LMFDB - Embedded newform 4007.2.a.b.1.12

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			1.12
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)

$f(q)$	$=$	$q-2.58803 q^{2} +0.217741 q^{3} +4.69789 q^{4} -3.50376 q^{5} -0.563520 q^{6} +3.48169 q^{7} -6.98221 q^{8} -2.95259 q^{9} +O(q^{10})$	\(q-2.58803 q^{2} +0.217741 q^{3} +4.69789 q^{4} -3.50376 q^{5} -0.563520 q^{6} +3.48169 q^{7} -6.98221 q^{8} -2.95259 q^{9} +9.06783 q^{10} +2.01611 q^{11} +1.02292 q^{12} -3.23824 q^{13} -9.01070 q^{14} -0.762912 q^{15} +8.67439 q^{16} -2.69049 q^{17} +7.64138 q^{18} -5.60494 q^{19} -16.4603 q^{20} +0.758106 q^{21} -5.21775 q^{22} -8.73576 q^{23} -1.52031 q^{24} +7.27632 q^{25} +8.38067 q^{26} -1.29612 q^{27} +16.3566 q^{28} -4.60270 q^{29} +1.97444 q^{30} -7.56059 q^{31} -8.48513 q^{32} +0.438990 q^{33} +6.96306 q^{34} -12.1990 q^{35} -13.8709 q^{36} +4.57216 q^{37} +14.5057 q^{38} -0.705098 q^{39} +24.4640 q^{40} +8.95960 q^{41} -1.96200 q^{42} -3.92387 q^{43} +9.47146 q^{44} +10.3452 q^{45} +22.6084 q^{46} +1.68707 q^{47} +1.88877 q^{48} +5.12215 q^{49} -18.8313 q^{50} -0.585830 q^{51} -15.2129 q^{52} -3.33422 q^{53} +3.35440 q^{54} -7.06396 q^{55} -24.3099 q^{56} -1.22043 q^{57} +11.9119 q^{58} -9.30415 q^{59} -3.58408 q^{60} +10.9909 q^{61} +19.5670 q^{62} -10.2800 q^{63} +4.61098 q^{64} +11.3460 q^{65} -1.13612 q^{66} +10.9468 q^{67} -12.6396 q^{68} -1.90213 q^{69} +31.5713 q^{70} -8.43776 q^{71} +20.6156 q^{72} +3.35436 q^{73} -11.8329 q^{74} +1.58435 q^{75} -26.3314 q^{76} +7.01946 q^{77} +1.82481 q^{78} -5.00504 q^{79} -30.3930 q^{80} +8.57555 q^{81} -23.1877 q^{82} -1.76152 q^{83} +3.56150 q^{84} +9.42682 q^{85} +10.1551 q^{86} -1.00220 q^{87} -14.0769 q^{88} +14.2315 q^{89} -26.7736 q^{90} -11.2746 q^{91} -41.0396 q^{92} -1.64625 q^{93} -4.36619 q^{94} +19.6384 q^{95} -1.84756 q^{96} +8.89259 q^{97} -13.2563 q^{98} -5.95274 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.58803	−1.83001	−0.915006	−	0.403440i	$-0.867814\pi$
$2$	−2.58803	−1.83001	−0.915006	+	0.403440i	$0.867814\pi$
$3$	0.217741	0.125713	0.0628564	−	0.998023i	$-0.479979\pi$
$3$	0.217741	0.125713	0.0628564	+	0.998023i	$0.479979\pi$
$4$	4.69789	2.34894
$5$	−3.50376	−1.56693	−0.783464	−	0.621437i	$-0.786549\pi$
$5$	−3.50376	−1.56693	−0.783464	+	0.621437i	$0.786549\pi$
$6$	−0.563520	−0.230056
$7$	3.48169	1.31595	0.657977	−	0.753038i	$-0.271412\pi$
$7$	3.48169	1.31595	0.657977	+	0.753038i	$0.271412\pi$
$8$	−6.98221	−2.46859
$9$	−2.95259	−0.984196
$10$	9.06783	2.86750
$11$	2.01611	0.607880	0.303940	−	0.952691i	$-0.401698\pi$
$11$	2.01611	0.607880	0.303940	+	0.952691i	$0.401698\pi$
$12$	1.02292	0.295292
$13$	−3.23824	−0.898127	−0.449064	−	0.893500i	$-0.648242\pi$
$13$	−3.23824	−0.898127	−0.449064	+	0.893500i	$0.648242\pi$
$14$	−9.01070	−2.40821
$15$	−0.762912	−0.196983
$16$	8.67439	2.16860
$17$	−2.69049	−0.652539	−0.326270	−	0.945277i	$-0.605792\pi$
$17$	−2.69049	−0.652539	−0.326270	+	0.945277i	$0.605792\pi$
$18$	7.64138	1.80109
$19$	−5.60494	−1.28586	−0.642931	−	0.765924i	$-0.722282\pi$
$19$	−5.60494	−1.28586	−0.642931	+	0.765924i	$0.722282\pi$
$20$	−16.4603	−3.68063
$21$	0.758106	0.165432
$22$	−5.21775	−1.11243
$23$	−8.73576	−1.82153	−0.910766	−	0.412922i	$-0.864508\pi$
$23$	−8.73576	−1.82153	−0.910766	+	0.412922i	$0.864508\pi$
$24$	−1.52031	−0.310333
$25$	7.27632	1.45526
$26$	8.38067	1.64358
$27$	−1.29612	−0.249439
$28$	16.3566	3.09110
$29$	−4.60270	−0.854701	−0.427350	−	0.904086i	$-0.640553\pi$
$29$	−4.60270	−0.854701	−0.427350	+	0.904086i	$0.640553\pi$
$30$	1.97444	0.360481
$31$	−7.56059	−1.35792	−0.678961	−	0.734174i	$-0.737570\pi$
$31$	−7.56059	−1.35792	−0.678961	+	0.734174i	$0.737570\pi$
$32$	−8.48513	−1.49997
$33$	0.438990	0.0764183
$34$	6.96306	1.19415
$35$	−12.1990	−2.06201
$36$	−13.8709	−2.31182
$37$	4.57216	0.751658	0.375829	−	0.926689i	$-0.377358\pi$
$37$	4.57216	0.751658	0.375829	+	0.926689i	$0.377358\pi$
$38$	14.5057	2.35314
$39$	−0.705098	−0.112906
$40$	24.4640	3.86810
$41$	8.95960	1.39925	0.699627	−	0.714508i	$-0.253349\pi$
$41$	8.95960	1.39925	0.699627	+	0.714508i	$0.253349\pi$
$42$	−1.96200	−0.302743
$43$	−3.92387	−0.598385	−0.299192	−	0.954193i	$-0.596717\pi$
$43$	−3.92387	−0.598385	−0.299192	+	0.954193i	$0.596717\pi$
$44$	9.47146	1.42788
$45$	10.3452	1.54217
$46$	22.6084	3.33343
$47$	1.68707	0.246085	0.123042	−	0.992401i	$-0.460735\pi$
$47$	1.68707	0.246085	0.123042	+	0.992401i	$0.460735\pi$
$48$	1.88877	0.272620
$49$	5.12215	0.731735
$50$	−18.8313	−2.66315
$51$	−0.585830	−0.0820326
$52$	−15.2129	−2.10965
$53$	−3.33422	−0.457990	−0.228995	−	0.973428i	$-0.573544\pi$
$53$	−3.33422	−0.457990	−0.228995	+	0.973428i	$0.573544\pi$
$54$	3.35440	0.456476
$55$	−7.06396	−0.952504
$56$	−24.3099	−3.24855
$57$	−1.22043	−0.161649
$58$	11.9119	1.56411
$59$	−9.30415	−1.21130	−0.605649	−	0.795732i	$-0.707086\pi$
$59$	−9.30415	−1.21130	−0.605649	+	0.795732i	$0.707086\pi$
$60$	−3.58408	−0.462702
$61$	10.9909	1.40724	0.703618	−	0.710578i	$-0.251566\pi$
$61$	10.9909	1.40724	0.703618	+	0.710578i	$0.251566\pi$
$62$	19.5670	2.48502
$63$	−10.2800	−1.29516
$64$	4.61098	0.576373
$65$	11.3460	1.40730
$66$	−1.13612	−0.139846
$67$	10.9468	1.33737	0.668683	−	0.743548i	$-0.266858\pi$
$67$	10.9468	1.33737	0.668683	+	0.743548i	$0.266858\pi$
$68$	−12.6396	−1.53278
$69$	−1.90213	−0.228990
$70$	31.5713	3.77350
$71$	−8.43776	−1.00138	−0.500689	−	0.865627i	$-0.666920\pi$
$71$	−8.43776	−1.00138	−0.500689	+	0.865627i	$0.666920\pi$
$72$	20.6156	2.42957
$73$	3.35436	0.392599	0.196299	−	0.980544i	$-0.437108\pi$
