LMFDB - Embedded newform 294.3.h.e.263.3

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			263.3
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	294.263
Dual form			294.3.h.e.275.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 - 0.707107i) q^{2} +(-2.28024 + 1.94949i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-3.46410 + 2.00000i) q^{5} +(-1.41421 + 4.00000i) q^{6} -2.82843i q^{8} +(1.39898 - 8.89060i) q^{9} +O(q^{10})$	\(q+(1.22474 - 0.707107i) q^{2} +(-2.28024 + 1.94949i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-3.46410 + 2.00000i) q^{5} +(-1.41421 + 4.00000i) q^{6} -2.82843i q^{8} +(1.39898 - 8.89060i) q^{9} +(-2.82843 + 4.89898i) q^{10} +(-8.57321 - 4.94975i) q^{11} +(1.09638 + 5.89898i) q^{12} +12.7279 q^{13} +(4.00000 - 11.3137i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(-27.7128 - 16.0000i) q^{17} +(-4.57321 - 11.8780i) q^{18} +(-14.1421 - 24.4949i) q^{19} +8.00000i q^{20} -14.0000 q^{22} +(-1.22474 + 0.707107i) q^{23} +(5.51399 + 6.44949i) q^{24} +(-4.50000 + 7.79423i) q^{25} +(15.5885 - 9.00000i) q^{26} +(14.1421 + 23.0000i) q^{27} -56.5685i q^{29} +(-3.10102 - 16.6848i) q^{30} +(-4.89898 - 2.82843i) q^{32} +(29.1985 - 5.42679i) q^{33} -45.2548 q^{34} +(-14.0000 - 11.3137i) q^{36} +(25.0000 + 43.3013i) q^{37} +(-34.6410 - 20.0000i) q^{38} +(-29.0227 + 24.8130i) q^{39} +(5.65685 + 9.79796i) q^{40} -16.0000i q^{41} -52.0000 q^{43} +(-17.1464 + 9.89949i) q^{44} +(12.9350 + 33.5959i) q^{45} +(-1.00000 + 1.73205i) q^{46} +(-29.4449 + 17.0000i) q^{47} +(11.3137 + 4.00000i) q^{48} +12.7279i q^{50} +(94.3837 - 17.5420i) q^{51} +(12.7279 - 22.0454i) q^{52} +(39.1918 + 22.6274i) q^{53} +(33.5840 + 18.1691i) q^{54} +39.5980 q^{55} +(80.0000 + 28.2843i) q^{57} +(-40.0000 - 69.2820i) q^{58} +(-27.7128 - 16.0000i) q^{59} +(-15.5959 - 18.2419i) q^{60} +(16.2635 + 28.1691i) q^{61} -8.00000 q^{64} +(-44.0908 + 25.4558i) q^{65} +(31.9233 - 27.2929i) q^{66} +(6.00000 - 10.3923i) q^{67} +(-55.4256 + 32.0000i) q^{68} +(1.41421 - 4.00000i) q^{69} +89.0955i q^{71} +(-25.1464 - 3.95691i) q^{72} +(16.2635 - 28.1691i) q^{73} +(61.2372 + 35.3553i) q^{74} +(-4.93369 - 26.5454i) q^{75} -56.5685 q^{76} +(-18.0000 + 50.9117i) q^{78} +(20.0000 + 34.6410i) q^{79} +(13.8564 + 8.00000i) q^{80} +(-77.0857 - 24.8755i) q^{81} +(-11.3137 - 19.5959i) q^{82} -62.0000i q^{83} +128.000 q^{85} +(-63.6867 + 36.7696i) q^{86} +(110.280 + 128.990i) 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} +(16.6848 - 3.10102i) 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
$3$	−2.28024	+	1.94949i	−0.760080	+	0.649830i
$3$	−2.28024	+	1.94949i	−0.760080	+	0.649830i
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$	−3.46410	+	2.00000i	−0.692820	+	0.400000i	−0.804668	−	0.593725i	$-0.797657\pi$
$5$	−3.46410	+	2.00000i	−0.692820	+	0.400000i	0.111847	+	0.993725i	$0.464323\pi$
$6$	−1.41421	+	4.00000i	−0.235702	+	0.666667i
$7$		0			0
$7$		0			0
$8$		−	2.82843i		−	0.353553i
$9$	1.39898	−	8.89060i	0.155442	−	0.987845i
$10$	−2.82843	+	4.89898i	−0.282843	+	0.489898i
$11$	−8.57321	−	4.94975i	−0.779383	−	0.449977i	0.0568285	−	0.998384i	$-0.481901\pi$
$11$	−8.57321	−	4.94975i	−0.779383	−	0.449977i	−0.836212	+	0.548407i	$0.815235\pi$
$12$	1.09638	+	5.89898i	0.0913647	+	0.491582i
$13$	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	$-0.943055\pi$
$17$	−27.7128	−	16.0000i	−1.63017	−	0.941176i	−0.646125	−	0.763232i	$-0.723612\pi$
$18$	−4.57321	−	11.8780i	−0.254067	−	0.659886i
$19$	−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	−0.526389	−	0.850244i	$-0.676454\pi$
$23$	−1.22474	+	0.707107i	−0.0532498	+	0.0307438i	0.473139	+	0.880988i	$0.343121\pi$
$24$	5.51399	+	6.44949i	0.229750	+	0.268729i
$25$	−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	$-0.570866\pi$
$29$		−	56.5685i		−	1.95064i	0.220797	−	0.975320i	$-0.429134\pi$
$30$	−3.10102	−	16.6848i	−0.103367	−	0.556161i
$31$		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
$33$	29.1985	−	5.42679i	0.884802	−	0.164448i
$34$	−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
$39$	−29.0227	+	24.8130i	−0.744172	+	0.636230i
$40$	5.65685	+	9.79796i	0.141421	+	0.244949i
$41$		−	16.0000i		−	0.390244i	−0.980779	−	0.195122i	$-0.937490\pi$
$41$		−	16.0000i		−	0.390244i	0.980779	−	0.195122i	$-0.0625103\pi$
$42$		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
$45$	12.9350	+	33.5959i	0.287445	+	0.746576i
$46$	−1.00000	+	1.73205i	−0.0217391	+	0.0376533i
$47$	−29.4449	+	17.0000i	−0.626486	+	0.361702i	−0.779390	−	0.626539i	$-0.784471\pi$
$47$	−29.4449	+	17.0000i	−0.626486	+	0.361702i	0.152904	+	0.988241i	$0.451138\pi$
$48$	11.3137	+	4.00000i	0.235702	+	0.0833333i
$49$		0			0
$50$			12.7279i			0.254558i
$51$	94.3837	−	17.5420i	1.85066	−	0.343961i
$52$	12.7279	−	22.0454i	0.244768	−	0.423950i
$53$	39.1918	+	22.6274i	0.739469	+	0.426932i	0.821876	−	0.569666i	$-0.192928\pi$
