LMFDB - Embedded newform 4007.2.a.b.1.3

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			1.3
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)

$f(q)$	$=$	$q-2.77052 q^{2} -1.23937 q^{3} +5.67576 q^{4} -3.30641 q^{5} +3.43369 q^{6} +0.994092 q^{7} -10.1837 q^{8} -1.46397 q^{9} +O(q^{10})$	\(q-2.77052 q^{2} -1.23937 q^{3} +5.67576 q^{4} -3.30641 q^{5} +3.43369 q^{6} +0.994092 q^{7} -10.1837 q^{8} -1.46397 q^{9} +9.16047 q^{10} +2.91316 q^{11} -7.03435 q^{12} +2.07626 q^{13} -2.75415 q^{14} +4.09786 q^{15} +16.8627 q^{16} +4.81136 q^{17} +4.05595 q^{18} +1.21446 q^{19} -18.7664 q^{20} -1.23204 q^{21} -8.07096 q^{22} +6.65884 q^{23} +12.6214 q^{24} +5.93236 q^{25} -5.75232 q^{26} +5.53250 q^{27} +5.64222 q^{28} -2.11829 q^{29} -11.3532 q^{30} +10.3256 q^{31} -26.3509 q^{32} -3.61048 q^{33} -13.3299 q^{34} -3.28688 q^{35} -8.30913 q^{36} +5.71649 q^{37} -3.36469 q^{38} -2.57325 q^{39} +33.6716 q^{40} +3.53656 q^{41} +3.41340 q^{42} +5.71015 q^{43} +16.5344 q^{44} +4.84048 q^{45} -18.4484 q^{46} +4.09201 q^{47} -20.8991 q^{48} -6.01178 q^{49} -16.4357 q^{50} -5.96304 q^{51} +11.7844 q^{52} -3.54063 q^{53} -15.3279 q^{54} -9.63211 q^{55} -10.1236 q^{56} -1.50517 q^{57} +5.86875 q^{58} -9.23267 q^{59} +23.2584 q^{60} -14.5531 q^{61} -28.6073 q^{62} -1.45532 q^{63} +39.2801 q^{64} -6.86498 q^{65} +10.0029 q^{66} +8.60276 q^{67} +27.3081 q^{68} -8.25274 q^{69} +9.10634 q^{70} +1.60963 q^{71} +14.9087 q^{72} +5.73619 q^{73} -15.8376 q^{74} -7.35237 q^{75} +6.89300 q^{76} +2.89595 q^{77} +7.12924 q^{78} +16.4185 q^{79} -55.7550 q^{80} -2.46489 q^{81} -9.79808 q^{82} -6.24645 q^{83} -6.99278 q^{84} -15.9083 q^{85} -15.8201 q^{86} +2.62534 q^{87} -29.6669 q^{88} -3.62229 q^{89} -13.4106 q^{90} +2.06400 q^{91} +37.7939 q^{92} -12.7972 q^{93} -11.3370 q^{94} -4.01552 q^{95} +32.6584 q^{96} -10.3255 q^{97} +16.6557 q^{98} -4.26478 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.77052	−1.95905	−0.979525	−	0.201322i	$-0.935476\pi$
$2$	−2.77052	−1.95905	−0.979525	+	0.201322i	$0.935476\pi$
$3$	−1.23937	−0.715549	−0.357774	−	0.933808i	$-0.616464\pi$
$3$	−1.23937	−0.715549	−0.357774	+	0.933808i	$0.616464\pi$
$4$	5.67576	2.83788
$5$	−3.30641	−1.47867	−0.739336	−	0.673336i	$-0.764861\pi$
$5$	−3.30641	−1.47867	−0.739336	+	0.673336i	$0.764861\pi$
$6$	3.43369	1.40180
$7$	0.994092	0.375731	0.187866	−	0.982195i	$-0.439843\pi$
$7$	0.994092	0.375731	0.187866	+	0.982195i	$0.439843\pi$
$8$	−10.1837	−3.60050
$9$	−1.46397	−0.487990
$10$	9.16047	2.89679
$11$	2.91316	0.878351	0.439176	−	0.898401i	$-0.355271\pi$
$11$	2.91316	0.878351	0.439176	+	0.898401i	$0.355271\pi$
$12$	−7.03435	−2.03064
$13$	2.07626	0.575852	0.287926	−	0.957653i	$-0.407034\pi$
$13$	2.07626	0.575852	0.287926	+	0.957653i	$0.407034\pi$
$14$	−2.75415	−0.736076
$15$	4.09786	1.05806
$16$	16.8627	4.21567
$17$	4.81136	1.16693	0.583463	−	0.812140i	$-0.301698\pi$
$17$	4.81136	1.16693	0.583463	+	0.812140i	$0.301698\pi$
$18$	4.05595	0.955996
$19$	1.21446	0.278617	0.139309	−	0.990249i	$-0.455512\pi$
$19$	1.21446	0.278617	0.139309	+	0.990249i	$0.455512\pi$
$20$	−18.7664	−4.19629
$21$	−1.23204	−0.268854
$22$	−8.07096	−1.72073
$23$	6.65884	1.38846	0.694232	−	0.719752i	$-0.255744\pi$
$23$	6.65884	1.38846	0.694232	+	0.719752i	$0.255744\pi$
$24$	12.6214	2.57633
$25$	5.93236	1.18647
$26$	−5.75232	−1.12812
$27$	5.53250	1.06473
$28$	5.64222	1.06628
$29$	−2.11829	−0.393356	−0.196678	−	0.980468i	$-0.563015\pi$
$29$	−2.11829	−0.393356	−0.196678	+	0.980468i	$0.563015\pi$
$30$	−11.3532	−2.07280
$31$	10.3256	1.85454	0.927269	−	0.374396i	$-0.122150\pi$
$31$	10.3256	1.85454	0.927269	+	0.374396i	$0.122150\pi$
$32$	−26.3509	−4.65822
$33$	−3.61048	−0.628503
$34$	−13.3299	−2.28606
$35$	−3.28688	−0.555583
$36$	−8.30913	−1.38486
$37$	5.71649	0.939785	0.469892	−	0.882724i	$-0.344293\pi$
$37$	5.71649	0.939785	0.469892	+	0.882724i	$0.344293\pi$
$38$	−3.36469	−0.545825
$39$	−2.57325	−0.412050
$40$	33.6716	5.32395
$41$	3.53656	0.552317	0.276159	−	0.961112i	$-0.410938\pi$
$41$	3.53656	0.552317	0.276159	+	0.961112i	$0.410938\pi$
$42$	3.41340	0.526699
$43$	5.71015	0.870790	0.435395	−	0.900239i	$-0.356609\pi$
$43$	5.71015	0.870790	0.435395	+	0.900239i	$0.356609\pi$
$44$	16.5344	2.49265
$45$	4.84048	0.721577
$46$	−18.4484	−2.72007
$47$	4.09201	0.596881	0.298440	−	0.954428i	$-0.403534\pi$
$47$	4.09201	0.596881	0.298440	+	0.954428i	$0.403534\pi$
$48$	−20.8991	−3.01652
$49$	−6.01178	−0.858826
$50$	−16.4357	−2.32436
$51$	−5.96304	−0.834992
$52$	11.7844	1.63420
$53$	−3.54063	−0.486342	−0.243171	−	0.969983i	$-0.578188\pi$
$53$	−3.54063	−0.486342	−0.243171	+	0.969983i	$0.578188\pi$
$54$	−15.3279	−2.08586
$55$	−9.63211	−1.29879
$56$	−10.1236	−1.35282
$57$	−1.50517	−0.199364
$58$	5.86875	0.770605
$59$	−9.23267	−1.20199	−0.600995	−	0.799252i	$-0.705229\pi$
$59$	−9.23267	−1.20199	−0.600995	+	0.799252i	$0.705229\pi$
$60$	23.2584	3.00265
$61$	−14.5531	−1.86334	−0.931669	−	0.363307i	$-0.881648\pi$
$61$	−14.5531	−1.86334	−0.931669	+	0.363307i	$0.881648\pi$
$62$	−28.6073	−3.63313
$63$	−1.45532	−0.183353
$64$	39.2801	4.91002
$65$	−6.86498	−0.851496
$66$	10.0029	1.23127
$67$	8.60276	1.05099	0.525497	−	0.850795i	$-0.323879\pi$
$67$	8.60276	1.05099	0.525497	+	0.850795i	$0.323879\pi$
$68$	27.3081	3.31159
$69$	−8.25274	−0.993513
$70$	9.10634	1.08842
$71$	1.60963	0.191028	0.0955140	−	0.995428i	$-0.469551\pi$
$71$	1.60963	0.191028	0.0955140	+	0.995428i	$0.469551\pi$
$72$	14.9087	1.75700
$73$	5.73619	0.671370	0.335685	−	0.941974i	$-0.391032\pi$
