LMFDB - Embedded newform 108.6.h.a.71.8

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			71.8
Character	$\chi$	$=$	108.71
Dual form			108.6.h.a.35.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.75843 - 4.22779i) q^{2} +(-3.74838 + 31.7797i) q^{4} +(-12.8631 - 7.42651i) q^{5} +(15.2989 - 8.83282i) q^{7} +(148.446 - 103.595i) q^{8} +O(q^{10})$	\(q+(-3.75843 - 4.22779i) q^{2} +(-3.74838 + 31.7797i) q^{4} +(-12.8631 - 7.42651i) q^{5} +(15.2989 - 8.83282i) q^{7} +(148.446 - 103.595i) q^{8} +(16.9473 + 82.2944i) q^{10} +(143.245 + 248.107i) q^{11} +(42.2460 - 73.1722i) q^{13} +(-94.8432 - 31.4829i) q^{14} +(-995.899 - 238.245i) q^{16} -1609.65i q^{17} -1669.01i q^{19} +(284.228 - 380.948i) q^{20} +(510.569 - 1538.10i) q^{22} +(-2324.29 + 4025.79i) q^{23} +(-1452.19 - 2515.27i) q^{25} +(-468.135 + 96.4056i) q^{26} +(223.358 + 519.303i) q^{28} +(-2414.87 + 1394.23i) q^{29} +(-2781.39 - 1605.84i) q^{31} +(2735.77 + 5105.88i) q^{32} +(-6805.24 + 6049.75i) q^{34} -262.388 q^{35} -4624.19 q^{37} +(-7056.20 + 6272.84i) q^{38} +(-2678.82 + 230.111i) q^{40} +(-9810.20 - 5663.92i) q^{41} +(-12396.0 + 7156.83i) q^{43} +(-8421.70 + 3622.27i) q^{44} +(25755.9 - 5304.05i) q^{46} +(-1695.63 - 2936.92i) q^{47} +(-8247.46 + 14285.0i) q^{49} +(-5176.07 + 15593.1i) q^{50} +(2167.04 + 1616.84i) q^{52} -31068.4i q^{53} -4255.23i q^{55} +(1356.03 - 2896.08i) q^{56} +(14970.6 + 4969.46i) q^{58} +(10900.3 - 18879.9i) q^{59} +(-17894.5 - 30994.2i) q^{61} +(3664.53 + 17794.5i) q^{62} +(11304.4 - 30756.4i) q^{64} +(-1086.83 + 627.480i) q^{65} +(18015.5 + 10401.2i) q^{67} +(51154.1 + 6033.56i) q^{68} +(986.168 + 1109.32i) q^{70} +42271.8 q^{71} -72975.6 q^{73} +(17379.7 + 19550.1i) q^{74} +(53040.5 + 6256.07i) q^{76} +(4382.97 + 2530.51i) q^{77} +(76047.9 - 43906.3i) q^{79} +(11041.0 + 10460.6i) q^{80} +(12925.1 + 62762.9i) q^{82} +(-12234.8 - 21191.3i) q^{83} +(-11954.1 + 20705.0i) q^{85} +(76847.0 + 25509.2i) q^{86} +(46966.6 + 21991.1i) q^{88} -119158. i q^{89} -1492.60i q^{91} +(-119226. - 88955.4i) q^{92} +(-6043.77 + 18207.0i) q^{94} +(-12394.9 + 21468.6i) q^{95} +(39575.0 + 68545.9i) q^{97} +(91391.6 - 18820.8i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−3.75843	−	4.22779i	−0.664403	−	0.747374i
$2$	−3.75843	−	4.22779i	−0.664403	−	0.747374i
$3$		0			0
$3$		0			0
$4$	−3.74838	+	31.7797i	−0.117137	+	0.993116i
$5$	−12.8631	−	7.42651i	−0.230102	−	0.132849i	0.380517	−	0.924774i	$-0.375746\pi$
$5$	−12.8631	−	7.42651i	−0.230102	−	0.132849i	−0.610619	+	0.791924i	$0.709079\pi$
$6$		0			0
$7$	15.2989	−	8.83282i	0.118009	−	0.0681325i	−0.439834	−	0.898079i	$-0.644963\pi$
$7$	15.2989	−	8.83282i	0.118009	−	0.0681325i	0.557843	+	0.829947i	$0.311629\pi$
$8$	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	$-0.0504863\pi$
$11$	143.245	+	248.107i	0.356941	+	0.618240i	−0.630507	+	0.776184i	$0.717153\pi$
$12$		0			0
$13$	42.2460	−	73.1722i	0.0693309	−	0.120085i	−0.829276	−	0.558839i	$-0.811247\pi$
$13$	42.2460	−	73.1722i	0.0693309	−	0.120085i	0.898607	+	0.438755i	$0.144580\pi$
$14$	−94.8432	−	31.4829i	−0.129326	−	0.0429294i
$15$		0			0
$16$	−995.899	−	238.245i	−0.972558	−	0.232661i
$17$		−	1609.65i		−	1.35085i	−0.737427	−	0.675427i	$-0.763960\pi$
$17$		−	1609.65i		−	1.35085i	0.737427	−	0.675427i	$-0.236040\pi$
$18$		0			0
$19$		−	1669.01i		−	1.06065i	−0.847793	−	0.530327i	$-0.822069\pi$
$19$		−	1669.01i		−	1.06065i	0.847793	−	0.530327i	$-0.177931\pi$
$20$	284.228	−	380.948i	0.158888	−	0.212956i
$21$		0			0
$22$	510.569	−	1538.10i	0.224904	−	0.677530i
$23$	−2324.29	+	4025.79i	−0.916159	+	1.58683i	−0.110963	+	0.993825i	$0.535394\pi$
$23$	−2324.29	+	4025.79i	−0.916159	+	1.58683i	−0.805196	+	0.593009i	$0.797940\pi$
$24$		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	−0.742323	−	0.670042i	$-0.766276\pi$
$29$	−2414.87	+	1394.23i	−0.533211	+	0.307850i	0.209112	+	0.977892i	$0.432943\pi$
$30$		0			0
$31$	−2781.39	−	1605.84i	−0.519825	−	0.300121i	0.217038	−	0.976163i	$-0.430360\pi$
$31$	−2781.39	−	1605.84i	−0.519825	−	0.300121i	−0.736863	+	0.676042i	$0.763694\pi$
$32$	2735.77	+	5105.88i	0.472286	+	0.881445i
$33$		0			0
$34$	−6805.24	+	6049.75i	−1.00959	+	0.897511i
$35$	−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	$0.589556\pi$
$38$	−7056.20	+	6272.84i	−0.792706	+	0.704702i
$39$		0			0
$40$	−2678.82	+	230.111i	−0.264724	+	0.0227398i
$41$	−9810.20	−	5663.92i	−0.911420	−	0.526208i	−0.0305320	−	0.999534i	$-0.509720\pi$
$41$	−9810.20	−	5663.92i	−0.911420	−	0.526208i	−0.880888	+	0.473325i	$0.843053\pi$
$42$		0			0
$43$	−12396.0	+	7156.83i	−1.02237	+	0.590268i	−0.914791	−	0.403928i	$-0.867645\pi$
$43$	−12396.0	+	7156.83i	−1.02237	+	0.590268i	−0.107584	+	0.994196i	$0.534311\pi$
$44$	−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	$-0.202382\pi$
$47$	−1695.63	−	2936.92i	−0.111966	−	0.193931i	−0.916563	+	0.399890i	$0.869048\pi$
$48$		0			0
$49$	−8247.46	+	14285.0i	−0.490716	+	0.849945i
$50$	−5176.07	+	15593.1i	−0.292803	+	0.882076i
$51$		0			0
$52$	2167.04	+	1616.84i	0.111137	+	0.0829200i
$53$		−	31068.4i		−	1.51925i	−0.650360	−	0.759626i	$-0.725382\pi$
$53$		−	31068.4i		−	1.51925i	0.650360	−	0.759626i	$-0.274618\pi$
$54$		0			0
$55$		−	4255.23i		−	0.189678i
$56$	1356.03	−	2896.08i	0.0577827	−	0.123407i
$57$		0			0
$58$	14970.6	+	4969.46i	0.584346	+	0.193972i
$59$	10900.3	−	18879.9i	0.407671	−	0.706107i	−0.586957	−	0.809618i	$-0.699674\pi$
$59$	10900.3	−	18879.9i	0.407671	−	0.706107i	0.994628	+	0.103511i	$0.0330077\pi$
$60$		0			0
$61$	−17894.5	−	30994.2i	−0.615736	−	1.06649i	−0.990255	−	0.139267i	$-0.955525\pi$
$61$	−17894.5	−	30994.2i	−0.615736	−	1.06649i	0.374519	−	0.927219i	$-0.377808\pi$
$62$	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	$-0.241980\pi$
$67$	18015.5	+	10401.2i	0.490296	+	0.283072i	−0.234401	+	0.972140i	$0.575313\pi$
$68$	51154.1	+	6033.56i	1.34155	+	0.158235i
$69$		0			0
$70$	986.168	+	1109.32i	0.0240550	+	0.0270590i
$71$	42271.8			0.995187			0.497593	−	0.867410i	$-0.334217\pi$
