LMFDB - Embedded newform 4007.2.a.b.1.16

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			1.16
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)

$f(q)$	$=$	$q-2.47249 q^{2} +0.496095 q^{3} +4.11323 q^{4} +2.63577 q^{5} -1.22659 q^{6} +3.34809 q^{7} -5.22495 q^{8} -2.75389 q^{9} +O(q^{10})$	\(q-2.47249 q^{2} +0.496095 q^{3} +4.11323 q^{4} +2.63577 q^{5} -1.22659 q^{6} +3.34809 q^{7} -5.22495 q^{8} -2.75389 q^{9} -6.51692 q^{10} +3.92765 q^{11} +2.04055 q^{12} +0.755716 q^{13} -8.27813 q^{14} +1.30759 q^{15} +4.69221 q^{16} -0.105502 q^{17} +6.80898 q^{18} -1.17107 q^{19} +10.8415 q^{20} +1.66097 q^{21} -9.71110 q^{22} +5.61960 q^{23} -2.59207 q^{24} +1.94728 q^{25} -1.86850 q^{26} -2.85447 q^{27} +13.7715 q^{28} -0.945939 q^{29} -3.23301 q^{30} +4.11733 q^{31} -1.15155 q^{32} +1.94849 q^{33} +0.260853 q^{34} +8.82478 q^{35} -11.3274 q^{36} -9.26281 q^{37} +2.89546 q^{38} +0.374907 q^{39} -13.7718 q^{40} -6.05072 q^{41} -4.10673 q^{42} -3.74994 q^{43} +16.1553 q^{44} -7.25862 q^{45} -13.8944 q^{46} +1.56189 q^{47} +2.32778 q^{48} +4.20968 q^{49} -4.81463 q^{50} -0.0523390 q^{51} +3.10843 q^{52} +5.62484 q^{53} +7.05767 q^{54} +10.3524 q^{55} -17.4936 q^{56} -0.580961 q^{57} +2.33883 q^{58} +10.6317 q^{59} +5.37842 q^{60} +12.3028 q^{61} -10.1801 q^{62} -9.22026 q^{63} -6.53721 q^{64} +1.99189 q^{65} -4.81762 q^{66} +5.74969 q^{67} -0.433954 q^{68} +2.78785 q^{69} -21.8192 q^{70} -9.07795 q^{71} +14.3889 q^{72} +6.73055 q^{73} +22.9023 q^{74} +0.966033 q^{75} -4.81688 q^{76} +13.1501 q^{77} -0.926955 q^{78} +15.0391 q^{79} +12.3676 q^{80} +6.84558 q^{81} +14.9604 q^{82} -15.3131 q^{83} +6.83194 q^{84} -0.278079 q^{85} +9.27171 q^{86} -0.469275 q^{87} -20.5218 q^{88} +4.08551 q^{89} +17.9469 q^{90} +2.53020 q^{91} +23.1147 q^{92} +2.04259 q^{93} -3.86178 q^{94} -3.08667 q^{95} -0.571278 q^{96} +17.6503 q^{97} -10.4084 q^{98} -10.8163 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.47249	−1.74832	−0.874159	−	0.485640i	$-0.838587\pi$
$2$	−2.47249	−1.74832	−0.874159	+	0.485640i	$0.838587\pi$
$3$	0.496095	0.286420	0.143210	−	0.989692i	$-0.454258\pi$
$3$	0.496095	0.286420	0.143210	+	0.989692i	$0.454258\pi$
$4$	4.11323	2.05662
$5$	2.63577	1.17875	0.589376	−	0.807859i	$-0.299374\pi$
$5$	2.63577	1.17875	0.589376	+	0.807859i	$0.299374\pi$
$6$	−1.22659	−0.500754
$7$	3.34809	1.26546	0.632729	−	0.774373i	$-0.281935\pi$
$7$	3.34809	1.26546	0.632729	+	0.774373i	$0.281935\pi$
$8$	−5.22495	−1.84730
$9$	−2.75389	−0.917963
$10$	−6.51692	−2.06083
$11$	3.92765	1.18423	0.592116	−	0.805853i	$-0.298293\pi$
$11$	3.92765	1.18423	0.592116	+	0.805853i	$0.298293\pi$
$12$	2.04055	0.589056
$13$	0.755716	0.209598	0.104799	−	0.994493i	$-0.466580\pi$
$13$	0.755716	0.209598	0.104799	+	0.994493i	$0.466580\pi$
$14$	−8.27813	−2.21242
$15$	1.30759	0.337618
$16$	4.69221	1.17305
$17$	−0.105502	−0.0255880	−0.0127940	−	0.999918i	$-0.504073\pi$
$17$	−0.105502	−0.0255880	−0.0127940	+	0.999918i	$0.504073\pi$
$18$	6.80898	1.60489
$19$	−1.17107	−0.268662	−0.134331	−	0.990937i	$-0.542888\pi$
$19$	−1.17107	−0.268662	−0.134331	+	0.990937i	$0.542888\pi$
$20$	10.8415	2.42424
$21$	1.66097	0.362453
$22$	−9.71110	−2.07041
$23$	5.61960	1.17177	0.585884	−	0.810395i	$-0.300748\pi$
$23$	5.61960	1.17177	0.585884	+	0.810395i	$0.300748\pi$
$24$	−2.59207	−0.529104
$25$	1.94728	0.389455
$26$	−1.86850	−0.366444
$27$	−2.85447	−0.549344
$28$	13.7715	2.60256
$29$	−0.945939	−0.175656	−0.0878282	−	0.996136i	$-0.527993\pi$
$29$	−0.945939	−0.175656	−0.0878282	+	0.996136i	$0.527993\pi$
$30$	−3.23301	−0.590264
$31$	4.11733	0.739494	0.369747	−	0.929132i	$-0.379444\pi$
$31$	4.11733	0.739494	0.369747	+	0.929132i	$0.379444\pi$
$32$	−1.15155	−0.203567
$33$	1.94849	0.339188
$34$	0.260853	0.0447359
$35$	8.82478	1.49166
$36$	−11.3274	−1.88790
$37$	−9.26281	−1.52280	−0.761398	−	0.648284i	$-0.775487\pi$
$37$	−9.26281	−1.52280	−0.761398	+	0.648284i	$0.775487\pi$
$38$	2.89546	0.469706
$39$	0.374907	0.0600331
$40$	−13.7718	−2.17751
$41$	−6.05072	−0.944964	−0.472482	−	0.881340i	$-0.656642\pi$
$41$	−6.05072	−0.944964	−0.472482	+	0.881340i	$0.656642\pi$
$42$	−4.10673	−0.633683
$43$	−3.74994	−0.571861	−0.285930	−	0.958250i	$-0.592303\pi$
$43$	−3.74994	−0.571861	−0.285930	+	0.958250i	$0.592303\pi$
$44$	16.1553	2.43551
$45$	−7.25862	−1.08205
$46$	−13.8944	−2.04862
$47$	1.56189	0.227826	0.113913	−	0.993491i	$-0.463662\pi$
$47$	1.56189	0.227826	0.113913	+	0.993491i	$0.463662\pi$
$48$	2.32778	0.335986
$49$	4.20968	0.601383
$50$	−4.81463	−0.680892
$51$	−0.0523390	−0.00732892
$52$	3.10843	0.431062
$53$	5.62484	0.772631	0.386315	−	0.922367i	$-0.373748\pi$
$53$	5.62484	0.772631	0.386315	+	0.922367i	$0.373748\pi$
$54$	7.05767	0.960427
$55$	10.3524	1.39591
$56$	−17.4936	−2.33768
$57$	−0.580961	−0.0769502
$58$	2.33883	0.307103
$59$	10.6317	1.38413	0.692066	−	0.721834i	$-0.256701\pi$
$59$	10.6317	1.38413	0.692066	+	0.721834i	$0.256701\pi$
$60$	5.37842	0.694351
$61$	12.3028	1.57521	0.787604	−	0.616182i	$-0.211321\pi$
$61$	12.3028	1.57521	0.787604	+	0.616182i	$0.211321\pi$
$62$	−10.1801	−1.29287
$63$	−9.22026	−1.16164
$64$	−6.53721	−0.817151
$65$	1.99189	0.247064
$66$	−4.81762	−0.593008
$67$	5.74969	0.702436	0.351218	−	0.936294i	$-0.385768\pi$
$67$	5.74969	0.702436	0.351218	+	0.936294i	$0.385768\pi$
$68$	−0.433954	−0.0526246
$69$	2.78785	0.335618
$70$	−21.8192	−2.60790
$71$	−9.07795	−1.07735	−0.538677	−	0.842512i	$-0.681076\pi$
$71$	−9.07795	−1.07735	−0.538677	+	0.842512i	$0.681076\pi$
$72$	14.3889	1.69575
$73$	6.73055	0.787751	0.393876	−	0.919164i	$-0.371134\pi$