$73$	5.73619	0.671370	0.335685	+	0.941974i	$0.391032\pi$
$74$	−15.8376	−1.84109
$75$	−7.35237	−0.848979
$76$	6.89300	0.790681
$77$	2.89595	0.330024
$78$	7.12924	0.807227
$79$	16.4185	1.84722	0.923611	−	0.383331i	$-0.125223\pi$
$79$	16.4185	1.84722	0.923611	+	0.383331i	$0.125223\pi$
$80$	−55.7550	−6.23360
$81$	−2.46489	−0.273876
$82$	−9.79808	−1.08202
$83$	−6.24645	−0.685637	−0.342818	−	0.939402i	$-0.611382\pi$
$83$	−6.24645	−0.685637	−0.342818	+	0.939402i	$0.611382\pi$
$84$	−6.99278	−0.762975
$85$	−15.9083	−1.72550
$86$	−15.8201	−1.70592
$87$	2.62534	0.281466
$88$	−29.6669	−3.16250
$89$	−3.62229	−0.383962	−0.191981	−	0.981399i	$-0.561491\pi$
$89$	−3.62229	−0.383962	−0.191981	+	0.981399i	$0.561491\pi$
$90$	−13.4106	−1.41361
$91$	2.06400	0.216366
$92$	37.7939	3.94029
$93$	−12.7972	−1.32701
$94$	−11.3370	−1.16932
$95$	−4.01552	−0.411984
$96$	32.6584	3.33319
$97$	−10.3255	−1.04840	−0.524199	−	0.851596i	$-0.675635\pi$
$97$	−10.3255	−1.04840	−0.524199	+	0.851596i	$0.675635\pi$
$98$	16.6557	1.68248
$99$	−4.26478	−0.428626
$100$	33.6706	3.36706
$101$	6.07427	0.604413	0.302206	−	0.953243i	$-0.402277\pi$
$101$	6.07427	0.604413	0.302206	+	0.953243i	$0.402277\pi$
$102$	16.5207	1.63579
$103$	9.62892	0.948766	0.474383	−	0.880319i	$-0.342671\pi$
$103$	9.62892	0.948766	0.474383	+	0.880319i	$0.342671\pi$
$104$	−21.1441	−2.07335
$105$	4.07365	0.397547
$106$	9.80936	0.952769
$107$	13.0355	1.26019	0.630096	−	0.776517i	$-0.283016\pi$
$107$	13.0355	1.26019	0.630096	+	0.776517i	$0.283016\pi$
$108$	31.4011	3.02157
$109$	5.73531	0.549343	0.274672	−	0.961538i	$-0.411431\pi$
$109$	5.73531	0.549343	0.274672	+	0.961538i	$0.411431\pi$
$110$	26.6859	2.54440
$111$	−7.08483	−0.672462
$112$	16.7631	1.58396
$113$	−11.8656	−1.11622	−0.558109	−	0.829768i	$-0.688473\pi$
$113$	−11.8656	−1.11622	−0.558109	+	0.829768i	$0.688473\pi$
$114$	4.17009	0.390565
$115$	−22.0169	−2.05308
$116$	−12.0229	−1.11630
$117$	−3.03958	−0.281010
$118$	25.5792	2.35476
$119$	4.78293	0.438450
$120$	−41.7315	−3.80955
$121$	−2.51349	−0.228499
$122$	40.3197	3.65037
$123$	−4.38309	−0.395210
$124$	58.6058	5.26295
$125$	−3.08277	−0.275731
$126$	4.03198	0.359198
$127$	16.5332	1.46708	0.733541	−	0.679645i	$-0.237866\pi$
$127$	16.5332	1.46708	0.733541	+	0.679645i	$0.237866\pi$
$128$	−56.1244	−4.96075
$129$	−7.07698	−0.623093
$130$	19.0195	1.66812
$131$	11.7205	1.02403	0.512013	−	0.858977i	$-0.328900\pi$
$131$	11.7205	1.02403	0.512013	+	0.858977i	$0.328900\pi$
$132$	−20.4922	−1.78362
$133$	1.20729	0.104685
$134$	−23.8341	−2.05895
$135$	−18.2927	−1.57439
$136$	−48.9976	−4.20151
$137$	1.51778	0.129673	0.0648365	−	0.997896i	$-0.479347\pi$
$137$	1.51778	0.129673	0.0648365	+	0.997896i	$0.479347\pi$
$138$	22.8643	1.94634
$139$	−15.5439	−1.31842	−0.659209	−	0.751960i	$-0.729109\pi$
$139$	−15.5439	−1.31842	−0.659209	+	0.751960i	$0.729109\pi$
$140$	−18.6555	−1.57668
$141$	−5.07150	−0.427098
$142$	−4.45951	−0.374233
$143$	6.04849	0.505800
$144$	−24.6865	−2.05721
$145$	7.00394	0.581645
$146$	−15.8922	−1.31525
$147$	7.45081	0.614532
$148$	32.4454	2.66699
$149$	3.00769	0.246400	0.123200	−	0.992382i	$-0.460684\pi$
$149$	3.00769	0.246400	0.123200	+	0.992382i	$0.460684\pi$
$150$	20.3699	1.66319
$151$	−5.08613	−0.413904	−0.206952	−	0.978351i	$-0.566354\pi$
$151$	−5.08613	−0.413904	−0.206952	+	0.978351i	$0.566354\pi$
$152$	−12.3678	−1.00316
$153$	−7.04367	−0.569447
$154$	−8.02327	−0.646534
$155$	−34.1408	−2.74225
$156$	−14.6052	−1.16935
$157$	9.43823	0.753253	0.376626	−	0.926365i	$-0.377084\pi$
$157$	9.43823	0.753253	0.376626	+	0.926365i	$0.377084\pi$
$158$	−45.4876	−3.61880
$159$	4.38814	0.348002
$160$	87.1269	6.88798
$161$	6.61949	0.521689
$162$	6.82901	0.536538
$163$	−4.63869	−0.363330	−0.181665	−	0.983360i	$-0.558149\pi$
$163$	−4.63869	−0.363330	−0.181665	+	0.983360i	$0.558149\pi$
$164$	20.0726	1.56741
$165$	11.9377	0.929351
$166$	17.3059	1.34320
$167$	−16.7707	−1.29776	−0.648879	−	0.760892i	$-0.724762\pi$
$167$	−16.7707	−1.29776	−0.648879	+	0.760892i	$0.724762\pi$
$168$	12.5468	0.968008
$169$	−8.68913	−0.668395
$170$	44.0743	3.38034
$171$	−1.77794	−0.135962
$172$	32.4094	2.47120
$173$	−1.46616	−0.111470	−0.0557352	−	0.998446i	$-0.517750\pi$
$173$	−1.46616	−0.111470	−0.0557352	+	0.998446i	$0.517750\pi$
$174$	−7.27354	−0.551406
$175$	5.89731	0.445795
$176$	49.1238	3.70284
$177$	11.4427	0.860083
$178$	10.0356	0.752201
$179$	−22.3085	−1.66742	−0.833708	−	0.552205i	$-0.813786\pi$
$179$	−22.3085	−1.66742	−0.833708	+	0.552205i	$0.813786\pi$
$180$	27.4734	2.04775
$181$	−1.89933	−0.141176	−0.0705882	−	0.997506i	$-0.522488\pi$
$181$	−1.89933	−0.141176	−0.0705882	+	0.997506i	$0.522488\pi$
$182$	−5.71833	−0.423871
$183$	18.0367	1.33331
$184$	−67.8118	−4.99916
$185$	−18.9011	−1.38963
$186$	35.4550	2.59968
$187$	14.0163	1.02497
$188$	23.2252	1.69388
$189$	5.49981	0.400052
$190$	11.1251	0.807096
$191$	0.205124	0.0148423	0.00742114	−	0.999972i	$-0.497638\pi$
$191$	0.205124	0.0148423	0.00742114	+	0.999972i	$0.497638\pi$
$192$	−48.6825	−3.51336
$193$	2.88113	0.207388	0.103694	−	0.994609i	$-0.466934\pi$
$193$	2.88113	0.207388	0.103694	+	0.994609i	$0.466934\pi$
$194$	28.6070	2.05387
$195$	8.50823	0.609287
$196$	−34.1214	−2.43724
$197$	3.47856	0.247837	0.123918	−	0.992292i	$-0.460454\pi$
$197$	3.47856	0.247837	0.123918	+	0.992292i	$0.460454\pi$
$198$	11.8156	0.839701
$199$	11.7514	0.833037	0.416519	−	0.909127i	$-0.363250\pi$
$199$	11.7514	0.833037	0.416519	+	0.909127i	$0.363250\pi$
$200$	−60.4136	−4.27189
$201$	−10.6620	−0.752038
$202$	−16.8289	−1.18407