$71$	42271.8			0.995187			0.497593	+	0.867410i	$0.334217\pi$
$72$		0			0
$73$	−72975.6			−1.60277			−0.801384	−	0.598150i	$-0.795903\pi$
$73$	−72975.6			−1.60277			−0.801384	+	0.598150i	$0.795903\pi$
$74$	17379.7	+	19550.1i	0.368946	+	0.415020i
$75$		0			0
$76$	53040.5	+	6256.07i	1.05335	+	0.124242i
$77$	4382.97	+	2530.51i	0.0842445	+	0.0486386i
$78$		0			0
$79$	76047.9	−	43906.3i	1.37094	−	0.791514i	0.379896	−	0.925029i	$-0.375960\pi$
$79$	76047.9	−	43906.3i	1.37094	−	0.791514i	0.991047	+	0.133515i	$0.0426263\pi$
$80$	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	$-0.229118\pi$
$83$	−12234.8	−	21191.3i	−0.194940	−	0.337646i	−0.946881	+	0.321585i	$0.895785\pi$
$84$		0			0
$85$	−11954.1	+	20705.0i	−0.179460	+	0.310834i
$86$	76847.0	+	25509.2i	1.12042	+	0.371920i
$87$		0			0
$88$	46966.6	+	21991.1i	0.646521	+	0.302719i
$89$		−	119158.i		−	1.59459i	−0.603588	−	0.797296i	$-0.706263\pi$
$89$		−	119158.i		−	1.59459i	0.603588	−	0.797296i	$-0.293737\pi$
$90$		0			0
$91$		−	1492.60i		−	0.0188948i
$92$	−119226.	−	88955.4i	−1.46859	−	1.09573i
$93$		0			0
$94$	−6043.77	+	18207.0i	−0.0705486	+	0.212529i
$95$	−12394.9	+	21468.6i	−0.140907	+	0.244059i
$96$		0			0
$97$	39575.0	+	68545.9i	0.427062	+	0.739694i	0.996611	−	0.0822641i	$-0.0262151\pi$
$97$	39575.0	+	68545.9i	0.427062	+	0.739694i	−0.569548	+	0.821958i	$0.692882\pi$
$98$	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	−0.945887	−	0.324495i	$-0.894806\pi$
$101$	−116647.	+	67346.1i	−1.13781	+	0.656915i	−0.191923	+	0.981410i	$0.561472\pi$
$102$		0			0
$103$	−87239.5	−	50367.8i	−0.810252	−	0.467799i	0.0367911	−	0.999323i	$-0.488286\pi$
$103$	−87239.5	−	50367.8i	−0.810252	−	0.467799i	−0.847044	+	0.531524i	$0.821620\pi$
$104$	−1308.99	−	15238.6i	−0.0118674	−	0.138153i
$105$		0			0
$106$	−131351.	+	116769.i	−1.13545	+	1.00940i
$107$	−14924.9			−0.126024			−0.0630118	−	0.998013i	$-0.520071\pi$
$107$	−14924.9			−0.126024			−0.0630118	+	0.998013i	$0.520071\pi$
$108$		0			0
$109$	34005.6			0.274148			0.137074	−	0.990561i	$-0.456230\pi$
$109$	34005.6			0.274148			0.137074	+	0.990561i	$0.456230\pi$
$110$	−17990.2	+	15993.0i	−0.141760	+	0.126022i
$111$		0			0
$112$	−17340.5	+	5151.72i	−0.130622	+	0.0388067i
$113$	89706.6	+	51792.2i	0.660889	+	0.381564i	0.792616	−	0.609722i	$-0.208719\pi$
$113$	89706.6	+	51792.2i	0.660889	+	0.381564i	−0.131727	+	0.991286i	$0.542052\pi$
$114$		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
$122$	−63781.5	+	192143.i	−0.387967	+	1.16876i
$123$		0			0
$124$	61458.7	−	82372.4i	0.358946	−	0.481091i
$125$			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	$0.650680\pi$
$128$	−172518.	+	67803.2i	−0.930700	+	0.365785i
$129$		0			0
$130$	6737.62	+	2236.53i	0.0349662	+	0.0116069i
$131$	−70996.7	+	122970.i	−0.361460	+	0.626066i	−0.988201	−	0.153161i	$-0.951055\pi$
$131$	−70996.7	+	122970.i	−0.361460	+	0.626066i	0.626742	+	0.779227i	$0.284388\pi$
$132$		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	−0.377663	−	0.925943i	$-0.623272\pi$
$137$	51712.9	−	29856.5i	0.235395	−	0.135906i	0.613059	+	0.790037i	$0.289939\pi$
$138$		0			0
$139$	−310879.	−	179486.i	−1.36475	−	0.787941i	−0.374501	−	0.927227i	$-0.622186\pi$
$139$	−310879.	−	179486.i	−1.36475	−	0.787941i	−0.990252	+	0.139286i	$0.955519\pi$
$140$	983.530	−	8338.62i	0.00424099	−	0.0359562i
$141$		0			0
$142$	−158876.	−	178716.i	−0.661205	−	0.743777i
$143$	24206.0			0.0989882
$144$		0			0
$145$	41417.0			0.163591
$146$	274274.	+	308526.i	1.06488	+	1.19787i
$147$		0			0
$148$	17333.2	−	146955.i	0.0650466	−	0.551481i
$149$	175221.	+	101164.i	0.646576	+	0.373301i	0.787143	−	0.616770i	$-0.211559\pi$
$149$	175221.	+	101164.i	0.646576	+	0.373301i	−0.140567	+	0.990071i	$0.544893\pi$
$150$		0			0
$151$	15615.5	−	9015.60i	0.0557331	−	0.0321775i	−0.471875	−	0.881666i	$-0.656422\pi$
$151$	15615.5	−	9015.60i	0.0557331	−	0.0321775i	0.527608	+	0.849488i	$0.323089\pi$
$152$	−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	−0.165590	−	0.986195i	$-0.552953\pi$
$157$	238209.	−	412590.i	0.771274	−	1.33589i	0.936865	−	0.349692i	$-0.113714\pi$
$158$	−471447.	−	156496.i	−1.50242	−	0.498723i
$159$		0			0
$160$	2728.37	−	85994.6i	0.00842565	−	0.265565i
$161$			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	$0.883104\pi$
$164$	216770.	−	290535.i	0.629347	−	0.843507i
$165$		0			0
$166$	−43608.6	+	131372.i	−0.122829	+	0.370026i
$167$	21086.7	−	36523.3i	0.0585083	−	0.101339i	−0.835288	−	0.549813i	$-0.814699\pi$
$167$	21086.7	−	36523.3i	0.0585083	−	0.101339i	0.893796	+	0.448474i	$0.148032\pi$
$168$		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	−0.615622	−	0.788042i	$-0.711095\pi$
$173$	−94858.3	+	54766.5i	−0.240968	+	0.139123i	0.374653	+	0.927165i	$0.377762\pi$
$174$		0			0
$175$	−44433.9	−	25653.9i	−0.109678	−	0.0633226i
$176$	−83547.0	−	281217.i	−0.203306	−	0.684321i
$177$		0			0
$178$	−503777.	+	447849.i	−1.19176	+	1.05945i
$179$	−264309.			−0.616566			−0.308283	−	0.951295i	$-0.599754\pi$
$179$	−264309.			−0.616566			−0.308283	+	0.951295i	$0.599754\pi$
$180$		0			0
$181$	508179.			1.15298			0.576488	−	0.817105i	$-0.304423\pi$
$181$	508179.			1.15298			0.576488	+	0.817105i	$0.304423\pi$
$182$	−6310.42	+	5609.85i	−0.0141215	+	0.0125537i
$183$		0			0
$184$	72018.3	+	838395.i	0.156819	+	1.82559i
$185$	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	$-0.133591\pi$
$191$	52294.2	+	90576.3i	0.103722	+	0.179652i	−0.809493	+	0.587129i	$0.800258\pi$
$192$		0			0
$193$	−271784.	+	470744.i	−0.525207	+	0.909685i	0.474362	+	0.880330i	$0.342679\pi$
$193$	−271784.	+	470744.i	−0.525207	+	0.909685i	−0.999569	+	0.0293554i	$0.990655\pi$
$194$	141058.	−	424940.i	0.269087	−	0.810631i
$195$		0			0
$196$	−423059.	−	315648.i	−0.786613	−	0.586898i
$197$			922105.i			1.69284i	0.532519	+	0.846418i	$0.321245\pi$
$197$			922105.i			1.69284i	−0.532519	+	0.846418i	$0.678755\pi$
$198$		0			0
$199$			93172.6i			0.166784i	0.996517	+	0.0833922i	$0.0265754\pi$
$199$			93172.6i			0.166784i	−0.996517	+	0.0833922i	$0.973425\pi$
$200$	−476141.	−	222943.i	−0.841706	−	0.394111i
