LMFDB - Embedded newform 1764.2.b.m.1567.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(1567,1764)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1764, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1764.1567");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.b (of order $2$, degree $1$, 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:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.15911316233388032.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 10 x^{10} - 20 x^{9} + 35 x^{8} - 56 x^{7} + 84 x^{6} - 112 x^{5} + 140 x^{4} + \cdots + 64 $ x^12 - 4x^11 + 10x^10 - 20x^9 + 35x^8 - 56x^7 + 84x^6 - 112x^5 + 140x^4 - 160x^3 + 160x^2 - 128*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 588)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1567.7
Root			$0.250649 - 1.39182i$ of defining polynomial
Character	$\chi$	$=$	1764.1567
Dual form			1764.2.b.m.1567.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.250649 - 1.39182i) q^{2} +(-1.87435 + 0.697718i) q^{4} +3.39209i q^{5} +(1.44090 + 2.43388i) q^{8} +O(q^{10})$	\(q+(-0.250649 - 1.39182i) q^{2} +(-1.87435 + 0.697718i) q^{4} +3.39209i q^{5} +(1.44090 + 2.43388i) q^{8} +(4.72119 - 0.850222i) q^{10} -1.94285i q^{11} -5.34172i q^{13} +(3.02638 - 2.61554i) q^{16} -1.74787i q^{17} +6.27143 q^{19} +(-2.36672 - 6.35796i) q^{20} +(-2.70411 + 0.486974i) q^{22} +8.39557i q^{23} -6.50626 q^{25} +(-7.43474 + 1.33890i) q^{26} -4.18824 q^{29} +4.59252 q^{31} +(-4.39892 - 3.55661i) q^{32} +(-2.43273 + 0.438101i) q^{34} -1.78336 q^{37} +(-1.57193 - 8.72873i) q^{38} +(-8.25595 + 4.88767i) q^{40} +1.32834i q^{41} +3.27318i q^{43} +(1.35556 + 3.64159i) q^{44} +(11.6852 - 2.10434i) q^{46} +8.22010 q^{47} +(1.63079 + 9.05557i) q^{50} +(3.72702 + 10.0123i) q^{52} +11.8665 q^{53} +6.59033 q^{55} +(1.04978 + 5.82930i) q^{58} +0.507814 q^{59} +7.63584i q^{61} +(-1.15111 - 6.39198i) q^{62} +(-3.84759 + 7.01399i) q^{64} +18.1196 q^{65} +16.1883i q^{67} +(1.21952 + 3.27612i) q^{68} -1.11861i q^{71} -3.06345i q^{73} +(0.446997 + 2.48212i) q^{74} +(-11.7549 + 4.37569i) q^{76} +6.77621i q^{79} +(8.87213 + 10.2657i) q^{80} +(1.84882 - 0.332947i) q^{82} +5.39583 q^{83} +5.92893 q^{85} +(4.55570 - 0.820419i) q^{86} +(4.72869 - 2.79947i) q^{88} +10.1060i q^{89} +(-5.85774 - 15.7362i) q^{92} +(-2.06036 - 11.4409i) q^{94} +21.2732i q^{95} -6.46434i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} - 4 q^{4} - 4 q^{8}+O(q^{10}) $ 12 * q - 4 * q^2 - 4 * q^4 - 4 * q^8	$ 12 q - 4 q^{2} - 4 q^{4} - 4 q^{8} - 4 q^{16} + 24 q^{20} - 12 q^{25} - 24 q^{26} - 32 q^{29} + 16 q^{31} - 4 q^{32} + 32 q^{34} + 32 q^{37} + 24 q^{38} - 32 q^{40} + 24 q^{44} + 24 q^{46} + 28 q^{50} + 32 q^{52} + 32 q^{53} + 16 q^{55} + 16 q^{58} + 16 q^{59} - 8 q^{62} - 4 q^{64} + 8 q^{68} + 32 q^{74} - 32 q^{76} + 16 q^{80} + 32 q^{82} + 16 q^{83} + 16 q^{85} + 24 q^{86} + 24 q^{88}+O(q^{100}) $ 12 * q - 4 * q^2 - 4 * q^4 - 4 * q^8 - 4 * q^16 + 24 * q^20 - 12 * q^25 - 24 * q^26 - 32 * q^29 + 16 * q^31 - 4 * q^32 + 32 * q^34 + 32 * q^37 + 24 * q^38 - 32 * q^40 + 24 * q^44 + 24 * q^46 + 28 * q^50 + 32 * q^52 + 32 * q^53 + 16 * q^55 + 16 * q^58 + 16 * q^59 - 8 * q^62 - 4 * q^64 + 8 * q^68 + 32 * q^74 - 32 * q^76 + 16 * q^80 + 32 * q^82 + 16 * q^83 + 16 * q^85 + 24 * q^86 + 24 * q^88

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.250649	−	1.39182i	−0.177235	−	0.984168i
$2$	−0.250649	−	1.39182i	−0.177235	−	0.984168i
$3$		0			0
$3$		0			0
$4$	−1.87435	+	0.697718i	−0.937175	+	0.348859i
$5$			3.39209i			1.51699i	0.651680	+	0.758494i	$0.274064\pi$
$5$			3.39209i			1.51699i	−0.651680	+	0.758494i	$0.725936\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	1.44090	+	2.43388i	0.509437	+	0.860508i
$9$		0			0
$10$	4.72119	−	0.850222i	1.49297	−	0.268864i
$11$		−	1.94285i		−	0.585793i	−0.956144	−	0.292896i	$-0.905381\pi$
$11$		−	1.94285i		−	0.585793i	0.956144	−	0.292896i	$-0.0946191\pi$
$12$		0			0
$13$		−	5.34172i		−	1.48153i	−0.671766	−	0.740764i	$-0.734464\pi$
$13$		−	5.34172i		−	1.48153i	0.671766	−	0.740764i	$-0.265536\pi$
$14$		0			0
$15$		0			0
$16$	3.02638	−	2.61554i	0.756595	−	0.653884i
$17$		−	1.74787i		−	0.423921i	−0.977278	−	0.211960i	$-0.932015\pi$
$17$		−	1.74787i		−	0.423921i	0.977278	−	0.211960i	$-0.0679847\pi$
$18$		0			0
$19$	6.27143			1.43876			0.719382	−	0.694614i	$-0.244425\pi$
$19$	6.27143			1.43876			0.719382	+	0.694614i	$0.244425\pi$
$20$	−2.36672	−	6.35796i	−0.529215	−	1.42168i
$21$		0			0
$22$	−2.70411	+	0.486974i	−0.576519	+	0.103823i
$23$			8.39557i			1.75060i	0.483582	+	0.875299i	$0.339335\pi$
$23$			8.39557i			1.75060i	−0.483582	+	0.875299i	$0.660665\pi$
$24$		0			0
$25$	−6.50626			−1.30125
$26$	−7.43474	+	1.33890i	−1.45807	+	0.262579i
$27$		0			0
$28$		0			0
$29$	−4.18824			−0.777737			−0.388869	−	0.921293i	$-0.627134\pi$
$29$	−4.18824			−0.777737			−0.388869	+	0.921293i	$0.627134\pi$
$30$		0			0
$31$	4.59252			0.824841			0.412421	−	0.910994i	$-0.364683\pi$
$31$	4.59252			0.824841			0.412421	+	0.910994i	$0.364683\pi$
$32$	−4.39892	−	3.55661i	−0.777627	−	0.628726i
$33$		0			0
$34$	−2.43273	+	0.438101i	−0.417209	+	0.0751337i
$35$		0			0
$36$		0			0
$37$	−1.78336			−0.293182			−0.146591	−	0.989197i	$-0.546830\pi$
$37$	−1.78336			−0.293182			−0.146591	+	0.989197i	$0.546830\pi$
$38$	−1.57193	−	8.72873i	−0.255000	−	1.41599i
$39$		0			0
$40$	−8.25595	+	4.88767i	−1.30538	+	0.772809i
$41$			1.32834i			0.207452i	0.994606	+	0.103726i	$0.0330765\pi$
$41$			1.32834i			0.207452i	−0.994606	+	0.103726i	$0.966923\pi$
$42$		0			0
$43$			3.27318i			0.499156i	0.968355	+	0.249578i	$0.0802919\pi$
$43$			3.27318i			0.499156i	−0.968355	+	0.249578i	$0.919708\pi$
$44$	1.35556	+	3.64159i	0.204359	+	0.548991i
$45$		0			0
$46$	11.6852	−	2.10434i	1.72288	−	0.310268i
$47$	8.22010			1.19902			0.599512	−	0.800366i	$-0.295361\pi$
$47$	8.22010			1.19902			0.599512	+	0.800366i	$0.295361\pi$
$48$		0			0
$49$		0			0
$50$	1.63079	+	9.05557i	0.230628	+	1.28065i
$51$		0			0
$52$	3.72702	+	10.0123i	0.516844	+	1.38845i
$53$	11.8665			1.63000			0.814998	−	0.579464i	$-0.196738\pi$
$53$	11.8665			1.63000			0.814998	+	0.579464i	$0.196738\pi$
$54$		0			0
$55$	6.59033			0.888641
$56$		0			0
$57$		0			0
$58$	1.04978	+	5.82930i	0.137842	+	0.765424i
$59$	0.507814			0.0661118			0.0330559	−	0.999454i	$-0.489476\pi$
$59$	0.507814			0.0661118			0.0330559	+	0.999454i	$0.489476\pi$
$60$		0			0
