LMFDB - Embedded newform 8035.2.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8035,2,Mod(1,8035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8035, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8035 = 5 \cdot 1607 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8035.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:	$64.1597980241$
Analytic rank:	$0$
Dimension:	$127$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	8035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.65256 q^{2} +2.52646 q^{3} +5.03608 q^{4} -1.00000 q^{5} -6.70158 q^{6} -1.65453 q^{7} -8.05337 q^{8} +3.38299 q^{9} +O(q^{10})$	\(q-2.65256 q^{2} +2.52646 q^{3} +5.03608 q^{4} -1.00000 q^{5} -6.70158 q^{6} -1.65453 q^{7} -8.05337 q^{8} +3.38299 q^{9} +2.65256 q^{10} -4.67182 q^{11} +12.7234 q^{12} -0.0867083 q^{13} +4.38874 q^{14} -2.52646 q^{15} +11.2899 q^{16} +1.54019 q^{17} -8.97358 q^{18} -6.51159 q^{19} -5.03608 q^{20} -4.18010 q^{21} +12.3923 q^{22} -0.876169 q^{23} -20.3465 q^{24} +1.00000 q^{25} +0.229999 q^{26} +0.967604 q^{27} -8.33233 q^{28} -0.142363 q^{29} +6.70158 q^{30} -6.12452 q^{31} -13.8404 q^{32} -11.8032 q^{33} -4.08544 q^{34} +1.65453 q^{35} +17.0370 q^{36} -10.3950 q^{37} +17.2724 q^{38} -0.219065 q^{39} +8.05337 q^{40} +6.16587 q^{41} +11.0880 q^{42} -0.545093 q^{43} -23.5277 q^{44} -3.38299 q^{45} +2.32409 q^{46} -9.14844 q^{47} +28.5235 q^{48} -4.26254 q^{49} -2.65256 q^{50} +3.89122 q^{51} -0.436669 q^{52} +11.2459 q^{53} -2.56663 q^{54} +4.67182 q^{55} +13.3245 q^{56} -16.4513 q^{57} +0.377626 q^{58} +4.85857 q^{59} -12.7234 q^{60} +2.34475 q^{61} +16.2457 q^{62} -5.59725 q^{63} +14.1327 q^{64} +0.0867083 q^{65} +31.3086 q^{66} -9.68205 q^{67} +7.75650 q^{68} -2.21360 q^{69} -4.38874 q^{70} +14.9100 q^{71} -27.2445 q^{72} +10.2564 q^{73} +27.5733 q^{74} +2.52646 q^{75} -32.7929 q^{76} +7.72966 q^{77} +0.581083 q^{78} +8.15334 q^{79} -11.2899 q^{80} -7.70436 q^{81} -16.3554 q^{82} +4.38070 q^{83} -21.0513 q^{84} -1.54019 q^{85} +1.44589 q^{86} -0.359674 q^{87} +37.6239 q^{88} +10.1419 q^{89} +8.97358 q^{90} +0.143461 q^{91} -4.41245 q^{92} -15.4733 q^{93} +24.2668 q^{94} +6.51159 q^{95} -34.9672 q^{96} +9.13925 q^{97} +11.3066 q^{98} -15.8047 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 127 q + 19 q^{2} + 10 q^{3} + 125 q^{4} - 127 q^{5} + 13 q^{7} + 54 q^{8} + 123 q^{9}+O(q^{10}) $ 127 * q + 19 * q^2 + 10 * q^3 + 125 * q^4 - 127 * q^5 + 13 * q^7 + 54 * q^8 + 123 * q^9	\( 127 q + 19 q^{2} + 10 q^{3} + 125 q^{4} - 127 q^{5} + 13 q^{7} + 54 q^{8} + 123 q^{9} - 19 q^{10} + 30 q^{11} + 35 q^{12} + 30 q^{13} + 39 q^{14} - 10 q^{15} + 121 q^{16} + 63 q^{17} + 53 q^{18} - 35 q^{19} - 125 q^{20} + 33 q^{21} + 49 q^{22} + 61 q^{23} - 5 q^{24} + 127 q^{25} + 10 q^{26} + 40 q^{27} + 32 q^{28} + 134 q^{29} - 25 q^{31} + 122 q^{32} + 48 q^{33} - 21 q^{34} - 13 q^{35} + 133 q^{36} + 60 q^{37} + 33 q^{38} + 26 q^{39} - 54 q^{40} + 9 q^{41} + 45 q^{42} + 48 q^{43} + 85 q^{44} - 123 q^{45} - 11 q^{46} + 57 q^{47} + 71 q^{48} + 70 q^{49} + 19 q^{50} + 45 q^{51} + 68 q^{52} + 182 q^{53} - 29 q^{54} - 30 q^{55} + 96 q^{56} + 74 q^{57} + 47 q^{58} + 19 q^{59} - 35 q^{60} + 16 q^{61} + 43 q^{62} + 73 q^{63} + 110 q^{64} - 30 q^{65} + 8 q^{66} + 40 q^{67} + 129 q^{68} + 2 q^{69} - 39 q^{70} + 48 q^{71} + 151 q^{72} + 30 q^{73} + 117 q^{74} + 10 q^{75} - 98 q^{76} + 134 q^{77} + 54 q^{78} + 23 q^{79} - 121 q^{80} + 111 q^{81} + 4 q^{82} + 92 q^{83} + 48 q^{84} - 63 q^{85} + 42 q^{86} + 69 q^{87} + 121 q^{88} + 12 q^{89} - 53 q^{90} - 30 q^{91} + 175 q^{92} + 82 q^{93} - 23 q^{94} + 35 q^{95} + 6 q^{96} + 67 q^{97} + 122 q^{98} + 73 q^{99}+O(q^{100}) \) 127 * q + 19 * q^2 + 10 * q^3 + 125 * q^4 - 127 * q^5 + 13 * q^7 + 54 * q^8 + 123 * q^9 - 19 * q^10 + 30 * q^11 + 35 * q^12 + 30 * q^13 + 39 * q^14 - 10 * q^15 + 121 * q^16 + 63 * q^17 + 53 * q^18 - 35 * q^19 - 125 * q^20 + 33 * q^21 + 49 * q^22 + 61 * q^23 - 5 * q^24 + 127 * q^25 + 10 * q^26 + 40 * q^27 + 32 * q^28 + 134 * q^29 - 25 * q^31 + 122 * q^32 + 48 * q^33 - 21 * q^34 - 13 * q^35 + 133 * q^36 + 60 * q^37 + 33 * q^38 + 26 * q^39 - 54 * q^40 + 9 * q^41 + 45 * q^42 + 48 * q^43 + 85 * q^44 - 123 * q^45 - 11 * q^46 + 57 * q^47 + 71 * q^48 + 70 * q^49 + 19 * q^50 + 45 * q^51 + 68 * q^52 + 182 * q^53 - 29 * q^54 - 30 * q^55 + 96 * q^56 + 74 * q^57 + 47 * q^58 + 19 * q^59 - 35 * q^60 + 16 * q^61 + 43 * q^62 + 73 * q^63 + 110 * q^64 - 30 * q^65 + 8 * q^66 + 40 * q^67 + 129 * q^68 + 2 * q^69 - 39 * q^70 + 48 * q^71 + 151 * q^72 + 30 * q^73 + 117 * q^74 + 10 * q^75 - 98 * q^76 + 134 * q^77 + 54 * q^78 + 23 * q^79 - 121 * q^80 + 111 * q^81 + 4 * q^82 + 92 * q^83 + 48 * q^84 - 63 * q^85 + 42 * q^86 + 69 * q^87 + 121 * q^88 + 12 * q^89 - 53 * q^90 - 30 * q^91 + 175 * q^92 + 82 * q^93 - 23 * q^94 + 35 * q^95 + 6 * q^96 + 67 * q^97 + 122 * q^98 + 73 * 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 $

$2$	−2.65256	−1.87564	−0.937822	−	0.347118i	$-0.887160\pi$
$2$	−2.65256	−1.87564	−0.937822	+	0.347118i	$0.887160\pi$
$3$	2.52646	1.45865	0.729326	−	0.684167i	$-0.239834\pi$
$3$	2.52646	1.45865	0.729326	+	0.684167i	$0.239834\pi$
$4$	5.03608	2.51804
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−6.70158	−2.73591
$7$	−1.65453	−0.625353	−0.312676	−	0.949860i	$-0.601226\pi$
$7$	−1.65453	−0.625353	−0.312676	+	0.949860i	$0.601226\pi$
$8$	−8.05337	−2.84730
$9$	3.38299	1.12766
$10$	2.65256	0.838813
$11$	−4.67182	−1.40861	−0.704304	−	0.709899i	$-0.748741\pi$
$11$	−4.67182	−1.40861	−0.704304	+	0.709899i	$0.748741\pi$
$12$	12.7234	3.67294
$13$	−0.0867083	−0.0240486	−0.0120243	−	0.999928i	$-0.503828\pi$
$13$	−0.0867083	−0.0240486	−0.0120243	+	0.999928i	$0.503828\pi$
$14$	4.38874	1.17294
$15$	−2.52646	−0.652329
$16$	11.2899	2.82248
$17$	1.54019	0.373550	0.186775	−	0.982403i	$-0.440196\pi$
$17$	1.54019	0.373550	0.186775	+	0.982403i	$0.440196\pi$
$18$	−8.97358	−2.11509
$19$	−6.51159	−1.49386	−0.746930	−	0.664902i	$-0.768473\pi$
$19$	−6.51159	−1.49386	−0.746930	+	0.664902i	$0.768473\pi$
$20$	−5.03608	−1.12610
$21$	−4.18010	−0.912172
$22$	12.3923	2.64205
$23$	−0.876169	−0.182694	−0.0913469	−	0.995819i	$-0.529117\pi$
$23$	−0.876169	−0.182694	−0.0913469	+	0.995819i	$0.529117\pi$