$201$		0			0
$202$	723135.	+	240043.i	1.24693	+	0.413914i
$203$	−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	$-0.334651\pi$
$211$	−4637.49	−	2677.46i	−0.00717096	−	0.00414015i	−0.503581	+	0.863948i	$0.667985\pi$
$212$	987346.	+	116456.i	1.50879	+	0.177960i
$213$		0			0
$214$	56094.2	+	63099.3i	0.0837305	+	0.0941868i
$215$	212601.			0.313667
$216$		0			0
$217$	−56736.2			−0.0817921
$218$	−127808.	−	143769.i	−0.182145	−	0.204891i
$219$		0			0
$220$	135230.	+	15950.2i	0.188372	+	0.0222183i
$221$	−117781.	−	68001.1i	−0.162217	−	0.0936559i
$222$		0			0
$223$	714552.	−	412547.i	0.962214	−	0.555535i	0.0653606	−	0.997862i	$-0.479180\pi$
$223$	714552.	−	412547.i	0.962214	−	0.555535i	0.896854	+	0.442327i	$0.145847\pi$
$224$	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	$-0.259328\pi$
$227$	−222824.	−	385943.i	−0.287011	−	0.497117i	−0.973095	+	0.230405i	$0.925995\pi$
$228$		0			0
$229$	121497.	−	210439.i	0.153101	−	0.265178i	−0.779265	−	0.626694i	$-0.784407\pi$
$229$	121497.	−	210439.i	0.153101	−	0.265178i	0.932366	+	0.361516i	$0.117741\pi$
$230$	−370691.	−	123050.i	−0.462053	−	0.153377i
$231$		0			0
$232$	−214044.	+	457135.i	−0.261085	+	0.557602i
$233$		−	483894.i		−	0.583930i	−0.956429	−	0.291965i	$-0.905691\pi$
$233$		−	483894.i		−	0.583930i	0.956429	−	0.291965i	$-0.0943091\pi$
$234$		0			0
$235$			50370.6i			0.0594987i
$236$	559140.	+	417179.i	0.653493	+	0.487576i
$237$		0			0
$238$	−50676.4	+	152664.i	−0.0579913	+	0.174700i
$239$	374928.	−	649395.i	0.424574	−	0.735384i	−0.571806	−	0.820389i	$-0.693757\pi$
$239$	374928.	−	649395.i	0.424574	−	0.735384i	0.996381	+	0.0850045i	$0.0270905\pi$
$240$		0			0
$241$	−214184.	−	370977.i	−0.237544	−	0.411438i	0.722465	−	0.691408i	$-0.243009\pi$
$241$	−214184.	−	370977.i	−0.237544	−	0.411438i	−0.960009	+	0.279969i	$0.909676\pi$
$242$	−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
$248$	−579241.	+	49756.9i	−0.598040	+	0.0513717i
$249$		0			0
$250$	378618.	−	336585.i	0.383134	−	0.340600i
$251$	168039.			0.168355			0.0841773	−	0.996451i	$-0.473174\pi$
$251$	168039.			0.168355			0.0841773	+	0.996451i	$0.473174\pi$
$252$		0			0
$253$	−1.33177e6			−1.30806
$254$	1.36792e6	−	1.21605e6i	1.33038	−	1.18268i
$255$		0			0
$256$	935055.	+	474536.i	0.891738	+	0.452552i
$257$	−1.21515e6	−	701569.i	−1.14762	−	0.662579i	−0.199314	−	0.979936i	$-0.563871\pi$
$257$	−1.21515e6	−	701569.i	−1.14762	−	0.662579i	−0.948306	+	0.317357i	$0.897205\pi$
$258$		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	$-0.0305316\pi$
$263$	465252.	+	805840.i	0.414762	+	0.718388i	−0.580642	+	0.814159i	$0.697198\pi$
$264$		0			0
$265$	−230730.	+	399636.i	−0.201832	+	0.349583i
$266$	−52545.2	+	158294.i	−0.0455333	+	0.137170i
$267$		0			0
$268$	−398077.	+	533538.i	−0.338555	+	0.453762i
$269$		−	1.02733e6i		−	0.865621i	−0.901485	−	0.432810i	$-0.857522\pi$
$269$		−	1.02733e6i		−	0.865621i	0.901485	−	0.432810i	$-0.142478\pi$
$270$		0			0
$271$			1.66981e6i			1.38116i	0.723255	+	0.690581i	$0.242645\pi$
$271$			1.66981e6i			1.38116i	−0.723255	+	0.690581i	$0.757355\pi$
$272$	−383490.	+	1.60305e6i	−0.314291	+	1.31378i
$273$		0			0
$274$	−320586.	−	106418.i	−0.257970	−	0.0856323i
$275$	416038.	−	720599.i	0.331743	−	0.574595i
$276$		0			0
$277$	−531248.	−	920149.i	−0.416004	−	0.720541i	0.579529	−	0.814952i	$-0.303237\pi$
$277$	−531248.	−	920149.i	−0.416004	−	0.720541i	−0.995533	+	0.0944109i	$0.969903\pi$
$278$	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	−0.198725	−	0.980055i	$-0.563680\pi$
$281$	728876.	−	420817.i	0.550666	−	0.317927i	0.749390	+	0.662128i	$0.230347\pi$
$282$		0			0
$283$	−1.59876e6	−	923047.i	−1.18664	−	0.685106i	−0.229097	−	0.973404i	$-0.573577\pi$
$283$	−1.59876e6	−	923047.i	−1.18664	−	0.685106i	−0.957541	+	0.288298i	$0.906911\pi$
$284$	−158451.	+	1.34338e6i	−0.116573	+	0.988336i
$285$		0			0
$286$	−90976.8	−	102338.i	−0.0657681	−	0.0739813i
$287$	−200114.			−0.143408
$288$		0			0
$289$	−1.17110e6			−0.824804
$290$	−155663.	−	175102.i	−0.108690	−	0.122263i
$291$		0			0
$292$	273540.	−	2.31914e6i	0.187743	−	1.59173i
$293$	−1.40490e6	−	811121.i	−0.956043	−	0.551972i	−0.0610899	−	0.998132i	$-0.519458\pi$
$293$	−1.40490e6	−	811121.i	−0.956043	−	0.551972i	−0.894953	+	0.446161i	$0.852791\pi$
$294$		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
$302$	−96805.8	−	32134.4i	−0.0610779	−	0.0202746i
$303$		0			0
$304$	−397632.	+	1.66216e6i	−0.246773	+	1.03155i
$305$			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	$-0.116588\pi$
$308$	−96847.9	+	129804.i	−0.0581719	+	0.0779672i
$309$		0			0
$310$	85014.2	−	256107.i	0.0502443	−	0.151362i
$311$	−685107.	+	1.18664e6i	−0.401659	+	0.695693i	−0.993926	−	0.110048i	$-0.964900\pi$
$311$	−685107.	+	1.18664e6i	−0.401659	+	0.695693i	0.592268	+	0.805741i	$0.298233\pi$
$312$		0			0
$313$	130578.	+	226168.i	0.0753372	+	0.130488i	0.901233	−	0.433335i	$-0.142663\pi$
$313$	130578.	+	226168.i	0.0753372	+	0.130488i	−0.825896	+	0.563823i	$0.809330\pi$
$314$	−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	−0.640667	−	0.767819i	$-0.721342\pi$
$317$	−529678.	+	305810.i	−0.296049	+	0.170924i	0.344618	+	0.938743i	$0.388009\pi$
$318$		0			0
$319$	−691835.	−	399431.i	−0.380650	−	0.219768i
$320$	−373821.	+	311670.i	−0.204075	+	0.170145i
$321$		0			0
$322$	347187.	−	308643.i	0.186605	−	0.165889i
$323$	−2.68651e6			−1.43279
$324$		0			0
$325$	−245397.			−0.128873
$326$	1.02980e6	−	915479.i	0.536674	−	0.477094i
$327$		0			0
$328$	−2.04304e6	+	175497.i	−1.04856	+	0.0900711i
$329$	−51882.7	−	29954.5i	−0.0264261	−	0.0152571i
$330$		0			0
$331$	853212.	−	492602.i	0.428043	−	0.247131i	−0.270470	−	0.962728i	$-0.587179\pi$
$331$	853212.	−	492602.i	0.428043	−	0.247131i	0.698512	+	0.715598i	$0.253846\pi$
$332$	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	−0.467142	−	0.884182i	$-0.654716\pi$
$337$	1.10946e6	−	1.92164e6i	0.532153	−	0.921716i	0.999295	−	0.0375341i	$-0.0119503\pi$
$338$	648979.	−	1.95507e6i	0.308986	−	0.930829i
$339$		0			0