$203$	−2.10577	−0.147796
$204$	−33.8447	−2.36961
$205$	−11.6933	−0.816696
$206$	−26.6771	−1.85868
$207$	−9.74833	−0.677556
$208$	35.0114	2.42760
$209$	3.53793	0.244724
$210$	−11.2861	−0.778815
$211$	−15.1168	−1.04068	−0.520340	−	0.853959i	$-0.674195\pi$
$211$	−15.1168	−1.04068	−0.520340	+	0.853959i	$0.674195\pi$
$212$	−20.0957	−1.38018
$213$	−1.99492	−0.136690
$214$	−36.1151	−2.46878
$215$	−18.8801	−1.28761
$216$	−56.3415	−3.83355
$217$	10.2646	0.696808
$218$	−15.8898	−1.07619
$219$	−7.10925	−0.480398
$220$	−54.6695	−3.68582
$221$	9.98964	0.671976
$222$	19.6286	1.31739
$223$	−1.10236	−0.0738195	−0.0369098	−	0.999319i	$-0.511751\pi$
$223$	−1.10236	−0.0738195	−0.0369098	+	0.999319i	$0.511751\pi$
$224$	−26.1952	−1.75024
$225$	−8.68479	−0.578986
$226$	32.8737	2.18673
$227$	13.1157	0.870517	0.435258	−	0.900306i	$-0.356657\pi$
$227$	13.1157	0.870517	0.435258	+	0.900306i	$0.356657\pi$
$228$	−8.54296	−0.565771
$229$	−12.1917	−0.805651	−0.402826	−	0.915277i	$-0.631972\pi$
$229$	−12.1917	−0.805651	−0.402826	+	0.915277i	$0.631972\pi$
$230$	60.9980	4.02209
$231$	−3.58914	−0.236148
$232$	21.5721	1.41628
$233$	−20.2198	−1.32464	−0.662322	−	0.749219i	$-0.730429\pi$
$233$	−20.2198	−1.32464	−0.662322	+	0.749219i	$0.730429\pi$
$234$	8.42122	0.550512
$235$	−13.5299	−0.882591
$236$	−52.4024	−3.41110
$237$	−20.3485	−1.32178
$238$	−13.2512	−0.858946
$239$	7.73971	0.500640	0.250320	−	0.968163i	$-0.419464\pi$
$239$	7.73971	0.500640	0.250320	+	0.968163i	$0.419464\pi$
$240$	69.1009	4.46045
$241$	−8.80975	−0.567486	−0.283743	−	0.958900i	$-0.591576\pi$
$241$	−8.80975	−0.567486	−0.283743	+	0.958900i	$0.591576\pi$
$242$	6.96366	0.447641
$243$	−13.5426	−0.868757
$244$	−82.6001	−5.28793
$245$	19.8774	1.26992
$246$	12.1434	0.774236
$247$	2.52155	0.160442
$248$	−105.154	−6.67726
$249$	7.74164	0.490607
$250$	8.54087	0.540172
$251$	29.6227	1.86977	0.934883	−	0.354956i	$-0.115504\pi$
$251$	29.6227	1.86977	0.934883	+	0.354956i	$0.115504\pi$
$252$	−8.26004	−0.520333
$253$	19.3983	1.21956
$254$	−45.8054	−2.87409
$255$	19.7163	1.23468
$256$	76.9334	4.80834
$257$	14.2007	0.885812	0.442906	−	0.896568i	$-0.353947\pi$
$257$	14.2007	0.885812	0.442906	+	0.896568i	$0.353947\pi$
$258$	19.6069	1.22067
$259$	5.68271	0.353107
$260$	−38.9640	−2.41644
$261$	3.10111	0.191954
$262$	−32.4719	−2.00612
$263$	31.6261	1.95015	0.975075	−	0.221875i	$-0.0712178\pi$
$263$	31.6261	1.95015	0.975075	+	0.221875i	$0.0712178\pi$
$264$	36.7682	2.26292
$265$	11.7068	0.719141
$266$	−3.34481	−0.205084
$267$	4.48935	0.274744
$268$	48.8272	2.98259
$269$	−20.9269	−1.27593	−0.637967	−	0.770064i	$-0.720224\pi$
$269$	−20.9269	−1.27593	−0.637967	+	0.770064i	$0.720224\pi$
$270$	50.6802	3.08430
$271$	−16.7834	−1.01952	−0.509759	−	0.860317i	$-0.670266\pi$
$271$	−16.7834	−1.01952	−0.509759	+	0.860317i	$0.670266\pi$
$272$	81.1324	4.91938
$273$	−2.55805	−0.154820
$274$	−4.20504	−0.254036
$275$	17.2819	1.04214
$276$	−46.8405	−2.81947
$277$	−23.7231	−1.42539	−0.712693	−	0.701476i	$-0.752525\pi$
$277$	−23.7231	−1.42539	−0.712693	+	0.701476i	$0.752525\pi$
$278$	43.0647	2.58285
$279$	−15.1164	−0.904995
$280$	33.4727	2.00038
$281$	15.7495	0.939537	0.469769	−	0.882790i	$-0.344337\pi$
$281$	15.7495	0.939537	0.469769	+	0.882790i	$0.344337\pi$
$282$	14.0507	0.836706
$283$	−22.7026	−1.34953	−0.674764	−	0.738034i	$-0.735754\pi$
$283$	−22.7026	−1.34953	−0.674764	+	0.738034i	$0.735754\pi$
$284$	9.13587	0.542114
$285$	4.97670	0.294794
$286$	−16.7574	−0.990888
$287$	3.51566	0.207523
$288$	38.5769	2.27316
$289$	6.14914	0.361714
$290$	−19.4045	−1.13947
$291$	12.7971	0.750180
$292$	32.5572	1.90527
$293$	−15.8556	−0.926295	−0.463148	−	0.886281i	$-0.653280\pi$
$293$	−15.8556	−0.926295	−0.463148	+	0.886281i	$0.653280\pi$
$294$	−20.6426	−1.20390
$295$	30.5270	1.77735
$296$	−58.2152	−3.38369
$297$	16.1171	0.935207
$298$	−8.33286	−0.482709
$299$	13.8255	0.799549
$300$	−41.7303	−2.40930
$301$	5.67641	0.327183
$302$	14.0912	0.810858
$303$	−7.52825	−0.432487
$304$	20.4791	1.17456
$305$	48.1187	2.75527
$306$	19.5146	1.11558
$307$	26.4237	1.50808	0.754039	−	0.656829i	$-0.228103\pi$
$307$	26.4237	1.50808	0.754039	+	0.656829i	$0.228103\pi$
$308$	16.4367	0.936568
$309$	−11.9338	−0.678888
$310$	94.5876	5.37221
$311$	18.8003	1.06607	0.533034	−	0.846094i	$-0.321052\pi$
$311$	18.8003	1.06607	0.533034	+	0.846094i	$0.321052\pi$
$312$	26.2053	1.48358
$313$	28.1506	1.59117	0.795584	−	0.605843i	$-0.207164\pi$
$313$	28.1506	1.59117	0.795584	+	0.605843i	$0.207164\pi$
$314$	−26.1488	−1.47566
$315$	4.81188	0.271119
$316$	93.1872	5.24219
$317$	10.3844	0.583246	0.291623	−	0.956533i	$-0.405805\pi$
$317$	10.3844	0.583246	0.291623	+	0.956533i	$0.405805\pi$
$318$	−12.1574	−0.681753
$319$	−6.17092	−0.345505
$320$	−129.876	−7.26031
$321$	−16.1558	−0.901729
$322$	−18.3394	−1.02202
$323$	5.84322	0.325125
$324$	−13.9901	−0.777228
$325$	12.3171	0.683232
$326$	12.8516	0.711783
$327$	−7.10816	−0.393082
$328$	−36.0154	−1.98862
$329$	4.06783	0.224267
$330$	−33.0737	−1.82064
$331$	5.48437	0.301448	0.150724	−	0.988576i	$-0.451839\pi$
$331$	5.48437	0.301448	0.150724	+	0.988576i	$0.451839\pi$
$332$	−35.4533	−1.94575
$333$	−8.36876	−0.458605
$334$	46.4636	2.54237
$335$	−28.4443	−1.55408
$336$	−20.7756	−1.13340
$337$	5.96960	0.325185	0.162593	−	0.986693i	$-0.448014\pi$
$337$	5.96960	0.325185	0.162593	+	0.986693i	$0.448014\pi$
$338$	24.0734	1.30942
$339$	14.7058	0.798708
$340$	−90.2918	−4.89676
$341$	30.0802	1.62894
$342$	4.92580	0.266357
$343$	−12.9349	−0.698419
$344$	−58.1507	−3.13528
$345$	27.2870	1.46908
