LMFDB - Embedded newform 21.7.h.a.2.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,7,Mod(2,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("21.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	21.h (of order $6$, degree $2$, 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:	$4.83113575602$
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			2.4
Character	$\chi$	$=$	21.2
Dual form			21.7.h.a.11.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.42751 - 4.28827i) q^{2} +(19.2952 + 18.8863i) q^{3} +(4.77856 + 8.27670i) q^{4} +(-88.3745 - 51.0231i) q^{5} +(-62.3258 - 223.022i) q^{6} +(-127.732 + 318.329i) q^{7} +466.932i q^{8} +(15.6130 + 728.833i) q^{9} +O(q^{10})$	\(q+(-7.42751 - 4.28827i) q^{2} +(19.2952 + 18.8863i) 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} +(15.6130 + 728.833i) q^{9} +(437.602 + 757.948i) q^{10} +(-1435.62 + 828.858i) q^{11} +(-64.1131 + 249.950i) 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} +(3009.47 - 5480.36i) q^{18} +(2933.29 - 5080.60i) q^{19} -975.266i q^{20} +(-8476.70 + 3729.84i) q^{21} +14217.5 q^{22} +(11371.0 + 6565.05i) q^{23} +(-8818.63 + 9009.56i) 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} +(-5871.23 + 22889.5i) q^{30} +(6289.55 + 10893.8i) q^{31} +(-8407.73 + 4854.20i) q^{32} +(-43354.8 - 11120.6i) 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} +(-5382.66 - 5268.58i) q^{39} +(23824.3 - 41264.9i) q^{40} +57478.9i q^{41} +(78955.3 + 8646.95i) q^{42} -2510.49 q^{43} +(-13720.4 - 7921.49i) q^{44} +(35807.5 - 65206.9i) 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} +(-149546. - 38359.0i) q^{51} +(-1333.04 - 2308.89i) q^{52} +(21710.2 - 12534.4i) q^{53} +(161572. - 48907.1i) 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} +(18419.2 - 18818.0i) q^{60} +(-73338.1 + 127025. i) q^{61} -107885. i q^{62} +(-234003. - 88125.4i) q^{63} -212180. q^{64} +(24653.2 + 14233.5i) q^{65} +(274330. + 268516. 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} +(-340315. + 7290.22i) q^{72} +(254284. + 440433. i) q^{73} +(566469. - 327051. i) q^{74} +(34961.5 - 136300. i) 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} +(-530953. + 22758.6i) q^{81} +(246485. - 426925. i) q^{82} -701690. i q^{83} +(-71377.2 - 52335.8i) q^{84} +583503. q^{85} +(18646.7 + 10765.7i) q^{86} +(732957. - 748827. 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} +(-84385.9 + 328986. i) q^{93} +(-206019. - 356835. i) q^{94} +(-518456. + 299331. i) q^{95} +(-253907. - 65128.1i) 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 $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

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

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	$-0.513411\pi$
$2$	−7.42751	−	4.28827i	−0.928438	−	0.536034i	−0.886317	+	0.463079i	$0.846745\pi$
$3$	19.2952	+	18.8863i	0.714639	+	0.699494i
$3$	19.2952	+	18.8863i	0.714639	+	0.699494i
$4$	4.77856	+	8.27670i	0.0746649	+	0.129323i
$5$	−88.3745	−	51.0231i	−0.706996	−	0.408185i	0.102952	−	0.994686i	$-0.467171\pi$
$5$	−88.3745	−	51.0231i	−0.706996	−	0.408185i	−0.809948	+	0.586502i	$0.800505\pi$
$6$	−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
$9$	15.6130	+	728.833i	0.0214170	+	0.999771i
$10$	437.602	+	757.948i	0.437602	+	0.757948i
$11$	−1435.62	+	828.858i	−1.07861	+	0.622733i	−0.930520	−	0.366242i	$-0.880644\pi$
$11$	−1435.62	+	828.858i	−1.07861	+	0.622733i	−0.148085	+	0.988975i	$0.547311\pi$
$12$	−64.1131	+	249.950i	−0.0371025	+	0.144647i
$13$	−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	$-0.864369\pi$
$17$	−4951.96	+	2859.02i	−1.00793	+	0.581929i	−0.0973456	+	0.995251i	$0.531035\pi$
$18$	3009.47	−	5480.36i	0.516027	−	0.939705i
$19$	2933.29	−	5080.60i	0.427655	−	0.740721i	−0.569009	−	0.822331i	$-0.692673\pi$
$19$	2933.29	−	5080.60i	0.427655	−	0.740721i	0.996664	+	0.0816105i	$0.0260063\pi$
$20$		−	975.266i		−	0.121908i
$21$	−8476.70	+	3729.84i	−0.915311	+	0.402747i
$22$	14217.5			1.33522
$23$	11371.0	+	6565.05i	0.934577	+	0.539578i	0.888256	−	0.459348i	$-0.151917\pi$
$23$	11371.0	+	6565.05i	0.934577	+	0.539578i	0.0463208	+	0.998927i	$0.485250\pi$
$24$	−8818.63	+	9009.56i	−0.637922	+	0.651734i
$25$	−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	$-0.292856\pi$
$30$	−5871.23	+	22889.5i	−0.217453	+	0.847759i
$31$	6289.55	+	10893.8i	0.211123	+	0.365675i	0.952066	−	0.305892i	$-0.0989547\pi$
$31$	6289.55	+	10893.8i	0.211123	+	0.365675i	−0.740944	+	0.671567i	$0.765621\pi$
$32$	−8407.73	+	4854.20i	−0.256584	+	0.148139i
$33$	−43354.8	−	11120.6i	−1.20641	−	0.309448i
$34$	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	0.193613	+	0.981078i	$0.437979\pi$
$37$	−38133.2	+	66048.7i	−0.752832	+	1.30394i	−0.946445	+	0.322866i	$0.895354\pi$
$38$	−43574.0	+	25157.5i	−0.794103	+	0.458476i
$39$	−5382.66	−	5268.58i	−0.0907409	−	0.0888178i
$40$	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	$0.863084\pi$
$42$	78955.3	+	8646.95i	1.06570	+	0.116712i
$43$	−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
$45$	35807.5	−	65206.9i	0.392949	−	0.715576i
$46$	−56305.4	−	97523.9i	−0.578465	−	1.00193i
$47$	41606.0	+	24021.2i	0.400739	+	0.231367i	0.686803	−	0.726844i	$-0.259014\pi$