$340$	−613191.	−	457507.i	−0.287673	−	0.214635i
$341$		−	920109.i		−	0.428503i
$342$		0			0
$343$			588300.i			0.270000i
$344$	−1.09873e6	+	2.34656e6i	−0.500602	+	1.06914i
$345$		0			0
$346$	588059.	+	195205.i	0.264077	+	0.0876597i
$347$	−1.28567e6	+	2.22684e6i	−0.573199	+	0.992810i	0.423036	+	0.906113i	$0.360964\pi$
$347$	−1.28567e6	+	2.22684e6i	−0.573199	+	0.992810i	−0.996235	+	0.0866969i	$0.972369\pi$
$348$		0			0
$349$	935689.	+	1.62066e6i	0.411214	+	0.712243i	0.995023	−	0.0996478i	$-0.0317716\pi$
$349$	935689.	+	1.62066e6i	0.411214	+	0.712243i	−0.583809	+	0.811891i	$0.698438\pi$
$350$	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	−0.733354	−	0.679847i	$-0.762046\pi$
$353$	−1.19697e6	+	691073.i	−0.511267	+	0.295180i	0.222087	+	0.975027i	$0.428713\pi$
$354$		0			0
$355$	−543746.	−	313932.i	−0.228994	−	0.132210i
$356$	3.78682e6	+	446651.i	1.58362	+	0.186786i
$357$		0			0
$358$	993388.	+	1.11744e6i	0.409648	+	0.460806i
$359$	4.58930e6			1.87936			0.939680	−	0.342054i	$-0.111123\pi$
$359$	4.58930e6			1.87936			0.939680	+	0.342054i	$0.111123\pi$
$360$		0			0
$361$	−309482.			−0.124988
$362$	−1.90996e6	−	2.14847e6i	−0.766041	−	0.861705i
$363$		0			0
$364$	47434.5	+	5594.85i	0.0187647	+	0.00221327i
$365$	938692.	+	541954.i	0.368800	+	0.212927i
$366$		0			0
$367$	318059.	−	183631.i	0.123266	−	0.0711675i	−0.437099	−	0.899413i	$-0.643994\pi$
$367$	318059.	−	183631.i	0.123266	−	0.0711675i	0.560365	+	0.828246i	$0.310661\pi$
$368$	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	0.456343	+	0.889804i	$0.349159\pi$
$373$	−1.45750e6	+	2.52447e6i	−0.542421	+	0.939501i	−0.998764	+	0.0496972i	$0.984174\pi$
$374$	−2.47580e6	−	821835.i	−0.915243	−	0.303812i
$375$		0			0
$376$	−555959.	−	260316.i	−0.202802	−	0.0949579i
$377$			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	$-0.113407\pi$
$380$	−635804.	−	474378.i	−0.225873	−	0.168526i
$381$		0			0
$382$	186393.	−	561514.i	0.0653538	−	0.196880i
$383$	1.91266e6	−	3.31282e6i	0.666254	−	1.15399i	−0.312690	−	0.949855i	$-0.601230\pi$
$383$	1.91266e6	−	3.31282e6i	0.666254	−	1.15399i	0.978944	−	0.204130i	$-0.0654367\pi$
$384$		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	−0.250506	−	0.968115i	$-0.580597\pi$
$389$	1.38080e6	−	797204.i	0.462654	−	0.267113i	0.713159	+	0.701002i	$0.247264\pi$
$390$		0			0
$391$	6.48010e6	+	3.74128e6i	2.14358	+	1.23760i
$392$	255548.	+	2.97494e6i	0.0839958	+	0.977831i
$393$		0			0
$394$	3.89846e6	−	3.46567e6i	1.26518	−	1.12473i
$395$	−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	$0.277575\pi$
$398$	393914.	−	350183.i	0.124650	−	0.110812i
$399$		0			0
$400$	846988.	+	2.85094e6i	0.264684	+	0.890918i
$401$	4.84780e6	+	2.79888e6i	1.50551	+	0.869207i	0.999980	+	0.00639934i	$0.00203699\pi$
$401$	4.84780e6	+	2.79888e6i	1.50551	+	0.869207i	0.505532	+	0.862808i	$0.331296\pi$
$402$		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	−0.620891	−	0.783897i	$-0.713229\pi$
$409$	1.24641e6	−	2.15885e6i	0.368429	−	0.638138i	0.989320	+	0.145759i	$0.0465625\pi$
$410$	299853.	−	903314.i	0.0880944	−	0.265387i
$411$		0			0
$412$	1.92768e6	−	2.58365e6i	0.559489	−	0.749878i
$413$		−	385123.i		−	0.111103i
$414$		0			0
$415$			363447.i			0.103591i
$416$	489183.	+	15520.4i	0.138592	+	0.00439714i
$417$		0			0
$418$	−2.56710e6	−	852142.i	−0.718625	−	0.238545i
$419$	−476950.	+	826102.i	−0.132720	+	0.229879i	−0.924724	−	0.380637i	$-0.875705\pi$
$419$	−476950.	+	826102.i	−0.132720	+	0.229879i	0.792004	+	0.610516i	$0.209038\pi$
$420$		0			0
$421$	−1.44880e6	−	2.50940e6i	−0.398386	−	0.690025i	0.595141	−	0.803621i	$-0.297096\pi$
$421$	−1.44880e6	−	2.50940e6i	−0.398386	−	0.690025i	−0.993527	+	0.113597i	$0.963763\pi$
$422$	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
$428$	55944.2	−	474309.i	0.0147620	−	0.125156i
$429$		0			0
$430$	−799046.	−	898832.i	−0.208401	−	0.234427i
$431$	3.72242e6			0.965234			0.482617	−	0.875831i	$-0.339686\pi$
$431$	3.72242e6			0.965234			0.482617	+	0.875831i	$0.339686\pi$
$432$		0			0
$433$	4.74890e6			1.21723			0.608616	−	0.793465i	$-0.291725\pi$
$433$	4.74890e6			1.21723			0.608616	+	0.793465i	$0.291725\pi$
$434$	213239.	+	239869.i	0.0543429	+	0.0611293i
$435$		0			0
$436$	−127466.	+	1.08069e6i	−0.0321128	+	0.272261i
$437$	6.71907e6	+	3.87925e6i	1.68308	+	0.971728i
$438$		0			0
$439$	−6.29205e6	+	3.63272e6i	−1.55823	+	0.899644i	−0.560802	+	0.827950i	$0.689507\pi$
$439$	−6.29205e6	+	3.63272e6i	−1.55823	+	0.899644i	−0.997427	+	0.0716934i	$0.977160\pi$
$440$	−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	−0.973203	−	0.229946i	$-0.926145\pi$
$443$	−2.83250e6	−	4.90603e6i	−0.685741	−	1.18774i	0.287463	−	0.957792i	$-0.407188\pi$
$444$		0			0
$445$	−884931.	+	1.53275e6i	−0.211841	+	0.366919i
$446$	−4.42976e6	−	1.47045e6i	−1.05449	−	0.350035i
$447$		0			0
$448$	−98721.2	−	570388.i	−0.0232389	−	0.134269i
$449$			4.08820e6i			0.957011i	0.878085	+	0.478505i	$0.158821\pi$
$449$			4.08820e6i			0.957011i	−0.878085	+	0.478505i	$0.841179\pi$
$450$		0			0
$451$		−	3.24531e6i		−	0.751302i
$452$	−1.98219e6	+	2.65671e6i	−0.456352	+	0.611644i
$453$		0			0
$454$	−794216.	+	2.39260e6i	−0.180842	+	0.544791i
$455$	−11084.8	+	19199.5i	−0.00251016	+	0.00434772i
$456$		0			0
$457$	2.07648e6	+	3.59658e6i	0.465091	+	0.805562i	0.999206	−	0.0398504i	$-0.0126881\pi$
$457$	2.07648e6	+	3.59658e6i	0.465091	+	0.805562i	−0.534114	+	0.845412i	$0.679355\pi$
$458$	−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	−0.531777	−	0.846884i	$-0.678476\pi$
$461$	−293141.	+	169245.i	−0.0642427	+	0.0370905i	0.467535	+	0.883975i	$0.345142\pi$
$462$		0			0
$463$	6.16958e6	+	3.56201e6i	1.33753	+	0.772223i	0.986441	−	0.164119i	$-0.0524781\pi$
$463$	6.16958e6	+	3.56201e6i	1.33753	+	0.772223i	0.351089	+	0.936342i	$0.385811\pi$
$464$	2.73714e6	−	813179.i	0.590203	−	0.175344i
$465$		0			0
$466$	−2.04580e6	+	1.81868e6i	−0.436414	+	0.387965i
$467$	−3.96727e6			−0.841782			−0.420891	−	0.907111i	$-0.638283\pi$
$467$	−3.96727e6			−0.841782			−0.420891	+	0.907111i	$0.638283\pi$
