LMFDB - Embedded newform 108.6.h.a.35.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,6,Mod(35,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("108.35");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	108.h (of order $6$, degree $2$, not 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:	$17.3214525398$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			35.10
Character	$\chi$	$=$	108.35
Dual form			108.6.h.a.71.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.66122 - 4.99179i) q^{2} +(-17.8359 + 26.5684i) q^{4} +(-3.68052 + 2.12495i) q^{5} +(13.9322 + 8.04377i) q^{7} +(180.089 + 18.3284i) q^{8} +O(q^{10})$	\(q+(-2.66122 - 4.99179i) q^{2} +(-17.8359 + 26.5684i) q^{4} +(-3.68052 + 2.12495i) q^{5} +(13.9322 + 8.04377i) q^{7} +(180.089 + 18.3284i) q^{8} +(20.4019 + 12.7174i) q^{10} +(43.3121 - 75.0187i) q^{11} +(162.502 + 281.462i) q^{13} +(3.07614 - 90.9529i) q^{14} +(-387.764 - 947.742i) q^{16} -1863.80i q^{17} -416.071i q^{19} +(9.18864 - 135.686i) q^{20} +(-489.740 - 16.5636i) q^{22} +(-1293.41 - 2240.24i) q^{23} +(-1553.47 + 2690.69i) q^{25} +(972.544 - 1560.21i) q^{26} +(-462.204 + 226.690i) q^{28} +(-4342.80 - 2507.32i) q^{29} +(6396.76 - 3693.17i) q^{31} +(-3699.00 + 4457.78i) q^{32} +(-9303.69 + 4959.98i) q^{34} -68.3704 q^{35} -10519.2 q^{37} +(-2076.94 + 1107.25i) q^{38} +(-701.768 + 315.222i) q^{40} +(-13207.4 + 7625.29i) q^{41} +(-6794.45 - 3922.78i) q^{43} +(1220.62 + 2488.76i) q^{44} +(-7740.79 + 12418.2i) q^{46} +(14244.6 - 24672.4i) q^{47} +(-8274.10 - 14331.2i) q^{49} +(17565.5 + 594.085i) q^{50} +(-10376.4 - 702.686i) q^{52} +5483.31i q^{53} +368.144i q^{55} +(2361.61 + 1703.95i) q^{56} +(-958.860 + 28350.9i) q^{58} +(-1901.12 - 3292.83i) q^{59} +(16590.1 - 28734.9i) q^{61} +(-35458.7 - 22102.9i) q^{62} +(32096.1 + 6601.49i) q^{64} +(-1196.18 - 690.617i) q^{65} +(57592.1 - 33250.8i) q^{67} +(49518.3 + 33242.5i) q^{68} +(181.948 + 341.290i) q^{70} -43573.3 q^{71} +22901.9 q^{73} +(27993.8 + 52509.6i) q^{74} +(11054.4 + 7420.98i) q^{76} +(1206.87 - 696.785i) q^{77} +(31941.7 + 18441.5i) q^{79} +(3441.08 + 2664.20i) q^{80} +(73211.6 + 45635.9i) q^{82} +(27504.3 - 47638.8i) q^{83} +(3960.48 + 6859.75i) q^{85} +(-1500.17 + 44355.8i) q^{86} +(9175.01 - 12716.2i) q^{88} -40969.8i q^{89} +5228.51i q^{91} +(82588.8 + 5592.90i) q^{92} +(-161068. - 5447.50i) q^{94} +(884.130 + 1531.36i) q^{95} +(23339.8 - 40425.7i) q^{97} +(-49518.9 + 79440.8i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 3 q^{2} - q^{4} + 6 q^{5}+O(q^{10}) $ 56 * q + 3 * q^2 - q^4 + 6 * q^5	$ 56 q + 3 q^{2} - q^{4} + 6 q^{5} - 68 q^{10} - 2 q^{13} + 1518 q^{14} - q^{16} + 1242 q^{20} + 63 q^{22} + 12498 q^{25} - 2052 q^{28} + 11946 q^{29} + 7233 q^{32} + 6361 q^{34} - 8 q^{37} + 14877 q^{38} - 1526 q^{40} + 43536 q^{41} - 26880 q^{46} + 38414 q^{49} - 38631 q^{50} + 24988 q^{52} - 21186 q^{56} - 3314 q^{58} - 2 q^{61} - 106342 q^{64} - 35970 q^{65} - 31413 q^{68} + 10524 q^{70} + 53620 q^{73} + 20406 q^{74} + 26193 q^{76} - 26178 q^{77} - 151286 q^{82} + 6248 q^{85} - 279237 q^{86} - 122541 q^{88} - 435804 q^{92} + 63480 q^{94} - 58148 q^{97}+O(q^{100}) $ 56 * q + 3 * q^2 - q^4 + 6 * q^5 - 68 * q^10 - 2 * q^13 + 1518 * q^14 - q^16 + 1242 * q^20 + 63 * q^22 + 12498 * q^25 - 2052 * q^28 + 11946 * q^29 + 7233 * q^32 + 6361 * q^34 - 8 * q^37 + 14877 * q^38 - 1526 * q^40 + 43536 * q^41 - 26880 * q^46 + 38414 * q^49 - 38631 * q^50 + 24988 * q^52 - 21186 * q^56 - 3314 * q^58 - 2 * q^61 - 106342 * q^64 - 35970 * q^65 - 31413 * q^68 + 10524 * q^70 + 53620 * q^73 + 20406 * q^74 + 26193 * q^76 - 26178 * q^77 - 151286 * q^82 + 6248 * q^85 - 279237 * q^86 - 122541 * q^88 - 435804 * q^92 + 63480 * q^94 - 58148 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.66122	−	4.99179i	−0.470441	−	0.882431i
$2$	−2.66122	−	4.99179i	−0.470441	−	0.882431i
$3$		0			0
$3$		0			0
$4$	−17.8359	+	26.5684i	−0.557371	+	0.830264i
$5$	−3.68052	+	2.12495i	−0.0658391	+	0.0380122i	−0.532558	−	0.846393i	$-0.678769\pi$
$5$	−3.68052	+	2.12495i	−0.0658391	+	0.0380122i	0.466719	+	0.884406i	$0.345436\pi$
$6$		0			0
$7$	13.9322	+	8.04377i	0.107467	+	0.0620461i	0.552770	−	0.833334i	$-0.313571\pi$
$7$	13.9322	+	8.04377i	0.107467	+	0.0620461i	−0.445303	+	0.895380i	$0.646904\pi$
$8$	180.089	+	18.3284i	0.994861	+	0.101251i
$9$		0			0
$10$	20.4019	+	12.7174i	0.0645166	+	0.0402160i
$11$	43.3121	−	75.0187i	0.107926	−	0.186934i	−0.807004	−	0.590546i	$-0.798912\pi$
$11$	43.3121	−	75.0187i	0.107926	−	0.186934i	0.914930	+	0.403613i	$0.132246\pi$
$12$		0			0
$13$	162.502	+	281.462i	0.266686	+	0.461914i	0.968004	−	0.250935i	$-0.0807380\pi$
$13$	162.502	+	281.462i	0.266686	+	0.461914i	−0.701318	+	0.712849i	$0.747405\pi$
$14$	3.07614	−	90.9529i	0.00419455	−	0.124021i
$15$		0			0
$16$	−387.764	−	947.742i	−0.378676	−	0.925529i
$17$		−	1863.80i		−	1.56415i	−0.623187	−	0.782073i	$-0.714163\pi$
$17$		−	1863.80i		−	1.56415i	0.623187	−	0.782073i	$-0.285837\pi$
$18$		0			0
$19$		−	416.071i		−	0.264413i	−0.991222	−	0.132207i	$-0.957794\pi$
$19$		−	416.071i		−	0.264413i	0.991222	−	0.132207i	$-0.0422063\pi$
$20$	9.18864	−	135.686i	0.00513660	−	0.0758508i
$21$		0			0
$22$	−489.740	−	16.5636i	−0.215729	−	0.00729623i
$23$	−1293.41	−	2240.24i	−0.509818	−	0.883030i	−0.999935	−	0.0113741i	$-0.996379\pi$
$23$	−1293.41	−	2240.24i	−0.509818	−	0.883030i	0.490117	−	0.871656i	$-0.336954\pi$
$24$		0			0
$25$	−1553.47	+	2690.69i	−0.497110	+	0.861020i
$26$	972.544	−	1560.21i	0.282147	−	0.452635i
$27$		0			0
$28$	−462.204	+	226.690i	−0.111414	+	0.0546433i
$29$	−4342.80	−	2507.32i	−0.958904	−	0.553623i	−0.0630683	−	0.998009i	$-0.520089\pi$
$29$	−4342.80	−	2507.32i	−0.958904	−	0.553623i	−0.895835	+	0.444386i	$0.853422\pi$
$30$		0			0
$31$	6396.76	−	3693.17i	1.19552	−	0.690232i	0.235964	−	0.971762i	$-0.424175\pi$
$31$	6396.76	−	3693.17i	1.19552	−	0.690232i	0.959553	+	0.281530i	$0.0908418\pi$
$32$	−3699.00	+	4457.78i	−0.638571	+	0.769563i
$33$		0			0
$34$	−9303.69	+	4959.98i	−1.38025	+	0.735838i
$35$	−68.3704			−0.00943405
$36$		0			0
$37$	−10519.2			−1.26322			−0.631609	−	0.775287i	$-0.717605\pi$
$37$	−10519.2			−1.26322			−0.631609	+	0.775287i	$0.717605\pi$
$38$	−2076.94	+	1107.25i	−0.233327	+	0.124391i
$39$		0			0
$40$	−701.768	+	315.222i	−0.0693496	+	0.0311506i
$41$	−13207.4	+	7625.29i	−1.22704	+	0.708430i	−0.966409	−	0.257009i	$-0.917263\pi$
$41$	−13207.4	+	7625.29i	−1.22704	+	0.708430i	−0.260628	+	0.965439i	$0.583930\pi$
$42$		0			0
$43$	−6794.45	−	3922.78i	−0.560381	−	0.323536i	0.192917	−	0.981215i	$-0.438205\pi$
$43$	−6794.45	−	3922.78i	−0.560381	−	0.323536i	−0.753298	+	0.657679i	$0.771538\pi$
$44$	1220.62	+	2488.76i	0.0950495	+	0.193799i
$45$		0			0
$46$	−7740.79	+	12418.2i	−0.539375	+	0.865293i
$47$	14244.6	−	24672.4i	0.940604	−	1.62917i	0.176280	−	0.984340i	$-0.443594\pi$
$47$	14244.6	−	24672.4i	0.940604	−	1.62917i	0.764323	−	0.644833i	$-0.223073\pi$
$48$		0			0
$49$	−8274.10	−	14331.2i	−0.492301	−	0.852690i
$50$	17565.5	+	594.085i	0.993652	+	0.0336065i
$51$		0			0
$52$	−10376.4	−	702.686i	−0.532153	−	0.0360373i
$53$			5483.31i			0.268135i	0.990972	+	0.134067i	$0.0428038\pi$
$53$			5483.31i			0.268135i	−0.990972	+	0.134067i	$0.957196\pi$
$54$		0			0
$55$			368.144i			0.0164101i
$56$	2361.61	+	1703.95i	0.100633	+	0.0726084i
$57$		0			0
$58$	−958.860	+	28350.9i	−0.0374270	+	1.10661i
$59$	−1901.12	−	3292.83i	−0.0711015	−	0.123151i	0.828283	−	0.560310i	$-0.189318\pi$
$59$	−1901.12	−	3292.83i	−0.0711015	−	0.123151i	−0.899384	+	0.437159i	$0.855985\pi$
$60$		0			0
$61$	16590.1	−	28734.9i	0.570853	−	0.988747i	−0.425625	−	0.904900i	$-0.639946\pi$
$61$	16590.1	−	28734.9i	0.570853	−	0.988747i	0.996479	−	0.0838475i	$-0.0267209\pi$
$62$	−35458.7	−	22102.9i	−1.17150	−	0.730248i
$63$		0			0
$64$	32096.1	+	6601.49i	0.979496	+	0.201462i