$53$	39.1918	+	22.6274i	0.739469	+	0.426932i	−0.0824075	+	0.996599i	$0.526261\pi$
$54$	33.5840	+	18.1691i	0.621925	+	0.336465i
$55$	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	0.246409	−	0.969166i	$-0.420749\pi$
$59$	−27.7128	−	16.0000i	−0.469709	−	0.271186i	−0.716118	+	0.697979i	$0.754083\pi$
$60$	−15.5959	−	18.2419i	−0.259932	−	0.304032i
$61$	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
$66$	31.9233	−	27.2929i	0.483687	−	0.413528i
$67$	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	$0.215894\pi$
$71$			89.0955i			1.25487i	−0.778671	+	0.627433i	$0.784106\pi$
$72$	−25.1464	−	3.95691i	−0.349256	−	0.0549571i
$73$	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
$75$	−4.93369	−	26.5454i	−0.0657826	−	0.353939i
$76$	−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
$81$	−77.0857	−	24.8755i	−0.951675	−	0.307106i
$82$	−11.3137	−	19.5959i	−0.137972	−	0.238975i
$83$		−	62.0000i		−	0.746988i	−0.927633	−	0.373494i	$-0.878160\pi$
$83$		−	62.0000i		−	0.746988i	0.927633	−	0.373494i	$-0.121840\pi$
$84$		0			0
$85$	128.000			1.50588
$86$	−63.6867	+	36.7696i	−0.740543	+	0.427553i
$87$	110.280	+	128.990i	1.26758	+	1.48264i
$88$	−14.0000	+	24.2487i	−0.159091	+	0.275554i
$89$	−48.4974	+	28.0000i	−0.544915	+	0.314607i	−0.747068	−	0.664747i	$-0.768539\pi$
$89$	−48.4974	+	28.0000i	−0.544915	+	0.314607i	0.202154	+	0.979354i	$0.435206\pi$
$90$	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
$96$	16.6848	−	3.10102i	0.173800	−	0.0323023i
$97$	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	0.646337	−	0.763052i	$-0.276300\pi$
$101$	31.1769	+	18.0000i	0.308682	+	0.178218i	−0.337654	+	0.941270i	$0.609633\pi$
$102$	103.192	−	88.2238i	1.01168	−	0.864940i
$103$	−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	−0.955774	−	0.294103i	$-0.904979\pi$
$107$	−126.149	+	72.8320i	−1.17896	+	0.680673i	−0.223186	+	0.974776i	$0.571646\pi$
$108$	53.9793	−	1.49490i	0.499808	−	0.0138416i
$109$	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	$0.0239247\pi$
$113$			16.9706i			0.150182i	−0.997177	+	0.0750910i	$0.976075\pi$
$114$	117.980	−	21.9275i	1.03491	−	0.192347i
$115$	2.82843	−	4.89898i	0.0245950	−	0.0425998i
$116$	−97.9796	−	56.5685i	−0.844652	−	0.487660i
$117$	17.8061	−	113.159i	0.152189	−	0.967170i
$118$	−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
$123$	31.1918	+	36.4838i	0.253592	+	0.296616i
$124$		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
$129$	118.572	−	101.373i	0.919166	−	0.785841i
$130$	−36.0000	+	62.3538i	−0.276923	+	0.479645i
$131$	−25.9808	+	15.0000i	−0.198326	+	0.114504i	−0.595875	−	0.803077i	$-0.703194\pi$
$131$	−25.9808	+	15.0000i	−0.198326	+	0.114504i	0.397548	+	0.917581i	$0.369861\pi$
$132$	19.7990	−	56.0000i	0.149992	−	0.424242i
$133$		0			0
$134$		−	16.9706i		−	0.126646i
$135$	−94.9898	−	51.3901i	−0.703628	−	0.380667i
$136$	−45.2548	+	78.3837i	−0.332756	+	0.576351i
$137$	58.7878	+	33.9411i	0.429108	+	0.247745i	0.698966	−	0.715154i	$-0.253644\pi$
$137$	58.7878	+	33.9411i	0.429108	+	0.247745i	−0.269859	+	0.962900i	$0.586977\pi$
$138$	−1.09638	−	5.89898i	−0.00794476	−	0.0427462i
$139$	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
$144$	−33.5959	+	12.9350i	−0.233305	+	0.0898264i
$145$	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	−0.213348	−	0.976976i	$-0.568437\pi$
$149$	78.3837	−	45.2548i	0.526065	−	0.303724i	0.739413	+	0.673253i	$0.235103\pi$
$150$	−24.8130	−	29.0227i	−0.165420	−	0.193485i
$151$	−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
$156$	13.9546	+	75.0818i	0.0894525	+	0.481293i
$157$	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
$159$	−133.479	+	24.8082i	−0.839488	+	0.156026i
$160$	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
$165$	−90.2929	+	77.1959i	−0.547229	+	0.467854i
$166$	−43.8406	−	75.9342i	−0.264100	−	0.457435i
$167$			226.000i			1.35329i	0.736308	+	0.676647i	$0.236568\pi$
$167$			226.000i			1.35329i	−0.736308	+	0.676647i	$0.763432\pi$
$168$		0			0
$169$	−7.00000			−0.0414201
$170$	156.767	−	90.5097i	0.922161	−	0.532410i
$171$	−237.559	+	91.4643i	−1.38923	+	0.534879i
$172$	−52.0000	+	90.0666i	−0.302326	+	0.523643i
$173$	114.315	−	66.0000i	0.660782	−	0.381503i	−0.131793	−	0.991277i	$-0.542073\pi$
$173$	114.315	−	66.0000i	0.660782	−	0.381503i	0.792575	+	0.609774i	$0.208740\pi$
$174$	226.274	+	80.0000i	1.30043	+	0.459770i
$175$		0			0
$176$			39.5980i			0.224989i
$177$	94.3837	−	17.5420i	0.533241	−	0.0991075i
$178$	−39.5980	+	68.5857i	−0.222461	+	0.385313i
$179$	−194.734	−	112.430i	−1.08790	−	0.628100i	−0.154885	−	0.987933i	$-0.549501\pi$
$179$	−194.734	−	112.430i	−1.08790	−	0.628100i	−0.933017	+	0.359832i	$0.882834\pi$
$180$	71.1248	+	11.1918i	0.395138	+	0.0621769i
$181$	−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	−0.522275	−	0.852777i	$-0.674917\pi$
