LMFDB - Embedded newform 165.6.c.b.34.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,6,Mod(34,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("165.34");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	165.c (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$26.4633302691$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			34.15
Character	$\chi$	$=$	165.34
Dual form			165.6.c.b.34.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.31741i q^{2} -9.00000i q^{3} +30.2644 q^{4} +(-35.6376 + 43.0693i) q^{5} +11.8567 q^{6} -87.4786i q^{7} +82.0279i q^{8} -81.0000 q^{9} +O(q^{10})$	\(q+1.31741i q^{2} -9.00000i q^{3} +30.2644 q^{4} +(-35.6376 + 43.0693i) q^{5} +11.8567 q^{6} -87.4786i q^{7} +82.0279i q^{8} -81.0000 q^{9} +(-56.7399 - 46.9494i) q^{10} +121.000 q^{11} -272.380i q^{12} -521.292i q^{13} +115.245 q^{14} +(387.623 + 320.739i) q^{15} +860.397 q^{16} -68.1523i q^{17} -106.710i q^{18} +1588.76 q^{19} +(-1078.55 + 1303.47i) q^{20} -787.308 q^{21} +159.407i q^{22} -191.904i q^{23} +738.251 q^{24} +(-584.921 - 3069.77i) q^{25} +686.756 q^{26} +729.000i q^{27} -2647.49i q^{28} +4252.98 q^{29} +(-422.545 + 510.659i) q^{30} -83.6771 q^{31} +3758.39i q^{32} -1089.00i q^{33} +89.7846 q^{34} +(3767.64 + 3117.53i) q^{35} -2451.42 q^{36} -14445.4i q^{37} +2093.06i q^{38} -4691.63 q^{39} +(-3532.88 - 2923.28i) q^{40} +6151.94 q^{41} -1037.21i q^{42} -1408.62i q^{43} +3662.00 q^{44} +(2886.65 - 3488.61i) q^{45} +252.816 q^{46} -14797.5i q^{47} -7743.57i q^{48} +9154.49 q^{49} +(4044.15 - 770.582i) q^{50} -613.371 q^{51} -15776.6i q^{52} -10938.4i q^{53} -960.393 q^{54} +(-4312.15 + 5211.38i) q^{55} +7175.69 q^{56} -14298.9i q^{57} +5602.92i q^{58} +16099.1 q^{59} +(11731.2 + 9706.97i) q^{60} +41095.0 q^{61} -110.237i q^{62} +7085.77i q^{63} +22581.4 q^{64} +(22451.7 + 18577.6i) q^{65} +1434.66 q^{66} -1254.02i q^{67} -2062.59i q^{68} -1727.14 q^{69} +(-4107.07 + 4963.53i) q^{70} +47638.4 q^{71} -6644.26i q^{72} +7358.01i q^{73} +19030.5 q^{74} +(-27627.9 + 5264.29i) q^{75} +48083.1 q^{76} -10584.9i q^{77} -6180.81i q^{78} -90184.5 q^{79} +(-30662.5 + 37056.7i) q^{80} +6561.00 q^{81} +8104.64i q^{82} -10857.0i q^{83} -23827.4 q^{84} +(2935.27 + 2428.79i) q^{85} +1855.73 q^{86} -38276.8i q^{87} +9925.37i q^{88} -112869. q^{89} +(4595.93 + 3802.90i) q^{90} -45601.9 q^{91} -5807.86i q^{92} +753.094i q^{93} +19494.4 q^{94} +(-56619.8 + 68426.9i) q^{95} +33825.5 q^{96} +96993.9i q^{97} +12060.2i q^{98} -9801.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 418 q^{4} - 98 q^{5} + 234 q^{6} - 2106 q^{9}+O(q^{10}) $ 26 * q - 418 * q^4 - 98 * q^5 + 234 * q^6 - 2106 * q^9	$ 26 q - 418 q^{4} - 98 q^{5} + 234 q^{6} - 2106 q^{9} + 236 q^{10} + 3146 q^{11} + 1220 q^{14} + 7002 q^{16} - 540 q^{19} + 4930 q^{20} + 5472 q^{21} - 7182 q^{24} + 218 q^{25} + 5304 q^{26} - 23904 q^{29} + 12114 q^{30} + 38192 q^{31} + 2604 q^{34} - 11988 q^{35} + 33858 q^{36} - 17748 q^{39} - 41096 q^{40} + 70368 q^{41} - 50578 q^{44} + 7938 q^{45} - 8240 q^{46} - 29114 q^{49} - 133876 q^{50} + 26568 q^{51} - 18954 q^{54} - 11858 q^{55} + 119604 q^{56} + 18384 q^{59} - 14148 q^{60} + 10876 q^{61} - 213114 q^{64} - 117068 q^{65} + 28314 q^{66} - 163512 q^{69} - 58660 q^{70} + 203400 q^{71} - 27352 q^{74} - 35352 q^{75} + 279932 q^{76} - 187908 q^{79} - 256654 q^{80} + 170586 q^{81} - 196560 q^{84} + 37396 q^{85} + 741860 q^{86} + 36836 q^{89} - 19116 q^{90} + 349072 q^{91} - 129040 q^{94} - 208284 q^{95} + 209898 q^{96} - 254826 q^{99}+O(q^{100}) $ 26 * q - 418 * q^4 - 98 * q^5 + 234 * q^6 - 2106 * q^9 + 236 * q^10 + 3146 * q^11 + 1220 * q^14 + 7002 * q^16 - 540 * q^19 + 4930 * q^20 + 5472 * q^21 - 7182 * q^24 + 218 * q^25 + 5304 * q^26 - 23904 * q^29 + 12114 * q^30 + 38192 * q^31 + 2604 * q^34 - 11988 * q^35 + 33858 * q^36 - 17748 * q^39 - 41096 * q^40 + 70368 * q^41 - 50578 * q^44 + 7938 * q^45 - 8240 * q^46 - 29114 * q^49 - 133876 * q^50 + 26568 * q^51 - 18954 * q^54 - 11858 * q^55 + 119604 * q^56 + 18384 * q^59 - 14148 * q^60 + 10876 * q^61 - 213114 * q^64 - 117068 * q^65 + 28314 * q^66 - 163512 * q^69 - 58660 * q^70 + 203400 * q^71 - 27352 * q^74 - 35352 * q^75 + 279932 * q^76 - 187908 * q^79 - 256654 * q^80 + 170586 * q^81 - 196560 * q^84 + 37396 * q^85 + 741860 * q^86 + 36836 * q^89 - 19116 * q^90 + 349072 * q^91 - 129040 * q^94 - 208284 * q^95 + 209898 * q^96 - 254826 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$			1.31741i			0.232888i	0.993197	+	0.116444i	$0.0371495\pi$
$2$			1.31741i			0.232888i	−0.993197	+	0.116444i	$0.962851\pi$
$3$		−	9.00000i		−	0.577350i
$3$		−	9.00000i		−	0.577350i
$4$	30.2644			0.945763
$5$	−35.6376	+	43.0693i	−0.637505	+	0.770446i
$5$	−35.6376	+	43.0693i	−0.637505	+	0.770446i
$6$	11.8567			0.134458
$7$		−	87.4786i		−	0.674772i	−0.941366	−	0.337386i	$-0.890457\pi$
$7$		−	87.4786i		−	0.674772i	0.941366	−	0.337386i	$-0.109543\pi$
$8$			82.0279i			0.453144i
$9$	−81.0000			−0.333333
$10$	−56.7399	−	46.9494i	−0.179427	−	0.148467i
$11$	121.000			0.301511
$11$	121.000			0.301511
$12$		−	272.380i		−	0.546037i
$13$		−	521.292i		−	0.855506i	−0.903896	−	0.427753i	$-0.859305\pi$
$13$		−	521.292i		−	0.855506i	0.903896	−	0.427753i	$-0.140695\pi$
$14$	115.245			0.157146
$15$	387.623	+	320.739i	0.444817	+	0.368064i
$16$	860.397			0.840232
$17$		−	68.1523i		−	0.0571950i	−0.999591	−	0.0285975i	$-0.990896\pi$
$17$		−	68.1523i		−	0.0571950i	0.999591	−	0.0285975i	$-0.00910411\pi$
$18$		−	106.710i		−	0.0776292i
$19$	1588.76			1.00966			0.504830	−	0.863219i	$-0.331555\pi$
$19$	1588.76			1.00966			0.504830	+	0.863219i	$0.331555\pi$
$20$	−1078.55	+	1303.47i	−0.602929	+	0.728660i
$21$	−787.308			−0.389580
$22$			159.407i			0.0702183i
$23$		−	191.904i		−	0.0756422i	−0.999285	−	0.0378211i	$-0.987958\pi$
$23$		−	191.904i		−	0.0756422i	0.999285	−	0.0378211i	$-0.0120417\pi$
$24$	738.251			0.261623
$25$	−584.921	−	3069.77i	−0.187175	−	0.982327i
$26$	686.756			0.199237
$27$			729.000i			0.192450i
$28$		−	2647.49i		−	0.638174i
$29$	4252.98			0.939071			0.469535	−	0.882914i	$-0.344421\pi$
