LMFDB - Embedded newform 369.3.l.b.55.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [369,3,Mod(55,369)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(369, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("369.55");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 369 = 3^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	369.l (of order $8$, degree $4$, 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:	$10.0545217549$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{8})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 66 x^{18} + 1853 x^{16} + 28868 x^{14} + 272678 x^{12} + 1600296 x^{10} + 5739482 x^{8} + \cdots + 776161 $ x^20 + 66x^18 + 1853x^16 + 28868x^14 + 272678x^12 + 1600296x^10 + 5739482x^8 + 11863964x^6 + 12547553x^4 + 5476470*x^2 + 776161
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 41)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			55.3
Root			$-1.38143i$ of defining polynomial
Character	$\chi$	$=$	369.55
Dual form			369.3.l.b.208.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.976817 + 0.976817i) q^{2} -2.09166i q^{4} +(-4.54303 + 4.54303i) q^{5} +(0.392560 + 0.947724i) q^{7} +(5.95043 - 5.95043i) q^{8} +O(q^{10})$	\(q+(0.976817 + 0.976817i) q^{2} -2.09166i q^{4} +(-4.54303 + 4.54303i) q^{5} +(0.392560 + 0.947724i) q^{7} +(5.95043 - 5.95043i) q^{8} -8.87541 q^{10} +(12.1914 - 5.04984i) q^{11} +(9.50068 + 22.9367i) q^{13} +(-0.542293 + 1.30921i) q^{14} +3.25833 q^{16} +(-0.0103812 + 0.0250625i) q^{17} +(-4.10513 + 9.91065i) q^{19} +(9.50246 + 9.50246i) q^{20} +(16.8415 + 6.97599i) q^{22} +26.1898i q^{23} -16.2782i q^{25} +(-13.1245 + 31.6853i) q^{26} +(1.98231 - 0.821101i) q^{28} +(9.09988 + 21.9691i) q^{29} +34.6509i q^{31} +(-20.6189 - 20.6189i) q^{32} +(-0.0346220 + 0.0143409i) q^{34} +(-6.08895 - 2.52212i) q^{35} +31.8640 q^{37} +(-13.6909 + 5.67094i) q^{38} +54.0660i q^{40} +(36.9925 - 17.6792i) q^{41} +(-26.6842 - 26.6842i) q^{43} +(-10.5625 - 25.5002i) q^{44} +(-25.5826 + 25.5826i) q^{46} +(5.31373 - 12.8285i) q^{47} +(33.9042 - 33.9042i) q^{49} +(15.9008 - 15.9008i) q^{50} +(47.9757 - 19.8722i) q^{52} +(44.5080 - 18.4358i) q^{53} +(-32.4443 + 78.3274i) q^{55} +(7.97527 + 3.30347i) q^{56} +(-12.5708 + 30.3487i) q^{58} +2.86012 q^{59} +(-29.7057 - 29.7057i) q^{61} +(-33.8476 + 33.8476i) q^{62} -53.3152i q^{64} +(-147.364 - 61.0401i) q^{65} +(14.9886 - 36.1856i) q^{67} +(0.0524222 + 0.0217140i) q^{68} +(-3.48413 - 8.41144i) q^{70} +(22.4314 + 54.1541i) q^{71} +(-56.7726 - 56.7726i) q^{73} +(31.1253 + 31.1253i) q^{74} +(20.7297 + 8.58652i) q^{76} +(9.57171 + 9.57171i) q^{77} +(-134.955 + 55.9004i) q^{79} +(-14.8027 + 14.8027i) q^{80} +(53.4042 + 18.8656i) q^{82} -127.971 q^{83} +(-0.0666974 - 0.161022i) q^{85} -52.1311i q^{86} +(42.4953 - 102.593i) q^{88} +(39.5582 + 95.5019i) q^{89} +(-18.0080 + 18.0080i) q^{91} +54.7801 q^{92} +(17.7216 - 7.34054i) q^{94} +(-26.3747 - 63.6741i) q^{95} +(109.949 + 45.5425i) q^{97} +66.2363 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 8 q^{2} + 12 q^{5} - 4 q^{7} - 36 q^{8}+O(q^{10}) $ 20 * q + 8 * q^2 + 12 * q^5 - 4 * q^7 - 36 * q^8	$ 20 q + 8 q^{2} + 12 q^{5} - 4 q^{7} - 36 q^{8} + 16 q^{10} + 12 q^{11} - 48 q^{13} - 88 q^{14} - 36 q^{16} + 28 q^{17} + 76 q^{19} + 16 q^{20} - 116 q^{22} - 40 q^{26} + 72 q^{28} + 24 q^{29} - 176 q^{32} + 80 q^{34} - 60 q^{35} + 208 q^{37} + 380 q^{38} + 116 q^{41} - 40 q^{43} - 116 q^{44} - 176 q^{46} + 64 q^{47} + 168 q^{49} + 148 q^{50} - 184 q^{52} + 120 q^{53} + 20 q^{55} - 188 q^{56} + 36 q^{58} + 512 q^{59} - 460 q^{61} - 68 q^{62} - 432 q^{65} + 300 q^{67} - 120 q^{68} + 308 q^{70} + 108 q^{71} + 60 q^{73} - 140 q^{74} + 872 q^{76} - 112 q^{77} - 208 q^{79} + 68 q^{80} - 376 q^{82} + 120 q^{83} + 172 q^{85} + 316 q^{88} - 268 q^{89} - 800 q^{91} + 448 q^{92} - 212 q^{94} + 184 q^{95} - 120 q^{97} + 20 q^{98}+O(q^{100}) $ 20 * q + 8 * q^2 + 12 * q^5 - 4 * q^7 - 36 * q^8 + 16 * q^10 + 12 * q^11 - 48 * q^13 - 88 * q^14 - 36 * q^16 + 28 * q^17 + 76 * q^19 + 16 * q^20 - 116 * q^22 - 40 * q^26 + 72 * q^28 + 24 * q^29 - 176 * q^32 + 80 * q^34 - 60 * q^35 + 208 * q^37 + 380 * q^38 + 116 * q^41 - 40 * q^43 - 116 * q^44 - 176 * q^46 + 64 * q^47 + 168 * q^49 + 148 * q^50 - 184 * q^52 + 120 * q^53 + 20 * q^55 - 188 * q^56 + 36 * q^58 + 512 * q^59 - 460 * q^61 - 68 * q^62 - 432 * q^65 + 300 * q^67 - 120 * q^68 + 308 * q^70 + 108 * q^71 + 60 * q^73 - 140 * q^74 + 872 * q^76 - 112 * q^77 - 208 * q^79 + 68 * q^80 - 376 * q^82 + 120 * q^83 + 172 * q^85 + 316 * q^88 - 268 * q^89 - 800 * q^91 + 448 * q^92 - 212 * q^94 + 184 * q^95 - 120 * q^97 + 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/369\mathbb{Z}\right)^\times$.

$n$	$83$	$334$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$

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 $

$2$	0.976817	+	0.976817i	0.488408	+	0.488408i	0.907804	−	0.419395i	$-0.137758\pi$
$2$	0.976817	+	0.976817i	0.488408	+	0.488408i	−0.419395	+	0.907804i	$0.637758\pi$
$3$		0			0
$3$		0			0
$4$		−	2.09166i		−	0.522915i
$5$	−4.54303	+	4.54303i	−0.908606	+	0.908606i	−0.996160	−	0.0875541i	$-0.972095\pi$
$5$	−4.54303	+	4.54303i	−0.908606	+	0.908606i	0.0875541	+	0.996160i	$0.472095\pi$
$6$		0			0
$7$	0.392560	+	0.947724i	0.0560800	+	0.135389i	0.949436	−	0.313960i	$-0.101656\pi$
$7$	0.392560	+	0.947724i	0.0560800	+	0.135389i	−0.893356	+	0.449349i	$0.851656\pi$
$8$	5.95043	−	5.95043i	0.743804	−	0.743804i
$9$		0			0
$10$	−8.87541			−0.887541
$11$	12.1914	−	5.04984i	1.10831	−	0.459076i	0.247953	−	0.968772i	$-0.420242\pi$
$11$	12.1914	−	5.04984i	1.10831	−	0.459076i	0.860355	+	0.509696i	$0.170242\pi$
$12$		0			0
$13$	9.50068	+	22.9367i	0.730821	+	1.76436i	0.639842	+	0.768506i	$0.279000\pi$
$13$	9.50068	+	22.9367i	0.730821	+	1.76436i	0.0909790	+	0.995853i	$0.471000\pi$
$14$	−0.542293	+	1.30921i	−0.0387352	+	0.0935151i
$15$		0			0
$16$	3.25833			0.203646
$17$	−0.0103812	+	0.0250625i	−0.000610660	+	0.00147426i	−0.924185	−	0.381946i	$-0.875254\pi$
$17$	−0.0103812	+	0.0250625i	−0.000610660	+	0.00147426i	0.923574	+	0.383420i	$0.125254\pi$
$18$		0			0
$19$	−4.10513	+	9.91065i	−0.216059	+	0.521613i	−0.994333	−	0.106312i	$-0.966096\pi$
$19$	−4.10513	+	9.91065i	−0.216059	+	0.521613i	0.778273	+	0.627925i	$0.216096\pi$
$20$	9.50246	+	9.50246i	0.475123	+	0.475123i
$21$		0			0
$22$	16.8415	+	6.97599i	0.765524	+	0.317090i
$23$			26.1898i			1.13869i	0.822100	+	0.569343i	$0.192803\pi$
$23$			26.1898i			1.13869i	−0.822100	+	0.569343i	$0.807197\pi$
$24$		0			0
$25$		−	16.2782i		−	0.651128i
$26$	−13.1245	+	31.6853i	−0.504788	+	1.21867i
$27$		0			0
$28$	1.98231	−	0.821101i	0.0707969	−	0.0293251i
$29$	9.09988	+	21.9691i	0.313789	+	0.757554i	0.999558	+	0.0297342i	$0.00946609\pi$
$29$	9.09988	+	21.9691i	0.313789	+	0.757554i	−0.685769	+	0.727819i	$0.740534\pi$
$30$		0			0
$31$			34.6509i			1.11777i	0.829245	+	0.558886i	$0.188771\pi$
$31$			34.6509i			1.11777i	−0.829245	+	0.558886i	$0.811229\pi$
$32$	−20.6189	−	20.6189i	−0.644342	−	0.644342i
$33$		0			0
$34$	−0.0346220	+	0.0143409i	−0.00101829	+	0.000421792i
$35$	−6.08895	−	2.52212i	−0.173970	−	0.0720607i
$36$		0			0
$37$	31.8640			0.861190			0.430595	−	0.902545i	$-0.358304\pi$
$37$	31.8640			0.861190			0.430595	+	0.902545i	$0.358304\pi$
$38$	−13.6909	+	5.67094i	−0.360286	+	0.149235i
$39$		0			0
$40$			54.0660i			1.35165i
$41$	36.9925	−	17.6792i	0.902256	−	0.431200i
$41$	36.9925	−	17.6792i	0.902256	−	0.431200i
$42$		0			0
$43$	−26.6842	−	26.6842i	−0.620562	−	0.620562i	0.325113	−	0.945675i	$-0.394598\pi$
$43$	−26.6842	−	26.6842i	−0.620562	−	0.620562i	−0.945675	+	0.325113i	$0.894598\pi$
$44$	−10.5625	−	25.5002i	−0.240058	−	0.579550i
$45$		0			0