$47$	41606.0	+	24021.2i	0.400739	+	0.231367i	−0.286064	+	0.958211i	$0.592347\pi$
$48$	120041.	−	33546.8i	1.08544	−	0.303338i
$49$	−85017.9	−	81321.9i	−0.722640	−	0.691224i
$50$			44697.4i			0.357579i
$51$	−149546.	−	38359.0i	−1.12736	−	0.289172i
$52$	−1333.04	−	2308.89i	−0.00948054	−	0.0164208i
$53$	21710.2	−	12534.4i	0.145826	−	0.0841928i	−0.425312	−	0.905047i	$-0.639835\pi$
$53$	21710.2	−	12534.4i	0.145826	−	0.0841928i	0.571138	+	0.820854i	$0.306502\pi$
$54$	161572.	−	48907.1i	1.02609	−	0.310593i
$55$	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	$-0.635684\pi$
$59$	34569.8	−	19958.9i	0.168322	−	0.0971808i	0.581794	+	0.813336i	$0.302351\pi$
$60$	18419.2	−	18818.0i	0.0852741	−	0.0871204i
$61$	−73338.1	+	127025.i	−0.323102	+	0.559630i	−0.981126	−	0.193367i	$-0.938059\pi$
$61$	−73338.1	+	127025.i	−0.323102	+	0.559630i	0.658024	+	0.752997i	$0.271392\pi$
$62$		−	107885.i		−	0.452676i
$63$	−234003.	−	88125.4i	−0.935836	−	0.352436i
$64$	−212180.			−0.809401
$65$	24653.2	+	14233.5i	0.0897705	+	0.0518290i
$66$	274330.	+	268516.i	0.954203	+	0.933981i
$67$	−71608.3	−	124029.i	−0.238089	−	0.412382i	0.722077	−	0.691813i	$-0.243188\pi$
$67$	−71608.3	−	124029.i	−0.238089	−	0.412382i	−0.960166	+	0.279431i	$0.909854\pi$
$68$	−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	$0.666768\pi$
$72$	−340315.	+	7290.22i	−0.911767	+	0.0195318i
$73$	254284.	+	440433.i	0.653657	+	1.13217i	0.982229	+	0.187689i	$0.0600996\pi$
$73$	254284.	+	440433.i	0.653657	+	1.13217i	−0.328571	+	0.944479i	$0.606567\pi$
$74$	566469.	−	327051.i	1.39792	−	0.807087i
$75$	34961.5	−	136300.i	0.0828717	−	0.323082i
$76$	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	−0.654356	−	0.756186i	$-0.727060\pi$
$79$	161568.	−	279844.i	0.327698	−	0.567590i	0.982055	+	0.188596i	$0.0603937\pi$
$80$	−407965.	+	235539.i	−0.796806	+	0.460036i
$81$	−530953.	+	22758.6i	−0.999083	+	0.0428243i
$82$	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	$-0.210277\pi$
$84$	−71377.2	−	52335.8i	−0.120426	−	0.0883001i
$85$	583503.			0.950138
$86$	18646.7	+	10765.7i	0.0293161	+	0.0169257i
$87$	732957.	−	748827.i	1.11307	−	1.13716i
$88$	−387020.	−	670338.i	−0.567918	−	0.983662i
$89$	630238.	+	363868.i	0.893994	+	0.516148i	0.875247	−	0.483676i	$-0.160699\pi$
$89$	630238.	+	363868.i	0.893994	+	0.516148i	0.0187473	+	0.999824i	$0.494032\pi$
$90$	−545585.	+	330772.i	−0.748402	+	0.453734i
$91$	35632.6	−	88802.0i	0.0472850	−	0.117842i
$92$			125486.i			0.161150i
$93$	−84385.9	+	328986.i	−0.104911	+	0.409004i
$94$	−206019.	−	356835.i	−0.248041	−	0.429620i
$95$	−518456.	+	299331.i	−0.604702	+	0.349125i
$96$	−253907.	−	65128.1i	−0.286987	−	0.0736130i
$97$	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	$-0.974000\pi$
$101$	−1.46750e6	+	847260.i	−1.42434	+	0.822343i	−0.427673	+	0.903933i	$0.640667\pi$
$102$	946258.	+	926204.i	0.891680	+	0.872783i
$103$	−603539.	+	1.04536e6i	−0.552323	+	0.956652i	0.445783	+	0.895141i	$0.352925\pi$
$103$	−603539.	+	1.04536e6i	−0.552323	+	0.956652i	−0.998106	+	0.0615111i	$0.980408\pi$
$104$		−	130257.i		−	0.115798i
$105$	939432.	+	102884.i	0.811517	+	0.0888749i
$106$	−215003.			−0.180521
$107$	1.05422e6	+	608652.i	0.860554	+	0.496841i	0.864198	−	0.503152i	$-0.167827\pi$
$107$	1.05422e6	+	608652.i	0.860554	+	0.496841i	−0.00364376	+	0.999993i	$0.501160\pi$
$108$	−183173.	−	42825.3i	−0.145409	−	0.0339961i
$109$	530058.	+	918087.i	0.409302	+	0.708931i	0.994812	−	0.101734i	$-0.0324390\pi$
$109$	530058.	+	918087.i	0.409302	+	0.708931i	−0.585510	+	0.810665i	$0.699106\pi$
$110$	−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	$-0.233743\pi$
$114$	−1.31590e6	−	337534.i	−0.888198	−	0.227826i
$115$	−669938.	−	1.16037e6i	−0.440495	−	0.762960i
$116$	321209.	−	185450.i	0.205785	−	0.118810i
$117$	−4355.45	−	203317.i	−0.00271942	−	0.126945i
$118$	−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
$123$	−1.08557e6	+	1.10907e6i	−0.583366	+	0.595997i
$124$	−60110.0	+	104114.i	−0.0315269	+	0.0546062i
$125$			2.12629e6i			1.08866i
$126$	1.36015e6	+	1.65802e6i	0.679949	+	0.828855i
$127$	−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
$129$	−48440.5	−	47413.9i	−0.0225652	−	0.0220870i
$130$	−122075.	−	211439.i	−0.0555642	−	0.0962400i
$131$	−382494.	−	220833.i	−0.170142	−	0.0982313i	0.412511	−	0.910953i	$-0.364652\pi$
$131$	−382494.	−	220833.i	−0.170142	−	0.0982313i	−0.582653	+	0.812721i	$0.697985\pi$
$132$	−115131.	−	411975.i	−0.0500577	−	0.179122i
$133$	1.24263e6	+	1.58271e6i	0.528185	+	0.672738i
$134$			1.22830e6i			0.510495i
$135$	1.92243e6	−	581911.i	0.781358	−	0.236513i
$136$	−1.33497e6	−	2.31223e6i	−0.530706	−	0.919209i
$137$	−397020.	+	229220.i	−0.154401	+	0.0891436i	−0.575210	−	0.818006i	$-0.695080\pi$
$137$	−397020.	+	229220.i	−0.154401	+	0.0891436i	0.420809	+	0.907149i	$0.361746\pi$
$138$	755441.	−	2.94515e6i	0.287451	−	1.12065i
$139$	−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
$144$	2.94980e6	+	1.61984e6i	0.987882	+	0.542482i
$145$	−1.98015e6	+	3.42972e6i	−0.649521	+	1.12500i
$146$		−	4.36175e6i		−	1.40153i
$147$	−104570.	−	3.17480e6i	−0.0329195	−	0.999458i
$148$	−728887.			−0.224841
$149$	−1.24914e6	−	721194.i	−0.377619	−	0.218019i	0.299163	−	0.954202i	$-0.403293\pi$