$468$		0			0
$469$	367489.			0.0771457
$470$	212956.	−	189314.i	0.0444678	−	0.0395311i
$471$		0			0
$472$	−337748.	−	3.93186e6i	−0.0697810	−	0.812351i
$473$	−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	0.939867	+	0.341540i	$0.110948\pi$
$479$	3.84509e6	+	6.65989e6i	0.765716	+	1.32626i	−0.174151	+	0.984719i	$0.555718\pi$
$480$		0			0
$481$	−195353.	+	338362.i	−0.0384997	+	0.0666835i
$482$	−763418.	+	2.29982e6i	−0.149673	+	0.450895i
$483$		0			0
$484$	2.02554e6	+	1.51127e6i	0.393031	+	0.293243i
$485$		−	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	$-0.0358634\pi$
$488$	−5.86719e6	−	2.74718e6i	−1.11527	−	0.522202i
$489$		0			0
$490$	−1.31535e6	−	436627.i	−0.247486	−	0.0821524i
$491$	−730305.	+	1.26493e6i	−0.136710	+	0.236789i	−0.926249	−	0.376911i	$-0.876986\pi$
$491$	−730305.	+	1.26493e6i	−0.136710	+	0.236789i	0.789539	+	0.613700i	$0.210320\pi$
$492$		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	$-0.455689\pi$
$499$	−3.61275e6	−	2.08582e6i	−0.649510	−	0.374995i	−0.788269	+	0.615331i	$0.789022\pi$
$500$	−2.84602e6	−	335685.i	−0.509111	−	0.0600491i
$501$		0			0
$502$	−631562.	−	710432.i	−0.111855	−	0.125824i
$503$	−3.55656e6			−0.626773			−0.313387	−	0.949626i	$-0.601464\pi$
$503$	−3.55656e6			−0.626773			−0.313387	+	0.949626i	$0.601464\pi$
$504$		0			0
$505$	2.00059e6			0.349083
$506$	5.00536e6	+	5.63043e6i	0.869079	+	0.977610i
$507$		0			0
$508$	−1.02824e7	−	1.21280e6i	−1.76781	−	0.208512i
$509$	−5.64282e6	−	3.25788e6i	−0.965388	−	0.557367i	−0.0675606	−	0.997715i	$-0.521522\pi$
$509$	−5.64282e6	−	3.25788e6i	−0.965388	−	0.557367i	−0.897827	+	0.440348i	$0.854855\pi$
$510$		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
$518$	438572.	+	145583.i	0.0718153	+	0.0238389i
$519$		0			0
$520$	−96331.6	+	205736.i	−0.0156229	+	0.0333659i
$521$			551264.i			0.0889744i	0.999010	+	0.0444872i	$0.0141654\pi$
$521$			551264.i			0.0889744i	−0.999010	+	0.0444872i	$0.985835\pi$
$522$		0			0
$523$		−	1.10624e7i		−	1.76846i	−0.467053	−	0.884230i	$-0.654684\pi$
$523$		−	1.10624e7i		−	1.76846i	0.467053	−	0.884230i	$-0.345316\pi$
$524$	−3.64182e6	−	2.71719e6i	−0.579416	−	0.432307i
$525$		0			0
$526$	1.65830e6	−	4.99568e6i	0.261336	−	0.787282i
$527$	−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
$536$	3.75183e6	−	322283.i	0.564068	−	0.0484535i
$537$		0			0
$538$	−4.34332e6	+	3.86114e6i	−0.646943	+	0.575121i
$539$	−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	$0.570886\pi$
$542$	7.05962e6	−	6.27588e6i	1.03225	−	0.917649i
$543$		0			0
$544$	8.21866e6	−	4.40362e6i	1.19070	−	0.637989i
$545$	−437418.	−	252543.i	−0.0630820	−	0.0364204i
$546$		0			0
$547$	−1.52151e6	+	878446.i	−0.217424	+	0.125530i	−0.604757	−	0.796410i	$-0.706730\pi$
$547$	−1.52151e6	+	878446.i	−0.217424	+	0.125530i	0.387333	+	0.921940i	$0.373396\pi$
$548$	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
$554$	−1.89353e6	+	5.70432e6i	−0.262119	+	0.789641i
$555$		0			0
$556$	6.86930e6	−	9.20686e6i	0.942379	−	1.26306i
$557$		−	1.04568e7i		−	1.42811i	−0.700090	−	0.714055i	$-0.746857\pi$
$557$		−	1.04568e7i		−	1.42811i	0.700090	−	0.714055i	$-0.253143\pi$
$558$		0			0
$559$			1.20939e6i			0.163695i
$560$	261312.	+	62512.6i	0.0352119	+	0.00842360i
$561$		0			0
$562$	−4.51856e6	−	1.49992e6i	−0.603474	−	0.200322i
$563$	−2.79625e6	+	4.84324e6i	−0.371796	+	0.643969i	−0.989842	−	0.142173i	$-0.954591\pi$
$563$	−2.79625e6	+	4.84324e6i	−0.371796	+	0.643969i	0.618046	+	0.786142i	$0.287925\pi$
$564$		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	−0.139613	−	0.990206i	$-0.544586\pi$
$569$	5.00540e6	−	2.88987e6i	0.648124	−	0.374195i	0.787737	+	0.616012i	$0.211253\pi$
$570$		0			0
$571$	2.38689e6	+	1.37807e6i	0.306367	+	0.176881i	0.645300	−	0.763930i	$-0.276733\pi$
$571$	2.38689e6	+	1.37807e6i	0.306367	+	0.176881i	−0.338933	+	0.940811i	$0.610066\pi$
$572$	−90733.4	+	769261.i	−0.0115952	+	0.0983068i
$573$		0			0
$574$	752114.	+	846038.i	0.0952805	+	0.107179i
$575$	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	$0.706437\pi$
$578$	4.40151e6	+	4.95118e6i	0.548002	+	0.616437i
$579$		0			0
$580$	−155246.	+	1.31622e6i	−0.0191625	+	0.162464i
$581$	−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	−0.996995	−	0.0774689i	$-0.975316\pi$
$587$	−4.72166e6	−	8.17816e6i	−0.565587	−	0.979626i	0.431407	−	0.902157i	$-0.358017\pi$
$588$		0			0
$589$	−2.68015e6	+	4.64215e6i	−0.318325	+	0.551355i
$590$	1.73845e6	+	577072.i	0.205604	+	0.0682496i
$591$		0			0
$592$	4.60522e6	+	1.10169e6i	0.540065	+	0.129198i
$593$		−	1.32881e6i		−	0.155177i	−0.996985	−	0.0775883i	$-0.975278\pi$
$593$		−	1.32881e6i		−	0.155177i	0.996985	−	0.0775883i	$-0.0247220\pi$
$594$		0			0
$595$			422352.i			0.0489083i
$596$	−3.87174e6	+	5.18926e6i	−0.446469	+	0.598397i
$597$		0			0
$598$	699973.	−	2.10869e6i	0.0800439	−	0.241134i
$599$	8.44536e6	−	1.46278e7i	0.961726	−	1.66576i	0.243560	−	0.969886i	$-0.421685\pi$
$599$	8.44536e6	−	1.46278e7i	0.961726	−	1.66576i	0.718166	−	0.695872i	$-0.244982\pi$
$600$		0			0
$601$	3.86305e6	+	6.69101e6i	0.436259	+	0.755623i	0.997397	−	0.0720990i	$-0.0229698\pi$
$601$	3.86305e6	+	6.69101e6i	0.436259	+	0.755623i	−0.561138	+	0.827722i	$0.689636\pi$
$602$	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	$-0.292841\pi$
$607$	1.99470e6	+	1.15164e6i	0.219739	+	0.126866i	−0.386091	+	0.922461i	$0.626175\pi$
$608$	8.52174e6	−	4.56602e6i	0.934909	−	0.500932i
$609$		0			0
$610$	2.24738e6	−	1.99789e6i	0.244541	−	0.217393i
$611$	−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	$0.720095\pi$
$614$	−5.00079e6	+	4.44562e6i	−0.535325	+	0.475895i
$615$		0			0
$616$	912781.	−	78408.0i	0.0969203	−	0.00832547i
$617$	−1.03585e7	−	5.98047e6i	−1.09543	−	0.632445i	−0.160410	−	0.987050i	$-0.551282\pi$
$617$	−1.03585e7	−	5.98047e6i	−1.09543	−	0.632445i	−0.935016	+	0.354606i	$0.884615\pi$
$618$		0			0
$619$	−6.60708e6	+	3.81460e6i	−0.693079	+	0.400149i	−0.804764	−	0.593594i	$-0.797708\pi$
$619$	−6.60708e6	+	3.81460e6i	−0.693079	+	0.400149i	0.111685	+	0.993744i	$0.464375\pi$