$73$	3.35436	0.392599	0.196299	+	0.980544i	$0.437108\pi$
$74$	−11.8329	−1.37554
$75$	1.58435	0.182945
$76$	−26.3314	−3.02042
$77$	7.01946	0.799942
$78$	1.82481	0.206620
$79$	−5.00504	−0.563110	−0.281555	−	0.959545i	$-0.590850\pi$
$79$	−5.00504	−0.563110	−0.281555	+	0.959545i	$0.590850\pi$
$80$	−30.3930	−3.39804
$81$	8.57555	0.952839
$82$	−23.1877	−2.56065
$83$	−1.76152	−0.193352	−0.0966762	−	0.995316i	$-0.530821\pi$
$83$	−1.76152	−0.193352	−0.0966762	+	0.995316i	$0.530821\pi$
$84$	3.56150	0.388591
$85$	9.42682	1.02248
$86$	10.1551	1.09505
$87$	−1.00220	−0.107447
$88$	−14.0769	−1.50060
$89$	14.2315	1.50854	0.754269	−	0.656565i	$-0.227991\pi$
$89$	14.2315	1.50854	0.754269	+	0.656565i	$0.227991\pi$
$90$	−26.7736	−2.82218
$91$	−11.2746	−1.18189
$92$	−41.0396	−4.27868
$93$	−1.64625	−0.170708
$94$	−4.36619	−0.450338
$95$	19.6384	2.01485
$96$	−1.84756	−0.188566
$97$	8.89259	0.902906	0.451453	−	0.892295i	$-0.350906\pi$
$97$	8.89259	0.902906	0.451453	+	0.892295i	$0.350906\pi$
$98$	−13.2563	−1.33908
$99$	−5.95274	−0.598273
$100$	34.1834	3.41834
$101$	−18.4057	−1.83144	−0.915718	−	0.401822i	$-0.868377\pi$
$101$	−18.4057	−1.83144	−0.915718	+	0.401822i	$0.868377\pi$
$102$	1.51614	0.150121
$103$	−5.13530	−0.505997	−0.252998	−	0.967467i	$-0.581417\pi$
$103$	−5.13530	−0.505997	−0.252998	+	0.967467i	$0.581417\pi$
$104$	22.6101	2.21710
$105$	−2.65622	−0.259221
$106$	8.62905	0.838127
$107$	−12.0850	−1.16830	−0.584151	−	0.811645i	$-0.698572\pi$
$107$	−12.0850	−1.16830	−0.584151	+	0.811645i	$0.698572\pi$
$108$	−6.08904	−0.585918
$109$	5.00164	0.479071	0.239535	−	0.970888i	$-0.423005\pi$
$109$	5.00164	0.479071	0.239535	+	0.970888i	$0.423005\pi$
$110$	18.2817	1.74309
$111$	0.995546	0.0944931
$112$	30.2015	2.85377
$113$	−11.0240	−1.03705	−0.518527	−	0.855061i	$-0.673519\pi$
$113$	−11.0240	−1.03705	−0.518527	+	0.855061i	$0.673519\pi$
$114$	3.15849	0.295820
$115$	30.6080	2.85421
$116$	−21.6230	−2.00764
$117$	9.56120	0.883933
$118$	24.0794	2.21669
$119$	−9.36744	−0.858712
$120$	5.32681	0.486269
$121$	−6.93530	−0.630482
$122$	−28.4447	−2.57526
$123$	1.95087	0.175904
$124$	−35.5188	−3.18969
$125$	−7.97568	−0.713367
$126$	26.6049	2.37015
$127$	0.338431	0.0300309	0.0150154	−	0.999887i	$-0.495220\pi$
$127$	0.338431	0.0300309	0.0150154	+	0.999887i	$0.495220\pi$
$128$	5.03691	0.445204
$129$	−0.854388	−0.0752247
$130$	−29.3638	−2.57538
$131$	19.1239	1.67087	0.835434	−	0.549591i	$-0.185217\pi$
$131$	19.1239	1.67087	0.835434	+	0.549591i	$0.185217\pi$
$132$	2.06232	0.179502
$133$	−19.5147	−1.69213
$134$	−28.3306	−2.44740
$135$	4.54130	0.390853
$136$	18.7856	1.61085
$137$	5.99924	0.512550	0.256275	−	0.966604i	$-0.417505\pi$
$137$	5.99924	0.512550	0.256275	+	0.966604i	$0.417505\pi$
$138$	4.92278	0.419054
$139$	−7.28301	−0.617737	−0.308868	−	0.951105i	$-0.599950\pi$
$139$	−7.28301	−0.617737	−0.308868	+	0.951105i	$0.599950\pi$
$140$	−57.3095	−4.84354
$141$	0.367344	0.0309360
$142$	21.8372	1.83253
$143$	−6.52865	−0.545953
$144$	−25.6119	−2.13433
$145$	16.1268	1.33925
$146$	−8.68119	−0.718460
$147$	1.11530	0.0919885
$148$	21.4795	1.76560
$149$	−0.542111	−0.0444115	−0.0222057	−	0.999753i	$-0.507069\pi$
$149$	−0.542111	−0.0444115	−0.0222057	+	0.999753i	$0.507069\pi$
$150$	−4.10035	−0.334792
$151$	6.48728	0.527928	0.263964	−	0.964533i	$-0.414970\pi$
$151$	6.48728	0.527928	0.263964	+	0.964533i	$0.414970\pi$
$152$	39.1349	3.17426
$153$	7.94391	0.642227
$154$	−18.1666	−1.46390
$155$	26.4905	2.12777
$156$	−3.31247	−0.265210
$157$	16.6935	1.33229	0.666145	−	0.745823i	$-0.267943\pi$
$157$	16.6935	1.33229	0.666145	+	0.745823i	$0.267943\pi$
$158$	12.9532	1.03050
$159$	−0.725996	−0.0575752
$160$	29.7299	2.35035
$161$	−30.4152	−2.39705
$162$	−22.1938	−1.74371
$163$	14.1523	1.10849	0.554246	−	0.832353i	$-0.313007\pi$
$163$	14.1523	1.10849	0.554246	+	0.832353i	$0.313007\pi$
$164$	42.0912	3.28677
$165$	−1.53811	−0.119742
$166$	4.55887	0.353837
$167$	1.95205	0.151054	0.0755269	−	0.997144i	$-0.475936\pi$
$167$	1.95205	0.151054	0.0755269	+	0.997144i	$0.475936\pi$
$168$	−5.29326	−0.408384
$169$	−2.51378	−0.193368
$170$	−24.3969	−1.87116
$171$	16.5491	1.26554
$172$	−18.4339	−1.40557
$173$	−4.07045	−0.309471	−0.154735	−	0.987956i	$-0.549452\pi$
$173$	−4.07045	−0.309471	−0.154735	+	0.987956i	$0.549452\pi$
$174$	2.59371	0.196629
$175$	25.3339	1.91506
$176$	17.4885	1.31825
$177$	−2.02590	−0.152276
$178$	−36.8316	−2.76064
$179$	−6.00807	−0.449064	−0.224532	−	0.974467i	$-0.572085\pi$
$179$	−6.00807	−0.449064	−0.224532	+	0.974467i	$0.572085\pi$
$180$	48.6004	3.62246
$181$	4.09874	0.304657	0.152328	−	0.988330i	$-0.451323\pi$
$181$	4.09874	0.304657	0.152328	+	0.988330i	$0.451323\pi$
$182$	29.1789	2.16288
$183$	2.39316	0.176908
$184$	60.9950	4.49661
$185$	−16.0197	−1.17779
$186$	4.26054	0.312398
$187$	−5.42432	−0.396665
$188$	7.92567	0.578039
$189$	−4.51269	−0.328250
$190$	−50.8246	−3.68721
$191$	26.0811	1.88716	0.943582	−	0.331138i	$-0.107433\pi$
$191$	26.0811	1.88716	0.943582	+	0.331138i	$0.107433\pi$
$192$	1.00400	0.0724575
$193$	−3.27262	−0.235568	−0.117784	−	0.993039i	$-0.537579\pi$
$193$	−3.27262	−0.235568	−0.117784	+	0.993039i	$0.537579\pi$
$194$	−23.0143	−1.65233
$195$	2.47049	0.176916
$196$	24.0633	1.71881
$197$	−17.3663	−1.23730	−0.618648	−	0.785668i	$-0.712319\pi$
$197$	−17.3663	−1.23730	−0.618648	+	0.785668i	$0.712319\pi$
$198$	15.4059	1.09485
$199$	−23.8961	−1.69395	−0.846974	−	0.531635i	$-0.821578\pi$
$199$	−23.8961	−1.69395	−0.846974	+	0.531635i	$0.821578\pi$
$200$	−50.8048	−3.59245
$201$	2.38357	0.168124