$24$	−20.3465	−4.15321
$25$	1.00000	0.200000
$26$	0.229999	0.0451065
$27$	0.967604	0.186215
$28$	−8.33233	−1.57466
$29$	−0.142363	−0.0264361	−0.0132181	−	0.999913i	$-0.504208\pi$
$29$	−0.142363	−0.0264361	−0.0132181	+	0.999913i	$0.504208\pi$
$30$	6.70158	1.22354
$31$	−6.12452	−1.10000	−0.549998	−	0.835166i	$-0.685372\pi$
$31$	−6.12452	−1.10000	−0.549998	+	0.835166i	$0.685372\pi$
$32$	−13.8404	−2.44666
$33$	−11.8032	−2.05467
$34$	−4.08544	−0.700647
$35$	1.65453	0.279666
$36$	17.0370	2.83950
$37$	−10.3950	−1.70892	−0.854461	−	0.519515i	$-0.826113\pi$
$37$	−10.3950	−1.70892	−0.854461	+	0.519515i	$0.826113\pi$
$38$	17.2724	2.80195
$39$	−0.219065	−0.0350784
$40$	8.05337	1.27335
$41$	6.16587	0.962948	0.481474	−	0.876460i	$-0.340102\pi$
$41$	6.16587	0.962948	0.481474	+	0.876460i	$0.340102\pi$
$42$	11.0880	1.71091
$43$	−0.545093	−0.0831259	−0.0415629	−	0.999136i	$-0.513234\pi$
$43$	−0.545093	−0.0831259	−0.0415629	+	0.999136i	$0.513234\pi$
$44$	−23.5277	−3.54693
$45$	−3.38299	−0.504306
$46$	2.32409	0.342669
$47$	−9.14844	−1.33444	−0.667219	−	0.744862i	$-0.732515\pi$
$47$	−9.14844	−1.33444	−0.667219	+	0.744862i	$0.732515\pi$
$48$	28.5235	4.11701
$49$	−4.26254	−0.608934
$50$	−2.65256	−0.375129
$51$	3.89122	0.544880
$52$	−0.436669	−0.0605552
$53$	11.2459	1.54475	0.772373	−	0.635169i	$-0.219070\pi$
$53$	11.2459	1.54475	0.772373	+	0.635169i	$0.219070\pi$
$54$	−2.56663	−0.349274
$55$	4.67182	0.629948
$56$	13.3245	1.78057
$57$	−16.4513	−2.17902
$58$	0.377626	0.0495848
$59$	4.85857	0.632532	0.316266	−	0.948671i	$-0.397571\pi$
$59$	4.85857	0.632532	0.316266	+	0.948671i	$0.397571\pi$
$60$	−12.7234	−1.64259
$61$	2.34475	0.300214	0.150107	−	0.988670i	$-0.452038\pi$
$61$	2.34475	0.300214	0.150107	+	0.988670i	$0.452038\pi$
$62$	16.2457	2.06320
$63$	−5.59725	−0.705187
$64$	14.1327	1.76659
$65$	0.0867083	0.0107548
$66$	31.3086	3.85382
$67$	−9.68205	−1.18285	−0.591426	−	0.806360i	$-0.701435\pi$
$67$	−9.68205	−1.18285	−0.591426	+	0.806360i	$0.701435\pi$
$68$	7.75650	0.940614
$69$	−2.21360	−0.266487
$70$	−4.38874	−0.524554
$71$	14.9100	1.76950	0.884748	−	0.466070i	$-0.154330\pi$
$71$	14.9100	1.76950	0.884748	+	0.466070i	$0.154330\pi$
$72$	−27.2445	−3.21079
$73$	10.2564	1.20042	0.600209	−	0.799843i	$-0.295084\pi$
$73$	10.2564	1.20042	0.600209	+	0.799843i	$0.295084\pi$
$74$	27.5733	3.20533
$75$	2.52646	0.291730
$76$	−32.7929	−3.76160
$77$	7.72966	0.880877
$78$	0.581083	0.0657946
$79$	8.15334	0.917322	0.458661	−	0.888611i	$-0.348329\pi$
$79$	8.15334	0.917322	0.458661	+	0.888611i	$0.348329\pi$
$80$	−11.2899	−1.26225
$81$	−7.70436	−0.856039
$82$	−16.3554	−1.80615
$83$	4.38070	0.480845	0.240422	−	0.970668i	$-0.422714\pi$
$83$	4.38070	0.480845	0.240422	+	0.970668i	$0.422714\pi$
$84$	−21.0513	−2.29688
$85$	−1.54019	−0.167057
$86$	1.44589	0.155914
$87$	−0.359674	−0.0385611
$88$	37.6239	4.01072
$89$	10.1419	1.07503	0.537517	−	0.843253i	$-0.319362\pi$
$89$	10.1419	1.07503	0.537517	+	0.843253i	$0.319362\pi$
$90$	8.97358	0.945898
$91$	0.143461	0.0150388
$92$	−4.41245	−0.460030
$93$	−15.4733	−1.60451
$94$	24.2668	2.50293
$95$	6.51159	0.668075
$96$	−34.9672	−3.56882
$97$	9.13925	0.927951	0.463975	−	0.885848i	$-0.346423\pi$
$97$	9.13925	0.927951	0.463975	+	0.885848i	$0.346423\pi$
$98$	11.3066	1.14214
$99$	−15.8047	−1.58843
$100$	5.03608	0.503608
$101$	2.58876	0.257592	0.128796	−	0.991671i	$-0.458889\pi$
$101$	2.58876	0.257592	0.128796	+	0.991671i	$0.458889\pi$
$102$	−10.3217	−1.02200
$103$	8.29267	0.817101	0.408550	−	0.912736i	$-0.366034\pi$
$103$	8.29267	0.817101	0.408550	+	0.912736i	$0.366034\pi$
$104$	0.698294	0.0684734
$105$	4.18010	0.407936
$106$	−29.8305	−2.89739
$107$	4.61606	0.446252	0.223126	−	0.974790i	$-0.428374\pi$
$107$	4.61606	0.446252	0.223126	+	0.974790i	$0.428374\pi$
$108$	4.87292	0.468897
$109$	4.08290	0.391071	0.195535	−	0.980697i	$-0.437356\pi$
$109$	4.08290	0.391071	0.195535	+	0.980697i	$0.437356\pi$
$110$	−12.3923	−1.18156
$111$	−26.2625	−2.49272
$112$	−18.6795	−1.76504
$113$	8.10281	0.762248	0.381124	−	0.924524i	$-0.375537\pi$
$113$	8.10281	0.762248	0.381124	+	0.924524i	$0.375537\pi$
$114$	43.6379	4.08707
$115$	0.876169	0.0817032
$116$	−0.716951	−0.0665672
$117$	−0.293333	−0.0271187
$118$	−12.8877	−1.18640
$119$	−2.54828	−0.233601
$120$	20.3465	1.85737
$121$	10.8259	0.984176
$122$	−6.21958	−0.563094
$123$	15.5778	1.40460
$124$	−30.8436	−2.76983
$125$	−1.00000	−0.0894427
$126$	14.8470	1.32268
$127$	−4.65988	−0.413498	−0.206749	−	0.978394i	$-0.566288\pi$
$127$	−4.65988	−0.413498	−0.206749	+	0.978394i	$0.566288\pi$
$128$	−9.80702	−0.866827
$129$	−1.37715	−0.121252
$130$	−0.229999	−0.0201722
$131$	4.33450	0.378707	0.189353	−	0.981909i	$-0.439361\pi$
$131$	4.33450	0.378707	0.189353	+	0.981909i	$0.439361\pi$
$132$	−59.4416	−5.17373
$133$	10.7736	0.934190
$134$	25.6822	2.21861
$135$	−0.967604	−0.0832781
$136$	−12.4037	−1.06361
$137$	−14.3279	−1.22411	−0.612056	−	0.790814i	$-0.709657\pi$
$137$	−14.3279	−1.22411	−0.612056	+	0.790814i	$0.709657\pi$
$138$	5.87172	0.499834
$139$	0.792279	0.0672002	0.0336001	−	0.999435i	$-0.489303\pi$
$139$	0.792279	0.0672002	0.0336001	+	0.999435i	$0.489303\pi$
$140$	8.33233	0.704210
$141$	−23.1131	−1.94648
$142$	−39.5498	−3.31894
$143$	0.405086	0.0338750
$144$	38.1936	3.18280
$145$	0.142363	0.0118226
$146$	−27.2057	−2.25156
$147$	−10.7691	−0.888222
$148$	−52.3499	−4.30313
$149$	−2.80984	−0.230191	−0.115095	−	0.993354i	$-0.536717\pi$
$149$	−2.80984	−0.230191	−0.115095	+	0.993354i	$0.536717\pi$
$150$	−6.70158	−0.547182
$151$	−6.27002	−0.510247	−0.255124	−	0.966908i	$-0.582116\pi$
$151$	−6.27002	−0.510247	−0.255124	+	0.966908i	$0.582116\pi$
$152$	52.4402	4.25347
$153$	5.21044	0.421239
$154$	−20.5034	−1.65221
$155$	6.12452	0.491933
$156$	−1.10323	−0.0883288
$157$	13.4866	1.07635	0.538174	−	0.842834i	$-0.319114\pi$
$157$	13.4866	1.07635	0.538174	+	0.842834i	$0.319114\pi$
$158$	−21.6272	−1.72057
$159$	28.4124	2.25325
$160$	13.8404	1.09418
$161$	1.44965	0.114248
$162$	20.4363	1.60562
$163$	6.24059	0.488801	0.244400	−	0.969674i	$-0.421409\pi$
$163$	6.24059	0.488801	0.244400	+	0.969674i	$0.421409\pi$
$164$	31.0518	2.42474
$165$	11.8032	0.918875
$166$	−11.6201	−0.901893
$167$	6.81984	0.527735	0.263868	−	0.964559i	$-0.415002\pi$