$620$	−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
$626$	465421.	−	1.40209e6i	0.0474690	−	0.143002i
$627$		0			0
$628$	1.22191e7	+	9.11675e6i	1.23635	+	0.922446i
$629$			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	$0.679636\pi$
$632$	6.74055e6	−	1.43958e7i	0.671278	−	1.43365i
$633$		0			0
$634$	3.28366e6	+	1.09000e6i	0.324440	+	0.107697i
$635$	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	−0.158565	−	0.987349i	$-0.550687\pi$
$641$	6.42076e6	−	3.70703e6i	0.617222	−	0.356353i	0.775787	+	0.630995i	$0.217353\pi$
$642$		0			0
$643$	−3.01403e6	−	1.74015e6i	−0.287488	−	0.165981i	0.349320	−	0.937003i	$-0.386413\pi$
$643$	−3.01403e6	−	1.74015e6i	−0.287488	−	0.165981i	−0.636809	+	0.771022i	$0.719746\pi$
$644$	−2.60975e6	−	307818.i	−0.247962	−	0.0292468i
$645$		0			0
$646$	1.00971e7	+	1.13580e7i	0.951949	+	1.07083i
$647$	2.88799e6			0.271229			0.135614	−	0.990762i	$-0.456699\pi$
$647$	2.88799e6			0.271229			0.135614	+	0.990762i	$0.456699\pi$
$648$		0			0
$649$	6.24566e6			0.582058
$650$	922309.	+	1.03749e6i	0.0856235	+	0.0963163i
$651$		0			0
$652$	−7.74090e6	−	913030.i	−0.713136	−	0.0841136i
$653$	−4.44008e6	−	2.56348e6i	−0.407482	−	0.235260i	0.282225	−	0.959348i	$-0.408927\pi$
$653$	−4.44008e6	−	2.56348e6i	−0.407482	−	0.235260i	−0.689707	+	0.724088i	$0.742261\pi$
$654$		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	$-0.203882\pi$
$659$	−1.30044e6	−	2.25243e6i	−0.116648	−	0.202041i	−0.918437	+	0.395566i	$0.870548\pi$
$660$		0			0
$661$	6.08660e6	−	1.05423e7i	0.541840	−	0.938494i	−0.456959	−	0.889488i	$-0.651061\pi$
$661$	6.08660e6	−	1.05423e7i	0.541840	−	0.938494i	0.998798	−	0.0490059i	$-0.0156053\pi$
$662$	−5.28936e6	−	1.75579e6i	−0.469092	−	0.155714i
$663$		0			0
$664$	−4.01150e6	−	1.87830e6i	−0.353091	−	0.165327i
$665$			437927.i			0.0384015i
$666$		0			0
$667$		−	1.29624e7i		−	1.12816i
$668$	1.08166e6	+	807033.i	0.0937883	+	0.0699761i
$669$		0			0
$670$	−550649.	+	1.65884e6i	−0.0473901	+	0.142764i
$671$	5.12658e6	−	8.87949e6i	0.439563	−	0.761346i
$672$		0			0
$673$	1.21145e6	+	2.09828e6i	0.103102	+	0.178577i	0.912961	−	0.408047i	$-0.133790\pi$
$673$	1.21145e6	+	2.09828e6i	0.103102	+	0.178577i	−0.809859	+	0.586624i	$0.800457\pi$
$674$	−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	−0.610966	−	0.791657i	$-0.709219\pi$
$677$	−2.75301e6	+	1.58945e6i	−0.230854	+	0.133283i	0.380112	+	0.924940i	$0.375885\pi$
$678$		0			0
$679$	1.21091e6	+	699118.i	0.100794	+	0.0581937i
$680$	370397.	+	4.31195e6i	0.0307182	+	0.357603i
$681$		0			0
$682$	−3.89003e6	+	3.45817e6i	−0.320252	+	0.284698i
$683$	−1.16442e7			−0.955123			−0.477562	−	0.878598i	$-0.658479\pi$
$683$	−1.16442e7			−0.955123			−0.477562	+	0.878598i	$0.658479\pi$
$684$		0			0
$685$	−886917.			−0.0722199
$686$	2.48721e6	−	2.21109e6i	0.201791	−	0.179389i
$687$		0			0
$688$	1.40502e7	−	4.17420e6i	1.13165	−	0.336203i
$689$	−2.27335e6	−	1.31252e6i	−0.182439	−	0.105331i
$690$		0			0
$691$	1.57763e7	−	9.10845e6i	1.25693	−	0.725687i	0.284451	−	0.958691i	$-0.408189\pi$
$691$	1.57763e7	−	9.10845e6i	1.25693	−	0.725687i	0.972476	+	0.233004i	$0.0748555\pi$
$692$	−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
$698$	3.33509e6	−	1.00470e7i	0.259101	−	0.780547i
$699$		0			0
$700$	981830.	−	1.31594e6i	0.0757341	−	0.101506i
$701$			8.51403e6i			0.654395i	0.944956	+	0.327197i	$0.106104\pi$
$701$			8.51403e6i			0.654395i	−0.944956	+	0.327197i	$0.893896\pi$
$702$		0			0
$703$			7.71779e6i			0.588986i
$704$	9.25016e6	−	1.60099e6i	0.703424	−	0.121747i
$705$		0			0
$706$	7.42045e6	+	2.46320e6i	0.560297	+	0.185989i
$707$	−1.18971e6	+	2.06064e6i	−0.0895145	+	0.155044i
$708$		0			0
$709$	−5.32118e6	−	9.21656e6i	−0.397551	−	0.688578i	0.595872	−	0.803079i	$-0.296806\pi$
$709$	−5.32118e6	−	9.21656e6i	−0.397551	−	0.688578i	−0.993423	+	0.114501i	$0.963473\pi$
$710$	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
$716$	990731.	−	8.39967e6i	0.0722226	−	0.612322i
$717$		0			0
$718$	−1.72486e7	−	1.94026e7i	−1.24865	−	1.40459i
$719$	−3.66390e6			−0.264315			−0.132157	−	0.991229i	$-0.542190\pi$
$719$	−3.66390e6			−0.264315			−0.132157	+	0.991229i	$0.542190\pi$
$720$		0			0
$721$	−1.77956e6			−0.127489
$722$	1.16317e6	+	1.30842e6i	0.0830422	+	0.0934125i
$723$		0			0
$724$	−1.90485e6	+	1.61498e7i	−0.135056	+	1.14504i
$725$	7.01372e6	+	4.04938e6i	0.495568	+	0.286117i
$726$		0			0
$727$	−5.20680e6	+	3.00615e6i	−0.365372	+	0.210948i	−0.671435	−	0.741064i	$-0.734322\pi$
$727$	−5.20680e6	+	3.00615e6i	−0.365372	+	0.210948i	0.306063	+	0.952011i	$0.400988\pi$
$728$	−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	−0.589720	−	0.807608i	$-0.700762\pi$
$733$	5.88479e6	−	1.01927e7i	0.404549	−	0.700699i	0.994269	+	0.106909i	$0.0340953\pi$
$734$	−1.97176e6	−	654520.i	−0.135087	−	0.0448418i
$735$		0			0
$736$	−2.69139e7	−	853904.i	−1.83140	−	0.0581051i
$737$			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	$-0.162295\pi$
$740$	−1.31432e6	+	1.76157e6i	−0.0882313	+	0.118256i
$741$		0			0
$742$	−978126.	+	2.94663e6i	−0.0652206	+	0.196479i
$743$	−1.03693e7	+	1.79602e7i	−0.689094	+	1.19355i	0.283038	+	0.959109i	$0.408658\pi$
$743$	−1.03693e7	+	1.79602e7i	−0.689094	+	1.19355i	−0.972131	+	0.234436i	$0.924676\pi$
$744$		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	$-0.334843\pi$
$751$	−126982.	−	73312.8i	−0.00821563	−	0.00474329i	−0.504102	+	0.863644i	$0.668177\pi$
$752$	988974.	+	3.32886e6i	0.0637735	+	0.214660i
$753$		0			0
$754$	996075.	−	885494.i	0.0638063	−	0.0567227i
$755$	−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	$0.192203\pi$
$758$	−8.24717e6	+	7.33159e6i	−0.521353	+	0.463474i
$759$		0			0
$760$	384056.	+	4.47096e6i	0.0241191	+	0.280781i
$761$	−3.55514e6	−	2.05256e6i	−0.222534	−	0.128480i	0.384589	−	0.923088i	$-0.374343\pi$
$761$	−3.55514e6	−	2.05256e6i	−0.222534	−	0.128480i	−0.607123	+	0.794608i	$0.707676\pi$
$762$		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	−0.345629	−	0.938371i	$-0.612334\pi$
