LMFDB - Embedded newform 171.3.ba.c.136.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,3,Mod(10,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 17]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("171.10");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	171.ba (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.65941252056$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{18})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 48 x^{16} + 936 x^{14} + 9539 x^{12} + 54576 x^{10} + 176517 x^{8} + 313396 x^{6} + 277917 x^{4} + \cdots + 8427 $ x^18 + 48x^16 + 936x^14 + 9539x^12 + 54576x^10 + 176517x^8 + 313396x^6 + 277917x^4 + 96435x^2 + 8427
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 57)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			136.1
Root			$3.09812i$ of defining polynomial
Character	$\chi$	$=$	171.136
Dual form			171.3.ba.c.127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.99143 + 2.37330i) q^{2} +(-0.972139 - 5.51328i) q^{4} +(-0.0525425 + 0.297983i) q^{5} +(-1.79984 - 3.11741i) q^{7} +(4.28839 + 2.47590i) q^{8} +O(q^{10})$	\(q+(-1.99143 + 2.37330i) q^{2} +(-0.972139 - 5.51328i) q^{4} +(-0.0525425 + 0.297983i) q^{5} +(-1.79984 - 3.11741i) q^{7} +(4.28839 + 2.47590i) q^{8} +(-0.602568 - 0.718112i) q^{10} +(9.85364 - 17.0670i) q^{11} +(-0.921973 + 2.53310i) q^{13} +(10.9828 + 1.93656i) q^{14} +(6.62675 - 2.41194i) q^{16} +(2.16287 + 1.81486i) q^{17} +(0.848719 - 18.9810i) q^{19} +1.69394 q^{20} +(20.8822 + 57.3733i) q^{22} +(-0.575632 - 3.26457i) q^{23} +(23.4063 + 8.51919i) q^{25} +(-4.17575 - 7.23260i) q^{26} +(-15.4375 + 12.9536i) q^{28} +(29.1735 + 34.7677i) q^{29} +(-15.0386 + 8.68256i) q^{31} +(-14.2469 + 39.1431i) q^{32} +(-8.61441 + 1.51895i) q^{34} +(1.02351 - 0.372526i) q^{35} -50.1934i q^{37} +(43.3574 + 39.8137i) q^{38} +(-0.963100 + 1.14778i) q^{40} +(-20.9363 - 57.5219i) q^{41} +(4.12466 - 23.3921i) q^{43} +(-103.674 - 37.7343i) q^{44} +(8.89413 + 5.13503i) q^{46} +(24.4852 - 20.5455i) q^{47} +(18.0212 - 31.2136i) q^{49} +(-66.8305 + 38.5846i) q^{50} +(14.8620 + 2.62056i) q^{52} +(-65.8534 + 11.6117i) q^{53} +(4.56795 + 3.83296i) q^{55} -17.8249i q^{56} -140.611 q^{58} +(65.2969 - 77.8178i) q^{59} +(-6.73733 - 38.2093i) q^{61} +(9.34213 - 52.9818i) q^{62} +(-50.4224 - 87.3341i) q^{64} +(-0.706379 - 0.407828i) q^{65} +(45.9957 + 54.8156i) q^{67} +(7.90322 - 13.6888i) q^{68} +(-1.15413 + 3.17094i) q^{70} +(-69.9337 - 12.3312i) q^{71} +(-96.9318 + 35.2803i) q^{73} +(119.124 + 99.9566i) q^{74} +(-105.473 + 13.7730i) q^{76} -70.9398 q^{77} +(28.5249 + 78.3715i) q^{79} +(0.370532 + 2.10139i) q^{80} +(178.210 + 64.8630i) q^{82} +(-32.6839 - 56.6101i) q^{83} +(-0.654441 + 0.549142i) q^{85} +(47.3024 + 56.3728i) q^{86} +(84.5124 - 48.7933i) q^{88} +(-28.1898 + 77.4508i) q^{89} +(9.55612 - 1.68500i) q^{91} +(-17.4389 + 6.34724i) q^{92} +99.0256i q^{94} +(5.61144 + 1.25022i) q^{95} +(-7.49384 + 8.93081i) q^{97} +(38.1911 + 104.929i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 9 q^{2} - 3 q^{4} - 9 q^{7} + 27 q^{8}+O(q^{10}) $ 18 * q - 9 * q^2 - 3 * q^4 - 9 * q^7 + 27 * q^8	$ 18 q - 9 q^{2} - 3 q^{4} - 9 q^{7} + 27 q^{8} - 78 q^{10} - 15 q^{11} + 36 q^{13} + 39 q^{14} - 3 q^{16} + 30 q^{17} + 54 q^{19} + 30 q^{20} + 132 q^{22} - 69 q^{23} + 138 q^{25} - 48 q^{26} - 246 q^{28} + 162 q^{29} + 72 q^{31} + 21 q^{32} - 285 q^{34} - 54 q^{35} + 204 q^{38} - 51 q^{40} - 30 q^{41} + 402 q^{43} - 471 q^{44} - 99 q^{46} + 105 q^{47} + 66 q^{49} - 567 q^{50} - 3 q^{52} + 36 q^{53} - 15 q^{55} - 48 q^{58} + 180 q^{59} + 93 q^{61} - 189 q^{62} - 183 q^{64} + 891 q^{65} - 354 q^{67} - 153 q^{68} + 372 q^{70} - 144 q^{71} - 453 q^{73} + 489 q^{74} - 150 q^{76} + 36 q^{77} - 96 q^{79} - 144 q^{80} + 249 q^{82} + 99 q^{83} - 573 q^{85} + 33 q^{86} + 360 q^{88} - 795 q^{89} + 414 q^{91} - 285 q^{92} - 198 q^{95} - 483 q^{97} + 39 q^{98}+O(q^{100}) $ 18 * q - 9 * q^2 - 3 * q^4 - 9 * q^7 + 27 * q^8 - 78 * q^10 - 15 * q^11 + 36 * q^13 + 39 * q^14 - 3 * q^16 + 30 * q^17 + 54 * q^19 + 30 * q^20 + 132 * q^22 - 69 * q^23 + 138 * q^25 - 48 * q^26 - 246 * q^28 + 162 * q^29 + 72 * q^31 + 21 * q^32 - 285 * q^34 - 54 * q^35 + 204 * q^38 - 51 * q^40 - 30 * q^41 + 402 * q^43 - 471 * q^44 - 99 * q^46 + 105 * q^47 + 66 * q^49 - 567 * q^50 - 3 * q^52 + 36 * q^53 - 15 * q^55 - 48 * q^58 + 180 * q^59 + 93 * q^61 - 189 * q^62 - 183 * q^64 + 891 * q^65 - 354 * q^67 - 153 * q^68 + 372 * q^70 - 144 * q^71 - 453 * q^73 + 489 * q^74 - 150 * q^76 + 36 * q^77 - 96 * q^79 - 144 * q^80 + 249 * q^82 + 99 * q^83 - 573 * q^85 + 33 * q^86 + 360 * q^88 - 795 * q^89 + 414 * q^91 - 285 * q^92 - 198 * q^95 - 483 * q^97 + 39 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$1$	$e\left(\frac{13}{18}\right)$

Coefficient data

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

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

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

$2$	−1.99143	+	2.37330i	−0.995716	+	1.18665i	−0.0133054	+	0.999911i	$0.504235\pi$
$2$	−1.99143	+	2.37330i	−0.995716	+	1.18665i	−0.982410	+	0.186736i	$0.940209\pi$
$3$		0			0
$3$		0			0
$4$	−0.972139	−	5.51328i	−0.243035	−	1.37832i
$5$	−0.0525425	+	0.297983i	−0.0105085	+	0.0595967i	−0.989611	−	0.143770i	$-0.954077\pi$
$5$	−0.0525425	+	0.297983i	−0.0105085	+	0.0595967i	0.979103	+	0.203367i	$0.0651885\pi$
$6$		0			0
$7$	−1.79984	−	3.11741i	−0.257120	−	0.445345i	0.708349	−	0.705862i	$-0.249440\pi$
$7$	−1.79984	−	3.11741i	−0.257120	−	0.445345i	−0.965469	+	0.260517i	$0.916107\pi$
$8$	4.28839	+	2.47590i	0.536048	+	0.309488i
$9$		0			0
$10$	−0.602568	−	0.718112i	−0.0602568	−	0.0718112i
$11$	9.85364	−	17.0670i	0.895785	−	1.55155i	0.0629550	−	0.998016i	$-0.479948\pi$
$11$	9.85364	−	17.0670i	0.895785	−	1.55155i	0.832830	−	0.553529i	$-0.186719\pi$
$12$		0			0
$13$	−0.921973	+	2.53310i	−0.0709210	+	0.194854i	−0.970089	−	0.242750i	$-0.921951\pi$
$13$	−0.921973	+	2.53310i	−0.0709210	+	0.194854i	0.899168	+	0.437604i	$0.144173\pi$
$14$	10.9828	+	1.93656i	0.784485	+	0.138326i
$15$		0			0
$16$	6.62675	−	2.41194i	0.414172	−	0.150746i
$17$	2.16287	+	1.81486i	0.127228	+	0.106757i	0.704181	−	0.710020i	$-0.251314\pi$
$17$	2.16287	+	1.81486i	0.127228	+	0.106757i	−0.576954	+	0.816777i	$0.695759\pi$
$18$		0			0
$19$	0.848719	−	18.9810i	0.0446694	−	0.999002i
$19$	0.848719	−	18.9810i	0.0446694	−	0.999002i
$20$	1.69394			0.0846972
$21$		0			0
$22$	20.8822	+	57.3733i	0.949190	+	2.60788i
$23$	−0.575632	−	3.26457i	−0.0250275	−	0.141938i	0.969734	−	0.244166i	$-0.0785141\pi$
$23$	−0.575632	−	3.26457i	−0.0250275	−	0.141938i	−0.994761	+	0.102228i	$0.967403\pi$
$24$		0			0
$25$	23.4063	+	8.51919i	0.936251	+	0.340768i
$26$	−4.17575	−	7.23260i	−0.160606	−	0.278177i
$27$		0			0
$28$	−15.4375	+	12.9536i	−0.551338	+	0.462627i
$29$	29.1735	+	34.7677i	1.00598	+	1.19888i	0.979954	+	0.199224i	$0.0638420\pi$
$29$	29.1735	+	34.7677i	1.00598	+	1.19888i	0.0260298	+	0.999661i	$0.491714\pi$
$30$		0			0
$31$	−15.0386	+	8.68256i	−0.485117	+	0.280083i	−0.722547	−	0.691322i	$-0.757029\pi$
$31$	−15.0386	+	8.68256i	−0.485117	+	0.280083i	0.237429	+	0.971405i	$0.423695\pi$
$32$	−14.2469	+	39.1431i	−0.445217	+	1.22322i
$33$		0			0
$34$	−8.61441	+	1.51895i	−0.253365	+	0.0446751i
$35$	1.02351	−	0.372526i	0.0292430	−	0.0106436i
$36$		0			0
$37$		−	50.1934i		−	1.35658i	−0.734795	−	0.678289i	$-0.762722\pi$
$37$		−	50.1934i		−	1.35658i	0.734795	−	0.678289i	$-0.237278\pi$
$38$	43.3574	+	39.8137i	1.14099	+	1.04773i
$39$		0			0
$40$	−0.963100	+	1.14778i	−0.0240775	+	0.0286945i
$41$	−20.9363	−	57.5219i	−0.510641	−	1.40297i	−0.880571	−	0.473915i	$-0.842841\pi$
$41$	−20.9363	−	57.5219i	−0.510641	−	1.40297i	0.369930	−	0.929060i	$-0.379382\pi$
$42$		0			0
$43$	4.12466	−	23.3921i	0.0959223	−	0.544002i	−0.898539	−	0.438895i	$-0.855370\pi$
$43$	4.12466	−	23.3921i	0.0959223	−	0.544002i	0.994461	−	0.105108i	$-0.0335188\pi$
$44$	−103.674	−	37.7343i	−2.35623	−	0.857598i
$45$		0			0
$46$	8.89413	+	5.13503i	0.193351	+	0.111631i