$167$	6.81984	0.527735	0.263868	+	0.964559i	$0.415002\pi$
$168$	33.6639	2.59722
$169$	−12.9925	−0.999422
$170$	4.08544	0.313339
$171$	−22.0286	−1.68457
$172$	−2.74513	−0.209314
$173$	1.07176	0.0814846	0.0407423	−	0.999170i	$-0.487028\pi$
$173$	1.07176	0.0814846	0.0407423	+	0.999170i	$0.487028\pi$
$174$	0.954057	0.0723269
$175$	−1.65453	−0.125071
$176$	−52.7444	−3.97576
$177$	12.2750	0.922644
$178$	−26.9019	−2.01638
$179$	−16.4873	−1.23232	−0.616161	−	0.787621i	$-0.711313\pi$
$179$	−16.4873	−1.23232	−0.616161	+	0.787621i	$0.711313\pi$
$180$	−17.0370	−1.26986
$181$	0.527337	0.0391966	0.0195983	−	0.999808i	$-0.493761\pi$
$181$	0.527337	0.0391966	0.0195983	+	0.999808i	$0.493761\pi$
$182$	−0.380540	−0.0282075
$183$	5.92390	0.437907
$184$	7.05612	0.520184
$185$	10.3950	0.764253
$186$	41.0440	3.00949
$187$	−7.19548	−0.526186
$188$	−46.0722	−3.36016
$189$	−1.60093	−0.116450
$190$	−17.2724	−1.25307
$191$	1.68558	0.121964	0.0609820	−	0.998139i	$-0.480577\pi$
$191$	1.68558	0.121964	0.0609820	+	0.998139i	$0.480577\pi$
$192$	35.7057	2.57683
$193$	−0.898573	−0.0646807	−0.0323404	−	0.999477i	$-0.510296\pi$
$193$	−0.898573	−0.0646807	−0.0323404	+	0.999477i	$0.510296\pi$
$194$	−24.2424	−1.74050
$195$	0.219065	0.0156876
$196$	−21.4665	−1.53332
$197$	12.0324	0.857271	0.428636	−	0.903477i	$-0.358994\pi$
$197$	12.0324	0.857271	0.428636	+	0.903477i	$0.358994\pi$
$198$	41.9230	2.97934
$199$	−6.96233	−0.493547	−0.246773	−	0.969073i	$-0.579370\pi$
$199$	−6.96233	−0.493547	−0.246773	+	0.969073i	$0.579370\pi$
$200$	−8.05337	−0.569459
$201$	−24.4613	−1.72537
$202$	−6.86685	−0.483150
$203$	0.235544	0.0165319
$204$	19.5965	1.37203
$205$	−6.16587	−0.430643
$206$	−21.9968	−1.53259
$207$	−2.96407	−0.206017
$208$	−0.978928	−0.0678765
$209$	30.4210	2.10426
$210$	−11.0880	−0.765142
$211$	−6.27496	−0.431986	−0.215993	−	0.976395i	$-0.569299\pi$
$211$	−6.27496	−0.431986	−0.215993	+	0.976395i	$0.569299\pi$
$212$	56.6353	3.88973
$213$	37.6696	2.58108
$214$	−12.2444	−0.837009
$215$	0.545093	0.0371750
$216$	−7.79247	−0.530211
$217$	10.1332	0.687886
$218$	−10.8301	−0.733509
$219$	25.9123	1.75099
$220$	23.5277	1.58623
$221$	−0.133547	−0.00898334
$222$	69.6627	4.67546
$223$	11.7840	0.789113	0.394556	−	0.918872i	$-0.370898\pi$
$223$	11.7840	0.789113	0.394556	+	0.918872i	$0.370898\pi$
$224$	22.8993	1.53003
$225$	3.38299	0.225533
$226$	−21.4932	−1.42971
$227$	28.5046	1.89192	0.945958	−	0.324290i	$-0.105125\pi$
$227$	28.5046	1.89192	0.945958	+	0.324290i	$0.105125\pi$
$228$	−82.8497	−5.48686
$229$	3.15182	0.208278	0.104139	−	0.994563i	$-0.466791\pi$
$229$	3.15182	0.208278	0.104139	+	0.994563i	$0.466791\pi$
$230$	−2.32409	−0.153246
$231$	19.5287	1.28489
$232$	1.14650	0.0752715
$233$	25.4876	1.66975	0.834873	−	0.550442i	$-0.185541\pi$
$233$	25.4876	1.66975	0.834873	+	0.550442i	$0.185541\pi$
$234$	0.778084	0.0508649
$235$	9.14844	0.596778
$236$	24.4681	1.59274
$237$	20.5991	1.33805
$238$	6.75948	0.438152
$239$	10.2504	0.663045	0.331522	−	0.943447i	$-0.392438\pi$
$239$	10.2504	0.663045	0.331522	+	0.943447i	$0.392438\pi$
$240$	−28.5235	−1.84118
$241$	−21.3893	−1.37780	−0.688902	−	0.724855i	$-0.741907\pi$
$241$	−21.3893	−1.37780	−0.688902	+	0.724855i	$0.741907\pi$
$242$	−28.7164	−1.84596
$243$	−22.3675	−1.43488
$244$	11.8083	0.755950
$245$	4.26254	0.272323
$246$	−41.3211	−2.63454
$247$	0.564609	0.0359252
$248$	49.3231	3.13202
$249$	11.0677	0.701385
$250$	2.65256	0.167763
$251$	5.68449	0.358802	0.179401	−	0.983776i	$-0.442584\pi$
$251$	5.68449	0.358802	0.179401	+	0.983776i	$0.442584\pi$
$252$	−28.1882	−1.77569
$253$	4.09331	0.257344
$254$	12.3606	0.775574
$255$	−3.89122	−0.243678
$256$	−2.25168	−0.140730
$257$	−18.9796	−1.18391	−0.591957	−	0.805970i	$-0.701644\pi$
$257$	−18.9796	−1.18391	−0.591957	+	0.805970i	$0.701644\pi$
$258$	3.65298	0.227425
$259$	17.1988	1.06868
$260$	0.436669	0.0270811
$261$	−0.481612	−0.0298111
$262$	−11.4975	−0.710319
$263$	30.6540	1.89020	0.945102	−	0.326775i	$-0.105962\pi$
$263$	30.6540	1.89020	0.945102	+	0.326775i	$0.105962\pi$
$264$	95.0553	5.85025
$265$	−11.2459	−0.690832
$266$	−28.5776	−1.75221
$267$	25.6230	1.56810
$268$	−48.7595	−2.97846
$269$	−13.7081	−0.835800	−0.417900	−	0.908493i	$-0.637234\pi$
$269$	−13.7081	−0.835800	−0.417900	+	0.908493i	$0.637234\pi$
$270$	2.56663	0.156200
$271$	−0.122442	−0.00743781	−0.00371891	−	0.999993i	$-0.501184\pi$
$271$	−0.122442	−0.00743781	−0.00371891	+	0.999993i	$0.501184\pi$
$272$	17.3886	1.05434
$273$	0.362449	0.0219364
$274$	38.0056	2.29600
$275$	−4.67182	−0.281722
$276$	−11.1479	−0.671023
$277$	−6.96257	−0.418340	−0.209170	−	0.977879i	$-0.567076\pi$
$277$	−6.96257	−0.418340	−0.209170	+	0.977879i	$0.567076\pi$
$278$	−2.10157	−0.126044
$279$	−20.7192	−1.24043
$280$	−13.3245	−0.796293
$281$	−16.5907	−0.989721	−0.494860	−	0.868973i	$-0.664781\pi$
$281$	−16.5907	−0.989721	−0.494860	+	0.868973i	$0.664781\pi$
$282$	61.3090	3.65090
$283$	2.62254	0.155894	0.0779469	−	0.996958i	$-0.475164\pi$
$283$	2.62254	0.155894	0.0779469	+	0.996958i	$0.475164\pi$
$284$	75.0881	4.45566
$285$	16.4513	0.974488
$286$	−1.07451	−0.0635374
$287$	−10.2016	−0.602182
$288$	−46.8219	−2.75901
$289$	−14.6278	−0.860460
$290$	−0.377626	−0.0221750
$291$	23.0899	1.35356
$292$	51.6519	3.02270
$293$	31.6257	1.84759	0.923796	−	0.382886i	$-0.125070\pi$
$293$	31.6257	1.84759	0.923796	+	0.382886i	$0.125070\pi$
$294$	28.5657	1.66599
$295$	−4.85857	−0.282877
$296$	83.7146	4.86581
$297$	−4.52047	−0.262304
$298$	7.45326	0.431756
$299$	0.0759711	0.00439352
$300$	12.7234	0.734588
$301$	0.901872	0.0519830
$302$	16.6316	0.957042
$303$	6.54040	0.375736
$304$	−73.5152	−4.21639
$305$	−2.34475	−0.134260
$306$	−13.8210	−0.790094
$307$	−5.61394	−0.320405	−0.160202	−	0.987084i	$-0.551215\pi$
$307$	−5.61394	−0.320405	−0.160202	+	0.987084i	$0.551215\pi$
$308$	38.9272	2.21808
$309$	20.9511	1.19186
$310$	−16.2457	−0.922692
$311$	−28.3357	−1.60677	−0.803385	−	0.595460i	$-0.796970\pi$
$311$	−28.3357	−1.60677	−0.803385	+	0.595460i	$0.796970\pi$
$312$	1.76421	0.0998787
$313$	16.4717	0.931034	0.465517	−	0.885039i	$-0.345868\pi$
$313$	16.4717	0.931034	0.465517	+	0.885039i	$0.345868\pi$
$314$	−35.7740	−2.01884
$315$	5.59725	0.315369
$316$	41.0608	2.30985
$317$	1.70193	0.0955896	0.0477948	−	0.998857i	$-0.484781\pi$