$73$	6.73055	0.787751	0.393876	+	0.919164i	$0.371134\pi$
$74$	22.9023	2.66233
$75$	0.966033	0.111548
$76$	−4.81688	−0.552534
$77$	13.1501	1.49859
$78$	−0.926955	−0.104957
$79$	15.0391	1.69203	0.846015	−	0.533158i	$-0.178995\pi$
$79$	15.0391	1.69203	0.846015	+	0.533158i	$0.178995\pi$
$80$	12.3676	1.38274
$81$	6.84558	0.760620
$82$	14.9604	1.65210
$83$	−15.3131	−1.68084	−0.840418	−	0.541938i	$-0.817691\pi$
$83$	−15.3131	−1.68084	−0.840418	+	0.541938i	$0.817691\pi$
$84$	6.83194	0.745426
$85$	−0.278079	−0.0301619
$86$	9.27171	0.999794
$87$	−0.469275	−0.0503116
$88$	−20.5218	−2.18763
$89$	4.08551	0.433064	0.216532	−	0.976276i	$-0.430525\pi$
$89$	4.08551	0.433064	0.216532	+	0.976276i	$0.430525\pi$
$90$	17.9469	1.89177
$91$	2.53020	0.265237
$92$	23.1147	2.40987
$93$	2.04259	0.211806
$94$	−3.86178	−0.398312
$95$	−3.08667	−0.316685
$96$	−0.571278	−0.0583058
$97$	17.6503	1.79211	0.896057	−	0.443939i	$-0.146419\pi$
$97$	17.6503	1.79211	0.896057	+	0.443939i	$0.146419\pi$
$98$	−10.4084	−1.05141
$99$	−10.8163	−1.08708
$100$	8.00960	0.800960
$101$	−13.9904	−1.39209	−0.696047	−	0.717996i	$-0.745060\pi$
$101$	−13.9904	−1.39209	−0.696047	+	0.717996i	$0.745060\pi$
$102$	0.129408	0.0128133
$103$	15.6251	1.53959	0.769795	−	0.638291i	$-0.220359\pi$
$103$	15.6251	1.53959	0.769795	+	0.638291i	$0.220359\pi$
$104$	−3.94858	−0.387190
$105$	4.37793	0.427242
$106$	−13.9074	−1.35080
$107$	2.17700	0.210458	0.105229	−	0.994448i	$-0.466442\pi$
$107$	2.17700	0.210458	0.105229	+	0.994448i	$0.466442\pi$
$108$	−11.7411	−1.12979
$109$	18.6843	1.78963	0.894816	−	0.446436i	$-0.147307\pi$
$109$	18.6843	1.78963	0.894816	+	0.446436i	$0.147307\pi$
$110$	−25.5962	−2.44050
$111$	−4.59523	−0.436160
$112$	15.7099	1.48445
$113$	−14.4641	−1.36067	−0.680335	−	0.732901i	$-0.738166\pi$
$113$	−14.4641	−1.36067	−0.680335	+	0.732901i	$0.738166\pi$
$114$	1.43642	0.134533
$115$	14.8120	1.38122
$116$	−3.89086	−0.361258
$117$	−2.08116	−0.192403
$118$	−26.2869	−2.41990
$119$	−0.353230	−0.0323805
$120$	−6.83210	−0.623682
$121$	4.42644	0.402403
$122$	−30.4185	−2.75396
$123$	−3.00173	−0.270657
$124$	16.9355	1.52086
$125$	−8.04627	−0.719680
$126$	22.7971	2.03092
$127$	6.55543	0.581700	0.290850	−	0.956769i	$-0.406062\pi$
$127$	6.55543	0.581700	0.290850	+	0.956769i	$0.406062\pi$
$128$	18.4663	1.63221
$129$	−1.86033	−0.163793
$130$	−4.92494	−0.431946
$131$	20.1124	1.75723	0.878616	−	0.477529i	$-0.158467\pi$
$131$	20.1124	1.75723	0.878616	+	0.477529i	$0.158467\pi$
$132$	8.01457	0.697579
$133$	−3.92084	−0.339980
$134$	−14.2161	−1.22808
$135$	−7.52373	−0.647540
$136$	0.551243	0.0472687
$137$	−10.9461	−0.935189	−0.467595	−	0.883943i	$-0.654879\pi$
$137$	−10.9461	−0.935189	−0.467595	+	0.883943i	$0.654879\pi$
$138$	−6.89295	−0.586767
$139$	17.4660	1.48145	0.740725	−	0.671808i	$-0.234482\pi$
$139$	17.4660	1.48145	0.740725	+	0.671808i	$0.234482\pi$
$140$	36.2984	3.06777
$141$	0.774847	0.0652539
$142$	22.4452	1.88356
$143$	2.96819	0.248212
$144$	−12.9218	−1.07682
$145$	−2.49328	−0.207055
$146$	−16.6413	−1.37724
$147$	2.08840	0.172248
$148$	−38.1001	−3.13181
$149$	−19.8580	−1.62683	−0.813416	−	0.581682i	$-0.802395\pi$
$149$	−19.8580	−1.62683	−0.813416	+	0.581682i	$0.802395\pi$
$150$	−2.38851	−0.195021
$151$	21.0825	1.71567	0.857836	−	0.513923i	$-0.171808\pi$
$151$	21.0825	1.71567	0.857836	+	0.513923i	$0.171808\pi$
$152$	6.11878	0.496299
$153$	0.290541	0.0234888
$154$	−32.5136	−2.62002
$155$	10.8523	0.871680
$156$	1.54208	0.123465
$157$	−2.06924	−0.165144	−0.0825718	−	0.996585i	$-0.526313\pi$
$157$	−2.06924	−0.165144	−0.0825718	+	0.996585i	$0.526313\pi$
$158$	−37.1841	−2.95821
$159$	2.79045	0.221297
$160$	−3.03522	−0.239955
$161$	18.8149	1.48282
$162$	−16.9257	−1.32981
$163$	−18.7389	−1.46774	−0.733872	−	0.679288i	$-0.762289\pi$
$163$	−18.7389	−1.46774	−0.733872	+	0.679288i	$0.762289\pi$
$164$	−24.8880	−1.94343
$165$	5.13576	0.399818
$166$	37.8617	2.93864
$167$	14.0126	1.08433	0.542163	−	0.840273i	$-0.317605\pi$
$167$	14.0126	1.08433	0.542163	+	0.840273i	$0.317605\pi$
$168$	−8.67848	−0.669559
$169$	−12.4289	−0.956069
$170$	0.687548	0.0527326
$171$	3.22500	0.246622
$172$	−15.4244	−1.17610
$173$	−25.7688	−1.95917	−0.979583	−	0.201042i	$-0.935567\pi$
$173$	−25.7688	−1.95917	−0.979583	+	0.201042i	$0.935567\pi$
$174$	1.16028	0.0879606
$175$	6.51965	0.492839
$176$	18.4293	1.38916
$177$	5.27434	0.396443
$178$	−10.1014	−0.757133
$179$	6.52385	0.487615	0.243808	−	0.969824i	$-0.421603\pi$
$179$	6.52385	0.487615	0.243808	+	0.969824i	$0.421603\pi$
$180$	−29.8564	−2.22536
$181$	−9.20670	−0.684329	−0.342164	−	0.939640i	$-0.611160\pi$
$181$	−9.20670	−0.684329	−0.342164	+	0.939640i	$0.611160\pi$
$182$	−6.25591	−0.463719
$183$	6.10333	0.451171
$184$	−29.3621	−2.16461
$185$	−24.4146	−1.79500
$186$	−5.05028	−0.370305
$187$	−0.414375	−0.0303021
$188$	6.42443	0.468550
$189$	−9.55703	−0.695171
$190$	7.63177	0.553667
$191$	−4.60483	−0.333194	−0.166597	−	0.986025i	$-0.553278\pi$
$191$	−4.60483	−0.333194	−0.166597	+	0.986025i	$0.553278\pi$
$192$	−3.24307	−0.234049
$193$	−3.14666	−0.226502	−0.113251	−	0.993566i	$-0.536126\pi$
$193$	−3.14666	−0.226502	−0.113251	+	0.993566i	$0.536126\pi$
$194$	−43.6402	−3.13318
$195$	0.988167	0.0707641
$196$	17.3154	1.23681
$197$	19.2263	1.36982	0.684910	−	0.728628i	$-0.259842\pi$
$197$	19.2263	1.36982	0.684910	+	0.728628i	$0.259842\pi$
$198$	26.7433	1.90056
$199$	16.0065	1.13467	0.567334	−	0.823488i	$-0.307975\pi$
$199$	16.0065	1.13467	0.567334	+	0.823488i	$0.307975\pi$
$200$	−10.1744	−0.719441
$201$	2.85239	0.201192
$202$	34.5911	2.43382
$203$	−3.16708	−0.222286
