LMFDB - Embedded newform 8007.2.a.i.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$0$
Dimension:	$63$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.21840 q^{2} +1.00000 q^{3} +2.92128 q^{4} -1.40773 q^{5} -2.21840 q^{6} +0.0138217 q^{7} -2.04376 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.21840 q^{2} +1.00000 q^{3} +2.92128 q^{4} -1.40773 q^{5} -2.21840 q^{6} +0.0138217 q^{7} -2.04376 q^{8} +1.00000 q^{9} +3.12290 q^{10} -6.42242 q^{11} +2.92128 q^{12} -5.42147 q^{13} -0.0306620 q^{14} -1.40773 q^{15} -1.30869 q^{16} +1.00000 q^{17} -2.21840 q^{18} -6.35449 q^{19} -4.11237 q^{20} +0.0138217 q^{21} +14.2475 q^{22} +2.20786 q^{23} -2.04376 q^{24} -3.01830 q^{25} +12.0270 q^{26} +1.00000 q^{27} +0.0403771 q^{28} -4.83007 q^{29} +3.12290 q^{30} -2.64215 q^{31} +6.99071 q^{32} -6.42242 q^{33} -2.21840 q^{34} -0.0194572 q^{35} +2.92128 q^{36} +8.05832 q^{37} +14.0968 q^{38} -5.42147 q^{39} +2.87706 q^{40} +8.62125 q^{41} -0.0306620 q^{42} -7.48231 q^{43} -18.7617 q^{44} -1.40773 q^{45} -4.89791 q^{46} -5.33441 q^{47} -1.30869 q^{48} -6.99981 q^{49} +6.69578 q^{50} +1.00000 q^{51} -15.8376 q^{52} -9.77211 q^{53} -2.21840 q^{54} +9.04103 q^{55} -0.0282483 q^{56} -6.35449 q^{57} +10.7150 q^{58} +3.17975 q^{59} -4.11237 q^{60} -11.1816 q^{61} +5.86134 q^{62} +0.0138217 q^{63} -12.8908 q^{64} +7.63196 q^{65} +14.2475 q^{66} -7.61654 q^{67} +2.92128 q^{68} +2.20786 q^{69} +0.0431638 q^{70} +4.93260 q^{71} -2.04376 q^{72} -8.44664 q^{73} -17.8765 q^{74} -3.01830 q^{75} -18.5633 q^{76} -0.0887689 q^{77} +12.0270 q^{78} +12.5753 q^{79} +1.84228 q^{80} +1.00000 q^{81} -19.1254 q^{82} -13.2876 q^{83} +0.0403771 q^{84} -1.40773 q^{85} +16.5987 q^{86} -4.83007 q^{87} +13.1259 q^{88} -5.96342 q^{89} +3.12290 q^{90} -0.0749340 q^{91} +6.44978 q^{92} -2.64215 q^{93} +11.8338 q^{94} +8.94541 q^{95} +6.99071 q^{96} -8.70293 q^{97} +15.5283 q^{98} -6.42242 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9}+O(q^{10}) $ 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9	\( 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9} + 4 q^{10} + 23 q^{11} + 70 q^{12} + 10 q^{13} + 18 q^{14} + 19 q^{15} + 72 q^{16} + 63 q^{17} + 10 q^{18} + 6 q^{19} + 48 q^{20} + 11 q^{21} + 21 q^{22} + 44 q^{23} + 27 q^{24} + 110 q^{25} + 41 q^{26} + 63 q^{27} + 26 q^{28} + 35 q^{29} + 4 q^{30} + q^{31} + 54 q^{32} + 23 q^{33} + 10 q^{34} + 47 q^{35} + 70 q^{36} + 40 q^{37} + 38 q^{38} + 10 q^{39} - 10 q^{40} + 35 q^{41} + 18 q^{42} + 27 q^{43} + 46 q^{44} + 19 q^{45} + 8 q^{46} + 29 q^{47} + 72 q^{48} + 114 q^{49} + 27 q^{50} + 63 q^{51} - q^{52} + 75 q^{53} + 10 q^{54} + 5 q^{55} + 24 q^{56} + 6 q^{57} + 41 q^{58} + 105 q^{59} + 48 q^{60} + 5 q^{61} + 22 q^{62} + 11 q^{63} + 61 q^{64} + 49 q^{65} + 21 q^{66} + 4 q^{67} + 70 q^{68} + 44 q^{69} - 16 q^{70} + 16 q^{71} + 27 q^{72} + 39 q^{73} + 54 q^{74} + 110 q^{75} + 6 q^{76} + 88 q^{77} + 41 q^{78} + 16 q^{79} + 102 q^{80} + 63 q^{81} - 29 q^{82} + 73 q^{83} + 26 q^{84} + 19 q^{85} + 46 q^{86} + 35 q^{87} + 18 q^{88} + 88 q^{89} + 4 q^{90} - 15 q^{91} + 110 q^{92} + q^{93} - 8 q^{94} + 28 q^{95} + 54 q^{96} + 70 q^{97} + 33 q^{98} + 23 q^{99}+O(q^{100}) \) 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9 + 4 * q^10 + 23 * q^11 + 70 * q^12 + 10 * q^13 + 18 * q^14 + 19 * q^15 + 72 * q^16 + 63 * q^17 + 10 * q^18 + 6 * q^19 + 48 * q^20 + 11 * q^21 + 21 * q^22 + 44 * q^23 + 27 * q^24 + 110 * q^25 + 41 * q^26 + 63 * q^27 + 26 * q^28 + 35 * q^29 + 4 * q^30 + q^31 + 54 * q^32 + 23 * q^33 + 10 * q^34 + 47 * q^35 + 70 * q^36 + 40 * q^37 + 38 * q^38 + 10 * q^39 - 10 * q^40 + 35 * q^41 + 18 * q^42 + 27 * q^43 + 46 * q^44 + 19 * q^45 + 8 * q^46 + 29 * q^47 + 72 * q^48 + 114 * q^49 + 27 * q^50 + 63 * q^51 - q^52 + 75 * q^53 + 10 * q^54 + 5 * q^55 + 24 * q^56 + 6 * q^57 + 41 * q^58 + 105 * q^59 + 48 * q^60 + 5 * q^61 + 22 * q^62 + 11 * q^63 + 61 * q^64 + 49 * q^65 + 21 * q^66 + 4 * q^67 + 70 * q^68 + 44 * q^69 - 16 * q^70 + 16 * q^71 + 27 * q^72 + 39 * q^73 + 54 * q^74 + 110 * q^75 + 6 * q^76 + 88 * q^77 + 41 * q^78 + 16 * q^79 + 102 * q^80 + 63 * q^81 - 29 * q^82 + 73 * q^83 + 26 * q^84 + 19 * q^85 + 46 * q^86 + 35 * q^87 + 18 * q^88 + 88 * q^89 + 4 * q^90 - 15 * q^91 + 110 * q^92 + q^93 - 8 * q^94 + 28 * q^95 + 54 * q^96 + 70 * q^97 + 33 * q^98 + 23 * 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 $

$2$	−2.21840	−1.56864	−0.784321	−	0.620355i	$-0.786989\pi$
$2$	−2.21840	−1.56864	−0.784321	+	0.620355i	$0.786989\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.92128	1.46064
$5$	−1.40773	−0.629556	−0.314778	−	0.949165i	$-0.601930\pi$
$5$	−1.40773	−0.629556	−0.314778	+	0.949165i	$0.601930\pi$
$6$	−2.21840	−0.905656
$7$	0.0138217	0.00522412	0.00261206	−	0.999997i	$-0.499169\pi$
$7$	0.0138217	0.00522412	0.00261206	+	0.999997i	$0.499169\pi$
$8$	−2.04376	−0.722579
$9$	1.00000	0.333333
$10$	3.12290	0.987548
$11$	−6.42242	−1.93643	−0.968217	−	0.250113i	$-0.919532\pi$
$11$	−6.42242	−1.93643	−0.968217	+	0.250113i	$0.919532\pi$
$12$	2.92128	0.843301
$13$	−5.42147	−1.50365	−0.751823	−	0.659366i	$-0.770825\pi$
$13$	−5.42147	−1.50365	−0.751823	+	0.659366i	$0.770825\pi$
$14$	−0.0306620	−0.00819477
$15$	−1.40773	−0.363474
$16$	−1.30869	−0.327172
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.21840	−0.522881
$19$	−6.35449	−1.45782	−0.728911	−	0.684609i	$-0.759973\pi$
$19$	−6.35449	−1.45782	−0.728911	+	0.684609i	$0.759973\pi$
$20$	−4.11237	−0.919554
$21$	0.0138217	0.00301614
$22$	14.2475	3.03757
$23$	2.20786	0.460371	0.230185	−	0.973147i	$-0.426067\pi$
$23$	2.20786	0.460371	0.230185	+	0.973147i	$0.426067\pi$
$24$	−2.04376	−0.417181
$25$	−3.01830	−0.603660
$26$	12.0270	2.35868
$27$	1.00000	0.192450
$28$	0.0403771	0.00763055
$29$	−4.83007	−0.896921	−0.448461	−	0.893803i	$-0.648028\pi$
$29$	−4.83007	−0.896921	−0.448461	+	0.893803i	$0.648028\pi$
$30$	3.12290	0.570161
$31$	−2.64215	−0.474545	−0.237272	−	0.971443i	$-0.576253\pi$
$31$	−2.64215	−0.474545	−0.237272	+	0.971443i	$0.576253\pi$
$32$	6.99071	1.23579
$33$	−6.42242	−1.11800
$34$	−2.21840	−0.380452
$35$	−0.0194572	−0.00328887
$36$	2.92128	0.486880
$37$	8.05832	1.32478	0.662390	−	0.749160i	$-0.269542\pi$
