LMFDB - Embedded newform 294.3.h.e.263.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,3,Mod(263,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("294.263");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	294.h (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.01091977219$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			263.1
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	294.263
Dual form			294.3.h.e.275.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 + 0.707107i) q^{2} +(-0.548188 + 2.94949i) q^{3} +(1.00000 - 1.73205i) q^{4} +(3.46410 - 2.00000i) q^{5} +(-1.41421 - 4.00000i) q^{6} +2.82843i q^{8} +(-8.39898 - 3.23375i) q^{9} +O(q^{10})$	\(q+(-1.22474 + 0.707107i) q^{2} +(-0.548188 + 2.94949i) q^{3} +(1.00000 - 1.73205i) q^{4} +(3.46410 - 2.00000i) q^{5} +(-1.41421 - 4.00000i) q^{6} +2.82843i q^{8} +(-8.39898 - 3.23375i) q^{9} +(-2.82843 + 4.89898i) q^{10} +(8.57321 + 4.94975i) q^{11} +(4.56048 + 3.89898i) q^{12} +12.7279 q^{13} +(4.00000 + 11.3137i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(27.7128 + 16.0000i) q^{17} +(12.5732 - 1.97846i) q^{18} +(-14.1421 - 24.4949i) q^{19} -8.00000i q^{20} -14.0000 q^{22} +(1.22474 - 0.707107i) q^{23} +(-8.34242 - 1.55051i) q^{24} +(-4.50000 + 7.79423i) q^{25} +(-15.5885 + 9.00000i) q^{26} +(14.1421 - 23.0000i) q^{27} +56.5685i q^{29} +(-12.8990 - 11.0280i) q^{30} +(4.89898 + 2.82843i) q^{32} +(-19.2990 + 22.5732i) q^{33} -45.2548 q^{34} +(-14.0000 + 11.3137i) q^{36} +(25.0000 + 43.3013i) q^{37} +(34.6410 + 20.0000i) q^{38} +(-6.97730 + 37.5409i) q^{39} +(5.65685 + 9.79796i) q^{40} +16.0000i q^{41} -52.0000 q^{43} +(17.1464 - 9.89949i) q^{44} +(-35.5624 + 5.59592i) q^{45} +(-1.00000 + 1.73205i) q^{46} +(29.4449 - 17.0000i) q^{47} +(11.3137 - 4.00000i) q^{48} -12.7279i q^{50} +(-62.3837 + 72.9676i) q^{51} +(12.7279 - 22.0454i) q^{52} +(-39.1918 - 22.6274i) q^{53} +(-1.05705 + 38.1691i) q^{54} +39.5980 q^{55} +(80.0000 - 28.2843i) q^{57} +(-40.0000 - 69.2820i) q^{58} +(27.7128 + 16.0000i) q^{59} +(23.5959 + 4.38551i) q^{60} +(16.2635 + 28.1691i) q^{61} -8.00000 q^{64} +(44.0908 - 25.4558i) q^{65} +(7.67463 - 41.2929i) q^{66} +(6.00000 - 10.3923i) q^{67} +(55.4256 - 32.0000i) q^{68} +(1.41421 + 4.00000i) q^{69} -89.0955i q^{71} +(9.14643 - 23.7559i) q^{72} +(16.2635 - 28.1691i) q^{73} +(-61.2372 - 35.3553i) q^{74} +(-20.5222 - 17.5454i) q^{75} -56.5685 q^{76} +(-18.0000 - 50.9117i) q^{78} +(20.0000 + 34.6410i) q^{79} +(-13.8564 - 8.00000i) q^{80} +(60.0857 + 54.3204i) q^{81} +(-11.3137 - 19.5959i) q^{82} +62.0000i q^{83} +128.000 q^{85} +(63.6867 - 36.7696i) q^{86} +(-166.848 - 31.0102i) q^{87} +(-14.0000 + 24.2487i) q^{88} +(48.4974 - 28.0000i) q^{89} +(39.5980 - 32.0000i) q^{90} -2.82843i q^{92} +(-24.0416 + 41.6413i) q^{94} +(-97.9796 - 56.5685i) q^{95} +(-11.0280 + 12.8990i) q^{96} +24.0416 q^{97} +(-56.0000 - 69.2965i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{4} - 28 q^{9}+O(q^{10}) $ 8 * q + 8 * q^4 - 28 * q^9	$ 8 q + 8 q^{4} - 28 q^{9} + 32 q^{15} - 16 q^{16} + 32 q^{18} - 112 q^{22} - 36 q^{25} - 64 q^{30} - 112 q^{36} + 200 q^{37} - 144 q^{39} - 416 q^{43} - 8 q^{46} + 128 q^{51} + 640 q^{57} - 320 q^{58} + 32 q^{60} - 64 q^{64} + 48 q^{67} - 64 q^{72} - 144 q^{78} + 160 q^{79} - 68 q^{81} + 1024 q^{85} - 112 q^{88} - 448 q^{99}+O(q^{100}) $ 8 * q + 8 * q^4 - 28 * q^9 + 32 * q^15 - 16 * q^16 + 32 * q^18 - 112 * q^22 - 36 * q^25 - 64 * q^30 - 112 * q^36 + 200 * q^37 - 144 * q^39 - 416 * q^43 - 8 * q^46 + 128 * q^51 + 640 * q^57 - 320 * q^58 + 32 * q^60 - 64 * q^64 + 48 * q^67 - 64 * q^72 - 144 * q^78 + 160 * q^79 - 68 * q^81 + 1024 * q^85 - 112 * q^88 - 448 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.22474	+	0.707107i	−0.612372	+	0.353553i
$2$	−1.22474	+	0.707107i	−0.612372	+	0.353553i
$3$	−0.548188	+	2.94949i	−0.182729	+	0.983163i
$3$	−0.548188	+	2.94949i	−0.182729	+	0.983163i
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$	3.46410	−	2.00000i	0.692820	−	0.400000i	−0.111847	−	0.993725i	$-0.535677\pi$
$5$	3.46410	−	2.00000i	0.692820	−	0.400000i	0.804668	+	0.593725i	$0.202343\pi$
$6$	−1.41421	−	4.00000i	−0.235702	−	0.666667i
$7$		0			0
$7$		0			0
$8$			2.82843i			0.353553i
$9$	−8.39898	−	3.23375i	−0.933220	−	0.359306i
$10$	−2.82843	+	4.89898i	−0.282843	+	0.489898i
$11$	8.57321	+	4.94975i	0.779383	+	0.449977i	0.836212	−	0.548407i	$-0.184765\pi$
$11$	8.57321	+	4.94975i	0.779383	+	0.449977i	−0.0568285	+	0.998384i	$0.518099\pi$
$12$	4.56048	+	3.89898i	0.380040	+	0.324915i
$13$	12.7279			0.979071			0.489535	−	0.871983i	$-0.337166\pi$
$13$	12.7279			0.979071			0.489535	+	0.871983i	$0.337166\pi$
$14$		0			0
$15$	4.00000	+	11.3137i	0.266667	+	0.754247i
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	27.7128	+	16.0000i	1.63017	+	0.941176i	0.984040	+	0.177945i	$0.0569449\pi$
$17$	27.7128	+	16.0000i	1.63017	+	0.941176i	0.646125	+	0.763232i	$0.276388\pi$
$18$	12.5732	−	1.97846i	0.698512	−	0.109914i
$19$	−14.1421	−	24.4949i	−0.744323	−	1.28921i	−0.950510	−	0.310693i	$-0.899439\pi$
$19$	−14.1421	−	24.4949i	−0.744323	−	1.28921i	0.206188	−	0.978512i	$-0.433894\pi$
$20$		−	8.00000i		−	0.400000i
$21$		0			0
$22$	−14.0000			−0.636364
$23$	1.22474	−	0.707107i	0.0532498	−	0.0307438i	−0.473139	−	0.880988i	$-0.656879\pi$
$23$	1.22474	−	0.707107i	0.0532498	−	0.0307438i	0.526389	+	0.850244i	$0.323546\pi$
$24$	−8.34242	−	1.55051i	−0.347601	−	0.0646046i
$25$	−4.50000	+	7.79423i	−0.180000	+	0.311769i
$26$	−15.5885	+	9.00000i	−0.599556	+	0.346154i
$27$	14.1421	−	23.0000i	0.523783	−	0.851852i
$28$		0			0
$29$			56.5685i			1.95064i	0.220797	+	0.975320i	$0.429134\pi$
$29$			56.5685i			1.95064i	−0.220797	+	0.975320i	$0.570866\pi$
$30$	−12.8990	−	11.0280i	−0.429966	−	0.367599i
$31$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$31$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$32$	4.89898	+	2.82843i	0.153093	+	0.0883883i
$33$	−19.2990	+	22.5732i	−0.584817	+	0.684037i
$34$	−45.2548			−1.33102
$35$		0			0
$36$	−14.0000	+	11.3137i	−0.388889	+	0.314270i
$37$	25.0000	+	43.3013i	0.675676	+	1.17030i	0.976271	+	0.216553i	$0.0694813\pi$
$37$	25.0000	+	43.3013i	0.675676	+	1.17030i	−0.300595	+	0.953752i	$0.597185\pi$
$38$	34.6410	+	20.0000i	0.911606	+	0.526316i
$39$	−6.97730	+	37.5409i	−0.178905	+	0.962587i
$40$	5.65685	+	9.79796i	0.141421	+	0.244949i
$41$			16.0000i			0.390244i	0.980779	+	0.195122i	$0.0625103\pi$
$41$			16.0000i			0.390244i	−0.980779	+	0.195122i	$0.937490\pi$
$42$		0			0
$43$	−52.0000			−1.20930			−0.604651	−	0.796490i	$-0.706687\pi$
$43$	−52.0000			−1.20930			−0.604651	+	0.796490i	$0.706687\pi$
$44$	17.1464	−	9.89949i	0.389692	−	0.224989i
$45$	−35.5624	+	5.59592i	−0.790276	+	0.124354i
$46$	−1.00000	+	1.73205i	−0.0217391	+	0.0376533i
$47$	29.4449	−	17.0000i	0.626486	−	0.361702i	−0.152904	−	0.988241i	$-0.548862\pi$
$47$	29.4449	−	17.0000i	0.626486	−	0.361702i	0.779390	+	0.626539i	$0.215529\pi$
$48$	11.3137	−	4.00000i	0.235702	−	0.0833333i
$49$		0			0
$50$		−	12.7279i		−	0.254558i
$51$	−62.3837	+	72.9676i	−1.22321	+	1.43074i
$52$	12.7279	−	22.0454i	0.244768	−	0.423950i
$53$	−39.1918	−	22.6274i	−0.739469	−	0.426932i	0.0824075	−	0.996599i	$-0.473739\pi$
$53$	−39.1918	−	22.6274i	−0.739469	−	0.426932i	−0.821876	+	0.569666i	$0.807072\pi$
$54$	−1.05705	+	38.1691i	−0.0195750	+	0.706836i
$55$	39.5980			0.719963
$56$		0			0
$57$	80.0000	−	28.2843i	1.40351	−	0.496215i
$58$	−40.0000	−	69.2820i	−0.689655	−	1.19452i
$59$	27.7128	+	16.0000i	0.469709	+	0.271186i	0.716118	−	0.697979i	$-0.245917\pi$
$59$	27.7128	+	16.0000i	0.469709	+	0.271186i	−0.246409	+	0.969166i	$0.579251\pi$
$60$	23.5959	+	4.38551i	0.393265	+	0.0730918i
$61$	16.2635	+	28.1691i	0.266614	+	0.461789i	0.967985	−	0.251007i	$-0.0807618\pi$
$61$	16.2635	+	28.1691i	0.266614	+	0.461789i	−0.701371	+	0.712796i	$0.747428\pi$
$62$		0			0
$63$		0			0
$64$	−8.00000			−0.125000
$65$	44.0908	−	25.4558i	0.678320	−	0.391628i
$66$	7.67463	−	41.2929i	0.116282	−	0.625649i
$67$	6.00000	−	10.3923i	0.0895522	−	0.155109i	−0.817770	−	0.575546i	$-0.804790\pi$
$67$	6.00000	−	10.3923i	0.0895522	−	0.155109i	0.907322	+	0.420437i	$0.138123\pi$
