LMFDB - Embedded newform 261.3.s.a.235.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [261,3,Mod(10,261)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(261, base_ring=CyclotomicField(28))

chi = DirichletCharacter(H, H._module([0, 23]))

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

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

chi := DirichletCharacter("261.10");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	261.s (of order $28$, degree $12$, 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:	$7.11173489980$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{28})$
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			235.4
Character	$\chi$	$=$	261.235
Dual form			261.3.s.a.10.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.24379 + 2.03821i) q^{2} +(4.63233 + 9.61914i) q^{4} +(5.12808 - 1.17045i) q^{5} +(-6.56728 - 3.16264i) q^{7} +(-2.86375 + 25.4165i) q^{8} +O(q^{10})$	\(q+(3.24379 + 2.03821i) q^{2} +(4.63233 + 9.61914i) q^{4} +(5.12808 - 1.17045i) q^{5} +(-6.56728 - 3.16264i) q^{7} +(-2.86375 + 25.4165i) q^{8} +(19.0200 + 6.65539i) q^{10} +(0.480789 + 4.26712i) q^{11} +(2.73044 + 2.17745i) q^{13} +(-14.8568 - 23.6444i) q^{14} +(-34.4669 + 43.2201i) q^{16} +(6.15599 - 6.15599i) q^{17} +(5.18330 - 14.8130i) q^{19} +(35.0137 + 43.9058i) q^{20} +(-7.13770 + 14.8216i) q^{22} +(3.58915 - 15.7251i) q^{23} +(2.40304 - 1.15724i) q^{25} +(4.41886 + 12.6284i) q^{26} -77.8220i q^{28} +(0.661611 - 28.9925i) q^{29} +(-34.6988 - 21.8027i) q^{31} +(-103.327 + 36.1556i) q^{32} +(32.5159 - 7.42154i) q^{34} +(-37.3793 - 8.53157i) q^{35} +(-5.62751 + 49.9455i) q^{37} +(47.0056 - 37.4857i) q^{38} +(15.0632 + 133.690i) q^{40} +(0.940907 + 0.940907i) q^{41} +(-10.2578 - 16.3252i) q^{43} +(-38.8189 + 24.3915i) q^{44} +(43.6934 - 43.6934i) q^{46} +(59.1758 - 6.66751i) q^{47} +(2.57590 + 3.23008i) q^{49} +(10.1536 + 1.14404i) q^{50} +(-8.29691 + 36.3511i) q^{52} +(8.89009 + 38.9500i) q^{53} +(7.45998 + 21.3194i) q^{55} +(99.1903 - 157.860i) q^{56} +(61.2387 - 92.6968i) q^{58} -6.74786 q^{59} +(74.0694 - 25.9180i) q^{61} +(-68.1170 - 141.446i) q^{62} +(-193.284 - 44.1159i) q^{64} +(16.5505 + 7.97030i) q^{65} +(29.6632 - 23.6556i) q^{67} +(87.7319 + 30.6987i) q^{68} +(-103.861 - 103.861i) q^{70} +(-65.3239 - 52.0941i) q^{71} +(-38.0089 + 23.8825i) q^{73} +(-120.054 + 150.543i) q^{74} +(166.499 - 18.7600i) q^{76} +(10.3379 - 29.5439i) q^{77} +(-120.957 - 13.6286i) q^{79} +(-126.162 + 261.978i) q^{80} +(1.13434 + 4.96987i) q^{82} +(-7.07418 + 3.40675i) q^{83} +(24.3631 - 38.7737i) q^{85} -73.8632i q^{86} -109.832 q^{88} +(94.3960 + 59.3130i) q^{89} +(-11.0451 - 22.9353i) q^{91} +(167.888 - 38.3193i) q^{92} +(205.543 + 98.9845i) q^{94} +(9.24248 - 82.0292i) q^{95} +(-13.0335 - 4.56061i) q^{97} +(1.77211 + 15.7279i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8}+O(q^{10}) $ 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8	$ 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8} - 20 q^{10} + 8 q^{11} - 14 q^{13} - 26 q^{14} + 18 q^{16} + 26 q^{17} + 2 q^{19} - 46 q^{20} + 154 q^{22} - 56 q^{23} - 34 q^{25} - 110 q^{26} + 170 q^{29} - 88 q^{31} + 132 q^{32} - 224 q^{34} + 210 q^{35} - 56 q^{37} + 294 q^{38} - 492 q^{40} + 34 q^{41} + 176 q^{43} - 126 q^{44} + 744 q^{46} - 208 q^{47} + 506 q^{49} - 732 q^{50} + 690 q^{52} + 14 q^{53} + 284 q^{55} - 332 q^{56} - 508 q^{58} + 44 q^{59} - 30 q^{61} + 504 q^{62} - 896 q^{64} + 554 q^{65} - 574 q^{67} + 796 q^{68} - 1066 q^{70} - 224 q^{71} - 22 q^{73} - 820 q^{74} + 514 q^{76} - 436 q^{77} + 564 q^{79} - 1162 q^{80} - 18 q^{82} + 126 q^{83} + 38 q^{85} - 384 q^{88} + 160 q^{89} - 434 q^{91} + 1022 q^{92} - 2 q^{94} + 642 q^{95} + 604 q^{97} + 102 q^{98}+O(q^{100}) $ 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8 - 20 * q^10 + 8 * q^11 - 14 * q^13 - 26 * q^14 + 18 * q^16 + 26 * q^17 + 2 * q^19 - 46 * q^20 + 154 * q^22 - 56 * q^23 - 34 * q^25 - 110 * q^26 + 170 * q^29 - 88 * q^31 + 132 * q^32 - 224 * q^34 + 210 * q^35 - 56 * q^37 + 294 * q^38 - 492 * q^40 + 34 * q^41 + 176 * q^43 - 126 * q^44 + 744 * q^46 - 208 * q^47 + 506 * q^49 - 732 * q^50 + 690 * q^52 + 14 * q^53 + 284 * q^55 - 332 * q^56 - 508 * q^58 + 44 * q^59 - 30 * q^61 + 504 * q^62 - 896 * q^64 + 554 * q^65 - 574 * q^67 + 796 * q^68 - 1066 * q^70 - 224 * q^71 - 22 * q^73 - 820 * q^74 + 514 * q^76 - 436 * q^77 + 564 * q^79 - 1162 * q^80 - 18 * q^82 + 126 * q^83 + 38 * q^85 - 384 * q^88 + 160 * q^89 - 434 * q^91 + 1022 * q^92 - 2 * q^94 + 642 * q^95 + 604 * q^97 + 102 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{5}{28}\right)$	$1$

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 $

$2$	3.24379	+	2.03821i	1.62189	+	1.01910i	0.963967	+	0.266021i	$0.0857091\pi$
$2$	3.24379	+	2.03821i	1.62189	+	1.01910i	0.657926	+	0.753082i	$0.271434\pi$
$3$		0			0
$3$		0			0
$4$	4.63233	+	9.61914i	1.15808	+	2.40479i
$5$	5.12808	−	1.17045i	1.02562	−	0.234090i	0.323557	−	0.946209i	$-0.395121\pi$
$5$	5.12808	−	1.17045i	1.02562	−	0.234090i	0.702059	+	0.712119i	$0.252264\pi$
$6$		0			0
$7$	−6.56728	−	3.16264i	−0.938183	−	0.451805i	−0.0986550	−	0.995122i	$-0.531454\pi$
$7$	−6.56728	−	3.16264i	−0.938183	−	0.451805i	−0.839528	+	0.543317i	$0.817168\pi$
$8$	−2.86375	+	25.4165i	−0.357969	+	3.17707i
$9$		0			0
$10$	19.0200	+	6.65539i	1.90200	+	0.665539i
$11$	0.480789	+	4.26712i	0.0437081	+	0.387920i	0.996453	+	0.0841491i	$0.0268172\pi$
$11$	0.480789	+	4.26712i	0.0437081	+	0.387920i	−0.952745	+	0.303771i	$0.901754\pi$
$12$		0			0
$13$	2.73044	+	2.17745i	0.210034	+	0.167496i	0.722856	−	0.690998i	$-0.242829\pi$
$13$	2.73044	+	2.17745i	0.210034	+	0.167496i	−0.512823	+	0.858494i	$0.671400\pi$
$14$	−14.8568	−	23.6444i	−1.06120	−	1.68888i
$15$		0			0
$16$	−34.4669	+	43.2201i	−2.15418	+	2.70126i
$17$	6.15599	−	6.15599i	0.362117	−	0.362117i	−0.502475	−	0.864592i	$-0.667577\pi$
$17$	6.15599	−	6.15599i	0.362117	−	0.362117i	0.864592	+	0.502475i	$0.167577\pi$
$18$		0			0
$19$	5.18330	−	14.8130i	0.272806	−	0.779633i	−0.723224	−	0.690613i	$-0.757341\pi$
$19$	5.18330	−	14.8130i	0.272806	−	0.779633i	0.996030	−	0.0890201i	$-0.0283736\pi$
$20$	35.0137	+	43.9058i	1.75069	+	2.19529i
$21$		0			0
$22$	−7.13770	+	14.8216i	−0.324441	+	0.673708i
$23$	3.58915	−	15.7251i	0.156050	−	0.683699i	−0.835005	−	0.550243i	$-0.814535\pi$
$23$	3.58915	−	15.7251i	0.156050	−	0.683699i	0.991055	−	0.133457i	$-0.0426077\pi$
$24$		0			0
$25$	2.40304	−	1.15724i	0.0961215	−	0.0462897i
$26$	4.41886	+	12.6284i	0.169956	+	0.485707i
$27$		0			0
$28$		−	77.8220i		−	2.77936i
$29$	0.661611	−	28.9925i	0.0228142	−	0.999740i
$29$	0.661611	−	28.9925i	0.0228142	−	0.999740i
$30$		0			0
$31$	−34.6988	−	21.8027i	−1.11931	−	0.703312i	−0.160413	−	0.987050i	$-0.551283\pi$
$31$	−34.6988	−	21.8027i	−1.11931	−	0.703312i	−0.958902	+	0.283738i	$0.908425\pi$
$32$	−103.327	+	36.1556i	−3.22896	+	1.12986i
$33$		0			0
$34$	32.5159	−	7.42154i	0.956350	−	0.218281i
$35$	−37.3793	−	8.53157i	−1.06798	−	0.243759i
$36$		0			0
$37$	−5.62751	+	49.9455i	−0.152095	+	1.34988i	0.653281	+	0.757115i	$0.273392\pi$
$37$	−5.62751	+	49.9455i	−0.152095	+	1.34988i	−0.805376	+	0.592764i	$0.798037\pi$
$38$	47.0056	−	37.4857i	1.23699	−	0.986465i
$39$		0			0
$40$	15.0632	+	133.690i	0.376581	+	3.34225i
$41$	0.940907	+	0.940907i	0.0229490	+	0.0229490i	0.718488	−	0.695539i	$-0.244834\pi$
$41$	0.940907	+	0.940907i	0.0229490	+	0.0229490i	−0.695539	+	0.718488i	$0.744834\pi$
$42$		0			0
$43$	−10.2578	−	16.3252i	−0.238554	−	0.379657i	0.705894	−	0.708318i	$-0.250546\pi$
$43$	−10.2578	−	16.3252i	−0.238554	−	0.379657i	−0.944448	+	0.328661i	$0.893403\pi$
$44$	−38.8189	+	24.3915i	−0.882247	+	0.554352i
$45$		0			0
$46$	43.6934	−	43.6934i	0.949857	−	0.949857i
$47$	59.1758	−	6.66751i	1.25906	−	0.141862i	0.542899	−	0.839798i	$-0.317327\pi$
$47$	59.1758	−	6.66751i	1.25906	−	0.141862i	0.716160	+	0.697936i	$0.245898\pi$
$48$		0			0
$49$	2.57590	+	3.23008i	0.0525694	+	0.0659199i
$50$	10.1536	+	1.14404i	0.203073	+	0.0228808i