$37$	8.05832	1.32478	0.662390	+	0.749160i	$0.269542\pi$
$38$	14.0968	2.28680
$39$	−5.42147	−0.868130
$40$	2.87706	0.454904
$41$	8.62125	1.34641	0.673207	−	0.739454i	$-0.264916\pi$
$41$	8.62125	1.34641	0.673207	+	0.739454i	$0.264916\pi$
$42$	−0.0306620	−0.00473125
$43$	−7.48231	−1.14104	−0.570521	−	0.821283i	$-0.693259\pi$
$43$	−7.48231	−1.14104	−0.570521	+	0.821283i	$0.693259\pi$
$44$	−18.7617	−2.82843
$45$	−1.40773	−0.209852
$46$	−4.89791	−0.722157
$47$	−5.33441	−0.778104	−0.389052	−	0.921216i	$-0.627197\pi$
$47$	−5.33441	−0.778104	−0.389052	+	0.921216i	$0.627197\pi$
$48$	−1.30869	−0.188893
$49$	−6.99981	−0.999973
$50$	6.69578	0.946927
$51$	1.00000	0.140028
$52$	−15.8376	−2.19628
$53$	−9.77211	−1.34230	−0.671151	−	0.741320i	$-0.734200\pi$
$53$	−9.77211	−1.34230	−0.671151	+	0.741320i	$0.734200\pi$
$54$	−2.21840	−0.301885
$55$	9.04103	1.21909
$56$	−0.0282483	−0.00377484
$57$	−6.35449	−0.841673
$58$	10.7150	1.40695
$59$	3.17975	0.413968	0.206984	−	0.978344i	$-0.433635\pi$
$59$	3.17975	0.413968	0.206984	+	0.978344i	$0.433635\pi$
$60$	−4.11237	−0.530905
$61$	−11.1816	−1.43166	−0.715829	−	0.698275i	$-0.753951\pi$
$61$	−11.1816	−1.43166	−0.715829	+	0.698275i	$0.753951\pi$
$62$	5.86134	0.744391
$63$	0.0138217	0.00174137
$64$	−12.8908	−1.61135
$65$	7.63196	0.946628
$66$	14.2475	1.75374
$67$	−7.61654	−0.930508	−0.465254	−	0.885177i	$-0.654037\pi$
$67$	−7.61654	−0.930508	−0.465254	+	0.885177i	$0.654037\pi$
$68$	2.92128	0.354257
$69$	2.20786	0.265795
$70$	0.0431638	0.00515906
$71$	4.93260	0.585392	0.292696	−	0.956206i	$-0.405448\pi$
$71$	4.93260	0.585392	0.292696	+	0.956206i	$0.405448\pi$
$72$	−2.04376	−0.240860
$73$	−8.44664	−0.988605	−0.494302	−	0.869290i	$-0.664576\pi$
$73$	−8.44664	−0.988605	−0.494302	+	0.869290i	$0.664576\pi$
$74$	−17.8765	−2.07810
$75$	−3.01830	−0.348523
$76$	−18.5633	−2.12935
$77$	−0.0887689	−0.0101162
$78$	12.0270	1.36179
$79$	12.5753	1.41484	0.707418	−	0.706795i	$-0.249860\pi$
$79$	12.5753	1.41484	0.707418	+	0.706795i	$0.249860\pi$
$80$	1.84228	0.205973
$81$	1.00000	0.111111
$82$	−19.1254	−2.11204
$83$	−13.2876	−1.45851	−0.729254	−	0.684243i	$-0.760133\pi$
$83$	−13.2876	−1.45851	−0.729254	+	0.684243i	$0.760133\pi$
$84$	0.0403771	0.00440550
$85$	−1.40773	−0.152690
$86$	16.5987	1.78989
$87$	−4.83007	−0.517838
$88$	13.1259	1.39923
$89$	−5.96342	−0.632121	−0.316061	−	0.948739i	$-0.602360\pi$
$89$	−5.96342	−0.632121	−0.316061	+	0.948739i	$0.602360\pi$
$90$	3.12290	0.329183
$91$	−0.0749340	−0.00785522
$92$	6.44978	0.672436
$93$	−2.64215	−0.273978
$94$	11.8338	1.22057
$95$	8.94541	0.917779
$96$	6.99071	0.713486
$97$	−8.70293	−0.883649	−0.441824	−	0.897102i	$-0.645669\pi$
$97$	−8.70293	−0.883649	−0.441824	+	0.897102i	$0.645669\pi$
$98$	15.5283	1.56860
$99$	−6.42242	−0.645478
$100$	−8.81729	−0.881729
$101$	9.58578	0.953821	0.476910	−	0.878952i	$-0.341757\pi$
$101$	9.58578	0.953821	0.476910	+	0.878952i	$0.341757\pi$
$102$	−2.21840	−0.219654
$103$	−14.9858	−1.47659	−0.738296	−	0.674477i	$-0.764369\pi$
$103$	−14.9858	−1.47659	−0.738296	+	0.674477i	$0.764369\pi$
$104$	11.0802	1.08650
$105$	−0.0194572	−0.00189883
$106$	21.6784	2.10559
$107$	10.5674	1.02159	0.510793	−	0.859703i	$-0.329352\pi$
$107$	10.5674	1.02159	0.510793	+	0.859703i	$0.329352\pi$
$108$	2.92128	0.281100
$109$	−6.30923	−0.604315	−0.302157	−	0.953258i	$-0.597707\pi$
$109$	−6.30923	−0.604315	−0.302157	+	0.953258i	$0.597707\pi$
$110$	−20.0566	−1.91232
$111$	8.05832	0.764862
$112$	−0.0180883	−0.00170918
$113$	5.50263	0.517644	0.258822	−	0.965925i	$-0.416666\pi$
$113$	5.50263	0.517644	0.258822	+	0.965925i	$0.416666\pi$
$114$	14.0968	1.32028
$115$	−3.10807	−0.289829
$116$	−14.1100	−1.31008
$117$	−5.42147	−0.501215
$118$	−7.05394	−0.649368
$119$	0.0138217	0.00126703
$120$	2.87706	0.262639
$121$	30.2475	2.74977
$122$	24.8052	2.24576
$123$	8.62125	0.777352
$124$	−7.71847	−0.693139
$125$	11.2876	1.00959
$126$	−0.0306620	−0.00273159
$127$	3.29841	0.292687	0.146343	−	0.989234i	$-0.453250\pi$
$127$	3.29841	0.292687	0.146343	+	0.989234i	$0.453250\pi$
$128$	14.6154	1.29183
$129$	−7.48231	−0.658780
$130$	−16.9307	−1.48492
$131$	−5.06091	−0.442174	−0.221087	−	0.975254i	$-0.570960\pi$
$131$	−5.06091	−0.442174	−0.221087	+	0.975254i	$0.570960\pi$
$132$	−18.7617	−1.63300
$133$	−0.0878300	−0.00761583
$134$	16.8965	1.45963
$135$	−1.40773	−0.121158
$136$	−2.04376	−0.175251
$137$	−1.91526	−0.163632	−0.0818160	−	0.996647i	$-0.526072\pi$
$137$	−1.91526	−0.163632	−0.0818160	+	0.996647i	$0.526072\pi$
$138$	−4.89791	−0.416938
$139$	−0.570656	−0.0484024	−0.0242012	−	0.999707i	$-0.507704\pi$
$139$	−0.570656	−0.0484024	−0.0242012	+	0.999707i	$0.507704\pi$
$140$	−0.0568400	−0.00480386
$141$	−5.33441	−0.449238
$142$	−10.9425	−0.918271
$143$	34.8190	2.91171
$144$	−1.30869	−0.109057
$145$	6.79943	0.564662
$146$	18.7380	1.55077
$147$	−6.99981	−0.577335
$148$	23.5406	1.93502
$149$	0.521602	0.0427313	0.0213656	−	0.999772i	$-0.493199\pi$
$149$	0.521602	0.0427313	0.0213656	+	0.999772i	$0.493199\pi$
$150$	6.69578	0.546708
$151$	4.07730	0.331806	0.165903	−	0.986142i	$-0.446946\pi$
$151$	4.07730	0.331806	0.165903	+	0.986142i	$0.446946\pi$
$152$	12.9871	1.05339
$153$	1.00000	0.0808452
$154$	0.196924	0.0158686
$155$	3.71944	0.298752
$156$	−15.8376	−1.26802
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	−27.8971	−2.21937
$159$	−9.77211	−0.774979
$160$	−9.84102	−0.778001
$161$	0.0305164	0.00240503
$162$	−2.21840	−0.174294
$163$	9.36029	0.733155	0.366577	−	0.930388i	$-0.380530\pi$
$163$	9.36029	0.733155	0.366577	+	0.930388i	$0.380530\pi$
$164$	25.1851	1.96663
$165$	9.04103	0.703843
$166$	29.4773	2.28788
$167$	13.4657	1.04201	0.521003	−	0.853555i	$-0.325558\pi$
$167$	13.4657	1.04201	0.521003	+	0.853555i	$0.325558\pi$
$168$	−0.0282483	−0.00217940
$169$	16.3923	1.26095
$170$	3.12290	0.239515
$171$	−6.35449	−0.485940
$172$	−21.8579	−1.66665
$173$	−3.22099	−0.244887	−0.122444	−	0.992475i	$-0.539073\pi$
$173$	−3.22099	−0.244887	−0.122444	+	0.992475i	$0.539073\pi$
$174$	10.7150	0.812302
$175$	−0.0417181	−0.00315359
$176$	8.40493	0.633546
$177$	3.17975	0.239004
$178$	13.2292	0.991572
$179$	−17.9376	−1.34072	−0.670358	−	0.742038i	$-0.733859\pi$
