	−	0.961758i	$-0.411686\pi$
$821$	15.6961	0.547799	0.273900	+	0.961758i	$0.411686\pi$
$822$	73.7023	2.57066
$823$	−5.70401	−0.198829	−0.0994147	−	0.995046i	$-0.531697\pi$
$823$	−5.70401	−0.198829	−0.0994147	+	0.995046i	$0.531697\pi$
$824$	82.3088	2.86736
$825$	42.8433	1.49161
$826$	25.1732	0.875887
$827$	5.14399	0.178874	0.0894370	−	0.995992i	$-0.471493\pi$
$827$	5.14399	0.178874	0.0894370	+	0.995992i	$0.471493\pi$
$828$	287.050	9.97568
$829$	−29.6018	−1.02811	−0.514057	−	0.857756i	$-0.671858\pi$
$829$	−29.6018	−1.02811	−0.514057	+	0.857756i	$0.671858\pi$
$830$	0.768939	0.0266903
$831$	81.9691	2.84348
$832$	−61.5769	−2.13479
$833$	−11.8646	−0.411084
$834$	48.8407	1.69121
$835$	−2.89256	−0.100101
$836$	93.3713	3.22931
$837$	149.507	5.16771
$838$	−34.8713	−1.20461
$839$	48.3492	1.66920	0.834599	−	0.550858i	$-0.185699\pi$
$839$	48.3492	1.66920	0.834599	+	0.550858i	$0.185699\pi$
$840$	−6.36967	−0.219774
$841$	−17.7003	−0.610357
$842$	35.3283	1.21749
$843$	89.9754	3.09892
$844$	−76.5877	−2.63626
$845$	0.833695	0.0286800
$846$	9.77681	0.336134
$847$	−6.22027	−0.213731
$848$	−69.0657	−2.37173
$849$	−85.7225	−2.94199
$850$	34.9979	1.20042
$851$	1.34898	0.0462424
$852$	211.786	7.25567
$853$	15.8370	0.542248	0.271124	−	0.962544i	$-0.412605\pi$
$853$	15.8370	0.542248	0.271124	+	0.962544i	$0.412605\pi$
$854$	−32.8585	−1.12439
$855$	−7.08740	−0.242384
$856$	−43.2677	−1.47886
$857$	−42.2545	−1.44339	−0.721693	−	0.692213i	$-0.756636\pi$
$857$	−42.2545	−1.44339	−0.721693	+	0.692213i	$0.756636\pi$
$858$	−61.8760	−2.11241
$859$	−29.6284	−1.01091	−0.505454	−	0.862854i	$-0.668675\pi$
$859$	−29.6284	−1.01091	−0.505454	+	0.862854i	$0.668675\pi$
$860$	2.78019	0.0948036
$861$	−41.8510	−1.42628
$862$	15.3129	0.521561
$863$	9.89783	0.336926	0.168463	−	0.985708i	$-0.446120\pi$
$863$	9.89783	0.336926	0.168463	+	0.985708i	$0.446120\pi$
$864$	273.370	9.30025
$865$	−1.38680	−0.0471525
$866$	−47.6816	−1.62029
$867$	33.2211	1.12825
$868$	−83.7646	−2.84316
$869$	−29.0340	−0.984911
$870$	−4.16014	−0.141042
$871$	33.4565	1.13363
$872$	−42.5255	−1.44009
$873$	40.0209	1.35450
$874$	−129.168	−4.36917
$875$	2.19969	0.0743631
$876$	264.653	8.94178
$877$	9.49136	0.320500	0.160250	−	0.987076i	$-0.448770\pi$
$877$	9.49136	0.320500	0.160250	+	0.987076i	$0.448770\pi$
$878$	−31.6915	−1.06954
$879$	27.5523	0.929316
$880$	−5.02600	−0.169427
$881$	−31.4492	−1.05955	−0.529776	−	0.848138i	$-0.677724\pi$
$881$	−31.4492	−1.05955	−0.529776	+	0.848138i	$0.677724\pi$
$882$	92.9342	3.12926
$883$	−5.35104	−0.180077	−0.0900384	−	0.995938i	$-0.528699\pi$
$883$	−5.35104	−0.180077	−0.0900384	+	0.995938i	$0.528699\pi$
$884$	−36.6876	−1.23394
$885$	−2.73397	−0.0919014
$886$	62.2160	2.09019
$887$	19.4539	0.653197	0.326599	−	0.945163i	$-0.394097\pi$
$887$	19.4539	0.653197	0.326599	+	0.945163i	$0.394097\pi$
$888$	5.42627	0.182094