$317$	1.70193	0.0955896	0.0477948	+	0.998857i	$0.484781\pi$
$318$	−75.3655	−4.22629
$319$	0.665095	0.0372382
$320$	−14.1327	−0.790042
$321$	11.6623	0.650926
$322$	−3.84528	−0.214289
$323$	−10.0291	−0.558032
$324$	−38.7997	−2.15554
$325$	−0.0867083	−0.00480971
$326$	−16.5535	−0.916816
$327$	10.3153	0.570436
$328$	−49.6561	−2.74180
$329$	15.1364	0.834494
$330$	−31.3086	−1.72348
$331$	13.3423	0.733358	0.366679	−	0.930348i	$-0.380495\pi$
$331$	13.3423	0.733358	0.366679	+	0.930348i	$0.380495\pi$
$332$	22.0616	1.21078
$333$	−35.1661	−1.92709
$334$	−18.0900	−0.989843
$335$	9.68205	0.528987
$336$	−47.1929	−2.57458
$337$	−13.7230	−0.747540	−0.373770	−	0.927521i	$-0.621935\pi$
$337$	−13.7230	−0.747540	−0.373770	+	0.927521i	$0.621935\pi$
$338$	34.4633	1.87456
$339$	20.4714	1.11185
$340$	−7.75650	−0.420655
$341$	28.6127	1.54946
$342$	58.4323	3.15965
$343$	18.6342	1.00615
$344$	4.38984	0.236684
$345$	2.21360	0.119176
$346$	−2.84291	−0.152836
$347$	17.5706	0.943239	0.471619	−	0.881802i	$-0.343670\pi$
$347$	17.5706	0.943239	0.471619	+	0.881802i	$0.343670\pi$
$348$	−1.81135	−0.0970983
$349$	10.6410	0.569602	0.284801	−	0.958587i	$-0.408072\pi$
$349$	10.6410	0.569602	0.284801	+	0.958587i	$0.408072\pi$
$350$	4.38874	0.234588
$351$	−0.0838992	−0.00447821
$352$	64.6599	3.44639
$353$	27.9398	1.48708	0.743542	−	0.668689i	$-0.233144\pi$
$353$	27.9398	1.48708	0.743542	+	0.668689i	$0.233144\pi$
$354$	−32.5601	−1.73055
$355$	−14.9100	−0.791343
$356$	51.0751	2.70698
$357$	−6.43813	−0.340742
$358$	43.7336	2.31139
$359$	−24.5775	−1.29715	−0.648576	−	0.761150i	$-0.724635\pi$
$359$	−24.5775	−1.29715	−0.648576	+	0.761150i	$0.724635\pi$
$360$	27.2445	1.43591
$361$	23.4008	1.23162
$362$	−1.39879	−0.0735189
$363$	27.3513	1.43557
$364$	0.722482	0.0378683
$365$	−10.2564	−0.536844
$366$	−15.7135	−0.821358
$367$	−6.06213	−0.316440	−0.158220	−	0.987404i	$-0.550576\pi$
$367$	−6.06213	−0.316440	−0.158220	+	0.987404i	$0.550576\pi$
$368$	−9.89187	−0.515649
$369$	20.8591	1.08588
$370$	−27.5733	−1.43347
$371$	−18.6067	−0.966012
$372$	−77.9249	−4.04022
$373$	−4.12735	−0.213706	−0.106853	−	0.994275i	$-0.534077\pi$
$373$	−4.12735	−0.213706	−0.106853	+	0.994275i	$0.534077\pi$
$374$	19.0865	0.986937
$375$	−2.52646	−0.130466
$376$	73.6758	3.79954
$377$	0.0123440	0.000635751 0
$378$	4.24656	0.218419
$379$	−1.14231	−0.0586768	−0.0293384	−	0.999570i	$-0.509340\pi$
$379$	−1.14231	−0.0586768	−0.0293384	+	0.999570i	$0.509340\pi$
$380$	32.7929	1.68224
$381$	−11.7730	−0.603149
$382$	−4.47109	−0.228761
$383$	−18.7361	−0.957372	−0.478686	−	0.877986i	$-0.658887\pi$
$383$	−18.7361	−0.957372	−0.478686	+	0.877986i	$0.658887\pi$
$384$	−24.7770	−1.26440
$385$	−7.72966	−0.393940
$386$	2.38352	0.121318
$387$	−1.84404	−0.0937380
$388$	46.0260	2.33661
$389$	15.8298	0.802603	0.401302	−	0.915946i	$-0.368558\pi$
$389$	15.8298	0.802603	0.401302	+	0.915946i	$0.368558\pi$
$390$	−0.581083	−0.0294243
$391$	−1.34946	−0.0682454
$392$	34.3278	1.73382
$393$	10.9509	0.552401
$394$	−31.9166	−1.60794
$395$	−8.15334	−0.410239
$396$	−79.5938	−3.99974
$397$	18.6048	0.933748	0.466874	−	0.884324i	$-0.345380\pi$
$397$	18.6048	0.933748	0.466874	+	0.884324i	$0.345380\pi$
$398$	18.4680	0.925718
$399$	27.2191	1.36266
$400$	11.2899	0.564495
$401$	−33.1701	−1.65643	−0.828217	−	0.560407i	$-0.810645\pi$
$401$	−33.1701	−1.65643	−0.828217	+	0.560407i	$0.810645\pi$
$402$	64.8851	3.23617
$403$	0.531047	0.0264533
$404$	13.0372	0.648625
$405$	7.70436	0.382832
$406$	−0.624794	−0.0310080
$407$	48.5635	2.40720
$408$	−31.3374	−1.55143
$409$	−5.28685	−0.261418	−0.130709	−	0.991421i	$-0.541725\pi$
$409$	−5.28685	−0.261418	−0.130709	+	0.991421i	$0.541725\pi$
$410$	16.3554	0.807733
$411$	−36.1988	−1.78555
$412$	41.7625	2.05749
$413$	−8.03864	−0.395556
$414$	7.86237	0.386415
$415$	−4.38070	−0.215040
$416$	1.20008	0.0588387
$417$	2.00166	0.0980217
$418$	−80.6935	−3.94685
$419$	−22.0012	−1.07483	−0.537416	−	0.843318i	$-0.680599\pi$
$419$	−22.0012	−1.07483	−0.537416	+	0.843318i	$0.680599\pi$
$420$	21.0513	1.02720
$421$	38.4644	1.87464	0.937320	−	0.348470i	$-0.113299\pi$
$421$	38.4644	1.87464	0.937320	+	0.348470i	$0.113299\pi$
$422$	16.6447	0.810252
$423$	−30.9491	−1.50480
$424$	−90.5676	−4.39835
$425$	1.54019	0.0747101
$426$	−99.9208	−4.84118
$427$	−3.87945	−0.187740
$428$	23.2468	1.12368
$429$	1.02343	0.0494118
$430$	−1.44589	−0.0697271
$431$	−21.5811	−1.03952	−0.519762	−	0.854311i	$-0.673979\pi$
$431$	−21.5811	−1.03952	−0.519762	+	0.854311i	$0.673979\pi$
$432$	10.9242	0.525588
$433$	26.4025	1.26882	0.634412	−	0.772995i	$-0.281242\pi$
$433$	26.4025	1.26882	0.634412	+	0.772995i	$0.281242\pi$
$434$	−26.8789	−1.29023
$435$	0.359674	0.0172450
$436$	20.5618	0.984731
$437$	5.70525	0.272919
$438$	−68.7340	−3.28424
$439$	−12.8579	−0.613675	−0.306837	−	0.951762i	$-0.599271\pi$
$439$	−12.8579	−0.613675	−0.306837	+	0.951762i	$0.599271\pi$
$440$	−37.6239	−1.79365
$441$	−14.4201	−0.686672
$442$	0.354241	0.0168495
$443$	−23.8380	−1.13258	−0.566289	−	0.824207i	$-0.691621\pi$
$443$	−23.8380	−1.13258	−0.566289	+	0.824207i	$0.691621\pi$
$444$	−132.260	−6.27677
$445$	−10.1419	−0.480770
$446$	−31.2577	−1.48009
$447$	−7.09893	−0.335768
$448$	−23.3830	−1.10474
$449$	13.2769	0.626576	0.313288	−	0.949658i	$-0.398570\pi$
$449$	13.2769	0.626576	0.313288	+	0.949658i	$0.398570\pi$
$450$	−8.97358	−0.423019
$451$	−28.8059	−1.35642
$452$	40.8064	1.91937
$453$	−15.8409	−0.744273
$454$	−75.6101	−3.54856
$455$	−0.143461	−0.00672557
$456$	132.488	6.20432
$457$	33.3070	1.55804	0.779018	−	0.627001i	$-0.215718\pi$
$457$	33.3070	1.55804	0.779018	+	0.627001i	$0.215718\pi$
$458$	−8.36039	−0.390655
$459$	1.49029	0.0695608
$460$	4.41245	0.205732
$461$	18.2543	0.850187	0.425094	−	0.905149i	$-0.360241\pi$
$461$	18.2543	0.850187	0.425094	+	0.905149i	$0.360241\pi$
$462$	−51.8010	−2.41000
$463$	−26.1409	−1.21487	−0.607436	−	0.794369i	$-0.707802\pi$
$463$	−26.1409	−1.21487	−0.607436	+	0.794369i	$0.707802\pi$
$464$	−1.60726	−0.0746154
$465$	15.4733	0.717559
$466$	−67.6073	−3.13185
$467$	−28.0150	−1.29638	−0.648191	−	0.761478i	$-0.724474\pi$
$467$	−28.0150	−1.29638	−0.648191	+	0.761478i	$0.724474\pi$
$468$	−1.47725	−0.0682858
$469$	16.0192	0.739699
$470$	−24.2668	−1.11934
$471$	34.0733	1.57002
