LMFDB - Embedded newform 8027.2.a.f.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, 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("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.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:	$64.0959177025$
Analytic rank:	$0$
Dimension:	$176$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.77677 q^{2} -3.10732 q^{3} +5.71046 q^{4} -0.966106 q^{5} +8.62833 q^{6} +4.66578 q^{7} -10.3031 q^{8} +6.65546 q^{9} +O(q^{10})$	\(q-2.77677 q^{2} -3.10732 q^{3} +5.71046 q^{4} -0.966106 q^{5} +8.62833 q^{6} +4.66578 q^{7} -10.3031 q^{8} +6.65546 q^{9} +2.68266 q^{10} +0.00376926 q^{11} -17.7442 q^{12} +6.25341 q^{13} -12.9558 q^{14} +3.00200 q^{15} +17.1884 q^{16} +4.19620 q^{17} -18.4807 q^{18} +2.54249 q^{19} -5.51691 q^{20} -14.4981 q^{21} -0.0104664 q^{22} +1.00000 q^{23} +32.0151 q^{24} -4.06664 q^{25} -17.3643 q^{26} -11.3587 q^{27} +26.6438 q^{28} +2.76292 q^{29} -8.33588 q^{30} -1.73444 q^{31} -27.1221 q^{32} -0.0117123 q^{33} -11.6519 q^{34} -4.50764 q^{35} +38.0057 q^{36} +9.51286 q^{37} -7.05992 q^{38} -19.4314 q^{39} +9.95389 q^{40} -2.36385 q^{41} +40.2579 q^{42} -5.09898 q^{43} +0.0215242 q^{44} -6.42988 q^{45} -2.77677 q^{46} -7.55988 q^{47} -53.4100 q^{48} +14.7695 q^{49} +11.2921 q^{50} -13.0390 q^{51} +35.7099 q^{52} +11.8266 q^{53} +31.5405 q^{54} -0.00364151 q^{55} -48.0720 q^{56} -7.90034 q^{57} -7.67200 q^{58} +9.51316 q^{59} +17.1428 q^{60} -11.2164 q^{61} +4.81615 q^{62} +31.0529 q^{63} +40.9351 q^{64} -6.04146 q^{65} +0.0325224 q^{66} +3.65836 q^{67} +23.9622 q^{68} -3.10732 q^{69} +12.5167 q^{70} +2.25856 q^{71} -68.5718 q^{72} +1.57815 q^{73} -26.4150 q^{74} +12.6364 q^{75} +14.5188 q^{76} +0.0175866 q^{77} +53.9565 q^{78} +0.604109 q^{79} -16.6058 q^{80} +15.3288 q^{81} +6.56388 q^{82} -15.9342 q^{83} -82.7908 q^{84} -4.05398 q^{85} +14.1587 q^{86} -8.58529 q^{87} -0.0388351 q^{88} -3.32964 q^{89} +17.8543 q^{90} +29.1771 q^{91} +5.71046 q^{92} +5.38948 q^{93} +20.9921 q^{94} -2.45632 q^{95} +84.2772 q^{96} +10.5025 q^{97} -41.0116 q^{98} +0.0250862 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9}+O(q^{10}) $ 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9	\( 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9} + 18 q^{10} + 11 q^{11} + 46 q^{12} + 87 q^{13} - 6 q^{14} + 29 q^{15} + 257 q^{16} + 14 q^{17} + 72 q^{18} + 34 q^{19} + 45 q^{20} + 23 q^{21} + 62 q^{22} + 176 q^{23} + 33 q^{24} + 272 q^{25} + 31 q^{26} + 82 q^{27} + 80 q^{28} + 75 q^{29} - 30 q^{30} + 73 q^{31} + 71 q^{32} + 30 q^{33} + 23 q^{34} + 44 q^{35} + 264 q^{36} + 236 q^{37} - 21 q^{38} + 17 q^{39} + 43 q^{40} + 51 q^{41} + 38 q^{42} + 51 q^{43} + 12 q^{44} + 127 q^{45} + 19 q^{46} + 45 q^{47} + 61 q^{48} + 268 q^{49} + 55 q^{50} - 3 q^{51} + 166 q^{52} + 63 q^{53} - 32 q^{54} + 11 q^{55} - 9 q^{56} + 72 q^{57} + 98 q^{58} + 95 q^{59} - 7 q^{60} + 73 q^{61} + 12 q^{62} + 19 q^{63} + 365 q^{64} + 19 q^{65} - 28 q^{66} + 138 q^{67} + 16 q^{68} + 22 q^{69} + 100 q^{70} + 85 q^{71} + 129 q^{72} + 118 q^{73} - 21 q^{74} - 12 q^{75} + 52 q^{76} + 75 q^{77} + 97 q^{78} + 74 q^{79} + 8 q^{80} + 280 q^{81} + 67 q^{82} + 10 q^{83} - 51 q^{84} + 169 q^{85} - 39 q^{86} - 6 q^{87} + 159 q^{88} + 38 q^{89} + 22 q^{90} + 90 q^{91} + 203 q^{92} + 230 q^{93} + 63 q^{94} + 30 q^{95} + 107 q^{96} + 161 q^{97} + 58 q^{98} + 7 q^{99}+O(q^{100}) \) 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9 + 18 * q^10 + 11 * q^11 + 46 * q^12 + 87 * q^13 - 6 * q^14 + 29 * q^15 + 257 * q^16 + 14 * q^17 + 72 * q^18 + 34 * q^19 + 45 * q^20 + 23 * q^21 + 62 * q^22 + 176 * q^23 + 33 * q^24 + 272 * q^25 + 31 * q^26 + 82 * q^27 + 80 * q^28 + 75 * q^29 - 30 * q^30 + 73 * q^31 + 71 * q^32 + 30 * q^33 + 23 * q^34 + 44 * q^35 + 264 * q^36 + 236 * q^37 - 21 * q^38 + 17 * q^39 + 43 * q^40 + 51 * q^41 + 38 * q^42 + 51 * q^43 + 12 * q^44 + 127 * q^45 + 19 * q^46 + 45 * q^47 + 61 * q^48 + 268 * q^49 + 55 * q^50 - 3 * q^51 + 166 * q^52 + 63 * q^53 - 32 * q^54 + 11 * q^55 - 9 * q^56 + 72 * q^57 + 98 * q^58 + 95 * q^59 - 7 * q^60 + 73 * q^61 + 12 * q^62 + 19 * q^63 + 365 * q^64 + 19 * q^65 - 28 * q^66 + 138 * q^67 + 16 * q^68 + 22 * q^69 + 100 * q^70 + 85 * q^71 + 129 * q^72 + 118 * q^73 - 21 * q^74 - 12 * q^75 + 52 * q^76 + 75 * q^77 + 97 * q^78 + 74 * q^79 + 8 * q^80 + 280 * q^81 + 67 * q^82 + 10 * q^83 - 51 * q^84 + 169 * q^85 - 39 * q^86 - 6 * q^87 + 159 * q^88 + 38 * q^89 + 22 * q^90 + 90 * q^91 + 203 * q^92 + 230 * q^93 + 63 * q^94 + 30 * q^95 + 107 * q^96 + 161 * q^97 + 58 * q^98 + 7 * 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 $

$2$	−2.77677	−1.96347	−0.981737	−	0.190244i	$-0.939072\pi$
$2$	−2.77677	−1.96347	−0.981737	+	0.190244i	$0.939072\pi$
$3$	−3.10732	−1.79401	−0.897007	−	0.442016i	$-0.854263\pi$
$3$	−3.10732	−1.79401	−0.897007	+	0.442016i	$0.854263\pi$
$4$	5.71046	2.85523
$5$	−0.966106	−0.432056	−0.216028	−	0.976387i	$-0.569310\pi$
$5$	−0.966106	−0.432056	−0.216028	+	0.976387i	$0.569310\pi$
$6$	8.62833	3.52250
$7$	4.66578	1.76350	0.881750	−	0.471717i	$-0.156366\pi$
$7$	4.66578	1.76350	0.881750	+	0.471717i	$0.156366\pi$
$8$	−10.3031	−3.64269
$9$	6.65546	2.21849
$10$	2.68266	0.848330
$11$	0.00376926	0.00113648	0.000568238	−	1.00000i	$-0.499819\pi$
$11$	0.00376926	0.00113648	0.000568238		1.00000i	$0.499819\pi$
$12$	−17.7442	−5.12232
$13$	6.25341	1.73438	0.867192	−	0.497974i	$-0.165922\pi$
$13$	6.25341	1.73438	0.867192	+	0.497974i	$0.165922\pi$
$14$	−12.9558	−3.46259
$15$	3.00200	0.775114
$16$	17.1884	4.29711
$17$	4.19620	1.01773	0.508864	−	0.860847i	$-0.330066\pi$
$17$	4.19620	1.01773	0.508864	+	0.860847i	$0.330066\pi$
$18$	−18.4807	−4.35594
$19$	2.54249	0.583288	0.291644	−	0.956527i	$-0.405798\pi$
$19$	2.54249	0.583288	0.291644	+	0.956527i	$0.405798\pi$
$20$	−5.51691	−1.23362
$21$	−14.4981	−3.16374
$22$	−0.0104664	−0.00223144
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	32.0151	6.53505
$25$	−4.06664	−0.813328
$26$	−17.3643	−3.40542
$27$	−11.3587	−2.18598
$28$	26.6438	5.03520
$29$	2.76292	0.513061	0.256531	−	0.966536i	$-0.417421\pi$
$29$	2.76292	0.513061	0.256531	+	0.966536i	$0.417421\pi$
$30$	−8.33588	−1.52192
