LMFDB - Embedded newform 225.2.h.e.46.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(46,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("225.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.h (of order $5$, 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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	16.0.1130304400000000000000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5x^{14} + 5x^{12} - 10x^{10} + 205x^{8} - 700x^{6} + 1250x^{4} - 1250x^{2} + 625 $ x^16 - 5x^14 + 5x^12 - 10x^10 + 205x^8 - 700x^6 + 1250x^4 - 1250*x^2 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			46.4
Root			$-1.85090 + 0.438393i$ of defining polynomial
Character	$\chi$	$=$	225.46
Dual form			225.2.h.e.181.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.670386 - 2.06324i) q^{2} +(-2.18949 - 1.59076i) q^{4} +(-1.69588 - 1.45739i) q^{5} -3.32440 q^{7} +(-1.23973 + 0.900718i) q^{8} +O(q^{10})$	\(q+(0.670386 - 2.06324i) q^{2} +(-2.18949 - 1.59076i) q^{4} +(-1.69588 - 1.45739i) q^{5} -3.32440 q^{7} +(-1.23973 + 0.900718i) q^{8} +(-4.14384 + 2.52199i) q^{10} +(1.18052 - 3.63326i) q^{11} +(0.819443 + 2.52199i) q^{13} +(-2.22863 + 6.85902i) q^{14} +(-0.645329 - 1.98612i) q^{16} +(3.82870 - 2.78171i) q^{17} +(2.95435 - 2.14646i) q^{19} +(1.39476 + 5.88869i) q^{20} +(-6.70487 - 4.87137i) q^{22} +(-1.11807 + 3.44107i) q^{23} +(0.752016 + 4.94312i) q^{25} +5.75280 q^{26} +(7.27874 + 5.28832i) q^{28} +(0.0281335 + 0.0204402i) q^{29} +(8.17609 - 5.94028i) q^{31} -7.59524 q^{32} +(-3.17262 - 9.76433i) q^{34} +(5.63778 + 4.84495i) q^{35} +(3.23366 + 9.95217i) q^{37} +(-2.44810 - 7.53447i) q^{38} +(3.41514 + 0.279266i) q^{40} +(-0.589966 - 1.81573i) q^{41} -2.27279 q^{43} +(-8.36438 + 6.07708i) q^{44} +(6.35020 + 4.61369i) q^{46} +(1.19421 + 0.867645i) q^{47} +4.05161 q^{49} +(10.7030 + 1.76221i) q^{50} +(2.21771 - 6.82541i) q^{52} +(-7.22046 - 5.24597i) q^{53} +(-7.29710 + 4.44110i) q^{55} +(4.12136 - 2.99434i) q^{56} +(0.0610333 - 0.0443433i) q^{58} +(-3.83193 - 11.7935i) q^{59} +(-1.59967 + 4.92329i) q^{61} +(-6.77506 - 20.8515i) q^{62} +(-3.80108 + 11.6985i) q^{64} +(2.28585 - 5.47123i) q^{65} +(4.39437 - 3.19269i) q^{67} -12.8079 q^{68} +(13.7758 - 8.38408i) q^{70} +(9.80619 + 7.12462i) q^{71} +(3.78817 - 11.6588i) q^{73} +22.7015 q^{74} -9.88302 q^{76} +(-3.92451 + 12.0784i) q^{77} +(5.86453 + 4.26083i) q^{79} +(-1.80015 + 4.30871i) q^{80} -4.14178 q^{82} +(-4.55307 + 3.30800i) q^{83} +(-10.5471 - 0.862466i) q^{85} +(-1.52364 + 4.68930i) q^{86} +(1.80902 + 5.56758i) q^{88} +(-5.50537 + 16.9438i) q^{89} +(-2.72415 - 8.38408i) q^{91} +(7.92192 - 5.75562i) q^{92} +(2.59074 - 1.88228i) q^{94} +(-8.13845 - 0.665506i) q^{95} +(6.69686 + 4.86555i) q^{97} +(2.71614 - 8.35943i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{4}+O(q^{10}) $ 16 * q - 2 * q^4	$ 16 q - 2 q^{4} + 14 q^{16} + 14 q^{19} - 30 q^{22} + 10 q^{25} + 30 q^{28} + 18 q^{31} - 20 q^{34} + 10 q^{37} - 10 q^{40} - 80 q^{43} - 32 q^{49} - 40 q^{52} - 70 q^{55} - 10 q^{58} + 32 q^{61} - 8 q^{64} - 40 q^{67} + 50 q^{70} + 60 q^{73} - 88 q^{76} + 36 q^{79} + 120 q^{82} + 20 q^{88} + 30 q^{91} + 30 q^{94} + 40 q^{97}+O(q^{100}) $ 16 * q - 2 * q^4 + 14 * q^16 + 14 * q^19 - 30 * q^22 + 10 * q^25 + 30 * q^28 + 18 * q^31 - 20 * q^34 + 10 * q^37 - 10 * q^40 - 80 * q^43 - 32 * q^49 - 40 * q^52 - 70 * q^55 - 10 * q^58 + 32 * q^61 - 8 * q^64 - 40 * q^67 + 50 * q^70 + 60 * q^73 - 88 * q^76 + 36 * q^79 + 120 * q^82 + 20 * q^88 + 30 * q^91 + 30 * q^94 + 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.670386	−	2.06324i	0.474035	−	1.45893i	−0.373221	−	0.927743i	$-0.621747\pi$
$2$	0.670386	−	2.06324i	0.474035	−	1.45893i	0.847255	−	0.531186i	$-0.178253\pi$
$3$		0			0
$3$		0			0
$4$	−2.18949	−	1.59076i	−1.09475	−	0.795380i
$5$	−1.69588	−	1.45739i	−0.758420	−	0.651766i
$5$	−1.69588	−	1.45739i	−0.758420	−	0.651766i
$6$		0			0
$7$	−3.32440			−1.25650			−0.628252	−	0.778010i	$-0.716229\pi$
$7$	−3.32440			−1.25650			−0.628252	+	0.778010i	$0.716229\pi$
$8$	−1.23973	+	0.900718i	−0.438311	+	0.318452i
$9$		0			0
$10$	−4.14384	+	2.52199i	−1.31040	+	0.797522i
$11$	1.18052	−	3.63326i	0.355940	−	1.09547i	−0.599523	−	0.800357i	$-0.704643\pi$
$11$	1.18052	−	3.63326i	0.355940	−	1.09547i	0.955463	−	0.295112i	$-0.0953569\pi$
$12$		0			0
$13$	0.819443	+	2.52199i	0.227273	+	0.699473i	0.998053	+	0.0623720i	$0.0198665\pi$
$13$	0.819443	+	2.52199i	0.227273	+	0.699473i	−0.770780	+	0.637101i	$0.780133\pi$
$14$	−2.22863	+	6.85902i	−0.595626	+	1.83315i
$15$		0			0
$16$	−0.645329	−	1.98612i	−0.161332	−	0.496530i
$17$	3.82870	−	2.78171i	0.928596	−	0.674664i	−0.0170528	−	0.999855i	$-0.505428\pi$
$17$	3.82870	−	2.78171i	0.928596	−	0.674664i	0.945649	+	0.325190i	$0.105428\pi$
$18$		0			0
$19$	2.95435	−	2.14646i	0.677773	−	0.492431i	−0.194845	−	0.980834i	$-0.562420\pi$
$19$	2.95435	−	2.14646i	0.677773	−	0.492431i	0.872618	+	0.488403i	$0.162420\pi$
$20$	1.39476	+	5.88869i	0.311877	+	1.31675i
$21$		0			0
$22$	−6.70487	−	4.87137i	−1.42948	−	1.03858i
$23$	−1.11807	+	3.44107i	−0.233134	+	0.717513i	0.764229	+	0.644944i	$0.223120\pi$
$23$	−1.11807	+	3.44107i	−0.233134	+	0.717513i	−0.997363	+	0.0725682i	$0.976880\pi$
$24$		0			0
$25$	0.752016	+	4.94312i	0.150403	+	0.988625i
$26$	5.75280			1.12822
$27$		0			0
$28$	7.27874	+	5.28832i	1.37555	+	0.999398i
$29$	0.0281335	+	0.0204402i	0.00522426	+	0.00379565i	0.590394	−	0.807115i	$-0.298972\pi$
$29$	0.0281335	+	0.0204402i	0.00522426	+	0.00379565i	−0.585170	+	0.810911i	$0.698972\pi$
$30$		0			0
$31$	8.17609	−	5.94028i	1.46847	−	1.06690i	0.487415	−	0.873171i	$-0.337940\pi$
$31$	8.17609	−	5.94028i	1.46847	−	1.06690i	0.981054	−	0.193734i	$-0.0620599\pi$
$32$	−7.59524			−1.34266
$33$		0			0
$34$	−3.17262	−	9.76433i	−0.544100	−	1.67457i
$35$	5.63778	+	4.84495i	0.952958	+	0.818946i
$36$		0			0
$37$	3.23366	+	9.95217i	0.531610	+	1.63613i	0.750862	+	0.660459i	$0.229638\pi$
$37$	3.23366	+	9.95217i	0.531610	+	1.63613i	−0.219252	+	0.975668i	$0.570362\pi$
$38$	−2.44810	−	7.53447i	−0.397134	−	1.22225i
$39$		0			0
$40$	3.41514	+	0.279266i	0.539980	+	0.0441559i
$41$	−0.589966	−	1.81573i	−0.0921371	−	0.283569i	0.894360	−	0.447348i	$-0.147632\pi$
$41$	−0.589966	−	1.81573i	−0.0921371	−	0.283569i	−0.986497	+	0.163779i	$0.947632\pi$
$42$		0			0
$43$	−2.27279			−0.346597			−0.173298	−	0.984869i	$-0.555442\pi$
$43$	−2.27279			−0.346597			−0.173298	+	0.984869i	$0.555442\pi$
$44$	−8.36438	+	6.07708i	−1.26098	+	0.916154i
$45$		0			0
$46$	6.35020	+	4.61369i	0.936286	+	0.680252i
$47$	1.19421	+	0.867645i	0.174194	+	0.126559i	0.671466	−	0.741036i	$-0.265665\pi$
$47$	1.19421	+	0.867645i	0.174194	+	0.126559i	−0.497272	+	0.867595i	$0.665665\pi$
$48$		0			0
$49$	4.05161			0.578801
$50$	10.7030	+	1.76221i	1.51363	+	0.249215i
$51$		0			0
$52$	2.21771	−	6.82541i	0.307541	−	0.946513i
$53$	−7.22046	−	5.24597i	−0.991806	−	0.720589i	−0.0314903	−	0.999504i	$-0.510025\pi$
$53$	−7.22046	−	5.24597i	−0.991806	−	0.720589i	−0.960316	+	0.278915i	$0.910025\pi$
$54$		0			0
$55$	−7.29710	+	4.44110i	−0.983941	+	0.598837i
$56$	4.12136	−	2.99434i	0.550740	−	0.400136i
$57$		0			0
$58$	0.0610333	−	0.0443433i	0.00801406	−	0.00582256i
$59$	−3.83193	−	11.7935i	−0.498875	−	1.53538i	−0.810830	−	0.585282i	$-0.800984\pi$
$59$	−3.83193	−	11.7935i	−0.498875	−	1.53538i	0.311955	−	0.950097i	$-0.399016\pi$
$60$		0			0
$61$	−1.59967	+	4.92329i	−0.204817	+	0.630363i	0.794903	+	0.606736i	$0.207521\pi$
$61$	−1.59967	+	4.92329i	−0.204817	+	0.630363i	−0.999721	+	0.0236271i	$0.992479\pi$
$62$	−6.77506	−	20.8515i	−0.860433	−	2.64814i