$769$	1.04927e7	−	1.81739e7i	0.639839	−	1.10823i	0.985468	−	0.169862i	$-0.0543323\pi$
$770$	−133967.	+	403580.i	−0.00814276	+	0.0245303i
$771$		0			0
$772$	−1.39413e7	−	1.04017e7i	−0.841902	−	0.628149i
$773$			4.46768e6i			0.268926i	0.990919	+	0.134463i	$0.0429310\pi$
$773$			4.46768e6i			0.268926i	−0.990919	+	0.134463i	$0.957069\pi$
$774$		0			0
$775$			9.32794e6i			0.557868i
$776$	1.29757e7	+	6.07560e6i	0.773530	+	0.362189i
$777$		0			0
$778$	−8.56004e6	−	2.84148e6i	−0.507022	−	0.168305i
$779$	−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	$-0.637250\pi$
$787$	−2.45633e7	−	1.41816e7i	−1.41368	−	0.816187i	−0.995733	+	0.0922851i	$0.970583\pi$
$788$	−2.93042e7	−	3.45640e6i	−1.68118	−	0.198293i
$789$		0			0
$790$	4.90205e6	+	5.51422e6i	0.279454	+	0.314352i
$791$	1.82988e6			0.103988
$792$		0			0
$793$	−3.02388e6			−0.170758
$794$	−1.51848e7	−	1.70811e7i	−0.854788	−	0.961535i
$795$		0			0
$796$	−2.96100e6	−	349246.i	−0.165636	−	0.0195366i
$797$	1.19538e7	+	6.90152e6i	0.666591	+	0.384857i	0.794784	−	0.606893i	$-0.207584\pi$
$797$	1.19538e7	+	6.90152e6i	0.666591	+	0.384857i	−0.128192	+	0.991749i	$0.540918\pi$
$798$		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
$806$	1.45688e6	+	483606.i	0.0789924	+	0.0262213i
$807$		0			0
$808$	−1.03391e7	+	2.20812e7i	−0.557125	+	1.18986i
$809$		−	9.63249e6i		−	0.517449i	−0.965951	−	0.258724i	$-0.916698\pi$
$809$		−	9.63249e6i		−	0.517449i	0.965951	−	0.258724i	$-0.0833022\pi$
$810$		0			0
$811$			2.76809e7i			1.47784i	0.673793	+	0.738920i	$0.264664\pi$
$811$			2.76809e7i			1.47784i	−0.673793	+	0.738920i	$0.735336\pi$
$812$	−1.26341e6	−	942638.i	−0.0672440	−	0.0501713i
$813$		0			0
$814$	−2.36096e6	+	7.11247e6i	−0.124890	+	0.376235i
$815$	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	−0.981586	−	0.191019i	$-0.938821\pi$
$821$	−2.52416e7	+	1.45733e7i	−1.30695	+	0.754569i	−0.325366	+	0.945588i	$0.605487\pi$
$822$		0			0
$823$	32905.4	+	18998.0i	0.00169343	+	0.000977704i	0.500846	−	0.865536i	$-0.333022\pi$
$823$	32905.4	+	18998.0i	0.00169343	+	0.000977704i	−0.499153	+	0.866514i	$0.666355\pi$
$824$	−1.81682e7	+	1.56065e6i	−0.932166	+	0.0800732i
$825$		0			0
$826$	−1.62822e6	+	1.44746e6i	−0.0830353	+	0.0738169i
$827$	−1.95942e7			−0.996238			−0.498119	−	0.867109i	$-0.665976\pi$
$827$	−1.95942e7			−0.996238			−0.498119	+	0.867109i	$0.665976\pi$
$828$		0			0
$829$	2.59138e7			1.30962			0.654809	−	0.755794i	$-0.272749\pi$
$829$	2.59138e7			1.30962			0.654809	+	0.755794i	$0.272749\pi$
$830$	1.53658e6	−	1.36599e6i	0.0774210	−	0.0688260i
$831$		0			0
$832$	−1.77295e6	−	2.12650e6i	−0.0887947	−	0.106502i
$833$	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	$-0.173070\pi$
$839$	−410110.	−	710332.i	−0.0201139	−	0.0348382i	−0.875907	+	0.482480i	$0.839736\pi$
$840$		0			0
$841$	−6.36784e6	+	1.10294e7i	−0.310457	+	0.537728i
$842$	−5.16398e6	+	1.55566e7i	−0.251018	+	0.756198i
$843$		0			0
$844$	102472.	−	137342.i	0.00495163	−	0.00663662i
$845$		−	5.40879e6i		−	0.260590i
$846$		0			0
$847$		−	1.39514e6i		−	0.0668205i
$848$	−7.40190e6	+	3.09410e7i	−0.353471	+	1.47756i
$849$		0			0
$850$	2.50993e7	+	8.33164e6i	1.19156	+	0.395534i
$851$	1.07479e7	−	1.86160e7i	0.508747	−	0.881175i
$852$		0			0
$853$	−8.23977e6	−	1.42717e7i	−0.387742	−	0.671588i	0.604404	−	0.796678i	$-0.293411\pi$
$853$	−8.23977e6	−	1.42717e7i	−0.387742	−	0.671588i	−0.992145	+	0.125090i	$0.960078\pi$
$854$	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	−0.614749	−	0.788723i	$-0.710743\pi$
$857$	−5.14015e6	+	2.96767e6i	−0.239069	+	0.138027i	0.375680	+	0.926750i	$0.377409\pi$
$858$		0			0
$859$	−1.26480e7	−	7.30230e6i	−0.584840	−	0.337658i	0.178214	−	0.983992i	$-0.442968\pi$
$859$	−1.26480e7	−	7.30230e6i	−0.584840	−	0.337658i	−0.763055	+	0.646334i	$0.776301\pi$
$860$	−796909.	+	6.75639e6i	−0.0367420	+	0.311508i
$861$		0			0
$862$	−1.39905e7	−	1.57376e7i	−0.641305	−	0.721391i
$863$	2.72449e7			1.24525			0.622626	−	0.782519i	$-0.286066\pi$
$863$	2.72449e7			1.24525			0.622626	+	0.782519i	$0.286066\pi$
$864$		0			0
$865$	1.62689e6			0.0739297
$866$	−1.78484e7	−	2.00773e7i	−0.808732	−	0.909728i
$867$		0			0
$868$	212669.	−	1.80306e6i	0.00958087	−	0.0812290i
$869$	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	−0.745766	−	0.666208i	$-0.767916\pi$
$877$	4.64812e6	−	8.05078e6i	0.204070	−	0.353459i	0.949836	+	0.312749i	$0.101250\pi$
$878$	3.90066e7	+	1.29481e7i	1.70766	+	0.566854i
$879$		0			0
$880$	−1.01379e6	+	4.23778e6i	−0.0441306	+	0.184473i
$881$			2.21047e7i			0.959499i	0.877406	+	0.479749i	$0.159272\pi$
$881$			2.21047e7i			0.959499i	−0.877406	+	0.479749i	$0.840728\pi$
$882$		0			0
$883$			4.54738e7i			1.96272i	0.192167	+	0.981362i	$0.438449\pi$
$883$			4.54738e7i			1.96272i	−0.192167	+	0.981362i	$0.561551\pi$
$884$	2.60254e6	−	3.48816e6i	0.112013	−	0.150129i
$885$		0			0
$886$	−1.00959e7	+	3.04142e7i	−0.432076	+	1.30164i
$887$	−3.80414e6	+	6.58897e6i	−0.162348	+	0.281195i	−0.935710	−	0.352769i	$-0.885240\pi$
$887$	−3.80414e6	+	6.58897e6i	−0.162348	+	0.281195i	0.773362	+	0.633964i	$0.218573\pi$
$888$		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
$896$	−2.04044e6	+	2.56114e6i	−0.0849091	+	0.106577i
$897$		0			0
$898$	1.72841e7	−	1.53652e7i	0.715245	−	0.635841i
$899$	8.95560e6			0.369569
$900$		0			0
$901$	−5.00092e7			−2.05229
$902$	−1.37205e7	+	1.21973e7i	−0.561504	+	0.499167i
$903$		0			0
$904$	1.86820e7	−	1.60478e6i	0.760329	−	0.0653124i
$905$	−6.53676e6	−	3.77400e6i	−0.265302	−	0.153172i
$906$		0			0
$907$	1.65581e7	−	9.55982e6i	0.668332	−	0.385862i	−0.127112	−	0.991888i	$-0.540571\pi$
$907$	1.65581e7	−	9.55982e6i	0.668332	−	0.385862i	0.795444	+	0.606027i	$0.207238\pi$
$908$	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	−0.998503	−	0.0546990i	$-0.982580\pi$
$911$	−1.36925e7	−	2.37161e7i	−0.546622	−	0.946777i	0.451881	−	0.892078i	$-0.350753\pi$
$912$		0			0
$913$	3.50513e6	−	6.07107e6i	0.139164	−	0.241039i
$914$	7.40124e6	−	2.22964e7i	0.293048	−	0.882815i
$915$		0			0
$916$	6.23228e6	+	4.64995e6i	0.245419	+	0.183109i