$149$	−1.24914e6	−	721194.i	−0.377619	−	0.218019i	−0.676782	+	0.736184i	$0.736626\pi$
$150$	−844170.	+	862447.i	−0.250124	+	0.255540i
$151$	−1.34562e6	−	2.33067e6i	−0.390832	−	0.676941i	0.601727	−	0.798701i	$-0.294479\pi$
$151$	−1.34562e6	−	2.33067e6i	−0.390832	−	0.676941i	−0.992560	+	0.121761i	$0.961146\pi$
$152$	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
$156$	17885.2	−	69726.9i	0.00471107	−	0.0183665i
$157$	2.76937e6	+	4.79669e6i	0.715619	+	1.23949i	0.962720	+	0.270498i	$0.0871885\pi$
$157$	2.76937e6	+	4.79669e6i	0.715619	+	1.23949i	−0.247102	+	0.968990i	$0.579478\pi$
$158$	−2.40009e6	+	1.38570e6i	−0.608495	+	0.351315i
$159$	655632.	+	168172.i	0.163105	+	0.0418371i
$160$	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	−0.622905	−	0.782297i	$-0.714048\pi$
$163$	1.58521e6	−	2.74567e6i	0.366037	−	0.633994i	0.988942	+	0.148303i	$0.0473812\pi$
$164$	−475736.	+	274666.i	−0.107854	+	0.0622693i
$165$	3.26405e6	+	3.19488e6i	0.726616	+	0.711217i
$166$	−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	$0.962923\pi$
$168$	−1.74158e6	−	3.95804e6i	−0.367296	−	0.834742i
$169$	−4.74899e6			−0.983877
$170$	−4.33397e6	−	2.50222e6i	−0.882144	−	0.509306i
$171$	3.74871e6	+	2.05855e6i	0.749710	+	0.411693i
$172$	−11996.5	−	20778.6i	−0.00235760	−	0.00408348i
$173$	4.10478e6	+	2.36989e6i	0.792777	+	0.457710i	0.840939	−	0.541129i	$-0.182003\pi$
$173$	4.10478e6	+	2.36989e6i	0.792777	+	0.457710i	−0.0481622	+	0.998840i	$0.515336\pi$
$174$	−8.65521e6	+	2.41879e6i	−1.64297	+	0.459146i
$175$	1.76958e6	−	252997.i	0.330184	−	0.0472065i
$176$			7.65254e6i			1.40368i
$177$	1.04398e6	+	267785.i	0.188267	+	0.0482911i
$178$	−3.12073e6	−	5.40527e6i	−0.553346	−	0.958423i
$179$	1.44503e6	−	834290.i	0.251952	−	0.145465i	−0.368706	−	0.929546i	$-0.620199\pi$
$179$	1.44503e6	−	834290.i	0.251952	−	0.145465i	0.620658	+	0.784082i	$0.286866\pi$
$180$	710806.	−	15226.9i	0.121880	−	0.00261092i
$181$	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
$186$	2.03756e6	−	2.08167e6i	0.316644	−	0.323499i
$187$	4.73944e6	−	8.20895e6i	0.724773	−	1.25534i
$188$			459147.i			0.0691000i
$189$	−2.85078e6	−	6.11986e6i	−0.422258	−	0.906476i
$190$	5.13445e6			0.748571
$191$	−3.58555e6	−	2.07012e6i	−0.514583	−	0.297095i	0.220132	−	0.975470i	$-0.429351\pi$
$191$	−3.58555e6	−	2.07012e6i	−0.514583	−	0.297095i	−0.734716	+	0.678375i	$0.762684\pi$
$192$	−4.09406e6	−	4.00730e6i	−0.578429	−	0.566171i
$193$	−3.10980e6	−	5.38633e6i	−0.432574	−	0.749240i	0.564520	−	0.825419i	$-0.309061\pi$
$193$	−3.10980e6	−	5.38633e6i	−0.432574	−	0.749240i	−0.997094	+	0.0761794i	$0.975728\pi$
$194$	−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	$-0.125581\pi$
$198$	221978.	+	1.03622e7i	0.0285966	+	1.33492i
$199$	1.16360e6	+	2.01542e6i	0.147654	+	0.255744i	0.930360	−	0.366648i	$-0.119495\pi$
$199$	1.16360e6	+	2.01542e6i	0.147654	+	0.255744i	−0.782706	+	0.622392i	$0.786161\pi$
$200$	2.10743e6	−	1.21673e6i	0.263429	−	0.152091i
$201$	960757.	−	3.74559e6i	0.118311	−	0.461246i
$202$	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
$207$	−4.60729e6	+	8.39006e6i	−0.519439	+	0.945919i
$208$	−643890.	+	1.11525e6i	−0.0715520	+	0.123932i
$209$			9.72511e6i			1.06526i
$210$	−6.53644e6	−	4.79271e6i	−0.705803	−	0.517516i
$211$	−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
$213$	−1.17059e7	+	1.19593e7i	−1.21133	+	1.23756i
$214$	−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
$219$	−3.41169e6	+	1.33007e7i	−0.324815	+	1.26632i
$220$	808357.	+	1.40012e6i	0.0759163	+	0.131491i
$221$	1.38141e6	−	797560.i	0.127981	−	0.0738901i
$222$	1.71070e7	+	4.38799e6i	1.56356	+	0.401058i
$223$	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	$-0.906430\pi$
$227$	−1.38579e7	+	8.00086e6i	−1.18473	+	0.684004i	−0.227626	+	0.973749i	$0.573096\pi$
$228$	1.08184e6	+	1.05891e6i	0.0912761	+	0.0893418i
$229$	−8.75867e6	+	1.51705e7i	−0.729343	+	1.26326i	0.227818	+	0.973704i	$0.426841\pi$
$229$	−8.75867e6	+	1.51705e7i	−0.729343	+	1.26326i	−0.957161	+	0.289556i	$0.906492\pi$
$230$			1.14915e7i			0.944481i
$231$	9.07784e6	−	1.23806e7i	0.736455	−	1.00440i
$232$	1.81211e7			1.45118
$233$	−8.78674e6	−	5.07303e6i	−0.694640	−	0.401051i	0.110708	−	0.993853i	$-0.464688\pi$
$233$	−8.78674e6	−	5.07303e6i	−0.694640	−	0.401051i	−0.805348	+	0.592802i	$0.798022\pi$
$234$	−839530.	+	1.52882e6i	−0.0655222	+	0.119319i
$235$	−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	$-0.0421070\pi$
$240$	−1.23202e7	−	3.16018e6i	−0.891221	−	0.228601i
$241$	−418915.	−	725582.i	−0.0299278	−	0.0518365i	0.850674	−	0.525694i	$-0.176194\pi$
$241$	−418915.	−	725582.i	−0.0299278	−	0.0518365i	−0.880601	+	0.473858i	$0.842861\pi$
$242$	−7.25266e6	+	4.18732e6i	−0.511742	+	0.295454i
$243$	−1.06747e7	−	9.58863e6i	−0.743938	−	0.668248i
$244$	−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
$249$	1.32524e7	−	1.35393e7i	0.858410	−	0.876996i
$250$	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	$-0.173461\pi$
$252$	−388809.	−	2.35789e6i	−0.0242960	−	0.147340i
$253$	−2.17660e7			−1.34405
$254$	1.29126e7	+	7.45509e6i	0.787975	+	0.454938i
$255$	1.12588e7	+	1.10202e7i	0.679005	+	0.664615i
$256$	−3.67838e6	−	6.37114e6i	−0.219249	−	0.379750i