$63$		0			0
$64$	−3.80108	+	11.6985i	−0.475135	+	1.46232i
$65$	2.28585	−	5.47123i	0.283524	−	0.678623i
$66$		0			0
$67$	4.39437	−	3.19269i	0.536857	−	0.390050i	−0.286059	−	0.958212i	$-0.592345\pi$
$67$	4.39437	−	3.19269i	0.536857	−	0.390050i	0.822916	+	0.568162i	$0.192345\pi$
$68$	−12.8079			−1.55319
$69$		0			0
$70$	13.7758	−	8.38408i	1.64652	−	1.00209i
$71$	9.80619	+	7.12462i	1.16378	+	0.845536i	0.990251	−	0.139292i	$-0.0444828\pi$
$71$	9.80619	+	7.12462i	1.16378	+	0.845536i	0.173530	+	0.984829i	$0.444483\pi$
$72$		0			0
$73$	3.78817	−	11.6588i	0.443371	−	1.36456i	−0.440889	−	0.897562i	$-0.645337\pi$
$73$	3.78817	−	11.6588i	0.443371	−	1.36456i	0.884260	−	0.466995i	$-0.154663\pi$
$74$	22.7015			2.63899
$75$		0			0
$76$	−9.88302			−1.13366
$77$	−3.92451	+	12.0784i	−0.447239	+	1.37646i
$78$		0			0
$79$	5.86453	+	4.26083i	0.659811	+	0.479381i	0.866599	−	0.499005i	$-0.166301\pi$
$79$	5.86453	+	4.26083i	0.659811	+	0.479381i	−0.206788	+	0.978386i	$0.566301\pi$
$80$	−1.80015	+	4.30871i	−0.201263	+	0.481729i
$81$		0			0
$82$	−4.14178			−0.457383
$83$	−4.55307	+	3.30800i	−0.499764	+	0.363100i	−0.808927	−	0.587909i	$-0.799951\pi$
$83$	−4.55307	+	3.30800i	−0.499764	+	0.363100i	0.309163	+	0.951009i	$0.399951\pi$
$84$		0			0
$85$	−10.5471	−	0.862466i	−1.14399	−	0.0935475i
$86$	−1.52364	+	4.68930i	−0.164299	+	0.505660i
$87$		0			0
$88$	1.80902	+	5.56758i	0.192842	+	0.593506i
$89$	−5.50537	+	16.9438i	−0.583568	+	1.79604i	0.0213784	+	0.999771i	$0.493195\pi$
$89$	−5.50537	+	16.9438i	−0.583568	+	1.79604i	−0.604946	+	0.796266i	$0.706805\pi$
$90$		0			0
$91$	−2.72415	−	8.38408i	−0.285569	−	0.878890i
$92$	7.92192	−	5.75562i	0.825918	−	0.600064i
$93$		0			0
$94$	2.59074	−	1.88228i	0.267214	−	0.194143i
$95$	−8.13845	−	0.665506i	−0.834987	−	0.0682795i
$96$		0			0
$97$	6.69686	+	4.86555i	0.679963	+	0.494022i	0.873345	−	0.487102i	$-0.161946\pi$
$97$	6.69686	+	4.86555i	0.679963	+	0.494022i	−0.193383	+	0.981123i	$0.561946\pi$
$98$	2.71614	−	8.35943i	0.274372	−	0.844430i
$99$		0			0
$100$	6.21679	−	12.0192i	0.621679	−	1.20192i
$101$	−3.57692			−0.355916			−0.177958	−	0.984038i	$-0.556949\pi$
$101$	−3.57692			−0.355916			−0.177958	+	0.984038i	$0.556949\pi$
$102$		0			0
$103$	−10.0800	−	7.32352i	−0.993208	−	0.721608i	−0.0325865	−	0.999469i	$-0.510374\pi$
$103$	−10.0800	−	7.32352i	−0.993208	−	0.721608i	−0.960621	+	0.277861i	$0.910374\pi$
$104$	−3.28749	−	2.38850i	−0.322365	−	0.234212i
$105$		0			0
$106$	−15.6642	+	11.3807i	−1.52144	+	1.10539i
$107$	0.574861			0.0555740			0.0277870	−	0.999614i	$-0.491154\pi$
$107$	0.574861			0.0555740			0.0277870	+	0.999614i	$0.491154\pi$
$108$		0			0
$109$	3.50801	+	10.7966i	0.336007	+	1.03412i	0.966224	+	0.257704i	$0.0829659\pi$
$109$	3.50801	+	10.7966i	0.336007	+	1.03412i	−0.630217	+	0.776419i	$0.717034\pi$
$110$	4.27115	+	18.0329i	0.407239	+	1.71937i
$111$		0			0
$112$	2.14533	+	6.60264i	0.202715	+	0.623891i
$113$	5.33988	+	16.4345i	0.502334	+	1.54603i	0.805207	+	0.592994i	$0.202054\pi$
$113$	5.33988	+	16.4345i	0.502334	+	1.54603i	−0.302873	+	0.953031i	$0.597946\pi$
$114$		0			0
$115$	6.91110	−	4.20617i	0.644464	−	0.392228i
$116$	−0.0290827	−	0.0895073i	−0.00270026	−	0.00831055i
$117$		0			0
$118$	−26.9016			−2.47649
$119$	−12.7281	+	9.24751i	−1.16678	+	0.847718i
$120$		0			0
$121$	−2.90777	−	2.11262i	−0.264343	−	0.192056i
$122$	9.08552	+	6.60101i	0.822564	+	0.597628i
$123$		0			0
$124$	−27.3510			−2.45620
$125$	5.92874	−	9.47893i	0.530283	−	0.847821i
$126$		0			0
$127$	−2.93011	+	9.01796i	−0.260005	+	0.800214i	0.732797	+	0.680448i	$0.238215\pi$
$127$	−2.93011	+	9.01796i	−0.260005	+	0.800214i	−0.992802	+	0.119767i	$0.961785\pi$
$128$	9.29929	+	6.75633i	0.821949	+	0.597181i
$129$		0			0
$130$	−9.75605	−	8.38408i	−0.855662	−	0.735332i
$131$	7.79027	−	5.65996i	0.680639	−	0.494513i	−0.192931	−	0.981212i	$-0.561799\pi$
$131$	7.79027	−	5.65996i	0.680639	−	0.494513i	0.873570	+	0.486699i	$0.161799\pi$
$132$		0			0
$133$	−9.82142	+	7.13568i	−0.851625	+	0.618742i
$134$	−3.64136	−	11.2070i	−0.314566	−	0.968133i
$135$		0			0
$136$	−2.24102	+	6.89715i	−0.192166	+	0.591426i
$137$	−0.440172	−	1.35471i	−0.0376064	−	0.115741i	0.930491	−	0.366315i	$-0.119381\pi$
$137$	−0.440172	−	1.35471i	−0.0376064	−	0.115741i	−0.968097	+	0.250574i	$0.919381\pi$
$138$		0			0
$139$	−0.508854	+	1.56609i	−0.0431605	+	0.132834i	−0.970315	−	0.241845i	$-0.922247\pi$
$139$	−0.508854	+	1.56609i	−0.0431605	+	0.132834i	0.927154	+	0.374680i	$0.122247\pi$
$140$	−4.63672	−	19.5763i	−0.391874	−	1.65450i
$141$		0			0
$142$	21.2737	−	15.4562i	1.78525	−	1.29706i
$143$	10.1304			0.847146
$144$		0			0
$145$	−0.0179217	−	0.0756657i	−0.00148831	−	0.00628369i
$146$	−21.5153	−	15.6318i	−1.78062	−	1.29369i
$147$		0			0
$148$	8.75145	−	26.9342i	0.719365	−	2.21398i
$149$	9.87569			0.809048			0.404524	−	0.914527i	$-0.367437\pi$
$149$	9.87569			0.809048			0.404524	+	0.914527i	$0.367437\pi$
$150$		0			0
$151$	−11.6003			−0.944021			−0.472011	−	0.881593i	$-0.656472\pi$
$151$	−11.6003			−0.944021			−0.472011	+	0.881593i	$0.656472\pi$
$152$	−1.72924	+	5.32206i	−0.140260	+	0.431676i
$153$		0			0
$154$	22.2897	+	16.1944i	1.79615	+	1.30498i
$155$	−22.5230	−	1.84177i	−1.80909	−	0.147935i
$156$		0			0
$157$	5.64993			0.450914			0.225457	−	0.974253i	$-0.427613\pi$
$157$	5.64993			0.450914			0.225457	+	0.974253i	$0.427613\pi$
$158$	12.7226	−	9.24351i	1.01216	−	0.735374i
$159$		0			0
$160$	12.8806	+	11.0692i	1.01830	+	0.875100i
$161$	3.71691	−	11.4395i	0.292934	−	0.901557i
$162$		0			0
$163$	−3.75451	−	11.5552i	−0.294076	−	0.905072i	−0.983530	−	0.180743i	$-0.942150\pi$
$163$	−3.75451	−	11.5552i	−0.294076	−	0.905072i	0.689455	−	0.724329i	$-0.257850\pi$
$164$	−1.59666	+	4.91402i	−0.124678	+	0.383720i
$165$		0			0
$166$	3.77287	+	11.6117i	0.292831	+	0.901242i
$167$	7.99263	−	5.80699i	0.618488	−	0.449358i	−0.233905	−	0.972260i	$-0.575150\pi$
$167$	7.99263	−	5.80699i	0.618488	−	0.449358i	0.852393	+	0.522901i	$0.175150\pi$
$168$		0			0
$169$	4.82830	−	3.50796i	0.371407	−	0.269843i
$170$	−8.85007	+	21.1829i	−0.678770	+	1.62465i
$171$		0			0
$172$	4.97625	+	3.61546i	0.379435	+	0.275676i
$173$	−0.0578028	+	0.177899i	−0.00439467	+	0.0135254i	−0.953230	−	0.302246i	$-0.902263\pi$
$173$	−0.0578028	+	0.177899i	−0.00439467	+	0.0135254i	0.948835	+	0.315772i	$0.102263\pi$
$174$		0			0
$175$	−2.50000	−	16.4329i	−0.188982	−	1.24221i
$176$	−7.97791			−0.601357
$177$		0			0
$178$	31.2683	+	22.7178i	2.34366	+	1.70277i
$179$	−12.8779	−	9.35635i	−0.962540	−	0.699326i	−0.00880060	−	0.999961i	$-0.502801\pi$
$179$	−12.8779	−	9.35635i	−0.962540	−	0.699326i	−0.953739	+	0.300635i	$0.902801\pi$
$180$		0			0
$181$	10.7058	−	7.77821i	0.795755	−	0.578150i	−0.113910	−	0.993491i	$-0.536338\pi$
$181$	10.7058	−	7.77821i	0.795755	−	0.578150i	0.909666	+	0.415341i	$0.136338\pi$
$182$	−19.1246			−1.41761
$183$		0			0
$184$	−1.71332	−	5.27307i	−0.126308	−	0.388736i
$185$	9.02033	−	21.5904i	0.663188	−	1.58736i
$186$		0			0
$187$	−5.58684	−	17.1945i	−0.408550	−	1.25739i
$188$	−1.23450	−	3.79941i	−0.0900353	−	0.277100i
$189$		0			0
$190$	−6.82900	+	16.3454i	−0.495428	+	1.18582i
$191$	0.818073	+	2.51777i	0.0591937	+	0.182179i	0.976281	−	0.216507i	$-0.0694663\pi$
$191$	0.818073	+	2.51777i	0.0591937	+	0.182179i	−0.917087	+	0.398686i	$0.869466\pi$
$192$		0			0
$193$	−8.29846			−0.597336			−0.298668	−	0.954357i	$-0.596542\pi$
$193$	−8.29846			−0.597336			−0.298668	+	0.954357i	$0.596542\pi$
$194$	14.5283	−	10.5554i	1.04307	−	0.757834i
$195$		0			0
$196$	−8.87097	−	6.44514i	−0.633641	−	0.460367i