$46$	−25.5826	+	25.5826i	−0.556144	+	0.556144i
$47$	5.31373	−	12.8285i	0.113058	−	0.272947i	−0.857215	−	0.514958i	$-0.827807\pi$
$47$	5.31373	−	12.8285i	0.113058	−	0.272947i	0.970273	+	0.242012i	$0.0778073\pi$
$48$		0			0
$49$	33.9042	−	33.9042i	0.691922	−	0.691922i
$50$	15.9008	−	15.9008i	0.318017	−	0.318017i
$51$		0			0
$52$	47.9757	−	19.8722i	0.922609	−	0.382157i
$53$	44.5080	−	18.4358i	0.839773	−	0.347845i	0.0790089	−	0.996874i	$-0.474824\pi$
$53$	44.5080	−	18.4358i	0.839773	−	0.347845i	0.760764	+	0.649029i	$0.224824\pi$
$54$		0			0
$55$	−32.4443	+	78.3274i	−0.589896	+	1.42413i
$56$	7.97527	+	3.30347i	0.142416	+	0.0589904i
$57$		0			0
$58$	−12.5708	+	30.3487i	−0.216738	+	0.523253i
$59$	2.86012			0.0484766			0.0242383	−	0.999706i	$-0.492284\pi$
$59$	2.86012			0.0484766			0.0242383	+	0.999706i	$0.492284\pi$
$60$		0			0
$61$	−29.7057	−	29.7057i	−0.486979	−	0.486979i	0.420373	−	0.907351i	$-0.361899\pi$
$61$	−29.7057	−	29.7057i	−0.486979	−	0.486979i	−0.907351	+	0.420373i	$0.861899\pi$
$62$	−33.8476	+	33.8476i	−0.545929	+	0.545929i
$63$		0			0
$64$		−	53.3152i		−	0.833050i
$65$	−147.364	−	61.0401i	−2.26713	−	0.939078i
$66$		0			0
$67$	14.9886	−	36.1856i	0.223710	−	0.540083i	−0.771678	−	0.636013i	$-0.780582\pi$
$67$	14.9886	−	36.1856i	0.223710	−	0.540083i	0.995388	+	0.0959298i	$0.0305824\pi$
$68$	0.0524222	+	0.0217140i	0.000770914	+	0.000319323i
$69$		0			0
$70$	−3.48413	−	8.41144i	−0.0497733	−	0.120163i
$71$	22.4314	+	54.1541i	0.315935	+	0.762734i	0.999462	+	0.0328086i	$0.0104452\pi$
$71$	22.4314	+	54.1541i	0.315935	+	0.762734i	−0.683527	+	0.729925i	$0.739555\pi$
$72$		0			0
$73$	−56.7726	−	56.7726i	−0.777707	−	0.777707i	0.201734	−	0.979440i	$-0.435342\pi$
$73$	−56.7726	−	56.7726i	−0.777707	−	0.777707i	−0.979440	+	0.201734i	$0.935342\pi$
$74$	31.1253	+	31.1253i	0.420612	+	0.420612i
$75$		0			0
$76$	20.7297	+	8.58652i	0.272759	+	0.112981i
$77$	9.57171	+	9.57171i	0.124308	+	0.124308i
$78$		0			0
$79$	−134.955	+	55.9004i	−1.70830	+	0.707600i	−0.708299	+	0.705913i	$0.750537\pi$
$79$	−134.955	+	55.9004i	−1.70830	+	0.707600i	−0.999999	+	0.00168717i	$0.999463\pi$
$80$	−14.8027	+	14.8027i	−0.185034	+	0.185034i
$81$		0			0
$82$	53.4042	+	18.8656i	0.651271	+	0.230068i
$83$	−127.971			−1.54182			−0.770910	−	0.636944i	$-0.780198\pi$
$83$	−127.971			−1.54182			−0.770910	+	0.636944i	$0.780198\pi$
$84$		0			0
$85$	−0.0666974	−	0.161022i	−0.000784676	−	0.00189437i
$86$		−	52.1311i		−	0.606175i
$87$		0			0
$88$	42.4953	−	102.593i	0.482901	−	1.16583i
$89$	39.5582	+	95.5019i	0.444474	+	1.07306i	0.974362	+	0.224987i	$0.0722341\pi$
$89$	39.5582	+	95.5019i	0.444474	+	1.07306i	−0.529888	+	0.848068i	$0.677766\pi$
$90$		0			0
$91$	−18.0080	+	18.0080i	−0.197891	+	0.197891i
$92$	54.7801			0.595436
$93$		0			0
$94$	17.7216	−	7.34054i	0.188528	−	0.0780908i
$95$	−26.3747	−	63.6741i	−0.277628	−	0.670254i
$96$		0			0
$97$	109.949	+	45.5425i	1.13350	+	0.469511i	0.868969	−	0.494867i	$-0.164783\pi$
$97$	109.949	+	45.5425i	1.13350	+	0.469511i	0.264530	+	0.964377i	$0.414783\pi$
$98$	66.2363			0.675881
$99$		0			0
$100$	−34.0485			−0.340485
$101$	−5.69079	+	13.7388i	−0.0563444	+	0.136028i	−0.949545	−	0.313631i	$-0.898454\pi$
$101$	−5.69079	+	13.7388i	−0.0563444	+	0.136028i	0.893200	+	0.449659i	$0.148454\pi$
$102$		0			0
$103$	−19.3162	+	19.3162i	−0.187536	+	0.187536i	−0.794630	−	0.607094i	$-0.792335\pi$
$103$	−19.3162	+	19.3162i	−0.187536	+	0.187536i	0.607094	+	0.794630i	$0.292335\pi$
$104$	193.016	+	79.9500i	1.85593	+	0.768750i
$105$		0			0
$106$	61.4845	+	25.4677i	0.580043	+	0.240262i
$107$		−	186.847i		−	1.74623i	−0.487513	−	0.873115i	$-0.662096\pi$
$107$		−	186.847i		−	1.74623i	0.487513	−	0.873115i	$-0.337904\pi$
$108$		0			0
$109$	−44.4400	−	18.4077i	−0.407706	−	0.168878i	0.169398	−	0.985548i	$-0.445818\pi$
$109$	−44.4400	−	18.4077i	−0.407706	−	0.168878i	−0.577105	+	0.816670i	$0.695818\pi$
$110$	−108.204	+	44.8194i	−0.983669	+	0.407449i
$111$		0			0
$112$	1.27909	+	3.08800i	0.0114205	+	0.0275714i
$113$		−	126.114i		−	1.11605i	−0.829824	−	0.558025i	$-0.811559\pi$
$113$		−	126.114i		−	1.11605i	0.829824	−	0.558025i	$-0.188441\pi$
$114$		0			0
$115$	−118.981	−	118.981i	−1.03462	−	1.03462i
$116$	45.9518	−	19.0338i	0.396136	−	0.164085i
$117$		0			0
$118$	2.79381	+	2.79381i	0.0236764	+	0.0236764i
$119$	−0.0278276			−0.000233845
$120$		0			0
$121$	37.5692	−	37.5692i	0.310489	−	0.310489i
$122$		−	58.0340i		−	0.475689i
$123$		0			0
$124$	72.4779			0.584499
$125$	−39.6233	−	39.6233i	−0.316987	−	0.316987i
$126$		0			0
$127$		−	134.706i		−	1.06068i	−0.847786	−	0.530338i	$-0.822065\pi$
$127$		−	134.706i		−	1.06068i	0.847786	−	0.530338i	$-0.177935\pi$
$128$	−30.3966	+	30.3966i	−0.237473	+	0.237473i
$129$		0			0
$130$	−84.3224	−	203.572i	−0.648634	−	1.56594i
$131$	−59.5935	+	59.5935i	−0.454912	+	0.454912i	−0.896981	−	0.442069i	$-0.854245\pi$
$131$	−59.5935	+	59.5935i	−0.454912	+	0.454912i	0.442069	+	0.896981i	$0.354245\pi$
$132$		0			0
$133$	−11.0041			−0.0827374
$134$	49.9878	−	20.7056i	0.373043	−	0.154519i
$135$		0			0
$136$	0.0873599	+	0.210906i	0.000642352	+	0.00155078i
$137$	19.9933	−	48.2682i	0.145937	−	0.352323i	−0.833961	−	0.551824i	$-0.813932\pi$
$137$	19.9933	−	48.2682i	0.145937	−	0.352323i	0.979898	+	0.199501i	$0.0639321\pi$
$138$		0			0
$139$	197.683			1.42218			0.711090	−	0.703101i	$-0.248202\pi$
$139$	197.683			1.42218			0.711090	+	0.703101i	$0.248202\pi$
$140$	−5.27542	+	12.7360i	−0.0376816	+	0.0909714i
$141$		0			0
$142$	−30.9873	+	74.8100i	−0.218220	+	0.526831i
$143$	231.653	+	231.653i	1.61995	+	1.61995i
$144$		0			0
$145$	−141.147	−	58.4650i	−0.973428	−	0.403207i
$146$		−	110.913i		−	0.759677i
$147$		0			0
$148$		−	66.6486i		−	0.450329i
$149$	−16.0243	+	38.6861i	−0.107546	+	0.259639i	−0.968486	−	0.249067i	$-0.919876\pi$
$149$	−16.0243	+	38.6861i	−0.107546	+	0.259639i	0.860940	+	0.508706i	$0.169876\pi$
$150$		0			0
$151$	205.755	−	85.2263i	1.36261	−	0.564413i	0.422838	−	0.906205i	$-0.361034\pi$
$151$	205.755	−	85.2263i	1.36261	−	0.564413i	0.939775	+	0.341793i	$0.111034\pi$
$152$	34.5454	+	83.4000i	0.227272	+	0.548684i
$153$		0			0
$154$			18.6996i			0.121426i
$155$	−157.420	−	157.420i	−1.01561	−	1.01561i
$156$		0			0
$157$	−49.9163	+	20.6760i	−0.317938	+	0.131694i	−0.535945	−	0.844253i	$-0.680045\pi$
$157$	−49.9163	+	20.6760i	−0.317938	+	0.131694i	0.218007	+	0.975947i	$0.430045\pi$
$158$	−186.431	−	77.2223i	−1.17994	−	0.488749i
$159$		0			0
$160$	187.345			1.17091
$161$	−24.8207	+	10.2811i	−0.154166	+	0.0638576i
$162$		0			0
$163$			173.848i			1.06655i	0.845942	+	0.533275i	$0.179039\pi$
$163$			173.848i			1.06655i	−0.845942	+	0.533275i	$0.820961\pi$
$164$	−36.9789	−	77.3757i	−0.225481	−	0.471803i
$165$		0			0
$166$	−125.004	−	125.004i	−0.753038	−	0.753038i
$167$	109.618	+	264.642i	0.656397	+	1.58468i	0.803328	+	0.595537i	$0.203061\pi$
$167$	109.618	+	264.642i	0.656397	+	1.58468i	−0.146931	+	0.989147i	$0.546939\pi$
$168$		0			0
$169$	−316.327	+	316.327i	−1.87176	+	1.87176i
$170$	0.0921377	−	0.222440i	0.000541986	−	0.00130847i
$171$		0			0
$172$	−55.8141	+	55.8141i	−0.324501	+	0.324501i
$173$	146.640	−	146.640i	0.847633	−	0.847633i	−0.142205	−	0.989837i	$-0.545419\pi$
$173$	146.640	−	146.640i	0.847633	−	0.847633i	0.989837	+	0.142205i	$0.0454191\pi$
$174$		0			0
$175$	15.4272	−	6.39018i	0.0881557	−	0.0365153i
$176$	39.7236	−	16.4541i	0.225702	−	0.0934890i
$177$		0			0
$178$	−54.6468	+	131.929i	−0.307004	+	0.741174i
$179$	−76.2003	−	31.5632i	−0.425700	−	0.176331i	0.159539	−	0.987192i	$-0.448999\pi$
$179$	−76.2003	−	31.5632i	−0.425700	−	0.176331i	−0.585239	+	0.810861i	$0.698999\pi$
$180$		0			0
$181$	9.24361	−	22.3160i	0.0510697	−	0.123293i	−0.896286	−	0.443477i	$-0.853745\pi$