$191$	−8.57321	+	4.94975i	−0.0448859	+	0.0259149i	0.477389	+	0.878692i	$0.341583\pi$
$192$	18.2419	−	15.5959i	0.0950100	−	0.0812287i
$193$	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	$-0.912053\pi$
$197$		−	107.480i		−	0.545585i	0.962073	−	0.272792i	$-0.0879472\pi$
$198$	−19.5857	+	124.468i	−0.0989177	+	0.628629i
$199$	−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
$201$	6.57826	+	35.3939i	0.0327277	+	0.176089i
$202$	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
$207$	4.57321	+	11.8780i	0.0220928	+	0.0573814i
$208$	−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
$213$	−173.691	−	203.159i	−0.815449	−	0.953798i
$214$	−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
$219$	17.8309	+	95.9378i	0.0814195	+	0.438072i
$220$	39.5980	−	68.5857i	0.179991	−	0.311753i
$221$	−352.727	−	203.647i	−1.59605	−	0.921479i
$222$	−208.560	+	38.7628i	−0.939461	+	0.174607i
$223$	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	0.999235	−	0.0390966i	$-0.0124480\pi$
$227$	332.554	+	192.000i	1.46499	+	0.845815i	0.465759	+	0.884912i	$0.345781\pi$
$228$	128.990	−	110.280i	0.565745	−	0.483683i
$229$	−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	0.238250	−	0.971204i	$-0.423426\pi$
$233$	279.242	−	161.220i	1.19846	−	0.691933i	0.960212	+	0.279271i	$0.0900928\pi$
$234$	−58.2075	−	151.182i	−0.248750	−	0.646075i
$235$	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	$-0.797279\pi$
$239$		−	284.257i		−	1.18936i	0.803963	−	0.594680i	$-0.202721\pi$
$240$	−47.1918	+	8.77101i	−0.196633	+	0.0365459i
$241$	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
$243$	224.268	−	93.5556i	0.922916	−	0.385003i
$244$	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
$249$	120.868	+	141.375i	0.485415	+	0.567770i
$250$	−96.1665	−	166.565i	−0.384666	−	0.666261i
$251$		−	224.000i		−	0.892430i	−0.894926	−	0.446215i	$-0.852772\pi$
$251$		−	224.000i		−	0.892430i	0.894926	−	0.446215i	$-0.147228\pi$
$252$		0			0
$253$	14.0000			0.0553360
$254$	−127.373	+	73.5391i	−0.501470	+	0.289524i
$255$	−291.871	+	249.535i	−1.14459	+	0.978567i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−103.923	+	60.0000i	−0.404370	+	0.233463i	−0.688368	−	0.725362i	$-0.741672\pi$
$257$	−103.923	+	60.0000i	−0.404370	+	0.233463i	0.283998	+	0.958825i	$0.408339\pi$
$258$	73.5391	−	208.000i	0.285035	−	0.806202i
$259$		0			0
$260$			101.823i			0.391628i
$261$	−502.929	−	79.1382i	−1.92693	−	0.303212i
$262$	−21.2132	+	36.7423i	−0.0809664	+	0.140238i
$263$	194.734	+	112.430i	0.740435	+	0.427490i	0.822227	−	0.569159i	$-0.192731\pi$
$263$	194.734	+	112.430i	0.740435	+	0.427490i	−0.0817924	+	0.996649i	$0.526064\pi$
$264$	−15.3493	−	82.5857i	−0.0581412	−	0.312825i
$265$	−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	0.740196	−	0.672391i	$-0.234733\pi$
$269$	142.028	+	82.0000i	0.527986	+	0.304833i	−0.212210	+	0.977224i	$0.568066\pi$
$270$	−152.677	+	4.22821i	−0.565469	+	0.0156600i
$271$	−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
$276$	−5.51399	−	6.44949i	−0.0199782	−	0.0233677i
$277$	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	$0.0224464\pi$
$281$			39.5980i			0.140918i	−0.997515	+	0.0704590i	$0.977554\pi$
$282$	−26.3587	−	141.821i	−0.0934705	−	0.502912i
$283$	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
$285$	−333.697	+	62.0204i	−1.17087	+	0.217615i
$286$	−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
$291$	−54.8207	+	46.8689i	−0.188387	+	0.161062i
$292$	−32.5269	−	56.3383i	−0.111394	−	0.192939i
$293$			316.000i			1.07850i	0.842146	+	0.539249i	$0.181292\pi$
$293$			316.000i			1.07850i	−0.842146	+	0.539249i	$0.818708\pi$
$294$		0			0
$295$	128.000			0.433898
$296$	122.474	−	70.7107i	0.413765	−	0.238887i
$297$	−7.39936	−	267.184i	−0.0249137	−	0.899609i
$298$	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
$303$	−106.182	+	19.7348i	−0.350434	+	0.0651313i
$304$	−56.5685	+	97.9796i	−0.186081	+	0.322301i
$305$	−112.677	−	65.0538i	−0.369431	−	0.213291i
$306$	−63.3106	+	402.343i	−0.206897	+	1.31485i
$307$	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	0.999629	−	0.0272286i	$-0.00866819\pi$
$311$	458.993	+	265.000i	1.47586	+	0.852090i	0.476234	+	0.879319i	$0.342002\pi$
$312$	70.1816	+	82.0886i	0.224941	+	0.263104i
$313$	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	−0.646516	−	0.762900i	$-0.723775\pi$
$317$	−97.9796	+	56.5685i	−0.309084	+	0.178450i	0.337433	+	0.941350i	$0.390441\pi$
$318$	−145.935	+	124.767i	−0.458916	+	0.392350i
$319$	−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
$324$	−120.171	+	108.641i	−0.370899	+	0.335311i
$325$	−57.2756	+	99.2043i	−0.176233	+	0.305244i
$326$	−298.838	−	172.534i	−0.916680	−	0.529246i
$327$	96.4811	+	519.110i	0.295049	+	1.58749i
$328$	−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
$333$	419.949	−	161.688i	1.26111	−	0.485548i
$334$	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