$61$			7.63584i			0.977669i	0.872377	+	0.488834i	$0.162578\pi$
$61$			7.63584i			0.977669i	−0.872377	+	0.488834i	$0.837422\pi$
$62$	−1.15111	−	6.39198i	−0.146191	−	0.811783i
$63$		0			0
$64$	−3.84759	+	7.01399i	−0.480949	+	0.876749i
$65$	18.1196			2.24746
$66$		0			0
$67$			16.1883i			1.97771i	0.148880	+	0.988855i	$0.452433\pi$
$67$			16.1883i			1.97771i	−0.148880	+	0.988855i	$0.547567\pi$
$68$	1.21952	+	3.27612i	0.147888	+	0.397288i
$69$		0			0
$70$		0			0
$71$		−	1.11861i		−	0.132755i	−0.997795	−	0.0663774i	$-0.978856\pi$
$71$		−	1.11861i		−	0.132755i	0.997795	−	0.0663774i	$-0.0211441\pi$
$72$		0			0
$73$		−	3.06345i		−	0.358550i	−0.983799	−	0.179275i	$-0.942625\pi$
$73$		−	3.06345i		−	0.358550i	0.983799	−	0.179275i	$-0.0573752\pi$
$74$	0.446997	+	2.48212i	0.0519623	+	0.288541i
$75$		0			0
$76$	−11.7549	+	4.37569i	−1.34837	+	0.501926i
$77$		0			0
$78$		0			0
$79$			6.77621i			0.762383i	0.924496	+	0.381192i	$0.124486\pi$
$79$			6.77621i			0.762383i	−0.924496	+	0.381192i	$0.875514\pi$
$80$	8.87213	+	10.2657i	0.991934	+	1.14775i
$81$		0			0
$82$	1.84882	−	0.332947i	0.204168	−	0.0367679i
$83$	5.39583			0.592269			0.296135	−	0.955146i	$-0.404302\pi$
$83$	5.39583			0.592269			0.296135	+	0.955146i	$0.404302\pi$
$84$		0			0
$85$	5.92893			0.643082
$86$	4.55570	−	0.820419i	0.491253	−	0.0884680i
$87$		0			0
$88$	4.72869	−	2.79947i	0.504080	−	0.298424i
$89$			10.1060i			1.07124i	0.844460	+	0.535619i	$0.179922\pi$
$89$			10.1060i			1.07124i	−0.844460	+	0.535619i	$0.820078\pi$
$90$		0			0
$91$		0			0
$92$	−5.85774	−	15.7362i	−0.610712	−	1.64062i
$93$		0			0
$94$	−2.06036	−	11.4409i	−0.212510	−	1.18004i
$95$			21.2732i			2.18259i
$96$		0			0
$97$		−	6.46434i		−	0.656355i	−0.944616	−	0.328177i	$-0.893566\pi$
$97$		−	6.46434i		−	0.656355i	0.944616	−	0.328177i	$-0.106434\pi$
$98$		0			0
$99$		0			0
$100$	12.1950	−	4.53953i	1.21950	−	0.453953i
$101$		−	2.45096i		−	0.243880i	−0.992537	−	0.121940i	$-0.961088\pi$
$101$		−	2.45096i		−	0.243880i	0.992537	−	0.121940i	$-0.0389115\pi$
$102$		0			0
$103$	7.79743			0.768304			0.384152	−	0.923270i	$-0.374494\pi$
$103$	7.79743			0.768304			0.384152	+	0.923270i	$0.374494\pi$
$104$	13.0011	−	7.69691i	1.27487	−	0.754744i
$105$		0			0
$106$	−2.97433	−	16.5162i	−0.288893	−	1.60419i
$107$		−	9.50235i		−	0.918627i	−0.888274	−	0.459313i	$-0.848096\pi$
$107$		−	9.50235i		−	0.918627i	0.888274	−	0.459313i	$-0.151904\pi$
$108$		0			0
$109$	8.90428			0.852875			0.426438	−	0.904517i	$-0.359768\pi$
$109$	8.90428			0.852875			0.426438	+	0.904517i	$0.359768\pi$
$110$	−1.65186	−	9.17259i	−0.157499	−	0.874572i
$111$		0			0
$112$		0			0
$113$	−0.499997			−0.0470357			−0.0235179	−	0.999723i	$-0.507487\pi$
$113$	−0.499997			−0.0470357			−0.0235179	+	0.999723i	$0.507487\pi$
$114$		0			0
$115$	−28.4785			−2.65564
$116$	7.85023	−	2.92221i	0.728876	−	0.271320i
$117$		0			0
$118$	−0.127283	−	0.706788i	−0.0117173	−	0.0650651i
$119$		0			0
$120$		0			0
$121$	7.22531			0.656847
$122$	10.6277	−	1.91391i	0.962191	−	0.173277i
$123$		0			0
$124$	−8.60800	+	3.20428i	−0.773021	+	0.287753i
$125$		−	5.10937i		−	0.456996i
$126$		0			0
$127$			15.5062i			1.37595i	0.725735	+	0.687975i	$0.241500\pi$
$127$			15.5062i			1.37595i	−0.725735	+	0.687975i	$0.758500\pi$
$128$	10.7266	+	3.59712i	0.948110	+	0.317944i
$129$		0			0
$130$	−4.54165	−	25.2193i	−0.398329	−	2.21188i
$131$	−9.44607			−0.825307			−0.412653	−	0.910888i	$-0.635398\pi$
$131$	−9.44607			−0.825307			−0.412653	+	0.910888i	$0.635398\pi$
$132$		0			0
$133$		0			0
$134$	22.5312	−	4.05756i	1.94640	−	0.350520i
$135$		0			0
$136$	4.25411	−	2.51851i	0.364787	−	0.215961i
$137$	−11.9959			−1.02487			−0.512437	−	0.858725i	$-0.671257\pi$
$137$	−11.9959			−1.02487			−0.512437	+	0.858725i	$0.671257\pi$
$138$		0			0
$139$	8.21228			0.696557			0.348278	−	0.937391i	$-0.386766\pi$
$139$	8.21228			0.696557			0.348278	+	0.937391i	$0.386766\pi$
$140$		0			0
$141$		0			0
$142$	−1.55691	+	0.280379i	−0.130653	+	0.0235289i
$143$	−10.3782			−0.867868
$144$		0			0
$145$		−	14.2069i		−	1.17982i
$146$	−4.26379	+	0.767850i	−0.352874	+	0.0635478i
$147$		0			0
$148$	3.34264	−	1.24428i	0.274763	−	0.102279i
$149$	−7.28962			−0.597189			−0.298594	−	0.954380i	$-0.596518\pi$
$149$	−7.28962			−0.597189			−0.298594	+	0.954380i	$0.596518\pi$
$150$		0			0
$151$		−	0.412747i		−	0.0335889i	−0.999859	−	0.0167944i	$-0.994654\pi$
$151$		−	0.412747i		−	0.0335889i	0.999859	−	0.0167944i	$-0.00534609\pi$
$152$	9.03653	+	15.2639i	0.732959	+	1.23807i
$153$		0			0
$154$		0			0
$155$			15.5782i			1.25127i
$156$		0			0
$157$		−	9.92944i		−	0.792456i	−0.918152	−	0.396228i	$-0.870319\pi$
$157$		−	9.92944i		−	0.792456i	0.918152	−	0.396228i	$-0.129681\pi$
$158$	9.43130	−	1.69845i	0.750314	−	0.135121i
$159$		0			0
$160$	12.0643	−	14.9215i	0.953769	−	1.17965i
$161$		0			0
$162$		0			0
$163$			6.66694i			0.522195i	0.965312	+	0.261098i	$0.0840845\pi$
$163$			6.66694i			0.522195i	−0.965312	+	0.261098i	$0.915916\pi$
$164$	−0.926808	−	2.48978i	−0.0723715	−	0.194419i
$165$		0			0
$166$	−1.35246	−	7.51005i	−0.104971	−	0.582893i
$167$	6.48631			0.501926			0.250963	−	0.967997i	$-0.419253\pi$
$167$	6.48631			0.501926			0.250963	+	0.967997i	$0.419253\pi$
$168$		0			0
$169$	−15.5340			−1.19492
$170$	−1.48608	−	8.25202i	−0.113977	−	0.632901i
$171$		0			0
$172$	−2.28376	−	6.13509i	−0.174135	−	0.467796i
$173$		−	6.25378i		−	0.475466i	−0.971331	−	0.237733i	$-0.923596\pi$
$173$		−	6.25378i		−	0.475466i	0.971331	−	0.237733i	$-0.0764043\pi$
$174$		0			0
$175$		0			0
$176$	−5.08161	−	5.87982i	−0.383040	−	0.443208i
$177$		0			0
$178$	14.0658	−	2.53306i	1.05428	−	0.189861i
$179$			2.42517i			0.181265i	0.995884	+	0.0906327i	$0.0288889\pi$
$179$			2.42517i			0.181265i	−0.995884	+	0.0906327i	$0.971111\pi$
$180$		0			0
$181$			8.19141i			0.608863i	0.952534	+	0.304431i	$0.0984664\pi$
$181$			8.19141i			0.608863i	−0.952534	+	0.304431i	$0.901534\pi$
$182$		0			0
$183$		0			0
$184$	−20.4339	+	12.0972i	−1.50640	+	0.891819i
$185$		−	6.04931i		−	0.444754i
$186$		0			0
$187$	−3.39586			−0.248330
$188$	−15.4073	+	5.73531i	−1.12370	+	0.418290i
$189$		0			0
$190$	29.6086	−	5.33211i	2.14804	−	0.386832i
$191$		−	7.01340i		−	0.507472i	−0.967274	−	0.253736i	$-0.918341\pi$
$191$		−	7.01340i		−	0.507472i	0.967274	−	0.253736i	$-0.0816594\pi$
$192$		0			0
$193$	−18.1003			−1.30289			−0.651445	−	0.758696i	$-0.725837\pi$
$193$	−18.1003			−1.30289			−0.651445	+	0.758696i	$0.725837\pi$