$202$	47.6345	3.35155
$203$	−16.0252	−1.12475
$204$	−2.75216	−0.192690
$205$	−31.3923	−2.19253
$206$	13.2903	0.925980
$207$	25.7931	1.79275
$208$	−28.0898	−1.94768
$209$	−11.3002	−0.781649
$210$	6.87437	0.474377
$211$	20.2383	1.39326	0.696631	−	0.717430i	$-0.254682\pi$
$211$	20.2383	1.39326	0.696631	+	0.717430i	$0.254682\pi$
$212$	−15.6638	−1.07579
$213$	−1.83725	−0.125886
$214$	31.2763	2.13801
$215$	13.7483	0.937626
$216$	9.04981	0.615761
$217$	−26.3236	−1.78696
$218$	−12.9444	−0.876705
$219$	0.730383	0.0493547
$220$	−33.1857	−2.23738
$221$	8.71246	0.586063
$222$	−2.57650	−0.172923
$223$	−10.0843	−0.675295	−0.337647	−	0.941273i	$-0.609631\pi$
$223$	−10.0843	−0.675295	−0.337647	+	0.941273i	$0.609631\pi$
$224$	−29.5426	−1.97390
$225$	−21.4840	−1.43227
$226$	28.5305	1.89782
$227$	−19.4937	−1.29384	−0.646922	−	0.762556i	$-0.723944\pi$
$227$	−19.4937	−1.29384	−0.646922	+	0.762556i	$0.723944\pi$
$228$	−5.73342	−0.379705
$229$	−18.4040	−1.21617	−0.608086	−	0.793871i	$-0.708063\pi$
$229$	−18.4040	−1.21617	−0.608086	+	0.793871i	$0.708063\pi$
$230$	−79.2144	−5.22324
$231$	1.52842	0.100563
$232$	32.1371	2.10990
$233$	15.8430	1.03791	0.518955	−	0.854802i	$-0.326321\pi$
$233$	15.8430	1.03791	0.518955	+	0.854802i	$0.326321\pi$
$234$	−24.7447	−1.61761
$235$	−5.91109	−0.385597
$236$	−43.7099	−2.84527
$237$	−1.08980	−0.0707902
$238$	24.2432	1.57145
$239$	−25.3437	−1.63935	−0.819674	−	0.572830i	$-0.805846\pi$
$239$	−25.3437	−1.63935	−0.819674	+	0.572830i	$0.805846\pi$
$240$	−6.61779	−0.427177
$241$	−5.15088	−0.331798	−0.165899	−	0.986143i	$-0.553053\pi$
$241$	−5.15088	−0.331798	−0.165899	+	0.986143i	$0.553053\pi$
$242$	17.9488	1.15379
$243$	5.75562	0.369223
$244$	51.6339	3.30552
$245$	−17.9468	−1.14658
$246$	−5.04891	−0.321907
$247$	18.1502	1.15487
$248$	52.7897	3.35215
$249$	−0.383556	−0.0243069
$250$	20.6413	1.30547
$251$	−8.44150	−0.532823	−0.266411	−	0.963859i	$-0.585838\pi$
$251$	−8.44150	−0.532823	−0.266411	+	0.963859i	$0.585838\pi$
$252$	−48.2943	−3.04225
$253$	−17.6122	−1.10727
$254$	−0.875869	−0.0549569
$255$	2.05261	0.128539
$256$	−22.2576	−1.39110
$257$	27.6004	1.72167	0.860834	−	0.508886i	$-0.169943\pi$
$257$	27.6004	1.72167	0.860834	+	0.508886i	$0.169943\pi$
$258$	2.21118	0.137662
$259$	15.9188	0.989148
$260$	53.3024	3.30567
$261$	13.5899	0.841193
$262$	−49.4933	−3.05771
$263$	16.5240	1.01891	0.509457	−	0.860496i	$-0.329846\pi$
$263$	16.5240	1.01891	0.509457	+	0.860496i	$0.329846\pi$
$264$	−3.06512	−0.188645
$265$	11.6823	0.717638
$266$	50.5045	3.09663
$267$	3.09879	0.189643
$268$	51.4269	3.14140
$269$	5.95937	0.363349	0.181675	−	0.983359i	$-0.441848\pi$
$269$	5.95937	0.363349	0.181675	+	0.983359i	$0.441848\pi$
$270$	−11.7530	−0.715266
$271$	6.38177	0.387665	0.193833	−	0.981035i	$-0.437908\pi$
$271$	6.38177	0.387665	0.193833	+	0.981035i	$0.437908\pi$
$272$	−23.3383	−1.41509
$273$	−2.45493	−0.148579
$274$	−15.5262	−0.937972
$275$	14.6699	0.884626
$276$	−8.93601	−0.537885
$277$	−8.16523	−0.490601	−0.245301	−	0.969447i	$-0.578887\pi$
$277$	−8.16523	−0.490601	−0.245301	+	0.969447i	$0.578887\pi$
$278$	18.8486	1.13047
$279$	22.3233	1.33646
$280$	85.1760	5.09024
$281$	11.5629	0.689782	0.344891	−	0.938643i	$-0.387916\pi$
$281$	11.5629	0.689782	0.344891	+	0.938643i	$0.387916\pi$
$282$	−0.950698	−0.0566132
$283$	11.7021	0.695620	0.347810	−	0.937565i	$-0.386925\pi$
$283$	11.7021	0.695620	0.347810	+	0.937565i	$0.386925\pi$
$284$	−39.6397	−2.35218
$285$	4.27608	0.253293
$286$	16.8963	0.999101
$287$	31.1945	1.84135
$288$	25.0531	1.47627
$289$	−9.76127	−0.574192
$290$	−41.7365	−2.45085
$291$	1.93628	0.113507
$292$	15.7584	0.922193
$293$	22.4509	1.31160	0.655798	−	0.754936i	$-0.272332\pi$
$293$	22.4509	1.31160	0.655798	+	0.754936i	$0.272332\pi$
$294$	−2.88643	−0.168340
$295$	32.5995	1.89802
$296$	−31.9238	−1.85553
$297$	−2.61312	−0.151629
$298$	1.40300	0.0812735
$299$	28.2885	1.63597
$300$	7.44312	0.429729
$301$	−13.6617	−0.787447
$302$	−16.7893	−0.966114
$303$	−4.00767	−0.230235
$304$	−48.6194	−2.78852
$305$	−38.5094	−2.20504
$306$	−20.5591	−1.17528
$307$	−28.4966	−1.62638	−0.813192	−	0.581995i	$-0.802272\pi$
$307$	−28.4966	−1.62638	−0.813192	+	0.581995i	$0.802272\pi$
$308$	32.9767	1.87902
$309$	−1.11817	−0.0636103
$310$	−68.5581	−3.89384
$311$	18.5297	1.05072	0.525361	−	0.850879i	$-0.323930\pi$
$311$	18.5297	1.05072	0.525361	+	0.850879i	$0.323930\pi$
$312$	4.92315	0.278718
$313$	9.57645	0.541293	0.270646	−	0.962679i	$-0.412763\pi$
$313$	9.57645	0.541293	0.270646	+	0.962679i	$0.412763\pi$
$314$	−43.2033	−2.43811
$315$	36.0186	2.02942
$316$	−23.5131	−1.32272
$317$	−5.04723	−0.283481	−0.141740	−	0.989904i	$-0.545270\pi$
$317$	−5.04723	−0.283481	−0.141740	+	0.989904i	$0.545270\pi$
$318$	1.87890	0.105363
$319$	−9.27955	−0.519555
$320$	−16.1558	−0.903135
$321$	−2.63140	−0.146870
$322$	78.7154	4.38664
$323$	15.0800	0.839075
$324$	40.2870	2.23817
$325$	−23.5625	−1.30701
$326$	−36.6265	−2.02855
$327$	1.08906	0.0602253
$328$	−62.5578	−3.45418
$329$	5.87385	0.323836
$330$	3.98068	0.219129
$331$	−20.8510	−1.14607	−0.573037	−	0.819529i	$-0.694235\pi$
$331$	−20.8510	−1.14607	−0.573037	+	0.819529i	$0.694235\pi$
$332$	−8.27545	−0.454174
$333$	−13.4997	−0.739779
$334$	−5.05195	−0.276430
$335$	−38.3550	−2.09556
$336$	6.57611	0.358756
$337$	30.6793	1.67121	0.835604	−	0.549333i	$-0.185118\pi$
$337$	30.6793	1.67121	0.835604	+	0.549333i	$0.185118\pi$
$338$	6.50573	0.353865
$339$	−2.40038	−0.130371
$340$	44.2862	2.40175
$341$	−15.2430	−0.825454
$342$	−42.8295	−2.31595
$343$	−6.53810	−0.353024