$339$	−33.0839	−	38.6969i	−0.0975927	−	0.114150i
$340$	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
$345$	3.10102	+	16.6848i	0.00898847	+	0.0483618i
$346$	93.3381	−	161.666i	0.269763	−	0.467244i
$347$	187.386	+	108.187i	0.540017	+	0.311779i	0.745086	−	0.666969i	$-0.232408\pi$
$347$	187.386	+	108.187i	0.540017	+	0.311779i	−0.205069	+	0.978748i	$0.565742\pi$
$348$	333.697	−	62.0204i	0.958898	−	0.178220i
$349$	−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	0.576448	−	0.817134i	$-0.304438\pi$
$353$	55.4256	+	32.0000i	0.157013	+	0.0906516i	−0.419435	+	0.907785i	$0.637772\pi$
$354$	103.192	−	88.2238i	0.291502	−	0.249220i
$355$	−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	−0.267471	−	0.963566i	$-0.586188\pi$
$359$	155.543	−	89.8026i	0.433266	−	0.250146i	0.700737	+	0.713420i	$0.252855\pi$
$360$	95.0236	−	36.5857i	0.263954	−	0.101627i
$361$	−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
$366$	−135.677	+	25.2167i	−0.370701	+	0.0688980i
$367$	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
$369$	−142.250	−	22.3837i	−0.385500	−	0.0606604i
$370$	−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
$375$	265.131	+	310.112i	0.707015	+	0.826967i
$376$	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
$381$	237.145	−	202.747i	0.622427	−	0.532144i
$382$	−7.00000	+	12.1244i	−0.0183246	+	0.0317392i
$383$	96.9948	−	56.0000i	0.253250	−	0.146214i	−0.368001	−	0.929825i	$-0.619958\pi$
$383$	96.9948	−	56.0000i	0.253250	−	0.146214i	0.621252	+	0.783611i	$0.286624\pi$
$384$	11.3137	−	32.0000i	0.0294628	−	0.0833333i
$385$		0			0
$386$		−	226.274i		−	0.586203i
$387$	−72.7469	+	462.311i	−0.187977	+	1.19460i
$388$	24.0416	−	41.6413i	0.0619630	−	0.107323i
$389$	372.322	+	214.960i	0.957127	+	0.552598i	0.895288	−	0.445489i	$-0.146970\pi$
$389$	372.322	+	214.960i	0.957127	+	0.552598i	0.0618394	+	0.998086i	$0.480303\pi$
$390$	−39.4695	−	212.363i	−0.101204	−	0.544521i
$391$	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
$396$	64.0250	+	166.291i	0.161679	+	0.419928i
$397$	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	−0.639387	−	0.768885i	$-0.720812\pi$
$401$	−117.576	+	67.8823i	−0.293206	+	0.169282i	0.346181	+	0.938168i	$0.387478\pi$
$402$	33.0839	+	38.6969i	0.0822984	+	0.0962610i
$403$		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
$408$	−49.6163	−	266.957i	−0.121609	−	0.654307i
$409$	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
$411$	−200.218	+	37.2122i	−0.487148	+	0.0905407i
$412$	−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
$417$	−490.161	+	419.063i	−1.17545	+	1.00495i
$418$	197.990	+	342.929i	0.473660	+	0.820403i
$419$		−	352.000i		−	0.840095i	−0.907502	−	0.420048i	$-0.862013\pi$
$419$		−	352.000i		−	0.840095i	0.907502	−	0.420048i	$-0.137987\pi$
$420$		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
$423$	109.948	+	285.565i	0.259923	+	0.675095i
$424$	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
$429$	371.636	−	69.0717i	0.866284	−	0.161006i
$430$	147.078	−	254.747i	0.342042	−	0.592435i
$431$	−635.643	−	366.988i	−1.47481	−	0.851481i	−0.475212	−	0.879871i	$-0.657629\pi$
$431$	−635.643	−	366.988i	−1.47481	−	0.851481i	−0.999597	+	0.0283901i	$0.990962\pi$
$432$	51.3901	−	94.9898i	0.118958	−	0.219884i
$433$	−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
$438$	89.6765	+	104.891i	0.204741	+	0.239477i
$439$	−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	−0.0584500	−	0.998290i	$-0.518616\pi$
$443$	344.153	−	198.697i	0.776870	−	0.448526i	0.835320	+	0.549764i	$0.185282\pi$
$444$	−228.024	+	194.949i	−0.513567	+	0.439074i
$445$	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	$0.00601583\pi$
$449$			16.9706i			0.0377964i	−0.999821	+	0.0188982i	$0.993984\pi$
$450$	113.159	+	17.8061i	0.251464	+	0.0395691i
$451$	−79.1960	+	137.171i	−0.175601	+	0.304150i
$452$	29.3939	+	16.9706i	0.0650307	+	0.0375455i
$453$	−83.3246	−	448.322i	−0.183940	−	0.989674i
$454$	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
$459$	−23.9184	−	863.669i	−0.0521097	−	1.88163i
$460$	−5.65685	−	9.79796i	−0.0122975	−	0.0212999i
$461$			580.000i			1.25813i	0.777351	+	0.629067i	$0.216563\pi$
$461$			580.000i			1.25813i	−0.777351	+	0.629067i	$0.783437\pi$
$462$		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	−0.376598	−	0.926377i	$-0.622906\pi$
$467$	110.851	−	64.0000i	0.237369	−	0.137045i	0.613967	+	0.789332i	$0.289573\pi$
$468$	−178.191	−	144.000i	−0.380750	−	0.307692i
$469$		0			0
$470$		−	192.333i		−	0.409219i
$471$	93.8059	+	504.716i	0.199163	+	1.07158i
$472$	−45.2548	+	78.3837i	−0.0958789	+	0.166067i
$473$	445.807	+	257.387i	0.942510	+	0.544158i
$474$	−166.848	+	31.0102i	−0.352001	+	0.0654224i
$475$	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	−0.00361975	−	0.999993i	$-0.501152\pi$
$479$	−417.424	−	241.000i	−0.871449	−	0.503132i	−0.867830	+	0.496862i	$0.834486\pi$
