LMFDB - Embedded newform 21.7.h.a.11.11

Newspace parameters

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	21.h (of order $6$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.83113575602$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.11
Character	$\chi$	$=$	21.11
Dual form			21.7.h.a.2.11

$q$-expansion

$f(q)$	$=$	$q+(7.42751 - 4.28827i) q^{2} +(6.70842 - 26.1533i) q^{3} +(4.77856 - 8.27670i) q^{4} +(88.3745 - 51.0231i) q^{5} +(-62.3258 - 223.022i) q^{6} +(-127.732 - 318.329i) q^{7} +466.932i q^{8} +(-638.994 - 350.895i) q^{9} +O(q^{10})$	\(q+(7.42751 - 4.28827i) q^{2} +(6.70842 - 26.1533i) q^{3} +(4.77856 - 8.27670i) q^{4} +(88.3745 - 51.0231i) q^{5} +(-62.3258 - 223.022i) q^{6} +(-127.732 - 318.329i) q^{7} +466.932i q^{8} +(-638.994 - 350.895i) q^{9} +(437.602 - 757.948i) q^{10} +(1435.62 + 828.858i) q^{11} +(-184.407 - 180.499i) q^{12} -278.963 q^{13} +(-2313.81 - 1816.64i) q^{14} +(-741.570 - 2653.57i) q^{15} +(2308.16 + 3997.85i) q^{16} +(4951.96 + 2859.02i) q^{17} +(-6250.87 + 133.906i) q^{18} +(2933.29 + 5080.60i) q^{19} -975.266i q^{20} +(-9182.25 + 1205.14i) q^{21} +14217.5 q^{22} +(-11371.0 + 6565.05i) q^{23} +(12211.8 + 3132.37i) q^{24} +(-2605.79 + 4513.37i) q^{25} +(-2072.00 + 1196.27i) q^{26} +(-13463.7 + 14357.9i) q^{27} +(-3245.09 - 463.951i) q^{28} -38808.9i q^{29} +(-16887.3 - 16529.4i) q^{30} +(6289.55 - 10893.8i) q^{31} +(8407.73 + 4854.20i) q^{32} +(31308.2 - 31986.0i) q^{33} +49041.0 q^{34} +(-27530.4 - 21614.9i) q^{35} +(-5957.72 + 3611.99i) q^{36} +(-38133.2 - 66048.7i) q^{37} +(43574.0 + 25157.5i) q^{38} +(-1871.40 + 7295.81i) q^{39} +(23824.3 + 41264.9i) q^{40} +57478.9i q^{41} +(-63033.2 + 48327.2i) q^{42} -2510.49 q^{43} +(13720.4 - 7921.49i) q^{44} +(-74374.6 + 1593.25i) q^{45} +(-56305.4 + 97523.9i) q^{46} +(-41606.0 + 24021.2i) q^{47} +(120041. - 33546.8i) q^{48} +(-85017.9 + 81321.9i) q^{49} +44697.4i q^{50} +(107993. - 110331. i) q^{51} +(-1333.04 + 2308.89i) q^{52} +(-21710.2 - 12534.4i) q^{53} +(-38431.4 + 164379. i) q^{54} +169163. q^{55} +(148638. - 59642.3i) q^{56} +(152552. - 42632.5i) q^{57} +(-166423. - 288253. i) q^{58} +(-34569.8 - 19958.9i) q^{59} +(-25506.5 - 6542.50i) q^{60} +(-73338.1 - 127025. i) q^{61} -107885. i q^{62} +(-30079.9 + 248231. i) q^{63} -212180. q^{64} +(-24653.2 + 14233.5i) q^{65} +(95376.7 - 371834. i) q^{66} +(-71608.3 + 124029. i) q^{67} +(47326.5 - 27324.0i) q^{68} +(95416.5 + 341431. i) q^{69} +(-297173. - 42486.8i) q^{70} +619806. i q^{71} +(163844. - 298367. i) q^{72} +(254284. - 440433. i) q^{73} +(-566469. - 327051. i) q^{74} +(100559. + 98427.7i) q^{75} +56067.5 q^{76} +(80474.0 - 562873. i) q^{77} +(17386.6 + 62214.7i) q^{78} +(161568. + 279844. i) q^{79} +(407965. + 235539. i) q^{80} +(285186. + 448440. i) q^{81} +(246485. + 426925. i) q^{82} -701690. i q^{83} +(-33903.3 + 81757.6i) q^{84} +583503. q^{85} +(-18646.7 + 10765.7i) q^{86} +(-1.01498e6 - 260346. i) q^{87} +(-387020. + 670338. i) q^{88} +(-630238. + 363868. i) q^{89} +(-545585. + 330772. i) q^{90} +(35632.6 + 88802.0i) q^{91} +125486. i q^{92} +(-242717. - 237573. i) q^{93} +(-206019. + 356835. i) q^{94} +(518456. + 299331. i) q^{95} +(183356. - 187326. i) q^{96} +1.47695e6 q^{97} +(-282741. + 968598. i) q^{98} +(-626513. - 1.03339e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - q^{3} + 382 q^{4} - 356 q^{6} + 1120 q^{7} + 1031 q^{9}+O(q^{10}) $ 28 * q - q^3 + 382 * q^4 - 356 * q^6 + 1120 * q^7 + 1031 * q^9	$ 28 q - q^{3} + 382 q^{4} - 356 q^{6} + 1120 q^{7} + 1031 q^{9} - 930 q^{10} - 404 q^{12} + 3632 q^{13} + 5450 q^{15} - 13706 q^{16} + 1612 q^{18} + 6830 q^{19} - 11333 q^{21} - 27348 q^{22} - 54498 q^{24} - 7640 q^{25} + 13268 q^{27} + 88522 q^{28} + 32380 q^{30} + 69410 q^{31} - 85459 q^{33} - 31344 q^{34} + 399028 q^{36} - 71830 q^{37} + 104570 q^{39} + 230250 q^{40} - 467782 q^{42} - 498904 q^{43} - 85375 q^{45} - 342660 q^{46} - 324728 q^{48} + 395668 q^{49} + 42177 q^{51} + 218000 q^{52} - 402122 q^{54} + 231660 q^{55} + 786782 q^{57} + 459522 q^{58} + 1021150 q^{60} + 153158 q^{61} + 179011 q^{63} - 1399412 q^{64} + 80896 q^{66} - 977098 q^{67} - 1520742 q^{69} - 139650 q^{70} - 1001352 q^{72} - 488350 q^{73} + 1434610 q^{75} + 6196280 q^{76} + 245176 q^{78} + 380762 q^{79} + 893531 q^{81} - 3665004 q^{82} + 1231496 q^{84} - 912540 q^{85} + 1452416 q^{87} - 1522482 q^{88} - 11713820 q^{90} - 1529416 q^{91} - 1690071 q^{93} - 3034044 q^{94} + 7549346 q^{96} + 7212176 q^{97} + 435866 q^{99}+O(q^{100}) $ 28 * q - q^3 + 382 * q^4 - 356 * q^6 + 1120 * q^7 + 1031 * q^9 - 930 * q^10 - 404 * q^12 + 3632 * q^13 + 5450 * q^15 - 13706 * q^16 + 1612 * q^18 + 6830 * q^19 - 11333 * q^21 - 27348 * q^22 - 54498 * q^24 - 7640 * q^25 + 13268 * q^27 + 88522 * q^28 + 32380 * q^30 + 69410 * q^31 - 85459 * q^33 - 31344 * q^34 + 399028 * q^36 - 71830 * q^37 + 104570 * q^39 + 230250 * q^40 - 467782 * q^42 - 498904 * q^43 - 85375 * q^45 - 342660 * q^46 - 324728 * q^48 + 395668 * q^49 + 42177 * q^51 + 218000 * q^52 - 402122 * q^54 + 231660 * q^55 + 786782 * q^57 + 459522 * q^58 + 1021150 * q^60 + 153158 * q^61 + 179011 * q^63 - 1399412 * q^64 + 80896 * q^66 - 977098 * q^67 - 1520742 * q^69 - 139650 * q^70 - 1001352 * q^72 - 488350 * q^73 + 1434610 * q^75 + 6196280 * q^76 + 245176 * q^78 + 380762 * q^79 + 893531 * q^81 - 3665004 * q^82 + 1231496 * q^84 - 912540 * q^85 + 1452416 * q^87 - 1522482 * q^88 - 11713820 * q^90 - 1529416 * q^91 - 1690071 * q^93 - 3034044 * q^94 + 7549346 * q^96 + 7212176 * q^97 + 435866 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	7.42751	−	4.28827i	0.928438	−	0.536034i	0.0421209	−	0.999113i	$-0.486589\pi$
$2$	7.42751	−	4.28827i	0.928438	−	0.536034i	0.886317	+	0.463079i	$0.153255\pi$
$3$	6.70842	−	26.1533i	0.248460	−	0.968642i
$3$	6.70842	−	26.1533i	0.248460	−	0.968642i
$4$	4.77856	−	8.27670i	0.0746649	−	0.129323i
$5$	88.3745	−	51.0231i	0.706996	−	0.408185i	−0.102952	−	0.994686i	$-0.532829\pi$
$5$	88.3745	−	51.0231i	0.706996	−	0.408185i	0.809948	+	0.586502i	$0.199495\pi$
$6$	−62.3258	−	223.022i	−0.288545	−	1.03251i
$7$	−127.732	−	318.329i	−0.372398	−	0.928073i
$7$	−127.732	−	318.329i	−0.372398	−	0.928073i
$8$			466.932i			0.911976i
$9$	−638.994	−	350.895i	−0.876535	−	0.481338i
$10$	437.602	−	757.948i	0.437602	−	0.757948i
$11$	1435.62	+	828.858i	1.07861	+	0.622733i	0.930520	−	0.366242i	$-0.119356\pi$
$11$	1435.62	+	828.858i	1.07861	+	0.622733i	0.148085	+	0.988975i	$0.452689\pi$
$12$	−184.407	−	180.499i	−0.106717	−	0.104455i
$13$	−278.963			−0.126974			−0.0634872	−	0.997983i	$-0.520222\pi$
$13$	−278.963			−0.126974			−0.0634872	+	0.997983i	$0.520222\pi$
$14$	−2313.81	−	1816.64i	−0.843227	−	0.662041i
$15$	−741.570	−	2653.57i	−0.219724	−	0.786244i
$16$	2308.16	+	3997.85i	0.563515	+	0.976037i
$17$	4951.96	+	2859.02i	1.00793	+	0.581929i	0.910585	−	0.413322i	$-0.135631\pi$
$17$	4951.96	+	2859.02i	1.00793	+	0.581929i	0.0973456	+	0.995251i	$0.468965\pi$
$18$	−6250.87	+	133.906i	−1.07182	+	0.0229605i
$19$	2933.29	+	5080.60i	0.427655	+	0.740721i	0.996664	−	0.0816105i	$-0.0260063\pi$
$19$	2933.29	+	5080.60i	0.427655	+	0.740721i	−0.569009	+	0.822331i	$0.692673\pi$
$20$		−	975.266i		−	0.121908i
$21$	−9182.25	+	1205.14i	−0.991497	+	0.130131i
$22$	14217.5			1.33522
$23$	−11371.0	+	6565.05i	−0.934577	+	0.539578i	−0.888256	−	0.459348i	$-0.848083\pi$
$23$	−11371.0	+	6565.05i	−0.934577	+	0.539578i	−0.0463208	+	0.998927i	$0.514750\pi$
$24$	12211.8	+	3132.37i	0.883379	+	0.226590i
$25$	−2605.79	+	4513.37i	−0.166771	+	0.288855i
$26$	−2072.00	+	1196.27i	−0.117888	+	0.0680626i
$27$	−13463.7	+	14357.9i	−0.684028	+	0.729456i
$28$	−3245.09	−	463.951i	−0.147827	−	0.0211348i
$29$		−	38808.9i		−	1.59124i	−0.605793	−	0.795622i	$-0.707144\pi$
$29$		−	38808.9i		−	1.59124i	0.605793	−	0.795622i	$-0.292856\pi$