$194$	−8.99723	+	1.62028i	−0.645963	+	0.116329i
$195$		0			0
$196$		0			0
$197$	19.2075			1.36848			0.684239	−	0.729258i	$-0.260135\pi$
$197$	19.2075			1.36848			0.684239	+	0.729258i	$0.260135\pi$
$198$		0			0
$199$	−17.0532			−1.20887			−0.604436	−	0.796654i	$-0.706601\pi$
$199$	−17.0532			−1.20887			−0.604436	+	0.796654i	$0.706601\pi$
$200$	−9.37490	−	15.8355i	−0.662905	−	1.11974i
$201$		0			0
$202$	−3.41131	+	0.614330i	−0.240019	+	0.0432241i
$203$		0			0
$204$		0			0
$205$	−4.50585			−0.314702
$206$	−1.95442	−	10.8527i	−0.136171	−	0.756141i
$207$		0			0
$208$	−13.9715	−	16.1661i	−0.968747	−	1.12092i
$209$		−	12.1845i		−	0.842818i
$210$		0			0
$211$		−	20.9435i		−	1.44181i	−0.693035	−	0.720904i	$-0.743727\pi$
$211$		−	20.9435i		−	1.44181i	0.693035	−	0.720904i	$-0.256273\pi$
$212$	−22.2421	+	8.27950i	−1.52759	+	0.568638i
$213$		0			0
$214$	−13.2256	+	2.38175i	−0.904083	+	0.162813i
$215$	−11.1029			−0.757213
$216$		0			0
$217$		0			0
$218$	−2.23184	−	12.3932i	−0.151160	−	0.839373i
$219$		0			0
$220$	−12.3526	+	4.59819i	−0.832812	+	0.310010i
$221$	−9.33663			−0.628050
$222$		0			0
$223$	15.2110			1.01861			0.509303	−	0.860587i	$-0.329903\pi$
$223$	15.2110			1.01861			0.509303	+	0.860587i	$0.329903\pi$
$224$		0			0
$225$		0			0
$226$	0.125323	+	0.695908i	0.00833639	+	0.0462911i
$227$	−0.420504			−0.0279099			−0.0139549	−	0.999903i	$-0.504442\pi$
$227$	−0.420504			−0.0279099			−0.0139549	+	0.999903i	$0.504442\pi$
$228$		0			0
$229$			25.7347i			1.70060i	0.526301	+	0.850298i	$0.323579\pi$
$229$			25.7347i			1.70060i	−0.526301	+	0.850298i	$0.676421\pi$
$230$	7.13810	+	39.6371i	0.470673	+	2.61359i
$231$		0			0
$232$	−6.03486	−	10.1937i	−0.396208	−	0.669249i
$233$	−11.8429			−0.775857			−0.387929	−	0.921689i	$-0.626809\pi$
$233$	−11.8429			−0.775857			−0.387929	+	0.921689i	$0.626809\pi$
$234$		0			0
$235$			27.8833i			1.81891i
$236$	−0.951822	+	0.354311i	−0.0619583	+	0.0230637i
$237$		0			0
$238$		0			0
$239$		−	8.11304i		−	0.524789i	−0.964961	−	0.262395i	$-0.915488\pi$
$239$		−	8.11304i		−	0.524789i	0.964961	−	0.262395i	$-0.0845122\pi$
$240$		0			0
$241$		−	3.28762i		−	0.211774i	−0.994378	−	0.105887i	$-0.966232\pi$
$241$		−	3.28762i		−	0.211774i	0.994378	−	0.105887i	$-0.0337682\pi$
$242$	−1.81102	−	10.0564i	−0.116416	−	0.646448i
$243$		0			0
$244$	−5.32766	−	14.3122i	−0.341068	−	0.916247i
$245$		0			0
$246$		0			0
$247$		−	33.5002i		−	2.13157i
$248$	6.61738	+	11.1777i	0.420204	+	0.709783i
$249$		0			0
$250$	−7.11134	+	1.28066i	−0.449761	+	0.0809958i
$251$	20.6150			1.30121			0.650603	−	0.759418i	$-0.274516\pi$
$251$	20.6150			1.30121			0.650603	+	0.759418i	$0.274516\pi$
$252$		0			0
$253$	16.3114			1.02549
$254$	21.5819	−	3.88660i	1.35417	−	0.243867i
$255$		0			0
$256$	2.31795	−	15.8312i	0.144872	−	0.989450i
$257$		−	14.3940i		−	0.897870i	−0.893564	−	0.448935i	$-0.851803\pi$
$257$		−	14.3940i		−	0.897870i	0.893564	−	0.448935i	$-0.148197\pi$
$258$		0			0
$259$		0			0
$260$	−33.9625	+	12.6424i	−2.10626	+	0.784046i
$261$		0			0
$262$	2.36764	+	13.1473i	0.146274	+	0.812241i
$263$		−	3.75215i		−	0.231367i	−0.993286	−	0.115684i	$-0.963094\pi$
$263$		−	3.75215i		−	0.231367i	0.993286	−	0.115684i	$-0.0369059\pi$
$264$		0			0
$265$			40.2524i			2.47268i
$266$		0			0
$267$		0			0
$268$	−11.2948	−	30.3425i	−0.689942	−	1.85346i
$269$			5.65458i			0.344766i	0.985030	+	0.172383i	$0.0551466\pi$
$269$			5.65458i			0.344766i	−0.985030	+	0.172383i	$0.944853\pi$
$270$		0			0
$271$	18.0423			1.09599			0.547995	−	0.836482i	$-0.315391\pi$
$271$	18.0423			1.09599			0.547995	+	0.836482i	$0.315391\pi$
$272$	−4.57161	−	5.28972i	−0.277195	−	0.320736i
$273$		0			0
$274$	3.00674	+	16.6961i	0.181644	+	1.00865i
$275$			12.6407i			0.762264i
$276$		0			0
$277$	25.7525			1.54732			0.773660	−	0.633601i	$-0.218424\pi$
$277$	25.7525			1.54732			0.773660	+	0.633601i	$0.218424\pi$
$278$	−2.05840	−	11.4301i	−0.123454	−	0.685529i
$279$		0			0
$280$		0			0
$281$	−11.5642			−0.689860			−0.344930	−	0.938628i	$-0.612097\pi$
$281$	−11.5642			−0.689860			−0.344930	+	0.938628i	$0.612097\pi$
$282$		0			0
$283$	30.2442			1.79783			0.898915	−	0.438124i	$-0.144357\pi$
$283$	30.2442			1.79783			0.898915	+	0.438124i	$0.144357\pi$
$284$	0.780476	+	2.09667i	0.0463127	+	0.124415i
$285$		0			0
$286$	2.60128	+	14.4446i	0.153817	+	0.854128i
$287$		0			0
$288$		0			0
$289$	13.9450			0.820291
$290$	−19.7735	+	3.56094i	−1.16114	+	0.209105i
$291$		0			0
$292$	2.13743	+	5.74199i	0.125083	+	0.336024i
$293$			7.74537i			0.452489i	0.974071	+	0.226245i	$0.0726448\pi$
$293$			7.74537i			0.452489i	−0.974071	+	0.226245i	$0.927355\pi$
$294$		0			0
$295$			1.72255i			0.100291i
$296$	−2.56965	−	4.34049i	−0.149358	−	0.252286i
$297$		0			0
$298$	1.82713	+	10.1459i	0.105843	+	0.587734i
$299$	44.8468			2.59356
$300$		0			0
$301$		0			0
$302$	−0.574471	+	0.103454i	−0.0330571	+	0.00595313i
$303$		0			0
$304$	18.9797	−	16.4031i	1.08856	−	0.940785i
$305$	−25.9014			−1.48311
$306$		0			0
$307$	−19.0435			−1.08687			−0.543435	−	0.839451i	$-0.682877\pi$
$307$	−19.0435			−1.08687			−0.543435	+	0.839451i	$0.682877\pi$
$308$		0			0
$309$		0			0
$310$	21.6822	−	3.90466i	1.23146	−	0.221770i
$311$	−6.90884			−0.391764			−0.195882	−	0.980627i	$-0.562757\pi$
$311$	−6.90884			−0.391764			−0.195882	+	0.980627i	$0.562757\pi$
$312$		0			0
$313$		−	4.16626i		−	0.235491i	−0.993044	−	0.117745i	$-0.962433\pi$
$313$		−	4.16626i		−	0.235491i	0.993044	−	0.117745i	$-0.0375667\pi$
$314$	−13.8200	+	2.48880i	−0.779910	+	0.140451i
$315$		0			0
$316$	−4.72788	−	12.7010i	−0.265964	−	0.714487i
$317$	−21.1478			−1.18778			−0.593890	−	0.804546i	$-0.702409\pi$
$317$	−21.1478			−1.18778			−0.593890	+	0.804546i	$0.702409\pi$
$318$		0			0
$319$			8.13715i			0.455593i
$320$	−23.7921	−	13.0514i	−1.33002	−	0.729594i
$321$		0			0
$322$		0			0
$323$		−	10.9616i		−	0.609922i
$324$		0			0
$325$			34.7546i			1.92784i
$326$	9.27921	−	1.67106i	0.513928	−	0.0925515i
$327$		0			0
$328$	−3.23303	+	1.91401i	−0.178514	+	0.105684i
$329$		0			0
$330$		0			0
$331$			25.9710i			1.42750i	0.700402	+	0.713749i	$0.253004\pi$
$331$			25.9710i			1.42750i	−0.700402	+	0.713749i	$0.746996\pi$
$332$	−10.1137	+	3.76477i	−0.555060	+	0.206618i
$333$		0			0
$334$	−1.62579	−	9.02781i	−0.0889590	−	0.493980i
$335$	−54.9120			−3.00016
$336$		0			0
$337$	−29.0557			−1.58276			−0.791381	−	0.611323i	$-0.790638\pi$
$337$	−29.0557			−1.58276			−0.791381	+	0.611323i	$0.790638\pi$