$197$	16.8564	+	12.2469i	1.20097	+	0.872555i	0.994380	−	0.105873i	$-0.0337637\pi$
$197$	16.8564	+	12.2469i	1.20097	+	0.872555i	0.206589	+	0.978428i	$0.433764\pi$
$198$		0			0
$199$	−3.31747			−0.235169			−0.117585	−	0.993063i	$-0.537515\pi$
$199$	−3.31747			−0.235169			−0.117585	+	0.993063i	$0.537515\pi$
$200$	−5.38466	−	5.45079i	−0.380753	−	0.385429i
$201$		0			0
$202$	−2.39791	+	7.38002i	−0.168717	+	0.519256i
$203$	−0.0935269	−	0.0679513i	−0.00656430	−	0.00476925i
$204$		0			0
$205$	−1.64572	+	3.93907i	−0.114942	+	0.275116i
$206$	−21.8676	+	15.8878i	−1.52359	+	1.10695i
$207$		0			0
$208$	4.48015	−	3.25502i	0.310643	−	0.225695i
$209$	−4.31098	−	13.2678i	−0.298197	−	0.917756i
$210$		0			0
$211$	3.29924	−	10.1540i	0.227129	−	0.699032i	−0.770939	−	0.636909i	$-0.780213\pi$
$211$	3.29924	−	10.1540i	0.227129	−	0.699032i	0.998068	−	0.0621231i	$-0.0197871\pi$
$212$	7.46406	+	22.9720i	0.512634	+	1.57773i
$213$		0			0
$214$	0.385379	−	1.18608i	0.0263440	−	0.0810784i
$215$	3.85437	+	3.31234i	0.262866	+	0.225900i
$216$		0			0
$217$	−27.1806	+	19.7478i	−1.84514	+	1.34057i
$218$	24.6276			1.66799
$219$		0			0
$220$	23.0417	+	1.88419i	1.55347	+	0.127032i
$221$	10.1528	+	7.37647i	0.682954	+	0.496195i
$222$		0			0
$223$	0.169512	−	0.521705i	0.0113514	−	0.0349359i	−0.945220	−	0.326433i	$-0.894153\pi$
$223$	0.169512	−	0.521705i	0.0113514	−	0.0349359i	0.956572	+	0.291497i	$0.0941533\pi$
$224$	25.2496			1.68706
$225$		0			0
$226$	37.4880			2.49366
$227$	−1.13841	+	3.50365i	−0.0755586	+	0.232546i	−0.981702	−	0.190426i	$-0.939013\pi$
$227$	−1.13841	+	3.50365i	−0.0755586	+	0.232546i	0.906143	+	0.422972i	$0.139013\pi$
$228$		0			0
$229$	1.39323	+	1.01224i	0.0920673	+	0.0668908i	0.632867	−	0.774261i	$-0.281878\pi$
$229$	1.39323	+	1.01224i	0.0920673	+	0.0668908i	−0.540799	+	0.841152i	$0.681878\pi$
$230$	−4.04522	−	17.0790i	−0.266734	−	1.12616i
$231$		0			0
$232$	−0.0532889			−0.00349858
$233$	−14.0037	+	10.1743i	−0.917412	+	0.666539i	−0.942879	−	0.333137i	$-0.891893\pi$
$233$	−14.0037	+	10.1743i	−0.917412	+	0.666539i	0.0254662	+	0.999676i	$0.491893\pi$
$234$		0			0
$235$	−0.760739	−	3.21185i	−0.0496251	−	0.209518i
$236$	−10.3706	+	31.9174i	−0.675068	+	2.07765i
$237$		0			0
$238$	10.5471	+	32.4605i	0.683664	+	2.10410i
$239$	3.14880	−	9.69101i	0.203679	−	0.626860i	−0.796086	−	0.605183i	$-0.793100\pi$
$239$	3.14880	−	9.69101i	0.203679	−	0.626860i	0.999765	−	0.0216761i	$-0.00690025\pi$
$240$		0			0
$241$	3.71188	+	11.4240i	0.239104	+	0.735885i	0.996551	+	0.0829883i	$0.0264464\pi$
$241$	3.71188	+	11.4240i	0.239104	+	0.735885i	−0.757447	+	0.652897i	$0.773554\pi$
$242$	−6.30816	+	4.58315i	−0.405504	+	0.294616i
$243$		0			0
$244$	11.3343	−	8.23482i	0.725601	−	0.527180i
$245$	−6.87104	−	5.90478i	−0.438975	−	0.377243i
$246$		0			0
$247$	7.83425	+	5.69192i	0.498482	+	0.362168i
$248$	−4.78564	+	14.7287i	−0.303889	+	0.935273i
$249$		0			0
$250$	−15.5827	−	18.5869i	−0.985538	−	1.17554i
$251$	8.68448			0.548159			0.274080	−	0.961707i	$-0.411627\pi$
$251$	8.68448			0.548159			0.274080	+	0.961707i	$0.411627\pi$
$252$		0			0
$253$	11.1824	+	8.12449i	0.703031	+	0.510782i
$254$	16.6419	+	12.0910i	1.04420	+	0.758659i
$255$		0			0
$256$	0.271296	−	0.197108i	0.0169560	−	0.0123193i
$257$	−8.45069			−0.527140			−0.263570	−	0.964640i	$-0.584900\pi$
$257$	−8.45069			−0.527140			−0.263570	+	0.964640i	$0.584900\pi$
$258$		0			0
$259$	−10.7500	−	33.0850i	−0.667970	−	2.05580i
$260$	−13.7083	+	8.34300i	−0.850150	+	0.517411i
$261$		0			0
$262$	−6.45535	−	19.8675i	−0.398813	−	1.22742i
$263$	−2.52357	−	7.76676i	−0.155610	−	0.478919i	0.842612	−	0.538521i	$-0.181017\pi$
$263$	−2.52357	−	7.76676i	−0.155610	−	0.478919i	−0.998222	+	0.0596022i	$0.981017\pi$
$264$		0			0
$265$	4.59959	+	19.4196i	0.282551	+	1.19293i
$266$	8.13845	+	25.0476i	0.499000	+	1.53576i
$267$		0			0
$268$	−14.7002			−0.897960
$269$	11.0322	−	8.01539i	0.672647	−	0.488707i	−0.198263	−	0.980149i	$-0.563530\pi$
$269$	11.0322	−	8.01539i	0.672647	−	0.488707i	0.870910	+	0.491442i	$0.163530\pi$
$270$		0			0
$271$	0.872330	+	0.633785i	0.0529902	+	0.0384997i	0.613965	−	0.789333i	$-0.289574\pi$
$271$	0.872330	+	0.633785i	0.0529902	+	0.0384997i	−0.560975	+	0.827833i	$0.689574\pi$
$272$	−7.99558	−	5.80913i	−0.484803	−	0.352230i
$273$		0			0
$274$	−3.09017			−0.186684
$275$	18.8474	+	3.10317i	1.13654	+	0.187128i
$276$		0			0
$277$	5.45470	−	16.7878i	0.327741	−	1.00868i	−0.642447	−	0.766330i	$-0.722081\pi$
$277$	5.45470	−	16.7878i	0.327741	−	1.00868i	0.970188	−	0.242353i	$-0.0779192\pi$
$278$	2.89009	+	2.09977i	0.173336	+	0.125936i
$279$		0			0
$280$	−11.3533	−	0.928391i	−0.678487	−	0.0554820i
$281$	−20.5184	+	14.9075i	−1.22402	+	0.889305i	−0.996428	−	0.0844503i	$-0.973087\pi$
$281$	−20.5184	+	14.9075i	−1.22402	+	0.889305i	−0.227596	+	0.973756i	$0.573087\pi$
$282$		0			0
$283$	8.81015	−	6.40095i	0.523709	−	0.380497i	−0.294290	−	0.955716i	$-0.595083\pi$
$283$	8.81015	−	6.40095i	0.523709	−	0.380497i	0.817999	+	0.575219i	$0.195083\pi$
$284$	−10.1370	−	31.1986i	−0.601523	−	1.85130i
$285$		0			0
$286$	6.79128	−	20.9014i	0.401577	−	1.23593i
$287$	1.96128	+	6.03620i	0.115771	+	0.356305i
$288$		0			0
$289$	1.66772	−	5.13272i	0.0981012	−	0.301924i
$290$	−0.168131	−	0.0137486i	−0.00987297	−	0.000807343i
$291$		0			0
$292$	−26.8405	+	19.5007i	−1.57072	+	1.14119i
$293$	−8.22487			−0.480502			−0.240251	−	0.970711i	$-0.577230\pi$
$293$	−8.22487			−0.480502			−0.240251	+	0.970711i	$0.577230\pi$
$294$		0			0
$295$	−10.6892	+	25.5849i	−0.622350	+	1.48961i
$296$	−12.9730	−	9.42541i	−0.754038	−	0.547841i
$297$		0			0
$298$	6.62053	−	20.3759i	0.383517	−	1.18034i
$299$	−9.59452			−0.554866
$300$		0			0
$301$	7.55564			0.435500
$302$	−7.77670	+	23.9342i	−0.447499	+	1.37726i
$303$		0			0
$304$	−6.16964	−	4.48251i	−0.353853	−	0.257089i
$305$	9.88802	−	6.01796i	0.566187	−	0.344587i
$306$		0			0
$307$	6.38809			0.364587			0.182294	−	0.983244i	$-0.441648\pi$
$307$	6.38809			0.364587			0.182294	+	0.983244i	$0.441648\pi$
$308$	27.8065	−	20.2026i	1.58442	−	1.15115i
$309$		0			0
$310$	−18.8991	+	45.2355i	−1.07340	+	2.56920i
$311$	5.80554	−	17.8676i	0.329202	−	1.01318i	−0.640306	−	0.768120i	$-0.721192\pi$
$311$	5.80554	−	17.8676i	0.329202	−	1.01318i	0.969508	−	0.245060i	$-0.0788077\pi$
$312$		0			0
$313$	6.73970	+	20.7427i	0.380950	+	1.17244i	0.939376	+	0.342890i	$0.111406\pi$
$313$	6.73970	+	20.7427i	0.380950	+	1.17244i	−0.558425	+	0.829555i	$0.688594\pi$
$314$	3.78764	−	11.6571i	0.213749	−	0.657851i
$315$		0			0
$316$	−6.06239	−	18.6581i	−0.341036	−	1.04960i
$317$	−8.90788	+	6.47195i	−0.500316	+	0.363501i	−0.809138	−	0.587619i	$-0.800065\pi$
$317$	−8.90788	+	6.47195i	−0.500316	+	0.363501i	0.308822	+	0.951120i	$0.400065\pi$
$318$		0			0
$319$	0.107477	−	0.0780864i	0.00601754	−	0.00437200i
$320$	23.4955	−	14.2996i	1.31344	−	0.799374i
$321$		0			0
$322$	−21.1106	−	15.3377i	−1.17645	−	0.854739i
$323$	5.34047	−	16.4363i	0.297152	−	0.914539i
$324$		0			0
$325$	−11.8503	+	5.94718i	−0.657334	+	0.329890i
$326$	−26.3581			−1.45984
$327$		0			0
$328$	2.36686	+	1.71962i	0.130688	+	0.0949503i
$329$	−3.97003	−	2.88440i	−0.218875	−	0.159022i
$330$		0			0
$331$	−7.08443	+	5.14714i	−0.389395	+	0.282912i	−0.765208	−	0.643784i	$-0.777364\pi$
$331$	−7.08443	+	5.14714i	−0.389395	+	0.282912i	0.375812	+	0.926696i	$0.377364\pi$
$332$	15.2311			0.835917
$333$		0			0
$334$	−6.62304	−	20.3836i	−0.362396	−	1.11534i
$335$	−12.1053	−	0.989890i	−0.661384	−	0.0540834i
$336$		0			0
$337$	−9.42596	−	29.0101i	−0.513465	−	1.58028i	−0.786058	−	0.618153i	$-0.787881\pi$
$337$	−9.42596	−	29.0101i	−0.513465	−	1.58028i	0.272593	−	0.962129i	$-0.412119\pi$