$257$	−3.24923e6	−	1.87594e6i	−0.191417	−	0.110515i	0.401229	−	0.915978i	$-0.368583\pi$
$257$	−3.24923e6	−	1.87594e6i	−0.191417	−	0.110515i	−0.592646	+	0.805463i	$0.701917\pi$
$258$	156468.	+	559893.i	0.00911102	+	0.0326021i
$259$	−1.61544e7	−	2.05755e7i	−0.929802	−	1.18427i
$260$			272063.i			0.0154792i
$261$	2.82852e7	−	605924.i	1.59088	−	0.0340798i
$262$	1.89398e6	+	3.28047e6i	0.105311	+	0.182403i
$263$	3.67446e6	−	2.12145e6i	0.201988	−	0.116618i	−0.395594	−	0.918425i	$-0.629461\pi$
$263$	3.67446e6	−	2.12145e6i	0.201988	−	0.116618i	0.597583	+	0.801807i	$0.296128\pi$
$264$	5.19259e6	−	2.02437e7i	0.282210	−	1.10022i
$265$	−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	$-0.686391\pi$
$269$	−2.08782e6	+	1.20540e6i	−0.107260	+	0.0619264i	0.445411	+	0.895326i	$0.353058\pi$
$270$	−1.67743e7	−	3.92177e6i	−0.852221	−	0.199247i
$271$	−4.37442e6	+	7.57672e6i	−0.219792	+	0.380692i	−0.954744	−	0.297427i	$-0.903871\pi$
$271$	−4.37442e6	+	7.57672e6i	−0.219792	+	0.380692i	0.734952	+	0.678119i	$0.237205\pi$
$272$			2.63963e7i			1.31170i
$273$	2.36468e6	−	1.04049e6i	0.116221	−	0.0511386i
$274$	3.93183e6			0.191136
$275$	7.48188e6	+	4.31966e6i	0.359760	+	0.207707i
$276$	−2.36997e6	+	2.42128e6i	−0.112724	+	0.115164i
$277$	−5.07001e6	−	8.78152e6i	−0.238545	−	0.413172i	0.721752	−	0.692152i	$-0.243337\pi$
$277$	−5.07001e6	−	8.78152e6i	−0.238545	−	0.413172i	−0.960297	+	0.278980i	$0.910004\pi$
$278$	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	$-0.00957132\pi$
$282$	2.76412e6	−	1.07762e7i	0.123257	−	0.480526i
$283$	7.51770e6	+	1.30210e7i	0.331685	+	0.574495i	0.982842	−	0.184448i	$-0.0590496\pi$
$283$	7.51770e6	+	1.30210e7i	0.331685	+	0.574495i	−0.651157	+	0.758943i	$0.725716\pi$
$284$	−5.12995e6	+	2.96178e6i	−0.223953	+	0.129300i
$285$	−1.56570e7	−	4.01607e6i	−0.676354	−	0.173487i
$286$	−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
$291$	2.84981e7	+	2.78942e7i	1.15648	+	1.13197i
$292$	−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	$-0.183285\pi$
$294$	−1.28377e7	+	2.40293e7i	−0.505180	+	0.945581i
$295$	−4.07346e6			−0.158671
$296$	−3.08402e7	−	1.78056e7i	−1.18917	−	0.686565i
$297$	7.42819e6	−	3.17720e7i	0.283540	−	1.21276i
$298$	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
$303$	−4.43174e7	−	1.13676e7i	−1.59311	−	0.408638i
$304$	−1.35410e7	−	2.34537e7i	−0.481981	−	0.834815i
$305$	1.29624e7	−	7.48387e6i	0.456864	−	0.263771i
$306$	765678.	+	3.57427e7i	0.0267228	+	1.24745i
$307$	−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	$-0.764983\pi$
$311$	−1.58376e7	+	9.14385e6i	−0.526512	+	0.303982i	0.213083	+	0.977034i	$0.431650\pi$
$312$	2.46007e6	−	2.51333e6i	0.0809997	−	0.0827535i
$313$	−5.92720e6	+	1.02662e7i	−0.193293	+	0.334794i	−0.946340	−	0.323174i	$-0.895250\pi$
$313$	−5.92720e6	+	1.02662e7i	−0.193293	+	0.334794i	0.753046	+	0.657967i	$0.228584\pi$
$314$		−	4.75032e7i		−	1.53438i
$315$	1.61835e7	+	1.97276e7i	0.517774	+	0.631164i
$316$	3.08825e6			0.0978703
$317$	1.38377e7	+	7.98923e6i	0.434398	+	0.250800i	0.701218	−	0.712947i	$-0.252640\pi$
$317$	1.38377e7	+	7.98923e6i	0.434398	+	0.250800i	−0.266821	+	0.963746i	$0.585973\pi$
$318$	−4.14854e6	−	4.06062e6i	−0.129007	−	0.126273i
$319$	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
$324$	−2.72556e6	−	4.28579e6i	−0.0801346	−	0.126007i
$325$	726920.	+	1.25906e6i	0.0211756	+	0.0366773i
$326$	−2.35483e7	+	1.35956e7i	−0.679685	+	0.392416i
$327$	−7.11170e6	+	2.77256e7i	−0.203390	+	0.792934i
$328$	−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	0.101559	−	0.994829i	$-0.467617\pi$
$331$	3.30853e7	−	5.73054e7i	0.912327	−	1.58020i	0.810768	−	0.585368i	$-0.199050\pi$
$332$	5.80768e6	−	3.35307e6i	0.158704	−	0.0916279i
$333$	−4.87338e7	−	2.67615e7i	−1.31977	−	0.724733i
$334$	4.64229e6	−	8.04069e6i	0.124593	−	0.215801i
$335$			1.46147e7i			0.388737i
$336$	−4.65421e6	+	4.24976e7i	−0.122695	+	1.12033i
$337$	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
$339$	3.65211e7	−	3.73118e7i	0.937442	−	0.957739i
$340$	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
$345$	8.98845e6	−	3.50422e7i	0.218891	−	0.853364i
$346$	−2.03255e7	−	3.52048e7i	−0.490696	−	0.849911i
$347$	−2.47273e6	+	1.42763e6i	−0.0591818	+	0.0341686i	−0.529299	−	0.848435i	$-0.677545\pi$
$347$	−2.47273e6	+	1.42763e6i	−0.0591818	+	0.0341686i	0.470117	+	0.882604i	$0.344212\pi$
$348$	9.70029e6	+	2.48816e6i	0.230169	+	0.0590391i
$349$	−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	$-0.767519\pi$
$353$	−2.37372e7	+	1.37047e7i	−0.539643	+	0.311563i	0.205291	+	0.978701i	$0.434186\pi$
$354$	−6.60586e6	−	6.46586e6i	−0.148908	−	0.145753i
$355$	3.16244e7	−	5.47750e7i	0.706866	−	1.22433i
$356$			6.95506e6i			0.154153i
$357$	3.13126e7	−	4.27051e7i	0.688200	−	0.938588i
$358$	−1.43106e7			−0.311896
$359$	4.06713e7	+	2.34816e7i	0.879032	+	0.507510i	0.870339	−	0.492453i	$-0.163900\pi$
$359$	4.06713e7	+	2.34816e7i	0.879032	+	0.507510i	0.00869313	+	0.999962i	$0.497233\pi$
$360$	3.04472e7	+	1.67197e7i	0.652589	+	0.358360i
$361$	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
$366$	3.29002e7	+	8.43902e6i	0.671052	+	0.172127i
$367$	1.64150e7	+	2.84317e7i	0.332081	+	0.575181i	0.982920	−	0.184035i	$-0.0589160\pi$
$367$	1.64150e7	+	2.84317e7i	0.332081	+	0.575181i	−0.650839	+	0.759216i	$0.725583\pi$
