LMFDB - Embedded newform 108.6.h.a.35.17

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			35.17
Character	$\chi$	$=$	108.35
Dual form			108.6.h.a.71.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.78216 - 5.36879i) q^{2} +(-25.6478 - 19.1360i) q^{4} +(-12.8631 + 7.42651i) q^{5} +(-15.2989 - 8.83282i) q^{7} +(-148.446 + 103.595i) q^{8} +O(q^{10})$	\(q+(1.78216 - 5.36879i) q^{2} +(-25.6478 - 19.1360i) q^{4} +(-12.8631 + 7.42651i) q^{5} +(-15.2989 - 8.83282i) q^{7} +(-148.446 + 103.595i) q^{8} +(16.9473 + 82.2944i) q^{10} +(-143.245 + 248.107i) q^{11} +(42.2460 + 73.1722i) q^{13} +(-74.6866 + 66.3951i) q^{14} +(291.624 + 981.596i) q^{16} +1609.65i q^{17} -1669.01i q^{19} +(472.025 + 55.6747i) q^{20} +(1076.75 + 1211.22i) q^{22} +(2324.29 + 4025.79i) q^{23} +(-1452.19 + 2515.27i) q^{25} +(468.135 - 96.4056i) q^{26} +(223.358 + 519.303i) q^{28} +(-2414.87 - 1394.23i) q^{29} +(2781.39 - 1605.84i) q^{31} +(5789.71 + 183.691i) q^{32} +(8641.85 + 2868.64i) q^{34} +262.388 q^{35} -4624.19 q^{37} +(-8960.54 - 2974.43i) q^{38} +(1140.13 - 2434.98i) q^{40} +(-9810.20 + 5663.92i) q^{41} +(12396.0 + 7156.83i) q^{43} +(8421.70 - 3622.27i) q^{44} +(25755.9 - 5304.05i) q^{46} +(1695.63 - 2936.92i) q^{47} +(-8247.46 - 14285.0i) q^{49} +(10915.9 + 12279.1i) q^{50} +(316.708 - 2685.13i) q^{52} +31068.4i q^{53} -4255.23i q^{55} +(3186.09 - 273.686i) q^{56} +(-11789.0 + 10480.2i) q^{58} +(-10900.3 - 18879.9i) q^{59} +(-17894.5 + 30994.2i) q^{61} +(-3664.53 - 17794.5i) q^{62} +(11304.4 - 30756.4i) q^{64} +(-1086.83 - 627.480i) q^{65} +(-18015.5 + 10401.2i) q^{67} +(30802.3 - 41283.9i) q^{68} +(467.617 - 1408.71i) q^{70} -42271.8 q^{71} -72975.6 q^{73} +(-8241.02 + 24826.3i) q^{74} +(-31938.2 + 42806.4i) q^{76} +(4382.97 - 2530.51i) q^{77} +(-76047.9 - 43906.3i) q^{79} +(-11041.0 - 10460.6i) q^{80} +(12925.1 + 62762.9i) q^{82} +(12234.8 - 21191.3i) q^{83} +(-11954.1 - 20705.0i) q^{85} +(60515.1 - 53796.9i) q^{86} +(-4438.45 - 51669.8i) q^{88} +119158. i q^{89} -1492.60i q^{91} +(17424.6 - 147731. i) q^{92} +(-12745.9 - 14337.6i) q^{94} +(12394.9 + 21468.6i) q^{95} +(39575.0 - 68545.9i) q^{97} +(-91391.6 + 18820.8i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.78216	−	5.36879i	0.315044	−	0.949077i
$2$	1.78216	−	5.36879i	0.315044	−	0.949077i
$3$		0			0
$3$		0			0
$4$	−25.6478	−	19.1360i	−0.801495	−	0.598001i
$5$	−12.8631	+	7.42651i	−0.230102	+	0.132849i	−0.610619	−	0.791924i	$-0.709079\pi$
$5$	−12.8631	+	7.42651i	−0.230102	+	0.132849i	0.380517	+	0.924774i	$0.375746\pi$
$6$		0			0
$7$	−15.2989	−	8.83282i	−0.118009	−	0.0681325i	0.439834	−	0.898079i	$-0.355037\pi$
$7$	−15.2989	−	8.83282i	−0.118009	−	0.0681325i	−0.557843	+	0.829947i	$0.688371\pi$
$8$	−148.446	+	103.595i	−0.820055	+	0.572284i
$9$		0			0
$10$	16.9473	+	82.2944i	0.0535922	+	0.260238i
$11$	−143.245	+	248.107i	−0.356941	+	0.618240i	−0.987448	−	0.157943i	$-0.949514\pi$
$11$	−143.245	+	248.107i	−0.356941	+	0.618240i	0.630507	+	0.776184i	$0.282847\pi$
$12$		0			0
$13$	42.2460	+	73.1722i	0.0693309	+	0.120085i	0.898607	−	0.438755i	$-0.144580\pi$
$13$	42.2460	+	73.1722i	0.0693309	+	0.120085i	−0.829276	+	0.558839i	$0.811247\pi$
$14$	−74.6866	+	66.3951i	−0.101841	+	0.0905349i
$15$		0			0
$16$	291.624	+	981.596i	0.284789	+	0.958590i
$17$			1609.65i			1.35085i	0.737427	+	0.675427i	$0.236040\pi$
$17$			1609.65i			1.35085i	−0.737427	+	0.675427i	$0.763960\pi$
$18$		0			0
$19$		−	1669.01i		−	1.06065i	−0.847793	−	0.530327i	$-0.822069\pi$
$19$		−	1669.01i		−	1.06065i	0.847793	−	0.530327i	$-0.177931\pi$
$20$	472.025	+	55.6747i	0.263870	+	0.0311231i
$21$		0			0
$22$	1076.75	+	1211.22i	0.474306	+	0.533537i
$23$	2324.29	+	4025.79i	0.916159	+	1.58683i	0.805196	+	0.593009i	$0.202060\pi$
$23$	2324.29	+	4025.79i	0.916159	+	1.58683i	0.110963	+	0.993825i	$0.464606\pi$
$24$		0			0
$25$	−1452.19	+	2515.27i	−0.464702	+	0.804888i
$26$	468.135	−	96.4056i	0.135812	−	0.0279685i
$27$		0			0
$28$	223.358	+	519.303i	0.0538403	+	0.125177i
$29$	−2414.87	−	1394.23i	−0.533211	−	0.307850i	0.209112	−	0.977892i	$-0.432943\pi$
$29$	−2414.87	−	1394.23i	−0.533211	−	0.307850i	−0.742323	+	0.670042i	$0.766276\pi$
$30$		0			0
$31$	2781.39	−	1605.84i	0.519825	−	0.300121i	−0.217038	−	0.976163i	$-0.569640\pi$
$31$	2781.39	−	1605.84i	0.519825	−	0.300121i	0.736863	+	0.676042i	$0.236306\pi$
$32$	5789.71	+	183.691i	0.999497	+	0.0317113i
$33$		0			0
$34$	8641.85	+	2868.64i	1.28206	+	0.425578i
$35$	262.388			0.0362055
$36$		0			0
$37$	−4624.19			−0.555304			−0.277652	−	0.960682i	$-0.589556\pi$
$37$	−4624.19			−0.555304			−0.277652	+	0.960682i	$0.589556\pi$
$38$	−8960.54	−	2974.43i	−1.00664	−	0.334152i
$39$		0			0
$40$	1140.13	−	2434.98i	0.112669	−	0.240628i
$41$	−9810.20	+	5663.92i	−0.911420	+	0.526208i	−0.880888	−	0.473325i	$-0.843053\pi$
$41$	−9810.20	+	5663.92i	−0.911420	+	0.526208i	−0.0305320	+	0.999534i	$0.509720\pi$
$42$		0			0
$43$	12396.0	+	7156.83i	1.02237	+	0.590268i	0.914791	−	0.403928i	$-0.132355\pi$
$43$	12396.0	+	7156.83i	1.02237	+	0.590268i	0.107584	+	0.994196i	$0.465689\pi$
$44$	8421.70	−	3622.27i	0.655795	−	0.282065i
$45$		0			0
$46$	25755.9	−	5304.05i	1.79466	−	0.369584i
$47$	1695.63	−	2936.92i	0.111966	−	0.193931i	−0.804597	−	0.593822i	$-0.797618\pi$
$47$	1695.63	−	2936.92i	0.111966	−	0.193931i	0.916563	+	0.399890i	$0.130952\pi$
$48$		0			0
$49$	−8247.46	−	14285.0i	−0.490716	−	0.849945i
$50$	10915.9	+	12279.1i	0.617499	+	0.694613i
$51$		0			0
$52$	316.708	−	2685.13i	0.0162424	−	0.137707i
$53$			31068.4i			1.51925i	0.650360	+	0.759626i	$0.274618\pi$
$53$			31068.4i			1.51925i	−0.650360	+	0.759626i	$0.725382\pi$
$54$		0			0
$55$		−	4255.23i		−	0.189678i
$56$	3186.09	−	273.686i	0.135765	−	0.0116622i
$57$		0			0
$58$	−11789.0	+	10480.2i	−0.460158	+	0.409072i
$59$	−10900.3	−	18879.9i	−0.407671	−	0.706107i	0.586957	−	0.809618i	$-0.300326\pi$
$59$	−10900.3	−	18879.9i	−0.407671	−	0.706107i	−0.994628	+	0.103511i	$0.966992\pi$
$60$		0			0
$61$	−17894.5	+	30994.2i	−0.615736	+	1.06649i	0.374519	+	0.927219i	$0.377808\pi$
$61$	−17894.5	+	30994.2i	−0.615736	+	1.06649i	−0.990255	+	0.139267i	$0.955525\pi$
$62$	−3664.53	−	17794.5i	−0.121071	−	0.587906i
$63$		0			0
$64$	11304.4	−	30756.4i	0.344982	−	0.938609i
$65$	−1086.83	−	627.480i	−0.0319064	−	0.0184211i
$66$		0			0
$67$	−18015.5	+	10401.2i	−0.490296	+	0.283072i	−0.724697	−	0.689068i	$-0.758020\pi$
$67$	−18015.5	+	10401.2i	−0.490296	+	0.283072i	0.234401	+	0.972140i	$0.424687\pi$
$68$	30802.3	−	41283.9i	0.807812	−	1.08270i
$69$		0			0
$70$	467.617	−	1408.71i	0.0114063	−	0.0343618i
$71$	−42271.8			−0.995187			−0.497593	−	0.867410i	$-0.665783\pi$
$71$	−42271.8			−0.995187			−0.497593	+	0.867410i	$0.665783\pi$
$72$		0			0
$73$	−72975.6			−1.60277			−0.801384	−	0.598150i	$-0.795903\pi$
$73$	−72975.6			−1.60277			−0.801384	+	0.598150i	$0.795903\pi$
$74$	−8241.02	+	24826.3i	−0.174945	+	0.527027i
$75$		0			0
$76$	−31938.2	+	42806.4i	−0.634273	+	0.850109i
$77$	4382.97	−	2530.51i	0.0842445	−	0.0486386i
$78$		0			0
$79$	−76047.9	−	43906.3i	−1.37094	−	0.791514i	−0.379896	−	0.925029i	$-0.624040\pi$
$79$	−76047.9	−	43906.3i	−1.37094	−	0.791514i	−0.991047	+	0.133515i	$0.957374\pi$
$80$	−11041.0	−	10460.6i	−0.192879	−	0.182739i
$81$		0			0
$82$	12925.1	+	62762.9i	0.212275	+	1.03079i
$83$	12234.8	−	21191.3i	0.194940	−	0.337646i	−0.751941	−	0.659231i	$-0.770882\pi$
$83$	12234.8	−	21191.3i	0.194940	−	0.337646i	0.946881	+	0.321585i	$0.104215\pi$
$84$		0			0
$85$	−11954.1	−	20705.0i	−0.179460	−	0.310834i