$30$	−16887.3	−	16529.4i	−0.625454	−	0.612199i
$31$	6289.55	−	10893.8i	0.211123	−	0.365675i	−0.740944	−	0.671567i	$-0.765621\pi$
$31$	6289.55	−	10893.8i	0.211123	−	0.365675i	0.952066	+	0.305892i	$0.0989547\pi$
$32$	8407.73	+	4854.20i	0.256584	+	0.148139i
$33$	31308.2	−	31986.0i	0.871196	−	0.890058i
$34$	49041.0			1.24774
$35$	−27530.4	−	21614.9i	−0.642109	−	0.504138i
$36$	−5957.72	+	3611.99i	−0.127695	+	0.0774175i
$37$	−38133.2	−	66048.7i	−0.752832	−	1.30394i	−0.946445	−	0.322866i	$-0.895354\pi$
$37$	−38133.2	−	66048.7i	−0.752832	−	1.30394i	0.193613	−	0.981078i	$-0.437979\pi$
$38$	43574.0	+	25157.5i	0.794103	+	0.458476i
$39$	−1871.40	+	7295.81i	−0.0315481	+	0.122993i
$40$	23824.3	+	41264.9i	0.372255	+	0.644764i
$41$			57478.9i			0.833983i	0.908910	+	0.416991i	$0.136916\pi$
$41$			57478.9i			0.833983i	−0.908910	+	0.416991i	$0.863084\pi$
$42$	−63033.2	+	48327.2i	−0.850789	+	0.652294i
$43$	−2510.49			−0.0315757			−0.0157879	−	0.999875i	$-0.505026\pi$
$43$	−2510.49			−0.0315757			−0.0157879	+	0.999875i	$0.505026\pi$
$44$	13720.4	−	7921.49i	0.161068	−	0.0929927i
$45$	−74374.6	+	1593.25i	−0.816182	+	0.0174842i
$46$	−56305.4	+	97523.9i	−0.578465	+	1.00193i
$47$	−41606.0	+	24021.2i	−0.400739	+	0.231367i	−0.686803	−	0.726844i	$-0.740986\pi$
$47$	−41606.0	+	24021.2i	−0.400739	+	0.231367i	0.286064	+	0.958211i	$0.407653\pi$
$48$	120041.	−	33546.8i	1.08544	−	0.303338i
$49$	−85017.9	+	81321.9i	−0.722640	+	0.691224i
$50$			44697.4i			0.357579i
$51$	107993.	−	110331.i	0.814111	−	0.831738i
$52$	−1333.04	+	2308.89i	−0.00948054	+	0.0164208i
$53$	−21710.2	−	12534.4i	−0.145826	−	0.0841928i	0.425312	−	0.905047i	$-0.360165\pi$
$53$	−21710.2	−	12534.4i	−0.145826	−	0.0841928i	−0.571138	+	0.820854i	$0.693498\pi$
$54$	−38431.4	+	164379.i	−0.244064	+	1.04392i
$55$	169163.			1.01676
$56$	148638.	−	59642.3i	0.846381	−	0.339618i
$57$	152552.	−	42632.5i	0.823749	−	0.230206i
$58$	−166423.	−	288253.i	−0.852961	−	1.47737i
$59$	−34569.8	−	19958.9i	−0.168322	−	0.0971808i	0.413472	−	0.910517i	$-0.364316\pi$
$59$	−34569.8	−	19958.9i	−0.168322	−	0.0971808i	−0.581794	+	0.813336i	$0.697649\pi$
$60$	−25506.5	−	6542.50i	−0.118086	−	0.0302893i
$61$	−73338.1	−	127025.i	−0.323102	−	0.559630i	0.658024	−	0.752997i	$-0.271392\pi$
$61$	−73338.1	−	127025.i	−0.323102	−	0.559630i	−0.981126	+	0.193367i	$0.938059\pi$
$62$		−	107885.i		−	0.452676i
$63$	−30079.9	+	248231.i	−0.120297	+	0.992738i
$64$	−212180.			−0.809401
$65$	−24653.2	+	14233.5i	−0.0897705	+	0.0518290i
$66$	95376.7	−	371834.i	0.331750	−	1.29335i
$67$	−71608.3	+	124029.i	−0.238089	+	0.412382i	−0.960166	−	0.279431i	$-0.909854\pi$
$67$	−71608.3	+	124029.i	−0.238089	+	0.412382i	0.722077	+	0.691813i	$0.243188\pi$
$68$	47326.5	−	27324.0i	0.150514	−	0.0868994i
$69$	95416.5	+	341431.i	0.290453	+	1.03933i
$70$	−297173.	−	42486.8i	−0.866393	−	0.123868i
$71$			619806.i			1.73173i	0.500277	+	0.865866i	$0.333232\pi$
$71$			619806.i			1.73173i	−0.500277	+	0.865866i	$0.666768\pi$
$72$	163844.	−	298367.i	0.438968	−	0.799379i
$73$	254284.	−	440433.i	0.653657	−	1.13217i	−0.328571	−	0.944479i	$-0.606567\pi$
$73$	254284.	−	440433.i	0.653657	−	1.13217i	0.982229	−	0.187689i	$-0.0600996\pi$
$74$	−566469.	−	327051.i	−1.39792	−	0.807087i
$75$	100559.	+	98427.7i	0.238362	+	0.233310i
$76$	56067.5			0.127723
$77$	80474.0	−	562873.i	0.176272	−	1.23293i
$78$	17386.6	+	62214.7i	0.0366379	+	0.131102i
$79$	161568.	+	279844.i	0.327698	+	0.567590i	0.982055	−	0.188596i	$-0.0603937\pi$
$79$	161568.	+	279844.i	0.327698	+	0.567590i	−0.654356	+	0.756186i	$0.727060\pi$
$80$	407965.	+	235539.i	0.796806	+	0.460036i
$81$	285186.	+	448440.i	0.536628	+	0.843819i
$82$	246485.	+	426925.i	0.447043	+	0.774302i
$83$		−	701690.i		−	1.22719i	−0.789622	−	0.613594i	$-0.789723\pi$
$83$		−	701690.i		−	1.22719i	0.789622	−	0.613594i	$-0.210277\pi$
$84$	−33903.3	+	81757.6i	−0.0572011	+	0.137940i
$85$	583503.			0.950138
$86$	−18646.7	+	10765.7i	−0.0293161	+	0.0169257i
$87$	−1.01498e6	−	260346.i	−1.54135	−	0.395361i
$88$	−387020.	+	670338.i	−0.567918	+	0.983662i
$89$	−630238.	+	363868.i	−0.893994	+	0.516148i	−0.875247	−	0.483676i	$-0.839301\pi$
$89$	−630238.	+	363868.i	−0.893994	+	0.516148i	−0.0187473	+	0.999824i	$0.505968\pi$
$90$	−545585.	+	330772.i	−0.748402	+	0.453734i
$91$	35632.6	+	88802.0i	0.0472850	+	0.117842i
$92$			125486.i			0.161150i
$93$	−242717.	−	237573.i	−0.301753	−	0.295358i
$94$	−206019.	+	356835.i	−0.248041	+	0.429620i
$95$	518456.	+	299331.i	0.604702	+	0.349125i
$96$	183356.	−	187326.i	0.207244	−	0.211731i
$97$	1.47695e6			1.61827			0.809135	−	0.587623i	$-0.199936\pi$
$97$	1.47695e6			1.61827			0.809135	+	0.587623i	$0.199936\pi$
$98$	−282741.	+	968598.i	−0.300407	+	1.02912i
$99$	−626513.	−	1.03339e6i	−0.645691	−	1.06502i
$100$	24903.9	+	43134.8i	0.0249039	+	0.0431348i
$101$	1.46750e6	+	847260.i	1.42434	+	0.822343i	0.996666	−	0.0815908i	$-0.0260001\pi$
$101$	1.46750e6	+	847260.i	1.42434	+	0.822343i	0.427673	+	0.903933i	$0.359333\pi$
$102$	328987.	−	1.28259e6i	0.310012	−	1.20861i
$103$	−603539.	−	1.04536e6i	−0.552323	−	0.956652i	−0.998106	−	0.0615111i	$-0.980408\pi$
$103$	−603539.	−	1.04536e6i	−0.552323	−	0.956652i	0.445783	−	0.895141i	$-0.352925\pi$
$104$		−	130257.i		−	0.115798i
$105$	−749987.	+	575011.i	−0.647867	+	0.496716i
$106$	−215003.			−0.180521
$107$	−1.05422e6	+	608652.i	−0.860554	+	0.496841i	−0.864198	−	0.503152i	$-0.832173\pi$
$107$	−1.05422e6	+	608652.i	−0.860554	+	0.496841i	0.00364376	+	0.999993i	$0.498840\pi$
$108$	54498.8	+	180045.i	0.0432629	+	0.142926i
$109$	530058.	−	918087.i	0.409302	−	0.708931i	−0.585510	−	0.810665i	$-0.699106\pi$
$109$	530058.	−	918087.i	0.409302	−	0.708931i	0.994812	+	0.101734i	$0.0324390\pi$
$110$	1.25646e6	−	725419.i	0.943999	−	0.545018i
$111$	−1.98321e6	+	554229.i	−1.45010	+	0.405247i
$112$	977805.	−	1.24541e6i	0.695982	−	0.886457i
$113$		−	1.93373e6i		−	1.34017i	−0.742283	−	0.670086i	$-0.766257\pi$
$113$		−	1.93373e6i		−	1.34017i	0.742283	−	0.670086i	$-0.233743\pi$
$114$	950265.	−	970839.i	0.641402	−	0.655289i
$115$	−669938.	+	1.16037e6i	−0.440495	+	0.762960i
$116$	−321209.	−	185450.i	−0.205785	−	0.118810i
$117$	178256.	+	97886.7i	0.111298	+	0.0611176i
$118$	−342357.			−0.208369
$119$	277583.	−	1.94154e6i	0.164722	−	1.15214i
$120$	1.23904e6	−	346263.i	0.717036	−	0.200383i
$121$	488230.	+	845638.i	0.275593	+	0.477341i
$122$	−1.08944e6	−	628988.i	−0.599961	−	0.346388i
$123$	1.50327e6	+	385593.i	0.807831	+	0.207211i
$124$	−60110.0	−	104114.i	−0.0315269	−	0.0546062i
$125$			2.12629e6i			1.08866i
$126$	841064.	+	1.97273e6i	0.420453	+	0.986179i
$127$	−1.73848e6			−0.848711			−0.424355	−	0.905496i	$-0.639499\pi$
$127$	−1.73848e6			−0.848711			−0.424355	+	0.905496i	$0.639499\pi$
$128$	−2.11406e6	+	1.22055e6i	−1.00806	+	0.582005i
$129$	−16841.4	+	65657.7i	−0.00784530	+	0.0305856i
$130$	−122075.	+	211439.i	−0.0555642	+	0.0962400i
$131$	382494.	−	220833.i	0.170142	−	0.0982313i	−0.412511	−	0.910953i	$-0.635348\pi$
$131$	382494.	−	220833.i	0.170142	−	0.0982313i	0.582653	+	0.812721i	$0.302015\pi$
$132$	−115131.	−	411975.i	−0.0500577	−	0.179122i
$133$	1.24263e6	−	1.58271e6i	0.528185	−	0.672738i
$134$			1.22830e6i			0.510495i
$135$	−457267.	+	1.95583e6i	−0.185853	+	0.794932i
$136$	−1.33497e6	+	2.31223e6i	−0.530706	+	0.919209i
$137$	397020.	+	229220.i	0.154401	+	0.0891436i	0.575210	−	0.818006i	$-0.304920\pi$
$137$	397020.	+	229220.i	0.154401	+	0.0891436i	−0.420809	+	0.907149i	$0.638254\pi$
$138$	2.17285e6	+	2.12681e6i	0.826786	+	0.809265i
$139$	−2.80243e6			−1.04349			−0.521747	−	0.853100i	$-0.674720\pi$
$139$	−2.80243e6			−1.04349			−0.521747	+	0.853100i	$0.674720\pi$
$140$	−310456.	+	124573.i	−0.113140	+	0.0453983i
$141$	349125.	+	1.24928e6i	0.124544	+	0.445659i
$142$	2.65790e6	+	4.60361e6i	0.928267	+	1.60781i
$143$	−400486.	−	231220.i	−0.136955	−	0.0790712i