$480$	−51.5959	+	44.1119i	−0.107491	+	0.0918998i
$481$	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
$486$	208.518	−	273.164i	0.429049	−	0.562065i
$487$	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	$-0.780959\pi$
$491$		−	623.668i		−	1.27020i	0.772430	−	0.635100i	$-0.219041\pi$
$492$	94.3837	−	17.5420i	0.191837	−	0.0356545i
$493$	−905.097	+	1567.67i	−1.83590	+	3.17986i
$494$	−440.908	−	254.558i	−0.892527	−	0.515300i
$495$	55.3968	−	352.050i	0.111913	−	0.711212i
$496$		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
$501$	−440.585	−	515.334i	−0.879411	−	1.02861i
$502$	−158.392	−	274.343i	−0.315522	−	0.546500i
$503$			16.0000i			0.0318091i	0.999874	+	0.0159046i	$0.00506280\pi$
$503$			16.0000i			0.0318091i	−0.999874	+	0.0159046i	$0.994937\pi$
$504$		0			0
$505$	−144.000			−0.285149
$506$	17.1464	−	9.89949i	0.0338862	−	0.0195642i
$507$	15.9617	−	13.6464i	0.0314826	−	0.0269160i
$508$	−104.000	+	180.133i	−0.204724	+	0.354593i
$509$	−308.305	+	178.000i	−0.605707	+	0.349705i	−0.771284	−	0.636492i	$-0.780385\pi$
$509$	−308.305	+	178.000i	−0.605707	+	0.349705i	0.165576	+	0.986197i	$0.447052\pi$
$510$	−181.019	+	512.000i	−0.354940	+	1.00392i
$511$		0			0
$512$			22.6274i			0.0441942i
$513$	363.383	−	671.679i	0.708348	−	1.30932i
$514$	−84.8528	+	146.969i	−0.165083	+	0.285933i
$515$	254.747	+	147.078i	0.494654	+	0.285589i
$516$	−57.0116	−	306.747i	−0.110488	−	0.594471i
$517$	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	0.279515	−	0.960141i	$-0.409826\pi$
$521$	−214.774	−	124.000i	−0.412235	−	0.238004i	−0.691749	+	0.722138i	$0.743160\pi$
$522$	−671.918	+	258.700i	−1.28720	+	0.495594i
$523$	−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
$528$	−77.1959	−	90.2929i	−0.146204	−	0.171009i
$529$	−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
$534$	−43.4143	−	233.588i	−0.0813002	−	0.437430i
$535$	291.328	−	504.595i	0.544538	−	0.943168i
$536$	−29.3939	−	16.9706i	−0.0548393	−	0.0316615i
$537$	663.222	−	123.266i	1.23505	−	0.229545i
$538$	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
$543$	415.992	−	355.652i	0.766100	−	0.654977i
$544$	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
$549$	273.193	−	105.184i	0.497619	−	0.191592i
$550$	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
$555$	589.898	−	109.638i	1.06288	−	0.197545i
$556$	214.960	−	372.322i	0.386620	−	0.669645i
$557$	−911.210	−	526.087i	−1.63592	−	0.944502i	−0.982216	−	0.187756i	$-0.939879\pi$
$557$	−911.210	−	526.087i	−1.63592	−	0.944502i	−0.653709	−	0.756746i	$-0.726788\pi$
$558$		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	$-0.916264\pi$
$563$	−942.236	−	544.000i	−1.67360	−	0.966252i	−0.708000	−	0.706212i	$-0.750402\pi$
$564$	−132.565	−	155.056i	−0.235045	−	0.274922i
$565$	−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	−0.831543	−	0.555460i	$-0.812542\pi$
$569$	−436.009	+	251.730i	−0.766273	+	0.442408i	0.0652707	+	0.997868i	$0.479209\pi$
$570$	−364.838	+	311.918i	−0.640067	+	0.547225i
$571$	−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
$576$	−11.1918	+	71.1248i	−0.0194303	+	0.123481i
$577$	−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
$579$	87.7101	+	471.918i	0.151486	+	0.815058i
$580$	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
$585$	164.636	+	427.606i	0.281429	+	0.730951i
$586$	223.446	+	387.019i	0.381307	+	0.660443i
$587$			480.000i			0.817717i	0.912598	+	0.408859i	$0.134073\pi$
$587$			480.000i			0.817717i	−0.912598	+	0.408859i	$0.865927\pi$
$588$		0			0
$589$		0			0
$590$	156.767	−	90.5097i	0.265707	−	0.153406i
$591$	209.532	+	245.081i	0.354537	+	0.414688i
$592$	100.000	−	173.205i	0.168919	−	0.292576i
$593$	928.379	−	536.000i	1.56556	−	0.903879i	0.568887	−	0.822416i	$-0.307374\pi$
$593$	928.379	−	536.000i	1.56556	−	0.903879i	0.996676	−	0.0814631i	$-0.0259593\pi$
$594$	−197.990	−	322.000i	−0.333316	−	0.542088i
$595$		0			0
$596$		−	181.019i		−	0.303724i
$597$	−120.940	−	650.709i	−0.202579	−	1.08996i
$598$	−12.7279	+	22.0454i	−0.0212842	+	0.0368652i
$599$	353.951	+	204.354i	0.590904	+	0.341158i	0.765455	−	0.643490i	$-0.222514\pi$
$599$	353.951	+	204.354i	0.590904	+	0.341158i	−0.174551	+	0.984648i	$0.555847\pi$
$600$	−75.0818	+	13.9546i	−0.125136	+	0.0232577i
$601$	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
$606$	−116.091	+	99.2518i	−0.191569	+	0.163782i
$607$	−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
$612$	206.960	+	537.535i	0.338170	+	0.878325i
$613$	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	$-0.899094\pi$
$617$		−	384.666i		−	0.623446i	0.950173	−	0.311723i	$-0.100906\pi$
$618$	306.747	−	57.0116i	0.496354	−	0.0922517i
$619$	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
$621$	−33.5840	−	18.1691i	−0.0540805	−	0.0292579i
$622$	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
$627$	−545.857	−	638.467i	−0.870586	−	1.01829i