$65$	−1196.18	−	690.617i	−0.0351168	−	0.0202747i
$66$		0			0
$67$	57592.1	−	33250.8i	1.56738	−	0.904930i	0.570912	−	0.821011i	$-0.306590\pi$
$67$	57592.1	−	33250.8i	1.56738	−	0.904930i	0.996473	−	0.0839192i	$-0.0267438\pi$
$68$	49518.3	+	33242.5i	1.29865	+	0.871809i
$69$		0			0
$70$	181.948	+	341.290i	0.00443816	+	0.00832490i
$71$	−43573.3			−1.02583			−0.512914	−	0.858440i	$-0.671434\pi$
$71$	−43573.3			−1.02583			−0.512914	+	0.858440i	$0.671434\pi$
$72$		0			0
$73$	22901.9			0.502996			0.251498	−	0.967858i	$-0.419077\pi$
$73$	22901.9			0.502996			0.251498	+	0.967858i	$0.419077\pi$
$74$	27993.8	+	52509.6i	0.594269	+	1.11470i
$75$		0			0
$76$	11054.4	+	7420.98i	0.219533	+	0.147376i
$77$	1206.87	−	696.785i	0.0231970	−	0.0133928i
$78$		0			0
$79$	31941.7	+	18441.5i	0.575824	+	0.332452i	0.759472	−	0.650540i	$-0.225457\pi$
$79$	31941.7	+	18441.5i	0.575824	+	0.332452i	−0.183648	+	0.982992i	$0.558791\pi$
$80$	3441.08	+	2664.20i	0.0601132	+	0.0465417i
$81$		0			0
$82$	73211.6	+	45635.9i	1.20239	+	0.749501i
$83$	27504.3	−	47638.8i	0.438233	−	0.759041i	−0.559321	−	0.828951i	$-0.688938\pi$
$83$	27504.3	−	47638.8i	0.438233	−	0.759041i	0.997553	+	0.0699102i	$0.0222713\pi$
$84$		0			0
$85$	3960.48	+	6859.75i	0.0594567	+	0.102982i
$86$	−1500.17	+	44355.8i	−0.0218723	+	0.646702i
$87$		0			0
$88$	9175.01	−	12716.2i	0.126299	−	0.175046i
$89$		−	40969.8i		−	0.548263i	−0.961692	−	0.274132i	$-0.911610\pi$
$89$		−	40969.8i		−	0.548263i	0.961692	−	0.274132i	$-0.0883904\pi$
$90$		0			0
$91$			5228.51i			0.0661873i
$92$	82588.8	+	5592.90i	1.01731	+	0.0688918i
$93$		0			0
$94$	−161068.	−	5447.50i	−1.88013	−	0.0635883i
$95$	884.130	+	1531.36i	0.0100509	+	0.0174087i
$96$		0			0
$97$	23339.8	−	40425.7i	0.251865	−	0.436243i	−0.712174	−	0.702003i	$-0.752289\pi$
$97$	23339.8	−	40425.7i	0.251865	−	0.436243i	0.964039	+	0.265760i	$0.0856227\pi$
$98$	−49518.9	+	79440.8i	−0.520842	+	0.835562i
$99$		0			0
$100$	−43779.9	−	89264.0i	−0.437799	−	0.892640i
$101$	65827.1	+	38005.3i	0.642098	+	0.370716i	0.785422	−	0.618960i	$-0.212446\pi$
$101$	65827.1	+	38005.3i	0.642098	+	0.370716i	−0.143324	+	0.989676i	$0.545779\pi$
$102$		0			0
$103$	−3270.29	+	1888.10i	−0.0303734	+	0.0175361i	−0.515110	−	0.857124i	$-0.672249\pi$
$103$	−3270.29	+	1888.10i	−0.0303734	+	0.0175361i	0.484736	+	0.874660i	$0.338916\pi$
$104$	24106.1	+	53666.6i	0.218546	+	0.486542i
$105$		0			0
$106$	27371.5	−	14592.3i	0.236610	−	0.126142i
$107$	−57656.6			−0.486844			−0.243422	−	0.969920i	$-0.578270\pi$
$107$	−57656.6			−0.486844			−0.243422	+	0.969920i	$0.578270\pi$
$108$		0			0
$109$	−176304.			−1.42133			−0.710667	−	0.703529i	$-0.751607\pi$
$109$	−176304.			−1.42133			−0.710667	+	0.703529i	$0.751607\pi$
$110$	1837.70	−	979.710i	0.0144808	−	0.00771998i
$111$		0			0
$112$	2221.00	−	16323.2i	0.0167303	−	0.122959i
$113$	−111854.	+	64579.2i	−0.824057	+	0.475769i	−0.851813	−	0.523845i	$-0.824497\pi$
$113$	−111854.	+	64579.2i	−0.824057	+	0.475769i	0.0277568	+	0.999615i	$0.491164\pi$
$114$		0			0
$115$	9520.81	+	5496.84i	0.0671319	+	0.0387586i
$116$	144073.	−	70661.3i	0.994118	−	0.487570i
$117$		0			0
$118$	−11377.8	+	18252.9i	−0.0752236	+	0.120678i
$119$	14992.0	−	25966.9i	0.0970491	−	0.168094i
$120$		0			0
$121$	76773.6	+	132976.i	0.476704	+	0.825675i
$122$	−187588.	−	6344.46i	−1.14105	−	0.0385918i
$123$		0			0
$124$	−15969.9	+	235823.i	−0.0932712	+	1.37731i
$125$		−	26485.1i		−	0.151610i
$126$		0			0
$127$		−	43254.5i		−	0.237970i	−0.992896	−	0.118985i	$-0.962036\pi$
$127$		−	43254.5i		−	0.237970i	0.992896	−	0.118985i	$-0.0379640\pi$
$128$	−52461.5	−	177785.i	−0.283019	−	0.959114i
$129$		0			0
$130$	−264.109	+	7808.97i	−0.00137064	+	0.0405262i
$131$	104818.	+	181550.i	0.533650	+	0.924309i	0.999227	+	0.0393020i	$0.0125135\pi$
$131$	104818.	+	181550.i	0.533650	+	0.924309i	−0.465577	+	0.885007i	$0.654153\pi$
$132$		0			0
$133$	3346.78	−	5796.79i	0.0164058	−	0.0284157i
$134$	−319246.	−	199000.i	−1.53590	−	0.957394i
$135$		0			0
$136$	34160.5	−	335650.i	0.158372	−	1.55611i
$137$	−99563.4	−	57483.0i	−0.453209	−	0.261660i	0.255976	−	0.966683i	$-0.417603\pi$
$137$	−99563.4	−	57483.0i	−0.453209	−	0.261660i	−0.709184	+	0.705023i	$0.750937\pi$
$138$		0			0
$139$	−186853.	+	107880.i	−0.820281	+	0.473590i	−0.850514	−	0.525953i	$-0.823709\pi$
$139$	−186853.	+	107880.i	−0.820281	+	0.473590i	0.0302321	+	0.999543i	$0.490375\pi$
$140$	1219.44	−	1816.50i	0.00525826	−	0.00783275i
$141$		0			0
$142$	115958.	+	217509.i	0.482592	+	0.905223i
$143$	28153.2			0.115130
$144$		0			0
$145$	21311.7			0.0841779
$146$	−60946.9	−	114321.i	−0.236630	−	0.443860i
$147$		0			0
$148$	187619.	−	279479.i	0.704080	−	1.04880i
$149$	192038.	−	110873.i	0.708633	−	0.409129i	−0.101922	−	0.994792i	$-0.532499\pi$
$149$	192038.	−	110873.i	0.708633	−	0.409129i	0.810555	+	0.585663i	$0.199166\pi$
$150$		0			0
$151$	−364405.	−	210389.i	−1.30059	−	0.750898i	−0.320088	−	0.947388i	$-0.603712\pi$
$151$	−364405.	−	210389.i	−1.30059	−	0.750898i	−0.980506	+	0.196490i	$0.937046\pi$
$152$	7625.92	−	74929.8i	0.0267722	−	0.263055i
$153$		0			0
$154$	−6689.94	−	4170.13i	−0.0227311	−	0.0141693i
$155$	−15695.6	+	27185.6i	−0.0524745	+	0.0908886i
$156$		0			0
$157$	110672.	+	191690.i	0.358335	+	0.620654i	0.987683	−	0.156470i	$-0.0500113\pi$
$157$	110672.	+	191690.i	0.358335	+	0.620654i	−0.629348	+	0.777124i	$0.716678\pi$
$158$	7052.50	−	208523.i	0.0224750	−	0.664525i
$159$		0			0
$160$	4141.68	−	24267.1i	0.0127902	−	0.0749409i
$161$		−	41615.4i		−	0.126529i
$162$		0			0
$163$			324082.i			0.955402i	0.878522	+	0.477701i	$0.158530\pi$
$163$			324082.i			0.955402i	−0.878522	+	0.477701i	$0.841470\pi$
$164$	32973.1	−	486904.i	0.0957303	−	1.41362i
$165$		0			0
$166$	−310997.	−	10518.3i	−0.875964	−	0.0296262i
$167$	125104.	+	216686.i	0.347120	+	0.601229i	0.985737	−	0.168296i	$-0.0538263\pi$
$167$	125104.	+	216686.i	0.347120	+	0.601229i	−0.638617	+	0.769525i	$0.720493\pi$
$168$		0			0
$169$	132833.	−	230073.i	0.357757	−	0.619654i
$170$	23702.7	−	38025.2i	0.0629037	−	0.100913i
$171$		0			0
$172$	225407.	−	110552.i	0.580960	−	0.284935i
$173$	267332.	+	154344.i	0.679102	+	0.392080i	0.799517	−	0.600644i	$-0.205089\pi$
$173$	267332.	+	154344.i	0.679102	+	0.392080i	−0.120414	+	0.992724i	$0.538422\pi$
$174$		0			0
$175$	−43286.5	+	24991.5i	−0.106846	+	0.0616875i
$176$	−87893.3	−	11959.1i	−0.213882	−	0.0291016i
$177$		0			0
$178$	−204513.	+	109030.i	−0.483805	+	0.257926i
$179$	−7856.73			−0.0183278			−0.00916388	−	0.999958i	$-0.502917\pi$
$179$	−7856.73			−0.0183278			−0.00916388	+	0.999958i	$0.502917\pi$
$180$		0			0
$181$	−449713.			−1.02033			−0.510163	−	0.860078i	$-0.670415\pi$
$181$	−449713.			−1.02033			−0.510163	+	0.860078i	$0.670415\pi$
$182$	26099.6	−	13914.2i	0.0584058	−	0.0311372i
$183$		0			0
$184$	−191868.	−	427149.i	−0.417790	−	0.930112i
$185$	38716.1	−	22352.7i	0.0831691	−	0.0480177i
$186$		0			0
$187$	−139820.	−	80725.1i	−0.292392	−	0.168812i
$188$	401443.	+	818512.i	0.828379	+	1.68900i
$189$		0			0
$190$	5291.35	−	8488.66i	0.0106337	−	0.0170591i
$191$	−255380.	+	442331.i	−0.506527	+	0.877331i	0.493444	+	0.869777i	$0.335738\pi$
$191$	−255380.	+	442331.i	−0.506527	+	0.877331i	−0.999971	+	0.00755354i	$0.997596\pi$
$192$		0			0
$193$	439991.	+	762087.i	0.850257	+	1.47269i	0.880976	+	0.473161i	$0.156887\pi$
$193$	439991.	+	762087.i	0.850257	+	1.47269i	−0.0307186	+	0.999528i	$0.509780\pi$
$194$	−263909.	−	8925.72i	−0.503442	−	0.0170270i
$195$		0			0
$196$	528332.	+	35778.6i	0.982351	+	0.0665247i
$197$			162799.i			0.298873i	0.988771	+	0.149437i	$0.0477460\pi$
$197$			162799.i			0.298873i	−0.988771	+	0.149437i	$0.952254\pi$
$198$		0			0
$199$			786472.i			1.40783i	0.710283	+	0.703916i	$0.248567\pi$
$199$			786472.i			1.40783i	−0.710283	+	0.703916i	$0.751433\pi$
$200$	−329079.	+	456091.i	−0.581735	+	0.806262i
$201$		0			0