$144$	−72074.7	−	3.36452e6i	−0.0241377	−	1.12677i
$145$	−1.98015e6	−	3.42972e6i	−0.649521	−	1.12500i
$146$		−	4.36175e6i		−	1.40153i
$147$	1.55650e6	+	2.76904e6i	0.490002	+	0.871721i
$148$	−728887.			−0.224841
$149$	1.24914e6	−	721194.i	0.377619	−	0.218019i	−0.299163	−	0.954202i	$-0.596707\pi$
$149$	1.24914e6	−	721194.i	0.377619	−	0.218019i	0.676782	+	0.736184i	$0.263374\pi$
$150$	1.16899e6	+	299849.i	0.346366	+	0.0888441i
$151$	−1.34562e6	+	2.33067e6i	−0.390832	+	0.676941i	−0.992560	−	0.121761i	$-0.961146\pi$
$151$	−1.34562e6	+	2.33067e6i	−0.390832	+	0.676941i	0.601727	+	0.798701i	$0.294479\pi$
$152$	−2.37230e6	+	1.36965e6i	−0.675520	+	0.390012i
$153$	−2.16106e6	−	3.56452e6i	−0.603383	−	0.995236i
$154$	−1.81603e6	−	4.52583e6i	−0.497234	−	1.23919i
$155$		−	1.28365e6i		−	0.344708i
$156$	51442.7	+	50352.5i	0.0135503	+	0.0132632i
$157$	2.76937e6	−	4.79669e6i	0.715619	−	1.23949i	−0.247102	−	0.968990i	$-0.579478\pi$
$157$	2.76937e6	−	4.79669e6i	0.715619	−	1.23949i	0.962720	−	0.270498i	$-0.0871885\pi$
$158$	2.40009e6	+	1.38570e6i	0.608495	+	0.351315i
$159$	−473457.	+	483708.i	−0.117785	+	0.120335i
$160$	990706.			0.241871
$161$	3.54229e6	+	2.78115e6i	0.848802	+	0.666418i
$162$	4.04125e6	+	2.10783e6i	0.950542	+	0.495783i
$163$	1.58521e6	+	2.74567e6i	0.366037	+	0.633994i	0.988942	−	0.148303i	$-0.0473812\pi$
$163$	1.58521e6	+	2.74567e6i	0.366037	+	0.633994i	−0.622905	+	0.782297i	$0.714048\pi$
$164$	475736.	+	274666.i	0.107854	+	0.0622693i
$165$	1.13482e6	−	4.42419e6i	0.252624	−	0.984877i
$166$	−3.00904e6	−	5.21181e6i	−0.657814	−	1.13937i
$167$			1.08256e6i			0.232435i	0.993224	+	0.116217i	$0.0370769\pi$
$167$			1.08256e6i			0.232435i	−0.993224	+	0.116217i	$0.962923\pi$
$168$	−562719.	−	4.28749e6i	−0.118676	−	0.904222i
$169$	−4.74899e6			−0.983877
$170$	4.33397e6	−	2.50222e6i	0.882144	−	0.509306i
$171$	−91595.0	−	4.27575e6i	−0.0183182	−	0.855115i
$172$	−11996.5	+	20778.6i	−0.00235760	+	0.00408348i
$173$	−4.10478e6	+	2.36989e6i	−0.792777	+	0.457710i	−0.840939	−	0.541129i	$-0.817997\pi$
$173$	−4.10478e6	+	2.36989e6i	−0.792777	+	0.457710i	0.0481622	+	0.998840i	$0.484664\pi$
$174$	−8.65521e6	+	2.41879e6i	−1.64297	+	0.459146i
$175$	1.76958e6	+	252997.i	0.330184	+	0.0472065i
$176$			7.65254e6i			1.40368i
$177$	−753901.	+	770223.i	−0.135955	+	0.138898i
$178$	−3.12073e6	+	5.40527e6i	−0.553346	+	0.958423i
$179$	−1.44503e6	−	834290.i	−0.251952	−	0.145465i	0.368706	−	0.929546i	$-0.379801\pi$
$179$	−1.44503e6	−	834290.i	−0.251952	−	0.145465i	−0.620658	+	0.784082i	$0.713134\pi$
$180$	−342216.	+	623190.i	−0.0586791	+	0.106857i
$181$	9.84153e6			1.65969			0.829845	−	0.557994i	$-0.188429\pi$
$181$	9.84153e6			1.65969			0.829845	+	0.557994i	$0.188429\pi$
$182$	645468.	+	506775.i	0.107068	+	0.0840623i
$183$	−3.81412e6	+	1.06590e6i	−0.622359	+	0.173925i
$184$	−3.06543e6	−	5.30948e6i	−0.492083	−	0.852312i
$185$	−6.74001e6	−	3.89135e6i	−1.06450	−	0.614589i
$186$	−2.82156e6	−	723740.i	−0.438481	−	0.112472i
$187$	4.73944e6	+	8.20895e6i	0.724773	+	1.25534i
$188$			459147.i			0.0691000i
$189$	6.29028e6	+	2.45193e6i	0.931719	+	0.363180i
$190$	5.13445e6			0.748571
$191$	3.58555e6	−	2.07012e6i	0.514583	−	0.297095i	−0.220132	−	0.975470i	$-0.570649\pi$
$191$	3.58555e6	−	2.07012e6i	0.514583	−	0.297095i	0.734716	+	0.678375i	$0.237316\pi$
$192$	−1.42339e6	+	5.54921e6i	−0.201104	+	0.784020i
$193$	−3.10980e6	+	5.38633e6i	−0.432574	+	0.749240i	−0.997094	−	0.0761794i	$-0.975728\pi$
$193$	−3.10980e6	+	5.38633e6i	−0.432574	+	0.749240i	0.564520	+	0.825419i	$0.309061\pi$
$194$	1.09701e7	−	6.33357e6i	1.50246	−	0.867448i
$195$	206870.	+	740248.i	0.0278994	+	0.0998329i
$196$	266814.	+	1.09227e6i	0.0354357	+	0.145065i
$197$		−	5.87728e6i		−	0.768737i	−0.923180	−	0.384368i	$-0.874419\pi$
$197$		−	5.87728e6i		−	0.768737i	0.923180	−	0.384368i	$-0.125581\pi$
$198$	−9.08488e6	−	4.98884e6i	−1.17037	−	0.642694i
$199$	1.16360e6	−	2.01542e6i	0.147654	−	0.255744i	−0.782706	−	0.622392i	$-0.786161\pi$
$199$	1.16360e6	−	2.01542e6i	0.147654	−	0.255744i	0.930360	+	0.366648i	$0.119495\pi$
$200$	−2.10743e6	−	1.21673e6i	−0.263429	−	0.152091i
$201$	2.76340e6	+	2.70484e6i	0.340295	+	0.333083i
$202$	1.45331e7			1.76321
$203$	−1.23540e7	+	4.95715e6i	−1.47679	+	0.592575i
$204$	−397127.	−	1.42105e6i	−0.0467777	−	0.167385i
$205$	2.93275e6	+	5.07968e6i	0.340419	+	0.589623i
$206$	−8.96557e6	−	5.17628e6i	−1.02560	−	0.592128i
$207$	9.56965e6	−	205001.i	1.07891	−	0.0231123i
$208$	−643890.	−	1.11525e6i	−0.0715520	−	0.123932i
$209$			9.72511e6i			1.06526i
$210$	−3.10473e6	+	7.48704e6i	−0.335248	+	0.808449i
$211$	−6.47376e6			−0.689143			−0.344572	−	0.938760i	$-0.611976\pi$
$211$	−6.47376e6			−0.689143			−0.344572	+	0.938760i	$0.611976\pi$
$212$	−207487.	+	119792.i	−0.0217762	+	0.0125725i
$213$	1.62100e7	+	4.15792e6i	1.67743	+	0.430266i
$214$	−5.22013e6	+	9.04153e6i	−0.532647	+	0.922572i
$215$	−221863.	+	128093.i	−0.0223239	+	0.0128887i
$216$	−6.70415e6	−	6.28664e6i	−0.665246	−	0.623817i
$217$	−4.27120e6	−	610654.i	−0.417995	−	0.0597608i
$218$		−	9.09213e6i		−	0.877599i
$219$	−9.81294e6	−	9.60498e6i	−0.934258	−	0.914459i
$220$	808357.	−	1.40012e6i	0.0759163	−	0.131491i
$221$	−1.38141e6	−	797560.i	−0.127981	−	0.0738901i
$222$	−1.23536e7	+	1.26211e7i	−1.12911	+	1.15355i
$223$	8.24843e6			0.743801			0.371901	−	0.928273i	$-0.378706\pi$
$223$	8.24843e6			0.743801			0.371901	+	0.928273i	$0.378706\pi$
$224$	471296.	−	3.29646e6i	0.0419324	−	0.293295i
$225$	3.24881e6	−	1.96965e6i	0.285217	−	0.172919i
$226$	−8.29237e6	−	1.43628e7i	−0.718378	−	1.24427i
$227$	1.38579e7	+	8.00086e6i	1.18473	+	0.684004i	0.957104	−	0.289744i	$-0.0935702\pi$
$227$	1.38579e7	+	8.00086e6i	1.18473	+	0.684004i	0.227626	+	0.973749i	$0.426904\pi$
$228$	376125.	−	1.46635e6i	0.0317342	−	0.123718i
$229$	−8.75867e6	−	1.51705e7i	−0.729343	−	1.26326i	−0.957161	−	0.289556i	$-0.906492\pi$
$229$	−8.75867e6	−	1.51705e7i	−0.729343	−	1.26326i	0.227818	−	0.973704i	$-0.426841\pi$
$230$			1.14915e7i			0.944481i
$231$	−1.41811e7	−	5.88065e6i	−1.15047	−	0.477078i
$232$	1.81211e7			1.45118
$233$	8.78674e6	−	5.07303e6i	0.694640	−	0.401051i	−0.110708	−	0.993853i	$-0.535312\pi$
$233$	8.78674e6	−	5.07303e6i	0.694640	−	0.401051i	0.805348	+	0.592802i	$0.201978\pi$
$234$	1.74376e6	−	37354.7i	0.136094	−	0.00291540i
$235$	−2.45127e6	+	4.24573e6i	−0.188881	+	0.327151i
$236$	−330388.	+	190749.i	−0.0251355	+	0.0145120i
$237$	8.40272e6	−	2.34823e6i	0.631212	−	0.176399i
$238$	−6.26412e6	−	1.56112e7i	−0.464653	−	1.15799i
$239$		−	3.60131e6i		−	0.263795i	−0.991263	−	0.131898i	$-0.957893\pi$
$239$		−	3.60131e6i		−	0.263795i	0.991263	−	0.131898i	$-0.0421070\pi$
$240$	8.89692e6	−	9.08955e6i	0.643585	−	0.657520i
$241$	−418915.	+	725582.i	−0.0299278	+	0.0518365i	−0.880601	−	0.473858i	$-0.842861\pi$
$241$	−418915.	+	725582.i	−0.0299278	+	0.0518365i	0.850674	+	0.525694i	$0.176194\pi$
$242$	7.25266e6	+	4.18732e6i	0.511742	+	0.295454i
$243$	1.36413e7	−	4.45025e6i	0.950689	−	0.310146i
$244$	−1.40180e6			−0.0964977
$245$	−3.36413e6	+	1.15247e7i	−0.228757	+	0.783664i
$246$	1.28190e7	−	3.58242e6i	0.861094	−	0.240642i
$247$	−818278.	−	1.41730e6i	−0.0543013	−	0.0940526i
$248$	5.08667e6	+	2.93679e6i	0.333487	+	0.192539i
$249$	−1.83515e7	−	4.70723e6i	−1.18871	−	0.304907i
$250$	9.11812e6	+	1.57931e7i	0.583560	+	1.01076i
$251$		−	1.63942e7i		−	1.03674i	−0.855157	−	0.518370i	$-0.826539\pi$
$251$		−	1.63942e7i		−	1.03674i	0.855157	−	0.518370i	$-0.173461\pi$
$252$	1.91080e6	+	1.43515e6i	0.119402	+	0.0896800i
$253$	−2.17660e7			−1.34405
$254$	−1.29126e7	+	7.45509e6i	−0.787975	+	0.454938i
$255$	3.91439e6	−	1.52606e7i	0.236071	−	0.920344i
$256$	−3.67838e6	+	6.37114e6i	−0.219249	+	0.379750i
$257$	3.24923e6	−	1.87594e6i	0.191417	−	0.110515i	−0.401229	−	0.915978i	$-0.631417\pi$
$257$	3.24923e6	−	1.87594e6i	0.191417	−	0.110515i	0.592646	+	0.805463i	$0.298083\pi$