$472$	−39.1279	−1.80101
$473$	2.54658	0.117092
$474$	−54.6403	−2.50971
$475$	−6.51159	−0.298772
$476$	−12.8333	−0.588216
$477$	38.0448	1.74195
$478$	−27.1899	−1.24364
$479$	−23.0586	−1.05357	−0.526787	−	0.849997i	$-0.676603\pi$
$479$	−23.0586	−1.05357	−0.526787	+	0.849997i	$0.676603\pi$
$480$	34.9672	1.59603
$481$	0.901330	0.0410971
$482$	56.7363	2.58427
$483$	3.66247	0.166648
$484$	54.5202	2.47819
$485$	−9.13925	−0.414992
$486$	59.3312	2.69132
$487$	−6.81935	−0.309014	−0.154507	−	0.987992i	$-0.549379\pi$
$487$	−6.81935	−0.309014	−0.154507	+	0.987992i	$0.549379\pi$
$488$	−18.8831	−0.854798
$489$	15.7666	0.712990
$490$	−11.3066	−0.510782
$491$	2.99530	0.135176	0.0675880	−	0.997713i	$-0.478470\pi$
$491$	2.99530	0.135176	0.0675880	+	0.997713i	$0.478470\pi$
$492$	78.4511	3.53685
$493$	−0.219266	−0.00987523
$494$	−1.49766	−0.0673828
$495$	15.8047	0.710369
$496$	−69.1453	−3.10471
$497$	−24.6691	−1.10656
$498$	−29.3576	−1.31555
$499$	−20.8199	−0.932029	−0.466014	−	0.884777i	$-0.654310\pi$
$499$	−20.8199	−0.932029	−0.466014	+	0.884777i	$0.654310\pi$
$500$	−5.03608	−0.225220
$501$	17.2300	0.769781
$502$	−15.0785	−0.672984
$503$	28.5734	1.27403	0.637013	−	0.770853i	$-0.280170\pi$
$503$	28.5734	1.27403	0.637013	+	0.770853i	$0.280170\pi$
$504$	45.0767	2.00788
$505$	−2.58876	−0.115198
$506$	−10.8577	−0.482686
$507$	−32.8250	−1.45781
$508$	−23.4675	−1.04120
$509$	−8.37842	−0.371367	−0.185684	−	0.982610i	$-0.559450\pi$
$509$	−8.37842	−0.371367	−0.185684	+	0.982610i	$0.559450\pi$
$510$	10.3217	0.457052
$511$	−16.9695	−0.750685
$512$	25.5868	1.13079
$513$	−6.30064	−0.278180
$514$	50.3445	2.22060
$515$	−8.29267	−0.365419
$516$	−6.93545	−0.305316
$517$	42.7399	1.87970
$518$	−45.6208	−2.00446
$519$	2.70776	0.118858
$520$	−0.698294	−0.0306222
$521$	10.3107	0.451720	0.225860	−	0.974160i	$-0.427481\pi$
$521$	10.3107	0.451720	0.225860	+	0.974160i	$0.427481\pi$
$522$	1.27751	0.0559149
$523$	5.08125	0.222188	0.111094	−	0.993810i	$-0.464565\pi$
$523$	5.08125	0.222188	0.111094	+	0.993810i	$0.464565\pi$
$524$	21.8288	0.953598
$525$	−4.18010	−0.182434
$526$	−81.3115	−3.54535
$527$	−9.43291	−0.410904
$528$	−133.257	−5.79925
$529$	−22.2323	−0.966623
$530$	29.8305	1.29575
$531$	16.4365	0.713283
$532$	54.2567	2.35233
$533$	−0.534632	−0.0231575
$534$	−67.9664	−2.94120
$535$	−4.61606	−0.199570
$536$	77.9732	3.36793
$537$	−41.6545	−1.79753
$538$	36.3616	1.56766
$539$	19.9138	0.857749
$540$	−4.87292	−0.209697
$541$	5.23805	0.225201	0.112601	−	0.993640i	$-0.464082\pi$
$541$	5.23805	0.225201	0.112601	+	0.993640i	$0.464082\pi$
$542$	0.324784	0.0139507
$543$	1.33229	0.0571742
$544$	−21.3168	−0.913951
$545$	−4.08290	−0.174892
$546$	−0.961418	−0.0411449
$547$	−15.5645	−0.665489	−0.332744	−	0.943017i	$-0.607975\pi$
$547$	−15.5645	−0.665489	−0.332744	+	0.943017i	$0.607975\pi$
$548$	−72.1563	−3.08236
$549$	7.93225	0.338540
$550$	12.3923	0.528409
$551$	0.927009	0.0394919
$552$	17.8270	0.758767
$553$	−13.4899	−0.573650
$554$	18.4686	0.784657
$555$	26.2625	1.11478
$556$	3.98998	0.169213
$557$	−26.0731	−1.10475	−0.552376	−	0.833595i	$-0.686279\pi$
$557$	−26.0731	−1.10475	−0.552376	+	0.833595i	$0.686279\pi$
$558$	54.9589	2.32660
$559$	0.0472641	0.00199906
$560$	18.6795	0.789352
$561$	−18.1791	−0.767521
$562$	44.0079	1.85636
$563$	0.625872	0.0263774	0.0131887	−	0.999913i	$-0.495802\pi$
$563$	0.625872	0.0263774	0.0131887	+	0.999913i	$0.495802\pi$
$564$	−116.400	−4.90131
$565$	−8.10281	−0.340888
$566$	−6.95644	−0.292401
$567$	12.7471	0.535327
$568$	−120.076	−5.03828
$569$	−16.8113	−0.704768	−0.352384	−	0.935856i	$-0.614629\pi$
$569$	−16.8113	−0.704768	−0.352384	+	0.935856i	$0.614629\pi$
$570$	−43.6379	−1.82779
$571$	16.3060	0.682385	0.341193	−	0.939993i	$-0.389169\pi$
$571$	16.3060	0.682385	0.341193	+	0.939993i	$0.389169\pi$
$572$	2.04004	0.0852985
$573$	4.25853	0.177903
$574$	27.0604	1.12948
$575$	−0.876169	−0.0365388
$576$	47.8108	1.99211
$577$	38.6490	1.60898	0.804490	−	0.593967i	$-0.202439\pi$
$577$	38.6490	1.60898	0.804490	+	0.593967i	$0.202439\pi$
$578$	38.8012	1.61392
$579$	−2.27021	−0.0943466
$580$	0.716951	0.0297698
$581$	−7.24800	−0.300698
$582$	−61.2475	−2.53879
$583$	−52.5390	−2.17594
$584$	−82.5985	−3.41795
$585$	0.293333	0.0121278
$586$	−83.8890	−3.46542
$587$	−19.1394	−0.789968	−0.394984	−	0.918688i	$-0.629250\pi$
$587$	−19.1394	−0.789968	−0.394984	+	0.918688i	$0.629250\pi$
$588$	−54.2341	−2.23658
$589$	39.8804	1.64324
$590$	12.8877	0.530576
$591$	30.3993	1.25046
$592$	−117.358	−4.82339
$593$	41.3485	1.69798	0.848990	−	0.528409i	$-0.177211\pi$
$593$	41.3485	1.69798	0.848990	+	0.528409i	$0.177211\pi$
$594$	11.9908	0.491990
$595$	2.54828	0.104469
$596$	−14.1505	−0.579629
$597$	−17.5900	−0.719912
$598$	−0.201518	−0.00824068
$599$	−11.1184	−0.454285	−0.227143	−	0.973862i	$-0.572938\pi$
$599$	−11.1184	−0.454285	−0.227143	+	0.973862i	$0.572938\pi$
$600$	−20.3465	−0.830643
$601$	22.3181	0.910376	0.455188	−	0.890395i	$-0.349572\pi$
$601$	22.3181	0.910376	0.455188	+	0.890395i	$0.349572\pi$
$602$	−2.39227	−0.0975016
$603$	−32.7543	−1.33386
$604$	−31.5763	−1.28482
$605$	−10.8259	−0.440137
$606$	−17.3488	−0.704747
$607$	−11.6058	−0.471066	−0.235533	−	0.971866i	$-0.575684\pi$
$607$	−11.6058	−0.471066	−0.235533	+	0.971866i	$0.575684\pi$
$608$	90.1230	3.65497
$609$	0.595091	0.0241143
$610$	6.21958	0.251823
$611$	0.793246	0.0320913
$612$	26.2401	1.06070
$613$	−32.9503	−1.33085	−0.665424	−	0.746465i	$-0.731749\pi$
$613$	−32.9503	−1.33085	−0.665424	+	0.746465i	$0.731749\pi$
$614$	14.8913	0.600965
$615$	−15.5778	−0.628158
$616$	−62.2499	−2.50812
$617$	−26.0563	−1.04899	−0.524494	−	0.851414i	$-0.675745\pi$
$617$	−26.0563	−1.04899	−0.524494	+	0.851414i	$0.675745\pi$
$618$	−55.5740	−2.23551
$619$	35.4398	1.42445	0.712223	−	0.701953i	$-0.247688\pi$
$619$	35.4398	1.42445	0.712223	+	0.701953i	$0.247688\pi$
$620$	30.8436	1.23871
$621$	−0.847784	−0.0340204
$622$	75.1621	3.01373
$623$	−16.7800	−0.672276
$624$	−2.47322	−0.0990081
$625$	1.00000	0.0400000
$626$	−43.6921	−1.74629
$627$	76.8573	3.06939
$628$	67.9195	2.71028
$629$	−16.0102	−0.638369
$630$	−14.8470	−0.591520
$631$	29.2491	1.16439	0.582194	−	0.813050i	$-0.302194\pi$
$631$	29.2491	1.16439	0.582194	+	0.813050i	$0.302194\pi$