$202$	14534.2	−	429735.i	0.0250618	−	0.741007i
$203$	−40336.6	−	69865.0i	−0.0687004	−	0.118993i
$204$		0			0
$205$	32406.7	−	56130.1i	0.0538580	−	0.0932848i
$206$	18128.0	+	11299.9i	0.0297633	+	0.0185527i
$207$		0			0
$208$	203741.	−	263151.i	0.326527	−	0.421741i
$209$	−31213.1	−	18020.9i	−0.0494278	−	0.0285372i
$210$		0			0
$211$	879851.	−	507982.i	1.36051	−	0.785493i	0.370821	−	0.928704i	$-0.379076\pi$
$211$	879851.	−	507982.i	1.36051	−	0.785493i	0.989692	+	0.143212i	$0.0457429\pi$
$212$	−145683.	−	97799.5i	−0.222623	−	0.149450i
$213$		0			0
$214$	153437.	+	287810.i	0.229031	+	0.429606i
$215$	33342.8			0.0491933
$216$		0			0
$217$	118828.			0.171305
$218$	469183.	+	880072.i	0.668654	+	1.25423i
$219$		0			0
$220$	−9781.01	−	6566.16i	−0.0136247	−	0.00914650i
$221$	524588.	−	302871.i	0.722500	−	0.417136i
$222$		0			0
$223$	−201948.	−	116595.i	−0.271942	−	0.157006i	0.357828	−	0.933788i	$-0.383518\pi$
$223$	−201948.	−	116595.i	−0.271942	−	0.157006i	−0.629770	+	0.776782i	$0.716851\pi$
$224$	−87392.7	+	32352.9i	−0.116374	+	0.0430817i
$225$		0			0
$226$	620034.	+	386494.i	0.807504	+	0.503352i
$227$	−439493.	+	761224.i	−0.566092	+	0.980501i	0.430855	+	0.902421i	$0.358212\pi$
$227$	−439493.	+	761224.i	−0.566092	+	0.980501i	−0.996947	+	0.0780796i	$0.975121\pi$
$228$		0			0
$229$	−191288.	−	331320.i	−0.241045	−	0.417503i	0.719967	−	0.694008i	$-0.244157\pi$
$229$	−191288.	−	331320.i	−0.241045	−	0.417503i	−0.961012	+	0.276506i	$0.910824\pi$
$230$	2102.13	−	62154.1i	0.00262023	−	0.0774730i
$231$		0			0
$232$	−736136.	−	531137.i	−0.897921	−	0.647868i
$233$			224357.i			0.270738i	0.990795	+	0.135369i	$0.0432220\pi$
$233$			224357.i			0.270738i	−0.990795	+	0.135369i	$0.956778\pi$
$234$		0			0
$235$			121076.i			0.143018i
$236$	121393.	+	8220.75i	0.141878	+	0.00960797i
$237$		0			0
$238$	−169518.	−	5733.30i	−0.193987	−	0.00656089i
$239$	−769108.	−	1.33213e6i	−0.870949	−	1.50853i	−0.861017	−	0.508577i	$-0.830172\pi$
$239$	−769108.	−	1.33213e6i	−0.870949	−	1.50853i	−0.00993200	−	0.999951i	$-0.503162\pi$
$240$		0			0
$241$	692903.	−	1.20014e6i	0.768475	−	1.33104i	−0.169914	−	0.985459i	$-0.554349\pi$
$241$	692903.	−	1.20014e6i	0.768475	−	1.33104i	0.938390	−	0.345579i	$-0.112318\pi$
$242$	459476.	−	737115.i	0.504341	−	0.809090i
$243$		0			0
$244$	467543.	+	953285.i	0.502744	+	1.02506i
$245$	60905.9	+	35164.1i	0.0648253	+	0.0374269i
$246$		0			0
$247$	117108.	−	67612.4i	0.122136	−	0.0705154i
$248$	1.21968e6	−	547857.i	1.25926	−	0.565637i
$249$		0			0
$250$	−132208.	+	70482.6i	−0.133785	+	0.0713234i
$251$	1.31402e6			1.31649			0.658246	−	0.752803i	$-0.271299\pi$
$251$	1.31402e6			1.31649			0.658246	+	0.752803i	$0.271299\pi$
$252$		0			0
$253$	−224080.			−0.220091
$254$	−215917.	+	115109.i	−0.209992	+	0.111951i
$255$		0			0
$256$	−747854.	+	735001.i	−0.713209	+	0.700952i
$257$	−542479.	+	313201.i	−0.512331	+	0.295794i	−0.733791	−	0.679375i	$-0.762251\pi$
$257$	−542479.	+	313201.i	−0.512331	+	0.295794i	0.221461	+	0.975169i	$0.428918\pi$
$258$		0			0
$259$	−146556.	−	84614.0i	−0.135754	−	0.0783777i
$260$	39683.6	−	19463.0i	0.0364064	−	0.0178557i
$261$		0			0
$262$	627315.	−	1.00637e6i	0.564589	−	0.905743i
$263$	750127.	−	1.29926e6i	0.668722	−	1.15826i	−0.309540	−	0.950887i	$-0.600175\pi$
$263$	750127.	−	1.29926e6i	0.668722	−	1.15826i	0.978262	−	0.207374i	$-0.0664917\pi$
$264$		0			0
$265$	−11651.8	−	20181.4i	−0.0101924	−	0.0176538i
$266$	−37842.9	−	1279.89i	−0.0327929	−	0.00110910i
$267$		0			0
$268$	−143782.	+	2.12319e6i	−0.122283	+	1.80572i
$269$			264637.i			0.222982i	0.993765	+	0.111491i	$0.0355626\pi$
$269$			264637.i			0.222982i	−0.993765	+	0.111491i	$0.964437\pi$
$270$		0			0
$271$		−	650898.i		−	0.538381i	−0.963087	−	0.269190i	$-0.913244\pi$
$271$		−	650898.i		−	0.538381i	0.963087	−	0.269190i	$-0.0867561\pi$
$272$	−1.76640e6	+	722715.i	−1.44766	+	0.592305i
$273$		0			0
$274$	−21982.9	+	649974.i	−0.0176892	+	0.523022i
$275$	134568.	+	233079.i	0.107303	+	0.185853i
$276$		0			0
$277$	237366.	−	411129.i	0.185874	−	0.321943i	−0.757997	−	0.652258i	$-0.773822\pi$
$277$	237366.	−	411129.i	0.185874	−	0.321943i	0.943871	+	0.330315i	$0.107155\pi$
$278$	1.03577e6	+	645639.i	0.803804	+	0.501046i
$279$		0			0
$280$	−12312.8	−	1253.12i	−0.00938557	−	0.000955208i
$281$	−1.41561e6	−	817304.i	−1.06949	−	0.617473i	−0.141451	−	0.989945i	$-0.545177\pi$
$281$	−1.41561e6	−	817304.i	−1.06949	−	0.617473i	−0.928043	+	0.372472i	$0.878510\pi$
$282$		0			0
$283$	1.06078e6	−	612441.i	0.787333	−	0.454567i	−0.0516895	−	0.998663i	$-0.516461\pi$
$283$	1.06078e6	−	612441.i	0.787333	−	0.454567i	0.839023	+	0.544096i	$0.183127\pi$
$284$	777167.	−	1.15767e6i	0.571766	−	0.851708i
$285$		0			0
$286$	−74921.7	−	140535.i	−0.0541618	−	0.101594i
$287$	−245345.			−0.175821
$288$		0			0
$289$	−2.05390e6			−1.44655
$290$	−56715.0	−	106383.i	−0.0396007	−	0.0742812i
$291$		0			0
$292$	−408475.	+	608468.i	−0.280355	+	0.417619i
$293$	−963120.	+	556058.i	−0.655407	+	0.378400i	−0.790525	−	0.612430i	$-0.790192\pi$
$293$	−963120.	+	556058.i	−0.655407	+	0.378400i	0.135117	+	0.990830i	$0.456859\pi$
$294$		0			0
$295$	13994.2	+	8079.55i	0.00936253	+	0.00540546i
$296$	−1.89439e6	−	192800.i	−1.25673	−	0.127902i
$297$		0			0
$298$	−1.06451e6	−	663555.i	−0.694399	−	0.432849i
$299$	420362.	−	728088.i	0.271923	−	0.470984i
$300$		0			0
$301$	−63107.9	−	109306.i	−0.0401483	−	0.0695389i
$302$	−80458.0	+	2.37892e6i	−0.0507635	+	1.50094i
$303$		0			0
$304$	−394328.	+	161338.i	−0.244722	+	0.100127i
$305$			141013.i			0.0867977i
$306$		0			0
$307$		−	1.54327e6i		−	0.934537i	−0.884115	−	0.467269i	$-0.845238\pi$
$307$		−	1.54327e6i		−	0.934537i	0.884115	−	0.467269i	$-0.154762\pi$
$308$	−3013.02	+	44492.3i	−0.00180978	+	0.0267244i
$309$		0			0
$310$	177474.	+	6002.38i	0.104889	+	0.00354748i
$311$	−1.17389e6	−	2.03323e6i	−0.688218	−	1.19203i	−0.972414	−	0.233262i	$-0.925060\pi$
$311$	−1.17389e6	−	2.03323e6i	−0.688218	−	1.19203i	0.284196	−	0.958766i	$-0.408273\pi$
$312$		0			0
$313$	−705005.	+	1.22110e6i	−0.406753	+	0.704517i	−0.994524	−	0.104510i	$-0.966672\pi$
$313$	−705005.	+	1.22110e6i	−0.406753	+	0.704517i	0.587770	+	0.809028i	$0.300006\pi$
$314$	662351.	−	1.06258e6i	0.379109	−	0.608187i
$315$		0			0
$316$	−1.05967e6	+	519720.i	−0.596971	+	0.292787i
$317$	−1.72360e6	−	995122.i	−0.963360	−	0.556196i	−0.0661546	−	0.997809i	$-0.521073\pi$
$317$	−1.72360e6	−	995122.i	−0.963360	−	0.556196i	−0.897206	+	0.441613i	$0.854406\pi$
$318$		0			0
$319$	−376192.	+	217194.i	−0.206982	+	0.119501i
$320$	−132158.	+	43905.7i	−0.0721472	+	0.0239688i
$321$		0			0
$322$	−207735.	+	110748.i	−0.111653	+	0.0595244i
$323$	−775473.			−0.413581
$324$		0			0
$325$	−1.00977e6			−0.530289
$326$	1.61775e6	−	862453.i	0.843077	−	0.449460i
$327$		0			0
$328$	−2.51827e6	+	1.13116e6i	−1.29246	+	0.580550i
$329$	396919.	−	229161.i	0.202168	−	0.116722i
$330$		0			0
$331$	2.45201e6	+	1.41567e6i	1.23013	+	0.710218i	0.967058	−	0.254557i	$-0.0819296\pi$
$331$	2.45201e6	+	1.41567e6i	1.23013	+	0.710218i	0.263076	+	0.964775i	$0.415263\pi$
$332$	775126.	+	1.58042e6i	0.385946	+	0.786916i
$333$		0			0
$334$	748723.	−	1.20114e6i	0.367244	−	0.589152i
$335$	−141312.	+	244760.i	−0.0687968	+	0.119160i
$336$		0			0
$337$	−360837.	−	624988.i	−0.173076	−	0.299776i	0.766418	−	0.642342i	$-0.222037\pi$
$337$	−360837.	−	624988.i	−0.173076	−	0.299776i	−0.939494	+	0.342566i	$0.888704\pi$
$338$	−1.50197e6	−	50798.5i	−0.715105	−	0.0241857i
$339$		0			0
$340$	−252892.	−	17125.8i	−0.118642	−	0.00803440i
$341$		−	639836.i		−	0.297977i
$342$		0			0
$343$		−	536603.i		−	0.246274i
$344$	−1.15171e6	−	830981.i	−0.524743	−	0.378613i
$345$		0			0
$346$	59024.9	−	1.74521e6i	0.0265061	−	0.783712i
$347$	751022.	+	1.30081e6i	0.334833	+	0.579948i	0.983453	−	0.181165i	$-0.0579866\pi$
$347$	751022.	+	1.30081e6i	0.334833	+	0.579948i	−0.648619	+	0.761113i	$0.724653\pi$