$29$	4252.98			0.939071			0.469535	+	0.882914i	$0.344421\pi$
$30$	−422.545	+	510.659i	−0.0857175	+	0.103592i
$31$	−83.6771			−0.0156388			−0.00781938	−	0.999969i	$-0.502489\pi$
$31$	−83.6771			−0.0156388			−0.00781938	+	0.999969i	$0.502489\pi$
$32$			3758.39i			0.648824i
$33$		−	1089.00i		−	0.174078i
$34$	89.7846			0.0133200
$35$	3767.64	+	3117.53i	0.519875	+	0.430170i
$36$	−2451.42			−0.315254
$37$		−	14445.4i		−	1.73470i	−0.497695	−	0.867352i	$-0.665820\pi$
$37$		−	14445.4i		−	1.73470i	0.497695	−	0.867352i	$-0.334180\pi$
$38$			2093.06i			0.235138i
$39$	−4691.63			−0.493926
$40$	−3532.88	−	2923.28i	−0.349123	−	0.288882i
$41$	6151.94			0.571548			0.285774	−	0.958297i	$-0.407749\pi$
$41$	6151.94			0.571548			0.285774	+	0.958297i	$0.407749\pi$
$42$		−	1037.21i		−	0.0907283i
$43$		−	1408.62i		−	0.116177i	−0.998311	−	0.0580886i	$-0.981499\pi$
$43$		−	1408.62i		−	0.116177i	0.998311	−	0.0580886i	$-0.0185006\pi$
$44$	3662.00			0.285158
$45$	2886.65	−	3488.61i	0.212502	−	0.256815i
$46$	252.816			0.0176161
$47$		−	14797.5i		−	0.977110i	−0.872533	−	0.488555i	$-0.837524\pi$
$47$		−	14797.5i		−	0.977110i	0.872533	−	0.488555i	$-0.162476\pi$
$48$		−	7743.57i		−	0.485108i
$49$	9154.49			0.544683
$50$	4044.15	−	770.582i	0.228772	−	0.0435907i
$51$	−613.371			−0.0330216
$52$		−	15776.6i		−	0.809106i
$53$		−	10938.4i		−	0.534891i	−0.963573	−	0.267445i	$-0.913820\pi$
$53$		−	10938.4i		−	0.534891i	0.963573	−	0.267445i	$-0.0861795\pi$
$54$	−960.393			−0.0448192
$55$	−4312.15	+	5211.38i	−0.192215	+	0.232298i
$56$	7175.69			0.305769
$57$		−	14298.9i		−	0.582928i
$58$			5602.92i			0.218698i
$59$	16099.1			0.602103			0.301052	−	0.953608i	$-0.402662\pi$
$59$	16099.1			0.602103			0.301052	+	0.953608i	$0.402662\pi$
$60$	11731.2	+	9706.97i	0.420692	+	0.348101i
$61$	41095.0			1.41405			0.707025	−	0.707189i	$-0.250037\pi$
$61$	41095.0			1.41405			0.707025	+	0.707189i	$0.250037\pi$
$62$		−	110.237i		−	0.00364208i
$63$			7085.77i			0.224924i
$64$	22581.4			0.689129
$65$	22451.7	+	18577.6i	0.659121	+	0.545389i
$66$	1434.66			0.0405405
$67$		−	1254.02i		−	0.0341286i	−0.999854	−	0.0170643i	$-0.994568\pi$
$67$		−	1254.02i		−	0.0341286i	0.999854	−	0.0170643i	$-0.00543199\pi$
$68$		−	2062.59i		−	0.0540930i
$69$	−1727.14			−0.0436721
$70$	−4107.07	+	4963.53i	−0.100181	+	0.121073i
$71$	47638.4			1.12153			0.560765	−	0.827975i	$-0.310507\pi$
$71$	47638.4			1.12153			0.560765	+	0.827975i	$0.310507\pi$
$72$		−	6644.26i		−	0.151048i
$73$			7358.01i			0.161604i	0.996730	+	0.0808022i	$0.0257482\pi$
$73$			7358.01i			0.161604i	−0.996730	+	0.0808022i	$0.974252\pi$
$74$	19030.5			0.403991
$75$	−27627.9	+	5264.29i	−0.567147	+	0.108065i
$76$	48083.1			0.954900
$77$		−	10584.9i		−	0.203451i
$78$		−	6180.81i		−	0.115029i
$79$	−90184.5			−1.62579			−0.812895	−	0.582411i	$-0.802110\pi$
$79$	−90184.5			−1.62579			−0.812895	+	0.582411i	$0.802110\pi$
$80$	−30662.5	+	37056.7i	−0.535652	+	0.647353i
$81$	6561.00			0.111111
$82$			8104.64i			0.133106i
$83$		−	10857.0i		−	0.172987i	−0.996252	−	0.0864935i	$-0.972434\pi$
$83$		−	10857.0i		−	0.172987i	0.996252	−	0.0864935i	$-0.0275662\pi$
$84$	−23827.4			−0.368450
$85$	2935.27	+	2428.79i	0.0440657	+	0.0364621i
$86$	1855.73			0.0270563
$87$		−	38276.8i		−	0.542173i
$88$			9925.37i			0.136628i
$89$	−112869.			−1.51043			−0.755216	−	0.655476i	$-0.772468\pi$
$89$	−112869.			−1.51043			−0.755216	+	0.655476i	$0.772468\pi$
$90$	4595.93	+	3802.90i	0.0598091	+	0.0494890i
$91$	−45601.9			−0.577271
$92$		−	5807.86i		−	0.0715396i
$93$			753.094i			0.00902905i
$94$	19494.4			0.227557
$95$	−56619.8	+	68426.9i	−0.643664	+	0.777889i
$96$	33825.5			0.374599
$97$			96993.9i			1.04668i	0.852123	+	0.523341i	$0.175315\pi$
$97$			96993.9i			1.04668i	−0.852123	+	0.523341i	$0.824685\pi$
$98$			12060.2i			0.126850i
$99$	−9801.00			−0.100504
$100$	−17702.3	−	92904.9i	−0.177023	−	0.929049i
$101$	−55750.8			−0.543810			−0.271905	−	0.962324i	$-0.587654\pi$
$101$	−55750.8			−0.543810			−0.271905	+	0.962324i	$0.587654\pi$
$102$		−	808.062i		−	0.00769031i
$103$		−	107469.i		−	0.998139i	−0.866562	−	0.499069i	$-0.833675\pi$
$103$		−	107469.i		−	0.998139i	0.866562	−	0.499069i	$-0.166325\pi$
$104$	42760.5			0.387667
$105$	28057.8	−	33908.8i	0.248359	−	0.300150i
$106$	14410.4			0.124569
$107$			25673.1i			0.216780i	0.994108	+	0.108390i	$0.0345696\pi$
$107$			25673.1i			0.216780i	−0.994108	+	0.108390i	$0.965430\pi$
$108$			22062.8i			0.182012i
$109$	−98829.6			−0.796748			−0.398374	−	0.917223i	$-0.630425\pi$
$109$	−98829.6			−0.796748			−0.398374	+	0.917223i	$0.630425\pi$
$110$	−6865.53	−	5680.88i	−0.0540994	−	0.0447645i
$111$	−130009.			−1.00153
$112$		−	75266.4i		−	0.566965i
$113$			12055.0i			0.0888120i	0.999014	+	0.0444060i	$0.0141395\pi$
$113$			12055.0i			0.0888120i	−0.999014	+	0.0444060i	$0.985860\pi$
$114$	18837.5			0.135757
$115$	8265.16	+	6839.00i	0.0582783	+	0.0482223i
$116$	128714.			0.888139
$117$			42224.7i			0.285169i
$118$			21209.1i			0.140222i
$119$	−5961.87			−0.0385936
$120$	−26309.5	+	31795.9i	−0.166786	+	0.201566i
$121$	14641.0			0.0909091
$122$			54139.1i			0.329315i
$123$		−	55367.5i		−	0.329983i
$124$	−2532.44			−0.0147906
$125$	153058.	+	84207.2i	0.876155	+	0.482030i
$126$	−9334.87			−0.0523820
$127$			57953.4i			0.318838i	0.987211	+	0.159419i	$0.0509620\pi$
$127$			57953.4i			0.318838i	−0.987211	+	0.159419i	$0.949038\pi$
$128$			150017.i			0.809313i
$129$	−12677.5			−0.0670750
$130$	−24474.4	+	29578.1i	−0.127014	+	0.153501i
$131$	−124350.			−0.633095			−0.316548	−	0.948577i	$-0.602524\pi$
$131$	−124350.			−0.633095			−0.316548	+	0.948577i	$0.602524\pi$
$132$		−	32958.0i		−	0.164636i
$133$		−	138983.i		−	0.681291i
$134$	1652.06			0.00794812
$135$	−31397.5	−	25979.8i	−0.148272	−	0.122688i
$136$	5590.39			0.0259176
$137$			408683.i			1.86031i	0.367170	+	0.930154i	$0.380327\pi$
$137$			408683.i			1.86031i	−0.367170	+	0.930154i	$0.619673\pi$
$138$		−	2275.35i		−	0.0101707i
$139$	−378463.			−1.66145			−0.830723	−	0.556686i	$-0.812073\pi$
$139$	−378463.			−1.66145			−0.830723	+	0.556686i	$0.812073\pi$