$47$	24.4852	−	20.5455i	0.520962	−	0.437139i	−0.344005	−	0.938968i	$-0.611784\pi$
$47$	24.4852	−	20.5455i	0.520962	−	0.437139i	0.864967	+	0.501829i	$0.167339\pi$
$48$		0			0
$49$	18.0212	−	31.2136i	0.367779	−	0.637011i
$50$	−66.8305	+	38.5846i	−1.33661	+	0.771693i
$51$		0			0
$52$	14.8620	+	2.62056i	0.285807	+	0.0503955i
$53$	−65.8534	+	11.6117i	−1.24252	+	0.219089i	−0.755994	−	0.654578i	$-0.772846\pi$
$53$	−65.8534	+	11.6117i	−1.24252	+	0.219089i	−0.486523	+	0.873668i	$0.661735\pi$
$54$		0			0
$55$	4.56795	+	3.83296i	0.0830536	+	0.0696902i
$56$		−	17.8249i		−	0.318302i
$57$		0			0
$58$	−140.611			−2.42433
$59$	65.2969	−	77.8178i	1.10673	−	1.31895i	0.163595	−	0.986528i	$-0.447691\pi$
$59$	65.2969	−	77.8178i	1.10673	−	1.31895i	0.943132	−	0.332418i	$-0.107865\pi$
$60$		0			0
$61$	−6.73733	−	38.2093i	−0.110448	−	0.626382i	−0.988904	−	0.148558i	$-0.952537\pi$
$61$	−6.73733	−	38.2093i	−0.110448	−	0.626382i	0.878456	−	0.477824i	$-0.158574\pi$
$62$	9.34213	−	52.9818i	0.150679	−	0.854546i
$63$		0			0
$64$	−50.4224	−	87.3341i	−0.787849	−	1.36459i
$65$	−0.706379	−	0.407828i	−0.0108674	−	0.00627428i
$66$		0			0
$67$	45.9957	+	54.8156i	0.686504	+	0.818143i	0.990928	−	0.134393i	$-0.0429086\pi$
$67$	45.9957	+	54.8156i	0.686504	+	0.818143i	−0.304424	+	0.952536i	$0.598464\pi$
$68$	7.90322	−	13.6888i	0.116224	−	0.201306i
$69$		0			0
$70$	−1.15413	+	3.17094i	−0.0164875	+	0.0452991i
$71$	−69.9337	−	12.3312i	−0.984982	−	0.173679i	−0.342116	−	0.939658i	$-0.611144\pi$
$71$	−69.9337	−	12.3312i	−0.984982	−	0.173679i	−0.642866	+	0.765979i	$0.722255\pi$
$72$		0			0
$73$	−96.9318	+	35.2803i	−1.32783	+	0.483292i	−0.905960	−	0.423363i	$-0.860849\pi$
$73$	−96.9318	+	35.2803i	−1.32783	+	0.483292i	−0.421873	+	0.906655i	$0.638627\pi$
$74$	119.124	+	99.9566i	1.60978	+	1.35077i
$75$		0			0
$76$	−105.473	+	13.7730i	−1.38780	+	0.181224i
$77$	−70.9398			−0.921297
$78$		0			0
$79$	28.5249	+	78.3715i	0.361074	+	0.992044i	0.978650	+	0.205532i	$0.0658926\pi$
$79$	28.5249	+	78.3715i	0.361074	+	0.992044i	−0.617576	+	0.786511i	$0.711885\pi$
$80$	0.370532	+	2.10139i	0.00463165	+	0.0262674i
$81$		0			0
$82$	178.210	+	64.8630i	2.17329	+	0.791013i
$83$	−32.6839	−	56.6101i	−0.393781	−	0.682049i	0.599163	−	0.800627i	$-0.295500\pi$
$83$	−32.6839	−	56.6101i	−0.393781	−	0.682049i	−0.992945	+	0.118577i	$0.962167\pi$
$84$		0			0
$85$	−0.654441	+	0.549142i	−0.00769931	+	0.00646049i
$86$	47.3024	+	56.3728i	0.550028	+	0.655498i
$87$		0			0
$88$	84.5124	−	48.7933i	0.960368	−	0.554469i
$89$	−28.1898	+	77.4508i	−0.316739	+	0.870234i	0.674514	+	0.738262i	$0.264353\pi$
$89$	−28.1898	+	77.4508i	−0.316739	+	0.870234i	−0.991253	+	0.131972i	$0.957869\pi$
$90$		0			0
$91$	9.55612	−	1.68500i	0.105012	−	0.0185165i
$92$	−17.4389	+	6.34724i	−0.189553	+	0.0689917i
$93$		0			0
$94$			99.0256i			1.05346i
$95$	5.61144	+	1.25022i	0.0590678	+	0.0131602i
$96$		0			0
$97$	−7.49384	+	8.93081i	−0.0772561	+	0.0920702i	−0.803288	−	0.595591i	$-0.796918\pi$
$97$	−7.49384	+	8.93081i	−0.0772561	+	0.0920702i	0.726032	+	0.687661i	$0.241362\pi$
$98$	38.1911	+	104.929i	0.389705	+	1.07071i
$99$		0			0
$100$	24.2145	−	137.327i	0.242145	−	1.37327i
$101$	76.9222	+	27.9974i	0.761606	+	0.277202i	0.693481	−	0.720475i	$-0.256076\pi$
$101$	76.9222	+	27.9974i	0.761606	+	0.277202i	0.0681250	+	0.997677i	$0.478298\pi$
$102$		0			0
$103$	78.3120	+	45.2135i	0.760311	+	0.438966i	0.829407	−	0.558644i	$-0.188678\pi$
$103$	78.3120	+	45.2135i	0.760311	+	0.438966i	−0.0690965	+	0.997610i	$0.522012\pi$
$104$	−10.2255	+	8.58020i	−0.0983219	+	0.0825019i
$105$		0			0
$106$	103.584	−	179.414i	0.977212	−	1.69258i
$107$	37.2909	−	21.5299i	0.348513	−	0.201214i	−0.315517	−	0.948920i	$-0.602178\pi$
$107$	37.2909	−	21.5299i	0.348513	−	0.201214i	0.664030	+	0.747706i	$0.268845\pi$
$108$		0			0
$109$	80.2597	+	14.1519i	0.736327	+	0.129834i	0.529221	−	0.848484i	$-0.322484\pi$
$109$	80.2597	+	14.1519i	0.736327	+	0.129834i	0.207106	+	0.978318i	$0.433595\pi$
$110$	−18.1935	+	3.20801i	−0.165396	+	0.0291637i
$111$		0			0
$112$	−19.4461	−	16.3172i	−0.173626	−	0.145689i
$113$		−	41.5216i		−	0.367448i	−0.982978	−	0.183724i	$-0.941185\pi$
$113$		−	41.5216i		−	0.367448i	0.982978	−	0.183724i	$-0.0588152\pi$
$114$		0			0
$115$	1.00303			0.00872203
$116$	163.323	−	194.641i	1.40796	−	1.67794i
$117$		0			0
$118$	54.6504	+	309.938i	0.463139	+	2.62659i
$119$	1.76486	−	10.0090i	0.0148307	−	0.0841094i
$120$		0			0
$121$	−133.688	−	231.555i	−1.10486	−	1.91368i
$122$	104.099	+	60.1015i	0.853270	+	0.492636i
$123$		0			0
$124$	62.4890	+	74.4715i	0.503943	+	0.600576i
$125$	−7.55066	+	13.0781i	−0.0604053	+	0.104625i
$126$		0			0
$127$	−64.7093	+	177.787i	−0.509522	+	1.39990i	0.372209	+	0.928149i	$0.378600\pi$
$127$	−64.7093	+	177.787i	−0.509522	+	1.39990i	−0.881731	+	0.471752i	$0.843622\pi$
$128$	143.592	+	25.3192i	1.12182	+	0.197806i
$129$		0			0
$130$	2.37460	−	0.864284i	0.0182662	−	0.00664834i
$131$	94.6174	+	79.3934i	0.722270	+	0.606057i	0.928012	−	0.372549i	$-0.121516\pi$
$131$	94.6174	+	79.3934i	0.722270	+	0.606057i	−0.205742	+	0.978606i	$0.565961\pi$
$132$		0			0
$133$	−60.6993	+	31.5170i	−0.456386	+	0.236970i
$134$	−221.691			−1.65441
$135$		0			0
$136$	4.78180	+	13.1379i	0.0351603	+	0.0966020i
$137$	13.4909	+	76.5107i	0.0984737	+	0.558472i	0.993627	+	0.112714i	$0.0359545\pi$
$137$	13.4909	+	76.5107i	0.0984737	+	0.558472i	−0.895154	+	0.445758i	$0.852934\pi$
$138$		0			0
$139$	−214.449	−	78.0530i	−1.54280	−	0.561533i	−0.576084	−	0.817391i	$-0.695420\pi$
$139$	−214.449	−	78.0530i	−1.54280	−	0.561533i	−0.966714	+	0.255858i	$0.917642\pi$
$140$	−3.04883	−	5.28072i	−0.0217773	−	0.0377194i
$141$		0			0
$142$	168.534	−	141.417i	1.18686	−	0.995892i
$143$	34.1476	+	40.6955i	0.238794	+	0.284584i
$144$		0			0
$145$	−11.8930	+	6.86645i	−0.0820210	+	0.0473548i
$146$	109.302	−	300.306i	0.748647	−	2.05689i
$147$		0			0
$148$	−276.730	+	48.7949i	−1.86980	+	0.329696i
$149$	−209.622	+	76.2961i	−1.40686	+	0.512055i	−0.930206	−	0.367037i	$-0.880372\pi$
$149$	−209.622	+	76.2961i	−1.40686	+	0.512055i	−0.476652	+	0.879092i	$0.658150\pi$
$150$		0			0
$151$		−	147.722i		−	0.978290i	−0.872203	−	0.489145i	$-0.837309\pi$
$151$		−	147.722i		−	0.978290i	0.872203	−	0.489145i	$-0.162691\pi$
$152$	50.6348	−	79.2967i	0.333124	−	0.521689i
$153$		0			0
$154$	141.272	−	168.361i	0.917349	−	1.09325i
$155$	−1.79709	−	4.93747i	−0.0115941	−	0.0318546i
$156$		0			0
$157$	−32.7935	+	185.981i	−0.208876	+	1.18459i	0.682347	+	0.731029i	$0.260959\pi$
$157$	−32.7935	+	185.981i	−0.208876	+	1.18459i	−0.891223	+	0.453566i	$0.850152\pi$
$158$	−242.804	−	88.3734i	−1.53673	−	0.559325i
$159$		0			0
$160$	−10.9154	−	6.30203i	−0.0682215	−	0.0393877i
$161$	−9.14098	+	7.67019i	−0.0567762	+	0.0476409i
$162$		0			0
$163$	9.22305	−	15.9748i	0.0565831	−	0.0980049i	−0.836346	−	0.548201i	$-0.815313\pi$
$163$	9.22305	−	15.9748i	0.0565831	−	0.0980049i	0.892930	+	0.450197i	$0.148646\pi$
$164$	−296.781	+	171.347i	−1.80964	+	1.04480i
$165$		0			0
$166$	199.440	+	35.1667i	1.20145	+	0.211847i
$167$	168.967	−	29.7935i	1.01178	−	0.178404i	0.356905	−	0.934141i	$-0.383832\pi$
$167$	168.967	−	29.7935i	1.01178	−	0.178404i	0.654876	+	0.755737i	$0.272721\pi$
$168$		0			0
$169$	123.895	+	103.960i	0.733106	+	0.615149i
$170$		−	2.64676i		−	0.0155692i
$171$		0			0
$172$	−132.977			−0.773121
$173$	31.1591	−	37.1340i	0.180111	−	0.214647i	−0.668434	−	0.743772i	$-0.733035\pi$
$173$	31.1591	−	37.1340i	0.180111	−	0.214647i	0.848544	+	0.529124i	$0.177479\pi$
$174$		0			0
$175$	−15.5697	−	88.3002i	−0.0889698	−	0.504573i
$176$	24.1330	−	136.865i	0.137119	−	0.777643i
$177$		0			0
$178$	−127.676	−	221.141i	−0.717278	−	1.24236i
$179$	139.421	+	80.4948i	0.778889	+	0.449692i	0.836036	−	0.548674i	$-0.184867\pi$
$179$	139.421	+	80.4948i	0.778889	+	0.449692i	−0.0571474	+	0.998366i	$0.518201\pi$
$180$		0			0
$181$	−126.375	−	150.608i	−0.698206	−	0.832089i	0.294116	−	0.955770i	$-0.404975\pi$
$181$	−126.375	−	150.608i	−0.698206	−	0.832089i	−0.992322	+	0.123680i	$0.960530\pi$