$86$	60515.1	−	53796.9i	0.882302	−	0.784352i
$87$		0			0
$88$	−4438.45	−	51669.8i	−0.0610976	−	0.711263i
$89$			119158.i			1.59459i	0.603588	+	0.797296i	$0.293737\pi$
$89$			119158.i			1.59459i	−0.603588	+	0.797296i	$0.706263\pi$
$90$		0			0
$91$		−	1492.60i		−	0.0188948i
$92$	17424.6	−	147731.i	0.214632	−	1.81970i
$93$		0			0
$94$	−12745.9	−	14337.6i	−0.148782	−	0.167362i
$95$	12394.9	+	21468.6i	0.140907	+	0.244059i
$96$		0			0
$97$	39575.0	−	68545.9i	0.427062	−	0.739694i	−0.569548	−	0.821958i	$-0.692882\pi$
$97$	39575.0	−	68545.9i	0.427062	−	0.739694i	0.996611	+	0.0822641i	$0.0262151\pi$
$98$	−91391.6	+	18820.8i	−0.961260	+	0.197958i
$99$		0			0
$100$	85378.0	−	36722.1i	0.853780	−	0.367221i
$101$	−116647.	−	67346.1i	−1.13781	−	0.656915i	−0.191923	−	0.981410i	$-0.561472\pi$
$101$	−116647.	−	67346.1i	−1.13781	−	0.656915i	−0.945887	+	0.324495i	$0.894806\pi$
$102$		0			0
$103$	87239.5	−	50367.8i	0.810252	−	0.467799i	−0.0367911	−	0.999323i	$-0.511714\pi$
$103$	87239.5	−	50367.8i	0.810252	−	0.467799i	0.847044	+	0.531524i	$0.178380\pi$
$104$	−13851.5	−	6485.66i	−0.125578	−	0.0587991i
$105$		0			0
$106$	166800.	+	55368.8i	1.44189	+	0.478631i
$107$	14924.9			0.126024			0.0630118	−	0.998013i	$-0.479929\pi$
$107$	14924.9			0.126024			0.0630118	+	0.998013i	$0.479929\pi$
$108$		0			0
$109$	34005.6			0.274148			0.137074	−	0.990561i	$-0.456230\pi$
$109$	34005.6			0.274148			0.137074	+	0.990561i	$0.456230\pi$
$110$	−22845.4	−	7583.48i	−0.180019	−	0.0597568i
$111$		0			0
$112$	4208.75	−	17593.2i	0.0317035	−	0.132526i
$113$	89706.6	−	51792.2i	0.660889	−	0.381564i	−0.131727	−	0.991286i	$-0.542052\pi$
$113$	89706.6	−	51792.2i	0.660889	−	0.381564i	0.792616	+	0.609722i	$0.208719\pi$
$114$		0			0
$115$	−59795.1	−	34522.7i	−0.421620	−	0.243422i
$116$	35256.3	+	81970.0i	0.243272	+	0.565601i
$117$		0			0
$118$	−120789.	+	24874.6i	−0.798584	+	0.164457i
$119$	14217.7	−	24625.8i	0.0920370	−	0.159413i
$120$		0			0
$121$	39487.4	+	68394.3i	0.245186	+	0.424674i
$122$	134510.	+	151308.i	0.818194	+	0.920371i
$123$		0			0
$124$	−102066.	−	12038.6i	−0.596110	−	0.0703105i
$125$		−	89554.6i		−	0.512640i
$126$		0			0
$127$			323553.i			1.78007i	0.455894	+	0.890034i	$0.349320\pi$
$127$			323553.i			1.78007i	−0.455894	+	0.890034i	$0.650680\pi$
$128$	−144978.	−	115503.i	−0.782129	−	0.623117i
$129$		0			0
$130$	−5305.71	+	4716.68i	−0.0275350	+	0.0244781i
$131$	70996.7	+	122970.i	0.361460	+	0.626066i	0.988201	−	0.153161i	$-0.0489452\pi$
$131$	70996.7	+	122970.i	0.361460	+	0.626066i	−0.626742	+	0.779227i	$0.715612\pi$
$132$		0			0
$133$	−14742.0	+	25534.0i	−0.0722650	+	0.125167i
$134$	23735.7	+	115258.i	0.114193	+	0.554509i
$135$		0			0
$136$	−166750.	−	238945.i	−0.773072	−	1.10777i
$137$	51712.9	+	29856.5i	0.235395	+	0.135906i	0.613059	−	0.790037i	$-0.289939\pi$
$137$	51712.9	+	29856.5i	0.235395	+	0.135906i	−0.377663	+	0.925943i	$0.623272\pi$
$138$		0			0
$139$	310879.	−	179486.i	1.36475	−	0.787941i	0.374501	−	0.927227i	$-0.377814\pi$
$139$	310879.	−	179486.i	1.36475	−	0.787941i	0.990252	+	0.139286i	$0.0444807\pi$
$140$	−6729.69	−	5021.07i	−0.0290185	−	0.0216509i
$141$		0			0
$142$	−75334.9	+	226948.i	−0.313527	+	0.944509i
$143$	−24206.0			−0.0989882
$144$		0			0
$145$	41417.0			0.163591
$146$	−130054.	+	391791.i	−0.504942	+	1.52115i
$147$		0			0
$148$	118600.	+	88488.6i	0.445074	+	0.332073i
$149$	175221.	−	101164.i	0.646576	−	0.373301i	−0.140567	−	0.990071i	$-0.544893\pi$
$149$	175221.	−	101164.i	0.646576	−	0.373301i	0.787143	+	0.616770i	$0.211559\pi$
$150$		0			0
$151$	−15615.5	−	9015.60i	−0.0557331	−	0.0321775i	0.471875	−	0.881666i	$-0.343578\pi$
$151$	−15615.5	−	9015.60i	−0.0557331	−	0.0321775i	−0.527608	+	0.849488i	$0.676911\pi$
$152$	172900.	+	247757.i	0.606996	+	0.869795i
$153$		0			0
$154$	−5774.64	−	28041.0i	−0.0196211	−	0.0952779i
$155$	−23851.5	+	41312.0i	−0.0797419	+	0.138117i
$156$		0			0
$157$	238209.	+	412590.i	0.771274	+	1.33589i	0.936865	+	0.349692i	$0.113714\pi$
$157$	238209.	+	412590.i	0.771274	+	1.33589i	−0.165590	+	0.986195i	$0.552953\pi$
$158$	−371253.	+	330037.i	−1.18312	+	1.05177i
$159$		0			0
$160$	−75837.7	+	40634.5i	−0.234199	+	0.125486i
$161$		−	82120.2i		−	0.249681i
$162$		0			0
$163$			243580.i			0.718080i	0.933322	+	0.359040i	$0.116896\pi$
$163$			243580.i			0.718080i	−0.933322	+	0.359040i	$0.883104\pi$
$164$	359996.	+	42461.1i	1.04517	+	0.123277i
$165$		0			0
$166$	−91967.2	−	103452.i	−0.259037	−	0.291386i
$167$	−21086.7	−	36523.3i	−0.0585083	−	0.101339i	0.835288	−	0.549813i	$-0.185301\pi$
$167$	−21086.7	−	36523.3i	−0.0585083	−	0.101339i	−0.893796	+	0.448474i	$0.851968\pi$
$168$		0			0
$169$	182077.	−	315367.i	0.490386	−	0.849374i
$170$	−132465.	+	27279.2i	−0.351543	+	0.0723952i
$171$		0			0
$172$	−180977.	−	420767.i	−0.466447	−	1.08448i
$173$	−94858.3	−	54766.5i	−0.240968	−	0.139123i	0.374653	−	0.927165i	$-0.377762\pi$
$173$	−94858.3	−	54766.5i	−0.240968	−	0.139123i	−0.615622	+	0.788042i	$0.711095\pi$
$174$		0			0
$175$	44433.9	−	25653.9i	0.109678	−	0.0633226i
$176$	−285314.	−	68254.6i	−0.694292	−	0.166093i
$177$		0			0
$178$	639737.	+	212359.i	1.51339	+	0.502366i
$179$	264309.			0.616566			0.308283	−	0.951295i	$-0.400246\pi$
$179$	264309.			0.616566			0.308283	+	0.951295i	$0.400246\pi$
$180$		0			0
$181$	508179.			1.15298			0.576488	−	0.817105i	$-0.304423\pi$
$181$	508179.			1.15298			0.576488	+	0.817105i	$0.304423\pi$
$182$	−8013.48	−	2660.05i	−0.0179326	−	0.00595267i
$183$		0			0
$184$	−762081.	−	356828.i	−1.65942	−	0.776988i
$185$	59481.3	−	34341.6i	0.127777	−	0.0737718i
$186$		0			0
$187$	−399364.	−	230573.i	−0.835152	−	0.482175i
$188$	−99690.5	+	42878.0i	−0.205712	+	0.0884790i
$189$		0			0
$190$	137350.	−	28285.2i	0.276022	−	0.0568428i
$191$	−52294.2	+	90576.3i	−0.103722	+	0.179652i	−0.913215	−	0.407477i	$-0.866409\pi$
$191$	−52294.2	+	90576.3i	−0.103722	+	0.179652i	0.809493	+	0.587129i	$0.199742\pi$
$192$		0			0
$193$	−271784.	−	470744.i	−0.525207	−	0.909685i	−0.999569	−	0.0293554i	$-0.990655\pi$
$193$	−271784.	−	470744.i	−0.525207	−	0.909685i	0.474362	−	0.880330i	$-0.342679\pi$
$194$	−297480.	−	334629.i	−0.567483	−	0.638351i
$195$		0			0
$196$	−61829.2	+	524204.i	−0.114962	+	0.974675i
$197$		−	922105.i		−	1.69284i	−0.532519	−	0.846418i	$-0.678755\pi$
$197$		−	922105.i		−	1.69284i	0.532519	−	0.846418i	$-0.321245\pi$
$198$		0			0
$199$			93172.6i			0.166784i	0.996517	+	0.0833922i	$0.0265754\pi$
$199$			93172.6i			0.166784i	−0.996517	+	0.0833922i	$0.973425\pi$
$200$	−44996.3	−	523821.i	−0.0795430	−	0.925994i
$201$		0			0
$202$	−569450.	+	506232.i	−0.981923	+	0.872913i
$203$	24629.9	+	42660.3i	0.0419491	+	0.0726580i
$204$		0			0
$205$	84126.4	−	145711.i	0.139813	−	0.242163i
$206$	−114940.	−	558134.i	−0.188713	−	0.916369i
$207$		0			0
$208$	−59505.6	+	62807.2i	−0.0953673	+	0.100659i
$209$	414092.	+	239076.i	0.655739	+	0.378591i
$210$		0			0
$211$	4637.49	−	2677.46i	0.00717096	−	0.00414015i	−0.496410	−	0.868088i	$-0.665349\pi$
$211$	4637.49	−	2677.46i	0.00717096	−	0.00414015i	0.503581	+	0.863948i	$0.332015\pi$
$212$	594527.	−	796839.i	0.908515	−	1.21767i
$213$		0			0
$214$	26598.5	−	80128.7i	0.0397029	−	0.119606i
$215$	−212601.			−0.313667
$216$		0			0
$217$	−56736.2			−0.0817921
$218$	60603.4	−	182569.i	0.0863685	−	0.260187i
$219$		0			0
$220$	−81428.3	+	109137.i	−0.113428	+	0.152026i
$221$	−117781.	+	68001.1i	−0.162217	+	0.0936559i
$222$		0			0
$223$	−714552.	−	412547.i	−0.962214	−	0.555535i	−0.0653606	−	0.997862i	$-0.520820\pi$