$140$	114025.	+	94350.2i	0.491679	+	0.406839i
$141$	−133177.			−0.564135
$142$			62759.4i			0.261191i
$143$		−	63076.4i		−	0.257945i
$144$	−69692.2			−0.280077
$145$	−151566.	+	183173.i	−0.598662	+	0.723503i
$146$	−9693.52			−0.0376357
$147$		−	82390.4i		−	0.314473i
$148$		−	437182.i		−	1.64062i
$149$	271317.			1.00118			0.500588	−	0.865686i	$-0.333117\pi$
$149$	271317.			1.00118			0.500588	+	0.865686i	$0.333117\pi$
$150$	−6935.24	−	36397.4i	−0.0251671	−	0.132081i
$151$	−146748.			−0.523758			−0.261879	−	0.965101i	$-0.584342\pi$
$151$	−146748.			−0.523758			−0.261879	+	0.965101i	$0.584342\pi$
$152$			130323.i			0.457522i
$153$			5520.34i			0.0190650i
$154$	13944.7			0.0473813
$155$	2982.05	−	3603.91i	0.00996979	−	0.0120488i
$156$	−141990.			−0.467138
$157$			365562.i			1.18362i	0.806077	+	0.591810i	$0.201586\pi$
$157$			365562.i			1.18362i	−0.806077	+	0.591810i	$0.798414\pi$
$158$		−	118810.i		−	0.378626i
$159$	−98445.8			−0.308819
$160$	−161871.	−	133940.i	−0.499884	−	0.413628i
$161$	−16787.5			−0.0510412
$162$			8643.54i			0.0258764i
$163$			16695.2i			0.0492180i	0.999697	+	0.0246090i	$0.00783408\pi$
$163$			16695.2i			0.0492180i	−0.999697	+	0.0246090i	$0.992166\pi$
$164$	186185.			0.540549
$165$	46902.4	+	38809.4i	0.134117	+	0.110975i
$166$	14303.1			0.0402865
$167$			568590.i			1.57764i	0.614623	+	0.788821i	$0.289308\pi$
$167$			568590.i			1.57764i	−0.614623	+	0.788821i	$0.710692\pi$
$168$		−	64581.2i		−	0.176536i
$169$	99547.4			0.268110
$170$	−3199.71	+	3866.96i	−0.00849157	+	0.0102624i
$171$	−128690.			−0.336554
$172$		−	42630.9i		−	0.109876i
$173$			552203.i			1.40276i	0.712788	+	0.701380i	$0.247432\pi$
$173$			552203.i			1.40276i	−0.712788	+	0.701380i	$0.752568\pi$
$174$	50426.3			0.126265
$175$	−268539.	+	51168.1i	−0.662846	+	0.126300i
$176$	104108.			0.253339
$177$		−	144892.i		−	0.347624i
$178$		−	148695.i		−	0.351761i
$179$	179962.			0.419807			0.209903	−	0.977722i	$-0.432685\pi$
$179$	179962.			0.419807			0.209903	+	0.977722i	$0.432685\pi$
$180$	87362.7	−	105581.i	0.200976	−	0.242887i
$181$	612439.			1.38953			0.694763	−	0.719239i	$-0.255509\pi$
$181$	612439.			1.38953			0.694763	+	0.719239i	$0.255509\pi$
$182$		−	60076.5i		−	0.134439i
$183$		−	369855.i		−	0.816402i
$184$	15741.5			0.0342768
$185$	622153.	+	514800.i	1.33650	+	1.10588i
$186$	−992.135			−0.00210275
$187$		−	8246.43i		−	0.0172449i
$188$		−	447838.i		−	0.924115i
$189$	63771.9			0.129860
$190$	−90146.4	−	74591.5i	−0.181161	−	0.149901i
$191$	65407.8			0.129732			0.0648659	−	0.997894i	$-0.479338\pi$
$191$	65407.8			0.129732			0.0648659	+	0.997894i	$0.479338\pi$
$192$		−	203232.i		−	0.397869i
$193$		−	661050.i		−	1.27744i	−0.769439	−	0.638721i	$-0.779464\pi$
$193$		−	661050.i		−	1.27744i	0.769439	−	0.638721i	$-0.220536\pi$
$194$	−127781.			−0.243759
$195$	167199.	−	202065.i	0.314881	−	0.380544i
$196$	277055.			0.515141
$197$		−	590186.i		−	1.08349i	−0.840544	−	0.541743i	$-0.817765\pi$
$197$		−	590186.i		−	1.08349i	0.840544	−	0.541743i	$-0.182235\pi$
$198$		−	12911.9i		−	0.0234061i
$199$	342750.			0.613543			0.306771	−	0.951783i	$-0.400751\pi$
$199$	342750.			0.613543			0.306771	+	0.951783i	$0.400751\pi$
$200$	251807.	−	47979.8i	0.445136	−	0.0848172i
$201$	−11286.2			−0.0197041
$202$		−	73446.7i		−	0.126647i
$203$		−	372045.i		−	0.633658i
$204$	−18563.3			−0.0312306
$205$	−219240.	+	264959.i	−0.364364	+	0.440347i
$206$	141581.			0.232454
$207$			15544.2i			0.0252141i
$208$		−	448518.i		−	0.718823i
$209$	192241.			0.304424
$210$	44671.8	+	36963.6i	0.0699013	+	0.0578397i
$211$	−214655.			−0.331921			−0.165960	−	0.986132i	$-0.553072\pi$
$211$	−214655.			−0.331921			−0.165960	+	0.986132i	$0.553072\pi$
$212$		−	331045.i		−	0.505880i
$213$		−	428746.i		−	0.647516i
$214$	−33822.1			−0.0504854
$215$	60668.0	+	50199.7i	0.0895083	+	0.0740636i
$216$	−59798.3			−0.0872076
$217$			7319.96i			0.0105526i
$218$		−	130199.i		−	0.185553i
$219$	66222.1			0.0933023
$220$	−130505.	+	157719.i	−0.181790	+	0.219699i
$221$	−35527.3			−0.0489307
$222$		−	171275.i		−	0.233244i
$223$			118747.i			0.159904i	0.996799	+	0.0799521i	$0.0254767\pi$
$223$			118747.i			0.159904i	−0.996799	+	0.0799521i	$0.974523\pi$
$224$	328779.			0.437808
$225$	47378.6	+	248651.i	0.0623916	+	0.327442i
$226$	−15881.4			−0.0206832
$227$			2183.16i			0.00281204i	0.999999	+	0.00140602i	$0.000447550\pi$
$227$			2183.16i			0.00281204i	−0.999999	+	0.00140602i	$0.999552\pi$
$228$		−	432747.i		−	0.551312i
$229$	−123704.			−0.155881			−0.0779407	−	0.996958i	$-0.524834\pi$
$229$	−123704.			−0.155881			−0.0779407	+	0.996958i	$0.524834\pi$
$230$	−9009.77	+	10888.6i	−0.0112304	+	0.0135723i
$231$	−95264.2			−0.117463
$232$			348863.i			0.425534i
$233$		−	1.16587e6i		−	1.40689i	−0.710748	−	0.703446i	$-0.751644\pi$
$233$		−	1.16587e6i		−	1.40689i	0.710748	−	0.703446i	$-0.248356\pi$
$234$	−55627.3			−0.0664122
$235$	637317.	+	527347.i	0.752811	+	0.622912i
$236$	487229.			0.569447
$237$			811661.i			0.938650i
$238$		−	7854.24i		−	0.00898797i
$239$	−770619.			−0.872659			−0.436330	−	0.899787i	$-0.643722\pi$
$239$	−770619.			−0.872659			−0.436330	+	0.899787i	$0.643722\pi$
$240$	333510.	+	275963.i	0.373750	+	0.309259i
$241$	−1.42541e6			−1.58087			−0.790434	−	0.612547i	$-0.790145\pi$
$241$	−1.42541e6			−1.58087			−0.790434	+	0.612547i	$0.790145\pi$
$242$			19288.2i			0.0211716i
$243$		−	59049.0i		−	0.0641500i
$244$	1.24372e6			1.33736
$245$	−326244.	+	394277.i	−0.347238	+	0.419649i
$246$	72941.7			0.0768490
$247$		−	828211.i		−	0.863771i
$248$		−	6863.86i		−	0.00708662i
$249$	−97712.7			−0.0998741
$250$	−110935.	+	201640.i	−0.112259	+	0.204046i
$251$	−668745.			−0.670002			−0.335001	−	0.942218i	$-0.608737\pi$
$251$	−668745.			−0.670002			−0.335001	+	0.942218i	$0.608737\pi$
$252$			214447.i			0.212725i
$253$		−	23220.4i		−	0.0228070i
$254$	−76348.5			−0.0742534
$255$	21859.1	−	26417.4i	0.0210514	−	0.0254413i
$256$	524969.			0.500650
$257$			1.08696e6i			1.02655i	0.858223	+	0.513276i	$0.171568\pi$
$257$			1.08696e6i			1.02655i	−0.858223	+	0.513276i	$0.828432\pi$
$258$		−	16701.5i		−	0.0156209i