$182$	−15.0313	+	26.0351i	−0.0825898	+	0.143050i
$183$		0			0
$184$	5.61423	−	15.4250i	0.0305121	−	0.0838313i
$185$	14.9568	+	2.63729i	0.0808475	+	0.0142556i
$186$		0			0
$187$	52.2864	−	19.0307i	0.279606	−	0.101768i
$188$	−137.076	−	115.021i	−0.729129	−	0.611812i
$189$		0			0
$190$	−14.1419	+	10.8279i	−0.0744312	+	0.0569889i
$191$	−112.912			−0.591162			−0.295581	−	0.955318i	$-0.595513\pi$
$191$	−112.912			−0.591162			−0.295581	+	0.955318i	$0.595513\pi$
$192$		0			0
$193$	92.6761	+	254.626i	0.480187	+	1.31930i	0.909333	+	0.416068i	$0.136592\pi$
$193$	92.6761	+	254.626i	0.480187	+	1.31930i	−0.429146	+	0.903235i	$0.641186\pi$
$194$	−6.27198	−	35.5702i	−0.0323298	−	0.183352i
$195$		0			0
$196$	−189.608	−	69.0117i	−0.967388	−	0.352100i
$197$	92.8769	+	160.868i	0.471457	+	0.816587i	0.999467	−	0.0326512i	$-0.0103951\pi$
$197$	92.8769	+	160.868i	0.471457	+	0.816587i	−0.528010	+	0.849238i	$0.677062\pi$
$198$		0			0
$199$	174.147	−	146.126i	0.875108	−	0.734303i	−0.0900589	−	0.995936i	$-0.528706\pi$
$199$	174.147	−	146.126i	0.875108	−	0.734303i	0.965167	+	0.261633i	$0.0842611\pi$
$200$	79.2825	+	94.4852i	0.396413	+	0.472426i
$201$		0			0
$202$	−219.631	+	126.804i	−1.08728	+	0.627744i
$203$	55.8775	−	153.522i	0.275259	−	0.756267i
$204$		0			0
$205$	18.2406	−	3.21632i	0.0889787	−	0.0156893i
$206$	−263.258	+	95.8180i	−1.27795	+	0.465136i
$207$		0			0
$208$			19.0100i			0.0913941i
$209$	−315.586	−	201.517i	−1.50998	−	0.964197i
$210$		0			0
$211$	−72.0941	+	85.9184i	−0.341678	+	0.407196i	−0.909332	−	0.416071i	$-0.863407\pi$
$211$	−72.0941	+	85.9184i	−0.341678	+	0.407196i	0.567654	+	0.823267i	$0.307851\pi$
$212$	128.037	+	351.780i	0.603950	+	1.65934i
$213$		0			0
$214$	−23.1654	+	131.378i	−0.108250	+	0.613914i
$215$	6.75374	+	2.45816i	0.0314127	+	0.0114333i
$216$		0			0
$217$	54.1342	+	31.2544i	0.249467	+	0.144030i
$218$	−193.418	+	162.297i	−0.887240	+	0.744483i
$219$		0			0
$220$	16.6915	−	28.9105i	0.0758705	−	0.131412i
$221$	−6.59133	+	3.80551i	−0.0298250	+	0.0172195i
$222$		0			0
$223$	429.451	+	75.7239i	1.92579	+	0.339569i	0.999323	−	0.0368036i	$-0.0117176\pi$
$223$	429.451	+	75.7239i	1.92579	+	0.339569i	0.926468	+	0.376372i	$0.122829\pi$
$224$	147.668	−	26.0378i	0.659230	−	0.116240i
$225$		0			0
$226$	98.5430	+	82.6874i	0.436031	+	0.365873i
$227$			190.582i			0.839569i	0.907624	+	0.419784i	$0.137894\pi$
$227$			190.582i			0.839569i	−0.907624	+	0.419784i	$0.862106\pi$
$228$		0			0
$229$	58.1740			0.254035			0.127017	−	0.991900i	$-0.459460\pi$
$229$	58.1740			0.254035			0.127017	+	0.991900i	$0.459460\pi$
$230$	−1.99747	+	2.38050i	−0.00868466	+	0.0103500i
$231$		0			0
$232$	39.0261	+	221.328i	0.168216	+	0.954000i
$233$	−2.19714	+	12.4606i	−0.00942979	+	0.0534790i	−0.989160	−	0.146845i	$-0.953088\pi$
$233$	−2.19714	+	12.4606i	−0.00942979	+	0.0534790i	0.979730	+	0.200324i	$0.0641994\pi$
$234$		0			0
$235$	4.83571	+	8.37570i	0.0205775	+	0.0356413i
$236$	−492.509	−	284.350i	−2.08690	−	1.20487i
$237$		0			0
$238$	20.2397	+	24.1208i	0.0850409	+	0.101348i
$239$	−16.2594	+	28.1621i	−0.0680310	+	0.117833i	−0.898035	−	0.439925i	$-0.855005\pi$
$239$	−16.2594	+	28.1621i	−0.0680310	+	0.117833i	0.830003	+	0.557758i	$0.188338\pi$
$240$		0			0
$241$	−34.3684	+	94.4264i	−0.142607	+	0.391811i	−0.990348	−	0.138600i	$-0.955740\pi$
$241$	−34.3684	+	94.4264i	−0.142607	+	0.391811i	0.847741	+	0.530410i	$0.177962\pi$
$242$	815.779	+	143.844i	3.37099	+	0.594396i
$243$		0			0
$244$	−204.109	+	74.2896i	−0.836512	+	0.304465i
$245$	8.35425	+	7.01005i	0.0340990	+	0.0286124i
$246$		0			0
$247$	47.2983	+	19.6499i	0.191491	+	0.0795542i
$248$	−85.9886			−0.346728
$249$		0			0
$250$	−16.0016	−	43.9641i	−0.0640065	−	0.175856i
$251$	50.8203	+	288.216i	0.202471	+	1.14827i	0.901370	+	0.433050i	$0.142563\pi$
$251$	50.8203	+	288.216i	0.202471	+	1.14827i	−0.698899	+	0.715221i	$0.746326\pi$
$252$		0			0
$253$	−61.3885	−	22.3436i	−0.242642	−	0.0883146i
$254$	−293.078	−	507.626i	−1.15385	−	1.99853i
$255$		0			0
$256$	−37.0383	+	31.0788i	−0.144681	+	0.121402i
$257$	−73.8389	−	87.9977i	−0.287311	−	0.342404i	0.603013	−	0.797731i	$-0.293967\pi$
$257$	−73.8389	−	87.9977i	−0.287311	−	0.342404i	−0.890324	+	0.455328i	$0.849522\pi$
$258$		0			0
$259$	−156.473	+	90.3400i	−0.604145	+	0.348803i
$260$	−1.56177	+	4.29093i	−0.00600681	+	0.0165036i
$261$		0			0
$262$	−376.848	+	66.4485i	−1.43835	+	0.253620i
$263$	114.104	−	41.5306i	0.433857	−	0.157911i	−0.115853	−	0.993266i	$-0.536960\pi$
$263$	114.104	−	41.5306i	0.433857	−	0.157911i	0.549710	+	0.835355i	$0.314738\pi$
$264$		0			0
$265$		−	20.2333i		−	0.0763522i
$266$	46.0793	−	206.821i	0.173230	−	0.777523i
$267$		0			0
$268$	257.499	−	306.876i	0.960818	−	1.14506i
$269$	26.5773	+	73.0206i	0.0988004	+	0.271452i	0.979239	−	0.202708i	$-0.0649741\pi$
$269$	26.5773	+	73.0206i	0.0988004	+	0.271452i	−0.880439	+	0.474160i	$0.842752\pi$
$270$		0			0
$271$	55.0466	−	312.185i	0.203124	−	1.15197i	−0.697240	−	0.716838i	$-0.745589\pi$
$271$	55.0466	−	312.185i	0.203124	−	1.15197i	0.900364	−	0.435137i	$-0.143300\pi$
$272$	18.7101	+	6.80993i	0.0687873	+	0.0250365i
$273$		0			0
$274$	−208.449	−	120.348i	−0.760761	−	0.439226i
$275$	376.034	−	315.530i	1.36740	−	1.14738i
$276$		0			0
$277$	−37.7290	+	65.3486i	−0.136206	+	0.235916i	−0.926057	−	0.377383i	$-0.876824\pi$
$277$	−37.7290	+	65.3486i	−0.136206	+	0.235916i	0.789852	+	0.613298i	$0.210158\pi$
$278$	612.303	−	353.513i	2.20253	−	1.27163i
$279$		0			0
$280$	5.31153	+	0.936565i	0.0189697	+	0.00334488i
$281$	−214.146	+	37.7597i	−0.762086	+	0.134376i	−0.541166	−	0.840916i	$-0.682017\pi$
$281$	−214.146	+	37.7597i	−0.762086	+	0.134376i	−0.220920	+	0.975292i	$0.570906\pi$
$282$		0			0
$283$	−62.6909	−	52.6039i	−0.221523	−	0.185880i	0.525272	−	0.850935i	$-0.323964\pi$
$283$	−62.6909	−	52.6039i	−0.221523	−	0.185880i	−0.746794	+	0.665055i	$0.768408\pi$
$284$			397.552i			1.39983i
$285$		0			0
$286$	−164.585			−0.575472
$287$	−141.638	+	168.797i	−0.493511	+	0.588144i
$288$		0			0
$289$	−48.8000	−	276.759i	−0.168858	−	0.957643i
$290$	7.38806	−	41.8998i	0.0254761	−	0.144482i
$291$		0			0
$292$	288.741	+	500.114i	0.988840	+	1.71272i
$293$	−228.088	−	131.687i	−0.778459	−	0.449443i	0.0574250	−	0.998350i	$-0.481711\pi$
$293$	−228.088	−	131.687i	−0.778459	−	0.449443i	−0.835884	+	0.548906i	$0.815044\pi$
$294$		0			0
$295$	19.7576	+	23.5461i	0.0669748	+	0.0798174i
$296$	124.274	−	215.249i	0.419844	−	0.727191i
$297$		0			0
$298$	236.374	−	649.433i	0.793202	−	2.17931i
$299$	8.80020	+	1.55171i	0.0294321	+	0.00518968i
$300$		0			0
$301$	−80.3466	+	29.2438i	−0.266932	+	0.0971554i
$302$	350.587	+	294.178i	1.16089	+	0.974098i
$303$		0			0
$304$	−40.1569	−	127.830i	−0.132095	−	0.420492i
$305$	11.7397			0.0384910
$306$		0			0
$307$	−95.6426	−	262.776i	−0.311539	−	0.855947i	−0.992346	−	0.123485i	$-0.960593\pi$
$307$	−95.6426	−	262.776i	−0.311539	−	0.855947i	0.680807	−	0.732463i	$-0.261629\pi$
$308$	68.9634	+	391.111i	0.223907	+	1.26984i
$309$		0			0
$310$	15.2969	+	5.56760i	0.0493447	+	0.0179600i
$311$	75.9361	+	131.525i	0.244167	+	0.422910i	0.961897	−	0.273411i	$-0.0881520\pi$
$311$	75.9361	+	131.525i	0.244167	+	0.422910i	−0.717730	+	0.696322i	$0.754819\pi$
$312$		0			0
$313$	−128.864	+	108.130i	−0.411707	+	0.345463i	−0.824998	−	0.565136i	$-0.808824\pi$
$313$	−128.864	+	108.130i	−0.411707	+	0.345463i	0.413291	+	0.910599i	$0.364379\pi$
$314$	−376.082	−	448.198i	−1.19771	−	1.42738i
$315$		0			0
$316$	404.353	−	233.453i	1.27960	−	0.738777i
$317$	9.89564	−	27.1880i	0.0312165	−	0.0857667i	−0.923105	−	0.384547i	$-0.874358\pi$
$317$	9.89564	−	27.1880i	0.0312165	−	0.0857667i	0.954322	+	0.298780i	$0.0965798\pi$
$318$		0			0
$319$	880.845	−	155.317i	2.76127	−	0.486886i
$320$	28.6734	−	10.4363i	0.0896045	−	0.0326134i
$321$		0			0
$322$		−	36.9689i		−	0.114810i
$323$	36.2836	−	39.5132i	0.112333	−	0.122332i
$324$		0			0
$325$	−43.1599	+	51.4360i	−0.132800	+	0.158265i
$326$	19.5458	+	53.7017i	0.0599565	+	0.164729i
$327$		0			0