$889$	15.6384	0.524496
$890$	−2.63534	−0.0883369
$891$	67.0299	2.24559
$892$	0.399017	0.0133601
$893$	−3.19324	−0.106858
$894$	−29.6954	−0.993164
$895$	2.25182	0.0752700
$896$	−39.7047	−1.32644
$897$	62.1300	2.07446
$898$	−39.9429	−1.33291
$899$	−34.0436	−1.13542
$900$	−198.977	−6.63256
$901$	−13.3649	−0.445250
$902$	−59.0306	−1.96550
$903$	18.8771	0.628191
$904$	99.3477	3.30425
$905$	−0.990243	−0.0329168
$906$	146.084	4.85331
$907$	55.8436	1.85425	0.927127	−	0.374746i	$-0.122270\pi$
$907$	55.8436	1.85425	0.927127	+	0.374746i	$0.122270\pi$
$908$	108.248	3.59234
$909$	−80.7969	−2.67987
$910$	−1.58527	−0.0525512
$911$	54.2673	1.79796	0.898978	−	0.437993i	$-0.144311\pi$
$911$	54.2673	1.79796	0.898978	+	0.437993i	$0.144311\pi$
$912$	−290.661	−9.62473
$913$	5.34518	0.176900
$914$	−104.809	−3.46679
$915$	3.56865	0.117976
$916$	−27.5451	−0.910115
$917$	26.3611	0.870521
$918$	103.744	3.42406
$919$	−39.4237	−1.30047	−0.650235	−	0.759733i	$-0.725329\pi$
$919$	−39.4237	−1.30047	−0.650235	+	0.759733i	$0.725329\pi$
$920$	9.02124	0.297422
$921$	−86.4516	−2.84868
$922$	−2.31478	−0.0762332
$923$	32.7995	1.07961
$924$	−71.1547	−2.34082
$925$	−0.935082	−0.0307453
$926$	22.3299	0.733807
$927$	−69.7923	−2.29228
$928$	−62.2481	−2.04339
$929$	34.2946	1.12517	0.562584	−	0.826740i	$-0.309807\pi$
$929$	34.2946	1.12517	0.562584	+	0.826740i	$0.309807\pi$
$930$	12.5337	0.410996
$931$	−30.3536	−0.994799
$932$	−35.1924	−1.15277
$933$	99.6314	3.26179
$934$	−56.6558	−1.85383
$935$	−0.972582	−0.0318068
$936$	178.824	5.84503
$937$	1.23585	0.0403735	0.0201867	−	0.999796i	$-0.493574\pi$
$937$	1.23585	0.0403735	0.0201867	+	0.999796i	$0.493574\pi$
$938$	53.0059	1.73070
$939$	40.8861	1.33427
$940$	0.358394	0.0116895
$941$	23.0976	0.752961	0.376480	−	0.926425i	$-0.377134\pi$
$941$	23.0976	0.752961	0.376480	+	0.926425i	$0.377134\pi$
$942$	−53.7486	−1.75122
$943$	59.2729	1.93019
$944$	−80.2268	−2.61116
$945$	3.25376	0.105845
$946$	26.6260	0.865687
$947$	−48.4334	−1.57387	−0.786937	−	0.617034i	$-0.788334\pi$
$947$	−48.4334	−1.57387	−0.786937	+	0.617034i	$0.788334\pi$
$948$	188.451	6.12061
$949$	40.9870	1.33049
$950$	89.5362	2.90494
$951$	35.6016	1.15446
$952$	−36.1698	−1.17227
$953$	23.3558	0.756569	0.378284	−	0.925689i	$-0.376514\pi$
$953$	23.3558	0.756569	0.378284	+	0.925689i	$0.376514\pi$
$954$	104.686	3.38933
$955$	−1.53493	−0.0496692
$956$	−126.251	−4.08326
$957$	−28.9187	−0.934808
$958$	64.2767	2.07668
$959$	13.1260	0.423861
$960$	10.5954	0.341965
$961$	71.5666	2.30860
$962$	1.35048	0.0435413
$963$	36.6880	1.18226
$964$	−68.0511	−2.19178
$965$	2.10139	0.0676460
$966$	98.4339	3.16706
$967$	−8.95012	−0.287816	−0.143908	−	0.989591i	$-0.545967\pi$
$967$	−8.95012	−0.287816	−0.143908	+	0.989591i	$0.545967\pi$
$968$	35.4369	1.13899
$969$	−56.2458	−1.80687
$970$	2.02122	0.0648973
$971$	−24.3309	−0.780816	−0.390408	−	0.920642i	$-0.627666\pi$