$344$	27.3973	1.47716
$345$	6.66462	0.358811
$346$	10.5344	0.566335
$347$	13.4091	0.719836	0.359918	−	0.932984i	$-0.382805\pi$
$347$	13.4091	0.719836	0.359918	+	0.932984i	$0.382805\pi$
$348$	−4.70821	−0.252387
$349$	−27.9959	−1.49859	−0.749293	−	0.662238i	$-0.769607\pi$
$349$	−27.9959	−1.49859	−0.749293	+	0.662238i	$0.769607\pi$
$350$	−65.5648	−3.50459
$351$	4.19716	0.224028
$352$	−17.1070	−0.911804
$353$	−18.6220	−0.991150	−0.495575	−	0.868565i	$-0.665043\pi$
$353$	−18.6220	−0.991150	−0.495575	+	0.868565i	$0.665043\pi$
$354$	5.24307	0.278666
$355$	29.5639	1.56909
$356$	66.8581	3.54347
$357$	−2.03968	−0.107951
$358$	15.5491	0.821793
$359$	−24.1199	−1.27300	−0.636500	−	0.771277i	$-0.719618\pi$
$359$	−24.1199	−1.27300	−0.636500	+	0.771277i	$0.719618\pi$
$360$	−72.2321	−3.80697
$361$	12.4154	0.653440
$362$	−10.6076	−0.557525
$363$	−1.51010	−0.0792597
$364$	−52.9666	−2.77620
$365$	−11.7529	−0.615174
$366$	−6.19357	−0.323743
$367$	−8.03613	−0.419482	−0.209741	−	0.977757i	$-0.567262\pi$
$367$	−8.03613	−0.419482	−0.209741	+	0.977757i	$0.567262\pi$
$368$	−75.7774	−3.95017
$369$	−26.4540	−1.37714
$370$	41.4595	2.15538
$371$	−11.6087	−0.602694
$372$	−7.73391	−0.400984
$373$	20.8271	1.07839	0.539194	−	0.842181i	$-0.318729\pi$
$373$	20.8271	1.07839	0.539194	+	0.842181i	$0.318729\pi$
$374$	14.0383	0.725903
$375$	−1.73663	−0.0896794
$376$	−11.7795	−0.607481
$377$	14.9047	0.767630
$378$	11.6790	0.600702
$379$	−23.6461	−1.21462	−0.607309	−	0.794466i	$-0.707751\pi$
$379$	−23.6461	−1.21462	−0.607309	+	0.794466i	$0.707751\pi$
$380$	92.2588	4.73278
$381$	0.0736903	0.00377527
$382$	−67.4987	−3.45353
$383$	3.97169	0.202944	0.101472	−	0.994838i	$-0.467645\pi$
$383$	3.97169	0.202944	0.101472	+	0.994838i	$0.467645\pi$
$384$	1.09674	0.0559678
$385$	−24.5945	−1.25345
$386$	8.46963	0.431093
$387$	11.5856	0.588928
$388$	41.7764	2.12088
$389$	−0.431877	−0.0218971	−0.0109485	−	0.999940i	$-0.503485\pi$
$389$	−0.431877	−0.0218971	−0.0109485	+	0.999940i	$0.503485\pi$
$390$	−6.39371	−0.323758
$391$	23.5035	1.18862
$392$	−35.7639	−1.80635
$393$	4.16407	0.210049
$394$	44.9444	2.26427
$395$	17.5364	0.882354
$396$	−27.9653	−1.40531
$397$	29.8229	1.49677	0.748384	−	0.663266i	$-0.230830\pi$
$397$	29.8229	1.49677	0.748384	+	0.663266i	$0.230830\pi$
$398$	61.8437	3.09995
$399$	−4.24914	−0.212723
$400$	63.1176	3.15588
$401$	28.7981	1.43811	0.719055	−	0.694953i	$-0.244575\pi$
$401$	28.7981	1.43811	0.719055	+	0.694953i	$0.244575\pi$
$402$	−6.16874	−0.307669
$403$	24.4830	1.21959
$404$	−86.4679	−4.30194
$405$	−30.0466	−1.49303
$406$	41.4736	2.05830
$407$	9.21797	0.456918
$408$	4.09039	0.202504
$409$	29.1474	1.44125	0.720623	−	0.693327i	$-0.243856\pi$
$409$	29.1474	1.44125	0.720623	+	0.693327i	$0.243856\pi$
$410$	81.2441	4.01236
$411$	1.30628	0.0644341
$412$	−24.1251	−1.18856
$413$	−32.3942	−1.59401
$414$	−66.7533	−3.28075
$415$	6.17196	0.302969
$416$	27.4769	1.34717
$417$	−1.58581	−0.0776574
$418$	29.2452	1.43043
$419$	−12.3791	−0.604761	−0.302380	−	0.953187i	$-0.597781\pi$
$419$	−12.3791	−0.604761	−0.302380	+	0.953187i	$0.597781\pi$
$420$	−12.4786	−0.608895
$421$	34.4197	1.67752	0.838758	−	0.544504i	$-0.183282\pi$
$421$	34.4197	1.67752	0.838758	+	0.544504i	$0.183282\pi$
$422$	−52.3773	−2.54969
$423$	−4.98123	−0.242196
$424$	23.2802	1.13059
$425$	−19.5769	−0.949617
$426$	4.75485	0.230373
$427$	38.2668	1.85186
$428$	−56.7740	−2.74428
$429$	−1.42156	−0.0686333
$430$	−35.5810	−1.71587
$431$	11.5685	0.557236	0.278618	−	0.960402i	$-0.410124\pi$
$431$	11.5685	0.557236	0.278618	+	0.960402i	$0.410124\pi$
$432$	−11.2431	−0.540932
$433$	18.1346	0.871493	0.435746	−	0.900069i	$-0.356484\pi$
$433$	18.1346	0.871493	0.435746	+	0.900069i	$0.356484\pi$
$434$	68.1263	3.27017
$435$	3.51146	0.168361
$436$	23.4972	1.12531
$437$	48.9634	2.34224
$438$	−1.89025	−0.0903197
$439$	2.30605	0.110062	0.0550308	−	0.998485i	$-0.482474\pi$
$439$	2.30605	0.110062	0.0550308	+	0.998485i	$0.482474\pi$
$440$	49.3221	2.35134
$441$	−15.1236	−0.720171
$442$	−22.5481	−1.07250
$443$	30.5121	1.44967	0.724836	−	0.688921i	$-0.241915\pi$
$443$	30.5121	1.44967	0.724836	+	0.688921i	$0.241915\pi$
$444$	4.67697	0.221959
$445$	−49.8638	−2.36377
$446$	26.0985	1.23580
$447$	−0.118040	−0.00558309
$448$	16.0540	0.758480
$449$	3.08543	0.145610	0.0728051	−	0.997346i	$-0.476805\pi$
$449$	3.08543	0.145610	0.0728051	+	0.997346i	$0.476805\pi$
$450$	55.6012	2.62106
$451$	18.0635	0.850578
$452$	−51.7897	−2.43598
$453$	1.41255	0.0663673
$454$	50.4503	2.36775
$455$	39.5033	1.85194
$456$	8.52127	0.399045
$457$	26.5971	1.24416	0.622080	−	0.782954i	$-0.286288\pi$
$457$	26.5971	1.24416	0.622080	+	0.782954i	$0.286288\pi$
$458$	47.6302	2.22561
$459$	3.48720	0.162769
$460$	143.793	6.70438
$461$	23.5443	1.09657	0.548284	−	0.836292i	$-0.315281\pi$
$461$	23.5443	1.09657	0.548284	+	0.836292i	$0.315281\pi$
$462$	−3.95561	−0.184031
$463$	10.6371	0.494346	0.247173	−	0.968971i	$-0.420498\pi$
$463$	10.6371	0.494346	0.247173	+	0.968971i	$0.420498\pi$
$464$	−39.9256	−1.85350
$465$	5.76807	0.267488
$466$	−41.0022	−1.89939
$467$	7.83779	0.362690	0.181345	−	0.983420i	$-0.441955\pi$
$467$	7.83779	0.362690	0.181345	+	0.983420i	$0.441955\pi$
$468$	44.9175	2.07631
$469$	38.1134	1.75991
$470$	15.2981	0.705647
$471$	3.63487	0.167486
$472$	64.9636	2.99019
$473$	−7.91095	−0.363746
$474$	2.82044	0.129547
$475$	−40.7834	−1.87127
$476$	−44.0072	−2.01707
$477$	9.84457	0.450752
$478$	65.5903	3.00003
$479$	15.7852	0.721243	0.360622	−	0.932712i	$-0.382565\pi$
$479$	15.7852	0.721243	0.360622	+	0.932712i	$0.382565\pi$