$31$	−1.73444	−0.311515	−0.155758	−	0.987795i	$-0.549782\pi$
$31$	−1.73444	−0.311515	−0.155758	+	0.987795i	$0.549782\pi$
$32$	−27.1221	−4.79456
$33$	−0.0117123	−0.00203885
$34$	−11.6519	−1.99828
$35$	−4.50764	−0.761930
$36$	38.0057	6.33429
$37$	9.51286	1.56390	0.781952	−	0.623338i	$-0.214224\pi$
$37$	9.51286	1.56390	0.781952	+	0.623338i	$0.214224\pi$
$38$	−7.05992	−1.14527
$39$	−19.4314	−3.11151
$40$	9.95389	1.57385
$41$	−2.36385	−0.369172	−0.184586	−	0.982816i	$-0.559094\pi$
$41$	−2.36385	−0.369172	−0.184586	+	0.982816i	$0.559094\pi$
$42$	40.2579	6.21193
$43$	−5.09898	−0.777588	−0.388794	−	0.921325i	$-0.627108\pi$
$43$	−5.09898	−0.777588	−0.388794	+	0.921325i	$0.627108\pi$
$44$	0.0215242	0.00324490
$45$	−6.42988	−0.958510
$46$	−2.77677	−0.409413
$47$	−7.55988	−1.10272	−0.551361	−	0.834267i	$-0.685891\pi$
$47$	−7.55988	−1.10272	−0.551361	+	0.834267i	$0.685891\pi$
$48$	−53.4100	−7.70907
$49$	14.7695	2.10993
$50$	11.2921	1.59695
$51$	−13.0390	−1.82582
$52$	35.7099	4.95207
$53$	11.8266	1.62451	0.812254	−	0.583304i	$-0.198240\pi$
$53$	11.8266	1.62451	0.812254	+	0.583304i	$0.198240\pi$
$54$	31.5405	4.29212
$55$	−0.00364151	−0.000491021 0
$56$	−48.0720	−6.42389
$57$	−7.90034	−1.04643
$58$	−7.67200	−1.00738
$59$	9.51316	1.23851	0.619254	−	0.785191i	$-0.287435\pi$
$59$	9.51316	1.23851	0.619254	+	0.785191i	$0.287435\pi$
$60$	17.1428	2.21313
$61$	−11.2164	−1.43611	−0.718053	−	0.695988i	$-0.754967\pi$
$61$	−11.2164	−1.43611	−0.718053	+	0.695988i	$0.754967\pi$
$62$	4.81615	0.611652
$63$	31.0529	3.91230
$64$	40.9351	5.11689
$65$	−6.04146	−0.749351
$66$	0.0325224	0.00400323
$67$	3.65836	0.446940	0.223470	−	0.974711i	$-0.428262\pi$
$67$	3.65836	0.446940	0.223470	+	0.974711i	$0.428262\pi$
$68$	23.9622	2.90585
$69$	−3.10732	−0.374078
$70$	12.5167	1.49603
$71$	2.25856	0.268042	0.134021	−	0.990979i	$-0.457211\pi$
$71$	2.25856	0.268042	0.134021	+	0.990979i	$0.457211\pi$
$72$	−68.5718	−8.08127
$73$	1.57815	0.184709	0.0923545	−	0.995726i	$-0.470561\pi$
$73$	1.57815	0.184709	0.0923545	+	0.995726i	$0.470561\pi$
$74$	−26.4150	−3.07069
$75$	12.6364	1.45912
$76$	14.5188	1.66542
$77$	0.0175866	0.00200417
$78$	53.9565	6.10937
$79$	0.604109	0.0679676	0.0339838	−	0.999422i	$-0.489181\pi$
$79$	0.604109	0.0679676	0.0339838	+	0.999422i	$0.489181\pi$
$80$	−16.6058	−1.85659
$81$	15.3288	1.70319
$82$	6.56388	0.724859
$83$	−15.9342	−1.74900	−0.874500	−	0.485025i	$-0.838810\pi$
$83$	−15.9342	−1.74900	−0.874500	+	0.485025i	$0.838810\pi$
$84$	−82.7908	−9.03321
$85$	−4.05398	−0.439715
$86$	14.1587	1.52677
$87$	−8.58529	−0.920439
$88$	−0.0388351	−0.00413983
$89$	−3.32964	−0.352941	−0.176471	−	0.984306i	$-0.556468\pi$
$89$	−3.32964	−0.352941	−0.176471	+	0.984306i	$0.556468\pi$
$90$	17.8543	1.88201
$91$	29.1771	3.05859
$92$	5.71046	0.595357
$93$	5.38948	0.558863
$94$	20.9921	2.16516
$95$	−2.45632	−0.252013
$96$	84.2772	8.60151
$97$	10.5025	1.06636	0.533182	−	0.846000i	$-0.320996\pi$
$97$	10.5025	1.06636	0.533182	+	0.846000i	$0.320996\pi$
$98$	−41.0116	−4.14280
$99$	0.0250862	0.00252126
$100$	−23.2224	−2.32224
$101$	7.22212	0.718627	0.359314	−	0.933217i	$-0.383011\pi$
$101$	7.22212	0.718627	0.359314	+	0.933217i	$0.383011\pi$
$102$	36.2062	3.58495
$103$	13.3741	1.31779	0.658895	−	0.752235i	$-0.271024\pi$
$103$	13.3741	1.31779	0.658895	+	0.752235i	$0.271024\pi$
$104$	−64.4295	−6.31783
$105$	14.0067	1.36691
$106$	−32.8398	−3.18968
$107$	−3.71905	−0.359534	−0.179767	−	0.983709i	$-0.557534\pi$
$107$	−3.71905	−0.359534	−0.179767	+	0.983709i	$0.557534\pi$
$108$	−64.8633	−6.24148
$109$	−8.34626	−0.799426	−0.399713	−	0.916640i	$-0.630890\pi$
$109$	−8.34626	−0.799426	−0.399713	+	0.916640i	$0.630890\pi$
$110$	0.0101116	0.000964107 0
$111$	−29.5595	−2.80567
$112$	80.1975	7.57795
$113$	19.5324	1.83746	0.918728	−	0.394891i	$-0.129218\pi$
$113$	19.5324	1.83746	0.918728	+	0.394891i	$0.129218\pi$
$114$	21.9374	2.05463
$115$	−0.966106	−0.0900899
$116$	15.7775	1.46491
$117$	41.6193	3.84771
$118$	−26.4159	−2.43178
$119$	19.5786	1.79476
$120$	−30.9299	−2.82350
$121$	−11.0000	−0.999999
$122$	31.1452	2.81976
$123$	7.34525	0.662299
$124$	−9.90447	−0.889447
$125$	8.75934	0.783459
$126$	−86.2269	−7.68170
$127$	3.50952	0.311419	0.155710	−	0.987803i	$-0.450234\pi$
$127$	3.50952	0.311419	0.155710	+	0.987803i	$0.450234\pi$
$128$	−59.4232	−5.25232
$129$	15.8442	1.39500
$130$	16.7758	1.47133
$131$	−2.74298	−0.239655	−0.119827	−	0.992795i	$-0.538234\pi$
$131$	−2.74298	−0.239655	−0.119827	+	0.992795i	$0.538234\pi$
$132$	−0.0668827	−0.00582139
$133$	11.8627	1.02863
$134$	−10.1584	−0.877554
$135$	10.9737	0.944466
$136$	−43.2339	−3.70727
$137$	7.87604	0.672895	0.336448	−	0.941702i	$-0.390774\pi$
$137$	7.87604	0.672895	0.336448	+	0.941702i	$0.390774\pi$
$138$	8.62833	0.734492
$139$	15.8297	1.34266	0.671330	−	0.741159i	$-0.265723\pi$
$139$	15.8297	1.34266	0.671330	+	0.741159i	$0.265723\pi$
$140$	−25.7407	−2.17549
$141$	23.4910	1.97830
$142$	−6.27150	−0.526292
$143$	0.0235708	0.00197109
$144$	114.397	9.53307
$145$	−2.66927	−0.221671
$146$	−4.38217	−0.362671
$147$	−45.8937	−3.78525
$148$	54.3228	4.46531
$149$	12.7538	1.04483	0.522415	−	0.852691i	$-0.325031\pi$
$149$	12.7538	1.04483	0.522415	+	0.852691i	$0.325031\pi$
$150$	−35.0883	−2.86495
$151$	−18.5514	−1.50969	−0.754844	−	0.655904i	$-0.772287\pi$
$151$	−18.5514	−1.50969	−0.754844	+	0.655904i	$0.772287\pi$
$152$	−26.1955	−2.12474
$153$	27.9276	2.25782
$154$	−0.0488339	−0.00393514
$155$	1.67566	0.134592
$156$	−110.962	−8.88408
$157$	16.1506	1.28896	0.644481	−	0.764620i	$-0.277074\pi$
$157$	16.1506	1.28896	0.644481	+	0.764620i	$0.277074\pi$
$158$	−1.67747	−0.133453
$159$	−36.7491	−2.91439
$160$	26.2029	2.07152
$161$	4.66578	0.367715
$162$	−42.5644	−3.34418
$163$	10.7399	0.841216	0.420608	−	0.907243i	$-0.361817\pi$
$163$	10.7399	0.841216	0.420608	+	0.907243i	$0.361817\pi$
$164$	−13.4987	−1.05407
$165$	0.0113153	0.000880898 0
$166$	44.2455	3.43412
$167$	13.6364	1.05522	0.527609	−	0.849487i	$-0.323089\pi$
$167$	13.6364	1.05522	0.527609	+	0.849487i	$0.323089\pi$
$168$	149.375	11.5246
$169$	26.1052	2.00809
$170$	11.2570	0.863370
$171$	16.9214	1.29402
$172$	−29.1175	−2.22019