$348$		0			0
$349$	−506792.	+	877790.i	−0.222724	+	0.385769i	−0.955634	−	0.294556i	$-0.904828\pi$
$349$	−506792.	+	877790.i	−0.222724	+	0.385769i	0.732910	+	0.680325i	$0.238161\pi$
$350$	239947.	+	149569.i	0.104700	+	0.0652638i
$351$		0			0
$352$	174206.	+	470570.i	0.0749387	+	0.202427i
$353$	1.78252e6	+	1.02914e6i	0.761374	+	0.439579i	0.829789	−	0.558077i	$-0.188461\pi$
$353$	1.78252e6	+	1.02914e6i	0.761374	+	0.439579i	−0.0684149	+	0.997657i	$0.521794\pi$
$354$		0			0
$355$	160372.	−	92591.0i	0.0675396	−	0.0389940i
$356$	1.08850e6	+	730732.i	0.455203	+	0.305586i
$357$		0			0
$358$	20908.5	+	39219.1i	0.00862213	+	0.0161730i
$359$	−301586.			−0.123502			−0.0617512	−	0.998092i	$-0.519669\pi$
$359$	−301586.			−0.123502			−0.0617512	+	0.998092i	$0.519669\pi$
$360$		0			0
$361$	2.30298e6			0.930086
$362$	1.19678e6	+	2.24487e6i	0.480003	+	0.900368i
$363$		0			0
$364$	−138913.	−	93255.0i	−0.0549529	−	0.0368909i
$365$	−84290.9	+	48665.4i	−0.0331168	+	0.0191200i
$366$		0			0
$367$	−1.93072e6	−	1.11470e6i	−0.748261	−	0.432009i	0.0768040	−	0.997046i	$-0.475528\pi$
$367$	−1.93072e6	−	1.11470e6i	−0.748261	−	0.432009i	−0.825065	+	0.565037i	$0.808862\pi$
$368$	−1.62164e6	+	2.09450e6i	−0.624215	+	0.806234i
$369$		0			0
$370$	−214612.	−	133777.i	−0.0814985	−	0.0508016i
$371$	−44106.5	+	76394.7i	−0.0166367	+	0.0288156i
$372$		0			0
$373$	898552.	+	1.55634e6i	0.334404	+	0.579204i	0.983370	−	0.181613i	$-0.0581318\pi$
$373$	898552.	+	1.55634e6i	0.334404	+	0.579204i	−0.648966	+	0.760817i	$0.724798\pi$
$374$	−30871.3	+	912778.i	−0.0114124	+	0.337432i
$375$		0			0
$376$	3.01751e6	−	4.18215e6i	1.10073	−	1.52556i
$377$		−	1.62978e6i		−	0.590574i
$378$		0			0
$379$			2.14708e6i			0.767804i	0.923374	+	0.383902i	$0.125420\pi$
$379$			2.14708e6i			0.767804i	−0.923374	+	0.383902i	$0.874580\pi$
$380$	−56455.0	−	3823.13i	−0.0200560	−	0.00135819i
$381$		0			0
$382$	2.88764e6	+	97663.5i	1.01248	+	0.0342431i
$383$	1.30237e6	+	2.25578e6i	0.453669	+	0.785777i	0.998611	−	0.0526965i	$-0.0167816\pi$
$383$	1.30237e6	+	2.25578e6i	0.453669	+	0.785777i	−0.544942	+	0.838474i	$0.683448\pi$
$384$		0			0
$385$	−2961.27	+	5129.06i	−0.00101818	+	0.00176354i
$386$	2.63326e6	−	4.22442e6i	0.899551	−	1.44311i
$387$		0			0
$388$	657764.	+	1.34113e6i	0.221815	+	0.452264i
$389$	3.00548e6	+	1.73521e6i	1.00702	+	0.581405i	0.910319	−	0.413908i	$-0.135836\pi$
$389$	3.00548e6	+	1.73521e6i	1.00702	+	0.581405i	0.0967049	+	0.995313i	$0.469170\pi$
$390$		0			0
$391$	−4.17537e6	+	2.41065e6i	−1.38119	+	0.797429i
$392$	−1.22741e6	−	2.73254e6i	−0.403435	−	0.898154i
$393$		0			0
$394$	812660.	−	433244.i	0.263735	−	0.140602i
$395$	−156749.			−0.0505490
$396$		0			0
$397$	5.78885e6			1.84338			0.921692	−	0.387922i	$-0.126807\pi$
$397$	5.78885e6			1.84338			0.921692	+	0.387922i	$0.126807\pi$
$398$	3.92590e6	−	2.09297e6i	1.24231	−	0.662302i
$399$		0			0
$400$	3.15246e6	+	428935.i	0.985143	+	0.134042i
$401$	2.02846e6	−	1.17113e6i	0.629950	−	0.363702i	−0.150782	−	0.988567i	$-0.548179\pi$
$401$	2.02846e6	−	1.17113e6i	0.629950	−	0.363702i	0.780733	+	0.624865i	$0.214846\pi$
$402$		0			0
$403$	2.07897e6	+	1.20029e6i	0.637655	+	0.368150i
$404$	−2.18382e6	+	1.07107e6i	−0.665678	+	0.326485i
$405$		0			0
$406$	−241407.	+	387278.i	−0.0726833	+	0.116602i
$407$	−455608.	+	789137.i	−0.136334	+	0.236138i
$408$		0			0
$409$	−1.17070e6	−	2.02771e6i	−0.346048	−	0.599373i	0.639495	−	0.768795i	$-0.279143\pi$
$409$	−1.17070e6	−	2.02771e6i	−0.346048	−	0.599373i	−0.985544	+	0.169422i	$0.945810\pi$
$410$	−366431.	−	12393.1i	−0.107655	−	0.00364101i
$411$		0			0
$412$	8164.48	−	120563.i	0.00236966	−	0.0349920i
$413$		−	61168.6i		−	0.0176463i
$414$		0			0
$415$			233781.i			0.0666328i
$416$	−1.85579e6	−	316728.i	−0.525770	−	0.0897333i
$417$		0			0
$418$	−6891.64	+	203767.i	−0.00192922	+	0.0570417i
$419$	2.33383e6	+	4.04232e6i	0.649434	+	1.12485i	0.983258	+	0.182217i	$0.0583274\pi$
$419$	2.33383e6	+	4.04232e6i	0.649434	+	1.12485i	−0.333824	+	0.942635i	$0.608339\pi$
$420$		0			0
$421$	2.03900e6	−	3.53165e6i	0.560676	−	0.971119i	−0.436762	−	0.899577i	$-0.643875\pi$
$421$	2.03900e6	−	3.53165e6i	0.560676	−	0.971119i	0.997438	−	0.0715416i	$-0.0227919\pi$
$422$	−4.87721e6	−	3.04018e6i	−1.33318	−	0.831032i
$423$		0			0
$424$	−100500.	+	987484.i	−0.0271489	+	0.266757i
$425$	5.01490e6	+	2.89536e6i	1.34676	+	0.777553i
$426$		0			0
$427$	462274.	−	266894.i	0.122696	−	0.0708385i
$428$	1.02836e6	−	1.53185e6i	0.271352	−	0.404209i
$429$		0			0
$430$	−88732.4	−	166440.i	−0.0231426	−	0.0434097i
$431$	−4.54361e6			−1.17817			−0.589085	−	0.808071i	$-0.700512\pi$
$431$	−4.54361e6			−1.17817			−0.589085	+	0.808071i	$0.700512\pi$
$432$		0			0
$433$	−6726.40			−0.00172410			−0.000862051	−	1.00000i	$-0.500274\pi$
$433$	−6726.40			−0.00172410			−0.000862051		1.00000i	$0.500274\pi$
$434$	−316227.	−	593164.i	−0.0805888	−	0.151165i
$435$		0			0
$436$	3.14453e6	−	4.68413e6i	0.792210	−	1.18008i
$437$	−932101.	+	538148.i	−0.233485	+	0.134803i
$438$		0			0
$439$	−4.27223e6	−	2.46657e6i	−1.05802	−	0.610847i	−0.133134	−	0.991098i	$-0.542504\pi$
$439$	−4.27223e6	−	2.46657e6i	−1.05802	−	0.610847i	−0.924883	+	0.380251i	$0.875838\pi$
$440$	−6747.49	+	66298.7i	−0.00166154	+	0.0163258i
$441$		0			0
$442$	−2.90791e6	−	1.81263e6i	−0.707987	−	0.441319i
$443$	−2.52747e6	+	4.37771e6i	−0.611895	+	1.05983i	0.379025	+	0.925386i	$0.376259\pi$
$443$	−2.52747e6	+	4.37771e6i	−0.611895	+	1.05983i	−0.990921	+	0.134448i	$0.957074\pi$
$444$		0			0
$445$	87058.8	+	150790.i	0.0208407	+	0.0360972i
$446$	−44588.7	+	1.31836e6i	−0.0106142	+	0.313833i
$447$		0			0
$448$	394070.	+	350147.i	0.0927637	+	0.0824244i
$449$			3.95256e6i			0.925257i	0.886552	+	0.462628i	$0.153094\pi$
$449$			3.95256e6i			0.925257i	−0.886552	+	0.462628i	$0.846906\pi$
$450$		0			0
$451$			1.32107e6i			0.305833i
$452$	279251.	−	4.12362e6i	0.0642908	−	0.949364i
$453$		0			0
$454$	4.96945e6	+	168073.i	1.13154	+	0.0382700i
$455$	−11110.3	−	19243.6i	−0.00251593	−	0.00435772i
$456$		0			0
$457$	−3.74368e6	+	6.48424e6i	−0.838509	+	1.45234i	0.0526320	+	0.998614i	$0.483239\pi$
$457$	−3.74368e6	+	6.48424e6i	−0.838509	+	1.45234i	−0.891141	+	0.453726i	$0.850094\pi$
$458$	−1.14482e6	+	1.83658e6i	−0.255020	+	0.409116i
$459$		0			0
$460$	−315854.	+	154912.i	−0.0695973	+	0.0341343i
$461$	−4.43539e6	−	2.56077e6i	−0.972029	−	0.561201i	−0.0721745	−	0.997392i	$-0.522994\pi$
$461$	−4.43539e6	−	2.56077e6i	−0.972029	−	0.561201i	−0.899854	+	0.436191i	$0.856327\pi$
$462$		0			0
$463$	−3.47662e6	+	2.00723e6i	−0.753711	+	0.435155i	−0.827033	−	0.562153i	$-0.809973\pi$
$463$	−3.47662e6	+	2.00723e6i	−0.753711	+	0.435155i	0.0733224	+	0.997308i	$0.476640\pi$
$464$	−692307.	+	5.08810e6i	−0.149281	+	1.09714i
$465$		0			0
$466$	1.11994e6	−	597062.i	0.238908	−	0.127366i
$467$	5.43636e6			1.15350			0.576748	−	0.816922i	$-0.304321\pi$
$467$	5.43636e6			1.15350			0.576748	+	0.816922i	$0.304321\pi$
$468$		0			0
$469$	1.06985e6			0.224590
$470$	604388.	−	322211.i	0.126203	−	0.0672814i
$471$		0			0
$472$	−282018.	−	627847.i	−0.0582669	−	0.129718i
$473$	−588564.	+	339807.i	−0.120960	+	0.0698361i
$474$		0			0
$475$	1.11952e6	+	646353.i	0.227665	+	0.131443i
$476$	422505.	+	861455.i	0.0854701	+	0.174267i
$477$		0			0
$478$	−4.60297e6	+	7.38432e6i	−0.921442	+	1.47823i
$479$	4.63944e6	−	8.03575e6i	0.923904	−	1.60025i	0.130589	−	0.991437i	$-0.458313\pi$
$479$	4.63944e6	−	8.03575e6i	0.923904	−	1.60025i	0.793315	−	0.608812i	$-0.208354\pi$
$480$		0			0
$481$	−1.70939e6	−	2.96075e6i	−0.336882	−	0.583497i
$482$	−7.83482e6	−	264983.i	−1.53607	−	0.0519518i
$483$		0			0
$484$	−4.90228e6	−	331982.i	−0.951229	−	0.0644171i
$485$			198384.i			0.0382958i
$486$		0			0
$487$			2.35999e6i			0.450908i	0.974254	+	0.225454i	$0.0723865\pi$
$487$			2.35999e6i			0.450908i	−0.974254	+	0.225454i	$0.927614\pi$