$628$	−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
$633$	848.249	−	725.210i	1.34005	−	1.14567i
$634$	−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
$639$	792.112	+	124.643i	1.23961	+	0.195059i
$640$	22.6274	−	39.1918i	0.0353553	−	0.0612372i
$641$	489.898	+	282.843i	0.764271	+	0.441252i	0.830827	−	0.556530i	$-0.187868\pi$
$641$	489.898	+	282.843i	0.764271	+	0.441252i	−0.0665559	+	0.997783i	$0.521201\pi$
$642$	−112.927	−	607.595i	−0.175898	−	0.946409i
$643$	−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	−0.274755	−	0.961514i	$-0.588597\pi$
$647$	−805.404	−	465.000i	−1.24483	−	0.718702i	−0.970073	+	0.242813i	$0.921930\pi$
$648$	−70.3587	+	218.031i	−0.108578	+	0.336468i
$649$	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	−0.806494	−	0.591242i	$-0.798638\pi$
$653$	−455.605	+	263.044i	−0.697711	+	0.402823i	0.108783	+	0.994065i	$0.465304\pi$
$654$	485.231	+	567.555i	0.741944	+	0.867821i
$655$	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	$0.0112734\pi$
$659$			46.6690i			0.0708180i	−0.999373	+	0.0354090i	$0.988727\pi$
$660$	43.4143	+	233.588i	0.0657792	+	0.353921i
$661$	−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
$663$	1201.31	−	223.273i	1.81193	−	0.336762i
$664$	−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
$669$	−38.6969	+	33.0839i	−0.0578430	+	0.0494528i
$670$	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
$675$	−242.907	+	6.72704i	−0.359862	+	0.00996598i
$676$	−7.00000	+	12.1244i	−0.0103550	+	0.0179354i
$677$	−883.346	+	510.000i	−1.30479	+	0.753323i	−0.981222	−	0.192880i	$-0.938217\pi$
$677$	−883.346	+	510.000i	−1.30479	+	0.753323i	−0.323572	+	0.946203i	$0.604884\pi$
$678$	−67.8823	−	24.0000i	−0.100121	−	0.0353982i
$679$		0			0
$680$		−	362.039i		−	0.532410i
$681$	−1132.60	+	210.504i	−1.66315	+	0.309111i
$682$		0			0
$683$	400.492	+	231.224i	0.586371	+	0.338542i	0.763661	−	0.645617i	$-0.223400\pi$
$683$	400.492	+	231.224i	0.586371	+	0.338542i	−0.177290	+	0.984159i	$0.556733\pi$
$684$	−79.1382	+	502.929i	−0.115699	+	0.735276i
$685$	−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
$690$	15.5959	+	18.2419i	0.0226028	+	0.0264376i
$691$	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
$696$	364.838	−	311.918i	0.524193	−	0.448159i
$697$	−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	$0.192636\pi$
$701$			797.616i			1.13783i	−0.822398	+	0.568913i	$0.807364\pi$
$702$	427.454	+	231.255i	0.608909	+	0.329423i
$703$	707.107	−	1224.74i	1.00584	−	1.74217i
$704$	68.5857	+	39.5980i	0.0974229	+	0.0562471i
$705$	74.5536	+	401.131i	0.105750	+	0.568980i
$706$	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
$711$	335.959	−	129.350i	0.472516	−	0.181927i
$712$	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
$717$	554.156	+	648.174i	0.772881	+	0.904008i
$718$	127.000	−	219.970i	0.176880	−	0.306366i
$719$	568.113	−	328.000i	0.790143	−	0.456189i	−0.0498700	−	0.998756i	$-0.515881\pi$
$719$	568.113	−	328.000i	0.790143	−	0.456189i	0.840013	+	0.542567i	$0.182547\pi$
$720$	90.5097	−	112.000i	0.125708	−	0.155556i
$721$		0			0
$722$			620.840i			0.859889i
$723$	25.5834	+	137.650i	0.0353851	+	0.190387i
$724$	−182.434	+	315.984i	−0.251980	+	0.436442i
$725$	440.908	+	254.558i	0.608149	+	0.351115i
$726$	95.9378	−	17.8309i	0.132146	−	0.0245604i
$727$	−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
$732$	−148.338	+	126.822i	−0.202648	+	0.173254i
$733$	−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
$738$	−190.047	+	73.1714i	−0.257517	+	0.0991483i
$739$	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	$0.196041\pi$
$743$			858.428i			1.15535i	−0.816266	+	0.577677i	$0.803959\pi$
$744$		0			0
$745$	−181.019	+	313.535i	−0.242979	+	0.420852i
$746$	17.1464	+	9.89949i	0.0229845	+	0.0132701i
$747$	−551.218	−	86.7367i	−0.737908	−	0.116113i
$748$	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
$753$	436.686	+	510.774i	0.579928	+	0.678318i
$754$	−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
$759$	−31.9233	+	27.2929i	−0.0420597	+	0.0359590i
$760$	160.000	−	277.128i	0.210526	−	0.364642i
$761$	−588.897	+	340.000i	−0.773847	+	0.446781i	−0.834245	−	0.551394i	$-0.814096\pi$
$761$	−588.897	+	340.000i	−0.773847	+	0.446781i	0.0603985	+	0.998174i	$0.480763\pi$
$762$	147.078	−	416.000i	0.193016	−	0.545932i
$763$		0			0
$764$			19.7990i			0.0259149i
$765$	179.069	−	1138.00i	0.234078	−	1.48758i
$766$	79.1960	−	137.171i	0.103389	−	0.179075i
$767$	−352.727	−	203.647i	−0.459878	−	0.265511i
$768$	−8.77101	−	47.1918i	−0.0114206	−	0.0614477i
$769$	−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	−0.315560	−	0.948905i	$-0.602193\pi$
$773$	−1001.13	−	578.000i	−1.29512	−	0.747736i	−0.979556	+	0.201169i	$0.935526\pi$
$774$	237.807	+	617.653i	0.307244	+	0.798002i
$775$		0			0
$776$		−	68.0000i		−	0.0876289i
$777$		0			0
$778$	608.000			0.781491