$68$	55.4256	−	32.0000i	0.815083	−	0.470588i
$69$	1.41421	+	4.00000i	0.0204958	+	0.0579710i
$70$		0			0
$71$		−	89.0955i		−	1.25487i	−0.778671	−	0.627433i	$-0.784106\pi$
$71$		−	89.0955i		−	1.25487i	0.778671	−	0.627433i	$-0.215894\pi$
$72$	9.14643	−	23.7559i	0.127034	−	0.329943i
$73$	16.2635	−	28.1691i	0.222787	−	0.385879i	−0.732866	−	0.680373i	$-0.761818\pi$
$73$	16.2635	−	28.1691i	0.222787	−	0.385879i	0.955653	+	0.294494i	$0.0951512\pi$
$74$	−61.2372	−	35.3553i	−0.827530	−	0.477775i
$75$	−20.5222	−	17.5454i	−0.273629	−	0.233939i
$76$	−56.5685			−0.744323
$77$		0			0
$78$	−18.0000	−	50.9117i	−0.230769	−	0.652714i
$79$	20.0000	+	34.6410i	0.253165	+	0.438494i	0.964395	−	0.264465i	$-0.0851953\pi$
$79$	20.0000	+	34.6410i	0.253165	+	0.438494i	−0.711231	+	0.702959i	$0.751862\pi$
$80$	−13.8564	−	8.00000i	−0.173205	−	0.100000i
$81$	60.0857	+	54.3204i	0.741799	+	0.670622i
$82$	−11.3137	−	19.5959i	−0.137972	−	0.238975i
$83$			62.0000i			0.746988i	0.927633	+	0.373494i	$0.121840\pi$
$83$			62.0000i			0.746988i	−0.927633	+	0.373494i	$0.878160\pi$
$84$		0			0
$85$	128.000			1.50588
$86$	63.6867	−	36.7696i	0.740543	−	0.427553i
$87$	−166.848	−	31.0102i	−1.91780	−	0.356439i
$88$	−14.0000	+	24.2487i	−0.159091	+	0.275554i
$89$	48.4974	−	28.0000i	0.544915	−	0.314607i	−0.202154	−	0.979354i	$-0.564794\pi$
$89$	48.4974	−	28.0000i	0.544915	−	0.314607i	0.747068	+	0.664747i	$0.231461\pi$
$90$	39.5980	−	32.0000i	0.439978	−	0.355556i
$91$		0			0
$92$		−	2.82843i		−	0.0307438i
$93$		0			0
$94$	−24.0416	+	41.6413i	−0.255762	+	0.442993i
$95$	−97.9796	−	56.5685i	−1.03136	−	0.595458i
$96$	−11.0280	+	12.8990i	−0.114875	+	0.134364i
$97$	24.0416			0.247852			0.123926	−	0.992291i	$-0.460451\pi$
$97$	24.0416			0.247852			0.123926	+	0.992291i	$0.460451\pi$
$98$		0			0
$99$	−56.0000	−	69.2965i	−0.565657	−	0.699964i
$100$	9.00000	+	15.5885i	0.0900000	+	0.155885i
$101$	−31.1769	−	18.0000i	−0.308682	−	0.178218i	0.337654	−	0.941270i	$-0.390367\pi$
$101$	−31.1769	−	18.0000i	−0.308682	−	0.178218i	−0.646337	+	0.763052i	$0.723700\pi$
$102$	24.8082	−	133.479i	0.243217	−	1.30861i
$103$	−36.7696	−	63.6867i	−0.356986	−	0.618318i	0.630470	−	0.776214i	$-0.282862\pi$
$103$	−36.7696	−	63.6867i	−0.356986	−	0.618318i	−0.987456	+	0.157896i	$0.949529\pi$
$104$			36.0000i			0.346154i
$105$		0			0
$106$	64.0000			0.603774
$107$	126.149	−	72.8320i	1.17896	−	0.680673i	0.223186	−	0.974776i	$-0.428354\pi$
$107$	126.149	−	72.8320i	1.17896	−	0.680673i	0.955774	+	0.294103i	$0.0950209\pi$
$108$	−25.6950	−	47.4949i	−0.237917	−	0.439768i
$109$	88.0000	−	152.420i	0.807339	−	1.39835i	−0.107361	−	0.994220i	$-0.534240\pi$
$109$	88.0000	−	152.420i	0.807339	−	1.39835i	0.914700	−	0.404133i	$-0.132427\pi$
$110$	−48.4974	+	28.0000i	−0.440886	+	0.254545i
$111$	−141.421	+	50.0000i	−1.27407	+	0.450450i
$112$		0			0
$113$		−	16.9706i		−	0.150182i	−0.997177	−	0.0750910i	$-0.976075\pi$
$113$		−	16.9706i		−	0.150182i	0.997177	−	0.0750910i	$-0.0239247\pi$
$114$	−77.9796	+	91.2096i	−0.684031	+	0.800084i
$115$	2.82843	−	4.89898i	0.0245950	−	0.0425998i
$116$	97.9796	+	56.5685i	0.844652	+	0.487660i
$117$	−106.902	−	41.1589i	−0.913689	−	0.351786i
$118$	−45.2548			−0.383516
$119$		0			0
$120$	−32.0000	+	11.3137i	−0.266667	+	0.0942809i
$121$	−11.5000	−	19.9186i	−0.0950413	−	0.164616i
$122$	−39.8372	−	23.0000i	−0.326534	−	0.188525i
$123$	−47.1918	−	8.77101i	−0.383673	−	0.0713090i
$124$		0			0
$125$			136.000i			1.08800i
$126$		0			0
$127$	−104.000			−0.818898			−0.409449	−	0.912333i	$-0.634279\pi$
$127$	−104.000			−0.818898			−0.409449	+	0.912333i	$0.634279\pi$
$128$	9.79796	−	5.65685i	0.0765466	−	0.0441942i
$129$	28.5058	−	153.373i	0.220975	−	1.18894i
$130$	−36.0000	+	62.3538i	−0.276923	+	0.479645i
$131$	25.9808	−	15.0000i	0.198326	−	0.114504i	−0.397548	−	0.917581i	$-0.630139\pi$
$131$	25.9808	−	15.0000i	0.198326	−	0.114504i	0.595875	+	0.803077i	$0.296806\pi$
$132$	19.7990	+	56.0000i	0.149992	+	0.424242i
$133$		0			0
$134$			16.9706i			0.126646i
$135$	2.98979	−	107.959i	0.0221466	−	0.799693i
$136$	−45.2548	+	78.3837i	−0.332756	+	0.576351i
$137$	−58.7878	−	33.9411i	−0.429108	−	0.247745i	0.269859	−	0.962900i	$-0.413023\pi$
$137$	−58.7878	−	33.9411i	−0.429108	−	0.247745i	−0.698966	+	0.715154i	$0.746356\pi$
$138$	−4.56048	−	3.89898i	−0.0330469	−	0.0282535i
$139$	214.960			1.54648			0.773239	−	0.634115i	$-0.218635\pi$
$139$	214.960			1.54648			0.773239	+	0.634115i	$0.218635\pi$
$140$		0			0
$141$	34.0000	+	96.1665i	0.241135	+	0.682032i
$142$	63.0000	+	109.119i	0.443662	+	0.768445i
$143$	109.119	+	63.0000i	0.763071	+	0.440559i
$144$	5.59592	+	35.5624i	0.0388605	+	0.246961i
$145$	113.137	+	195.959i	0.780256	+	1.35144i
$146$			46.0000i			0.315068i
$147$		0			0
$148$	100.000			0.675676
$149$	−78.3837	+	45.2548i	−0.526065	+	0.303724i	−0.739413	−	0.673253i	$-0.764897\pi$
$149$	−78.3837	+	45.2548i	−0.526065	+	0.303724i	0.213348	+	0.976976i	$0.431563\pi$
$150$	37.5409	+	6.97730i	0.250273	+	0.0465153i
$151$	−76.0000	+	131.636i	−0.503311	+	0.871761i	0.496681	+	0.867933i	$0.334552\pi$
$151$	−76.0000	+	131.636i	−0.503311	+	0.871761i	−0.999993	+	0.00382774i	$0.998782\pi$
$152$	69.2820	−	40.0000i	0.455803	−	0.263158i
$153$	−181.019	−	224.000i	−1.18313	−	1.46405i
$154$		0			0
$155$		0			0
$156$	58.0454	+	49.6259i	0.372086	+	0.318115i
$157$	85.5599	−	148.194i	0.544968	−	0.943912i	−0.453641	−	0.891184i	$-0.649875\pi$
$157$	85.5599	−	148.194i	0.544968	−	0.943912i	0.998609	−	0.0527273i	$-0.0167914\pi$
$158$	−48.9898	−	28.2843i	−0.310062	−	0.179014i
$159$	88.2238	−	103.192i	0.554867	−	0.649005i
$160$	22.6274			0.141421
$161$		0			0
$162$	−112.000	−	24.0416i	−0.691358	−	0.148405i
$163$	−122.000	−	211.310i	−0.748466	−	1.29638i	−0.948558	−	0.316604i	$-0.897457\pi$
$163$	−122.000	−	211.310i	−0.748466	−	1.29638i	0.200091	−	0.979777i	$-0.435876\pi$
$164$	27.7128	+	16.0000i	0.168981	+	0.0975610i
$165$	−21.7071	+	116.794i	−0.131558	+	0.707841i
$166$	−43.8406	−	75.9342i	−0.264100	−	0.457435i
$167$		−	226.000i		−	1.35329i	−0.736308	−	0.676647i	$-0.763432\pi$
$167$		−	226.000i		−	1.35329i	0.736308	−	0.676647i	$-0.236568\pi$
$168$		0			0
$169$	−7.00000			−0.0414201
$170$	−156.767	+	90.5097i	−0.922161	+	0.532410i
$171$	39.5691	+	251.464i	0.231398	+	1.47055i
$172$	−52.0000	+	90.0666i	−0.302326	+	0.523643i
$173$	−114.315	+	66.0000i	−0.660782	+	0.381503i	−0.792575	−	0.609774i	$-0.791260\pi$
$173$	−114.315	+	66.0000i	−0.660782	+	0.381503i	0.131793	+	0.991277i	$0.457927\pi$
$174$	226.274	−	80.0000i	1.30043	−	0.459770i
$175$		0			0
$176$		−	39.5980i		−	0.224989i
$177$	−62.3837	+	72.9676i	−0.352450	+	0.412247i
$178$	−39.5980	+	68.5857i	−0.222461	+	0.385313i
$179$	194.734	+	112.430i	1.08790	+	0.628100i	0.933017	−	0.359832i	$-0.117166\pi$
$179$	194.734	+	112.430i	1.08790	+	0.628100i	0.154885	+	0.987933i	$0.450499\pi$
$180$	−25.8700	+	67.1918i	−0.143722	+	0.373288i
$181$	−182.434			−1.00792			−0.503960	−	0.863727i	$-0.668124\pi$
$181$	−182.434			−1.00792			−0.503960	+	0.863727i	$0.668124\pi$
$182$		0			0
$183$	−92.0000	+	32.5269i	−0.502732	+	0.177743i
$184$	2.00000	+	3.46410i	0.0108696	+	0.0188266i
$185$	173.205	+	100.000i	0.936244	+	0.540541i
$186$		0			0
$187$	158.392	+	274.343i	0.847016	+	1.46707i
$188$		−	68.0000i		−	0.361702i
$189$		0			0
$190$	160.000			0.842105
$191$	8.57321	−	4.94975i	0.0448859	−	0.0259149i	−0.477389	−	0.878692i	$-0.658417\pi$
$191$	8.57321	−	4.94975i	0.0448859	−	0.0259149i	0.522275	+	0.852777i	$0.325083\pi$
$192$	4.38551	−	23.5959i	0.0228412	−	0.122895i
$193$	80.0000	−	138.564i	0.414508	−	0.717949i	−0.580869	−	0.813997i	$-0.697287\pi$
$193$	80.0000	−	138.564i	0.414508	−	0.717949i	0.995377	+	0.0960486i	$0.0306204\pi$
$194$	−29.4449	+	17.0000i	−0.151778	+	0.0876289i
$195$	50.9117	+	144.000i	0.261086	+	0.738462i
$196$		0			0
$197$			107.480i			0.545585i	0.962073	+	0.272792i	$0.0879472\pi$
$197$			107.480i			0.545585i	−0.962073	+	0.272792i	$0.912053\pi$
$198$	117.586	+	45.2725i	0.593867	+	0.228649i
$199$	−110.309	+	191.060i	−0.554315	+	0.960102i	0.443642	+	0.896204i	$0.353686\pi$
$199$	−110.309	+	191.060i	−0.554315	+	0.960102i	−0.997956	+	0.0638972i	$0.979647\pi$
$200$	−22.0454	−	12.7279i	−0.110227	−	0.0636396i
$201$	27.3629	+	23.3939i	0.136134	+	0.116387i