$179$	−17.9376	−1.34072	−0.670358	+	0.742038i	$0.733859\pi$
$180$	−4.11237	−0.306518
$181$	−2.00710	−0.149186	−0.0745932	−	0.997214i	$-0.523766\pi$
$181$	−2.00710	−0.149186	−0.0745932	+	0.997214i	$0.523766\pi$
$182$	0.166233	0.0123220
$183$	−11.1816	−0.826569
$184$	−4.51234	−0.332654
$185$	−11.3439	−0.834022
$186$	5.86134	0.429774
$187$	−6.42242	−0.469654
$188$	−15.5833	−1.13653
$189$	0.0138217	0.00100538
$190$	−19.8444	−1.43967
$191$	11.4400	0.827767	0.413883	−	0.910330i	$-0.364172\pi$
$191$	11.4400	0.827767	0.413883	+	0.910330i	$0.364172\pi$
$192$	−12.8908	−0.930312
$193$	−0.153205	−0.0110279	−0.00551396	−	0.999985i	$-0.501755\pi$
$193$	−0.153205	−0.0110279	−0.00551396	+	0.999985i	$0.501755\pi$
$194$	19.3065	1.38613
$195$	7.63196	0.546536
$196$	−20.4484	−1.46060
$197$	−5.13556	−0.365894	−0.182947	−	0.983123i	$-0.558564\pi$
$197$	−5.13556	−0.365894	−0.182947	+	0.983123i	$0.558564\pi$
$198$	14.2475	1.01252
$199$	−23.7111	−1.68084	−0.840419	−	0.541938i	$-0.817691\pi$
$199$	−23.7111	−1.68084	−0.840419	+	0.541938i	$0.817691\pi$
$200$	6.16868	0.436192
$201$	−7.61654	−0.537229
$202$	−21.2650	−1.49620
$203$	−0.0667598	−0.00468562
$204$	2.92128	0.204530
$205$	−12.1364	−0.847642
$206$	33.2444	2.31624
$207$	2.20786	0.153457
$208$	7.09500	0.491950
$209$	40.8113	2.82297
$210$	0.0431638	0.00297859
$211$	27.4085	1.88688	0.943440	−	0.331545i	$-0.107570\pi$
$211$	27.4085	1.88688	0.943440	+	0.331545i	$0.107570\pi$
$212$	−28.5471	−1.96062
$213$	4.93260	0.337976
$214$	−23.4426	−1.60250
$215$	10.5331	0.718349
$216$	−2.04376	−0.139060
$217$	−0.0365191	−0.00247908
$218$	13.9964	0.947954
$219$	−8.44664	−0.570771
$220$	26.4114	1.78065
$221$	−5.42147	−0.364687
$222$	−17.8765	−1.19979
$223$	−27.0117	−1.80884	−0.904420	−	0.426643i	$-0.859696\pi$
$223$	−27.0117	−1.80884	−0.904420	+	0.426643i	$0.859696\pi$
$224$	0.0966235	0.00645593
$225$	−3.01830	−0.201220
$226$	−12.2070	−0.811998
$227$	−14.0354	−0.931561	−0.465781	−	0.884900i	$-0.654226\pi$
$227$	−14.0354	−0.931561	−0.465781	+	0.884900i	$0.654226\pi$
$228$	−18.5633	−1.22938
$229$	16.3542	1.08072	0.540358	−	0.841435i	$-0.318289\pi$
$229$	16.3542	1.08072	0.540358	+	0.841435i	$0.318289\pi$
$230$	6.89493	0.454638
$231$	−0.0887689	−0.00584056
$232$	9.87151	0.648096
$233$	8.27508	0.542119	0.271059	−	0.962563i	$-0.412626\pi$
$233$	8.27508	0.542119	0.271059	+	0.962563i	$0.412626\pi$
$234$	12.0270	0.786227
$235$	7.50941	0.489860
$236$	9.28893	0.604658
$237$	12.5753	0.816856
$238$	−0.0306620	−0.00198752
$239$	−1.01315	−0.0655353	−0.0327676	−	0.999463i	$-0.510432\pi$
$239$	−1.01315	−0.0655353	−0.0327676	+	0.999463i	$0.510432\pi$
$240$	1.84228	0.118918
$241$	−4.39105	−0.282852	−0.141426	−	0.989949i	$-0.545169\pi$
$241$	−4.39105	−0.282852	−0.141426	+	0.989949i	$0.545169\pi$
$242$	−67.1010	−4.31341
$243$	1.00000	0.0641500
$244$	−32.6646	−2.09114
$245$	9.85383	0.629538
$246$	−19.1254	−1.21939
$247$	34.4507	2.19205
$248$	5.39993	0.342896
$249$	−13.2876	−0.842070
$250$	−25.0403	−1.58369
$251$	8.15117	0.514497	0.257249	−	0.966345i	$-0.417184\pi$
$251$	8.15117	0.514497	0.257249	+	0.966345i	$0.417184\pi$
$252$	0.0403771	0.00254352
$253$	−14.1798	−0.891477
$254$	−7.31718	−0.459121
$255$	−1.40773	−0.0881554
$256$	−6.64127	−0.415079
$257$	8.54838	0.533233	0.266617	−	0.963803i	$-0.414094\pi$
$257$	8.54838	0.533233	0.266617	+	0.963803i	$0.414094\pi$
$258$	16.5987	1.03339
$259$	0.111380	0.00692080
$260$	22.2951	1.38268
$261$	−4.83007	−0.298974
$262$	11.2271	0.693613
$263$	−2.69736	−0.166327	−0.0831633	−	0.996536i	$-0.526502\pi$
$263$	−2.69736	−0.166327	−0.0831633	+	0.996536i	$0.526502\pi$
$264$	13.1259	0.807843
$265$	13.7565	0.845054
$266$	0.194842	0.0119465
$267$	−5.96342	−0.364955
$268$	−22.2500	−1.35914
$269$	−15.8438	−0.966016	−0.483008	−	0.875616i	$-0.660456\pi$
$269$	−15.8438	−0.966016	−0.483008	+	0.875616i	$0.660456\pi$
$270$	3.12290	0.190054
$271$	−19.9297	−1.21064	−0.605321	−	0.795982i	$-0.706955\pi$
$271$	−19.9297	−1.21064	−0.605321	+	0.795982i	$0.706955\pi$
$272$	−1.30869	−0.0793507
$273$	−0.0749340	−0.00453521
$274$	4.24881	0.256680
$275$	19.3848	1.16895
$276$	6.44978	0.388231
$277$	14.5338	0.873253	0.436626	−	0.899643i	$-0.356173\pi$
$277$	14.5338	0.873253	0.436626	+	0.899643i	$0.356173\pi$
$278$	1.26594	0.0759260
$279$	−2.64215	−0.158182
$280$	0.0397659	0.00237647
$281$	14.1334	0.843130	0.421565	−	0.906798i	$-0.361481\pi$
$281$	14.1334	0.843130	0.421565	+	0.906798i	$0.361481\pi$
$282$	11.8338	0.704695
$283$	−3.06051	−0.181928	−0.0909641	−	0.995854i	$-0.528995\pi$
$283$	−3.06051	−0.181928	−0.0909641	+	0.995854i	$0.528995\pi$
$284$	14.4095	0.855047
$285$	8.94541	0.529880
$286$	−77.2422	−4.56743
$287$	0.119160	0.00703382
$288$	6.99071	0.411931
$289$	1.00000	0.0588235
$290$	−15.0838	−0.885752
$291$	−8.70293	−0.510175
$292$	−24.6750	−1.44400
$293$	−31.1704	−1.82099	−0.910497	−	0.413516i	$-0.864300\pi$
$293$	−31.1704	−1.82099	−0.910497	+	0.413516i	$0.864300\pi$
$294$	15.5283	0.905632
$295$	−4.47622	−0.260616
$296$	−16.4693	−0.957257
$297$	−6.42242	−0.372667
$298$	−1.15712	−0.0670301
$299$	−11.9698	−0.692234
$300$	−8.81729	−0.509067
$301$	−0.103418	−0.00596093
$302$	−9.04508	−0.520486
$303$	9.58578	0.550689
$304$	8.31604	0.476957
$305$	15.7407	0.901309
$306$	−2.21840	−0.126817
$307$	−21.5447	−1.22962	−0.614810	−	0.788676i	$-0.710767\pi$
$307$	−21.5447	−1.22962	−0.614810	+	0.788676i	$0.710767\pi$
$308$	−0.259319	−0.0147761
$309$	−14.9858	−0.852511
$310$	−8.25118	−0.468635
$311$	22.5939	1.28118	0.640591	−	0.767882i	$-0.278689\pi$
$311$	22.5939	1.28118	0.640591	+	0.767882i	$0.278689\pi$
$312$	11.0802	0.627292
$313$	7.90290	0.446698	0.223349	−	0.974739i	$-0.428301\pi$
$313$	7.90290	0.446698	0.223349	+	0.974739i	$0.428301\pi$
$314$	−2.21840	−0.125191
$315$	−0.0194572	−0.00109629
$316$	36.7361	2.06657
$317$	18.9196	1.06263	0.531316	−	0.847173i	$-0.321698\pi$
$317$	18.9196	1.06263	0.531316	+	0.847173i	$0.321698\pi$
$318$	21.6784	1.21566
$319$	31.0207	1.73683
$320$	18.1467	1.01443
$321$	10.5674	0.589813
$322$	−0.0676975	−0.00377263
$323$	−6.35449	−0.353574
$324$	2.92128	0.162293
$325$	16.3636	0.907690
$326$	−20.7648	−1.15006
$327$	−6.30923	−0.348901
$328$	−17.6198	−0.972890