$480$	6.47341	0.295469
$481$	−14.8058	−0.675085
$482$	13.3306	0.607194
$483$	−6.62263	−0.301340
$484$	−32.5813	−1.48097
$485$	−31.1575	−1.41479
$486$	−14.8957	−0.675682
$487$	−19.5665	−0.886644	−0.443322	−	0.896362i	$-0.646200\pi$
$487$	−19.5665	−0.886644	−0.443322	+	0.896362i	$0.646200\pi$
$488$	−76.7406	−3.47388
$489$	3.08153	0.139352
$490$	46.4467	2.09825
$491$	−0.404136	−0.0182384	−0.00911921	−	0.999958i	$-0.502903\pi$
$491$	−0.404136	−0.0182384	−0.00911921	+	0.999958i	$0.502903\pi$
$492$	9.16498	0.413189
$493$	12.3835	0.557726
$494$	−46.9731	−2.11342
$495$	20.8570	0.937451
$496$	−65.5835	−2.94479
$497$	−29.3777	−1.31777
$498$	0.992654	0.0444819
$499$	21.9623	0.983169	0.491585	−	0.870830i	$-0.336418\pi$
$499$	21.9623	0.983169	0.491585	+	0.870830i	$0.336418\pi$
$500$	−37.4689	−1.67566
$501$	0.425040	0.0189894
$502$	21.8468	0.975072
$503$	20.5687	0.917113	0.458557	−	0.888665i	$-0.348367\pi$
$503$	20.5687	0.917113	0.458557	+	0.888665i	$0.348367\pi$
$504$	71.7771	3.19721
$505$	64.4891	2.86973
$506$	45.5810	2.02632
$507$	−0.547353	−0.0243088
$508$	1.58991	0.0705409
$509$	13.7620	0.609989	0.304994	−	0.952354i	$-0.401345\pi$
$509$	13.7620	0.609989	0.304994	+	0.952354i	$0.401345\pi$
$510$	−5.31220	−0.235228
$511$	11.6788	0.516642
$512$	47.5295	2.10053
$513$	7.26469	0.320744
$514$	−71.4307	−3.15067
$515$	17.9929	0.792860
$516$	−4.01382	−0.176699
$517$	3.40132	0.149590
$518$	−41.1984	−1.81015
$519$	−0.886304	−0.0389044
$520$	−79.2204	−3.47404
$521$	3.83224	0.167894	0.0839468	−	0.996470i	$-0.473247\pi$
$521$	3.83224	0.167894	0.0839468	+	0.996470i	$0.473247\pi$
$522$	−35.1710	−1.53939
$523$	−42.0132	−1.83711	−0.918553	−	0.395297i	$-0.870642\pi$
$523$	−42.0132	−1.83711	−0.918553	+	0.395297i	$0.870642\pi$
$524$	89.8422	3.92477
$525$	5.51622	0.240748
$526$	−42.7646	−1.86463
$527$	20.3417	0.886098
$528$	3.80797	0.165720
$529$	53.3135	2.31798
$530$	−30.2341	−1.31329
$531$	27.4713	1.19215
$532$	−91.6777	−3.97473
$533$	−29.0134	−1.25671
$534$	−8.01974	−0.347048
$535$	42.3429	1.83065
$536$	−76.4330	−3.30140
$537$	−1.30820	−0.0564531
$538$	−15.4230	−0.664933
$539$	10.3268	0.444807
$540$	21.3345	0.918092
$541$	−18.9784	−0.815945	−0.407972	−	0.912994i	$-0.633764\pi$
$541$	−18.9784	−0.815945	−0.407972	+	0.912994i	$0.633764\pi$
$542$	−16.5162	−0.709432
$543$	0.892463	0.0382992
$544$	22.8292	0.978792
$545$	−17.5246	−0.750669
$546$	6.35343	0.271902
$547$	−5.15145	−0.220260	−0.110130	−	0.993917i	$-0.535127\pi$
$547$	−5.15145	−0.220260	−0.110130	+	0.993917i	$0.535127\pi$
$548$	28.1838	1.20395
$549$	−32.4515	−1.38500
$550$	−37.9660	−1.61888
$551$	25.7979	1.09903
$552$	13.2811	0.565281
$553$	−17.4260	−0.741028
$554$	21.1318	0.897806
$555$	−3.48815	−0.148064
$556$	−34.2148	−1.45103
$557$	16.3308	0.691956	0.345978	−	0.938243i	$-0.387547\pi$
$557$	16.3308	0.691956	0.345978	+	0.938243i	$0.387547\pi$
$558$	−57.7734	−2.44574
$559$	12.7065	0.537426
$560$	−105.819	−4.47166
$561$	−1.18110	−0.0498659
$562$	−29.9250	−1.26231
$563$	−5.26332	−0.221823	−0.110911	−	0.993830i	$-0.535377\pi$
$563$	−5.26332	−0.221823	−0.110911	+	0.993830i	$0.535377\pi$
$564$	1.72574	0.0726669
$565$	38.6255	1.62499
$566$	−30.2855	−1.27299
$567$	29.8574	1.25389
$568$	58.9143	2.47199
$569$	0.863494	0.0361995	0.0180998	−	0.999836i	$-0.494238\pi$
$569$	0.863494	0.0361995	0.0180998	+	0.999836i	$0.494238\pi$
$570$	−11.0666	−0.463529
$571$	−4.70104	−0.196733	−0.0983663	−	0.995150i	$-0.531362\pi$
$571$	−4.70104	−0.196733	−0.0983663	+	0.995150i	$0.531362\pi$
$572$	−30.6709	−1.28241
$573$	5.67893	0.237241
$574$	−80.7323	−3.36970
$575$	−63.5642	−2.65081
$576$	−13.6143	−0.567264
$577$	−31.9286	−1.32921	−0.664603	−	0.747196i	$-0.731399\pi$
$577$	−31.9286	−1.32921	−0.664603	+	0.747196i	$0.731399\pi$
$578$	25.2624	1.05078
$579$	−0.712583	−0.0296139
$580$	75.7617	3.14584
$581$	−6.13308	−0.254443
$582$	−5.01115	−0.207719
$583$	−6.72215	−0.278403
$584$	−23.4209	−0.969163
$585$	−33.5001	−1.38506
$586$	−58.1036	−2.40024
$587$	−4.70779	−0.194311	−0.0971556	−	0.995269i	$-0.530974\pi$
$587$	−4.70779	−0.194311	−0.0971556	+	0.995269i	$0.530974\pi$
$588$	5.23956	0.216076
$589$	42.3767	1.74610
$590$	−84.3684	−3.47339
$591$	−3.78135	−0.155544
$592$	39.6607	1.63004
$593$	24.6932	1.01403	0.507014	−	0.861938i	$-0.330749\pi$
$593$	24.6932	1.01403	0.507014	+	0.861938i	$0.330749\pi$
$594$	6.76284	0.277483
$595$	32.8212	1.34554
$596$	−2.54678	−0.104320
$597$	−5.20315	−0.212951
$598$	−73.2115	−2.99384
$599$	19.2591	0.786906	0.393453	−	0.919345i	$-0.371280\pi$
$599$	19.2591	0.786906	0.393453	+	0.919345i	$0.371280\pi$
$600$	−11.0623	−0.451616
$601$	−37.4052	−1.52579	−0.762895	−	0.646522i	$-0.776223\pi$
$601$	−37.4052	−1.52579	−0.762895	+	0.646522i	$0.776223\pi$
$602$	35.3569	1.44104
$603$	−32.3214	−1.31623
$604$	30.4765	1.24007
$605$	24.2996	0.987921
$606$	10.3720	0.421333
$607$	26.3608	1.06995	0.534976	−	0.844867i	$-0.320320\pi$
$607$	26.3608	1.06995	0.534976	+	0.844867i	$0.320320\pi$
$608$	47.5587	1.92876
$609$	−3.48934	−0.141395
$610$	99.6633	4.03525
$611$	−5.46315	−0.221015
$612$	37.3196	1.50856
$613$	−17.9569	−0.725271	−0.362636	−	0.931931i	$-0.618123\pi$
$613$	−17.9569	−0.725271	−0.362636	+	0.931931i	$0.618123\pi$
$614$	73.7499	2.97630
$615$	−6.83538	−0.275629
$616$	−49.0114	−1.97472
$617$	8.75306	0.352385	0.176192	−	0.984356i	$-0.443622\pi$
$617$	8.75306	0.352385	0.176192	+	0.984356i	$0.443622\pi$
$618$	2.89385	0.116408
$619$	−11.8912	−0.477947	−0.238973	−	0.971026i	$-0.576811\pi$
$619$	−11.8912	−0.477947	−0.238973	+	0.971026i	$0.576811\pi$