$202$	50.9117			0.252038
$203$		0			0
$204$	64.0000	+	181.019i	0.313725	+	0.887350i
$205$	32.0000	+	55.4256i	0.156098	+	0.270369i
$206$	90.0666	+	52.0000i	0.437217	+	0.252427i
$207$	−12.5732	+	1.97846i	−0.0607402	+	0.00955776i
$208$	−25.4558	−	44.0908i	−0.122384	−	0.211975i
$209$		−	280.000i		−	1.33971i
$210$		0			0
$211$	−372.000			−1.76303			−0.881517	−	0.472153i	$-0.843477\pi$
$211$	−372.000			−1.76303			−0.881517	+	0.472153i	$0.843477\pi$
$212$	−78.3837	+	45.2548i	−0.369734	+	0.213466i
$213$	262.786	+	48.8411i	1.23374	+	0.229301i
$214$	−103.000	+	178.401i	−0.481308	+	0.833651i
$215$	−180.133	+	104.000i	−0.837829	+	0.483721i
$216$	65.0538	+	40.0000i	0.301175	+	0.185185i
$217$		0			0
$218$			248.902i			1.14175i
$219$	74.1691	+	63.4109i	0.338672	+	0.289547i
$220$	39.5980	−	68.5857i	0.179991	−	0.311753i
$221$	352.727	+	203.647i	1.59605	+	0.921479i
$222$	137.850	−	161.237i	0.620945	−	0.726294i
$223$	16.9706			0.0761012			0.0380506	−	0.999276i	$-0.487885\pi$
$223$	16.9706			0.0761012			0.0380506	+	0.999276i	$0.487885\pi$
$224$		0			0
$225$	63.0000	−	50.9117i	0.280000	−	0.226274i
$226$	12.0000	+	20.7846i	0.0530973	+	0.0919673i
$227$	−332.554	−	192.000i	−1.46499	−	0.845815i	−0.465759	−	0.884912i	$-0.654219\pi$
$227$	−332.554	−	192.000i	−1.46499	−	0.845815i	−0.999235	+	0.0390966i	$0.987552\pi$
$228$	31.0102	−	166.848i	0.136010	−	0.731791i
$229$	−125.158	−	216.780i	−0.546541	−	0.946637i	−0.998508	−	0.0546023i	$-0.982611\pi$
$229$	−125.158	−	216.780i	−0.546541	−	0.946637i	0.451967	−	0.892035i	$-0.350722\pi$
$230$			8.00000i			0.0347826i
$231$		0			0
$232$	−160.000			−0.689655
$233$	−279.242	+	161.220i	−1.19846	+	0.691933i	−0.960212	−	0.279271i	$-0.909907\pi$
$233$	−279.242	+	161.220i	−1.19846	+	0.691933i	−0.238250	+	0.971204i	$0.576574\pi$
$234$	160.031	−	25.1816i	0.683893	−	0.107614i
$235$	68.0000	−	117.779i	0.289362	−	0.501189i
$236$	55.4256	−	32.0000i	0.234854	−	0.135593i
$237$	−113.137	+	40.0000i	−0.477372	+	0.168776i
$238$		0			0
$239$			284.257i			1.18936i	0.803963	+	0.594680i	$0.202721\pi$
$239$			284.257i			1.18936i	−0.803963	+	0.594680i	$0.797279\pi$
$240$	31.1918	−	36.4838i	0.129966	−	0.152016i
$241$	23.3345	−	40.4166i	0.0968238	−	0.167704i	−0.813545	−	0.581503i	$-0.802465\pi$
$241$	23.3345	−	40.4166i	0.0968238	−	0.167704i	0.910368	+	0.413799i	$0.135798\pi$
$242$	28.1691	+	16.2635i	0.116401	+	0.0672044i
$243$	−193.156	+	147.444i	−0.794880	+	0.606767i
$244$	65.0538			0.266614
$245$		0			0
$246$	64.0000	−	22.6274i	0.260163	−	0.0919814i
$247$	−180.000	−	311.769i	−0.728745	−	1.26222i
$248$		0			0
$249$	−182.868	−	33.9877i	−0.734411	−	0.136497i
$250$	−96.1665	−	166.565i	−0.384666	−	0.666261i
$251$			224.000i			0.892430i	0.894926	+	0.446215i	$0.147228\pi$
$251$			224.000i			0.892430i	−0.894926	+	0.446215i	$0.852772\pi$
$252$		0			0
$253$	14.0000			0.0553360
$254$	127.373	−	73.5391i	0.501470	−	0.289524i
$255$	−70.1681	+	377.535i	−0.275169	+	1.48053i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	103.923	−	60.0000i	0.404370	−	0.233463i	−0.283998	−	0.958825i	$-0.591661\pi$
$257$	103.923	−	60.0000i	0.404370	−	0.233463i	0.688368	+	0.725362i	$0.258328\pi$
$258$	73.5391	+	208.000i	0.285035	+	0.806202i
$259$		0			0
$260$		−	101.823i		−	0.391628i
$261$	182.929	−	475.118i	0.700876	−	1.82038i
$262$	−21.2132	+	36.7423i	−0.0809664	+	0.140238i
$263$	−194.734	−	112.430i	−0.740435	−	0.427490i	0.0817924	−	0.996649i	$-0.473936\pi$
$263$	−194.734	−	112.430i	−0.740435	−	0.427490i	−0.822227	+	0.569159i	$0.807269\pi$
$264$	−63.8467	−	54.5857i	−0.241844	−	0.206764i
$265$	−181.019			−0.683092
$266$		0			0
$267$	56.0000	+	158.392i	0.209738	+	0.593228i
$268$	−12.0000	−	20.7846i	−0.0447761	−	0.0775545i
$269$	−142.028	−	82.0000i	−0.527986	−	0.304833i	0.212210	−	0.977224i	$-0.431934\pi$
$269$	−142.028	−	82.0000i	−0.527986	−	0.304833i	−0.740196	+	0.672391i	$0.765267\pi$
$270$	72.6765	+	134.336i	0.269172	+	0.497540i
$271$	−115.966	−	200.858i	−0.427917	−	0.741174i	0.568771	−	0.822496i	$-0.307419\pi$
$271$	−115.966	−	200.858i	−0.427917	−	0.741174i	−0.996688	+	0.0813220i	$0.974086\pi$
$272$		−	128.000i		−	0.470588i
$273$		0			0
$274$	96.0000			0.350365
$275$	−77.1589	+	44.5477i	−0.280578	+	0.161992i
$276$	8.34242	+	1.55051i	0.0302261	+	0.00561779i
$277$	232.000	−	401.836i	0.837545	−	1.45067i	−0.0543961	−	0.998519i	$-0.517323\pi$
$277$	232.000	−	401.836i	0.837545	−	1.45067i	0.891941	−	0.452151i	$-0.149343\pi$
$278$	−263.272	+	152.000i	−0.947021	+	0.546763i
$279$		0			0
$280$		0			0
$281$		−	39.5980i		−	0.140918i	−0.997515	−	0.0704590i	$-0.977554\pi$
$281$		−	39.5980i		−	0.140918i	0.997515	−	0.0704590i	$-0.0224464\pi$
$282$	−109.641	−	93.7378i	−0.388799	−	0.332404i
$283$	124.451	−	215.555i	0.439755	−	0.761679i	−0.557915	−	0.829898i	$-0.688398\pi$
$283$	124.451	−	215.555i	0.439755	−	0.761679i	0.997670	+	0.0682194i	$0.0217318\pi$
$284$	−154.318	−	89.0955i	−0.543373	−	0.313716i
$285$	220.560	−	257.980i	0.773893	−	0.905192i
$286$	−178.191			−0.623045
$287$		0			0
$288$	−32.0000	−	39.5980i	−0.111111	−	0.137493i
$289$	367.500	+	636.529i	1.27163	+	2.20252i
$290$	−277.128	−	160.000i	−0.955614	−	0.551724i
$291$	−13.1793	+	70.9105i	−0.0452898	+	0.243679i
$292$	−32.5269	−	56.3383i	−0.111394	−	0.192939i
$293$		−	316.000i		−	1.07850i	−0.842146	−	0.539249i	$-0.818708\pi$
$293$		−	316.000i		−	1.07850i	0.842146	−	0.539249i	$-0.181292\pi$
$294$		0			0
$295$	128.000			0.433898
$296$	−122.474	+	70.7107i	−0.413765	+	0.238887i
$297$	235.088	−	127.184i	0.791541	−	0.428229i
$298$	64.0000	−	110.851i	0.214765	−	0.371984i
$299$	15.5885	−	9.00000i	0.0521353	−	0.0301003i
$300$	−50.9117	+	18.0000i	−0.169706	+	0.0600000i
$301$		0			0
$302$		−	214.960i		−	0.711790i
$303$	70.1816	−	82.0886i	0.231623	−	0.270919i
$304$	−56.5685	+	97.9796i	−0.186081	+	0.322301i
$305$	112.677	+	65.0538i	0.369431	+	0.213291i
$306$	380.094	+	146.343i	1.24214	+	0.478245i
$307$	345.068			1.12400			0.562000	−	0.827137i	$-0.310032\pi$
$307$	345.068			1.12400			0.562000	+	0.827137i	$0.310032\pi$
$308$		0			0
$309$	208.000	−	73.5391i	0.673139	−	0.237991i
$310$		0			0
$311$	−458.993	−	265.000i	−1.47586	−	0.852090i	−0.476234	−	0.879319i	$-0.657998\pi$
$311$	−458.993	−	265.000i	−1.47586	−	0.852090i	−0.999629	+	0.0272286i	$0.991332\pi$
$312$	−106.182	−	19.7348i	−0.340326	−	0.0632525i
$313$	74.2462	+	128.598i	0.237208	+	0.410857i	0.959912	−	0.280301i	$-0.0904343\pi$
$313$	74.2462	+	128.598i	0.237208	+	0.410857i	−0.722704	+	0.691158i	$0.757101\pi$
$314$			242.000i			0.770701i
$315$		0			0
$316$	80.0000			0.253165
$317$	97.9796	−	56.5685i	0.309084	−	0.178450i	−0.337433	−	0.941350i	$-0.609559\pi$
$317$	97.9796	−	56.5685i	0.309084	−	0.178450i	0.646516	+	0.762900i	$0.276225\pi$
$318$	−35.0840	+	188.767i	−0.110327	+	0.593608i
$319$	−280.000	+	484.974i	−0.877743	+	1.52030i
$320$	−27.7128	+	16.0000i	−0.0866025	+	0.0500000i
$321$	145.664	+	412.000i	0.453782	+	1.28349i
$322$		0			0
$323$		−	905.097i		−	2.80216i
$324$	154.171	−	49.7511i	0.475838	−	0.153553i
$325$	−57.2756	+	99.2043i	−0.176233	+	0.305244i
$326$	298.838	+	172.534i	0.916680	+	0.529246i
$327$	401.322	+	343.110i	1.22728	+	1.04927i
$328$	−45.2548			−0.137972
$329$		0			0
$330$	−56.0000	−	158.392i	−0.169697	−	0.479976i
$331$	−26.0000	−	45.0333i	−0.0785498	−	0.136052i	0.824075	−	0.566481i	$-0.191696\pi$
$331$	−26.0000	−	45.0333i	−0.0785498	−	0.136052i	−0.902624	+	0.430429i	$0.858362\pi$
$332$	107.387	+	62.0000i	0.323455	+	0.186747i
$333$	−69.9490	−	444.530i	−0.210057	−	1.33493i
$334$	159.806	+	276.792i	0.478461	+	0.828720i
$335$		−	48.0000i		−	0.143284i
$336$		0			0
$337$	80.0000			0.237389			0.118694	−	0.992931i	$-0.462129\pi$
$337$	80.0000			0.237389			0.118694	+	0.992931i	$0.462129\pi$
$338$	8.57321	−	4.94975i	0.0253645	−	0.0146442i
$339$	50.0545	+	9.30306i	0.147653	+	0.0274427i
$340$	128.000	−	221.703i	0.376471	−	0.652066i
$341$		0			0
$342$	−226.274	−	280.000i	−0.661620	−	0.818713i
$343$		0			0
$344$		−	147.078i		−	0.427553i
$345$	12.8990	+	11.0280i	0.0373883	+	0.0319652i
$346$	93.3381	−	161.666i	0.269763	−	0.467244i
$347$	−187.386	−	108.187i	−0.540017	−	0.311779i	0.205069	−	0.978748i	$-0.434258\pi$