$488$	3.51436e6	−	4.87077e6i	0.668031	−	0.925866i
$489$		0			0
$490$	13447.6	−	397609.i	0.00253020	−	0.0748110i
$491$	4.26271e6	+	7.38323e6i	0.797961	+	1.38211i	0.920942	+	0.389701i	$0.127421\pi$
$491$	4.26271e6	+	7.38323e6i	0.797961	+	1.38211i	−0.122980	+	0.992409i	$0.539245\pi$
$492$		0			0
$493$	−4.67314e6	+	8.09412e6i	−0.865947	+	1.49986i
$494$	−649156.	−	404647.i	−0.119683	−	0.0746035i
$495$		0			0
$496$	−5.98061e6	−	4.63040e6i	−1.09154	−	0.845111i
$497$	−607073.	−	350494.i	−0.110243	−	0.0636486i
$498$		0			0
$499$	−218746.	+	126293.i	−0.0393268	+	0.0227054i	−0.519535	−	0.854449i	$-0.673895\pi$
$499$	−218746.	+	126293.i	−0.0393268	+	0.0227054i	0.480208	+	0.877155i	$0.340561\pi$
$500$	703668.	+	472385.i	0.125876	+	0.0845027i
$501$		0			0
$502$	−3.49689e6	−	6.55931e6i	−0.619332	−	1.16171i
$503$	−6.25307e6			−1.10198			−0.550989	−	0.834512i	$-0.685749\pi$
$503$	−6.25307e6			−1.10198			−0.550989	+	0.834512i	$0.685749\pi$
$504$		0			0
$505$	−323037.			−0.0563669
$506$	596326.	+	1.11856e6i	0.103540	+	0.194215i
$507$		0			0
$508$	1.14920e6	+	771481.i	0.197578	+	0.132637i
$509$	−431856.	+	249332.i	−0.0738830	+	0.0426564i	−0.536486	−	0.843909i	$-0.680249\pi$
$509$	−431856.	+	249332.i	−0.0738830	+	0.0426564i	0.462603	+	0.886565i	$0.346915\pi$
$510$		0			0
$511$	319074.	+	184218.i	0.0540555	+	0.0312090i
$512$	5.65917e6	+	1.77713e6i	0.954064	+	0.299601i
$513$		0			0
$514$	3.00708e6	+	1.87445e6i	0.502039	+	0.312943i
$515$	8024.25	−	13898.4i	0.00133317	−	0.00230912i
$516$		0			0
$517$	−1.23393e6	−	2.13723e6i	−0.203032	−	0.351661i
$518$	−32358.5	+	956751.i	−0.00529863	+	0.156666i
$519$		0			0
$520$	−202762.	−	146297.i	−0.0328835	−	0.0237261i
$521$		−	9.81352e6i		−	1.58391i	−0.610579	−	0.791955i	$-0.709063\pi$
$521$		−	9.81352e6i		−	1.58391i	0.610579	−	0.791955i	$-0.290937\pi$
$522$		0			0
$523$		−	1.10853e7i		−	1.77211i	−0.463576	−	0.886057i	$-0.653434\pi$
$523$		−	1.10853e7i		−	1.77211i	0.463576	−	0.886057i	$-0.346566\pi$
$524$	−6.69301e6	−	453250.i	−1.06486	−	0.0721123i
$525$		0			0
$526$	−8.48187e6	−	286867.i	−1.33668	−	0.0452081i
$527$	−6.88333e6	−	1.19223e7i	−1.07962	−	1.86996i
$528$		0			0
$529$	−127624.	+	221050.i	−0.0198286	+	0.0343441i
$530$	−69733.5	+	111870.i	−0.0107833	+	0.0172991i
$531$		0			0
$532$	94319.1	+	192310.i	0.0144484	+	0.0294592i
$533$	−4.29246e6	−	2.47825e6i	−0.654467	−	0.377857i
$534$		0			0
$535$	212206.	−	122517.i	0.0320534	−	0.0185060i
$536$	1.09811e7	−	4.93253e6i	1.65096	−	0.741580i
$537$		0			0
$538$	1.32101e6	−	704257.i	0.196766	−	0.104900i
$539$	−1.43347e6			−0.212529
$540$		0			0
$541$	2.27509e6			0.334200			0.167100	−	0.985940i	$-0.446560\pi$
$541$	2.27509e6			0.334200			0.167100	+	0.985940i	$0.446560\pi$
$542$	−3.24914e6	+	1.73218e6i	−0.475084	+	0.253276i
$543$		0			0
$544$	8.30842e6	+	6.89420e6i	1.20371	+	0.998818i
$545$	648891.	−	374637.i	0.0935794	−	0.0540281i
$546$		0			0
$547$	7.20659e6	+	4.16072e6i	1.02982	+	0.594567i	0.916933	−	0.399041i	$-0.130657\pi$
$547$	7.20659e6	+	4.16072e6i	1.02982	+	0.594567i	0.112887	+	0.993608i	$0.463990\pi$
$548$	3.30303e6	−	1.61999e6i	0.469852	−	0.230441i
$549$		0			0
$550$	805364.	−	1.29201e6i	0.113523	−	0.182120i
$551$	−1.04322e6	+	1.80691e6i	−0.146385	+	0.253547i
$552$		0			0
$553$	296679.	+	513863.i	0.0412547	+	0.0714553i
$554$	−2.68395e6	−	90774.4i	−0.371535	−	0.0125658i
$555$		0			0
$556$	466489.	−	6.88852e6i	0.0639963	−	0.945015i
$557$		−	1.46783e6i		−	0.200465i	−0.994964	−	0.100232i	$-0.968041\pi$
$557$		−	1.46783e6i		−	0.200465i	0.994964	−	0.100232i	$-0.0319586\pi$
$558$		0			0
$559$		−	2.54984e6i		−	0.345130i
$560$	26511.6	+	64797.5i	0.00357245	+	0.00873149i
$561$		0			0
$562$	−312557.	+	9.24146e6i	−0.0417435	+	1.23424i
$563$	−1.07987e6	−	1.87039e6i	−0.143582	−	0.248691i	0.785261	−	0.619165i	$-0.212529\pi$
$563$	−1.07987e6	−	1.87039e6i	−0.143582	−	0.248691i	−0.928843	+	0.370474i	$0.879195\pi$
$564$		0			0
$565$	274455.	−	475370.i	0.0361701	−	0.0626485i
$566$	−5.88014e6	−	3.66534e6i	−0.771518	−	0.480921i
$567$		0			0
$568$	−7.84707e6	−	798630.i	−1.02056	−	0.103866i
$569$	−2.42463e6	−	1.39986e6i	−0.313954	−	0.181261i	0.334741	−	0.942310i	$-0.391351\pi$
$569$	−2.42463e6	−	1.39986e6i	−0.313954	−	0.181261i	−0.648694	+	0.761049i	$0.724685\pi$
$570$		0			0
$571$	9.90022e6	−	5.71589e6i	1.27073	−	0.733658i	0.295607	−	0.955310i	$-0.404478\pi$
$571$	9.90022e6	−	5.71589e6i	1.27073	−	0.733658i	0.975126	+	0.221651i	$0.0711447\pi$
$572$	−502136.	+	747987.i	−0.0641699	+	0.0955881i
$573$		0			0
$574$	652915.	+	1.22471e6i	0.0827136	+	0.155150i
$575$	8.03706e6			1.01374
$576$		0			0
$577$	669533.			0.0837206			0.0418603	−	0.999123i	$-0.486672\pi$
$577$	669533.			0.0837206			0.0418603	+	0.999123i	$0.486672\pi$
$578$	5.46586e6	+	1.02526e7i	0.680517	+	1.27648i
$579$		0			0
$580$	−380112.	+	566218.i	−0.0469183	+	0.0698898i
$581$	766391.	−	442476.i	0.0941911	−	0.0543813i
$582$		0			0
$583$	411351.	+	237494.i	0.0501235	+	0.0289388i
$584$	4.12438e6	+	419756.i	0.500411	+	0.0509289i
$585$		0			0
$586$	5.33879e6	+	3.32790e6i	0.642242	+	0.400337i
$587$	−197174.	+	341516.i	−0.0236187	+	0.0409087i	−0.877593	−	0.479406i	$-0.840852\pi$
$587$	−197174.	+	341516.i	−0.0236187	+	0.0409087i	0.853974	+	0.520315i	$0.174185\pi$
$588$		0			0
$589$	−1.53662e6	−	2.66151e6i	−0.182507	−	0.316111i
$590$	3089.82	−	91357.5i	0.000365429	−	0.0108047i
$591$		0			0
$592$	4.07897e6	+	9.96948e6i	0.478350	+	1.16914i
$593$			5.00148e6i			0.584066i	0.956408	+	0.292033i	$0.0943317\pi$
$593$			5.00148e6i			0.584066i	−0.956408	+	0.292033i	$0.905668\pi$
$594$		0			0
$595$			127429.i			0.0147562i
$596$	−479434.	+	7.07967e6i	−0.0552858	+	0.816389i
$597$		0			0
$598$	−4.75313e6	−	160757.i	−0.543534	−	0.0183830i
$599$	−5.30363e6	−	9.18615e6i	−0.603957	−	1.04608i	−0.992215	−	0.124533i	$-0.960257\pi$
$599$	−5.30363e6	−	9.18615e6i	−0.603957	−	1.04608i	0.388259	−	0.921550i	$-0.373077\pi$
$600$		0			0
$601$	3.48253e6	−	6.03191e6i	0.393286	−	0.681191i	−0.599595	−	0.800304i	$-0.704672\pi$
$601$	3.48253e6	−	6.03191e6i	0.393286	−	0.681191i	0.992881	+	0.119113i	$0.0380050\pi$
$602$	−377689.	+	605908.i	−0.0424759	+	0.0681421i
$603$		0			0
$604$	1.20892e7	−	5.92919e6i	1.34836	−	0.661307i
$605$	−565134.	−	326280.i	−0.0627715	−	0.0362412i
$606$		0			0
$607$	−1.36935e7	+	7.90597e6i	−1.50850	+	0.870930i	−0.508544	+	0.861036i	$0.669816\pi$
$607$	−1.36935e7	+	7.90597e6i	−1.50850	+	0.870930i	−0.999951	+	0.00989422i	$0.996851\pi$
$608$	1.85475e6	+	1.53905e6i	0.203483	+	0.168847i
$609$		0			0
$610$	703904.	−	375265.i	0.0765930	−	0.0408332i
$611$	9.25912e6			1.00338
$612$		0			0
$613$	133521.			0.0143515			0.00717575	−	0.999974i	$-0.497716\pi$
$613$	133521.			0.0143515			0.00717575	+	0.999974i	$0.497716\pi$
$614$	−7.70369e6	+	4.10698e6i	−0.824665	+	0.439645i
$615$		0			0
$616$	230115.	−	103363.i	0.0244339	−	0.0109753i
$617$	−1.06772e7	+	6.16447e6i	−1.12913	+	0.651902i	−0.943715	−	0.330758i	$-0.892696\pi$
$617$	−1.06772e7	+	6.16447e6i	−1.12913	+	0.651902i	−0.185413	+	0.982661i	$0.559362\pi$
$618$		0			0
$619$	8.56059e6	+	4.94246e6i	0.898001	+	0.518461i	0.876551	−	0.481309i	$-0.159838\pi$
$619$	8.56059e6	+	4.94246e6i	0.898001	+	0.518461i	0.0214502	+	0.999770i	$0.493172\pi$
$620$	−442334.	−	901886.i	−0.0462137	−	0.0942263i
$621$		0			0
$622$	−7.02550e6	+	1.12707e7i	−0.728117	+	1.16808i
$623$	329552.	−	570801.i	0.0340176	−	0.0589202i
$624$		0			0
$625$	−4.79831e6	−	8.31092e6i	−0.491347	−	0.851038i
$626$	7.97166e6	+	269611.i	0.813042	+	0.0274981i
$627$		0			0
$628$	−7.06683e6	−	478565.i	−0.715032	−	0.0484219i
$629$			1.96057e7i			1.97586i
$630$		0			0
$631$		−	1.28910e7i		−	1.28888i	−0.764653	−	0.644442i	$-0.777090\pi$
$631$		−	1.28910e7i		−	1.28888i	0.764653	−	0.644442i	$-0.222910\pi$
$632$	5.41434e6	+	3.90656e6i	0.539204	+	0.389047i
$633$		0			0
$634$	−380559.	+	1.12521e7i	−0.0376010	+	1.11176i