$632$	−65.6619	−2.61189
$633$	−15.8534	−0.630117
$634$	−4.51446	−0.179292
$635$	4.65988	0.184922
$636$	143.087	5.67376
$637$	0.369597	0.0146440
$638$	−1.76420	−0.0698455
$639$	50.4405	1.99539
$640$	9.80702	0.387657
$641$	−0.869329	−0.0343364	−0.0171682	−	0.999853i	$-0.505465\pi$
$641$	−0.869329	−0.0343364	−0.0171682	+	0.999853i	$0.505465\pi$
$642$	−30.9349	−1.22090
$643$	−20.8015	−0.820333	−0.410166	−	0.912011i	$-0.634529\pi$
$643$	−20.8015	−0.820333	−0.410166	+	0.912011i	$0.634529\pi$
$644$	7.30053	0.287681
$645$	1.37715	0.0542254
$646$	26.6027	1.04667
$647$	−11.4962	−0.451962	−0.225981	−	0.974132i	$-0.572559\pi$
$647$	−11.4962	−0.451962	−0.225981	+	0.974132i	$0.572559\pi$
$648$	62.0460	2.43740
$649$	−22.6984	−0.890990
$650$	0.229999	0.00902130
$651$	25.6011	1.00339
$652$	31.4281	1.23082
$653$	3.16725	0.123944	0.0619721	−	0.998078i	$-0.480261\pi$
$653$	3.16725	0.123944	0.0619721	+	0.998078i	$0.480261\pi$
$654$	−27.3619	−1.06993
$655$	−4.33450	−0.169363
$656$	69.6121	2.71790
$657$	34.6972	1.35367
$658$	−40.1501	−1.56521
$659$	22.8110	0.888589	0.444295	−	0.895881i	$-0.353454\pi$
$659$	22.8110	0.888589	0.444295	+	0.895881i	$0.353454\pi$
$660$	59.4416	2.31376
$661$	23.6256	0.918928	0.459464	−	0.888197i	$-0.348042\pi$
$661$	23.6256	0.918928	0.459464	+	0.888197i	$0.348042\pi$
$662$	−35.3912	−1.37552
$663$	−0.337401	−0.0131036
$664$	−35.2794	−1.36911
$665$	−10.7736	−0.417783
$666$	93.2801	3.61453
$667$	0.124734	0.00482972
$668$	34.3452	1.32886
$669$	29.7717	1.15104
$670$	−25.6822	−0.992191
$671$	−10.9542	−0.422884
$672$	57.8542	2.23178
$673$	−48.8545	−1.88320	−0.941602	−	0.336727i	$-0.890680\pi$
$673$	−48.8545	−1.88320	−0.941602	+	0.336727i	$0.890680\pi$
$674$	36.4011	1.40212
$675$	0.967604	0.0372431
$676$	−65.4311	−2.51658
$677$	−28.4710	−1.09423	−0.547115	−	0.837058i	$-0.684274\pi$
$677$	−28.4710	−1.09423	−0.547115	+	0.837058i	$0.684274\pi$
$678$	−54.3017	−2.08544
$679$	−15.1212	−0.580297
$680$	12.4037	0.475660
$681$	72.0156	2.75964
$682$	−75.8969	−2.90624
$683$	−26.6255	−1.01880	−0.509398	−	0.860531i	$-0.670132\pi$
$683$	−26.6255	−1.01880	−0.509398	+	0.860531i	$0.670132\pi$
$684$	−110.938	−4.24181
$685$	14.3279	0.547440
$686$	−49.4283	−1.88718
$687$	7.96294	0.303805
$688$	−6.15405	−0.234621
$689$	−0.975115	−0.0371489
$690$	−5.87172	−0.223532
$691$	6.61836	0.251774	0.125887	−	0.992045i	$-0.459822\pi$
$691$	6.61836	0.251774	0.125887	+	0.992045i	$0.459822\pi$
$692$	5.39748	0.205181
$693$	26.1494	0.993332
$694$	−46.6070	−1.76918
$695$	−0.792279	−0.0300529
$696$	2.89659	0.109795
$697$	9.49660	0.359709
$698$	−28.2260	−1.06837
$699$	64.3933	2.43558
$700$	−8.33233	−0.314932
$701$	−48.6296	−1.83671	−0.918356	−	0.395754i	$-0.870483\pi$
$701$	−48.6296	−1.83671	−0.918356	+	0.395754i	$0.870483\pi$
$702$	0.222548	0.00839952
$703$	67.6878	2.55289
$704$	−66.0255	−2.48843
$705$	23.1131	0.870492
$706$	−74.1119	−2.78924
$707$	−4.28318	−0.161086
$708$	61.8177	2.32325
$709$	30.8783	1.15966	0.579829	−	0.814738i	$-0.303119\pi$
$709$	30.8783	1.15966	0.579829	+	0.814738i	$0.303119\pi$
$710$	39.5498	1.48428
$711$	27.5827	1.03443
$712$	−81.6761	−3.06094
$713$	5.36612	0.200963
$714$	17.0775	0.639111
$715$	−0.405086	−0.0151493
$716$	−83.0315	−3.10303
$717$	25.8973	0.967151
$718$	65.1933	2.43299
$719$	24.9699	0.931220	0.465610	−	0.884990i	$-0.345835\pi$
$719$	24.9699	0.931220	0.465610	+	0.884990i	$0.345835\pi$
$720$	−38.1936	−1.42339
$721$	−13.7205	−0.510976
$722$	−62.0720	−2.31008
$723$	−54.0391	−2.00973
$724$	2.65571	0.0986986
$725$	−0.142363	−0.00528723
$726$	−72.5508	−2.69261
$727$	48.9203	1.81435	0.907177	−	0.420748i	$-0.138232\pi$
$727$	48.9203	1.81435	0.907177	+	0.420748i	$0.138232\pi$
$728$	−1.15535	−0.0428200
$729$	−33.3976	−1.23695
$730$	27.2057	1.00693
$731$	−0.839545	−0.0310517
$732$	29.8332	1.10267
$733$	−27.3910	−1.01171	−0.505854	−	0.862619i	$-0.668823\pi$
$733$	−27.3910	−1.01171	−0.505854	+	0.862619i	$0.668823\pi$
$734$	16.0802	0.593529
$735$	10.7691	0.397225
$736$	12.1265	0.446990
$737$	45.2328	1.66617
$738$	−55.3300	−2.03672
$739$	33.8258	1.24430	0.622152	−	0.782897i	$-0.286259\pi$
$739$	33.8258	1.24430	0.622152	+	0.782897i	$0.286259\pi$
$740$	52.3499	1.92442
$741$	1.42646	0.0524023
$742$	49.3554	1.81189
$743$	−19.5793	−0.718293	−0.359147	−	0.933281i	$-0.616932\pi$
$743$	−19.5793	−0.718293	−0.359147	+	0.933281i	$0.616932\pi$
$744$	124.613	4.56852
$745$	2.80984	0.102944
$746$	10.9480	0.400836
$747$	14.8199	0.542231
$748$	−36.2370	−1.32496
$749$	−7.63741	−0.279065
$750$	6.70158	0.244707
$751$	−7.28859	−0.265964	−0.132982	−	0.991118i	$-0.542455\pi$
$751$	−7.28859	−0.265964	−0.132982	+	0.991118i	$0.542455\pi$
$752$	−103.285	−3.76642
$753$	14.3616	0.523367
$754$	−0.0327433	−0.00119244
$755$	6.27002	0.228189
$756$	−8.06239	−0.293226
$757$	18.6304	0.677133	0.338566	−	0.940943i	$-0.390058\pi$
$757$	18.6304	0.677133	0.338566	+	0.940943i	$0.390058\pi$
$758$	3.03006	0.110057
$759$	10.3416	0.375375
$760$	−52.4402	−1.90221
$761$	−22.2817	−0.807712	−0.403856	−	0.914822i	$-0.632330\pi$
$761$	−22.2817	−0.807712	−0.403856	+	0.914822i	$0.632330\pi$
$762$	31.2286	1.13129
$763$	−6.75527	−0.244557
$764$	8.48868	0.307110
$765$	−5.21044	−0.188384
$766$	49.6988	1.79569
$767$	−0.421278	−0.0152115
$768$	−5.68877	−0.205276
$769$	3.24409	0.116985	0.0584924	−	0.998288i	$-0.481371\pi$
$769$	3.24409	0.116985	0.0584924	+	0.998288i	$0.481371\pi$
$770$	20.5034	0.738891
$771$	−47.9511	−1.72692
$772$	−4.52528	−0.162868
$773$	31.7287	1.14120	0.570601	−	0.821228i	$-0.306710\pi$
$773$	31.7287	1.14120	0.570601	+	0.821228i	$0.306710\pi$
$774$	4.89143	0.175819
$775$	−6.12452	−0.219999
$776$	−73.6018	−2.64215
$777$	43.4520	1.55883
$778$	−41.9895	−1.50540
$779$	−40.1496	−1.43851
$780$	1.10323	0.0395019
$781$	−69.6571	−2.49253
$782$	3.57954	0.128004
$783$	−0.137751	−0.00492282
$784$	−48.1236	−1.71870
$785$	−13.4866	−0.481357
$786$	−29.0480	−1.03611
$787$	1.72478	0.0614819	0.0307409	−	0.999527i	$-0.490213\pi$
$787$	1.72478	0.0614819	0.0307409	+	0.999527i	$0.490213\pi$
$788$	60.5960	2.15864
$789$	77.4459	2.75715
$790$	21.6272	0.769462
$791$	−13.4063	−0.476674
$792$	127.281	4.52274
$793$	−0.203309	−0.00721971
$794$	−49.3503	−1.75138
$795$	−28.4124	−1.00768
$796$	−35.0628	−1.24277