$328$	52.6358	−	298.513i	0.160475	−	0.910099i
$329$	−108.118	−	39.3519i	−0.328627	−	0.119610i
$330$		0			0
$331$	86.5069	+	49.9448i	0.261350	+	0.150891i	0.624950	−	0.780664i	$-0.285119\pi$
$331$	86.5069	+	49.9448i	0.261350	+	0.150891i	−0.363600	+	0.931555i	$0.618453\pi$
$332$	−280.334	+	235.228i	−0.844379	+	0.708518i
$333$		0			0
$334$	−265.778	+	460.341i	−0.795743	+	1.37827i
$335$	−18.7509	+	10.8258i	−0.0559728	+	0.0323159i
$336$		0			0
$337$	−25.2851	−	4.45844i	−0.0750299	−	0.0132298i	0.136007	−	0.990708i	$-0.456573\pi$
$337$	−25.2851	−	4.45844i	−0.0750299	−	0.0132298i	−0.211037	+	0.977478i	$0.567684\pi$
$338$	−493.457	+	87.0097i	−1.45993	+	0.257425i
$339$		0			0
$340$	3.66378	+	3.07427i	0.0107758	+	0.00904198i
$341$			342.219i			1.00357i
$342$		0			0
$343$	−306.125			−0.892493
$344$	75.6047	−	90.1021i	0.219781	−	0.261925i
$345$		0			0
$346$	26.0787	+	147.900i	0.0753719	+	0.427456i
$347$	−41.7996	+	237.057i	−0.120460	+	0.683162i	0.863441	+	0.504449i	$0.168304\pi$
$347$	−41.7996	+	237.057i	−0.120460	+	0.683162i	−0.983901	+	0.178713i	$0.942807\pi$
$348$		0			0
$349$	239.280	+	414.445i	0.685615	+	1.18752i	0.973243	+	0.229778i	$0.0738000\pi$
$349$	239.280	+	414.445i	0.685615	+	1.18752i	−0.287628	+	0.957742i	$0.592867\pi$
$350$	240.568	+	138.892i	0.687339	+	0.396835i
$351$		0			0
$352$	527.672	+	628.855i	1.49907	+	1.78652i
$353$	143.458	−	248.476i	0.406396	−	0.703898i	−0.588087	−	0.808798i	$-0.700119\pi$
$353$	143.458	−	248.476i	0.406396	−	0.703898i	0.994483	+	0.104899i	$0.0334520\pi$
$354$		0			0
$355$	7.34899	−	20.1912i	0.0207014	−	0.0568766i
$356$	454.412	+	80.1251i	1.27644	+	0.225070i
$357$		0			0
$358$	−468.686	+	170.588i	−1.30918	+	0.476502i
$359$	333.582	+	279.908i	0.929198	+	0.779689i	0.975673	−	0.219230i	$-0.0703545\pi$
$359$	333.582	+	279.908i	0.929198	+	0.779689i	−0.0464755	+	0.998919i	$0.514799\pi$
$360$		0			0
$361$	−359.559	−	32.2191i	−0.996009	−	0.0892496i
$362$	609.105			1.68261
$363$		0			0
$364$	−18.5798	−	51.0475i	−0.0510433	−	0.140240i
$365$	−5.41990	−	30.7378i	−0.0148490	−	0.0842131i
$366$		0			0
$367$	−166.482	−	60.5943i	−0.453628	−	0.165107i	0.105094	−	0.994462i	$-0.466486\pi$
$367$	−166.482	−	60.5943i	−0.453628	−	0.165107i	−0.558722	+	0.829355i	$0.688708\pi$
$368$	−11.6885	−	20.2451i	−0.0317623	−	0.0550139i
$369$		0			0
$370$	−36.0445	+	30.2449i	−0.0974175	+	0.0817430i
$371$	154.724	+	184.393i	0.417046	+	0.497016i
$372$		0			0
$373$	−527.476	+	304.538i	−1.41414	+	0.816457i	−0.995776	−	0.0918207i	$-0.970731\pi$
$373$	−527.476	+	304.538i	−1.41414	+	0.816457i	−0.418369	+	0.908277i	$0.637398\pi$
$374$	−58.9593	+	161.989i	−0.157645	+	0.433126i
$375$		0			0
$376$	155.871	−	27.4842i	0.414550	−	0.0730963i
$377$	−114.967	+	41.8446i	−0.304953	+	0.110994i
$378$		0			0
$379$			648.960i			1.71229i	0.516732	+	0.856147i	$0.327148\pi$
$379$			648.960i			1.71229i	−0.516732	+	0.856147i	$0.672852\pi$
$380$	1.43768	−	32.1528i	0.00378337	−	0.0846126i
$381$		0			0
$382$	224.856	−	267.973i	0.588629	−	0.701501i
$383$	−207.474	−	570.031i	−0.541708	−	1.48833i	−0.844648	−	0.535321i	$-0.820190\pi$
$383$	−207.474	−	570.031i	−0.541708	−	1.48833i	0.302940	−	0.953010i	$-0.402032\pi$
$384$		0			0
$385$	3.72736	−	21.1389i	0.00968145	−	0.0549062i
$386$	−788.860	−	287.121i	−2.04368	−	0.743838i
$387$		0			0
$388$	56.5231	+	32.6336i	0.145678	+	0.0841073i
$389$	363.699	−	305.179i	0.934958	−	0.784523i	−0.0417431	−	0.999128i	$-0.513291\pi$
$389$	363.699	−	305.179i	0.934958	−	0.784523i	0.976701	+	0.214606i	$0.0688467\pi$
$390$		0			0
$391$	4.67973	−	8.10553i	0.0119686	−	0.0207303i
$392$	154.563	−	89.2372i	0.394294	−	0.227646i
$393$		0			0
$394$	−566.744	−	99.9323i	−1.43844	−	0.253635i
$395$	−24.8522	+	4.38211i	−0.0629169	+	0.0110939i
$396$		0			0
$397$	547.573	+	459.469i	1.37928	+	1.15735i	0.969479	+	0.245176i	$0.0788456\pi$
$397$	547.573	+	459.469i	1.37928	+	1.15735i	0.409799	+	0.912176i	$0.365599\pi$
$398$			704.302i			1.76960i
$399$		0			0
$400$	175.655			0.439139
$401$	281.167	−	335.081i	0.701164	−	0.835614i	−0.291494	−	0.956573i	$-0.594152\pi$
$401$	281.167	−	335.081i	0.701164	−	0.835614i	0.992658	+	0.120958i	$0.0385967\pi$
$402$		0			0
$403$	−8.12857	−	46.0994i	−0.0201702	−	0.114391i
$404$	79.5783	−	451.311i	0.196976	−	1.11711i
$405$		0			0
$406$	253.077	+	438.343i	0.623343	+	1.07966i
$407$	−856.650	−	494.587i	−2.10479	−	1.21520i
$408$		0			0
$409$	−487.244	−	580.674i	−1.19130	−	1.41974i	−0.883589	−	0.468263i	$-0.844880\pi$
$409$	−487.244	−	580.674i	−1.19130	−	1.41974i	−0.307716	−	0.951478i	$-0.599565\pi$
$410$	−28.6917	+	49.6955i	−0.0699798	+	0.121208i
$411$		0			0
$412$	173.144	−	475.709i	0.420253	−	1.15463i
$413$	−360.114	−	63.4978i	−0.871947	−	0.153748i
$414$		0			0
$415$	18.5862	−	6.76481i	0.0447859	−	0.0163007i
$416$	−86.0182	−	72.1778i	−0.206774	−	0.173504i
$417$		0			0
$418$	1106.73	−	347.672i	2.64768	−	0.831750i
$419$	3.36928			0.00804125			0.00402062	−	0.999992i	$-0.498720\pi$
$419$	3.36928			0.00804125			0.00402062	+	0.999992i	$0.498720\pi$
$420$		0			0
$421$	−21.9861	−	60.4063i	−0.0522235	−	0.143483i	0.910838	−	0.412763i	$-0.135436\pi$
$421$	−21.9861	−	60.4063i	−0.0522235	−	0.143483i	−0.963062	+	0.269281i	$0.913214\pi$
$422$	−60.3393	−	342.201i	−0.142984	−	0.810903i
$423$		0			0
$424$	−311.155	−	113.251i	−0.733855	−	0.267101i
$425$	35.1635	+	60.9051i	0.0827378	+	0.143306i
$426$		0			0
$427$	−106.988	+	89.7737i	−0.250558	+	0.210243i
$428$	−154.952	−	184.665i	−0.362038	−	0.431460i
$429$		0			0
$430$	−19.2835	+	11.1334i	−0.0448455	+	0.0258915i
$431$	−117.504	+	322.839i	−0.272631	+	0.749047i	0.725517	+	0.688205i	$0.241601\pi$
$431$	−117.504	+	322.839i	−0.272631	+	0.749047i	−0.998147	+	0.0608424i	$0.980621\pi$
$432$		0			0
$433$	78.6148	−	13.8619i	0.181558	−	0.0320137i	−0.0821296	−	0.996622i	$-0.526172\pi$
$433$	78.6148	−	13.8619i	0.181558	−	0.0320137i	0.263688	+	0.964608i	$0.415061\pi$
$434$	−181.981	+	66.2355i	−0.419310	+	0.152616i
$435$		0			0
$436$		−	456.251i		−	1.04645i
$437$	−62.4535	+	8.15539i	−0.142914	+	0.0186622i
$438$		0			0
$439$	−193.621	+	230.749i	−0.441051	+	0.525624i	−0.940077	−	0.340963i	$-0.889247\pi$
$439$	−193.621	+	230.749i	−0.441051	+	0.525624i	0.499026	+	0.866587i	$0.333691\pi$
$440$	10.0991	+	27.7470i	0.0229525	+	0.0630614i
$441$		0			0
$442$	4.09459	−	23.2216i	0.00926378	−	0.0525375i
$443$	657.518	+	239.317i	1.48424	+	0.540219i	0.951926	−	0.306328i	$-0.0991004\pi$
$443$	657.518	+	239.317i	1.48424	+	0.540219i	0.532314	+	0.846547i	$0.321323\pi$
$444$		0			0
$445$	−21.5979	−	12.4695i	−0.0485346	−	0.0280215i
$446$	−1034.94	+	868.416i	−2.32049	+	1.94712i
$447$		0			0
$448$	−181.504	+	314.375i	−0.405143	+	0.701729i
$449$	−229.255	+	132.361i	−0.510591	+	0.294790i	−0.733077	−	0.680146i	$-0.761916\pi$
$449$	−229.255	+	132.361i	−0.510591	+	0.294790i	0.222485	+	0.974936i	$0.428583\pi$
$450$		0			0
$451$	−1188.03	−	209.481i	−2.63420	−	0.464481i
$452$	−228.920	+	40.3648i	−0.506460	+	0.0893026i
$453$		0			0
$454$	−452.308	−	379.531i	−0.996272	−	0.835972i
$455$			2.93610i			0.00645297i
$456$		0			0
$457$	91.6885			0.200631			0.100316	−	0.994956i	$-0.468015\pi$
$457$	91.6885			0.200631			0.100316	+	0.994956i	$0.468015\pi$
$458$	−115.849	+	138.064i	−0.252946	+	0.301450i
$459$		0			0
$460$	−0.975089	−	5.53000i	−0.00211976	−	0.0120217i
$461$	−109.505	+	621.035i	−0.237538	+	1.34715i	0.599663	+	0.800252i	$0.295301\pi$
$461$	−109.505	+	621.035i	−0.237538	+	1.34715i	−0.837202	+	0.546894i	$0.815810\pi$
$462$		0			0
$463$	−329.338	−	570.431i	−0.711314	−	1.23203i	−0.964364	−	0.264578i	$-0.914767\pi$
$463$	−329.338	−	570.431i	−0.711314	−	1.23203i	0.253050	−	0.967453i	$-0.418566\pi$
$464$	277.183	+	160.032i	0.597378	+	0.344896i
$465$		0			0
$466$	−25.1972	−	30.0289i	−0.0540713	−	0.0644397i
$467$	410.867	−	711.642i	0.879800	−	1.52386i	0.0282409	−	0.999601i	$-0.491009\pi$
$467$	410.867	−	711.642i	0.879800	−	1.52386i	0.851560	−	0.524258i	$-0.175657\pi$
$468$		0			0
$469$	88.0979	−	242.047i	0.187842	−	0.516092i
$470$	−29.5080	−	5.20306i	−0.0627830	−	0.0110703i