$635$	91913.5	+	159199.i	0.00904576	+	0.0156677i
$636$		0			0
$637$	2.68911e6	−	4.65768e6i	0.262579	−	0.454801i
$638$	2.08532e6	+	1.29987e6i	0.202824	+	0.126429i
$639$		0			0
$640$	570870.	+	542863.i	0.0550918	+	0.0523891i
$641$	7.67906e6	+	4.43351e6i	0.738181	+	0.426189i	0.821408	−	0.570342i	$-0.193189\pi$
$641$	7.67906e6	+	4.43351e6i	0.738181	+	0.426189i	−0.0832264	+	0.996531i	$0.526522\pi$
$642$		0			0
$643$	9.18917e6	−	5.30537e6i	0.876494	−	0.506044i	0.00699288	−	0.999976i	$-0.497774\pi$
$643$	9.18917e6	−	5.30537e6i	0.876494	−	0.506044i	0.869501	+	0.493932i	$0.164441\pi$
$644$	1.10566e6	+	742247.i	0.105052	+	0.0705235i
$645$		0			0
$646$	2.06370e6	+	3.87100e6i	0.194565	+	0.364957i
$647$	−2.37142e6			−0.222714			−0.111357	−	0.993780i	$-0.535520\pi$
$647$	−2.37142e6			−0.222714			−0.111357	+	0.993780i	$0.535520\pi$
$648$		0			0
$649$	−329365.			−0.0306949
$650$	2.68721e6	+	5.04054e6i	0.249470	+	0.467944i
$651$		0			0
$652$	−8.61036e6	−	5.78028e6i	−0.793236	−	0.532513i
$653$	8.07136e6	−	4.66000e6i	0.740737	−	0.427665i	−0.0816004	−	0.996665i	$-0.526003\pi$
$653$	8.07136e6	−	4.66000e6i	0.740737	−	0.427665i	0.822337	+	0.569001i	$0.192670\pi$
$654$		0			0
$655$	−771568.	−	445465.i	−0.0702701	−	0.0405705i
$656$	1.23482e7	+	9.56039e6i	1.12032	+	0.867393i
$657$		0			0
$658$	−2.20021e6	−	1.37149e6i	−0.198107	−	0.123489i
$659$	−971185.	+	1.68214e6i	−0.0871141	+	0.150886i	−0.906290	−	0.422656i	$-0.861098\pi$
$659$	−971185.	+	1.68214e6i	−0.0871141	+	0.150886i	0.819176	+	0.573542i	$0.194431\pi$
$660$		0			0
$661$	−8.93142e6	−	1.54697e7i	−0.795091	−	1.37714i	−0.922781	−	0.385324i	$-0.874090\pi$
$661$	−8.93142e6	−	1.54697e7i	−0.795091	−	1.37714i	0.127690	−	0.991814i	$-0.459244\pi$
$662$	541387.	−	1.60073e7i	0.0480134	−	1.41962i
$663$		0			0
$664$	5.82636e6	−	8.07511e6i	0.512834	−	0.710769i
$665$			28446.9i			0.00249449i
$666$		0			0
$667$			1.29719e7i			1.12899i
$668$	−7.98835e6	−	540970.i	−0.692653	−	0.0469064i
$669$		0			0
$670$	1.59785e6	+	54041.4i	0.137515	+	0.00465093i
$671$	−1.43710e6	−	2.48914e6i	−0.123220	−	0.213424i
$672$		0			0
$673$	3.31863e6	−	5.74803e6i	0.282436	−	0.489194i	−0.689548	−	0.724240i	$-0.742191\pi$
$673$	3.31863e6	−	5.74803e6i	0.282436	−	0.489194i	0.971984	+	0.235046i	$0.0755241\pi$
$674$	−2.15954e6	+	3.46445e6i	−0.183110	+	0.293754i
$675$		0			0
$676$	3.74350e6	+	7.63271e6i	0.315073	+	0.642409i
$677$	2.38918e6	+	1.37940e6i	0.200345	+	0.115669i	0.596816	−	0.802378i	$-0.296432\pi$
$677$	2.38918e6	+	1.37940e6i	0.200345	+	0.115669i	−0.396472	+	0.918047i	$0.629765\pi$
$678$		0			0
$679$	650351.	−	375480.i	0.0541344	−	0.0312545i
$680$	587511.	+	1.30796e6i	0.0487241	+	0.108473i
$681$		0			0
$682$	−3.19392e6	+	1.70274e6i	−0.262944	+	0.140181i
$683$	−462361.			−0.0379253			−0.0189627	−	0.999820i	$-0.506036\pi$
$683$	−462361.			−0.0379253			−0.0189627	+	0.999820i	$0.506036\pi$
$684$		0			0
$685$	488594.			0.0397852
$686$	−2.67861e6	+	1.42802e6i	−0.217320	+	0.115857i
$687$		0			0
$688$	−1.08314e6	+	7.96050e6i	−0.0872392	+	0.641164i
$689$	−1.54334e6	+	891048.i	−0.123855	+	0.0715078i
$690$		0			0
$691$	−4.14382e6	−	2.39243e6i	−0.330146	−	0.190610i	0.325760	−	0.945452i	$-0.394380\pi$
$691$	−4.14382e6	−	2.39243e6i	−0.330146	−	0.190610i	−0.655906	+	0.754843i	$0.727713\pi$
$692$	−8.86877e6	+	4.34973e6i	−0.704041	+	0.345300i
$693$		0			0
$694$	4.49472e6	−	7.21067e6i	0.354245	−	0.568299i
$695$	458477.	−	794106.i	0.0360044	−	0.0623615i
$696$		0			0
$697$	1.42120e7	+	2.46160e7i	1.10809	+	1.91926i
$698$	5.73042e6	+	193810.i	0.445193	+	0.0150570i
$699$		0			0
$700$	108067.	−	1.59580e6i	0.00833585	−	0.123093i
$701$		−	1.31247e7i		−	1.00877i	−0.863478	−	0.504387i	$-0.831719\pi$
$701$		−	1.31247e7i		−	1.00877i	0.863478	−	0.504387i	$-0.168281\pi$
$702$		0			0
$703$			4.37673e6i			0.334012i
$704$	1.88539e6	−	2.12189e6i	0.143373	−	0.161358i
$705$		0			0
$706$	393568.	−	1.16367e7i	0.0297172	−	0.878657i
$707$	611412.	+	1.05900e6i	0.0460029	+	0.0796794i
$708$		0			0
$709$	−3.98415e6	+	6.90074e6i	−0.297659	+	0.515561i	−0.975600	−	0.219555i	$-0.929539\pi$
$709$	−3.98415e6	+	6.90074e6i	−0.297659	+	0.515561i	0.677941	+	0.735117i	$0.262873\pi$
$710$	−888980.	−	554140.i	−0.0661830	−	0.0412547i
$711$		0			0
$712$	750912.	−	7.37822e6i	0.0555123	−	0.545446i
$713$	−1.65472e7	−	9.55353e6i	−1.21899	−	0.703785i
$714$		0			0
$715$	−103618.	+	59824.1i	−0.00758004	+	0.00437634i
$716$	140132.	−	208741.i	0.0102154	−	0.0152169i
$717$		0			0
$718$	802586.	+	1.50545e6i	0.0581006	+	0.108982i
$719$	−5.58804e6			−0.403123			−0.201561	−	0.979476i	$-0.564602\pi$
$719$	−5.58804e6			−0.403123			−0.201561	+	0.979476i	$0.564602\pi$
$720$		0			0
$721$	−60749.9			−0.00435219
$722$	−6.12874e6	−	1.14960e7i	−0.437550	−	0.820737i
$723$		0			0
$724$	8.02102e6	−	1.19482e7i	0.568700	−	0.847140i
$725$	1.34928e7	−	7.79008e6i	0.953362	−	0.550424i
$726$		0			0
$727$	−2.72597e6	−	1.57384e6i	−0.191287	−	0.110439i	0.401298	−	0.915948i	$-0.368559\pi$
$727$	−2.72597e6	−	1.57384e6i	−0.191287	−	0.110439i	−0.592585	+	0.805508i	$0.701893\pi$
$728$	−95830.4	+	941598.i	−0.00670154	+	0.0658472i
$729$		0			0
$730$	467244.	+	291253.i	0.0324516	+	0.0202285i
$731$	−7.31128e6	+	1.26635e7i	−0.506057	+	0.876517i
$732$		0			0
$733$	1.20330e7	+	2.08418e7i	0.827209	+	1.43277i	0.900219	+	0.435438i	$0.143406\pi$
$733$	1.20330e7	+	2.08418e7i	0.827209	+	1.43277i	−0.0730095	+	0.997331i	$0.523260\pi$
$734$	−426289.	+	1.26042e7i	−0.0292054	+	0.863524i
$735$		0			0
$736$	1.47708e7	+	2.52094e6i	1.00510	+	0.171541i
$737$		−	5.76065e6i		−	0.390663i
$738$		0			0
$739$		−	4.89450e6i		−	0.329683i	−0.986320	−	0.164842i	$-0.947289\pi$
$739$		−	4.89450e6i		−	0.329683i	0.986320	−	0.164842i	$-0.0527113\pi$
$740$	−96657.0	+	1.42731e6i	−0.00648865	+	0.0958160i
$741$		0			0
$742$	498723.	+	16867.4i	0.0332544	+	0.00112470i
$743$	2.80417e6	+	4.85696e6i	0.186351	+	0.322770i	0.944031	−	0.329857i	$-0.107000\pi$
$743$	2.80417e6	+	4.85696e6i	0.186351	+	0.322770i	−0.757680	+	0.652626i	$0.773667\pi$
$744$		0			0
$745$	−471200.	+	816142.i	−0.0311039	+	0.0538735i
$746$	5.37766e6	−	8.62713e6i	0.353791	−	0.567570i
$747$		0			0
$748$	4.63855e6	−	2.27500e6i	0.303129	−	0.148671i
$749$	−803285.	−	463777.i	−0.0523197	−	0.0302068i
$750$		0			0
$751$	1.23051e7	−	7.10437e6i	0.796134	−	0.459648i	−0.0459832	−	0.998942i	$-0.514642\pi$
$751$	1.23051e7	−	7.10437e6i	0.796134	−	0.459648i	0.842118	+	0.539294i	$0.181309\pi$
$752$	−2.89067e7	−	3.93315e6i	−1.86403	−	0.253627i
$753$		0			0
$754$	−8.13550e6	+	4.33719e6i	−0.521141	+	0.277830i
$755$	1.78826e6			0.114173
$756$		0			0
$757$	−1.75241e7			−1.11147			−0.555733	−	0.831361i	$-0.687562\pi$
$757$	−1.75241e7			−1.11147			−0.555733	+	0.831361i	$0.687562\pi$
$758$	1.07178e7	−	5.71385e6i	0.677534	−	0.361206i
$759$		0			0
$760$	131155.	+	291985.i	0.00823664	+	0.0183370i
$761$	9.78403e6	−	5.64882e6i	0.612430	−	0.353587i	−0.161486	−	0.986875i	$-0.551629\pi$
$761$	9.78403e6	−	5.64882e6i	0.612430	−	0.353587i	0.773916	+	0.633288i	$0.218295\pi$
$762$		0			0
$763$	−2.45631e6	−	1.41815e6i	−0.152747	−	0.0881883i
$764$	−7.19712e6	−	1.46744e7i	−0.446093	−	0.909550i
$765$		0			0
$766$	7.79446e6	−	1.25043e7i	0.479970	−	0.769993i
$767$	617871.	−	1.07018e6i	0.0379236	−	0.0656855i
$768$		0			0
$769$	−465579.	−	806407.i	−0.0283908	−	0.0491743i	0.851481	−	0.524386i	$-0.175705\pi$
$769$	−465579.	−	806407.i	−0.0283908	−	0.0491743i	−0.879872	+	0.475211i	$0.842372\pi$
$770$	33483.7	+	1132.46i	0.00203520	+	6.88329e-5i
$771$		0			0
$772$	−2.80951e7	−	1.90259e6i	−1.69663	−	0.114896i
$773$			4.59758e6i			0.276745i	0.990380	+	0.138373i	$0.0441872\pi$
$773$			4.59758e6i			0.276745i	−0.990380	+	0.138373i	$0.955813\pi$
$774$		0			0
$775$			2.29489e7i			1.37249i
$776$	4.94419e6	−	6.85245e6i	0.294741	−	0.408500i
$777$		0			0
$778$	663589.	−	1.96205e7i	0.0393052	−	1.16215i
$779$	3.17266e6	+	5.49522e6i	0.187318	+	0.324445i