$258$	156468.	+	559893.i	0.00911102	+	0.0326021i
$259$	−1.61544e7	+	2.05755e7i	−0.929802	+	1.18427i
$260$			272063.i			0.0154792i
$261$	−1.36178e7	+	2.47986e7i	−0.765926	+	1.39478i
$262$	1.89398e6	−	3.28047e6i	0.105311	−	0.182403i
$263$	−3.67446e6	−	2.12145e6i	−0.201988	−	0.116618i	0.395594	−	0.918425i	$-0.370539\pi$
$263$	−3.67446e6	−	2.12145e6i	−0.201988	−	0.116618i	−0.597583	+	0.801807i	$0.703872\pi$
$264$	1.49353e7	+	1.46188e7i	0.811712	+	0.794510i
$265$	−2.55817e6			−0.137465
$266$	2.44255e6	−	1.70843e7i	0.129777	−	0.907721i
$267$	5.28847e6	+	1.89238e7i	0.277841	+	0.994203i
$268$	684368.	+	1.18536e6i	0.0355538	+	0.0615809i
$269$	2.08782e6	+	1.20540e6i	0.107260	+	0.0619264i	0.552670	−	0.833400i	$-0.313609\pi$
$269$	2.08782e6	+	1.20540e6i	0.107260	+	0.0619264i	−0.445411	+	0.895326i	$0.646942\pi$
$270$	4.99078e6	+	1.64878e7i	0.253558	+	0.837669i
$271$	−4.37442e6	−	7.57672e6i	−0.219792	−	0.380692i	0.734952	−	0.678119i	$-0.237205\pi$
$271$	−4.37442e6	−	7.57672e6i	−0.219792	−	0.380692i	−0.954744	+	0.297427i	$0.903871\pi$
$272$			2.63963e7i			1.31170i
$273$	2.56151e6	−	336190.i	0.125895	−	0.0165233i
$274$	3.93183e6			0.191136
$275$	−7.48188e6	+	4.31966e6i	−0.359760	+	0.207707i
$276$	3.28187e6	+	841812.i	0.156097	+	0.0400394i
$277$	−5.07001e6	+	8.78152e6i	−0.238545	+	0.413172i	−0.960297	−	0.278980i	$-0.910004\pi$
$277$	−5.07001e6	+	8.78152e6i	−0.238545	+	0.413172i	0.721752	+	0.692152i	$0.243337\pi$
$278$	−2.08151e7	+	1.20176e7i	−0.968820	+	0.559349i
$279$	−7.84158e6	+	4.75412e6i	−0.361070	+	0.218906i
$280$	1.00927e7	−	1.28548e7i	0.459761	−	0.585588i
$281$		−	1.33415e6i		−	0.0601293i	−0.999548	−	0.0300646i	$-0.990429\pi$
$281$		−	1.33415e6i		−	0.0601293i	0.999548	−	0.0300646i	$-0.00957132\pi$
$282$	7.95038e6	+	7.78189e6i	0.354520	+	0.347006i
$283$	7.51770e6	−	1.30210e7i	0.331685	−	0.574495i	−0.651157	−	0.758943i	$-0.725716\pi$
$283$	7.51770e6	−	1.30210e7i	0.331685	−	0.574495i	0.982842	+	0.184448i	$0.0590496\pi$
$284$	5.12995e6	+	2.96178e6i	0.223953	+	0.129300i
$285$	1.13065e7	−	1.15513e7i	0.488421	−	0.498996i
$286$	−3.96615e6			−0.169539
$287$	1.82972e7	−	7.34192e6i	0.773997	−	0.310573i
$288$	−3.66917e6	−	6.05204e6i	−0.153600	−	0.253352i
$289$	4.27918e6	+	7.41176e6i	0.177283	+	0.307063i
$290$	−2.94151e7	−	1.69828e7i	−1.20608	−	0.696331i
$291$	9.90801e6	−	3.86272e7i	0.402075	−	1.56752i
$292$	−2.43022e6	−	4.20926e6i	−0.0976106	−	0.169067i
$293$		−	2.73930e7i		−	1.08902i	−0.838754	−	0.544511i	$-0.816715\pi$
$293$		−	2.73930e7i		−	1.08902i	0.838754	−	0.544511i	$-0.183285\pi$
$294$	2.34353e7	+	1.38924e7i	0.922209	+	0.546682i
$295$	−4.07346e6			−0.158671
$296$	3.08402e7	−	1.78056e7i	1.18917	−	0.686565i
$297$	−3.12295e7	+	9.45300e6i	−1.19205	+	0.360828i
$298$	6.18535e6	−	1.07133e7i	0.233731	−	0.404833i
$299$	3.17209e6	−	1.83140e6i	0.118667	−	0.0685126i
$300$	1.29518e6	−	361953.i	0.0479698	−	0.0134057i
$301$	320671.	+	799162.i	0.0117587	+	0.0293046i
$302$			2.30815e7i			0.837997i
$303$	3.20033e7	−	3.26962e7i	1.15045	−	1.17536i
$304$	−1.35410e7	+	2.34537e7i	−0.481981	+	0.834815i
$305$	−1.29624e7	−	7.48387e6i	−0.456864	−	0.263771i
$306$	−3.13369e7	−	1.72082e7i	−1.09368	−	0.600582i
$307$	−552266.			−0.0190868			−0.00954339	−	0.999954i	$-0.503038\pi$
$307$	−552266.			−0.0190868			−0.00954339	+	0.999954i	$0.503038\pi$
$308$	−4.27418e6	−	3.35578e6i	−0.146285	−	0.114853i
$309$	−3.13884e7	+	8.77184e6i	−1.06388	+	0.297314i
$310$	−5.50464e6	−	9.53431e6i	−0.184775	−	0.320040i
$311$	1.58376e7	+	9.14385e6i	0.526512	+	0.303982i	0.739595	−	0.673052i	$-0.235017\pi$
$311$	1.58376e7	+	9.14385e6i	0.526512	+	0.303982i	−0.213083	+	0.977034i	$0.568350\pi$
$312$	−3.40665e6	−	873816.i	−0.112167	−	0.0287711i
$313$	−5.92720e6	−	1.02662e7i	−0.193293	−	0.334794i	0.753046	−	0.657967i	$-0.228584\pi$
$313$	−5.92720e6	−	1.02662e7i	−0.193293	−	0.334794i	−0.946340	+	0.323174i	$0.895250\pi$
$314$		−	4.75032e7i		−	1.53438i
$315$	1.00072e7	+	2.34721e7i	0.320171	+	0.750965i
$316$	3.08825e6			0.0978703
$317$	−1.38377e7	+	7.98923e6i	−0.434398	+	0.250800i	−0.701218	−	0.712947i	$-0.747360\pi$
$317$	−1.38377e7	+	7.98923e6i	−0.434398	+	0.250800i	0.266821	+	0.963746i	$0.414027\pi$
$318$	−1.44233e6	+	5.62305e6i	−0.0448522	+	0.174860i
$319$	3.21670e7	−	5.57149e7i	0.990920	−	1.71632i
$320$	−1.87513e7	+	1.08261e7i	−0.572244	+	0.330385i
$321$	8.84615e6	+	3.16544e7i	0.267448	+	0.957014i
$322$	3.82367e7	+	5.46671e6i	1.14528	+	0.163741i
$323$			3.35453e7i			0.995460i
$324$	5.07438e6	−	217506.i	0.149193	−	0.00639494i
$325$	726920.	−	1.25906e6i	0.0211756	−	0.0366773i
$326$	2.35483e7	+	1.35956e7i	0.679685	+	0.392416i
$327$	−2.04552e7	−	2.00217e7i	−0.585006	−	0.572608i
$328$	−2.68387e7			−0.760573
$329$	1.29611e7	+	1.01761e7i	0.363960	+	0.285755i
$330$	−1.05432e7	−	3.77271e7i	−0.293381	−	1.04981i
$331$	3.30853e7	+	5.73054e7i	0.912327	+	1.58020i	0.810768	+	0.585368i	$0.199050\pi$
$331$	3.30853e7	+	5.73054e7i	0.912327	+	1.58020i	0.101559	+	0.994829i	$0.467617\pi$
$332$	−5.80768e6	−	3.35307e6i	−0.158704	−	0.0916279i
$333$	1.19075e6	+	5.55855e7i	0.0322469	+	1.50532i
$334$	4.64229e6	+	8.04069e6i	0.124593	+	0.215801i
$335$			1.46147e7i			0.388737i
$336$	−2.60121e7	−	3.39276e7i	−0.685736	−	0.894407i
$337$	6.95350e6			0.181683			0.0908414	−	0.995865i	$-0.471044\pi$
$337$	6.95350e6			0.181683			0.0908414	+	0.995865i	$0.471044\pi$
$338$	−3.52731e7	+	2.03650e7i	−0.913469	+	0.527392i
$339$	−5.05735e7	−	1.29723e7i	−1.29815	−	0.332979i
$340$	2.78830e6	−	4.82948e6i	0.0709420	−	0.122875i
$341$	1.80589e7	−	1.04263e7i	0.455436	−	0.262946i
$342$	−1.90159e7	−	3.13654e7i	−0.475378	−	0.784102i
$343$	3.67467e7	+	1.66762e7i	0.910616	+	0.413253i
$344$		−	1.17223e6i		−	0.0287963i
$345$	2.58532e7	+	2.53053e7i	0.629590	+	0.616247i
$346$	−2.03255e7	+	3.52048e7i	−0.490696	+	0.849911i
$347$	2.47273e6	+	1.42763e6i	0.0591818	+	0.0341686i	0.529299	−	0.848435i	$-0.322455\pi$
$347$	2.47273e6	+	1.42763e6i	0.0591818	+	0.0341686i	−0.470117	+	0.882604i	$0.655788\pi$
$348$	−7.00495e6	+	7.15662e6i	−0.166214	+	0.169813i
$349$	−2.10065e7			−0.494171			−0.247086	−	0.968994i	$-0.579473\pi$
$349$	−2.10065e7			−0.494171			−0.247086	+	0.968994i	$0.579473\pi$
$350$	1.42285e7	−	5.70930e6i	0.331860	−	0.133162i
$351$	3.75588e6	−	4.00532e6i	0.0868540	−	0.0926223i
$352$	8.04689e6	+	1.39376e7i	0.184502	+	0.319566i
$353$	2.37372e7	+	1.37047e7i	0.539643	+	0.311563i	0.744934	−	0.667138i	$-0.232481\pi$
$353$	2.37372e7	+	1.37047e7i	0.539643	+	0.311563i	−0.205291	+	0.978701i	$0.565814\pi$
$354$	−2.29667e6	+	8.95377e6i	−0.0517713	+	0.201835i
$355$	3.16244e7	+	5.47750e7i	0.706866	+	1.22433i
$356$			6.95506e6i			0.154153i
$357$	−4.89157e7	−	2.02844e7i	−1.07509	−	0.445818i
$358$	−1.43106e7			−0.311896
$359$	−4.06713e7	+	2.34816e7i	−0.879032	+	0.507510i	−0.870339	−	0.492453i	$-0.836100\pi$
$359$	−4.06713e7	+	2.34816e7i	−0.879032	+	0.507510i	−0.00869313	+	0.999962i	$0.502767\pi$
$360$	−743939.	−	3.47279e7i	−0.0159452	−	0.744338i
$361$	6.31458e6	−	1.09372e7i	0.134222	−	0.232479i
$362$	7.30980e7	−	4.22032e7i	1.54092	−	0.889650i
$363$	2.53915e7	−	7.09594e6i	0.530846	−	0.148351i
$364$	905260.	+	129425.i	0.0187702	+	0.00268358i
$365$		−	5.18974e7i		−	1.06725i
$366$	−2.37585e7	+	2.42729e7i	−0.484592	+	0.495084i
$367$	1.64150e7	−	2.84317e7i	0.332081	−	0.575181i	−0.650839	−	0.759216i	$-0.725583\pi$
$367$	1.64150e7	−	2.84317e7i	0.332081	−	0.575181i	0.982920	+	0.184035i	$0.0589160\pi$
$368$	−5.24921e7	−	3.03063e7i	−1.05330	−	0.608121i
$369$	2.01691e7	−	3.67287e7i	0.401427	−	0.731015i
$370$	−6.67486e7			−1.31776
$371$	−1.21697e6	+	8.51203e6i	−0.0238318	+	0.166691i
$372$	−3.12616e6	+	873639.i	−0.0607271	+	0.0169708i
$373$	−4.34777e6	−	7.53055e6i	−0.0837799	−	0.145111i	0.821091	−	0.570798i	$-0.193366\pi$
$373$	−4.34777e6	−	7.53055e6i	−0.0837799	−	0.145111i	−0.904871	+	0.425687i	$0.860033\pi$