$779$	−391.918	+	226.274i	−0.503104	+	0.290467i
$780$	−198.504	−	232.182i	−0.254492	−	0.297669i
$781$	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
$786$	−23.2577	−	125.136i	−0.0295899	−	0.159206i
$787$	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
$789$	−663.222	+	123.266i	−0.840586	+	0.156230i
$790$	−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
$795$	412.767	−	352.895i	0.519204	−	0.443894i
$796$	220.617	+	382.120i	0.277157	+	0.480051i
$797$			60.0000i			0.0752823i	0.999291	+	0.0376412i	$0.0119844\pi$
$797$			60.0000i			0.0752823i	−0.999291	+	0.0376412i	$0.988016\pi$
$798$		0			0
$799$	1088.00			1.36170
$800$	44.0908	−	25.4558i	0.0551135	−	0.0318198i
$801$	181.090	+	470.343i	0.226080	+	0.587195i
$802$	−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
$807$	−483.716	+	89.9029i	−0.599401	+	0.111404i
$808$	50.9117	−	88.1816i	0.0630095	−	0.109136i
$809$	−553.585	−	319.612i	−0.684283	−	0.395071i	0.117184	−	0.993110i	$-0.462613\pi$
$809$	−553.585	−	319.612i	−0.684283	−	0.395071i	−0.801467	+	0.598039i	$0.795947\pi$
$810$	339.896	−	307.283i	0.419625	−	0.379361i
$811$	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
$816$	−249.535	−	291.871i	−0.305802	−	0.357685i
$817$	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	−0.289990	−	0.957030i	$-0.593652\pi$
$821$	323.333	−	186.676i	0.393828	−	0.227377i	0.683817	+	0.729653i	$0.260318\pi$
$822$	−218.903	+	187.151i	−0.266305	+	0.227678i
$823$	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	$0.0106163\pi$
$827$			55.1543i			0.0666921i	−0.999444	+	0.0333460i	$0.989384\pi$
$828$	25.1464	+	3.95691i	0.0303701	+	0.00477888i
$829$	−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
$831$	254.359	+	1368.56i	0.306088	+	1.64689i
$832$	−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	$0.267519\pi$
$839$			1250.00i			1.48987i	−0.667138	+	0.744934i	$0.732481\pi$
$840$		0			0
$841$	−2359.00			−2.80499
$842$	293.939	−	169.706i	0.349096	−	0.201551i
$843$	−77.1959	−	90.2929i	−0.0915728	−	0.107109i
$844$	−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
$849$	136.445	+	734.133i	0.160712	+	0.864703i
$850$	203.647	−	352.727i	0.239584	−	0.414972i
$851$	−61.2372	−	35.3553i	−0.0719592	−	0.0415456i
$852$	−525.572	+	97.6821i	−0.616869	+	0.114650i
$853$	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	0.365044	−	0.930990i	$-0.381054\pi$
$857$	−221.703	−	128.000i	−0.258696	−	0.149358i	−0.623740	+	0.781632i	$0.714387\pi$
$858$	406.318	−	347.381i	0.473564	−	0.404873i
$859$	−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	$-0.279190\pi$
$863$	1402.33	−	809.637i	1.62495	−	0.938166i	0.985568	−	0.169277i	$-0.0541434\pi$
$864$	−4.22821	−	152.677i	−0.00489376	−	0.176709i
$865$	−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
$870$	−943.837	+	175.420i	−1.08487	+	0.201632i
$871$	76.3675	−	132.272i	0.0876780	−	0.151863i
$872$	−431.110	−	248.902i	−0.494392	−	0.285438i
$873$	33.6337	−	213.745i	0.0385266	−	0.244839i
$874$	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
$879$	−616.039	−	720.556i	−0.700840	−	0.819745i
$880$	−79.1960	−	137.171i	−0.0899954	−	0.155877i
$881$		−	264.000i		−	0.299659i	−0.988712	−	0.149830i	$-0.952127\pi$
$881$		−	264.000i		−	0.299659i	0.988712	−	0.149830i	$-0.0478726\pi$
$882$		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
$885$	−291.871	+	249.535i	−0.329797	+	0.281960i
$886$	281.000	−	486.706i	0.317156	−	0.549330i
$887$	1110.24	−	641.000i	1.25168	−	0.722661i	0.280241	−	0.959930i	$-0.409586\pi$
$887$	1110.24	−	641.000i	1.25168	−	0.722661i	0.971444	+	0.237269i	$0.0762523\pi$
$888$	−141.421	+	400.000i	−0.159258	+	0.450450i
$889$		0			0
$890$		−	316.784i		−	0.355937i
$891$	537.745	+	594.818i	0.603529	+	0.667585i
$892$	16.9706	−	29.3939i	0.0190253	−	0.0329528i
$893$	832.827	+	480.833i	0.932616	+	0.538446i
$894$	70.1681	+	377.535i	0.0784878	+	0.422298i
$895$	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
$900$	151.182	−	58.2075i	0.167980	−	0.0646750i
$901$	−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
$906$	−419.063	−	490.161i	−0.462542	−	0.541017i
$907$	−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	$-0.763686\pi$
$911$		−	1231.78i		−	1.35212i	0.736847	−	0.676059i	$-0.236314\pi$
$912$	−62.0204	−	333.697i	−0.0680048	−	0.365895i
$913$	−306.884	+	531.539i	−0.336127	+	0.582190i
$914$	154.318	+	89.0955i	0.168838	+	0.0974786i
$915$	383.751	−	71.3235i	0.419400	−	0.0779491i
$916$	−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
$921$	−786.838	+	672.707i	−0.854330	+	0.730409i
$922$	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
$927$	−617.653	+	237.807i	−0.666293	+	0.256534i
$928$	−160.000	+	277.128i	−0.172414	+	0.298629i
$929$	1274.79	−	736.000i	1.37222	−	0.792250i	0.381010	−	0.924571i	$-0.375576\pi$
$929$	1274.79	−	736.000i	1.37222	−	0.792250i	0.991207	+	0.132321i	$0.0422430\pi$