$223$	−714552.	−	412547.i	−0.962214	−	0.555535i	−0.896854	+	0.442327i	$0.854153\pi$
$224$	−86953.6	−	53949.7i	−0.115789	−	0.0718405i
$225$		0			0
$226$	−118190.	−	573918.i	−0.153925	−	0.747444i
$227$	222824.	−	385943.i	0.287011	−	0.497117i	−0.686084	−	0.727522i	$-0.740672\pi$
$227$	222824.	−	385943.i	0.287011	−	0.497117i	0.973095	+	0.230405i	$0.0740051\pi$
$228$		0			0
$229$	121497.	+	210439.i	0.153101	+	0.265178i	0.932366	−	0.361516i	$-0.117741\pi$
$229$	121497.	+	210439.i	0.153101	+	0.265178i	−0.779265	+	0.626694i	$0.784407\pi$
$230$	−291910.	+	259503.i	−0.363855	+	0.323461i
$231$		0			0
$232$	502912.	−	43200.2i	0.613440	−	0.0526946i
$233$			483894.i			0.583930i	0.956429	+	0.291965i	$0.0943091\pi$
$233$			483894.i			0.583930i	−0.956429	+	0.291965i	$0.905691\pi$
$234$		0			0
$235$			50370.6i			0.0594987i
$236$	−81717.2	+	692819.i	−0.0955066	+	0.809729i
$237$		0			0
$238$	−106873.	−	120219.i	−0.122299	−	0.137572i
$239$	−374928.	−	649395.i	−0.424574	−	0.735384i	0.571806	−	0.820389i	$-0.306243\pi$
$239$	−374928.	−	649395.i	−0.424574	−	0.735384i	−0.996381	+	0.0850045i	$0.972910\pi$
$240$		0			0
$241$	−214184.	+	370977.i	−0.237544	+	0.411438i	−0.960009	−	0.279969i	$-0.909676\pi$
$241$	−214184.	+	370977.i	−0.237544	+	0.411438i	0.722465	+	0.691408i	$0.243009\pi$
$242$	437567.	−	90110.6i	0.480293	−	0.0989094i
$243$		0			0
$244$	1.05206e6	−	452504.i	1.13127	−	0.486572i
$245$	212176.	+	122500.i	0.225829	+	0.130383i
$246$		0			0
$247$	122125.	−	70508.8i	0.127368	−	0.0735361i
$248$	−246530.	+	526516.i	−0.254531	+	0.543604i
$249$		0			0
$250$	−480800.	−	159600.i	−0.486535	−	0.161504i
$251$	−168039.			−0.168355			−0.0841773	−	0.996451i	$-0.526826\pi$
$251$	−168039.			−0.168355			−0.0841773	+	0.996451i	$0.526826\pi$
$252$		0			0
$253$	−1.33177e6			−1.30806
$254$	1.73709e6	+	576623.i	1.68942	+	0.560799i
$255$		0			0
$256$	−878487.	+	572513.i	−0.837791	+	0.545991i
$257$	−1.21515e6	+	701569.i	−1.14762	+	0.662579i	−0.948306	−	0.317357i	$-0.897205\pi$
$257$	−1.21515e6	+	701569.i	−1.14762	+	0.662579i	−0.199314	+	0.979936i	$0.563871\pi$
$258$		0			0
$259$	70744.9	+	40844.6i	0.0655309	+	0.0378343i
$260$	15867.3	+	36891.1i	0.0145569	+	0.0338445i
$261$		0			0
$262$	786727.	−	162015.i	0.708061	−	0.145815i
$263$	−465252.	+	805840.i	−0.414762	+	0.718388i	−0.995403	−	0.0957708i	$-0.969468\pi$
$263$	−465252.	+	805840.i	−0.414762	+	0.718388i	0.580642	+	0.814159i	$0.302802\pi$
$264$		0			0
$265$	−230730.	−	399636.i	−0.201832	−	0.349583i
$266$	110814.	+	124652.i	0.0960263	+	0.108018i
$267$		0			0
$268$	661096.	+	77975.5i	0.562247	+	0.0663164i
$269$			1.02733e6i			0.865621i	0.901485	+	0.432810i	$0.142478\pi$
$269$			1.02733e6i			0.865621i	−0.901485	+	0.432810i	$0.857522\pi$
$270$		0			0
$271$			1.66981e6i			1.38116i	0.723255	+	0.690581i	$0.242645\pi$
$271$			1.66981e6i			1.38116i	−0.723255	+	0.690581i	$0.757355\pi$
$272$	−1.58002e6	+	469411.i	−1.29491	+	0.384708i
$273$		0			0
$274$	252454.	−	224427.i	0.203145	−	0.180592i
$275$	−416038.	−	720599.i	−0.331743	−	0.574595i
$276$		0			0
$277$	−531248.	+	920149.i	−0.416004	+	0.720541i	−0.995533	−	0.0944109i	$-0.969903\pi$
$277$	−531248.	+	920149.i	−0.416004	+	0.720541i	0.579529	+	0.814952i	$0.303237\pi$
$278$	−409588.	−	1.98892e6i	−0.317860	−	1.54349i
$279$		0			0
$280$	−38950.4	+	27182.0i	−0.0296905	+	0.0207198i
$281$	728876.	+	420817.i	0.550666	+	0.317927i	0.749390	−	0.662128i	$-0.230347\pi$
$281$	728876.	+	420817.i	0.550666	+	0.317927i	−0.198725	+	0.980055i	$0.563680\pi$
$282$		0			0
$283$	1.59876e6	−	923047.i	1.18664	−	0.685106i	0.229097	−	0.973404i	$-0.426423\pi$
$283$	1.59876e6	−	923047.i	1.18664	−	0.685106i	0.957541	+	0.288298i	$0.0930893\pi$
$284$	1.08418e6	+	808914.i	0.797637	+	0.595123i
$285$		0			0
$286$	−43138.9	+	129957.i	−0.0311856	+	0.0939475i
$287$	200114.			0.143408
$288$		0			0
$289$	−1.17110e6			−0.824804
$290$	73811.5	−	222359.i	0.0515381	−	0.155260i
$291$		0			0
$292$	1.87167e6	+	1.39647e6i	1.28461	+	0.958458i
$293$	−1.40490e6	+	811121.i	−0.956043	+	0.551972i	−0.894953	−	0.446161i	$-0.852791\pi$
$293$	−1.40490e6	+	811121.i	−0.956043	+	0.551972i	−0.0610899	+	0.998132i	$0.519458\pi$
$294$		0			0
$295$	280424.	+	161903.i	0.187612	+	0.108318i
$296$	686441.	−	479040.i	0.455380	−	0.317792i
$297$		0			0
$298$	−230856.	−	1.12101e6i	−0.150592	−	0.731256i
$299$	−196384.	+	340147.i	−0.127036	+	0.220033i
$300$		0			0
$301$	−126430.	−	218983.i	−0.0804329	−	0.139314i
$302$	−76232.1	+	67769.1i	−0.0480973	+	0.0427577i
$303$		0			0
$304$	1.63829e6	−	486722.i	1.01673	−	0.302062i
$305$		−	531574.i		−	0.327201i
$306$		0			0
$307$		−	1.18284e6i		−	0.716275i	−0.933669	−	0.358137i	$-0.883412\pi$
$307$		−	1.18284e6i		−	0.716275i	0.933669	−	0.358137i	$-0.116588\pi$
$308$	−160838.	−	18970.6i	−0.0966075	−	0.0113947i
$309$		0			0
$310$	179288.	+	201678.i	0.105962	+	0.119194i
$311$	685107.	+	1.18664e6i	0.401659	+	0.695693i	0.993926	−	0.110048i	$-0.0351005\pi$
$311$	685107.	+	1.18664e6i	0.401659	+	0.695693i	−0.592268	+	0.805741i	$0.701767\pi$
$312$		0			0
$313$	130578.	−	226168.i	0.0753372	−	0.130488i	−0.825896	−	0.563823i	$-0.809330\pi$
$313$	130578.	−	226168.i	0.0753372	−	0.130488i	0.901233	+	0.433335i	$0.142663\pi$
$314$	2.63963e6	−	543594.i	1.51084	−	0.311136i
$315$		0			0
$316$	1.11027e6	+	2.58136e6i	0.625478	+	1.45422i
$317$	−529678.	−	305810.i	−0.296049	−	0.170924i	0.344618	−	0.938743i	$-0.388009\pi$
$317$	−529678.	−	305810.i	−0.296049	−	0.170924i	−0.640667	+	0.767819i	$0.721342\pi$
$318$		0			0
$319$	691835.	−	399431.i	0.380650	−	0.219768i
$320$	83003.4	+	479574.i	0.0453128	+	0.261806i
$321$		0			0
$322$	−440886.	−	146351.i	−0.236966	−	0.0786603i
$323$	2.68651e6			1.43279
$324$		0			0
$325$	−245397.			−0.128873
$326$	1.30773e6	+	434098.i	0.681513	+	0.226226i
$327$		0			0
$328$	869533.	−	1.85707e6i	0.446274	−	0.953111i
$329$	−51882.7	+	29954.5i	−0.0264261	+	0.0152571i
$330$		0			0
$331$	−853212.	−	492602.i	−0.428043	−	0.247131i	0.270470	−	0.962728i	$-0.412821\pi$
$331$	−853212.	−	492602.i	−0.428043	−	0.247131i	−0.698512	+	0.715598i	$0.746154\pi$
$332$	−719312.	+	309385.i	−0.358156	+	0.154047i
$333$		0			0
$334$	−233666.	+	48120.0i	−0.114612	+	0.0236026i
$335$	154490.	−	267584.i	0.0752120	−	0.130271i
$336$		0			0
$337$	1.10946e6	+	1.92164e6i	0.532153	+	0.921716i	0.999295	+	0.0375341i	$0.0119503\pi$
$337$	1.10946e6	+	1.92164e6i	0.532153	+	0.921716i	−0.467142	+	0.884182i	$0.654716\pi$
$338$	−1.36865e6	−	1.53957e6i	−0.651629	−	0.733005i
$339$		0			0
$340$	−89616.6	+	759792.i	−0.0420428	+	0.356449i
$341$			920109.i			0.428503i
$342$		0			0
$343$			588300.i			0.270000i
$344$	−2.58154e6	+	221755.i	−1.17620	+	0.101036i
$345$		0			0
$346$	−463082.	+	411672.i	−0.207954	+	0.184868i
$347$	1.28567e6	+	2.22684e6i	0.573199	+	0.992810i	0.996235	+	0.0866969i	$0.0276312\pi$
$347$	1.28567e6	+	2.22684e6i	0.573199	+	0.992810i	−0.423036	+	0.906113i	$0.639036\pi$
$348$		0			0
$349$	935689.	−	1.62066e6i	0.411214	−	0.712243i	−0.583809	−	0.811891i	$-0.698438\pi$
$349$	935689.	−	1.62066e6i	0.411214	−	0.712243i	0.995023	+	0.0996478i	$0.0317716\pi$
$350$	−58542.5	−	284276.i	−0.0255447	−	0.124042i
$351$		0			0
$352$	−874919.	+	1.41015e6i	−0.376367	+	0.606610i
$353$	−1.19697e6	−	691073.i	−0.511267	−	0.295180i	0.222087	−	0.975027i	$-0.428713\pi$
$353$	−1.19697e6	−	691073.i	−0.511267	−	0.295180i	−0.733354	+	0.679847i	$0.762046\pi$
$354$		0			0
$355$	543746.	−	313932.i	0.228994	−	0.132210i
$356$	2.28022e6	−	3.05616e6i	0.953569	−	1.27806i
$357$		0			0