$374$	7.04044e7	+	4.06480e7i	1.34581	+	0.777006i
$375$	5.56097e7	+	1.42641e7i	1.05452	+	0.270489i
$376$	−1.12163e7	−	1.94272e7i	−0.211001	−	0.365465i
$377$			1.08262e7i			0.202047i
$378$	5.72357e7	−	8.76274e6i	1.05972	−	0.162242i
$379$	5.92421e7			1.08821			0.544106	−	0.839017i	$-0.316869\pi$
$379$	5.92421e7			1.08821			0.544106	+	0.839017i	$0.316869\pi$
$380$	4.95494e6	−	2.86074e6i	0.0903000	−	0.0521347i
$381$	−1.16625e7	+	4.54672e7i	−0.210871	+	0.822097i
$382$	1.77545e7	−	3.07516e7i	0.318506	−	0.551668i
$383$	−6.91860e7	+	3.99446e7i	−1.23146	+	0.710987i	−0.967335	−	0.253501i	$-0.918418\pi$
$383$	−6.91860e7	+	3.99446e7i	−1.23146	+	0.710987i	−0.264130	+	0.964487i	$0.585085\pi$
$384$	1.77395e7	+	6.34777e7i	0.313292	+	1.12106i
$385$	−2.16076e7	−	5.38497e7i	−0.378639	−	0.943628i
$386$			5.33426e7i			0.927497i
$387$	1.60419e6	+	880918.i	0.0276772	+	0.0151986i
$388$	7.05769e6	−	1.22243e7i	0.120828	−	0.209280i
$389$	−5.62167e7	−	3.24567e7i	−0.955029	−	0.551386i	−0.0603893	−	0.998175i	$-0.519234\pi$
$389$	−5.62167e7	−	3.24567e7i	−0.955029	−	0.551386i	−0.894639	+	0.446789i	$0.852568\pi$
$390$	4.71092e6	+	4.61108e6i	0.0794167	+	0.0777336i
$391$	−7.50784e7			−1.25599
$392$	−3.79718e7	−	3.96976e7i	−0.630380	−	0.659031i
$393$	−3.20959e6	−	1.14849e7i	−0.0528776	−	0.189213i
$394$	−2.52034e7	−	4.36535e7i	−0.412069	−	0.713724i
$395$	2.85570e7	+	1.64874e7i	0.463363	+	0.267523i
$396$	−1.15469e7	+	247357.i	−0.185943	+	0.00398326i
$397$	−2.19560e7	−	3.80290e7i	−0.350899	−	0.607776i	0.635508	−	0.772094i	$-0.280791\pi$
$397$	−2.19560e7	−	3.80290e7i	−0.350899	−	0.607776i	−0.986407	+	0.164319i	$0.947457\pi$
$398$		−	1.99593e7i		−	0.316590i
$399$	−3.30570e7	−	4.31164e7i	−0.520410	−	0.678771i
$400$	−2.40583e7			−0.375911
$401$	−313037.	+	180732.i	−0.00485470	+	0.00280286i	−0.502425	−	0.864621i	$-0.667559\pi$
$401$	−313037.	+	180732.i	−0.00485470	+	0.00280286i	0.497571	+	0.867423i	$0.334226\pi$
$402$	3.21242e7	+	8.23997e6i	0.494487	+	0.126837i
$403$	−1.75455e6	+	3.03897e6i	−0.0268072	+	0.0464314i
$404$	1.40250e7	−	8.09736e6i	0.212696	−	0.122800i
$405$	4.80840e7	+	2.50796e7i	0.723828	+	0.377533i
$406$	−7.05017e7	+	8.97965e7i	−1.05347	+	1.34178i
$407$		−	1.26428e8i		−	1.87525i
$408$	5.15170e7	+	5.04252e7i	0.758525	+	0.742450i
$409$	2.82790e7	−	4.89806e7i	0.413327	−	0.715903i	−0.581924	−	0.813243i	$-0.697700\pi$
$409$	2.82790e7	−	4.89806e7i	0.413327	−	0.715903i	0.995251	+	0.0973398i	$0.0310334\pi$
$410$	4.35661e7	+	2.51529e7i	0.632116	+	0.364952i
$411$	8.65824e6	−	8.84570e6i	0.124711	−	0.127411i
$412$	−1.15362e7			−0.164957
$413$	−1.93781e6	+	1.35540e7i	−0.0275082	+	0.192405i
$414$	7.01995e7	−	4.25599e7i	0.989311	−	0.599790i
$415$	−3.58024e7	−	6.20115e7i	−0.500919	−	0.867617i
$416$	−2.34544e6	−	1.35414e6i	−0.0325795	−	0.0188098i
$417$	−1.87999e7	+	7.32929e7i	−0.259267	+	1.01077i
$418$	4.17039e7	+	7.22333e7i	0.571016	+	0.989029i
$419$		−	8.40770e7i		−	1.14297i	−0.820612	−	0.571486i	$-0.806367\pi$
$419$		−	8.40770e7i		−	1.14297i	0.820612	−	0.571486i	$-0.193633\pi$
$420$	1.17533e6	+	8.95514e6i	0.0158640	+	0.120872i
$421$	2.82795e7			0.378988			0.189494	−	0.981882i	$-0.439315\pi$
$421$	2.82795e7			0.378988			0.189494	+	0.981882i	$0.439315\pi$
$422$	−4.80839e7	+	2.77613e7i	−0.639827	+	0.369404i
$423$	3.50149e7	−	750088.i	0.462628	−	0.00991039i
$424$	5.85270e6	−	1.01372e7i	0.0767819	−	0.132990i
$425$	−2.58076e7	+	1.49000e7i	−0.336187	+	0.194098i
$426$	1.38230e8	−	3.86299e7i	1.78802	−	0.499683i
$427$	−3.10682e7	+	3.95709e7i	−0.399055	+	0.508267i
$428$			1.16339e7i			0.148386i
$429$	−8.73381e6	+	8.92291e6i	−0.110620	+	0.113015i
$430$	−1.09859e6	+	1.90282e6i	−0.0138176	+	0.0239327i
$431$	1.11174e8	+	6.41866e7i	1.38859	+	0.801701i	0.993156	−	0.116795i	$-0.0372620\pi$
$431$	1.11174e8	+	6.41866e7i	1.38859	+	0.801701i	0.395431	+	0.918496i	$0.370595\pi$
$432$	−8.84770e7	−	2.06856e7i	−1.09744	−	0.256577i
$433$	1.58472e7			0.195204			0.0976020	−	0.995226i	$-0.468883\pi$
$433$	1.58472e7			0.195204			0.0976020	+	0.995226i	$0.468883\pi$
$434$	−3.43430e7	+	1.37804e7i	−0.420116	+	0.168575i
$435$	−1.02982e8	+	2.87795e7i	−1.25111	+	0.349635i
$436$	−5.06582e6	−	8.77426e6i	−0.0611210	−	0.105865i
$437$	−6.67088e7	−	3.85144e7i	−0.799354	−	0.461507i
$438$	−1.14074e8	−	2.92605e7i	−1.35758	−	0.348224i
$439$	3.23972e7	+	5.61137e7i	0.382926	+	0.663247i	0.991479	−	0.130266i	$-0.0415832\pi$
$439$	3.23972e7	+	5.61137e7i	0.382926	+	0.663247i	−0.608553	+	0.793513i	$0.708250\pi$
$440$			7.89878e7i			0.927261i
$441$	8.28614e7	−	2.21318e7i	0.966132	−	0.258049i
$442$	−1.36806e7			−0.158430
$443$	6.45405e7	−	3.72625e7i	0.742371	−	0.428608i	−0.0805598	−	0.996750i	$-0.525671\pi$
$443$	6.45405e7	−	3.72625e7i	0.742371	−	0.428608i	0.822931	+	0.568142i	$0.192337\pi$
$444$	−4.88968e6	+	1.90628e7i	−0.0558639	+	0.217790i
$445$	−3.71313e7	+	6.43134e7i	−0.421367	+	0.729829i
$446$	6.12653e7	−	3.53715e7i	0.690573	−	0.398703i
$447$	−1.04818e7	−	3.75074e7i	−0.117359	−	0.419947i
$448$	2.71022e7	+	6.75430e7i	0.301419	+	0.751184i
$449$			1.66886e8i			1.84366i	0.387600	+	0.921828i	$0.373304\pi$
$449$			1.66886e8i			1.84366i	−0.387600	+	0.921828i	$0.626696\pi$
$450$	1.56841e7	−	2.85614e7i	0.172116	−	0.313431i
$451$	−4.76419e7	+	8.25181e7i	−0.519349	+	0.899538i
$452$	−1.60049e7	−	9.24044e6i	−0.173316	−	0.100064i
$453$	5.19280e7	+	5.08275e7i	0.558607	+	0.546769i
$454$	1.37239e8			1.46660
$455$	7.67996e6	+	6.02975e6i	0.0815314	+	0.0640126i
$456$	1.99065e7	+	7.12316e7i	0.209942	+	0.751239i
$457$	−9.22998e7	−	1.59868e8i	−0.967058	−	1.67499i	−0.703982	−	0.710217i	$-0.748597\pi$
$457$	−9.22998e7	−	1.59868e8i	−0.967058	−	1.67499i	−0.263075	−	0.964775i	$-0.584737\pi$
$458$	−1.30110e8	−	7.51192e7i	−1.35430	−	0.781906i
$459$	−1.07721e8	+	3.26067e7i	−1.11394	+	0.337185i
$460$	6.40267e6	+	1.10898e7i	0.0657791	+	0.113933i
$461$			1.22227e8i			1.24756i	0.781598	+	0.623782i	$0.214405\pi$
$461$			1.22227e8i			1.24756i	−0.781598	+	0.623782i	$0.785595\pi$
$462$	−1.30548e8	+	1.71341e7i	−1.32387	+	0.173754i
$463$	−8.10536e6			−0.0816637			−0.0408319	−	0.999166i	$-0.513001\pi$
$463$	−8.10536e6			−0.0816637			−0.0408319	+	0.999166i	$0.513001\pi$
$464$	1.55152e8	−	8.95770e7i	1.55311	−	0.896690i
$465$	−3.35717e7	−	8.61126e6i	−0.333899	−	0.0856461i
$466$	4.35090e7	−	7.53599e7i	0.429954	−	0.744702i
$467$	−1.08903e8	+	6.28750e7i	−1.06927	+	0.617344i	−0.927982	−	0.372624i	$-0.878458\pi$
$467$	−1.08903e8	+	6.28750e7i	−1.06927	+	0.617344i	−0.141289	+	0.989968i	$0.545125\pi$
$468$	1.66198e6	−	1.00761e6i	0.0162140	−	0.00983005i
$469$	4.86288e7	+	6.95247e6i	0.471384	+	0.0673939i
$470$			4.20469e7i			0.404986i
$471$	−1.06871e8	−	1.04606e8i	−1.02282	−	1.00114i
$472$	9.31944e6	−	1.61417e7i	0.0886266	−	0.153506i
$473$	−3.60412e6	−	2.08084e6i	−0.0340577	−	0.0196632i
$474$	5.23414e7	−	5.34747e7i	0.491485	−	0.502126i
$475$	−3.05742e7			−0.285282
$476$	−1.47431e7	−	1.15752e7i	−0.136700	−	0.107327i
$477$	9.47443e6	+	1.56274e7i	0.0872967	+	0.143990i
$478$	−1.54434e7	−	2.67488e7i	−0.141403	−	0.244918i
$479$	−1.93355e7	−	1.11634e7i	−0.175934	−	0.101575i	0.409447	−	0.912334i	$-0.365722\pi$
$479$	−1.93355e7	−	1.11634e7i	−0.175934	−	0.101575i	−0.585381	+	0.810758i	$0.699055\pi$
$480$	6.64607e6	−	2.59103e7i	0.0600954	−	0.234287i
$481$	1.06377e7	+	1.84251e7i	0.0955904	+	0.165568i
$482$			7.18569e6i			0.0641693i
$483$	9.64996e7	−	7.39856e7i	0.856414	−	0.656607i
$484$	9.33213e6			0.0823085
$485$	1.30525e8	−	7.53586e7i	1.14411	−	0.660553i
$486$	8.22373e7	−	9.15521e7i	0.716407	−	0.797553i
$487$	227444.	−	393944.i	0.00196919	−	0.00341074i	−0.865039	−	0.501704i	$-0.832707\pi$
$487$	227444.	−	393944.i	0.00196919	−	0.00341074i	0.867008	+	0.498294i	$0.166040\pi$
$488$	5.93122e7	−	3.42439e7i	0.510369	−	0.294662i
$489$	8.24426e7	−	2.30395e7i	0.705059	−	0.197036i
$490$	2.44338e7	+	1.00026e8i	0.207684	+	0.850205i