$797$	42.7313	1.51362	0.756810	−	0.653635i	$-0.226757\pi$
$797$	42.7313	1.51362	0.756810	+	0.653635i	$0.226757\pi$
$798$	−72.2002	−2.55586
$799$	−14.0903	−0.498479
$800$	−13.8404	−0.489332
$801$	34.3098	1.21228
$802$	87.9856	3.10688
$803$	−47.9160	−1.69092
$804$	−123.189	−4.34454
$805$	−1.44965	−0.0510933
$806$	−1.40863	−0.0496170
$807$	−34.6330	−1.21914
$808$	−20.8483	−0.733440
$809$	−2.36144	−0.0830238	−0.0415119	−	0.999138i	$-0.513217\pi$
$809$	−2.36144	−0.0830238	−0.0415119	+	0.999138i	$0.513217\pi$
$810$	−20.4363	−0.718057
$811$	−3.74117	−0.131370	−0.0656850	−	0.997840i	$-0.520923\pi$
$811$	−3.74117	−0.131370	−0.0656850	+	0.997840i	$0.520923\pi$
$812$	1.18622	0.0416280
$813$	−0.309344	−0.0108492
$814$	−128.817	−4.51505
$815$	−6.24059	−0.218598
$816$	43.9315	1.53791
$817$	3.54942	0.124178
$818$	14.0237	0.490327
$819$	0.485328	0.0169587
$820$	−31.0518	−1.08438
$821$	−4.63726	−0.161842	−0.0809208	−	0.996721i	$-0.525786\pi$
$821$	−4.63726	−0.161842	−0.0809208	+	0.996721i	$0.525786\pi$
$822$	96.0194	3.34906
$823$	−28.5872	−0.996488	−0.498244	−	0.867037i	$-0.666022\pi$
$823$	−28.5872	−0.996488	−0.498244	+	0.867037i	$0.666022\pi$
$824$	−66.7839	−2.32653
$825$	−11.8032	−0.410933
$826$	21.3230	0.741922
$827$	−14.7878	−0.514222	−0.257111	−	0.966382i	$-0.582771\pi$
$827$	−14.7878	−0.514222	−0.257111	+	0.966382i	$0.582771\pi$
$828$	−14.9273	−0.518759
$829$	35.0207	1.21632	0.608160	−	0.793814i	$-0.291908\pi$
$829$	35.0207	1.21632	0.608160	+	0.793814i	$0.291908\pi$
$830$	11.6201	0.403339
$831$	−17.5906	−0.610212
$832$	−1.22542	−0.0424839
$833$	−6.56510	−0.227467
$834$	−5.30952	−0.183854
$835$	−6.81984	−0.236010
$836$	153.202	5.29862
$837$	−5.92611	−0.204836
$838$	58.3596	2.01600
$839$	18.5188	0.639340	0.319670	−	0.947529i	$-0.396428\pi$
$839$	18.5188	0.639340	0.319670	+	0.947529i	$0.396428\pi$
$840$	−33.6639	−1.16151
$841$	−28.9797	−0.999301
$842$	−102.029	−3.51616
$843$	−41.9158	−1.44366
$844$	−31.6012	−1.08776
$845$	12.9925	0.446955
$846$	82.0943	2.82246
$847$	−17.9118	−0.615457
$848$	126.965	4.36001
$849$	6.62573	0.227395
$850$	−4.08544	−0.140129
$851$	9.10775	0.312210
$852$	189.707	6.49925
$853$	46.0373	1.57629	0.788144	−	0.615491i	$-0.211042\pi$
$853$	46.0373	1.57629	0.788144	+	0.615491i	$0.211042\pi$
$854$	10.2905	0.352133
$855$	22.0286	0.753363
$856$	−37.1749	−1.27061
$857$	43.7658	1.49501	0.747506	−	0.664255i	$-0.231251\pi$
$857$	43.7658	1.49501	0.747506	+	0.664255i	$0.231251\pi$
$858$	−2.71471	−0.0926788
$859$	−9.65049	−0.329270	−0.164635	−	0.986355i	$-0.552645\pi$
$859$	−9.65049	−0.329270	−0.164635	+	0.986355i	$0.552645\pi$
$860$	2.74513	0.0936081
$861$	−25.7739	−0.878374
$862$	57.2451	1.94978
$863$	−46.4597	−1.58151	−0.790753	−	0.612135i	$-0.790311\pi$
$863$	−46.4597	−1.58151	−0.790753	+	0.612135i	$0.790311\pi$
$864$	−13.3920	−0.455606
$865$	−1.07176	−0.0364410
$866$	−70.0342	−2.37986
$867$	−36.9566	−1.25511
$868$	51.0315	1.73212
$869$	−38.0910	−1.29215
$870$	−0.954057	−0.0323456
$871$	0.839514	0.0284459
$872$	−32.8811	−1.11349
$873$	30.9180	1.04642
$874$	−15.1335	−0.511899
$875$	1.65453	0.0559333
$876$	130.496	4.40906
$877$	5.34579	0.180515	0.0902573	−	0.995918i	$-0.471231\pi$
$877$	5.34579	0.180515	0.0902573	+	0.995918i	$0.471231\pi$
$878$	34.1064	1.15103
$879$	79.9009	2.69499
$880$	52.7444	1.77801
$881$	−36.4895	−1.22936	−0.614681	−	0.788776i	$-0.710715\pi$
$881$	−36.4895	−1.22936	−0.614681	+	0.788776i	$0.710715\pi$
$882$	38.2502	1.28795
$883$	53.1610	1.78901	0.894505	−	0.447057i	$-0.147528\pi$
$883$	53.1610	1.78901	0.894505	+	0.447057i	$0.147528\pi$
$884$	−0.672553	−0.0226204
$885$	−12.2750	−0.412619
$886$	63.2317	2.12431
$887$	3.41682	0.114725	0.0573627	−	0.998353i	$-0.481731\pi$
$887$	3.41682	0.114725	0.0573627	+	0.998353i	$0.481731\pi$
$888$	211.501	7.09752
$889$	7.70990	0.258582
$890$	26.9019	0.901753
$891$	35.9934	1.20582
$892$	59.3449	1.98702
$893$	59.5709	1.99346
$894$	18.8303	0.629781
$895$	16.4873	0.551111
$896$	16.2260	0.542073
$897$	0.191938	0.00640862
$898$	−35.2178	−1.17523
$899$	0.871905	0.0290797
$900$	17.0370	0.567899
$901$	17.3208	0.577041
$902$	76.4093	2.54415
$903$	2.27854	0.0758251
$904$	−65.2550	−2.17035
$905$	−0.527337	−0.0175293
$906$	42.0191	1.39599
$907$	−44.7655	−1.48641	−0.743207	−	0.669062i	$-0.766696\pi$
$907$	−44.7655	−1.48641	−0.743207	+	0.669062i	$0.766696\pi$
$908$	143.551	4.76391
$909$	8.75776	0.290477
$910$	0.380540	0.0126148
$911$	20.6689	0.684793	0.342396	−	0.939556i	$-0.388761\pi$
$911$	20.6689	0.684793	0.342396	+	0.939556i	$0.388761\pi$
$912$	−185.733	−6.15024
$913$	−20.4659	−0.677321
$914$	−88.3488	−2.92232
$915$	−5.92390	−0.195838
$916$	15.8728	0.524452
$917$	−7.17155	−0.236825
$918$	−3.95309	−0.130471
$919$	0.0482347	0.00159112	0.000795558	−	1.00000i	$-0.499747\pi$
$919$	0.0482347	0.00159112	0.000795558		1.00000i	$0.499747\pi$
$920$	−7.05612	−0.232633
$921$	−14.1834	−0.467359
$922$	−48.4206	−1.59465
$923$	−1.29282	−0.0425538
$924$	98.3479	3.23541
$925$	−10.3950	−0.341785
$926$	69.3404	2.27867
$927$	28.0540	0.921414
$928$	1.97036	0.0646803
$929$	−13.6234	−0.446970	−0.223485	−	0.974707i	$-0.571743\pi$
$929$	−13.6234	−0.446970	−0.223485	+	0.974707i	$0.571743\pi$
$930$	−41.0440	−1.34589
$931$	27.7559	0.909662
$932$	128.357	4.20449
$933$	−71.5889	−2.34372
$934$	74.3116	2.43155
$935$	7.19548	0.235317
$936$	2.36232	0.0772149
$937$	−15.0932	−0.493072	−0.246536	−	0.969134i	$-0.579292\pi$
$937$	−15.0932	−0.493072	−0.246536	+	0.969134i	$0.579292\pi$
$938$	−42.4920	−1.38741
$939$	41.6150	1.35805
$940$	46.0722	1.50271
$941$	45.8115	1.49341	0.746706	−	0.665154i	$-0.231634\pi$
$941$	45.8115	1.49341	0.746706	+	0.665154i	$0.231634\pi$
$942$	−90.3815	−2.94479
$943$	−5.40235	−0.175925
$944$	54.8528	1.78531
$945$	1.60093	0.0520782
$946$	−6.75495	−0.219622
$947$	47.4567	1.54214	0.771068	−	0.636753i	$-0.219723\pi$
$947$	47.4567	1.54214	0.771068	+	0.636753i	$0.219723\pi$
$948$	103.738	3.36927
$949$	−0.889313	−0.0288683
$950$	17.2724	0.560390
$951$	4.29984	0.139432
$952$	20.5223	0.665131
$953$	54.6777	1.77119	0.885593	−	0.464462i	$-0.153752\pi$
$953$	54.6777	1.77119	0.885593	+	0.464462i	$0.153752\pi$
$954$	−100.916	−3.26728
$955$	−1.68558	−0.0545439
$956$	51.6219	1.66957
$957$	1.68033	0.0543175
$958$	61.1643	1.97613