$259$	−1.26366e6			−1.17053
$260$	679487.	+	562241.i	0.623373	+	0.515809i
$261$	−344491.			−0.313024
$262$		−	163821.i		−	0.147440i
$263$		−	865881.i		−	0.771914i	−0.922517	−	0.385957i	$-0.873871\pi$
$263$		−	865881.i		−	0.771914i	0.922517	−	0.385957i	$-0.126129\pi$
$264$	89328.3			0.0788823
$265$	471110.	+	389819.i	0.412105	+	0.340996i
$266$	183098.			0.158664
$267$			1.01582e6i			0.872049i
$268$		−	37952.2i		−	0.0322775i
$269$	−455847.			−0.384094			−0.192047	−	0.981386i	$-0.561513\pi$
$269$	−455847.			−0.384094			−0.192047	+	0.981386i	$0.561513\pi$
$270$	34226.1	−	41363.4i	0.0285725	−	0.0345308i
$271$	1.93670e6			1.60191			0.800955	−	0.598725i	$-0.204326\pi$
$271$	1.93670e6			1.60191			0.800955	+	0.598725i	$0.204326\pi$
$272$		−	58638.1i		−	0.0480571i
$273$			410417.i			0.333288i
$274$	−538403.			−0.433243
$275$	−70775.5	−	371442.i	−0.0564353	−	0.296183i
$276$	−52270.8			−0.0413034
$277$		−	1.67891e6i		−	1.31470i	−0.753584	−	0.657352i	$-0.771677\pi$
$277$		−	1.67891e6i		−	1.31470i	0.753584	−	0.657352i	$-0.228323\pi$
$278$		−	498591.i		−	0.386930i
$279$	6777.85			0.00521292
$280$	−255724.	+	309051.i	−0.194929	+	0.235578i
$281$	−1.66433e6			−1.25740			−0.628700	−	0.777648i	$-0.716413\pi$
$281$	−1.66433e6			−1.25740			−0.628700	+	0.777648i	$0.716413\pi$
$282$		−	175449.i		−	0.131380i
$283$		−	529051.i		−	0.392673i	−0.980537	−	0.196337i	$-0.937095\pi$
$283$		−	529051.i		−	0.392673i	0.980537	−	0.196337i	$-0.0629045\pi$
$284$	1.44175e6			1.06070
$285$	615842.	+	509578.i	0.449115	+	0.371620i
$286$	83097.5			0.0600721
$287$		−	538163.i		−	0.385664i
$288$		−	304430.i		−	0.216275i
$289$	1.41521e6			0.996729
$290$	−241314.	−	199675.i	−0.168495	−	0.139421i
$291$	872945.			0.604302
$292$			222686.i			0.152839i
$293$			1.17586e6i			0.800178i	0.916476	+	0.400089i	$0.131021\pi$
$293$			1.17586e6i			0.800178i	−0.916476	+	0.400089i	$0.868979\pi$
$294$	108542.			0.0732369
$295$	−573733.	+	693375.i	−0.383844	+	0.463888i
$296$	1.18493e6			0.786071
$297$			88209.0i			0.0580259i
$298$			357436.i			0.233162i
$299$	−100038.			−0.0647123
$300$	−836144.	+	159321.i	−0.536386	+	0.102204i
$301$	−123224.			−0.0783931
$302$		−	193328.i		−	0.121977i
$303$			501757.i			0.313969i
$304$	1.36697e6			0.848349
$305$	−1.46453e6	+	1.76993e6i	−0.901464	+	1.08945i
$306$	−7272.55			−0.00444000
$307$			1.53089e6i			0.927037i	0.886087	+	0.463518i	$0.153413\pi$
$307$			1.53089e6i			0.927037i	−0.886087	+	0.463518i	$0.846587\pi$
$308$		−	320346.i		−	0.192417i
$309$	−967223.			−0.576276
$310$	4747.83	+	3928.59i	0.00280602	+	0.00232184i
$311$	−1.11621e6			−0.654400			−0.327200	−	0.944955i	$-0.606105\pi$
$311$	−1.11621e6			−0.654400			−0.327200	+	0.944955i	$0.606105\pi$
$312$		−	384844.i		−	0.223820i
$313$		−	864587.i		−	0.498824i	−0.968397	−	0.249412i	$-0.919763\pi$
$313$		−	864587.i		−	0.498824i	0.968397	−	0.249412i	$-0.0802374\pi$
$314$	−481596.			−0.275651
$315$	−305179.	−	252520.i	−0.173292	−	0.143390i
$316$	−2.72938e6			−1.53761
$317$		−	1.80604e6i		−	1.00943i	−0.863285	−	0.504717i	$-0.831597\pi$
$317$		−	1.80604e6i		−	1.00943i	0.863285	−	0.504717i	$-0.168403\pi$
$318$		−	129694.i		−	0.0719202i
$319$	514611.			0.283140
$320$	−804746.	+	972563.i	−0.439323	+	0.530937i
$321$	231058.			0.125158
$322$		−	22116.0i		−	0.0118869i
$323$		−	108278.i		−	0.0577476i
$324$	198565.			0.105085
$325$	−1.60025e6	+	304915.i	−0.840386	+	0.160129i
$326$	−21994.5			−0.0114623
$327$			889466.i			0.460003i
$328$			504630.i			0.258994i
$329$	−1.29446e6			−0.659326
$330$	−51127.9	+	61789.8i	−0.0258448	+	0.0312343i
$331$	1.85701e6			0.931634			0.465817	−	0.884881i	$-0.345761\pi$
$331$	1.85701e6			0.931634			0.465817	+	0.884881i	$0.345761\pi$
$332$		−	328580.i		−	0.163605i
$333$			1.17008e6i			0.578235i
$334$	−749068.			−0.367413
$335$	54009.8	+	44690.3i	0.0262942	+	0.0217571i
$336$	−677397.			−0.327337
$337$			2.18068e6i			1.04597i	0.852343	+	0.522983i	$0.175181\pi$
$337$			2.18068e6i			1.04597i	−0.852343	+	0.522983i	$0.824819\pi$
$338$			131145.i			0.0624395i
$339$	108495.			0.0512757
$340$	88834.2	+	73505.8i	0.0416757	+	0.0344845i
$341$	−10124.9			−0.00471527
$342$		−	169538.i		−	0.0783792i
$343$		−	2.27108e6i		−	1.04231i
$344$	115546.			0.0526451
$345$	61551.0	−	74386.4i	0.0278411	−	0.0336470i
$346$	−727478.			−0.326685
$347$			2.59930e6i			1.15886i	0.815021	+	0.579432i	$0.196726\pi$
$347$			2.59930e6i			1.15886i	−0.815021	+	0.579432i	$0.803274\pi$
$348$		−	1.15843e6i		−	0.512767i
$349$	−1.17216e6			−0.515138			−0.257569	−	0.966260i	$-0.582921\pi$
$349$	−1.17216e6			−0.515138			−0.257569	+	0.966260i	$0.582921\pi$
$350$	−67409.5	−	353777.i	−0.0294138	−	0.154369i
$351$	380022.			0.164642
$352$			454765.i			0.195628i
$353$		−	1.57881e6i		−	0.674364i	−0.941440	−	0.337182i	$-0.890526\pi$
$353$		−	1.57881e6i		−	0.674364i	0.941440	−	0.337182i	$-0.109474\pi$
$354$	190882.			0.0809574
$355$	−1.69772e6	+	2.05175e6i	−0.714982	+	0.864079i
$356$	−3.41593e6			−1.42851
$357$			53656.8i			0.0222820i
$358$			237085.i			0.0977678i
$359$	−3.19520e6			−1.30847			−0.654233	−	0.756293i	$-0.727008\pi$
$359$	−3.19520e6			−1.30847			−0.654233	+	0.756293i	$0.727008\pi$
$360$	286163.	+	236785.i	0.116374	+	0.0962939i
$361$	48073.9			0.0194152
$362$			806834.i			0.323603i
$363$		−	131769.i		−	0.0524864i
$364$	−1.38012e6			−0.545962
$365$	−316904.	−	262222.i	−0.124507	−	0.103024i
$366$	487252.			0.190130
$367$			2.52046e6i			0.976819i	0.872615	+	0.488409i	$0.162423\pi$
$367$			2.52046e6i			0.976819i	−0.872615	+	0.488409i	$0.837577\pi$
$368$		−	165114.i		−	0.0635570i
$369$	−498307.			−0.190516
$370$	−678203.	+	819631.i	−0.257546	+	0.311253i
$371$	−956879.			−0.360929
$372$			22792.0i			0.00853934i
$373$		−	1.66879e6i		−	0.621053i	−0.950565	−	0.310527i	$-0.899495\pi$
$373$		−	1.66879e6i		−	0.621053i	0.950565	−	0.310527i	$-0.100505\pi$
$374$	10863.9			0.00401614
$375$	757865.	−	1.37752e6i	0.278300	−	0.505848i
$376$	1.21381e6			0.442772
$377$		−	2.21705e6i		−	0.803380i
$378$			84013.9i			0.0302428i
$379$	3.13030e6			1.11941			0.559704	−	0.828692i	$-0.310915\pi$