$204$	−0.215282	−0.0150728
$205$	−15.9483	−1.11388
$206$	−38.6331	−2.69169
$207$	−15.4758	−1.07564
$208$	3.54598	0.245869
$209$	−4.59955	−0.318158
$210$	−10.8244	−0.746955
$211$	−22.8735	−1.57468	−0.787338	−	0.616522i	$-0.788541\pi$
$211$	−22.8735	−1.57468	−0.787338	+	0.616522i	$0.788541\pi$
$212$	23.1363	1.58900
$213$	−4.50352	−0.308576
$214$	−5.38261	−0.367948
$215$	−9.88398	−0.674082
$216$	14.9145	1.01480
$217$	13.7852	0.935799
$218$	−46.1968	−3.12884
$219$	3.33899	0.225628
$220$	42.5817	2.87086
$221$	−0.0797295	−0.00536319
$222$	11.3617	0.762546
$223$	18.7405	1.25496	0.627479	−	0.778633i	$-0.284087\pi$
$223$	18.7405	1.25496	0.627479	+	0.778633i	$0.284087\pi$
$224$	−3.85549	−0.257606
$225$	−5.36259	−0.357506
$226$	35.7625	2.37888
$227$	26.5099	1.75952	0.879761	−	0.475416i	$-0.157702\pi$
$227$	26.5099	1.75952	0.879761	+	0.475416i	$0.157702\pi$
$228$	−2.38963	−0.158257
$229$	−5.80211	−0.383414	−0.191707	−	0.981452i	$-0.561402\pi$
$229$	−5.80211	−0.383414	−0.191707	+	0.981452i	$0.561402\pi$
$230$	−36.6225	−2.41482
$231$	6.52370	0.429228
$232$	4.94248	0.324490
$233$	−11.4132	−0.747706	−0.373853	−	0.927488i	$-0.621964\pi$
$233$	−11.4132	−0.747706	−0.373853	+	0.927488i	$0.621964\pi$
$234$	5.14566	0.336382
$235$	4.11679	0.268550
$236$	43.7307	2.84663
$237$	7.46082	0.484632
$238$	0.873359	0.0566114
$239$	−18.9887	−1.22828	−0.614140	−	0.789197i	$-0.710497\pi$
$239$	−18.9887	−1.22828	−0.614140	+	0.789197i	$0.710497\pi$
$240$	6.13548	0.396044
$241$	−25.6064	−1.64945	−0.824726	−	0.565533i	$-0.808670\pi$
$241$	−25.6064	−1.64945	−0.824726	+	0.565533i	$0.808670\pi$
$242$	−10.9443	−0.703529
$243$	11.9595	0.767201
$244$	50.6041	3.23960
$245$	11.0958	0.708882
$246$	7.42176	0.473194
$247$	−0.884996	−0.0563109
$248$	−21.5129	−1.36607
$249$	−7.59677	−0.481426
$250$	19.8944	1.25823
$251$	−28.9015	−1.82425	−0.912123	−	0.409916i	$-0.865558\pi$
$251$	−28.9015	−1.82425	−0.912123	+	0.409916i	$0.865558\pi$
$252$	−37.9251	−2.38905
$253$	22.0718	1.38764
$254$	−16.2083	−1.01700
$255$	−0.137953	−0.00863898
$256$	−32.5835	−2.03647
$257$	12.4613	0.777314	0.388657	−	0.921382i	$-0.372939\pi$
$257$	12.4613	0.777314	0.388657	+	0.921382i	$0.372939\pi$
$258$	4.59965	0.286361
$259$	−31.0127	−1.92703
$260$	8.19312	0.508115
$261$	2.60501	0.161246
$262$	−49.7279	−3.07220
$263$	16.7106	1.03042	0.515211	−	0.857063i	$-0.327714\pi$
$263$	16.7106	1.03042	0.515211	+	0.857063i	$0.327714\pi$
$264$	−10.1807	−0.626582
$265$	14.8258	0.910740
$266$	9.69426	0.594393
$267$	2.02680	0.124038
$268$	23.6498	1.44464
$269$	−16.3809	−0.998764	−0.499382	−	0.866382i	$-0.666440\pi$
$269$	−16.3809	−0.998764	−0.499382	+	0.866382i	$0.666440\pi$
$270$	18.6024	1.13211
$271$	−7.20598	−0.437732	−0.218866	−	0.975755i	$-0.570236\pi$
$271$	−7.20598	−0.437732	−0.218866	+	0.975755i	$0.570236\pi$
$272$	−0.495037	−0.0300160
$273$	1.25522	0.0759694
$274$	27.0642	1.63501
$275$	7.64822	0.461205
$276$	11.4671	0.690237
$277$	−19.5528	−1.17481	−0.587407	−	0.809292i	$-0.699851\pi$
$277$	−19.5528	−1.17481	−0.587407	+	0.809292i	$0.699851\pi$
$278$	−43.1847	−2.59005
$279$	−11.3387	−0.678829
$280$	−46.1091	−2.75554
$281$	7.22061	0.430746	0.215373	−	0.976532i	$-0.430903\pi$
$281$	7.22061	0.430746	0.215373	+	0.976532i	$0.430903\pi$
$282$	−1.91581	−0.114085
$283$	−7.34392	−0.436551	−0.218275	−	0.975887i	$-0.570043\pi$
$283$	−7.34392	−0.436551	−0.218275	+	0.975887i	$0.570043\pi$
$284$	−37.3397	−2.21570
$285$	−1.53128	−0.0907051
$286$	−7.33883	−0.433954
$287$	−20.2583	−1.19581
$288$	3.17125	0.186867
$289$	−16.9889	−0.999345
$290$	6.16461	0.361998
$291$	8.75620	0.513298
$292$	27.6843	1.62010
$293$	−9.46552	−0.552982	−0.276491	−	0.961017i	$-0.589172\pi$
$293$	−9.46552	−0.552982	−0.276491	+	0.961017i	$0.589172\pi$
$294$	−5.16356	−0.301145
$295$	28.0227	1.63155
$296$	48.3977	2.81306
$297$	−11.2114	−0.650550
$298$	49.0988	2.84422
$299$	4.24682	0.245600
$300$	3.97352	0.229411
$301$	−12.5551	−0.723666
$302$	−52.1265	−2.99954
$303$	−6.94055	−0.398724
$304$	−5.49490	−0.315154
$305$	32.4272	1.85678
$306$	−0.718361	−0.0410659
$307$	8.82020	0.503395	0.251698	−	0.967806i	$-0.419011\pi$
$307$	8.82020	0.503395	0.251698	+	0.967806i	$0.419011\pi$
$308$	54.0895	3.08203
$309$	7.75154	0.440970
$310$	−26.8323	−1.52397
$311$	0.951163	0.0539355	0.0269678	−	0.999636i	$-0.491415\pi$
$311$	0.951163	0.0539355	0.0269678	+	0.999636i	$0.491415\pi$
$312$	−1.95887	−0.110899
$313$	−20.7355	−1.17204	−0.586021	−	0.810296i	$-0.699306\pi$
$313$	−20.7355	−1.17204	−0.586021	+	0.810296i	$0.699306\pi$
$314$	5.11619	0.288723
$315$	−24.3025	−1.36929
$316$	61.8593	3.47986
$317$	18.7532	1.05328	0.526641	−	0.850087i	$-0.323451\pi$
$317$	18.7532	1.05328	0.526641	+	0.850087i	$0.323451\pi$
$318$	−6.89938	−0.386898
$319$	−3.71532	−0.208018
$320$	−17.2306	−0.963218
$321$	1.08000	0.0602795
$322$	−46.5198	−2.59244
$323$	0.123550	0.00687451
$324$	28.1575	1.56430
$325$	1.47159	0.0816290
$326$	46.3318	2.56608
$327$	9.26918	0.512587
$328$	31.6147	1.74563
$329$	5.22936	0.288304
$330$	−12.6981	−0.699009
$331$	18.8583	1.03655	0.518274	−	0.855215i	$-0.326575\pi$
$331$	18.8583	1.03655	0.518274	+	0.855215i	$0.326575\pi$
$332$	−62.9865	−3.45683
$333$	25.5088	1.39787
$334$	−34.6460	−1.89575
$335$	15.1548	0.827997
$336$	7.79360	0.425176
$337$	−12.2484	−0.667211	−0.333605	−	0.942713i	$-0.608265\pi$
$337$	−12.2484	−0.667211	−0.333605	+	0.942713i	$0.608265\pi$
$338$	30.7304	1.67151
$339$	−7.17557	−0.389723
$340$	−1.14380	−0.0620314
$341$	16.1714	0.875732
$342$	−7.97379	−0.431173
$343$	−9.34222	−0.504432
$344$	19.5933	1.05640