$971$	−24.3309	−0.780816	−0.390408	+	0.920642i	$0.627666\pi$
$972$	−200.576	−6.43347
$973$	8.69827	0.278854
$974$	79.7731	2.55610
$975$	−43.0671	−1.37925
$976$	104.720	3.35200
$977$	−53.7984	−1.72116	−0.860581	−	0.509313i	$-0.829899\pi$
$977$	−53.7984	−1.72116	−0.860581	+	0.509313i	$0.829899\pi$
$978$	−56.1673	−1.79603
$979$	−18.3192	−0.585485
$980$	3.40674	0.108824
$981$	36.0587	1.15126
$982$	38.4979	1.22852
$983$	21.3096	0.679672	0.339836	−	0.940485i	$-0.389629\pi$
$983$	21.3096	0.679672	0.339836	+	0.940485i	$0.389629\pi$
$984$	238.426	7.60073
$985$	0.733048	0.0233568
$986$	−23.6231	−0.752314
$987$	2.43345	0.0774575
$988$	−93.8590	−2.98605
$989$	−26.7353	−0.850133
$990$	7.61813	0.242120
$991$	21.0149	0.667561	0.333781	−	0.942651i	$-0.391676\pi$
$991$	21.0149	0.667561	0.333781	+	0.942651i	$0.391676\pi$
$992$	187.541	5.95444
$993$	−64.5475	−2.04835
$994$	51.9650	1.64823
$995$	1.61835	0.0513053
$996$	−34.6940	−1.09932
$997$	47.6008	1.50753	0.753766	−	0.657143i	$-0.228235\pi$
$997$	47.6008	1.50753	0.753766	+	0.657143i	$0.228235\pi$
$998$	67.1145	2.12447
$999$	−2.77185	−0.0876975

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4007.2.a.a.1.4	✓	139

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4007.2.a.a.1.4	✓	139	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)

\(f(q)\)	\(=\)	\(q-2.70090 q^{2} -3.24744 q^{3} +5.29488 q^{4} -0.141100 q^{5} +8.77102 q^{6} +1.56207 q^{7} -8.89915 q^{8} +7.54587 q^{9} +O(q^{10})\)	\(q-2.70090 q^{2} -3.24744 q^{3} +5.29488 q^{4} -0.141100 q^{5} +8.77102 q^{6} +1.56207 q^{7} -8.89915 q^{8} +7.54587 q^{9} +0.381096 q^{10} +2.64914 q^{11} -17.1948 q^{12} -2.66298 q^{13} -4.21901 q^{14} +0.458212 q^{15} +13.4460 q^{16} +2.60193 q^{17} -20.3807 q^{18} +6.65660 q^{19} -0.747105 q^{20} -5.07274 q^{21} -7.15507 q^{22} +7.18444 q^{23} +28.8994 q^{24} -4.98009 q^{25} +7.19244 q^{26} -14.7624 q^{27} +8.27099 q^{28} +3.36150 q^{29} -1.23759 q^{30} -10.1275 q^{31} -18.5180 q^{32} -8.60292 q^{33} -7.02757 q^{34} -0.220408 q^{35} +39.9544 q^{36} +0.187764 q^{37} -17.9788 q^{38} +8.64786 q^{39} +1.25567 q^{40} +8.25018 q^{41} +13.7010 q^{42} -3.72128 q^{43} +14.0269 q^{44} -1.06472 q^{45} -19.4045 q^{46} -0.479710 q^{47} -43.6650 q^{48} -4.55992 q^{49} +13.4507 q^{50} -8.44962 q^{51} -14.1001 q^{52} -5.13653 q^{53} +39.8719 q^{54} -0.373792 q^{55} -13.9011 q^{56} -21.6169 q^{57} -9.07907 q^{58} -5.96660 q^{59} +2.42618 q^{60} +7.78820 q^{61} +27.3534 q^{62} +11.7872 q^{63} +23.1233 q^{64} +0.375745 q^{65} +23.2357 q^{66} -12.5636 q^{67} +13.7769 q^{68} -23.3310 q^{69} +0.595300 q^{70} -12.3169 q^{71} -67.1518 q^{72} -15.3914 q^{73} -0.507132 q^{74} +16.1725 q^{75} +35.2459 q^{76} +4.13815 q^{77} -23.3570 q^{78} -10.9598 q^{79} -1.89722 q^{80} +25.3025 q^{81} -22.2829 q^{82} +2.01770 q^{83} -26.8596 q^{84} -0.367131 