$620$	124.449	4.99801
$621$	11.3226	0.454361
$622$	−47.9554	−1.92284
$623$	49.5497	1.98517
$624$	−6.11630	−0.244848
$625$	−8.43674	−0.337470
$626$	−24.7841	−0.990572
$627$	−2.46051	−0.0982633
$628$	78.4244	3.12947
$629$	−12.3013	−0.490487
$630$	−93.2172	−3.71386
$631$	3.84539	0.153083	0.0765413	−	0.997066i	$-0.475612\pi$
$631$	3.84539	0.153083	0.0765413	+	0.997066i	$0.475612\pi$
$632$	34.9462	1.39009
$633$	4.40671	0.175151
$634$	13.0624	0.518773
$635$	−1.18578	−0.0470563
$636$	−3.41065	−0.135241
$637$	−16.5868	−0.657191
$638$	24.0157	0.950792
$639$	24.9132	0.985553
$640$	−17.6481	−0.697603
$641$	3.95167	0.156081	0.0780407	−	0.996950i	$-0.475134\pi$
$641$	3.95167	0.156081	0.0780407	+	0.996950i	$0.475134\pi$
$642$	6.81014	0.268775
$643$	−12.5572	−0.495208	−0.247604	−	0.968861i	$-0.579643\pi$
$643$	−12.5572	−0.495208	−0.247604	+	0.968861i	$0.579643\pi$
$644$	−142.887	−5.63055
$645$	2.99357	0.117872
$646$	−39.0275	−1.53552
$647$	6.64509	0.261245	0.130623	−	0.991432i	$-0.458302\pi$
$647$	6.64509	0.261245	0.130623	+	0.991432i	$0.458302\pi$
$648$	−59.8763	−2.35216
$649$	−18.7582	−0.736323
$650$	60.9804	2.39185
$651$	−5.73173	−0.224644
$652$	66.4858	2.60379
$653$	5.23275	0.204773	0.102387	−	0.994745i	$-0.467352\pi$
$653$	5.23275	0.204773	0.102387	+	0.994745i	$0.467352\pi$
$654$	−2.81853	−0.110213
$655$	−67.0057	−2.61813
$656$	77.7190	3.03442
$657$	−9.90406	−0.386394
$658$	−15.2017	−0.592624
$659$	−7.08020	−0.275806	−0.137903	−	0.990446i	$-0.544036\pi$
$659$	−7.08020	−0.275806	−0.137903	+	0.990446i	$0.544036\pi$
$660$	−7.22589	−0.281267
$661$	−32.7771	−1.27488	−0.637441	−	0.770500i	$-0.720007\pi$
$661$	−32.7771	−1.27488	−0.637441	+	0.770500i	$0.720007\pi$
$662$	53.9630	2.09733
$663$	1.89706	0.0736757
$664$	12.2993	0.477307
$665$	68.3746	2.65145
$666$	34.9376	1.35381
$667$	40.2081	1.55686
$668$	9.17049	0.354817
$669$	−2.19577	−0.0848932
$670$	99.2637	3.83489
$671$	22.1588	0.855431
$672$	−6.43263	−0.248144
$673$	38.2414	1.47410	0.737048	−	0.675840i	$-0.236219\pi$
$673$	38.2414	1.47410	0.737048	+	0.675840i	$0.236219\pi$
$674$	−79.3989	−3.05833
$675$	−9.43101	−0.363000
$676$	−11.8095	−0.454210
$677$	26.2199	1.00771	0.503856	−	0.863787i	$-0.331914\pi$
$677$	26.2199	1.00771	0.503856	+	0.863787i	$0.331914\pi$
$678$	6.21226	0.238580
$679$	30.9612	1.18818
$680$	−65.8201	−2.52409
$681$	−4.24458	−0.162653
$682$	39.4493	1.51059
$683$	11.4507	0.438150	0.219075	−	0.975708i	$-0.429696\pi$
$683$	11.4507	0.438150	0.219075	+	0.975708i	$0.429696\pi$
$684$	77.7458	2.97268
$685$	−21.0199	−0.803128
$686$	16.9208	0.646038
$687$	−4.00731	−0.152888
$688$	−34.0372	−1.29766
$689$	10.7970	0.411333
$690$	−17.2482	−0.656628
$691$	6.29313	0.239402	0.119701	−	0.992810i	$-0.461806\pi$
$691$	6.29313	0.239402	0.119701	+	0.992810i	$0.461806\pi$
$692$	−19.1225	−0.726929
$693$	−20.7256	−0.787300
$694$	−34.7030	−1.31731
$695$	25.5179	0.967949
$696$	6.99756	0.265242
$697$	−24.1057	−0.913068
$698$	72.4542	2.74243
$699$	3.44967	0.130479
$700$	119.016	4.49837
$701$	−28.6461	−1.08195	−0.540974	−	0.841039i	$-0.681944\pi$
$701$	−28.6461	−1.08195	−0.540974	+	0.841039i	$0.681944\pi$
$702$	−10.8624	−0.409974
$703$	−25.6267	−0.966528
$704$	9.29625	0.350365
$705$	−1.28709	−0.0484745
$706$	48.1943	1.81382
$707$	−64.0829	−2.41008
$708$	−9.51743	−0.357687
$709$	−29.5245	−1.10882	−0.554409	−	0.832245i	$-0.687055\pi$
$709$	−29.5245	−1.10882	−0.554409	+	0.832245i	$0.687055\pi$
$710$	−76.5122	−2.87145
$711$	14.7778	0.554211
$712$	−99.3675	−3.72396
$713$	66.0476	2.47350
$714$	5.27874	0.197552
$715$	22.8748	0.855470
$716$	−28.2252	−1.05483
$717$	−5.51837	−0.206087
$718$	62.4230	2.32960
$719$	34.3481	1.28097	0.640485	−	0.767971i	$-0.278733\pi$
$719$	34.3481	1.28097	0.640485	+	0.767971i	$0.278733\pi$
$720$	89.7379	3.34433
$721$	−17.8795	−0.665868
$722$	−32.1313	−1.19580
$723$	−1.12156	−0.0417112
$724$	19.2554	0.715622
$725$	−33.4908	−1.24382
$726$	3.90818	0.145046
$727$	−2.17129	−0.0805288	−0.0402644	−	0.999189i	$-0.512820\pi$
$727$	−2.17129	−0.0805288	−0.0402644	+	0.999189i	$0.512820\pi$
$728$	78.7213	2.91761
$729$	−24.4734	−0.906423
$730$	30.4168	1.12578
$731$	10.5571	0.390470
$732$	11.2428	0.415546
$733$	23.3531	0.862567	0.431283	−	0.902217i	$-0.358061\pi$
$733$	23.3531	0.862567	0.431283	+	0.902217i	$0.358061\pi$
$734$	20.7977	0.767658
$735$	−3.90775	−0.144139
$736$	74.1241	2.73225
$737$	22.0700	0.812957
$738$	68.4637	2.52018
$739$	−42.2615	−1.55461	−0.777306	−	0.629122i	$-0.783414\pi$
$739$	−42.2615	−1.55461	−0.777306	+	0.629122i	$0.783414\pi$
$740$	−75.2590	−2.76657
$741$	3.95203	0.145182
$742$	30.0436	1.10294
$743$	−31.0840	−1.14036	−0.570181	−	0.821519i	$-0.693127\pi$
$743$	−31.0840	−1.14036	−0.570181	+	0.821519i	$0.693127\pi$
$744$	11.4945	0.421408
$745$	1.89943	0.0695896
$746$	−53.9012	−1.97346
$747$	5.20106	0.190297
$748$	−25.4828	−0.931745
$749$	−42.0762	−1.53743
$750$	4.49446	0.164114
$751$	−19.0030	−0.693429	−0.346714	−	0.937971i	$-0.612703\pi$
$751$	−19.0030	−0.693429	−0.346714	+	0.937971i	$0.612703\pi$
$752$	14.6343	0.533658
$753$	−1.83806	−0.0669826
$754$	−38.5737	−1.40477
$755$	−22.7299	−0.827225
$756$	−21.2001	−0.771042
$757$	42.3088	1.53774	0.768871	−	0.639404i	$-0.220819\pi$
$757$	42.3088	1.53774	0.768871	+	0.639404i	$0.220819\pi$
$758$	61.1968	2.22277
$759$	−3.83491	−0.139198
$760$	−137.119	−4.97384
$761$	18.7177	0.678515	0.339258	−	0.940693i	$-0.389824\pi$
$761$	18.7177	0.678515	0.339258	+	0.940693i	$0.389824\pi$
$762$	−0.190713	−0.00690879
$763$	17.4142	0.630435
$764$	122.526	4.43285