$471$		0			0
$472$	472.688	−	172.044i	1.00146	−	0.364500i
$473$	−358.590	−	300.893i	−0.758119	−	0.636137i
$474$		0			0
$475$	181.568	−	437.045i	0.382249	−	0.920095i
$476$	−56.8981			−0.119534
$477$		0			0
$478$	−34.4576	−	94.6713i	−0.0720869	−	0.198057i
$479$	−52.5190	−	297.850i	−0.109643	−	0.621816i	−0.989264	−	0.146141i	$-0.953315\pi$
$479$	−52.5190	−	297.850i	−0.109643	−	0.621816i	0.879621	−	0.475676i	$-0.157796\pi$
$480$		0			0
$481$	127.145	+	46.2769i	0.264334	+	0.0962098i
$482$	−155.659	−	269.610i	−0.322945	−	0.559357i
$483$		0			0
$484$	−1146.66	+	962.164i	−2.36914	+	1.98794i
$485$	−2.26749	−	2.70229i	−0.00467524	−	0.00557173i
$486$		0			0
$487$	570.524	−	329.392i	1.17151	−	0.676370i	0.217472	−	0.976067i	$-0.430219\pi$
$487$	570.524	−	329.392i	1.17151	−	0.676370i	0.954034	+	0.299697i	$0.0968856\pi$
$488$	65.7102	−	180.537i	0.134652	−	0.369954i
$489$		0			0
$490$	−33.2738	+	5.86707i	−0.0679057	+	0.0119736i
$491$	126.665	−	46.1024i	0.257974	−	0.0938949i	−0.209796	−	0.977745i	$-0.567280\pi$
$491$	126.665	−	46.1024i	0.257974	−	0.0938949i	0.467770	+	0.883850i	$0.345058\pi$
$492$		0			0
$493$			128.144i			0.259927i
$494$	−140.826	+	73.1215i	−0.285074	+	0.148019i
$495$		0			0
$496$	−78.7155	+	93.8095i	−0.158701	+	0.189132i
$497$	87.4280	+	240.206i	0.175911	+	0.483313i
$498$		0			0
$499$	−59.5919	+	337.962i	−0.119423	+	0.677279i	0.865043	+	0.501699i	$0.167291\pi$
$499$	−59.5919	+	337.962i	−0.119423	+	0.677279i	−0.984465	+	0.175580i	$0.943820\pi$
$500$	79.4436	+	28.9151i	0.158887	+	0.0578302i
$501$		0			0
$502$	−785.227	−	453.351i	−1.56420	−	0.903089i
$503$	−665.358	+	558.302i	−1.32278	+	1.10994i	−0.337072	+	0.941479i	$0.609436\pi$
$503$	−665.358	+	558.302i	−1.32278	+	1.10994i	−0.985708	+	0.168465i	$0.946119\pi$
$504$		0			0
$505$	−12.3844	+	21.4505i	−0.0245237	+	0.0424762i
$506$	175.279	−	101.197i	0.346401	−	0.199995i
$507$		0			0
$508$	1043.10	+	183.926i	2.05334	+	0.362059i
$509$	751.794	−	132.562i	1.47700	−	0.260435i	0.623623	−	0.781725i	$-0.285660\pi$
$509$	751.794	−	132.562i	1.47700	−	0.260435i	0.853380	+	0.521290i	$0.174549\pi$
$510$		0			0
$511$	284.445	+	238.678i	0.556644	+	0.467080i
$512$			433.436i			0.846555i
$513$		0			0
$514$	355.890			0.692392
$515$	−17.5876	+	20.9601i	−0.0341506	+	0.0406991i
$516$		0			0
$517$	−109.382	−	620.337i	−0.211571	−	1.19988i
$518$	97.2026	−	551.264i	0.187650	−	1.06422i
$519$		0			0
$520$	−2.01948	−	3.49785i	−0.00388362	−	0.00672663i
$521$	−7.23934	−	4.17964i	−0.0138951	−	0.00802233i	0.493036	−	0.870009i	$-0.335887\pi$
$521$	−7.23934	−	4.17964i	−0.0138951	−	0.00802233i	−0.506931	+	0.861986i	$0.669220\pi$
$522$		0			0
$523$	−176.158	−	209.937i	−0.336822	−	0.401409i	0.570874	−	0.821038i	$-0.306605\pi$
$523$	−176.158	−	209.937i	−0.336822	−	0.401409i	−0.907696	+	0.419629i	$0.862160\pi$
$524$	345.737	−	598.833i	0.659803	−	1.14281i
$525$		0			0
$526$	−128.667	+	353.509i	−0.244613	+	0.672070i
$527$	−48.2842	−	8.51381i	−0.0916209	−	0.0161552i
$528$		0			0
$529$	486.771	−	177.170i	0.920173	−	0.334915i
$530$	48.0197	+	40.2933i	0.0906032	+	0.0760251i
$531$		0			0
$532$	232.770	+	304.013i	0.437538	+	0.571453i
$533$	165.011			0.309590
$534$		0			0
$535$	4.45620	+	12.2433i	0.00832934	+	0.0228847i
$536$	61.5296	+	348.951i	0.114794	+	0.651029i
$537$		0			0
$538$	−226.226	−	82.3396i	−0.420495	−	0.153048i
$539$	−355.148	−	615.134i	−0.658901	−	1.14125i
$540$		0			0
$541$	−20.8027	+	17.4555i	−0.0384523	+	0.0322653i	−0.661811	−	0.749670i	$-0.730212\pi$
$541$	−20.8027	+	17.4555i	−0.0384523	+	0.0322653i	0.623359	+	0.781936i	$0.285768\pi$
$542$	631.286	+	752.337i	1.16473	+	1.38808i
$543$		0			0
$544$	−101.854	+	58.8052i	−0.187231	+	0.108098i
$545$	−8.43409	+	23.1725i	−0.0154754	+	0.0425183i
$546$		0			0
$547$	526.779	−	92.8853i	0.963032	−	0.169809i	0.330040	−	0.943967i	$-0.392938\pi$
$547$	526.779	−	92.8853i	0.963032	−	0.169809i	0.632992	+	0.774158i	$0.281827\pi$
$548$	408.709	−	148.758i	0.745820	−	0.271456i
$549$		0			0
$550$			1520.80i			2.76508i
$551$	684.686	−	524.236i	1.24262	−	0.951426i
$552$		0			0
$553$	192.976	−	229.980i	0.348962	−	0.415877i
$554$	−79.9567	−	219.679i	−0.144326	−	0.396533i
$555$		0			0
$556$	−221.854	+	1258.19i	−0.399017	+	2.26294i
$557$	−121.698	−	44.2944i	−0.218488	−	0.0795232i	0.230457	−	0.973083i	$-0.425978\pi$
$557$	−121.698	−	44.2944i	−0.218488	−	0.0795232i	−0.448945	+	0.893559i	$0.648200\pi$
$558$		0			0
$559$	55.4517	+	32.0150i	0.0991980	+	0.0572720i
$560$	5.88401	−	4.93727i	0.0105072	−	0.00881655i
$561$		0			0
$562$	336.842	−	583.428i	0.599363	−	1.03813i
$563$	−380.804	+	219.857i	−0.676384	+	0.390511i	−0.798491	−	0.602006i	$-0.794368\pi$
$563$	−380.804	+	219.857i	−0.676384	+	0.390511i	0.122107	+	0.992517i	$0.461035\pi$
$564$		0			0
$565$	12.3727	+	2.18165i	0.0218987	+	0.00386133i
$566$	249.689	−	44.0270i	0.441147	−	0.0777862i
$567$		0			0
$568$	−269.372	−	226.030i	−0.474247	−	0.397940i
$569$		−	91.6743i		−	0.161115i	−0.996750	−	0.0805574i	$-0.974330\pi$
$569$		−	91.6743i		−	0.161115i	0.996750	−	0.0805574i	$-0.0256700\pi$
$570$		0			0
$571$	966.550			1.69273			0.846366	−	0.532601i	$-0.178786\pi$
$571$	966.550			1.69273			0.846366	+	0.532601i	$0.178786\pi$
$572$	191.169	−	227.827i	0.334212	−	0.398299i
$573$		0			0
$574$	−118.544	−	672.296i	−0.206523	−	1.17125i
$575$	14.3381	−	81.3154i	0.0249358	−	0.141418i
$576$		0			0
$577$	193.473	+	335.104i	0.335308	+	0.580770i	0.983544	−	0.180669i	$-0.0578264\pi$
$577$	193.473	+	335.104i	0.335308	+	0.580770i	−0.648236	+	0.761439i	$0.724493\pi$
$578$	754.012	+	435.329i	1.30452	+	0.753165i
$579$		0			0
$580$	49.4183	+	58.8945i	0.0852040	+	0.101542i
$581$	−117.651	+	203.778i	−0.202498	+	0.350737i
$582$		0			0
$583$	−450.718	+	1238.34i	−0.773102	+	2.12408i
$584$	−503.032	−	88.6981i	−0.861356	−	0.151880i
$585$		0			0
$586$	766.754	−	279.076i	1.30845	−	0.476238i
$587$	300.982	+	252.554i	0.512746	+	0.430245i	0.862094	−	0.506748i	$-0.169152\pi$
$587$	300.982	+	252.554i	0.512746	+	0.430245i	−0.349348	+	0.936993i	$0.613597\pi$
$588$		0			0
$589$	152.040	+	292.818i	0.258133	+	0.497144i
$590$	−95.2277			−0.161403
$591$		0			0
$592$	−121.063	−	332.619i	−0.204499	−	0.561857i
$593$	−171.326	−	971.636i	−0.288913	−	1.63851i	−0.690962	−	0.722891i	$-0.742813\pi$
$593$	−171.326	−	971.636i	−0.288913	−	1.63851i	0.402048	−	0.915618i	$-0.368298\pi$
$594$		0			0
$595$	2.88979	+	1.05180i	0.00485679	+	0.00176773i
$596$	624.423	+	1081.53i	1.04769	+	1.81465i
$597$		0			0
$598$	−21.2077	+	17.7953i	−0.0354643	+	0.0297581i
$599$	224.924	+	268.054i	0.375499	+	0.447503i	0.920388	−	0.391006i	$-0.127873\pi$
$599$	224.924	+	268.054i	0.375499	+	0.447503i	−0.544889	+	0.838508i	$0.683428\pi$
$600$		0			0
$601$	−117.781	+	68.0006i	−0.195974	+	0.113146i	−0.594776	−	0.803891i	$-0.702759\pi$
$601$	−117.781	+	68.0006i	−0.195974	+	0.113146i	0.398802	+	0.917037i	$0.369426\pi$
$602$	90.6006	−	248.923i	0.150499	−	0.413493i
$603$		0			0
$604$	−814.431	+	143.606i	−1.34840	+	0.237758i
$605$	76.0238	−	27.6704i	0.125659	−	0.0457362i
$606$		0			0
$607$			297.039i			0.489355i	0.969604	+	0.244678i	$0.0786821\pi$
$607$			297.039i			0.489355i	−0.969604	+	0.244678i	$0.921318\pi$
$608$	730.886	+	303.643i	1.20211	+	0.499413i
$609$		0			0
$610$	−23.3789	+	27.8619i	−0.0383260	+	0.0456752i
$611$	29.4692	+	80.9659i	0.0482310	+	0.132514i
$612$		0			0
$613$	140.181	−	795.006i	0.228680	−	1.29691i	−0.626843	−	0.779146i	$-0.715653\pi$
$613$	140.181	−	795.006i	0.228680	−	1.29691i	0.855523	−	0.517765i	$-0.173236\pi$
$614$	814.110	+	296.312i	1.32591	+	0.482593i
$615$		0			0
$616$	−304.217	−	175.640i	−0.493860	−	0.285130i
$617$	−142.756	+	119.787i	−0.231372	+	0.194144i	−0.751101	−	0.660187i	$-0.770477\pi$
$617$	−142.756	+	119.787i	−0.231372	+	0.194144i	0.519730	+	0.854331i	$0.326033\pi$
$618$		0			0
$619$	43.2410	−	74.8957i	0.0698563	−	0.120995i	−0.828982	−	0.559276i	$-0.811079\pi$
$619$	43.2410	−	74.8957i	0.0698563	−	0.120995i	0.898838	+	0.438281i	$0.144413\pi$
$620$	−25.4746	+	14.7078i	−0.0410881	+	0.0237222i