$346$	4.06203	0.218376
$347$	6.44036	0.345737	0.172868	−	0.984945i	$-0.444696\pi$
$347$	6.44036	0.345737	0.172868	+	0.984945i	$0.444696\pi$
$348$	14.9008	0.798766
$349$	−27.3391	−1.46343	−0.731714	−	0.681611i	$-0.761280\pi$
$349$	−27.3391	−1.46343	−0.731714	+	0.681611i	$0.761280\pi$
$350$	−16.3386	−0.873334
$351$	11.4869	0.613126
$352$	−76.7644	−4.09155
$353$	−8.29497	−0.441497	−0.220748	−	0.975331i	$-0.570850\pi$
$353$	−8.29497	−0.441497	−0.220748	+	0.975331i	$0.570850\pi$
$354$	−31.7021	−1.68495
$355$	−5.32210	−0.282468
$356$	−20.5592	−1.08964
$357$	−5.92780	−0.313733
$358$	61.8061	3.26655
$359$	1.02179	0.0539280	0.0269640	−	0.999636i	$-0.491416\pi$
$359$	1.02179	0.0539280	0.0269640	+	0.999636i	$0.491416\pi$
$360$	−49.2942	−2.59803
$361$	−17.5251	−0.922372
$362$	5.26214	0.276572
$363$	3.11513	0.163502
$364$	11.7147	0.614019
$365$	−18.9662	−0.992737
$366$	−49.9709	−2.61202
$367$	34.3198	1.79148	0.895740	−	0.444579i	$-0.146647\pi$
$367$	34.3198	1.79148	0.895740	+	0.444579i	$0.146647\pi$
$368$	112.286	5.85331
$369$	−5.17741	−0.269525
$370$	52.3657	2.72236
$371$	−3.51971	−0.182734
$372$	−72.6341	−3.76590
$373$	16.9249	0.876336	0.438168	−	0.898893i	$-0.355628\pi$
$373$	16.9249	0.876336	0.438168	+	0.898893i	$0.355628\pi$
$374$	−38.8323	−2.00797
$375$	3.82069	0.197299
$376$	−41.6720	−2.14907
$377$	−4.39813	−0.226515
$378$	−15.2373	−0.783722
$379$	38.8632	1.99627	0.998134	−	0.0610647i	$-0.0194496\pi$
$379$	38.8632	1.99627	0.998134	+	0.0610647i	$0.0194496\pi$
$380$	−22.7911	−1.16916
$381$	−20.4907	−1.04977
$382$	−0.568300	−0.0290768
$383$	−11.6681	−0.596214	−0.298107	−	0.954532i	$-0.596355\pi$
$383$	−11.6681	−0.596214	−0.298107	+	0.954532i	$0.596355\pi$
$384$	69.5588	3.54966
$385$	−9.57520	−0.487998
$386$	−7.98221	−0.406284
$387$	−8.35949	−0.424937
$388$	−58.6052	−2.97523
$389$	−32.1958	−1.63239	−0.816196	−	0.577775i	$-0.803921\pi$
$389$	−32.1958	−1.63239	−0.816196	+	0.577775i	$0.803921\pi$
$390$	−23.5722	−1.19362
$391$	32.0380	1.62023
$392$	61.2224	3.09220
$393$	−14.5260	−0.732741
$394$	−9.63739	−0.485525
$395$	−54.2862	−2.73144
$396$	−24.2058	−1.21639
$397$	−3.85497	−0.193476	−0.0967378	−	0.995310i	$-0.530841\pi$
$397$	−3.85497	−0.193476	−0.0967378	+	0.995310i	$0.530841\pi$
$398$	−32.5575	−1.63196
$399$	−1.49627	−0.0749074
$400$	100.036	5.00178
$401$	1.19710	0.0597804	0.0298902	−	0.999553i	$-0.490484\pi$
$401$	1.19710	0.0597804	0.0298902	+	0.999553i	$0.490484\pi$
$402$	29.5392	1.47328
$403$	21.4387	1.06794
$404$	34.4761	1.71525
$405$	8.14994	0.404974
$406$	5.83408	0.289540
$407$	16.6531	0.825461
$408$	60.7260	3.00638
$409$	18.8864	0.933873	0.466937	−	0.884291i	$-0.345358\pi$
$409$	18.8864	0.933873	0.466937	+	0.884291i	$0.345358\pi$
$410$	32.3965	1.59995
$411$	−1.88109	−0.0927873
$412$	54.6514	2.69248
$413$	−9.17812	−0.451626
$414$	27.0079	1.32737
$415$	20.6533	1.01383
$416$	−54.7114	−2.68244
$417$	19.2646	0.943393
$418$	−9.80189	−0.479426
$419$	16.1793	0.790411	0.395205	−	0.918593i	$-0.370673\pi$
$419$	16.1793	0.790411	0.395205	+	0.918593i	$0.370673\pi$
$420$	23.1210	1.12819
$421$	−14.7816	−0.720409	−0.360204	−	0.932873i	$-0.617293\pi$
$421$	−14.7816	−0.720409	−0.360204	+	0.932873i	$0.617293\pi$
$422$	41.8812	2.03875
$423$	−5.99058	−0.291272
$424$	36.0568	1.75107
$425$	28.5427	1.38452
$426$	5.52697	0.267782
$427$	−14.4672	−0.700115
$428$	73.9865	3.57627
$429$	−7.49630	−0.361925
$430$	52.3077	2.52250
$431$	−7.87624	−0.379385	−0.189693	−	0.981844i	$-0.560749\pi$
$431$	−7.87624	−0.379385	−0.189693	+	0.981844i	$0.560749\pi$
$432$	93.2928	4.48855
$433$	−12.1158	−0.582248	−0.291124	−	0.956685i	$-0.594029\pi$
$433$	−12.1158	−0.582248	−0.291124	+	0.956685i	$0.594029\pi$
$434$	−28.4383	−1.36508
$435$	−8.68045	−0.416196
$436$	32.5522	1.55897
$437$	8.08692	0.386850
$438$	19.6963	0.941125
$439$	36.1669	1.72615	0.863075	−	0.505075i	$-0.168535\pi$
$439$	36.1669	1.72615	0.863075	+	0.505075i	$0.168535\pi$
$440$	98.0909	4.67630
$441$	8.80106	0.419098
$442$	−27.6765	−1.31643
$443$	39.6356	1.88315	0.941573	−	0.336809i	$-0.109348\pi$
$443$	39.6356	1.88315	0.941573	+	0.336809i	$0.109348\pi$
$444$	−40.2118	−1.90837
$445$	11.9768	0.567754
$446$	3.05411	0.144616
$447$	−3.72763	−0.176311
$448$	39.0480	1.84485
$449$	−20.3594	−0.960820	−0.480410	−	0.877044i	$-0.659512\pi$
$449$	−20.3594	−0.960820	−0.480410	+	0.877044i	$0.659512\pi$
$450$	24.0614	1.13426
$451$	10.3026	0.485129
$452$	−67.3460	−3.16769
$453$	6.30359	0.296168
$454$	−36.3371	−1.70539
$455$	−6.82442	−0.319934
$456$	15.3282	0.717810
$457$	−1.35708	−0.0634814	−0.0317407	−	0.999496i	$-0.510105\pi$
$457$	−1.35708	−0.0634814	−0.0317407	+	0.999496i	$0.510105\pi$
$458$	33.7773	1.57831
$459$	26.6188	1.24246
$460$	−124.962	−5.82640
$461$	−16.5480	−0.770716	−0.385358	−	0.922767i	$-0.625922\pi$
$461$	−16.5480	−0.770716	−0.385358	+	0.922767i	$0.625922\pi$
$462$	9.94378	0.462627
$463$	−4.37814	−0.203469	−0.101735	−	0.994812i	$-0.532439\pi$
$463$	−4.37814	−0.203469	−0.101735	+	0.994812i	$0.532439\pi$
$464$	−35.7201	−1.65826
$465$	42.3130	1.96222
$466$	56.0193	2.59505
$467$	38.6359	1.78785	0.893927	−	0.448212i	$-0.147939\pi$
$467$	38.6359	1.78785	0.893927	+	0.448212i	$0.147939\pi$
$468$	−17.2519	−0.797471
$469$	8.55193	0.394892
$470$	37.4847	1.72904
$471$	−11.6974	−0.538989
$472$	94.0231	4.32776
$473$	16.6346	0.764860
$474$	56.3759	2.58943
$475$	7.20464	0.330572
$476$	27.1467	1.24427
$477$	5.18337	0.237330
$478$	−21.4430	−0.980780
$479$	−25.4982	−1.16504	−0.582521	−	0.812816i	$-0.697934\pi$
$479$	−25.4982	−1.16504	−0.582521	+	0.812816i	$0.697934\pi$