$368$	5.24921e7	−	3.03063e7i	1.05330	−	0.608121i
$369$	−4.18925e7	+	897420.i	−0.833792	+	0.0178614i
$370$	−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	−0.904871	−	0.425687i	$-0.860033\pi$
$373$	−4.34777e6	+	7.53055e6i	−0.0837799	+	0.145111i	0.821091	+	0.570798i	$0.193366\pi$
$374$	−7.04044e7	+	4.06480e7i	−1.34581	+	0.777006i
$375$	−4.01579e7	+	4.10273e7i	−0.761512	+	0.778000i
$376$	−1.12163e7	+	1.94272e7i	−0.211001	+	0.365465i
$377$			1.08262e7i			0.202047i
$378$	−5.06945e6	+	5.76802e7i	−0.0938610	+	1.06795i
$379$	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
$381$	−3.35445e7	−	3.28336e7i	−0.606522	−	0.593668i
$382$	1.77545e7	+	3.07516e7i	0.318506	+	0.551668i
$383$	6.91860e7	+	3.99446e7i	1.23146	+	0.710987i	0.967335	−	0.253501i	$-0.0815820\pi$
$383$	6.91860e7	+	3.99446e7i	1.23146	+	0.710987i	0.264130	+	0.964487i	$0.414915\pi$
$384$	1.77395e7	+	6.34777e7i	0.313292	+	1.12106i
$385$	−2.16076e7	+	5.38497e7i	−0.378639	+	0.943628i
$386$			5.33426e7i			0.927497i
$387$	−39196.3	−	1.82973e6i	−0.000676258	−	0.0315685i
$388$	7.05769e6	+	1.22243e7i	0.120828	+	0.209280i
$389$	5.62167e7	−	3.24567e7i	0.955029	−	0.551386i	0.0603893	−	0.998175i	$-0.480766\pi$
$389$	5.62167e7	−	3.24567e7i	0.955029	−	0.551386i	0.894639	+	0.446789i	$0.147432\pi$
$390$	1.63785e6	−	6.38532e6i	0.0276110	−	0.107644i
$391$	−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
$396$	5.55922e6	−	1.01236e7i	0.0895217	−	0.163023i
$397$	−2.19560e7	+	3.80290e7i	−0.350899	+	0.607776i	−0.986407	−	0.164319i	$-0.947457\pi$
$397$	−2.19560e7	+	3.80290e7i	−0.350899	+	0.607776i	0.635508	+	0.772094i	$0.280791\pi$
$398$		−	1.99593e7i		−	0.316590i
$399$	−5.91473e6	+	5.40075e7i	−0.0931143	+	0.850227i
$400$	−2.40583e7			−0.375911
$401$	313037.	+	180732.i	0.00485470	+	0.00280286i	0.502425	−	0.864621i	$-0.332441\pi$
$401$	313037.	+	180732.i	0.00485470	+	0.00280286i	−0.497571	+	0.867423i	$0.665774\pi$
$402$	−2.31981e7	+	2.37004e7i	−0.357088	+	0.364819i
$403$	−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
$408$	1.79110e7	−	6.98277e7i	0.263718	−	1.02813i
$409$	2.82790e7	+	4.89806e7i	0.413327	+	0.715903i	0.995251	−	0.0973398i	$-0.0310334\pi$
$409$	2.82790e7	+	4.89806e7i	0.413327	+	0.715903i	−0.581924	+	0.813243i	$0.697700\pi$
$410$	−4.35661e7	+	2.51529e7i	−0.632116	+	0.364952i
$411$	−1.19897e7	−	3.07540e6i	−0.172697	−	0.0442972i
$412$	−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
$417$	−5.40736e7	−	5.29276e7i	−0.745722	−	0.729918i
$418$	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	$-0.193633\pi$
$420$	3.63759e6	+	8.26704e6i	0.0490983	+	0.111584i
$421$	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
$423$	−1.68579e7	+	3.06988e7i	−0.222731	+	0.405603i
$424$	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
$429$	1.20944e7	+	3.10225e6i	0.153183	+	0.0392920i
$430$	−1.09859e6	−	1.90282e6i	−0.0138176	−	0.0239327i
$431$	−1.11174e8	+	6.41866e7i	−1.38859	+	0.801701i	−0.993156	−	0.116795i	$-0.962738\pi$
$431$	−1.11174e8	+	6.41866e7i	−1.38859	+	0.801701i	−0.395431	+	0.918496i	$0.629405\pi$
$432$	2.63242e7	+	8.69662e7i	0.326516	+	1.07870i
$433$	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
$438$	8.23775e7	−	8.41611e7i	0.980362	−	1.00159i
$439$	3.23972e7	−	5.61137e7i	0.382926	−	0.663247i	−0.608553	−	0.793513i	$-0.708250\pi$
$439$	3.23972e7	−	5.61137e7i	0.382926	−	0.663247i	0.991479	+	0.130266i	$0.0415832\pi$
$440$			7.89878e7i			0.927261i
$441$	5.79427e7	−	6.32335e7i	0.675589	−	0.737278i
$442$	−1.36806e7			−0.158430
$443$	−6.45405e7	−	3.72625e7i	−0.742371	−	0.428608i	0.0805598	−	0.996750i	$-0.474329\pi$
$443$	−6.45405e7	−	3.72625e7i	−0.742371	−	0.428608i	−0.822931	+	0.568142i	$0.807663\pi$
$444$	−1.40640e7	−	1.37660e7i	−0.160680	−	0.157275i
$445$	−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	$0.626696\pi$
$450$	−3.25769e7	+	697862.i	−0.357497	+	0.00765829i
$451$	−4.76419e7	−	8.25181e7i	−0.519349	−	0.899538i
$452$	1.60049e7	−	9.24044e6i	0.173316	−	0.100064i
$453$	1.80539e7	−	7.03847e7i	0.194212	−	0.757153i
$454$	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	−0.263075	+	0.964775i	$0.584737\pi$
$457$	−9.22998e7	+	1.59868e8i	−0.967058	+	1.67499i	−0.703982	+	0.710217i	$0.748597\pi$
$458$	1.30110e8	−	7.51192e7i	1.35430	−	0.781906i
$459$	2.56224e7	−	1.09593e8i	0.264961	−	1.13330i
$460$	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	$0.785595\pi$
$462$	−1.20517e8	+	5.30289e7i	−1.22215	+	0.537758i
$463$	−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
$465$	2.42434e7	−	2.47683e7i	0.241121	−	0.246342i
$466$	4.35090e7	+	7.53599e7i	0.429954	+	0.744702i
$467$	1.08903e8	+	6.28750e7i	1.06927	+	0.617344i	0.927982	−	0.372624i	$-0.121542\pi$
$467$	1.08903e8	+	6.28750e7i	1.06927	+	0.617344i	0.141289	+	0.989968i	$0.454875\pi$
$468$	1.66198e6	−	1.00761e6i	0.0162140	−	0.00983005i
$469$	4.86288e7	−	6.95247e6i	0.471384	−	0.0673939i
$470$			4.20469e7i			0.404986i
$471$	−3.71562e7	+	1.44856e8i	−0.355605	+	1.38636i
$472$	9.31944e6	+	1.61417e7i	0.0886266	+	0.153506i
$473$	3.60412e6	−	2.08084e6i	0.0340577	−	0.0196632i
$474$	−7.24811e7	−	1.85917e7i	−0.680597	−	0.174575i
$475$	−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	$-0.634278\pi$