$329$	−0.0737307	−0.00406490
$330$	−20.0566	−1.10408
$331$	0.434987	0.0239090	0.0119545	−	0.999929i	$-0.496195\pi$
$331$	0.434987	0.0239090	0.0119545	+	0.999929i	$0.496195\pi$
$332$	−38.8169	−2.13036
$333$	8.05832	0.441593
$334$	−29.8722	−1.63453
$335$	10.7220	0.585807
$336$	−0.0180883	−0.000986797 0
$337$	−29.5129	−1.60767	−0.803835	−	0.594852i	$-0.797211\pi$
$337$	−29.5129	−1.60767	−0.803835	+	0.594852i	$0.797211\pi$
$338$	−36.3647	−1.97798
$339$	5.50263	0.298862
$340$	−4.11237	−0.223025
$341$	16.9690	0.918924
$342$	14.0968	0.762267
$343$	−0.193501	−0.0104481
$344$	15.2921	0.824492
$345$	−3.10807	−0.167333
$346$	7.14543	0.384141
$347$	16.2682	0.873325	0.436663	−	0.899625i	$-0.356160\pi$
$347$	16.2682	0.873325	0.436663	+	0.899625i	$0.356160\pi$
$348$	−14.1100	−0.756374
$349$	−27.1372	−1.45262	−0.726311	−	0.687366i	$-0.758767\pi$
$349$	−27.1372	−1.45262	−0.726311	+	0.687366i	$0.758767\pi$
$350$	0.0925472	0.00494685
$351$	−5.42147	−0.289377
$352$	−44.8973	−2.39303
$353$	−8.69632	−0.462858	−0.231429	−	0.972852i	$-0.574340\pi$
$353$	−8.69632	−0.462858	−0.231429	+	0.972852i	$0.574340\pi$
$354$	−7.05394	−0.374913
$355$	−6.94377	−0.368537
$356$	−17.4208	−0.923302
$357$	0.0138217	0.000731523 0
$358$	39.7926	2.10310
$359$	−12.2523	−0.646650	−0.323325	−	0.946288i	$-0.604801\pi$
$359$	−12.2523	−0.646650	−0.323325	+	0.946288i	$0.604801\pi$
$360$	2.87706	0.151635
$361$	21.3796	1.12524
$362$	4.45254	0.234020
$363$	30.2475	1.58758
$364$	−0.218903	−0.0114736
$365$	11.8906	0.622382
$366$	24.8052	1.29659
$367$	23.5515	1.22938	0.614690	−	0.788769i	$-0.289281\pi$
$367$	23.5515	1.22938	0.614690	+	0.788769i	$0.289281\pi$
$368$	−2.88940	−0.150620
$369$	8.62125	0.448805
$370$	25.1653	1.30828
$371$	−0.135067	−0.00701235
$372$	−7.71847	−0.400184
$373$	34.8114	1.80247	0.901233	−	0.433335i	$-0.142663\pi$
$373$	34.8114	1.80247	0.901233	+	0.433335i	$0.142663\pi$
$374$	14.2475	0.736719
$375$	11.2876	0.582889
$376$	10.9023	0.562241
$377$	26.1861	1.34865
$378$	−0.0306620	−0.00157708
$379$	14.6813	0.754129	0.377065	−	0.926187i	$-0.376933\pi$
$379$	14.6813	0.754129	0.377065	+	0.926187i	$0.376933\pi$
$380$	26.1320	1.34054
$381$	3.29841	0.168983
$382$	−25.3784	−1.29847
$383$	26.0579	1.33150	0.665749	−	0.746176i	$-0.268112\pi$
$383$	26.0579	1.33150	0.665749	+	0.746176i	$0.268112\pi$
$384$	14.6154	0.745841
$385$	0.124963	0.00636868
$386$	0.339869	0.0172989
$387$	−7.48231	−0.380347
$388$	−25.4237	−1.29069
$389$	36.6327	1.85735	0.928676	−	0.370891i	$-0.120948\pi$
$389$	36.6327	1.85735	0.928676	+	0.370891i	$0.120948\pi$
$390$	−16.9307	−0.857320
$391$	2.20786	0.111656
$392$	14.3059	0.722559
$393$	−5.06091	−0.255289
$394$	11.3927	0.573957
$395$	−17.7027	−0.890718
$396$	−18.7617	−0.942810
$397$	−21.9601	−1.10215	−0.551073	−	0.834457i	$-0.685781\pi$
$397$	−21.9601	−1.10215	−0.551073	+	0.834457i	$0.685781\pi$
$398$	52.6007	2.63663
$399$	−0.0878300	−0.00439700
$400$	3.95001	0.197500
$401$	11.3085	0.564718	0.282359	−	0.959309i	$-0.408883\pi$
$401$	11.3085	0.564718	0.282359	+	0.959309i	$0.408883\pi$
$402$	16.8965	0.842721
$403$	14.3244	0.713547
$404$	28.0027	1.39319
$405$	−1.40773	−0.0699506
$406$	0.148100	0.00735006
$407$	−51.7539	−2.56535
$408$	−2.04376	−0.101181
$409$	7.33255	0.362571	0.181286	−	0.983430i	$-0.441974\pi$
$409$	7.33255	0.362571	0.181286	+	0.983430i	$0.441974\pi$
$410$	26.9233	1.32965
$411$	−1.91526	−0.0944730
$412$	−43.7776	−2.15677
$413$	0.0439495	0.00216262
$414$	−4.89791	−0.240719
$415$	18.7054	0.918212
$416$	−37.8999	−1.85820
$417$	−0.570656	−0.0279451
$418$	−90.5355	−4.42824
$419$	−24.2018	−1.18234	−0.591169	−	0.806548i	$-0.701333\pi$
$419$	−24.2018	−1.18234	−0.591169	+	0.806548i	$0.701333\pi$
$420$	−0.0568400	−0.00277351
$421$	9.01769	0.439495	0.219748	−	0.975557i	$-0.429477\pi$
$421$	9.01769	0.439495	0.219748	+	0.975557i	$0.429477\pi$
$422$	−60.8029	−2.95984
$423$	−5.33441	−0.259368
$424$	19.9719	0.969920
$425$	−3.01830	−0.146409
$426$	−10.9425	−0.530164
$427$	−0.154549	−0.00747915
$428$	30.8703	1.49217
$429$	34.8190	1.68108
$430$	−23.3665	−1.12683
$431$	18.9278	0.911718	0.455859	−	0.890052i	$-0.349332\pi$
$431$	18.9278	0.911718	0.455859	+	0.890052i	$0.349332\pi$
$432$	−1.30869	−0.0629642
$433$	40.6680	1.95438	0.977191	−	0.212364i	$-0.0681163\pi$
$433$	40.6680	1.95438	0.977191	+	0.212364i	$0.0681163\pi$
$434$	0.0810138	0.00388878
$435$	6.79943	0.326008
$436$	−18.4310	−0.882686
$437$	−14.0298	−0.671138
$438$	18.7380	0.895336
$439$	22.4370	1.07086	0.535430	−	0.844579i	$-0.320149\pi$
$439$	22.4370	1.07086	0.535430	+	0.844579i	$0.320149\pi$
$440$	−18.4777	−0.880890
$441$	−6.99981	−0.333324
$442$	12.0270	0.572064
$443$	−6.05298	−0.287586	−0.143793	−	0.989608i	$-0.545930\pi$
$443$	−6.05298	−0.287586	−0.143793	+	0.989608i	$0.545930\pi$
$444$	23.5406	1.11719
$445$	8.39488	0.397955
$446$	59.9227	2.83742
$447$	0.521602	0.0246709
$448$	−0.178173	−0.00841787
$449$	4.28758	0.202344	0.101172	−	0.994869i	$-0.467741\pi$
$449$	4.28758	0.202344	0.101172	+	0.994869i	$0.467741\pi$
$450$	6.69578	0.315642
$451$	−55.3693	−2.60724
$452$	16.0747	0.756091
$453$	4.07730	0.191568
$454$	31.1360	1.46129
$455$	0.105487	0.00494529
$456$	12.9871	0.608175
$457$	−19.7169	−0.922319	−0.461159	−	0.887317i	$-0.652566\pi$
$457$	−19.7169	−0.922319	−0.461159	+	0.887317i	$0.652566\pi$
$458$	−36.2801	−1.69526
$459$	1.00000	0.0466760
$460$	−9.07954	−0.423336
$461$	−39.6447	−1.84644	−0.923218	−	0.384277i	$-0.874451\pi$
$461$	−39.6447	−1.84644	−0.923218	+	0.384277i	$0.874451\pi$
$462$	0.196924	0.00916176
$463$	6.92680	0.321916	0.160958	−	0.986961i	$-0.448542\pi$
$463$	6.92680	0.321916	0.160958	+	0.986961i	$0.448542\pi$
$464$	6.32104	0.293447
$465$	3.71944	0.172485
$466$	−18.3574	−0.850390
$467$	−5.49809	−0.254421	−0.127211	−	0.991876i	$-0.540602\pi$
$467$	−5.49809	−0.254421	−0.127211	+	0.991876i	$0.540602\pi$
$468$	−15.8376	−0.732095
$469$	−0.105274	−0.00486108
$470$	−16.6588	−0.768415
$471$	1.00000	0.0460776
$472$	−6.49865	−0.299124
$473$	48.0545	2.20955
$474$	−27.8971	−1.28136
$475$	19.1798	0.880028
$476$	0.0403771	0.00185068
$477$	−9.77211	−0.447434
$478$	2.24757	0.102801
$479$	−35.8908	−1.63989	−0.819947	−	0.572439i	$-0.805997\pi$