$338$	−4.00093	−	12.3136i	−0.217622	−	0.669772i
$339$		0			0
$340$	21.7207	+	18.6662i	1.17797	+	1.01232i
$341$	−11.9305	−	36.7185i	−0.646075	−	1.98842i
$342$		0			0
$343$	9.80162			0.529238
$344$	2.81765	−	2.04714i	0.151917	−	0.110374i
$345$		0			0
$346$	0.328297	+	0.238522i	0.0176494	+	0.0128230i
$347$	10.2956	+	7.48018i	0.552696	+	0.401557i	0.828778	−	0.559577i	$-0.189036\pi$
$347$	10.2956	+	7.48018i	0.552696	+	0.401557i	−0.276083	+	0.961134i	$0.589036\pi$
$348$		0			0
$349$	−22.2817			−1.19271			−0.596357	−	0.802720i	$-0.703386\pi$
$349$	−22.2817			−1.19271			−0.596357	+	0.802720i	$0.703386\pi$
$350$	−35.5809	−	5.85830i	−1.90188	−	0.313139i
$351$		0			0
$352$	−8.96631	+	27.5955i	−0.477906	+	1.47084i
$353$	13.7602	+	9.99740i	0.732384	+	0.532108i	0.890317	−	0.455342i	$-0.150483\pi$
$353$	13.7602	+	9.99740i	0.732384	+	0.532108i	−0.157933	+	0.987450i	$0.550483\pi$
$354$		0			0
$355$	−6.24676	−	26.3740i	−0.331544	−	1.39978i
$356$	39.0075	−	28.3406i	2.06739	−	1.50205i
$357$		0			0
$358$	−27.9375	+	20.2978i	−1.47654	+	1.07277i
$359$	6.24572	+	19.2223i	0.329636	+	1.01452i	0.969304	+	0.245865i	$0.0790719\pi$
$359$	6.24572	+	19.2223i	0.329636	+	1.01452i	−0.639668	+	0.768651i	$0.720928\pi$
$360$		0			0
$361$	−1.75044	+	5.38732i	−0.0921287	+	0.283543i
$362$	−8.87128	−	27.3030i	−0.466264	−	1.43501i
$363$		0			0
$364$	−7.37254	+	22.6904i	−0.386426	+	1.18930i
$365$	−23.4157	+	14.2510i	−1.22563	+	0.745933i
$366$		0			0
$367$	−11.7853	+	8.56250i	−0.615186	+	0.446959i	−0.851237	−	0.524782i	$-0.824147\pi$
$367$	−11.7853	+	8.56250i	−0.615186	+	0.446959i	0.236051	+	0.971741i	$0.424147\pi$
$368$	7.55589			0.393878
$369$		0			0
$370$	−38.4990	−	33.0850i	−2.00147	−	1.72001i
$371$	24.0037	+	17.4397i	1.24621	+	0.905423i
$372$		0			0
$373$	−1.75150	+	5.39055i	−0.0906891	+	0.279112i	−0.986106	−	0.166116i	$-0.946877\pi$
$373$	−1.75150	+	5.39055i	−0.0906891	+	0.279112i	0.895417	+	0.445228i	$0.146877\pi$
$374$	−39.2217			−2.02811
$375$		0			0
$376$	−2.26200			−0.116654
$377$	−0.0284961	+	0.0877019i	−0.00146762	+	0.00451688i
$378$		0			0
$379$	−7.27243	−	5.28373i	−0.373560	−	0.271407i	0.385126	−	0.922864i	$-0.374158\pi$
$379$	−7.27243	−	5.28373i	−0.373560	−	0.271407i	−0.758685	+	0.651457i	$0.774158\pi$
$380$	16.7604	+	14.4034i	0.859791	+	0.738881i
$381$		0			0
$382$	5.74318			0.293847
$383$	−18.7825	+	13.6463i	−0.959741	+	0.697292i	−0.953090	−	0.302686i	$-0.902117\pi$
$383$	−18.7825	+	13.6463i	−0.959741	+	0.697292i	−0.00665004	+	0.999978i	$0.502117\pi$
$384$		0			0
$385$	24.2585	−	14.7640i	1.23633	−	0.752441i
$386$	−5.56317	+	17.1217i	−0.283158	+	0.871471i
$387$		0			0
$388$	−6.92280	−	21.3062i	−0.351452	−	1.08166i
$389$	3.27362	−	10.0752i	0.165979	−	0.510831i	−0.833128	−	0.553080i	$-0.813452\pi$
$389$	3.27362	−	10.0752i	0.165979	−	0.510831i	0.999107	+	0.0422493i	$0.0134524\pi$
$390$		0			0
$391$	5.29131	+	16.2850i	0.267593	+	0.823566i
$392$	−5.02291	+	3.64936i	−0.253695	+	0.184320i
$393$		0			0
$394$	36.5685	−	26.5686i	1.84230	−	1.33851i
$395$	−3.73584	−	15.7728i	−0.187970	−	0.793614i
$396$		0			0
$397$	2.19339	+	1.59359i	0.110083	+	0.0799802i	0.641465	−	0.767152i	$-0.278327\pi$
$397$	2.19339	+	1.59359i	0.110083	+	0.0799802i	−0.531382	+	0.847133i	$0.678327\pi$
$398$	−2.22399	+	6.84472i	−0.111478	+	0.343095i
$399$		0			0
$400$	9.33233	−	4.68353i	0.466616	−	0.234177i
$401$	−8.49932			−0.424436			−0.212218	−	0.977222i	$-0.568069\pi$
$401$	−8.49932			−0.424436			−0.212218	+	0.977222i	$0.568069\pi$
$402$		0			0
$403$	21.6811	+	15.7523i	1.08001	+	0.784676i
$404$	7.83163	+	5.69001i	0.389638	+	0.283089i
$405$		0			0
$406$	−0.202899	+	0.147415i	−0.0100697	+	0.00731606i
$407$	39.9762			1.98155
$408$		0			0
$409$	4.96087	+	15.2680i	0.245299	+	0.754954i	0.995587	+	0.0938422i	$0.0299149\pi$
$409$	4.96087	+	15.2680i	0.245299	+	0.754954i	−0.750288	+	0.661111i	$0.770085\pi$
$410$	7.02396	+	6.03620i	0.346889	+	0.298107i
$411$		0			0
$412$	10.4200	+	32.0696i	0.513358	+	1.57995i
$413$	12.7389	+	39.2062i	0.626838	+	1.92921i
$414$		0			0
$415$	12.5425	+	1.02564i	0.615687	+	0.0503467i
$416$	−6.22386	−	19.1551i	−0.305150	−	0.939155i
$417$		0			0
$418$	−30.2647			−1.48030
$419$	−22.0512	+	16.0212i	−1.07727	+	0.782685i	−0.977205	−	0.212296i	$-0.931906\pi$
$419$	−22.0512	+	16.0212i	−1.07727	+	0.782685i	−0.100068	+	0.994981i	$0.531906\pi$
$420$		0			0
$421$	−2.42210	−	1.75976i	−0.118046	−	0.0857653i	0.527196	−	0.849744i	$-0.323243\pi$
$421$	−2.42210	−	1.75976i	−0.118046	−	0.0857653i	−0.645242	+	0.763978i	$0.723243\pi$
$422$	−18.7384	−	13.6142i	−0.912170	−	0.662730i
$423$		0			0
$424$	13.6766			0.664193
$425$	16.6296	+	16.8338i	0.806654	+	0.816561i
$426$		0			0
$427$	5.31795	−	16.3670i	0.257354	−	0.792053i
$428$	−1.25866	−	0.914466i	−0.0608394	−	0.0442024i
$429$		0			0
$430$	9.41806	−	5.73193i	0.454179	−	0.276418i
$431$	−27.7155	+	20.1365i	−1.33501	+	0.969940i	−0.335395	+	0.942077i	$0.608870\pi$
$431$	−27.7155	+	20.1365i	−1.33501	+	0.969940i	−0.999612	+	0.0278621i	$0.991130\pi$
$432$		0			0
$433$	8.32935	−	6.05163i	0.400283	−	0.290823i	−0.369373	−	0.929281i	$-0.620428\pi$
$433$	8.32935	−	6.05163i	0.400283	−	0.290823i	0.769656	+	0.638458i	$0.220428\pi$
$434$	22.5230	+	69.3186i	1.08114	+	3.32740i
$435$		0			0
$436$	9.49396	−	29.2194i	0.454678	−	1.39936i
$437$	4.08294	+	12.5660i	0.195314	+	0.601113i
$438$		0			0
$439$	−12.1458	+	37.3810i	−0.579688	+	1.78410i	0.0399418	+	0.999202i	$0.487283\pi$
$439$	−12.1458	+	37.3810i	−0.579688	+	1.78410i	−0.619630	+	0.784894i	$0.712717\pi$
$440$	5.04627	−	12.0784i	0.240572	−	0.575815i
$441$		0			0
$442$	22.0257	−	16.0026i	1.04766	−	0.761167i
$443$	−0.749909			−0.0356293			−0.0178146	−	0.999841i	$-0.505671\pi$
$443$	−0.749909			−0.0356293			−0.0178146	+	0.999841i	$0.505671\pi$
$444$		0			0
$445$	34.0302	−	20.7111i	1.61319	−	0.981802i
$446$	−0.962762	−	0.699487i	−0.0455881	−	0.0331217i
$447$		0			0
$448$	12.6363	−	38.8906i	0.597009	−	1.83741i
$449$	−6.79987			−0.320906			−0.160453	−	0.987043i	$-0.551295\pi$
$449$	−6.79987			−0.320906			−0.160453	+	0.987043i	$0.551295\pi$
$450$		0			0
$451$	−7.29348			−0.343436
$452$	14.4517	−	44.4776i	0.679749	−	2.09205i
$453$		0			0
$454$	6.46569	+	4.69760i	0.303450	+	0.220469i
$455$	−7.59906	+	18.1885i	−0.356249	+	0.852692i
$456$		0			0
$457$	17.4455			0.816065			0.408033	−	0.912967i	$-0.366215\pi$
$457$	17.4455			0.816065			0.408033	+	0.912967i	$0.366215\pi$
$458$	3.02250	−	2.19597i	0.141232	−	0.102611i
$459$		0			0
$460$	−21.8228	−	1.78452i	−1.01749	−	0.0832037i
$461$	11.8487	−	36.4666i	0.551850	−	1.69842i	−0.152271	−	0.988339i	$-0.548659\pi$
$461$	11.8487	−	36.4666i	0.551850	−	1.69842i	0.704121	−	0.710080i	$-0.251341\pi$
$462$		0			0
$463$	4.66531	+	14.3583i	0.216815	+	0.667289i	0.999020	+	0.0442671i	$0.0140953\pi$
$463$	4.66531	+	14.3583i	0.216815	+	0.667289i	−0.782204	+	0.623022i	$0.785905\pi$
$464$	0.0224413	−	0.0690671i	0.00104181	−	0.00320636i
$465$		0			0
$466$	11.6041	+	35.7136i	0.537548	+	1.65440i
$467$	−4.51552	+	3.28072i	−0.208953	+	0.151814i	−0.687340	−	0.726336i	$-0.741222\pi$
$467$	−4.51552	+	3.28072i	−0.208953	+	0.151814i	0.478387	+	0.878149i	$0.341222\pi$
$468$		0			0
$469$	−14.6086	+	10.6138i	−0.674563	+	0.490099i
$470$	−7.13681	−	0.583599i	−0.329196	−	0.0269194i
$471$		0			0
$472$	15.3732	+	11.1693i	0.707607	+	0.514107i
$473$	−2.68306	+	8.25762i	−0.123367	+	0.379686i
$474$		0			0
$475$	12.8319	+	12.9895i	0.588769	+	0.596000i
$476$	42.5787			1.95159
$477$		0			0
$478$	−17.8839	−	12.9934i	−0.817992	−	0.594306i