$780$		0			0
$781$	−1.88725e6	+	3.26881e6i	−0.110714	+	0.191762i
$782$	2.31450e7	+	1.44273e7i	1.35344	+	0.843660i
$783$		0			0
$784$	−1.03738e7	+	1.33988e7i	−0.602767	+	0.778532i
$785$	−814662.	−	470345.i	−0.0471849	−	0.0272422i
$786$		0			0
$787$	−7.46443e6	+	4.30959e6i	−0.429596	+	0.248027i	−0.699174	−	0.714951i	$-0.746449\pi$
$787$	−7.46443e6	+	4.30959e6i	−0.429596	+	0.248027i	0.269579	+	0.962978i	$0.413116\pi$
$788$	−4.32533e6	−	2.90367e6i	−0.248144	−	0.166583i
$789$		0			0
$790$	417144.	+	782459.i	0.0237803	+	0.0446061i
$791$	−2.07784e6			−0.118079
$792$		0			0
$793$	1.07837e7			0.608954
$794$	−1.54054e7	−	2.88967e7i	−0.867204	−	1.62666i
$795$		0			0
$796$	−2.08953e7	−	1.40274e7i	−1.16887	−	0.784684i
$797$	−7.54210e6	+	4.35443e6i	−0.420578	+	0.242821i	−0.695324	−	0.718696i	$-0.744739\pi$
$797$	−7.54210e6	+	4.35443e6i	−0.420578	+	0.242821i	0.274747	+	0.961517i	$0.411406\pi$
$798$		0			0
$799$	−4.59845e7	−	2.65492e7i	−2.54826	−	1.47124i
$800$	−6.24822e6	−	1.68779e7i	−0.345169	−	0.932380i
$801$		0			0
$802$	−1.12442e7	−	7.00902e6i	−0.617297	−	0.384788i
$803$	991930.	−	1.71807e6i	0.0542865	−	0.0940270i
$804$		0			0
$805$	88430.7	+	153166.i	0.00480965	+	0.00833055i
$806$	459022.	−	1.35720e7i	0.0248884	−	0.735880i
$807$		0			0
$808$	1.11582e7	+	8.05085e6i	0.601263	+	0.433824i
$809$		−	1.21590e7i		−	0.653169i	−0.945168	−	0.326584i	$-0.894102\pi$
$809$		−	1.21590e7i		−	0.653169i	0.945168	−	0.326584i	$-0.105898\pi$
$810$		0			0
$811$			2.14341e7i			1.14433i	0.820137	+	0.572167i	$0.193897\pi$
$811$			2.14341e7i			1.14433i	−0.820137	+	0.572167i	$0.806103\pi$
$812$	2.57564e6	+	174422.i	0.137087	+	0.00928350i
$813$		0			0
$814$	5.15167e6	+	174236.i	0.272513	+	0.00921672i
$815$	−688658.	−	1.19279e6i	−0.0363170	−	0.0629029i
$816$		0			0
$817$	−1.63215e6	+	2.82697e6i	−0.0855473	+	0.148172i
$818$	−7.00641e6	+	1.12400e7i	−0.366110	+	0.587333i
$819$		0			0
$820$	913287.	+	1.86212e6i	0.0474322	+	0.0967106i
$821$	1.88546e7	+	1.08857e7i	0.976248	+	0.563637i	0.901135	−	0.433538i	$-0.142735\pi$
$821$	1.88546e7	+	1.08857e7i	0.976248	+	0.563637i	0.0751127	+	0.997175i	$0.476068\pi$
$822$		0			0
$823$	−1.63030e7	+	9.41255e6i	−0.839012	+	0.484404i	−0.856928	−	0.515436i	$-0.827630\pi$
$823$	−1.63030e7	+	9.41255e6i	−0.839012	+	0.484404i	0.0179161	+	0.999839i	$0.494297\pi$
$824$	−623550.	+	280088.i	−0.0319929	+	0.0143706i
$825$		0			0
$826$	−305341.	+	162783.i	−0.0155716	+	0.00830154i
$827$	2.05084e7			1.04272			0.521361	−	0.853336i	$-0.325424\pi$
$827$	2.05084e7			1.04272			0.521361	+	0.853336i	$0.325424\pi$
$828$		0			0
$829$	−3.27151e7			−1.65334			−0.826669	−	0.562688i	$-0.809767\pi$
$829$	−3.27151e7			−1.65334			−0.826669	+	0.562688i	$0.809767\pi$
$830$	1.16698e6	−	622141.i	0.0587989	−	0.0313468i
$831$		0			0
$832$	3.35762e6	+	1.01066e7i	0.168160	+	0.506170i
$833$	−2.67104e7	+	1.54213e7i	−1.33373	+	0.770030i
$834$		0			0
$835$	−920894.	−	531679.i	−0.0457082	−	0.0263896i
$836$	1.03550e6	−	507866.i	0.0512430	−	0.0251324i
$837$		0			0
$838$	1.39676e7	−	2.24075e7i	0.687085	−	1.10226i
$839$	−1.82802e6	+	3.16623e6i	−0.0896555	+	0.155288i	−0.907366	−	0.420342i	$-0.861910\pi$
$839$	−1.82802e6	+	3.16623e6i	−0.0896555	+	0.155288i	0.817710	+	0.575630i	$0.195243\pi$
$840$		0			0
$841$	2.31771e6	+	4.01440e6i	0.112998	+	0.195718i
$842$	−2.30555e7	−	779763.i	−1.12071	−	0.0379038i
$843$		0			0
$844$	−2.19660e6	+	3.24366e7i	−0.106144	+	1.56740i
$845$			1.12905e6i			0.0543966i
$846$		0			0
$847$			2.47020e6i			0.118310i
$848$	5.19676e6	−	2.12623e6i	0.248167	−	0.101536i
$849$		0			0
$850$	1.10726e6	−	3.27385e7i	0.0525655	−	1.55422i
$851$	1.36056e7	+	2.35656e7i	0.644011	+	1.11546i
$852$		0			0
$853$	1.25006e7	−	2.16517e7i	0.588245	−	1.01887i	−0.406217	−	0.913777i	$-0.633152\pi$
$853$	1.25006e7	−	2.16517e7i	0.588245	−	1.01887i	0.994462	−	0.105094i	$-0.0335144\pi$
$854$	−2.56249e6	−	1.59731e6i	−0.120231	−	0.0749453i
$855$		0			0
$856$	−1.03833e7	−	1.05675e6i	−0.484342	−	0.0492935i
$857$	1.66895e7	+	9.63570e6i	0.776233	+	0.448158i	0.835093	−	0.550108i	$-0.185414\pi$
$857$	1.66895e7	+	9.63570e6i	0.776233	+	0.448158i	−0.0588609	+	0.998266i	$0.518747\pi$
$858$		0			0
$859$	1.12055e7	−	6.46950e6i	0.518142	−	0.299149i	−0.218032	−	0.975942i	$-0.569964\pi$
$859$	1.12055e7	−	6.46950e6i	0.518142	−	0.299149i	0.736174	+	0.676792i	$0.236630\pi$
$860$	−594698.	+	885867.i	−0.0274189	+	0.0408434i
$861$		0			0
$862$	1.20915e7	+	2.26807e7i	0.554259	+	1.03965i
$863$	−8.69765e6			−0.397535			−0.198767	−	0.980047i	$-0.563694\pi$
$863$	−8.69765e6			−0.397535			−0.198767	+	0.980047i	$0.563694\pi$
$864$		0			0
$865$	−1.31189e6			−0.0596153
$866$	17900.4	+	33576.8i	0.000811088	+	0.00152140i
$867$		0			0
$868$	−2.11940e6	+	3.15708e6i	−0.0954803	+	0.142228i
$869$	2.76692e6	−	1.59748e6i	0.124293	−	0.0717607i
$870$		0			0
$871$	1.87176e7	+	1.08066e7i	0.835999	+	0.482664i
$872$	−3.17504e7	−	3.23138e6i	−1.41403	−	0.143912i
$873$		0			0
$874$	5.16684e6	+	3.22072e6i	0.228795	+	0.142618i
$875$	213040.	−	368996.i	0.00940679	−	0.0162930i
$876$		0			0
$877$	1.12877e7	+	1.95509e7i	0.495573	+	0.858357i	0.999987	−	0.00510463i	$-0.00162486\pi$
$877$	1.12877e7	+	1.95509e7i	0.495573	+	0.858357i	−0.504414	+	0.863462i	$0.668292\pi$
$878$	−943278.	+	2.78901e7i	−0.0412955	+	1.22100i
$879$		0			0
$880$	348905.	−	142753.i	0.0151880	−	0.00621411i
$881$			1.89558e7i			0.822816i	0.911451	+	0.411408i	$0.134963\pi$
$881$			1.89558e7i			0.822816i	−0.911451	+	0.411408i	$0.865037\pi$
$882$		0			0
$883$		−	2.38595e7i		−	1.02981i	−0.857246	−	0.514907i	$-0.827826\pi$
$883$		−	2.38595e7i		−	1.02981i	0.857246	−	0.514907i	$-0.172174\pi$
$884$	−1.30967e6	+	1.93395e7i	−0.0563677	+	0.832365i
$885$		0			0
$886$	2.85787e7	+	966568.i	1.22309	+	0.0413664i
$887$	1.14641e7	+	1.98564e7i	0.489249	+	0.847405i	0.999923	−	0.0123696i	$-0.00393747\pi$
$887$	1.14641e7	+	1.98564e7i	0.489249	+	0.847405i	−0.510674	+	0.859774i	$0.670604\pi$
$888$		0			0
$889$	347929.	−	602631.i	0.0147651	−	0.0255739i
$890$	521030.	−	835864.i	0.0220490	−	0.0353721i
$891$		0			0
$892$	6.69965e6	−	3.28587e6i	0.281929	−	0.138273i
$893$	−1.02655e7	−	5.92678e6i	−0.430775	−	0.248708i
$894$		0			0
$895$	28916.9	−	16695.2i	0.00120668	−	0.000696679i
$896$	699157.	−	2.89893e6i	0.0290941	−	0.120633i
$897$		0			0
$898$	1.97303e7	−	1.05186e7i	0.816476	−	0.435279i
$899$	−3.70398e7			−1.52851
$900$		0			0
$901$	1.02198e7			0.419402
$902$	6.59450e6	−	3.51565e6i	0.269877	−	0.143876i
$903$		0			0
$904$	−2.13274e7	+	9.57989e6i	−0.867994	+	0.389888i
$905$	1.65518e6	−	955617.i	0.0671774	−	0.0387849i
$906$		0			0
$907$	−9.34957e6	−	5.39798e6i	−0.377375	−	0.217878i	0.299300	−	0.954159i	$-0.403247\pi$
$907$	−9.34957e6	−	5.39798e6i	−0.377375	−	0.217878i	−0.676676	+	0.736281i	$0.736580\pi$
$908$	−1.23858e7	−	2.52537e7i	−0.498551	−	1.01651i
$909$		0			0
$910$	−66493.2	+	106672.i	−0.00266179	+	0.00427018i
$911$	1.46710e6	−	2.54108e6i	0.0585683	−	0.101443i	−0.835255	−	0.549863i	$-0.814680\pi$
$911$	1.46710e6	−	2.54108e6i	0.0585683	−	0.101443i	0.893823	+	0.448420i	$0.148013\pi$
$912$		0			0
$913$	−2.38253e6	−	4.12667e6i	−0.0945937	−	0.163841i
$914$	4.23307e7	+	1.43167e6i	1.67606	+	0.0566864i
$915$		0			0
$916$	1.22145e7	+	827161.i	0.480989	+	0.0325725i
$917$			3.37252e6i			0.132444i
$918$		0			0
$919$			2.10763e7i			0.823201i	0.911364	+	0.411600i	$0.135030\pi$
$919$			2.10763e7i			0.823201i	−0.911364	+	0.411600i	$0.864970\pi$
$920$	1.61384e6	+	1.16442e6i	0.0628626	+	0.0453566i
$921$		0			0
$922$	−979302.	+	2.89553e7i	−0.0379393	+	1.12176i
$923$	−7.08075e6	−	1.22642e7i	−0.273574	−	0.473844i
$924$		0			0
$925$	1.63412e7	−	2.83039e7i	0.627958	−	1.08766i
$926$	1.92717e7	+	1.20129e7i	0.738571	+	0.460383i
$927$		0			0
$928$	2.72411e7	−	1.00847e7i	1.03838	−	0.384409i
$929$	1.43110e7	+	8.26248e6i	0.544041	+	0.314102i	0.746715	−	0.665144i	$-0.231630\pi$