$173$	12.8624	0.977912	0.488956	−	0.872308i	$-0.337378\pi$
$173$	12.8624	0.977912	0.488956	+	0.872308i	$0.337378\pi$
$174$	23.8394	1.80726
$175$	−18.9741	−1.43430
$176$	0.0647877	0.00488356
$177$	−29.5605	−2.22190
$178$	9.24566	0.692991
$179$	21.2095	1.58527	0.792637	−	0.609693i	$-0.208707\pi$
$179$	21.2095	1.58527	0.792637	+	0.609693i	$0.208707\pi$
$180$	−36.7176	−2.73677
$181$	−16.4164	−1.22022	−0.610110	−	0.792317i	$-0.708875\pi$
$181$	−16.4164	−1.22022	−0.610110	+	0.792317i	$0.708875\pi$
$182$	−81.0180	−6.00546
$183$	34.8528	2.57640
$184$	−10.3031	−0.759554
$185$	−9.19043	−0.675694
$186$	−14.9653	−1.09731
$187$	0.0158166	0.00115662
$188$	−43.1704	−3.14852
$189$	−52.9972	−3.85498
$190$	6.82063	0.494820
$191$	9.12693	0.660401	0.330201	−	0.943911i	$-0.392884\pi$
$191$	9.12693	0.660401	0.330201	+	0.943911i	$0.392884\pi$
$192$	−127.199	−9.17977
$193$	16.3956	1.18018	0.590091	−	0.807337i	$-0.299092\pi$
$193$	16.3956	1.18018	0.590091	+	0.807337i	$0.299092\pi$
$194$	−29.1630	−2.09378
$195$	18.7728	1.34435
$196$	84.3408	6.02434
$197$	−5.22362	−0.372168	−0.186084	−	0.982534i	$-0.559580\pi$
$197$	−5.22362	−0.372168	−0.186084	+	0.982534i	$0.559580\pi$
$198$	−0.0696586	−0.00495042
$199$	−7.55778	−0.535757	−0.267879	−	0.963453i	$-0.586323\pi$
$199$	−7.55778	−0.535757	−0.267879	+	0.963453i	$0.586323\pi$
$200$	41.8990	2.96270
$201$	−11.3677	−0.801816
$202$	−20.0542	−1.41101
$203$	12.8912	0.904784
$204$	−74.4584	−5.21313
$205$	2.28373	0.159503
$206$	−37.1369	−2.58745
$207$	6.65546	0.462586
$208$	107.486	7.45283
$209$	0.00958332	0.000662892 0
$210$	−38.8934	−2.68390
$211$	−16.3145	−1.12314	−0.561570	−	0.827429i	$-0.689802\pi$
$211$	−16.3145	−1.12314	−0.561570	+	0.827429i	$0.689802\pi$
$212$	67.5353	4.63834
$213$	−7.01807	−0.480870
$214$	10.3270	0.705936
$215$	4.92616	0.335961
$216$	117.030	7.96286
$217$	−8.09253	−0.549357
$218$	23.1756	1.56965
$219$	−4.90384	−0.331370
$220$	−0.0207947	−0.00140198
$221$	26.2406	1.76513
$222$	82.0801	5.50885
$223$	10.5430	0.706009	0.353004	−	0.935622i	$-0.385160\pi$
$223$	10.5430	0.706009	0.353004	+	0.935622i	$0.385160\pi$
$224$	−126.546	−8.45521
$225$	−27.0653	−1.80436
$226$	−54.2371	−3.60780
$227$	−21.8618	−1.45102	−0.725508	−	0.688214i	$-0.758395\pi$
$227$	−21.8618	−1.45102	−0.725508	+	0.688214i	$0.758395\pi$
$228$	−45.1146	−2.98779
$229$	6.79922	0.449305	0.224653	−	0.974439i	$-0.427875\pi$
$229$	6.79922	0.449305	0.224653	+	0.974439i	$0.427875\pi$
$230$	2.68266	0.176889
$231$	−0.0546471	−0.00359552
$232$	−28.4666	−1.86893
$233$	−24.7658	−1.62246	−0.811231	−	0.584726i	$-0.801202\pi$
$233$	−24.7658	−1.62246	−0.811231	+	0.584726i	$0.801202\pi$
$234$	−115.567	−7.55487
$235$	7.30364	0.476437
$236$	54.3245	3.53622
$237$	−1.87716	−0.121935
$238$	−54.3652	−3.52397
$239$	14.5875	0.943584	0.471792	−	0.881710i	$-0.343607\pi$
$239$	14.5875	0.943584	0.471792	+	0.881710i	$0.343607\pi$
$240$	51.5997	3.33075
$241$	−4.10431	−0.264382	−0.132191	−	0.991224i	$-0.542201\pi$
$241$	−4.10431	−0.264382	−0.132191	+	0.991224i	$0.542201\pi$
$242$	30.5444	1.96347
$243$	−13.5553	−0.869574
$244$	−64.0505	−4.10041
$245$	−14.2689	−0.911609
$246$	−20.3961	−1.30041
$247$	15.8992	1.01164
$248$	17.8701	1.13475
$249$	49.5126	3.13773
$250$	−24.3227	−1.53830
$251$	−19.9574	−1.25970	−0.629850	−	0.776716i	$-0.716884\pi$
$251$	−19.9574	−1.25970	−0.629850	+	0.776716i	$0.716884\pi$
$252$	177.326	11.1705
$253$	0.00376926	0.000236972 0
$254$	−9.74513	−0.611464
$255$	12.5970	0.788856
$256$	83.1344	5.19590
$257$	−26.6907	−1.66492	−0.832460	−	0.554086i	$-0.813068\pi$
$257$	−26.6907	−1.66492	−0.832460	+	0.554086i	$0.813068\pi$
$258$	−43.9957	−2.73905
$259$	44.3849	2.75795
$260$	−34.4995	−2.13957
$261$	18.3885	1.13822
$262$	7.61662	0.470556
$263$	−15.6514	−0.965105	−0.482553	−	0.875867i	$-0.660290\pi$
$263$	−15.6514	−0.965105	−0.482553	+	0.875867i	$0.660290\pi$
$264$	0.120673	0.00742692
$265$	−11.4258	−0.701878
$266$	−32.9400	−2.01968
$267$	10.3463	0.633182
$268$	20.8909	1.27612
$269$	5.45580	0.332646	0.166323	−	0.986071i	$-0.446811\pi$
$269$	5.45580	0.332646	0.166323	+	0.986071i	$0.446811\pi$
$270$	−30.4715	−1.85443
$271$	−11.3918	−0.692006	−0.346003	−	0.938233i	$-0.612461\pi$
$271$	−11.3918	−0.692006	−0.346003	+	0.938233i	$0.612461\pi$
$272$	72.1261	4.37329
$273$	−90.6626	−5.48715
$274$	−21.8700	−1.32121
$275$	−0.0153282	−0.000924327 0
$276$	−17.7442	−1.06808
$277$	−15.3705	−0.923524	−0.461762	−	0.887004i	$-0.652783\pi$
$277$	−15.3705	−0.923524	−0.461762	+	0.887004i	$0.652783\pi$
$278$	−43.9555	−2.63628
$279$	−11.5435	−0.691092
$280$	46.4427	2.77548
$281$	−24.2522	−1.44677	−0.723383	−	0.690447i	$-0.757414\pi$
$281$	−24.2522	−1.44677	−0.723383	+	0.690447i	$0.757414\pi$
$282$	−65.2291	−3.88434
$283$	−15.0284	−0.893345	−0.446673	−	0.894697i	$-0.647391\pi$
$283$	−15.0284	−0.893345	−0.446673	+	0.894697i	$0.647391\pi$
$284$	12.8974	0.765320
$285$	7.63257	0.452114
$286$	−0.0654506	−0.00387017
$287$	−11.0292	−0.651034
$288$	−180.510	−10.6367
$289$	0.608105	0.0357709
$290$	7.41197	0.435246
$291$	−32.6346	−1.91307
$292$	9.01199	0.527387
$293$	−17.3221	−1.01197	−0.505983	−	0.862543i	$-0.668870\pi$
$293$	−17.3221	−1.01197	−0.505983	+	0.862543i	$0.668870\pi$
$294$	127.436	7.43224
$295$	−9.19072	−0.535104
$296$	−98.0119	−5.69683
$297$	−0.0428139	−0.00248431
$298$	−35.4143	−2.05150
$299$	6.25341	0.361644
$300$	72.1594	4.16613
$301$	−23.7908	−1.37128
$302$	51.5129	2.96423
$303$	−22.4415	−1.28923
$304$	43.7014	2.50645
$305$	10.8362	0.620478
$306$	−77.5487	−4.43316
$307$	28.5097	1.62713	0.813567	−	0.581471i	$-0.197523\pi$
$307$	28.5097	1.62713	0.813567	+	0.581471i	$0.197523\pi$
$308$	0.100427	0.00572238
$309$	−41.5577	−2.36413
$310$	−4.65291	−0.264268
$311$	−17.0880	−0.968972	−0.484486	−	0.874799i	$-0.660993\pi$
$311$	−17.0880	−0.968972	−0.484486	+	0.874799i	$0.660993\pi$
$312$	200.203	11.3343
$313$	−3.60663	−0.203859	−0.101929	−	0.994792i	$-0.532502\pi$
$313$	−3.60663	−0.203859	−0.101929	+	0.994792i	$0.532502\pi$
$314$	−44.8467	−2.53084
$315$	−30.0004	−1.69033
$316$	3.44974	0.194063
$317$	24.7512	1.39017	0.695084	−	0.718929i	$-0.255367\pi$
$317$	24.7512	1.39017	0.695084	+	0.718929i	$0.255367\pi$
$318$	102.044	5.72233