$479$	−2.38091	−	1.72983i	−0.108786	−	0.0790380i	0.532062	−	0.846705i	$-0.321417\pi$
$479$	−2.38091	−	1.72983i	−0.108786	−	0.0790380i	−0.640848	+	0.767667i	$0.721417\pi$
$480$		0			0
$481$	−22.4494	+	16.3105i	−1.02361	+	0.743693i
$482$	26.0588			1.18695
$483$		0			0
$484$	3.00587	+	9.25113i	0.136631	+	0.420506i
$485$	−4.26605	−	18.0113i	−0.193711	−	0.817853i
$486$		0			0
$487$	−1.76445	−	5.43042i	−0.0799549	−	0.246076i	0.903087	−	0.429458i	$-0.141295\pi$
$487$	−1.76445	−	5.43042i	−0.0799549	−	0.246076i	−0.983042	+	0.183382i	$0.941295\pi$
$488$	−2.45133	−	7.54442i	−0.110966	−	0.341520i
$489$		0			0
$490$	−16.7892	+	10.2181i	−0.758460	+	0.461607i
$491$	12.7515	+	39.2451i	0.575467	+	1.77111i	0.634583	+	0.772855i	$0.281172\pi$
$491$	12.7515	+	39.2451i	0.575467	+	1.77111i	−0.0591157	+	0.998251i	$0.518828\pi$
$492$		0			0
$493$	0.164573			0.00741202
$494$	16.9957	−	12.3481i	0.764675	−	0.555569i
$495$		0			0
$496$	−17.0744	−	12.4052i	−0.766661	−	0.557012i
$497$	−32.5997	−	23.6850i	−1.46229	−	1.06242i
$498$		0			0
$499$	34.8039			1.55804			0.779018	−	0.627002i	$-0.215718\pi$
$499$	34.8039			1.55804			0.779018	+	0.627002i	$0.215718\pi$
$500$	−28.0596	+	11.3228i	−1.25486	+	0.506373i
$501$		0			0
$502$	5.82195	−	17.9181i	0.259847	−	0.799725i
$503$	−22.7485	−	16.5278i	−1.01431	−	0.736937i	−0.0491992	−	0.998789i	$-0.515667\pi$
$503$	−22.7485	−	16.5278i	−1.01431	−	0.736937i	−0.965108	+	0.261852i	$0.915667\pi$
$504$		0			0
$505$	6.06602	+	5.21297i	0.269934	+	0.231974i
$506$	24.2593	−	17.6254i	1.07846	−	0.783544i
$507$		0			0
$508$	20.7609	−	15.0837i	0.921114	−	0.669229i
$509$	9.80583	+	30.1792i	0.434636	+	1.33767i	0.893459	+	0.449144i	$0.148271\pi$
$509$	9.80583	+	30.1792i	0.434636	+	1.33767i	−0.458824	+	0.888527i	$0.651729\pi$
$510$		0			0
$511$	−12.5934	+	38.7584i	−0.557098	+	1.71457i
$512$	6.87922	+	21.1721i	0.304021	+	0.935682i
$513$		0			0
$514$	−5.66523	+	17.4358i	−0.249883	+	0.769059i
$515$	6.42116	+	27.1103i	0.282950	+	1.19462i
$516$		0			0
$517$	4.56217	−	3.31461i	0.200644	−	0.145776i
$518$	−75.4687			−3.31591
$519$		0			0
$520$	2.09420	+	8.84176i	0.0918369	+	0.387737i
$521$	1.06229	+	0.771800i	0.0465398	+	0.0338132i	0.610812	−	0.791776i	$-0.290843\pi$
$521$	1.06229	+	0.771800i	0.0465398	+	0.0338132i	−0.564272	+	0.825589i	$0.690843\pi$
$522$		0			0
$523$	−0.223533	+	0.687963i	−0.00977441	+	0.0300825i	−0.955825	−	0.293937i	$-0.905034\pi$
$523$	−0.223533	+	0.687963i	−0.00977441	+	0.0300825i	0.946050	+	0.324020i	$0.105034\pi$
$524$	−26.0604			−1.13845
$525$		0			0
$526$	−17.7164			−0.772473
$527$	14.7796	−	45.4870i	0.643811	−	1.98145i
$528$		0			0
$529$	8.01651	+	5.82434i	0.348544	+	0.253232i
$530$	43.1507	+	3.52856i	1.87435	+	0.153271i
$531$		0			0
$532$	32.8551			1.42445
$533$	4.09579	−	2.97577i	0.177409	−	0.128895i
$534$		0			0
$535$	−0.974896	−	0.837799i	−0.0421484	−	0.0362212i
$536$	−2.57212	+	7.91617i	−0.111099	+	0.341926i
$537$		0			0
$538$	−9.14178	−	28.1355i	−0.394130	−	1.21301i
$539$	4.78300	−	14.7206i	0.206018	−	0.634059i
$540$		0			0
$541$	−13.5264	−	41.6301i	−0.581546	−	1.78982i	−0.612718	−	0.790302i	$-0.709924\pi$
$541$	−13.5264	−	41.6301i	−0.581546	−	1.78982i	0.0311714	−	0.999514i	$-0.490076\pi$
$542$	1.89244	−	1.37494i	0.0812875	−	0.0590588i
$543$		0			0
$544$	−29.0799	+	21.1278i	−1.24679	+	0.905845i
$545$	9.78565	−	23.4222i	0.419171	−	1.00330i
$546$		0			0
$547$	18.0077	+	13.0834i	0.769954	+	0.559405i	0.901947	−	0.431846i	$-0.142138\pi$
$547$	18.0077	+	13.0834i	0.769954	+	0.559405i	−0.131993	+	0.991251i	$0.542138\pi$
$548$	−1.19126	+	3.66633i	−0.0508883	+	0.156618i
$549$		0			0
$550$	19.0376	−	36.8064i	0.811767	−	1.56943i
$551$	0.126990			0.00540996
$552$		0			0
$553$	−19.4960	−	14.1647i	−0.829055	−	0.602344i
$554$	−30.9805	−	22.5087i	−1.31624	−	0.956301i
$555$		0			0
$556$	3.60541	−	2.61948i	0.152903	−	0.111091i
$557$	−40.8497			−1.73086			−0.865429	−	0.501032i	$-0.832954\pi$
$557$	−40.8497			−1.73086			−0.865429	+	0.501032i	$0.832954\pi$
$558$		0			0
$559$	−1.86242	−	5.73193i	−0.0787719	−	0.242435i
$560$	5.98442	−	14.3239i	0.252888	−	0.605294i
$561$		0			0
$562$	17.0024	+	52.3280i	0.717203	+	2.20732i
$563$	−11.6682	−	35.9110i	−0.491756	−	1.51347i	−0.821952	−	0.569557i	$-0.807115\pi$
$563$	−11.6682	−	35.9110i	−0.491756	−	1.51347i	0.330195	−	0.943913i	$-0.392885\pi$
$564$		0			0
$565$	14.8957	−	35.6532i	0.626666	−	1.49994i
$566$	−7.30047	−	22.4685i	−0.306862	−	0.944423i
$567$		0			0
$568$	−18.5743			−0.779361
$569$	22.0522	−	16.0218i	0.924476	−	0.671671i	−0.0201584	−	0.999797i	$-0.506417\pi$
$569$	22.0522	−	16.0218i	0.924476	−	0.671671i	0.944634	+	0.328126i	$0.106417\pi$
$570$		0			0
$571$	32.4321	+	23.5633i	1.35724	+	0.986094i	0.998615	+	0.0526136i	$0.0167552\pi$
$571$	32.4321	+	23.5633i	1.35724	+	0.986094i	0.358628	+	0.933481i	$0.383245\pi$
$572$	−22.1804	−	16.1150i	−0.927410	−	0.673803i
$573$		0			0
$574$	13.7689			0.574703
$575$	−17.8504	−	2.93902i	−0.744415	−	0.122566i
$576$		0			0
$577$	5.13837	−	15.8143i	0.213913	−	0.658357i	−0.785316	−	0.619095i	$-0.787500\pi$
$577$	5.13837	−	15.8143i	0.213913	−	0.658357i	0.999229	−	0.0392614i	$-0.0125005\pi$
$578$	−9.47199	−	6.88180i	−0.393983	−	0.286245i
$579$		0			0
$580$	−0.0811265	+	0.194179i	−0.00336860	+	0.00806282i
$581$	15.1362	−	10.9971i	0.627956	−	0.456236i
$582$		0			0
$583$	−27.5839	+	20.0408i	−1.14241	+	0.830007i
$584$	5.80496	+	17.8658i	0.240211	+	0.739293i
$585$		0			0
$586$	−5.51384	+	16.9699i	−0.227775	+	0.701018i
$587$	3.31218	+	10.1938i	0.136708	+	0.420745i	0.995852	−	0.0909899i	$-0.0290031\pi$
$587$	3.31218	+	10.1938i	0.136708	+	0.420745i	−0.859144	+	0.511735i	$0.829003\pi$
$588$		0			0
$589$	11.4044	−	35.0993i	0.469912	−	1.44624i
$590$	45.6219	+	39.2062i	1.87822	+	1.61409i
$591$		0			0
$592$	17.6794	−	12.8448i	0.726620	−	0.527920i
$593$	30.3399			1.24591			0.622954	−	0.782258i	$-0.285932\pi$
$593$	30.3399			1.24591			0.622954	+	0.782258i	$0.285932\pi$
$594$		0			0
$595$	35.0626	+	2.86718i	1.43743	+	0.117543i
$596$	−21.6228	−	15.7099i	−0.885703	−	0.643501i
$597$		0			0
$598$	−6.43204	+	19.7958i	−0.263025	+	0.809509i
$599$	−38.5303			−1.57431			−0.787153	−	0.616758i	$-0.788446\pi$
$599$	−38.5303			−1.57431			−0.787153	+	0.616758i	$0.788446\pi$
$600$		0			0
$601$	−12.5110			−0.510333			−0.255166	−	0.966897i	$-0.582130\pi$
$601$	−12.5110			−0.510333			−0.255166	+	0.966897i	$0.582130\pi$
$602$	5.06520	−	15.5891i	0.206442	−	0.635363i
$603$		0			0
$604$	25.3988	+	18.4533i	1.03346	+	0.750855i
$605$	1.85232	+	7.82051i	0.0753073	+	0.317949i
$606$		0			0
$607$	−8.69260			−0.352822			−0.176411	−	0.984317i	$-0.556449\pi$
$607$	−8.69260			−0.352822			−0.176411	+	0.984317i	$0.556449\pi$
$608$	−22.4390	+	16.3029i	−0.910020	+	0.661168i
$609$		0			0
$610$	−5.78768	−	24.4357i	−0.234336	−	0.989372i
$611$	−1.20960	+	3.72277i	−0.0489352	+	0.150607i
$612$		0			0
$613$	−0.883537	−	2.71925i	−0.0356857	−	0.109829i	0.931627	−	0.363416i	$-0.118390\pi$
$613$	−0.883537	−	2.71925i	−0.0356857	−	0.109829i	−0.967313	+	0.253587i	$0.918390\pi$
$614$	4.28249	−	13.1801i	0.172827	−	0.531907i
$615$		0			0
$616$	−6.01389	−	18.5088i	−0.242306	−	0.745743i
$617$	−32.1143	+	23.3324i	−1.29287	+	0.939326i	−0.999859	−	0.0167825i	$-0.994658\pi$
$617$	−32.1143	+	23.3324i	−1.29287	+	0.939326i	−0.293012	+	0.956109i	$0.594658\pi$
$618$		0			0
$619$	−17.5615	+	12.7592i	−0.705857	+	0.512835i	−0.881834	−	0.471559i	$-0.843691\pi$
$619$	−17.5615	+	12.7592i	−0.705857	+	0.512835i	0.175978	+	0.984394i	$0.443691\pi$
$620$	46.3841	+	39.8612i	1.86283	+	1.60086i
$621$		0			0
$622$	−32.9732	−	23.9564i	−1.32210	−	0.960565i