$51$		0			0
$52$	−8.29691	+	36.3511i	−0.159556	+	0.699060i
$53$	8.89009	+	38.9500i	0.167738	+	0.734906i	0.986898	+	0.161342i	$0.0515823\pi$
$53$	8.89009	+	38.9500i	0.167738	+	0.734906i	−0.819161	+	0.573564i	$0.805561\pi$
$54$		0			0
$55$	7.45998	+	21.3194i	0.135636	+	0.387625i
$56$	99.1903	−	157.860i	1.77125	−	2.81894i
$57$		0			0
$58$	61.2387	−	92.6968i	1.05584	−	1.59822i
$59$	−6.74786			−0.114371			−0.0571853	−	0.998364i	$-0.518213\pi$
$59$	−6.74786			−0.114371			−0.0571853	+	0.998364i	$0.518213\pi$
$60$		0			0
$61$	74.0694	−	25.9180i	1.21425	−	0.424885i	0.354238	−	0.935155i	$-0.384740\pi$
$61$	74.0694	−	25.9180i	1.21425	−	0.424885i	0.860014	+	0.510270i	$0.170454\pi$
$62$	−68.1170	−	141.446i	−1.09866	−	2.28139i
$63$		0			0
$64$	−193.284	−	44.1159i	−3.02007	−	0.689311i
$65$	16.5505	+	7.97030i	0.254623	+	0.122620i
$66$		0			0
$67$	29.6632	−	23.6556i	0.442735	−	0.353069i	−0.376609	−	0.926373i	$-0.622910\pi$
$67$	29.6632	−	23.6556i	0.442735	−	0.353069i	0.819343	+	0.573303i	$0.194338\pi$
$68$	87.7319	+	30.6987i	1.29018	+	0.451452i
$69$		0			0
$70$	−103.861	−	103.861i	−1.48373	−	1.48373i
$71$	−65.3239	−	52.0941i	−0.920055	−	0.733719i	0.0441092	−	0.999027i	$-0.485955\pi$
$71$	−65.3239	−	52.0941i	−0.920055	−	0.733719i	−0.964164	+	0.265308i	$0.914526\pi$
$72$		0			0
$73$	−38.0089	+	23.8825i	−0.520669	+	0.327158i	−0.766595	−	0.642130i	$-0.778051\pi$
$73$	−38.0089	+	23.8825i	−0.520669	+	0.327158i	0.245926	+	0.969289i	$0.420908\pi$
$74$	−120.054	+	150.543i	−1.62235	+	2.03436i
$75$		0			0
$76$	166.499	−	18.7600i	2.19078	−	0.246842i
$77$	10.3379	−	29.5439i	0.134258	−	0.383687i
$78$		0			0
$79$	−120.957	−	13.6286i	−1.53111	−	0.172514i	−0.694169	−	0.719813i	$-0.744228\pi$
$79$	−120.957	−	13.6286i	−1.53111	−	0.172514i	−0.836938	+	0.547298i	$0.815656\pi$
$80$	−126.162	+	261.978i	−1.57703	+	3.27473i
$81$		0			0
$82$	1.13434	+	4.96987i	0.0138334	+	0.0606081i
$83$	−7.07418	+	3.40675i	−0.0852311	+	0.0410451i	−0.476014	−	0.879438i	$-0.657919\pi$
$83$	−7.07418	+	3.40675i	−0.0852311	+	0.0410451i	0.390783	+	0.920483i	$0.372204\pi$
$84$		0			0
$85$	24.3631	−	38.7737i	0.286625	−	0.456161i
$86$		−	73.8632i		−	0.858875i
$87$		0			0
$88$	−109.832			−1.24809
$89$	94.3960	+	59.3130i	1.06063	+	0.666438i	0.945072	−	0.326863i	$-0.105992\pi$
$89$	94.3960	+	59.3130i	1.06063	+	0.666438i	0.115558	+	0.993301i	$0.463134\pi$
$90$		0			0
$91$	−11.0451	−	22.9353i	−0.121374	−	0.252036i
$92$	167.888	−	38.3193i	1.82487	−	0.416515i
$93$		0			0
$94$	205.543	+	98.9845i	2.18663	+	1.05303i
$95$	9.24248	−	82.0292i	0.0972892	−	0.863466i
$96$		0			0
$97$	−13.0335	−	4.56061i	−0.134366	−	0.0470166i	0.262259	−	0.964998i	$-0.415533\pi$
$97$	−13.0335	−	4.56061i	−0.134366	−	0.0470166i	−0.396624	+	0.917981i	$0.629818\pi$
$98$	1.77211	+	15.7279i	0.0180827	+	0.160489i
$99$		0			0
$100$	22.2633	+	17.7544i	0.222633	+	0.177544i
$101$	63.8690	+	101.647i	0.632366	+	1.00640i	0.997160	+	0.0753164i	$0.0239967\pi$
$101$	63.8690	+	101.647i	0.632366	+	1.00640i	−0.364794	+	0.931088i	$0.618860\pi$
$102$		0			0
$103$	−26.7668	+	33.5645i	−0.259872	+	0.325869i	−0.894601	−	0.446866i	$-0.852540\pi$
$103$	−26.7668	+	33.5645i	−0.259872	+	0.325869i	0.634729	+	0.772734i	$0.281112\pi$
$104$	−63.1625	+	63.1625i	−0.607332	+	0.607332i
$105$		0			0
$106$	−50.5506	+	144.465i	−0.476893	+	1.36288i
$107$	−3.07678	−	3.85816i	−0.0287549	−	0.0360575i	0.767246	−	0.641353i	$-0.221626\pi$
$107$	−3.07678	−	3.85816i	−0.0287549	−	0.0360575i	−0.796001	+	0.605295i	$0.793055\pi$
$108$		0			0
$109$	−91.6589	+	190.332i	−0.840907	+	1.74616i	−0.198024	+	0.980197i	$0.563452\pi$
$109$	−91.6589	+	190.332i	−0.840907	+	1.74616i	−0.642883	+	0.765964i	$0.722262\pi$
$110$	−19.2548	+	84.3606i	−0.175043	+	0.766914i
$111$		0			0
$112$	363.043	−	174.833i	3.24146	−	1.56100i
$113$	−32.9621	−	94.2003i	−0.291700	−	0.833631i	−0.992715	−	0.120484i	$-0.961555\pi$
$113$	−32.9621	−	94.2003i	−0.291700	−	0.833631i	0.701015	−	0.713146i	$-0.252730\pi$
$114$		0			0
$115$		−	84.8404i		−	0.737743i
$116$	281.947	−	127.939i	2.43058	−	1.10292i
$117$		0			0
$118$	−21.8886	−	13.7535i	−0.185497	−	0.116555i
$119$	−59.8973	+	20.9590i	−0.503338	+	0.176126i
$120$		0			0
$121$	99.9891	−	22.8219i	0.826356	−	0.188610i
$122$	293.092	+	66.8963i	2.40239	+	0.548330i
$123$		0			0
$124$	48.9868	−	434.770i	0.395055	−	3.50621i
$125$	−91.8416	+	73.2412i	−0.734733	+	0.585930i
$126$		0			0
$127$	12.5115	+	111.043i	0.0985161	+	0.874355i	0.941637	+	0.336630i	$0.109287\pi$
$127$	12.5115	+	111.043i	0.0985161	+	0.874355i	−0.843121	+	0.537724i	$0.819284\pi$
$128$	−227.428	−	227.428i	−1.77678	−	1.77678i
$129$		0			0
$130$	37.4412	+	59.5873i	0.288009	+	0.458364i
$131$	−162.714	+	102.240i	−1.24209	+	0.780456i	−0.982680	−	0.185311i	$-0.940671\pi$
$131$	−162.714	+	102.240i	−1.24209	+	0.780456i	−0.259409	+	0.965768i	$0.583528\pi$
$132$		0			0
$133$	−80.8884	+	80.8884i	−0.608184	+	0.608184i
$134$	144.436	−	16.2741i	1.07788	−	0.121448i
$135$		0			0
$136$	138.835	+	174.093i	1.02084	+	1.28010i
$137$	−211.263	−	23.8036i	−1.54206	−	0.173749i	−0.700400	−	0.713750i	$-0.746995\pi$
$137$	−211.263	−	23.8036i	−1.54206	−	0.173749i	−0.841664	+	0.540002i	$0.818424\pi$
$138$		0			0
$139$	−44.5635	+	195.245i	−0.320601	+	1.40464i	0.515887	+	0.856657i	$0.327463\pi$
$139$	−44.5635	+	195.245i	−0.320601	+	1.40464i	−0.836487	+	0.547986i	$0.815395\pi$
$140$	−91.0868	−	399.077i	−0.650620	−	2.85055i
$141$		0			0
$142$	−105.718	−	302.126i	−0.744495	−	2.12764i
$143$	−7.97868	+	12.6980i	−0.0557950	+	0.0887972i
$144$		0			0
$145$	−30.5414	−	149.450i	−0.210631	−	1.03069i
$146$	−171.970			−1.17788
$147$		0			0
$148$	−506.502	+	177.233i	−3.42231	+	1.19752i
$149$	113.849	+	236.410i	0.764087	+	1.58664i	0.809110	+	0.587657i	$0.199949\pi$
$149$	113.849	+	236.410i	0.764087	+	1.58664i	−0.0450238	+	0.998986i	$0.514336\pi$
$150$		0			0
$151$	126.068	+	28.7742i	0.834887	+	0.190558i	0.618534	−	0.785758i	$-0.287727\pi$
$151$	126.068	+	28.7742i	0.834887	+	0.190558i	0.216353	+	0.976315i	$0.430584\pi$
$152$	361.652	+	174.162i	2.37929	+	1.14581i
$153$		0			0
$154$	93.7505	−	74.7635i	0.608769	−	0.485477i
$155$	−203.457	−	71.1927i	−1.31263	−	0.459308i
$156$		0			0
$157$	−68.2720	−	68.2720i	−0.434854	−	0.434854i	0.455422	−	0.890276i	$-0.349488\pi$
$157$	−68.2720	−	68.2720i	−0.434854	−	0.434854i	−0.890276	+	0.455422i	$0.849488\pi$
$158$	−364.582	−	290.744i	−2.30748	−	1.84016i
$159$		0			0
$160$	−487.550	+	306.348i	−3.04719	+	1.91467i
$161$	−73.3037	+	91.9199i	−0.455302	+	0.570931i
$162$		0			0
$163$	−91.2607	+	10.2826i	−0.559882	+	0.0630835i	−0.387371	−	0.921924i	$-0.626617\pi$
$163$	−91.2607	+	10.2826i	−0.559882	+	0.0630835i	−0.172511	+	0.985008i	$0.555188\pi$
$164$	−4.69212	+	13.4093i	−0.0286105	+	0.0817641i
$165$		0			0
$166$	−29.8908	−	3.36788i	−0.180065	−	0.0202885i
$167$	49.7396	−	103.285i	0.297842	−	0.618475i	−0.697316	−	0.716764i	$-0.745623\pi$
$167$	49.7396	−	103.285i	0.297842	−	0.618475i	0.995158	+	0.0982887i	$0.0313368\pi$
$168$		0			0
$169$	−34.8920	−	152.872i	−0.206462	−	0.904568i
$170$	158.058	−	76.1165i	0.929751	−	0.447744i
$171$		0			0
$172$	109.517	−	174.296i	0.636728	−	1.01335i
$173$		−	85.8359i		−	0.496161i	−0.968739	−	0.248081i	$-0.920200\pi$
$173$		−	85.8359i		−	0.496161i	0.968739	−	0.248081i	$-0.0797998\pi$
$174$		0			0
$175$	−19.4414			−0.111093
$176$	−200.997	−	126.295i	−1.14203	−	0.717584i
$177$		0			0
$178$	185.309	+	384.797i	1.04106	+	2.16178i
$179$	82.0781	−	18.7338i	0.458537	−	0.104658i	0.0129880	−	0.999916i	$-0.495866\pi$
$179$	82.0781	−	18.7338i	0.458537	−	0.104658i	0.445549	+	0.895258i	$0.353009\pi$
$180$		0			0
$181$	−34.3159	−	16.5257i	−0.189591	−	0.0913021i	0.336680	−	0.941619i	$-0.390696\pi$
$181$	−34.3159	−	16.5257i	−0.189591	−	0.0913021i	−0.526271	+	0.850317i	$0.676410\pi$
$182$	10.9191	−	96.9094i	0.0599949	−	0.532469i
$183$		0			0
$184$	389.399	+	136.256i	2.11630	+	0.740524i
$185$	29.6005	+	262.712i	0.160003	+	1.42006i
$186$		0			0
$187$	29.2281	+	23.3086i	0.156300	+	0.124645i
$188$	338.258	+	538.334i	1.79924	+	2.86348i