$765$	−27.8335	−1.00632
$766$	−10.2788	−0.371390
$767$	30.1291	1.08790
$768$	−4.84640	−0.174879
$769$	−26.0267	−0.938546	−0.469273	−	0.883053i	$-0.655484\pi$
$769$	−26.0267	−0.938546	−0.469273	+	0.883053i	$0.655484\pi$
$770$	63.6512	2.29383
$771$	6.00975	0.216436
$772$	−15.3744	−0.553337
$773$	25.3625	0.912227	0.456113	−	0.889922i	$-0.349241\pi$
$773$	25.3625	0.912227	0.456113	+	0.889922i	$0.349241\pi$
$774$	−29.9838	−1.07775
$775$	−55.0133	−1.97614
$776$	−62.0900	−2.22890
$777$	3.46618	0.124349
$778$	1.11771	0.0400719
$779$	−50.2180	−1.79925
$780$	11.6061	0.415565
$781$	−17.0115	−0.608718
$782$	−60.8276	−2.17519
$783$	5.96567	0.213196
$784$	44.4315	1.58684
$785$	−58.4901	−2.08760
$786$	−10.7767	−0.384393
$787$	−25.8286	−0.920689	−0.460344	−	0.887740i	$-0.652274\pi$
$787$	−25.8286	−0.920689	−0.460344	+	0.887740i	$0.652274\pi$
$788$	−81.5849	−2.90634
$789$	3.59796	0.128091
$790$	−45.3848	−1.61472
$791$	−38.3822	−1.36472
$792$	41.5633	1.47689
$793$	−35.5911	−1.26388
$794$	−77.1825	−2.73910
$795$	2.54371	0.0902162
$796$	−112.261	−3.97899
$797$	27.0992	0.959902	0.479951	−	0.877295i	$-0.340654\pi$
$797$	27.0992	0.959902	0.479951	+	0.877295i	$0.340654\pi$
$798$	10.9969	0.389286
$799$	−4.53904	−0.160580
$800$	−61.7406	−2.18286
$801$	−42.0198	−1.48470
$802$	−74.5304	−2.63176
$803$	6.76276	0.238653
$804$	11.1977	0.394914
$805$	106.567	3.75601
$806$	−63.3628	−2.23186
$807$	1.29760	0.0456776
$808$	128.513	4.52105
$809$	9.66528	0.339813	0.169907	−	0.985460i	$-0.445653\pi$
$809$	9.66528	0.339813	0.169907	+	0.985460i	$0.445653\pi$
$810$	77.7616	2.73226
$811$	−2.78573	−0.0978202	−0.0489101	−	0.998803i	$-0.515575\pi$
$811$	−2.78573	−0.0978202	−0.0489101	+	0.998803i	$0.515575\pi$
$812$	−75.2845	−2.64197
$813$	1.38957	0.0487345
$814$	−23.8564	−0.836165
$815$	−49.5862	−1.73693
$816$	−5.08171	−0.177896
$817$	21.9931	0.769440
$818$	−75.4343	−2.63750
$819$	33.2891	1.16322
$820$	−147.477	−5.15013
$821$	−44.0032	−1.53572	−0.767862	−	0.640616i	$-0.778679\pi$
$821$	−44.0032	−1.53572	−0.767862	+	0.640616i	$0.778679\pi$
$822$	−3.38069	−0.117915
$823$	50.6667	1.76613	0.883065	−	0.469250i	$-0.155476\pi$
$823$	50.6667	1.76613	0.883065	+	0.469250i	$0.155476\pi$
$824$	35.8558	1.24910
$825$	3.19423	0.111209
$826$	83.8370	2.91706
$827$	53.9112	1.87468	0.937338	−	0.348421i	$-0.113282\pi$
$827$	53.9112	1.87468	0.937338	+	0.348421i	$0.113282\pi$
$828$	121.173	4.21106
$829$	25.9812	0.902364	0.451182	−	0.892432i	$-0.351002\pi$
$829$	25.9812	0.902364	0.451182	+	0.892432i	$0.351002\pi$
$830$	−15.9732	−0.554438
$831$	−1.77791	−0.0616748
$832$	−14.9315	−0.517656
$833$	−13.7811	−0.477486
$834$	4.10412	0.142114
$835$	−6.83950	−0.236690
$836$	−53.0870	−1.83605
$837$	9.79946	0.338719
$838$	32.0376	1.10672
$839$	41.5683	1.43510	0.717549	−	0.696508i	$-0.245264\pi$
$839$	41.5683	1.43510	0.717549	+	0.696508i	$0.245264\pi$
$840$	18.5463	0.639908
$841$	−7.81512	−0.269487
$842$	−89.0793	−3.06987
$843$	2.51771	0.0867144
$844$	95.0773	3.27270
$845$	8.80767	0.302993
$846$	12.8916	0.443221
$847$	−24.1466	−0.829686
$848$	−28.9223	−0.993196
$849$	2.54803	0.0874483
$850$	50.6655	1.73781
$851$	−39.9413	−1.36917
$852$	−8.63118	−0.295699
$853$	−25.6856	−0.879458	−0.439729	−	0.898130i	$-0.644926\pi$
$853$	−25.6856	−0.879458	−0.439729	+	0.898130i	$0.644926\pi$
$854$	−99.0355	−3.38893
$855$	−57.9840	−1.98301
$856$	84.3801	2.88405
$857$	−16.0010	−0.546582	−0.273291	−	0.961931i	$-0.588112\pi$
$857$	−16.0010	−0.546582	−0.273291	+	0.961931i	$0.588112\pi$
$858$	3.67902	0.125600
$859$	5.26894	0.179774	0.0898869	−	0.995952i	$-0.471349\pi$
$859$	5.26894	0.179774	0.0898869	+	0.995952i	$0.471349\pi$
$860$	64.5880	2.20243
$861$	6.79233	0.231482
$862$	−29.9397	−1.01975
$863$	−21.5857	−0.734786	−0.367393	−	0.930066i	$-0.619750\pi$
$863$	−21.5857	−0.734786	−0.367393	+	0.930066i	$0.619750\pi$
$864$	10.9978	0.374152
$865$	14.2619	0.484918
$866$	−46.9328	−1.59484
$867$	−2.12543	−0.0721833
$868$	−123.665	−4.19748
$869$	−10.0907	−0.342303
$870$	−9.08775	−0.308104
$871$	−35.4484	−1.20112
$872$	−34.9226	−1.18263
$873$	−26.2562	−0.888637
$874$	−126.719	−4.28633
$875$	−27.7688	−0.938758
$876$	3.43126	0.115931
$877$	−53.5275	−1.80749	−0.903747	−	0.428067i	$-0.859195\pi$
$877$	−53.5275	−1.80749	−0.903747	+	0.428067i	$0.859195\pi$
$878$	−5.96811	−0.201414
$879$	4.88848	0.164884
$880$	−61.2755	−2.06560
$881$	8.72154	0.293836	0.146918	−	0.989149i	$-0.453065\pi$
$881$	8.72154	0.293836	0.146918	+	0.989149i	$0.453065\pi$
$882$	39.1403	1.31792
$883$	27.5353	0.926635	0.463318	−	0.886192i	$-0.346659\pi$
$883$	27.5353	0.926635	0.463318	+	0.886192i	$0.346659\pi$
$884$	40.9302	1.37663
$885$	7.09825	0.238605
$886$	−78.9661	−2.65292
$887$	−6.66636	−0.223834	−0.111917	−	0.993718i	$-0.535699\pi$
$887$	−6.66636	−0.223834	−0.111917	+	0.993718i	$0.535699\pi$
$888$	−6.95112	−0.233264
$889$	1.17831	0.0395193
$890$	129.049	4.32573
$891$	17.2892	0.579211
$892$	−47.3749	−1.58623
$893$	−9.45593	−0.316431
$894$	0.305490	0.0102171
$895$	21.0508	0.703651
$896$	17.5369	0.585868
$897$	6.15957	0.205662
$898$	−7.98517	−0.266468
$899$	34.7992	1.16062
$900$	−100.929	−3.36431
$901$	8.97067	0.298856
$902$	−46.7489	−1.55657
$903$	−2.97471	−0.0989922
$904$	76.9722	2.56006
$905$	−14.3610	−0.477375
$906$	−3.65571	−0.121453
$907$	−43.2015	−1.43448	−0.717242	−	0.696825i	$-0.754596\pi$
$907$	−43.2015	−1.43448	−0.717242	+	0.696825i	$0.754596\pi$
$908$	−91.5794	−3.03917
$909$	54.3445	1.80249
$910$	−102.236	−3.38908
$911$	−47.9137	−1.58745	−0.793727	−	0.608275i	$-0.791862\pi$