$623$	18.3020	−	56.3279i	0.733255	−	2.25673i
$624$		0			0
$625$	−23.8689	+	7.43462i	−0.954758	+	0.297385i
$626$	47.3152			1.89110
$627$		0			0
$628$	−12.3705	−	8.98768i	−0.493636	−	0.358648i
$629$	40.0648	+	29.1088i	1.59749	+	1.16064i
$630$		0			0
$631$	3.42841	−	2.49089i	0.136483	−	0.0991606i	−0.517449	−	0.855714i	$-0.673118\pi$
$631$	3.42841	−	2.49089i	0.136483	−	0.0991606i	0.653932	+	0.756553i	$0.273118\pi$
$632$	−11.1082			−0.441862
$633$		0			0
$634$	7.38145	+	22.7178i	0.293155	+	0.902237i
$635$	18.1118	−	11.0231i	0.718746	−	0.437436i
$636$		0			0
$637$	3.32006	+	10.2181i	0.131546	+	0.404856i
$638$	−0.0890598	−	0.274098i	−0.00352591	−	0.0108516i
$639$		0			0
$640$	−5.92386	−	25.0106i	−0.234161	−	0.988633i
$641$	7.99569	+	24.6082i	0.315811	+	0.971965i	0.975419	+	0.220356i	$0.0707220\pi$
$641$	7.99569	+	24.6082i	0.315811	+	0.971965i	−0.659609	+	0.751609i	$0.729278\pi$
$642$		0			0
$643$	3.38669			0.133558			0.0667790	−	0.997768i	$-0.478728\pi$
$643$	3.38669			0.133558			0.0667790	+	0.997768i	$0.478728\pi$
$644$	−26.3356	+	19.1339i	−1.03777	+	0.753983i
$645$		0			0
$646$	−30.3318	−	22.0373i	−1.19339	−	0.867046i
$647$	−5.38122	−	3.90969i	−0.211558	−	0.153706i	0.476960	−	0.878925i	$-0.341738\pi$
$647$	−5.38122	−	3.90969i	−0.211558	−	0.153706i	−0.688518	+	0.725219i	$0.741738\pi$
$648$		0			0
$649$	−47.3724			−1.85953
$650$	4.32620	+	28.4368i	0.169687	+	1.11538i
$651$		0			0
$652$	−10.1611	+	31.2725i	−0.397938	+	1.22473i
$653$	−15.9053	−	11.5559i	−0.622424	−	0.452218i	0.231343	−	0.972872i	$-0.425688\pi$
$653$	−15.9053	−	11.5559i	−0.622424	−	0.452218i	−0.853767	+	0.520654i	$0.825688\pi$
$654$		0			0
$655$	−21.4601	−	1.75486i	−0.838517	−	0.0685681i
$656$	−3.22553	+	2.34348i	−0.125936	+	0.0914976i
$657$		0			0
$658$	−8.61264	+	6.25745i	−0.335756	+	0.243941i
$659$	0.0777271	+	0.239219i	0.00302782	+	0.00931866i	0.952559	−	0.304354i	$-0.0984406\pi$
$659$	0.0777271	+	0.239219i	0.00302782	+	0.00931866i	−0.949531	+	0.313673i	$0.898441\pi$
$660$		0			0
$661$	−14.5495	+	44.7788i	−0.565911	+	1.74169i	0.0993193	+	0.995056i	$0.468333\pi$
$661$	−14.5495	+	44.7788i	−0.565911	+	1.74169i	−0.665230	+	0.746638i	$0.731667\pi$
$662$	5.87046	+	18.0674i	0.228162	+	0.702210i
$663$		0			0
$664$	2.66501	−	8.20206i	0.103422	−	0.318302i
$665$	27.0554	+	2.21241i	1.04916	+	0.0857934i
$666$		0			0
$667$	−0.101791	+	0.0739558i	−0.00394138	+	0.00286358i
$668$	−26.7373			−1.03450
$669$		0			0
$670$	−10.1576	+	24.3125i	−0.392423	+	0.939275i
$671$	15.9992	+	11.6241i	0.617641	+	0.448742i
$672$		0			0
$673$	4.65524	−	14.3273i	0.179446	−	0.552278i	−0.820362	−	0.571844i	$-0.806228\pi$
$673$	4.65524	−	14.3273i	0.179446	−	0.552278i	0.999809	+	0.0195655i	$0.00622828\pi$
$674$	−66.1738			−2.54892
$675$		0			0
$676$	−16.1518			−0.621225
$677$	1.91183	−	5.88401i	0.0734776	−	0.226141i	−0.907572	−	0.419896i	$-0.862067\pi$
$677$	1.91183	−	5.88401i	0.0734776	−	0.226141i	0.981050	+	0.193755i	$0.0620666\pi$
$678$		0			0
$679$	−22.2630	−	16.1750i	−0.854376	−	0.620740i
$680$	13.8524	−	8.43070i	0.531214	−	0.323303i
$681$		0			0
$682$	−83.7569			−3.20722
$683$	−10.0722	+	7.31789i	−0.385403	+	0.280011i	−0.763569	−	0.645726i	$-0.776555\pi$
$683$	−10.0722	+	7.31789i	−0.385403	+	0.280011i	0.378166	+	0.925738i	$0.376555\pi$
$684$		0			0
$685$	−1.22786	+	2.93893i	−0.0469143	+	0.112291i
$686$	6.57087	−	20.2231i	0.250877	−	0.772120i
$687$		0			0
$688$	1.46669	+	4.51402i	0.0559172	+	0.172095i
$689$	7.31351	−	22.5087i	0.278622	−	0.857512i
$690$		0			0
$691$	−8.44383	−	25.9875i	−0.321219	−	0.988609i	−0.973119	−	0.230304i	$-0.926028\pi$
$691$	−8.44383	−	25.9875i	−0.321219	−	0.988609i	0.651900	−	0.758305i	$-0.273972\pi$
$692$	0.409553	−	0.297558i	0.0155689	−	0.0113114i
$693$		0			0
$694$	22.3354	−	16.2276i	0.847840	−	0.615992i
$695$	3.14537	−	1.91430i	0.119311	−	0.0726137i
$696$		0			0
$697$	−7.30963	−	5.31076i	−0.276872	−	0.201159i
$698$	−14.9374	+	45.9725i	−0.565387	+	1.74008i
$699$		0			0
$700$	−20.6671	+	39.9566i	−0.781142	+	1.51022i
$701$	−27.7130			−1.04671			−0.523353	−	0.852116i	$-0.675319\pi$
$701$	−27.7130			−1.04671			−0.523353	+	0.852116i	$0.675319\pi$
$702$		0			0
$703$	30.9153	+	22.4613i	1.16599	+	0.847142i
$704$	38.0166	+	27.6207i	1.43280	+	1.04099i
$705$		0			0
$706$	29.8517	−	21.6885i	1.12348	−	0.816258i
$707$	11.8911			0.447210
$708$		0			0
$709$	2.47850	+	7.62803i	0.0930819	+	0.286477i	0.986749	−	0.162254i	$-0.0518763\pi$
$709$	2.47850	+	7.62803i	0.0930819	+	0.286477i	−0.893667	+	0.448731i	$0.851876\pi$
$710$	−58.6035	−	4.79219i	−2.19935	−	0.179848i
$711$		0			0
$712$	−8.43639	−	25.9645i	−0.316167	−	0.973062i
$713$	11.2995	+	34.7761i	0.423168	+	1.30238i
$714$		0			0
$715$	−17.1799	−	14.7640i	−0.642493	−	0.552141i
$716$	13.3124	+	40.9713i	0.497507	+	1.53117i
$717$		0			0
$718$	43.8473			1.63637
$719$	12.9705	−	9.42361i	0.483717	−	0.351441i	−0.319046	−	0.947739i	$-0.603362\pi$
$719$	12.9705	−	9.42361i	0.483717	−	0.351441i	0.802763	+	0.596298i	$0.203362\pi$
$720$		0			0
$721$	33.5098	+	24.3463i	1.24797	+	0.906703i
$722$	9.94183	+	7.22316i	0.369997	+	0.268818i
$723$		0			0
$724$	−35.8135			−1.33100
$725$	−0.0798815	+	0.154439i	−0.00296673	+	0.00573571i
$726$		0			0
$727$	−1.17061	+	3.60278i	−0.0434157	+	0.133620i	−0.970415	−	0.241444i	$-0.922379\pi$
$727$	−1.17061	+	3.60278i	−0.0434157	+	0.133620i	0.926999	+	0.375063i	$0.122379\pi$
$728$	10.9289	+	7.94032i	0.405052	+	0.294288i
$729$		0			0
$730$	13.7057	+	57.8658i	0.507271	+	2.14171i
$731$	−8.70181	+	6.32224i	−0.321848	+	0.233836i
$732$		0			0
$733$	34.3518	−	24.9581i	1.26881	−	0.921847i	0.269659	−	0.962956i	$-0.413089\pi$
$733$	34.3518	−	24.9581i	1.26881	−	0.921847i	0.999155	+	0.0411091i	$0.0130891\pi$
$734$	9.76578	+	30.0560i	0.360461	+	1.10939i
$735$		0			0
$736$	8.49202	−	26.1357i	0.313020	−	0.963376i
$737$	−6.41226	−	19.7349i	−0.236199	−	0.726945i
$738$		0			0
$739$	−0.356025	+	1.09573i	−0.0130966	+	0.0403072i	−0.957391	−	0.288794i	$-0.906746\pi$
$739$	−0.356025	+	1.09573i	−0.0130966	+	0.0403072i	0.944295	+	0.329101i	$0.106746\pi$
$740$	−54.0951	+	32.9228i	−1.98857	+	1.21027i
$741$		0			0
$742$	52.0739	−	37.8339i	1.91169	−	1.38893i
$743$	39.7658			1.45887			0.729433	−	0.684053i	$-0.239784\pi$
$743$	39.7658			1.45887			0.729433	+	0.684053i	$0.239784\pi$
$744$		0			0
$745$	−16.7480	−	14.3928i	−0.613599	−	0.527310i
$746$	9.94781	+	7.22751i	0.364215	+	0.264618i
$747$		0			0
$748$	−15.1200	+	46.5346i	−0.552842	+	1.70147i
$749$	−1.91107			−0.0698289
$750$		0			0
$751$	−26.2947			−0.959506			−0.479753	−	0.877404i	$-0.659274\pi$
$751$	−26.2947			−0.959506			−0.479753	+	0.877404i	$0.659274\pi$
$752$	0.952587	−	2.93176i	0.0347373	−	0.106910i
$753$		0			0
$754$	0.161846	+	0.117588i	0.00589410	+	0.00428231i
$755$	19.6728	+	16.9062i	0.715965	+	0.615280i
$756$		0			0
$757$	−24.5334			−0.891681			−0.445840	−	0.895113i	$-0.647095\pi$
$757$	−24.5334			−0.891681			−0.445840	+	0.895113i	$0.647095\pi$
$758$	−15.7769	+	11.4626i	−0.573044	+	0.416341i
$759$		0			0
$760$	10.6889	−	6.50540i	0.387728	−	0.235975i
$761$	5.81060	−	17.8832i	0.210634	−	0.648265i	−0.788801	−	0.614649i	$-0.789298\pi$
$761$	5.81060	−	17.8832i	0.210634	−	0.648265i	0.999435	−	0.0336159i	$-0.0107023\pi$
$762$		0			0
$763$	−11.6620	−	35.8920i	−0.422194	−	1.29938i
$764$	2.21400	−	6.81400i	0.0800998	−	0.246522i
$765$		0			0
$766$	15.5640	+	47.9010i	0.562349	+	1.73073i
$767$	26.6029	−	19.3281i	0.960576	−	0.697899i
$768$		0			0
$769$	25.8086	−	18.7510i	0.930681	−	0.676179i	−0.0154785	−	0.999880i	$-0.504927\pi$
$769$	25.8086	−	18.7510i	0.930681	−	0.676179i	0.946159	+	0.323701i	$0.104927\pi$