$189$		0			0
$190$	197.173	−	247.247i	1.03775	−	1.30130i
$191$	189.648	−	189.648i	0.992922	−	0.992922i	−0.00705344	−	0.999975i	$-0.502245\pi$
$191$	189.648	−	189.648i	0.992922	−	0.992922i	0.999975	+	0.00705344i	$0.00224520\pi$
$192$		0			0
$193$	58.8988	−	168.323i	0.305175	−	0.872141i	−0.684525	−	0.728989i	$-0.739991\pi$
$193$	58.8988	−	168.323i	0.305175	−	0.872141i	0.989701	−	0.143152i	$-0.0457237\pi$
$194$	−32.9823	−	41.3585i	−0.170012	−	0.213188i
$195$		0			0
$196$	−19.1381	+	39.7408i	−0.0976436	+	0.202759i
$197$	32.7329	−	143.412i	0.166157	−	0.727980i	−0.821353	−	0.570421i	$-0.806780\pi$
$197$	32.7329	−	143.412i	0.166157	−	0.727980i	0.987509	−	0.157560i	$-0.0503626\pi$
$198$		0			0
$199$	−192.699	+	92.7988i	−0.968335	+	0.466326i	−0.850078	−	0.526657i	$-0.823445\pi$
$199$	−192.699	+	92.7988i	−0.968335	+	0.466326i	−0.118257	+	0.992983i	$0.537731\pi$
$200$	22.5314	+	64.3909i	0.112657	+	0.321955i
$201$		0			0
$202$			459.899i			2.27673i
$203$	−96.0375	+	188.309i	−0.473091	+	0.927631i
$204$		0			0
$205$	5.92633	+	3.72376i	0.0289089	+	0.0181647i
$206$	−155.237	+	54.3198i	−0.753578	+	0.263688i
$207$		0			0
$208$	−188.220	+	42.9599i	−0.904901	+	0.206538i
$209$	65.7011	+	14.9958i	0.314359	+	0.0717504i
$210$		0			0
$211$	−1.09661	+	9.73273i	−0.00519723	+	0.0461267i	−0.996043	−	0.0888710i	$-0.971674\pi$
$211$	−1.09661	+	9.73273i	−0.00519723	+	0.0461267i	0.990846	+	0.134998i	$0.0431027\pi$
$212$	−333.484	+	265.945i	−1.57304	+	1.25446i
$213$		0			0
$214$	−2.11669	−	18.7861i	−0.00989107	−	0.0877857i
$215$	−71.7109	−	71.7109i	−0.333539	−	0.333539i
$216$		0			0
$217$	158.923	+	252.924i	0.732362	+	1.16555i
$218$	−685.257	+	430.576i	−3.14338	+	1.97512i
$219$		0			0
$220$	−170.517	+	170.517i	−0.775078	+	0.775078i
$221$	30.2129	−	3.40418i	0.136710	−	0.0154035i
$222$		0			0
$223$	−200.825	−	251.827i	−0.900562	−	1.12927i	−0.991066	−	0.133373i	$-0.957419\pi$
$223$	−200.825	−	251.827i	−0.900562	−	1.12927i	0.0905034	−	0.995896i	$-0.471152\pi$
$224$	792.923	+	89.3410i	3.53984	+	0.398844i
$225$		0			0
$226$	85.0776	−	372.749i	0.376449	−	1.64933i
$227$	57.8450	+	253.436i	0.254824	+	1.11646i	0.926703	+	0.375796i	$0.122630\pi$
$227$	57.8450	+	253.436i	0.254824	+	1.11646i	−0.671879	+	0.740661i	$0.734512\pi$
$228$		0			0
$229$	96.5555	+	275.940i	0.421640	+	1.20498i	0.937403	+	0.348246i	$0.113223\pi$
$229$	96.5555	+	275.940i	0.421640	+	1.20498i	−0.515764	+	0.856731i	$0.672492\pi$
$230$	172.922	−	275.204i	0.751836	−	1.19654i
$231$		0			0
$232$	734.993	+	99.8431i	3.16807	+	0.430358i
$233$	8.24553			0.0353885			0.0176943	−	0.999843i	$-0.494367\pi$
$233$	8.24553			0.0353885			0.0176943	+	0.999843i	$0.494367\pi$
$234$		0			0
$235$	295.654	−	103.454i	1.25810	−	0.440229i
$236$	−31.2584	−	64.9086i	−0.132451	−	0.275037i
$237$		0			0
$238$	−237.013	−	54.0966i	−0.995851	−	0.227297i
$239$	144.107	+	69.3984i	0.602959	+	0.290370i	0.710352	−	0.703847i	$-0.248536\pi$
$239$	144.107	+	69.3984i	0.602959	+	0.290370i	−0.107392	+	0.994217i	$0.534250\pi$
$240$		0			0
$241$	−85.1309	+	67.8896i	−0.353240	+	0.281700i	−0.783992	−	0.620771i	$-0.786820\pi$
$241$	−85.1309	+	67.8896i	−0.353240	+	0.281700i	0.430752	+	0.902470i	$0.358248\pi$
$242$	370.859	+	129.769i	1.53248	+	0.536236i
$243$		0			0
$244$	592.423	+	592.423i	2.42796	+	2.42796i
$245$	16.9901	+	13.5491i	0.0693472	+	0.0553026i
$246$		0			0
$247$	46.4073	−	29.1597i	0.187884	−	0.118055i
$248$	653.517	−	819.484i	2.63515	−	3.30437i
$249$		0			0
$250$	−447.195	+	50.3868i	−1.78878	+	0.201547i
$251$	−3.89158	+	11.1215i	−0.0155043	+	0.0443088i	−0.951375	−	0.308034i	$-0.900329\pi$
$251$	−3.89158	+	11.1215i	−0.0155043	+	0.0443088i	0.935871	+	0.352342i	$0.114615\pi$
$252$		0			0
$253$	68.8265	+	7.75488i	0.272041	+	0.0306517i
$254$	−185.744	+	385.701i	−0.731275	+	1.51851i
$255$		0			0
$256$	−97.7195	−	428.137i	−0.381717	−	1.67241i
$257$	−63.5682	+	30.6128i	−0.247347	+	0.119116i	−0.553450	−	0.832882i	$-0.686689\pi$
$257$	−63.5682	+	30.6128i	−0.247347	+	0.119116i	0.306103	+	0.951998i	$0.400975\pi$
$258$		0			0
$259$	194.917	−	310.209i	0.752575	−	1.19772i
$260$			196.123i			0.754318i
$261$		0			0
$262$	−736.194			−2.80990
$263$	50.8493	+	31.9507i	0.193343	+	0.121486i	0.625225	−	0.780445i	$-0.285007\pi$
$263$	50.8493	+	31.9507i	0.193343	+	0.121486i	−0.431881	+	0.901930i	$0.642150\pi$
$264$		0			0
$265$	91.1782	+	189.333i	0.344069	+	0.714466i
$266$	−427.252	+	97.5175i	−1.60621	+	0.366607i
$267$		0			0
$268$	364.957	+	175.754i	1.36178	+	0.655798i
$269$	18.2957	−	162.379i	0.0680138	−	0.603640i	−0.912761	−	0.408495i	$-0.866054\pi$
$269$	18.2957	−	162.379i	0.0680138	−	0.603640i	0.980774	−	0.195145i	$-0.0625176\pi$
$270$		0			0
$271$	−198.079	−	69.3110i	−0.730920	−	0.255760i	−0.0609426	−	0.998141i	$-0.519411\pi$
$271$	−198.079	−	69.3110i	−0.730920	−	0.255760i	−0.669978	+	0.742381i	$0.733696\pi$
$272$	53.8848	+	478.241i	0.198106	+	1.75824i
$273$		0			0
$274$	−636.775	−	507.811i	−2.32400	−	1.85332i
$275$	6.09344	+	9.69766i	0.0221580	+	0.0352642i
$276$		0			0
$277$	35.9969	−	45.1387i	0.129953	−	0.162956i	−0.712598	−	0.701573i	$-0.752482\pi$
$277$	35.9969	−	45.1387i	0.129953	−	0.162956i	0.842551	+	0.538617i	$0.181053\pi$
$278$	−542.505	+	542.505i	−1.95146	+	1.95146i
$279$		0			0
$280$	323.888	−	925.618i	1.15674	−	3.30578i
$281$	−176.539	−	221.372i	−0.628251	−	0.787802i	0.361228	−	0.932478i	$-0.382358\pi$
$281$	−176.539	−	221.372i	−0.628251	−	0.787802i	−0.989479	+	0.144675i	$0.953786\pi$
$282$		0			0
$283$	96.2836	−	199.935i	0.340225	−	0.706484i	−0.658721	−	0.752387i	$-0.728902\pi$
$283$	96.2836	−	199.935i	0.340225	−	0.706484i	0.998946	+	0.0459032i	$0.0146166\pi$
$284$	198.498	−	869.677i	0.698937	−	3.06224i
$285$		0			0
$286$	−51.7623	+	24.9274i	−0.180987	+	0.0871588i
$287$	−3.20345	−	9.15495i	−0.0111619	−	0.0318988i
$288$		0			0
$289$			213.208i			0.737742i
$290$	205.540	−	547.034i	0.708759	−	1.88632i
$291$		0			0
$292$	−405.799	−	254.981i	−1.38972	−	0.873221i
$293$	−23.2034	+	8.11923i	−0.0791926	+	0.0277107i	−0.369585	−	0.929197i	$-0.620500\pi$
$293$	−23.2034	+	8.11923i	−0.0791926	+	0.0277107i	0.290392	+	0.956908i	$0.406214\pi$
$294$		0			0
$295$	−34.6036	+	7.89804i	−0.117300	+	0.0267730i
$296$	−1253.33	−	286.064i	−4.23421	−	0.966431i
$297$		0			0
$298$	−112.550	+	998.910i	−0.377685	+	3.35205i
$299$	44.0406	−	35.1212i	0.147293	−	0.117462i
$300$		0			0
$301$	15.7353	+	139.654i	0.0522766	+	0.463968i
$302$	350.290	+	350.290i	1.15990	+	1.15990i
$303$		0			0
$304$	461.569	+	734.583i	1.51832	+	2.41639i
$305$	349.498	−	219.604i	1.14590	−	0.720014i
$306$		0			0
$307$	−96.2745	+	96.2745i	−0.313598	+	0.313598i	−0.846302	−	0.532704i	$-0.821176\pi$
$307$	−96.2745	+	96.2745i	−0.313598	+	0.313598i	0.532704	+	0.846302i	$0.321176\pi$
$308$	332.076	−	37.4160i	1.07817	−	0.121480i
$309$		0			0
$310$	−514.866	−	645.621i	−1.66086	−	2.08265i
$311$	305.576	+	34.4302i	0.982561	+	0.110708i	0.588604	−	0.808421i	$-0.299678\pi$
$311$	305.576	+	34.4302i	0.982561	+	0.110708i	0.393956	+	0.919129i	$0.371106\pi$
$312$		0			0
$313$	77.7372	−	340.589i	0.248362	−	1.08814i	−0.684813	−	0.728719i	$-0.740116\pi$
$313$	77.7372	−	340.589i	0.248362	−	1.08814i	0.933174	−	0.359424i	$-0.117027\pi$
$314$	−82.3074	−	360.612i	−0.262126	−	1.14845i
$315$		0			0
$316$	−429.219	−	1226.64i	−1.35829	−	3.88177i
$317$	158.784	−	252.704i	0.500896	−	0.797172i	−0.496593	−	0.867983i	$-0.665416\pi$
$317$	158.784	−	252.704i	0.500896	−	0.797172i	0.997490	+	0.0708112i	$0.0225588\pi$
$318$		0			0
$319$	124.032	−	11.1161i	0.388816	−	0.0348466i
$320$	−1042.81			−3.25879
$321$		0			0
$322$	−425.133	+	148.761i	−1.32029	+	0.461989i
$323$	−59.2805	−	123.097i	−0.183531	−	0.381106i
$324$		0			0
$325$	9.08118	+	2.07272i	0.0279421	+	0.00637760i
$326$	−316.988	−	152.654i	−0.972357	−	0.468262i
$327$		0			0
$328$	−26.6091	+	21.2201i	−0.0811254	+	0.0646953i
$329$	−409.711	−	143.364i	−1.24532	−	0.435757i
$330$		0			0
$331$	−26.9231	−	26.9231i	−0.0813386	−	0.0813386i	0.665267	−	0.746606i	$-0.268318\pi$