$338$	3.89358	+	21.6206i	0.211783	+	1.17601i
$339$		0			0
$340$	−11.1129	+	4.13672i	−0.602681	+	0.224345i
$341$		−	8.92260i		−	0.483186i
$342$		0			0
$343$		0			0
$344$	−7.96655	+	4.71634i	−0.429528	+	0.254288i
$345$		0			0
$346$	−8.70416	+	1.56750i	−0.467938	+	0.0842693i
$347$		−	30.8353i		−	1.65532i	−0.561226	−	0.827662i	$-0.689670\pi$
$347$		−	30.8353i		−	1.65532i	0.561226	−	0.827662i	$-0.310330\pi$
$348$		0			0
$349$			7.97277i			0.426772i	0.976968	+	0.213386i	$0.0684493\pi$
$349$			7.97277i			0.426772i	−0.976968	+	0.213386i	$0.931551\pi$
$350$		0			0
$351$		0			0
$352$	−6.90998	+	8.54647i	−0.368303	+	0.455528i
$353$		−	14.8383i		−	0.789765i	−0.918732	−	0.394883i	$-0.870785\pi$
$353$		−	14.8383i		−	0.789765i	0.918732	−	0.394883i	$-0.129215\pi$
$354$		0			0
$355$	3.79443			0.201388
$356$	−7.05116	−	18.9423i	−0.373711	−	1.00394i
$357$		0			0
$358$	3.37541	−	0.607865i	0.178396	−	0.0321266i
$359$			12.9057i			0.681139i	0.940219	+	0.340570i	$0.110620\pi$
$359$			12.9057i			0.681139i	−0.940219	+	0.340570i	$0.889380\pi$
$360$		0			0
$361$	20.3308			1.07004
$362$	11.4010	−	2.05317i	0.599223	−	0.107912i
$363$		0			0
$364$		0			0
$365$	10.3915			0.543916
$366$		0			0
$367$	−9.99357			−0.521660			−0.260830	−	0.965385i	$-0.583996\pi$
$367$	−9.99357			−0.521660			−0.260830	+	0.965385i	$0.583996\pi$
$368$	21.9589	+	25.4082i	1.14469	+	1.32449i
$369$		0			0
$370$	−8.41958	+	1.51625i	−0.437713	+	0.0788262i
$371$		0			0
$372$		0			0
$373$	−7.43350			−0.384892			−0.192446	−	0.981308i	$-0.561642\pi$
$373$	−7.43350			−0.384892			−0.192446	+	0.981308i	$0.561642\pi$
$374$	0.851167	+	4.72644i	0.0440128	+	0.244398i
$375$		0			0
$376$	11.8444	+	20.0068i	0.610827	+	1.03177i
$377$			22.3724i			1.15224i
$378$		0			0
$379$		−	7.11645i		−	0.365547i	−0.983155	−	0.182774i	$-0.941492\pi$
$379$		−	7.11645i		−	0.365547i	0.983155	−	0.182774i	$-0.0585076\pi$
$380$	−14.8427	−	39.8735i	−0.761416	−	2.04547i
$381$		0			0
$382$	−9.76142	+	1.75790i	−0.499438	+	0.0899419i
$383$	1.60485			0.0820043			0.0410021	−	0.999159i	$-0.486945\pi$
$383$	1.60485			0.0820043			0.0410021	+	0.999159i	$0.486945\pi$
$384$		0			0
$385$		0			0
$386$	4.53682	+	25.1925i	0.230918	+	1.28226i
$387$		0			0
$388$	4.51029	+	12.1164i	0.228975	+	0.615119i
$389$	29.2060			1.48080			0.740402	−	0.672165i	$-0.234635\pi$
$389$	29.2060			1.48080			0.740402	+	0.672165i	$0.234635\pi$
$390$		0			0
$391$	14.6744			0.742114
$392$		0			0
$393$		0			0
$394$	−4.81433	−	26.7335i	−0.242543	−	1.34681i
$395$	−22.9855			−1.15653
$396$		0			0
$397$		−	28.4412i		−	1.42742i	−0.700439	−	0.713712i	$-0.747013\pi$
$397$		−	28.4412i		−	1.42742i	0.700439	−	0.713712i	$-0.252987\pi$
$398$	4.27437	+	23.7351i	0.214255	+	1.18973i
$399$		0			0
$400$	−19.6904	+	17.0174i	−0.984521	+	0.850868i
$401$	−25.2054			−1.25870			−0.629348	−	0.777124i	$-0.716678\pi$
$401$	−25.2054			−1.25870			−0.629348	+	0.777124i	$0.716678\pi$
$402$		0			0
$403$		−	24.5320i		−	1.22203i
$404$	1.71008	+	4.59396i	0.0850796	+	0.228558i
$405$		0			0
$406$		0			0
$407$			3.46481i			0.171744i
$408$		0			0
$409$		−	9.88943i		−	0.489001i	−0.969649	−	0.244500i	$-0.921376\pi$
$409$		−	9.88943i		−	0.489001i	0.969649	−	0.244500i	$-0.0786239\pi$
$410$	1.12939	+	6.27136i	0.0557764	+	0.309720i
$411$		0			0
$412$	−14.6151	+	5.44041i	−0.720035	+	0.268030i
$413$		0			0
$414$		0			0
$415$			18.3031i			0.898465i
$416$	−18.9984	+	23.4978i	−0.931474	+	1.15208i
$417$		0			0
$418$	−16.9587	+	3.05402i	−0.829475	+	0.149377i
$419$	34.8874			1.70436			0.852180	−	0.523249i	$-0.175280\pi$
$419$	34.8874			1.70436			0.852180	+	0.523249i	$0.175280\pi$
$420$		0			0
$421$	−2.79181			−0.136065			−0.0680323	−	0.997683i	$-0.521672\pi$
$421$	−2.79181			−0.136065			−0.0680323	+	0.997683i	$0.521672\pi$
$422$	−29.1496	+	5.24945i	−1.41898	+	0.255539i
$423$		0			0
$424$	17.0986	+	28.8818i	0.830379	+	1.40262i
$425$			11.3721i			0.551627i
$426$		0			0
$427$		0			0
$428$	6.62996	+	17.8107i	0.320471	+	0.860914i
$429$		0			0
$430$	2.78293	+	15.4533i	0.134205	+	0.745225i
$431$			4.56631i			0.219951i	0.993934	+	0.109976i	$0.0350773\pi$
$431$			4.56631i			0.219951i	−0.993934	+	0.109976i	$0.964923\pi$
$432$		0			0
$433$		−	36.3666i		−	1.74767i	−0.486223	−	0.873835i	$-0.661626\pi$
$433$		−	36.3666i		−	1.74767i	0.486223	−	0.873835i	$-0.338374\pi$
$434$		0			0
$435$		0			0
$436$	−16.6897	+	6.21267i	−0.799293	+	0.297533i
$437$			52.6523i			2.51870i
$438$		0			0
$439$	12.6737			0.604883			0.302442	−	0.953168i	$-0.402198\pi$
$439$	12.6737			0.604883			0.302442	+	0.953168i	$0.402198\pi$
$440$	9.49604	+	16.0401i	0.452706	+	0.764683i
$441$		0			0
$442$	2.34021	+	12.9950i	0.111313	+	0.618107i
$443$		−	11.8926i		−	0.565035i	−0.959262	−	0.282518i	$-0.908830\pi$
$443$		−	11.8926i		−	0.565035i	0.959262	−	0.282518i	$-0.0911696\pi$
$444$		0			0
$445$	−34.2806			−1.62505
$446$	−3.81263	−	21.1711i	−0.180533	−	1.00248i
$447$		0			0
$448$		0			0
$449$	−17.6510			−0.833001			−0.416500	−	0.909135i	$-0.636744\pi$
$449$	−17.6510			−0.833001			−0.416500	+	0.909135i	$0.636744\pi$
$450$		0			0
$451$	2.58078			0.121524
$452$	0.937169	−	0.348857i	0.0440807	−	0.0164088i
$453$		0			0
$454$	0.105399	+	0.585268i	0.00494661	+	0.0274680i
$455$		0			0
$456$		0			0
$457$	−20.1718			−0.943597			−0.471798	−	0.881706i	$-0.656395\pi$
$457$	−20.1718			−0.943597			−0.471798	+	0.881706i	$0.656395\pi$
$458$	35.8182	−	6.45037i	1.67367	−	0.301406i
$459$		0			0
$460$	53.3787	−	19.8700i	2.48880	−	0.926442i
$461$		−	14.4743i		−	0.674135i	−0.941481	−	0.337067i	$-0.890565\pi$
$461$		−	14.4743i		−	0.674135i	0.941481	−	0.337067i	$-0.109435\pi$
$462$		0			0
$463$			18.3259i			0.851675i	0.904800	+	0.425837i	$0.140020\pi$
$463$			18.3259i			0.851675i	−0.904800	+	0.425837i	$0.859980\pi$
$464$	−12.6752	+	10.9545i	−0.588432	+	0.508550i
$465$		0			0
$466$	2.96842	+	16.4833i	0.137509	+	0.763574i
$467$	15.2717			0.706690			0.353345	−	0.935493i	$-0.385044\pi$
$467$	15.2717			0.706690			0.353345	+	0.935493i	$0.385044\pi$
$468$		0			0
$469$		0			0
$470$	38.8087	−	6.98891i	1.79011	−	0.322374i
$471$		0			0
$472$	0.731711	+	1.23596i	0.0336797	+	0.0568897i
$473$	6.35932			0.292402
$474$		0			0
$475$	−40.8036			−1.87220
$476$		0			0
$477$		0			0
$478$	−11.2919	+	2.03352i	−0.516481	+	0.0930112i
$479$	36.5797			1.67137			0.835684	−	0.549211i	$-0.185072\pi$
$479$	36.5797			1.67137			0.835684	+	0.549211i	$0.185072\pi$
$480$		0			0
$481$			9.52621i			0.434358i