$480$	−107.982	−4.92869
$481$	11.8689	0.541177
$482$	24.4075	1.11173
$483$	−8.20398	−0.373294
$484$	−14.2659	−0.648452
$485$	34.1405	1.55024
$486$	37.5200	1.70194
$487$	−29.3505	−1.33000	−0.664999	−	0.746844i	$-0.731568\pi$
$487$	−29.3505	−1.33000	−0.664999	+	0.746844i	$0.731568\pi$
$488$	148.205	6.70894
$489$	5.74904	0.259981
$490$	−55.0707	−2.48784
$491$	6.33901	0.286075	0.143038	−	0.989717i	$-0.454313\pi$
$491$	6.33901	0.286075	0.143038	+	0.989717i	$0.454313\pi$
$492$	−24.8774	−1.12156
$493$	−10.1918	−0.459017
$494$	−6.98598	−0.314314
$495$	14.1011	0.633798
$496$	174.118	7.81813
$497$	1.60012	0.0717752
$498$	−21.4483	−0.961123
$499$	12.2642	0.549019	0.274510	−	0.961584i	$-0.411484\pi$
$499$	12.2642	0.549019	0.274510	+	0.961584i	$0.411484\pi$
$500$	−17.4971	−0.782492
$501$	20.7851	0.928609
$502$	−82.0701	−3.66297
$503$	15.0338	0.670324	0.335162	−	0.942161i	$-0.391209\pi$
$503$	15.0338	0.670324	0.335162	+	0.942161i	$0.391209\pi$
$504$	14.8206	0.660162
$505$	−20.0840	−0.893728
$506$	−53.7432	−2.38918
$507$	10.7690	0.478269
$508$	93.8383	4.16340
$509$	5.58218	0.247426	0.123713	−	0.992318i	$-0.460520\pi$
$509$	5.58218	0.247426	0.123713	+	0.992318i	$0.460520\pi$
$510$	−54.6242	−2.41880
$511$	5.70230	0.252255
$512$	−100.896	−4.45903
$513$	6.71902	0.296652
$514$	−39.3431	−1.73535
$515$	−31.8372	−1.40291
$516$	−40.1672	−1.76826
$517$	11.9207	0.524271
$518$	−15.7440	−0.691753
$519$	1.81712	0.0797625
$520$	69.9112	3.06581
$521$	10.6706	0.467489	0.233745	−	0.972298i	$-0.424902\pi$
$521$	10.6706	0.467489	0.233745	+	0.972298i	$0.424902\pi$
$522$	−8.59167	−0.376047
$523$	−19.5622	−0.855396	−0.427698	−	0.903922i	$-0.640675\pi$
$523$	−19.5622	−0.855396	−0.427698	+	0.903922i	$0.640675\pi$
$524$	66.5228	2.90606
$525$	−7.30893	−0.318988
$526$	−87.6207	−3.82044
$527$	49.6803	2.16411
$528$	−60.8824	−2.64957
$529$	21.3401	0.927830
$530$	−32.4338	−1.40883
$531$	13.5163	0.586559
$532$	6.85227	0.297084
$533$	7.34282	0.318053
$534$	−12.4378	−0.538237
$535$	−43.1008	−1.86341
$536$	−87.6083	−3.78410
$537$	27.6484	1.19312
$538$	57.9782	2.49962
$539$	−17.5133	−0.754351
$540$	−103.825	−4.46792
$541$	−16.7851	−0.721648	−0.360824	−	0.932634i	$-0.617505\pi$
$541$	−16.7851	−0.721648	−0.360824	+	0.932634i	$0.617505\pi$
$542$	46.4987	1.99729
$543$	2.35397	0.101019
$544$	−126.783	−5.43579
$545$	−18.9633	−0.812299
$546$	7.08711	0.303300
$547$	−8.29108	−0.354501	−0.177251	−	0.984166i	$-0.556720\pi$
$547$	−8.29108	−0.354501	−0.177251	+	0.984166i	$0.556720\pi$
$548$	8.61457	0.367996
$549$	21.3053	0.909290
$550$	−47.8799	−2.04160
$551$	−2.57259	−0.109596
$552$	84.0438	3.57714
$553$	16.3215	0.694059
$554$	65.7253	2.79240
$555$	23.4254	0.994351
$556$	−88.2235	−3.74151
$557$	2.90235	0.122977	0.0614883	−	0.998108i	$-0.480415\pi$
$557$	2.90235	0.122977	0.0614883	+	0.998108i	$0.480415\pi$
$558$	41.8802	1.77293
$559$	11.8558	0.501446
$560$	−55.4256	−2.34216
$561$	−17.3713	−0.733416
$562$	−43.6343	−1.84060
$563$	40.1832	1.69352	0.846761	−	0.531974i	$-0.178550\pi$
$563$	40.1832	1.69352	0.846761	+	0.531974i	$0.178550\pi$
$564$	−28.7846	−1.21205
$565$	39.2324	1.65052
$566$	62.8978	2.64379
$567$	−2.45032	−0.102904
$568$	−16.3921	−0.687795
$569$	−0.650783	−0.0272823	−0.0136411	−	0.999907i	$-0.504342\pi$
$569$	−0.650783	−0.0272823	−0.0136411	+	0.999907i	$0.504342\pi$
$570$	−13.7880	−0.577517
$571$	10.7445	0.449642	0.224821	−	0.974400i	$-0.427820\pi$
$571$	10.7445	0.449642	0.224821	+	0.974400i	$0.427820\pi$
$572$	34.3298	1.43540
$573$	−0.254225	−0.0106204
$574$	−9.74019	−0.406548
$575$	39.5026	1.64737
$576$	−57.5049	−2.39604
$577$	−34.9364	−1.45442	−0.727210	−	0.686415i	$-0.759183\pi$
$577$	−34.9364	−1.45442	−0.727210	+	0.686415i	$0.759183\pi$
$578$	−17.0363	−0.708616
$579$	−3.57077	−0.148396
$580$	39.7526	1.65064
$581$	−6.20954	−0.257615
$582$	−35.4546	−1.46964
$583$	−10.3144	−0.427180
$584$	−58.4159	−2.41727
$585$	10.0501	0.415521
$586$	43.9283	1.81466
$587$	−8.91214	−0.367843	−0.183922	−	0.982941i	$-0.558879\pi$
$587$	−8.91214	−0.367843	−0.183922	+	0.982941i	$0.558879\pi$
$588$	42.2890	1.74397
$589$	12.5401	0.516706
$590$	−84.5755	−3.48192
$591$	−4.31121	−0.177339
$592$	96.3954	3.96183
$593$	34.4392	1.41425	0.707124	−	0.707090i	$-0.249992\pi$
$593$	34.4392	1.41425	0.707124	+	0.707090i	$0.249992\pi$
$594$	−44.6526	−1.83212
$595$	−15.8143	−0.648324
$596$	17.0709	0.699252
$597$	−14.5643	−0.596079
$598$	−38.3037	−1.56636
$599$	43.1271	1.76213	0.881063	−	0.472999i	$-0.156829\pi$
$599$	43.1271	1.76213	0.881063	+	0.472999i	$0.156829\pi$
$600$	74.8747	3.05675
$601$	43.4254	1.77136	0.885679	−	0.464297i	$-0.153693\pi$
$601$	43.4254	1.77136	0.885679	+	0.464297i	$0.153693\pi$
$602$	−15.7266	−0.640968
$603$	−12.5942	−0.512874
$604$	−28.8677	−1.17461
$605$	8.31063	0.337875
$606$	20.8571	0.847263
$607$	−26.7000	−1.08372	−0.541859	−	0.840469i	$-0.682279\pi$
$607$	−26.7000	−1.08372	−0.541859	+	0.840469i	$0.682279\pi$
$608$	−32.0022	−1.29786
$609$	2.60983	0.105755
$610$	−133.314	−5.39771
$611$	8.49609	0.343715
$612$	−39.9782	−1.61602
$613$	−3.16393	−0.127790	−0.0638949	−	0.997957i	$-0.520352\pi$
$613$	−3.16393	−0.127790	−0.0638949	+	0.997957i	$0.520352\pi$
$614$	−73.2072	−2.95440
$615$	14.4923	0.584386
$616$	−29.4916	−1.18825
$617$	−10.2086	−0.410981	−0.205491	−	0.978659i	$-0.565879\pi$
$617$	−10.2086	−0.410981	−0.205491	+	0.978659i	$0.565879\pi$
$618$	33.0627	1.32998
$619$	−38.1505	−1.53340	−0.766700	−	0.642006i	$-0.778103\pi$
$619$	−38.1505	−1.53340	−0.766700	+	0.642006i	$0.778103\pi$