$331$	−26.9231	−	26.9231i	−0.0813386	−	0.0813386i	−0.746606	+	0.665267i	$0.768318\pi$
$332$	−65.5400	−	52.2664i	−0.197410	−	0.157429i
$333$		0			0
$334$	371.862	−	233.656i	1.11336	−	0.699569i
$335$	124.428	−	156.027i	0.371426	−	0.465753i
$336$		0			0
$337$	68.6759	−	7.73791i	0.203786	−	0.0229612i	−0.00948132	−	0.999955i	$-0.503018\pi$
$337$	68.6759	−	7.73791i	0.203786	−	0.0229612i	0.213267	+	0.976994i	$0.431589\pi$
$338$	198.402	−	567.002i	0.586989	−	1.67752i
$339$		0			0
$340$	485.828	+	54.7397i	1.42891	+	0.160999i
$341$	76.3519	−	158.546i	0.223906	−	0.464945i
$342$		0			0
$343$	72.7761	+	318.853i	0.212175	+	0.929601i
$344$	444.307	−	213.967i	1.29159	−	0.621997i
$345$		0			0
$346$	174.951	−	278.433i	0.505639	−	0.804720i
$347$			255.048i			0.735009i	0.930022	+	0.367505i	$0.119788\pi$
$347$			255.048i			0.735009i	−0.930022	+	0.367505i	$0.880212\pi$
$348$		0			0
$349$	402.926			1.15451			0.577257	−	0.816562i	$-0.304123\pi$
$349$	402.926			1.15451			0.577257	+	0.816562i	$0.304123\pi$
$350$	−63.0636	−	39.6255i	−0.180182	−	0.113216i
$351$		0			0
$352$	−203.959	−	423.525i	−0.579428	−	1.20320i
$353$	630.205	−	143.840i	1.78528	−	0.407479i	0.803167	−	0.595754i	$-0.203147\pi$
$353$	630.205	−	143.840i	1.78528	−	0.407479i	0.982116	+	0.188274i	$0.0602894\pi$
$354$		0			0
$355$	−395.960	−	190.684i	−1.11538	−	0.537138i
$356$	−133.266	+	1182.77i	−0.374342	+	3.32238i
$357$		0			0
$358$	304.427	+	106.524i	0.850356	+	0.297552i
$359$	1.72924	+	15.3474i	0.00481682	+	0.0427505i	0.995891	−	0.0905633i	$-0.0288668\pi$
$359$	1.72924	+	15.3474i	0.00481682	+	0.0427505i	−0.991074	+	0.133314i	$0.957438\pi$
$360$		0			0
$361$	89.6819	+	71.5189i	0.248426	+	0.198113i
$362$	−77.6308	−	123.549i	−0.214450	−	0.341295i
$363$		0			0
$364$	169.454	−	212.488i	0.465532	−	0.583758i
$365$	−166.959	+	166.959i	−0.457422	+	0.457422i
$366$		0			0
$367$	218.637	−	624.829i	0.595741	−	1.70253i	−0.109883	−	0.993945i	$-0.535048\pi$
$367$	218.637	−	624.829i	0.595741	−	1.70253i	0.705624	−	0.708586i	$-0.250667\pi$
$368$	555.934	+	697.119i	1.51069	+	1.89434i
$369$		0			0
$370$	−439.443	+	912.512i	−1.18768	+	2.46625i
$371$	64.8010	−	283.912i	0.174666	−	0.765261i
$372$		0			0
$373$	398.567	−	191.940i	1.06854	−	0.514584i	0.184907	−	0.982756i	$-0.440802\pi$
$373$	398.567	−	191.940i	1.06854	−	0.514584i	0.883637	+	0.468173i	$0.155087\pi$
$374$	47.3019	+	135.181i	0.126476	+	0.361447i
$375$		0			0
$376$			1523.14i			4.05090i
$377$	64.9361	−	77.7214i	0.172244	−	0.206158i
$378$		0			0
$379$	−78.5862	−	49.3790i	−0.207352	−	0.130288i	0.424353	−	0.905497i	$-0.360502\pi$
$379$	−78.5862	−	49.3790i	−0.207352	−	0.130288i	−0.631705	+	0.775209i	$0.717644\pi$
$380$	831.865	−	291.082i	2.18912	−	0.766006i
$381$		0			0
$382$	1001.72	−	228.636i	2.62230	−	0.598524i
$383$	−52.6752	−	12.0228i	−0.137533	−	0.0313911i	0.153200	−	0.988195i	$-0.451042\pi$
$383$	−52.6752	−	12.0228i	−0.137533	−	0.0313911i	−0.290733	+	0.956804i	$0.593899\pi$
$384$		0			0
$385$	18.4337	−	163.604i	0.0478798	−	0.424945i
$386$	534.133	−	425.957i	1.38376	−	1.10351i
$387$		0			0
$388$	−16.5062	−	146.497i	−0.0425419	−	0.377570i
$389$	220.798	+	220.798i	0.567605	+	0.567605i	0.931457	−	0.363852i	$-0.118539\pi$
$389$	220.798	+	220.798i	0.567605	+	0.567605i	−0.363852	+	0.931457i	$0.618539\pi$
$390$		0			0
$391$	−74.7087	−	118.898i	−0.191071	−	0.304088i
$392$	−89.4741	+	56.2203i	−0.228250	+	0.143419i
$393$		0			0
$394$	398.482	−	398.482i	1.01138	−	1.01138i
$395$	−636.231	+	71.6860i	−1.61071	+	0.181484i
$396$		0			0
$397$	487.205	+	610.936i	1.22722	+	1.53888i	0.752251	+	0.658876i	$0.228968\pi$
$397$	487.205	+	610.936i	1.22722	+	1.53888i	0.474965	+	0.880005i	$0.342461\pi$
$398$	−814.217	−	91.7402i	−2.04577	−	0.230503i
$399$		0			0
$400$	−32.8091	+	143.746i	−0.0820228	+	0.359366i
$401$	28.0626	+	122.950i	0.0699815	+	0.306609i	0.997790	−	0.0664482i	$-0.0211667\pi$
$401$	28.0626	+	122.950i	0.0699815	+	0.306609i	−0.927808	+	0.373057i	$0.878310\pi$
$402$		0			0
$403$	−47.2685	−	135.086i	−0.117292	−	0.335200i
$404$	−681.893	+	1085.23i	−1.68785	+	2.68621i
$405$		0			0
$406$	−695.338	+	415.090i	−1.71266	+	1.02239i
$407$	−215.829			−0.530293
$408$		0			0
$409$	−115.947	+	40.5715i	−0.283488	+	0.0991968i	−0.468278	−	0.883581i	$-0.655125\pi$
$409$	−115.947	+	40.5715i	−0.283488	+	0.0991968i	0.184790	+	0.982778i	$0.440840\pi$
$410$	11.6340	+	24.1582i	0.0283755	+	0.0589224i
$411$		0			0
$412$	−446.854	−	101.992i	−1.08460	−	0.247552i
$413$	44.3151	+	21.3410i	0.107300	+	0.0516732i
$414$		0			0
$415$	−32.2896	+	25.7501i	−0.0778061	+	0.0620483i
$416$	−360.854	−	126.268i	−0.867439	−	0.303530i
$417$		0			0
$418$	182.556	+	182.556i	0.436736	+	0.436736i
$419$	209.191	+	166.825i	0.499263	+	0.398149i	0.840486	−	0.541833i	$-0.182270\pi$
$419$	209.191	+	166.825i	0.499263	+	0.398149i	−0.341223	+	0.939983i	$0.610841\pi$
$420$		0			0
$421$	−301.780	+	189.621i	−0.716818	+	0.450407i	−0.840427	−	0.541924i	$-0.817696\pi$
$421$	−301.780	+	189.621i	−0.716818	+	0.450407i	0.123609	+	0.992331i	$0.460553\pi$
$422$	−23.3945	+	29.3358i	−0.0554372	+	0.0695160i
$423$		0			0
$424$	−1015.43	+	114.412i	−2.39489	+	0.269839i
$425$	7.66911	−	21.9170i	0.0180450	−	0.0515695i
$426$		0			0
$427$	−568.404	−	64.0437i	−1.33116	−	0.149985i
$428$	22.8595	−	47.4682i	0.0534100	−	0.110907i
$429$		0			0
$430$	−86.4533	−	378.777i	−0.201054	−	0.880876i
$431$	−124.980	+	60.1870i	−0.289976	+	0.139645i	−0.573217	−	0.819404i	$-0.694305\pi$
$431$	−124.980	+	60.1870i	−0.289976	+	0.139645i	0.283241	+	0.959049i	$0.408590\pi$
$432$		0			0
$433$	107.372	−	170.882i	0.247973	−	0.394647i	−0.699424	−	0.714707i	$-0.746560\pi$
$433$	107.372	−	170.882i	0.247973	−	0.394647i	0.947397	+	0.320060i	$0.103703\pi$
$434$			1144.35i			2.63675i
$435$		0			0
$436$	−2255.42			−5.17298
$437$	−214.333	−	134.674i	−0.490464	−	0.308179i
$438$		0			0
$439$	70.9416	+	147.312i	0.161598	+	0.335562i	0.966008	−	0.258513i	$-0.0832325\pi$
$439$	70.9416	+	147.312i	0.161598	+	0.335562i	−0.804410	+	0.594075i	$0.797518\pi$
$440$	−563.228	+	128.553i	−1.28006	+	0.292166i
$441$		0			0
$442$	104.943	+	50.5377i	0.237427	+	0.114339i
$443$	71.6573	−	635.976i	0.161755	−	1.43561i	−0.606304	−	0.795233i	$-0.707349\pi$
$443$	71.6573	−	635.976i	0.161755	−	1.43561i	0.768059	−	0.640379i	$-0.221223\pi$
$444$		0			0
$445$	553.493	+	193.676i	1.24381	+	0.435226i
$446$	−138.159	−	1226.20i	−0.309774	−	2.74932i
$447$		0			0
$448$	1129.83	+	901.009i	2.52194	+	2.01118i
$449$	149.510	+	237.943i	0.332984	+	0.529941i	0.970689	−	0.240340i	$-0.0772589\pi$
$449$	149.510	+	237.943i	0.332984	+	0.529941i	−0.637705	+	0.770281i	$0.720116\pi$
$450$		0			0
$451$	−3.56259	+	4.46734i	−0.00789931	+	0.00990542i
$452$	753.434	−	753.434i	1.66689	−	1.66689i
$453$		0			0
$454$	−328.917	+	939.992i	−0.724487	+	2.07047i
$455$	−83.4846	−	104.686i	−0.183483	−	0.230080i
$456$		0			0
$457$	209.594	−	435.225i	0.458629	−	0.952353i	−0.535539	−	0.844511i	$-0.679891\pi$
$457$	209.594	−	435.225i	0.458629	−	0.952353i	0.994168	−	0.107843i	$-0.0343943\pi$
$458$	−249.217	+	1091.89i	−0.544141	+	2.38404i
$459$		0			0
$460$	816.092	−	393.009i	1.77411	−	0.854368i
$461$	107.774	+	308.000i	0.233783	+	0.668114i	0.999684	+	0.0251545i	$0.00800777\pi$
$461$	107.774	+	308.000i	0.233783	+	0.668114i	−0.765901	+	0.642959i	$0.777707\pi$
$462$		0			0
$463$		−	332.607i		−	0.718374i	−0.933266	−	0.359187i	$-0.883054\pi$
$463$		−	332.607i		−	0.718374i	0.933266	−	0.359187i	$-0.116946\pi$
$464$	1230.25	+	1027.88i	2.65141	+	2.21525i
$465$		0			0
$466$	26.7467	+	16.8061i	0.0573965	+	0.0360646i
$467$	182.053	−	63.7030i	0.389835	−	0.136409i	−0.128243	−	0.991743i	$-0.540934\pi$
$467$	182.053	−	63.7030i	0.389835	−	0.136409i	0.518077	+	0.855334i	$0.326648\pi$
$468$		0			0
$469$	−269.621	+	61.5392i	−0.574884	+	0.131214i
$470$	1169.90	+	267.022i	2.48915	+	0.568132i
$471$		0			0
$472$	19.3242	−	171.507i	0.0409411	−	0.363363i
$473$	64.7299	−	51.6204i	0.136850	−	0.109134i
$474$		0			0
$475$	−4.68659	−	41.5946i	−0.00986650	−	0.0875676i
$476$	−479.071	−	479.071i	−1.00645	−	1.00645i
$477$		0			0