$479$	−35.8908	−1.63989	−0.819947	+	0.572439i	$0.805997\pi$
$480$	−9.84102	−0.449179
$481$	−43.6879	−1.99200
$482$	9.74108	0.443694
$483$	0.0305164	0.00138854
$484$	88.3614	4.01643
$485$	12.2514	0.556306
$486$	−2.21840	−0.100628
$487$	−6.84807	−0.310316	−0.155158	−	0.987890i	$-0.549589\pi$
$487$	−6.84807	−0.310316	−0.155158	+	0.987890i	$0.549589\pi$
$488$	22.8526	1.03449
$489$	9.36029	0.423287
$490$	−21.8597	−0.987521
$491$	−40.1583	−1.81232	−0.906158	−	0.422938i	$-0.860999\pi$
$491$	−40.1583	−1.81232	−0.906158	+	0.422938i	$0.860999\pi$
$492$	25.1851	1.13543
$493$	−4.83007	−0.217535
$494$	−76.4253	−3.43854
$495$	9.04103	0.406364
$496$	3.45775	0.155257
$497$	0.0681770	0.00305816
$498$	29.4773	1.32091
$499$	−31.1014	−1.39229	−0.696145	−	0.717901i	$-0.745103\pi$
$499$	−31.1014	−1.39229	−0.696145	+	0.717901i	$0.745103\pi$
$500$	32.9742	1.47465
$501$	13.4657	0.601602
$502$	−18.0825	−0.807062
$503$	−41.8019	−1.86385	−0.931927	−	0.362645i	$-0.881874\pi$
$503$	−41.8019	−1.86385	−0.931927	+	0.362645i	$0.881874\pi$
$504$	−0.0282483	−0.00125828
$505$	−13.4942	−0.600483
$506$	31.4564	1.39841
$507$	16.3923	0.728009
$508$	9.63558	0.427510
$509$	30.5710	1.35504	0.677518	−	0.735506i	$-0.263055\pi$
$509$	30.5710	1.35504	0.677518	+	0.735506i	$0.263055\pi$
$510$	3.12290	0.138284
$511$	−0.116747	−0.00516459
$512$	−14.4979	−0.640724
$513$	−6.35449	−0.280558
$514$	−18.9637	−0.836452
$515$	21.0959	0.929597
$516$	−21.8579	−0.962241
$517$	34.2598	1.50675
$518$	−0.247084	−0.0108563
$519$	−3.22099	−0.141386
$520$	−15.5979	−0.684014
$521$	23.5011	1.02960	0.514800	−	0.857310i	$-0.327866\pi$
$521$	23.5011	1.02960	0.514800	+	0.857310i	$0.327866\pi$
$522$	10.7150	0.468983
$523$	−11.0314	−0.482368	−0.241184	−	0.970479i	$-0.577536\pi$
$523$	−11.0314	−0.482368	−0.241184	+	0.970479i	$0.577536\pi$
$524$	−14.7843	−0.645856
$525$	−0.0417181	−0.00182073
$526$	5.98382	0.260907
$527$	−2.64215	−0.115094
$528$	8.40493	0.365778
$529$	−18.1254	−0.788059
$530$	−30.5173	−1.32559
$531$	3.17975	0.137989
$532$	−0.256576	−0.0111240
$533$	−46.7399	−2.02453
$534$	13.2292	0.572485
$535$	−14.8760	−0.643146
$536$	15.5664	0.672366
$537$	−17.9376	−0.774063
$538$	35.1479	1.51533
$539$	44.9557	1.93638
$540$	−4.11237	−0.176968
$541$	−18.5870	−0.799119	−0.399559	−	0.916707i	$-0.630837\pi$
$541$	−18.5870	−0.799119	−0.399559	+	0.916707i	$0.630837\pi$
$542$	44.2119	1.89906
$543$	−2.00710	−0.0861328
$544$	6.99071	0.299724
$545$	8.88168	0.380450
$546$	0.166233	0.00711413
$547$	−14.8186	−0.633600	−0.316800	−	0.948492i	$-0.602608\pi$
$547$	−14.8186	−0.633600	−0.316800	+	0.948492i	$0.602608\pi$
$548$	−5.59502	−0.239008
$549$	−11.1816	−0.477220
$550$	−43.0031	−1.83366
$551$	30.6926	1.30755
$552$	−4.51234	−0.192058
$553$	0.173813	0.00739127
$554$	−32.2418	−1.36982
$555$	−11.3439	−0.481523
$556$	−1.66704	−0.0706984
$557$	27.7452	1.17560	0.587800	−	0.809006i	$-0.299994\pi$
$557$	27.7452	1.17560	0.587800	+	0.809006i	$0.299994\pi$
$558$	5.86134	0.248130
$559$	40.5651	1.71572
$560$	0.0254634	0.00107602
$561$	−6.42242	−0.271155
$562$	−31.3536	−1.32257
$563$	−32.1169	−1.35357	−0.676783	−	0.736183i	$-0.736626\pi$
$563$	−32.1169	−1.35357	−0.676783	+	0.736183i	$0.736626\pi$
$564$	−15.5833	−0.656176
$565$	−7.74621	−0.325885
$566$	6.78942	0.285380
$567$	0.0138217	0.000580457 0
$568$	−10.0811	−0.422992
$569$	−22.0455	−0.924196	−0.462098	−	0.886829i	$-0.652903\pi$
$569$	−22.0455	−0.924196	−0.462098	+	0.886829i	$0.652903\pi$
$570$	−19.8444	−0.831193
$571$	29.4428	1.23214	0.616072	−	0.787690i	$-0.288723\pi$
$571$	29.4428	1.23214	0.616072	+	0.787690i	$0.288723\pi$
$572$	101.716	4.25296
$573$	11.4400	0.477911
$574$	−0.264345	−0.0110336
$575$	−6.66398	−0.277907
$576$	−12.8908	−0.537116
$577$	4.70156	0.195728	0.0978642	−	0.995200i	$-0.468799\pi$
$577$	4.70156	0.195728	0.0978642	+	0.995200i	$0.468799\pi$
$578$	−2.21840	−0.0922731
$579$	−0.153205	−0.00636697
$580$	19.8630	0.824767
$581$	−0.183658	−0.00761942
$582$	19.3065	0.800282
$583$	62.7606	2.59928
$584$	17.2629	0.714345
$585$	7.63196	0.315543
$586$	69.1483	2.85649
$587$	−44.6192	−1.84163	−0.920815	−	0.390000i	$-0.872475\pi$
$587$	−44.6192	−1.84163	−0.920815	+	0.390000i	$0.872475\pi$
$588$	−20.4484	−0.843278
$589$	16.7895	0.691801
$590$	9.93003	0.408813
$591$	−5.13556	−0.211249
$592$	−10.5458	−0.433430
$593$	−22.3793	−0.919009	−0.459504	−	0.888176i	$-0.651973\pi$
$593$	−22.3793	−0.919009	−0.459504	+	0.888176i	$0.651973\pi$
$594$	14.2475	0.584581
$595$	−0.0194572	−0.000797668 0
$596$	1.52374	0.0624150
$597$	−23.7111	−0.970432
$598$	26.5539	1.08587
$599$	−6.89506	−0.281724	−0.140862	−	0.990029i	$-0.544987\pi$
$599$	−6.89506	−0.281724	−0.140862	+	0.990029i	$0.544987\pi$
$600$	6.16868	0.251836
$601$	−44.8043	−1.82760	−0.913802	−	0.406160i	$-0.866868\pi$
$601$	−44.8043	−1.82760	−0.913802	+	0.406160i	$0.866868\pi$
$602$	0.229423	0.00935057
$603$	−7.61654	−0.310169
$604$	11.9109	0.484650
$605$	−42.5803	−1.73114
$606$	−21.2650	−0.863833
$607$	8.39850	0.340885	0.170442	−	0.985368i	$-0.445480\pi$
$607$	8.39850	0.340885	0.170442	+	0.985368i	$0.445480\pi$
$608$	−44.4224	−1.80157
$609$	−0.0667598	−0.00270524
$610$	−34.9191	−1.41383
$611$	28.9203	1.16999
$612$	2.92128	0.118086
$613$	47.1830	1.90570	0.952852	−	0.303434i	$-0.0981333\pi$
$613$	47.1830	1.90570	0.952852	+	0.303434i	$0.0981333\pi$
$614$	47.7946	1.92883
$615$	−12.1364	−0.489386
$616$	0.181422	0.00730972
$617$	−2.75950	−0.111093	−0.0555466	−	0.998456i	$-0.517690\pi$
$617$	−2.75950	−0.111093	−0.0555466	+	0.998456i	$0.517690\pi$
$618$	33.2444	1.33728
$619$	36.9288	1.48429	0.742146	−	0.670238i	$-0.233808\pi$
$619$	36.9288	1.48429	0.742146	+	0.670238i	$0.233808\pi$
$620$	10.8655	0.436369
$621$	2.20786	0.0885984
$622$	−50.1222	−2.00972
$623$	−0.0824247	−0.00330228
$624$	7.09500	0.284027
$625$	−0.798374	−0.0319349
$626$	−17.5318	−0.700710
$627$	40.8113	1.62984
$628$	2.92128	0.116572
$629$	8.05832	0.321306
$630$	0.0431638	0.00171969
$631$	−19.2190	−0.765094	−0.382547	−	0.923936i	$-0.624953\pi$
$631$	−19.2190	−0.765094	−0.382547	+	0.923936i	$0.624953\pi$
$632$	−25.7010	−1.02233
$633$	27.4085	1.08939
$634$	−41.9712	−1.66689
$635$	−4.64327	−0.184262
$636$	−28.5471	−1.13196