$620$	−193.775	−7.78218
$621$	36.8400	1.47834
$622$	−52.0866	−2.08848
$623$	−3.60089	−0.144267
$624$	−43.3920	−1.73707
$625$	−19.4689	−0.778756
$626$	−77.9918	−3.11718
$627$	−4.38479	−0.175112
$628$	53.5691	2.13764
$629$	27.5041	1.09666
$630$	−13.3314	−0.531136
$631$	34.3996	1.36942	0.684712	−	0.728813i	$-0.259928\pi$
$631$	34.3996	1.36942	0.684712	+	0.728813i	$0.259928\pi$
$632$	−167.201	−6.65092
$633$	18.7352	0.744658
$634$	−28.7702	−1.14261
$635$	−54.6655	−2.16933
$636$	24.9060	0.987587
$637$	−12.4820	−0.494556
$638$	17.0966	0.676862
$639$	−2.35645	−0.0932197
$640$	185.571	7.33532
$641$	17.8686	0.705769	0.352885	−	0.935667i	$-0.385201\pi$
$641$	17.8686	0.705769	0.352885	+	0.935667i	$0.385201\pi$
$642$	44.7599	1.76653
$643$	−16.4515	−0.648784	−0.324392	−	0.945923i	$-0.605160\pi$
$643$	−16.4515	−0.648784	−0.324392	+	0.945923i	$0.605160\pi$
$644$	37.5706	1.48049
$645$	23.3994	0.921350
$646$	−16.1887	−0.636937
$647$	11.5109	0.452542	0.226271	−	0.974064i	$-0.427347\pi$
$647$	11.5109	0.452542	0.226271	+	0.974064i	$0.427347\pi$
$648$	25.1018	0.986091
$649$	−26.8963	−1.05577
$650$	−34.1248	−1.33849
$651$	−12.7216	−0.498600
$652$	−26.3281	−1.03109
$653$	−13.1104	−0.513050	−0.256525	−	0.966538i	$-0.582578\pi$
$653$	−13.1104	−0.513050	−0.256525	+	0.966538i	$0.582578\pi$
$654$	19.6933	0.770068
$655$	−38.7529	−1.51420
$656$	59.6359	2.32839
$657$	−8.39761	−0.327622
$658$	−11.2700	−0.439350
$659$	−16.4133	−0.639369	−0.319685	−	0.947524i	$-0.603577\pi$
$659$	−16.4133	−0.639369	−0.319685	+	0.947524i	$0.603577\pi$
$660$	67.7556	2.63738
$661$	1.40641	0.0547029	0.0273514	−	0.999626i	$-0.491293\pi$
$661$	1.40641	0.0547029	0.0273514	+	0.999626i	$0.491293\pi$
$662$	−15.1945	−0.590552
$663$	−12.3808	−0.480832
$664$	63.6122	2.46863
$665$	−3.99179	−0.154795
$666$	23.1858	0.898431
$667$	−14.1053	−0.546161
$668$	−95.1865	−3.68288
$669$	1.36623	0.0528215
$670$	78.8053	3.04451
$671$	−42.3957	−1.63667
$672$	32.4655	1.25238
$673$	−1.68108	−0.0648011	−0.0324005	−	0.999475i	$-0.510315\pi$
$673$	−1.68108	−0.0648011	−0.0324005	+	0.999475i	$0.510315\pi$
$674$	−16.5389	−0.637054
$675$	32.8208	1.26327
$676$	−49.3174	−1.89682
$677$	32.6504	1.25486	0.627428	−	0.778674i	$-0.284107\pi$
$677$	32.6504	1.25486	0.627428	+	0.778674i	$0.284107\pi$
$678$	−40.7426	−1.56471
$679$	−10.2645	−0.393916
$680$	162.006	6.21265
$681$	−16.2551	−0.622897
$682$	−83.3377	−3.19117
$683$	−30.9987	−1.18613	−0.593067	−	0.805153i	$-0.702083\pi$
$683$	−30.9987	−1.18613	−0.593067	+	0.805153i	$0.702083\pi$
$684$	−10.0911	−0.385844
$685$	−5.01842	−0.191744
$686$	35.8363	1.36824
$687$	15.1100	0.576483
$688$	96.2886	3.67097
$689$	−7.35127	−0.280061
$690$	−75.5990	−2.87800
$691$	−29.8119	−1.13410	−0.567049	−	0.823684i	$-0.691915\pi$
$691$	−29.8119	−1.13410	−0.567049	+	0.823684i	$0.691915\pi$
$692$	−8.32159	−0.316339
$693$	−4.23958	−0.161048
$694$	−17.8431	−0.677316
$695$	51.3946	1.94951
$696$	−26.7358	−1.01342
$697$	17.0156	0.644513
$698$	75.7434	2.86693
$699$	25.0598	0.947848
$700$	33.4717	1.26511
$701$	−21.0046	−0.793334	−0.396667	−	0.917963i	$-0.629833\pi$
$701$	−21.0046	−0.793334	−0.396667	+	0.917963i	$0.629833\pi$
$702$	−31.8247	−1.20115
$703$	6.94247	0.261840
$704$	114.429	4.31272
$705$	16.7685	0.631537
$706$	22.9814	0.864915
$707$	6.03838	0.227097
$708$	64.9458	2.44081
$709$	26.7448	1.00442	0.502210	−	0.864745i	$-0.332520\pi$
$709$	26.7448	1.00442	0.502210	+	0.864745i	$0.332520\pi$
$710$	14.7450	0.553369
$711$	−24.0361	−0.901425
$712$	36.8885	1.38245
$713$	68.7567	2.57496
$714$	16.4231	0.614618
$715$	−19.9988	−0.747913
$716$	−126.618	−4.73192
$717$	−9.59235	−0.358233
$718$	−2.83088	−0.105648
$719$	−25.7531	−0.960430	−0.480215	−	0.877151i	$-0.659441\pi$
$719$	−25.7531	−0.960430	−0.480215	+	0.877151i	$0.659441\pi$
$720$	81.6236	3.04193
$721$	9.57203	0.356481
$722$	48.5535	1.80697
$723$	10.9185	0.406064
$724$	−10.7802	−0.400641
$725$	−12.5665	−0.466706
$726$	−8.63053	−0.320309
$727$	−24.6883	−0.915637	−0.457819	−	0.889046i	$-0.651369\pi$
$727$	−24.6883	−0.915637	−0.457819	+	0.889046i	$0.651369\pi$
$728$	−21.0192	−0.779023
$729$	24.1789	0.895515
$730$	52.5462	1.94482
$731$	27.4736	1.01615
$732$	102.372	3.78377
$733$	−43.1386	−1.59336	−0.796679	−	0.604402i	$-0.793412\pi$
$733$	−43.1386	−1.59336	−0.796679	+	0.604402i	$0.793412\pi$
$734$	−95.0835	−3.50960
$735$	−24.6354	−0.908692
$736$	−175.466	−6.46777
$737$	25.0612	0.923142
$738$	14.3441	0.528013
$739$	5.54957	0.204144	0.102072	−	0.994777i	$-0.467453\pi$
$739$	5.54957	0.204144	0.102072	+	0.994777i	$0.467453\pi$
$740$	−107.278	−3.94361
$741$	−3.12512	−0.114804
$742$	9.75140	0.357985
$743$	14.2930	0.524358	0.262179	−	0.965019i	$-0.415559\pi$
$743$	14.2930	0.524358	0.262179	+	0.965019i	$0.415559\pi$
$744$	130.324	4.77790
$745$	−9.94467	−0.364344
$746$	−46.8906	−1.71679
$747$	9.14460	0.334584
$748$	79.5529	2.90874
$749$	12.9585	0.473493
$750$	−10.5853	−0.386519
$751$	28.9497	1.05639	0.528195	−	0.849123i	$-0.322869\pi$
$751$	28.9497	1.05639	0.528195	+	0.849123i	$0.322869\pi$
$752$	69.0023	2.51626
$753$	−36.7134	−1.33791
$754$	12.1851	0.443754
$755$	16.8169	0.612028
$756$	31.2156	1.13530
$757$	42.5901	1.54796	0.773982	−	0.633207i	$-0.218262\pi$
$757$	42.5901	1.54796	0.773982	+	0.633207i	$0.218262\pi$
$758$	−107.671	−3.91079
$759$	−24.0416	−0.872654
$760$	40.8930	1.48334
$761$	−20.6990	−0.750337	−0.375168	−	0.926957i	$-0.622415\pi$
$761$	−20.6990	−0.750337	−0.375168	+	0.926957i	$0.622415\pi$
$762$	56.7697	2.05655
$763$	5.70143	0.206405
$764$	1.16424	0.0421206