$319$	0.0104142	0.000583082 0
$320$	−39.5477	−2.21078
$321$	11.5563	0.645009
$322$	−12.9558	−0.721999
$323$	10.6688	0.593628
$324$	87.5342	4.86301
$325$	−25.4304	−1.41062
$326$	−29.8223	−1.65170
$327$	25.9345	1.43418
$328$	24.3550	1.34478
$329$	−35.2727	−1.94465
$330$	−0.0314201	−0.00172962
$331$	−12.4592	−0.684821	−0.342410	−	0.939550i	$-0.611243\pi$
$331$	−12.4592	−0.684821	−0.342410	+	0.939550i	$0.611243\pi$
$332$	−90.9913	−4.99380
$333$	63.3125	3.46950
$334$	−37.8652	−2.07189
$335$	−3.53436	−0.193103
$336$	−249.199	−13.5949
$337$	−3.12830	−0.170409	−0.0852046	−	0.996363i	$-0.527154\pi$
$337$	−3.12830	−0.170409	−0.0852046	+	0.996363i	$0.527154\pi$
$338$	−72.4881	−3.94283
$339$	−60.6936	−3.29642
$340$	−23.1501	−1.25549
$341$	−0.00653757	−0.000354029 0
$342$	−46.9870	−2.54077
$343$	36.2509	1.95737
$344$	52.5353	2.83252
$345$	3.00200	0.161622
$346$	−35.7160	−1.92011
$347$	35.7568	1.91953	0.959763	−	0.280812i	$-0.0906038\pi$
$347$	35.7568	1.91953	0.959763	+	0.280812i	$0.0906038\pi$
$348$	−49.0259	−2.62807
$349$	−1.00000	−0.0535288
$349$	−1.00000	−0.0535288
$350$	52.6866	2.81622
$351$	−71.0306	−3.79133
$352$	−0.102230	−0.00544890
$353$	13.8709	0.738272	0.369136	−	0.929375i	$-0.379654\pi$
$353$	13.8709	0.738272	0.369136	+	0.929375i	$0.379654\pi$
$354$	82.0826	4.36264
$355$	−2.18201	−0.115809
$356$	−19.0138	−1.00773
$357$	−60.8369	−3.21983
$358$	−58.8940	−3.11265
$359$	−3.68549	−0.194513	−0.0972563	−	0.995259i	$-0.531007\pi$
$359$	−3.68549	−0.194513	−0.0972563	+	0.995259i	$0.531007\pi$
$360$	66.2477	3.49156
$361$	−12.5357	−0.659776
$362$	45.5845	2.39587
$363$	34.1805	1.79401
$364$	166.614	8.73297
$365$	−1.52466	−0.0798046
$366$	−96.7784	−5.05869
$367$	−10.0369	−0.523920	−0.261960	−	0.965079i	$-0.584369\pi$
$367$	−10.0369	−0.523920	−0.261960	+	0.965079i	$0.584369\pi$
$368$	17.1884	0.896009
$369$	−15.7325	−0.819002
$370$	25.5197	1.32671
$371$	55.1803	2.86482
$372$	30.7764	1.59568
$373$	12.2772	0.635692	0.317846	−	0.948142i	$-0.397041\pi$
$373$	12.2772	0.635692	0.317846	+	0.948142i	$0.397041\pi$
$374$	−0.0439190	−0.00227100
$375$	−27.2181	−1.40554
$376$	77.8901	4.01688
$377$	17.2777	0.889846
$378$	147.161	7.56915
$379$	19.6035	1.00696	0.503481	−	0.864006i	$-0.332052\pi$
$379$	19.6035	1.00696	0.503481	+	0.864006i	$0.332052\pi$
$380$	−14.0267	−0.719554
$381$	−10.9052	−0.558691
$382$	−25.3434	−1.29668
$383$	−2.26773	−0.115876	−0.0579378	−	0.998320i	$-0.518453\pi$
$383$	−2.26773	−0.115876	−0.0579378	+	0.998320i	$0.518453\pi$
$384$	184.647	9.42273
$385$	−0.0169905	−0.000865915 0
$386$	−45.5269	−2.31726
$387$	−33.9361	−1.72507
$388$	59.9739	3.04471
$389$	9.45152	0.479211	0.239606	−	0.970870i	$-0.422982\pi$
$389$	9.45152	0.479211	0.239606	+	0.970870i	$0.422982\pi$
$390$	−52.1277	−2.63959
$391$	4.19620	0.212211
$392$	−152.172	−7.68584
$393$	8.52331	0.429944
$394$	14.5048	0.730741
$395$	−0.583634	−0.0293658
$396$	0.143254	0.00719876
$397$	29.5184	1.48149	0.740743	−	0.671789i	$-0.234474\pi$
$397$	29.5184	1.48149	0.740743	+	0.671789i	$0.234474\pi$
$398$	20.9862	1.05195
$399$	−36.8613	−1.84537
$400$	−69.8991	−3.49496
$401$	28.7987	1.43814	0.719070	−	0.694937i	$-0.244568\pi$
$401$	28.7987	1.43814	0.719070	+	0.694937i	$0.244568\pi$
$402$	31.5655	1.57434
$403$	−10.8462	−0.540287
$404$	41.2416	2.05185
$405$	−14.8092	−0.735875
$406$	−35.7959	−1.77652
$407$	0.0358565	0.00177734
$408$	134.342	6.65090
$409$	−25.3140	−1.25169	−0.625847	−	0.779945i	$-0.715247\pi$
$409$	−25.3140	−1.25169	−0.625847	+	0.779945i	$0.715247\pi$
$410$	−6.34140	−0.313179
$411$	−24.4734	−1.20718
$412$	76.3723	3.76259
$413$	44.3863	2.18411
$414$	−18.4807	−0.908276
$415$	15.3941	0.755666
$416$	−169.606	−8.31561
$417$	−49.1881	−2.40875
$418$	−0.0266107	−0.00130157
$419$	−2.74753	−0.134225	−0.0671127	−	0.997745i	$-0.521379\pi$
$419$	−2.74753	−0.134225	−0.0671127	+	0.997745i	$0.521379\pi$
$420$	79.9847	3.90285
$421$	0.573424	0.0279470	0.0139735	−	0.999902i	$-0.495552\pi$
$421$	0.573424	0.0279470	0.0139735	+	0.999902i	$0.495552\pi$
$422$	45.3018	2.20526
$423$	−50.3144	−2.44637
$424$	−121.851	−5.91759
$425$	−17.0644	−0.827747
$426$	19.4876	0.944176
$427$	−52.3331	−2.53257
$428$	−21.2375	−1.02655
$429$	−0.0732419	−0.00353615
$430$	−13.6788	−0.659651
$431$	−19.3644	−0.932750	−0.466375	−	0.884587i	$-0.654440\pi$
$431$	−19.3644	−0.932750	−0.466375	+	0.884587i	$0.654440\pi$
$432$	−195.238	−9.39339
$433$	−13.3963	−0.643787	−0.321893	−	0.946776i	$-0.604319\pi$
$433$	−13.3963	−0.643787	−0.321893	+	0.946776i	$0.604319\pi$
$434$	22.4711	1.07865
$435$	8.29430	0.397681
$436$	−47.6610	−2.28255
$437$	2.54249	0.121624
$438$	13.6168	0.650637
$439$	−9.02989	−0.430973	−0.215487	−	0.976507i	$-0.569134\pi$
$439$	−9.02989	−0.430973	−0.215487	+	0.976507i	$0.569134\pi$
$440$	0.0375188	0.00178864
$441$	98.2980	4.68086
$442$	−72.8641	−3.46579
$443$	−26.0447	−1.23742	−0.618712	−	0.785618i	$-0.712345\pi$
$443$	−26.0447	−1.23742	−0.618712	+	0.785618i	$0.712345\pi$
$444$	−168.799	−8.01082
$445$	3.21679	0.152490
$446$	−29.2754	−1.38623
$447$	−39.6301	−1.87444
$448$	190.994	9.02363
$449$	−13.9042	−0.656181	−0.328090	−	0.944646i	$-0.606405\pi$
$449$	−13.9042	−0.656181	−0.328090	+	0.944646i	$0.606405\pi$
$450$	75.1543	3.54281
$451$	−0.00890998	−0.000419555 0
$452$	111.539	5.24636
$453$	57.6451	2.70840
$454$	60.7051	2.84903
$455$	−28.1881	−1.32148
$456$	81.3980	3.81181
$457$	−6.47558	−0.302915	−0.151457	−	0.988464i	$-0.548397\pi$
$457$	−6.47558	−0.302915	−0.151457	+	0.988464i	$0.548397\pi$
$458$	−18.8799	−0.882199
$459$	−47.6634	−2.22474
$460$	−5.51691	−0.257227
$461$	−15.1618	−0.706157	−0.353078	−	0.935594i	$-0.614865\pi$
$461$	−15.1618	−0.706157	−0.353078	+	0.935594i	$0.614865\pi$
$462$	0.151743	0.00705970
$463$	19.1112	0.888171	0.444086	−	0.895984i	$-0.353529\pi$
$463$	19.1112	0.888171	0.444086	+	0.895984i	$0.353529\pi$
$464$	47.4903	2.20468
$465$	−5.20681	−0.241460
$466$	68.7690	3.18566
$467$	15.7093	0.726938	0.363469	−	0.931606i	$-0.381592\pi$
$467$	15.7093	0.726938	0.363469	+	0.931606i	$0.381592\pi$
$468$	237.665	10.9861
$469$	17.0691	0.788178
$470$	−20.2805	−0.935472
$471$	−50.1853	−2.31242
$472$	−98.0150	−4.51150
$473$	−0.0192194	−0.000883710 0
$474$	5.21245	0.239416