$478$	326.005	+	518.834i	0.682019	+	1.08543i
$479$	−149.906	+	94.1921i	−0.312956	+	0.196643i	−0.679346	−	0.733818i	$-0.737736\pi$
$479$	−149.906	+	94.1921i	−0.312956	+	0.196643i	0.366390	+	0.930461i	$0.380594\pi$
$480$		0			0
$481$	−124.120	+	124.120i	−0.258045	+	0.258045i
$482$	−414.520	+	46.7052i	−0.859999	+	0.0968987i
$483$		0			0
$484$	682.710	+	856.091i	1.41056	+	1.76878i
$485$	−72.1746	−	8.13213i	−0.148814	−	0.0167673i
$486$		0			0
$487$	10.4608	−	45.8320i	0.0214802	−	0.0941108i	−0.963052	−	0.269317i	$-0.913202\pi$
$487$	10.4608	−	45.8320i	0.0214802	−	0.0941108i	0.984532	+	0.175206i	$0.0560592\pi$
$488$	446.629	+	1956.81i	0.915223	+	4.00986i
$489$		0			0
$490$	27.4963	+	78.5798i	0.0561148	+	0.160367i
$491$	308.602	−	491.137i	0.628517	−	1.00028i	−0.368971	−	0.929441i	$-0.620290\pi$
$491$	308.602	−	491.137i	0.628517	−	1.00028i	0.997488	−	0.0708376i	$-0.0225672\pi$
$492$		0			0
$493$	−174.404	−	182.550i	−0.353761	−	0.370284i
$494$	209.969			0.425038
$495$		0			0
$496$	2138.27	−	748.214i	4.31104	−	1.50850i
$497$	264.246	+	548.712i	0.531681	+	1.10405i
$498$		0			0
$499$	−927.838	−	211.773i	−1.85939	−	0.424395i	−0.862706	−	0.505706i	$-0.831232\pi$
$499$	−927.838	−	211.773i	−1.85939	−	0.424395i	−0.996689	+	0.0813113i	$0.974089\pi$
$500$	−1129.96	−	544.159i	−2.25992	−	1.08832i
$501$		0			0
$502$	−35.2914	+	28.1439i	−0.0703016	+	0.0560636i
$503$	199.435	+	69.7852i	0.396490	+	0.138738i	0.521157	−	0.853461i	$-0.325501\pi$
$503$	199.435	+	69.7852i	0.396490	+	0.138738i	−0.124667	+	0.992199i	$0.539786\pi$
$504$		0			0
$505$	446.498	+	446.498i	0.884154	+	0.884154i
$506$	207.452	+	165.438i	0.409985	+	0.326952i
$507$		0			0
$508$	−1010.18	+	634.739i	−1.98855	+	1.24949i
$509$	−41.2535	+	51.7302i	−0.0810481	+	0.101631i	−0.820702	−	0.571356i	$-0.806418\pi$
$509$	−41.2535	+	51.7302i	−0.0810481	+	0.101631i	0.739654	+	0.672987i	$0.234989\pi$
$510$		0			0
$511$	325.147	−	36.6352i	0.636295	−	0.0716932i
$512$	130.737	−	373.625i	0.255346	−	0.729737i
$513$		0			0
$514$	−268.597	−	30.2636i	−0.522562	−	0.0588786i
$515$	−97.9766	+	203.451i	−0.190246	+	0.395050i
$516$		0			0
$517$	56.9021	+	249.305i	0.110062	+	0.482214i
$518$	1264.54	−	608.970i	2.44119	−	1.17562i
$519$		0			0
$520$	−249.974	+	397.831i	−0.480719	+	0.765060i
$521$		−	926.186i		−	1.77771i	−0.458190	−	0.888854i	$-0.651502\pi$
$521$		−	926.186i		−	1.77771i	0.458190	−	0.888854i	$-0.348498\pi$
$522$		0			0
$523$	711.936			1.36125			0.680627	−	0.732630i	$-0.261707\pi$
$523$	711.936			1.36125			0.680627	+	0.732630i	$0.261707\pi$
$524$	−1737.20	−	1091.56i	−3.31527	−	2.08312i
$525$		0			0
$526$	99.8221	+	207.283i	0.189776	+	0.394074i
$527$	−347.822	+	79.3882i	−0.660004	+	0.150642i
$528$		0			0
$529$	242.216	+	116.645i	0.457875	+	0.220501i
$530$	−90.1381	+	799.997i	−0.170072	+	1.50943i
$531$		0			0
$532$	−1152.78	−	403.375i	−2.16688	−	0.758224i
$533$	0.520309	+	4.61787i	0.000976189	+	0.00866392i
$534$		0			0
$535$	−20.2937	−	16.1837i	−0.0379322	−	0.0302499i
$536$	516.296	+	821.680i	0.963238	+	1.53298i
$537$		0			0
$538$	390.309	−	489.433i	0.725482	−	0.909726i
$539$	−12.5447	+	12.5447i	−0.0232740	+	0.0232740i
$540$		0			0
$541$	51.9016	−	148.326i	0.0959364	−	0.274170i	−0.885907	−	0.463862i	$-0.846463\pi$
$541$	51.9016	−	148.326i	0.0959364	−	0.274170i	0.981844	+	0.189692i	$0.0607489\pi$
$542$	−501.257	−	628.557i	−0.924829	−	1.15970i
$543$		0			0
$544$	−413.505	+	858.652i	−0.760120	+	1.57841i
$545$	−247.260	+	1083.32i	−0.453689	+	1.98774i
$546$		0			0
$547$	249.900	−	120.346i	0.456856	−	0.220010i	−0.191279	−	0.981536i	$-0.561263\pi$
$547$	249.900	−	120.346i	0.456856	−	0.220010i	0.648135	+	0.761525i	$0.275549\pi$
$548$	−749.670	−	2142.43i	−1.36801	−	3.90955i
$549$		0			0
$550$			43.8768i			0.0797761i
$551$	−426.037	−	160.077i	−0.773207	−	0.290521i
$552$		0			0
$553$	751.259	+	472.047i	1.35851	+	0.853611i
$554$	208.768	−	73.0512i	0.376838	−	0.131861i
$555$		0			0
$556$	−2084.53	+	475.780i	−3.74915	+	0.855719i
$557$	−114.217	−	26.0694i	−0.205058	−	0.0468032i	0.118758	−	0.992923i	$-0.462109\pi$
$557$	−114.217	−	26.0694i	−0.205058	−	0.0468032i	−0.323816	+	0.946120i	$0.604966\pi$
$558$		0			0
$559$	7.53906	−	66.9110i	0.0134867	−	0.119698i
$560$	1657.08	−	1321.48i	2.95908	−	2.35979i
$561$		0			0
$562$	−121.451	−	1077.91i	−0.216105	−	1.91798i
$563$	−544.911	−	544.911i	−0.967871	−	0.967871i	0.0316292	−	0.999500i	$-0.489930\pi$
$563$	−544.911	−	544.911i	−0.967871	−	0.967871i	−0.999500	+	0.0316292i	$0.989930\pi$
$564$		0			0
$565$	−279.289	−	444.486i	−0.494317	−	0.786701i
$566$	719.832	−	452.301i	1.27179	−	0.799118i
$567$		0			0
$568$	1511.12	−	1511.12i	2.66042	−	2.66042i
$569$	−877.995	+	98.9262i	−1.54305	+	0.173860i	−0.842088	−	0.539340i	$-0.818674\pi$
$569$	−877.995	+	98.9262i	−1.54305	+	0.173860i	−0.700960	+	0.713200i	$0.747245\pi$
$570$		0			0
$571$	−118.851	−	149.035i	−0.208146	−	0.261007i	0.666790	−	0.745246i	$-0.267668\pi$
$571$	−118.851	−	149.035i	−0.208146	−	0.261007i	−0.874936	+	0.484239i	$0.839096\pi$
$572$	−159.104	−	17.9267i	−0.278153	−	0.0313404i
$573$		0			0
$574$	8.26835	−	36.2260i	0.0144048	−	0.0631115i
$575$	−9.57287	−	41.9415i	−0.0166485	−	0.0729417i
$576$		0			0
$577$	105.425	+	301.288i	0.182713	+	0.522163i	0.998413	−	0.0563115i	$-0.0179340\pi$
$577$	105.425	+	301.288i	0.182713	+	0.522163i	−0.815701	+	0.578474i	$0.803648\pi$
$578$	−434.561	+	691.600i	−0.751836	+	1.19654i
$579$		0			0
$580$	1296.10	−	986.085i	2.23466	−	1.70015i
$581$	57.2324			0.0985068
$582$		0			0
$583$	−161.930	+	56.6618i	−0.277753	+	0.0971901i
$584$	−498.163	−	1034.45i	−0.853019	−	1.77131i
$585$		0			0
$586$	−91.8156	−	20.9563i	−0.156682	−	0.0357616i
$587$	927.516	+	446.668i	1.58009	+	0.760934i	0.998614	−	0.0526268i	$-0.0167594\pi$
$587$	927.516	+	446.668i	1.58009	+	0.760934i	0.581481	+	0.813560i	$0.302474\pi$
$588$		0			0
$589$	−502.818	+	400.984i	−0.853681	+	0.680788i
$590$	−128.345	−	44.9097i	−0.217533	−	0.0761181i
$591$		0			0
$592$	−1964.69	−	1964.69i	−3.31873	−	3.31873i
$593$	720.843	+	574.853i	1.21559	+	0.969398i	0.999975	−	0.00708137i	$-0.00225409\pi$
$593$	720.843	+	574.853i	1.21559	+	0.969398i	0.215612	+	0.976479i	$0.430826\pi$
$594$		0			0
$595$	−282.627	+	177.586i	−0.475003	+	0.298464i
$596$	−1746.67	+	2190.26i	−2.93066	+	3.67493i
$597$		0			0
$598$	214.442	−	24.1619i	0.358599	−	0.0404044i
$599$	−53.8833	+	153.989i	−0.0899553	+	0.257078i	−0.980068	−	0.198663i	$-0.936340\pi$
$599$	−53.8833	+	153.989i	−0.0899553	+	0.257078i	0.890112	+	0.455741i	$0.150626\pi$
$600$		0			0
$601$	−863.514	−	97.2947i	−1.43680	−	0.161888i	−0.641041	−	0.767507i	$-0.721497\pi$
$601$	−863.514	−	97.2947i	−1.43680	−	0.161888i	−0.795755	+	0.605619i	$0.792926\pi$
$602$	−233.602	+	485.080i	−0.388044	+	0.805781i
$603$		0			0
$604$	307.206	+	1345.96i	0.508619	+	2.22841i
$605$	486.040	−	234.065i	0.803373	−	0.386884i
$606$		0			0
$607$	−310.491	+	494.143i	−0.511517	+	0.814075i	−0.998229	−	0.0594878i	$-0.981053\pi$
$607$	−310.491	+	494.143i	−0.511517	+	0.814075i	0.486712	+	0.873562i	$0.338196\pi$
$608$			1717.99i			2.82564i
$609$		0			0
$610$	1581.30			2.59229
$611$	176.094	+	110.647i	0.288206	+	0.181092i
$612$		0			0
$613$	−246.942	−	512.779i	−0.402841	−	0.836508i	−0.999423	−	0.0339560i	$-0.989189\pi$
$613$	−246.942	−	512.779i	−0.402841	−	0.836508i	0.596582	−	0.802552i	$-0.296525\pi$
$614$	−508.521	+	116.067i	−0.828211	+	0.189034i
$615$		0			0
$616$	721.299	+	347.359i	1.17094	+	0.563895i
$617$	−30.7744	+	273.130i	−0.0498775	+	0.442675i	0.943810	+	0.330489i	$0.107214\pi$
$617$	−30.7744	+	273.130i	−0.0498775	+	0.442675i	−0.993687	+	0.112186i	$0.964215\pi$
$618$		0			0
$619$	−477.311	−	167.018i	−0.771100	−	0.269820i	−0.0840811	−	0.996459i	$-0.526795\pi$
$619$	−477.311	−	167.018i	−0.771100	−	0.269820i	−0.687019	+	0.726639i	$0.741081\pi$
$620$	−257.668	−	2286.87i	−0.415594	−	3.68850i
$621$		0			0
$622$	921.049	+	734.512i	1.48079	+	1.18089i
$623$	−432.340	−	688.065i	−0.693965	−	1.10444i
$624$		0			0
$625$	−426.820	+	535.215i	−0.682911	+	0.856344i