$930$		0			0
$931$		0			0
$932$		−	644.881i		−	0.691933i
$933$	−1563.23	+	290.540i	−1.67549	+	0.311404i
$934$	90.5097	−	156.767i	0.0969054	−	0.167845i
$935$	−1097.37	−	633.568i	−1.17366	−	0.677612i
$936$	−320.062	−	50.3633i	−0.341946	−	0.0538069i
$937$	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	0.914023	−	0.405663i	$-0.132959\pi$
$941$	959.556	+	554.000i	1.01972	+	0.588735i	0.105697	+	0.994398i	$0.466293\pi$
$942$	471.777	+	551.818i	0.500824	+	0.585794i
$943$	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	−0.381158	−	0.924510i	$-0.624475\pi$
$947$	216.780	−	125.158i	0.228912	−	0.132163i	0.610070	+	0.792347i	$0.291141\pi$
$948$	−182.419	+	155.959i	−0.192425	+	0.164514i
$949$	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	$0.0841106\pi$
$953$			497.803i			0.522354i	−0.965291	+	0.261177i	$0.915889\pi$
$954$	89.5347	−	568.999i	0.0938519	−	0.596435i
$955$	19.7990	−	34.2929i	0.0207319	−	0.0359088i
$956$	−492.347	−	284.257i	−0.515008	−	0.297340i
$957$	−306.985	−	1651.71i	−0.320779	−	1.72593i
$958$	−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
$963$	471.041	+	1223.43i	0.489139	+	1.27044i
$964$	−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
$969$	−1764.48	−	2063.84i	−1.82093	−	2.12986i
$970$	−68.0000	+	117.779i	−0.0701031	+	0.121422i
$971$	−289.252	+	167.000i	−0.297891	+	0.171988i	−0.641495	−	0.767127i	$-0.721686\pi$
$971$	−289.252	+	167.000i	−0.297891	+	0.171988i	0.343604	+	0.939115i	$0.388352\pi$
$972$	62.2254	−	482.000i	0.0640179	−	0.495885i
$973$		0			0
$974$		−	169.706i		−	0.174236i
$975$	−62.7957	−	337.868i	−0.0644058	−	0.346531i
$976$	65.0538	−	112.677i	0.0666535	−	0.115447i
$977$	−44.0908	−	25.4558i	−0.0451288	−	0.0260551i	0.477266	−	0.878759i	$-0.341628\pi$
$977$	−44.0908	−	25.4558i	−0.0451288	−	0.0260551i	−0.522395	+	0.852704i	$0.674961\pi$
$978$	1017.77	−	189.162i	1.04067	−	0.193417i
$979$	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	−0.0824297	−	0.996597i	$-0.526268\pi$
$983$	−969.948	−	560.000i	−0.986723	−	0.569685i	−0.904293	+	0.426912i	$0.859601\pi$
$984$	103.192	−	88.2238i	0.104870	−	0.0896584i
$985$	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
$990$	−181.090	−	470.343i	−0.182919	−	0.475094i
$991$	−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
$996$	365.737	−	67.9753i	0.367206	−	0.0682483i
$997$	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
$999$	−642.376	+	1187.37i	−0.643019	+	1.18856i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.22474 - 0.707107i) q^{2} +(-2.28024 + 1.94949i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-3.46410 + 2.00000i) q^{5} +(-1.41421 + 4.00000i) q^{6} -2.82843i q^{8} +(1.39898 - 8.89060i) q^{9} +O(q^{10})\)	\(q+(1.22474 - 0.707107i) q^{2} +(-2.28024 + 1.94949i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-3.46410 + 2.00000i) q^{5} +(-1.41421 + 4.00000i) q^{6} -2.82843i q^{8} +(1.39898 - 8.89060i) q^{9} +(-2.82843 + 4.89898i) q^{10} +(-8.57321 - 4.94975i) q^{11} +(1.09638 + 5.89898i) q^{12} +12.7279 q^{13} +(4.00000 - 11.3137i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(-27.7128 - 16.0000i) q^{17} +(-4.57321 - 11.8780i) q^{18} +(-14.1421 - 24.4949i) q^{19} +8.00000i q^{20} -14.0000 q^{22} +(-1.22474 + 0.707107i) q^{23} +(5.51399 + 6.44949i) q^{24} +(-4.50000 + 7.79423i) q^{25} +(15.5885 - 9.00000i) q^{26} +(14.1421 + 23.0000i) q^{27} -56.5685i q^{29} +(-3.10102 - 16.6848i) q^{30} +(-4.89898 - 2.82843i) q^{32} +(29.1985 - 5.42679i) q^{33} -45.2548 q^{34} +(-14.0000 - 11.3137i) q^{36} +(25.0000 + 43.3013i) q^{37} +(-34.6410 - 20.0000i) q^{38} +(-29.0227 + 24.8130i) q^{39} +(5.65685 + 9.79796i) q^{40} -16.0000i q^{41} -52.0000 q^{43} +(-17.1464 + 9.89949i) q^{44} +(12.9350 + 33.5959i) q^{45} +(-1.00000 + 1.73205i) q^{46} +(-29.4449 + 17.0000i) q^{47} +(11.3137 + 4.00000i) q^{48} +12.7279i q^{50} +(94.3837 - 17.5420i) q^{51} +(12.7279 - 22.0454i) q^{52} +(39.1918 + 22.6274i) q^{53} +(33.5840 + 18.1691i) q^{54} +39.5980 q^{55} +(80.0000 + 28.2843i) q^{57} +(-40.0000 - 69.2820i) q^{58} +(-27.7128 - 16.0000i) q^{59} +(-15.5959 - 18.2419i) q^{60} +(16.2635 + 28.1691i) q^{61} -8.00000 q^{64} +(-44.0908 + 25.4558i) q^{65} +(31.9233 - 27.2929i) q^{66} +(6.00000 - 10.3923i) q^{67} +(-55.4256 + 32.0000i) q^{68} +(1.41421 - 4.00000i) q^{69} +89.0955i q^{71} +(-25.1464 - 3.95691i) q^{72} +(16.2635 - 28.1691i) q^{73} +(61.2372 + 35.3553i) q^{74} +(-4.93369 - 26.5454i) q^{75} -56.5685 q^{76} +(-18.0000 + 50.9117i) q^{78} +(20.0000 + 34.6410i) q^{79} +(13.8564 + 8.00000i) q^{80} +(-77.0857 - 24.8755i) q^{81} +(-11.3137 - 19.5959i) q^{82} -62.0000i q^{83} +128.000 q^{85} +(-63.6867 + 36.7696i) q^{86} +(110.280 + 128.990i) 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} +(16.6848 - 3.10102i) 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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