$491$		−	1.40943e8i		−	1.19069i	−0.803469	−	0.595347i	$-0.797015\pi$
$491$		−	1.40943e8i		−	1.19069i	0.803469	−	0.595347i	$-0.202985\pi$
$492$	1.03749e7	−	1.05995e7i	0.0871140	−	0.0890001i
$493$	1.10955e8	−	1.92180e8i	0.925991	−	1.60386i
$494$	−1.21555e7	−	7.01800e6i	−0.100831	−	0.0582147i
$495$	−1.08094e8	−	5.93586e7i	−0.891226	−	0.489405i
$496$	5.80691e7			0.475883
$497$	1.97302e8	−	7.91692e7i	1.60717	−	0.644892i
$498$	−1.56492e8	+	4.37334e7i	−1.26708	+	0.354099i
$499$	6.54628e7	+	1.13385e8i	0.526857	+	0.912543i	0.999510	+	0.0312944i	$0.00996293\pi$
$499$	6.54628e7	+	1.13385e8i	0.526857	+	0.912543i	−0.472653	+	0.881248i	$0.656704\pi$
$500$	1.75987e7	+	1.01606e7i	0.140790	+	0.0812849i
$501$	2.83124e7	+	7.26223e6i	0.225146	+	0.0577507i
$502$	−7.03029e7	−	1.21768e8i	−0.555728	−	0.962549i
$503$			5.96687e7i			0.468859i	0.972133	+	0.234430i	$0.0753223\pi$
$503$			5.96687e7i			0.468859i	−0.972133	+	0.234430i	$0.924678\pi$
$504$	−1.15907e8	−	1.40453e7i	−0.905353	−	0.109708i
$505$	1.72919e8			1.34267
$506$	−1.61667e8	+	9.33384e7i	−1.24787	+	0.720458i
$507$	−3.18582e7	+	1.24202e8i	−0.244454	+	0.953025i
$508$	−8.30745e6	+	1.43889e7i	−0.0633689	+	0.109758i
$509$	−9.49105e7	+	5.47966e7i	−0.719715	+	0.415528i	−0.814648	−	0.579956i	$-0.803070\pi$
$509$	−9.49105e7	+	5.47966e7i	−0.719715	+	0.415528i	0.0949326	+	0.995484i	$0.469736\pi$
$510$	−3.63673e7	−	1.30134e8i	−0.274158	−	0.981024i
$511$	−1.72683e8	−	2.46885e7i	−1.29416	−	0.185026i
$512$		−	9.31352e7i		−	0.693912i
$513$	−1.12440e8	−	2.62880e7i	−0.832851	−	0.194718i
$514$	1.60891e7	−	2.78671e7i	0.118479	−	0.205212i
$515$	−1.06675e8	−	6.15888e7i	−0.780981	−	0.450900i
$516$	462951.	+	453140.i	0.00336966	+	0.00329825i
$517$	−7.96407e7			−0.576319
$518$	−3.17535e7	+	2.22099e8i	−0.228456	+	1.59793i
$519$	3.44441e7	+	1.23252e8i	0.246384	+	0.881640i
$520$	−6.64609e6	−	1.15114e7i	−0.0472668	−	0.0818685i
$521$	−4.66166e7	−	2.69141e7i	−0.329631	−	0.190312i	0.326046	−	0.945354i	$-0.394283\pi$
$521$	−4.66166e7	−	2.69141e7i	−0.329631	−	0.190312i	−0.655677	+	0.755041i	$0.727617\pi$
$522$	5.19673e6	+	2.42589e8i	0.0365358	+	1.70553i
$523$	1.36233e8	+	2.35962e8i	0.952306	+	1.64944i	0.740415	+	0.672149i	$0.234629\pi$
$523$	1.36233e8	+	2.35962e8i	0.952306	+	1.64944i	0.211891	+	0.977293i	$0.432038\pi$
$524$		−	4.22105e6i		−	0.0293377i
$525$	1.84878e7	−	4.45832e7i	0.127764	−	0.308101i
$526$	−3.63894e7			−0.250045
$527$	6.22913e7	−	3.59639e7i	0.425594	−	0.245717i
$528$	2.00139e8	+	5.13364e7i	1.35966	+	0.348758i
$529$	1.21818e7	−	2.10995e7i	0.0822894	−	0.142529i
$530$	−1.90008e7	+	1.09701e7i	−0.127628	+	0.0736858i
$531$	1.50864e7	+	2.48840e7i	0.100763	+	0.166202i
$532$	−7.16164e6	−	1.78479e7i	−0.0475639	−	0.118537i
$533$		−	1.60345e7i		−	0.105895i
$534$	1.20431e8	+	1.17878e8i	0.790884	+	0.774124i
$535$	−6.21106e7	+	1.07579e8i	−0.405606	+	0.702530i
$536$	−5.79132e7	−	3.34362e7i	−0.376082	−	0.217131i
$537$	−3.15133e7	+	3.21956e7i	−0.203503	+	0.207909i
$538$	2.06764e7			0.132779
$539$	−1.89458e8	+	4.62798e7i	−1.20989	+	0.295546i
$540$	1.40028e7	+	1.31307e7i	0.0889267	+	0.0833887i
$541$	6.80986e7	+	1.17950e8i	0.430077	+	0.744916i	0.996880	−	0.0789380i	$-0.0251529\pi$
$541$	6.80986e7	+	1.17950e8i	0.430077	+	0.744916i	−0.566802	+	0.823854i	$0.691820\pi$
$542$	−6.49821e7	−	3.75174e7i	−0.408127	−	0.235632i
$543$	6.60211e7	−	2.57389e8i	0.412366	−	1.60765i
$544$	2.77565e7	+	4.80757e7i	0.172412	+	0.298627i
$545$		−	1.08181e8i		−	0.668283i
$546$	1.75839e7	−	1.34815e7i	0.108028	−	0.0828247i
$547$	4.57100e7			0.279286			0.139643	−	0.990202i	$-0.455404\pi$
$547$	4.57100e7			0.279286			0.139643	+	0.990202i	$0.455404\pi$
$548$	3.79437e6	−	2.19068e6i	0.0230567	−	0.0133118i
$549$	2.29006e6	+	1.06902e8i	0.0138398	+	0.646057i
$550$	−3.70478e7	+	6.41686e7i	−0.222676	+	0.385687i
$551$	1.97172e8	−	1.13838e8i	1.17867	−	0.680504i
$552$	−1.59425e8	+	4.45530e7i	−0.947848	+	0.264886i
$553$	6.84450e7	−	8.71769e7i	0.404731	−	0.515497i
$554$			8.69664e7i			0.511472i
$555$	−1.46987e8	+	1.50169e8i	−0.859802	+	0.878418i
$556$	−1.33916e7	+	2.31949e7i	−0.0779125	+	0.134948i
$557$	2.01129e8	+	1.16122e8i	1.16388	+	0.671968i	0.952232	−	0.305377i	$-0.0987825\pi$
$557$	2.01129e8	+	1.16122e8i	1.16388	+	0.671968i	0.211651	+	0.977345i	$0.432116\pi$
$558$	−3.78564e7	+	6.89381e7i	−0.217890	+	0.396786i
$559$	700333.			0.00400931
$560$	2.28685e7	−	1.59953e8i	0.130219	−	0.910811i
$561$	2.46485e8	−	6.88831e7i	1.39606	−	0.390143i
$562$	−5.72120e6	−	9.90942e6i	−0.0322314	−	0.0558263i
$563$	4.40626e7	+	2.54395e7i	0.246913	+	0.142555i	0.618350	−	0.785903i	$-0.287801\pi$
$563$	4.40626e7	+	2.54395e7i	0.246913	+	0.142555i	−0.371437	+	0.928458i	$0.621135\pi$
$564$	1.20082e7	+	3.08015e6i	0.0669332	+	0.0171686i
$565$	−9.86649e7	−	1.70893e8i	−0.547038	−	0.947497i
$566$		−	1.28952e8i		−	0.711177i
$567$	1.06324e8	−	1.48063e8i	0.583287	−	0.812266i
$568$	−2.89407e8			−1.57930
$569$	−1.20964e8	+	6.98384e7i	−0.656626	+	0.379103i	−0.790990	−	0.611829i	$-0.790434\pi$
$569$	−1.20964e8	+	6.98384e7i	−0.656626	+	0.379103i	0.134364	+	0.990932i	$0.457101\pi$
$570$	3.44440e7	−	1.34283e8i	0.185990	−	0.725097i
$571$	−1.08542e8	+	1.88000e8i	−0.583027	+	1.00983i	0.412092	+	0.911142i	$0.364798\pi$
$571$	−1.08542e8	+	1.88000e8i	−0.583027	+	1.00983i	−0.995118	+	0.0986895i	$0.968535\pi$
$572$	−3.82749e6	+	2.20980e6i	−0.0204515	+	0.0118077i
$573$	−3.00871e7	−	1.07661e8i	−0.159925	−	0.572263i
$574$	1.04419e8	−	1.32996e8i	0.552131	−	0.703237i
$575$		−	6.84286e7i		−	0.359944i
$576$	1.35582e8	+	7.44528e7i	0.709469	+	0.389595i
$577$	−3.81534e7	+	6.60837e7i	−0.198612	+	0.344007i	−0.948079	−	0.318036i	$-0.896977\pi$
$577$	−3.81534e7	+	6.60837e7i	−0.198612	+	0.344007i	0.749466	+	0.662042i	$0.230310\pi$
$578$	6.35672e7	+	3.67006e7i	0.329192	+	0.190059i
$579$	1.20009e8	+	1.17465e8i	0.618268	+	0.605165i
$580$	−3.78490e7			−0.193986
$581$	−2.23368e8	+	8.96285e7i	−1.13892	+	0.457002i
$582$	−9.20522e7	−	3.29392e8i	−0.466944	−	1.67088i
$583$	−2.07784e7	−	3.59893e7i	−0.104859	−	0.181622i
$584$	2.05652e8	+	1.18733e8i	1.03251	+	0.596120i
$585$	2.07477e7	−	444457.i	0.103634	−	0.00222005i
$586$	−1.17469e8	−	2.03462e8i	−0.583753	−	1.01109i
$587$			3.46645e8i			1.71384i	0.515447	+	0.856921i	$0.327626\pi$
$587$			3.46645e8i			1.71384i	−0.515447	+	0.856921i	$0.672374\pi$
$588$	3.03564e7	+	349320.i	0.149320	+	0.00171827i
$589$	7.37963e7			0.361151
$590$	−3.02556e7	+	1.74681e7i	−0.147316	+	0.0850529i
$591$	−1.53710e8	−	3.94272e7i	−0.744631	−	0.191000i
$592$	1.76035e8	−	3.04902e8i	0.848465	−	1.46958i
$593$	2.16280e8	−	1.24869e8i	1.03718	−	0.598813i	0.118143	−	0.992997i	$-0.462306\pi$
$593$	2.16280e8	−	1.24869e8i	1.03718	−	0.598813i	0.919032	+	0.394183i	$0.128972\pi$
$594$	−1.91420e8	+	2.04133e8i	−0.913331	+	0.973987i
$595$	−7.45323e7	−	1.85746e8i	−0.353829	−	0.881798i
$596$		−	1.37851e7i		−	0.0651134i
$597$	−4.49039e7	−	4.39523e7i	−0.211038	−	0.206566i
$598$	1.57071e7	−	2.72055e7i	0.0734502	−	0.127220i
$599$	1.62210e7	+	9.36522e6i	0.0754741	+	0.0435750i	0.537262	−	0.843415i	$-0.319459\pi$
$599$	1.62210e7	+	9.36522e6i	0.0754741	+	0.0435750i	−0.461788	+	0.886990i	$0.652792\pi$
$600$	−4.59590e7	+	4.69541e7i	−0.212773	+	0.217380i
$601$	−3.43299e8			−1.58143			−0.790714	−	0.612185i	$-0.790291\pi$
$601$	−3.43299e8			−1.58143			−0.790714	+	0.612185i	$0.790291\pi$
$602$	5.80881e6	+	4.56066e6i	0.0266255	+	0.0209044i
$603$	8.92785e7	−	5.41269e7i	0.407188	−	0.246866i
$604$	1.28602e7	+	2.22745e7i	0.0583629	+	0.101088i
$605$	8.62941e7	+	4.98219e7i	0.389686	+	0.224985i
$606$	9.74943e7	−	3.80090e8i	0.438088	−	1.70792i
$607$	−7.52753e7	−	1.30381e8i	−0.336579	−	0.582971i	0.647208	−	0.762313i	$-0.275936\pi$
$607$	−7.52753e7	−	1.30381e8i	−0.336579	−	0.582971i	−0.983787	+	0.179342i	$0.942603\pi$
$608$			5.69551e7i			0.253409i
$609$	4.67702e7	+	3.56353e8i	0.207070	+	1.57771i