$626$	946.353	−	946.353i	1.51175	−	1.51175i
$627$		0			0
$628$	340.459	−	972.977i	0.542133	−	1.54933i
$629$	272.821	+	342.107i	0.433738	+	0.543891i
$630$		0			0
$631$	−251.062	+	521.335i	−0.397879	+	0.826205i	0.601742	+	0.798690i	$0.294473\pi$
$631$	−251.062	+	521.335i	−0.397879	+	0.826205i	−0.999621	+	0.0275142i	$0.991241\pi$
$632$	692.784	−	3035.29i	1.09618	−	4.80267i
$633$		0			0
$634$	1030.12	−	496.082i	1.62480	−	0.782463i
$635$	194.131	+	554.794i	0.305718	+	0.873691i
$636$		0			0
$637$			14.4284i			0.0226506i
$638$	424.992	+	216.745i	0.666131	+	0.339726i
$639$		0			0
$640$	−1432.46	−	900.076i	−2.23822	−	1.40637i
$641$	354.797	−	124.149i	0.553505	−	0.193680i	−0.0390104	−	0.999239i	$-0.512421\pi$
$641$	354.797	−	124.149i	0.553505	−	0.193680i	0.592516	+	0.805559i	$0.298135\pi$
$642$		0			0
$643$	−13.7935	+	3.14829i	−0.0214519	+	0.00489625i	−0.233233	−	0.972421i	$-0.574931\pi$
$643$	−13.7935	+	3.14829i	−0.0214519	+	0.00489625i	0.211782	+	0.977317i	$0.432073\pi$
$644$	−1223.76	−	279.315i	−1.90024	−	0.433718i
$645$		0			0
$646$	58.6043	−	520.127i	0.0907187	−	0.805151i
$647$	−778.933	+	621.178i	−1.20391	+	0.960090i	−0.999822	−	0.0188619i	$-0.993996\pi$
$647$	−778.933	+	621.178i	−1.20391	+	0.960090i	−0.204092	+	0.978952i	$0.565424\pi$
$648$		0			0
$649$	−3.24430	−	28.7939i	−0.00499892	−	0.0443666i
$650$	25.2328	+	25.2328i	0.0388197	+	0.0388197i
$651$		0			0
$652$	−521.660	−	830.217i	−0.800092	−	1.27334i
$653$	240.927	−	151.384i	0.368954	−	0.231829i	−0.334774	−	0.942298i	$-0.608660\pi$
$653$	240.927	−	151.384i	0.368954	−	0.231829i	0.703728	+	0.710469i	$0.251517\pi$
$654$		0			0
$655$	−714.742	+	714.742i	−1.09121	+	1.09121i
$656$	−73.0963	+	8.23598i	−0.111427	+	0.0125548i
$657$		0			0
$658$	−1036.81	−	1300.12i	−1.57570	−	1.97586i
$659$	−1062.63	−	119.729i	−1.61249	−	0.181684i	−0.740792	−	0.671734i	$-0.765550\pi$
$659$	−1062.63	−	119.729i	−1.61249	−	0.181684i	−0.871694	+	0.490050i	$0.836978\pi$
$660$		0			0
$661$	100.223	−	439.106i	0.151624	−	0.664306i	−0.840790	−	0.541361i	$-0.817909\pi$
$661$	100.223	−	439.106i	0.151624	−	0.664306i	0.992414	−	0.122945i	$-0.0392337\pi$
$662$	−32.4579	−	142.207i	−0.0490301	−	0.214815i
$663$		0			0
$664$	−66.3289	−	189.557i	−0.0998930	−	0.285478i
$665$	−320.126	+	509.478i	−0.481393	+	0.766133i
$666$		0			0
$667$	−453.534	−	114.462i	−0.679961	−	0.171607i
$668$	1223.93			1.83223
$669$		0			0
$670$	721.633	−	252.510i	1.07706	−	0.376881i
$671$	146.207	+	303.602i	0.217894	+	0.452462i
$672$		0			0
$673$	−665.540	−	151.905i	−0.988915	−	0.225713i	−0.302679	−	0.953092i	$-0.597881\pi$
$673$	−665.540	−	151.905i	−0.988915	−	0.225713i	−0.686236	+	0.727379i	$0.740738\pi$
$674$	238.541	+	114.875i	0.353919	+	0.170438i
$675$		0			0
$676$	1308.87	−	1043.79i	1.93619	−	1.54406i
$677$	−140.624	−	49.2065i	−0.207716	−	0.0726831i	0.224415	−	0.974494i	$-0.427953\pi$
$677$	−140.624	−	49.2065i	−0.207716	−	0.0726831i	−0.432132	+	0.901810i	$0.642238\pi$
$678$		0			0
$679$	71.1709	+	71.1709i	0.104817	+	0.104817i
$680$	915.722	+	730.264i	1.34665	+	1.07392i
$681$		0			0
$682$	570.819	−	358.670i	0.836978	−	0.525908i
$683$	562.476	−	705.323i	0.823538	−	1.03268i	−0.175301	−	0.984515i	$-0.556090\pi$
$683$	562.476	−	705.323i	0.823538	−	1.03268i	0.998839	−	0.0481690i	$-0.0153386\pi$
$684$		0			0
$685$	−1111.23	+	125.206i	−1.62224	+	0.182782i
$686$	−413.818	+	1182.62i	−0.603233	+	1.72394i
$687$		0			0
$688$	1059.14	+	119.336i	1.53944	+	0.173453i
$689$	−60.5379	+	125.708i	−0.0878635	+	0.182450i
$690$		0			0
$691$	174.983	+	766.650i	0.253231	+	1.10948i	0.928332	+	0.371753i	$0.121243\pi$
$691$	174.983	+	766.650i	0.253231	+	1.10948i	−0.675101	+	0.737726i	$0.735900\pi$
$692$	825.667	−	397.620i	1.19316	−	0.574596i
$693$		0			0
$694$	−519.841	+	827.322i	−0.749050	+	1.19211i
$695$			1053.39i			1.51567i
$696$		0			0
$697$	11.5844			0.0166204
$698$	1307.01	+	821.246i	1.87250	+	1.17657i
$699$		0			0
$700$	−90.0589	−	187.009i	−0.128656	−	0.267156i
$701$	−1133.94	+	258.815i	−1.61761	+	0.369208i	−0.933048	−	0.359751i	$-0.882862\pi$
$701$	−1133.94	+	258.815i	−1.61761	+	0.369208i	−0.684557	+	0.728959i	$0.740005\pi$
$702$		0			0
$703$	710.676	+	342.243i	1.01092	+	0.486833i
$704$	95.3188	−	845.978i	0.135396	−	1.20167i
$705$		0			0
$706$	2337.43	+	817.901i	3.31080	+	1.15850i
$707$	−97.9734	−	869.538i	−0.138576	−	1.22990i
$708$		0			0
$709$	70.9559	+	56.5854i	0.100079	+	0.0798102i	0.672251	−	0.740323i	$-0.265328\pi$
$709$	70.9559	+	56.5854i	0.100079	+	0.0798102i	−0.572172	+	0.820134i	$0.693899\pi$
$710$	−895.755	−	1425.59i	−1.26163	−	2.00787i
$711$		0			0
$712$	−1777.86	+	2229.36i	−2.49699	+	3.13112i
$713$	−467.388	+	467.388i	−0.655523	+	0.655523i
$714$		0			0
$715$	−26.0529	+	74.4550i	−0.0364377	+	0.104133i
$716$	560.416	+	702.740i	0.782704	+	0.981480i
$717$		0			0
$718$	−25.6719	+	53.3083i	−0.0357548	+	0.0742456i
$719$	−8.99364	+	39.4037i	−0.0125085	+	0.0548035i	−0.980797	−	0.195031i	$-0.937519\pi$
$719$	−8.99364	+	39.4037i	−0.0125085	+	0.0548035i	0.968288	+	0.249835i	$0.0803763\pi$
$720$		0			0
$721$	281.937	−	135.774i	0.391036	−	0.188313i
$722$	145.139	+	414.782i	0.201023	+	0.574491i
$723$		0			0
$724$		−	406.642i		−	0.561661i
$725$	−31.9614	−	70.4356i	−0.0440847	−	0.0971525i
$726$		0			0
$727$	−358.094	−	225.005i	−0.492564	−	0.309498i	0.262747	−	0.964865i	$-0.415371\pi$
$727$	−358.094	−	225.005i	−0.492564	−	0.309498i	−0.755311	+	0.655366i	$0.772514\pi$
$728$	614.566	−	215.046i	0.844184	−	0.295393i
$729$		0			0
$730$	−881.877	+	201.283i	−1.20805	+	0.275730i
$731$	−163.645	−	37.3509i	−0.223865	−	0.0510957i
$732$		0			0
$733$	−14.7149	+	130.599i	−0.0200749	+	0.178170i	−0.999748	−	0.0224286i	$-0.992860\pi$
$733$	−14.7149	+	130.599i	−0.0200749	+	0.178170i	0.979673	+	0.200599i	$0.0642887\pi$
$734$	1982.74	−	1581.18i	2.70128	−	2.15420i
$735$		0			0
$736$	197.695	+	1754.59i	0.268607	+	2.38396i
$737$	115.203	+	115.203i	0.156314	+	0.156314i
$738$		0			0
$739$	−152.535	−	242.758i	−0.206407	−	0.328495i	0.727438	−	0.686174i	$-0.240711\pi$
$739$	−152.535	−	242.758i	−0.206407	−	0.328495i	−0.933845	+	0.357679i	$0.883568\pi$
$740$	−2389.94	+	1501.70i	−3.22965	+	2.02932i
$741$		0			0
$742$	788.872	−	788.872i	1.06317	−	1.06317i
$743$	−286.805	+	32.3151i	−0.386009	+	0.0434928i	−0.302837	−	0.953042i	$-0.597934\pi$
$743$	−286.805	+	32.3151i	−0.386009	+	0.0434928i	−0.0831723	+	0.996535i	$0.526505\pi$
$744$		0			0
$745$	860.533	+	1079.07i	1.15508	+	1.44842i
$746$	1684.08	+	189.750i	2.25748	+	0.254357i
$747$		0			0
$748$	−88.8146	+	389.122i	−0.118736	+	0.520217i
$749$	8.00411	+	35.0683i	0.0106864	+	0.0468202i
$750$		0			0
$751$	14.9942	+	42.8510i	0.0199657	+	0.0570586i	0.953435	−	0.301599i	$-0.0975203\pi$
$751$	14.9942	+	42.8510i	0.0199657	+	0.0570586i	−0.933469	+	0.358657i	$0.883235\pi$
$752$	−1751.44	+	2787.40i	−2.32904	+	3.70664i
$753$		0			0
$754$	369.051	−	119.759i	0.489458	−	0.158831i
$755$	680.165			0.900881
$756$		0			0
$757$	−467.425	+	163.559i	−0.617470	+	0.216062i	−0.620846	−	0.783932i	$-0.713211\pi$
$757$	−467.425	+	163.559i	−0.617470	+	0.216062i	0.00337645	+	0.999994i	$0.498925\pi$
$758$	−154.272	−	320.350i	−0.203526	−	0.422625i
$759$		0			0
$760$	2058.43	+	469.823i	2.70846	+	0.618188i
$761$	−1035.64	−	498.740i	−1.36090	−	0.655375i	−0.396062	−	0.918224i	$-0.629624\pi$
$761$	−1035.64	−	498.740i	−1.36090	−	0.655375i	−0.964837	+	0.262849i	$0.915338\pi$
$762$		0			0
$763$	1203.90	−	960.077i	1.57785	−	1.25829i
$764$	2702.76	+	945.738i	3.53765	+	1.23788i
$765$		0			0
$766$	−146.362	−	146.362i	−0.191074	−	0.191074i
$767$	−18.4246	−	14.6931i	−0.0240217	−	0.0191566i
$768$		0			0
$769$	1078.65	−	677.762i	1.40267	−	0.881355i	0.403239	−	0.915095i	$-0.367884\pi$
$769$	1078.65	−	677.762i	1.40267	−	0.881355i	0.999431	+	0.0337394i	$0.0107416\pi$
$770$	393.253	−	493.124i	0.510718	−	0.640420i
$771$		0			0
$772$	1891.96	−	213.173i	2.45073	−	0.276131i
$773$	101.777	−	290.863i	0.131666	−	0.376279i	−0.859110	−	0.511791i	$-0.828982\pi$
$773$	101.777	−	290.863i	0.131666	−	0.376279i	0.990776	+	0.135512i	$0.0432680\pi$