$475$	−10.3394	−0.474404
$476$	111.803	5.12446
$477$	78.7115	3.60395
$478$	−40.5060	−1.85270
$479$	−38.0748	−1.73968	−0.869840	−	0.493334i	$-0.835778\pi$
$479$	−38.0748	−1.73968	−0.869840	+	0.493334i	$0.835778\pi$
$480$	−81.4208	−3.71633
$481$	59.4878	2.71241
$482$	11.3967	0.519106
$483$	−14.4981	−0.659686
$484$	−62.8150	−2.85523
$485$	−10.1465	−0.460729
$486$	37.6400	1.70739
$487$	10.0164	0.453885	0.226942	−	0.973908i	$-0.427127\pi$
$487$	10.0164	0.453885	0.226942	+	0.973908i	$0.427127\pi$
$488$	115.563	5.23130
$489$	−33.3724	−1.50915
$490$	39.6216	1.78992
$491$	−20.0866	−0.906495	−0.453248	−	0.891385i	$-0.649735\pi$
$491$	−20.0866	−0.906495	−0.453248	+	0.891385i	$0.649735\pi$
$492$	41.9448	1.89102
$493$	11.5938	0.522157
$494$	−44.1486	−1.98634
$495$	−0.0242359	−0.00108932
$496$	−29.8123	−1.33861
$497$	10.5379	0.472691
$498$	−137.485	−6.16085
$499$	−27.1958	−1.21745	−0.608725	−	0.793382i	$-0.708319\pi$
$499$	−27.1958	−1.21745	−0.608725	+	0.793382i	$0.708319\pi$
$500$	50.0198	2.23695
$501$	−42.3728	−1.89308
$502$	55.4172	2.47339
$503$	−12.6464	−0.563875	−0.281938	−	0.959433i	$-0.590977\pi$
$503$	−12.6464	−0.563875	−0.281938	+	0.959433i	$0.590977\pi$
$504$	−319.941	−14.2513
$505$	−6.97733	−0.310487
$506$	−0.0104664	−0.000465287 0
$507$	−81.1172	−3.60254
$508$	20.0410	0.889174
$509$	31.2951	1.38713	0.693566	−	0.720393i	$-0.256039\pi$
$509$	31.2951	1.38713	0.693566	+	0.720393i	$0.256039\pi$
$510$	−34.9790	−1.54890
$511$	7.36332	0.325734
$512$	−111.999	−4.94969
$513$	−28.8794	−1.27506
$514$	74.1139	3.26903
$515$	−12.9208	−0.569359
$516$	90.4776	3.98306
$517$	−0.0284952	−0.00125322
$518$	−123.247	−5.41516
$519$	−39.9677	−1.75439
$520$	62.2457	2.72966
$521$	39.1149	1.71366	0.856828	−	0.515603i	$-0.172432\pi$
$521$	39.1149	1.71366	0.856828	+	0.515603i	$0.172432\pi$
$522$	−51.0607	−2.23486
$523$	−9.51402	−0.416019	−0.208010	−	0.978127i	$-0.566699\pi$
$523$	−9.51402	−0.416019	−0.208010	+	0.978127i	$0.566699\pi$
$524$	−15.6637	−0.684270
$525$	58.9585	2.57316
$526$	43.4603	1.89496
$527$	−7.27807	−0.317038
$528$	−0.201316	−0.00876117
$529$	1.00000	0.0434783
$530$	31.7267	1.37812
$531$	63.3144	2.74761
$532$	67.7415	2.93697
$533$	−14.7821	−0.640286
$534$	−28.7292	−1.24324
$535$	3.59300	0.155339
$536$	−37.6924	−1.62806
$537$	−65.9049	−2.84401
$538$	−15.1495	−0.653142
$539$	0.0556702	0.00239789
$540$	62.6649	2.69667
$541$	−16.1246	−0.693250	−0.346625	−	0.938004i	$-0.612672\pi$
$541$	−16.1246	−0.693250	−0.346625	+	0.938004i	$0.612672\pi$
$542$	31.6326	1.35873
$543$	51.0110	2.18909
$544$	−113.810	−4.87956
$545$	8.06337	0.345397
$546$	251.749	10.7739
$547$	12.5283	0.535673	0.267836	−	0.963464i	$-0.413691\pi$
$547$	12.5283	0.535673	0.267836	+	0.963464i	$0.413691\pi$
$548$	44.9758	1.92127
$549$	−74.6500	−3.18598
$550$	0.0425630	0.00181489
$551$	7.02470	0.299262
$552$	32.0151	1.36265
$553$	2.81864	0.119861
$554$	42.6804	1.81332
$555$	28.5577	1.21220
$556$	90.3950	3.83360
$557$	−5.87314	−0.248853	−0.124427	−	0.992229i	$-0.539709\pi$
$557$	−5.87314	−0.248853	−0.124427	+	0.992229i	$0.539709\pi$
$558$	32.0537	1.35694
$559$	−31.8861	−1.34864
$560$	−77.4793	−3.27410
$561$	−0.0491472	−0.00207500
$562$	67.3428	2.84069
$563$	34.6058	1.45846	0.729231	−	0.684267i	$-0.239878\pi$
$563$	34.6058	1.45846	0.729231	+	0.684267i	$0.239878\pi$
$564$	134.144	5.64849
$565$	−18.8704	−0.793884
$566$	41.7304	1.75406
$567$	71.5206	3.00358
$568$	−23.2701	−0.976393
$569$	−15.4399	−0.647273	−0.323637	−	0.946181i	$-0.604906\pi$
$569$	−15.4399	−0.647273	−0.323637	+	0.946181i	$0.604906\pi$
$570$	−21.1939	−0.887715
$571$	44.4391	1.85972	0.929858	−	0.367918i	$-0.119929\pi$
$571$	44.4391	1.85972	0.929858	+	0.367918i	$0.119929\pi$
$572$	0.134600	0.00562790
$573$	−28.3603	−1.18477
$574$	30.6256	1.27829
$575$	−4.06664	−0.169591
$576$	272.442	11.3517
$577$	−37.5616	−1.56371	−0.781855	−	0.623460i	$-0.785726\pi$
$577$	−37.5616	−1.56371	−0.781855	+	0.623460i	$0.785726\pi$
$578$	−1.68857	−0.0702352
$579$	−50.9465	−2.11726
$580$	−15.2428	−0.632922
$581$	−74.3453	−3.08436
$582$	90.6187	3.75627
$583$	0.0445776	0.00184621
$584$	−16.2599	−0.672838
$585$	−40.2087	−1.66242
$586$	48.0995	1.98697
$587$	6.98871	0.288455	0.144227	−	0.989545i	$-0.453930\pi$
$587$	6.98871	0.288455	0.144227	+	0.989545i	$0.453930\pi$
$588$	−262.074	−10.8078
$589$	−4.40981	−0.181703
$590$	25.5205	1.05066
$591$	16.2315	0.667674
$592$	163.511	6.72027
$593$	41.4073	1.70039	0.850197	−	0.526465i	$-0.176483\pi$
$593$	41.4073	1.70039	0.850197	+	0.526465i	$0.176483\pi$
$594$	0.118884	0.00487789
$595$	−18.9150	−0.775438
$596$	72.8299	2.98323
$597$	23.4845	0.961156
$598$	−17.3643	−0.710079
$599$	2.15507	0.0880539	0.0440270	−	0.999030i	$-0.485981\pi$
$599$	2.15507	0.0880539	0.0440270	+	0.999030i	$0.485981\pi$
$600$	−130.194	−5.31513
$601$	−30.3806	−1.23925	−0.619625	−	0.784898i	$-0.712715\pi$
$601$	−30.3806	−1.23925	−0.619625	+	0.784898i	$0.712715\pi$
$602$	66.0615	2.69247
$603$	24.3481	0.991529
$604$	−105.937	−4.31051
$605$	10.6272	0.432055
$606$	62.3148	2.53137
$607$	23.1999	0.941653	0.470827	−	0.882226i	$-0.343956\pi$
$607$	23.1999	0.941653	0.470827	+	0.882226i	$0.343956\pi$
$608$	−68.9578	−2.79661
$609$	−40.0571	−1.62320
$610$	−30.0896	−1.21829
$611$	−47.2750	−1.91254
$612$	159.480	6.44658
$613$	26.2793	1.06141	0.530706	−	0.847556i	$-0.321927\pi$
$613$	26.2793	1.06141	0.530706	+	0.847556i	$0.321927\pi$
$614$	−79.1649	−3.19484
$615$	−7.09629	−0.286150
$616$	−0.181196	−0.00730060
$617$	8.59311	0.345946	0.172973	−	0.984927i	$-0.444663\pi$
$617$	8.59311	0.345946	0.172973	+	0.984927i	$0.444663\pi$
$618$	115.396	4.64192
$619$	47.5426	1.91090	0.955448	−	0.295159i	$-0.0953725\pi$
$619$	47.5426	1.91090	0.955448	+	0.295159i	$0.0953725\pi$
$620$	9.56877	0.384291
$621$	−11.3587	−0.455809
$622$	47.4495	1.90255
$623$	−15.5354	−0.622412
$624$	−333.995	−13.3705
$625$	11.8707	0.474830
$626$	10.0148	0.400271
$627$	−0.0297785	−0.00118924
$628$	92.2276	3.68028
$629$	39.9179	1.59163
$630$	83.3043	3.31892
$631$	−36.5823	−1.45632	−0.728160	−	0.685408i	$-0.759624\pi$
$631$	−36.5823	−1.45632	−0.728160	+	0.685408i	$0.759624\pi$
$632$	−6.22419	−0.247585
$633$	50.6946	2.01493
$634$	−68.7285	−2.72956