$610$	−1.28371e8			−0.565561
$611$	1.16065e7	−	6.70103e6i	0.0508837	−	0.0293777i
$612$	−3.98292e7	+	853219.i	−0.173759	+	0.00372226i
$613$	1.53242e7	−	2.65423e7i	0.0665267	−	0.115228i	−0.830843	−	0.556506i	$-0.812142\pi$
$613$	1.53242e7	−	2.65423e7i	0.0665267	−	0.115228i	0.897370	+	0.441279i	$0.145475\pi$
$614$	−4.10196e6	+	2.36826e6i	−0.0177209	+	0.0102312i
$615$	1.52525e8	−	4.26247e7i	0.655714	−	0.183246i
$616$	2.62823e8	+	3.75759e7i	1.12440	+	0.160756i
$617$			1.82214e8i			0.775758i	0.921710	+	0.387879i	$0.126792\pi$
$617$			1.82214e8i			0.775758i	−0.921710	+	0.387879i	$0.873208\pi$
$618$	−1.95522e8	+	1.99755e8i	−0.828380	+	0.846316i
$619$	−1.32745e8	+	2.29921e8i	−0.559688	+	0.969409i	0.437834	+	0.899056i	$0.355746\pi$
$619$	−1.32745e8	+	2.29921e8i	−0.559688	+	0.969409i	−0.997522	+	0.0703528i	$0.977588\pi$
$620$	−1.06244e7	−	6.13399e6i	−0.0445788	−	0.0257376i
$621$	5.88357e7	−	2.51653e8i	0.245678	−	1.05082i
$622$	1.56845e8			0.651779
$623$	1.96332e8	+	1.54145e8i	0.811944	+	0.637480i
$624$	−3.34870e7	+	9.35831e6i	−0.137823	+	0.0385162i
$625$	6.77745e7	+	1.17389e8i	0.277604	+	0.480825i
$626$	−8.80486e7	−	5.08349e7i	−0.358922	−	0.207223i
$627$	2.54344e8	+	6.52401e7i	1.03186	+	0.264675i
$628$	−2.64672e7	−	4.58425e7i	−0.106863	−	0.185093i
$629$		−	4.36094e8i		−	1.75238i
$630$	1.74983e8	+	1.31425e8i	0.699802	+	0.525603i
$631$	−1.33736e8			−0.532304			−0.266152	−	0.963931i	$-0.585752\pi$
$631$	−1.33736e8			−0.532304			−0.266152	+	0.963931i	$0.585752\pi$
$632$	−1.30668e8	+	7.54413e7i	−0.517629	+	0.298853i
$633$	−4.34287e7	+	1.69311e8i	−0.171224	+	0.667533i
$634$	−6.85199e7	+	1.18680e8i	−0.268874	+	0.465704i
$635$	−1.53638e8	+	8.87028e7i	−0.600035	+	0.346431i
$636$	1.74107e6	+	6.23009e6i	0.00676774	+	0.0242171i
$637$	2.37168e7	−	2.26858e7i	0.0917568	−	0.0877678i
$638$		−	5.51764e8i		−	2.12467i
$639$	2.17487e8	−	3.96052e8i	0.833547	−	1.51792i
$640$	−1.24553e8	+	2.15732e8i	−0.475131	+	0.822951i
$641$	−4.04341e8	−	2.33447e8i	−1.53523	−	0.886366i	−0.999108	−	0.0422269i	$-0.986555\pi$
$641$	−4.04341e8	−	2.33447e8i	−1.53523	−	0.886366i	−0.536124	−	0.844140i	$-0.680112\pi$
$642$	2.01447e8	+	1.97178e8i	0.761301	+	0.745167i
$643$	1.02012e8			0.383723			0.191862	−	0.981422i	$-0.438548\pi$
$643$	1.02012e8			0.383723			0.191862	+	0.981422i	$0.438548\pi$
$644$	3.99458e7	−	1.60286e7i	0.149559	−	0.0600120i
$645$	1.86170e6	+	6.66177e6i	0.00693795	+	0.0248262i
$646$	1.43851e8	+	2.49158e8i	0.533601	+	0.924223i
$647$	−2.00170e8	−	1.15568e8i	−0.739070	−	0.426702i	0.0826612	−	0.996578i	$-0.473658\pi$
$647$	−2.00170e8	−	1.15568e8i	−0.739070	−	0.426702i	−0.821731	+	0.569876i	$0.806991\pi$
$648$	−2.09391e8	+	1.33163e8i	−0.769543	+	0.489392i
$649$	−3.30862e7	−	5.73069e7i	−0.121035	−	0.209639i
$650$		−	1.24689e7i		−	0.0454034i
$651$	−4.46237e7	+	1.07610e8i	−0.161742	+	0.390039i
$652$	3.03001e7			0.109320
$653$	8.60382e7	−	4.96742e7i	0.308995	−	0.178398i	−0.337482	−	0.941332i	$-0.609575\pi$
$653$	8.60382e7	−	4.96742e7i	0.308995	−	0.178398i	0.646477	+	0.762934i	$0.276242\pi$
$654$	−2.37789e8	−	6.09938e7i	−0.850079	−	0.218048i
$655$	2.25351e7	−	3.90320e7i	0.0801930	−	0.138898i
$656$	−2.29792e8	+	1.32670e8i	−0.813998	+	0.469962i
$657$	−3.17032e8	+	1.92207e8i	−1.11791	+	0.677755i
$658$	1.39906e8	+	2.00024e7i	0.491089	+	0.0702110i
$659$			3.56396e8i			1.24531i	0.782498	+	0.622653i	$0.213945\pi$
$659$			3.56396e8i			1.24531i	−0.782498	+	0.622653i	$0.786055\pi$
$660$	−3.11949e7	−	3.05338e7i	−0.108505	−	0.106206i
$661$	−2.85691e6	+	4.94832e6i	−0.00989219	+	0.0171338i	−0.870929	−	0.491409i	$-0.836482\pi$
$661$	−2.85691e6	+	4.94832e6i	−0.00989219	+	0.0171338i	0.861037	+	0.508542i	$0.169815\pi$
$662$	4.91482e8	+	2.83757e8i	1.69408	+	0.978077i
$663$	−3.01260e7	+	3.07782e7i	−0.103371	+	0.105609i
$664$	3.27641e8			1.11917
$665$	2.90621e7	−	2.03274e8i	0.0988239	−	0.691221i
$666$	2.47210e8	+	4.07755e8i	0.836841	+	1.38031i
$667$	2.54782e8	+	4.41295e8i	0.858601	+	1.48714i
$668$	8.95999e6	+	5.17305e6i	0.0300592	+	0.0173547i
$669$	5.53339e7	−	2.15724e8i	0.184805	−	0.720477i
$670$	6.26718e7	+	1.08551e8i	0.208376	+	0.360918i
$671$		−	2.43147e8i		−	0.804826i
$672$	−8.30519e7	−	3.44400e7i	−0.273679	−	0.113489i
$673$	3.58623e7			0.117650			0.0588251	−	0.998268i	$-0.481265\pi$
$673$	3.58623e7			0.117650			0.0588251	+	0.998268i	$0.481265\pi$
$674$	5.16472e7	−	2.98185e7i	0.168681	−	0.0973881i
$675$	−2.97187e7	−	9.81804e7i	−0.0966315	−	0.319237i
$676$	−2.26933e7	+	3.93060e7i	−0.0734612	+	0.127238i
$677$	−1.91967e8	+	1.10832e8i	−0.618671	+	0.357190i	−0.776352	−	0.630300i	$-0.782932\pi$
$677$	−1.91967e8	+	1.10832e8i	−0.618671	+	0.357190i	0.157680	+	0.987490i	$0.449599\pi$
$678$	−4.31264e8	+	1.20521e8i	−1.38374	+	0.386701i
$679$	−1.88654e8	−	4.70157e8i	−0.602640	−	1.50187i
$680$			2.72456e8i			0.866503i
$681$	3.02214e8	−	3.08757e8i	0.956914	−	0.977632i
$682$	8.94215e7	−	1.54883e8i	0.281896	−	0.488258i
$683$	−1.47158e8	−	8.49617e7i	−0.461872	−	0.266662i	0.250959	−	0.967998i	$-0.419254\pi$
$683$	−1.47158e8	−	8.49617e7i	−0.461872	−	0.266662i	−0.712831	+	0.701336i	$0.752587\pi$
$684$	−3.58268e7	−	1.96738e7i	−0.111954	−	0.0614781i
$685$	4.67820e7			0.145548
$686$	3.44448e8	−	3.37168e7i	1.06697	−	0.104442i
$687$	−4.55515e8	+	1.27299e8i	−1.40486	+	0.392603i
$688$	−5.79461e6	−	1.00366e7i	−0.0177934	−	0.0308191i
$689$	6.05633e6	+	3.49663e6i	0.0185162	+	0.0106903i
$690$	3.00541e8	+	7.70898e7i	0.914864	+	0.234666i
$691$	−2.24103e6	−	3.88158e6i	−0.00679226	−	0.0117645i	0.862609	−	0.505871i	$-0.168829\pi$
$691$	−2.24103e6	−	3.88158e6i	−0.00679226	−	0.0117645i	−0.869402	+	0.494106i	$0.835495\pi$
$692$			4.52987e7i			0.136700i
$693$	−2.48932e8	+	3.31435e8i	−0.747964	+	0.995859i
$694$	2.44883e7			0.0732622
$695$	−2.47663e8	+	1.42989e8i	−0.737747	+	0.425938i
$696$	1.21564e8	−	4.73927e8i	0.360559	−	1.40567i
$697$	−1.64333e8	+	2.84634e8i	−0.485319	+	0.840597i
$698$	−1.56026e8	+	9.00816e7i	−0.458808	+	0.264893i
$699$	−7.37314e7	−	2.63835e8i	−0.215884	−	0.772503i
$700$	1.05500e7	−	1.34373e7i	0.0307581	−	0.0391759i
$701$			3.03741e8i			0.881758i	0.897567	+	0.440879i	$0.145333\pi$
$701$			3.03741e8i			0.881758i	−0.897567	+	0.440879i	$0.854667\pi$
$702$	1.07209e7	−	4.58557e7i	0.0309899	−	0.132551i
$703$	2.23711e8	−	3.87479e8i	0.643905	−	1.11528i
$704$	−3.04610e8	−	1.75867e8i	−0.873024	−	0.504041i
$705$	9.45958e7	+	9.25911e7i	0.269963	+	0.264242i
$706$	2.35078e8			0.668033
$707$	8.22607e7	−	5.75370e8i	0.232774	−	1.62813i
$708$	2.77235e6	+	9.92037e6i	0.00781176	+	0.0279530i
$709$	−8.39000e7	−	1.45319e8i	−0.235409	−	0.407741i	0.723982	−	0.689819i	$-0.242310\pi$
$709$	−8.39000e7	−	1.45319e8i	−0.235409	−	0.407741i	−0.959392	+	0.282078i	$0.908976\pi$
$710$	4.69781e8	+	2.71228e8i	1.31256	+	0.757808i
$711$	−5.04513e6	−	2.35512e8i	−0.0140367	−	0.655246i
$712$	−1.69902e8	−	2.94278e8i	−0.470715	−	0.815301i
$713$			1.65165e8i			0.455669i
$714$	−4.50307e8	+	5.91013e7i	−1.23713	+	0.162369i
$715$	−4.71903e7			−0.129103
$716$	−1.38103e7	+	7.97340e6i	−0.0376240	+	0.0217222i
$717$	−9.41864e7	−	2.41591e7i	−0.255523	−	0.0655426i
$718$	−2.01391e8	+	3.48819e8i	−0.544085	+	0.942383i
$719$	5.06681e8	−	2.92532e8i	1.36316	−	0.787022i	0.373119	−	0.927784i	$-0.378288\pi$
$719$	5.06681e8	−	2.92532e8i	1.36316	−	0.787022i	0.990044	+	0.140762i	$0.0449551\pi$
$720$	−1.78038e8	−	2.93661e8i	−0.476996	−	0.786771i
$721$	−2.55677e8	+	3.25650e8i	−0.682159	+	0.868851i
$722$		−	1.08315e8i		−	0.287790i
$723$	1.61661e7	+	1.58235e7i	0.0427752	+	0.0418686i
$724$	4.70283e7	−	8.14554e7i	0.123921	−	0.214637i
$725$	1.75159e8	+	1.01128e8i	0.459640	+	0.265373i
$726$	1.58166e8	−	1.61591e8i	0.413337	−	0.422286i
$727$	6.59467e8			1.71629			0.858144	−	0.513409i	$-0.171618\pi$
$727$	6.59467e8			1.71629			0.858144	+	0.513409i	$0.171618\pi$
$728$	−4.14645e7	+	1.66380e7i	−0.107469	+	0.0431228i