$181$	9.24361	−	22.3160i	0.0510697	−	0.123293i	0.947355	+	0.320184i	$0.103745\pi$
$182$	−35.1811			−0.193303
$183$		0			0
$184$	155.841	+	155.841i	0.846960	+	0.846960i
$185$	−144.759	+	144.759i	−0.782482	+	0.782482i
$186$		0			0
$187$			0.357970i			0.00191428i
$188$	−26.8328	−	11.1145i	−0.142728	−	0.0591197i
$189$		0			0
$190$	36.4347	−	87.9611i	0.191762	−	0.462953i
$191$	−29.2722	−	12.1249i	−0.153258	−	0.0634814i	0.304736	−	0.952437i	$-0.401432\pi$
$191$	−29.2722	−	12.1249i	−0.153258	−	0.0634814i	−0.457994	+	0.888955i	$0.651432\pi$
$192$		0			0
$193$	−11.5961	−	27.9955i	−0.0600836	−	0.145055i	0.890987	−	0.454030i	$-0.150014\pi$
$193$	−11.5961	−	27.9955i	−0.0600836	−	0.145055i	−0.951070	+	0.308975i	$0.900014\pi$
$194$	62.9137	+	151.887i	0.324298	+	0.782923i
$195$		0			0
$196$	−70.9159	−	70.9159i	−0.361816	−	0.361816i
$197$	20.2031	+	20.2031i	0.102554	+	0.102554i	0.756522	−	0.653968i	$-0.226897\pi$
$197$	20.2031	+	20.2031i	0.102554	+	0.102554i	−0.653968	+	0.756522i	$0.726897\pi$
$198$		0			0
$199$	−340.170	−	140.903i	−1.70940	−	0.708055i	−0.999995	−	0.00325106i	$-0.998965\pi$
$199$	−340.170	−	140.903i	−1.70940	−	0.708055i	−0.709402	−	0.704804i	$-0.751035\pi$
$200$	−96.8624	−	96.8624i	−0.484312	−	0.484312i
$201$		0			0
$202$	−18.9791	+	7.86141i	−0.0939561	+	0.0389179i
$203$	−17.2483	+	17.2483i	−0.0849672	+	0.0849672i
$204$		0			0
$205$	−87.7409	+	248.375i	−0.428004	+	1.21159i
$206$	−37.7367			−0.183188
$207$		0			0
$208$	30.9564	+	74.7353i	0.148829	+	0.359304i
$209$			141.555i			0.677296i
$210$		0			0
$211$	125.807	−	303.724i	0.596240	−	1.43945i	−0.281147	−	0.959665i	$-0.590715\pi$
$211$	125.807	−	303.724i	0.596240	−	1.43945i	0.877386	−	0.479785i	$-0.159285\pi$
$212$	−38.5614	−	93.0955i	−0.181893	−	0.439129i
$213$		0			0
$214$	182.515	−	182.515i	0.852874	−	0.852874i
$215$	242.454			1.12769
$216$		0			0
$217$	−32.8395	+	13.6026i	−0.151334	+	0.0626846i
$218$	−25.4288	−	61.3906i	−0.116646	−	0.281608i
$219$		0			0
$220$	163.834	+	67.8623i	0.744701	+	0.308465i
$221$	−0.673479			−0.00304742
$222$		0			0
$223$	−58.2357			−0.261147			−0.130573	−	0.991439i	$-0.541682\pi$
$223$	−58.2357			−0.261147			−0.130573	+	0.991439i	$0.541682\pi$
$224$	11.4469	−	27.6352i	0.0511022	−	0.123372i
$225$		0			0
$226$	123.190	−	123.190i	0.545088	−	0.545088i
$227$	−126.084	−	52.2256i	−0.555435	−	0.230069i	0.0872669	−	0.996185i	$-0.472187\pi$
$227$	−126.084	−	52.2256i	−0.555435	−	0.230069i	−0.642702	+	0.766116i	$0.722187\pi$
$228$		0			0
$229$	237.862	+	98.5256i	1.03870	+	0.430243i	0.835845	−	0.548966i	$-0.184978\pi$
$229$	237.862	+	98.5256i	1.03870	+	0.430243i	0.202854	+	0.979209i	$0.434978\pi$
$230$		−	232.445i		−	1.01063i
$231$		0			0
$232$	184.874	+	76.5772i	0.796869	+	0.330074i
$233$	18.3963	−	7.61999i	0.0789540	−	0.0327038i	−0.342857	−	0.939388i	$-0.611395\pi$
$233$	18.3963	−	7.61999i	0.0789540	−	0.0327038i	0.421811	+	0.906684i	$0.361395\pi$
$234$		0			0
$235$	34.1397	+	82.4206i	0.145275	+	0.350726i
$236$		−	5.98239i		−	0.0253491i
$237$		0			0
$238$	−0.0271824	−	0.0271824i	−0.000114212	−	0.000114212i
$239$	−270.876	+	112.201i	−1.13337	+	0.469458i	−0.868926	−	0.494942i	$-0.835189\pi$
$239$	−270.876	+	112.201i	−1.13337	+	0.469458i	−0.264446	+	0.964400i	$0.585189\pi$
$240$		0			0
$241$	202.230	+	202.230i	0.839130	+	0.839130i	0.988744	−	0.149614i	$-0.0478032\pi$
$241$	202.230	+	202.230i	0.839130	+	0.839130i	−0.149614	+	0.988744i	$0.547803\pi$
$242$	73.3964			0.303291
$243$		0			0
$244$	−62.1341	+	62.1341i	−0.254648	+	0.254648i
$245$			308.055i			1.25737i
$246$		0			0
$247$	−266.319			−1.07821
$248$	206.188	+	206.188i	0.831403	+	0.831403i
$249$		0			0
$250$		−	77.4095i		−	0.309638i
$251$	66.1533	−	66.1533i	0.263559	−	0.263559i	−0.562939	−	0.826498i	$-0.690330\pi$
$251$	66.1533	−	66.1533i	0.263559	−	0.263559i	0.826498	+	0.562939i	$0.190330\pi$
$252$		0			0
$253$	132.254	+	319.290i	0.522744	+	1.26202i
$254$	131.583	−	131.583i	0.518043	−	0.518043i
$255$		0			0
$256$	−272.645			−1.06502
$257$	85.0452	−	35.2269i	0.330915	−	0.137070i	−0.211039	−	0.977478i	$-0.567685\pi$
$257$	85.0452	−	35.2269i	0.330915	−	0.137070i	0.541954	+	0.840408i	$0.317685\pi$
$258$		0			0
$259$	12.5085	+	30.1983i	0.0482955	+	0.116596i
$260$	−127.675	+	308.235i	−0.491058	+	1.18552i
$261$		0			0
$262$	−116.424			−0.444366
$263$	64.9572	−	156.821i	0.246986	−	0.596276i	−0.750960	−	0.660348i	$-0.770409\pi$
$263$	64.9572	−	156.821i	0.246986	−	0.596276i	0.997945	+	0.0640720i	$0.0204087\pi$
$264$		0			0
$265$	−118.447	+	285.955i	−0.446968	+	1.07908i
$266$	−10.7490	−	10.7490i	−0.0404096	−	0.0404096i
$267$		0			0
$268$	−75.6879	−	31.3509i	−0.282417	−	0.116981i
$269$			48.3404i			0.179704i	0.995955	+	0.0898521i	$0.0286394\pi$
$269$			48.3404i			0.179704i	−0.995955	+	0.0898521i	$0.971361\pi$
$270$		0			0
$271$		−	34.7684i		−	0.128297i	−0.997940	−	0.0641484i	$-0.979567\pi$
$271$		−	34.7684i		−	0.128297i	0.997940	−	0.0641484i	$-0.0204331\pi$
$272$	−0.0338255	+	0.0816620i	−0.000124358	+	0.000300228i
$273$		0			0
$274$	66.6790	−	27.6193i	0.243354	−	0.100801i
$275$	−82.2023	−	198.454i	−0.298918	−	0.721651i
$276$		0			0
$277$		−	282.188i		−	1.01873i	−0.860551	−	0.509364i	$-0.829881\pi$
$277$		−	282.188i		−	1.01873i	0.860551	−	0.509364i	$-0.170119\pi$
$278$	193.100	+	193.100i	0.694605	+	0.694605i
$279$		0			0
$280$	−51.2396	+	21.2241i	−0.182999	+	0.0758005i
$281$	−171.362	−	70.9804i	−0.609829	−	0.252599i	0.0563266	−	0.998412i	$-0.482061\pi$
$281$	−171.362	−	70.9804i	−0.609829	−	0.252599i	−0.666155	+	0.745813i	$0.732061\pi$
$282$		0			0
$283$	39.0466			0.137974			0.0689869	−	0.997618i	$-0.478023\pi$
$283$	39.0466			0.137974			0.0689869	+	0.997618i	$0.478023\pi$
$284$	113.272	−	46.9188i	0.398845	−	0.165207i
$285$		0			0
$286$			452.565i			1.58239i
$287$	31.2768	+	28.1185i	0.108978	+	0.0979740i
$288$		0			0
$289$	204.353	+	204.353i	0.707105	+	0.707105i
$290$	−80.7652	−	194.984i	−0.278501	−	0.672360i
$291$		0			0
$292$	−118.749	+	118.749i	−0.406674	+	0.406674i
$293$	−6.24629	+	15.0799i	−0.0213184	+	0.0514672i	−0.934180	−	0.356801i	$-0.883867\pi$
$293$	−6.24629	+	15.0799i	−0.0213184	+	0.0514672i	0.912862	+	0.408269i	$0.133867\pi$
$294$		0			0
$295$	−12.9936	+	12.9936i	−0.0440461	+	0.0440461i
$296$	189.605	−	189.605i	0.640556	−	0.640556i
$297$		0			0
$298$	−53.4421	+	22.1364i	−0.179336	+	0.0742834i
$299$	−600.707	+	248.821i	−2.00905	+	0.832177i
$300$		0			0
$301$	14.8141	−	35.7644i	0.0492162	−	0.118818i
$302$	284.235	+	117.734i	0.941176	+	0.389848i
$303$		0			0
$304$	−13.3759	+	32.2922i	−0.0439996	+	0.106224i
$305$	269.908			0.884943
$306$		0			0
$307$	61.0974	+	61.0974i	0.199014	+	0.199014i	0.799577	−	0.600563i	$-0.205057\pi$
$307$	61.0974	+	61.0974i	0.199014	+	0.199014i	−0.600563	+	0.799577i	$0.705057\pi$
$308$	20.0207	−	20.0207i	0.0650024	−	0.0650024i
$309$		0			0
$310$		−	307.541i		−	0.992068i
$311$	186.824	+	77.3851i	0.600720	+	0.248827i	0.662255	−	0.749278i	$-0.269599\pi$
$311$	186.824	+	77.3851i	0.600720	+	0.248827i	−0.0615347	+	0.998105i	$0.519599\pi$
$312$		0			0
$313$	120.502	−	290.918i	0.384991	−	0.929451i	−0.605993	−	0.795470i	$-0.707224\pi$
$313$	120.502	−	290.918i	0.384991	−	0.929451i	0.990984	−	0.133981i	$-0.0427760\pi$
$314$	−68.9558	−	28.5624i	−0.219604	−	0.0909631i
$315$		0			0
$316$	116.925	+	282.281i	0.370014	+	0.893294i
$317$	−134.543	−	324.816i	−0.424427	−	1.02466i	−0.981026	−	0.193876i	$-0.937894\pi$
$317$	−134.543	−	324.816i	−0.424427	−	1.02466i	0.556599	−	0.830781i	$-0.312106\pi$
$318$		0			0
$319$	221.880	+	221.880i	0.695550	+	0.695550i
$320$	242.212	+	242.212i	0.756914	+	0.756914i
$321$		0			0
$322$	−34.2880	−	14.2026i	−0.106484	−	0.0441073i
$323$	−0.205770	−	0.205770i	−0.000637057	−	0.000637057i
$324$		0			0