$765$	23.2893	0.842026
$766$	32.3268	1.16801
$767$	−19.1694	−0.692169
$768$	−95.3487	−3.44060
$769$	52.8861	1.90712	0.953561	−	0.301199i	$-0.0973869\pi$
$769$	52.8861	1.90712	0.953561	+	0.301199i	$0.0973869\pi$
$770$	26.5282	0.956012
$771$	−17.5998	−0.633842
$772$	16.3526	0.588542
$773$	17.4646	0.628156	0.314078	−	0.949397i	$-0.398305\pi$
$773$	17.4646	0.628156	0.314078	+	0.949397i	$0.398305\pi$
$774$	23.1601	0.832472
$775$	61.2554	2.20036
$776$	105.152	3.77475
$777$	−7.04297	−0.252665
$778$	89.1990	3.19794
$779$	4.29502	0.153885
$780$	48.2907	1.72908
$781$	4.68911	0.167790
$782$	−88.7618	−3.17412
$783$	−11.7194	−0.418818
$784$	−101.375	−3.62053
$785$	−31.2067	−1.11381
$786$	40.2446	1.43548
$787$	−20.2259	−0.720976	−0.360488	−	0.932764i	$-0.617390\pi$
$787$	−20.2259	−0.720976	−0.360488	+	0.932764i	$0.617390\pi$
$788$	19.7434	0.703331
$789$	−39.1964	−1.39543
$790$	150.401	5.35102
$791$	−11.7954	−0.419398
$792$	43.4314	1.54327
$793$	−30.2162	−1.07301
$794$	10.6803	0.379028
$795$	−14.5090	−0.514581
$796$	66.6983	2.36406
$797$	11.5428	0.408868	0.204434	−	0.978880i	$-0.434465\pi$
$797$	11.5428	0.408868	0.204434	+	0.978880i	$0.434465\pi$
$798$	4.14545	0.146747
$799$	19.6881	0.696515
$800$	−156.323	−5.52685
$801$	5.30292	0.187370
$802$	−3.31659	−0.117113
$803$	16.7105	0.589699
$804$	−60.5148	−2.13419
$805$	−21.8868	−0.771407
$806$	−59.3963	−2.09215
$807$	25.9361	0.912993
$808$	−61.8588	−2.17618
$809$	−50.5446	−1.77705	−0.888526	−	0.458826i	$-0.848270\pi$
$809$	−50.5446	−1.77705	−0.888526	+	0.458826i	$0.848270\pi$
$810$	−22.5795	−0.793364
$811$	4.62428	0.162380	0.0811902	−	0.996699i	$-0.474128\pi$
$811$	4.62428	0.162380	0.0811902	+	0.996699i	$0.474128\pi$
$812$	−11.9519	−0.419428
$813$	20.8008	0.729516
$814$	−46.1375	−1.61712
$815$	15.3374	0.537247
$816$	−100.553	−3.52005
$817$	6.93478	0.242617
$818$	−52.3251	−1.82950
$819$	−3.02163	−0.105584
$820$	−66.3684	−2.31768
$821$	8.33512	0.290898	0.145449	−	0.989366i	$-0.453537\pi$
$821$	8.33512	0.290898	0.145449	+	0.989366i	$0.453537\pi$
$822$	5.21159	0.181775
$823$	−52.0095	−1.81294	−0.906469	−	0.422272i	$-0.861233\pi$
$823$	−52.0095	−1.81294	−0.906469	+	0.422272i	$0.861233\pi$
$824$	−98.0584	−3.41603
$825$	−21.4187	−0.745702
$826$	25.4281	0.884757
$827$	20.7693	0.722219	0.361110	−	0.932523i	$-0.382398\pi$
$827$	20.7693	0.722219	0.361110	+	0.932523i	$0.382398\pi$
$828$	−55.3291	−1.92282
$829$	−35.7403	−1.24131	−0.620657	−	0.784082i	$-0.713134\pi$
$829$	−35.7403	−1.24131	−0.620657	+	0.784082i	$0.713134\pi$
$830$	−57.2204	−1.98615
$831$	29.4017	1.01993
$832$	81.5559	2.82744
$833$	−28.9248	−1.00219
$834$	−53.3729	−1.84815
$835$	55.4509	1.91896
$836$	20.0804	0.694496
$837$	57.1265	1.97458
$838$	−44.8250	−1.54845
$839$	−14.6182	−0.504675	−0.252338	−	0.967639i	$-0.581199\pi$
$839$	−14.6182	−0.504675	−0.252338	+	0.967639i	$0.581199\pi$
$840$	−41.4850	−1.43137
$841$	−24.5129	−0.845271
$842$	40.9525	1.41132
$843$	−19.5194	−0.672285
$844$	−85.7990	−2.95332
$845$	28.7298	0.988337
$846$	16.5970	0.570616
$847$	−2.49864	−0.0858542
$848$	−59.7045	−2.05026
$849$	28.1368	0.965653
$850$	−79.0780	−2.71235
$851$	38.0651	1.30486
$852$	−11.3227	−0.387909
$853$	−26.5056	−0.907535	−0.453768	−	0.891120i	$-0.649920\pi$
$853$	−26.5056	−0.907535	−0.453768	+	0.891120i	$0.649920\pi$
$854$	40.0815	1.37156
$855$	5.87859	0.201044
$856$	−132.750	−4.53731
$857$	−1.52870	−0.0522193	−0.0261096	−	0.999659i	$-0.508312\pi$
$857$	−1.52870	−0.0522193	−0.0261096	+	0.999659i	$0.508312\pi$
$858$	20.7686	0.709029
$859$	38.2527	1.30516	0.652582	−	0.757718i	$-0.273686\pi$
$859$	38.2527	1.30516	0.652582	+	0.757718i	$0.273686\pi$
$860$	−107.159	−3.65409
$861$	−4.35719	−0.148493
$862$	21.8212	0.743234
$863$	34.7680	1.18352	0.591758	−	0.806116i	$-0.298434\pi$
$863$	34.7680	1.18352	0.591758	+	0.806116i	$0.298434\pi$
$864$	−145.786	−4.95975
$865$	4.84774	0.164828
$866$	33.5670	1.14065
$867$	−7.62104	−0.258824
$868$	58.2595	1.97746
$869$	47.8297	1.62251
$870$	24.0493	0.815348
$871$	17.8616	0.605217
$872$	−58.4069	−1.97791
$873$	15.1163	0.511608
$874$	−22.4049	−0.757858
$875$	−3.06456	−0.103601
$876$	−40.3504	−1.36331
$877$	−10.2852	−0.347305	−0.173653	−	0.984807i	$-0.555557\pi$
$877$	−10.2852	−0.347305	−0.173653	+	0.984807i	$0.555557\pi$
$878$	−100.201	−3.38162
$879$	19.6509	0.662810
$880$	−162.423	−5.47529
$881$	−11.5947	−0.390634	−0.195317	−	0.980740i	$-0.562574\pi$
$881$	−11.5947	−0.390634	−0.195317	+	0.980740i	$0.562574\pi$
$882$	−24.3835	−0.821034
$883$	−10.0511	−0.338247	−0.169124	−	0.985595i	$-0.554094\pi$
$883$	−10.0511	−0.338247	−0.169124	+	0.985595i	$0.554094\pi$
$884$	56.6988	1.90699
$885$	−37.8342	−1.27178
$886$	−109.811	−3.68918
$887$	−55.7582	−1.87218	−0.936088	−	0.351766i	$-0.885581\pi$
$887$	−55.7582	−1.87218	−0.936088	+	0.351766i	$0.885581\pi$
$888$	72.1500	2.42120
$889$	16.4355	0.551229
$890$	−33.1819	−1.11226
$891$	−7.18062	−0.240560
$892$	−6.25673	−0.209491
$893$	4.96960	0.166301
$894$	10.3275	0.345402
$895$	73.7611	2.46556
$896$	−55.7928	−1.86391
$897$	−17.1349	−0.572116
$898$	56.4061	1.88230
$899$	−21.8727	−0.729494
$900$	−49.2928	−1.64309
$901$	−17.0352	−0.567525
$902$	−28.5434	−0.950391
$903$	−7.03516	−0.234116
$904$	120.836	4.01894
$905$	6.27998	0.208754
$906$	−17.4642	−0.580209
$907$	−35.7345	−1.18654	−0.593272	−	0.805002i	$-0.702164\pi$
$907$	−35.7345	−1.18654	−0.593272	+	0.805002i	$0.702164\pi$
$908$	74.4413	2.47042
$909$	−8.89255	−0.294947
$910$	18.9072	0.626766
$911$	42.4552	1.40660	0.703302	−	0.710891i	$-0.251708\pi$