$358$	471040.	−	1.41902e6i	0.194245	−	0.585169i
$359$	−4.58930e6			−1.87936			−0.939680	−	0.342054i	$-0.888877\pi$
$359$	−4.58930e6			−1.87936			−0.939680	+	0.342054i	$0.888877\pi$
$360$		0			0
$361$	−309482.			−0.124988
$362$	905655.	−	2.72831e6i	0.363238	−	1.09426i
$363$		0			0
$364$	−28562.6	+	38282.1i	−0.0112991	+	0.0151441i
$365$	938692.	−	541954.i	0.368800	−	0.212927i
$366$		0			0
$367$	−318059.	−	183631.i	−0.123266	−	0.0711675i	0.437099	−	0.899413i	$-0.356006\pi$
$367$	−318059.	−	183631.i	−0.123266	−	0.0711675i	−0.560365	+	0.828246i	$0.689339\pi$
$368$	−3.27388e6	+	3.45553e6i	−1.26021	+	1.33013i
$369$		0			0
$370$	−78367.7	−	380545.i	−0.0297600	−	0.144511i
$371$	274422.	−	475313.i	0.103510	−	0.179285i
$372$		0			0
$373$	−1.45750e6	−	2.52447e6i	−0.542421	−	0.939501i	−0.998764	−	0.0496972i	$-0.984174\pi$
$373$	−1.45750e6	−	2.52447e6i	−0.542421	−	0.939501i	0.456343	−	0.889804i	$-0.349159\pi$
$374$	−1.94963e6	+	1.73319e6i	−0.720731	+	0.640717i
$375$		0			0
$376$	52539.3	+	611633.i	0.0191653	+	0.223111i
$377$		−	235602.i		−	0.0853740i
$378$		0			0
$379$		−	1.95071e6i		−	0.697579i	−0.937201	−	0.348790i	$-0.886593\pi$
$379$		−	1.95071e6i		−	0.697579i	0.937201	−	0.348790i	$-0.113407\pi$
$380$	92921.5	−	787812.i	0.0330109	−	0.279875i
$381$		0			0
$382$	393089.	+	442178.i	0.137826	+	0.155038i
$383$	−1.91266e6	−	3.31282e6i	−0.666254	−	1.15399i	−0.978944	−	0.204130i	$-0.934563\pi$
$383$	−1.91266e6	−	3.31282e6i	−0.666254	−	1.15399i	0.312690	−	0.949855i	$-0.398770\pi$
$384$		0			0
$385$	−37585.7	+	65100.3i	−0.0129232	+	0.0223837i
$386$	−3.01169e6	+	620213.i	−1.02882	+	0.211872i
$387$		0			0
$388$	−2.32671e6	+	1.00075e6i	−0.784626	+	0.337477i
$389$	1.38080e6	+	797204.i	0.462654	+	0.267113i	0.713159	−	0.701002i	$-0.247264\pi$
$389$	1.38080e6	+	797204.i	0.462654	+	0.267113i	−0.250506	+	0.968115i	$0.580597\pi$
$390$		0			0
$391$	−6.48010e6	+	3.74128e6i	−2.14358	+	1.23760i
$392$	2.70415e6	+	1.26616e6i	0.888824	+	0.416173i
$393$		0			0
$394$	−4.95059e6	−	1.64333e6i	−1.60663	−	0.533317i
$395$	1.30428e6			0.420609
$396$		0			0
$397$	4.04020e6			1.28655			0.643275	−	0.765635i	$-0.277575\pi$
$397$	4.04020e6			1.28655			0.643275	+	0.765635i	$0.277575\pi$
$398$	500224.	+	166048.i	0.158291	+	0.0525444i
$399$		0			0
$400$	−2.89248e6	−	691955.i	−0.903899	−	0.216236i
$401$	4.84780e6	−	2.79888e6i	1.50551	−	0.869207i	0.505532	−	0.862808i	$-0.331296\pi$
$401$	4.84780e6	−	2.79888e6i	1.50551	−	0.869207i	0.999980	−	0.00639934i	$-0.00203699\pi$
$402$		0			0
$403$	235005.	+	135680.i	0.0720799	+	0.0416154i
$404$	1.70300e6	+	3.95944e6i	0.519113	+	1.20693i
$405$		0			0
$406$	272928.	−	56205.7i	0.0821739	−	0.0169225i
$407$	662390.	−	1.14729e6i	0.198211	−	0.343311i
$408$		0			0
$409$	1.24641e6	+	2.15885e6i	0.368429	+	0.638138i	0.989320	−	0.145759i	$-0.0465625\pi$
$409$	1.24641e6	+	2.15885e6i	0.368429	+	0.638138i	−0.620891	+	0.783897i	$0.713229\pi$
$410$	−632366.	−	711337.i	−0.185784	−	0.208985i
$411$		0			0
$412$	−3.20135e6	−	377595.i	−0.929158	−	0.109593i
$413$			385123.i			0.111103i
$414$		0			0
$415$			363447.i			0.103591i
$416$	231151.	+	431406.i	0.0654880	+	0.122223i
$417$		0			0
$418$	2.02153e6	−	1.79710e6i	0.565899	−	0.503074i
$419$	476950.	+	826102.i	0.132720	+	0.229879i	0.924724	−	0.380637i	$-0.124295\pi$
$419$	476950.	+	826102.i	0.132720	+	0.229879i	−0.792004	+	0.610516i	$0.790962\pi$
$420$		0			0
$421$	−1.44880e6	+	2.50940e6i	−0.398386	+	0.690025i	−0.993527	−	0.113597i	$-0.963763\pi$
$421$	−1.44880e6	+	2.50940e6i	−0.398386	+	0.690025i	0.595141	+	0.803621i	$0.297096\pi$
$422$	−6109.98	−	29669.4i	−0.00167016	−	0.00811012i
$423$		0			0
$424$	−3.21852e6	−	4.61198e6i	−0.869444	−	1.24587i
$425$	−4.04870e6	−	2.33752e6i	−1.08728	−	0.627744i
$426$		0			0
$427$	547532.	−	316118.i	0.145325	−	0.0839033i
$428$	−382791.	−	285604.i	−0.101007	−	0.0753623i
$429$		0			0
$430$	−378888.	+	1.14141e6i	−0.0988188	+	0.297694i
$431$	−3.72242e6			−0.965234			−0.482617	−	0.875831i	$-0.660314\pi$
$431$	−3.72242e6			−0.965234			−0.482617	+	0.875831i	$0.660314\pi$
$432$		0			0
$433$	4.74890e6			1.21723			0.608616	−	0.793465i	$-0.291725\pi$
$433$	4.74890e6			1.21723			0.608616	+	0.793465i	$0.291725\pi$
$434$	−101113.	+	304605.i	−0.0257681	+	0.0776270i
$435$		0			0
$436$	−872172.	−	650734.i	−0.219728	−	0.163941i
$437$	6.71907e6	−	3.87925e6i	1.68308	−	0.971728i
$438$		0			0
$439$	6.29205e6	+	3.63272e6i	1.55823	+	0.899644i	0.997427	+	0.0716934i	$0.0228403\pi$
$439$	6.29205e6	+	3.63272e6i	1.55823	+	0.899644i	0.560802	+	0.827950i	$0.310493\pi$
$440$	440819.	+	631671.i	0.108550	+	0.155546i
$441$		0			0
$442$	155179.	+	753532.i	0.0377813	+	0.183462i
$443$	2.83250e6	−	4.90603e6i	0.685741	−	1.18774i	−0.287463	−	0.957792i	$-0.592812\pi$
$443$	2.83250e6	−	4.90603e6i	0.685741	−	1.18774i	0.973203	−	0.229946i	$-0.0738549\pi$
$444$		0			0
$445$	−884931.	−	1.53275e6i	−0.211841	−	0.366919i
$446$	−3.48832e6	+	3.10106e6i	−0.830385	+	0.738198i
$447$		0			0
$448$	−444610.	+	370689.i	−0.104661	+	0.0872599i
$449$		−	4.08820e6i		−	0.957011i	−0.878085	−	0.478505i	$-0.841179\pi$
$449$		−	4.08820e6i		−	0.957011i	0.878085	−	0.478505i	$-0.158821\pi$
$450$		0			0
$451$		−	3.24531e6i		−	0.751302i
$452$	−3.29188e6	−	388273.i	−0.757875	−	0.0893905i
$453$		0			0
$454$	−1.67494e6	−	1.88411e6i	−0.381382	−	0.429009i
$455$	11084.8	+	19199.5i	0.00251016	+	0.00434772i
$456$		0			0
$457$	2.07648e6	−	3.59658e6i	0.465091	−	0.805562i	−0.534114	−	0.845412i	$-0.679355\pi$
$457$	2.07648e6	−	3.59658e6i	0.465091	−	0.805562i	0.999206	+	0.0398504i	$0.0126881\pi$
$458$	1.34633e6	−	277257.i	0.299908	−	0.0617617i
$459$		0			0
$460$	872987.	+	2.02968e6i	0.192359	+	0.447231i
$461$	−293141.	−	169245.i	−0.0642427	−	0.0370905i	0.467535	−	0.883975i	$-0.345142\pi$
$461$	−293141.	−	169245.i	−0.0642427	−	0.0370905i	−0.531777	+	0.846884i	$0.678476\pi$
$462$		0			0
$463$	−6.16958e6	+	3.56201e6i	−1.33753	+	0.772223i	−0.986441	−	0.164119i	$-0.947522\pi$
$463$	−6.16958e6	+	3.56201e6i	−1.33753	+	0.772223i	−0.351089	+	0.936342i	$0.614189\pi$
$464$	664335.	−	2.77702e6i	0.143249	−	0.598803i
$465$		0			0
$466$	2.59793e6	+	862375.i	0.554195	+	0.183963i
$467$	3.96727e6			0.841782			0.420891	−	0.907111i	$-0.361717\pi$
$467$	3.96727e6			0.841782			0.420891	+	0.907111i	$0.361717\pi$
$468$		0			0
$469$	367489.			0.0771457
$470$	270429.	+	89768.2i	0.0564688	+	0.0187447i
$471$		0			0
$472$	3.57397e6	+	1.67343e6i	0.738407	+	0.345743i
$473$	−3.55132e6	+	2.05035e6i	−0.729855	+	0.421382i
$474$		0			0
$475$	4.19801e6	+	2.42372e6i	0.853707	+	0.492888i
$476$	−835894.	+	359528.i	−0.169096	+	0.0727303i
$477$		0			0
$478$	−4.15465e6	+	855589.i	−0.831696	+	0.171276i
$479$	−3.84509e6	+	6.65989e6i	−0.765716	+	1.32626i	0.174151	+	0.984719i	$0.444282\pi$
$479$	−3.84509e6	+	6.65989e6i	−0.765716	+	1.32626i	−0.939867	+	0.341540i	$0.889052\pi$
$480$		0			0
$481$	−195353.	−	338362.i	−0.0384997	−	0.0666835i
$482$	1.60999e6	+	1.81105e6i	0.315650	+	0.355069i
$483$		0			0
$484$	296028.	−	2.50980e6i	0.0574406	−	0.486996i
$485$			1.17562e6i			0.226940i
$486$		0			0
$487$		−	1.17689e6i		−	0.224860i	−0.993660	−	0.112430i	$-0.964137\pi$
$487$		−	1.17689e6i		−	0.224860i	0.993660	−	0.112430i	$-0.0358634\pi$
$488$	−554462.	−	6.45472e6i	−0.105395	−	1.22695i
$489$		0			0
$490$	1.03581e6	−	920814.i	0.194889	−	0.173253i
$491$	730305.	+	1.26493e6i	0.136710	+	0.236789i	0.926249	−	0.376911i	$-0.123014\pi$
$491$	730305.	+	1.26493e6i	0.136710	+	0.236789i	−0.789539	+	0.613700i	$0.789680\pi$
$492$		0			0