$325$	373.368	−	154.654i	1.14882	−	0.475859i
$326$	−169.817	+	169.817i	−0.520912	+	0.520912i
$327$		0			0
$328$	114.922	−	325.320i	0.350373	−	0.991831i
$329$	14.2438			0.0432943
$330$		0			0
$331$	−211.171	−	509.812i	−0.637979	−	1.54022i	−0.829367	−	0.558704i	$-0.811299\pi$
$331$	−211.171	−	509.812i	−0.637979	−	1.54022i	0.191388	−	0.981515i	$-0.438701\pi$
$332$			267.672i			0.806240i
$333$		0			0
$334$	−151.430	+	365.584i	−0.453383	+	1.09456i
$335$	96.2987	+	232.486i	0.287459	+	0.693987i
$336$		0			0
$337$	−53.5413	+	53.5413i	−0.158876	+	0.158876i	−0.782069	−	0.623192i	$-0.785835\pi$
$337$	−53.5413	+	53.5413i	−0.158876	+	0.158876i	0.623192	+	0.782069i	$0.285835\pi$
$338$	−617.986			−1.82836
$339$		0			0
$340$	−0.336803	+	0.139508i	−0.000990596	+	0.000410318i
$341$	174.982	+	422.443i	0.513142	+	1.23884i
$342$		0			0
$343$	91.8797	+	38.0578i	0.267871	+	0.110956i
$344$	−317.565			−0.923153
$345$		0			0
$346$	286.482			0.827982
$347$	−3.37585	+	8.15002i	−0.00972867	+	0.0234871i	−0.928669	−	0.370909i	$-0.879046\pi$
$347$	−3.37585	+	8.15002i	−0.00972867	+	0.0234871i	0.918941	+	0.394396i	$0.129046\pi$
$348$		0			0
$349$	−260.720	+	260.720i	−0.747049	+	0.747049i	−0.973924	−	0.226875i	$-0.927149\pi$
$349$	−260.720	+	260.720i	−0.747049	+	0.747049i	0.226875	+	0.973924i	$0.427149\pi$
$350$	21.3116	+	8.82756i	0.0608904	+	0.0252216i
$351$		0			0
$352$	−355.496	−	147.251i	−1.00993	−	0.418327i
$353$		−	60.9340i		−	0.172618i	−0.996268	−	0.0863088i	$-0.972493\pi$
$353$		−	60.9340i		−	0.172618i	0.996268	−	0.0863088i	$-0.0275072\pi$
$354$		0			0
$355$	−347.930	−	144.117i	−0.980084	−	0.405964i
$356$	199.757	−	82.7422i	0.561116	−	0.232422i
$357$		0			0
$358$	−43.6023	−	105.265i	−0.121794	−	0.294037i
$359$		−	86.3019i		−	0.240395i	−0.992750	−	0.120198i	$-0.961647\pi$
$359$		−	86.3019i		−	0.240395i	0.992750	−	0.120198i	$-0.0383528\pi$
$360$		0			0
$361$	173.897	+	173.897i	0.481708	+	0.481708i
$362$	30.8280	−	12.7694i	0.0851602	−	0.0352745i
$363$		0			0
$364$	37.6667	+	37.6667i	0.103480	+	0.103480i
$365$	515.839			1.41326
$366$		0			0
$367$	306.208	−	306.208i	0.834354	−	0.834354i	−0.153755	−	0.988109i	$-0.549137\pi$
$367$	306.208	−	306.208i	0.834354	−	0.834354i	0.988109	+	0.153755i	$0.0491366\pi$
$368$			85.3351i			0.231889i
$369$		0			0
$370$	−282.806			−0.764341
$371$	34.9441	+	34.9441i	0.0941890	+	0.0941890i
$372$		0			0
$373$			478.326i			1.28238i	0.767384	+	0.641188i	$0.221558\pi$
$373$			478.326i			1.28238i	−0.767384	+	0.641188i	$0.778442\pi$
$374$	−0.349671	+	0.349671i	−0.000934950	+	0.000934950i
$375$		0			0
$376$	−44.7160	−	107.954i	−0.118926	−	0.287112i
$377$	−417.442	+	417.442i	−1.10727	+	1.10727i
$378$		0			0
$379$	40.5044			0.106872			0.0534358	−	0.998571i	$-0.482983\pi$
$379$	40.5044			0.106872			0.0534358	+	0.998571i	$0.482983\pi$
$380$	−133.184	+	55.1668i	−0.350485	+	0.145176i
$381$		0			0
$382$	−16.7497	−	40.4374i	−0.0438475	−	0.105857i
$383$	198.505	−	479.232i	0.518289	−	1.25126i	−0.420665	−	0.907216i	$-0.638203\pi$
$383$	198.505	−	479.232i	0.518289	−	1.25126i	0.938954	−	0.344043i	$-0.111797\pi$
$384$		0			0
$385$	−86.9691			−0.225894
$386$	16.0192	−	38.6738i	0.0415006	−	0.100191i
$387$		0			0
$388$	95.2594	−	229.977i	0.245514	−	0.592723i
$389$	−233.701	−	233.701i	−0.600774	−	0.600774i	0.339744	−	0.940518i	$-0.389659\pi$
$389$	−233.701	−	233.701i	−0.600774	−	0.600774i	−0.940518	+	0.339744i	$0.889659\pi$
$390$		0			0
$391$	−0.656382	−	0.271882i	−0.00167873	−	0.000695351i
$392$		−	403.489i		−	1.02931i
$393$		0			0
$394$			39.4695i			0.100176i
$395$	359.150	−	867.064i	0.909239	−	2.19510i
$396$		0			0
$397$	118.294	−	48.9989i	0.297970	−	0.123423i	−0.228690	−	0.973499i	$-0.573444\pi$
$397$	118.294	−	48.9989i	0.297970	−	0.123423i	0.526660	+	0.850076i	$0.323444\pi$
$398$	−194.647	−	469.920i	−0.489063	−	1.18070i
$399$		0			0
$400$		−	53.0398i		−	0.132600i
$401$	440.267	+	440.267i	1.09792	+	1.09792i	0.994653	+	0.103270i	$0.0329304\pi$
$401$	440.267	+	440.267i	1.09792	+	1.09792i	0.103270	+	0.994653i	$0.467070\pi$
$402$		0			0
$403$	−794.776	+	329.207i	−1.97215	+	0.816891i
$404$	28.7368	+	11.9032i	0.0711308	+	0.0294633i
$405$		0			0
$406$	−33.6969			−0.0829974
$407$	388.467	−	160.908i	0.954463	−	0.395352i
$408$		0			0
$409$		−	444.887i		−	1.08774i	−0.839169	−	0.543871i	$-0.816958\pi$
$409$		−	444.887i		−	1.08774i	0.839169	−	0.543871i	$-0.183042\pi$
$410$	−328.324	+	156.910i	−0.800790	+	0.382708i
$411$		0			0
$412$	40.4028	+	40.4028i	0.0980650	+	0.0980650i
$413$	1.12277	+	2.71060i	0.00271857	+	0.00656320i
$414$		0			0
$415$	581.376	−	581.376i	1.40091	−	1.40091i
$416$	277.036	−	668.824i	0.665952	−	1.60775i
$417$		0			0
$418$	−138.273	+	138.273i	−0.330797	+	0.330797i
$419$	−434.530	+	434.530i	−1.03706	+	1.03706i	−0.0377779	+	0.999286i	$0.512028\pi$
$419$	−434.530	+	434.530i	−1.03706	+	1.03706i	−0.999286	+	0.0377779i	$0.987972\pi$
$420$		0			0
$421$	390.608	−	161.795i	0.927811	−	0.384312i	0.132963	−	0.991121i	$-0.457551\pi$
$421$	390.608	−	161.795i	0.927811	−	0.384312i	0.794848	+	0.606809i	$0.207551\pi$
$422$	419.572	−	173.793i	0.994248	−	0.411831i
$423$		0			0
$424$	155.141	−	374.543i	0.365898	−	0.883355i
$425$	0.407973	+	0.168988i	0.000959936	+	0.000397618i
$426$		0			0
$427$	16.4915	−	39.8141i	0.0386218	−	0.0932414i
$428$	−390.819			−0.913130
$429$		0			0
$430$	236.833	+	236.833i	0.550774	+	0.550774i
$431$	487.076	−	487.076i	1.13011	−	1.13011i	0.139949	−	0.990159i	$-0.455306\pi$
$431$	487.076	−	487.076i	1.13011	−	1.13011i	0.990159	−	0.139949i	$-0.0446938\pi$
$432$		0			0
$433$		−	461.455i		−	1.06572i	−0.846204	−	0.532858i	$-0.821118\pi$
$433$		−	461.455i		−	1.06572i	0.846204	−	0.532858i	$-0.178882\pi$
$434$	−45.3654	−	18.7910i	−0.104529	−	0.0432971i
$435$		0			0
$436$	−38.5025	+	92.9533i	−0.0883085	+	0.213196i
$437$	−259.558	−	107.512i	−0.593954	−	0.246024i
$438$		0			0
$439$	−168.872	−	407.694i	−0.384675	−	0.928688i	−0.991048	−	0.133508i	$-0.957376\pi$
$439$	−168.872	−	407.694i	−0.384675	−	0.928688i	0.606373	−	0.795181i	$-0.292624\pi$
$440$	273.024	+	659.139i	0.620510	+	1.49804i
$441$		0			0
$442$	−0.657865	−	0.657865i	−0.00148838	−	0.00148838i
$443$	−330.755	−	330.755i	−0.746625	−	0.746625i	0.227219	−	0.973844i	$-0.427037\pi$
$443$	−330.755	−	330.755i	−0.746625	−	0.746625i	−0.973844	+	0.227219i	$0.927037\pi$
$444$		0			0
$445$	−613.582	−	254.154i	−1.37884	−	0.571132i
$446$	−56.8856	−	56.8856i	−0.127546	−	0.127546i
$447$		0			0
$448$	50.5281	−	20.9294i	0.112786	−	0.0467174i
$449$	−52.0447	+	52.0447i	−0.115912	+	0.115912i	−0.762684	−	0.646771i	$-0.776119\pi$
$449$	−52.0447	+	52.0447i	−0.115912	+	0.115912i	0.646771	+	0.762684i	$0.276119\pi$
$450$		0			0
$451$	361.713	−	402.340i	0.802024	−	0.892107i
$452$	−263.786			−0.583598
$453$		0			0
$454$	−72.1459	−	174.176i	−0.158912	−	0.383647i
$455$		−	163.622i		−	0.359609i
$456$		0			0
$457$	248.956	−	601.032i	0.544761	−	1.31517i	−0.376570	−	0.926388i	$-0.622897\pi$
$457$	248.956	−	601.032i	0.544761	−	1.31517i	0.921331	−	0.388780i	$-0.127103\pi$
$458$	136.106	+	328.589i	0.297175	+	0.717443i
$459$		0			0
$460$	−248.868	+	248.868i	−0.541016	+	0.541016i
$461$	−484.023			−1.04994			−0.524971	−	0.851120i	$-0.675924\pi$
$461$	−484.023			−1.04994			−0.524971	+	0.851120i	$0.675924\pi$
$462$		0			0
$463$	−565.792	+	234.359i	−1.22201	+	0.506174i	−0.898049	−	0.439895i	$-0.855016\pi$
$463$	−565.792	+	234.359i	−1.22201	+	0.506174i	−0.323964	+	0.946070i	$0.605016\pi$
$464$	29.6504	+	71.5825i	0.0639018	+	0.154273i
$465$		0			0
$466$	25.4131	+	10.5265i	0.0545346	+	0.0225890i
$467$	47.4463			0.101598			0.0507990	−	0.998709i	$-0.483823\pi$
$467$	47.4463			0.101598			0.0507990	+	0.998709i	$0.483823\pi$
$468$		0			0
$469$	40.1778			0.0856671
$470$	−47.1616	+	113.858i	−0.100344	+	0.242251i