$637$	37.9493	1.50360
$638$	−68.8163	−2.72446
$639$	4.93260	0.195131
$640$	−20.5746	−0.813282
$641$	−25.0698	−0.990199	−0.495100	−	0.868836i	$-0.664868\pi$
$641$	−25.0698	−0.990199	−0.495100	+	0.868836i	$0.664868\pi$
$642$	−23.4426	−0.925206
$643$	33.8454	1.33473	0.667366	−	0.744730i	$-0.267422\pi$
$643$	33.8454	1.33473	0.667366	+	0.744730i	$0.267422\pi$
$644$	0.0891469	0.00351288
$645$	10.5331	0.414739
$646$	14.0968	0.554631
$647$	39.6881	1.56030	0.780151	−	0.625592i	$-0.215142\pi$
$647$	39.6881	1.56030	0.780151	+	0.625592i	$0.215142\pi$
$648$	−2.04376	−0.0802866
$649$	−20.4217	−0.801621
$650$	−36.3010	−1.42384
$651$	−0.0365191	−0.00143130
$652$	27.3440	1.07087
$653$	17.9565	0.702692	0.351346	−	0.936246i	$-0.385724\pi$
$653$	17.9565	0.702692	0.351346	+	0.936246i	$0.385724\pi$
$654$	13.9964	0.547301
$655$	7.12439	0.278373
$656$	−11.2825	−0.440508
$657$	−8.44664	−0.329535
$658$	0.163564	0.00637638
$659$	23.2444	0.905472	0.452736	−	0.891645i	$-0.350448\pi$
$659$	23.2444	0.905472	0.452736	+	0.891645i	$0.350448\pi$
$660$	26.4114	1.02806
$661$	−14.2852	−0.555628	−0.277814	−	0.960635i	$-0.589610\pi$
$661$	−14.2852	−0.555628	−0.277814	+	0.960635i	$0.589610\pi$
$662$	−0.964973	−0.0375048
$663$	−5.42147	−0.210552
$664$	27.1568	1.05389
$665$	0.123641	0.00479459
$666$	−17.8765	−0.692702
$667$	−10.6641	−0.412916
$668$	39.3370	1.52199
$669$	−27.0117	−1.04433
$670$	−23.7857	−0.918921
$671$	71.8130	2.77231
$672$	0.0966235	0.00372733
$673$	49.0322	1.89005	0.945026	−	0.326994i	$-0.106036\pi$
$673$	49.0322	1.89005	0.945026	+	0.326994i	$0.106036\pi$
$674$	65.4713	2.52186
$675$	−3.01830	−0.116174
$676$	47.8866	1.84179
$677$	38.0638	1.46291	0.731455	−	0.681889i	$-0.238841\pi$
$677$	38.0638	1.46291	0.731455	+	0.681889i	$0.238841\pi$
$678$	−12.2070	−0.468807
$679$	−0.120289	−0.00461628
$680$	2.87706	0.110330
$681$	−14.0354	−0.537837
$682$	−37.6440	−1.44146
$683$	0.812946	0.0311065	0.0155532	−	0.999879i	$-0.495049\pi$
$683$	0.812946	0.0311065	0.0155532	+	0.999879i	$0.495049\pi$
$684$	−18.5633	−0.709784
$685$	2.69617	0.103015
$686$	0.429262	0.0163893
$687$	16.3542	0.623952
$688$	9.79199	0.373316
$689$	52.9792	2.01835
$690$	6.89493	0.262485
$691$	−26.0681	−0.991676	−0.495838	−	0.868415i	$-0.665139\pi$
$691$	−26.0681	−0.991676	−0.495838	+	0.868415i	$0.665139\pi$
$692$	−9.40941	−0.357692
$693$	−0.0887689	−0.00337205
$694$	−36.0894	−1.36993
$695$	0.803328	0.0304720
$696$	9.87151	0.374179
$697$	8.62125	0.326553
$698$	60.2011	2.27865
$699$	8.27508	0.312992
$700$	−0.121870	−0.00460626
$701$	4.28119	0.161698	0.0808492	−	0.996726i	$-0.474237\pi$
$701$	4.28119	0.161698	0.0808492	+	0.996726i	$0.474237\pi$
$702$	12.0270	0.453929
$703$	−51.2065	−1.93129
$704$	82.7901	3.12027
$705$	7.50941	0.282821
$706$	19.2919	0.726059
$707$	0.132492	0.00498287
$708$	9.28893	0.349099
$709$	2.98529	0.112115	0.0560574	−	0.998428i	$-0.482147\pi$
$709$	2.98529	0.112115	0.0560574	+	0.998428i	$0.482147\pi$
$710$	15.4040	0.578103
$711$	12.5753	0.471612
$712$	12.1878	0.456758
$713$	−5.83350	−0.218466
$714$	−0.0306620	−0.00114750
$715$	−49.0157	−1.83308
$716$	−52.4006	−1.95830
$717$	−1.01315	−0.0378368
$718$	27.1804	1.01436
$719$	19.6103	0.731342	0.365671	−	0.930744i	$-0.380839\pi$
$719$	19.6103	0.731342	0.365671	+	0.930744i	$0.380839\pi$
$720$	1.84228	0.0686575
$721$	−0.207129	−0.00771389
$722$	−47.4284	−1.76510
$723$	−4.39105	−0.163305
$724$	−5.86329	−0.217908
$725$	14.5786	0.541435
$726$	−67.1010	−2.49035
$727$	24.4383	0.906365	0.453182	−	0.891418i	$-0.350289\pi$
$727$	24.4383	0.906365	0.453182	+	0.891418i	$0.350289\pi$
$728$	0.153147	0.00567601
$729$	1.00000	0.0370370
$730$	−26.3780	−0.976294
$731$	−7.48231	−0.276743
$732$	−32.6646	−1.20732
$733$	−31.7208	−1.17164	−0.585818	−	0.810443i	$-0.699227\pi$
$733$	−31.7208	−1.17164	−0.585818	+	0.810443i	$0.699227\pi$
$734$	−52.2466	−1.92846
$735$	9.85383	0.363464
$736$	15.4345	0.568923
$737$	48.9166	1.80187
$738$	−19.1254	−0.704014
$739$	−31.3219	−1.15220	−0.576098	−	0.817381i	$-0.695425\pi$
$739$	−31.3219	−1.15220	−0.576098	+	0.817381i	$0.695425\pi$
$740$	−33.1388	−1.21821
$741$	34.4507	1.26558
$742$	0.299633	0.0109999
$743$	29.6724	1.08857	0.544287	−	0.838899i	$-0.316800\pi$
$743$	29.6724	1.08857	0.544287	+	0.838899i	$0.316800\pi$
$744$	5.39993	0.197971
$745$	−0.734274	−0.0269017
$746$	−77.2254	−2.82742
$747$	−13.2876	−0.486170
$748$	−18.7617	−0.685995
$749$	0.146059	0.00533689
$750$	−25.0403	−0.914344
$751$	−33.9515	−1.23891	−0.619454	−	0.785033i	$-0.712646\pi$
$751$	−33.9515	−1.23891	−0.619454	+	0.785033i	$0.712646\pi$
$752$	6.98107	0.254573
$753$	8.15117	0.297045
$754$	−58.0911	−2.11555
$755$	−5.73974	−0.208891
$756$	0.0403771	0.00146850
$757$	6.67927	0.242762	0.121381	−	0.992606i	$-0.461268\pi$
$757$	6.67927	0.242762	0.121381	+	0.992606i	$0.461268\pi$
$758$	−32.5690	−1.18296
$759$	−14.1798	−0.514695
$760$	−18.2823	−0.663168
$761$	−46.0573	−1.66958	−0.834788	−	0.550571i	$-0.814410\pi$
$761$	−46.0573	−1.66958	−0.834788	+	0.550571i	$0.814410\pi$
$762$	−7.31718	−0.265073
$763$	−0.0872043	−0.00315701
$764$	33.4193	1.20907
$765$	−1.40773	−0.0508965
$766$	−57.8068	−2.08864
$767$	−17.2389	−0.622461
$768$	−6.64127	−0.239646
$769$	−47.8409	−1.72519	−0.862593	−	0.505898i	$-0.831161\pi$
$769$	−47.8409	−1.72519	−0.862593	+	0.505898i	$0.831161\pi$
$770$	−0.277216	−0.00999018
$771$	8.54838	0.307862
$772$	−0.447554	−0.0161078
$773$	−13.8497	−0.498138	−0.249069	−	0.968486i	$-0.580125\pi$
$773$	−13.8497	−0.498138	−0.249069	+	0.968486i	$0.580125\pi$
$774$	16.5987	0.596629
$775$	7.97481	0.286464
$776$	17.7867	0.638506
$777$	0.111380	0.00399573
$778$	−81.2659	−2.91352
$779$	−54.7837	−1.96283
$780$	22.2951	0.798292
$781$	−31.6793	−1.13357
$782$	−4.89791	−0.175149
$783$	−4.83007	−0.172613
$784$	9.16055	0.327163
$785$	−1.40773	−0.0502440
$786$	11.2271	0.400457
$787$	13.4438	0.479218	0.239609	−	0.970869i	$-0.422981\pi$
$787$	13.4438	0.479218	0.239609	+	0.970869i	$0.422981\pi$
$788$	−15.0024	−0.534439
$789$	−2.69736	−0.0960287
$790$	39.2715	1.39722
$791$	0.0760557	0.00270423
$792$	13.1259	0.466409
$793$	60.6208	2.15271
$794$	48.7162	1.72887
$795$	13.7565	0.487892
$796$	−69.2668	−2.45510