$479$	1.93355e7	−	1.11634e7i	0.175934	−	0.101575i	0.585381	+	0.810758i	$0.300945\pi$
$480$	1.91159e7	+	1.87108e7i	0.172851	+	0.169188i
$481$	1.06377e7	−	1.84251e7i	0.0955904	−	0.165568i
$482$			7.18569e6i			0.0641693i
$483$	−1.20875e8	−	1.32379e7i	−1.07274	−	0.117484i
$484$	9.33213e6			0.0823085
$485$	−1.30525e8	−	7.53586e7i	−1.14411	−	0.660553i
$486$	3.81678e7	+	1.16996e8i	0.332497	+	1.01920i
$487$	227444.	+	393944.i	0.00196919	+	0.00341074i	0.867008	−	0.498294i	$-0.166040\pi$
$487$	227444.	+	393944.i	0.00196919	+	0.00341074i	−0.865039	+	0.501704i	$0.832707\pi$
$488$	−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	$-0.202985\pi$
$492$	−1.43669e7	−	3.68515e6i	−0.120633	−	0.0309429i
$493$	1.10955e8	+	1.92180e8i	0.925991	+	1.60386i
$494$	1.21555e7	−	7.01800e6i	0.100831	−	0.0582147i
$495$	2.64115e6	+	1.23292e8i	0.0217760	+	1.01653i
$496$	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	−0.472653	−	0.881248i	$-0.656704\pi$
$499$	6.54628e7	−	1.13385e8i	0.526857	−	0.912543i	0.999510	−	0.0312944i	$-0.00996293\pi$
$500$	−1.75987e7	+	1.01606e7i	−0.140790	+	0.0812849i
$501$	−2.04455e7	+	2.08882e7i	−0.162587	+	0.166107i
$502$	−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	$0.924678\pi$
$504$	4.11486e7	−	1.09263e8i	0.321413	−	0.853460i
$505$	1.72919e8			1.34267
$506$	1.61667e8	+	9.33384e7i	1.24787	+	0.720458i
$507$	−9.16329e7	−	8.96910e7i	−0.703117	−	0.688216i
$508$	−8.30745e6	−	1.43889e7i	−0.0633689	−	0.109758i
$509$	9.49105e7	+	5.47966e7i	0.719715	+	0.415528i	0.814648	−	0.579956i	$-0.196930\pi$
$509$	9.49105e7	+	5.47966e7i	0.719715	+	0.415528i	−0.0949326	+	0.995484i	$0.530264\pi$
$510$	−3.63673e7	−	1.30134e8i	−0.274158	−	0.981024i
$511$	−1.72683e8	+	2.46885e7i	−1.29416	+	0.185026i
$512$		−	9.31352e7i		−	0.693912i
$513$	3.34537e7	+	1.10520e8i	0.247795	+	0.818629i
$514$	1.60891e7	+	2.78671e7i	0.118479	+	0.205212i
$515$	1.06675e8	−	6.15888e7i	0.780981	−	0.450900i
$516$	160955.	−	627498.i	0.00117154	−	0.00456734i
$517$	−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	$-0.605717\pi$
$521$	4.66166e7	−	2.69141e7i	0.329631	−	0.190312i	0.655677	+	0.755041i	$0.272383\pi$
$522$	−2.12687e8	−	1.16794e8i	−1.49530	−	0.821125i
$523$	1.36233e8	−	2.35962e8i	0.952306	−	1.64944i	0.211891	−	0.977293i	$-0.432038\pi$
$523$	1.36233e8	−	2.35962e8i	0.952306	−	1.64944i	0.740415	−	0.672149i	$-0.234629\pi$
$524$		−	4.22105e6i		−	0.0293377i
$525$	3.89227e7	+	2.85392e7i	0.268983	+	0.197226i
$526$	−3.63894e7			−0.250045
$527$	−6.22913e7	−	3.59639e7i	−0.425594	−	0.245717i
$528$	−1.44528e8	+	1.47658e8i	−0.981864	+	1.00312i
$529$	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
$534$	4.18704e7	−	1.63235e8i	0.274968	−	1.07199i
$535$	−6.21106e7	−	1.07579e8i	−0.405606	−	0.702530i
$536$	5.79132e7	−	3.34362e7i	0.376082	−	0.217131i
$537$	4.36389e7	+	1.11935e7i	0.281807	+	0.0722843i
$538$	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	−0.566802	−	0.823854i	$-0.691820\pi$
$541$	6.80986e7	−	1.17950e8i	0.430077	−	0.744916i	0.996880	+	0.0789380i	$0.0251529\pi$
$542$	6.49821e7	−	3.75174e7i	0.408127	−	0.235632i
$543$	1.89895e8	+	1.85870e8i	1.18608	+	1.16094i
$544$	2.77565e7	−	4.80757e7i	0.172412	−	0.298627i
$545$		−	1.08181e8i		−	0.668283i
$546$	−2.20256e7	−	2.41218e6i	−0.135316	−	0.0148194i
$547$	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
$549$	−9.37253e7	−	5.14680e7i	−0.566421	−	0.311043i
$550$	−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
$555$	2.03543e8	+	5.22096e7i	1.19063	+	0.305401i
$556$	−1.33916e7	−	2.31949e7i	−0.0779125	−	0.134948i
$557$	−2.01129e8	+	1.16122e8i	−1.16388	+	0.671968i	−0.952232	−	0.305377i	$-0.901217\pi$
$557$	−2.01129e8	+	1.16122e8i	−1.16388	+	0.671968i	−0.211651	+	0.977345i	$0.567884\pi$
$558$	7.86303e7	−	1.68442e6i	0.452572	−	0.00969497i
$559$	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	$-0.712199\pi$
$563$	−4.40626e7	+	2.54395e7i	−0.246913	+	0.142555i	0.371437	+	0.928458i	$0.378865\pi$
$564$	−8.67160e6	+	8.85935e6i	−0.0483350	+	0.0493815i
$565$	−9.86649e7	+	1.70893e8i	−0.547038	+	0.947497i
$566$		−	1.28952e8i		−	0.711177i
$567$	6.05752e7	−	1.71925e8i	0.332312	−	0.943170i
$568$	−2.89407e8			−1.57930
$569$	1.20964e8	+	6.98384e7i	0.656626	+	0.379103i	0.790990	−	0.611829i	$-0.209566\pi$
$569$	1.20964e8	+	6.98384e7i	0.656626	+	0.379103i	−0.134364	+	0.990932i	$0.542899\pi$
$570$	9.90704e7	+	9.69709e7i	0.534958	+	0.523621i
$571$	−1.08542e8	−	1.88000e8i	−0.583027	−	1.00983i	−0.995118	−	0.0986895i	$-0.968535\pi$
$571$	−1.08542e8	−	1.88000e8i	−0.583027	−	1.00983i	0.412092	−	0.911142i	$-0.364798\pi$
$572$	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
$576$	−3.31277e6	−	1.54644e8i	−0.0173350	−	0.809216i
$577$	−3.81534e7	−	6.60837e7i	−0.198612	−	0.344007i	0.749466	−	0.662042i	$-0.230310\pi$
$577$	−3.81534e7	−	6.60837e7i	−0.198612	−	0.344007i	−0.948079	+	0.318036i	$0.896977\pi$
$578$	−6.35672e7	+	3.67006e7i	−0.329192	+	0.190059i
$579$	4.17237e7	−	1.62663e8i	0.214955	−	0.838018i
$580$	−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
$585$	−9.98896e6	+	1.81903e7i	−0.0498945	+	0.0908599i
$586$	−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	$0.672374\pi$
$588$	2.57772e7	−	1.60365e7i	0.126795	−	0.0788817i