$635$	−3.39057	−0.134551
$636$	−209.854	−8.32126
$637$	92.3599	3.65943
$638$	−0.0289178	−0.00114487
$639$	15.0317	0.594646
$640$	57.4091	2.26929
$641$	−7.49147	−0.295895	−0.147948	−	0.988995i	$-0.547267\pi$
$641$	−7.49147	−0.295895	−0.147948	+	0.988995i	$0.547267\pi$
$642$	−32.0892	−1.26646
$643$	8.82930	0.348193	0.174097	−	0.984729i	$-0.444299\pi$
$643$	8.82930	0.348193	0.174097	+	0.984729i	$0.444299\pi$
$644$	26.6438	1.04991
$645$	−15.3072	−0.602719
$646$	−29.6248	−1.16557
$647$	47.8933	1.88288	0.941439	−	0.337182i	$-0.109474\pi$
$647$	47.8933	1.88288	0.941439	+	0.337182i	$0.109474\pi$
$648$	−157.934	−6.20422
$649$	0.0358576	0.00140753
$650$	70.6143	2.76972
$651$	25.1461	0.985554
$652$	61.3299	2.40186
$653$	27.8575	1.09015	0.545074	−	0.838388i	$-0.316502\pi$
$653$	27.8575	1.09015	0.545074	+	0.838388i	$0.316502\pi$
$654$	−72.0142	−2.81598
$655$	2.65001	0.103544
$656$	−40.6309	−1.58637
$657$	10.5033	0.409774
$658$	97.9443	3.81827
$659$	14.8348	0.577882	0.288941	−	0.957347i	$-0.406697\pi$
$659$	14.8348	0.577882	0.288941	+	0.957347i	$0.406697\pi$
$660$	0.0646158	0.00251517
$661$	8.31497	0.323415	0.161707	−	0.986839i	$-0.448300\pi$
$661$	8.31497	0.323415	0.161707	+	0.986839i	$0.448300\pi$
$662$	34.5964	1.34463
$663$	−81.5380	−3.16667
$664$	164.171	6.37107
$665$	−11.4606	−0.444425
$666$	−175.804	−6.81228
$667$	2.76292	0.106981
$668$	77.8702	3.01289
$669$	−32.7604	−1.26659
$670$	9.81412	0.379152
$671$	−0.0422774	−0.00163210
$672$	393.219	15.1688
$673$	−13.4063	−0.516774	−0.258387	−	0.966041i	$-0.583191\pi$
$673$	−13.4063	−0.516774	−0.258387	+	0.966041i	$0.583191\pi$
$674$	8.68657	0.334594
$675$	46.1917	1.77792
$676$	149.072	5.73356
$677$	−2.56649	−0.0986382	−0.0493191	−	0.998783i	$-0.515705\pi$
$677$	−2.56649	−0.0986382	−0.0493191	+	0.998783i	$0.515705\pi$
$678$	168.532	6.47244
$679$	49.0022	1.88053
$680$	41.7685	1.60175
$681$	67.9316	2.60314
$682$	0.0181533	0.000695127 0
$683$	−22.5405	−0.862488	−0.431244	−	0.902235i	$-0.641925\pi$
$683$	−22.5405	−0.862488	−0.431244	+	0.902235i	$0.641925\pi$
$684$	96.6292	3.69471
$685$	−7.60909	−0.290728
$686$	−100.661	−3.84324
$687$	−21.1274	−0.806060
$688$	−87.6435	−3.34138
$689$	73.9566	2.81752
$690$	−8.33588	−0.317342
$691$	6.49505	0.247083	0.123542	−	0.992339i	$-0.460575\pi$
$691$	6.49505	0.247083	0.123542	+	0.992339i	$0.460575\pi$
$692$	73.4504	2.79216
$693$	0.117047	0.00444623
$694$	−99.2884	−3.76894
$695$	−15.2932	−0.580104
$696$	88.4551	3.35288
$697$	−9.91920	−0.375716
$698$	2.77677	0.105102
$699$	76.9553	2.91072
$700$	−108.351	−4.09527
$701$	15.9523	0.602511	0.301256	−	0.953543i	$-0.402594\pi$
$701$	15.9523	0.602511	0.301256	+	0.953543i	$0.402594\pi$
$702$	197.236	7.44418
$703$	24.1864	0.912206
$704$	0.154295	0.00581522
$705$	−22.6948	−0.854735
$706$	−38.5162	−1.44958
$707$	33.6968	1.26730
$708$	−168.804	−6.34403
$709$	14.1416	0.531098	0.265549	−	0.964097i	$-0.414447\pi$
$709$	14.1416	0.531098	0.265549	+	0.964097i	$0.414447\pi$
$710$	6.05893	0.227388
$711$	4.02062	0.150785
$712$	34.3056	1.28566
$713$	−1.73444	−0.0649554
$714$	168.930	6.32206
$715$	−0.0227718	−0.000851619 0
$716$	121.116	4.52632
$717$	−45.3279	−1.69280
$718$	10.2338	0.381920
$719$	31.9387	1.19111	0.595557	−	0.803313i	$-0.296931\pi$
$719$	31.9387	1.19111	0.595557	+	0.803313i	$0.296931\pi$
$720$	−110.520	−4.11882
$721$	62.4007	2.32392
$722$	34.8089	1.29545
$723$	12.7534	0.474304
$724$	−93.7450	−3.48401
$725$	−11.2358	−0.417287
$726$	−94.9115	−3.52250
$727$	−22.3862	−0.830258	−0.415129	−	0.909762i	$-0.636264\pi$
$727$	−22.3862	−0.830258	−0.415129	+	0.909762i	$0.636264\pi$
$728$	−300.614	−11.1415
$729$	−3.86550	−0.143167
$730$	4.23364	0.156694
$731$	−21.3964	−0.791373
$732$	199.026	7.35620
$733$	−3.63197	−0.134150	−0.0670750	−	0.997748i	$-0.521367\pi$
$733$	−3.63197	−0.134150	−0.0670750	+	0.997748i	$0.521367\pi$
$734$	27.8701	1.02870
$735$	44.3382	1.63544
$736$	−27.1221	−0.999735
$737$	0.0137893	0.000507936 0
$738$	43.6856	1.60809
$739$	3.00310	0.110471	0.0552355	−	0.998473i	$-0.482409\pi$
$739$	3.00310	0.110471	0.0552355	+	0.998473i	$0.482409\pi$
$740$	−52.4816	−1.92926
$741$	−49.4041	−1.81490
$742$	−153.223	−5.62500
$743$	−18.2384	−0.669101	−0.334550	−	0.942378i	$-0.608584\pi$
$743$	−18.2384	−0.669101	−0.334550	+	0.942378i	$0.608584\pi$
$744$	−55.5283	−2.03577
$745$	−12.3215	−0.451425
$746$	−34.0911	−1.24816
$747$	−106.049	−3.88013
$748$	0.0903200	0.00330242
$749$	−17.3523	−0.634039
$750$	75.5784	2.75973
$751$	−28.7223	−1.04809	−0.524046	−	0.851690i	$-0.675578\pi$
$751$	−28.7223	−1.04809	−0.524046	+	0.851690i	$0.675578\pi$
$752$	−129.942	−4.73851
$753$	62.0141	2.25992
$754$	−47.9762	−1.74719
$755$	17.9226	0.652269
$756$	−302.638	−11.0068
$757$	−15.7574	−0.572712	−0.286356	−	0.958123i	$-0.592444\pi$
$757$	−15.7574	−0.572712	−0.286356	+	0.958123i	$0.592444\pi$
$758$	−54.4344	−1.97715
$759$	−0.0117123	−0.000425130 0
$760$	25.3077	0.918006
$761$	−27.0461	−0.980421	−0.490210	−	0.871604i	$-0.663080\pi$
$761$	−27.0461	−0.980421	−0.490210	+	0.871604i	$0.663080\pi$
$762$	30.2813	1.09697
$763$	−38.9418	−1.40979
$764$	52.1190	1.88560
$765$	−26.9811	−0.975503
$766$	6.29697	0.227519
$767$	59.4897	2.14805
$768$	−258.325	−9.32151
$769$	11.8466	0.427199	0.213600	−	0.976921i	$-0.431481\pi$
$769$	11.8466	0.427199	0.213600	+	0.976921i	$0.431481\pi$
$770$	0.0471787	0.00170020
$771$	82.9366	2.98689
$772$	93.6264	3.36969
$773$	30.6942	1.10399	0.551997	−	0.833846i	$-0.313866\pi$
$773$	30.6942	1.10399	0.551997	+	0.833846i	$0.313866\pi$
$774$	94.2327	3.38713
$775$	7.05335	0.253364
$776$	−108.208	−3.88444
$777$	−137.918	−4.94779
$778$	−26.2447	−0.940919
$779$	−6.01007	−0.215333
$780$	107.201	3.83842
$781$	0.00851310	0.000304623 0
$782$	−11.6519	−0.416671
$783$	−31.3832	−1.12154
$784$	253.865	9.06660
$785$	−15.6032	−0.556903
$786$	−23.6673	−0.844184
$787$	−22.4534	−0.800376	−0.400188	−	0.916433i	$-0.631055\pi$
$787$	−22.4534	−0.800376	−0.400188	+	0.916433i	$0.631055\pi$
$788$	−29.8293	−1.06262
$789$	48.6339	1.73141
$790$	1.62062	0.0576590
$791$	91.1340	3.24035
$792$	−0.258465	−0.00918416
$793$	−70.1405	−2.49076
$794$	−81.9658	−2.90886
$795$	35.5035	1.25918
$796$	−43.1584	−1.52971