$911$	−47.9137	−1.58745	−0.793727	+	0.608275i	$0.791862\pi$
$912$	−10.5864	−0.350552
$913$	−3.55143	−0.117535
$914$	−68.8340	−2.27683
$915$	−8.38507	−0.277202
$916$	−86.4601	−2.85672
$917$	66.5836	2.19878
$918$	−9.02498	−0.297869
$919$	32.6829	1.07811	0.539054	−	0.842271i	$-0.318782\pi$
$919$	32.6829	1.07811	0.539054	+	0.842271i	$0.318782\pi$
$920$	−213.712	−7.04586
$921$	−6.20487	−0.204457
$922$	−60.9333	−2.00673
$923$	27.3235	0.899365
$924$	7.18037	0.236217
$925$	33.2685	1.09386
$926$	−27.5290	−0.904659
$927$	15.1624	0.498000
$928$	39.0545	1.28203
$929$	−33.2258	−1.09010	−0.545052	−	0.838402i	$-0.683490\pi$
$929$	−33.2258	−1.09010	−0.545052	+	0.838402i	$0.683490\pi$
$930$	−14.9279	−0.489506
$931$	−28.7093	−0.940910
$932$	74.4287	2.43799
$933$	4.03467	0.132089
$934$	−20.2844	−0.663726
$935$	19.0055	0.621546
$936$	−66.7584	−2.18207
$937$	−47.9947	−1.56792	−0.783959	−	0.620813i	$-0.786803\pi$
$937$	−47.9947	−1.56792	−0.783959	+	0.620813i	$0.786803\pi$
$938$	−98.6385	−3.22066
$939$	2.08518	0.0680474
$940$	−27.7696	−0.905746
$941$	−42.2621	−1.37771	−0.688853	−	0.724901i	$-0.741886\pi$
$941$	−42.2621	−1.37771	−0.688853	+	0.724901i	$0.741886\pi$
$942$	−9.40714	−0.306501
$943$	−78.2689	−2.54879
$944$	−80.7078	−2.62682
$945$	15.8114	0.514344
$946$	20.4738	0.665660
$947$	42.3642	1.37665	0.688326	−	0.725401i	$-0.258346\pi$
$947$	42.3642	1.37665	0.688326	+	0.725401i	$0.258346\pi$
$948$	−5.11977	−0.166282
$949$	−10.8622	−0.352603
$950$	105.548	3.42444
$951$	−1.09899	−0.0356372
$952$	65.4055	2.11980
$953$	43.2080	1.39964	0.699822	−	0.714317i	$-0.253263\pi$
$953$	43.2080	1.39964	0.699822	+	0.714317i	$0.253263\pi$
$954$	−25.4780	−0.824882
$955$	−91.3820	−2.95705
$956$	−119.062	−3.85074
$957$	−2.02054	−0.0653147
$958$	−40.8525	−1.31988
$959$	20.8875	0.674492
$960$	−3.51777	−0.113536
$961$	26.1626	0.843954
$962$	38.3177	1.23541
$963$	35.6821	1.14984
$964$	−24.1983	−0.779374
$965$	11.4665	0.369118
$966$	17.1396	0.551456
$967$	−50.5061	−1.62417	−0.812083	−	0.583542i	$-0.801667\pi$
$967$	−50.5061	−1.62417	−0.812083	+	0.583542i	$0.801667\pi$
$968$	48.4238	1.55640
$969$	3.28354	0.105483
$970$	80.6365	2.58908
$971$	−50.4599	−1.61933	−0.809667	−	0.586889i	$-0.800353\pi$
$971$	−50.4599	−1.61933	−0.809667	+	0.586889i	$0.800353\pi$
$972$	27.0392	0.867284
$973$	−25.3572	−0.812913
$974$	50.6387	1.62257
$975$	−5.13052	−0.164308
$976$	95.3391	3.05173
$977$	23.0128	0.736246	0.368123	−	0.929777i	$-0.380001\pi$
$977$	23.0128	0.736246	0.368123	+	0.929777i	$0.380001\pi$
$978$	−7.97509	−0.255015
$979$	28.6923	0.917010
$980$	−84.3119	−2.69325
$981$	−14.7678	−0.471500
$982$	1.04592	0.0333765
$983$	24.3011	0.775086	0.387543	−	0.921852i	$-0.373324\pi$
$983$	24.3011	0.775086	0.387543	+	0.921852i	$0.373324\pi$
$984$	−13.6214	−0.434235
$985$	60.8473	1.93875
$986$	−32.0489	−1.02064
$987$	1.27898	0.0407103
$988$	85.2675	2.71272
$989$	34.2780	1.08998
$990$	−53.9784	−1.71555
$991$	17.5945	0.558908	0.279454	−	0.960159i	$-0.409846\pi$
$991$	17.5945	0.558908	0.279454	+	0.960159i	$0.409846\pi$
$992$	64.1526	2.03685
$993$	−4.54012	−0.144076
$994$	76.0302	2.41153
$995$	83.7261	2.65429
$996$	−1.80190	−0.0570955
$997$	−18.9712	−0.600823	−0.300412	−	0.953810i	$-0.597124\pi$
$997$	−18.9712	−0.600823	−0.300412	+	0.953810i	$0.597124\pi$
$998$	−56.8391	−1.79921
$999$	−5.92608	−0.187493

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4007.2.a.b.1.12	✓	195

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4007.2.a.b.1.12	✓	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)

\(f(q)\)	\(=\)	\(q-2.58803 q^{2} +0.217741 q^{3} +4.69789 q^{4} -3.50376 q^{5} -0.563520 q^{6} +3.48169 q^{7} -6.98221 q^{8} -2.95259 q^{9} +O(q^{10})\)	\(q-2.58803 q^{2} +0.217741 q^{3} +4.69789 q^{4} -3.50376 q^{5} -0.563520 q^{6} +3.48169 q^{7} -6.98221 q^{8} -2.95259 q^{9} +9.06783 q^{10} +2.01611 q^{11} +1.02292 q^{12} -3.23824 q^{13} -9.01070 q^{14} -0.762912 q^{15} +8.67439 q^{16} -2.69049 q^{17} +7.64138 q^{18} -5.60494 q^{19} -16.4603 q^{20} +0.758106 q^{21} -5.21775 q^{22} -8.73576 q^{23} -1.52031 q^{24} +7.27632 q^{25} +8.38067 q^{26} -1.29612 q^{27} +16.3566 q^{28} -4.60270 q^{29} +1.97444 q^{30} -7.56059 q^{31} -8.48513 q^{32} +0.438990 q^{33} +6.96306 q^{34} -12.1990 q^{35} -13.8709 q^{36} +4.57216 q^{37} +14.5057 q^{38} -0.705098 q^{39} +24.4640 q^{40} +8.95960 q^{41} -1.96200 q^{42} -3.92387 q^{43} +9.47146 q^{44} +10.3452 q^{45} +22.6084 q^{46} +1.68707 q^{47} +1.88877 q^{48} +5.12215 q^{49} -18.8313 q^{50} -0.585830 q^{51} -15.2129 q^{52} -3.33422 q^{53} +3.35440 q^{54} -7.06396 q^{55} -24.3099 q^{56} -1.22043 q^{57} +11.9119 q^{58} -9.30415 q^{59} -3.58408 q^{60} +10.9909 q^{61} +19.5670 q^{62} -10.2800 q^{63} +4.61098 q^{64} +11.3460 q^{65} -1.13612 q^{66} +10.9468 q^{67} -12.6396 q^{68} -1.90213 q^{69} +31.5713 q^{70} -8.43776 q^{71} +20.6156 q^{72} +3.35436 q^{73} -11.8329 q^{74} +1.58435 q^{75} -26.3314 q^{76} +7.01946 q^{77} +1.82481 q^{78} -5.00504 q^{79} -30.3930 q^{80} +8.57555 q^{81} -23.1877 q^{82} -1.76152 q^{83} +3.56150 q^{84} +9.42682 q^{85} +10.1551 q^{86} -1.00220 q^{87} -14.0769 q^{88} +14.2315 q^{89} -26.7736 q^{90} -11.2746 q^{91} -41.0396 q^{92} -1.64625 q^{93} -4.36619 q^{94} +19.6384 q^{95} -1.84756 q^{96} +8.89259 q^{97} -13.2563 q^{98} -5.95274 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 195 q + 14 q^{2} + 22 q^{3} + 220 q^{4} + 14 q^{5} + 13 q^{6} + 48 q^{7} + 39 q^{8} + 245 q^{9}+O(q^{10}) \) 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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