$347$	−187.386	−	108.187i	−0.540017	−	0.311779i	−0.745086	+	0.666969i	$0.767592\pi$
$348$	−220.560	+	257.980i	−0.633792	+	0.741321i
$349$	−12.7279			−0.0364697			−0.0182348	−	0.999834i	$-0.505805\pi$
$349$	−12.7279			−0.0364697			−0.0182348	+	0.999834i	$0.505805\pi$
$350$		0			0
$351$	180.000	−	292.742i	0.512821	−	0.834023i
$352$	28.0000	+	48.4974i	0.0795455	+	0.137777i
$353$	−55.4256	−	32.0000i	−0.157013	−	0.0906516i	0.419435	−	0.907785i	$-0.362228\pi$
$353$	−55.4256	−	32.0000i	−0.157013	−	0.0906516i	−0.576448	+	0.817134i	$0.695562\pi$
$354$	24.8082	−	133.479i	0.0700796	−	0.377058i
$355$	−178.191	−	308.636i	−0.501946	−	0.869396i
$356$		−	112.000i		−	0.314607i
$357$		0			0
$358$	−318.000			−0.888268
$359$	−155.543	+	89.8026i	−0.433266	+	0.250146i	−0.700737	−	0.713420i	$-0.747145\pi$
$359$	−155.543	+	89.8026i	−0.433266	+	0.250146i	0.267471	+	0.963566i	$0.413812\pi$
$360$	−15.8276	−	100.586i	−0.0439657	−	0.279405i
$361$	−219.500	+	380.185i	−0.608033	+	1.05314i
$362$	223.435	−	129.000i	0.617223	−	0.356354i
$363$	65.0538	−	23.0000i	0.179212	−	0.0633609i
$364$		0			0
$365$		−	130.108i		−	0.356459i
$366$	89.6765	−	104.891i	0.245018	−	0.286587i
$367$	65.0538	−	112.677i	0.177258	−	0.307021i	−0.763682	−	0.645592i	$-0.776611\pi$
$367$	65.0538	−	112.677i	0.177258	−	0.307021i	0.940941	+	0.338572i	$0.109944\pi$
$368$	−4.89898	−	2.82843i	−0.0133124	−	0.00768594i
$369$	51.7400	−	134.384i	0.140217	−	0.364183i
$370$	−282.843			−0.764440
$371$		0			0
$372$		0			0
$373$	7.00000	+	12.1244i	0.0187668	+	0.0325050i	0.875256	−	0.483659i	$-0.160693\pi$
$373$	7.00000	+	12.1244i	0.0187668	+	0.0325050i	−0.856490	+	0.516164i	$0.827359\pi$
$374$	−387.979	−	224.000i	−1.03738	−	0.598930i
$375$	−401.131	−	74.5536i	−1.06968	−	0.198810i
$376$	48.0833	+	83.2827i	0.127881	+	0.221496i
$377$			720.000i			1.90981i
$378$		0			0
$379$	148.000			0.390501			0.195251	−	0.980753i	$-0.437448\pi$
$379$	148.000			0.390501			0.195251	+	0.980753i	$0.437448\pi$
$380$	−195.959	+	113.137i	−0.515682	+	0.297729i
$381$	57.0116	−	306.747i	0.149637	−	0.805110i
$382$	−7.00000	+	12.1244i	−0.0183246	+	0.0317392i
$383$	−96.9948	+	56.0000i	−0.253250	+	0.146214i	−0.621252	−	0.783611i	$-0.713376\pi$
$383$	−96.9948	+	56.0000i	−0.253250	+	0.146214i	0.368001	+	0.929825i	$0.380042\pi$
$384$	11.3137	+	32.0000i	0.0294628	+	0.0833333i
$385$		0			0
$386$			226.274i			0.586203i
$387$	436.747	+	168.155i	1.12855	+	0.434509i
$388$	24.0416	−	41.6413i	0.0619630	−	0.107323i
$389$	−372.322	−	214.960i	−0.957127	−	0.552598i	−0.0618394	−	0.998086i	$-0.519697\pi$
$389$	−372.322	−	214.960i	−0.957127	−	0.552598i	−0.895288	+	0.445489i	$0.853030\pi$
$390$	−164.177	−	140.363i	−0.420967	−	0.359906i
$391$	45.2548			0.115741
$392$		0			0
$393$	30.0000	+	84.8528i	0.0763359	+	0.215910i
$394$	−76.0000	−	131.636i	−0.192893	−	0.334101i
$395$	138.564	+	80.0000i	0.350795	+	0.202532i
$396$	−176.025	+	27.6984i	−0.444508	+	0.0699454i
$397$	17.6777	+	30.6186i	0.0445281	+	0.0771250i	0.887430	−	0.460942i	$-0.152488\pi$
$397$	17.6777	+	30.6186i	0.0445281	+	0.0771250i	−0.842902	+	0.538067i	$0.819155\pi$
$398$		−	312.000i		−	0.783920i
$399$		0			0
$400$	36.0000			0.0900000
$401$	117.576	−	67.8823i	0.293206	−	0.169282i	−0.346181	−	0.938168i	$-0.612522\pi$
$401$	117.576	−	67.8823i	0.293206	−	0.169282i	0.639387	+	0.768885i	$0.279188\pi$
$402$	−50.0545	−	9.30306i	−0.124514	−	0.0231419i
$403$		0			0
$404$	−62.3538	+	36.0000i	−0.154341	+	0.0891089i
$405$	316.784	+	68.0000i	0.782182	+	0.167901i
$406$		0			0
$407$			494.975i			1.21615i
$408$	−206.384	−	176.448i	−0.505842	−	0.432470i
$409$	163.342	−	282.916i	0.399368	−	0.691726i	−0.594280	−	0.804258i	$-0.702563\pi$
$409$	163.342	−	282.916i	0.399368	−	0.691726i	0.993648	+	0.112532i	$0.0358961\pi$
$410$	−78.3837	−	45.2548i	−0.191180	−	0.110378i
$411$	132.336	−	154.788i	0.321985	−	0.376613i
$412$	−147.078			−0.356986
$413$		0			0
$414$	14.0000	−	11.3137i	0.0338164	−	0.0273278i
$415$	124.000	+	214.774i	0.298795	+	0.517528i
$416$	62.3538	+	36.0000i	0.149889	+	0.0865385i
$417$	−117.839	+	634.024i	−0.282587	+	1.52044i
$418$	197.990	+	342.929i	0.473660	+	0.820403i
$419$			352.000i			0.840095i	0.907502	+	0.420048i	$0.137987\pi$
$419$			352.000i			0.840095i	−0.907502	+	0.420048i	$0.862013\pi$
$420$		0			0
$421$	240.000			0.570071			0.285036	−	0.958517i	$-0.407995\pi$
$421$	240.000			0.570071			0.285036	+	0.958517i	$0.407995\pi$
$422$	455.605	−	263.044i	1.07963	−	0.623326i
$423$	−302.281	+	47.5653i	−0.714611	+	0.112448i
$424$	64.0000	−	110.851i	0.150943	−	0.261442i
$425$	−249.415	+	144.000i	−0.586860	+	0.338824i
$426$	−356.382	+	126.000i	−0.836577	+	0.295775i
$427$		0			0
$428$		−	291.328i		−	0.680673i
$429$	−245.636	+	287.310i	−0.572577	+	0.669721i
$430$	147.078	−	254.747i	0.342042	−	0.592435i
$431$	635.643	+	366.988i	1.47481	+	0.851481i	0.999597	−	0.0283901i	$-0.00903808\pi$
$431$	635.643	+	366.988i	1.47481	+	0.851481i	0.475212	+	0.879871i	$0.342371\pi$
$432$	−107.959	−	2.98979i	−0.249904	−	0.00692082i
$433$	−428.507			−0.989623			−0.494811	−	0.869000i	$-0.664763\pi$
$433$	−428.507			−0.989623			−0.494811	+	0.869000i	$0.664763\pi$
$434$		0			0
$435$	−640.000	+	226.274i	−1.47126	+	0.520171i
$436$	−176.000	−	304.841i	−0.403670	−	0.699176i
$437$	−34.6410	−	20.0000i	−0.0792701	−	0.0457666i
$438$	−135.677	−	25.2167i	−0.309764	−	0.0575723i
$439$	−203.647	−	352.727i	−0.463888	−	0.803477i	0.535263	−	0.844686i	$-0.320213\pi$
$439$	−203.647	−	352.727i	−0.463888	−	0.803477i	−0.999151	+	0.0412083i	$0.986879\pi$
$440$			112.000i			0.254545i
$441$		0			0
$442$	−576.000			−1.30317
$443$	−344.153	+	198.697i	−0.776870	+	0.448526i	−0.835320	−	0.549764i	$-0.814718\pi$
$443$	−344.153	+	198.697i	−0.776870	+	0.448526i	0.0584500	+	0.998290i	$0.481384\pi$
$444$	−54.8188	+	294.949i	−0.123466	+	0.664299i
$445$	112.000	−	193.990i	0.251685	−	0.435932i
$446$	−20.7846	+	12.0000i	−0.0466023	+	0.0269058i
$447$	−90.5097	−	256.000i	−0.202482	−	0.572707i
$448$		0			0
$449$		−	16.9706i		−	0.0377964i	−0.999821	−	0.0188982i	$-0.993984\pi$
$449$		−	16.9706i		−	0.0377964i	0.999821	−	0.0188982i	$-0.00601583\pi$
$450$	−41.1589	+	106.902i	−0.0914643	+	0.237559i
$451$	−79.1960	+	137.171i	−0.175601	+	0.304150i
$452$	−29.3939	−	16.9706i	−0.0650307	−	0.0375455i
$453$	−346.596	−	296.322i	−0.765113	−	0.654133i
$454$	543.058			1.19616
$455$		0			0
$456$	80.0000	+	226.274i	0.175439	+	0.496215i
$457$	63.0000	+	109.119i	0.137856	+	0.238773i	0.926685	−	0.375840i	$-0.122646\pi$
$457$	63.0000	+	109.119i	0.137856	+	0.238773i	−0.788829	+	0.614613i	$0.789312\pi$
$458$	306.573	+	177.000i	0.669373	+	0.386463i
$459$	759.918	−	411.121i	1.65560	−	0.895687i
$460$	−5.65685	−	9.79796i	−0.0122975	−	0.0212999i
$461$		−	580.000i		−	1.25813i	−0.777351	−	0.629067i	$-0.783437\pi$
$461$		−	580.000i		−	1.25813i	0.777351	−	0.629067i	$-0.216563\pi$
$462$		0			0
$463$	112.000			0.241901			0.120950	−	0.992659i	$-0.461406\pi$
$463$	112.000			0.241901			0.120950	+	0.992659i	$0.461406\pi$
$464$	195.959	−	113.137i	0.422326	−	0.243830i
$465$		0			0
$466$	228.000	−	394.908i	0.489270	−	0.847441i
$467$	−110.851	+	64.0000i	−0.237369	+	0.137045i	−0.613967	−	0.789332i	$-0.710427\pi$
$467$	−110.851	+	64.0000i	−0.237369	+	0.137045i	0.376598	+	0.926377i	$0.377094\pi$
$468$	−178.191	+	144.000i	−0.380750	+	0.307692i
$469$		0			0
$470$			192.333i			0.409219i
$471$	390.194	+	333.596i	0.828438	+	0.708273i
$472$	−45.2548	+	78.3837i	−0.0958789	+	0.166067i
$473$	−445.807	−	257.387i	−0.942510	−	0.544158i
$474$	110.280	−	128.990i	0.232658	−	0.272130i
$475$	254.558			0.535913
$476$		0			0
$477$	256.000	+	316.784i	0.536688	+	0.664117i
$478$	−201.000	−	348.142i	−0.420502	−	0.728331i
$479$	417.424	+	241.000i	0.871449	+	0.503132i	0.867830	−	0.496862i	$-0.165514\pi$
$479$	417.424	+	241.000i	0.871449	+	0.503132i	0.00361975	+	0.999993i	$0.498848\pi$
$480$	−12.4041	+	66.7393i	−0.0258418	+	0.139040i
$481$	318.198	+	551.135i	0.661534	+	1.14581i
$482$			66.0000i			0.136929i
$483$		0			0
$484$	−46.0000			−0.0950413
$485$	83.2827	−	48.0833i	0.171717	−	0.0991407i
$486$	132.308	−	317.164i	0.272238	−	0.652600i
$487$	60.0000	−	103.923i	0.123203	−	0.213394i	−0.797826	−	0.602888i	$-0.794017\pi$