$770$	−14.1990	−	59.9485i	−0.511697	−	2.16039i
$771$		0			0
$772$	18.1694	+	13.2009i	0.653932	+	0.475109i
$773$	−1.57099	+	4.83500i	−0.0565045	+	0.173903i	−0.975326	−	0.220771i	$-0.929143\pi$
$773$	−1.57099	+	4.83500i	−0.0565045	+	0.173903i	0.918821	+	0.394674i	$0.129143\pi$
$774$		0			0
$775$	35.5121	+	35.9482i	1.27563	+	1.29130i
$776$	−12.6848			−0.455358
$777$		0			0
$778$	−18.5928	−	13.5085i	−0.666586	−	0.484303i
$779$	−5.64034	−	4.09795i	−0.202086	−	0.146824i
$780$		0			0
$781$	37.4620	−	27.2177i	1.34049	−	0.973926i
$782$	37.1470			1.32837
$783$		0			0
$784$	−2.61462	−	8.04698i	−0.0933793	−	0.287392i
$785$	−9.58160	−	8.23416i	−0.341982	−	0.293890i
$786$		0			0
$787$	−9.73607	−	29.9645i	−0.347053	−	1.06812i	−0.960475	−	0.278365i	$-0.910207\pi$
$787$	−9.73607	−	29.9645i	−0.347053	−	1.06812i	0.613422	−	0.789755i	$-0.289793\pi$
$788$	−17.4251	−	53.6290i	−0.620744	−	1.91045i
$789$		0			0
$790$	−35.0474	−	2.86593i	−1.24693	−	0.101965i
$791$	−17.7519	−	54.6347i	−0.631185	−	1.94259i
$792$		0			0
$793$	−13.7273			−0.487471
$794$	4.75838	−	3.45717i	0.168869	−	0.122690i
$795$		0			0
$796$	7.26358	+	5.27730i	0.257451	+	0.187049i
$797$	−14.2273	−	10.3368i	−0.503958	−	0.366147i	0.306569	−	0.951849i	$-0.400819\pi$
$797$	−14.2273	−	10.3368i	−0.503958	−	0.366147i	−0.810527	+	0.585701i	$0.800819\pi$
$798$		0			0
$799$	6.98581			0.247140
$800$	−5.71174	−	37.5442i	−0.201941	−	1.32739i
$801$		0			0
$802$	−5.69783	+	17.5361i	−0.201197	+	0.619222i
$803$	−37.8874	−	27.5268i	−1.33702	−	0.971399i
$804$		0			0
$805$	−22.9752	+	13.9830i	−0.809771	+	0.492835i
$806$	47.0354	−	34.1732i	1.65675	−	1.20370i
$807$		0			0
$808$	4.43442	−	3.22179i	0.156002	−	0.113342i
$809$	4.46737	+	13.7491i	0.157064	+	0.483394i	0.998364	−	0.0571746i	$-0.0182092\pi$
$809$	4.46737	+	13.7491i	0.157064	+	0.483394i	−0.841300	+	0.540569i	$0.818209\pi$
$810$		0			0
$811$	7.90971	−	24.3436i	0.277748	−	0.854819i	−0.710732	−	0.703463i	$-0.751636\pi$
$811$	7.90971	−	24.3436i	0.277748	−	0.854819i	0.988479	−	0.151356i	$-0.0483640\pi$
$812$	0.0966824	+	0.297558i	0.00339289	+	0.0104422i
$813$		0			0
$814$	26.7995	−	82.4804i	0.939322	−	2.89094i
$815$	−10.4732	+	25.0680i	−0.366862	+	0.878094i
$816$		0			0
$817$	−6.71460	+	4.87844i	−0.234914	+	0.170675i
$818$	34.8272			1.21770
$819$		0			0
$820$	9.86939	−	6.00662i	0.344654	−	0.209760i
$821$	−9.29237	−	6.75130i	−0.324306	−	0.235622i	0.413705	−	0.910411i	$-0.364235\pi$
$821$	−9.29237	−	6.75130i	−0.324306	−	0.235622i	−0.738011	+	0.674789i	$0.764235\pi$
$822$		0			0
$823$	−17.2352	+	53.0444i	−0.600781	+	1.84901i	−0.0772383	+	0.997013i	$0.524610\pi$
$823$	−17.2352	+	53.0444i	−0.600781	+	1.84901i	−0.523542	+	0.852000i	$0.675390\pi$
$824$	19.0929			0.665132
$825$		0			0
$826$	89.4316			3.11172
$827$	1.60407	−	4.93680i	0.0557788	−	0.171670i	−0.919286	−	0.393591i	$-0.871233\pi$
$827$	1.60407	−	4.93680i	0.0557788	−	0.171670i	0.975065	+	0.221921i	$0.0712327\pi$
$828$		0			0
$829$	−24.1809	−	17.5685i	−0.839838	−	0.610178i	0.0824876	−	0.996592i	$-0.473714\pi$
$829$	−24.1809	−	17.5685i	−0.839838	−	0.610178i	−0.922325	+	0.386414i	$0.873714\pi$
$830$	10.5245	−	25.1906i	0.365309	−	0.874378i
$831$		0			0
$832$	−32.6183			−1.13084
$833$	15.5124	−	11.2704i	0.537473	−	0.390497i
$834$		0			0
$835$	−22.0176	−	1.80045i	−0.761951	−	0.0623071i
$836$	−11.6671	+	35.9076i	−0.403514	+	1.24189i
$837$		0			0
$838$	18.2726	+	56.2373i	0.631216	+	1.94268i
$839$	−13.0615	+	40.1991i	−0.450932	+	1.38783i	0.424913	+	0.905234i	$0.360305\pi$
$839$	−13.0615	+	40.1991i	−0.450932	+	1.38783i	−0.875845	+	0.482592i	$0.839695\pi$
$840$		0			0
$841$	−8.96112	−	27.5795i	−0.309004	−	0.951017i
$842$	−5.25454	+	3.81764i	−0.181083	+	0.131565i
$843$		0			0
$844$	−23.3763	+	16.9839i	−0.804645	+	0.584609i
$845$	−13.3007	−	1.08764i	−0.457558	−	0.0374159i
$846$		0			0
$847$	9.66658	+	7.02318i	0.332148	+	0.241319i
$848$	−5.75955	+	17.7261i	−0.197784	+	0.608715i
$849$		0			0
$850$	45.8804	−	23.0256i	1.57369	−	0.789772i
$851$	−37.8616			−1.29788
$852$		0			0
$853$	4.51616	+	3.28118i	0.154630	+	0.112346i	0.662410	−	0.749141i	$-0.269534\pi$
$853$	4.51616	+	3.28118i	0.154630	+	0.112346i	−0.507780	+	0.861487i	$0.669534\pi$
$854$	−30.2039	−	21.9444i	−1.03355	−	0.750921i
$855$		0			0
$856$	−0.712674	+	0.517788i	−0.0243587	+	0.0176976i
$857$	40.9218			1.39786			0.698930	−	0.715190i	$-0.253660\pi$
$857$	40.9218			1.39786			0.698930	+	0.715190i	$0.253660\pi$
$858$		0			0
$859$	1.94601	+	5.98920i	0.0663970	+	0.204349i	0.978751	−	0.205054i	$-0.0657370\pi$
$859$	1.94601	+	5.98920i	0.0663970	+	0.204349i	−0.912354	+	0.409403i	$0.865737\pi$
$860$	−3.16998	−	13.3837i	−0.108096	−	0.456381i
$861$		0			0
$862$	22.9662	+	70.6828i	0.782233	+	2.40746i
$863$	5.91389	+	18.2011i	0.201311	+	0.619572i	0.999845	+	0.0176217i	$0.00560946\pi$
$863$	5.91389	+	18.2011i	0.201311	+	0.619572i	−0.798534	+	0.601950i	$0.794391\pi$
$864$		0			0
$865$	0.357295	−	0.217454i	0.0121484	−	0.00739364i
$866$	−6.90206	−	21.2423i	−0.234541	−	0.721844i
$867$		0			0
$868$	90.9257			3.08622
$869$	22.4039	−	16.2774i	0.760000	−	0.552172i
$870$		0			0
$871$	11.6529	+	8.46630i	0.394842	+	0.286869i
$872$	−14.0737	−	10.2251i	−0.476594	−	0.346266i
$873$		0			0
$874$	28.6638			0.969567
$875$	−19.7095	+	31.5117i	−0.666302	+	1.06529i
$876$		0			0
$877$	4.11847	−	12.6753i	0.139071	−	0.428016i	−0.857130	−	0.515100i	$-0.827755\pi$
$877$	4.11847	−	12.6753i	0.139071	−	0.428016i	0.996201	+	0.0870840i	$0.0277549\pi$
$878$	68.9834	+	50.1194i	2.32808	+	1.69145i
$879$		0			0
$880$	13.5296	+	11.6269i	0.456082	+	0.391944i
$881$	−26.5565	+	19.2944i	−0.894711	+	0.650046i	−0.937102	−	0.349055i	$-0.886502\pi$
$881$	−26.5565	+	19.2944i	−0.894711	+	0.650046i	0.0423910	+	0.999101i	$0.486502\pi$
$882$		0			0
$883$	5.89651	−	4.28406i	0.198433	−	0.144170i	−0.484132	−	0.874995i	$-0.660864\pi$
$883$	5.89651	−	4.28406i	0.198433	−	0.144170i	0.682565	+	0.730825i	$0.260864\pi$
$884$	−10.4954	−	32.3015i	−0.352998	−	1.08642i
$885$		0			0
$886$	−0.502729	+	1.54724i	−0.0168895	+	0.0519806i
$887$	−9.84779	−	30.3084i	−0.330656	−	1.01766i	−0.968822	−	0.247757i	$-0.920307\pi$
$887$	−9.84779	−	30.3084i	−0.330656	−	1.01766i	0.638166	−	0.769899i	$-0.279693\pi$
$888$		0			0
$889$	9.74085	−	29.9793i	0.326698	−	1.00547i
$890$	−19.9186	−	84.0968i	−0.667673	−	2.81893i
$891$		0			0
$892$	−1.20105	+	0.872616i	−0.0402142	+	0.0292173i
$893$	5.39048			0.180385
$894$		0			0
$895$	8.20351	+	34.6354i	0.274213	+	1.15773i
$896$	−30.9145	−	22.4607i	−1.03278	−	0.750360i
$897$		0			0
$898$	−4.55854	+	14.0297i	−0.152120	+	0.468179i
$899$	0.351442			0.0117213
$900$		0			0
$901$	−42.2377			−1.40714
$902$	−4.88944	+	15.0482i	−0.162801	+	0.501049i
$903$		0			0
$904$	−21.4229	−	15.5646i	−0.712513	−	0.517671i
$905$	−29.4916	−	2.41162i	−0.980335	−	0.0801651i
$906$		0			0
$907$	−40.7506			−1.35310			−0.676551	−	0.736396i	$-0.736526\pi$
$907$	−40.7506			−1.35310			−0.676551	+	0.736396i	$0.736526\pi$
$908$	8.06600	−	5.86029i	0.267680	−	0.194481i
$909$		0			0
$910$	32.4330	+	27.8720i	1.07514	+	0.923948i
$911$	−7.78362	+	23.9555i	−0.257883	+	0.793682i	0.735365	+	0.677671i	$0.237011\pi$
$911$	−7.78362	+	23.9555i	−0.257883	+	0.793682i	−0.993248	+	0.116011i	$0.962989\pi$
$912$		0			0
$913$	6.64384	+	20.4476i	0.219879	+	0.676718i
$914$	11.6952	−	35.9942i	0.386843	−	1.19058i
$915$		0			0
$916$	−1.44024	−	4.43259i	−0.0475868	−	0.146457i
$917$	−25.8979	+	18.8159i	−0.855225	+	0.621357i
$918$		0			0
$919$	1.94774	−	1.41512i	0.0642500	−	0.0466804i	−0.555197	−	0.831719i	$-0.687357\pi$
$919$	1.94774	−	1.41512i	0.0642500	−	0.0466804i	0.619447	+	0.785039i	$0.287357\pi$