$345$	7.34813	0.395610
$346$	63.7132	3.42524
$347$	−4.38543	−0.235422	−0.117711	−	0.993048i	$-0.537556\pi$
$347$	−4.38543	−0.235422	−0.117711	+	0.993048i	$0.537556\pi$
$348$	−1.93024	−0.103472
$349$	21.0962	1.12926	0.564628	−	0.825346i	$-0.309020\pi$
$349$	21.0962	1.12926	0.564628	+	0.825346i	$0.309020\pi$
$350$	−16.1198	−0.861640
$351$	−2.15717	−0.115141
$352$	−4.52289	−0.241071
$353$	21.5447	1.14671	0.573353	−	0.819308i	$-0.305642\pi$
$353$	21.5447	1.14671	0.573353	+	0.819308i	$0.305642\pi$
$354$	−13.0408	−0.693109
$355$	−23.9274	−1.26993
$356$	16.8047	0.890645
$357$	−0.175235	−0.00927444
$358$	−16.1302	−0.852507
$359$	−12.6947	−0.669999	−0.335000	−	0.942218i	$-0.608736\pi$
$359$	−12.6947	−0.669999	−0.335000	+	0.942218i	$0.608736\pi$
$360$	37.9259	1.99887
$361$	−17.6286	−0.927821
$362$	22.7635	1.19642
$363$	2.19593	0.115257
$364$	10.4073	0.545491
$365$	17.7402	0.928563
$366$	−15.0905	−0.788791
$367$	17.2665	0.901307	0.450653	−	0.892699i	$-0.351191\pi$
$367$	17.2665	0.901307	0.450653	+	0.892699i	$0.351191\pi$
$368$	26.3683	1.37454
$369$	16.6630	0.867442
$370$	60.3650	3.13823
$371$	18.8324	0.977732
$372$	8.40163	0.435604
$373$	3.64003	0.188473	0.0942367	−	0.995550i	$-0.469959\pi$
$373$	3.64003	0.188473	0.0942367	+	0.995550i	$0.469959\pi$
$374$	1.02454	0.0529777
$375$	−3.99171	−0.206131
$376$	−8.16082	−0.420862
$377$	−0.714861	−0.0368172
$378$	23.6297	1.21538
$379$	−36.9362	−1.89728	−0.948642	−	0.316352i	$-0.897542\pi$
$379$	−36.9362	−1.89728	−0.948642	+	0.316352i	$0.897542\pi$
$380$	−12.6962	−0.651300
$381$	3.25211	0.166611
$382$	11.3854	0.582529
$383$	28.8802	1.47571	0.737854	−	0.674960i	$-0.235839\pi$
$383$	28.8802	1.47571	0.737854	+	0.674960i	$0.235839\pi$
$384$	9.16104	0.467497
$385$	34.6607	1.76647
$386$	7.78010	0.395997
$387$	10.3269	0.524947
$388$	72.5996	3.68569
$389$	10.6974	0.542380	0.271190	−	0.962526i	$-0.412583\pi$
$389$	10.6974	0.542380	0.271190	+	0.962526i	$0.412583\pi$
$390$	−2.44324	−0.123718
$391$	−0.592879	−0.0299832
$392$	−21.9954	−1.11094
$393$	9.97767	0.503307
$394$	−47.5370	−2.39488
$395$	39.6396	1.99448
$396$	−44.4900	−2.23571
$397$	18.8432	0.945713	0.472856	−	0.881139i	$-0.343223\pi$
$397$	18.8432	0.945713	0.472856	+	0.881139i	$0.343223\pi$
$398$	−39.5759	−1.98376
$399$	−1.94511	−0.0973772
$400$	9.13702	0.456851
$401$	−15.8866	−0.793338	−0.396669	−	0.917962i	$-0.629834\pi$
$401$	−15.8866	−0.793338	−0.396669	+	0.917962i	$0.629834\pi$
$402$	−7.05251	−0.351747
$403$	3.11153	0.154997
$404$	−57.5456	−2.86300
$405$	18.0434	0.896582
$406$	7.83060	0.388626
$407$	−36.3811	−1.80334
$408$	0.273469	0.0135387
$409$	22.0297	1.08930	0.544649	−	0.838664i	$-0.316663\pi$
$409$	22.0297	1.08930	0.544649	+	0.838664i	$0.316663\pi$
$410$	39.4321	1.94741
$411$	−5.43031	−0.267857
$412$	64.2698	3.16634
$413$	35.5959	1.75156
$414$	38.2637	1.88056
$415$	−40.3619	−1.98129
$416$	−0.870246	−0.0426673
$417$	8.66481	0.424318
$418$	11.3724	0.556240
$419$	10.3666	0.506444	0.253222	−	0.967408i	$-0.418510\pi$
$419$	10.3666	0.506444	0.253222	+	0.967408i	$0.418510\pi$
$420$	18.0074	0.878672
$421$	25.4060	1.23821	0.619107	−	0.785307i	$-0.287495\pi$
$421$	25.4060	1.23821	0.619107	+	0.785307i	$0.287495\pi$
$422$	56.5546	2.75303
$423$	−4.30129	−0.209136
$424$	−29.3895	−1.42728
$425$	−0.205442	−0.00996538
$426$	11.1349	0.539489
$427$	41.1907	1.99336
$428$	8.95449	0.432832
$429$	1.47250	0.0710931
$430$	24.4381	1.17851
$431$	−16.4925	−0.794418	−0.397209	−	0.917728i	$-0.630021\pi$
$431$	−16.4925	−0.794418	−0.397209	+	0.917728i	$0.630021\pi$
$432$	−13.3938	−0.644409
$433$	−0.601567	−0.0289095	−0.0144547	−	0.999896i	$-0.504601\pi$
$433$	−0.601567	−0.0289095	−0.0144547	+	0.999896i	$0.504601\pi$
$434$	−34.0838	−1.63607
$435$	−1.23690	−0.0593048
$436$	76.8528	3.68058
$437$	−6.58094	−0.314809
$438$	−8.25564	−0.394470
$439$	27.3100	1.30343	0.651716	−	0.758463i	$-0.274049\pi$
$439$	27.3100	1.30343	0.651716	+	0.758463i	$0.274049\pi$
$440$	−54.0907	−2.57867
$441$	−11.5930	−0.552048
$442$	0.197131	0.00937656
$443$	4.92743	0.234109	0.117055	−	0.993125i	$-0.462655\pi$
$443$	4.92743	0.234109	0.117055	+	0.993125i	$0.462655\pi$
$444$	−18.9012	−0.897013
$445$	10.7685	0.510474
$446$	−46.3358	−2.19407
$447$	−9.85145	−0.465958
$448$	−21.8871	−1.03407
$449$	−6.46136	−0.304930	−0.152465	−	0.988309i	$-0.548721\pi$
$449$	−6.46136	−0.304930	−0.152465	+	0.988309i	$0.548721\pi$
$450$	13.2590	0.625034
$451$	−23.7651	−1.11906
$452$	−59.4943	−2.79837
$453$	10.4589	0.491404
$454$	−65.5455	−3.07620
$455$	6.66903	0.312649
$456$	3.03549	0.142150
$457$	29.3918	1.37489	0.687445	−	0.726236i	$-0.258732\pi$
$457$	29.3918	1.37489	0.687445	+	0.726236i	$0.258732\pi$
$458$	14.3457	0.670330
$459$	0.301153	0.0140566
$460$	60.9250	2.84064
$461$	−2.47840	−0.115430	−0.0577152	−	0.998333i	$-0.518382\pi$
$461$	−2.47840	−0.115430	−0.0577152	+	0.998333i	$0.518382\pi$
$462$	−16.1298	−0.750427
$463$	−13.1119	−0.609361	−0.304681	−	0.952455i	$-0.598550\pi$
$463$	−13.1119	−0.609361	−0.304681	+	0.952455i	$0.598550\pi$
$464$	−4.43854	−0.206054
$465$	5.38378	0.249667
$466$	28.2192	1.30723
$467$	−0.857019	−0.0396581	−0.0198291	−	0.999803i	$-0.506312\pi$
$467$	−0.857019	−0.0396581	−0.0198291	+	0.999803i	$0.506312\pi$
$468$	−8.56029	−0.395699
$469$	19.2504	0.888903
$470$	−10.1787	−0.469511
$471$	−1.02654	−0.0473005
$472$	−55.5502	−2.55691
$473$	−14.7285	−0.677215
$474$	−18.4468	−0.847291
$475$	−2.28040	−0.104632
$476$	−1.45292	−0.0665943
$477$	−15.4902	−0.709247
$478$	46.9496	2.14742
$479$	−5.81040	−0.265484	−0.132742	−	0.991151i	$-0.542378\pi$