$482$	−4.57578	+	0.824036i	−0.208421	+	0.0375338i
$483$		0			0
$484$	−13.5428	+	5.04123i	−0.615581	+	0.229147i
$485$	21.9276			0.995682
$486$		0			0
$487$		−	21.5707i		−	0.977460i	−0.872435	−	0.488730i	$-0.837460\pi$
$487$		−	21.5707i		−	0.977460i	0.872435	−	0.488730i	$-0.162540\pi$
$488$	−18.5847	+	11.0025i	−0.841292	+	0.498060i
$489$		0			0
$490$		0			0
$491$			19.2285i			0.867768i	0.900969	+	0.433884i	$0.142857\pi$
$491$			19.2285i			0.867768i	−0.900969	+	0.433884i	$0.857143\pi$
$492$		0			0
$493$			7.32050i			0.329699i
$494$	−46.6265	+	8.39679i	−2.09782	+	0.377789i
$495$		0			0
$496$	13.8987	−	12.0119i	0.624071	−	0.539350i
$497$		0			0
$498$		0			0
$499$		−	7.65808i		−	0.342823i	−0.985200	−	0.171411i	$-0.945167\pi$
$499$		−	7.65808i		−	0.342823i	0.985200	−	0.171411i	$-0.0548327\pi$
$500$	3.56490	+	9.57675i	0.159427	+	0.428285i
$501$		0			0
$502$	−5.16712	−	28.6924i	−0.230620	−	1.28061i
$503$	−5.00763			−0.223279			−0.111640	−	0.993749i	$-0.535610\pi$
$503$	−5.00763			−0.223279			−0.111640	+	0.993749i	$0.535610\pi$
$504$		0			0
$505$	8.31388			0.369963
$506$	−4.08843	−	22.7026i	−0.181753	−	1.00925i
$507$		0			0
$508$	−10.8189	−	29.0640i	−0.480012	−	1.28951i
$509$		−	20.5448i		−	0.910634i	−0.890329	−	0.455317i	$-0.849526\pi$
$509$		−	20.5448i		−	0.910634i	0.890329	−	0.455317i	$-0.150474\pi$
$510$		0			0
$511$		0			0
$512$	−22.6153	+	0.741893i	−0.999462	+	0.0327874i
$513$		0			0
$514$	−20.0339	+	3.60783i	−0.883656	+	0.159134i
$515$			26.4496i			1.16551i
$516$		0			0
$517$		−	15.9705i		−	0.702380i
$518$		0			0
$519$		0			0
$520$	26.1086	+	44.1010i	1.14494	+	1.93396i
$521$		−	2.35833i		−	0.103320i	−0.998665	−	0.0516601i	$-0.983549\pi$
$521$		−	2.35833i		−	0.103320i	0.998665	−	0.0516601i	$-0.0164512\pi$
$522$		0			0
$523$	−15.5762			−0.681101			−0.340551	−	0.940226i	$-0.610613\pi$
$523$	−15.5762			−0.681101			−0.340551	+	0.940226i	$0.610613\pi$
$524$	17.7052	−	6.59069i	0.773457	−	0.287916i
$525$		0			0
$526$	−5.22233	+	0.940471i	−0.227705	+	0.0410065i
$527$		−	8.02713i		−	0.349667i
$528$		0			0
$529$	−47.4856			−2.06459
$530$	56.0242	−	10.0892i	2.43354	−	0.438247i
$531$		0			0
$532$		0			0
$533$	7.09564			0.307346
$534$		0			0
$535$	32.2328			1.39355
$536$	−39.4004	+	23.3257i	−1.70184	+	1.00752i
$537$		0			0
$538$	7.87018	−	1.41731i	0.339308	−	0.0611047i
$539$		0			0
$540$		0			0
$541$	−25.8631			−1.11194			−0.555971	−	0.831202i	$-0.687653\pi$
$541$	−25.8631			−1.11194			−0.555971	+	0.831202i	$0.687653\pi$
$542$	−4.52227	−	25.1117i	−0.194248	−	1.07864i
$543$		0			0
$544$	−6.21649	+	7.68874i	−0.266530	+	0.329652i
$545$			30.2041i			1.29380i
$546$		0			0
$547$			20.0667i			0.857991i	0.903307	+	0.428996i	$0.141132\pi$
$547$			20.0667i			0.857991i	−0.903307	+	0.428996i	$0.858868\pi$
$548$	22.4844	−	8.36972i	0.960487	−	0.357537i
$549$		0			0
$550$	17.5937	−	3.16838i	0.750196	−	0.135100i
$551$	−26.2663			−1.11898
$552$		0			0
$553$		0			0
$554$	−6.45484	−	35.8430i	−0.274240	−	1.52282i
$555$		0			0
$556$	−15.3927	+	5.72985i	−0.652796	+	0.243000i
$557$	4.58648			0.194335			0.0971676	−	0.995268i	$-0.469022\pi$
$557$	4.58648			0.194335			0.0971676	+	0.995268i	$0.469022\pi$
$558$		0			0
$559$	17.4844			0.739513
$560$		0			0
$561$		0			0
$562$	2.89854	+	16.0953i	0.122268	+	0.678939i
$563$	43.8053			1.84617			0.923086	−	0.384594i	$-0.125658\pi$
$563$	43.8053			1.84617			0.923086	+	0.384594i	$0.125658\pi$
$564$		0			0
$565$		−	1.69603i		−	0.0713526i
$566$	−7.58066	−	42.0946i	−0.318639	−	1.76937i
$567$		0			0
$568$	2.72257	−	1.61181i	0.114237	−	0.0676302i
$569$	−6.51122			−0.272964			−0.136482	−	0.990643i	$-0.543580\pi$
$569$	−6.51122			−0.272964			−0.136482	+	0.990643i	$0.543580\pi$
$570$		0			0
$571$		−	20.3469i		−	0.851490i	−0.904843	−	0.425745i	$-0.860012\pi$
$571$		−	20.3469i		−	0.851490i	0.904843	−	0.425745i	$-0.139988\pi$
$572$	19.4524	−	7.24105i	0.813344	−	0.302764i
$573$		0			0
$574$		0			0
$575$		−	54.6238i		−	2.27797i
$576$		0			0
$577$		−	12.8766i		−	0.536058i	−0.963411	−	0.268029i	$-0.913628\pi$
$577$		−	12.8766i		−	0.536058i	0.963411	−	0.268029i	$-0.0863723\pi$
$578$	−3.49528	−	19.4089i	−0.145385	−	0.807305i
$579$		0			0
$580$	9.91240	+	26.6287i	0.411590	+	1.10570i
$581$		0			0
$582$		0			0
$583$		−	23.0550i		−	0.954840i
$584$	7.45609	−	4.41414i	0.308535	−	0.182659i
$585$		0			0
$586$	10.7802	−	1.94137i	0.445326	−	0.0801971i
$587$	−38.1676			−1.57534			−0.787672	−	0.616094i	$-0.788714\pi$
$587$	−38.1676			−1.57534			−0.787672	+	0.616094i	$0.788714\pi$
$588$		0			0
$589$	28.8017			1.18675
$590$	2.39749	−	0.431755i	0.0987030	−	0.0177751i
$591$		0			0
$592$	−5.39712	+	4.66444i	−0.221820	+	0.191707i
$593$		−	1.82872i		−	0.0750964i	−0.999295	−	0.0375482i	$-0.988045\pi$
$593$		−	1.82872i		−	0.0750964i	0.999295	−	0.0375482i	$-0.0119548\pi$
$594$		0			0
$595$		0			0
$596$	13.6633	−	5.08610i	0.559671	−	0.208335i
$597$		0			0
$598$	−11.2408	−	62.4189i	−0.459670	−	2.55250i
$599$			3.83867i			0.156844i	0.996920	+	0.0784219i	$0.0249881\pi$
$599$			3.83867i			0.156844i	−0.996920	+	0.0784219i	$0.975012\pi$
$600$		0			0
$601$		−	6.74051i		−	0.274951i	−0.990505	−	0.137475i	$-0.956101\pi$
$601$		−	6.74051i		−	0.274951i	0.990505	−	0.137475i	$-0.0438988\pi$
$602$		0			0
$603$		0			0
$604$	0.287981	+	0.773632i	0.0117178	+	0.0314787i
$605$			24.5089i			0.996429i
$606$		0			0
$607$	−36.8900			−1.49732			−0.748658	−	0.662956i	$-0.769302\pi$
$607$	−36.8900			−1.49732			−0.748658	+	0.662956i	$0.769302\pi$
$608$	−27.5875	−	22.3050i	−1.11882	−	0.904588i
$609$		0			0
$610$	6.49216	+	36.0502i	0.262860	+	1.45963i
$611$		−	43.9095i		−	1.77639i
$612$		0			0
$613$	40.8439			1.64967			0.824834	−	0.565375i	$-0.191268\pi$
$613$	40.8439			1.64967			0.824834	+	0.565375i	$0.191268\pi$
$614$	4.77323	+	26.5052i	0.192632	+	1.06966i
$615$		0			0
$616$		0			0
$617$	−30.4463			−1.22572			−0.612860	−	0.790192i	$-0.709981\pi$
$617$	−30.4463			−1.22572			−0.612860	+	0.790192i	$0.709981\pi$
$618$		0			0
$619$	3.76171			0.151196			0.0755979	−	0.997138i	$-0.475913\pi$
$619$	3.76171			0.151196			0.0755979	+	0.997138i	$0.475913\pi$
$620$	−10.8692	−	29.1991i	−0.436518	−	1.17266i
$621$		0			0
$622$	1.73169	+	9.61589i	0.0694345	+	0.385562i
$623$		0			0
$624$		0			0
$625$	−15.1999			−0.607995
$626$	−5.79870	+	1.04427i	−0.231763	+	0.0417373i
$627$		0			0
$628$	6.92795	+	18.6113i	0.276455	+	0.742670i
$629$			3.11708i			0.124286i
$630$		0			0
$631$		−	1.46463i		−	0.0583061i	−0.999575	−	0.0291531i	$-0.990719\pi$