$589$	7.37963e7			0.361151
$590$	3.02556e7	+	1.74681e7i	0.147316	+	0.0850529i
$591$	1.11000e8	−	1.13404e8i	0.537726	−	0.549369i
$592$	1.76035e8	+	3.04902e8i	0.848465	+	1.46958i
$593$	−2.16280e8	−	1.24869e8i	−1.03718	−	0.598813i	−0.118143	−	0.992997i	$-0.537694\pi$
$593$	−2.16280e8	−	1.24869e8i	−1.03718	−	0.598813i	−0.919032	+	0.394183i	$0.871028\pi$
$594$	−1.91420e8	+	2.04133e8i	−0.913331	+	0.973987i
$595$	−7.45323e7	+	1.85746e8i	−0.353829	+	0.881798i
$596$		−	1.37851e7i		−	0.0651134i
$597$	−1.56118e7	+	6.08641e7i	−0.0733721	+	0.286047i
$598$	1.57071e7	+	2.72055e7i	0.0734502	+	0.127220i
$599$	−1.62210e7	+	9.36522e6i	−0.0754741	+	0.0435750i	−0.537262	−	0.843415i	$-0.680541\pi$
$599$	−1.62210e7	+	9.36522e6i	−0.0754741	+	0.0435750i	0.461788	+	0.886990i	$0.347208\pi$
$600$	6.36430e7	+	1.63246e7i	0.294643	+	0.0755770i
$601$	−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
$606$	2.80420e8	+	2.74478e8i	1.26006	+	1.23336i
$607$	−7.52753e7	+	1.30381e8i	−0.336579	+	0.582971i	−0.983787	−	0.179342i	$-0.942603\pi$
$607$	−7.52753e7	+	1.30381e8i	−0.336579	+	0.582971i	0.647208	+	0.762313i	$0.275936\pi$
$608$			5.69551e7i			0.253409i
$609$	1.44751e8	+	3.28971e8i	0.640870	+	1.45648i
$610$	−1.28371e8			−0.565561
$611$	−1.16065e7	−	6.70103e6i	−0.0508837	−	0.0293777i
$612$	1.91757e7	−	3.49197e7i	0.0836559	−	0.152341i
$613$	1.53242e7	+	2.65423e7i	0.0665267	+	0.115228i	0.897370	−	0.441279i	$-0.145475\pi$
$613$	1.53242e7	+	2.65423e7i	0.0665267	+	0.115228i	−0.830843	+	0.556506i	$0.812142\pi$
$614$	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	$0.873208\pi$
$618$	2.70754e8	+	6.94493e7i	1.14712	+	0.294240i
$619$	−1.32745e8	−	2.29921e8i	−0.559688	−	0.969409i	−0.997522	−	0.0703528i	$-0.977588\pi$
$619$	−1.32745e8	−	2.29921e8i	−0.559688	−	0.969409i	0.437834	−	0.899056i	$-0.355746\pi$
$620$	1.06244e7	−	6.13399e6i	0.0445788	−	0.0257376i
$621$	−2.47356e8	+	7.48735e7i	−1.03288	+	0.312646i
$622$	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
$627$	−1.83672e8	+	1.87648e8i	−0.745143	+	0.761276i
$628$	−2.64672e7	+	4.58425e7i	−0.106863	+	0.185093i
$629$		−	4.36094e8i		−	1.75238i
$630$	−3.56056e7	−	2.15926e8i	−0.142396	−	0.863542i
$631$	−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
$633$	−1.24913e8	−	1.22266e8i	−0.492488	−	0.482051i
$634$	−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
$639$	−4.51735e8	+	9.67704e6i	−1.73133	+	0.0370886i
$640$	−1.24553e8	−	2.15732e8i	−0.475131	−	0.822951i
$641$	4.04341e8	−	2.33447e8i	1.53523	−	0.886366i	0.536124	−	0.844140i	$-0.319888\pi$
$641$	4.04341e8	−	2.33447e8i	1.53523	−	0.886366i	0.999108	−	0.0422269i	$-0.0134452\pi$
$642$	7.00376e7	−	2.73048e8i	0.264683	−	1.03189i
$643$	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	$-0.526342\pi$
$647$	2.00170e8	−	1.15568e8i	0.739070	−	0.426702i	0.821731	+	0.569876i	$0.193009\pi$
$648$	−1.06267e7	−	2.47919e8i	−0.0390547	−	0.911140i
$649$	−3.30862e7	+	5.73069e7i	−0.121035	+	0.209639i
$650$		−	1.24689e7i		−	0.0454034i
$651$	−9.39469e7	−	6.88846e7i	−0.340518	−	0.249677i
$652$	3.03001e7			0.109320
$653$	−8.60382e7	−	4.96742e7i	−0.308995	−	0.178398i	0.337482	−	0.941332i	$-0.390425\pi$
$653$	−8.60382e7	−	4.96742e7i	−0.308995	−	0.178398i	−0.646477	+	0.762934i	$0.723758\pi$
$654$	1.71717e8	−	1.75435e8i	0.613875	−	0.627166i
$655$	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	$0.786055\pi$
$660$	−1.08456e7	+	4.22825e7i	−0.0377243	+	0.147072i
$661$	−2.85691e6	−	4.94832e6i	−0.00989219	−	0.0171338i	0.861037	−	0.508542i	$-0.169815\pi$
$661$	−2.85691e6	−	4.94832e6i	−0.00989219	−	0.0171338i	−0.870929	+	0.491409i	$0.836482\pi$
$662$	−4.91482e8	+	2.83757e8i	−1.69408	+	0.978077i
$663$	4.17177e7	+	1.07007e7i	0.143146	+	0.0367175i
$664$	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
$669$	1.59156e8	+	1.55783e8i	0.531549	+	0.520284i
$670$	6.26718e7	−	1.08551e8i	0.208376	−	0.360918i
$671$		−	2.43147e8i		−	0.804826i
$672$	5.31643e7	−	7.25071e7i	0.175191	−	0.238931i
$673$	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
$675$	9.98860e7	+	2.33530e7i	0.324783	+	0.0759332i
$676$	−2.26933e7	−	3.93060e7i	−0.0734612	−	0.127238i
$677$	1.91967e8	+	1.10832e8i	0.618671	+	0.357190i	0.776352	−	0.630300i	$-0.217068\pi$
$677$	1.91967e8	+	1.10832e8i	0.618671	+	0.357190i	−0.157680	+	0.987490i	$0.550401\pi$
$678$	−4.31264e8	+	1.20521e8i	−1.38374	+	0.386701i
$679$	−1.88654e8	+	4.70157e8i	−0.602640	+	1.50187i
$680$			2.72456e8i			0.866503i
$681$	−4.18498e8	−	1.07346e8i	−1.32511	−	0.339895i
$682$	8.94215e7	+	1.54883e8i	0.281896	+	0.488258i
$683$	1.47158e8	−	8.49617e7i	0.461872	−	0.266662i	−0.250959	−	0.967998i	$-0.580746\pi$
$683$	1.47158e8	−	8.49617e7i	0.461872	−	0.266662i	0.712831	+	0.701336i	$0.247413\pi$
$684$	875384.	+	4.08639e7i	0.00273546	+	0.127694i
$685$	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
$690$	−2.17032e8	+	2.21731e8i	−0.660659	+	0.674963i
$691$	−2.24103e6	+	3.88158e6i	−0.00679226	+	0.0117645i	−0.869402	−	0.494106i	$-0.835495\pi$
$691$	−2.24103e6	+	3.88158e6i	−0.00679226	+	0.0117645i	0.862609	+	0.505871i	$0.168829\pi$
$692$			4.52987e7i			0.136700i
$693$	4.08984e8	−	6.74402e7i	1.22887	−	0.202637i
$694$	2.44883e7			0.0732622
$695$	2.47663e8	+	1.42989e8i	0.737747	+	0.425938i