$479$	−5.81040	−0.265484	−0.132742	+	0.991151i	$0.542378\pi$
$480$	−1.50576	−0.0687281
$481$	−7.00006	−0.319175
$482$	63.3116	2.88377
$483$	9.33397	0.424710
$484$	18.2070	0.827589
$485$	46.5220	2.11246
$486$	−29.5697	−1.34131
$487$	34.8474	1.57909	0.789544	−	0.613694i	$-0.210317\pi$
$487$	34.8474	1.57909	0.789544	+	0.613694i	$0.210317\pi$
$488$	−64.2814	−2.90988
$489$	−9.29627	−0.420392
$490$	−27.4342	−1.23935
$491$	−22.1808	−1.00101	−0.500503	−	0.865735i	$-0.666852\pi$
$491$	−22.1808	−1.00101	−0.500503	+	0.865735i	$0.666852\pi$
$492$	−12.3468	−0.556637
$493$	0.0997984	0.00449469
$494$	2.18815	0.0984494
$495$	−28.5093	−1.28140
$496$	19.3194	0.867465
$497$	−30.3938	−1.36335
$498$	18.7830	0.841685
$499$	−23.6274	−1.05771	−0.528853	−	0.848713i	$-0.677378\pi$
$499$	−23.6274	−1.05771	−0.528853	+	0.848713i	$0.677378\pi$
$500$	−33.0962	−1.48011
$501$	6.95157	0.310573
$502$	71.4588	3.18936
$503$	20.3956	0.909394	0.454697	−	0.890646i	$-0.349747\pi$
$503$	20.3956	0.909394	0.454697	+	0.890646i	$0.349747\pi$
$504$	48.1754	2.14590
$505$	−36.8754	−1.64093
$506$	−54.5725	−2.42604
$507$	−6.16591	−0.273838
$508$	26.9640	1.19633
$509$	−19.9018	−0.882131	−0.441065	−	0.897475i	$-0.645399\pi$
$509$	−19.9018	−0.882131	−0.441065	+	0.897475i	$0.645399\pi$
$510$	0.341089	0.0151037
$511$	22.5345	0.996866
$512$	43.6298	1.92818
$513$	3.34279	0.147588
$514$	−30.8105	−1.35899
$515$	41.1842	1.81479
$516$	−7.65195	−0.336858
$517$	6.13458	0.269798
$518$	76.6787	3.36907
$519$	−12.7838	−0.561145
$520$	−10.4075	−0.456401
$521$	18.5240	0.811550	0.405775	−	0.913973i	$-0.367002\pi$
$521$	18.5240	0.811550	0.405775	+	0.913973i	$0.367002\pi$
$522$	−6.44088	−0.281910
$523$	−32.6775	−1.42889	−0.714445	−	0.699692i	$-0.753321\pi$
$523$	−32.6775	−1.42889	−0.714445	+	0.699692i	$0.753321\pi$
$524$	82.7271	3.61395
$525$	3.23436	0.141159
$526$	−41.3170	−1.80151
$527$	−0.434386	−0.0189222
$528$	9.14270	0.397885
$529$	8.57990	0.373039
$530$	−36.6566	−1.59226
$531$	−29.2786	−1.27058
$532$	−16.1273	−0.699208
$533$	−4.57263	−0.198063
$534$	−5.01126	−0.216858
$535$	5.73806	0.248078
$536$	−30.0418	−1.29761
$537$	3.23645	0.139663
$538$	40.5018	1.74616
$539$	16.5342	0.712177
$540$	−30.9468	−1.33174
$541$	27.6267	1.18776	0.593882	−	0.804552i	$-0.297595\pi$
$541$	27.6267	1.18776	0.593882	+	0.804552i	$0.297595\pi$
$542$	17.8167	0.765295
$543$	−4.56740	−0.196006
$544$	0.121491	0.00520888
$545$	49.2475	2.10953
$546$	−3.10352	−0.132819
$547$	10.1172	0.432582	0.216291	−	0.976329i	$-0.430604\pi$
$547$	10.1172	0.432582	0.216291	+	0.976329i	$0.430604\pi$
$548$	−45.0239	−1.92332
$549$	−33.8805	−1.44598
$550$	−18.9102	−0.806333
$551$	1.10776	0.0471921
$552$	−14.5664	−0.619987
$553$	50.3522	2.14119
$554$	48.3442	2.05395
$555$	−12.1120	−0.514124
$556$	71.8419	3.04677
$557$	−17.6928	−0.749667	−0.374834	−	0.927092i	$-0.622300\pi$
$557$	−17.6928	−0.749667	−0.374834	+	0.927092i	$0.622300\pi$
$558$	28.0348	1.18681
$559$	−2.83389	−0.119861
$560$	41.4077	1.74979
$561$	−0.205569	−0.00867913
$562$	−17.8529	−0.753080
$563$	2.69537	0.113596	0.0567981	−	0.998386i	$-0.481911\pi$
$563$	2.69537	0.113596	0.0567981	+	0.998386i	$0.481911\pi$
$564$	3.18713	0.134202
$565$	−38.1241	−1.60389
$566$	18.1578	0.763229
$567$	22.9196	0.962533
$568$	47.4319	1.99020
$569$	−18.4348	−0.772827	−0.386413	−	0.922326i	$-0.626286\pi$
$569$	−18.4348	−0.772827	−0.386413	+	0.922326i	$0.626286\pi$
$570$	3.78608	0.158581
$571$	−26.5493	−1.11105	−0.555526	−	0.831499i	$-0.687483\pi$
$571$	−26.5493	−1.11105	−0.555526	+	0.831499i	$0.687483\pi$
$572$	12.2088	0.510477
$573$	−2.28443	−0.0954335
$574$	50.0886	2.09066
$575$	10.9429	0.456351
$576$	18.0028	0.750115
$577$	−3.64707	−0.151830	−0.0759148	−	0.997114i	$-0.524188\pi$
$577$	−3.64707	−0.151830	−0.0759148	+	0.997114i	$0.524188\pi$
$578$	42.0049	1.74717
$579$	−1.56104	−0.0648747
$580$	−10.2554	−0.425833
$581$	−51.2697	−2.12703
$582$	−21.6497	−0.897408
$583$	22.0924	0.914974
$584$	−35.1668	−1.45521
$585$	−5.48545	−0.226796
$586$	23.4035	0.966788
$587$	−9.53340	−0.393486	−0.196743	−	0.980455i	$-0.563036\pi$
$587$	−9.53340	−0.393486	−0.196743	+	0.980455i	$0.563036\pi$
$588$	8.59008	0.354249
$589$	−4.82168	−0.198674
$590$	−69.2861	−2.85246
$591$	9.53808	0.392344
$592$	−43.4630	−1.78632
$593$	−30.3290	−1.24546	−0.622731	−	0.782436i	$-0.713977\pi$
$593$	−30.3290	−1.24546	−0.622731	+	0.782436i	$0.713977\pi$
$594$	27.7201	1.13737
$595$	−0.931032	−0.0381686
$596$	−81.6806	−3.34577
$597$	7.94072	0.324992
$598$	−10.5002	−0.429387
$599$	−10.9233	−0.446314	−0.223157	−	0.974783i	$-0.571636\pi$
$599$	−10.9233	−0.446314	−0.223157	+	0.974783i	$0.571636\pi$
$600$	−5.04748	−0.206062
$601$	11.5877	0.472671	0.236336	−	0.971671i	$-0.424054\pi$
$601$	11.5877	0.472671	0.236336	+	0.971671i	$0.424054\pi$
$602$	31.0425	1.26520
$603$	−15.8340	−0.644810
$604$	86.7173	3.52848
$605$	11.6671	0.474334
$606$	17.1605	0.697097
$607$	6.03636	0.245008	0.122504	−	0.992468i	$-0.460908\pi$
$607$	6.03636	0.245008	0.122504	+	0.992468i	$0.460908\pi$
$608$	1.34855	0.0546908
$609$	−1.57117	−0.0636672
$610$	−80.1762	−3.24624
$611$	1.18035	0.0477518
$612$	1.19506	0.0483075
$613$	−2.67163	−0.107906	−0.0539530	−	0.998543i	$-0.517182\pi$
$613$	−2.67163	−0.107906	−0.0539530	+	0.998543i	$0.517182\pi$
$614$	−21.8079	−0.880095
$615$	−7.91187	−0.319037
$616$	−68.7087	−2.76835
$617$	−8.75672	−0.352532	−0.176266	−	0.984343i	$-0.556402\pi$
$617$	−8.75672	−0.352532	−0.176266	+	0.984343i	$0.556402\pi$
$618$	−19.1656	−0.770955
$619$	6.40415	0.257405	0.128702	−	0.991683i	$-0.458919\pi$
$619$	6.40415	0.257405	0.128702	+	0.991683i	$0.458919\pi$