$379$	3.13030e6			1.11941			0.559704	+	0.828692i	$0.310915\pi$
$380$	−1.71357e6	+	2.07090e6i	−0.608754	+	0.735699i
$381$	521581.			0.184081
$382$			86169.0i			0.0302129i
$383$		−	4.30969e6i		−	1.50124i	−0.660737	−	0.750618i	$-0.729756\pi$
$383$		−	4.30969e6i		−	1.50124i	0.660737	−	0.750618i	$-0.270244\pi$
$384$	1.35016e6			0.467257
$385$	455884.	+	377221.i	0.156748	+	0.129701i
$386$	870875.			0.297500
$387$			114098.i			0.0387258i
$388$			2.93546e6i			0.989914i
$389$	2.45755e6			0.823432			0.411716	−	0.911312i	$-0.364929\pi$
$389$	2.45755e6			0.823432			0.411716	+	0.911312i	$0.364929\pi$
$390$	266203.	+	220269.i	0.0886239	+	0.0733318i
$391$	−13078.7			−0.00432636
$392$			750923.i			0.246820i
$393$			1.11915e6i			0.365518i
$394$	777518.			0.252330
$395$	3.21396e6	−	3.88418e6i	1.03645	−	1.25258i
$396$	−296622.			−0.0950528
$397$			5.93203e6i			1.88898i	0.328544	+	0.944489i	$0.393442\pi$
$397$			5.93203e6i			1.88898i	−0.328544	+	0.944489i	$0.606558\pi$
$398$			451543.i			0.142887i
$399$	−1.25085e6			−0.393343
$400$	−503265.	−	2.64122e6i	−0.157270	−	0.825382i
$401$	4.56758e6			1.41849			0.709243	−	0.704964i	$-0.249037\pi$
$401$	4.56758e6			1.41849			0.709243	+	0.704964i	$0.249037\pi$
$402$		−	14868.6i		−	0.00458885i
$403$			43620.2i			0.0133791i
$404$	−1.68727e6			−0.514316
$405$	−233818.	+	282577.i	−0.0708339	+	0.0856051i
$406$	490136.			0.147571
$407$		−	1.74789e6i		−	0.523033i
$408$		−	50313.5i		−	0.0149635i
$409$	5.87934e6			1.73788			0.868941	−	0.494915i	$-0.164801\pi$
$409$	5.87934e6			1.73788			0.868941	+	0.494915i	$0.164801\pi$
$410$	−349061.	−	288830.i	−0.102551	−	0.0848560i
$411$	3.67814e6			1.07405
$412$		−	3.25249e6i		−	0.944003i
$413$		−	1.40833e6i		−	0.406282i
$414$	−20478.1			−0.00587205
$415$	467601.	+	386916.i	0.133277	+	0.110280i
$416$	1.95922e6			0.555072
$417$			3.40616e6i			0.959236i
$418$			253260.i			0.0708966i
$419$	−6.12464e6			−1.70430			−0.852149	−	0.523299i	$-0.824701\pi$
$419$	−6.12464e6			−1.70430			−0.852149	+	0.523299i	$0.824701\pi$
$420$	849152.	−	1.02623e6i	0.234889	−	0.283871i
$421$	−2.83114e6			−0.778495			−0.389248	−	0.921133i	$-0.627265\pi$
$421$	−2.83114e6			−0.778495			−0.389248	+	0.921133i	$0.627265\pi$
$422$		−	282789.i		−	0.0773003i
$423$			1.19860e6i			0.325703i
$424$	897256.			0.242383
$425$	−209212.	+	39863.7i	−0.0561842	+	0.0107055i
$426$	564834.			0.150799
$427$		−	3.59494e6i		−	0.954161i
$428$			776983.i			0.205023i
$429$	−567687.			−0.148924
$430$	−66133.6	+	79924.7i	−0.0172485	+	0.0208454i
$431$	6.20538e6			1.60907			0.804536	−	0.593904i	$-0.202414\pi$
$431$	6.20538e6			1.60907			0.804536	+	0.593904i	$0.202414\pi$
$432$			627230.i			0.161703i
$433$		−	422736.i		−	0.108355i	−0.998531	−	0.0541775i	$-0.982746\pi$
$433$		−	422736.i		−	0.108355i	0.998531	−	0.0541775i	$-0.0172537\pi$
$434$	−9643.40			−0.00245757
$435$	1.64855e6	+	1.36409e6i	0.417715	+	0.345638i
$436$	−2.99102e6			−0.753535
$437$		−	304890.i		−	0.0763730i
$438$			87241.7i			0.0217290i
$439$	4.07012e6			1.00797			0.503983	−	0.863713i	$-0.331867\pi$
$439$	4.07012e6			1.00797			0.503983	+	0.863713i	$0.331867\pi$
$440$	−427478.	−	353717.i	−0.105265	−	0.0871011i
$441$	−741514.			−0.181561
$442$		−	46804.0i		−	0.0113953i
$443$		−	4.95245e6i		−	1.19898i	−0.800384	−	0.599488i	$-0.795371\pi$
$443$		−	4.95245e6i		−	1.19898i	0.800384	−	0.599488i	$-0.204629\pi$
$444$	−3.93464e6			−0.947212
$445$	4.02240e6	−	4.86120e6i	0.962908	−	1.16371i
$446$	−156438.			−0.0372397
$447$		−	2.44185e6i		−	0.578029i
$448$		−	1.97539e6i		−	0.465004i
$449$	−7.34037e6			−1.71831			−0.859157	−	0.511713i	$-0.829011\pi$
$449$	−7.34037e6			−1.71831			−0.859157	+	0.511713i	$0.829011\pi$
$450$	−327576.	+	62417.1i	−0.0762572	+	0.0145302i
$451$	744385.			0.172328
$452$			364838.i			0.0839952i
$453$			1.32073e6i			0.302392i
$454$	−2876.12			−0.000654888
$455$	1.62514e6	−	1.96404e6i	0.368013	−	0.444756i
$456$	1.17291e6			0.264150
$457$			2.07655e6i			0.465106i	0.972584	+	0.232553i	$0.0747080\pi$
$457$			2.07655e6i			0.465106i	−0.972584	+	0.232553i	$0.925292\pi$
$458$		−	162969.i		−	0.0363029i
$459$	49683.0			0.0110072
$460$	250140.	+	206978.i	0.0551174	+	0.0456069i
$461$	−1.68917e6			−0.370186			−0.185093	−	0.982721i	$-0.559259\pi$
$461$	−1.68917e6			−0.370186			−0.185093	+	0.982721i	$0.559259\pi$
$462$		−	125502.i		−	0.0273556i
$463$			1.35953e6i			0.294739i	0.989082	+	0.147369i	$0.0470806\pi$
$463$			1.35953e6i			0.294739i	−0.989082	+	0.147369i	$0.952919\pi$
$464$	3.65925e6			0.789037
$465$	−32435.2	−	26838.5i	−0.00695639	−	0.00575606i
$466$	1.53593e6			0.327648
$467$		−	8.47580e6i		−	1.79841i	−0.437528	−	0.899205i	$-0.644146\pi$
$467$		−	8.47580e6i		−	1.79841i	0.437528	−	0.899205i	$-0.355854\pi$
$468$			1.27791e6i			0.269702i
$469$	−109700.			−0.0230290
$470$	−694733.	+	839608.i	−0.145069	+	0.175320i
$471$	3.29006e6			0.683363
$472$			1.32057e6i			0.272840i
$473$		−	170442.i		−	0.0350288i
$474$	−1.06929e6			−0.218600
$475$	−929302.	−	4.87714e6i	−0.188983	−	0.991817i
$476$	−180433.			−0.0365004
$477$			886013.i			0.178297i
$478$		−	1.01522e6i		−	0.203232i
$479$	3.52896e6			0.702762			0.351381	−	0.936233i	$-0.385712\pi$
$479$	3.52896e6			0.702762			0.351381	+	0.936233i	$0.385712\pi$
$480$	−1.20546e6	+	1.45684e6i	−0.238808	+	0.288608i
$481$	−7.53028e6			−1.48405
$482$		−	1.87784e6i		−	0.368165i
$483$			151087.i			0.0294687i
$484$	443101.			0.0859785
$485$	−4.17745e6	−	3.45663e6i	−0.806413	−	0.667265i
$486$	77791.8			0.0149397
$487$			4.66713e6i			0.891719i	0.895103	+	0.445859i	$0.147102\pi$
$487$			4.66713e6i			0.891719i	−0.895103	+	0.445859i	$0.852898\pi$
$488$			3.37094e6i			0.640768i
$489$	150257.			0.0284160
$490$	−519425.	−	429798.i	−0.0977311	−	0.0808675i
$491$	−7.22516e6			−1.35252			−0.676260	−	0.736663i	$-0.736400\pi$
$491$	−7.22516e6			−1.35252			−0.676260	+	0.736663i	$0.736400\pi$
$492$		−	1.67566e6i		−	0.312086i
$493$		−	289850.i		−	0.0537102i
$494$	1.09109e6			0.201162
$495$	349284.	−	422122.i	0.0640717	−	0.0774328i
$496$	−71995.6			−0.0131402
$497$		−	4.16734e6i		−	0.756777i
$498$		−	128728.i		−	0.0232594i