$621$		0			0
$622$	−463.369	−	81.7045i	−0.744967	−	0.131358i
$623$	292.183	−	51.5198i	0.468994	−	0.0826963i
$624$		0			0
$625$	473.524	+	397.334i	0.757639	+	0.635734i
$626$		−	521.167i		−	0.832534i
$627$		0			0
$628$	1057.25			1.68351
$629$	91.0940	−	108.562i	0.144824	−	0.172594i
$630$		0			0
$631$	80.5639	+	456.900i	0.127677	+	0.724089i	0.979682	+	0.200557i	$0.0642751\pi$
$631$	80.5639	+	456.900i	0.127677	+	0.724089i	−0.852006	+	0.523533i	$0.824614\pi$
$632$	−71.7143	+	406.712i	−0.113472	+	0.643532i
$633$		0			0
$634$	44.8188	+	77.6284i	0.0706921	+	0.122442i
$635$	−49.5777	−	28.6237i	−0.0780751	−	0.0450767i
$636$		0			0
$637$	62.4520	+	74.4274i	0.0980409	+	0.116841i
$638$	−1385.53	+	2399.81i	−2.17168	+	3.76145i
$639$		0			0
$640$	−15.0894	+	41.4578i	−0.0235772	+	0.0647779i
$641$	−646.115	−	113.928i	−1.00798	−	0.177734i	−0.354804	−	0.934941i	$-0.615453\pi$
$641$	−646.115	−	113.928i	−1.00798	−	0.177734i	−0.653176	+	0.757206i	$0.726564\pi$
$642$		0			0
$643$	−231.285	+	84.1809i	−0.359697	+	0.130919i	−0.515546	−	0.856862i	$-0.672411\pi$
$643$	−231.285	+	84.1809i	−0.359697	+	0.130919i	0.155849	+	0.987781i	$0.450189\pi$
$644$	51.1742	+	42.9402i	0.0794630	+	0.0666774i
$645$		0			0
$646$	21.5201	+	164.799i	0.0333128	+	0.255108i
$647$	−269.364			−0.416328			−0.208164	−	0.978094i	$-0.566749\pi$
$647$	−269.364			−0.416328			−0.208164	+	0.978094i	$0.566749\pi$
$648$		0			0
$649$	−684.704	−	1881.21i	−1.05501	−	2.89863i
$650$	−36.1228	−	204.862i	−0.0555735	−	0.315173i
$651$		0			0
$652$	−97.0395	−	35.3195i	−0.148834	−	0.0541710i
$653$	346.957	+	600.946i	0.531327	+	0.920285i	0.999331	+	0.0365593i	$0.0116398\pi$
$653$	346.957	+	600.946i	0.531327	+	0.920285i	−0.468004	+	0.883726i	$0.655027\pi$
$654$		0			0
$655$	−28.6294	+	24.0229i	−0.0437090	+	0.0366762i
$656$	−277.479	−	330.687i	−0.422986	−	0.504096i
$657$		0			0
$658$	308.704	−	178.230i	0.469155	−	0.270867i
$659$	−13.0692	+	35.9073i	−0.0198319	+	0.0544876i	−0.949214	−	0.314633i	$-0.898119\pi$
$659$	−13.0692	+	35.9073i	−0.0198319	+	0.0544876i	0.929382	+	0.369120i	$0.120341\pi$
$660$		0			0
$661$	391.118	−	68.9646i	0.591706	−	0.104334i	0.130226	−	0.991484i	$-0.458430\pi$
$661$	391.118	−	68.9646i	0.591706	−	0.104334i	0.461480	+	0.887151i	$0.347319\pi$
$662$	−290.806	+	105.845i	−0.439285	+	0.159887i
$663$		0			0
$664$		−	323.688i		−	0.487482i
$665$	−6.20225	−	19.7434i	−0.00932670	−	0.0296893i
$666$		0			0
$667$	96.7083	−	115.253i	0.144990	−	0.172792i
$668$	−328.520	−	902.600i	−0.491796	−	1.35120i
$669$		0			0
$670$	11.6482	−	66.0602i	0.0173854	−	0.0985974i
$671$	−718.506	−	261.515i	−1.07080	−	0.389739i
$672$		0			0
$673$	154.322	+	89.0978i	0.229304	+	0.132389i	0.610251	−	0.792208i	$-0.291069\pi$
$673$	154.322	+	89.0978i	0.229304	+	0.132389i	−0.380947	+	0.924597i	$0.624402\pi$
$674$	60.9347	−	51.1303i	0.0904075	−	0.0758609i
$675$		0			0
$676$	452.718	−	784.131i	0.669701	−	1.15996i
$677$	−410.338	+	236.909i	−0.606112	+	0.349939i	−0.771442	−	0.636299i	$-0.780464\pi$
$677$	−410.338	+	236.909i	−0.606112	+	0.349939i	0.165330	+	0.986238i	$0.447131\pi$
$678$		0			0
$679$	41.3287	+	7.28737i	0.0608671	+	0.0107325i
$680$	−4.16612	+	0.734599i	−0.00612664	+	0.00108029i
$681$		0			0
$682$	−812.187	−	681.506i	−1.19089	−	0.999275i
$683$		−	1189.49i		−	1.74157i	−0.491667	−	0.870783i	$-0.663612\pi$
$683$		−	1189.49i		−	1.74157i	0.491667	−	0.870783i	$-0.336388\pi$
$684$		0			0
$685$	−23.5078			−0.0343179
$686$	609.627	−	726.525i	0.888669	−	1.05907i
$687$		0			0
$688$	−29.0873	−	164.962i	−0.0422780	−	0.239771i
$689$	31.3014	−	177.519i	0.0454302	−	0.257647i
$690$		0			0
$691$	143.081	+	247.823i	0.207063	+	0.358644i	0.950788	−	0.309842i	$-0.100276\pi$
$691$	143.081	+	247.823i	0.207063	+	0.358644i	−0.743725	+	0.668486i	$0.766943\pi$
$692$	−235.021	−	135.689i	−0.339626	−	0.196083i
$693$		0			0
$694$	−479.366	−	571.286i	−0.690729	−	0.823179i
$695$	34.5262	−	59.8011i	0.0496780	−	0.0860448i
$696$		0			0
$697$	59.1120	−	162.409i	0.0848092	−	0.233011i
$698$	−1460.11	−	257.456i	−2.09185	−	0.368849i
$699$		0			0
$700$	−471.688	+	171.680i	−0.673839	+	0.245257i
$701$	811.369	+	680.819i	1.15744	+	0.971211i	0.999867	−	0.0162952i	$-0.00518717\pi$
$701$	811.369	+	680.819i	1.15744	+	0.971211i	0.157577	+	0.987507i	$0.449632\pi$
$702$		0			0
$703$	−952.722	−	42.6000i	−1.35522	−	0.0605975i
$704$	−1987.37			−2.82297
$705$		0			0
$706$	304.021	+	835.291i	0.430625	+	1.18313i
$707$	−51.1682	−	290.189i	−0.0723737	−	0.410451i
$708$		0			0
$709$	379.035	+	137.958i	0.534605	+	0.194580i	0.595194	−	0.803582i	$-0.297075\pi$
$709$	379.035	+	137.958i	0.534605	+	0.194580i	−0.0605881	+	0.998163i	$0.519298\pi$
$710$	33.2846	+	57.6507i	0.0468798	+	0.0811981i
$711$		0			0
$712$	−312.649	+	262.344i	−0.439114	+	0.368460i
$713$	37.0016	+	44.0967i	0.0518956	+	0.0618468i
$714$		0			0
$715$	−13.9208	+	8.03718i	−0.0194696	+	0.0112408i
$716$	308.253	−	846.919i	0.430522	−	1.18285i
$717$		0			0
$718$	−1328.61	+	234.270i	−1.85043	+	0.326281i
$719$	414.223	−	150.765i	0.576109	−	0.209687i	−0.0374997	−	0.999297i	$-0.511939\pi$
$719$	414.223	−	150.765i	0.576109	−	0.209687i	0.613609	+	0.789610i	$0.289717\pi$
$720$		0			0
$721$		−	325.508i		−	0.451467i
$722$	792.503	−	789.178i	1.09765	−	1.09304i
$723$		0			0
$724$	−707.490	+	843.154i	−0.977196	+	1.16458i
$725$	386.652	+	1062.32i	0.533313	+	1.46526i
$726$		0			0
$727$	94.2684	−	534.622i	0.129668	−	0.735382i	−0.848758	−	0.528782i	$-0.822649\pi$
$727$	94.2684	−	534.622i	0.129668	−	0.735382i	0.978426	−	0.206600i	$-0.0662399\pi$
$728$	45.1522	+	16.4341i	0.0620223	+	0.0225743i
$729$		0			0
$730$	83.7432	+	48.3492i	0.114717	+	0.0662317i
$731$	51.3745	−	43.1084i	0.0702798	−	0.0589718i
$732$		0			0
$733$	198.967	−	344.622i	0.271443	−	0.470152i	−0.697789	−	0.716303i	$-0.745833\pi$
$733$	198.967	−	344.622i	0.271443	−	0.470152i	0.969231	+	0.246151i	$0.0791660\pi$
$734$	475.345	−	274.440i	0.647609	−	0.373897i
$735$		0			0
$736$	135.987	+	23.9781i	0.184764	+	0.0325790i
$737$	1388.76	−	244.876i	1.88435	−	0.332261i
$738$		0			0
$739$	344.867	+	289.378i	0.466668	+	0.391581i	0.845577	−	0.533853i	$-0.179256\pi$
$739$	344.867	+	289.378i	0.466668	+	0.391581i	−0.378910	+	0.925434i	$0.623701\pi$
$740$		−	85.0247i		−	0.114898i
$741$		0			0
$742$	−745.742			−1.00504
$743$	−802.892	+	956.850i	−1.08061	+	1.28782i	−0.125329	+	0.992115i	$0.539999\pi$
$743$	−802.892	+	956.850i	−1.08061	+	1.28782i	−0.955279	+	0.295704i	$0.904446\pi$
$744$		0			0
$745$	−11.7209	−	66.4727i	−0.0157328	−	0.0892250i
$746$	327.672	−	1858.32i	0.439239	−	2.49105i
$747$		0			0
$748$	−155.751	−	269.769i	−0.208223	−	0.360653i
$749$	−134.235	−	77.5007i	−0.179219	−	0.103472i
$750$		0			0
$751$	−16.5483	−	19.7215i	−0.0220351	−	0.0262604i	0.754914	−	0.655823i	$-0.227678\pi$
$751$	−16.5483	−	19.7215i	−0.0220351	−	0.0262604i	−0.776949	+	0.629563i	$0.783234\pi$
$752$	112.703	−	195.207i	0.149871	−	0.259584i
$753$		0			0
$754$	129.639	−	356.182i	0.171936	−	0.472389i
$755$	44.0186	+	7.76167i	0.0583028	+	0.0102804i
$756$		0			0
$757$	−1209.21	+	440.117i	−1.59737	+	0.581396i	−0.978887	−	0.204400i	$-0.934476\pi$
$757$	−1209.21	+	440.117i	−1.59737	+	0.581396i	−0.618485	+	0.785796i	$0.712253\pi$
$758$	−1540.17	−	1292.36i	−2.03189	−	1.70496i
$759$		0			0
$760$	20.9686	+	19.2548i	0.0275903	+	0.0253352i
$761$	768.122			1.00936			0.504679	−	0.863307i	$-0.331611\pi$
$761$	768.122			1.00936			0.504679	+	0.863307i	$0.331611\pi$
$762$		0			0
$763$	−100.337	−	275.674i	−0.131503	−	0.361303i
$764$	109.766	+	622.515i	0.143673	+	0.814810i
$765$		0			0
$766$	1766.02	+	642.779i	2.30551	+	0.839138i
$767$	136.918	+	237.149i	0.178511	+	0.309191i
$768$		0			0
$769$	−257.017	+	215.663i	−0.334222	+	0.280446i	−0.794418	−	0.607372i	$-0.792224\pi$
$769$	−257.017	+	215.663i	−0.334222	+	0.280446i	0.460195	+	0.887818i	$0.347779\pi$
$770$	42.7461	+	50.9428i	0.0555144	+	0.0661595i
$771$		0			0
$772$	1313.73	−	758.480i	1.70172	−	0.982488i
$773$	−288.933	+	793.836i	−0.373781	+	1.02695i	0.600106	+	0.799920i	$0.295125\pi$