$911$	42.4552	1.40660	0.703302	+	0.710891i	$0.251708\pi$
$912$	−25.3812	−0.840454
$913$	−18.1969	−0.602230
$914$	3.75981	0.124363
$915$	−59.6367	−1.97153
$916$	−69.1972	−2.28634
$917$	11.6513	0.384759
$918$	−73.7478	−2.43404
$919$	−52.4298	−1.72950	−0.864750	−	0.502202i	$-0.832523\pi$
$919$	−52.4298	−1.72950	−0.864750	+	0.502202i	$0.832523\pi$
$920$	224.214	7.39211
$921$	−32.7486	−1.07910
$922$	45.8464	1.50987
$923$	3.34202	0.110004
$924$	−20.3711	−0.670160
$925$	33.9123	1.11503
$926$	12.1297	0.398607
$927$	−14.0964	−0.462988
$928$	55.8188	1.83234
$929$	38.3706	1.25890	0.629449	−	0.777041i	$-0.283280\pi$
$929$	38.3706	1.25890	0.629449	+	0.777041i	$0.283280\pi$
$930$	−117.229	−3.84408
$931$	−7.30109	−0.239284
$932$	−114.763	−3.75918
$933$	−23.3005	−0.762824
$934$	−107.041	−3.50250
$935$	−46.3435	−1.51560
$936$	30.9543	1.01177
$937$	−25.5850	−0.835825	−0.417913	−	0.908487i	$-0.637238\pi$
$937$	−25.5850	−0.835825	−0.417913	+	0.908487i	$0.637238\pi$
$938$	−23.6933	−0.773612
$939$	−34.8890	−1.13856
$940$	−76.7922	−2.50469
$941$	−33.3218	−1.08626	−0.543131	−	0.839648i	$-0.682761\pi$
$941$	−33.3218	−1.08626	−0.543131	+	0.839648i	$0.682761\pi$
$942$	32.4079	1.05591
$943$	23.5493	0.766872
$944$	−155.688	−5.06720
$945$	−18.1846	−0.591546
$946$	−46.0864	−1.49840
$947$	−8.75634	−0.284543	−0.142271	−	0.989828i	$-0.545441\pi$
$947$	−8.75634	−0.284543	−0.142271	+	0.989828i	$0.545441\pi$
$948$	−115.493	−3.75104
$949$	11.9098	0.386610
$950$	−19.9606	−0.647606
$951$	−12.8701	−0.417341
$952$	−48.7081	−1.57864
$953$	47.3454	1.53367	0.766834	−	0.641845i	$-0.221831\pi$
$953$	47.3454	1.53367	0.766834	+	0.641845i	$0.221831\pi$
$954$	−14.3606	−0.464942
$955$	−0.678226	−0.0219469
$956$	43.9287	1.42076
$957$	7.64803	0.247226
$958$	70.6431	2.28238
$959$	1.50882	0.0487222
$960$	160.964	5.19510
$961$	75.6186	2.43931
$962$	−32.8831	−1.06019
$963$	−19.0836	−0.614961
$964$	−50.0020	−1.61045
$965$	−9.52619	−0.306659
$966$	22.7293	0.731302
$967$	−1.01063	−0.0324996	−0.0162498	−	0.999868i	$-0.505173\pi$
$967$	−1.01063	−0.0324996	−0.0162498	+	0.999868i	$0.505173\pi$
$968$	25.5967	0.822709
$969$	−7.24189	−0.232643
$970$	−94.5866	−3.03699
$971$	−6.31925	−0.202795	−0.101397	−	0.994846i	$-0.532331\pi$
$971$	−6.31925	−0.202795	−0.101397	+	0.994846i	$0.532331\pi$
$972$	−76.8644	−2.46543
$973$	−15.4521	−0.495371
$974$	81.3160	2.60553
$975$	−15.2655	−0.488886
$976$	−245.405	−7.85523
$977$	8.48019	0.271305	0.135653	−	0.990756i	$-0.456687\pi$
$977$	8.48019	0.271305	0.135653	+	0.990756i	$0.456687\pi$
$978$	−15.9278	−0.509315
$979$	−10.5523	−0.337254
$980$	112.819	3.60388
$981$	−8.39632	−0.268074
$982$	−17.5623	−0.560436
$983$	−9.57551	−0.305411	−0.152706	−	0.988272i	$-0.548799\pi$
$983$	−9.57551	−0.305411	−0.152706	+	0.988272i	$0.548799\pi$
$984$	44.6363	1.42295
$985$	−11.5015	−0.366469
$986$	28.2367	0.899238
$987$	−5.04154	−0.160474
$988$	14.3117	0.455315
$989$	38.0230	1.20906
$990$	−39.0674	−1.24164
$991$	−32.9046	−1.04525	−0.522624	−	0.852563i	$-0.675047\pi$
$991$	−32.9046	−1.04525	−0.522624	+	0.852563i	$0.675047\pi$
$992$	−272.089	−8.63885
$993$	−6.79715	−0.215701
$994$	−4.43316	−0.140611
$995$	−38.8551	−1.23179
$996$	43.9397	1.39228
$997$	6.86670	0.217470	0.108735	−	0.994071i	$-0.465320\pi$
$997$	6.86670	0.217470	0.108735	+	0.994071i	$0.465320\pi$
$998$	−33.9781	−1.07556
$999$	31.6264	1.00062

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4007.2.a.b.1.3	✓	195

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4007.2.a.b.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-2.77052 q^{2} -1.23937 q^{3} +5.67576 q^{4} -3.30641 q^{5} +3.43369 q^{6} +0.994092 q^{7} -10.1837 q^{8} -1.46397 q^{9} +O(q^{10})\)	\(q-2.77052 q^{2} -1.23937 q^{3} +5.67576 q^{4} -3.30641 q^{5} +3.43369 q^{6} +0.994092 q^{7} -10.1837 q^{8} -1.46397 q^{9} +9.16047 q^{10} +2.91316 q^{11} -7.03435 q^{12} +2.07626 q^{13} -2.75415 q^{14} +4.09786 q^{15} +16.8627 q^{16} +4.81136 q^{17} +4.05595 q^{18} +1.21446 q^{19} -18.7664 q^{20} -1.23204 q^{21} -8.07096 q^{22} +6.65884 q^{23} +12.6214 q^{24} +5.93236 q^{25} -5.75232 q^{26} +5.53250 q^{27} +5.64222 q^{28} -2.11829 q^{29} -11.3532 q^{30} +10.3256 q^{31} -26.3509 q^{32} -3.61048 q^{33} -13.3299 q^{34} -3.28688 q^{35} -8.30913 q^{36} +5.71649 q^{37} -3.36469 q^{38} -2.57325 q^{39} +33.6716 q^{40} +3.53656 q^{41} +3.41340 q^{42} +5.71015 q^{43} +16.5344 q^{44} +4.84048 q^{45} -18.4484 q^{46} +4.09201 q^{47} -20.8991 q^{48} -6.01178 q^{49} -16.4357 q^{50} -5.96304 q^{51} +11.7844 q^{52} -3.54063 q^{53} -15.3279 q^{54} -9.63211 q^{55} -10.1236 q^{56} -1.50517 q^{57} +5.86875 q^{58} -9.23267 q^{59} +23.2584 q^{60} -14.5531 q^{61} -28.6073 q^{62} -1.45532 q^{63} +39.2801 q^{64} -6.86498 q^{65} +10.0029 q^{66} +8.60276 q^{67} +27.3081 q^{68} -8.25274 q^{69} +9.10634 q^{70} +1.60963 q^{71} +14.9087 q^{72} +5.73619 q^{73} -15.8376 q^{74} -7.35237 q^{75} +6.89300 q^{76} +2.89595 q^{77} +7.12924 q^{78} +16.4185 q^{79} -55.7550 q^{80} -2.46489 q^{81} -9.79808 q^{82} -6.24645 q^{83} -6.99278 q^{84} -15.9083 q^{85} -15.8201 q^{86} +2.62534 q^{87} -29.6669 q^{88} -3.62229 q^{89} -13.4106 q^{90} +2.06400 q^{91} +37.7939 q^{92} -12.7972 q^{93} -11.3370 q^{94} -4.01552 q^{95} +32.6584 q^{96} -10.3255 q^{97} +16.6557 q^{98} -4.26478 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 195 q + 14 q^{2} + 22 q^{3} + 220 q^{4} + 14 q^{5} + 13 q^{6} + 48 q^{7} + 39 q^{8} + 245 q^{9}+O(q^{10}) \) 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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