$499$	1.04815e7			1.88440			0.942202	−	0.335046i	$-0.108752\pi$
$499$	1.04815e7			1.88440			0.942202	+	0.335046i	$0.108752\pi$
$500$	4.63221e6	+	2.54848e6i	0.828635	+	0.455886i
$501$	5.11731e6			0.910852
$502$		−	881012.i		−	0.156035i
$503$			8.37701e6i			1.47628i	0.674647	+	0.738140i	$0.264296\pi$
$503$			8.37701e6i			1.47628i	−0.674647	+	0.738140i	$0.735704\pi$
$504$	−581230.			−0.101923
$505$	1.98682e6	−	2.40114e6i	0.346682	−	0.418977i
$506$	30590.8			0.00531146
$507$		−	895926.i		−	0.154793i
$508$			1.75393e6i			0.301545i
$509$	−3.17550e6			−0.543272			−0.271636	−	0.962400i	$-0.587565\pi$
$509$	−3.17550e6			−0.543272			−0.271636	+	0.962400i	$0.587565\pi$
$510$	34802.6	+	28797.4i	0.00592497	+	0.00490261i
$511$	643668.			0.109046
$512$			5.49216e6i			0.925908i
$513$			1.15821e6i			0.194309i
$514$	−1.43198e6			−0.239071
$515$	4.62862e6	+	3.82995e6i	0.769012	+	0.636318i
$516$	−383678.			−0.0634371
$517$		−	1.79050e6i		−	0.294610i
$518$		−	1.66477e6i		−	0.272602i
$519$	4.96982e6			0.809884
$520$	−1.52388e6	+	1.84166e6i	−0.247140	+	0.298677i
$521$	3.72507e6			0.601230			0.300615	−	0.953746i	$-0.402808\pi$
$521$	3.72507e6			0.601230			0.300615	+	0.953746i	$0.402808\pi$
$522$		−	453837.i		−	0.0728993i
$523$			3.77963e6i			0.604219i	0.953273	+	0.302110i	$0.0976909\pi$
$523$			3.77963e6i			0.604219i	−0.953273	+	0.302110i	$0.902309\pi$
$524$	−3.76339e6			−0.598758
$525$	460513.	+	2.41685e6i	0.0729195	+	0.382694i
$526$	1.14072e6			0.179769
$527$			5702.79i			0.000894460i
$528$		−	936973.i		−	0.146266i
$529$	6.39952e6			0.994278
$530$	−513553.	+	620646.i	−0.0794137	+	0.0959741i
$531$	−1.30403e6			−0.200701
$532$		−	4.20624e6i		−	0.644340i
$533$		−	3.20696e6i		−	0.488962i
$534$	−1.33826e6			−0.203089
$535$	−1.10572e6	−	914929.i	−0.167017	−	0.138198i
$536$	102865.			0.0154652
$537$		−	1.61966e6i		−	0.242375i
$538$		−	600538.i		−	0.0894509i
$539$	1.10769e6			0.164228
$540$	−950227.	−	786264.i	−0.140231	−	0.116034i
$541$	−6.08511e6			−0.893871			−0.446936	−	0.894566i	$-0.647485\pi$
$541$	−6.08511e6			−0.893871			−0.446936	+	0.894566i	$0.647485\pi$
$542$			2.55142e6i			0.373065i
$543$		−	5.51195e6i		−	0.802243i
$544$	256143.			0.0371095
$545$	3.52205e6	−	4.25652e6i	0.507931	−	0.613851i
$546$	−540689.			−0.0776186
$547$		−	2.49034e6i		−	0.355870i	−0.984042	−	0.177935i	$-0.943058\pi$
$547$		−	2.49034e6i		−	0.355870i	0.984042	−	0.177935i	$-0.0569416\pi$
$548$			1.23685e7i			1.75941i
$549$	−3.32870e6			−0.471350
$550$	489342.	−	93240.4i	0.0689773	−	0.0131431i
$551$	6.75698e6			0.948143
$552$		−	141673.i		−	0.0197897i
$553$			7.88922e6i			1.09704i
$554$	2.21181e6			0.306178
$555$	4.63320e6	−	5.59937e6i	0.638481	−	0.771626i
$556$	−1.14540e7			−1.57133
$557$			5.36235e6i			0.732347i	0.930547	+	0.366173i	$0.119332\pi$
$557$			5.36235e6i			0.732347i	−0.930547	+	0.366173i	$0.880668\pi$
$558$			8929.21i			0.00121403i
$559$	−734300.			−0.0993903
$560$	3.24167e6	+	2.68231e6i	0.436816	+	0.361443i
$561$	−74217.9			−0.00995638
$562$		−	2.19261e6i		−	0.292833i
$563$			479316.i			0.0637310i	0.999492	+	0.0318655i	$0.0101448\pi$
$563$			479316.i			0.0637310i	−0.999492	+	0.0318655i	$0.989855\pi$
$564$	−4.03054e6			−0.533538
$565$	−519201.	−	429612.i	−0.0684249	−	0.0566181i
$566$	696978.			0.0914488
$567$		−	573947.i		−	0.0749746i
$568$			3.90768e6i			0.508215i
$569$	−3.08333e6			−0.399245			−0.199623	−	0.979873i	$-0.563972\pi$
$569$	−3.08333e6			−0.399245			−0.199623	+	0.979873i	$0.563972\pi$
$570$	−671324.	+	811317.i	−0.0865456	+	0.104593i
$571$	−5.85646e6			−0.751701			−0.375850	−	0.926680i	$-0.622649\pi$
$571$	−5.85646e6			−0.751701			−0.375850	+	0.926680i	$0.622649\pi$
$572$		−	1.90897e6i		−	0.243955i
$573$		−	588670.i		−	0.0749007i
$574$	708982.			0.0898164
$575$	−589101.	+	112249.i	−0.0743054	+	0.0141583i
$576$	−1.82909e6			−0.229710
$577$		−	5.66144e6i		−	0.707925i	−0.935260	−	0.353963i	$-0.884834\pi$
$577$		−	5.66144e6i		−	0.707925i	0.935260	−	0.353963i	$-0.115166\pi$
$578$			1.86442e6i			0.232126i
$579$	−5.94945e6			−0.737531
$580$	−4.58706e6	+	5.54362e6i	−0.566193	+	0.684263i
$581$	−949753.			−0.116727
$582$			1.15003e6i			0.140735i
$583$		−	1.32355e6i		−	0.161276i
$584$	−603562.			−0.0732301
$585$	−1.81859e6	−	1.50479e6i	−0.219707	−	0.181796i
$586$	−1.54909e6			−0.186352
$587$		−	1.39978e7i		−	1.67674i	−0.545104	−	0.838368i	$-0.683510\pi$
$587$		−	1.39978e7i		−	1.67674i	0.545104	−	0.838368i	$-0.316490\pi$
$588$		−	2.49350e6i		−	0.297417i
$589$	−132943.			−0.0157899
$590$	−913460.	−	755842.i	−0.108034	−	0.0893925i
$591$	−5.31167e6			−0.625551
$592$		−	1.24288e7i		−	1.45755i
$593$			1.27936e7i			1.49402i	0.664810	+	0.747012i	$0.268512\pi$
$593$			1.27936e7i			1.49402i	−0.664810	+	0.747012i	$0.731488\pi$
$594$	−116208.			−0.0135135
$595$	212467.	−	256773.i	0.0246036	−	0.0297343i
$596$	8.21124e6			0.946876
$597$		−	3.08475e6i		−	0.354229i
$598$		−	131791.i		−	0.0150707i
$599$	1.21733e7			1.38625			0.693125	−	0.720818i	$-0.256234\pi$
$599$	1.21733e7			1.38625			0.693125	+	0.720818i	$0.256234\pi$
$600$	−431819.	−	2.26626e6i	−0.0489692	−	0.256999i
$601$	−6.74801e6			−0.762060			−0.381030	−	0.924563i	$-0.624431\pi$
$601$	−6.74801e6			−0.762060			−0.381030	+	0.924563i	$0.624431\pi$
$602$		−	162336.i		−	0.0182568i
$603$			101576.i			0.0113762i
$604$	−4.44125e6			−0.495351
$605$	−521770.	+	630577.i	−0.0579550	+	0.0700406i
$606$	−661020.			−0.0731195
$607$			1.16658e7i			1.28512i	0.766234	+	0.642561i	$0.222128\pi$
$607$			1.16658e7i			1.28512i	−0.766234	+	0.642561i	$0.777872\pi$
$608$			5.97120e6i			0.655092i
$609$	−3.34840e6			−0.365843
$610$	−2.33173e6	−	1.92939e6i	−0.253719	−	0.209940i
$611$	−7.71382e6			−0.835923
$612$			167070.i			0.0180310i
$613$			1.36615e7i			1.46841i	0.678928	+	0.734204i	$0.262445\pi$
$613$			1.36615e7i			1.46841i	−0.678928	+	0.734204i	$0.737555\pi$
$614$	−2.01681e6			−0.215895
$615$	2.38464e6	+	1.97316e6i	0.254234	+	0.210366i
$616$	868258.			0.0921928
$617$			1.15742e7i			1.22399i	0.790862	+	0.611995i	$0.209633\pi$
$617$			1.15742e7i			1.22399i	−0.790862	+	0.611995i	$0.790367\pi$