$959$	23.7059	0.765503
$960$	−35.7057	−1.15240
$961$	6.50977	0.209993
$962$	−2.39083	−0.0770835
$963$	15.6161	0.503221
$964$	−107.718	−3.46936
$965$	0.898573	0.0289261
$966$	−9.71492	−0.312573
$967$	52.7375	1.69592	0.847962	−	0.530057i	$-0.177829\pi$
$967$	52.7375	1.69592	0.847962	+	0.530057i	$0.177829\pi$
$968$	−87.1853	−2.80224
$969$	−25.3380	−0.813974
$970$	24.2424	0.778377
$971$	41.8956	1.34449	0.672247	−	0.740327i	$-0.265329\pi$
$971$	41.8956	1.34449	0.672247	+	0.740327i	$0.265329\pi$
$972$	−112.645	−3.61308
$973$	−1.31085	−0.0420239
$974$	18.0887	0.579601
$975$	−0.219065	−0.00701569
$976$	26.4719	0.847346
$977$	7.68455	0.245851	0.122925	−	0.992416i	$-0.460772\pi$
$977$	7.68455	0.245851	0.122925	+	0.992416i	$0.460772\pi$
$978$	−41.8218	−1.33731
$979$	−47.3809	−1.51430
$980$	21.4665	0.685721
$981$	13.8124	0.440996
$982$	−7.94522	−0.253542
$983$	9.71363	0.309817	0.154908	−	0.987929i	$-0.450492\pi$
$983$	9.71363	0.309817	0.154908	+	0.987929i	$0.450492\pi$
$984$	−125.454	−3.99933
$985$	−12.0324	−0.383383
$986$	0.581615	0.0185224
$987$	38.2414	1.21724
$988$	2.84341	0.0904610
$989$	0.477593	0.0151866
$990$	−41.9230	−1.33240
$991$	42.5874	1.35283	0.676416	−	0.736520i	$-0.263532\pi$
$991$	42.5874	1.35283	0.676416	+	0.736520i	$0.263532\pi$
$992$	84.7659	2.69132
$993$	33.7087	1.06971
$994$	65.4362	2.07551
$995$	6.96233	0.220721
$996$	55.7376	1.76611
$997$	39.5026	1.25106	0.625530	−	0.780200i	$-0.284883\pi$
$997$	39.5026	1.25106	0.625530	+	0.780200i	$0.284883\pi$
$998$	55.2261	1.74815
$999$	−10.0582	−0.318228

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.c.1.3	✓	127

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.c.1.3	✓	127	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:	\( N \)	\(=\)	\( 8035 = 5 \cdot 1607 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.65256 q^{2} +2.52646 q^{3} +5.03608 q^{4} -1.00000 q^{5} -6.70158 q^{6} -1.65453 q^{7} -8.05337 q^{8} +3.38299 q^{9} +O(q^{10})\)	\(q-2.65256 q^{2} +2.52646 q^{3} +5.03608 q^{4} -1.00000 q^{5} -6.70158 q^{6} -1.65453 q^{7} -8.05337 q^{8} +3.38299 q^{9} +2.65256 q^{10} -4.67182 q^{11} +12.7234 q^{12} -0.0867083 q^{13} +4.38874 q^{14} -2.52646 q^{15} +11.2899 q^{16} +1.54019 q^{17} -8.97358 q^{18} -6.51159 q^{19} -5.03608 q^{20} -4.18010 q^{21} +12.3923 q^{22} -0.876169 q^{23} -20.3465 q^{24} +1.00000 q^{25} +0.229999 q^{26} +0.967604 q^{27} -8.33233 q^{28} -0.142363 q^{29} +6.70158 q^{30} -6.12452 q^{31} -13.8404 q^{32} -11.8032 q^{33} -4.08544 q^{34} +1.65453 q^{35} +17.0370 q^{36} -10.3950 q^{37} +17.2724 q^{38} -0.219065 q^{39} +8.05337 q^{40} +6.16587 q^{41} +11.0880 q^{42} -0.545093 q^{43} -23.5277 q^{44} -3.38299 q^{45} +2.32409 q^{46} -9.14844 q^{47} +28.5235 q^{48} -4.26254 q^{49} -2.65256 q^{50} +3.89122 q^{51} -0.436669 q^{52} +11.2459 q^{53} -2.56663 q^{54} +4.67182 q^{55} +13.3245 q^{56} -16.4513 q^{57} +0.377626 q^{58} +4.85857 q^{59} -12.7234 q^{60} +2.34475 q^{61} +16.2457 q^{62} -5.59725 q^{63} +14.1327 q^{64} +0.0867083 q^{65} +31.3086 q^{66} -9.68205 q^{67} +7.75650 q^{68} -2.21360 q^{69} -4.38874 q^{70} +14.9100 q^{71} -27.2445 q^{72} +10.2564 q^{73} +27.5733 q^{74} +2.52646 q^{75} -32.7929 q^{76} +7.72966 q^{77} +0.581083 q^{78} +8.15334 q^{79} -11.2899 q^{80} -7.70436 q^{81} -16.3554 q^{82} +4.38070 q^{83} -21.0513 q^{84} -1.54019 q^{85} +1.44589 q^{86} -0.359674 q^{87} +37.6239 q^{88} +10.1419 q^{89} +8.97358 q^{90} +0.143461 q^{91} -4.41245 q^{92} -15.4733 q^{93} +24.2668 q^{94} +6.51159 q^{95} -34.9672 q^{96} +9.13925 q^{97} +11.3066 q^{98} -15.8047 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 127 q + 19 q^{2} + 10 q^{3} + 125 q^{4} - 127 q^{5} + 13 q^{7} + 54 q^{8} + 123 q^{9}+O(q^{10}) \) 127 * q + 19 * q^2 + 10 * q^3 + 125 * q^4 - 127 * q^5 + 13 * q^7 + 54 * q^8 + 123 * q^9	\( 127 q + 19 q^{2} + 10 q^{3} + 125 q^{4} - 127 q^{5} + 13 q^{7} + 54 q^{8} + 123 q^{9} - 19 q^{10} + 30 q^{11} + 35 q^{12} + 30 q^{13} + 39 q^{14} - 10 q^{15} + 121 q^{16} + 63 q^{17} + 53 q^{18} - 35 q^{19} - 125 q^{20} + 33 q^{21} + 49 q^{22} + 61 q^{23} - 5 q^{24} + 127 q^{25} + 10 q^{26} + 40 q^{27} + 32 q^{28} + 134 q^{29} - 25 q^{31} + 122 q^{32} + 48 q^{33} - 21 q^{34} - 13 q^{35} + 133 q^{36} + 60 q^{37} + 33 q^{38} + 26 q^{39} - 54 q^{40} + 9 q^{41} + 45 q^{42} + 48 q^{43} + 85 q^{44} - 123 q^{45} - 11 q^{46} + 57 q^{47} + 71 q^{48} + 70 q^{49} + 19 q^{50} + 45 q^{51} + 68 q^{52} + 182 q^{53} - 29 q^{54} - 30 q^{55} + 96 q^{56} + 74 q^{57} + 47 q^{58} + 19 q^{59} - 35 q^{60} + 16 q^{61} + 43 q^{62} + 73 q^{63} + 110 q^{64} - 30 q^{65} + 8 q^{66} + 40 q^{67} + 129 q^{68} + 2 q^{69} - 39 q^{70} + 48 q^{71} + 151 q^{72} + 30 q^{73} + 117 q^{74} + 10 q^{75} - 98 q^{76} + 134 q^{77} + 54 q^{78} + 23 q^{79} - 121 q^{80} + 111 q^{81} + 4 q^{82} + 92 q^{83} + 48 q^{84} - 63 q^{85} + 42 q^{86} + 69 q^{87} + 121 q^{88} + 12 q^{89} - 53 q^{90} - 30 q^{91} + 175 q^{92} + 82 q^{93} - 23 q^{94} + 35 q^{95} + 6 q^{96} + 67 q^{97} + 122 q^{98} + 73 q^{99}+O(q^{100}) \) 127 * q + 19 * q^2 + 10 * q^3 + 125 * q^4 - 127 * q^5 + 13 * q^7 + 54 * q^8 + 123 * q^9 - 19 * q^10 + 30 * q^11 + 35 * q^12 + 30 * q^13 + 39 * q^14 - 10 * q^15 + 121 * q^16 + 63 * q^17 + 53 * q^18 - 35 * q^19 - 125 * q^20 + 33 * q^21 + 49 * q^22 + 61 * q^23 - 5 * q^24 + 127 * q^25 + 10 * q^26 + 40 * q^27 + 32 * q^28 + 134 * q^29 - 25 * q^31 + 122 * q^32 + 48 * q^33 - 21 * q^34 - 13 * q^35 + 133 * q^36 + 60 * q^37 + 33 * q^38 + 26 * q^39 - 54 * q^40 + 9 * q^41 + 45 * q^42 + 48 * q^43 + 85 * q^44 - 123 * q^45 - 11 * q^46 + 57 * q^47 + 71 * q^48 + 70 * q^49 + 19 * q^50 + 45 * q^51 + 68 * q^52 + 182 * q^53 - 29 * q^54 - 30 * q^55 + 96 * q^56 + 74 * q^57 + 47 * q^58 + 19 * q^59 - 35 * q^60 + 16 * q^61 + 43 * q^62 + 73 * q^63 + 110 * q^64 - 30 * q^65 + 8 * q^66 + 40 * q^67 + 129 * q^68 + 2 * q^69 - 39 * q^70 + 48 * q^71 + 151 * q^72 + 30 * q^73 + 117 * q^74 + 10 * q^75 - 98 * q^76 + 134 * q^77 + 54 * q^78 + 23 * q^79 - 121 * q^80 + 111 * q^81 + 4 * q^82 + 92 * q^83 + 48 * q^84 - 63 * q^85 + 42 * q^86 + 69 * q^87 + 121 * q^88 + 12 * q^89 - 53 * q^90 - 30 * q^91 + 175 * q^92 + 82 * q^93 - 23 * q^94 + 35 * q^95 + 6 * q^96 + 67 * q^97 + 122 * q^98 + 73 * q^99

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