$493$	2.24421e6	−	3.88709e6i	0.415859	−	0.720290i
$494$	−160902.	−	781320.i	−0.0296649	−	0.144049i
$495$		0			0
$496$	2.38740e6	+	2.26190e6i	0.435734	+	0.412828i
$497$	646711.	+	373379.i	0.117441	+	0.0678046i
$498$		0			0
$499$	3.61275e6	−	2.08582e6i	0.649510	−	0.374995i	−0.138758	−	0.990326i	$-0.544311\pi$
$499$	3.61275e6	−	2.08582e6i	0.649510	−	0.374995i	0.788269	+	0.615331i	$0.210978\pi$
$500$	−1.71372e6	+	2.29688e6i	−0.306560	+	0.410879i
$501$		0			0
$502$	−299471.	+	902165.i	−0.0530390	+	0.159782i
$503$	3.55656e6			0.626773			0.313387	−	0.949626i	$-0.398536\pi$
$503$	3.55656e6			0.626773			0.313387	+	0.949626i	$0.398536\pi$
$504$		0			0
$505$	2.00059e6			0.349083
$506$	−2.37342e6	+	7.14999e6i	−0.412096	+	1.24145i
$507$		0			0
$508$	6.19153e6	−	8.29845e6i	1.06448	−	1.42672i
$509$	−5.64282e6	+	3.25788e6i	−0.965388	+	0.557367i	−0.897827	−	0.440348i	$-0.854855\pi$
$509$	−5.64282e6	+	3.25788e6i	−0.965388	+	0.557367i	−0.0675606	+	0.997715i	$0.521522\pi$
$510$		0			0
$511$	1.11645e6	+	644581.i	0.189141	+	0.109201i
$512$	1.50810e6	+	5.73672e6i	0.254247	+	0.967139i
$513$		0			0
$514$	1.60099e6	+	7.77421e6i	0.267288	+	1.29792i
$515$	−748113.	+	1.29577e6i	−0.124294	+	0.215283i
$516$		0			0
$517$	485781.	+	841397.i	0.0799308	+	0.138444i
$518$	345365.	−	307023.i	0.0565527	−	0.0502744i
$519$		0			0
$520$	226339.	−	19442.5i	0.0367071	−	0.00315315i
$521$		−	551264.i		−	0.0889744i	−0.999010	−	0.0444872i	$-0.985835\pi$
$521$		−	551264.i		−	0.0889744i	0.999010	−	0.0444872i	$-0.0141654\pi$
$522$		0			0
$523$		−	1.10624e7i		−	1.76846i	−0.467053	−	0.884230i	$-0.654684\pi$
$523$		−	1.10624e7i		−	1.76846i	0.467053	−	0.884230i	$-0.345316\pi$
$524$	532245.	−	4.51251e6i	0.0846805	−	0.717942i
$525$		0			0
$526$	3.49723e6	+	3.93397e6i	0.551138	+	0.619965i
$527$	2.58483e6	+	4.47705e6i	0.405420	+	0.702208i
$528$		0			0
$529$	−7.58648e6	+	1.31402e7i	−1.17869	+	2.04156i
$530$	−2.55676e6	+	526528.i	−0.395367	+	0.0814201i
$531$		0			0
$532$	866720.	−	372787.i	0.132770	−	0.0571059i
$533$	−828883.	−	478556.i	−0.126379	−	0.0729650i
$534$		0			0
$535$	−191980.	+	110840.i	−0.0289983	+	0.0167422i
$536$	1.59681e6	−	3.41032e6i	0.240072	−	0.512724i
$537$		0			0
$538$	5.51550e6	+	1.83086e6i	0.821541	+	0.272708i
$539$	4.72562e6			0.700627
$540$		0			0
$541$	−3.00701e6			−0.441715			−0.220858	−	0.975306i	$-0.570886\pi$
$541$	−3.00701e6			−0.441715			−0.220858	+	0.975306i	$0.570886\pi$
$542$	8.96488e6	+	2.97587e6i	1.31083	+	0.435126i
$543$		0			0
$544$	−295678.	+	9.31938e6i	−0.0428373	+	1.35017i
$545$	−437418.	+	252543.i	−0.0630820	+	0.0364204i
$546$		0			0
$547$	1.52151e6	+	878446.i	0.217424	+	0.125530i	0.604757	−	0.796410i	$-0.293270\pi$
$547$	1.52151e6	+	878446.i	0.217424	+	0.125530i	−0.387333	+	0.921940i	$0.626604\pi$
$548$	−754990.	−	1.75533e6i	−0.107396	−	0.249694i
$549$		0			0
$550$	−4.61019e6	+	949402.i	−0.649849	+	0.133827i
$551$	−2.32697e6	+	4.03044e6i	−0.326522	+	0.565553i
$552$		0			0
$553$	775633.	+	1.34344e6i	0.107856	+	0.186812i
$554$	3.99332e6	+	4.49201e6i	0.552789	+	0.621822i
$555$		0			0
$556$	−1.14080e7	−	1.34556e6i	−1.56503	−	0.184594i
$557$			1.04568e7i			1.42811i	0.700090	+	0.714055i	$0.253143\pi$
$557$			1.04568e7i			1.42811i	−0.700090	+	0.714055i	$0.746857\pi$
$558$		0			0
$559$			1.20939e6i			0.163695i
$560$	76518.6	+	257559.i	0.0103109	+	0.0347062i
$561$		0			0
$562$	3.55825e6	−	3.16322e6i	0.475221	−	0.422463i
$563$	2.79625e6	+	4.84324e6i	0.371796	+	0.643969i	0.989842	−	0.142173i	$-0.0454088\pi$
$563$	2.79625e6	+	4.84324e6i	0.371796	+	0.643969i	−0.618046	+	0.786142i	$0.712075\pi$
$564$		0			0
$565$	−769270.	+	1.33241e6i	−0.101381	+	0.175597i
$566$	−2.10640e6	−	1.02284e7i	−0.276376	−	1.34205i
$567$		0			0
$568$	6.27507e6	−	4.37912e6i	0.816108	−	0.569530i
$569$	5.00540e6	+	2.88987e6i	0.648124	+	0.374195i	0.787737	−	0.616012i	$-0.211253\pi$
$569$	5.00540e6	+	2.88987e6i	0.648124	+	0.374195i	−0.139613	+	0.990206i	$0.544586\pi$
$570$		0			0
$571$	−2.38689e6	+	1.37807e6i	−0.306367	+	0.176881i	−0.645300	−	0.763930i	$-0.723267\pi$
$571$	−2.38689e6	+	1.37807e6i	−0.306367	+	0.176881i	0.338933	+	0.940811i	$0.389934\pi$
$572$	620833.	+	463208.i	0.0793386	+	0.0591951i
$573$		0			0
$574$	356634.	−	1.07437e6i	0.0451796	−	0.136105i
$575$	−1.35013e7			−1.70296
$576$		0			0
$577$	−9.66103e6			−1.20805			−0.604024	−	0.796966i	$-0.706437\pi$
$577$	−9.66103e6			−1.20805			−0.604024	+	0.796966i	$0.706437\pi$
$578$	−2.08709e6	+	6.28741e6i	−0.259849	+	0.782803i
$579$		0			0
$580$	−1.06226e6	−	792557.i	−0.131117	−	0.0978274i
$581$	−374357.	+	216135.i	−0.0460093	+	0.0265635i
$582$		0			0
$583$	−7.70830e6	−	4.45039e6i	−0.939263	−	0.542284i
$584$	1.08329e7	−	7.55987e6i	1.31436	−	0.917239i
$585$		0			0
$586$	1.85098e6	+	8.98818e6i	0.222668	+	1.08125i
$587$	4.72166e6	−	8.17816e6i	0.565587	−	0.979626i	−0.431407	−	0.902157i	$-0.641983\pi$
$587$	4.72166e6	−	8.17816e6i	0.565587	−	0.979626i	0.996995	−	0.0774689i	$-0.0246838\pi$
$588$		0			0
$589$	−2.68015e6	−	4.64215e6i	−0.318325	−	0.551355i
$590$	1.36898e6	−	1.21700e6i	0.161908	−	0.143933i
$591$		0			0
$592$	−1.34852e6	−	4.53908e6i	−0.158144	−	0.532309i
$593$			1.32881e6i			0.155177i	0.996985	+	0.0775883i	$0.0247220\pi$
$593$			1.32881e6i			0.155177i	−0.996985	+	0.0775883i	$0.975278\pi$
$594$		0			0
$595$			422352.i			0.0489083i
$596$	−6.42990e6	−	758399.i	−0.741462	−	0.0874545i
$597$		0			0
$598$	1.47619e6	+	1.66054e6i	0.168807	+	0.189887i
$599$	−8.44536e6	−	1.46278e7i	−0.961726	−	1.66576i	−0.718166	−	0.695872i	$-0.755018\pi$
$599$	−8.44536e6	−	1.46278e7i	−0.961726	−	1.66576i	−0.243560	−	0.969886i	$-0.578315\pi$
$600$		0			0
$601$	3.86305e6	−	6.69101e6i	0.436259	−	0.755623i	−0.561138	−	0.827722i	$-0.689636\pi$
$601$	3.86305e6	−	6.69101e6i	0.436259	−	0.755623i	0.997397	+	0.0720990i	$0.0229698\pi$
$602$	−1.40099e6	+	288514.i	−0.157559	+	0.0324471i
$603$		0			0
$604$	227980.	+	530049.i	0.0254276	+	0.0591186i
$605$	−1.01586e6	−	586508.i	−0.112836	−	0.0651456i
$606$		0			0
$607$	−1.99470e6	+	1.15164e6i	−0.219739	+	0.126866i	−0.605829	−	0.795595i	$-0.707159\pi$
$607$	−1.99470e6	+	1.15164e6i	−0.219739	+	0.126866i	0.386091	+	0.922461i	$0.373825\pi$
$608$	306582.	−	9.66305e6i	0.0336347	−	1.06012i
$609$		0			0
$610$	−2.85391e6	−	947348.i	−0.310539	−	0.103082i
$611$	286535.			0.0310509
$612$		0			0
$613$	−1.18649e7			−1.27531			−0.637653	−	0.770324i	$-0.720095\pi$
$613$	−1.18649e7			−1.27531			−0.637653	+	0.770324i	$0.720095\pi$
$614$	−6.35042e6	−	2.10800e6i	−0.679800	−	0.225658i
$615$		0			0
$616$	−388487.	+	829695.i	−0.0412501	+	0.0880982i
$617$	−1.03585e7	+	5.98047e6i	−1.09543	+	0.632445i	−0.935016	−	0.354606i	$-0.884615\pi$
$617$	−1.03585e7	+	5.98047e6i	−1.09543	+	0.632445i	−0.160410	+	0.987050i	$0.551282\pi$
$618$		0			0
$619$	6.60708e6	+	3.81460e6i	0.693079	+	0.400149i	0.804764	−	0.593594i	$-0.202292\pi$
$619$	6.60708e6	+	3.81460e6i	0.693079	+	0.400149i	−0.111685	+	0.993744i	$0.535625\pi$
$620$	1.40229e6	−	603141.i	0.146507	−	0.0630143i
$621$		0			0
$622$	7.59179e6	−	1.56342e6i	0.786807	−	0.162031i
$623$	1.05251e6	−	1.82299e6i	0.108644	−	0.188176i
$624$		0			0
$625$	−3.87303e6	−	6.70828e6i	−0.396598	−	0.686928i
$626$	−981538.	−	1.10411e6i	−0.100109	−	0.112610i
$627$		0			0
$628$	1.78579e6	−	1.51404e7i	0.180689	−	1.53193i
$629$		−	7.44330e6i		−	0.750134i
$630$		0			0
$631$			1.69017e7i			1.68988i	0.534861	+	0.844940i	$0.320364\pi$
$631$			1.69017e7i			1.68988i	−0.534861	+	0.844940i	$0.679636\pi$
$632$	1.58374e7	−	1.36044e6i	1.57722	−	0.135483i