$487$	60.0000	−	103.923i	0.123203	−	0.213394i	0.921029	+	0.389494i	$0.127350\pi$
$488$	−79.6743	+	46.0000i	−0.163267	+	0.0942623i
$489$	690.136	−	244.000i	1.41132	−	0.498978i
$490$		0			0
$491$			623.668i			1.27020i	0.772430	+	0.635100i	$0.219041\pi$
$491$			623.668i			1.27020i	−0.772430	+	0.635100i	$0.780959\pi$
$492$	−62.3837	+	72.9676i	−0.126796	+	0.148308i
$493$	−905.097	+	1567.67i	−1.83590	+	3.17986i
$494$	440.908	+	254.558i	0.892527	+	0.515300i
$495$	−332.583	−	128.050i	−0.671884	−	0.258687i
$496$		0			0
$497$		0			0
$498$	248.000	−	87.6812i	0.497992	−	0.176067i
$499$	−142.000	−	245.951i	−0.284569	−	0.492888i	0.687935	−	0.725772i	$-0.258517\pi$
$499$	−142.000	−	245.951i	−0.284569	−	0.492888i	−0.972505	+	0.232884i	$0.925184\pi$
$500$	235.559	+	136.000i	0.471118	+	0.272000i
$501$	666.585	+	123.891i	1.33051	+	0.247286i
$502$	−158.392	−	274.343i	−0.315522	−	0.546500i
$503$		−	16.0000i		−	0.0318091i	−0.999874	−	0.0159046i	$-0.994937\pi$
$503$		−	16.0000i		−	0.0318091i	0.999874	−	0.0159046i	$-0.00506280\pi$
$504$		0			0
$505$	−144.000			−0.285149
$506$	−17.1464	+	9.89949i	−0.0338862	+	0.0195642i
$507$	3.83732	−	20.6464i	0.00756867	−	0.0407227i
$508$	−104.000	+	180.133i	−0.204724	+	0.354593i
$509$	308.305	−	178.000i	0.605707	−	0.349705i	−0.165576	−	0.986197i	$-0.552948\pi$
$509$	308.305	−	178.000i	0.605707	−	0.349705i	0.771284	+	0.636492i	$0.219615\pi$
$510$	−181.019	−	512.000i	−0.354940	−	1.00392i
$511$		0			0
$512$		−	22.6274i		−	0.0441942i
$513$	−763.383	−	21.1410i	−1.48808	−	0.0412106i
$514$	−84.8528	+	146.969i	−0.165083	+	0.285933i
$515$	−254.747	−	147.078i	−0.494654	−	0.285589i
$516$	−237.145	−	202.747i	−0.459583	−	0.392920i
$517$	336.583			0.651031
$518$		0			0
$519$	−132.000	−	373.352i	−0.254335	−	0.719369i
$520$	72.0000	+	124.708i	0.138462	+	0.239822i
$521$	214.774	+	124.000i	0.412235	+	0.238004i	0.691749	−	0.722138i	$-0.256840\pi$
$521$	214.774	+	124.000i	0.412235	+	0.238004i	−0.279515	+	0.960141i	$0.590174\pi$
$522$	111.918	+	711.248i	0.214403	+	1.36254i
$523$	−25.4558	−	44.0908i	−0.0486727	−	0.0843037i	0.840663	−	0.541559i	$-0.182166\pi$
$523$	−25.4558	−	44.0908i	−0.0486727	−	0.0843037i	−0.889335	+	0.457256i	$0.848832\pi$
$524$		−	60.0000i		−	0.114504i
$525$		0			0
$526$	318.000			0.604563
$527$		0			0
$528$	116.794	+	21.7071i	0.221200	+	0.0411120i
$529$	−263.500	+	456.395i	−0.498110	+	0.862751i
$530$	221.703	−	128.000i	0.418307	−	0.241509i
$531$	−181.019	−	224.000i	−0.340903	−	0.421846i
$532$		0			0
$533$			203.647i			0.382076i
$534$	−180.586	−	154.392i	−0.338175	−	0.289123i
$535$	291.328	−	504.595i	0.544538	−	0.943168i
$536$	29.3939	+	16.9706i	0.0548393	+	0.0316615i
$537$	−438.362	+	512.734i	−0.816317	+	0.954813i
$538$	231.931			0.431099
$539$		0			0
$540$	−184.000	−	113.137i	−0.340741	−	0.209513i
$541$	−200.000	−	346.410i	−0.369686	−	0.640315i	0.619831	−	0.784736i	$-0.287201\pi$
$541$	−200.000	−	346.410i	−0.369686	−	0.640315i	−0.989516	+	0.144421i	$0.953868\pi$
$542$	284.056	+	164.000i	0.524089	+	0.302583i
$543$	100.008	−	538.086i	0.184177	−	0.990950i
$544$	90.5097	+	156.767i	0.166378	+	0.288175i
$545$		−	704.000i		−	1.29174i
$546$		0			0
$547$	820.000			1.49909			0.749543	−	0.661956i	$-0.230273\pi$
$547$	820.000			1.49909			0.749543	+	0.661956i	$0.230273\pi$
$548$	−117.576	+	67.8823i	−0.214554	+	0.123873i
$549$	−45.5045	−	289.184i	−0.0828861	−	0.526747i
$550$	63.0000	−	109.119i	0.114545	−	0.198399i
$551$	1385.64	−	800.000i	2.51477	−	1.45191i
$552$	−11.3137	+	4.00000i	−0.0204958	+	0.00724638i
$553$		0			0
$554$			656.195i			1.18447i
$555$	−389.898	+	456.048i	−0.702519	+	0.821708i
$556$	214.960	−	372.322i	0.386620	−	0.669645i
$557$	911.210	+	526.087i	1.63592	+	0.944502i	0.982216	+	0.187756i	$0.0601214\pi$
$557$	911.210	+	526.087i	1.63592	+	0.944502i	0.653709	+	0.756746i	$0.273212\pi$
$558$		0			0
$559$	−661.852			−1.18399
$560$		0			0
$561$	−896.000	+	316.784i	−1.59715	+	0.564677i
$562$	28.0000	+	48.4974i	0.0498221	+	0.0862943i
$563$	942.236	+	544.000i	1.67360	+	0.966252i	0.965598	+	0.260040i	$0.0837357\pi$
$563$	942.236	+	544.000i	1.67360	+	0.966252i	0.708000	+	0.706212i	$0.249598\pi$
$564$	200.565	+	37.2768i	0.355612	+	0.0660936i
$565$	−33.9411	−	58.7878i	−0.0600728	−	0.104049i
$566$			352.000i			0.621908i
$567$		0			0
$568$	252.000			0.443662
$569$	436.009	−	251.730i	0.766273	−	0.442408i	−0.0652707	−	0.997868i	$-0.520791\pi$
$569$	436.009	−	251.730i	0.766273	−	0.442408i	0.831543	+	0.555460i	$0.187458\pi$
$570$	−87.7101	+	471.918i	−0.153877	+	0.827927i
$571$	−410.000	+	710.141i	−0.718039	+	1.24368i	0.243737	+	0.969841i	$0.421627\pi$
$571$	−410.000	+	710.141i	−0.718039	+	1.24368i	−0.961776	+	0.273838i	$0.911707\pi$
$572$	218.238	−	126.000i	0.381536	−	0.220280i
$573$	9.89949	+	28.0000i	0.0172766	+	0.0488656i
$574$		0			0
$575$			12.7279i			0.0221355i
$576$	67.1918	+	25.8700i	0.116652	+	0.0449132i
$577$	−146.371	+	253.522i	−0.253676	+	0.439380i	−0.964535	−	0.263955i	$-0.914973\pi$
$577$	−146.371	+	253.522i	−0.253676	+	0.439380i	0.710859	+	0.703335i	$0.248306\pi$
$578$	−900.187	−	519.723i	−1.55742	−	0.899176i
$579$	364.838	+	311.918i	0.630118	+	0.538719i
$580$	452.548			0.780256
$581$		0			0
$582$	−34.0000	−	96.1665i	−0.0584192	−	0.165235i
$583$	−224.000	−	387.979i	−0.384220	−	0.665488i
$584$	79.6743	+	46.0000i	0.136429	+	0.0787671i
$585$	−452.636	+	71.2244i	−0.773736	+	0.121751i
$586$	223.446	+	387.019i	0.381307	+	0.660443i
$587$		−	480.000i		−	0.817717i	−0.912598	−	0.408859i	$-0.865927\pi$
$587$		−	480.000i		−	0.817717i	0.912598	−	0.408859i	$-0.134073\pi$
$588$		0			0
$589$		0			0
$590$	−156.767	+	90.5097i	−0.265707	+	0.153406i
$591$	−317.012	−	58.9194i	−0.536399	−	0.0996944i
$592$	100.000	−	173.205i	0.168919	−	0.292576i
$593$	−928.379	+	536.000i	−1.56556	+	0.903879i	−0.568887	+	0.822416i	$0.692626\pi$
$593$	−928.379	+	536.000i	−1.56556	+	0.903879i	−0.996676	+	0.0814631i	$0.974041\pi$
$594$	−197.990	+	322.000i	−0.333316	+	0.542088i
$595$		0			0
$596$			181.019i			0.303724i
$597$	−503.060	−	430.091i	−0.842647	−	0.720421i
$598$	−12.7279	+	22.0454i	−0.0212842	+	0.0368652i
$599$	−353.951	−	204.354i	−0.590904	−	0.341158i	0.174551	−	0.984648i	$-0.444153\pi$
$599$	−353.951	−	204.354i	−0.590904	−	0.341158i	−0.765455	+	0.643490i	$0.777486\pi$
$600$	49.6259	−	58.0454i	0.0827098	−	0.0967423i
$601$	326.683			0.543566			0.271783	−	0.962359i	$-0.412387\pi$
$601$	326.683			0.543566			0.271783	+	0.962359i	$0.412387\pi$
$602$		0			0
$603$	−84.0000	+	67.8823i	−0.139303	+	0.112574i
$604$	152.000	+	263.272i	0.251656	+	0.435880i
$605$	−79.6743	−	46.0000i	−0.131693	−	0.0760331i
$606$	−27.9092	+	150.164i	−0.0460548	+	0.247795i
$607$	−127.279	−	220.454i	−0.209686	−	0.363186i	0.741930	−	0.670478i	$-0.233911\pi$
$607$	−127.279	−	220.454i	−0.209686	−	0.363186i	−0.951616	+	0.307291i	$0.900577\pi$
$608$		−	160.000i		−	0.263158i
$609$		0			0
$610$	−184.000			−0.301639
$611$	374.772	−	216.375i	0.613375	−	0.354132i
$612$	−568.999	+	89.5347i	−0.929736	+	0.146299i
$613$	168.000	−	290.985i	0.274062	−	0.474689i	−0.695836	−	0.718201i	$-0.744966\pi$
$613$	168.000	−	290.985i	0.274062	−	0.474689i	0.969898	+	0.243511i	$0.0782993\pi$
$614$	−422.620	+	244.000i	−0.688307	+	0.397394i
$615$	−181.019	+	64.0000i	−0.294340	+	0.104065i
$616$		0			0
$617$			384.666i			0.623446i	0.950173	+	0.311723i	$0.100906\pi$
$617$			384.666i			0.623446i	−0.950173	+	0.311723i	$0.899094\pi$
$618$	−202.747	+	237.145i	−0.328069	+	0.383730i
$619$	308.299	−	533.989i	0.498059	−	0.862664i	−0.501938	−	0.864903i	$-0.667380\pi$
$619$	308.299	−	533.989i	0.498059	−	0.862664i	0.999997	+	0.00223976i	$0.000712938\pi$
$620$		0			0
$621$	1.05705	−	38.1691i	0.00170218	−	0.0614640i
$622$	749.533			1.20504
$623$		0			0
$624$	144.000	−	50.9117i	0.230769	−	0.0815892i
$625$	159.500	+	276.262i	0.255200	+	0.442019i
$626$	−181.865	−	105.000i	−0.290520	−	0.167732i
$627$	825.857	+	153.493i	1.31716	+	0.244805i
$628$	−171.120	−	296.388i	−0.272484	−	0.471956i
$629$			1600.00i			2.54372i
$630$		0			0
$631$	−712.000			−1.12837			−0.564184	−	0.825649i	$-0.690809\pi$
$631$	−712.000			−1.12837			−0.564184	+	0.825649i	$0.690809\pi$
$632$	−97.9796	+	56.5685i	−0.155031	+	0.0895072i
$633$	203.926	−	1097.21i	0.322158	−	1.73335i