$620$	44.6381	1.79271
$621$	−16.0410	−0.643703
$622$	−2.35175	−0.0942964
$623$	13.6787	0.548024
$624$	1.75914	0.0704219
$625$	−30.9445	−1.23778
$626$	51.2685	2.04910
$627$	−2.28181	−0.0911268
$628$	−8.51127	−0.339637
$629$	0.977245	0.0389653
$630$	60.0878	2.39395
$631$	−32.9109	−1.31016	−0.655081	−	0.755559i	$-0.727365\pi$
$631$	−32.9109	−1.31016	−0.655081	+	0.755559i	$0.727365\pi$
$632$	−78.5786	−3.12569
$633$	−11.3474	−0.451019
$634$	−46.3671	−1.84147
$635$	17.2786	0.685680
$636$	11.4778	0.455123
$637$	3.18133	0.126049
$638$	9.18610	0.363681
$639$	24.9997	0.988972
$640$	48.6729	1.92397
$641$	−10.0646	−0.397527	−0.198763	−	0.980047i	$-0.563693\pi$
$641$	−10.0646	−0.397527	−0.198763	+	0.980047i	$0.563693\pi$
$642$	−2.67029	−0.105388
$643$	−13.8610	−0.546623	−0.273312	−	0.961926i	$-0.588119\pi$
$643$	−13.8610	−0.546623	−0.273312	+	0.961926i	$0.588119\pi$
$644$	77.3900	3.04960
$645$	−4.90339	−0.193071
$646$	−0.305477	−0.0120188
$647$	17.5198	0.688774	0.344387	−	0.938828i	$-0.388087\pi$
$647$	17.5198	0.688774	0.344387	+	0.938828i	$0.388087\pi$
$648$	−35.7678	−1.40509
$649$	41.7577	1.63913
$650$	−3.63849	−0.142714
$651$	6.83875	0.268032
$652$	−77.0774	−3.01859
$653$	−11.4749	−0.449048	−0.224524	−	0.974469i	$-0.572083\pi$
$653$	−11.4749	−0.449048	−0.224524	+	0.974469i	$0.572083\pi$
$654$	−22.9180	−0.896165
$655$	53.0117	2.07134
$656$	−28.3912	−1.10849
$657$	−18.5352	−0.723127
$658$	−12.9296	−0.504047
$659$	40.2214	1.56680	0.783402	−	0.621515i	$-0.213482\pi$
$659$	40.2214	1.56680	0.783402	+	0.621515i	$0.213482\pi$
$660$	21.1246	0.822272
$661$	17.9585	0.698504	0.349252	−	0.937029i	$-0.386436\pi$
$661$	17.9585	0.698504	0.349252	+	0.937029i	$0.386436\pi$
$662$	−46.6272	−1.81222
$663$	−0.0395534	−0.00153613
$664$	80.0105	3.10501
$665$	−10.3344	−0.400752
$666$	−63.0703	−2.44392
$667$	−5.31580	−0.205828
$668$	57.6370	2.23004
$669$	9.29707	0.359446
$670$	−37.4703	−1.44760
$671$	48.3210	1.86541
$672$	−1.91269	−0.0737836
$673$	44.6266	1.72023	0.860114	−	0.510101i	$-0.170392\pi$
$673$	44.6266	1.72023	0.860114	+	0.510101i	$0.170392\pi$
$674$	30.2840	1.16650
$675$	−5.55845	−0.213945
$676$	−51.1229	−1.96627
$677$	−8.00580	−0.307688	−0.153844	−	0.988095i	$-0.549165\pi$
$677$	−8.00580	−0.307688	−0.153844	+	0.988095i	$0.549165\pi$
$678$	17.7416	0.681360
$679$	59.0946	2.26784
$680$	1.45295	0.0557180
$681$	13.1514	0.503963
$682$	−39.9838	−1.53106
$683$	−15.0576	−0.576162	−0.288081	−	0.957606i	$-0.593017\pi$
$683$	−15.0576	−0.576162	−0.288081	+	0.957606i	$0.593017\pi$
$684$	13.2652	0.507206
$685$	−28.8514	−1.10236
$686$	23.0986	0.881908
$687$	−2.87840	−0.109818
$688$	−17.5955	−0.670822
$689$	4.25078	0.161942
$690$	−18.1682	−0.691653
$691$	−34.0869	−1.29673	−0.648363	−	0.761331i	$-0.724546\pi$
$691$	−34.0869	−1.29673	−0.648363	+	0.761331i	$0.724546\pi$
$692$	−105.993	−4.02925
$693$	−36.2140	−1.37565
$694$	10.8430	0.411593
$695$	46.0365	1.74626
$696$	2.45194	0.0929405
$697$	0.638363	0.0241797
$698$	−52.1603	−1.97430
$699$	−5.66205	−0.214158
$700$	26.8168	1.01358
$701$	16.7130	0.631240	0.315620	−	0.948886i	$-0.397788\pi$
$701$	16.7130	0.631240	0.315620	+	0.948886i	$0.397788\pi$
$702$	5.33360	0.201304
$703$	10.8474	0.409117
$704$	−25.6759	−0.967696
$705$	2.04232	0.0769182
$706$	−53.2691	−2.00481
$707$	−46.8410	−1.76164
$708$	21.6946	0.815332
$709$	30.2917	1.13763	0.568814	−	0.822466i	$-0.307402\pi$
$709$	30.2917	1.13763	0.568814	+	0.822466i	$0.307402\pi$
$710$	59.1603	2.22025
$711$	−41.4160	−1.55322
$712$	−21.3466	−0.799998
$713$	23.1377	0.866515
$714$	0.433268	0.0162147
$715$	7.82346	0.292581
$716$	26.8341	1.00284
$717$	−9.42021	−0.351804
$718$	31.3875	1.17137
$719$	−4.03793	−0.150589	−0.0752947	−	0.997161i	$-0.523990\pi$
$719$	−4.03793	−0.150589	−0.0752947	+	0.997161i	$0.523990\pi$
$720$	−34.0589	−1.26930
$721$	52.3143	1.94829
$722$	43.5866	1.62213
$723$	−12.7032	−0.472436
$724$	−37.8693	−1.40740
$725$	−1.84200	−0.0684103
$726$	−5.42943	−0.201505
$727$	10.4292	0.386798	0.193399	−	0.981120i	$-0.438049\pi$
$727$	10.4292	0.386798	0.193399	+	0.981120i	$0.438049\pi$
$728$	−13.2202	−0.489973
$729$	−14.6037	−0.540878
$730$	−43.8625	−1.62342
$731$	0.395626	0.0146328
$732$	25.1044	0.927886
$733$	−9.67843	−0.357481	−0.178741	−	0.983896i	$-0.557202\pi$
$733$	−9.67843	−0.357481	−0.178741	+	0.983896i	$0.557202\pi$
$734$	−42.6915	−1.57577
$735$	5.50454	0.203038
$736$	−6.47126	−0.238534
$737$	22.5828	0.831846
$738$	−41.1992	−1.51657
$739$	−40.5729	−1.49250	−0.746249	−	0.665666i	$-0.768147\pi$
$739$	−40.5729	−1.49250	−0.746249	+	0.665666i	$0.768147\pi$
$740$	−100.423	−3.69162
$741$	−0.439042	−0.0161286
$742$	−46.5631	−1.70939
$743$	8.88134	0.325825	0.162912	−	0.986641i	$-0.447911\pi$
$743$	8.88134	0.325825	0.162912	+	0.986641i	$0.447911\pi$
$744$	−10.6724	−0.391270
$745$	−52.3411	−1.91763
$746$	−8.99995	−0.329512
$747$	42.1707	1.54295
$748$	−1.70442	−0.0623197
$749$	7.28877	0.266326
$750$	9.86949	0.360383
$751$	−37.6287	−1.37309	−0.686545	−	0.727087i	$-0.740873\pi$
$751$	−37.6287	−1.37309	−0.686545	+	0.727087i	$0.740873\pi$
$752$	7.32873	0.267251
$753$	−14.3379	−0.522501
$754$	1.76749	0.0643682
$755$	55.5687	2.02235
$756$	−39.3103	−1.42970
$757$	35.0567	1.27416	0.637078	−	0.770799i	$-0.280143\pi$
$757$	35.0567	1.27416	0.637078	+	0.770799i	$0.280143\pi$
$758$	91.3245	3.31706
$759$	10.9497	0.397449
$760$	16.1277	0.585013
$761$	−20.8928	−0.757364	−0.378682	−	0.925527i	$-0.623623\pi$
$761$	−20.8928	−0.757364	−0.378682	+	0.925527i	$0.623623\pi$
$762$	−8.04083	−0.291289
$763$	62.5567	2.26470
$764$	−18.9407	−0.685251