$773$	−288.933	+	793.836i	−0.373781	+	1.02695i	−0.973887	+	0.227034i	$0.927097\pi$
$774$		0			0
$775$	−425.967	+	75.1094i	−0.549635	+	0.0969154i
$776$	−54.2483	+	19.7448i	−0.0699076	+	0.0254443i
$777$		0			0
$778$			1470.91i			1.89063i
$779$	−1109.60	+	348.572i	−1.42438	+	0.447461i
$780$		0			0
$781$	−899.558	+	1072.05i	−1.15180	+	1.37267i
$782$	9.91746	+	27.2480i	0.0126822	+	0.0348440i
$783$		0			0
$784$	44.1365	−	250.311i	0.0562966	−	0.319274i
$785$	−53.6963	−	19.5439i	−0.0684029	−	0.0248966i
$786$		0			0
$787$	−464.975	−	268.454i	−0.590820	−	0.341110i	0.174602	−	0.984639i	$-0.444136\pi$
$787$	−464.975	−	268.454i	−0.590820	−	0.341110i	−0.765422	+	0.643529i	$0.777470\pi$
$788$	796.618	−	668.442i	1.01094	−	0.848277i
$789$		0			0
$790$	39.0913	−	67.7082i	0.0494827	−	0.0857066i
$791$	−129.440	+	74.7322i	−0.163641	+	0.0944781i
$792$		0			0
$793$	103.000	+	18.1616i	0.129886	+	0.0229024i
$794$	−2180.91	+	384.553i	−2.74674	+	0.484324i
$795$		0			0
$796$	−974.929	−	818.063i	−1.22479	−	1.02772i
$797$		−	17.0032i		−	0.0213340i	−0.999943	−	0.0106670i	$-0.996605\pi$
$797$		−	17.0032i		−	0.0213340i	0.999943	−	0.0106670i	$-0.00339548\pi$
$798$		0			0
$799$	90.2456			0.112948
$800$	−666.936	+	794.823i	−0.833670	+	0.993529i
$801$		0			0
$802$	235.323	+	1334.58i	0.293420	+	1.66407i
$803$	−353.002	+	2001.97i	−0.439604	+	2.49312i
$804$		0			0
$805$	−1.80530	−	3.12687i	−0.00224261	−	0.00388431i
$806$	125.595	+	72.5123i	0.155825	+	0.0899657i
$807$		0			0
$808$	260.553	+	310.516i	0.322467	+	0.384301i
$809$	−78.2195	+	135.480i	−0.0966866	+	0.167466i	−0.910311	−	0.413924i	$-0.864158\pi$
$809$	−78.2195	+	135.480i	−0.0966866	+	0.167466i	0.813625	+	0.581391i	$0.197491\pi$
$810$		0			0
$811$	−353.700	+	971.782i	−0.436128	+	1.19825i	0.505863	+	0.862614i	$0.331174\pi$
$811$	−353.700	+	971.782i	−0.436128	+	1.19825i	−0.941991	+	0.335638i	$0.891048\pi$
$812$	−900.731	−	158.823i	−1.10927	−	0.195595i
$813$		0			0
$814$	2879.76	−	1048.15i	3.53779	−	1.28765i
$815$	4.27562	+	3.58767i	0.00524616	+	0.00440205i
$816$		0			0
$817$	−440.506	−	98.1436i	−0.539175	−	0.120127i
$818$	2348.42			2.87093
$819$		0			0
$820$	−35.4649	−	97.4389i	−0.0432498	−	0.118828i
$821$	152.593	+	865.398i	0.185862	+	1.05408i	0.924842	+	0.380350i	$0.124197\pi$
$821$	152.593	+	865.398i	0.185862	+	1.05408i	−0.738980	+	0.673727i	$0.764692\pi$
$822$		0			0
$823$	−384.829	−	140.066i	−0.467593	−	0.170190i	0.0974687	−	0.995239i	$-0.468925\pi$
$823$	−384.829	−	140.066i	−0.467593	−	0.170190i	−0.565062	+	0.825049i	$0.691148\pi$
$824$	223.888	+	387.786i	0.271709	+	0.470614i
$825$		0			0
$826$	867.842	−	728.206i	1.05066	−	0.881605i
$827$	−283.373	−	337.710i	−0.342651	−	0.408356i	0.567007	−	0.823713i	$-0.308101\pi$
$827$	−283.373	−	337.710i	−0.342651	−	0.408356i	−0.909659	+	0.415357i	$0.863657\pi$
$828$		0			0
$829$	1111.02	−	641.449i	1.34020	−	0.773763i	0.353360	−	0.935487i	$-0.385039\pi$
$829$	1111.02	−	641.449i	1.34020	−	0.773763i	0.986836	+	0.161725i	$0.0517057\pi$
$830$	−20.9582	+	57.5821i	−0.0252508	+	0.0693760i
$831$		0			0
$832$	267.714	−	47.2052i	0.321771	−	0.0567370i
$833$	95.6257	−	34.8049i	0.114797	−	0.0417826i
$834$		0			0
$835$			51.9149i			0.0621735i
$836$	−804.226	+	1935.82i	−0.961993	+	2.31557i
$837$		0			0
$838$	−6.70969	+	7.99630i	−0.00800680	+	0.00954213i
$839$	−289.529	−	795.475i	−0.345089	−	0.948123i	−0.983894	−	0.178755i	$-0.942793\pi$
$839$	−289.529	−	795.475i	−0.345089	−	0.948123i	0.638805	−	0.769369i	$-0.279429\pi$
$840$		0			0
$841$	−211.657	+	1200.37i	−0.251673	+	1.42731i
$842$	187.146	+	68.1155i	0.222263	+	0.0808972i
$843$		0			0
$844$	543.777	+	313.950i	0.644286	+	0.371979i
$845$	−37.4882	+	31.4563i	−0.0443647	+	0.0372264i
$846$		0			0
$847$	−481.235	+	833.523i	−0.568164	+	0.984089i
$848$	−408.388	+	235.783i	−0.481589	+	0.278046i
$849$		0			0
$850$	−214.571	−	37.8347i	−0.252437	−	0.0445115i
$851$	−163.860	+	28.8929i	−0.192550	+	0.0339517i
$852$		0			0
$853$	941.082	+	789.662i	1.10326	+	0.925746i	0.997640	−	0.0686600i	$-0.0218724\pi$
$853$	941.082	+	789.662i	1.10326	+	0.925746i	0.105621	+	0.994406i	$0.466317\pi$
$854$		−	432.692i		−	0.506666i
$855$		0			0
$856$	213.224			0.249093
$857$	290.944	−	346.734i	0.339491	−	0.404590i	−0.569105	−	0.822265i	$-0.692710\pi$
$857$	290.944	−	346.734i	0.339491	−	0.404590i	0.908597	+	0.417675i	$0.137155\pi$
$858$		0			0
$859$	−104.435	−	592.281i	−0.121577	−	0.689500i	−0.983282	−	0.182090i	$-0.941714\pi$
$859$	−104.435	−	592.281i	−0.121577	−	0.689500i	0.861704	−	0.507410i	$-0.169397\pi$
$860$	6.98694	−	39.6249i	0.00812435	−	0.0460755i
$861$		0			0
$862$	−532.192	−	921.784i	−0.617392	−	1.06935i
$863$	912.067	+	526.582i	1.05686	+	0.610176i	0.924561	−	0.381034i	$-0.124432\pi$
$863$	912.067	+	526.582i	1.05686	+	0.610176i	0.132295	+	0.991210i	$0.457765\pi$
$864$		0			0
$865$	9.42814	+	11.2360i	0.0108996	+	0.0129896i
$866$	−123.658	+	214.181i	−0.142792	+	0.247322i
$867$		0			0
$868$	119.688	−	328.841i	0.137890	−	0.378849i
$869$	1618.64	+	285.410i	1.86265	+	0.328435i
$870$		0			0
$871$	−181.260	+	65.9733i	−0.208106	+	0.0757443i
$872$	309.146	+	259.404i	0.354525	+	0.297482i
$873$		0			0
$874$	105.017	−	164.462i	0.120156	−	0.188171i
$875$	54.3599			0.0621256
$876$		0			0
$877$	518.252	+	1423.89i	0.590938	+	1.62359i	0.768769	+	0.639527i	$0.220870\pi$
$877$	518.252	+	1423.89i	0.590938	+	1.62359i	−0.177831	+	0.984061i	$0.556908\pi$
$878$	−162.052	−	919.042i	−0.184569	−	1.04674i
$879$		0			0
$880$	39.5156	+	14.3825i	0.0449040	+	0.0163437i
$881$	−59.9188	−	103.782i	−0.0680123	−	0.117801i	0.830014	−	0.557743i	$-0.188332\pi$
$881$	−59.9188	−	103.782i	−0.0680123	−	0.117801i	−0.898026	+	0.439942i	$0.854999\pi$
$882$		0			0
$883$	557.642	−	467.917i	0.631531	−	0.529917i	−0.269874	−	0.962896i	$-0.586982\pi$
$883$	557.642	−	467.917i	0.631531	−	0.529917i	0.901404	+	0.432979i	$0.142537\pi$
$884$	27.3885	+	32.6403i	0.0309825	+	0.0369235i
$885$		0			0
$886$	−1877.37	+	1083.90i	−2.11893	+	1.22337i
$887$	−25.7297	+	70.6918i	−0.0290076	+	0.0796976i	−0.953351	−	0.301864i	$-0.902391\pi$
$887$	−25.7297	+	70.6918i	−0.0290076	+	0.0796976i	0.924344	+	0.381561i	$0.124613\pi$
$888$		0			0
$889$	670.703	−	118.263i	0.754447	−	0.133029i
$890$	72.6046	−	26.4259i	0.0815782	−	0.0296920i
$891$		0			0
$892$		−	2441.30i		−	2.73688i
$893$	−369.194	−	482.192i	−0.413431	−	0.539969i
$894$		0			0
$895$	−31.3117	+	37.3158i	−0.0349851	+	0.0416936i
$896$	−179.513	−	493.207i	−0.200349	−	0.550455i
$897$		0			0
$898$	142.415	−	807.678i	0.158592	−	0.899419i
$899$	−740.602	−	269.557i	−0.823807	−	0.299841i
$900$		0			0
$901$	−163.506	−	94.4002i	−0.181472	−	0.104773i
$902$	2863.03	−	2402.37i	3.17409	−	2.66338i
$903$		0			0
$904$	102.803	−	178.061i	0.113721	−	0.196970i
$905$	51.5188	−	29.7444i	0.0569269	−	0.0328667i
$906$		0			0
$907$	−417.341	−	73.5884i	−0.460133	−	0.0811339i	−0.0612233	−	0.998124i	$-0.519500\pi$
$907$	−417.341	−	73.5884i	−0.460133	−	0.0811339i	−0.398910	+	0.916990i	$0.630611\pi$
$908$	1050.73	−	185.272i	1.15719	−	0.204044i
$909$		0			0
$910$	−6.96823	−	5.84704i	−0.00765740	−	0.00642532i
$911$		−	20.4534i		−	0.0224516i	−0.999937	−	0.0112258i	$-0.996427\pi$
$911$		−	20.4534i		−	0.0224516i	0.999937	−	0.0112258i	$-0.00357336\pi$
$912$		0			0
$913$	−1288.22			−1.41097
$914$	−182.591	+	217.604i	−0.199772	+	0.238079i
$915$		0			0
$916$	−56.5532	−	320.729i	−0.0617393	−	0.350141i
$917$	77.2060	−	437.857i	0.0841941	−	0.477489i
$918$		0			0
$919$	34.6720	+	60.0537i	0.0377280	+	0.0653468i	0.884273	−	0.466971i	$-0.154655\pi$
$919$	34.6720	+	60.0537i	0.0377280	+	0.0653468i	−0.846545	+	0.532317i	$0.821321\pi$
$920$	4.30140	+	2.48341i	0.00467543	+	0.00269936i
$921$		0			0
$922$	−1255.83	−	1496.64i	−1.36207	−	1.62325i
$923$	95.7131	−	165.780i	0.103698	−	0.179610i
$924$		0			0
$925$	427.607	−	1174.84i	0.462278	−	1.27010i
$926$	2009.65	+	354.356i	2.17025	+	0.382674i
$927$		0			0
$928$	−1776.55	+	646.611i	−1.91438	+	0.696779i
$929$	−941.192	−	789.754i	−1.01312	−	0.850112i	−0.0243761	−	0.999703i	$-0.507760\pi$