$729$	−2.48770e7	−	3.86621e8i	−0.0642118	−	0.997936i
$730$	−2.22550e8	−	3.85468e8i	−0.572083	−	0.990877i
$731$	−1.24319e7	−	7.17753e6i	−0.0318261	−	0.0183748i
$732$	−9.40387e6	+	3.66618e7i	−0.0239758	+	0.0934717i
$733$	7.82392e7	+	1.35514e8i	0.198661	+	0.344091i	0.948094	−	0.317989i	$-0.103007\pi$
$733$	7.82392e7	+	1.35514e8i	0.198661	+	0.344091i	−0.749434	+	0.662079i	$0.769674\pi$
$734$		−	2.81569e8i		−	0.712026i
$735$	2.78840e8	+	1.65295e8i	0.702253	+	0.416293i
$736$	−1.27472e8			−0.319729
$737$	−2.05605e8	+	1.18706e8i	−0.513608	+	0.296531i
$738$	−7.69676e6	−	3.59293e8i	−0.0191487	−	0.893881i
$739$	1.52213e8	−	2.63641e8i	0.377155	−	0.653251i	−0.613492	−	0.789701i	$-0.710236\pi$
$739$	1.52213e8	−	2.63641e8i	0.377155	−	0.653251i	0.990647	+	0.136450i	$0.0435692\pi$
$740$	−6.44150e7	+	3.71900e7i	−0.158962	+	0.0917765i
$741$	−4.25565e7	+	1.18929e7i	−0.104595	+	0.0292302i
$742$	2.74629e7	+	6.84418e7i	0.0672255	+	0.167537i
$743$			2.42933e8i			0.592272i	0.955146	+	0.296136i	$0.0956981\pi$
$743$			2.42933e8i			0.592272i	−0.955146	+	0.296136i	$0.904302\pi$
$744$	1.10930e8	−	1.13332e8i	0.269359	−	0.275191i
$745$	7.35951e7	−	1.27470e8i	0.177984	−	0.308277i
$746$	−6.45861e7	−	3.72888e7i	−0.155569	−	0.0898177i
$747$	−2.46220e8	+	4.48376e8i	−0.590692	+	1.07567i
$748$	9.05907e7			0.216461
$749$	3.28409e8	+	2.57843e8i	0.781573	+	0.613635i
$750$	4.74209e8	−	1.32523e8i	1.12405	−	0.314128i
$751$	−1.14814e8	−	1.98864e8i	−0.271066	−	0.469501i	0.698069	−	0.716031i	$-0.254043\pi$
$751$	−1.14814e8	−	1.98864e8i	−0.271066	−	0.469501i	−0.969135	+	0.246530i	$0.920710\pi$
$752$	−1.92066e8	−	1.10890e8i	−0.451646	−	0.260758i
$753$	−4.28764e8	−	1.09979e8i	−1.00423	−	0.257588i
$754$	4.64258e7	+	8.04119e7i	0.108304	+	0.187588i
$755$			2.74630e8i			0.638126i
$756$	5.03524e7	−	4.03461e7i	0.116534	−	0.0933763i
$757$	8.30994e8			1.91562			0.957812	−	0.287395i	$-0.0927892\pi$
$757$	8.30994e8			1.91562			0.957812	+	0.287395i	$0.0927892\pi$
$758$	4.40021e8	−	2.54046e8i	1.01034	−	0.583318i
$759$	−1.46015e8	+	5.69253e8i	−0.333943	+	1.30191i
$760$	−1.39767e8	+	2.42084e8i	−0.318393	+	0.551473i
$761$	−9.38045e7	+	5.41581e7i	−0.212848	+	0.122888i	−0.602634	−	0.798017i	$-0.705882\pi$
$761$	−9.38045e7	+	5.41581e7i	−0.212848	+	0.122888i	0.389786	+	0.920905i	$0.372549\pi$
$762$	1.08352e8	+	3.87720e8i	0.244892	+	0.876300i
$763$	−3.59959e8	−	5.14634e7i	−0.810363	−	0.115858i
$764$

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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	21.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(7.42751 - 4.28827i) q^{2} +(6.70842 - 26.1533i) q^{3} +(4.77856 - 8.27670i) q^{4} +(88.3745 - 51.0231i) q^{5} +(-62.3258 - 223.022i) q^{6} +(-127.732 - 318.329i) q^{7} +466.932i q^{8} +(-638.994 - 350.895i) q^{9} +O(q^{10})\)	\(q+(7.42751 - 4.28827i) q^{2} +(6.70842 - 26.1533i) q^{3} +(4.77856 - 8.27670i) q^{4} +(88.3745 - 51.0231i) q^{5} +(-62.3258 - 223.022i) q^{6} +(-127.732 - 318.329i) q^{7} +466.932i q^{8} +(-638.994 - 350.895i) q^{9} +(437.602 - 757.948i) q^{10} +(1435.62 + 828.858i) q^{11} +(-184.407 - 180.499i) q^{12} -278.963 q^{13} +(-2313.81 - 1816.64i) q^{14} +(-741.570 - 2653.57i) q^{15} +(2308.16 + 3997.85i) q^{16} +(4951.96 + 2859.02i) q^{17} +(-6250.87 + 133.906i) q^{18} +(2933.29 + 5080.60i) q^{19} -975.266i q^{20} +(-9182.25 + 1205.14i) q^{21} +14217.5 q^{22} +(-11371.0 + 6565.05i) q^{23} +(12211.8 + 3132.37i) q^{24} +(-2605.79 + 4513.37i) q^{25} +(-2072.00 + 1196.27i) q^{26} +(-13463.7 + 14357.9i) q^{27} +(-3245.09 - 463.951i) q^{28} -38808.9i q^{29} +(-16887.3 - 16529.4i) q^{30} +(6289.55 - 10893.8i) q^{31} +(8407.73 + 4854.20i) q^{32} +(31308.2 - 31986.0i) q^{33} +49041.0 q^{34} +(-27530.4 - 21614.9i) q^{35} +(-5957.72 + 3611.99i) q^{36} +(-38133.2 - 66048.7i) q^{37} +(43574.0 + 25157.5i) q^{38} +(-1871.40 + 7295.81i) q^{39} +(23824.3 + 41264.9i) q^{40} +57478.9i q^{41} +(-63033.2 + 48327.2i) q^{42} -2510.49 q^{43} +(13720.4 - 7921.49i) q^{44} +(-74374.6 + 1593.25i) q^{45} +(-56305.4 + 97523.9i) q^{46} +(-41606.0 + 24021.2i) q^{47} +(120041. - 33546.8i) q^{48} +(-85017.9 + 81321.9i) q^{49} +44697.4i q^{50} +(107993. - 110331. i) q^{51} +(-1333.04 + 2308.89i) q^{52} +(-21710.2 - 12534.4i) q^{53} +(-38431.4 + 164379. i) q^{54} +169163. q^{55} +(148638. - 59642.3i) q^{56} +(152552. - 42632.5i) q^{57} +(-166423. - 288253. i) q^{58} +(-34569.8 - 19958.9i) q^{59} +(-25506.5 - 6542.50i) q^{60} +(-73338.1 - 127025. i) q^{61} -107885. i q^{62} +(-30079.9 + 248231. i) q^{63} -212180. q^{64} +(-24653.2 + 14233.5i) q^{65} +(95376.7 - 371834. i) q^{66} +(-71608.3 + 124029. i) q^{67} +(47326.5 - 27324.0i) q^{68} +(95416.5 + 341431. i) q^{69} +(-297173. - 42486.8i) q^{70} +619806. i q^{71} +(163844. - 298367. i) q^{72} +(254284. - 440433. i) q^{73} +(-566469. - 327051. i) q^{74} +(100559. + 98427.7i) q^{75} +56067.5 q^{76} +(80474.0 - 562873. i) q^{77} +(17386.6 + 62214.7i) q^{78} +(161568. + 279844. i) q^{79} +(407965. + 235539. i) q^{80} +(285186. + 448440. i) q^{81} +(246485. + 426925. i) q^{82} -701690. i q^{83} +(-33903.3 + 81757.6i) q^{84} +583503. q^{85} +(-18646.7 + 10765.7i) q^{86} +(-1.01498e6 - 260346. i) q^{87} +(-387020. + 670338. i) q^{88} +(-630238. + 363868. i) q^{89} +(-545585. + 330772. i) q^{90} +(35632.6 + 88802.0i) q^{91} +125486. i q^{92} +(-242717. - 237573. i) q^{93} +(-206019. + 356835. i) q^{94} +(518456. + 299331. i) q^{95} +(183356. - 187326. i) q^{96} +1.47695e6 q^{97} +(-282741. + 968598. i) q^{98} +(-626513. - 1.03339e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - q^{3} + 382 q^{4} - 356 q^{6} + 1120 q^{7} + 1031 q^{9}+O(q^{10}) \) 28 * q - q^3 + 382 * q^4 - 356 * q^6 + 1120 * q^7 + 1031 * q^9	\( 28 q - q^{3} + 382 q^{4} - 356 q^{6} + 1120 q^{7} + 1031 q^{9} - 930 q^{10} - 404 q^{12} + 3632 q^{13} + 5450 q^{15} - 13706 q^{16} + 1612 q^{18} + 6830 q^{19} - 11333 q^{21} - 27348 q^{22} - 54498 q^{24} - 7640 q^{25} + 13268 q^{27} + 88522 q^{28} + 32380 q^{30} + 69410 q^{31} - 85459 q^{33} - 31344 q^{34} + 399028 q^{36} - 71830 q^{37} + 104570 q^{39} + 230250 q^{40} - 467782 q^{42} - 498904 q^{43} - 85375 q^{45} - 342660 q^{46} - 324728 q^{48} + 395668 q^{49} + 42177 q^{51} + 218000 q^{52} - 402122 q^{54} + 231660 q^{55} + 786782 q^{57} + 459522 q^{58} + 1021150 q^{60} + 153158 q^{61} + 179011 q^{63} - 1399412 q^{64} + 80896 q^{66} - 977098 q^{67} - 1520742 q^{69} - 139650 q^{70} - 1001352 q^{72} - 488350 q^{73} + 1434610 q^{75} + 6196280 q^{76} + 245176 q^{78} + 380762 q^{79} + 893531 q^{81} - 3665004 q^{82} + 1231496 q^{84} - 912540 q^{85} + 1452416 q^{87} - 1522482 q^{88} - 11713820 q^{90} - 1529416 q^{91} - 1690071 q^{93} - 3034044 q^{94} + 7549346 q^{96} + 7212176 q^{97} + 435866 q^{99}+O(q^{100}) \) 28 * q - q^3 + 382 * q^4 - 356 * q^6 + 1120 * q^7 + 1031 * q^9 - 930 * q^10 - 404 * q^12 + 3632 * q^13 + 5450 * q^15 - 13706 * q^16 + 1612 * q^18 + 6830 * q^19 - 11333 * q^21 - 27348 * q^22 - 54498 * q^24 - 7640 * q^25 + 13268 * q^27 + 88522 * q^28 + 32380 * q^30 + 69410 * q^31 - 85459 * q^33 - 31344 * q^34 + 399028 * q^36 - 71830 * q^37 + 104570 * q^39 + 230250 * q^40 - 467782 * q^42 - 498904 * q^43 - 85375 * q^45 - 342660 * q^46 - 324728 * q^48 + 395668 * q^49 + 42177 * q^51 + 218000 * q^52 - 402122 * q^54 + 231660 * q^55 + 786782 * q^57 + 459522 * q^58 + 1021150 * q^60 + 153158 * q^61 + 179011 * q^63 - 1399412 * q^64 + 80896 * q^66 - 977098 * q^67 - 1520742 * q^69 - 139650 * q^70 - 1001352 * q^72 - 488350 * q^73 + 1434610 * q^75 + 6196280 * q^76 + 245176 * q^78 + 380762 * q^79 + 893531 * q^81 - 3665004 * q^82 + 1231496 * q^84 - 912540 * q^85 + 1452416 * q^87 - 1522482 * q^88 - 11713820 * q^90 - 1529416 * q^91 - 1690071 * q^93 - 3034044 * q^94 + 7549346 * q^96 + 7212176 * q^97 + 435866 * q^99

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