$797$	−10.8627	−0.384777	−0.192388	−	0.981319i	$-0.561623\pi$
$797$	−10.8627	−0.384777	−0.192388	+	0.981319i	$0.561623\pi$
$798$	0.194842	0.00689732
$799$	−5.33441	−0.188718
$800$	−21.1000	−0.745999
$801$	−5.96342	−0.210707
$802$	−25.0867	−0.885841
$803$	54.2479	1.91437
$804$	−22.2500	−0.784698
$805$	−0.0429588	−0.00151410
$806$	−31.7771	−1.11930
$807$	−15.8438	−0.557730
$808$	−19.5910	−0.689211
$809$	−7.13120	−0.250720	−0.125360	−	0.992111i	$-0.540009\pi$
$809$	−7.13120	−0.250720	−0.125360	+	0.992111i	$0.540009\pi$
$810$	3.12290	0.109728
$811$	46.6196	1.63704	0.818518	−	0.574480i	$-0.194796\pi$
$811$	46.6196	1.63704	0.818518	+	0.574480i	$0.194796\pi$
$812$	−0.195024	−0.00684400
$813$	−19.9297	−0.698964
$814$	114.811	4.02411
$815$	−13.1768	−0.461562
$816$	−1.30869	−0.0458132
$817$	47.5463	1.66343
$818$	−16.2665	−0.568745
$819$	−0.0749340	−0.00261841
$820$	−35.4538	−1.23810
$821$	−4.65128	−0.162331	−0.0811653	−	0.996701i	$-0.525864\pi$
$821$	−4.65128	−0.162331	−0.0811653	+	0.996701i	$0.525864\pi$
$822$	4.24881	0.148194
$823$	−23.5825	−0.822036	−0.411018	−	0.911627i	$-0.634827\pi$
$823$	−23.5825	−0.822036	−0.411018	+	0.911627i	$0.634827\pi$
$824$	30.6273	1.06695
$825$	19.3848	0.674892
$826$	−0.0974975	−0.00339237
$827$	38.6110	1.34264	0.671318	−	0.741170i	$-0.265729\pi$
$827$	38.6110	1.34264	0.671318	+	0.741170i	$0.265729\pi$
$828$	6.44978	0.224145
$829$	−6.68042	−0.232021	−0.116010	−	0.993248i	$-0.537011\pi$
$829$	−6.68042	−0.232021	−0.116010	+	0.993248i	$0.537011\pi$
$830$	−41.4960	−1.44035
$831$	14.5338	0.504173
$832$	69.8870	2.42290
$833$	−6.99981	−0.242529
$834$	1.26594	0.0438359
$835$	−18.9560	−0.656000
$836$	119.221	4.12335
$837$	−2.64215	−0.0913262
$838$	53.6893	1.85466
$839$	−6.84967	−0.236477	−0.118238	−	0.992985i	$-0.537725\pi$
$839$	−6.84967	−0.236477	−0.118238	+	0.992985i	$0.537725\pi$
$840$	0.0397659	0.00137205
$841$	−5.67044	−0.195533
$842$	−20.0048	−0.689411
$843$	14.1334	0.486781
$844$	80.0679	2.75605
$845$	−23.0760	−0.793837
$846$	11.8338	0.406856
$847$	0.418072	0.0143651
$848$	12.7886	0.439163
$849$	−3.06051	−0.105036
$850$	6.69578	0.229663
$851$	17.7916	0.609889
$852$	14.4095	0.493662
$853$	12.7881	0.437855	0.218927	−	0.975741i	$-0.429744\pi$
$853$	12.7881	0.437855	0.218927	+	0.975741i	$0.429744\pi$
$854$	0.342851	0.0117321
$855$	8.94541	0.305926
$856$	−21.5972	−0.738177
$857$	56.6934	1.93661	0.968304	−	0.249774i	$-0.0803562\pi$
$857$	56.6934	1.93661	0.968304	+	0.249774i	$0.0803562\pi$
$858$	−77.2422	−2.63701
$859$	−20.4337	−0.697190	−0.348595	−	0.937273i	$-0.613341\pi$
$859$	−20.4337	−0.697190	−0.348595	+	0.937273i	$0.613341\pi$
$860$	30.7700	1.04925
$861$	0.119160	0.00406098
$862$	−41.9892	−1.43016
$863$	−55.5310	−1.89030	−0.945148	−	0.326643i	$-0.894082\pi$
$863$	−55.5310	−1.89030	−0.945148	+	0.326643i	$0.894082\pi$
$864$	6.99071	0.237829
$865$	4.53428	0.154170
$866$	−90.2178	−3.06573
$867$	1.00000	0.0339618
$868$	−0.106682	−0.00362104
$869$	−80.7641	−2.73974
$870$	−15.0838	−0.511389
$871$	41.2928	1.39915
$872$	12.8946	0.436665
$873$	−8.70293	−0.294550
$874$	31.1237	1.05278
$875$	0.156014	0.00527423
$876$	−24.6750	−0.833691
$877$	−17.2160	−0.581345	−0.290672	−	0.956823i	$-0.593879\pi$
$877$	−17.2160	−0.581345	−0.290672	+	0.956823i	$0.593879\pi$
$878$	−49.7742	−1.67980
$879$	−31.1704	−1.05135
$880$	−11.8319	−0.398852
$881$	24.7699	0.834518	0.417259	−	0.908788i	$-0.362991\pi$
$881$	24.7699	0.834518	0.417259	+	0.908788i	$0.362991\pi$
$882$	15.5283	0.522867
$883$	−7.98755	−0.268802	−0.134401	−	0.990927i	$-0.542911\pi$
$883$	−7.98755	−0.268802	−0.134401	+	0.990927i	$0.542911\pi$
$884$	−15.8376	−0.532677
$885$	−4.47622	−0.150467
$886$	13.4279	0.451119
$887$	−2.44826	−0.0822046	−0.0411023	−	0.999155i	$-0.513087\pi$
$887$	−2.44826	−0.0822046	−0.0411023	+	0.999155i	$0.513087\pi$
$888$	−16.4693	−0.552673
$889$	0.0455897	0.00152903
$890$	−18.6232	−0.624250
$891$	−6.42242	−0.215159
$892$	−78.9089	−2.64206
$893$	33.8975	1.13434
$894$	−1.15712	−0.0386999
$895$	25.2512	0.844055
$896$	0.202010	0.00674869
$897$	−11.9698	−0.399662
$898$	−9.51156	−0.317405
$899$	12.7618	0.425629
$900$	−8.81729	−0.293910
$901$	−9.77211	−0.325556
$902$	122.831	4.08983
$903$	−0.103418	−0.00344154
$904$	−11.2461	−0.374038
$905$	2.82545	0.0939211
$906$	−9.04508	−0.300503
$907$	10.9073	0.362170	0.181085	−	0.983467i	$-0.442039\pi$
$907$	10.9073	0.362170	0.181085	+	0.983467i	$0.442039\pi$
$908$	−41.0013	−1.36068
$909$	9.58578	0.317940
$910$	−0.234011	−0.00775740
$911$	−17.2741	−0.572315	−0.286158	−	0.958183i	$-0.592378\pi$
$911$	−17.2741	−0.572315	−0.286158	+	0.958183i	$0.592378\pi$
$912$	8.31604	0.275372
$913$	85.3389	2.82430
$914$	43.7399	1.44679
$915$	15.7407	0.520371
$916$	47.7752	1.57854
$917$	−0.0699504	−0.00230997
$918$	−2.21840	−0.0732180
$919$	−18.0817	−0.596460	−0.298230	−	0.954494i	$-0.596396\pi$
$919$	−18.0817	−0.596460	−0.298230	+	0.954494i	$0.596396\pi$
$920$	6.35215	0.209424
$921$	−21.5447	−0.709921
$922$	87.9475	2.89640
$923$	−26.7419	−0.880222
$924$	−0.259319	−0.00853096
$925$	−24.3224	−0.799716
$926$	−15.3664	−0.504971
$927$	−14.9858	−0.492197
$928$	−33.7656	−1.10841
$929$	18.8416	0.618171	0.309086	−	0.951034i	$-0.399977\pi$
$929$	18.8416	0.618171	0.309086	+	0.951034i	$0.399977\pi$
$930$	−8.25118	−0.270567
$931$	44.4802	1.45778
$932$	24.1738	0.791840
$933$	22.5939	0.739691
$934$	12.1969	0.399096
$935$	9.04103	0.295673
$936$	11.0802	0.362167
$937$	2.57770	0.0842097	0.0421048	−	0.999113i	$-0.486594\pi$
$937$	2.57770	0.0842097	0.0421048	+	0.999113i	$0.486594\pi$
$938$	0.233538	0.00762530
$939$	7.90290	0.257901
$940$	21.9371	0.715508
$941$	20.4872	0.667864	0.333932	−	0.942597i	$-0.391624\pi$
$941$	20.4872	0.667864	0.333932	+	0.942597i	$0.391624\pi$
$942$	−2.21840	−0.0722792
$943$	19.0345	0.619849
$944$	−4.16129	−0.135438
$945$	−0.0194572	−0.000632944 0
$946$	−106.604	−3.46599
$947$	−2.57727	−0.0837500	−0.0418750	−	0.999123i	$-0.513333\pi$
$947$	−2.57727	−0.0837500	−0.0418750	+	0.999123i	$0.513333\pi$
$948$	36.7361	1.19313
$949$	45.7932	1.48651
$950$	−42.5483	−1.38045
$951$	18.9196	0.613511
$952$	−0.0282483	−0.000915532 0
$953$	51.8225	1.67869	0.839347	−	0.543596i	$-0.182937\pi$