$929$	−941.192	−	789.754i	−1.01312	−	0.850112i	−0.988748	+	0.149591i	$0.952204\pi$
$930$		0			0
$931$	−577.171	−	368.552i	−0.619947	−	0.395867i
$932$	70.8347			0.0760029
$933$		0			0
$934$	870.724	+	2392.29i	0.932253	+	2.56134i
$935$	2.92357	+	16.5804i	0.00312681	+	0.0177330i
$936$		0			0
$937$	1143.65	+	416.255i	1.22055	+	0.444242i	0.870350	−	0.492434i	$-0.163893\pi$
$937$	1143.65	+	416.255i	1.22055	+	0.444242i	0.350196	+	0.936676i	$0.386115\pi$
$938$	399.008	+	691.102i	0.425382	+	0.736783i
$939$		0			0
$940$	41.4766	−	34.8030i	0.0441240	−	0.0370244i
$941$	−103.582	−	123.444i	−0.110076	−	0.131184i	0.708193	−	0.706019i	$-0.249511\pi$
$941$	−103.582	−	123.444i	−0.110076	−	0.131184i	−0.818269	+	0.574835i	$0.805066\pi$
$942$		0			0
$943$	−175.733	+	101.459i	−0.186355	+	0.107592i
$944$	245.014	−	673.172i	0.259549	−	0.713106i
$945$		0			0
$946$	1428.21	−	251.833i	1.50974	−	0.266208i
$947$	−1305.76	+	475.259i	−1.37884	+	0.501857i	−0.921827	−	0.387602i	$-0.873303\pi$
$947$	−1305.76	+	475.259i	−1.37884	+	0.501857i	−0.457014	+	0.889459i	$0.651081\pi$
$948$		0			0
$949$		−	278.065i		−	0.293009i
$950$	675.656	+	1301.26i	0.711217	+	1.36975i
$951$		0			0
$952$	32.3497	−	38.5529i	0.0339808	−	0.0404967i
$953$	−290.781	−	798.914i	−0.305121	−	0.838314i	−0.993590	−	0.113048i	$-0.963939\pi$
$953$	−290.781	−	798.914i	−0.305121	−	0.838314i	0.688468	−	0.725267i	$-0.258284\pi$
$954$		0			0
$955$	5.93268	−	33.6459i	0.00621223	−	0.0352313i
$956$	171.072	+	62.2651i	0.178946	+	0.0651309i
$957$		0			0
$958$	811.474	+	468.505i	0.847050	+	0.489045i
$959$	214.234	−	179.764i	0.223393	−	0.187449i
$960$		0			0
$961$	−329.726	+	571.103i	−0.343108	+	0.594280i
$962$	−363.029	+	209.595i	−0.377369	+	0.217874i
$963$		0			0
$964$	554.009	+	97.6868i	0.574699	+	0.101335i
$965$	−80.7436	+	14.2373i	−0.0836722	+	0.0147537i
$966$		0			0
$967$	−953.387	−	799.987i	−0.985923	−	0.827287i	−0.000950336	−	1.00000i	$-0.500303\pi$
$967$	−953.387	−	799.987i	−0.985923	−	0.827287i	−0.984972	+	0.172712i	$0.944747\pi$
$968$		−	1324.00i		−	1.36776i
$969$		0			0
$970$	10.9289			0.0112669
$971$	−180.961	+	215.661i	−0.186366	+	0.222102i	−0.851135	−	0.524947i	$-0.824085\pi$
$971$	−180.961	+	215.661i	−0.186366	+	0.222102i	0.664770	+	0.747048i	$0.268530\pi$
$972$		0			0
$973$	142.650	+	809.009i	0.146608	+	0.831458i
$974$	−354.414	+	2009.98i	−0.363875	+	2.06364i
$975$		0			0
$976$	−136.805	−	236.954i	−0.140169	−	0.242780i
$977$	−694.199	−	400.796i	−0.710542	−	0.410232i	0.100720	−	0.994915i	$-0.467885\pi$
$977$	−694.199	−	400.796i	−0.710542	−	0.410232i	−0.811262	+	0.584683i	$0.801219\pi$
$978$		0			0
$979$	1044.08	+	1244.29i	1.06648	+	1.27098i
$980$	30.5268	−	52.8740i	0.0311498	−	0.0539531i
$981$		0			0
$982$	−142.831	+	392.424i	−0.145449	+	0.399617i
$983$	−245.393	−	43.2695i	−0.249637	−	0.0440178i	0.0474291	−	0.998875i	$-0.484897\pi$
$983$	−245.393	−	43.2695i	−0.249637	−	0.0440178i	−0.297066	+	0.954857i	$0.596008\pi$
$984$		0			0
$985$	−52.8159	+	19.2234i	−0.0536202	+	0.0195161i
$986$	−304.123	−	255.190i	−0.308441	−	0.258813i
$987$		0			0
$988$	62.3546	−	279.871i	0.0631120	−	0.283270i
$989$	−78.7395			−0.0796153
$990$		0			0
$991$	212.972	+	585.137i	0.214907	+	0.590451i	0.999565	−	0.0294767i	$-0.00938408\pi$
$991$	212.972	+	585.137i	0.214907	+	0.590451i	−0.784659	+	0.619928i	$0.787162\pi$
$992$	−125.608	−	712.359i	−0.126621	−	0.718104i
$993$		0			0
$994$	−744.188	−	270.862i	−0.748680	−	0.272497i
$995$	34.3931	+	59.5706i	0.0345660	+	0.0598700i
$996$		0			0
$997$	1198.80	−	1005.91i	1.20241	−	1.00894i	0.202850	−	0.979210i	$-0.434980\pi$
$997$	1198.80	−	1005.91i	1.20241	−	1.00894i	0.999558	−	0.0297299i	$-0.00946472\pi$
$998$	−683.411	−	814.458i	−0.684781	−	0.816090i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.3.ba.c.136.1		18
3.2	odd	2		57.3.k.a.22.3	yes	18
19.13	odd	18	inner	171.3.ba.c.127.1		18
57.32	even	18		57.3.k.a.13.3	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.3.k.a.13.3	✓	18	57.32	even	18
57.3.k.a.22.3	yes	18	3.2	odd	2
171.3.ba.c.127.1		18	19.13	odd	18	inner
171.3.ba.c.136.1		18	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	171.ba (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.99143 + 2.37330i) q^{2} +(-0.972139 - 5.51328i) q^{4} +(-0.0525425 + 0.297983i) q^{5} +(-1.79984 - 3.11741i) q^{7} +(4.28839 + 2.47590i) q^{8} +O(q^{10})\)	\(q+(-1.99143 + 2.37330i) q^{2} +(-0.972139 - 5.51328i) q^{4} +(-0.0525425 + 0.297983i) q^{5} +(-1.79984 - 3.11741i) q^{7} +(4.28839 + 2.47590i) q^{8} +(-0.602568 - 0.718112i) q^{10} +(9.85364 - 17.0670i) q^{11} +(-0.921973 + 2.53310i) q^{13} +(10.9828 + 1.93656i) q^{14} +(6.62675 - 2.41194i) q^{16} +(2.16287 + 1.81486i) q^{17} +(0.848719 - 18.9810i) q^{19} +1.69394 q^{20} +(20.8822 + 57.3733i) q^{22} +(-0.575632 - 3.26457i) q^{23} +(23.4063 + 8.51919i) q^{25} +(-4.17575 - 7.23260i) q^{26} +(-15.4375 + 12.9536i) q^{28} +(29.1735 + 34.7677i) q^{29} +(-15.0386 + 8.68256i) q^{31} +(-14.2469 + 39.1431i) q^{32} +(-8.61441 + 1.51895i) q^{34} +(1.02351 - 0.372526i) q^{35} -50.1934i q^{37} +(43.3574 + 39.8137i) q^{38} +(-0.963100 + 1.14778i) q^{40} +(-20.9363 - 57.5219i) q^{41} +(4.12466 - 23.3921i) q^{43} +(-103.674 - 37.7343i) q^{44} +(8.89413 + 5.13503i) q^{46} +(24.4852 - 20.5455i) q^{47} +(18.0212 - 31.2136i) q^{49} +(-66.8305 + 38.5846i) q^{50} +(14.8620 + 2.62056i) q^{52} +(-65.8534 + 11.6117i) q^{53} +(4.56795 + 3.83296i) q^{55} -17.8249i q^{56} -140.611 q^{58} +(65.2969 - 77.8178i) q^{59} +(-6.73733 - 38.2093i) q^{61} +(9.34213 - 52.9818i) q^{62} +(-50.4224 - 87.3341i) q^{64} +(-0.706379 - 0.407828i) q^{65} +(45.9957 + 54.8156i) q^{67} +(7.90322 - 13.6888i) q^{68} +(-1.15413 + 3.17094i) q^{70} +(-69.9337 - 12.3312i) q^{71} +(-96.9318 + 35.2803i) q^{73} +(119.124 + 99.9566i) q^{74} +(-105.473 + 13.7730i) q^{76} -70.9398 q^{77} +(28.5249 + 78.3715i) q^{79} +(0.370532 + 2.10139i) q^{80} +(178.210 + 64.8630i) q^{82} +(-32.6839 - 56.6101i) q^{83} +(-0.654441 + 0.549142i) q^{85} +(47.3024 + 56.3728i) q^{86} +(84.5124 - 48.7933i) q^{88} +(-28.1898 + 77.4508i) q^{89} +(9.55612 - 1.68500i) q^{91} +(-17.4389 + 6.34724i) q^{92} +99.0256i q^{94} +(5.61144 + 1.25022i) q^{95} +(-7.49384 + 8.93081i) q^{97} +(38.1911 + 104.929i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 9 q^{2} - 3 q^{4} - 9 q^{7} + 27 q^{8}+O(q^{10}) \) 18 * q - 9 * q^2 - 3 * q^4 - 9 * q^7 + 27 * q^8	\( 18 q - 9 q^{2} - 3 q^{4} - 9 q^{7} + 27 q^{8} - 78 q^{10} - 15 q^{11} + 36 q^{13} + 39 q^{14} - 3 q^{16} + 30 q^{17} + 54 q^{19} + 30 q^{20} + 132 q^{22} - 69 q^{23} + 138 q^{25} - 48 q^{26} - 246 q^{28} + 162 q^{29} + 72 q^{31} + 21 q^{32} - 285 q^{34} - 54 q^{35} + 204 q^{38} - 51 q^{40} - 30 q^{41} + 402 q^{43} - 471 q^{44} - 99 q^{46} + 105 q^{47} + 66 q^{49} - 567 q^{50} - 3 q^{52} + 36 q^{53} - 15 q^{55} - 48 q^{58} + 180 q^{59} + 93 q^{61} - 189 q^{62} - 183 q^{64} + 891 q^{65} - 354 q^{67} - 153 q^{68} + 372 q^{70} - 144 q^{71} - 453 q^{73} + 489 q^{74} - 150 q^{76} + 36 q^{77} - 96 q^{79} - 144 q^{80} + 249 q^{82} + 99 q^{83} - 573 q^{85} + 33 q^{86} + 360 q^{88} - 795 q^{89} + 414 q^{91} - 285 q^{92} - 198 q^{95} - 483 q^{97} + 39 q^{98}+O(q^{100}) \) 18 * q - 9 * q^2 - 3 * q^4 - 9 * q^7 + 27 * q^8 - 78 * q^10 - 15 * q^11 + 36 * q^13 + 39 * q^14 - 3 * q^16 + 30 * q^17 + 54 * q^19 + 30 * q^20 + 132 * q^22 - 69 * q^23 + 138 * q^25 - 48 * q^26 - 246 * q^28 + 162 * q^29 + 72 * q^31 + 21 * q^32 - 285 * q^34 - 54 * q^35 + 204 * q^38 - 51 * q^40 - 30 * q^41 + 402 * q^43 - 471 * q^44 - 99 * q^46 + 105 * q^47 + 66 * q^49 - 567 * q^50 - 3 * q^52 + 36 * q^53 - 15 * q^55 - 48 * q^58 + 180 * q^59 + 93 * q^61 - 189 * q^62 - 183 * q^64 + 891 * q^65 - 354 * q^67 - 153 * q^68 + 372 * q^70 - 144 * q^71 - 453 * q^73 + 489 * q^74 - 150 * q^76 + 36 * q^77 - 96 * q^79 - 144 * q^80 + 249 * q^82 + 99 * q^83 - 573 * q^85 + 33 * q^86 + 360 * q^88 - 795 * q^89 + 414 * q^91 - 285 * q^92 - 198 * q^95 - 483 * q^97 + 39 * q^98

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