$471$		0			0
$472$	17.0189	−	17.0189i	0.0360571	−	0.0360571i
$473$	−460.068	−	190.566i	−0.972659	−	0.402889i
$474$		0			0
$475$	161.328	+	66.8241i	0.339637	+	0.140682i
$476$			0.0582058i			0.000122281i
$477$		0			0
$478$	−374.196	−	154.997i	−0.782836	−	0.324261i
$479$	525.724	−	217.762i	1.09754	−	0.454618i	0.240913	−	0.970547i	$-0.422553\pi$
$479$	525.724	−	217.762i	1.09754	−	0.454618i	0.856631	+	0.515929i	$0.172553\pi$
$480$		0			0
$481$	302.730	+	730.854i	0.629376	+	1.51945i
$482$			395.084i			0.819676i
$483$		0			0
$484$	−78.5819	−	78.5819i	−0.162359	−	0.162359i
$485$	−706.404	+	292.602i	−1.45650	+	0.603304i
$486$		0			0
$487$	−383.555	−	383.555i	−0.787588	−	0.787588i	0.193510	−	0.981098i	$-0.438013\pi$
$487$	−383.555	−	383.555i	−0.787588	−	0.787588i	−0.981098	+	0.193510i	$0.938013\pi$
$488$	−353.523			−0.724433
$489$		0			0
$490$	−300.913	+	300.913i	−0.614109	+	0.614109i
$491$			413.228i			0.841604i	0.907152	+	0.420802i	$0.138251\pi$
$491$			413.228i			0.841604i	−0.907152	+	0.420802i	$0.861749\pi$
$492$		0			0
$493$	−0.645067			−0.00130845
$494$	−260.145	−	260.145i	−0.526609	−	0.526609i
$495$		0			0
$496$			112.904i			0.227630i
$497$	−42.5175	+	42.5175i	−0.0855483	+	0.0855483i
$498$		0			0
$499$	279.118	+	673.850i	0.559354	+	1.35040i	0.910279	+	0.413996i	$0.135867\pi$
$499$	279.118	+	673.850i	0.559354	+	1.35040i	−0.350925	+	0.936404i	$0.614133\pi$
$500$	−82.8785	+	82.8785i	−0.165757	+	0.165757i
$501$		0			0
$502$	129.239			0.257449
$503$	57.0309	−	23.6230i	0.113381	−	0.0469641i	−0.325272	−	0.945621i	$-0.605456\pi$
$503$	57.0309	−	23.6230i	0.113381	−	0.0469641i	0.438653	+	0.898657i	$0.355456\pi$
$504$		0			0
$505$	−36.5623	−	88.2691i	−0.0724005	−	0.174790i
$506$	−182.700	+	441.076i	−0.361067	+	0.871692i
$507$		0			0
$508$	−281.759			−0.554643
$509$	122.461	−	295.647i	0.240591	−	0.580838i	−0.756751	−	0.653703i	$-0.773214\pi$
$509$	122.461	−	295.647i	0.240591	−	0.580838i	0.997342	+	0.0728654i	$0.0232144\pi$
$510$		0			0
$511$	31.5181	−	76.0914i	0.0616792	−	0.148907i
$512$	−144.737	−	144.737i	−0.282690	−	0.282690i
$513$		0			0
$514$	117.484	+	48.6634i	0.228568	+	0.0946758i
$515$		−	175.508i		−	0.340792i
$516$		0			0
$517$		−	183.231i		−	0.354411i
$518$	−17.2796	+	41.7167i	−0.0333584	+	0.0805343i
$519$		0			0
$520$	−1240.09	+	513.663i	−2.38479	+	0.987814i
$521$	35.0257	+	84.5595i	0.0672278	+	0.162302i	0.953922	−	0.300053i	$-0.0970044\pi$
$521$	35.0257	+	84.5595i	0.0672278	+	0.162302i	−0.886695	+	0.462355i	$0.847004\pi$
$522$		0			0
$523$		−	273.269i		−	0.522502i	−0.965271	−	0.261251i	$-0.915865\pi$
$523$		−	273.269i		−	0.522502i	0.965271	−	0.261251i	$-0.0841351\pi$
$524$	124.649	+	124.649i	0.237880	+	0.237880i
$525$		0			0
$526$	216.636	−	89.7337i	0.411856	−	0.170596i
$527$	−0.868439	−	0.359719i	−0.00164789	−	0.000682579i
$528$		0			0
$529$	−156.906			−0.296608
$530$	−395.027	+	163.625i	−0.745333	+	0.308727i
$531$		0			0
$532$			23.0168i			0.0432646i
$533$	756.956	+	680.520i	1.42018	+	1.27677i
$534$		0			0
$535$	848.850	+	848.850i	1.58664	+	1.58664i
$536$	−126.131	−	304.508i	−0.235320	−	0.568113i
$537$		0			0
$538$	−47.2197	+	47.2197i	−0.0877690	+	0.0877690i
$539$	242.128	−	584.549i	0.449218	−	1.08451i
$540$		0			0
$541$	−280.642	+	280.642i	−0.518746	+	0.518746i	−0.917192	−	0.398446i	$-0.869550\pi$
$541$	−280.642	+	280.642i	−0.518746	+	0.518746i	0.398446	+	0.917192i	$0.369550\pi$
$542$	33.9624	−	33.9624i	0.0626612	−	0.0626612i
$543$		0			0
$544$	0.730812	−	0.302712i	0.00134340	−	0.000556456i
$545$	285.519	−	118.266i	0.523887	−	0.217001i
$546$		0			0
$547$	59.5360	−	143.733i	0.108841	−	0.262765i	−0.860070	−	0.510177i	$-0.829580\pi$
$547$	59.5360	−	143.733i	0.108841	−	0.262765i	0.968910	+	0.247412i	$0.0795800\pi$
$548$	−100.961	−	41.8192i	−0.184235	−	0.0763125i
$549$		0			0
$550$	113.557	−	274.150i	0.206466	−	0.498454i
$551$	−255.084			−0.462947
$552$		0			0
$553$	−105.956	−	105.956i	−0.191603	−	0.191603i
$554$	275.646	−	275.646i	0.497555	−	0.497555i
$555$		0			0
$556$		−	413.485i		−	0.743679i
$557$	457.414	+	189.467i	0.821210	+	0.340156i	0.753417	−	0.657543i	$-0.228404\pi$
$557$	457.414	+	189.467i	0.821210	+	0.340156i	0.0677932	+	0.997699i	$0.478404\pi$
$558$		0			0
$559$	358.528	−	865.563i	0.641374	−	1.54841i
$560$	−19.8398	−	8.21792i	−0.0354283	−	0.0146749i
$561$		0			0
$562$	−98.0543	−	236.724i	−0.174474	−	0.421217i
$563$	−283.085	−	683.428i	−0.502816	−	1.21390i	−0.947944	−	0.318438i	$-0.896842\pi$
$563$	−283.085	−	683.428i	−0.502816	−	1.21390i	0.445128	−	0.895467i	$-0.353158\pi$
$564$		0			0
$565$	572.937	+	572.937i	1.01405	+	1.01405i
$566$	38.1413	+	38.1413i	0.0673875	+	0.0673875i
$567$		0			0
$568$	455.717	+	188.764i	0.802318	+	0.332331i
$569$	414.050	+	414.050i	0.727679	+	0.727679i	0.970157	−	0.242478i	$-0.0779601\pi$
$569$	414.050	+	414.050i	0.727679	+	0.727679i	−0.242478	+	0.970157i	$0.577960\pi$
$570$		0			0
$571$	311.694	−	129.108i	0.545875	−	0.226109i	−0.0926654	−	0.995697i	$-0.529539\pi$
$571$	311.694	−	129.108i	0.545875	−	0.226109i	0.638540	+	0.769589i	$0.279539\pi$
$572$	484.539	−	484.539i	0.847096	−	0.847096i
$573$		0			0
$574$	3.08504	+	58.0183i	0.00537464	+	0.101077i
$575$	426.323			0.741431
$576$		0			0
$577$	328.629	+	793.380i	0.569547	+	1.37501i	0.901937	+	0.431867i	$0.142145\pi$
$577$	328.629	+	793.380i	0.569547	+	1.37501i	−0.332390	+	0.943142i	$0.607855\pi$
$578$			399.232i			0.690712i
$579$		0			0
$580$	−122.289	+	295.231i	−0.210843	+	0.509020i
$581$	−50.2363	−	121.281i	−0.0864653	−	0.208746i
$582$		0			0
$583$	449.516	−	449.516i	0.771040	−	0.771040i
$584$	−675.643			−1.15692
$585$		0			0
$586$	−20.8318	+	8.62880i	−0.0355491	+	0.0147249i
$587$	−370.983	−	895.633i	−0.631999	−	1.52578i	−0.837106	−	0.547041i	$-0.815754\pi$
$587$	−370.983	−	895.633i	−0.631999	−	1.52578i	0.205107	−	0.978740i	$-0.434246\pi$
$588$		0			0
$589$	−343.413	−	142.246i	−0.583045	−	0.241505i
$590$	−25.3847			−0.0430250
$591$		0			0
$592$	103.824			0.175378
$593$	15.7851	−	38.1085i	0.0266190	−	0.0642639i	−0.910011	−	0.414584i	$-0.863927\pi$
$593$	15.7851	−	38.1085i	0.0266190	−	0.0642639i	0.936630	+	0.350320i	$0.113927\pi$
$594$		0			0
$595$	0.126421	−	0.126421i	0.000212473	−	0.000212473i
$596$	80.9182	+	33.5174i	0.135769	+	0.0562373i
$597$		0			0
$598$	−829.833	−	343.728i	−1.38768	−	0.574796i
$599$			845.159i			1.41095i	0.708734	+	0.705475i	$0.249266\pi$
$599$			845.159i			1.41095i	−0.708734	+	0.705475i	$0.750734\pi$
$600$		0			0
$601$	−357.015	−	147.880i	−0.594034	−	0.246057i	0.0653509	−	0.997862i	$-0.479183\pi$
$601$	−357.015	−	147.880i	−0.594034	−	0.246057i	−0.659385	+	0.751805i	$0.729183\pi$
$602$	49.4059	−	20.4646i	0.0820695	−	0.0339943i
$603$		0			0
$604$	−178.264	−	430.368i	−0.295140	−	0.712530i
$605$			341.356i			0.564224i
$606$		0			0
$607$	295.420	+	295.420i	0.486689	+	0.486689i	0.907260	−	0.420571i	$-0.138170\pi$
$607$	295.420	+	295.420i	0.486689	+	0.486689i	−0.420571	+	0.907260i	$0.638170\pi$
$608$	288.991	−	119.704i	0.475313	−	0.196881i
$609$		0			0
$610$	263.650	+	263.650i	0.432213	+	0.432213i
$611$	344.727			0.564201
$612$		0			0
$613$	−830.468	+	830.468i	−1.35476	+	1.35476i	−0.474512	+	0.880249i	$0.657375\pi$
$613$	−830.468	+	830.468i	−1.35476	+	1.35476i	−0.880249	+	0.474512i	$0.842625\pi$
$614$			119.362i			0.194400i
$615$		0			0
$616$	113.912			0.184921
$617$	42.2366	+	42.2366i	0.0684548	+	0.0684548i	0.740505	−	0.672050i	$-0.234586\pi$
$617$	42.2366	+	42.2366i	0.0684548	+	0.0684548i	−0.672050	+	0.740505i	$0.734586\pi$
$618$		0			0
$619$			304.461i			0.491860i	0.969288	+	0.245930i	$0.0790933\pi$
$619$			304.461i			0.491860i	−0.969288	+	0.245930i	$0.920907\pi$
$620$	−329.269	+	329.269i	−0.531079	+	0.531079i
$621$		0			0