$774$		0			0
$775$	−108.613	−	12.2378i	−0.140146	−	0.0157907i
$776$	153.239	−	318.205i	0.197473	−	0.410058i
$777$		0			0
$778$	266.190	+	1166.26i	0.342147	+	1.49904i
$779$	18.8147	−	9.06068i	0.0241524	−	0.0116312i
$780$		0			0
$781$	190.885	−	303.791i	0.244410	−	0.388977i
$782$		−	537.952i		−	0.687919i
$783$		0			0
$784$	−228.388			−0.291311
$785$	−430.013	−	270.195i	−0.547788	−	0.344198i
$786$		0			0
$787$	418.692	+	869.423i	0.532010	+	1.10473i	0.977790	+	0.209588i	$0.0672121\pi$
$787$	418.692	+	869.423i	0.532010	+	1.10473i	−0.445780	+	0.895143i	$0.647074\pi$
$788$	1531.13	−	349.471i	1.94306	−	0.443491i
$789$		0			0
$790$	−2209.91	−	1064.24i	−2.79735	−	1.34713i
$791$	−81.4498	+	722.887i	−0.102971	+	0.913889i
$792$		0			0
$793$	258.677	+	90.5150i	0.326201	+	0.114143i
$794$	335.176	+	2974.77i	0.422136	+	3.74656i
$795$		0			0
$796$	−1785.29	−	1423.72i	−2.24283	−	1.78859i
$797$	86.2069	+	137.197i	0.108164	+	0.172142i	0.896420	−	0.443205i	$-0.146159\pi$
$797$	86.2069	+	137.197i	0.108164	+	0.172142i	−0.788256	+	0.615347i	$0.789016\pi$
$798$		0			0
$799$	323.240	−	405.331i	0.404556	−	0.507297i
$800$	−206.457	+	206.457i	−0.258072	+	0.258072i
$801$		0			0
$802$	−159.569	+	456.021i	−0.198964	+	0.568605i
$803$	−120.184	−	150.706i	−0.149669	−	0.187679i
$804$		0			0
$805$	−268.319	+	557.171i	−0.333316	+	0.692138i
$806$	122.003	−	534.532i	0.151369	−	0.663191i
$807$		0			0
$808$	−2766.42	+	1332.24i	−3.42378	+	1.64881i
$809$	161.421	+	461.316i	0.199532	+	0.570230i	0.999558	−	0.0297360i	$-0.00946665\pi$
$809$	161.421	+	461.316i	0.199532	+	0.570230i	−0.800026	+	0.599966i	$0.795181\pi$
$810$		0			0
$811$		−	1265.57i		−	1.56051i	−0.625462	−	0.780255i	$-0.715089\pi$
$811$		−	1265.57i		−	1.56051i	0.625462	−	0.780255i	$-0.284911\pi$
$812$	−2256.25	−	51.4879i	−2.77863	−	0.0634087i
$813$		0			0
$814$	−700.104	−	439.905i	−0.860079	−	0.540423i
$815$	−455.957	+	159.546i	−0.559456	+	0.195762i
$816$		0			0
$817$	−294.996	+	67.3309i	−0.361072	+	0.0824124i
$818$	−458.799	−	104.718i	−0.560879	−	0.128017i
$819$		0			0
$820$	−8.36664	+	74.2560i	−0.0102032	+	0.0905561i
$821$	388.526	−	309.839i	0.473235	−	0.377392i	−0.357633	−	0.933862i	$-0.616416\pi$
$821$	388.526	−	309.839i	0.473235	−	0.377392i	0.830868	+	0.556470i	$0.187845\pi$
$822$		0			0
$823$	−6.16192	−	54.6885i	−0.00748714	−	0.0664502i	0.989413	−	0.145127i	$-0.0463591\pi$
$823$	−6.16192	−	54.6885i	−0.00748714	−	0.0664502i	−0.996900	+	0.0786768i	$0.974930\pi$
$824$	−776.439	−	776.439i	−0.942280	−	0.942280i
$825$		0			0
$826$	100.251	+	159.549i	0.121370	+	0.193159i
$827$	690.518	−	433.881i	0.834967	−	0.524645i	−0.0453827	−	0.998970i	$-0.514451\pi$
$827$	690.518	−	433.881i	0.834967	−	0.524645i	0.880350	+	0.474325i	$0.157308\pi$
$828$		0			0
$829$	−479.385	+	479.385i	−0.578270	+	0.578270i	−0.934426	−	0.356157i	$-0.884087\pi$
$829$	−479.385	+	479.385i	−0.578270	+	0.578270i	0.356157	+	0.934426i	$0.384087\pi$
$830$	−157.224	+	17.7149i	−0.189427	+	0.0213433i
$831$		0			0
$832$	−431.690	−	541.323i	−0.518859	−	0.650628i
$833$	35.7415	+	4.02710i	0.0429070	+	0.00483446i
$834$		0			0
$835$	134.178	−	587.873i	0.160693	−	0.704040i
$836$	160.102	+	701.454i	0.191510	+	0.839059i
$837$		0			0
$838$	338.549	+	967.519i	0.403997	+	1.15456i
$839$	346.951	−	552.169i	0.413529	−	0.658127i	−0.573402	−	0.819274i	$-0.694377\pi$
$839$	346.951	−	552.169i	0.413529	−	0.658127i	0.986930	+	0.161147i	$0.0515194\pi$
$840$		0			0
$841$	−840.125	−	38.3635i	−0.998959	−	0.0456165i
$842$	−1365.40			−1.62161
$843$		0			0
$844$	−98.7004	+	34.5368i	−0.116944	+	0.0409203i
$845$	−357.858	−	743.101i	−0.423501	−	0.879409i
$846$		0			0
$847$	−728.834	−	166.352i	−0.860488	−	0.196401i
$848$	−1989.84	−	958.256i	−2.34651	−	1.13002i
$849$		0			0
$850$	69.5484	−	55.4630i	0.0818217	−	0.0652506i
$851$	765.200	+	267.755i	0.899178	+	0.314636i
$852$		0			0
$853$	−1023.16	−	1023.16i	−1.19949	−	1.19949i	−0.974321	−	0.225165i	$-0.927708\pi$
$853$	−1023.16	−	1023.16i	−1.19949	−	1.19949i	−0.225165	−	0.974321i	$-0.572292\pi$
$854$	−1713.25	−	1366.27i	−2.00614	−	1.59985i
$855$		0			0
$856$	106.872	−	67.1521i	0.124851	−	0.0784488i
$857$	564.699	−	708.110i	0.658925	−	0.826266i	−0.334301	−	0.942467i	$-0.608500\pi$
$857$	564.699	−	708.110i	0.658925	−	0.826266i	0.993226	+	0.116200i	$0.0370715\pi$
$858$		0			0
$859$	447.480	−	50.4189i	0.520931	−	0.0586949i	0.152416	−	0.988316i	$-0.451295\pi$
$859$	447.480	−	50.4189i	0.520931	−	0.0586949i	0.368516	+	0.929622i	$0.379866\pi$
$860$	357.608	−	1021.99i	0.415824	−	1.18836i
$861$		0			0
$862$	−528.081	−	59.5004i	−0.612623	−	0.0690260i
$863$	−73.4373	+	152.494i	−0.0850954	+	0.176702i	−0.939174	−	0.343441i	$-0.888407\pi$
$863$	−73.4373	+	152.494i	−0.0850954	+	0.176702i	0.854079	+	0.520144i	$0.174122\pi$
$864$		0			0
$865$	−100.467	−	440.173i	−0.116146	−	0.508871i
$866$	696.587	−	335.459i	0.804373	−	0.387366i
$867$		0			0
$868$	−1696.73	+	2700.33i	−1.95476	+	3.11097i
$869$		−	522.692i		−	0.601487i
$870$		0			0
$871$	132.503			0.152127
$872$	−4575.08	−	2874.71i	−5.24665	−	3.29669i
$873$		0			0
$874$	−420.756	−	873.708i	−0.481414	−	0.999666i
$875$	834.784	−	190.534i	0.954039	−	0.217753i
$876$		0			0
$877$	733.377	+	353.176i	0.836233	+	0.402709i	0.802449	−	0.596720i	$-0.203530\pi$
$877$	733.377	+	353.176i	0.836233	+	0.402709i	0.0337841	+	0.999429i	$0.489244\pi$
$878$	−70.1324	+	622.442i	−0.0798774	+	0.708932i
$879$		0			0
$880$	−1178.55	−	412.393i	−1.33926	−	0.468628i
$881$	−119.626	−	1061.71i	−0.135785	−	1.20512i	−0.858072	−	0.513530i	$-0.828338\pi$
$881$	−119.626	−	1061.71i	−0.135785	−	1.20512i	0.722287	−	0.691593i	$-0.243091\pi$
$882$		0			0
$883$	−247.657	−	197.500i	−0.280472	−	0.223669i	0.473142	−	0.880986i	$-0.343120\pi$
$883$	−247.657	−	197.500i	−0.280472	−	0.223669i	−0.753614	+	0.657317i	$0.771691\pi$
$884$	172.702	+	274.853i	0.195364	+	0.310920i
$885$		0			0
$886$	1528.69	−	1916.92i	1.72539	−	2.16357i
$887$	−643.743	+	643.743i	−0.725753	+	0.725753i	−0.969771	−	0.244018i	$-0.921534\pi$
$887$	−643.743	+	643.743i	−0.725753	+	0.725753i	0.244018	+	0.969771i	$0.421534\pi$
$888$		0			0
$889$	269.022	−	768.820i	0.302612	−	0.864815i
$890$	1400.66	+	1756.38i	1.57378	+	1.97346i
$891$		0			0
$892$	1492.07	−	3098.32i	1.67272	−	3.47345i
$893$	207.960	−	911.133i	0.232878	−	1.02031i
$894$		0			0
$895$	398.976	−	192.137i	0.445784	−	0.214678i
$896$	774.312	+	2212.86i	0.864187	+	2.46971i
$897$		0			0
$898$			1076.57i			1.19885i
$899$	−655.070	+	991.577i	−0.728665	+	1.10298i
$900$		0			0
$901$	294.503	+	185.049i	0.326863	+	0.205381i
$902$	−20.6616	+	7.22982i	−0.0229065	+	0.00801532i
$903$		0			0
$904$	2488.64	−	568.015i	2.75292	−	0.628336i
$905$	−195.317	−	44.5799i	−0.215820	−	0.0492596i
$906$		0			0
$907$	−106.225	+	942.772i	−0.117117	+	1.03944i	0.788410	+	0.615150i	$0.210905\pi$
$907$	−106.225	+	942.772i	−0.117117	+	1.03944i	−0.905527	+	0.424290i	$0.860524\pi$
$908$	−2169.88	+	1730.42i	−2.38973	+	1.90575i
$909$		0			0
$910$	−57.4338	−	509.739i	−0.0631141	−	0.560153i
$911$	291.791	+	291.791i	0.320297	+	0.320297i	0.848881	−	0.528584i	$-0.177277\pi$
$911$	291.791	+	291.791i	0.320297	+	0.320297i	−0.528584	+	0.848881i	$0.677277\pi$
$912$		0			0
$913$	−17.9382	−	28.5485i	−0.0196475	−	0.0312689i
$914$	1566.96	−	984.584i	1.71439	−	1.07723i
$915$		0			0
$916$	−2207.03	+	2207.03i	−2.40942	+	2.40942i
$917$	1391.93	−	156.833i	1.51792	−	0.171029i
$918$		0			0
$919$	710.166	+	890.520i	0.772760	+	0.969010i	0.999988	−	0.00483126i	$-0.00153784\pi$
$919$	710.166	+	890.520i	0.772760	+	0.969010i	−0.227228	+	0.973841i	$0.572966\pi$
$920$	2156.35	+	242.962i	2.34386	+	0.264089i
$921$		0			0
$922$	−278.172	+	1218.75i	−0.301706	+	1.32186i
$923$	−64.9305	−	284.479i	−0.0703472	−	0.308211i
$924$		0			0
$925$	44.2760	+	126.533i	0.0478659	+	0.136793i
$926$	677.922	−	1078.91i	0.732098	−	1.16513i
$927$		0			0
$928$	979.878	+	3019.62i	1.05590	+	3.25390i
$929$	755.257			0.812979			0.406489	−	0.913655i	$-0.366753\pi$
$929$	755.257			0.812979			0.406489	+	0.913655i	$0.366753\pi$