$696$	3.49651e8	+	3.42241e8i	1.03707	+	1.01509i
$697$	−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	$0.854667\pi$
$702$	−4.50727e7	+	1.36433e7i	−0.130287	+	0.0394373i
$703$	2.23711e8	+	3.87479e8i	0.643905	+	1.11528i
$704$	3.04610e8	−	1.75867e8i	0.873024	−	0.504041i
$705$	3.28883e7	−	1.28218e8i	0.0938587	−	0.365916i
$706$	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	−0.959392	−	0.282078i	$-0.908976\pi$
$709$	−8.39000e7	+	1.45319e8i	−0.235409	+	0.407741i	0.723982	+	0.689819i	$0.242310\pi$
$710$	−4.69781e8	+	2.71228e8i	−1.31256	+	0.757808i
$711$	2.06482e8	+	1.13387e8i	0.574478	+	0.315467i
$712$	−1.69902e8	+	2.94278e8i	−0.470715	+	0.815301i
$713$			1.65165e8i			0.455669i
$714$	−4.15706e8	+	1.82915e8i	−1.14207	+	0.502522i
$715$	−4.71903e7			−0.129103
$716$	1.38103e7	+	7.97340e6i	0.0376240	+	0.0217222i
$717$	6.80156e7	−	6.94882e7i	0.184523	−	0.188518i
$718$	−2.01391e8	−	3.48819e8i	−0.544085	−	0.942383i
$719$	−5.06681e8	−	2.92532e8i	−1.36316	−	0.787022i	−0.373119	−	0.927784i	$-0.621712\pi$
$719$	−5.06681e8	−	2.92532e8i	−1.36316	−	0.787022i	−0.990044	+	0.140762i	$0.955045\pi$
$720$	−1.78038e8	−	2.93661e8i	−0.476996	−	0.786771i
$721$	−2.55677e8	−	3.25650e8i	−0.682159	−	0.868851i
$722$		−	1.08315e8i		−	0.287790i
$723$	5.62052e6	−	2.19121e7i	0.0148717	−	0.0579787i
$724$	4.70283e7	+	8.14554e7i	0.123921	+	0.214637i
$725$	−1.75159e8	+	1.01128e8i	−0.459640	+	0.265373i
$726$	−2.19025e8	−	5.61806e7i	−0.572379	−	0.146817i
$727$	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
$732$	−2.70481e7	−	2.64749e7i	−0.0689610	−	0.0674995i
$733$	7.82392e7	−	1.35514e8i	0.198661	−	0.344091i	−0.749434	−	0.662079i	$-0.769674\pi$
$733$	7.82392e7	−	1.35514e8i	0.198661	−	0.344091i	0.948094	+	0.317989i	$0.103007\pi$
$734$		−	2.81569e8i		−	0.712026i
$735$	−1.52747e8	+	2.85907e8i	−0.384689	+	0.720050i
$736$	−1.27472e8			−0.319729
$737$	2.05605e8	+	1.18706e8i	0.513608	+	0.296531i
$738$	3.15005e8	+	1.72981e8i	0.783698	+	0.430357i
$739$	1.52213e8	+	2.63641e8i	0.377155	+	0.653251i	0.990647	−	0.136450i	$-0.0435692\pi$
$739$	1.52213e8	+	2.63641e8i	0.377155	+	0.653251i	−0.613492	+	0.789701i	$0.710236\pi$
$740$	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	$0.904302\pi$
$744$	−1.53614e8	−	3.94025e7i	−0.373002	−	0.0956764i
$745$	7.35951e7	+	1.27470e8i	0.177984	+	0.308277i
$746$	6.45861e7	−	3.72888e7i	0.155569	−	0.0898177i
$747$	5.11415e8	−	1.09555e7i	1.22691	−	0.0262827i
$748$	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	−0.969135	−	0.246530i	$-0.920710\pi$
$751$	−1.14814e8	+	1.98864e8i	−0.271066	+	0.469501i	0.698069	+	0.716031i	$0.254043\pi$
$752$	1.92066e8	−	1.10890e8i	0.451646	−	0.260758i
$753$	3.09627e8	−	3.16331e8i	0.725193	−	0.740894i
$754$	4.64258e7	−	8.04119e7i	0.108304	−	0.187588i
$755$			2.74630e8i			0.638126i
$756$	3.70297e7	−	5.28392e7i	0.0857007	−	0.122290i
$757$	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
$759$	−4.19980e8	−	4.11079e8i	−0.960512	−	0.940157i
$760$	−1.39767e8	−	2.42084e8i

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)

\(f(q)\)	\(=\)	\(q+(-7.42751 - 4.28827i) q^{2} +(19.2952 + 18.8863i) q^{3} +(4.77856 + 8.27670i) q^{4} +(-88.3745 - 51.0231i) q^{5} +(-62.3258 - 223.022i) q^{6} +(-127.732 + 318.329i) q^{7} +466.932i q^{8} +(15.6130 + 728.833i) q^{9} +O(q^{10})\)	\(q+(-7.42751 - 4.28827i) q^{2} +(19.2952 + 18.8863i) 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} +(15.6130 + 728.833i) q^{9} +(437.602 + 757.948i) q^{10} +(-1435.62 + 828.858i) q^{11} +(-64.1131 + 249.950i) 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} +(3009.47 - 5480.36i) q^{18} +(2933.29 - 5080.60i) q^{19} -975.266i q^{20} +(-8476.70 + 3729.84i) q^{21} +14217.5 q^{22} +(11371.0 + 6565.05i) q^{23} +(-8818.63 + 9009.56i) 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} +(-5871.23 + 22889.5i) q^{30} +(6289.55 + 10893.8i) q^{31} +(-8407.73 + 4854.20i) q^{32} +(-43354.8 - 11120.6i) 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} +(-5382.66 - 5268.58i) q^{39} +(23824.3 - 41264.9i) q^{40} +57478.9i q^{41} +(78955.3 + 8646.95i) q^{42} -2510.49 q^{43} +(-13720.4 - 7921.49i) q^{44} +(35807.5 - 65206.9i) 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} +(-149546. - 38359.0i) q^{51} +(-1333.04 - 2308.89i) q^{52} +(21710.2 - 12534.4i) q^{53} +(161572. - 48907.1i) 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} +(18419.2 - 18818.0i) q^{60} +(-73338.1 + 127025. i) q^{61} -107885. i q^{62} +(-234003. - 88125.4i) q^{63} -212180. q^{64} +(24653.2 + 14233.5i) q^{65} +(274330. + 268516. 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} +(-340315. + 7290.22i) q^{72} +(254284. + 440433. i) q^{73} +(566469. - 327051. i) q^{74} +(34961.5 - 136300. i) 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} +(-530953. + 22758.6i) q^{81} +(246485. - 426925. i) q^{82} -701690. i q^{83} +(-71377.2 - 52335.8i) q^{84} +583503. q^{85} +(18646.7 + 10765.7i) q^{86} +(732957. - 748827. 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} +(-84385.9 + 328986. i) q^{93} +(-206019. - 356835. i) q^{94} +(-518456. + 299331. i) q^{95} +(-253907. - 65128.1i) 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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