$622$	106.902	+	258.084i	0.171868	+	0.414926i
$623$	−74.9805	+	74.9805i	−0.120354	+	0.120354i
$624$		0			0
$625$	766.975			1.22716
$626$	401.882	−	166.465i	0.641984	−	0.265919i
$627$		0			0
$628$	43.2471	+	104.408i	0.0688649	+	0.166255i
$629$	−0.330788	+	0.798592i	−0.000525894	+	0.00126962i
$630$		0			0
$631$	822.716			1.30383			0.651914	−	0.758292i	$-0.273966\pi$
$631$	822.716			1.30383			0.651914	+	0.758292i	$0.273966\pi$
$632$	−470.412	+	1135.68i	−0.744323	+	1.79695i
$633$		0			0
$634$	185.862	−	448.710i	0.293157	−	0.707745i
$635$	611.972	+	611.972i	0.963736	+	0.963736i
$636$		0			0
$637$	1099.76	+	455.536i	1.72647	+	0.715127i
$638$			433.473i			0.679425i
$639$		0			0
$640$		−	276.185i		−	0.431539i
$641$	199.884	−	482.562i	0.311831	−	0.752827i	−0.687806	−	0.725894i	$-0.741426\pi$
$641$	199.884	−	482.562i	0.311831	−	0.752827i	0.999637	−	0.0269325i	$-0.00857393\pi$
$642$		0			0
$643$	−84.4747	+	34.9906i	−0.131376	+	0.0544177i	−0.447403	−	0.894333i	$-0.647651\pi$
$643$	−84.4747	+	34.9906i	−0.131376	+	0.0544177i	0.316027	+	0.948750i	$0.397651\pi$
$644$	21.5045	+	51.9164i	0.0333921	+	0.0806155i
$645$		0			0
$646$		−	0.401998i		−	0.000622288i
$647$	−9.46916	−	9.46916i	−0.0146355	−	0.0146355i	0.699751	−	0.714387i	$-0.253294\pi$
$647$	−9.46916	−	9.46916i	−0.0146355	−	0.0146355i	−0.714387	+	0.699751i	$0.753294\pi$
$648$		0			0
$649$	34.8688	−	14.4431i	0.0537270	−	0.0222545i
$650$	515.781	+	213.643i	0.793509	+	0.328682i
$651$		0			0
$652$	363.630			0.557715
$653$	−24.5236	+	10.1580i	−0.0375552	+	0.0155559i	−0.401382	−	0.915911i	$-0.631470\pi$
$653$	−24.5236	+	10.1580i	−0.0375552	+	0.0155559i	0.363827	+	0.931467i	$0.381470\pi$
$654$		0			0
$655$		−	541.470i		−	0.826671i
$656$	120.534	−	57.6048i	0.183741	−	0.0878121i
$657$		0			0
$658$	13.9136	+	13.9136i	0.0211453	+	0.0211453i
$659$	261.932	+	632.360i	0.397469	+	0.959576i	0.988264	+	0.152754i	$0.0488142\pi$
$659$	261.932	+	632.360i	0.397469	+	0.959576i	−0.590795	+	0.806822i	$0.701186\pi$
$660$		0			0
$661$	173.459	−	173.459i	0.262419	−	0.262419i	−0.563617	−	0.826036i	$-0.690591\pi$
$661$	173.459	−	173.459i	0.262419	−	0.262419i	0.826036	+	0.563617i	$0.190591\pi$
$662$	291.718	−	704.269i	0.440661	−	1.06385i
$663$		0			0
$664$	−761.483	+	761.483i	−1.14681	+	1.14681i
$665$	49.9918	−	49.9918i	0.0751757	−	0.0751757i
$666$		0			0
$667$	−575.365	+	238.324i	−0.862616	+	0.357307i
$668$	553.541	−	229.284i	0.828654	−	0.343240i
$669$		0			0
$670$	−133.030	+	321.162i	−0.198552	+	0.479346i
$671$	−512.163	−	212.145i	−0.763283	−	0.316162i
$672$		0			0
$673$	−395.832	+	955.624i	−0.588161	+	1.41995i	0.297098	+	0.954847i	$0.403981\pi$
$673$	−395.832	+	955.624i	−0.588161	+	1.41995i	−0.885259	+	0.465099i	$0.846019\pi$
$674$	−104.600			−0.155193
$675$		0			0
$676$	661.647	+	661.647i	0.978768	+	0.978768i
$677$	147.000	−	147.000i	0.217134	−	0.217134i	−0.590156	−	0.807289i	$-0.700934\pi$
$677$	147.000	−	147.000i	0.217134	−	0.217134i	0.807289	+	0.590156i	$0.200934\pi$
$678$		0			0
$679$			122.080i			0.179794i
$680$	−1.35503	−	0.561271i	−0.00199269	−	0.000825399i
$681$		0			0
$682$	−241.724	+	583.574i	−0.354434	+	0.855680i
$683$	89.3993	+	37.0304i	0.130892	+	0.0542173i	0.447168	−	0.894450i	$-0.352433\pi$
$683$	89.3993	+	37.0304i	0.130892	+	0.0542173i	−0.316276	+	0.948667i	$0.602433\pi$
$684$		0			0
$685$	128.453	+	310.114i	0.187523	+	0.452721i
$686$	52.5741	+	126.925i	0.0766386	+	0.185022i
$687$		0			0
$688$	−86.9459	−	86.9459i	−0.126375	−	0.126375i
$689$	845.712	+	845.712i	1.22745	+	1.22745i
$690$		0			0
$691$	−313.507	−	129.859i	−0.453700	−	0.187929i	0.144118	−	0.989561i	$-0.453966\pi$
$691$	−313.507	−	129.859i	−0.453700	−	0.187929i	−0.597818	+	0.801632i	$0.703966\pi$
$692$	−306.722	−	306.722i	−0.443239	−	0.443239i
$693$		0			0
$694$	−11.2587	+	4.66349i	−0.0162228	+	0.00671972i
$695$	−898.080	+	898.080i	−1.29220	+	1.29220i
$696$		0			0
$697$	0.0590576	+	1.11066i	8.47311e−5	+	0.00159348i
$698$	−509.351			−0.729730
$699$		0			0
$700$	−13.3661	−	32.2685i	−0.0190944	−	0.0460979i
$701$		−	300.567i		−	0.428769i	−0.976749	−	0.214384i	$-0.931226\pi$
$701$		−	300.567i		−	0.428769i	0.976749	−	0.214384i	$-0.0687745\pi$
$702$		0			0
$703$	−130.806	+	315.793i	−0.186068	+	0.449208i
$704$	−269.233	−	649.986i	−0.382433	−	0.923276i
$705$		0			0
$706$	59.5214	−	59.5214i	0.0843079	−	0.0843079i
$707$	−15.2545			−0.0215764
$708$		0			0
$709$	−57.2248	+	23.7033i	−0.0807121	+	0.0334320i	−0.422674	−	0.906282i	$-0.638909\pi$
$709$	−57.2248	+	23.7033i	−0.0807121	+	0.0334320i	0.341962	+	0.939714i	$0.388909\pi$
$710$	−199.088	−	480.640i	−0.280405	−	0.676958i
$711$		0			0
$712$	803.666	+	332.889i	1.12874	+	0.467541i
$713$	−907.500			−1.27279
$714$		0			0
$715$	−2104.81			−2.94379
$716$	−66.0194	+	159.385i	−0.0922059	+	0.222605i
$717$		0			0
$718$	84.3011	−	84.3011i	0.117411	−	0.117411i
$719$	−594.299	−	246.167i	−0.826564	−	0.342374i	−0.0710222	−	0.997475i	$-0.522626\pi$
$719$	−594.299	−	246.167i	−0.826564	−	0.342374i	−0.755541	+	0.655101i	$0.772626\pi$
$720$		0			0
$721$	−25.8891	−	10.7236i	−0.0359073	−	0.0148733i
$722$			339.730i			0.470540i
$723$		0			0
$724$	−46.6775	−	19.3345i	−0.0644717	−	0.0267051i
$725$	357.617	−	148.130i	0.493265	−	0.204317i
$726$		0			0
$727$	−43.6860	−	105.467i	−0.0600907	−	0.145072i	0.890982	−	0.454038i	$-0.150017\pi$
$727$	−43.6860	−	105.467i	−0.0600907	−	0.145072i	−0.951073	+	0.308966i	$0.900017\pi$
$728$			214.311i			0.294384i
$729$		0			0
$730$	503.880	+	503.880i	0.690247	+	0.690247i
$731$	0.945786	−	0.391757i	0.00129383	−	0.000535920i
$732$		0			0
$733$	−527.305	−	527.305i	−0.719380	−	0.719380i	0.249098	−	0.968478i	$-0.419866\pi$
$733$	−527.305	−	527.305i	−0.719380	−	0.719380i	−0.968478	+	0.249098i	$0.919866\pi$
$734$	598.218			0.815011
$735$		0			0
$736$	540.006	−	540.006i	0.733704	−	0.733704i
$737$		−	516.842i		−	0.701279i
$738$		0			0
$739$	164.452			0.222533			0.111267	−	0.993791i	$-0.464509\pi$
$739$	164.452			0.222533			0.111267	+	0.993791i	$0.464509\pi$
$740$	302.787	+	302.787i	0.409171	+	0.409171i
$741$		0			0
$742$			68.2680i			0.0920053i
$743$	−82.4432	+	82.4432i	−0.110960	+	0.110960i	−0.760407	−	0.649447i	$-0.775000\pi$
$743$	−82.4432	+	82.4432i	−0.110960	+	0.110960i	0.649447	+	0.760407i	$0.275000\pi$
$744$		0			0
$745$	−102.953	−	248.551i	−0.138192	−	0.333626i
$746$	−467.237	+	467.237i	−0.626323	+	0.626323i
$747$		0			0
$748$	0.748751			0.00100100
$749$	177.079	−	73.3486i	0.236421	−	0.0979286i
$750$		0			0
$751$	−302.607	−	730.559i	−0.402939	−	0.972781i	−0.986949	−	0.161034i	$-0.948517\pi$
$751$	−302.607	−	730.559i	−0.402939	−	0.972781i	0.584010	−	0.811747i	$-0.301483\pi$
$752$	17.3139	−	41.7995i	0.0230238	−	0.0555844i
$753$		0			0
$754$	−815.528			−1.08160
$755$	−547.563	+	1321.93i	−0.725249	+	1.75091i
$756$		0			0
$757$	−82.7473	+	199.770i	−0.109309	+	0.263896i	−0.969063	−	0.246812i	$-0.920617\pi$
$757$	−82.7473	+	199.770i	−0.109309	+	0.263896i	0.859754	+	0.510709i	$0.170617\pi$
$758$	39.5653	+	39.5653i	0.0521970	+	0.0521970i
$759$		0			0
$760$	−535.829	−	221.948i	−0.705038	−	0.292036i
$761$		−	638.280i		−	0.838739i	−0.907816	−	0.419370i	$-0.862251\pi$
$761$		−	638.280i		−	0.838739i	0.907816	−	0.419370i	$-0.137749\pi$
$762$		0			0
$763$		−	49.3430i		−	0.0646697i
$764$	−25.3612	+	61.2274i	−0.0331953	+	0.0801406i
$765$		0			0
$766$	662.025	−	274.220i	0.864262	−	0.357989i
$767$	27.1731	+	65.6016i	0.0354277	+	0.0855301i
$768$		0			0
$769$			321.513i			0.418092i	0.977906	+	0.209046i	$0.0670359\pi$
$769$			321.513i			0.418092i	−0.977906	+	0.209046i	$0.932964\pi$
$770$	−84.9528	−	84.9528i	−0.110328	−	0.110328i
$771$		0			0
$772$	−58.5571	+	24.2552i	−0.0758512	+	0.0314186i
$773$	644.760	+	267.068i	0.834101	+	0.345496i	0.758525	−	0.651644i	$-0.225920\pi$