$631$		−	1.46463i		−	0.0583061i	0.999575	−	0.0291531i	$-0.00928102\pi$
$632$	−16.4925	+	9.76387i	−0.656037	+	0.388386i
$633$		0			0
$634$	5.30067	+	29.4341i	0.210517	+	1.16898i
$635$	−52.5983			−2.08730
$636$		0			0
$637$		0			0
$638$	11.3255	−	2.03956i	0.448380	−	0.0807471i
$639$		0			0
$640$	−12.2018	+	36.3857i	−0.482317	+	1.43827i
$641$	−19.1077			−0.754711			−0.377355	−	0.926069i	$-0.623166\pi$
$641$	−19.1077			−0.754711			−0.377355	+	0.926069i	$0.623166\pi$
$642$		0			0
$643$	−45.6476			−1.80016			−0.900082	−	0.435720i	$-0.856494\pi$
$643$	−45.6476			−1.80016			−0.900082	+	0.435720i	$0.856494\pi$
$644$		0			0
$645$		0			0
$646$	−15.2567	+	2.74752i	−0.600266	+	0.108100i
$647$	−22.1741			−0.871753			−0.435877	−	0.900006i	$-0.643562\pi$
$647$	−22.1741			−0.871753			−0.435877	+	0.900006i	$0.643562\pi$
$648$		0			0
$649$		−	0.986609i		−	0.0387278i
$650$	48.3724	−	8.71120i	1.89732	−	0.341682i
$651$		0			0
$652$	−4.65164	−	12.4962i	−0.182172	−	0.489388i
$653$	36.5117			1.42881			0.714407	−	0.699730i	$-0.246696\pi$
$653$	36.5117			1.42881			0.714407	+	0.699730i	$0.246696\pi$
$654$		0			0
$655$		−	32.0419i		−	1.25198i
$656$	3.47433	+	4.02007i	0.135650	+	0.156957i
$657$		0			0
$658$		0			0
$659$			48.5539i			1.89139i	0.325054	+	0.945695i	$0.394617\pi$
$659$			48.5539i			1.89139i	−0.325054	+	0.945695i	$0.605383\pi$
$660$		0			0
$661$			1.63245i			0.0634950i	0.999496	+	0.0317475i	$0.0101072\pi$
$661$			1.63245i			0.0634950i	−0.999496	+	0.0317475i	$0.989893\pi$
$662$	36.1471	−	6.50961i	1.40490	−	0.253003i
$663$		0			0
$664$	7.77487	+	13.1328i	0.301724	+	0.509653i
$665$		0			0
$666$		0			0
$667$		−	35.1627i		−	1.36150i
$668$	−12.1576	+	4.52562i	−0.470393	+	0.175101i
$669$		0			0
$670$	13.7636	+	76.4279i	0.531735	+	2.95267i
$671$	14.8353			0.572711
$672$		0			0
$673$	34.2503			1.32025			0.660127	−	0.751154i	$-0.270502\pi$
$673$	34.2503			1.32025			0.660127	+	0.751154i	$0.270502\pi$
$674$	7.28276	+	40.4404i	0.280522	+	1.55771i
$675$		0			0
$676$	29.1162	−	10.8384i	1.11985	−	0.416860i
$677$			31.2214i			1.19994i	0.800023	+	0.599969i	$0.204820\pi$
$677$			31.2214i			1.19994i	−0.800023	+	0.599969i	$0.795180\pi$
$678$		0			0
$679$		0			0
$680$	8.54301	+	14.4303i	0.327610	+	0.553378i
$681$		0			0
$682$	−12.4187	+	2.23644i	−0.475537	+	0.0856377i
$683$		−	34.0957i		−	1.30464i	−0.757945	−	0.652318i	$-0.773797\pi$
$683$		−	34.0957i		−	1.30464i	0.757945	−	0.652318i	$-0.226203\pi$
$684$		0			0
$685$		−	40.6910i		−	1.55472i
$686$		0			0
$687$		0			0
$688$	8.56113	+	9.90589i	0.326390	+	0.377659i
$689$		−	63.3878i		−	2.41488i
$690$		0			0
$691$	−37.2594			−1.41741			−0.708707	−	0.705503i	$-0.750721\pi$
$691$	−37.2594			−1.41741			−0.708707	+	0.705503i	$0.750721\pi$
$692$	4.36337	+	11.7218i	0.165870	+	0.445595i
$693$		0			0
$694$	−42.9173	+	7.72882i	−1.62912	+	0.293382i
$695$			27.8568i			1.05667i
$696$		0			0
$697$	2.32177			0.0879432
$698$	11.0967	−	1.99836i	0.420016	−	0.0756392i
$699$		0			0
$700$		0			0
$701$	−26.4576			−0.999289			−0.499645	−	0.866230i	$-0.666536\pi$
$701$	−26.4576			−0.999289			−0.499645	+	0.866230i	$0.666536\pi$
$702$		0			0
$703$	−11.1842			−0.421821
$704$	13.6272	+	7.47531i	0.513593	+	0.281736i
$705$		0			0
$706$	−20.6524	+	3.71921i	−0.777262	+	0.139974i
$707$		0			0
$708$		0			0
$709$	37.1128			1.39380			0.696901	−	0.717167i	$-0.254562\pi$
$709$	37.1128			1.39380			0.696901	+	0.717167i	$0.254562\pi$
$710$	−0.951069	−	5.28118i	−0.0356930	−	0.198199i
$711$		0			0
$712$	−24.5969	+	14.5618i	−0.921809	+	0.545728i
$713$			38.5569i			1.44397i
$714$		0			0
$715$		−	35.2037i		−	1.31655i
$716$	−1.69208	−	4.54561i	−0.0632361	−	0.169878i
$717$		0			0
$718$	17.9625	−	3.23481i	0.670356	−	0.120722i
$719$	−34.8323			−1.29903			−0.649513	−	0.760350i	$-0.725027\pi$
$719$	−34.8323			−1.29903			−0.649513	+	0.760350i	$0.725027\pi$
$720$		0			0
$721$		0			0
$722$	−5.09590	−	28.2970i	−0.189650	−	1.05310i
$723$		0			0
$724$	−5.71529	−	15.3536i	−0.212407	−	0.570611i
$725$	27.2498			1.01203
$726$		0			0
$727$	−4.03273			−0.149566			−0.0747828	−	0.997200i	$-0.523826\pi$
$727$	−4.03273			−0.149566			−0.0747828	+	0.997200i	$0.523826\pi$
$728$		0			0
$729$		0			0
$730$	−2.60462	−	14.4631i	−0.0964012	−	0.535305i
$731$	5.72110			0.211602
$732$		0			0
$733$		−	28.2304i		−	1.04271i	−0.853339	−	0.521356i	$-0.825426\pi$
$733$		−	28.2304i		−	1.04271i	0.853339	−	0.521356i	$-0.174574\pi$
$734$	2.50487	+	13.9093i	0.0924566	+	0.513401i
$735$		0			0
$736$	29.8598	−	36.9315i	1.10065	−	1.36131i
$737$	31.4514			1.15853
$738$		0			0
$739$			5.62943i			0.207082i	0.994625	+	0.103541i	$0.0330173\pi$
$739$			5.62943i			0.207082i	−0.994625	+	0.103541i	$0.966983\pi$
$740$	4.22071	+	11.3385i	0.155156	+	0.416813i
$741$		0			0
$742$		0			0
$743$			3.58126i			0.131384i	0.997840	+	0.0656918i	$0.0209254\pi$
$743$			3.58126i			0.131384i	−0.997840	+	0.0656918i	$0.979075\pi$
$744$		0			0
$745$		−	24.7270i		−	0.905928i
$746$	1.86320	+	10.3461i	0.0682165	+	0.378799i
$747$		0			0
$748$	6.36502	−	2.36935i	0.232728	−	0.0866320i
$749$		0			0
$750$		0			0
$751$			24.0072i			0.876036i	0.898966	+	0.438018i	$0.144319\pi$
$751$			24.0072i			0.876036i	−0.898966	+	0.438018i	$0.855681\pi$
$752$	24.8771	−	21.5000i	0.907176	−	0.784023i
$753$		0			0
$754$	31.1385	−	5.60762i	1.13400	−	0.204217i
$755$	1.40007			0.0509539
$756$		0			0
$757$	−33.1227			−1.20386			−0.601932	−	0.798548i	$-0.705602\pi$
$757$	−33.1227			−1.20386			−0.601932	+	0.798548i	$0.705602\pi$
$758$	−9.90485	+	1.78373i	−0.359760	+	0.0647879i
$759$		0			0
$760$	−51.7766	+	30.6527i	−1.87814	+	1.11189i
$761$			30.0275i			1.08850i	0.838924	+	0.544249i	$0.183185\pi$
$761$			30.0275i			1.08850i	−0.838924	+	0.544249i	$0.816815\pi$
$762$		0			0
$763$		0			0
$764$	4.89337	+	13.1456i	0.177036	+	0.475590i
$765$		0			0
$766$	−0.402255	−	2.23368i	−0.0145341	−	0.0807060i
$767$		−	2.71260i		−	0.0979464i
$768$		0			0
$769$			10.2525i			0.369715i	0.982765	+	0.184857i	$0.0591823\pi$
$769$			10.2525i			0.369715i	−0.982765	+	0.184857i	$0.940818\pi$
$770$		0			0
$771$		0			0
$772$	33.9264	−	12.6289i	1.22104	−	0.454525i
$773$		−	43.9887i		−	1.58216i	−0.611711	−	0.791082i	$-0.709518\pi$
$773$		−	43.9887i		−	1.58216i	0.611711	−	0.791082i	$-0.290482\pi$
$774$		0			0
$775$	−29.8801			−1.07333
$776$	15.7335	−	9.31450i	0.564798	−	0.334371i
$777$		0			0
$778$	−7.32045	−	40.6496i	−0.262451	−	1.45736i
$779$			8.33061i			0.298475i