$618$		−	1.27423e6i		−	0.134207i
$619$	−9.22658e6			−0.967863			−0.483932	−	0.875106i	$-0.660792\pi$
$619$	−9.22658e6			−0.967863			−0.483932	+	0.875106i	$0.660792\pi$
$620$	90250.1	−	109070.i	0.00942906	−	0.0113953i
$621$	139898.			0.0145574
$622$		−	1.47050e6i		−	0.152402i
$623$			9.87366e6i			1.01920i
$624$	−4.03667e6			−0.415013
$625$	−9.08136e6	+	3.59115e6i	−0.929931	+	0.367734i
$626$	1.13902e6			0.116170
$627$		−	1.73016e6i		−	0.175759i
$628$			1.10635e7i			1.11942i
$629$	−984487.			−0.0992164
$630$	332673.	−	402046.i	0.0333938	−	0.0403575i
$631$	1.03002e7			1.02985			0.514923	−	0.857237i	$-0.327821\pi$
$631$	1.03002e7			1.02985			0.514923	+	0.857237i	$0.327821\pi$
$632$		−	7.39764e6i		−	0.736717i
$633$			1.93189e6i			0.191635i
$634$	2.37929e6			0.235085
$635$	−2.49601e6	−	2.06532e6i	−0.245647	−	0.203261i
$636$	−2.97941e6			−0.292070
$637$		−	4.77217e6i		−	0.465980i
$638$			677954.i			0.0659399i
$639$	−3.85871e6			−0.373844
$640$	−6.46114e6	−	5.34626e6i	−0.623532	−	0.515941i
$641$	−3.06165e6			−0.294313			−0.147157	−	0.989113i	$-0.547012\pi$
$641$	−3.06165e6			−0.294313			−0.147157	+	0.989113i	$0.547012\pi$
$642$			304399.i			0.0291478i
$643$			1.62044e6i			0.154563i	0.997009	+	0.0772813i	$0.0246240\pi$
$643$			1.62044e6i			0.154563i	−0.997009	+	0.0772813i	$0.975376\pi$
$644$	−508064.			−0.0482729
$645$	451797.	−	546012.i	0.0427606	−	0.0516777i
$646$	142647.			0.0134487
$647$			1.57992e6i			0.148380i	0.997244	+	0.0741900i	$0.0236371\pi$
$647$			1.57992e6i			0.148380i	−0.997244	+	0.0741900i	$0.976363\pi$
$648$			538185.i			0.0503494i
$649$	1.94799e6			0.181541
$650$	−401698.	−	2.10818e6i	−0.0372921	−	0.195716i
$651$	65879.6			0.00609254
$652$			505272.i			0.0465486i
$653$		−	1.29080e6i		−	0.118462i	−0.998244	−	0.0592308i	$-0.981135\pi$
$653$		−	1.29080e6i		−	0.118462i	0.998244	−	0.0592308i	$-0.0188648\pi$
$654$	−1.17179e6			−0.107129
$655$	4.43155e6	−	5.35568e6i	0.403601	−	0.487766i
$656$	5.29311e6			0.480232
$657$		−	595999.i		−	0.0538681i
$658$		−	1.70534e6i		−	0.153549i
$659$	−1.44401e7			−1.29525			−0.647627	−	0.761957i	$-0.724239\pi$
$659$	−1.44401e7			−1.29525			−0.647627	+	0.761957i	$0.724239\pi$
$660$	1.41947e6	+	1.17454e6i	0.126843	+	0.104956i
$661$	8.80403e6			0.783751			0.391875	−	0.920018i	$-0.371826\pi$
$661$	8.80403e6			0.783751			0.391875	+	0.920018i	$0.371826\pi$
$662$			2.44645e6i			0.216966i
$663$			319745.i			0.0282501i
$664$	890574.			0.0783880
$665$	5.98589e6	+	4.95302e6i	0.524898	+	0.434326i
$666$	−1.54147e6			−0.134664
$667$		−	816163.i		−	0.0710334i
$668$			1.72081e7i			1.49208i
$669$	1.06872e6			0.0923207
$670$	−58875.5	+	71153.1i	−0.00506697	+	0.00612360i
$671$	4.97250e6			0.426352
$672$		−	2.95901e6i		−	0.252769i
$673$		−	1.43891e7i		−	1.22461i	−0.790623	−	0.612303i	$-0.790243\pi$
$673$		−	1.43891e7i		−	1.22461i	0.790623	−	0.612303i	$-0.209757\pi$
$674$	−2.87286e6			−0.243593
$675$	2.23786e6	−	426408.i	0.189049	−	0.0360218i
$676$	3.01274e6			0.253569
$677$			1.21710e7i			1.02060i	0.859997	+	0.510299i	$0.170465\pi$
$677$			1.21710e7i			1.02060i	−0.859997	+	0.510299i	$0.829535\pi$
$678$			142933.i			0.0119415i
$679$	8.48489e6			0.706272
$680$	−199228.	+	240774.i	−0.0165226	+	0.0199681i
$681$	19648.4			0.00162353
$682$		−	13338.7i		−	0.00109813i
$683$			5.96383e6i			0.489186i	0.969626	+	0.244593i	$0.0786543\pi$
$683$			5.96383e6i			0.489186i	−0.969626	+	0.244593i	$0.921346\pi$
$684$	−3.89473e6			−0.318300
$685$	−1.76017e7	−	1.45645e7i	−1.43327	−	1.18596i
$686$	2.99194e6			0.242741
$687$			1.11333e6i			0.0899982i
$688$		−	1.21197e6i		−	0.0976158i
$689$	−5.70212e6			−0.457602
$690$	97997.5	+	81088.0i	0.00783596	+	0.00648386i
$691$	−1.10524e7			−0.880565			−0.440283	−	0.897859i	$-0.645122\pi$
$691$	−1.10524e7			−0.880565			−0.440283	+	0.897859i	$0.645122\pi$
$692$			1.67121e7i			1.32668i
$693$			857378.i			0.0678171i
$694$	−3.42434e6			−0.269885
$695$	1.34875e7	−	1.63001e7i	1.05918	−	1.28005i
$696$	3.13977e6			0.245682
$697$		−	419269.i		−	0.0326897i
$698$		−	1.54422e6i		−	0.119969i
$699$	−1.04928e7			−0.812270
$700$	−8.12719e6	+	1.54857e6i	−0.626896	+	0.119450i
$701$	−9.86637e6			−0.758337			−0.379168	−	0.925328i	$-0.623790\pi$
$701$	−9.86637e6			−0.758337			−0.379168	+	0.925328i	$0.623790\pi$
$702$			500645.i			0.0383431i
$703$		−	2.29503e7i		−	1.75146i
$704$	2.73235e6			0.207780
$705$	4.74612e6	−	5.73585e6i	0.359639	−	0.434635i
$706$	2.07995e6			0.157051
$707$			4.87700e6i			0.366948i
$708$		−	4.38506e6i		−	0.328770i
$709$	1.65852e7			1.23910			0.619550	−	0.784957i	$-0.287315\pi$
$709$	1.65852e7			1.23910			0.619550	+	0.784957i	$0.287315\pi$
$710$	−2.70300e6	−	2.23659e6i	−0.201233	−	0.166510i
$711$	7.30495e6			0.541930
$712$		−	9.25844e6i		−	0.684444i
$713$			16058.0i			0.00118295i
$714$	−70688.1			−0.00518921
$715$	2.71665e6	+	2.24789e6i	0.198733	+	0.164441i
$716$	5.44646e6			0.397038
$717$			6.93557e6i			0.503830i
$718$		−	4.20940e6i		−	0.304725i
$719$	1.70621e6			0.123086			0.0615430	−	0.998104i	$-0.480398\pi$
$719$	1.70621e6			0.123086			0.0615430	+	0.998104i	$0.480398\pi$
$720$	2.48366e6	−	3.00159e6i	0.178551	−	0.215784i
$721$	−9.40126e6			−0.673516
$722$			63333.1i			0.00452156i
$723$			1.28286e7i			0.912715i
$724$	1.85351e7			1.31416
$725$	−2.48766e6	−	1.30557e7i	−0.175770	−	0.922474i
$726$	173594.			0.0122234
$727$			4.79877e6i			0.336739i	0.985724	+	0.168370i	$0.0538502\pi$
$727$			4.79877e6i			0.336739i	−0.985724	+	0.168370i	$0.946150\pi$
$728$		−	3.74063e6i		−	0.261587i
$729$	−531441.			−0.0370370
$730$	345454.	−	417493.i	0.0239929	−	0.0289962i
$731$	−96000.4			−0.00664476
$732$		−	1.11935e7i		−	0.772123i
$733$			2.10050e7i			1.44398i	0.691902	+	0.721991i	$0.256773\pi$
$733$			2.10050e7i			1.44398i	−0.691902	+	0.721991i	$0.743227\pi$
$734$	−3.32048e6			−0.227489
$735$	3.54849e6	+	2.93620e6i	0.242285	+	0.200478i
$736$	721250.			0.0490785
$737$		−	151737.i		−	0.0102901i
$738$		−	656475.i		−	0.0443688i
$739$	1.45144e7			0.977660			0.488830	−	0.872379i	$-0.337424\pi$
$739$	1.45144e7			0.977660			0.488830	+	0.872379i	$0.337424\pi$