$633$		0			0
$634$	−2.58580e6	+	2.29873e6i	−0.255488	+	0.227125i
$635$	−2.40287e6	−	4.16190e6i	−0.236481	−	0.409597i
$636$		0			0
$637$	696844.	−	1.20697e6i	0.0680436	−	0.117855i
$638$	−911505.	−	4.42617e6i	−0.0886558	−	0.430503i
$639$		0			0
$640$	2.72266e6	+	409047.i	0.262750	+	0.0394751i
$641$	6.42076e6	+	3.70703e6i	0.617222	+	0.356353i	0.775787	−	0.630995i	$-0.217353\pi$
$641$	6.42076e6	+	3.70703e6i	0.617222	+	0.356353i	−0.158565	+	0.987349i	$0.550687\pi$
$642$		0			0
$643$	3.01403e6	−	1.74015e6i	0.287488	−	0.165981i	−0.349320	−	0.937003i	$-0.613587\pi$
$643$	3.01403e6	−	1.74015e6i	0.287488	−	0.165981i	0.636809	+	0.771022i	$0.280254\pi$
$644$	−1.57146e6	+	2.10621e6i	−0.149309	+	0.200118i
$645$		0			0
$646$	4.78778e6	−	1.44233e7i	0.451391	−	1.35983i
$647$	−2.88799e6			−0.271229			−0.135614	−	0.990762i	$-0.543301\pi$
$647$	−2.88799e6			−0.271229			−0.135614	+	0.990762i	$0.543301\pi$
$648$		0			0
$649$	6.24566e6			0.582058
$650$	−437336.	+	1.31749e6i	−0.0406006	+	0.122310i
$651$		0			0
$652$	4.66116e6	−	6.24730e6i	0.429413	−	0.575537i
$653$	−4.44008e6	+	2.56348e6i	−0.407482	+	0.235260i	−0.689707	−	0.724088i	$-0.742261\pi$
$653$	−4.44008e6	+	2.56348e6i	−0.407482	+	0.235260i	0.282225	+	0.959348i	$0.408927\pi$
$654$		0			0
$655$	−1.82647e6	−	1.05451e6i	−0.166345	−	0.0960394i
$656$	−8.42058e6	−	7.97793e6i	−0.763980	−	0.723820i
$657$		0			0
$658$	68356.3	+	331931.i	0.00615480	+	0.0298870i
$659$	1.30044e6	−	2.25243e6i	0.116648	−	0.202041i	−0.801789	−	0.597607i	$-0.796118\pi$
$659$	1.30044e6	−	2.25243e6i	0.116648	−	0.202041i	0.918437	+	0.395566i	$0.129452\pi$
$660$		0			0
$661$	6.08660e6	+	1.05423e7i	0.541840	+	0.938494i	0.998798	+	0.0490059i	$0.0156053\pi$
$661$	6.08660e6	+	1.05423e7i	0.541840	+	0.938494i	−0.456959	+	0.889488i	$0.651061\pi$
$662$	−4.16524e6	+	3.70283e6i	−0.369398	+	0.328389i
$663$		0			0
$664$	379095.	+	4.41321e6i	0.0333679	+	0.388449i
$665$		−	437927.i		−	0.0384015i
$666$		0			0
$667$		−	1.29624e7i		−	1.12816i
$668$	−158082.	+	1.34026e6i	−0.0137070	+	0.116211i
$669$		0			0
$670$	−1.16128e6	−	1.30630e6i	−0.0999422	−	0.112423i
$671$	−5.12658e6	−	8.87949e6i	−0.439563	−	0.761346i
$672$		0			0
$673$	1.21145e6	−	2.09828e6i	0.103102	−	0.178577i	−0.809859	−	0.586624i	$-0.800457\pi$
$673$	1.21145e6	−	2.09828e6i	0.103102	−	0.178577i	0.912961	+	0.408047i	$0.133790\pi$
$674$	1.22941e7	−	2.53179e6i	1.04243	−	0.214674i
$675$		0			0
$676$	−1.07048e7	+	4.60424e6i	−0.900969	+	0.387517i
$677$	−2.75301e6	−	1.58945e6i	−0.230854	−	0.133283i	0.380112	−	0.924940i	$-0.375885\pi$
$677$	−2.75301e6	−	1.58945e6i	−0.230854	−	0.133283i	−0.610966	+	0.791657i	$0.709219\pi$
$678$		0			0
$679$	−1.21091e6	+	699118.i	−0.100794	+	0.0581937i
$680$	3.91946e6	+	1.83520e6i	0.325053	+	0.152199i
$681$		0			0
$682$	4.93987e6	+	1.63978e6i	0.406682	+	0.134997i
$683$	1.16442e7			0.955123			0.477562	−	0.878598i	$-0.341521\pi$
$683$	1.16442e7			0.955123			0.477562	+	0.878598i	$0.341521\pi$
$684$		0			0
$685$	−886917.			−0.0722199
$686$	3.15846e6	+	1.04844e6i	0.256251	+	0.0850617i
$687$		0			0
$688$	−3.41015e6	+	1.42550e7i	−0.274665	+	1.14814i
$689$	−2.27335e6	+	1.31252e6i	−0.182439	+	0.105331i
$690$		0			0
$691$	−1.57763e7	−	9.10845e6i	−1.25693	−	0.725687i	−0.284451	−	0.958691i	$-0.591811\pi$
$691$	−1.57763e7	−	9.10845e6i	−1.25693	−	0.725687i	−0.972476	+	0.233004i	$0.925145\pi$
$692$	1.38490e6	+	3.21985e6i	0.109939	+	0.255606i
$693$		0			0
$694$	1.42467e7	−	2.93391e6i	1.12284	−	0.231232i
$695$	−2.66591e6	+	4.61749e6i	−0.209355	+	0.362613i
$696$		0			0
$697$	−9.11691e6	−	1.57910e7i	−0.710830	−	1.23119i
$698$	−7.03344e6	−	7.91179e6i	−0.546424	−	0.614661i
$699$		0			0
$700$	−1.63055e6	−	192321.i	−0.125773	−	0.0148348i
$701$		−	8.51403e6i		−	0.654395i	−0.944956	−	0.327197i	$-0.893896\pi$
$701$		−	8.51403e6i		−	0.654395i	0.944956	−	0.327197i	$-0.106104\pi$
$702$		0			0
$703$			7.71779e6i			0.588986i
$704$	6.01158e6	+	7.21037e6i	0.457148	+	0.548310i
$705$		0			0
$706$	−5.84342e6	+	5.19470e6i	−0.441220	+	0.392237i
$707$	1.18971e6	+	2.06064e6i	0.0895145	+	0.155044i
$708$		0			0
$709$	−5.32118e6	+	9.21656e6i	−0.397551	+	0.688578i	−0.993423	−	0.114501i	$-0.963473\pi$
$709$	−5.32118e6	+	9.21656e6i	−0.397551	+	0.688578i	0.595872	+	0.803079i	$0.296806\pi$
$710$	−716394.	−	3.47873e6i	−0.0533343	−	0.258985i
$711$		0			0
$712$	−1.23442e7	−	1.76886e7i	−0.912560	−	1.30765i
$713$	1.29295e7	+	7.46485e6i	0.952485	+	0.549918i
$714$		0			0
$715$	311364.	−	179766.i	0.0227774	−	0.0131505i
$716$	−6.77896e6	−	5.05783e6i	−0.494175	−	0.368707i
$717$		0			0
$718$	−8.17884e6	+	2.46390e7i	−0.592081	+	1.78366i
$719$	3.66390e6			0.264315			0.132157	−	0.991229i	$-0.457810\pi$
$719$	3.66390e6			0.264315			0.132157	+	0.991229i	$0.457810\pi$
$720$		0			0
$721$	−1.77956e6			−0.127489
$722$	−551544.	+	1.66154e6i	−0.0393765	+	0.118623i
$723$		0			0
$724$	−1.30337e7	−	9.72454e6i	−0.924105	−	0.689482i
$725$	7.01372e6	−	4.04938e6i	0.495568	−	0.286117i
$726$		0			0
$727$	5.20680e6	+	3.00615e6i	0.365372	+	0.210948i	0.671435	−	0.741064i	$-0.265678\pi$
$727$	5.20680e6	+	3.00615e6i	0.365372	+	0.210948i	−0.306063	+	0.952011i	$0.599012\pi$
$728$	154626.	+	221571.i	0.0108132	+	0.0154947i
$729$		0			0
$730$	−1.23674e6	−	6.00549e6i	−0.0858959	−	0.417101i
$731$	−1.15200e7	+	1.99532e7i	−0.797365	+	1.38108i
$732$		0			0
$733$	5.88479e6	+	1.01927e7i	0.404549	+	0.700699i	0.994269	−	0.106909i	$-0.0340953\pi$
$733$	5.88479e6	+	1.01927e7i	0.404549	+	0.700699i	−0.589720	+	0.807608i	$0.700762\pi$
$734$	−1.55271e6	+	1.38033e6i	−0.106378	+	0.0945679i
$735$		0			0
$736$	1.27175e7	+	2.37351e7i	0.865378	+	1.61509i
$737$		−	5.95968e6i		−	0.404161i
$738$		0			0
$739$		−	1.44915e7i		−	0.976118i	−0.872811	−	0.488059i	$-0.837705\pi$
$739$		−	1.44915e7i		−	0.976118i	0.872811	−	0.488059i	$-0.162295\pi$
$740$	−2.18273e6	−	257450.i	−0.146528	−	0.0172828i
$741$		0			0
$742$	−2.06279e6	−	2.32040e6i	−0.137545	−	0.154722i
$743$	1.03693e7	+	1.79602e7i	0.689094	+	1.19355i	0.972131	+	0.234436i	$0.0753245\pi$
$743$	1.03693e7	+	1.79602e7i	0.689094	+	1.19355i	−0.283038	+	0.959109i	$0.591342\pi$
$744$		0			0
$745$	−1.50259e6	+	2.60255e6i	−0.0991856	+	0.171794i
$746$	−1.61508e7	+	3.32603e6i	−1.06255	+	0.218816i
$747$		0			0
$748$	5.83058e6	+	1.35560e7i	0.381029	+	0.885883i
$749$	−228335.	−	131829.i	−0.0148719	−	0.00858631i
$750$		0			0
$751$	126982.	−	73312.8i	0.00821563	−	0.00474329i	−0.495887	−	0.868387i	$-0.665157\pi$
$751$	126982.	−	73312.8i	0.00821563	−	0.00474329i	0.504102	+	0.863644i	$0.331823\pi$
$752$	3.37736e6	+	807952.i	0.217788	+	0.0521004i
$753$		0			0
$754$	−1.26490e6	−	419879.i	−0.0810265	−	0.0268965i
$755$	267818.			0.0170991
$756$		0			0
$757$	2.59573e7			1.64634			0.823170	−	0.567795i	$-0.192203\pi$
$757$	2.59573e7			1.64634			0.823170	+	0.567795i	$0.192203\pi$
$758$	−1.04729e7	−	3.47646e6i	−0.662057	−	0.219768i
$759$		0			0
$760$	−4.06400e6	−	1.90288e6i	−0.255223	−	0.119503i
$761$	−3.55514e6	+	2.05256e6i	−0.222534	+	0.128480i	−0.607123	−	0.794608i	$-0.707676\pi$
$761$	−3.55514e6	+	2.05256e6i	−0.222534	+	0.128480i	0.384589	+	0.923088i	$0.374343\pi$
$762$		0			0
$763$	−520249.	−	300366.i	−0.0323519	−	0.0186784i
$764$	3.07451e6	−	1.32238e6i	0.190564	−	0.0819640i
$765$		0			0
$766$	−2.11945e7	+	4.36469e6i	−1.30512	+	0.268771i
$767$	920991.	−	1.59520e6i	0.0565284	−	0.0979101i
$768$		0			0
$769$	1.04927e7	+	1.81739e7i	0.639839	+	1.10823i	0.985468	+	0.169862i	$0.0543323\pi$
$769$	1.04927e7	+	1.81739e7i	0.639839	+	1.10823i	−0.345629	+	0.938371i	$0.612334\pi$