$780$		0			0
$781$	−2.17330			−0.0777669
$782$	−3.67811	−	20.4241i	−0.131529	−	0.730366i
$783$		0			0
$784$		0			0
$785$	33.6815			1.20215
$786$		0			0
$787$	−13.2340			−0.471743			−0.235871	−	0.971784i	$-0.575794\pi$
$787$	−13.2340			−0.471743			−0.235871	+	0.971784i	$0.575794\pi$
$788$	−36.0016	+	13.4014i	−1.28250	+	0.477406i
$789$		0			0
$790$	5.76129	+	31.9918i	0.204977	+	1.13822i
$791$		0			0
$792$		0			0
$793$	40.7885			1.44844
$794$	−39.5852	+	7.12875i	−1.40483	+	0.252990i
$795$		0			0
$796$	31.9637	−	11.8983i	1.13292	−	0.421726i
$797$		−	27.3445i		−	0.968592i	−0.874904	−	0.484296i	$-0.839076\pi$
$797$		−	27.3445i		−	0.968592i	0.874904	−	0.484296i	$-0.160924\pi$
$798$		0			0
$799$		−	14.3677i		−	0.508291i
$800$	28.6205	+	23.1402i	1.01189	+	0.818130i
$801$		0			0
$802$	6.31769	+	35.0814i	0.223085	+	1.23877i
$803$	−5.95185			−0.210036
$804$		0			0
$805$		0			0
$806$	−34.1442	+	6.14891i	−1.20268	+	0.216586i
$807$		0			0
$808$	5.96536	−	3.53160i	0.209861	−	0.124241i
$809$	13.5236			0.475463			0.237731	−	0.971331i	$-0.423596\pi$
$809$	13.5236			0.475463			0.237731	+	0.971331i	$0.423596\pi$
$810$		0			0
$811$	41.3899			1.45340			0.726699	−	0.686956i	$-0.241054\pi$
$811$	41.3899			1.45340			0.726699	+	0.686956i	$0.241054\pi$
$812$		0			0
$813$		0			0
$814$	4.82240	−	0.868449i	0.169025	−	0.0304391i
$815$	−22.6149			−0.792164
$816$		0			0
$817$			20.5275i			0.718168i
$818$	−13.7643	+	2.47877i	−0.481259	+	0.0866682i
$819$		0			0
$820$	8.44555	−	3.14381i	0.294931	−	0.109787i
$821$	23.9567			0.836095			0.418048	−	0.908425i	$-0.362714\pi$
$821$	23.9567			0.836095			0.418048	+	0.908425i	$0.362714\pi$
$822$		0			0
$823$		−	39.8179i		−	1.38797i	−0.719991	−	0.693983i	$-0.755854\pi$
$823$		−	39.8179i		−	1.38797i	0.719991	−	0.693983i	$-0.244146\pi$
$824$	11.2354	+	18.9781i	0.391402	+	0.661132i
$825$		0			0
$826$		0			0
$827$		−	30.8244i		−	1.07187i	−0.844259	−	0.535935i	$-0.819959\pi$
$827$		−	30.8244i		−	1.07187i	0.844259	−	0.535935i	$-0.180041\pi$
$828$		0			0
$829$			31.7804i			1.10378i	0.833917	+	0.551890i	$0.186093\pi$
$829$			31.7804i			1.10378i	−0.833917	+	0.551890i	$0.813907\pi$
$830$	25.4747	−	4.58765i	0.884241	−	0.159240i
$831$		0			0
$832$	37.4668	+	20.5528i	1.29893	+	0.712539i
$833$		0			0
$834$		0			0
$835$			22.0021i			0.761416i
$836$	8.50133	+	22.8380i	0.294025	+	0.789868i
$837$		0			0
$838$	−8.74447	−	48.5571i	−0.302073	−	1.67738i
$839$	−25.7224			−0.888036			−0.444018	−	0.896018i	$-0.646447\pi$
$839$	−25.7224			−0.888036			−0.444018	+	0.896018i	$0.646447\pi$
$840$		0			0
$841$	−11.4586			−0.395125
$842$	0.699763	+	3.88571i	0.0241154	+	0.133910i
$843$		0			0
$844$	14.6126	+	39.2554i	0.502987	+	1.35123i
$845$		−	52.6927i		−	1.81268i
$846$		0			0
$847$		0			0
$848$	35.9127	−	31.0374i	1.23325	−	1.06583i
$849$		0			0
$850$	15.8280	−	2.85040i	0.542894	−	0.0977679i
$851$		−	14.9723i		−	0.513245i
$852$		0			0
$853$			49.7192i			1.70235i	0.524880	+	0.851177i	$0.324110\pi$
$853$			49.7192i			1.70235i	−0.524880	+	0.851177i	$0.675890\pi$
$854$		0			0
$855$		0			0
$856$	23.1276	−	13.6920i	0.790486	−	0.467982i
$857$			49.9604i			1.70661i	0.521408	+	0.853307i	$0.325407\pi$
$857$			49.9604i			1.70661i	−0.521408	+	0.853307i	$0.674593\pi$
$858$		0			0
$859$	−15.5401			−0.530221			−0.265110	−	0.964218i	$-0.585408\pi$
$859$	−15.5401			−0.530221			−0.265110	+	0.964218i	$0.585408\pi$
$860$	20.8108	−	7.74671i	0.709641	−	0.264161i
$861$		0			0
$862$	6.35550	−	1.14454i	0.216469	−	0.0389832i
$863$		−	1.17256i		−	0.0399143i	−0.999801	−	0.0199571i	$-0.993647\pi$
$863$		−	1.17256i		−	0.0399143i	0.999801	−	0.0199571i	$-0.00635297\pi$
$864$		0			0
$865$	21.2134			0.721276
$866$	−50.6160	+	9.11525i	−1.72000	+	0.309749i
$867$		0			0
$868$		0			0
$869$	13.1652			0.446599
$870$		0			0
$871$	86.4732			2.93003
$872$	12.8302	+	21.6720i	0.434486	+	0.733906i
$873$		0			0
$874$	73.2827	−	13.1972i	2.47882	−	0.446402i
$875$		0			0
$876$		0			0
$877$	−6.53264			−0.220592			−0.110296	−	0.993899i	$-0.535180\pi$
$877$	−6.53264			−0.220592			−0.110296	+	0.993899i	$0.535180\pi$
$878$	−3.17665	−	17.6396i	−0.107207	−	0.595307i
$879$		0			0
$880$	19.9449	−	17.2373i	0.672341	−	0.581068i
$881$		−	47.3252i		−	1.59442i	−0.603699	−	0.797212i	$-0.706307\pi$
$881$		−	47.3252i		−	1.59442i	0.603699	−	0.797212i	$-0.293693\pi$
$882$		0			0
$883$		−	12.5720i		−	0.423081i	−0.977369	−	0.211541i	$-0.932152\pi$
$883$		−	12.5720i		−	0.423081i	0.977369	−	0.211541i	$-0.0678481\pi$
$884$	17.5001	−	6.51433i	0.588593	−	0.219101i
$885$		0			0
$886$	−16.5524	+	2.98087i	−0.556090	+	0.100144i
$887$	34.5685			1.16070			0.580348	−	0.814369i	$-0.302917\pi$
$887$	34.5685			1.16070			0.580348	+	0.814369i	$0.302917\pi$
$888$		0			0
$889$		0			0
$890$	8.59238	+	47.7125i	0.288017	+	1.59933i
$891$		0			0
$892$	−28.5108	+	10.6130i	−0.954613	+	0.355350i
$893$	51.5518			1.72511
$894$		0			0
$895$	−8.22638			−0.274978
$896$		0			0
$897$		0			0
$898$	4.42419	+	24.5671i	0.147637	+	0.819813i
$899$	−19.2346			−0.641510
$900$		0			0
$901$		−	20.7412i		−	0.690989i
$902$	−0.646868	−	3.59199i	−0.0215384	−	0.119600i
$903$		0			0
$904$	−0.720447	−	1.21693i	−0.0239617	−	0.0404746i
$905$	−27.7860			−0.923637
$906$		0			0
$907$			29.6575i			0.984761i	0.870380	+	0.492380i	$0.163873\pi$
$907$			29.6575i			0.984761i	−0.870380	+	0.492380i	$0.836127\pi$
$908$	0.788173	−	0.293393i	0.0261564	−	0.00973660i
$909$		0			0
$910$		0			0
$911$			41.3321i			1.36939i	0.728828	+	0.684697i	$0.240066\pi$
$911$			41.3321i			1.36939i	−0.728828	+	0.684697i	$0.759934\pi$
$912$		0			0
$913$		−	10.4833i		−	0.346947i
$914$	5.05603	+	28.0756i	0.167239	+	0.928658i
$915$		0			0
$916$	−17.9556	−	48.2359i	−0.593268	−	1.59376i
$917$		0			0
$918$		0			0
$919$		−	18.5693i		−	0.612546i	−0.951944	−	0.306273i	$-0.900918\pi$
$919$		−	18.5693i		−	0.612546i	0.951944	−	0.306273i	$-0.0990820\pi$
$920$	−41.0348	−	69.3134i	−1.35288	−	2.28520i
$921$		0			0
$922$	−20.1457	+	3.62796i	−0.663462	+	0.119480i
$923$	−5.97532			−0.196680
$924$		0			0
$925$	11.6030			0.381504
$926$	25.5064	−	4.59335i	0.838191	−	0.150947i
$927$		0			0
$928$	18.4238	+	14.8959i	0.604790	+	0.488983i
$929$			54.4539i			1.78657i	0.449487	+	0.893287i	$0.351607\pi$
$929$			54.4539i			1.78657i	−0.449487	+	0.893287i	$0.648393\pi$
$930$		0			0
$931$		0			0
$932$	22.1978	−	8.26303i	0.727114	−	0.270665i
$933$		0			0
$934$	−3.82783	−	21.2555i	−0.125250	−	0.695502i