$740$	1.88291e7	+	1.55801e7i	1.26401	+	1.04590i
$741$	−7.45390e6			−0.498698
$742$		−	1.26060e6i		−	0.0840560i
$743$		−	1.33510e7i		−	0.887245i	−0.896214	−	0.443622i	$-0.853693\pi$
$743$		−	1.33510e7i		−	0.887245i	0.896214	−	0.443622i	$-0.146307\pi$
$744$	−61774.7			−0.00409146
$745$	−9.66907e6	+	1.16854e7i	−0.638255	+	0.771353i
$746$	2.19848e6			0.144636
$747$			879414.i			0.0576623i
$748$		−	249573.i		−	0.0163096i
$749$	2.24585e6			0.146277
$750$	1.81476e6	+	998419.i	0.117806	+	0.0648127i
$751$	1.03902e7			0.672242			0.336121	−	0.941819i	$-0.390885\pi$
$751$	1.03902e7			0.672242			0.336121	+	0.941819i	$0.390885\pi$
$752$		−	1.27317e7i		−	0.820999i
$753$			6.01870e6i			0.386826i
$754$	2.92076e6			0.187097
$755$	5.22976e6	−	6.32034e6i	0.333898	−	0.403527i
$756$	1.93002e6			0.122817
$757$		−	1.09141e7i		−	0.692227i	−0.938193	−	0.346113i	$-0.887501\pi$
$757$		−	1.09141e7i		−	0.692227i	0.938193	−	0.346113i	$-0.112499\pi$
$758$			4.12390e6i			0.260696i
$759$	−208983.			−0.0131676
$760$	−5.61291e6	−	4.64440e6i	−0.352496	−	0.291673i
$761$	1.04145e7			0.651894			0.325947	−	0.945388i	$-0.394317\pi$
$761$	1.04145e7			0.651894			0.325947	+	0.945388i	$0.394317\pi$
$762$			687136.i			0.0428702i
$763$			8.64548e6i			0.537623i
$764$	1.97953e6			0.122696
$765$	−237757.	−	196732.i	−0.0146886	−	0.0121540i
$766$	5.67763e6			0.349619
$767$		−	8.39232e6i		−	0.515103i
$768$		−	4.72472e6i		−	0.289050i
$769$	9.42825e6			0.574930			0.287465	−	0.957791i	$-0.407187\pi$
$769$	9.42825e6			0.574930			0.287465	+	0.957791i	$0.407187\pi$
$770$	−496955.	+	600587.i	−0.0302058	+	0.0365047i
$771$	9.78265e6			0.592681
$772$		−	2.00063e7i		−	1.20816i
$773$			1.18529e7i			0.713469i	0.934206	+	0.356734i	$0.116110\pi$
$773$			1.18529e7i			0.713469i	−0.934206	+	0.356734i	$0.883890\pi$
$774$	−150314.			−0.00901875
$775$	48944.5	+	256870.i	0.00292718	+	0.0153624i
$776$	−7.95620e6			−0.474298

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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	165.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.31741i q^{2} -9.00000i q^{3} +30.2644 q^{4} +(-35.6376 + 43.0693i) q^{5} +11.8567 q^{6} -87.4786i q^{7} +82.0279i q^{8} -81.0000 q^{9} +O(q^{10})\)	\(q+1.31741i q^{2} -9.00000i q^{3} +30.2644 q^{4} +(-35.6376 + 43.0693i) q^{5} +11.8567 q^{6} -87.4786i q^{7} +82.0279i q^{8} -81.0000 q^{9} +(-56.7399 - 46.9494i) q^{10} +121.000 q^{11} -272.380i q^{12} -521.292i q^{13} +115.245 q^{14} +(387.623 + 320.739i) q^{15} +860.397 q^{16} -68.1523i q^{17} -106.710i q^{18} +1588.76 q^{19} +(-1078.55 + 1303.47i) q^{20} -787.308 q^{21} +159.407i q^{22} -191.904i q^{23} +738.251 q^{24} +(-584.921 - 3069.77i) q^{25} +686.756 q^{26} +729.000i q^{27} -2647.49i q^{28} +4252.98 q^{29} +(-422.545 + 510.659i) q^{30} -83.6771 q^{31} +3758.39i q^{32} -1089.00i q^{33} +89.7846 q^{34} +(3767.64 + 3117.53i) q^{35} -2451.42 q^{36} -14445.4i q^{37} +2093.06i q^{38} -4691.63 q^{39} +(-3532.88 - 2923.28i) q^{40} +6151.94 q^{41} -1037.21i q^{42} -1408.62i q^{43} +3662.00 q^{44} +(2886.65 - 3488.61i) q^{45} +252.816 q^{46} -14797.5i q^{47} -7743.57i q^{48} +9154.49 q^{49} +(4044.15 - 770.582i) q^{50} -613.371 q^{51} -15776.6i q^{52} -10938.4i q^{53} -960.393 q^{54} +(-4312.15 + 5211.38i) q^{55} +7175.69 q^{56} -14298.9i q^{57} +5602.92i q^{58} +16099.1 q^{59} +(11731.2 + 9706.97i) q^{60} +41095.0 q^{61} -110.237i q^{62} +7085.77i q^{63} +22581.4 q^{64} +(22451.7 + 18577.6i) q^{65} +1434.66 q^{66} -1254.02i q^{67} -2062.59i q^{68} -1727.14 q^{69} +(-4107.07 + 4963.53i) q^{70} +47638.4 q^{71} -6644.26i q^{72} +7358.01i q^{73} +19030.5 q^{74} +(-27627.9 + 5264.29i) q^{75} +48083.1 q^{76} -10584.9i q^{77} -6180.81i q^{78} -90184.5 q^{79} +(-30662.5 + 37056.7i) q^{80} +6561.00 q^{81} +8104.64i q^{82} -10857.0i q^{83} -23827.4 q^{84} +(2935.27 + 2428.79i) q^{85} +1855.73 q^{86} -38276.8i q^{87} +9925.37i q^{88} -112869. q^{89} +(4595.93 + 3802.90i) q^{90} -45601.9 q^{91} -5807.86i q^{92} +753.094i q^{93} +19494.4 q^{94} +(-56619.8 + 68426.9i) q^{95} +33825.5 q^{96} +96993.9i q^{97} +12060.2i q^{98} -9801.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 418 q^{4} - 98 q^{5} + 234 q^{6} - 2106 q^{9}+O(q^{10}) \) 26 * q - 418 * q^4 - 98 * q^5 + 234 * q^6 - 2106 * q^9	\( 26 q - 418 q^{4} - 98 q^{5} + 234 q^{6} - 2106 q^{9} + 236 q^{10} + 3146 q^{11} + 1220 q^{14} + 7002 q^{16} - 540 q^{19} + 4930 q^{20} + 5472 q^{21} - 7182 q^{24} + 218 q^{25} + 5304 q^{26} - 23904 q^{29} + 12114 q^{30} + 38192 q^{31} + 2604 q^{34} - 11988 q^{35} + 33858 q^{36} - 17748 q^{39} - 41096 q^{40} + 70368 q^{41} - 50578 q^{44} + 7938 q^{45} - 8240 q^{46} - 29114 q^{49} - 133876 q^{50} + 26568 q^{51} - 18954 q^{54} - 11858 q^{55} + 119604 q^{56} + 18384 q^{59} - 14148 q^{60} + 10876 q^{61} - 213114 q^{64} - 117068 q^{65} + 28314 q^{66} - 163512 q^{69} - 58660 q^{70} + 203400 q^{71} - 27352 q^{74} - 35352 q^{75} + 279932 q^{76} - 187908 q^{79} - 256654 q^{80} + 170586 q^{81} - 196560 q^{84} + 37396 q^{85} + 741860 q^{86} + 36836 q^{89} - 19116 q^{90} + 349072 q^{91} - 129040 q^{94} - 208284 q^{95} + 209898 q^{96} - 254826 q^{99}+O(q^{100}) \) 26 * q - 418 * q^4 - 98 * q^5 + 234 * q^6 - 2106 * q^9 + 236 * q^10 + 3146 * q^11 + 1220 * q^14 + 7002 * q^16 - 540 * q^19 + 4930 * q^20 + 5472 * q^21 - 7182 * q^24 + 218 * q^25 + 5304 * q^26 - 23904 * q^29 + 12114 * q^30 + 38192 * q^31 + 2604 * q^34 - 11988 * q^35 + 33858 * q^36 - 17748 * q^39 - 41096 * q^40 + 70368 * q^41 - 50578 * q^44 + 7938 * q^45 - 8240 * q^46 - 29114 * q^49 - 133876 * q^50 + 26568 * q^51 - 18954 * q^54 - 11858 * q^55 + 119604 * q^56 + 18384 * q^59 - 14148 * q^60 + 10876 * q^61 - 213114 * q^64 - 117068 * q^65 + 28314 * q^66 - 163512 * q^69 - 58660 * q^70 + 203400 * q^71 - 27352 * q^74 - 35352 * q^75 + 279932 * q^76 - 187908 * q^79 - 256654 * q^80 + 170586 * q^81 - 196560 * q^84 + 37396 * q^85 + 741860 * q^86 + 36836 * q^89 - 19116 * q^90 + 349072 * q^91 - 129040 * q^94 - 208284 * q^95 + 209898 * q^96 - 254826 * q^99

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