$953$	51.8225	1.67869	0.839347	+	0.543596i	$0.182937\pi$
$954$	21.6784	0.701864
$955$	−16.1044	−0.521125
$956$	−2.95970	−0.0957234
$957$	31.0207	1.00276
$958$	79.6201	2.57241
$959$	−0.0264722	−0.000854833 0
$960$	18.1467	0.585683
$961$	−24.0190	−0.774807
$962$	96.9171	3.12473
$963$	10.5674	0.340529
$964$	−12.8275	−0.413145
$965$	0.215671	0.00694269
$966$	−0.0676975	−0.00217813
$967$	−52.4246	−1.68586	−0.842931	−	0.538022i	$-0.819172\pi$
$967$	−52.4246	−1.68586	−0.842931	+	0.538022i	$0.819172\pi$
$968$	−61.8187	−1.98693
$969$	−6.35449	−0.204136
$970$	−27.1784	−0.872645
$971$	2.34578	0.0752797	0.0376398	−	0.999291i	$-0.488016\pi$
$971$	2.34578	0.0752797	0.0376398	+	0.999291i	$0.488016\pi$
$972$	2.92128	0.0937001
$973$	−0.00788744	−0.000252860 0
$974$	15.1917	0.486775
$975$	16.3636	0.524055
$976$	14.6332	0.468398
$977$	−18.5048	−0.592022	−0.296011	−	0.955185i	$-0.595657\pi$
$977$	−18.5048	−0.592022	−0.296011	+	0.955185i	$0.595657\pi$
$978$	−20.7648	−0.663986
$979$	38.2996	1.22406
$980$	28.7858	0.919529
$981$	−6.30923	−0.201438
$982$	89.0869	2.84288
$983$	50.8801	1.62282	0.811412	−	0.584474i	$-0.198699\pi$
$983$	50.8801	1.62282	0.811412	+	0.584474i	$0.198699\pi$
$984$	−17.6198	−0.561698
$985$	7.22948	0.230350
$986$	10.7150	0.341235
$987$	−0.0737307	−0.00234687
$988$	100.640	3.20179
$989$	−16.5199	−0.525302
$990$	−20.0566	−0.637440
$991$	33.4800	1.06353	0.531763	−	0.846893i	$-0.321530\pi$
$991$	33.4800	1.06353	0.531763	+	0.846893i	$0.321530\pi$
$992$	−18.4705	−0.586440
$993$	0.434987	0.0138039
$994$	−0.151244	−0.00479715
$995$	33.3788	1.05818
$996$	−38.8169	−1.22996
$997$	18.0283	0.570962	0.285481	−	0.958384i	$-0.407847\pi$
$997$	18.0283	0.570962	0.285481	+	0.958384i	$0.407847\pi$
$998$	68.9952	2.18400
$999$	8.05832	0.254954

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.i.1.7	✓	63

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.i.1.7	✓	63	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.21840 q^{2} +1.00000 q^{3} +2.92128 q^{4} -1.40773 q^{5} -2.21840 q^{6} +0.0138217 q^{7} -2.04376 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.21840 q^{2} +1.00000 q^{3} +2.92128 q^{4} -1.40773 q^{5} -2.21840 q^{6} +0.0138217 q^{7} -2.04376 q^{8} +1.00000 q^{9} +3.12290 q^{10} -6.42242 q^{11} +2.92128 q^{12} -5.42147 q^{13} -0.0306620 q^{14} -1.40773 q^{15} -1.30869 q^{16} +1.00000 q^{17} -2.21840 q^{18} -6.35449 q^{19} -4.11237 q^{20} +0.0138217 q^{21} +14.2475 q^{22} +2.20786 q^{23} -2.04376 q^{24} -3.01830 q^{25} +12.0270 q^{26} +1.00000 q^{27} +0.0403771 q^{28} -4.83007 q^{29} +3.12290 q^{30} -2.64215 q^{31} +6.99071 q^{32} -6.42242 q^{33} -2.21840 q^{34} -0.0194572 q^{35} +2.92128 q^{36} +8.05832 q^{37} +14.0968 q^{38} -5.42147 q^{39} +2.87706 q^{40} +8.62125 q^{41} -0.0306620 q^{42} -7.48231 q^{43} -18.7617 q^{44} -1.40773 q^{45} -4.89791 q^{46} -5.33441 q^{47} -1.30869 q^{48} -6.99981 q^{49} +6.69578 q^{50} +1.00000 q^{51} -15.8376 q^{52} -9.77211 q^{53} -2.21840 q^{54} +9.04103 q^{55} -0.0282483 q^{56} -6.35449 q^{57} +10.7150 q^{58} +3.17975 q^{59} -4.11237 q^{60} -11.1816 q^{61} +5.86134 q^{62} +0.0138217 q^{63} -12.8908 q^{64} +7.63196 q^{65} +14.2475 q^{66} -7.61654 q^{67} +2.92128 q^{68} +2.20786 q^{69} +0.0431638 q^{70} +4.93260 q^{71} -2.04376 q^{72} -8.44664 q^{73} -17.8765 q^{74} -3.01830 q^{75} -18.5633 q^{76} -0.0887689 q^{77} +12.0270 q^{78} +12.5753 q^{79} +1.84228 q^{80} +1.00000 q^{81} -19.1254 q^{82} -13.2876 q^{83} +0.0403771 q^{84} -1.40773 q^{85} +16.5987 q^{86} -4.83007 q^{87} +13.1259 q^{88} -5.96342 q^{89} +3.12290 q^{90} -0.0749340 q^{91} +6.44978 q^{92} -2.64215 q^{93} +11.8338 q^{94} +8.94541 q^{95} +6.99071 q^{96} -8.70293 q^{97} +15.5283 q^{98} -6.42242 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9}+O(q^{10}) \) 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9	\( 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9} + 4 q^{10} + 23 q^{11} + 70 q^{12} + 10 q^{13} + 18 q^{14} + 19 q^{15} + 72 q^{16} + 63 q^{17} + 10 q^{18} + 6 q^{19} + 48 q^{20} + 11 q^{21} + 21 q^{22} + 44 q^{23} + 27 q^{24} + 110 q^{25} + 41 q^{26} + 63 q^{27} + 26 q^{28} + 35 q^{29} + 4 q^{30} + q^{31} + 54 q^{32} + 23 q^{33} + 10 q^{34} + 47 q^{35} + 70 q^{36} + 40 q^{37} + 38 q^{38} + 10 q^{39} - 10 q^{40} + 35 q^{41} + 18 q^{42} + 27 q^{43} + 46 q^{44} + 19 q^{45} + 8 q^{46} + 29 q^{47} + 72 q^{48} + 114 q^{49} + 27 q^{50} + 63 q^{51} - q^{52} + 75 q^{53} + 10 q^{54} + 5 q^{55} + 24 q^{56} + 6 q^{57} + 41 q^{58} + 105 q^{59} + 48 q^{60} + 5 q^{61} + 22 q^{62} + 11 q^{63} + 61 q^{64} + 49 q^{65} + 21 q^{66} + 4 q^{67} + 70 q^{68} + 44 q^{69} - 16 q^{70} + 16 q^{71} + 27 q^{72} + 39 q^{73} + 54 q^{74} + 110 q^{75} + 6 q^{76} + 88 q^{77} + 41 q^{78} + 16 q^{79} + 102 q^{80} + 63 q^{81} - 29 q^{82} + 73 q^{83} + 26 q^{84} + 19 q^{85} + 46 q^{86} + 35 q^{87} + 18 q^{88} + 88 q^{89} + 4 q^{90} - 15 q^{91} + 110 q^{92} + q^{93} - 8 q^{94} + 28 q^{95} + 54 q^{96} + 70 q^{97} + 33 q^{98} + 23 q^{99}+O(q^{100}) \) 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9 + 4 * q^10 + 23 * q^11 + 70 * q^12 + 10 * q^13 + 18 * q^14 + 19 * q^15 + 72 * q^16 + 63 * q^17 + 10 * q^18 + 6 * q^19 + 48 * q^20 + 11 * q^21 + 21 * q^22 + 44 * q^23 + 27 * q^24 + 110 * q^25 + 41 * q^26 + 63 * q^27 + 26 * q^28 + 35 * q^29 + 4 * q^30 + q^31 + 54 * q^32 + 23 * q^33 + 10 * q^34 + 47 * q^35 + 70 * q^36 + 40 * q^37 + 38 * q^38 + 10 * q^39 - 10 * q^40 + 35 * q^41 + 18 * q^42 + 27 * q^43 + 46 * q^44 + 19 * q^45 + 8 * q^46 + 29 * q^47 + 72 * q^48 + 114 * q^49 + 27 * q^50 + 63 * q^51 - q^52 + 75 * q^53 + 10 * q^54 + 5 * q^55 + 24 * q^56 + 6 * q^57 + 41 * q^58 + 105 * q^59 + 48 * q^60 + 5 * q^61 + 22 * q^62 + 11 * q^63 + 61 * q^64 + 49 * q^65 + 21 * q^66 + 4 * q^67 + 70 * q^68 + 44 * q^69 - 16 * q^70 + 16 * q^71 + 27 * q^72 + 39 * q^73 + 54 * q^74 + 110 * q^75 + 6 * q^76 + 88 * q^77 + 41 * q^78 + 16 * q^79 + 102 * q^80 + 63 * q^81 - 29 * q^82 + 73 * q^83 + 26 * q^84 + 19 * q^85 + 46 * q^86 + 35 * q^87 + 18 * q^88 + 88 * q^89 + 4 * q^90 - 15 * q^91 + 110 * q^92 + q^93 - 8 * q^94 + 28 * q^95 + 54 * q^96 + 70 * q^97 + 33 * q^98 + 23 * q^99

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