$935$		−	11.5190i		−	0.376713i
$936$		0			0
$937$			8.99502i			0.293854i	0.989147	+	0.146927i	$0.0469383\pi$
$937$			8.99502i			0.293854i	−0.989147	+	0.146927i	$0.953062\pi$
$938$		0			0
$939$		0			0
$940$	−19.4547	−	52.2631i	−0.634541	−	1.70463i
$941$			20.1241i			0.656027i	0.944673	+	0.328014i	$0.106379\pi$
$941$			20.1241i			0.656027i	−0.944673	+	0.328014i	$0.893621\pi$
$942$		0			0
$943$	−11.1522			−0.363165
$944$	1.53684	−	1.32821i	0.0500198	−	0.0432294i
$945$		0			0
$946$	−1.59395	−	8.85106i	−0.0518239	−	0.287773i
$947$			16.4190i			0.533546i	0.963759	+	0.266773i	$0.0859574\pi$
$947$			16.4190i			0.533546i	−0.963759	+	0.266773i	$0.914043\pi$
$948$		0			0
$949$	−16.3641			−0.531202
$950$	10.2274	+	56.7914i	0.331819	+	1.84256i
$951$		0			0
$952$		0			0
$953$	34.1899			1.10752			0.553760	−	0.832677i	$-0.313193\pi$
$953$	34.1899			1.10752			0.553760	+	0.832677i	$0.313193\pi$
$954$		0			0
$955$	23.7901			0.769828
$956$	5.66061	+	15.2067i	0.183077	+	0.491819i
$957$		0			0
$958$	−9.16864	−	50.9125i	−0.296225	−	1.64491i
$959$		0			0
$960$		0			0
$961$	−9.90874			−0.319637
$962$	13.2588	−	2.38773i	0.427481	−	0.0769836i
$963$		0			0
$964$	2.29383	+	6.16214i	0.0738792	+	0.198469i
$965$		−	61.3979i		−	1.97647i
$966$		0			0
$967$		−	36.7457i		−	1.18166i	−0.806795	−	0.590831i	$-0.798800\pi$
$967$		−	36.7457i		−	1.18166i	0.806795	−	0.590831i	$-0.201200\pi$
$968$	10.4110	+	17.5856i	0.334622	+	0.565222i
$969$		0			0
$970$	−5.49613	−	30.5194i	−0.176470	−	0.979919i
$971$	−45.7602			−1.46851			−0.734257	−	0.678872i	$-0.762469\pi$
$971$	−45.7602			−1.46851			−0.734257	+	0.678872i	$0.762469\pi$
$972$		0			0
$973$		0			0
$974$	−30.0226	+	5.40666i	−0.961985	+	0.173240i
$975$		0			0
$976$	19.9718	+	23.1089i	0.639282	+	0.739699i
$977$	−42.3974			−1.35641			−0.678206	−	0.734872i	$-0.737242\pi$
$977$	−42.3974			−1.35641			−0.678206	+	0.734872i	$0.737242\pi$
$978$		0			0
$979$	19.6346			0.627523
$980$		0			0
$981$		0			0
$982$	26.7626	−	4.81959i	0.854030	−	0.153799i
$983$	32.2906			1.02991			0.514955	−	0.857217i	$-0.327809\pi$
$983$	32.2906			1.02991			0.514955	+	0.857217i	$0.327809\pi$
$984$		0			0
$985$			65.1535i			2.07596i
$986$	10.1888	−	1.83487i	0.324479	−	0.0584343i
$987$		0			0
$988$	23.3737	+	62.7912i	0.743617	+	1.99765i
$989$	−27.4802			−0.873821
$990$		0			0
$991$		−	33.9150i		−	1.07735i	−0.842515	−	0.538673i	$-0.818926\pi$
$991$		−	33.9150i		−	1.07735i	0.842515	−	0.538673i	$-0.181074\pi$
$992$	−20.2022	−	16.3338i	−0.641419	−	0.518599i
$993$		0			0
$994$		0			0
$995$		−	57.8461i		−	1.83384i
$996$		0			0
$997$		−	39.0420i		−	1.23647i	−0.785992	−	0.618236i	$-0.787848\pi$
$997$		−	39.0420i		−	1.23647i	0.785992	−	0.618236i	$-0.212152\pi$
$998$	−10.6587	+	1.91949i	−0.337396	+	0.0607603i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.b.m.1567.7		12
3.2	odd	2		588.2.b.d.391.6	yes	12
4.3	odd	2		1764.2.b.l.1567.8		12
7.6	odd	2		1764.2.b.l.1567.7		12
12.11	even	2		588.2.b.c.391.5	✓	12
21.2	odd	6		588.2.o.e.31.10		24
21.5	even	6		588.2.o.f.31.10		24
21.11	odd	6		588.2.o.e.19.2		24
21.17	even	6		588.2.o.f.19.2		24
21.20	even	2		588.2.b.c.391.6	yes	12
28.27	even	2	inner	1764.2.b.m.1567.8		12
84.11	even	6		588.2.o.f.19.10		24
84.23	even	6		588.2.o.f.31.2		24
84.47	odd	6		588.2.o.e.31.2		24
84.59	odd	6		588.2.o.e.19.10		24
84.83	odd	2		588.2.b.d.391.5	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.b.c.391.5	✓	12	12.11	even	2
588.2.b.c.391.6	yes	12	21.20	even	2
588.2.b.d.391.5	yes	12	84.83	odd	2
588.2.b.d.391.6	yes	12	3.2	odd	2
588.2.o.e.19.2		24	21.11	odd	6
588.2.o.e.19.10		24	84.59	odd	6
588.2.o.e.31.2		24	84.47	odd	6
588.2.o.e.31.10		24	21.2	odd	6
588.2.o.f.19.2		24	21.17	even	6
588.2.o.f.19.10		24	84.11	even	6
588.2.o.f.31.2		24	84.23	even	6
588.2.o.f.31.10		24	21.5	even	6
1764.2.b.l.1567.7		12	7.6	odd	2
1764.2.b.l.1567.8		12	4.3	odd	2
1764.2.b.m.1567.7		12	1.1	even	1	trivial
1764.2.b.m.1567.8		12	28.27	even	2	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:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.250649 - 1.39182i) q^{2} +(-1.87435 + 0.697718i) q^{4} +3.39209i q^{5} +(1.44090 + 2.43388i) q^{8} +O(q^{10})\)	\(q+(-0.250649 - 1.39182i) q^{2} +(-1.87435 + 0.697718i) q^{4} +3.39209i q^{5} +(1.44090 + 2.43388i) q^{8} +(4.72119 - 0.850222i) q^{10} -1.94285i q^{11} -5.34172i q^{13} +(3.02638 - 2.61554i) q^{16} -1.74787i q^{17} +6.27143 q^{19} +(-2.36672 - 6.35796i) q^{20} +(-2.70411 + 0.486974i) q^{22} +8.39557i q^{23} -6.50626 q^{25} +(-7.43474 + 1.33890i) q^{26} -4.18824 q^{29} +4.59252 q^{31} +(-4.39892 - 3.55661i) q^{32} +(-2.43273 + 0.438101i) q^{34} -1.78336 q^{37} +(-1.57193 - 8.72873i) q^{38} +(-8.25595 + 4.88767i) q^{40} +1.32834i q^{41} +3.27318i q^{43} +(1.35556 + 3.64159i) q^{44} +(11.6852 - 2.10434i) q^{46} +8.22010 q^{47} +(1.63079 + 9.05557i) q^{50} +(3.72702 + 10.0123i) q^{52} +11.8665 q^{53} +6.59033 q^{55} +(1.04978 + 5.82930i) q^{58} +0.507814 q^{59} +7.63584i q^{61} +(-1.15111 - 6.39198i) q^{62} +(-3.84759 + 7.01399i) q^{64} +18.1196 q^{65} +16.1883i q^{67} +(1.21952 + 3.27612i) q^{68} -1.11861i q^{71} -3.06345i q^{73} +(0.446997 + 2.48212i) q^{74} +(-11.7549 + 4.37569i) q^{76} +6.77621i q^{79} +(8.87213 + 10.2657i) q^{80} +(1.84882 - 0.332947i) q^{82} +5.39583 q^{83} +5.92893 q^{85} +(4.55570 - 0.820419i) q^{86} +(4.72869 - 2.79947i) q^{88} +10.1060i q^{89} +(-5.85774 - 15.7362i) q^{92} +(-2.06036 - 11.4409i) q^{94} +21.2732i q^{95} -6.46434i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} - 4 q^{4} - 4 q^{8}+O(q^{10}) \) 12 * q - 4 * q^2 - 4 * q^4 - 4 * q^8	\( 12 q - 4 q^{2} - 4 q^{4} - 4 q^{8} - 4 q^{16} + 24 q^{20} - 12 q^{25} - 24 q^{26} - 32 q^{29} + 16 q^{31} - 4 q^{32} + 32 q^{34} + 32 q^{37} + 24 q^{38} - 32 q^{40} + 24 q^{44} + 24 q^{46} + 28 q^{50} + 32 q^{52} + 32 q^{53} + 16 q^{55} + 16 q^{58} + 16 q^{59} - 8 q^{62} - 4 q^{64} + 8 q^{68} + 32 q^{74} - 32 q^{76} + 16 q^{80} + 32 q^{82} + 16 q^{83} + 16 q^{85} + 24 q^{86} + 24 q^{88}+O(q^{100}) \) 12 * q - 4 * q^2 - 4 * q^4 - 4 * q^8 - 4 * q^16 + 24 * q^20 - 12 * q^25 - 24 * q^26 - 32 * q^29 + 16 * q^31 - 4 * q^32 + 32 * q^34 + 32 * q^37 + 24 * q^38 - 32 * q^40 + 24 * q^44 + 24 * q^46 + 28 * q^50 + 32 * q^52 + 32 * q^53 + 16 * q^55 + 16 * q^58 + 16 * q^59 - 8 * q^62 - 4 * q^64 + 8 * q^68 + 32 * q^74 - 32 * q^76 + 16 * q^80 + 32 * q^82 + 16 * q^83 + 16 * q^85 + 24 * q^86 + 24 * q^88

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