$797$	−33.1848	−1.17547	−0.587733	−	0.809055i	$-0.699979\pi$
$797$	−33.1848	−1.17547	−0.587733	+	0.809055i	$0.699979\pi$
$798$	102.355	3.62334
$799$	−31.7228	−1.12227
$800$	110.296	3.89955
$801$	−22.1603	−0.782996
$802$	−79.9675	−2.82375
$803$	0.00594848	0.000209917 0
$804$	−64.9148	−2.28937
$805$	−4.50764	−0.158873
$806$	30.1174	1.06084
$807$	−16.9529	−0.596772
$808$	−74.4102	−2.61774
$809$	−34.4832	−1.21236	−0.606182	−	0.795326i	$-0.707300\pi$
$809$	−34.4832	−1.21236	−0.606182	+	0.795326i	$0.707300\pi$
$810$	41.1218	1.44487
$811$	−12.2159	−0.428958	−0.214479	−	0.976729i	$-0.568805\pi$
$811$	−12.2159	−0.428958	−0.214479	+	0.976729i	$0.568805\pi$
$812$	73.6146	2.58337
$813$	35.3982	1.24147
$814$	−0.0995652	−0.00348976
$815$	−10.3759	−0.363452
$816$	−224.119	−7.84574
$817$	−12.9641	−0.453557
$818$	70.2911	2.45767
$819$	194.187	6.78543
$820$	13.0412	0.455417
$821$	−11.2220	−0.391651	−0.195826	−	0.980639i	$-0.562739\pi$
$821$	−11.2220	−0.391651	−0.195826	+	0.980639i	$0.562739\pi$
$822$	67.9570	2.37027
$823$	4.48470	0.156327	0.0781635	−	0.996941i	$-0.475094\pi$
$823$	4.48470	0.156327	0.0781635	+	0.996941i	$0.475094\pi$
$824$	−137.795	−4.80031
$825$	0.0476298	0.00165826
$826$	−123.251	−4.28844
$827$	1.94021	0.0674679	0.0337339	−	0.999431i	$-0.489260\pi$
$827$	1.94021	0.0674679	0.0337339	+	0.999431i	$0.489260\pi$
$828$	38.0057	1.32079
$829$	22.3122	0.774934	0.387467	−	0.921884i	$-0.373350\pi$
$829$	22.3122	0.774934	0.387467	+	0.921884i	$0.373350\pi$
$830$	−42.7458	−1.48373
$831$	47.7611	1.65681
$832$	255.984	8.87465
$833$	61.9759	2.14734
$834$	136.584	4.72952
$835$	−13.1742	−0.455913
$836$	0.0547251	0.00189271
$837$	19.7010	0.680966
$838$	7.62925	0.263548
$839$	−20.7837	−0.717533	−0.358766	−	0.933427i	$-0.616803\pi$
$839$	−20.7837	−0.717533	−0.358766	+	0.933427i	$0.616803\pi$
$840$	−144.312	−4.97925
$841$	−21.3663	−0.736768
$842$	−1.59227	−0.0548731
$843$	75.3594	2.59552
$844$	−93.1635	−3.20682
$845$	−25.2204	−0.867607
$846$	139.712	4.80339
$847$	−51.3235	−1.76350
$848$	203.281	6.98069
$849$	46.6981	1.60267
$850$	47.3840	1.62526
$851$	9.51286	0.326097
$852$	−40.0764	−1.37299
$853$	−16.5772	−0.567592	−0.283796	−	0.958885i	$-0.591594\pi$
$853$	−16.5772	−0.567592	−0.283796	+	0.958885i	$0.591594\pi$
$854$	145.317	4.97264
$855$	−16.3479	−0.559087
$856$	38.3177	1.30967
$857$	−1.99969	−0.0683081	−0.0341540	−	0.999417i	$-0.510874\pi$
$857$	−1.99969	−0.0683081	−0.0341540	+	0.999417i	$0.510874\pi$
$858$	0.203376	0.00694315
$859$	−55.5358	−1.89486	−0.947428	−	0.319969i	$-0.896327\pi$
$859$	−55.5358	−1.89486	−0.947428	+	0.319969i	$0.896327\pi$
$860$	28.1306	0.959247
$861$	34.2713	1.16796
$862$	53.7705	1.83143
$863$	−52.5776	−1.78976	−0.894882	−	0.446304i	$-0.852740\pi$
$863$	−52.5776	−1.78976	−0.894882	+	0.446304i	$0.852740\pi$
$864$	308.072	10.4808
$865$	−12.4265	−0.422513
$866$	37.1986	1.26406
$867$	−1.88958	−0.0641735
$868$	−46.2121	−1.56854
$869$	0.00227705	7.72435e−5 0
$870$	−23.0314	−0.780837
$871$	22.8772	0.775165
$872$	85.9923	2.91207
$873$	69.8988	2.36571
$874$	−7.05992	−0.238805
$875$	40.8692	1.38163
$876$	−28.0032	−0.946139
$877$	21.4147	0.723122	0.361561	−	0.932349i	$-0.382244\pi$
$877$	21.4147	0.723122	0.361561	+	0.932349i	$0.382244\pi$
$878$	25.0739	0.846205
$879$	53.8253	1.81548
$880$	−0.0625918	−0.00210997
$881$	46.1941	1.55632	0.778159	−	0.628068i	$-0.216154\pi$
$881$	46.1941	1.55632	0.778159	+	0.628068i	$0.216154\pi$
$882$	−272.951	−9.19074
$883$	−37.3661	−1.25747	−0.628734	−	0.777620i	$-0.716427\pi$
$883$	−37.3661	−1.25747	−0.628734	+	0.777620i	$0.716427\pi$
$884$	149.846	5.03986
$885$	28.5585	0.959985
$886$	72.3203	2.42965
$887$	−9.32904	−0.313238	−0.156619	−	0.987659i	$-0.550060\pi$
$887$	−9.32904	−0.313238	−0.156619	+	0.987659i	$0.550060\pi$
$888$	304.555	10.2202
$889$	16.3747	0.549188
$890$	−8.93229	−0.299411
$891$	0.0577781	0.00193564
$892$	60.2051	2.01582
$893$	−19.2209	−0.643204
$894$	110.044	3.68041
$895$	−20.4907	−0.684927
$896$	−277.256	−9.26246
$897$	−19.4314	−0.648795
$898$	38.6088	1.28839
$899$	−4.79213	−0.159826
$900$	−154.556	−5.15185
$901$	49.6268	1.65331
$902$	0.0247410	0.000823784 0
$903$	73.9256	2.46009
$904$	−201.244	−6.69329
$905$	15.8600	0.527203
$906$	−160.067	−5.31788
$907$	−34.5079	−1.14582	−0.572908	−	0.819620i	$-0.694185\pi$
$907$	−34.5079	−1.14582	−0.572908	+	0.819620i	$0.694185\pi$
$908$	−124.841	−4.14298
$909$	48.0665	1.59427
$910$	78.2720	2.59469
$911$	7.67345	0.254233	0.127116	−	0.991888i	$-0.459428\pi$
$911$	7.67345	0.254233	0.127116	+	0.991888i	$0.459428\pi$
$912$	−135.794	−4.49660
$913$	−0.0600600	−0.00198770
$914$	17.9812	0.594766
$915$	−33.6715	−1.11315
$916$	38.8267	1.28287
$917$	−12.7981	−0.422632
$918$	132.350	4.36821
$919$	53.5890	1.76774	0.883868	−	0.467736i	$-0.154930\pi$
$919$	53.5890	1.76774	0.883868	+	0.467736i	$0.154930\pi$
$920$	9.95389	0.328170
$921$	−88.5888	−2.91910
$922$	42.1009	1.38652
$923$	14.1237	0.464887
$924$	−0.312060	−0.0102660
$925$	−38.6854	−1.27197
$926$	−53.0673	−1.74390
$927$	89.0109	2.92350
$928$	−74.9363	−2.45990
$929$	17.6799	0.580058	0.290029	−	0.957018i	$-0.406335\pi$
$929$	17.6799	0.580058	0.290029	+	0.957018i	$0.406335\pi$
$930$	14.4581	0.474100
$931$	37.5514	1.23070
$932$	−141.424	−4.63250
$933$	53.0980	1.73835
$934$	−43.6210	−1.42732
$935$	−0.0152805	−0.000499726 0
$936$	−428.808	−14.0160
$937$	−23.6700	−0.773266	−0.386633	−	0.922234i	$-0.626362\pi$
$937$	−23.6700	−0.773266	−0.386633	+	0.922234i	$0.626362\pi$
$938$	−47.3970	−1.54757
$939$	11.2070	0.365725
$940$	41.7072	1.36034
$941$	8.42218	0.274555	0.137278	−	0.990533i	$-0.456165\pi$
$941$	8.42218	0.274555	0.137278	+	0.990533i	$0.456165\pi$
$942$	139.353	4.54037
$943$	−2.36385	−0.0769776
$944$	163.516	5.32200
$945$	51.2009	1.66557
$946$	0.0533679	0.00173514
$947$	−2.56544	−0.0833655	−0.0416827	−	0.999131i	$-0.513272\pi$
$947$	−2.56544	−0.0833655	−0.0416827	+	0.999131i	$0.513272\pi$
$948$	−10.7195	−0.348152
$949$	9.86885	0.320356
$950$	28.7101	0.931480
$951$	−76.9100	−2.49398
$952$	−201.720	−6.53778
$953$	28.2310	0.914490	0.457245	−	0.889341i	$-0.348836\pi$
$953$	28.2310	0.914490	0.457245	+	0.889341i	$0.348836\pi$
$954$	−218.564	−7.07626