$773$	644.760	+	267.068i	0.834101	+	0.345496i	0.0755763	+	0.997140i	$0.475920\pi$
$774$		0			0
$775$	564.055			0.727813
$776$	925.245	−	383.249i	1.19233	−	0.493877i
$777$		0			0
$778$		−	456.566i		−	0.586846i
$779$	23.3536	+	439.195i	0.0299789	+	0.563794i
$780$		0			0
$781$	546.939	+	546.939i	0.700306	+	0.700306i
$782$	−0.375586	−	0.906744i	−0.000480288	−	0.00115952i
$783$		0			0
$784$	110.471	−	110.471i	0.140907	−	0.140907i
$785$	132.839	−	320.703i	0.169222	−	0.408539i
$786$		0			0
$787$	−38.3399	+	38.3399i	−0.0487165	+	0.0487165i	−0.731045	−	0.682329i	$-0.760967\pi$
$787$	−38.3399	+	38.3399i	−0.0487165	+	0.0487165i	0.682329	+	0.731045i	$0.260967\pi$
$788$	42.2581	−	42.2581i	0.0536270	−	0.0536270i
$789$		0			0
$790$	1197.79	−	496.139i	1.51618	−	0.628024i
$791$	119.521	−	49.5071i	0.151101	−	0.0625881i
$792$		0			0
$793$	399.125	−	963.574i	0.503311	−	1.21510i
$794$	163.414	+	67.6885i	0.205812	+	0.0852500i
$795$		0			0
$796$	−294.721	+	711.519i	−0.370252	+	0.893868i
$797$	−1549.66			−1.94437			−0.972186	−	0.234209i	$-0.924750\pi$
$797$	−1549.66			−1.94437			−0.972186	+	0.234209i	$0.924750\pi$
$798$		0			0
$799$	0.266351	+	0.266351i	0.000333355	+	0.000333355i
$800$	−335.639	+	335.639i	−0.419549	+	0.419549i
$801$		0			0
$802$			860.121i			1.07247i
$803$	−978.829	−	405.444i	−1.21897	−	0.504912i
$804$		0			0
$805$	66.0539	−	159.468i	0.0820546	−	0.198097i
$806$	−1097.93	−	454.776i	−1.36219	−	0.564238i
$807$		0			0
$808$	47.8890	+	115.614i	0.0592686	+	0.143087i
$809$	22.2664	+	53.7559i	0.0275234	+	0.0664474i	0.937044	−	0.349212i	$-0.113551\pi$
$809$	22.2664	+	53.7559i	0.0275234	+	0.0664474i	−0.909520	+	0.415660i	$0.863551\pi$
$810$		0			0
$811$	−661.326	−	661.326i	−0.815446	−	0.815446i	0.169999	−	0.985444i	$-0.445624\pi$
$811$	−661.326	−	661.326i	−0.815446	−	0.815446i	−0.985444	+	0.169999i	$0.945624\pi$
$812$	36.0776	+	36.0776i	0.0444306	+	0.0444306i
$813$		0			0
$814$	536.638	+	222.283i	0.659261	+	0.273075i
$815$	−789.795	−	789.795i	−0.969073	−	0.969073i
$816$		0			0
$817$	373.999	−	154.916i	0.457772	−	0.189615i
$818$	434.573	−	434.573i	0.531262	−	0.531262i
$819$		0			0
$820$	519.516	+	183.524i	0.633556	+	0.223810i
$821$	394.722			0.480783			0.240391	−	0.970676i	$-0.422724\pi$
$821$	394.722			0.480783			0.240391	+	0.970676i	$0.422724\pi$
$822$		0			0
$823$	−83.3051	−	201.116i	−0.101221	−	0.244370i	0.865154	−	0.501507i	$-0.167221\pi$
$823$	−83.3051	−	201.116i	−0.101221	−	0.244370i	−0.966375	+	0.257137i	$0.917221\pi$
$824$			229.879i			0.278979i
$825$		0			0
$826$	−1.55102	+	3.74450i	−0.00187775	+	0.00453330i
$827$	142.591	+	344.244i	0.172419	+	0.416256i	0.986341	−	0.164718i	$-0.0526715\pi$
$827$	142.591	+	344.244i	0.172419	+	0.416256i	−0.813922	+	0.580975i	$0.802672\pi$
$828$		0			0
$829$	−1023.38	+	1023.38i	−1.23448	+	1.23448i	−0.272256	+	0.962225i	$0.587770\pi$
$829$	−1023.38	+	1023.38i	−1.23448	+	1.23448i	−0.962225	+	0.272256i	$0.912230\pi$
$830$	1135.80			1.36843
$831$		0			0
$832$	1222.87	−	506.530i	1.46980	−	0.608811i
$833$	0.497756	+	1.20169i	0.000597546	+	0.00144260i
$834$		0			0
$835$	−1700.28	−	704.277i	−2.03626	−	0.843446i
$836$	296.084			0.354168
$837$		0			0
$838$	−848.912			−1.01302
$839$	478.975	−	1156.35i	0.570888	−	1.37825i	−0.329912	−	0.944012i	$-0.607019\pi$
$839$	478.975	−	1156.35i	0.570888	−	1.37825i	0.900800	−	0.434234i	$-0.142981\pi$
$840$		0			0
$841$	194.845	−	194.845i	0.231683	−	0.231683i
$842$	539.597	+	223.509i	0.640852	+	0.265450i
$843$		0			0
$844$	−635.287	−	263.144i	−0.752709	−	0.311782i
$845$		−	2874.16i		−	3.40138i
$846$		0			0
$847$	50.3534	+	20.8571i	0.0594491	+	0.0246246i
$848$	145.022	−	60.0700i	0.171016	−	0.0708373i
$849$		0			0
$850$	0.233444	+	0.563585i	0.000274640	+	0.000663041i
$851$			834.512i			0.980625i
$852$		0			0
$853$	−422.076	−	422.076i	−0.494814	−	0.494814i	0.415005	−	0.909819i	$-0.363780\pi$
$853$	−422.076	−	422.076i	−0.494814	−	0.494814i	−0.909819	+	0.415005i	$0.863780\pi$
$854$	55.0002	−	22.7818i	0.0644031	−	0.0266766i
$855$		0			0
$856$	−1111.82	−	1111.82i	−1.29885	−	1.29885i
$857$	619.431			0.722790			0.361395	−	0.932413i	$-0.382301\pi$
$857$	619.431			0.722790			0.361395	+	0.932413i	$0.382301\pi$
$858$		0			0
$859$	788.572	−	788.572i	0.918012	−	0.918012i	−0.0788731	−	0.996885i	$-0.525132\pi$
$859$	788.572	−	788.572i	0.918012	−	0.918012i	0.996885	+	0.0788731i	$0.0251322\pi$
$860$		−	507.130i		−	0.589687i
$861$		0			0
$862$	951.569			1.10391
$863$	−755.576	−	755.576i	−0.875522	−	0.875522i	0.117545	−	0.993068i	$-0.462498\pi$
$863$	−755.576	−	755.576i	−0.875522	−	0.875522i	−0.993068	+	0.117545i	$0.962498\pi$
$864$		0			0
$865$			1332.38i			1.54033i
$866$	450.757	−	450.757i	0.520505	−	0.520505i
$867$		0			0
$868$	28.4519	+	68.6890i	0.0327787	+	0.0791348i
$869$	−1363.01	+	1363.01i	−1.56848	+	1.56848i
$870$		0			0
$871$	972.378			1.11639
$872$	−373.971	+	154.904i	−0.428866	+	0.177642i
$873$		0			0
$874$	−148.521	−	358.561i	−0.169932	−	0.410252i
$875$	21.9974	−	53.1065i	0.0251399	−	0.0606932i
$876$		0			0
$877$	83.1296			0.0947886			0.0473943	−	0.998876i	$-0.484908\pi$
$877$	83.1296			0.0947886			0.0473943	+	0.998876i	$0.484908\pi$
$878$	233.285	−	563.200i	0.265700	−	0.641458i
$879$		0			0
$880$	−105.714	+	255.217i	−0.120130	+	0.290019i
$881$	456.680	+	456.680i	0.518365	+	0.518365i	0.917076	−	0.398711i	$-0.130542\pi$
$881$	456.680	+	456.680i	0.518365	+	0.518365i	−0.398711	+	0.917076i	$0.630542\pi$
$882$		0			0
$883$	−834.298	−	345.578i	−0.944845	−	0.391368i	−0.143554	−	0.989642i	$-0.545853\pi$
$883$	−834.298	−	345.578i	−0.944845	−	0.391368i	−0.801291	+	0.598275i	$0.795853\pi$
$884$			1.40869i			0.00159354i
$885$		0			0
$886$		−	646.174i		−	0.729316i
$887$	−210.758	+	508.814i	−0.237607	+	0.573635i	−0.997034	−	0.0769576i	$-0.975479\pi$
$887$	−210.758	+	508.814i	−0.237607	+	0.573635i	0.759427	+	0.650593i	$0.225479\pi$
$888$		0			0
$889$	127.664	−	52.8801i	0.143604	−	0.0594827i
$890$	−351.095	−	847.619i	−0.394489	−	0.952381i
$891$		0			0
$892$			121.809i			0.136557i
$893$	105.325	+	105.325i	0.117945	+	0.117945i
$894$		0			0
$895$	489.573	−	202.788i	0.547009	−	0.226578i
$896$	−40.7401	−	16.8751i	−0.0454688	−	0.0188338i
$897$		0			0
$898$	−101.676			−0.113225
$899$	−761.248	+	315.319i	−0.846772	+	0.350744i
$900$		0			0
$901$			1.30687i			0.00145046i
$902$	746.340	−	39.6856i	0.827428	−	0.0439973i
$903$		0			0
$904$	−750.430	−	750.430i	−0.830122	−	0.830122i
$905$	59.3884	+	143.376i	0.0656226	+	0.158427i
$906$		0			0
$907$	−406.812	+	406.812i	−0.448525	+	0.448525i	−0.894864	−	0.446339i	$-0.852727\pi$
$907$	−406.812	+	406.812i	−0.448525	+	0.448525i	0.446339	+	0.894864i	$0.352727\pi$
$908$	−109.238	+	263.724i	−0.120306	+	0.290445i
$909$		0			0
$910$	159.829	−	159.829i	0.175636	−	0.175636i
$911$	797.009	−	797.009i	0.874873	−	0.874873i	−0.118126	−	0.992999i	$-0.537689\pi$
$911$	797.009	−	797.009i	0.874873	−	0.874873i	0.992999	+	0.118126i	$0.0376885\pi$
$912$		0			0
$913$	−1560.15	+	646.233i	−1.70881	+	0.707813i
$914$	830.282	−	343.914i	0.908405	−	0.376274i
$915$		0			0
$916$	206.082	−	497.526i	0.224980	−	0.543150i
$917$	−79.8722	−	33.0841i	−0.0871016	−	0.0360787i
$918$		0			0
$919$	−292.232	+	705.510i	−0.317989	+	0.767693i	0.681372	+	0.731937i	$0.261384\pi$
$919$	−292.232	+	705.510i	−0.317989	+	0.767693i	−0.999361	+	0.0357553i	$0.988616\pi$
$920$	−1415.98			−1.53911
$921$		0			0
$922$	−472.802	−	472.802i	−0.512800	−	0.512800i
$923$	−1029.00	+	1029.00i	−1.11484	+	1.11484i
$924$		0			0
$925$		−	518.689i		−	0.560745i
$926$	−781.600	−	323.749i	−0.844061	−	0.349621i
$927$		0			0
$928$	265.349	−	640.609i	0.285936	−	0.690311i
$929$	405.195	+	167.837i	0.436163	+	0.180665i	0.589951	−	0.807439i	$-0.299147\pi$