$930$		0			0
$931$	61.1989	−	21.4144i	0.0657346	−	0.0230015i
$932$	38.1961	+	79.3149i	0.0409829	+	0.0851019i
$933$		0			0
$934$	720.381	+	164.422i	0.771285	+	0.176041i
$935$	177.166	+	85.3184i	0.189482	+	0.0912497i
$936$		0			0
$937$	−557.789	+	444.822i	−0.595293	+	0.474730i	−0.874185	−	0.485592i	$-0.838604\pi$
$937$	−557.789	+	444.822i	−0.595293	+	0.474730i	0.278893	+	0.960322i	$0.410033\pi$
$938$	−1000.02	−	349.923i	−1.06612	−	0.373052i
$939$		0			0
$940$	2364.71	+	2364.71i	2.51565	+	2.51565i
$941$	−226.705	−	180.791i	−0.240920	−	0.192127i	0.495585	−	0.868559i	$-0.334954\pi$
$941$	−226.705	−	180.791i	−0.240920	−	0.192127i	−0.736505	+	0.676432i	$0.763525\pi$
$942$		0			0
$943$	18.1729	−	11.4188i	0.0192714	−	0.0121090i
$944$	232.578	−	291.644i	0.246375	−	0.308945i
$945$		0			0
$946$	315.183	−	35.5126i	0.333175	−	0.0375398i
$947$	587.677	−	1679.48i	0.620567	−	1.77348i	−0.0131502	−	0.999914i	$-0.504186\pi$
$947$	587.677	−	1679.48i	0.620567	−	1.77348i	0.633717	−	0.773565i	$-0.281528\pi$
$948$		0			0
$949$	−155.784	−	17.5526i	−0.164156	−	0.0184959i
$950$	69.5761	−	144.476i	0.0732380	−	0.152080i
$951$		0			0
$952$	−361.173	−	1582.40i	−0.379383	−	1.66219i
$953$	−197.375	+	95.0507i	−0.207109	+	0.0997385i	−0.534563	−	0.845129i	$-0.679524\pi$
$953$	−197.375	+	95.0507i	−0.207109	+	0.0997385i	0.327454	+	0.944867i	$0.393809\pi$
$954$		0			0
$955$	750.557	−	1194.50i	0.785923	−	1.25079i
$956$			1707.67i			1.78626i
$957$		0			0
$958$	−678.246			−0.707981
$959$	1312.14	+	824.472i	1.36824	+	0.859721i
$960$		0			0
$961$	311.685	+	647.221i	0.324334	+	0.673486i
$962$	−655.599	+	149.636i	−0.681495	+	0.155547i
$963$		0			0
$964$	−1047.39	−	504.399i	−1.08651	−	0.523235i
$965$	105.024	−	932.113i	0.108833	−	0.965920i
$966$		0			0
$967$	−1599.47	−	559.679i	−1.65405	−	0.578779i	−0.667848	−	0.744298i	$-0.732784\pi$
$967$	−1599.47	−	559.679i	−1.65405	−	0.578779i	−0.986207	+	0.165519i	$0.947070\pi$
$968$	293.708	+	2606.73i	0.303417	+	2.69290i
$969$		0			0
$970$	−217.544	−	173.486i	−0.224272	−	0.178851i
$971$	307.298	+	489.062i	0.316476	+	0.503668i	0.966645	−	0.256122i	$-0.0824447\pi$
$971$	307.298	+	489.062i	0.316476	+	0.503668i	−0.650169	+	0.759790i	$0.725302\pi$
$972$		0			0
$973$	910.151	−	1141.29i	0.935407	−	1.17296i
$974$	127.348	−	127.348i	0.130747	−	0.130747i
$975$		0			0
$976$	−1432.76	+	4094.61i	−1.46800	+	4.19529i
$977$	9.36795	+	11.7470i	0.00958848	+	0.0120236i	0.786603	−	0.617460i	$-0.211838\pi$
$977$	9.36795	+	11.7470i	0.00958848	+	0.0120236i	−0.777014	+	0.629483i	$0.783267\pi$
$978$		0			0
$979$	−207.711	+	431.316i	−0.212166	+	0.440568i
$980$	−51.6273	+	226.194i	−0.0526809	+	0.230810i
$981$		0			0
$982$	2002.08	−	964.149i	2.03877	−	0.981822i
$983$	−351.298	−	1003.95i	−0.357373	−	1.02131i	−0.972504	−	0.232888i	$-0.925182\pi$
$983$	−351.298	−	1003.95i	−0.357373	−	1.02131i	0.615130	−	0.788425i	$-0.289103\pi$
$984$		0			0
$985$		−	773.741i		−	0.785524i
$986$	−193.656	−	947.626i	−0.196405	−	0.961081i
$987$		0			0
$988$	495.465	+	311.321i	0.501483	+	0.315103i
$989$	−293.533	+	102.712i	−0.296798	+	0.103854i
$990$		0			0
$991$	1086.17	−	247.912i	1.09604	−	0.250164i	0.363981	−	0.931406i	$-0.381417\pi$
$991$	1086.17	−	247.912i	1.09604	−	0.250164i	0.732058	+	0.681243i	$0.238560\pi$
$992$	4373.60	+	998.246i	4.40887	+	1.00630i
$993$		0			0
$994$	−261.231	+	2318.49i	−0.262808	+	2.33249i
$995$	−879.558	+	701.424i	−0.883978	+	0.704949i
$996$		0			0
$997$	−61.5936	−	546.658i	−0.0617790	−	0.548303i	−0.986036	−	0.166533i	$-0.946743\pi$
$997$	−61.5936	−	546.658i	−0.0617790	−	0.548303i	0.924257	−	0.381771i	$-0.124686\pi$
$998$	−2578.07	−	2578.07i	−2.58324	−	2.58324i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.3.s.a.235.4		48
3.2	odd	2		29.3.f.a.3.1	✓	48
29.10	odd	28	inner	261.3.s.a.10.4		48
87.68	even	28		29.3.f.a.10.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.3.f.a.3.1	✓	48	3.2	odd	2
29.3.f.a.10.1	yes	48	87.68	even	28
261.3.s.a.10.4		48	29.10	odd	28	inner
261.3.s.a.235.4		48	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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	261.s (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(3.24379 + 2.03821i) q^{2} +(4.63233 + 9.61914i) q^{4} +(5.12808 - 1.17045i) q^{5} +(-6.56728 - 3.16264i) q^{7} +(-2.86375 + 25.4165i) q^{8} +O(q^{10})\)	\(q+(3.24379 + 2.03821i) q^{2} +(4.63233 + 9.61914i) q^{4} +(5.12808 - 1.17045i) q^{5} +(-6.56728 - 3.16264i) q^{7} +(-2.86375 + 25.4165i) q^{8} +(19.0200 + 6.65539i) q^{10} +(0.480789 + 4.26712i) q^{11} +(2.73044 + 2.17745i) q^{13} +(-14.8568 - 23.6444i) q^{14} +(-34.4669 + 43.2201i) q^{16} +(6.15599 - 6.15599i) q^{17} +(5.18330 - 14.8130i) q^{19} +(35.0137 + 43.9058i) q^{20} +(-7.13770 + 14.8216i) q^{22} +(3.58915 - 15.7251i) q^{23} +(2.40304 - 1.15724i) q^{25} +(4.41886 + 12.6284i) q^{26} -77.8220i q^{28} +(0.661611 - 28.9925i) q^{29} +(-34.6988 - 21.8027i) q^{31} +(-103.327 + 36.1556i) q^{32} +(32.5159 - 7.42154i) q^{34} +(-37.3793 - 8.53157i) q^{35} +(-5.62751 + 49.9455i) q^{37} +(47.0056 - 37.4857i) q^{38} +(15.0632 + 133.690i) q^{40} +(0.940907 + 0.940907i) q^{41} +(-10.2578 - 16.3252i) q^{43} +(-38.8189 + 24.3915i) q^{44} +(43.6934 - 43.6934i) q^{46} +(59.1758 - 6.66751i) q^{47} +(2.57590 + 3.23008i) q^{49} +(10.1536 + 1.14404i) q^{50} +(-8.29691 + 36.3511i) q^{52} +(8.89009 + 38.9500i) q^{53} +(7.45998 + 21.3194i) q^{55} +(99.1903 - 157.860i) q^{56} +(61.2387 - 92.6968i) q^{58} -6.74786 q^{59} +(74.0694 - 25.9180i) q^{61} +(-68.1170 - 141.446i) q^{62} +(-193.284 - 44.1159i) q^{64} +(16.5505 + 7.97030i) q^{65} +(29.6632 - 23.6556i) q^{67} +(87.7319 + 30.6987i) q^{68} +(-103.861 - 103.861i) q^{70} +(-65.3239 - 52.0941i) q^{71} +(-38.0089 + 23.8825i) q^{73} +(-120.054 + 150.543i) q^{74} +(166.499 - 18.7600i) q^{76} +(10.3379 - 29.5439i) q^{77} +(-120.957 - 13.6286i) q^{79} +(-126.162 + 261.978i) q^{80} +(1.13434 + 4.96987i) q^{82} +(-7.07418 + 3.40675i) q^{83} +(24.3631 - 38.7737i) q^{85} -73.8632i q^{86} -109.832 q^{88} +(94.3960 + 59.3130i) q^{89} +(-11.0451 - 22.9353i) q^{91} +(167.888 - 38.3193i) q^{92} +(205.543 + 98.9845i) q^{94} +(9.24248 - 82.0292i) q^{95} +(-13.0335 - 4.56061i) q^{97} +(1.77211 + 15.7279i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8}+O(q^{10}) \) 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8	\( 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8} - 20 q^{10} + 8 q^{11} - 14 q^{13} - 26 q^{14} + 18 q^{16} + 26 q^{17} + 2 q^{19} - 46 q^{20} + 154 q^{22} - 56 q^{23} - 34 q^{25} - 110 q^{26} + 170 q^{29} - 88 q^{31} + 132 q^{32} - 224 q^{34} + 210 q^{35} - 56 q^{37} + 294 q^{38} - 492 q^{40} + 34 q^{41} + 176 q^{43} - 126 q^{44} + 744 q^{46} - 208 q^{47} + 506 q^{49} - 732 q^{50} + 690 q^{52} + 14 q^{53} + 284 q^{55} - 332 q^{56} - 508 q^{58} + 44 q^{59} - 30 q^{61} + 504 q^{62} - 896 q^{64} + 554 q^{65} - 574 q^{67} + 796 q^{68} - 1066 q^{70} - 224 q^{71} - 22 q^{73} - 820 q^{74} + 514 q^{76} - 436 q^{77} + 564 q^{79} - 1162 q^{80} - 18 q^{82} + 126 q^{83} + 38 q^{85} - 384 q^{88} + 160 q^{89} - 434 q^{91} + 1022 q^{92} - 2 q^{94} + 642 q^{95} + 604 q^{97} + 102 q^{98}+O(q^{100}) \) 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8 - 20 * q^10 + 8 * q^11 - 14 * q^13 - 26 * q^14 + 18 * q^16 + 26 * q^17 + 2 * q^19 - 46 * q^20 + 154 * q^22 - 56 * q^23 - 34 * q^25 - 110 * q^26 + 170 * q^29 - 88 * q^31 + 132 * q^32 - 224 * q^34 + 210 * q^35 - 56 * q^37 + 294 * q^38 - 492 * q^40 + 34 * q^41 + 176 * q^43 - 126 * q^44 + 744 * q^46 - 208 * q^47 + 506 * q^49 - 732 * q^50 + 690 * q^52 + 14 * q^53 + 284 * q^55 - 332 * q^56 - 508 * q^58 + 44 * q^59 - 30 * q^61 + 504 * q^62 - 896 * q^64 + 554 * q^65 - 574 * q^67 + 796 * q^68 - 1066 * q^70 - 224 * q^71 - 22 * q^73 - 820 * q^74 + 514 * q^76 - 436 * q^77 + 564 * q^79 - 1162 * q^80 - 18 * q^82 + 126 * q^83 + 38 * q^85 - 384 * q^88 + 160 * q^89 - 434 * q^91 + 1022 * q^92 - 2 * q^94 + 642 * q^95 + 604 * q^97 + 102 * q^98

Introduction

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