$634$	−80.0000	+	138.564i	−0.126183	+	0.218555i
$635$	−360.267	+	208.000i	−0.567349	+	0.327559i
$636$	−90.5097	−	256.000i	−0.142311	−	0.402516i
$637$		0			0
$638$		−	791.960i		−	1.24132i
$639$	−288.112	+	748.311i	−0.450880	+	1.17107i
$640$	22.6274	−	39.1918i	0.0353553	−	0.0612372i
$641$	−489.898	−	282.843i	−0.764271	−	0.441252i	0.0665559	−	0.997783i	$-0.478799\pi$
$641$	−489.898	−	282.843i	−0.764271	−	0.441252i	−0.830827	+	0.556530i	$0.812132\pi$
$642$	−469.729	−	401.595i	−0.731665	−	0.625537i
$643$	−837.214			−1.30204			−0.651022	−	0.759059i	$-0.725659\pi$
$643$	−837.214			−1.30204			−0.651022	+	0.759059i	$0.725659\pi$
$644$		0			0
$645$	−208.000	−	588.313i	−0.322481	−	0.912113i
$646$	640.000	+	1108.51i	0.990712	+	1.71596i
$647$	805.404	+	465.000i	1.24483	+	0.718702i	0.970073	−	0.242813i	$-0.0780700\pi$
$647$	805.404	+	465.000i	1.24483	+	0.718702i	0.274755	+	0.961514i	$0.411403\pi$
$648$	−153.641	+	169.948i	−0.237101	+	0.262266i
$649$	158.392	+	274.343i	0.244055	+	0.422716i
$650$		−	162.000i		−	0.249231i
$651$		0			0
$652$	−488.000			−0.748466
$653$	455.605	−	263.044i	0.697711	−	0.402823i	−0.108783	−	0.994065i	$-0.534696\pi$
$653$	455.605	−	263.044i	0.697711	−	0.402823i	0.806494	+	0.591242i	$0.201362\pi$
$654$	−734.133	−	136.445i	−1.12253	−	0.208631i
$655$	60.0000	−	103.923i	0.0916031	−	0.158661i
$656$	55.4256	−	32.0000i	0.0844903	−	0.0487805i
$657$	−227.688	+	184.000i	−0.346558	+	0.280061i
$658$		0			0
$659$		−	46.6690i		−	0.0708180i	−0.999373	−	0.0354090i	$-0.988727\pi$
$659$		−	46.6690i		−	0.0708180i	0.999373	−	0.0354090i	$-0.0112734\pi$
$660$	180.586	+	154.392i	0.273615	+	0.233927i
$661$	−248.194	+	429.885i	−0.375483	+	0.650356i	−0.990399	−	0.138236i	$-0.955857\pi$
$661$	−248.194	+	429.885i	−0.375483	+	0.650356i	0.614916	+	0.788593i	$0.289190\pi$
$662$	63.6867	+	36.7696i	0.0962035	+	0.0555431i
$663$	−794.015	+	928.727i	−1.19761	+	1.40079i
$664$	−175.362			−0.264100
$665$		0			0
$666$	400.000	+	494.975i	0.600601	+	0.743205i
$667$	40.0000	+	69.2820i	0.0599700	+	0.103871i
$668$	−391.443	−	226.000i	−0.585993	−	0.338323i
$669$	−9.30306	+	50.0545i	−0.0139059	+	0.0748199i
$670$	33.9411	+	58.7878i	0.0506584	+	0.0877429i
$671$			322.000i			0.479881i
$672$		0			0
$673$	−498.000			−0.739970			−0.369985	−	0.929038i	$-0.620637\pi$
$673$	−498.000			−0.739970			−0.369985	+	0.929038i	$0.620637\pi$
$674$	−97.9796	+	56.5685i	−0.145370	+	0.0839296i
$675$	115.628	+	213.727i	0.171300	+	0.316633i
$676$	−7.00000	+	12.1244i	−0.0103550	+	0.0179354i
$677$	883.346	−	510.000i	1.30479	−	0.753323i	0.323572	−	0.946203i	$-0.395116\pi$
$677$	883.346	−	510.000i	1.30479	−	0.753323i	0.981222	+	0.192880i	$0.0617828\pi$
$678$	−67.8823	+	24.0000i	−0.100121	+	0.0353982i
$679$		0			0
$680$			362.039i			0.532410i
$681$	748.604	−	875.612i	1.09927	−	1.28577i
$682$		0			0
$683$	−400.492	−	231.224i	−0.586371	−	0.338542i	0.177290	−	0.984159i	$-0.443267\pi$
$683$	−400.492	−	231.224i	−0.586371	−	0.338542i	−0.763661	+	0.645617i	$0.776600\pi$
$684$	475.118	+	182.929i	0.694617	+	0.267439i
$685$	−271.529			−0.396393
$686$		0			0
$687$	708.000	−	250.316i	1.03057	−	0.364361i
$688$	104.000	+	180.133i	0.151163	+	0.261822i
$689$	−498.831	−	288.000i	−0.723992	−	0.417997i
$690$	−23.5959	−	4.38551i	−0.0341970	−	0.00635580i
$691$	271.529	+	470.302i	0.392951	+	0.680611i	0.992837	−	0.119474i	$-0.0381209\pi$
$691$	271.529	+	470.302i	0.392951	+	0.680611i	−0.599886	+	0.800085i	$0.704788\pi$
$692$			264.000i			0.381503i
$693$		0			0
$694$	306.000			0.440922
$695$	744.645	−	429.921i	1.07143	−	0.618591i
$696$	87.7101	−	471.918i	0.126020	−	0.678044i
$697$	−256.000	+	443.405i	−0.367288	+	0.636162i
$698$	15.5885	−	9.00000i	0.0223330	−	0.0128940i
$699$	−322.441	−	912.000i	−0.461289	−	1.30472i
$700$		0			0
$701$		−	797.616i		−	1.13783i	−0.822398	−	0.568913i	$-0.807364\pi$
$701$		−	797.616i		−	1.13783i	0.822398	−	0.568913i	$-0.192636\pi$
$702$	−13.4541	+	485.814i	−0.0191654	+	0.692042i
$703$	707.107	−	1224.74i	1.00584	−	1.74217i
$704$	−68.5857	−	39.5980i	−0.0974229	−	0.0562471i
$705$	310.112	+	265.131i	0.439876	+	0.376072i
$706$	90.5097			0.128201
$707$		0			0
$708$	64.0000	+	181.019i	0.0903955	+	0.255677i
$709$	−440.000	−	762.102i	−0.620592	−	1.07490i	−0.989376	−	0.145382i	$-0.953559\pi$
$709$	−440.000	−	762.102i	−0.620592	−	1.07490i	0.368783	−	0.929515i	$-0.379774\pi$
$710$	436.477	+	252.000i	0.614756	+	0.354930i
$711$	−55.9592	−	355.624i	−0.0787049	−	0.500175i
$712$	79.1960	+	137.171i	0.111230	+	0.192656i
$713$		0			0
$714$		0			0
$715$	504.000			0.704895
$716$	389.469	−	224.860i	0.543951	−	0.314050i
$717$	−838.413	−	155.826i	−1.16933	−	0.217331i
$718$	127.000	−	219.970i	0.176880	−	0.306366i
$719$	−568.113	+	328.000i	−0.790143	+	0.456189i	−0.840013	−	0.542567i	$-0.817453\pi$
$719$	−568.113	+	328.000i	−0.790143	+	0.456189i	0.0498700	+	0.998756i	$0.484119\pi$
$720$	90.5097	+	112.000i	0.125708	+	0.155556i
$721$		0			0
$722$		−	620.840i		−	0.859889i
$723$	106.417	+	90.9808i	0.147188	+	0.125838i
$724$	−182.434	+	315.984i	−0.251980	+	0.436442i
$725$	−440.908	−	254.558i	−0.608149	−	0.351115i
$726$	−63.4109	+	74.1691i	−0.0873428	+	0.102161i
$727$	−786.303			−1.08157			−0.540786	−	0.841160i	$-0.681873\pi$
$727$	−786.303			−1.08157			−0.540786	+	0.841160i	$0.681873\pi$
$728$		0			0
$729$	−329.000	−	650.538i	−0.451303	−	0.892371i
$730$	92.0000	+	159.349i	0.126027	+	0.218286i
$731$	−1441.07	−	832.000i	−1.97136	−	1.13817i
$732$	−35.6617	+	191.876i	−0.0487182	+	0.262125i
$733$	−617.304	−	1069.20i	−0.842161	−	1.45867i	−0.888064	−	0.459720i	$-0.847950\pi$
$733$	−617.304	−	1069.20i	−0.842161	−	1.45867i	0.0459025	−	0.998946i	$-0.485384\pi$
$734$			184.000i			0.250681i
$735$		0			0
$736$	8.00000			0.0108696
$737$	102.879	−	59.3970i	0.139591	−	0.0805929i
$738$	31.6553	+	201.171i	0.0428933	+	0.272590i
$739$	78.0000	−	135.100i	0.105548	−	0.182815i	−0.808414	−	0.588614i	$-0.799674\pi$
$739$	78.0000	−	135.100i	0.105548	−	0.182815i	0.913962	+	0.405800i	$0.133007\pi$
$740$	346.410	−	200.000i	0.468122	−	0.270270i
$741$	1018.23	−	360.000i	1.37413	−	0.485830i
$742$		0			0
$743$		−	858.428i		−	1.15535i	−0.816266	−	0.577677i	$-0.803959\pi$
$743$		−	858.428i		−	1.15535i	0.816266	−	0.577677i	$-0.196041\pi$
$744$		0			0
$745$	−181.019	+	313.535i	−0.242979	+	0.420852i
$746$	−17.1464	−	9.89949i	−0.0229845	−	0.0132701i
$747$	200.493	−	520.737i	0.268397	−	0.697104i
$748$	633.568			0.847016
$749$		0			0
$750$	544.000	−	192.333i	0.725333	−	0.256444i
$751$	−40.0000	−	69.2820i	−0.0532623	−	0.0922530i	0.838165	−	0.545417i	$-0.183629\pi$
$751$	−40.0000	−	69.2820i	−0.0532623	−	0.0922530i	−0.891427	+	0.453164i	$0.850295\pi$
$752$	−117.779	−	68.0000i	−0.156622	−	0.0904255i
$753$	−660.686	−	122.794i	−0.877405	−	0.163073i
$754$	−509.117	−	881.816i	−0.675221	−	1.16952i
$755$			608.000i			0.805298i
$756$		0			0
$757$	−16.0000			−0.0211361			−0.0105680	−	0.999944i	$-0.503364\pi$
$757$	−16.0000			−0.0211361			−0.0105680	+	0.999944i	$0.503364\pi$
$758$	−181.262	+	104.652i	−0.239132	+	0.138063i
$759$	−7.67463	+	41.2929i	−0.0101115	+	0.0544043i
$760$	160.000	−	277.128i	0.210526	−	0.364642i
$761$	588.897	−	340.000i	0.773847	−	0.446781i	−0.0603985	−	0.998174i	$-0.519237\pi$
$761$	588.897	−	340.000i	0.773847	−	0.446781i	0.834245	+	0.551394i	$0.185904\pi$
$762$	147.078	+	416.000i	0.193016	+	0.545932i
$763$		0			0
$764$		−	19.7990i		−	0.0259149i
$765$	−1075.07	−	413.920i	−1.40532	−	0.541072i
$766$	79.1960	−	137.171i	0.103389	−	0.179075i
$767$	352.727	+	203.647i	0.459878	+	0.265511i
$768$	−36.4838	−	31.1918i	−0.0475050	−	0.0406144i
$769$	−1336.43			−1.73788			−0.868941	−	0.494915i	$-0.835199\pi$
$769$	−1336.43			−1.73788			−0.868941	+	0.494915i	$0.835199\pi$
$770$		0			0
$771$	120.000	+	339.411i	0.155642	+	0.440222i
$772$	−160.000	−	277.128i	−0.207254	−	0.358974i
$773$	1001.13	+	578.000i	1.29512	+	0.747736i	0.979556	−	0.201169i	$-0.0644742\pi$
$773$	1001.13	+	578.000i	1.29512	+	0.747736i	0.315560	+	0.948905i	$0.397807\pi$
$774$	−653.807	+	102.880i	−0.844712	+	0.132920i
$775$		0			0
$776$			68.0000i			0.0876289i
$777$		0			0
$778$	608.000			0.781491
$779$	391.918	−	226.274i	0.503104	−	0.290467i