$920$	−4.77934	+	11.4395i	−0.157570	+	0.377148i
$921$		0			0
$922$	−67.2960	−	48.8934i	−2.21628	−	1.61022i
$923$	−9.93256	+	30.5693i	−0.326934	+	1.00620i
$924$		0			0
$925$	−46.7631	+	23.4686i	−1.53756	+	0.771642i
$926$	32.7522			1.07630
$927$		0			0
$928$	−0.213681	−	0.155248i	−0.00701441	−	0.00509627i
$929$	8.92928	+	6.48750i	0.292960	+	0.212848i	0.724551	−	0.689222i	$-0.242047\pi$
$929$	8.92928	+	6.48750i	0.292960	+	0.212848i	−0.431590	+	0.902070i	$0.642047\pi$
$930$		0			0
$931$	11.9699	−	8.69661i	0.392296	−	0.285020i
$932$	46.8458			1.53449
$933$		0			0
$934$	3.74176	+	11.5159i	0.122434	+	0.376813i
$935$	−15.5846	+	37.3021i	−0.509669	+	1.21991i
$936$		0			0
$937$	0.492148	+	1.51468i	0.0160778	+	0.0494823i	0.958774	−	0.284171i	$-0.0917184\pi$
$937$	0.492148	+	1.51468i	0.0160778	+	0.0494823i	−0.942696	+	0.333654i	$0.891718\pi$
$938$	12.1053	+	37.2563i	0.395253	+	1.21646i
$939$		0			0
$940$	−3.44366	+	8.24249i	−0.112320	+	0.268840i
$941$	−2.47918	−	7.63013i	−0.0808189	−	0.248735i	0.902480	−	0.430731i	$-0.141744\pi$
$941$	−2.47918	−	7.63013i	−0.0808189	−	0.248735i	−0.983299	+	0.181996i	$0.941744\pi$
$942$		0			0
$943$	6.90767			0.224945
$944$	−20.9504	+	15.2213i	−0.681877	+	0.495412i
$945$		0			0
$946$	15.2387	+	11.0716i	0.495454	+	0.359969i
$947$	9.39328	+	6.82462i	0.305241	+	0.221770i	0.729852	−	0.683606i	$-0.239589\pi$
$947$	9.39328	+	6.82462i	0.305241	+	0.221770i	−0.424611	+	0.905376i	$0.639589\pi$
$948$		0			0
$949$	32.5074			1.05524
$950$	35.4028	−	17.7673i	1.14862	−	0.576447i
$951$		0			0
$952$	7.45004	−	22.9289i	0.241457	−	0.743129i
$953$	0.743091	+	0.539888i	0.0240711	+	0.0174887i	0.599756	−	0.800183i	$-0.295264\pi$
$953$	0.743091	+	0.539888i	0.0240711	+	0.0174887i	−0.575685	+	0.817672i	$0.695264\pi$
$954$		0			0
$955$	2.28203	−	5.46209i	0.0738446	−	0.176749i
$956$	−22.3104	+	16.2094i	−0.721568	+	0.524250i
$957$		0			0
$958$	−5.16518	+	3.75272i	−0.166879	+	0.121245i
$959$	1.46330	+	4.50359i	0.0472526	+	0.145428i
$960$		0			0
$961$	21.9820	−	67.6537i	0.709097	−	2.18238i
$962$	18.6026	+	57.2528i	0.599771	+	1.84590i
$963$		0			0
$964$	10.0457	−	30.9175i	0.323550	−	0.995786i
$965$	14.0732	+	12.0941i	0.453032	+	0.389323i
$966$		0			0
$967$	−18.2399	+	13.2521i	−0.586555	+	0.426157i	−0.841081	−	0.540909i	$-0.818080\pi$
$967$	−18.2399	+	13.2521i	−0.586555	+	0.426157i	0.254526	+	0.967066i	$0.418080\pi$
$968$	5.50773			0.177025
$969$		0			0
$970$	−40.0215	−	3.27269i	−1.28501	−	0.105080i
$971$	45.4353	+	33.0106i	1.45809	+	1.05936i	0.983856	+	0.178962i	$0.0572738\pi$
$971$	45.4353	+	33.0106i	1.45809	+	1.05936i	0.474231	+	0.880401i	$0.342726\pi$
$972$		0			0
$973$	1.69163	−	5.20631i	0.0542313	−	0.166907i
$974$	−12.3871			−0.396909
$975$		0			0
$976$	10.8106			0.346038
$977$	−15.3303	+	47.1818i	−0.490459	+	1.50948i	0.333456	+	0.942766i	$0.391785\pi$
$977$	−15.3303	+	47.1818i	−0.490459	+	1.50948i	−0.823915	+	0.566713i	$0.808215\pi$
$978$		0			0
$979$	55.0620	+	40.0049i	1.75979	+	1.27856i
$980$	5.65101	+	23.8587i	0.180515	+	0.762137i
$981$		0			0
$982$	89.5203			2.85671
$983$	45.4691	−	33.0352i	1.45024	−	1.05366i	0.464464	−	0.885592i	$-0.346247\pi$
$983$	45.4691	−	33.0352i	1.45024	−	1.05366i	0.985775	−	0.168069i	$-0.0537530\pi$
$984$		0			0
$985$	−10.7379	−	45.3356i	−0.342138	−	1.44451i
$986$	0.110328	−	0.339554i	0.00351355	−	0.0108136i
$987$		0			0
$988$	−8.09857	−	24.9248i	−0.257650	−	0.792964i
$989$	2.54114	−	7.82082i	0.0808035	−	0.248688i
$990$		0			0
$991$	−5.32519	−	16.3892i	−0.169160	−	0.520621i	0.830159	−	0.557527i	$-0.188250\pi$
$991$	−5.32519	−	16.3892i	−0.169160	−	0.520621i	−0.999319	+	0.0369060i	$0.988250\pi$
$992$	−62.0993	+	45.1178i	−1.97166	+	1.43249i
$993$		0			0
$994$	−70.7222	+	51.3827i	−2.24317	+	1.62976i
$995$	5.62603	+	4.83485i	0.178357	+	0.153275i
$996$		0			0
$997$	−1.28873	−	0.936317i	−0.0408145	−	0.0296535i	0.567191	−	0.823586i	$-0.308030\pi$
$997$	−1.28873	−	0.936317i	−0.0408145	−	0.0296535i	−0.608005	+	0.793933i	$0.708030\pi$
$998$	23.3320	−	71.8086i	0.738563	−	2.27306i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.h.e.46.4	yes	16
3.2	odd	2	inner	225.2.h.e.46.1	✓	16
25.6	even	5	inner	225.2.h.e.181.4	yes	16
25.9	even	10		5625.2.a.v.1.1		8
25.16	even	5		5625.2.a.w.1.8		8
75.41	odd	10		5625.2.a.w.1.1		8
75.56	odd	10	inner	225.2.h.e.181.1	yes	16
75.59	odd	10		5625.2.a.v.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.h.e.46.1	✓	16	3.2	odd	2	inner
225.2.h.e.46.4	yes	16	1.1	even	1	trivial
225.2.h.e.181.1	yes	16	75.56	odd	10	inner
225.2.h.e.181.4	yes	16	25.6	even	5	inner
5625.2.a.v.1.1		8	25.9	even	10
5625.2.a.v.1.8		8	75.59	odd	10
5625.2.a.w.1.1		8	75.41	odd	10
5625.2.a.w.1.8		8	25.16	even	5

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.670386 - 2.06324i) q^{2} +(-2.18949 - 1.59076i) q^{4} +(-1.69588 - 1.45739i) q^{5} -3.32440 q^{7} +(-1.23973 + 0.900718i) q^{8} +O(q^{10})\)	\(q+(0.670386 - 2.06324i) q^{2} +(-2.18949 - 1.59076i) q^{4} +(-1.69588 - 1.45739i) q^{5} -3.32440 q^{7} +(-1.23973 + 0.900718i) q^{8} +(-4.14384 + 2.52199i) q^{10} +(1.18052 - 3.63326i) q^{11} +(0.819443 + 2.52199i) q^{13} +(-2.22863 + 6.85902i) q^{14} +(-0.645329 - 1.98612i) q^{16} +(3.82870 - 2.78171i) q^{17} +(2.95435 - 2.14646i) q^{19} +(1.39476 + 5.88869i) q^{20} +(-6.70487 - 4.87137i) q^{22} +(-1.11807 + 3.44107i) q^{23} +(0.752016 + 4.94312i) q^{25} +5.75280 q^{26} +(7.27874 + 5.28832i) q^{28} +(0.0281335 + 0.0204402i) q^{29} +(8.17609 - 5.94028i) q^{31} -7.59524 q^{32} +(-3.17262 - 9.76433i) q^{34} +(5.63778 + 4.84495i) q^{35} +(3.23366 + 9.95217i) q^{37} +(-2.44810 - 7.53447i) q^{38} +(3.41514 + 0.279266i) q^{40} +(-0.589966 - 1.81573i) q^{41} -2.27279 q^{43} +(-8.36438 + 6.07708i) q^{44} +(6.35020 + 4.61369i) q^{46} +(1.19421 + 0.867645i) q^{47} +4.05161 q^{49} +(10.7030 + 1.76221i) q^{50} +(2.21771 - 6.82541i) q^{52} +(-7.22046 - 5.24597i) q^{53} +(-7.29710 + 4.44110i) q^{55} +(4.12136 - 2.99434i) q^{56} +(0.0610333 - 0.0443433i) q^{58} +(-3.83193 - 11.7935i) q^{59} +(-1.59967 + 4.92329i) q^{61} +(-6.77506 - 20.8515i) q^{62} +(-3.80108 + 11.6985i) q^{64} +(2.28585 - 5.47123i) q^{65} +(4.39437 - 3.19269i) q^{67} -12.8079 q^{68} +(13.7758 - 8.38408i) q^{70} +(9.80619 + 7.12462i) q^{71} +(3.78817 - 11.6588i) q^{73} +22.7015 q^{74} -9.88302 q^{76} +(-3.92451 + 12.0784i) q^{77} +(5.86453 + 4.26083i) q^{79} +(-1.80015 + 4.30871i) q^{80} -4.14178 q^{82} +(-4.55307 + 3.30800i) q^{83} +(-10.5471 - 0.862466i) q^{85} +(-1.52364 + 4.68930i) q^{86} +(1.80902 + 5.56758i) q^{88} +(-5.50537 + 16.9438i) q^{89} +(-2.72415 - 8.38408i) q^{91} +(7.92192 - 5.75562i) q^{92} +(2.59074 - 1.88228i) q^{94} +(-8.13845 - 0.665506i) q^{95} +(6.69686 + 4.86555i) q^{97} +(2.71614 - 8.35943i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{4}+O(q^{10}) \) 16 * q - 2 * q^4	\( 16 q - 2 q^{4} + 14 q^{16} + 14 q^{19} - 30 q^{22} + 10 q^{25} + 30 q^{28} + 18 q^{31} - 20 q^{34} + 10 q^{37} - 10 q^{40} - 80 q^{43} - 32 q^{49} - 40 q^{52} - 70 q^{55} - 10 q^{58} + 32 q^{61} - 8 q^{64} - 40 q^{67} + 50 q^{70} + 60 q^{73} - 88 q^{76} + 36 q^{79} + 120 q^{82} + 20 q^{88} + 30 q^{91} + 30 q^{94} + 40 q^{97}+O(q^{100}) \) 16 * q - 2 * q^4 + 14 * q^16 + 14 * q^19 - 30 * q^22 + 10 * q^25 + 30 * q^28 + 18 * q^31 - 20 * q^34 + 10 * q^37 - 10 * q^40 - 80 * q^43 - 32 * q^49 - 40 * q^52 - 70 * q^55 - 10 * q^58 + 32 * q^61 - 8 * q^64 - 40 * q^67 + 50 * q^70 + 60 * q^73 - 88 * q^76 + 36 * q^79 + 120 * q^82 + 20 * q^88 + 30 * q^91 + 30 * q^94 + 40 * q^97

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