$929$	1.43110e7	+	8.26248e6i	0.544041	+	0.314102i	−0.202674	+	0.979246i	$0.564963\pi$
$930$		0			0
$931$	−5.96278e6	+	3.44261e6i	−0.225463	+	0.130171i
$932$	−5.96081e6	−	4.00160e6i	−0.224784	−	0.150901i
$933$		0			0
$934$	−1.44673e7	−	2.71372e7i	−0.542652	−	1.01788i
$935$	686147.			0.0256678
$936$		0			0
$937$	1.09551e7			0.407633			0.203816	−	0.979009i	$-0.434665\pi$
$937$	1.09551e7			0.407633			0.203816	+	0.979009i	$0.434665\pi$
$938$	−2.84709e6	−	5.34045e6i	−0.105656	−	0.198185i
$939$		0			0
$940$	−3.21681e6	−	2.15950e6i	−0.118743	−	0.0797139i
$941$	3.02898e7	−	1.74878e7i	1.11512	−	0.643815i	0.174970	−	0.984574i	$-0.444017\pi$
$941$	3.02898e7	−	1.74878e7i	1.11512	−	0.643815i	0.940151	+	0.340759i	$0.110684\pi$
$942$		0			0
$943$	3.41650e7	+	1.97252e7i	1.25113	+	0.722341i
$944$	−2.38357e6	+	3.07861e6i	−0.0870558	+	0.112441i
$945$		0			0
$946$	3.26254e6	+	2.03368e6i	0.118530	+	0.0738849i
$947$	1.20408e7	−	2.08553e7i	0.436296	−	0.755687i	−0.561104	−	0.827745i	$-0.689623\pi$
$947$	1.20408e7	−	2.08553e7i	0.436296	−	0.755687i	0.997400	+	0.0720580i	$0.0229567\pi$
$948$		0			0
$949$	3.72161e6	+	6.44601e6i	0.134142	+	0.232341i
$950$	247181.	−	7.30848e6i	0.00888601	−	0.262735i
$951$		0			0
$952$	3.17582e6	−	4.40157e6i	0.113570	−	0.157404i
$953$		−	3.19780e7i		−	1.14056i	−0.821450	−	0.570281i	$-0.806834\pi$
$953$		−	3.19780e7i		−	1.14056i	0.821450	−	0.570281i	$-0.193166\pi$
$954$		0			0
$955$		−	2.17067e6i		−	0.0770170i
$956$	4.91104e7	+	3.32575e6i	1.73792	+	0.117692i
$957$		0			0
$958$	−5.24593e7	−	1.77424e6i	−1.84675	−	0.0624594i
$959$	−924760.	−	1.60173e6i	−0.0324700	−	0.0562397i
$960$		0			0
$961$	1.29644e7	−	2.24551e7i	0.452840	−	0.784343i
$962$	−1.02304e7	+	1.64121e7i	−0.356413	+	0.571777i
$963$		0			0
$964$	1.95274e7	+	3.98149e7i	0.676787	+	1.37992i
$965$	−3.23879e6	−	1.86992e6i	−0.111960	−	0.0646404i
$966$		0			0
$967$	2.45189e7	−	1.41560e7i	0.843209	−	0.486827i	−0.0151446	−	0.999885i	$-0.504821\pi$
$967$	2.45189e7	−	1.41560e7i	0.843209	−	0.486827i	0.858354	+	0.513058i	$0.171488\pi$
$968$	1.13889e7	+	2.53546e7i	0.390653	+	0.869699i
$969$		0			0
$970$	990289.	−	527942.i	0.0337935	−	0.0180159i
$971$	−1.79971e7			−0.612567			−0.306284	−	0.951940i	$-0.599086\pi$
$971$	−1.79971e7			−0.612567			−0.306284	+	0.951940i	$0.599086\pi$
$972$		0			0
$973$	−3.47103e6			−0.117538
$974$	1.17806e7	−	6.28044e6i	0.397895	−	0.212125i
$975$		0			0
$976$	−3.36663e7	−	4.58077e6i	−1.13128	−	0.153927i
$977$	6.10203e6	−	3.52301e6i	0.204521	−	0.118080i	−0.394242	−	0.919007i	$-0.628993\pi$
$977$	6.10203e6	−	3.52301e6i	0.204521	−	0.118080i	0.598763	+	0.800927i	$0.295659\pi$
$978$		0			0
$979$	−3.07350e6	−	1.77449e6i	−0.102489	−	0.0591720i
$980$	−2.02056e6	+	990995.i	−0.0672059	+	0.0329614i
$981$		0			0
$982$	2.55115e7	−	4.09269e7i	0.844223	−	1.35435i
$983$	1.13029e7	−	1.95773e7i	0.373085	−	0.646202i	−0.616954	−	0.787000i	$-0.711633\pi$
$983$	1.13029e7	−	1.95773e7i	0.373085	−	0.646202i	0.990038	+	0.140798i	$0.0449667\pi$
$984$		0			0
$985$	−345940.	−	599186.i	−0.0113608	−	0.0196776i
$986$	5.28403e7	+	1.78712e6i	1.73091	+	0.0585413i
$987$		0			0
$988$	−292367.	+	4.31730e6i	−0.00952876	+	0.140708i
$989$			2.02950e7i			0.659778i
$990$		0			0
$991$		−	3.05378e7i		−	0.987765i	−0.869529	−	0.493883i	$-0.835577\pi$
$991$		−	3.05378e7i		−	0.987765i	0.869529	−	0.493883i	$-0.164423\pi$
$992$	−7.19826e6	+	4.21764e7i	−0.232246	+	1.36079i
$993$		0			0
$994$	−134037.	+	3.96312e6i	−0.00430289	+	0.127225i
$995$	−1.67121e6	−	2.89463e6i	−0.0535148	−	0.0926904i
$996$		0			0
$997$	−1.05531e7	+	1.82786e7i	−0.336236	+	0.582377i	−0.983721	−	0.179700i	$-0.942487\pi$
$997$	−1.05531e7	+	1.82786e7i	−0.336236	+	0.582377i	0.647486	+	0.762078i	$0.275821\pi$
$998$	1.21256e6	+	755841.i	0.0385369	+	0.0240217i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.6.h.a.35.10		56
3.2	odd	2		36.6.h.a.11.19	✓	56
4.3	odd	2	inner	108.6.h.a.35.1		56
9.4	even	3		36.6.h.a.23.28	yes	56
9.5	odd	6	inner	108.6.h.a.71.1		56
12.11	even	2		36.6.h.a.11.28	yes	56
36.23	even	6	inner	108.6.h.a.71.10		56
36.31	odd	6		36.6.h.a.23.19	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.6.h.a.11.19	✓	56	3.2	odd	2
36.6.h.a.11.28	yes	56	12.11	even	2
36.6.h.a.23.19	yes	56	36.31	odd	6
36.6.h.a.23.28	yes	56	9.4	even	3
108.6.h.a.35.1		56	4.3	odd	2	inner
108.6.h.a.35.10		56	1.1	even	1	trivial
108.6.h.a.71.1		56	9.5	odd	6	inner
108.6.h.a.71.10		56	36.23	even	6	inner

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	108.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.66122 - 4.99179i) q^{2} +(-17.8359 + 26.5684i) q^{4} +(-3.68052 + 2.12495i) q^{5} +(13.9322 + 8.04377i) q^{7} +(180.089 + 18.3284i) q^{8} +O(q^{10})\)	\(q+(-2.66122 - 4.99179i) q^{2} +(-17.8359 + 26.5684i) q^{4} +(-3.68052 + 2.12495i) q^{5} +(13.9322 + 8.04377i) q^{7} +(180.089 + 18.3284i) q^{8} +(20.4019 + 12.7174i) q^{10} +(43.3121 - 75.0187i) q^{11} +(162.502 + 281.462i) q^{13} +(3.07614 - 90.9529i) q^{14} +(-387.764 - 947.742i) q^{16} -1863.80i q^{17} -416.071i q^{19} +(9.18864 - 135.686i) q^{20} +(-489.740 - 16.5636i) q^{22} +(-1293.41 - 2240.24i) q^{23} +(-1553.47 + 2690.69i) q^{25} +(972.544 - 1560.21i) q^{26} +(-462.204 + 226.690i) q^{28} +(-4342.80 - 2507.32i) q^{29} +(6396.76 - 3693.17i) q^{31} +(-3699.00 + 4457.78i) q^{32} +(-9303.69 + 4959.98i) q^{34} -68.3704 q^{35} -10519.2 q^{37} +(-2076.94 + 1107.25i) q^{38} +(-701.768 + 315.222i) q^{40} +(-13207.4 + 7625.29i) q^{41} +(-6794.45 - 3922.78i) q^{43} +(1220.62 + 2488.76i) q^{44} +(-7740.79 + 12418.2i) q^{46} +(14244.6 - 24672.4i) q^{47} +(-8274.10 - 14331.2i) q^{49} +(17565.5 + 594.085i) q^{50} +(-10376.4 - 702.686i) q^{52} +5483.31i q^{53} +368.144i q^{55} +(2361.61 + 1703.95i) q^{56} +(-958.860 + 28350.9i) q^{58} +(-1901.12 - 3292.83i) q^{59} +(16590.1 - 28734.9i) q^{61} +(-35458.7 - 22102.9i) q^{62} +(32096.1 + 6601.49i) q^{64} +(-1196.18 - 690.617i) q^{65} +(57592.1 - 33250.8i) q^{67} +(49518.3 + 33242.5i) q^{68} +(181.948 + 341.290i) q^{70} -43573.3 q^{71} +22901.9 q^{73} +(27993.8 + 52509.6i) q^{74} +(11054.4 + 7420.98i) q^{76} +(1206.87 - 696.785i) q^{77} +(31941.7 + 18441.5i) q^{79} +(3441.08 + 2664.20i) q^{80} +(73211.6 + 45635.9i) q^{82} +(27504.3 - 47638.8i) q^{83} +(3960.48 + 6859.75i) q^{85} +(-1500.17 + 44355.8i) q^{86} +(9175.01 - 12716.2i) q^{88} -40969.8i q^{89} +5228.51i q^{91} +(82588.8 + 5592.90i) q^{92} +(-161068. - 5447.50i) q^{94} +(884.130 + 1531.36i) q^{95} +(23339.8 - 40425.7i) q^{97} +(-49518.9 + 79440.8i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 3 q^{2} - q^{4} + 6 q^{5}+O(q^{10}) \) 56 * q + 3 * q^2 - q^4 + 6 * q^5	\( 56 q + 3 q^{2} - q^{4} + 6 q^{5} - 68 q^{10} - 2 q^{13} + 1518 q^{14} - q^{16} + 1242 q^{20} + 63 q^{22} + 12498 q^{25} - 2052 q^{28} + 11946 q^{29} + 7233 q^{32} + 6361 q^{34} - 8 q^{37} + 14877 q^{38} - 1526 q^{40} + 43536 q^{41} - 26880 q^{46} + 38414 q^{49} - 38631 q^{50} + 24988 q^{52} - 21186 q^{56} - 3314 q^{58} - 2 q^{61} - 106342 q^{64} - 35970 q^{65} - 31413 q^{68} + 10524 q^{70} + 53620 q^{73} + 20406 q^{74} + 26193 q^{76} - 26178 q^{77} - 151286 q^{82} + 6248 q^{85} - 279237 q^{86} - 122541 q^{88} - 435804 q^{92} + 63480 q^{94} - 58148 q^{97}+O(q^{100}) \) 56 * q + 3 * q^2 - q^4 + 6 * q^5 - 68 * q^10 - 2 * q^13 + 1518 * q^14 - q^16 + 1242 * q^20 + 63 * q^22 + 12498 * q^25 - 2052 * q^28 + 11946 * q^29 + 7233 * q^32 + 6361 * q^34 - 8 * q^37 + 14877 * q^38 - 1526 * q^40 + 43536 * q^41 - 26880 * q^46 + 38414 * q^49 - 38631 * q^50 + 24988 * q^52 - 21186 * q^56 - 3314 * q^58 - 2 * q^61 - 106342 * q^64 - 35970 * q^65 - 31413 * q^68 + 10524 * q^70 + 53620 * q^73 + 20406 * q^74 + 26193 * q^76 - 26178 * q^77 - 151286 * q^82 + 6248 * q^85 - 279237 * q^86 - 122541 * q^88 - 435804 * q^92 + 63480 * q^94 - 58148 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more