$955$	−8.81758	−0.285330
$956$	83.3011	2.69415
$957$	−0.0323602	−0.00104606
$958$	105.725	3.41582
$959$	36.7479	1.18665
$960$	122.887	3.96617
$961$	−27.9917	−0.902958
$962$	−165.184	−5.32575
$963$	−24.7520	−0.797622
$964$	−23.4375	−0.754870
$965$	−15.8399	−0.509904
$966$	40.2579	1.29528
$967$	−46.6689	−1.50077	−0.750385	−	0.661001i	$-0.770132\pi$
$967$	−46.6689	−1.50077	−0.750385	+	0.661001i	$0.770132\pi$
$968$	113.334	3.64269
$969$	−33.1514	−1.06498
$970$	28.1745	0.904629
$971$	21.4465	0.688252	0.344126	−	0.938923i	$-0.388175\pi$
$971$	21.4465	0.688252	0.344126	+	0.938923i	$0.388175\pi$
$972$	−77.4071	−2.48283
$973$	73.8580	2.36778
$974$	−27.8132	−0.891191
$975$	79.0204	2.53068
$976$	−192.791	−6.17110
$977$	36.1272	1.15581	0.577906	−	0.816104i	$-0.303870\pi$
$977$	36.1272	1.15581	0.577906	+	0.816104i	$0.303870\pi$
$978$	92.6676	2.96318
$979$	−0.0125503	−0.000401109 0
$980$	−81.4822	−2.60285
$981$	−55.5482	−1.77352
$982$	55.7759	1.77988
$983$	10.8979	0.347588	0.173794	−	0.984782i	$-0.444397\pi$
$983$	10.8979	0.347588	0.173794	+	0.984782i	$0.444397\pi$
$984$	−75.6788	−2.41255
$985$	5.04657	0.160797
$986$	−32.1933	−1.02524
$987$	109.604	3.48873
$988$	90.7920	2.88848
$989$	−5.09898	−0.162138
$990$	0.0672976	0.00213886
$991$	31.8596	1.01205	0.506026	−	0.862518i	$-0.331114\pi$
$991$	31.8596	1.01205	0.506026	+	0.862518i	$0.331114\pi$
$992$	47.0418	1.49358
$993$	38.7148	1.22858
$994$	−29.2615	−0.928117
$995$	7.30162	0.231477
$996$	282.739	8.95894
$997$	−7.65486	−0.242432	−0.121216	−	0.992626i	$-0.538679\pi$
$997$	−7.65486	−0.242432	−0.121216	+	0.992626i	$0.538679\pi$
$998$	75.5164	2.39043
$999$	−108.054	−3.41867

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.f.1.3	✓	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.f.1.3	✓	176	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:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.77677 q^{2} -3.10732 q^{3} +5.71046 q^{4} -0.966106 q^{5} +8.62833 q^{6} +4.66578 q^{7} -10.3031 q^{8} +6.65546 q^{9} +O(q^{10})\)	\(q-2.77677 q^{2} -3.10732 q^{3} +5.71046 q^{4} -0.966106 q^{5} +8.62833 q^{6} +4.66578 q^{7} -10.3031 q^{8} +6.65546 q^{9} +2.68266 q^{10} +0.00376926 q^{11} -17.7442 q^{12} +6.25341 q^{13} -12.9558 q^{14} +3.00200 q^{15} +17.1884 q^{16} +4.19620 q^{17} -18.4807 q^{18} +2.54249 q^{19} -5.51691 q^{20} -14.4981 q^{21} -0.0104664 q^{22} +1.00000 q^{23} +32.0151 q^{24} -4.06664 q^{25} -17.3643 q^{26} -11.3587 q^{27} +26.6438 q^{28} +2.76292 q^{29} -8.33588 q^{30} -1.73444 q^{31} -27.1221 q^{32} -0.0117123 q^{33} -11.6519 q^{34} -4.50764 q^{35} +38.0057 q^{36} +9.51286 q^{37} -7.05992 q^{38} -19.4314 q^{39} +9.95389 q^{40} -2.36385 q^{41} +40.2579 q^{42} -5.09898 q^{43} +0.0215242 q^{44} -6.42988 q^{45} -2.77677 q^{46} -7.55988 q^{47} -53.4100 q^{48} +14.7695 q^{49} +11.2921 q^{50} -13.0390 q^{51} +35.7099 q^{52} +11.8266 q^{53} +31.5405 q^{54} -0.00364151 q^{55} -48.0720 q^{56} -7.90034 q^{57} -7.67200 q^{58} +9.51316 q^{59} +17.1428 q^{60} -11.2164 q^{61} +4.81615 q^{62} +31.0529 q^{63} +40.9351 q^{64} -6.04146 q^{65} +0.0325224 q^{66} +3.65836 q^{67} +23.9622 q^{68} -3.10732 q^{69} +12.5167 q^{70} +2.25856 q^{71} -68.5718 q^{72} +1.57815 q^{73} -26.4150 q^{74} +12.6364 q^{75} +14.5188 q^{76} +0.0175866 q^{77} +53.9565 q^{78} +0.604109 q^{79} -16.6058 q^{80} +15.3288 q^{81} +6.56388 q^{82} -15.9342 q^{83} -82.7908 q^{84} -4.05398 q^{85} +14.1587 q^{86} -8.58529 q^{87} -0.0388351 q^{88} -3.32964 q^{89} +17.8543 q^{90} +29.1771 q^{91} +5.71046 q^{92} +5.38948 q^{93} +20.9921 q^{94} -2.45632 q^{95} +84.2772 q^{96} +10.5025 q^{97} -41.0116 q^{98} +0.0250862 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9}+O(q^{10}) \) 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9	\( 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9} + 18 q^{10} + 11 q^{11} + 46 q^{12} + 87 q^{13} - 6 q^{14} + 29 q^{15} + 257 q^{16} + 14 q^{17} + 72 q^{18} + 34 q^{19} + 45 q^{20} + 23 q^{21} + 62 q^{22} + 176 q^{23} + 33 q^{24} + 272 q^{25} + 31 q^{26} + 82 q^{27} + 80 q^{28} + 75 q^{29} - 30 q^{30} + 73 q^{31} + 71 q^{32} + 30 q^{33} + 23 q^{34} + 44 q^{35} + 264 q^{36} + 236 q^{37} - 21 q^{38} + 17 q^{39} + 43 q^{40} + 51 q^{41} + 38 q^{42} + 51 q^{43} + 12 q^{44} + 127 q^{45} + 19 q^{46} + 45 q^{47} + 61 q^{48} + 268 q^{49} + 55 q^{50} - 3 q^{51} + 166 q^{52} + 63 q^{53} - 32 q^{54} + 11 q^{55} - 9 q^{56} + 72 q^{57} + 98 q^{58} + 95 q^{59} - 7 q^{60} + 73 q^{61} + 12 q^{62} + 19 q^{63} + 365 q^{64} + 19 q^{65} - 28 q^{66} + 138 q^{67} + 16 q^{68} + 22 q^{69} + 100 q^{70} + 85 q^{71} + 129 q^{72} + 118 q^{73} - 21 q^{74} - 12 q^{75} + 52 q^{76} + 75 q^{77} + 97 q^{78} + 74 q^{79} + 8 q^{80} + 280 q^{81} + 67 q^{82} + 10 q^{83} - 51 q^{84} + 169 q^{85} - 39 q^{86} - 6 q^{87} + 159 q^{88} + 38 q^{89} + 22 q^{90} + 90 q^{91} + 203 q^{92} + 230 q^{93} + 63 q^{94} + 30 q^{95} + 107 q^{96} + 161 q^{97} + 58 q^{98} + 7 q^{99}+O(q^{100}) \) 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9 + 18 * q^10 + 11 * q^11 + 46 * q^12 + 87 * q^13 - 6 * q^14 + 29 * q^15 + 257 * q^16 + 14 * q^17 + 72 * q^18 + 34 * q^19 + 45 * q^20 + 23 * q^21 + 62 * q^22 + 176 * q^23 + 33 * q^24 + 272 * q^25 + 31 * q^26 + 82 * q^27 + 80 * q^28 + 75 * q^29 - 30 * q^30 + 73 * q^31 + 71 * q^32 + 30 * q^33 + 23 * q^34 + 44 * q^35 + 264 * q^36 + 236 * q^37 - 21 * q^38 + 17 * q^39 + 43 * q^40 + 51 * q^41 + 38 * q^42 + 51 * q^43 + 12 * q^44 + 127 * q^45 + 19 * q^46 + 45 * q^47 + 61 * q^48 + 268 * q^49 + 55 * q^50 - 3 * q^51 + 166 * q^52 + 63 * q^53 - 32 * q^54 + 11 * q^55 - 9 * q^56 + 72 * q^57 + 98 * q^58 + 95 * q^59 - 7 * q^60 + 73 * q^61 + 12 * q^62 + 19 * q^63 + 365 * q^64 + 19 * q^65 - 28 * q^66 + 138 * q^67 + 16 * q^68 + 22 * q^69 + 100 * q^70 + 85 * q^71 + 129 * q^72 + 118 * q^73 - 21 * q^74 - 12 * q^75 + 52 * q^76 + 75 * q^77 + 97 * q^78 + 74 * q^79 + 8 * q^80 + 280 * q^81 + 67 * q^82 + 10 * q^83 - 51 * q^84 + 169 * q^85 - 39 * q^86 - 6 * q^87 + 159 * q^88 + 38 * q^89 + 22 * q^90 + 90 * q^91 + 203 * q^92 + 230 * q^93 + 63 * q^94 + 30 * q^95 + 107 * q^96 + 161 * q^97 + 58 * q^98 + 7 * q^99

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