$765$	0.765798	0.0276875
$766$	−71.4061	−2.58001
$767$	8.03456	0.290111
$768$	−16.1645	−0.583285
$769$	25.5493	0.921331	0.460665	−	0.887574i	$-0.347611\pi$
$769$	25.5493	0.921331	0.460665	+	0.887574i	$0.347611\pi$
$770$	−85.6983	−3.08835
$771$	6.18198	0.222639
$772$	−12.9429	−0.465827
$773$	−38.5254	−1.38566	−0.692832	−	0.721099i	$-0.743637\pi$
$773$	−38.5254	−1.38566	−0.692832	+	0.721099i	$0.743637\pi$
$774$	−25.5333	−0.917775
$775$	8.01758	0.288000
$776$	−92.2218	−3.31057
$777$	−15.3852	−0.551942
$778$	−26.4493	−0.948253
$779$	7.08581	0.253876
$780$	4.06456	0.145535
$781$	−35.6550	−1.27584
$782$	1.46589	0.0524201
$783$	2.70016	0.0964957
$784$	19.7527	0.705454
$785$	−5.45405	−0.194663
$786$	−24.6697	−0.879941
$787$	15.9637	0.569046	0.284523	−	0.958669i	$-0.408165\pi$
$787$	15.9637	0.569046	0.284523	+	0.958669i	$0.408165\pi$
$788$	79.0823	2.81719
$789$	8.29006	0.295134
$790$	−98.0087	−3.48699
$791$	−48.4271	−1.72187
$792$	56.5147	2.00816
$793$	9.29740	0.330160
$794$	−46.5897	−1.65341
$795$	7.35498	0.260854
$796$	65.8383	2.33358
$797$	−1.05354	−0.0373184	−0.0186592	−	0.999826i	$-0.505940\pi$
$797$	−1.05354	−0.0373184	−0.0186592	+	0.999826i	$0.505940\pi$
$798$	4.80927	0.170246
$799$	−0.164783	−0.00582960
$800$	−2.24239	−0.0792804
$801$	−11.2511	−0.397537
$802$	39.2795	1.38701
$803$	26.4353	0.932880
$804$	11.7325	0.413774
$805$	49.5917	1.74788
$806$	−7.69325	−0.270983
$807$	−8.12650	−0.286066
$808$	73.0991	2.57162
$809$	−3.33641	−0.117302	−0.0586509	−	0.998279i	$-0.518680\pi$
$809$	−3.33641	−0.117302	−0.0586509	+	0.998279i	$0.518680\pi$
$810$	−44.6121	−1.56751
$811$	27.8552	0.978130	0.489065	−	0.872247i	$-0.337338\pi$
$811$	27.8552	0.978130	0.489065	+	0.872247i	$0.337338\pi$
$812$	−13.0270	−0.457156
$813$	−3.57485	−0.125375
$814$	89.9520	3.15282
$815$	−49.3914	−1.73011
$816$	−0.245585	−0.00859720
$817$	4.39144	0.153637
$818$	−54.4683	−1.90444
$819$	−6.96790	−0.243478
$820$	−65.5991	−2.29082
$821$	37.8753	1.32186	0.660929	−	0.750449i	$-0.270163\pi$
$821$	37.8753	1.32186	0.660929	+	0.750449i	$0.270163\pi$
$822$	13.4264	0.468300
$823$	8.18496	0.285310	0.142655	−	0.989772i	$-0.454436\pi$
$823$	8.18496	0.285310	0.142655	+	0.989772i	$0.454436\pi$
$824$	−81.6406	−2.84408
$825$	3.79424	0.132099
$826$	−88.0107	−3.06228
$827$	−49.8538	−1.73359	−0.866794	−	0.498666i	$-0.833823\pi$
$827$	−49.8538	−1.73359	−0.866794	+	0.498666i	$0.833823\pi$
$828$	−63.6554	−2.21218
$829$	−30.0281	−1.04292	−0.521459	−	0.853276i	$-0.674612\pi$
$829$	−30.0281	−1.04292	−0.521459	+	0.853276i	$0.674612\pi$
$830$	99.7946	3.46392
$831$	−9.70004	−0.336491
$832$	−4.94027	−0.171273
$833$	−0.444130	−0.0153882
$834$	−21.4237	−0.741842
$835$	36.9339	1.27815
$836$	−18.9190	−0.654328
$837$	−11.7528	−0.406237
$838$	−25.6315	−0.885425
$839$	−45.9351	−1.58586	−0.792928	−	0.609316i	$-0.791444\pi$
$839$	−45.9351	−1.58586	−0.792928	+	0.609316i	$0.791444\pi$
$840$	−22.8745	−0.789244
$841$	−28.1052	−0.969145
$842$	−62.8163	−2.16479
$843$	3.58211	0.123374
$844$	−94.0839	−3.23850
$845$	−32.7597	−1.12697
$846$	10.6349	0.365636
$847$	14.8201	0.509225
$848$	26.3929	0.906336
$849$	−3.64328	−0.125037
$850$	0.507953	0.0174226
$851$	−52.0533	−1.78436
$852$	−18.5240	−0.634623
$853$	30.8161	1.05512	0.527561	−	0.849517i	$-0.323107\pi$
$853$	30.8161	1.05512	0.527561	+	0.849517i	$0.323107\pi$
$854$	−101.844	−3.48502
$855$	8.50034	0.290706
$856$	−11.3747	−0.388779
$857$	3.17028	0.108295	0.0541473	−	0.998533i	$-0.482756\pi$
$857$	3.17028	0.108295	0.0541473	+	0.998533i	$0.482756\pi$
$858$	−3.64075	−0.124293
$859$	−16.4535	−0.561385	−0.280692	−	0.959798i	$-0.590564\pi$
$859$	−16.4535	−0.561385	−0.280692	+	0.959798i	$0.590564\pi$
$860$	−40.6551	−1.38633
$861$	−10.0501	−0.342505
$862$	40.7777	1.38889
$863$	−38.9331	−1.32530	−0.662649	−	0.748930i	$-0.730568\pi$
$863$	−38.9331	−1.32530	−0.662649	+	0.748930i	$0.730568\pi$
$864$	3.28707	0.111828
$865$	−67.9206	−2.30937
$866$	1.48737	0.0505430
$867$	−8.42809	−0.286233
$868$	56.7016	1.92458
$869$	59.0683	2.00376
$870$	3.05823	0.103684
$871$	4.34513	0.147229
$872$	−97.6246	−3.30599
$873$	−48.6069	−1.64509
$874$	16.2713	0.550386
$875$	−26.9396	−0.910725
$876$	13.7340	0.464030
$877$	6.33229	0.213826	0.106913	−	0.994268i	$-0.465903\pi$
$877$	6.33229	0.213826	0.106913	+	0.994268i	$0.465903\pi$
$878$	−67.5237	−2.27882
$879$	−4.69580	−0.158385
$880$	48.5755	1.63748
$881$	32.6580	1.10028	0.550139	−	0.835073i	$-0.314575\pi$
$881$	32.6580	1.10028	0.550139	+	0.835073i	$0.314575\pi$
$882$	28.6637	0.965155
$883$	−15.1040	−0.508289	−0.254145	−	0.967166i	$-0.581794\pi$
$883$	−15.1040	−0.508289	−0.254145	+	0.967166i	$0.581794\pi$
$884$	−0.327946	−0.0110300
$885$	13.9019	0.467308
$886$	−12.1830	−0.409298
$887$	−40.4864	−1.35940	−0.679700	−	0.733491i	$-0.737890\pi$
$887$	−40.4864	−1.35940	−0.679700	+	0.733491i	$0.737890\pi$
$888$	24.0099	0.805718
$889$	21.9481	0.736117
$890$	−26.6250	−0.892472
$891$	26.8871	0.900750
$892$	77.0841	2.58097
$893$	−1.82909	−0.0612080
$894$	24.3577	0.814642
$895$	17.1954	0.574777
$896$	61.8268	2.06549
$897$	2.10683	0.0703448
$898$	15.9757	0.533115
$899$	−3.89474	−0.129897
$900$	−22.0576	−0.735252
$901$	−0.593431	−0.0197701
$902$	58.7591	1.95647
$903$	−6.22853	−0.207273
$904$	75.5743	2.51356
$905$	−24.2667	−0.806654
$906$	−25.8597	−0.859130
$907$	28.2010	0.936399	0.468199	−	0.883623i	$-0.344903\pi$
$907$	28.2010	0.936399	0.468199	+	0.883623i	$0.344903\pi$
$908$	109.041	3.61866
$909$	38.5280	1.27789
$910$	−16.4891	−0.546610
$911$	7.86351	0.260530	0.130265	−	0.991479i	$-0.458417\pi$