$770$	282527.	+	317809.i	0.0171725	+	0.0193170i
$771$		0			0
$772$	−2.03750e6	+	1.72744e7i	−0.123042	+	1.04318i
$773$		−	4.46768e6i		−	0.268926i	−0.990919	−	0.134463i	$-0.957069\pi$
$773$		−	4.46768e6i		−	0.268926i	0.990919	−	0.134463i	$-0.0429310\pi$
$774$		0			0
$775$			9.32794e6i			0.557868i
$776$	1.22623e6	+	1.42751e7i	0.0731003	+	0.850991i
$777$		0			0
$778$	6.74082e6	−	5.99247e6i	0.399267	−	0.354942i
$779$	9.45312e6	+	1.63733e7i	0.558125	+	0.966701i
$780$		0			0
$781$	6.05520e6	−	1.04879e7i	0.355223	−	0.615265i
$782$	8.53764e6	+	4.14578e7i	0.499253	+	2.42432i
$783$		0			0
$784$	1.16170e7	−	1.22615e7i	0.674999	−	0.712450i
$785$	−6.12821e6	−	3.53812e6i	−0.354943	−	0.204927i
$786$		0			0
$787$	2.45633e7	−	1.41816e7i	1.41368	−	0.816187i	0.417945	−	0.908472i	$-0.362750\pi$
$787$	2.45633e7	−	1.41816e7i	1.41368	−	0.816187i	0.995733	+	0.0922851i	$0.0294171\pi$
$788$	−1.76454e7	+	2.36500e7i	−1.01232	+	1.35680i
$789$		0			0
$790$	2.32443e6	−	7.00241e6i	0.132510	−	0.399190i
$791$	−1.82988e6			−0.103988
$792$		0			0
$793$	−3.02388e6			−0.170758
$794$	7.20027e6	−	2.16910e7i	0.405320	−	1.22104i
$795$		0			0
$796$	1.78296e6	−	2.38968e6i	0.0997374	−	0.133677i
$797$	1.19538e7	−	6.90152e6i	0.666591	−	0.384857i	−0.128192	−	0.991749i	$-0.540918\pi$
$797$	1.19538e7	−	6.90152e6i	0.666591	−	0.384857i	0.794784	+	0.606893i	$0.207584\pi$
$798$		0			0
$799$	4.72741e6	+	2.72937e6i	0.261973	+	0.151250i
$800$	−8.86981e6	+	1.42959e7i	−0.489992	+	0.789746i
$801$		0			0
$802$	−6.38706e6	−	3.10149e7i	−0.350643	−	1.70268i
$803$	1.04534e7	−	1.81058e7i	0.572094	−	0.990896i
$804$		0			0
$805$	609866.	+	1.05632e6i	0.0331700	+	0.0574520i
$806$	1.14725e6	−	1.01989e6i	0.0622045	−	0.0552988i
$807$		0			0
$808$	2.42924e7	−	2.08672e6i	1.30901	−	0.112444i
$809$			9.63249e6i			0.517449i	0.965951	+	0.258724i	$0.0833022\pi$
$809$			9.63249e6i			0.517449i	−0.965951	+	0.258724i	$0.916698\pi$
$810$		0			0
$811$			2.76809e7i			1.47784i	0.673793	+	0.738920i	$0.264664\pi$
$811$			2.76809e7i			1.47784i	−0.673793	+	0.738920i	$0.735336\pi$
$812$	184645.	−	1.56546e6i	0.00982758	−	0.0833207i
$813$		0			0
$814$	−4.97909e6	−	5.60089e6i	−0.263384	−	0.296276i
$815$	−1.80895e6	−	3.13319e6i	−0.0953965	−	0.165232i
$816$		0			0
$817$	1.19448e7	−	2.06890e7i	0.626070	−	1.08439i
$818$	1.38117e7	−	2.84432e6i	0.721713	−	0.148626i
$819$		0			0
$820$	−4.94599e6	+	2.12733e6i	−0.256873	+	0.110484i
$821$	−2.52416e7	−	1.45733e7i	−1.30695	−	0.754569i	−0.325366	−	0.945588i	$-0.605487\pi$
$821$	−2.52416e7	−	1.45733e7i	−1.30695	−	0.754569i	−0.981586	+	0.191019i	$0.938821\pi$
$822$		0			0
$823$	−32905.4	+	18998.0i	−0.00169343	+	0.000977704i	−0.500846	−	0.865536i	$-0.666978\pi$
$823$	−32905.4	+	18998.0i	−0.00169343	+	0.000977704i	0.499153	+	0.866514i	$0.333645\pi$
$824$	−7.73253e6	+	1.65144e7i	−0.396738	+	0.847316i
$825$		0			0
$826$	2.06765e6	+	686349.i	0.105445	+	0.0350022i
$827$	1.95942e7			0.996238			0.498119	−	0.867109i	$-0.334024\pi$
$827$	1.95942e7			0.996238			0.498119	+	0.867109i	$0.334024\pi$
$828$		0			0
$829$	2.59138e7			1.30962			0.654809	−	0.755794i	$-0.272749\pi$
$829$	2.59138e7			1.30962			0.654809	+	0.755794i	$0.272749\pi$
$830$	1.95127e6	+	647719.i	0.0983155	+	0.0326356i
$831$		0			0
$832$	2.72807e6	−	472168.i	0.136630	−	0.0236477i
$833$	2.29938e7	−	1.32755e7i	1.14815	−	0.662885i
$834$		0			0
$835$	542481.	+	313201.i	0.0269258	+	0.0155456i
$836$	−6.04560e6	−	1.40559e7i	−0.299174	−	0.695572i
$837$		0			0
$838$	5.28517e6	−	1.08840e6i	0.259985	−	0.0535402i
$839$	410110.	−	710332.i	0.0201139	−	0.0348382i	−0.855793	−	0.517318i	$-0.826930\pi$
$839$	410110.	−	710332.i	0.0201139	−	0.0348382i	0.875907	+	0.482480i	$0.160264\pi$
$840$		0			0
$841$	−6.36784e6	−	1.10294e7i	−0.310457	−	0.537728i
$842$	1.08904e7	+	1.22505e7i	0.529378	+	0.595487i
$843$		0			0
$844$	−170178.	−	20072.3i	−0.00822330	−	0.000969929i
$845$			5.40879e6i			0.260590i
$846$		0			0
$847$		−	1.39514e6i		−	0.0668205i
$848$	−3.04967e7	+	9.06029e6i	−1.45634	+	0.432666i
$849$		0			0
$850$	−1.97651e7	+	1.75708e7i	−0.938320	+	0.834150i
$851$	−1.07479e7	−	1.86160e7i	−0.508747	−	0.881175i
$852$		0			0
$853$	−8.23977e6	+	1.42717e7i	−0.387742	+	0.671588i	−0.992145	−	0.125090i	$-0.960078\pi$
$853$	−8.23977e6	+	1.42717e7i	−0.387742	+	0.671588i	0.604404	+	0.796678i	$0.293411\pi$
$854$	−721383.	−	3.50295e6i	−0.0338471	−	0.164358i
$855$		0			0
$856$	−2.21554e6	+	1.54614e6i	−0.103346	+	0.0721213i
$857$	−5.14015e6	−	2.96767e6i	−0.239069	−	0.138027i	0.375680	−	0.926750i	$-0.377409\pi$
$857$	−5.14015e6	−	2.96767e6i	−0.239069	−	0.138027i	−0.614749	+	0.788723i	$0.710743\pi$
$858$		0			0
$859$	1.26480e7	−	7.30230e6i	0.584840	−	0.337658i	−0.178214	−	0.983992i	$-0.557032\pi$
$859$	1.26480e7	−	7.30230e6i	0.584840	−	0.337658i	0.763055	+	0.646334i	$0.223699\pi$
$860$	5.45276e6	+	4.06834e6i	0.251403	+	0.187573i
$861$		0			0
$862$	−6.63394e6	+	1.99849e7i	−0.304091	+	0.916082i
$863$	−2.72449e7			−1.24525			−0.622626	−	0.782519i	$-0.713934\pi$
$863$	−2.72449e7			−1.24525			−0.622626	+	0.782519i	$0.713934\pi$
$864$		0			0
$865$	1.62689e6			0.0739297
$866$	8.46328e6	−	2.54958e7i	0.383481	−	1.15525i
$867$		0			0
$868$	1.45516e6	+	1.08571e6i	0.0655559	+	0.0489118i
$869$	2.17869e7	−	1.25787e7i	0.978692	−	0.565048i
$870$		0			0
$871$	−1.52216e6	−	878820.i	−0.0679853	−	0.0392513i
$872$	−5.04800e6	+	3.52280e6i	−0.224816	+	0.156890i
$873$		0			0
$874$	−8.85249e6	−	4.29867e7i	−0.392001	−	1.90351i
$875$	−791020.	+	1.37009e6i	−0.0349275	+	0.0604962i
$876$		0			0
$877$	4.64812e6	+	8.05078e6i	0.204070	+	0.353459i	0.949836	−	0.312749i	$-0.101250\pi$
$877$	4.64812e6	+	8.05078e6i	0.204070	+	0.353459i	−0.745766	+	0.666208i	$0.767916\pi$
$878$	3.07167e7	−	2.73067e7i	1.34474	−	1.19545i
$879$		0			0
$880$	4.17692e6	−	1.24093e6i	0.181823	−	0.0540181i
$881$		−	2.21047e7i		−	0.959499i	−0.877406	−	0.479749i	$-0.840728\pi$
$881$		−	2.21047e7i		−	0.959499i	0.877406	−	0.479749i	$-0.159272\pi$
$882$		0			0
$883$			4.54738e7i			1.96272i	0.192167	+	0.981362i	$0.438449\pi$
$883$			4.54738e7i			1.96272i	−0.192167	+	0.981362i	$0.561551\pi$
$884$	4.32211e6	+	509788.i	0.186022	+	0.0219411i
$885$		0			0
$886$	−2.12915e7	−	2.39504e7i	−0.911217	−	1.02501i
$887$	3.80414e6	+	6.58897e6i	0.162348	+	0.281195i	0.935710	−	0.352769i	$-0.114760\pi$
$887$	3.80414e6	+	6.58897e6i	0.162348	+	0.281195i	−0.773362	+	0.633964i	$0.781427\pi$
$888$		0			0
$889$	2.85789e6	−	4.95001e6i	0.121281	−	0.210064i
$890$	−9.80608e6	+	2.01942e6i	−0.414973	+	0.0854578i
$891$		0			0
$892$	1.04322e7	+	2.42546e7i	0.439000	+	1.02066i
$893$	−4.90174e6	−	2.83002e6i	−0.205694	−	0.118758i
$894$		0			0
$895$	−3.39983e6	+	1.96289e6i	−0.141873	+	0.0819105i
$896$	1.19779e6	+	3.04764e6i	0.0498437	+	0.126822i
$897$		0			0
$898$	−2.19487e7	−	7.28582e6i	−0.908277	−	0.301500i
$899$	−8.95560e6			−0.369569
$900$		0			0
$901$	−5.00092e7			−2.05229
$902$	−1.74234e7	−	5.78364e6i	−0.713043	−	0.236693i
$903$		0			0
$904$	−7.95120e6	+	1.69814e7i	−0.323602	+	0.691120i
$905$	−6.53676e6	+	3.77400e6i	−0.265302	+	0.153172i
$906$		0			0
$907$	−1.65581e7	−	9.55982e6i	−0.668332	−	0.385862i	0.127112	−	0.991888i	$-0.459429\pi$
$907$	−1.65581e7	−	9.55982e6i	−0.668332	−	0.385862i	−0.795444	+	0.606027i	$0.792762\pi$
$908$	−1.31004e7	+	5.63463e6i	−0.527314	+	0.226804i
$909$		0			0
$910$	122833.	−	25295.7i	0.00491713	−	0.00101261i
$911$	1.36925e7	−	2.37161e7i	0.546622	−	0.946777i	−0.451881	−	0.892078i	$-0.649247\pi$
$911$	1.36925e7	−	2.37161e7i	0.546622	−	0.946777i	0.998503	−	0.0546990i	$-0.0174199\pi$