q^{85} +10.0508 q^{86} -10.9163 q^{87} -23.5751 q^{88} -6.91516 q^{89} +2.87570 q^{90} -4.15977 q^{91} +38.0407 q^{92} +32.8885 q^{93} +1.29565 q^{94} -0.939243 q^{95} +60.1360 q^{96} +5.30369 q^{97} +12.3159 q^{98} +19.9901 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9}+O(q^{10}) \) 139 * q - 13 * q^2 - 22 * q^3 + 113 * q^4 - 16 * q^5 - 15 * q^6 - 44 * q^7 - 36 * q^8 + 87 * q^9	\( 139 q - 13 q^{2} - 22 q^{3} + 113 q^{4} - 16 q^{5} - 15 q^{6} - 44 q^{7} - 36 q^{8} + 87 q^{9} - 40 q^{10} - 17 q^{11} - 59 q^{12} - 89 q^{13} - 15 q^{14} - 29 q^{15} + 73 q^{16} - 58 q^{17} - 51 q^{18} - 37 q^{19} - 24 q^{20} - 37 q^{21} - 99 q^{22} - 42 q^{23} - 27 q^{24} - 11 q^{25} + 2 q^{26} - 73 q^{27} - 113 q^{28} - 57 q^{29} - 29 q^{30} - 51 q^{31} - 80 q^{32} - 78 q^{33} - 28 q^{34} - 34 q^{35} + 28 q^{36} - 117 q^{37} - 31 q^{38} - 36 q^{39} - 107 q^{40} - 60 q^{41} - 41 q^{42} - 109 q^{43} - 21 q^{44} - 62 q^{45} - 92 q^{46} - 26 q^{47} - 90 q^{48} - 7 q^{49} - 22 q^{50} - 47 q^{51} - 182 q^{52} - 83 q^{53} - 19 q^{54} - 53 q^{55} - 23 q^{56} - 201 q^{57} - 112 q^{58} + 14 q^{59} - 64 q^{60} - 73 q^{61} - 21 q^{62} - 94 q^{63} + 14 q^{64} - 123 q^{65} - 10 q^{66} - 135 q^{67} - 84 q^{68} - 50 q^{69} - 35 q^{70} - 29 q^{71} - 143 q^{72} - 266 q^{73} - 53 q^{74} - 32 q^{75} - 66 q^{76} - 69 q^{77} - 59 q^{78} - 124 q^{79} - 20 q^{80} - 33 q^{81} - 93 q^{82} - 28 q^{83} - 4 q^{84} - 179 q^{85} + 6 q^{86} - 40 q^{87} - 259 q^{88} - 41 q^{89} + 2 q^{90} - 50 q^{91} - 77 q^{92} - 60 q^{93} - 48 q^{94} - 37 q^{95} + 3 q^{96} - 220 q^{97} - 9 q^{98} - 35 q^{99}+O(q^{100}) \) 139 * q - 13 * q^2 - 22 * q^3 + 113 * q^4 - 16 * q^5 - 15 * q^6 - 44 * q^7 - 36 * q^8 + 87 * q^9 - 40 * q^10 - 17 * q^11 - 59 * q^12 - 89 * q^13 - 15 * q^14 - 29 * q^15 + 73 * q^16 - 58 * q^17 - 51 * q^18 - 37 * q^19 - 24 * q^20 - 37 * q^21 - 99 * q^22 - 42 * q^23 - 27 * q^24 - 11 * q^25 + 2 * q^26 - 73 * q^27 - 113 * q^28 - 57 * q^29 - 29 * q^30 - 51 * q^31 - 80 * q^32 - 78 * q^33 - 28 * q^34 - 34 * q^35 + 28 * q^36 - 117 * q^37 - 31 * q^38 - 36 * q^39 - 107 * q^40 - 60 * q^41 - 41 * q^42 - 109 * q^43 - 21 * q^44 - 62 * q^45 - 92 * q^46 - 26 * q^47 - 90 * q^48 - 7 * q^49 - 22 * q^50 - 47 * q^51 - 182 * q^52 - 83 * q^53 - 19 * q^54 - 53 * q^55 - 23 * q^56 - 201 * q^57 - 112 * q^58 + 14 * q^59 - 64 * q^60 - 73 * q^61 - 21 * q^62 - 94 * q^63 + 14 * q^64 - 123 * q^65 - 10 * q^66 - 135 * q^67 - 84 * q^68 - 50 * q^69 - 35 * q^70 - 29 * q^71 - 143 * q^72 - 266 * q^73 - 53 * q^74 - 32 * q^75 - 66 * q^76 - 69 * q^77 - 59 * q^78 - 124 * q^79 - 20 * q^80 - 33 * q^81 - 93 * q^82 - 28 * q^83 - 4 * q^84 - 179 * q^85 + 6 * q^86 - 40 * q^87 - 259 * q^88 - 41 * q^89 + 2 * q^90 - 50 * q^91 - 77 * q^92 - 60 * q^93 - 48 * q^94 - 37 * q^95 + 3 * q^96 - 220 * q^97 - 9 * q^98 - 35 * q^99

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