$911$	7.86351	0.260530	0.130265	+	0.991479i	$0.458417\pi$
$912$	−2.72599	−0.0902665
$913$	−60.1447	−1.99050
$914$	−72.6711	−2.40375
$915$	16.0870	0.531819
$916$	−23.8654	−0.788536
$917$	67.3382	2.22370
$918$	−0.744598	−0.0245754
$919$	42.2837	1.39481	0.697406	−	0.716676i	$-0.254337\pi$
$919$	42.2837	1.39481	0.697406	+	0.716676i	$0.254337\pi$
$920$	−77.3918	−2.55153
$921$	4.37565	0.144183
$922$	6.12782	0.201809
$923$	−6.86035	−0.225811
$924$	26.8335	0.882757
$925$	−18.0373	−0.593061
$926$	32.4191	1.06536
$927$	−43.0299	−1.41329
$928$	1.08930	0.0357579
$929$	−9.25791	−0.303742	−0.151871	−	0.988400i	$-0.548530\pi$
$929$	−9.25791	−0.303742	−0.151871	+	0.988400i	$0.548530\pi$
$930$	−13.3114	−0.436497
$931$	−4.92983	−0.161569
$932$	−46.9453	−1.53774
$933$	0.471867	0.0154482
$934$	2.11897	0.0693350
$935$	−1.09220	−0.0357186
$936$	10.8740	0.355426
$937$	−23.2462	−0.759421	−0.379710	−	0.925105i	$-0.623976\pi$
$937$	−23.2462	−0.759421	−0.379710	+	0.925105i	$0.623976\pi$
$938$	−47.5966	−1.55408
$939$	−10.2868	−0.335697
$940$	16.9333	0.552304
$941$	49.6685	1.61915	0.809574	−	0.587018i	$-0.199698\pi$
$941$	49.6685	1.61915	0.809574	+	0.587018i	$0.199698\pi$
$942$	2.53812	0.0826963
$943$	−34.0026	−1.10728
$944$	49.8862	1.62366
$945$	−25.1901	−0.819434
$946$	36.4160	1.18399
$947$	6.30487	0.204881	0.102440	−	0.994739i	$-0.467335\pi$
$947$	6.30487	0.204881	0.102440	+	0.994739i	$0.467335\pi$
$948$	30.6881	0.996702
$949$	5.08639	0.165111
$950$	5.63827	0.182930
$951$	9.30335	0.301682
$952$	1.84561	0.0598165
$953$	−28.4229	−0.920709	−0.460355	−	0.887735i	$-0.652278\pi$
$953$	−28.4229	−0.920709	−0.460355	+	0.887735i	$0.652278\pi$
$954$	38.2994	1.23999
$955$	−12.1373	−0.392753
$956$	−78.1051	−2.52610
$957$	−1.84315	−0.0595805
$958$	14.3662	0.464150
$959$	−36.6485	−1.18344
$960$	−8.54799	−0.275885
$961$	−14.0476	−0.453148
$962$	17.3076	0.558019
$963$	−5.99521	−0.193193
$964$	−105.325	−3.39229
$965$	−8.29387	−0.266989
$966$	−23.0782	−0.742529
$967$	2.01733	0.0648729	0.0324365	−	0.999474i	$-0.489673\pi$
$967$	2.01733	0.0648729	0.0324365	+	0.999474i	$0.489673\pi$
$968$	−23.1279	−0.743360
$969$	0.0612925	0.00196900
$970$	−115.026	−3.69325
$971$	32.8261	1.05344	0.526720	−	0.850039i	$-0.323422\pi$
$971$	32.8261	1.05344	0.526720	+	0.850039i	$0.323422\pi$
$972$	49.1921	1.57784
$973$	58.4778	1.87471
$974$	−86.1601	−2.76075
$975$	0.730047	0.0233802
$976$	57.7271	1.84780
$977$	23.9141	0.765080	0.382540	−	0.923939i	$-0.375049\pi$
$977$	23.9141	0.765080	0.382540	+	0.923939i	$0.375049\pi$
$978$	22.9850	0.734979
$979$	16.0465	0.512847
$980$	45.6394	1.45790
$981$	−51.4545	−1.64282
$982$	54.8420	1.75008
$983$	25.0094	0.797677	0.398838	−	0.917021i	$-0.369413\pi$
$983$	25.0094	0.797677	0.398838	+	0.917021i	$0.369413\pi$
$984$	15.6839	0.499984
$985$	50.6762	1.61468
$986$	−0.246751	−0.00785815
$987$	2.59426	0.0825761
$988$	−3.64019	−0.115810
$989$	−21.0732	−0.670088
$990$	70.4891	2.24029
$991$	−36.3212	−1.15378	−0.576890	−	0.816822i	$-0.695734\pi$
$991$	−36.3212	−1.15378	−0.576890	+	0.816822i	$0.695734\pi$
$992$	−4.74132	−0.150537
$993$	9.35552	0.296889
$994$	75.1484	2.38356
$995$	42.1894	1.33749
$996$	−31.2473	−0.990108
$997$	−44.4145	−1.40662	−0.703310	−	0.710883i	$-0.748296\pi$
$997$	−44.4145	−1.40662	−0.703310	+	0.710883i	$0.748296\pi$
$998$	58.4185	1.84921
$999$	26.4404	0.836539

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4007.2.a.b.1.16	✓	195

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4007.2.a.b.1.16	✓	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)

\(f(q)\)	\(=\)	\(q-2.47249 q^{2} +0.496095 q^{3} +4.11323 q^{4} +2.63577 q^{5} -1.22659 q^{6} +3.34809 q^{7} -5.22495 q^{8} -2.75389 q^{9} +O(q^{10})\)	\(q-2.47249 q^{2} +0.496095 q^{3} +4.11323 q^{4} +2.63577 q^{5} -1.22659 q^{6} +3.34809 q^{7} -5.22495 q^{8} -2.75389 q^{9} -6.51692 q^{10} +3.92765 q^{11} +2.04055 q^{12} +0.755716 q^{13} -8.27813 q^{14} +1.30759 q^{15} +4.69221 q^{16} -0.105502 q^{17} +6.80898 q^{18} -1.17107 q^{19} +10.8415 q^{20} +1.66097 q^{21} -9.71110 q^{22} +5.61960 q^{23} -2.59207 q^{24} +1.94728 q^{25} -1.86850 q^{26} -2.85447 q^{27} +13.7715 q^{28} -0.945939 q^{29} -3.23301 q^{30} +4.11733 q^{31} -1.15155 q^{32} +1.94849 q^{33} +0.260853 q^{34} +8.82478 q^{35} -11.3274 q^{36} -9.26281 q^{37} +2.89546 q^{38} +0.374907 q^{39} -13.7718 q^{40} -6.05072 q^{41} -4.10673 q^{42} -3.74994 q^{43} +16.1553 q^{44} -7.25862 q^{45} -13.8944 q^{46} +1.56189 q^{47} +2.32778 q^{48} +4.20968 q^{49} -4.81463 q^{50} -0.0523390 q^{51} +3.10843 q^{52} +5.62484 q^{53} +7.05767 q^{54} +10.3524 q^{55} -17.4936 q^{56} -0.580961 q^{57} +2.33883 q^{58} +10.6317 q^{59} +5.37842 q^{60} +12.3028 q^{61} -10.1801 q^{62} -9.22026 q^{63} -6.53721 q^{64} +1.99189 q^{65} -4.81762 q^{66} +5.74969 q^{67} -0.433954 q^{68} +2.78785 q^{69} -21.8192 q^{70} -9.07795 q^{71} +14.3889 q^{72} +6.73055 q^{73} +22.9023 q^{74} +0.966033 q^{75} -4.81688 q^{76} +13.1501 q^{77} -0.926955 q^{78} +15.0391 q^{79} +12.3676 q^{80} +6.84558 q^{81} +14.9604 q^{82} -15.3131 q^{83} +6.83194 q^{84} -0.278079 q^{85} +9.27171 q^{86} -0.469275 q^{87} -20.5218 q^{88} +4.08551 q^{89} +17.9469 q^{90} +2.53020 q^{91} +23.1147 q^{92} +2.04259 q^{93} -3.86178 q^{94} -3.08667 q^{95} -0.571278 q^{96} +17.6503 q^{97} -10.4084 q^{98} -10.8163 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 195 q + 14 q^{2} + 22 q^{3} + 220 q^{4} + 14 q^{5} + 13 q^{6} + 48 q^{7} + 39 q^{8} + 245 q^{9}+O(q^{10}) \) 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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