$917$			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	$-0.158276\pi$
$920$	5.29997e6	−	1.13192e7i	0.206445	−	0.440906i
$921$		0			0
$922$	1.81728e6	+	603241.i	0.0704035	+	0.0233703i
$923$	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	−0.0104821	−	0.999945i	$-0.503337\pi$
$929$	2.23660e7	−	1.29130e7i	0.850255	−	0.490895i	0.860737	+	0.509050i	$0.170003\pi$
$930$		0			0
$931$	2.38418e7	+	1.37651e7i	0.901498	+	0.520480i
$932$	1.53780e7	+	1.81382e6i	0.579910	+	0.0683997i
$933$		0			0
$934$	1.49107e7	+	1.67728e7i	0.559283	+	0.629126i
$935$	−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	$0.386039\pi$
$938$	−1.38118e6	−	1.55366e6i	−0.0512559	−	0.0576567i
$939$		0			0
$940$	−1.60076e6	−	188808.i	−0.0590891	−	0.00696949i
$941$	−1.01451e7	−	5.85728e6i	−0.373493	−	0.215636i	0.301490	−	0.953469i	$-0.402516\pi$
$941$	−1.01451e7	−	5.85728e6i	−0.373493	−	0.215636i	−0.674983	+	0.737833i	$0.735849\pi$
$942$		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	$-0.192502\pi$
$947$	−2.23751e6	−	3.87549e6i	−0.0810757	−	0.140427i	−0.903712	+	0.428140i	$0.859169\pi$
$948$		0			0
$949$	−3.08293e6	+	5.33979e6i	−0.111121	+	0.192468i
$950$	2.60249e7	+	8.63889e6i	0.935578	+	0.310563i
$951$		0			0
$952$	−4.66166e6	−	2.18272e6i	−0.166705	−	0.0780560i
$953$		−	3.35437e7i		−	1.19641i	−0.801344	−	0.598203i	$-0.795881\pi$
$953$		−	3.35437e7i		−	1.19641i	0.801344	−	0.598203i	$-0.204119\pi$
$954$		0			0
$955$		−	1.55345e6i		−	0.0551176i
$956$	1.92322e7	+	1.43493e7i	0.680588	+	0.507792i
$957$		0			0
$958$	1.37051e7	−	4.12870e7i	0.482468	−	1.45345i
$959$	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	$-0.557953\pi$
$967$	−3.26635e7	−	1.88583e7i	−1.12330	−	0.648539i	−0.942242	+	0.334932i	$0.891287\pi$
$968$	−1.22352e6	−	1.42435e7i	−0.0419685	−	0.488573i
$969$		0			0
$970$	−4.97025e6	+	4.41847e6i	−0.169609	+	0.150780i
$971$	5.05249e7			1.71972			0.859860	−	0.510530i	$-0.170551\pi$
$971$	5.05249e7			1.71972			0.859860	+	0.510530i	$0.170551\pi$
$972$		0			0
$973$	−6.34147e6			−0.214737
$974$	−4.97562e6	+	4.42324e6i	−0.168054	+	0.149398i
$975$		0			0
$976$	1.04369e7	+	3.51303e7i	0.350709	+	1.18048i
$977$	−2.68169e7	−	1.54827e7i	−0.898818	−	0.518933i	−0.0220017	−	0.999758i	$-0.507004\pi$
$977$	−2.68169e7	−	1.54827e7i	−0.898818	−	0.518933i	−0.876817	+	0.480825i	$0.840337\pi$
$978$		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	0.934098	+	0.357016i	$0.116206\pi$
$983$	2.35167e7	+	4.07321e7i	0.776234	+	1.34448i	−0.157864	+	0.987461i	$0.550461\pi$
$984$		0			0
$985$	6.84802e6	−	1.18611e7i	0.224892	−	0.389525i
$986$	7.99907e6	−	2.40974e7i	0.262028	−	0.789365i
$987$		0			0
$988$	2.69852e6	−	3.61680e6i	0.0879494	−	0.117878i
$989$		−	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	$0.897602\pi$
$992$	589956.	−	1.85946e7i	0.0190345	−	0.599941i
$993$		0			0
$994$	−4.00919e6	−	1.33084e6i	−0.128704	−	0.0427228i
$995$	691947.	−	1.19849e6i	0.0221572	−	0.0383774i
$996$		0			0
$997$	1.49630e7	+	2.59167e7i	0.476740	+	0.825739i	0.999645	−	0.0266527i	$-0.00848483\pi$
$997$	1.49630e7	+	2.59167e7i	0.476740	+	0.825739i	−0.522904	+	0.852391i	$0.675151\pi$
$998$	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.71.8		56
3.2	odd	2		36.6.h.a.23.21	yes	56
4.3	odd	2	inner	108.6.h.a.71.17		56
9.2	odd	6	inner	108.6.h.a.35.17		56
9.7	even	3		36.6.h.a.11.12	✓	56
12.11	even	2		36.6.h.a.23.12	yes	56
36.7	odd	6		36.6.h.a.11.21	yes	56
36.11	even	6	inner	108.6.h.a.35.8		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.6.h.a.11.12	✓	56	9.7	even	3
36.6.h.a.11.21	yes	56	36.7	odd	6
36.6.h.a.23.12	yes	56	12.11	even	2
36.6.h.a.23.21	yes	56	3.2	odd	2
108.6.h.a.35.8		56	36.11	even	6	inner
108.6.h.a.35.17		56	9.2	odd	6	inner
108.6.h.a.71.8		56	1.1	even	1	trivial
108.6.h.a.71.17		56	4.3	odd	2	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)

\(f(q)\)	\(=\)	\(q+(-3.75843 - 4.22779i) q^{2} +(-3.74838 + 31.7797i) q^{4} +(-12.8631 - 7.42651i) q^{5} +(15.2989 - 8.83282i) q^{7} +(148.446 - 103.595i) q^{8} +O(q^{10})\)	\(q+(-3.75843 - 4.22779i) q^{2} +(-3.74838 + 31.7797i) q^{4} +(-12.8631 - 7.42651i) q^{5} +(15.2989 - 8.83282i) q^{7} +(148.446 - 103.595i) q^{8} +(16.9473 + 82.2944i) q^{10} +(143.245 + 248.107i) q^{11} +(42.2460 - 73.1722i) q^{13} +(-94.8432 - 31.4829i) q^{14} +(-995.899 - 238.245i) q^{16} -1609.65i q^{17} -1669.01i q^{19} +(284.228 - 380.948i) q^{20} +(510.569 - 1538.10i) q^{22} +(-2324.29 + 4025.79i) q^{23} +(-1452.19 - 2515.27i) q^{25} +(-468.135 + 96.4056i) q^{26} +(223.358 + 519.303i) q^{28} +(-2414.87 + 1394.23i) q^{29} +(-2781.39 - 1605.84i) q^{31} +(2735.77 + 5105.88i) q^{32} +(-6805.24 + 6049.75i) q^{34} -262.388 q^{35} -4624.19 q^{37} +(-7056.20 + 6272.84i) q^{38} +(-2678.82 + 230.111i) q^{40} +(-9810.20 - 5663.92i) q^{41} +(-12396.0 + 7156.83i) q^{43} +(-8421.70 + 3622.27i) q^{44} +(25755.9 - 5304.05i) q^{46} +(-1695.63 - 2936.92i) q^{47} +(-8247.46 + 14285.0i) q^{49} +(-5176.07 + 15593.1i) q^{50} +(2167.04 + 1616.84i) q^{52} -31068.4i q^{53} -4255.23i q^{55} +(1356.03 - 2896.08i) q^{56} +(14970.6 + 4969.46i) q^{58} +(10900.3 - 18879.9i) q^{59} +(-17894.5 - 30994.2i) q^{61} +(3664.53 + 17794.5i) q^{62} +(11304.4 - 30756.4i) q^{64} +(-1086.83 + 627.480i) q^{65} +(18015.5 + 10401.2i) q^{67} +(51154.1 + 6033.56i) q^{68} +(986.168 + 1109.32i) q^{70} +42271.8 q^{71} -72975.6 q^{73} +(17379.7 + 19550.1i) q^{74} +(53040.5 + 6256.07i) q^{76} +(4382.97 + 2530.51i) q^{77} +(76047.9 - 43906.3i) q^{79} +(11041.0 + 10460.6i) q^{80} +(12925.1 + 62762.9i) q^{82} +(-12234.8 - 21191.3i) q^{83} +(-11954.1 + 20705.0i) q^{85} +(76847.0 + 25509.2i) q^{86} +(46966.6 + 21991.1i) q^{88} -119158. i q^{89} -1492.60i q^{91} +(-119226. - 88955.4i) q^{92} +(-6043.77 + 18207.0i) q^{94} +(-12394.9 + 21468.6i) q^{95} +(39575.0 + 68545.9i) q^{97} +(91391.6 - 18820.8i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 3 q^{2} - q^{4} + 6 q^{5}+O(q^{10}) \) 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

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