$912$		0			0
$913$	3.50513e6	+	6.07107e6i	0.139164	+	0.241039i
$914$	−1.56087e7	−	1.75579e7i	−0.618016	−	0.695195i
$915$		0			0
$916$	910835.	−	7.72229e6i	0.0358675	−	0.304094i
$917$		−	2.50840e6i		−	0.0985086i
$918$		0			0
$919$		−	2.44251e7i		−	0.953999i	−0.878904	−	0.476999i	$-0.841724\pi$
$919$		−	2.44251e7i		−	0.953999i	0.878904	−	0.476999i	$-0.158276\pi$
$920$	1.24527e7	−	1.06969e6i	0.485058	−	0.0416666i
$921$		0			0
$922$	−1.43106e6	+	1.27219e6i	−0.0554410	+	0.0492861i
$923$	−1.78581e6	−	3.09312e6i	−0.0689972	−	0.119507i
$924$		0			0
$925$	6.71521e6	−	1.16311e7i	0.258051	−	0.446957i
$926$	8.12853e6	+	3.94713e7i	0.311519	+	1.51270i
$927$		0			0
$928$	−1.37253e7	−	8.51575e6i	−0.523181	−	0.324603i
$929$	2.23660e7	+	1.29130e7i	0.850255	+	0.490895i	0.860737	−	0.509050i	$-0.170003\pi$
$929$	2.23660e7	+	1.29130e7i	0.850255	+	0.490895i	−0.0104821	+	0.999945i	$0.503337\pi$
$930$		0			0
$931$	−2.38418e7	+	1.37651e7i	−0.901498	+	0.520480i
$932$	9.25982e6	−	1.24108e7i	0.349191	−	0.468017i
$933$		0			0
$934$	7.07030e6	−	2.12995e7i	0.265198	−	0.798916i
$935$	6.84942e6			0.256227
$936$		0			0
$937$	1.88351e7			0.700838			0.350419	−	0.936593i	$-0.386039\pi$
$937$	1.88351e7			0.700838			0.350419	+	0.936593i	$0.386039\pi$
$938$	654922.	−	1.97297e6i	0.0243043	−	0.0732173i
$939$		0			0
$940$	963893.	−	1.29190e6i	0.0355803	−	0.0476879i
$941$	−1.01451e7	+	5.85728e6i	−0.373493	+	0.215636i	−0.674983	−	0.737833i	$-0.735849\pi$
$941$	−1.01451e7	+	5.85728e6i	−0.373493	+	0.215636i	0.301490	+	0.953469i	$0.402516\pi$
$942$		0			0
$943$	−4.56035e7	−	2.63292e7i	−1.67001	−	0.964181i
$944$	1.53537e7	−	1.62056e7i	0.560767	−	0.591881i
$945$		0			0
$946$	4.67892e6	+	2.27203e7i	0.169988	+	0.825443i
$947$	2.23751e6	−	3.87549e6i	0.0810757	−	0.140427i	−0.822637	−	0.568568i	$-0.807498\pi$
$947$	2.23751e6	−	3.87549e6i	0.0810757	−	0.140427i	0.903712	+	0.428140i	$0.140831\pi$
$948$		0			0
$949$	−3.08293e6	−	5.33979e6i	−0.111121	−	0.192468i
$950$	2.04939e7	−	1.82188e7i	0.736744	−	0.654953i
$951$		0			0
$952$	440537.	+	5.12848e6i	0.0157540	+	0.183399i
$953$			3.35437e7i			1.19641i	0.801344	+	0.598203i	$0.204119\pi$
$953$			3.35437e7i			1.19641i	−0.801344	+	0.598203i	$0.795881\pi$
$954$		0			0
$955$		−	1.55345e6i		−	0.0551176i
$956$	−2.81075e6	+	2.38302e7i	−0.0994666	+	0.843303i
$957$		0			0
$958$	2.89030e7	+	3.25124e7i	1.01749	+	1.14455i
$959$	−527434.	−	913542.i	−0.0185192	−	0.0320761i
$960$		0			0
$961$	−9.15716e6	+	1.58607e7i	−0.319854	+	0.554004i
$962$	−2.16474e6	+	445797.i	−0.0754169	+	0.0155310i
$963$		0			0
$964$	1.25924e7	−	5.41614e6i	0.436431	−	0.187714i
$965$	6.99196e6	+	4.03681e6i	0.241702	+	0.139547i
$966$		0			0
$967$	3.26635e7	−	1.88583e7i	1.12330	−	0.648539i	0.181061	−	0.983472i	$-0.442047\pi$
$967$	3.26635e7	−	1.88583e7i	1.12330	−	0.648539i	0.942242	+	0.334932i	$0.108713\pi$
$968$	−1.29470e7	−	6.06216e6i	−0.444101	−	0.207941i
$969$		0			0
$970$	6.31164e6	+	2.09513e6i	0.215384	+	0.0714960i
$971$	−5.05249e7			−1.71972			−0.859860	−	0.510530i	$-0.829449\pi$
$971$	−5.05249e7			−1.71972			−0.859860	+	0.510530i	$0.829449\pi$
$972$		0			0
$973$	−6.34147e6			−0.214737
$974$	−6.31845e6	−	2.09739e6i	−0.213409	−	0.0708406i
$975$		0			0
$976$	−3.56422e7	−	8.52653e6i	−1.19768	−	0.286515i
$977$	−2.68169e7	+	1.54827e7i	−0.898818	+	0.518933i	−0.876817	−	0.480825i	$-0.840337\pi$
$977$	−2.68169e7	+	1.54827e7i	−0.898818	+	0.518933i	−0.0220017	+	0.999758i	$0.507004\pi$
$978$		0			0
$979$	−2.95640e7	−	1.70688e7i	−0.985842	−	0.569176i
$980$	−3.09769e6	−	7.20206e6i	−0.103032	−	0.239547i
$981$		0			0
$982$	8.09264e6	−	1.66656e6i	0.267801	−	0.0551497i
$983$	−2.35167e7	+	4.07321e7i	−0.776234	+	1.34448i	0.157864	+	0.987461i	$0.449539\pi$
$983$	−2.35167e7	+	4.07321e7i	−0.776234	+	1.34448i	−0.934098	+	0.357016i	$0.883794\pi$
$984$		0			0
$985$	6.84802e6	+	1.18611e7i	0.224892	+	0.389525i
$986$	−1.68694e7	−	1.89761e7i	−0.552597	−	0.621605i
$987$		0			0
$988$	−4.48150e6	−	528587.i	−0.146060	−	0.0172276i
$989$			6.65382e7i			2.16312i
$990$		0			0
$991$			1.95496e7i			0.632346i	0.948702	+	0.316173i	$0.102398\pi$
$991$			1.95496e7i			0.632346i	−0.948702	+	0.316173i	$0.897602\pi$
$992$	1.63984e7	−	8.78640e6i	0.529081	−	0.283486i
$993$		0			0
$994$	3.15713e6	−	2.80664e6i	0.101351	−	0.0900991i
$995$	−691947.	−	1.19849e6i	−0.0221572	−	0.0383774i
$996$		0			0
$997$	1.49630e7	−	2.59167e7i	0.476740	−	0.825739i	−0.522904	−	0.852391i	$-0.675151\pi$
$997$	1.49630e7	−	2.59167e7i	0.476740	−	0.825739i	0.999645	+	0.0266527i	$0.00848483\pi$
$998$	−4.75986e6	−	2.31133e7i	−0.151275	−	0.734575i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.6.h.a.35.17		56
3.2	odd	2		36.6.h.a.11.12	✓	56
4.3	odd	2	inner	108.6.h.a.35.8		56
9.4	even	3		36.6.h.a.23.21	yes	56
9.5	odd	6	inner	108.6.h.a.71.8		56
12.11	even	2		36.6.h.a.11.21	yes	56
36.23	even	6	inner	108.6.h.a.71.17		56
36.31	odd	6		36.6.h.a.23.12	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.6.h.a.11.12	✓	56	3.2	odd	2
36.6.h.a.11.21	yes	56	12.11	even	2
36.6.h.a.23.12	yes	56	36.31	odd	6
36.6.h.a.23.21	yes	56	9.4	even	3
108.6.h.a.35.8		56	4.3	odd	2	inner
108.6.h.a.35.17		56	1.1	even	1	trivial
108.6.h.a.71.8		56	9.5	odd	6	inner
108.6.h.a.71.17		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)

\(f(q)\)	\(=\)	\(q+(1.78216 - 5.36879i) q^{2} +(-25.6478 - 19.1360i) q^{4} +(-12.8631 + 7.42651i) q^{5} +(-15.2989 - 8.83282i) q^{7} +(-148.446 + 103.595i) q^{8} +O(q^{10})\)	\(q+(1.78216 - 5.36879i) q^{2} +(-25.6478 - 19.1360i) q^{4} +(-12.8631 + 7.42651i) q^{5} +(-15.2989 - 8.83282i) q^{7} +(-148.446 + 103.595i) q^{8} +(16.9473 + 82.2944i) q^{10} +(-143.245 + 248.107i) q^{11} +(42.2460 + 73.1722i) q^{13} +(-74.6866 + 66.3951i) q^{14} +(291.624 + 981.596i) q^{16} +1609.65i q^{17} -1669.01i q^{19} +(472.025 + 55.6747i) q^{20} +(1076.75 + 1211.22i) q^{22} +(2324.29 + 4025.79i) q^{23} +(-1452.19 + 2515.27i) q^{25} +(468.135 - 96.4056i) q^{26} +(223.358 + 519.303i) q^{28} +(-2414.87 - 1394.23i) q^{29} +(2781.39 - 1605.84i) q^{31} +(5789.71 + 183.691i) q^{32} +(8641.85 + 2868.64i) q^{34} +262.388 q^{35} -4624.19 q^{37} +(-8960.54 - 2974.43i) q^{38} +(1140.13 - 2434.98i) q^{40} +(-9810.20 + 5663.92i) q^{41} +(12396.0 + 7156.83i) q^{43} +(8421.70 - 3622.27i) q^{44} +(25755.9 - 5304.05i) q^{46} +(1695.63 - 2936.92i) q^{47} +(-8247.46 - 14285.0i) q^{49} +(10915.9 + 12279.1i) q^{50} +(316.708 - 2685.13i) q^{52} +31068.4i q^{53} -4255.23i q^{55} +(3186.09 - 273.686i) q^{56} +(-11789.0 + 10480.2i) q^{58} +(-10900.3 - 18879.9i) q^{59} +(-17894.5 + 30994.2i) q^{61} +(-3664.53 - 17794.5i) q^{62} +(11304.4 - 30756.4i) q^{64} +(-1086.83 - 627.480i) q^{65} +(-18015.5 + 10401.2i) q^{67} +(30802.3 - 41283.9i) q^{68} +(467.617 - 1408.71i) q^{70} -42271.8 q^{71} -72975.6 q^{73} +(-8241.02 + 24826.3i) q^{74} +(-31938.2 + 42806.4i) q^{76} +(4382.97 - 2530.51i) q^{77} +(-76047.9 - 43906.3i) q^{79} +(-11041.0 - 10460.6i) q^{80} +(12925.1 + 62762.9i) q^{82} +(12234.8 - 21191.3i) q^{83} +(-11954.1 - 20705.0i) q^{85} +(60515.1 - 53796.9i) q^{86} +(-4438.45 - 51669.8i) q^{88} +119158. i q^{89} -1492.60i q^{91} +(17424.6 - 147731. i) q^{92} +(-12745.9 - 14337.6i) q^{94} +(12394.9 + 21468.6i) q^{95} +(39575.0 - 68545.9i) q^{97} +(-91391.6 + 18820.8i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 3 q^{2} - q^{4} + 6 q^{5}+O(q^{10}) \) 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

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