$780$	300.327	+	55.8184i	0.385035	+	0.0715620i
$781$	441.000	−	763.834i	0.564661	−	0.978021i
$782$	−55.4256	+	32.0000i	−0.0708768	+	0.0409207i
$783$	1301.08	+	800.000i	1.66166	+	1.02171i
$784$		0			0
$785$		−	684.479i		−	0.871948i
$786$	−96.7423	−	82.7098i	−0.123082	−	0.105229i
$787$	260.215	−	450.706i	0.330642	−	0.572689i	−0.651996	−	0.758223i	$-0.726068\pi$
$787$	260.215	−	450.706i	0.330642	−	0.572689i	0.982638	+	0.185534i	$0.0594014\pi$
$788$	186.161	+	107.480i	0.236245	+	0.136396i
$789$	438.362	−	512.734i	0.555592	−	0.649854i
$790$	−226.274			−0.286423
$791$		0			0
$792$	196.000	−	158.392i	0.247475	−	0.199990i
$793$	207.000	+	358.535i	0.261034	+	0.452124i
$794$	−43.3013	−	25.0000i	−0.0545356	−	0.0314861i
$795$	99.2327	−	533.915i	0.124821	−	0.671591i
$796$	220.617	+	382.120i	0.277157	+	0.480051i
$797$		−	60.0000i		−	0.0752823i	−0.999291	−	0.0376412i	$-0.988016\pi$
$797$		−	60.0000i		−	0.0752823i	0.999291	−	0.0376412i	$-0.0119844\pi$
$798$		0			0
$799$	1088.00			1.36170
$800$	−44.0908	+	25.4558i	−0.0551135	+	0.0318198i
$801$	−497.874	+	78.3429i	−0.621565	+	0.0978063i
$802$	−96.0000	+	166.277i	−0.119701	+	0.207328i
$803$	278.860	−	161.000i	0.347273	−	0.200498i
$804$	67.8823	−	24.0000i	0.0844307	−	0.0298507i
$805$		0			0
$806$		0			0
$807$	319.716	−	373.959i	0.396179	−	0.463394i
$808$	50.9117	−	88.1816i	0.0630095	−	0.109136i
$809$	553.585	+	319.612i	0.684283	+	0.395071i	0.801467	−	0.598039i	$-0.204053\pi$
$809$	553.585	+	319.612i	0.684283	+	0.395071i	−0.117184	+	0.993110i	$0.537387\pi$
$810$	−436.063	+	140.717i	−0.538349	+	0.173725i
$811$	458.205			0.564988			0.282494	−	0.959269i	$-0.408838\pi$
$811$	458.205			0.564988			0.282494	+	0.959269i	$0.408838\pi$
$812$		0			0
$813$	656.000	−	231.931i	0.806888	−	0.285278i
$814$	−350.000	−	606.218i	−0.429975	−	0.744739i
$815$	−845.241	−	488.000i	−1.03711	−	0.598773i
$816$	377.535	+	70.1681i	0.462665	+	0.0859903i
$817$	735.391	+	1273.73i	0.900111	+	1.55904i
$818$			462.000i			0.564792i
$819$		0			0
$820$	128.000			0.156098
$821$	−323.333	+	186.676i	−0.393828	+	0.227377i	−0.683817	−	0.729653i	$-0.739682\pi$
$821$	−323.333	+	186.676i	−0.393828	+	0.227377i	0.289990	+	0.957030i	$0.406348\pi$
$822$	−52.6261	+	283.151i	−0.0640220	+	0.344466i
$823$	700.000	−	1212.44i	0.850547	−	1.47319i	−0.0301688	−	0.999545i	$-0.509604\pi$
$823$	700.000	−	1212.44i	0.850547	−	1.47319i	0.880716	−	0.473645i	$-0.157062\pi$
$824$	180.133	−	104.000i	0.218608	−	0.126214i
$825$	−89.0955	−	252.000i	−0.107994	−	0.305455i
$826$		0			0
$827$		−	55.1543i		−	0.0666921i	−0.999444	−	0.0333460i	$-0.989384\pi$
$827$		−	55.1543i		−	0.0666921i	0.999444	−	0.0333460i	$-0.0106163\pi$
$828$	−9.14643	+	23.7559i	−0.0110464	+	0.0286907i
$829$	−548.008	+	949.177i	−0.661047	+	1.14497i	0.319294	+	0.947656i	$0.396554\pi$
$829$	−548.008	+	949.177i	−0.661047	+	1.14497i	−0.980341	+	0.197311i	$0.936779\pi$
$830$	−303.737	−	175.362i	−0.365948	−	0.211280i
$831$	1058.03	+	904.563i	1.27320	+	1.08852i
$832$	−101.823			−0.122384
$833$		0			0
$834$	−304.000	−	859.842i	−0.364508	−	1.03099i
$835$	−452.000	−	782.887i	−0.541317	−	0.937589i
$836$	−484.974	−	280.000i	−0.580113	−	0.334928i
$837$		0			0
$838$	−248.902	−	431.110i	−0.297019	−	0.514451i
$839$		−	1250.00i		−	1.48987i	−0.667138	−	0.744934i	$-0.732481\pi$
$839$		−	1250.00i		−	1.48987i	0.667138	−	0.744934i	$-0.267519\pi$
$840$		0			0
$841$	−2359.00			−2.80499
$842$	−293.939	+	169.706i	−0.349096	+	0.201551i
$843$	116.794	+	21.7071i	0.138545	+	0.0257499i
$844$	−372.000	+	644.323i	−0.440758	+	0.763416i
$845$	−24.2487	+	14.0000i	−0.0286967	+	0.0165680i
$846$	336.583	−	272.000i	0.397852	−	0.321513i
$847$		0			0
$848$			181.019i			0.213466i
$849$	567.555	+	485.231i	0.668498	+	0.571532i
$850$	203.647	−	352.727i	0.239584	−	0.414972i
$851$	61.2372	+	35.3553i	0.0719592	+	0.0415456i
$852$	347.381	−	406.318i	0.407725	−	0.476899i
$853$	250.316			0.293453			0.146727	−	0.989177i	$-0.453126\pi$
$853$	250.316			0.293453			0.146727	+	0.989177i	$0.453126\pi$
$854$		0			0
$855$	640.000	+	791.960i	0.748538	+	0.926269i
$856$	206.000	+	356.802i	0.240654	+	0.416825i
$857$	221.703	+	128.000i	0.258696	+	0.149358i	0.623740	−	0.781632i	$-0.285613\pi$
$857$	221.703	+	128.000i	0.258696	+	0.149358i	−0.365044	+	0.930990i	$0.618946\pi$
$858$	97.6821	−	525.572i	0.113849	−	0.612555i
$859$	−393.151	−	680.958i	−0.457685	−	0.792734i	0.541153	−	0.840924i	$-0.317988\pi$
$859$	−393.151	−	680.958i	−0.457685	−	0.792734i	−0.998838	+	0.0481904i	$0.984655\pi$
$860$			416.000i			0.483721i
$861$		0			0
$862$	−1038.00			−1.20418
$863$	−1402.33	+	809.637i	−1.62495	+	0.938166i	−0.639383	+	0.768889i	$0.720810\pi$
$863$	−1402.33	+	809.637i	−1.62495	+	0.938166i	−0.985568	+	0.169277i	$0.945857\pi$
$864$	134.336	−	72.6765i	0.155481	−	0.0841164i
$865$	−264.000	+	457.261i	−0.305202	+	0.528626i
$866$	524.811	−	303.000i	0.606018	−	0.349885i
$867$	−2078.89	+	735.000i	−2.39780	+	0.847751i
$868$		0			0
$869$			395.980i			0.455673i
$870$	623.837	−	729.676i	0.717054	−	0.838709i
$871$	76.3675	−	132.272i	0.0876780	−	0.151863i
$872$	431.110	+	248.902i	0.494392	+	0.285438i
$873$	−201.925	−	77.7446i	−0.231300	−	0.0890546i
$874$	56.5685			0.0647237
$875$		0			0
$876$	184.000	−	65.0538i	0.210046	−	0.0742624i
$877$	632.000	+	1094.66i	0.720639	+	1.24818i	0.960744	+	0.277436i	$0.0894846\pi$
$877$	632.000	+	1094.66i	0.720639	+	1.24818i	−0.240106	+	0.970747i	$0.577182\pi$
$878$	498.831	+	288.000i	0.568144	+	0.328018i
$879$	932.039	+	173.227i	1.06034	+	0.197073i
$880$	−79.1960	−	137.171i	−0.0899954	−	0.155877i
$881$			264.000i			0.299659i	0.988712	+	0.149830i	$0.0478726\pi$
$881$			264.000i			0.299659i	−0.988712	+	0.149830i	$0.952127\pi$
$882$		0			0
$883$	1148.00			1.30011			0.650057	−	0.759886i	$-0.274745\pi$
$883$	1148.00			1.30011			0.650057	+	0.759886i	$0.274745\pi$
$884$	705.453	−	407.294i	0.798024	−	0.460739i
$885$	−70.1681	+	377.535i	−0.0792860	+	0.426593i
$886$	281.000	−	486.706i	0.317156	−	0.549330i
$887$	−1110.24	+	641.000i	−1.25168	+	0.722661i	−0.971444	−	0.237269i	$-0.923748\pi$
$887$	−1110.24	+	641.000i	−1.25168	+	0.722661i	−0.280241	+	0.959930i	$0.590414\pi$
$888$	−141.421	−	400.000i	−0.159258	−	0.450450i
$889$		0			0
$890$			316.784i			0.355937i
$891$	246.255	+	763.110i	0.276381	+	0.856464i
$892$	16.9706	−	29.3939i	0.0190253	−	0.0329528i
$893$	−832.827	−	480.833i	−0.932616	−	0.538446i
$894$	291.871	+	249.535i	0.326477	+	0.279122i
$895$	899.440			1.00496
$896$		0			0
$897$	18.0000	+	50.9117i	0.0200669	+	0.0567577i
$898$	12.0000	+	20.7846i	0.0133630	+	0.0231454i
$899$		0			0
$900$	−25.1816	−	160.031i	−0.0279796	−	0.177812i
$901$	−724.077	−	1254.14i	−0.803637	−	1.39194i
$902$		−	224.000i		−	0.248337i
$903$		0			0
$904$	48.0000			0.0530973
$905$	−631.968	+	364.867i	−0.698308	+	0.403168i
$906$	634.024	+	117.839i	0.699805	+	0.130065i
$907$	−434.000	+	751.710i	−0.478501	+	0.828787i	−0.999696	−	0.0246500i	$-0.992153\pi$
$907$	−434.000	+	751.710i	−0.478501	+	0.828787i	0.521196	+	0.853437i	$0.325486\pi$
$908$	−665.108	+	384.000i	−0.732497	+	0.422907i
$909$	203.647	+	252.000i	0.224034	+	0.277228i
$910$		0			0
$911$			1231.78i			1.35212i	0.736847	+	0.676059i	$0.236314\pi$
$911$			1231.78i			1.35212i	−0.736847	+	0.676059i	$0.763686\pi$
$912$	−257.980	−	220.560i	−0.282872	−	0.241842i
$913$	−306.884	+	531.539i	−0.336127	+	0.582190i
$914$	−154.318	−	89.0955i	−0.168838	−	0.0974786i
$915$	−253.644	+	296.677i	−0.277206	+	0.324237i
$916$	−500.632			−0.546541
$917$		0			0
$918$	−640.000	+	1040.86i	−0.697168	+	1.13384i
$919$	64.0000	+	110.851i	0.0696409	+	0.120622i	0.898743	−	0.438475i	$-0.144481\pi$
$919$	64.0000	+	110.851i	0.0696409	+	0.120622i	−0.829102	+	0.559097i	$0.811148\pi$
$920$	13.8564	+	8.00000i	0.0150613	+	0.00869565i
$921$	−189.162	+	1017.77i	−0.205388	+	1.10508i
$922$	410.122	+	710.352i	0.444818	+	0.770447i
$923$		−	1134.00i		−	1.22860i
$924$		0			0
$925$	−450.000			−0.486486
$926$	−137.171	+	79.1960i	−0.148133	+	0.0855248i
$927$	102.880	+	653.807i	0.110981	+	0.705294i
$928$	−160.000	+	277.128i	−0.172414	+	0.298629i
$929$	−1274.79	+	736.000i	−1.37222	+	0.792250i	−0.991207	−	0.132321i	$-0.957757\pi$
$929$	−1274.79	+	736.000i	−1.37222	+	0.792250i	−0.381010	+	0.924571i	$0.624424\pi$