$929$	405.195	+	167.837i	0.436163	+	0.180665i	−0.153788	+	0.988104i	$0.549147\pi$
$930$		0			0
$931$	196.831	+	475.193i	0.211419	+	0.510412i
$932$	−15.9384	−	38.4787i	−0.0171013	−	0.0412862i
$933$		0			0
$934$	46.3463	+	46.3463i	0.0496213	+	0.0496213i
$935$	−1.62627	−	1.62627i	−0.00173932	−	0.00173932i
$936$		0			0
$937$	712.976	+	295.324i	0.760914	+	0.315181i	0.729186	−	0.684316i	$-0.239899\pi$
$937$	712.976	+	295.324i	0.760914	+	0.315181i	0.0317279	+	0.999497i	$0.489899\pi$
$938$	39.2464	+	39.2464i	0.0418405	+	0.0418405i
$939$		0			0
$940$	172.396	−	71.4087i	0.183400	−	0.0759667i
$941$	−236.692	+	236.692i	−0.251532	+	0.251532i	−0.821599	−	0.570067i	$-0.806917\pi$
$941$	−236.692	+	236.692i	−0.251532	+	0.251532i	0.570067	+	0.821599i	$0.306917\pi$
$942$		0			0
$943$	463.015	+	968.826i	0.491002	+	1.02739i
$944$	9.31922			0.00987206
$945$		0			0
$946$	−263.254	−	635.550i	−0.278281	−	0.671829i
$947$			1505.59i			1.58985i	0.606705	+	0.794927i	$0.292491\pi$
$947$			1505.59i			1.58985i	−0.606705	+	0.794927i	$0.707509\pi$
$948$		0			0
$949$	762.796	−	1841.55i	0.803789	−	1.94052i
$950$	92.3127	+	222.863i	0.0971713	+	0.234592i
$951$		0			0
$952$	−0.165586	+	0.165586i	−0.000173935	+	0.000173935i
$953$	1012.29			1.06221			0.531107	−	0.847305i	$-0.321776\pi$
$953$	1012.29			1.06221			0.531107	+	0.847305i	$0.321776\pi$
$954$		0			0
$955$	188.068	−	77.9005i	0.196930	−	0.0815712i
$956$	234.685	+	566.580i	0.245487	+	0.592657i
$957$		0			0
$958$	726.249	+	300.822i	0.758089	+	0.314011i
$959$	53.5935			0.0558848
$960$		0			0
$961$	−239.686			−0.249413
$962$	−418.199	+	1009.62i	−0.434719	+	1.04950i
$963$		0			0
$964$	422.997	−	422.997i	0.438793	−	0.438793i
$965$	179.866	+	74.5030i	0.186390	+	0.0772052i
$966$		0			0
$967$	1357.57	+	562.326i	1.40390	+	0.581516i	0.950762	−	0.309922i	$-0.100303\pi$
$967$	1357.57	+	562.326i	1.40390	+	0.581516i	0.453142	+	0.891438i	$0.350303\pi$
$968$		−	447.106i		−	0.461886i
$969$		0			0
$970$	−975.846	−	404.209i	−1.00603	−	0.416710i
$971$	−705.780	+	292.344i	−0.726859	+	0.301075i	−0.715260	−	0.698858i	$-0.753692\pi$
$971$	−705.780	+	292.344i	−0.726859	+	0.301075i	−0.0115983	+	0.999933i	$0.503692\pi$
$972$		0			0
$973$	77.6025	+	187.349i	0.0797559	+	0.192548i
$974$		−	749.327i		−	0.769329i
$975$		0			0
$976$	−96.7910	−	96.7910i	−0.0991712	−	0.0991712i
$977$	−826.431	+	342.319i	−0.845887	+	0.350378i	−0.763172	−	0.646196i	$-0.776359\pi$
$977$	−826.431	+	342.319i	−0.845887	+	0.350378i	−0.0827148	+	0.996573i	$0.526359\pi$
$978$		0			0
$979$	964.539	+	964.539i	0.985228	+	0.985228i
$980$	644.346			0.657496
$981$		0			0
$982$	−403.648	+	403.648i	−0.411046	+	0.411046i
$983$			991.810i			1.00896i	0.863423	+	0.504481i	$0.168316\pi$
$983$			991.810i			1.00896i	−0.863423	+	0.504481i	$0.831684\pi$
$984$		0			0
$985$	−183.567			−0.186362
$986$	−0.630113	−	0.630113i	−0.000639059	−	0.000639059i
$987$		0			0
$988$			557.048i			0.563814i
$989$	698.853	−	698.853i	0.706626	−	0.706626i
$990$		0			0
$991$	−194.045	−	468.466i	−0.195807	−	0.472720i	0.795230	−	0.606308i	$-0.207350\pi$
$991$	−194.045	−	468.466i	−0.195807	−	0.472720i	−0.991037	+	0.133588i	$0.957350\pi$
$992$	714.465	−	714.465i	0.720227	−	0.720227i
$993$		0			0
$994$	−83.0636			−0.0835650
$995$	2185.53	−	905.275i	2.19651	−	0.909824i
$996$		0			0
$997$	−93.4694	−	225.655i	−0.0937507	−	0.226334i	0.870047	−	0.492969i	$-0.164088\pi$
$997$	−93.4694	−	225.655i	−0.0937507	−	0.226334i	−0.963798	+	0.266635i	$0.914088\pi$
$998$	−385.581	+	930.874i	−0.386353	+	0.932740i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	369.3.l.b.55.3		20
3.2	odd	2		41.3.e.b.14.3	yes	20
41.3	odd	8	inner	369.3.l.b.208.3		20
123.44	even	8		41.3.e.b.3.3	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.3.e.b.3.3	✓	20	123.44	even	8
41.3.e.b.14.3	yes	20	3.2	odd	2
369.3.l.b.55.3		20	1.1	even	1	trivial
369.3.l.b.208.3		20	41.3	odd	8	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:	\( N \)	\(=\)	\( 369 = 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	369.l (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.976817 + 0.976817i) q^{2} -2.09166i q^{4} +(-4.54303 + 4.54303i) q^{5} +(0.392560 + 0.947724i) q^{7} +(5.95043 - 5.95043i) q^{8} +O(q^{10})\)	\(q+(0.976817 + 0.976817i) q^{2} -2.09166i q^{4} +(-4.54303 + 4.54303i) q^{5} +(0.392560 + 0.947724i) q^{7} +(5.95043 - 5.95043i) q^{8} -8.87541 q^{10} +(12.1914 - 5.04984i) q^{11} +(9.50068 + 22.9367i) q^{13} +(-0.542293 + 1.30921i) q^{14} +3.25833 q^{16} +(-0.0103812 + 0.0250625i) q^{17} +(-4.10513 + 9.91065i) q^{19} +(9.50246 + 9.50246i) q^{20} +(16.8415 + 6.97599i) q^{22} +26.1898i q^{23} -16.2782i q^{25} +(-13.1245 + 31.6853i) q^{26} +(1.98231 - 0.821101i) q^{28} +(9.09988 + 21.9691i) q^{29} +34.6509i q^{31} +(-20.6189 - 20.6189i) q^{32} +(-0.0346220 + 0.0143409i) q^{34} +(-6.08895 - 2.52212i) q^{35} +31.8640 q^{37} +(-13.6909 + 5.67094i) q^{38} +54.0660i q^{40} +(36.9925 - 17.6792i) q^{41} +(-26.6842 - 26.6842i) q^{43} +(-10.5625 - 25.5002i) q^{44} +(-25.5826 + 25.5826i) q^{46} +(5.31373 - 12.8285i) q^{47} +(33.9042 - 33.9042i) q^{49} +(15.9008 - 15.9008i) q^{50} +(47.9757 - 19.8722i) q^{52} +(44.5080 - 18.4358i) q^{53} +(-32.4443 + 78.3274i) q^{55} +(7.97527 + 3.30347i) q^{56} +(-12.5708 + 30.3487i) q^{58} +2.86012 q^{59} +(-29.7057 - 29.7057i) q^{61} +(-33.8476 + 33.8476i) q^{62} -53.3152i q^{64} +(-147.364 - 61.0401i) q^{65} +(14.9886 - 36.1856i) q^{67} +(0.0524222 + 0.0217140i) q^{68} +(-3.48413 - 8.41144i) q^{70} +(22.4314 + 54.1541i) q^{71} +(-56.7726 - 56.7726i) q^{73} +(31.1253 + 31.1253i) q^{74} +(20.7297 + 8.58652i) q^{76} +(9.57171 + 9.57171i) q^{77} +(-134.955 + 55.9004i) q^{79} +(-14.8027 + 14.8027i) q^{80} +(53.4042 + 18.8656i) q^{82} -127.971 q^{83} +(-0.0666974 - 0.161022i) q^{85} -52.1311i q^{86} +(42.4953 - 102.593i) q^{88} +(39.5582 + 95.5019i) q^{89} +(-18.0080 + 18.0080i) q^{91} +54.7801 q^{92} +(17.7216 - 7.34054i) q^{94} +(-26.3747 - 63.6741i) q^{95} +(109.949 + 45.5425i) q^{97} +66.2363 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 8 q^{2} + 12 q^{5} - 4 q^{7} - 36 q^{8}+O(q^{10}) \) 20 * q + 8 * q^2 + 12 * q^5 - 4 * q^7 - 36 * q^8	\( 20 q + 8 q^{2} + 12 q^{5} - 4 q^{7} - 36 q^{8} + 16 q^{10} + 12 q^{11} - 48 q^{13} - 88 q^{14} - 36 q^{16} + 28 q^{17} + 76 q^{19} + 16 q^{20} - 116 q^{22} - 40 q^{26} + 72 q^{28} + 24 q^{29} - 176 q^{32} + 80 q^{34} - 60 q^{35} + 208 q^{37} + 380 q^{38} + 116 q^{41} - 40 q^{43} - 116 q^{44} - 176 q^{46} + 64 q^{47} + 168 q^{49} + 148 q^{50} - 184 q^{52} + 120 q^{53} + 20 q^{55} - 188 q^{56} + 36 q^{58} + 512 q^{59} - 460 q^{61} - 68 q^{62} - 432 q^{65} + 300 q^{67} - 120 q^{68} + 308 q^{70} + 108 q^{71} + 60 q^{73} - 140 q^{74} + 872 q^{76} - 112 q^{77} - 208 q^{79} + 68 q^{80} - 376 q^{82} + 120 q^{83} + 172 q^{85} + 316 q^{88} - 268 q^{89} - 800 q^{91} + 448 q^{92} - 212 q^{94} + 184 q^{95} - 120 q^{97} + 20 q^{98}+O(q^{100}) \) 20 * q + 8 * q^2 + 12 * q^5 - 4 * q^7 - 36 * q^8 + 16 * q^10 + 12 * q^11 - 48 * q^13 - 88 * q^14 - 36 * q^16 + 28 * q^17 + 76 * q^19 + 16 * q^20 - 116 * q^22 - 40 * q^26 + 72 * q^28 + 24 * q^29 - 176 * q^32 + 80 * q^34 - 60 * q^35 + 208 * q^37 + 380 * q^38 + 116 * q^41 - 40 * q^43 - 116 * q^44 - 176 * q^46 + 64 * q^47 + 168 * q^49 + 148 * q^50 - 184 * q^52 + 120 * q^53 + 20 * q^55 - 188 * q^56 + 36 * q^58 + 512 * q^59 - 460 * q^61 - 68 * q^62 - 432 * q^65 + 300 * q^67 - 120 * q^68 + 308 * q^70 + 108 * q^71 + 60 * q^73 - 140 * q^74 + 872 * q^76 - 112 * q^77 - 208 * q^79 + 68 * q^80 - 376 * q^82 + 120 * q^83 + 172 * q^85 + 316 * q^88 - 268 * q^89 - 800 * q^91 + 448 * q^92 - 212 * q^94 + 184 * q^95 - 120 * q^97 + 20 * q^98

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