$930$		0			0
$931$		0			0
$932$			644.881i			0.691933i
$933$	1033.23	−	1208.53i	1.10743	−	1.29531i
$934$	90.5097	−	156.767i	0.0969054	−	0.167845i
$935$	1097.37	+	633.568i	1.17366	+	0.677612i
$936$	116.415	−	302.363i	0.124375	−	0.323038i
$937$	507.703			0.541838			0.270919	−	0.962602i	$-0.412672\pi$
$937$	507.703			0.541838			0.270919	+	0.962602i	$0.412672\pi$
$938$		0			0
$939$	−420.000	+	148.492i	−0.447284	+	0.158139i
$940$	−136.000	−	235.559i	−0.144681	−	0.250595i
$941$	−959.556	−	554.000i	−1.01972	−	0.588735i	−0.105697	−	0.994398i	$-0.533707\pi$
$941$	−959.556	−	554.000i	−1.01972	−	0.588735i	−0.914023	+	0.405663i	$0.867041\pi$
$942$	−713.777	−	132.662i	−0.757725	−	0.140830i
$943$	11.3137	+	19.5959i	0.0119976	+	0.0207804i
$944$		−	128.000i		−	0.135593i
$945$		0			0
$946$	728.000			0.769556
$947$	−216.780	+	125.158i	−0.228912	+	0.132163i	−0.610070	−	0.792347i	$-0.708859\pi$
$947$	−216.780	+	125.158i	−0.228912	+	0.132163i	0.381158	+	0.924510i	$0.375525\pi$
$948$	−43.8551	+	235.959i	−0.0462606	+	0.248902i
$949$	207.000	−	358.535i	0.218124	−	0.377802i
$950$	−311.769	+	180.000i	−0.328178	+	0.189474i
$951$	113.137	+	320.000i	0.118966	+	0.336488i
$952$		0			0
$953$		−	497.803i		−	0.522354i	−0.965291	−	0.261177i	$-0.915889\pi$
$953$		−	497.803i		−	0.522354i	0.965291	−	0.261177i	$-0.0841106\pi$
$954$	−537.535	−	206.960i	−0.563454	−	0.216939i
$955$	19.7990	−	34.2929i	0.0207319	−	0.0359088i
$956$	492.347	+	284.257i	0.515008	+	0.297340i
$957$	−1276.93	−	1091.71i	−1.33431	−	1.14077i
$958$	−681.651			−0.711535
$959$		0			0
$960$	−32.0000	−	90.5097i	−0.0333333	−	0.0942809i
$961$	480.500	+	832.250i	0.500000	+	0.866025i
$962$	−779.423	−	450.000i	−0.810211	−	0.467775i
$963$	−1295.04	+	203.781i	−1.34480	+	0.211611i
$964$	−46.6690	−	80.8332i	−0.0484119	−	0.0838518i
$965$		−	640.000i		−	0.663212i
$966$		0			0
$967$	−384.000			−0.397104			−0.198552	−	0.980090i	$-0.563624\pi$
$967$	−384.000			−0.397104			−0.198552	+	0.980090i	$0.563624\pi$
$968$	56.3383	−	32.5269i	0.0582007	−	0.0336022i
$969$	2669.57	+	496.163i	2.75498	+	0.512036i
$970$	−68.0000	+	117.779i	−0.0701031	+	0.121422i
$971$	289.252	−	167.000i	0.297891	−	0.171988i	−0.343604	−	0.939115i	$-0.611648\pi$
$971$	289.252	−	167.000i	0.297891	−	0.171988i	0.641495	+	0.767127i	$0.278314\pi$
$972$	62.2254	+	482.000i	0.0640179	+	0.495885i
$973$		0			0
$974$			169.706i			0.174236i
$975$	−261.204	−	223.317i	−0.267902	−	0.229043i
$976$	65.0538	−	112.677i	0.0666535	−	0.115447i
$977$	44.0908	+	25.4558i	0.0451288	+	0.0260551i	0.522395	−	0.852704i	$-0.325039\pi$
$977$	44.0908	+	25.4558i	0.0451288	+	0.0260551i	−0.477266	+	0.878759i	$0.658372\pi$
$978$	−672.707	+	786.838i	−0.687839	+	0.804538i
$979$	554.372			0.566263
$980$		0			0
$981$	−1232.00	+	995.606i	−1.25586	+	1.01489i
$982$	−441.000	−	763.834i	−0.449084	−	0.777835i
$983$	969.948	+	560.000i	0.986723	+	0.569685i	0.904293	−	0.426912i	$-0.140399\pi$
$983$	969.948	+	560.000i	0.986723	+	0.569685i	0.0824297	+	0.996597i	$0.473732\pi$
$984$	24.8082	−	133.479i	0.0252115	−	0.135649i
$985$	214.960	+	372.322i	0.218234	+	0.377992i
$986$		−	2560.00i		−	2.59635i
$987$		0			0
$988$	−720.000			−0.728745
$989$	−63.6867	+	36.7696i	−0.0643951	+	0.0371785i
$990$	497.874	−	78.3429i	0.502903	−	0.0791342i
$991$	−508.000	+	879.882i	−0.512614	+	0.887873i	0.487280	+	0.873246i	$0.337989\pi$
$991$	−508.000	+	879.882i	−0.512614	+	0.887873i	−0.999893	+	0.0146266i	$0.995344\pi$
$992$		0			0
$993$	147.078	−	52.0000i	0.148115	−	0.0523666i
$994$		0			0
$995$			882.469i			0.886904i
$996$	−241.737	+	282.750i	−0.242708	+	0.283885i
$997$	610.233	−	1056.95i	0.612069	−	1.06014i	−0.378822	−	0.925470i	$-0.623671\pi$
$997$	610.233	−	1056.95i	0.612069	−	1.06014i	0.990891	−	0.134666i	$-0.0429960\pi$
$998$	347.828	+	200.818i	0.348525	+	0.201221i
$999$	1349.48	+	37.3724i	1.35083	+	0.0374098i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.3.h.e.263.1		8
3.2	odd	2	inner	294.3.h.e.263.3		8
7.2	even	3	inner	294.3.h.e.275.3		8
7.3	odd	6		294.3.b.g.197.1	✓	4
7.4	even	3		294.3.b.g.197.2	yes	4
7.5	odd	6	inner	294.3.h.e.275.4		8
7.6	odd	2	inner	294.3.h.e.263.2		8
21.2	odd	6	inner	294.3.h.e.275.1		8
21.5	even	6	inner	294.3.h.e.275.2		8
21.11	odd	6		294.3.b.g.197.4	yes	4
21.17	even	6		294.3.b.g.197.3	yes	4
21.20	even	2	inner	294.3.h.e.263.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.3.b.g.197.1	✓	4	7.3	odd	6
294.3.b.g.197.2	yes	4	7.4	even	3
294.3.b.g.197.3	yes	4	21.17	even	6
294.3.b.g.197.4	yes	4	21.11	odd	6
294.3.h.e.263.1		8	1.1	even	1	trivial
294.3.h.e.263.2		8	7.6	odd	2	inner
294.3.h.e.263.3		8	3.2	odd	2	inner
294.3.h.e.263.4		8	21.20	even	2	inner
294.3.h.e.275.1		8	21.2	odd	6	inner
294.3.h.e.275.2		8	21.5	even	6	inner
294.3.h.e.275.3		8	7.2	even	3	inner
294.3.h.e.275.4		8	7.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	294.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 0.707107i) q^{2} +(-0.548188 + 2.94949i) q^{3} +(1.00000 - 1.73205i) q^{4} +(3.46410 - 2.00000i) q^{5} +(-1.41421 - 4.00000i) q^{6} +2.82843i q^{8} +(-8.39898 - 3.23375i) q^{9} +O(q^{10})\)	\(q+(-1.22474 + 0.707107i) q^{2} +(-0.548188 + 2.94949i) q^{3} +(1.00000 - 1.73205i) q^{4} +(3.46410 - 2.00000i) q^{5} +(-1.41421 - 4.00000i) q^{6} +2.82843i q^{8} +(-8.39898 - 3.23375i) q^{9} +(-2.82843 + 4.89898i) q^{10} +(8.57321 + 4.94975i) q^{11} +(4.56048 + 3.89898i) q^{12} +12.7279 q^{13} +(4.00000 + 11.3137i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(27.7128 + 16.0000i) q^{17} +(12.5732 - 1.97846i) q^{18} +(-14.1421 - 24.4949i) q^{19} -8.00000i q^{20} -14.0000 q^{22} +(1.22474 - 0.707107i) q^{23} +(-8.34242 - 1.55051i) q^{24} +(-4.50000 + 7.79423i) q^{25} +(-15.5885 + 9.00000i) q^{26} +(14.1421 - 23.0000i) q^{27} +56.5685i q^{29} +(-12.8990 - 11.0280i) q^{30} +(4.89898 + 2.82843i) q^{32} +(-19.2990 + 22.5732i) q^{33} -45.2548 q^{34} +(-14.0000 + 11.3137i) q^{36} +(25.0000 + 43.3013i) q^{37} +(34.6410 + 20.0000i) q^{38} +(-6.97730 + 37.5409i) q^{39} +(5.65685 + 9.79796i) q^{40} +16.0000i q^{41} -52.0000 q^{43} +(17.1464 - 9.89949i) q^{44} +(-35.5624 + 5.59592i) q^{45} +(-1.00000 + 1.73205i) q^{46} +(29.4449 - 17.0000i) q^{47} +(11.3137 - 4.00000i) q^{48} -12.7279i q^{50} +(-62.3837 + 72.9676i) q^{51} +(12.7279 - 22.0454i) q^{52} +(-39.1918 - 22.6274i) q^{53} +(-1.05705 + 38.1691i) q^{54} +39.5980 q^{55} +(80.0000 - 28.2843i) q^{57} +(-40.0000 - 69.2820i) q^{58} +(27.7128 + 16.0000i) q^{59} +(23.5959 + 4.38551i) q^{60} +(16.2635 + 28.1691i) q^{61} -8.00000 q^{64} +(44.0908 - 25.4558i) q^{65} +(7.67463 - 41.2929i) q^{66} +(6.00000 - 10.3923i) q^{67} +(55.4256 - 32.0000i) q^{68} +(1.41421 + 4.00000i) q^{69} -89.0955i q^{71} +(9.14643 - 23.7559i) q^{72} +(16.2635 - 28.1691i) q^{73} +(-61.2372 - 35.3553i) q^{74} +(-20.5222 - 17.5454i) q^{75} -56.5685 q^{76} +(-18.0000 - 50.9117i) q^{78} +(20.0000 + 34.6410i) q^{79} +(-13.8564 - 8.00000i) q^{80} +(60.0857 + 54.3204i) q^{81} +(-11.3137 - 19.5959i) q^{82} +62.0000i q^{83} +128.000 q^{85} +(63.6867 - 36.7696i) q^{86} +(-166.848 - 31.0102i) q^{87} +(-14.0000 + 24.2487i) q^{88} +(48.4974 - 28.0000i) q^{89} +(39.5980 - 32.0000i) q^{90} -2.82843i q^{92} +(-24.0416 + 41.6413i) q^{94} +(-97.9796 - 56.5685i) q^{95} +(-11.0280 + 12.8990i) q^{96} +24.0416 q^{97} +(-56.0000 - 69.2965i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{4} - 28 q^{9}+O(q^{10}) \) 8 * q + 8 * q^4 - 28 * q^9	\( 8 q + 8 q^{4} - 28 q^{9} + 32 q^{15} - 16 q^{16} + 32 q^{18} - 112 q^{22} - 36 q^{25} - 64 q^{30} - 112 q^{36} + 200 q^{37} - 144 q^{39} - 416 q^{43} - 8 q^{46} + 128 q^{51} + 640 q^{57} - 320 q^{58} + 32 q^{60} - 64 q^{64} + 48 q^{67} - 64 q^{72} - 144 q^{78} + 160 q^{79} - 68 q^{81} + 1024 q^{85} - 112 q^{88} - 448 q^{99}+O(q^{100}) \) 8 * q + 8 * q^4 - 28 * q^9 + 32 * q^15 - 16 * q^16 + 32 * q^18 - 112 * q^22 - 36 * q^25 - 64 * q^30 - 112 * q^36 + 200 * q^37 - 144 * q^39 - 416 * q^43 - 8 * q^46 + 128 * q^51 + 640 * q^57 - 320 * q^58 + 32 * q^60 - 64 * q^64 + 48 * q^67 - 64 * q^72 - 144 * q^78 + 160 * q^79 - 68 * q^81 + 1024 * q^85 - 112 * q^88 - 448 * q^99

Introduction

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